**Optical Network Optimization Based on Particle Swarm Intelligence**

Fábio Renan Durand, Larissa Melo, Lucas Ricken Garcia, Alysson José dos Santos and Taufik Abrão

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/52225

## **1. Introduction**

34 Search Algorithms

142 Search Algorithms for Engineering Optimization

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Modern optical communication networks are expected to meet a broad range of services with different and variable demands of bit rate, connection (session) duration, frequency of use, and set up time [1]. Thus, it is necessary to build flexible all-optical networks that allow dynamic resources sharing between different users and clients in an efficient way. The alloptical network is able to implement ultrahigh speed transmitting, routing and switching of data in the optical domain, presenting the transparency to data formats and protocols which increases network flexibility and functionality such that future network requirements can be met [2]. Optical code division multiplexing access (OCDMA) based technology has attracted a lot of interests due to its various advantages including asynchronous operation, high net‐ work flexibility, protocol transparency, simplified network control and potentially enhanced security [3]. Therefore, recent developments and researches on OCDMA have been experi‐ enced an expansion of interest, from short-range networks, such as access networks, to highcapacity medium/large networks.

The optical network presents two promising scenarios: the transport (backbone) networks with optical code division multiplexing/wavelength division multiplexing (OCDM/WDM) technology and the access network with OCDMA technology. In both, transport OCDM/WDM and access OCDMA networks, each different code defines a specific user or logic channel transmitted in a common channel. In a common channel, the interference that may arise between different user codes is known as multiple access interference (MAI), and it can limit the number of users utilizing the channel simultaneously [3]. In this work we

© 2013 Durand et al.; licensee InTech. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2013 Durand et al.; licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

have focus on hybrid OCDM/WDM systems. In this one, data signals in routing network configuration are carried on optical code path (OCP) from a source node to a destination node passing through nodes where the signals are optically routed and switched without re‐ generation in the electrical domain. Hence, in routing and channel (code/wavelength) as‐ signment (RCA) problem, suitable paths and channels are carefully selected among the many possible choices for the required connections [2].

limiters is needed [13]. On the other hand, in [14] a multi rate and multi power level scheme using adaptive overlapping pulse-position modulator (OPPM) and optical power controller was proposed. The bit rate varies depending on the number of slots in the optical OPPM system and has the advantage that it is not required to change the code sequence depending on the required user's information rate. The power level can be achieved by accommodating users with the different transmitted power. The power controller requires only power at‐ tenuator, and the difference of the power does not cause the change of the bit rate. In [15] a hybrid power and rate control nonlinear programming algorithm for overlapped optical fast frequency hopping (OFFH) was proposed. The multi rate transmission is achieved by over‐ lapping consecutive bits while coded using fiber Bragg grating (FBG). The intensity of the transmitted optical signal is directly adjusted from the laser source with respect to the trans‐ mission data rate. The proposed algorithm provides a joint transmission power and overlap‐ ping coefficient allocation strategy, which has been obtained via the solution of a constrained optimization problem, which maximizes the aggregate system throughput sub‐ ject to a peak laser transmission power constraint. In [9], a control algorithm to solve the un‐ fairness in the resource allocation strategy presented in [10] has been analyzed. Also, a unified framework for allocating and controlling the transmission rate and power in a way

Optical Network Optimization Based on Particle Swarm Intelligence

http://dx.doi.org/10.5772/52225

145

that it can be applied for any expression of the system capacity was implemented.

gated under an analytical perspective in [6].

Besides, recently researches have showed the utilization of resource allocation and optimiza‐ tion algorithms such as Local Search, Simulated Annealing, GA, Particle Swarm optimiza‐ tion (PSO), Ant Colony optimization (ACO) and Game Theory to regulate the transmitted power, bit rate variation and the number of active users in order to maximize the aggregate throughput of the optical networks [16-17]. However, the complexity and unfairness in the strategies presented are aspects to be improved. On the other hand, resource allocation has not been largely investigated considering energy efficiency aspects. This issue has become paramount since energy consumption is dominated by the access segment due to the large amount of distributed network elements. The related works have showed the utilization of resource allocation and optimization algorithms to optimization of the access network; how‐ ever, these issues have not been largely investigated considering routed OCDM/WDM net‐ works [6]. In the case of the OCP networks optimization, it is necessary to consider the use of distributed iterative algorithms with high performance-complexity tradeoffs and the im‐ perfections of physical layer, which constitute a new research area so far, which was investi‐

It is worth noting the routed OCDM/WDM networks brings a new combination of challenges with the power control, like amplified spans, multiple links, accumulation, and self-generation of the optical spontaneous noise power (ASE) noise, as well as the MAI generated by the OCPs. On the other hand, the dispersive effects, such as chromatic or group velocity dispersion (GVD) and polarization mode dispersion (PMD), are signal degradation mechanisms that sig‐

In this chapter, optimization procedures based on PSO are investigated in details, aiming to efficiently solve the optimal resource allocation for SNIR optimization of OCPs from OCDM/WDM networks under QoS restrictions and energy efficiency constraint problem,

nificantly affect the overall performance of optical communication systems [6, 18-21].

Establishing OCP with higher optical signal-to-noise plus interference ratio (SNIR) allows reducing the number of retransmissions by higher layers, thus increasing network through‐ put. Therefore, RCA techniques that consider physical layer impairments for the establish‐ ment of an OCP, namely Quality of Transmission-Aware (QoT-aware) RCA, could be much more practical [4-5]. For a dynamic traffic scenario the objective is to minimize the blocking probability of the connections by routing, assigning channels, and to maintain an acceptable level of optical power and adequate SNIR all over the network [6]. Furthermore, different channels can travel via different optical paths and also have different levels of quality of service (QoS) requirements. The QoS depends on SNIR, dispersion, and nonlinear effects [6]. Therefore, it is desirable to adjust network parameters in an optimal way, based on on-line decentralized iterative algorithms to accomplish such adjustment [7].

As a result, this dynamic optimization allows an increased network flexibility and capacity [6-7]. The SNIR optimization problem appears to be a huge challenge, since the MAI intro‐ duces the near-far problem [7]. Furthermore, if the distances between the nodes are quite different, like in real optical networks, the signal power received from various nodes will be significantly distinct. Thus, considering an optical node as the reference, the performance of closer nodes is many orders of magnitude better than that of far ones. Then, an efficient power control is needed to overcome this problem and enhance the performance and throughput of the network; this could be achieved through the SNIR optimization [6]. In this case, which is analogous to the CDMA cellular system, the power control (centralized or dis‐ tributed) is one of the most important issues, because it has a significant impact on both net‐ work performance and capacity. It is the most effective way to avoid the near-far problem and to increase the SNIR [6-7].

The optical power control problem has been recently investigated in the context of access networks aiming at solving the near-far problem [7-8] and establishing the QoS at the physi‐ cal layer [9-11]. In [7], the impact of power control on the random access protocol was inves‐ tigated. In [8], the effect of near-far problem and a detailed review of the power control were presented including the use of distributed algorithms. On the other hand, in [9-12] the con‐ cept that users of various classes should transmit at different power levels was applied. Dis‐ tinct power levels were obtained with power attenuators [10], adjustable encoders/decoders [11], and adjustable transmitters [12]. Furthermore, the optimal selection of the system's pa‐ rameters such as the transmitted power and the information rate would improve their per‐ formances [9, 13-15]. In [13], optical power control and time hopping for multimedia applications using single wavelength was proposed. The approach accommodates various data rates using only one sequence by changing the time-hopping rate. However, in order to implement such system an optical selector device that consists of a number of optical hardlimiters is needed [13]. On the other hand, in [14] a multi rate and multi power level scheme using adaptive overlapping pulse-position modulator (OPPM) and optical power controller was proposed. The bit rate varies depending on the number of slots in the optical OPPM system and has the advantage that it is not required to change the code sequence depending on the required user's information rate. The power level can be achieved by accommodating users with the different transmitted power. The power controller requires only power at‐ tenuator, and the difference of the power does not cause the change of the bit rate. In [15] a hybrid power and rate control nonlinear programming algorithm for overlapped optical fast frequency hopping (OFFH) was proposed. The multi rate transmission is achieved by over‐ lapping consecutive bits while coded using fiber Bragg grating (FBG). The intensity of the transmitted optical signal is directly adjusted from the laser source with respect to the trans‐ mission data rate. The proposed algorithm provides a joint transmission power and overlap‐ ping coefficient allocation strategy, which has been obtained via the solution of a constrained optimization problem, which maximizes the aggregate system throughput sub‐ ject to a peak laser transmission power constraint. In [9], a control algorithm to solve the un‐ fairness in the resource allocation strategy presented in [10] has been analyzed. Also, a unified framework for allocating and controlling the transmission rate and power in a way that it can be applied for any expression of the system capacity was implemented.

have focus on hybrid OCDM/WDM systems. In this one, data signals in routing network configuration are carried on optical code path (OCP) from a source node to a destination node passing through nodes where the signals are optically routed and switched without re‐ generation in the electrical domain. Hence, in routing and channel (code/wavelength) as‐ signment (RCA) problem, suitable paths and channels are carefully selected among the

Establishing OCP with higher optical signal-to-noise plus interference ratio (SNIR) allows reducing the number of retransmissions by higher layers, thus increasing network through‐ put. Therefore, RCA techniques that consider physical layer impairments for the establish‐ ment of an OCP, namely Quality of Transmission-Aware (QoT-aware) RCA, could be much more practical [4-5]. For a dynamic traffic scenario the objective is to minimize the blocking probability of the connections by routing, assigning channels, and to maintain an acceptable level of optical power and adequate SNIR all over the network [6]. Furthermore, different channels can travel via different optical paths and also have different levels of quality of service (QoS) requirements. The QoS depends on SNIR, dispersion, and nonlinear effects [6]. Therefore, it is desirable to adjust network parameters in an optimal way, based on on-line

As a result, this dynamic optimization allows an increased network flexibility and capacity [6-7]. The SNIR optimization problem appears to be a huge challenge, since the MAI intro‐ duces the near-far problem [7]. Furthermore, if the distances between the nodes are quite different, like in real optical networks, the signal power received from various nodes will be significantly distinct. Thus, considering an optical node as the reference, the performance of closer nodes is many orders of magnitude better than that of far ones. Then, an efficient power control is needed to overcome this problem and enhance the performance and throughput of the network; this could be achieved through the SNIR optimization [6]. In this case, which is analogous to the CDMA cellular system, the power control (centralized or dis‐ tributed) is one of the most important issues, because it has a significant impact on both net‐ work performance and capacity. It is the most effective way to avoid the near-far problem

The optical power control problem has been recently investigated in the context of access networks aiming at solving the near-far problem [7-8] and establishing the QoS at the physi‐ cal layer [9-11]. In [7], the impact of power control on the random access protocol was inves‐ tigated. In [8], the effect of near-far problem and a detailed review of the power control were presented including the use of distributed algorithms. On the other hand, in [9-12] the con‐ cept that users of various classes should transmit at different power levels was applied. Dis‐ tinct power levels were obtained with power attenuators [10], adjustable encoders/decoders [11], and adjustable transmitters [12]. Furthermore, the optimal selection of the system's pa‐ rameters such as the transmitted power and the information rate would improve their per‐ formances [9, 13-15]. In [13], optical power control and time hopping for multimedia applications using single wavelength was proposed. The approach accommodates various data rates using only one sequence by changing the time-hopping rate. However, in order to implement such system an optical selector device that consists of a number of optical hard-

many possible choices for the required connections [2].

144 Search Algorithms for Engineering Optimization

decentralized iterative algorithms to accomplish such adjustment [7].

and to increase the SNIR [6-7].

Besides, recently researches have showed the utilization of resource allocation and optimiza‐ tion algorithms such as Local Search, Simulated Annealing, GA, Particle Swarm optimiza‐ tion (PSO), Ant Colony optimization (ACO) and Game Theory to regulate the transmitted power, bit rate variation and the number of active users in order to maximize the aggregate throughput of the optical networks [16-17]. However, the complexity and unfairness in the strategies presented are aspects to be improved. On the other hand, resource allocation has not been largely investigated considering energy efficiency aspects. This issue has become paramount since energy consumption is dominated by the access segment due to the large amount of distributed network elements. The related works have showed the utilization of resource allocation and optimization algorithms to optimization of the access network; how‐ ever, these issues have not been largely investigated considering routed OCDM/WDM net‐ works [6]. In the case of the OCP networks optimization, it is necessary to consider the use of distributed iterative algorithms with high performance-complexity tradeoffs and the im‐ perfections of physical layer, which constitute a new research area so far, which was investi‐ gated under an analytical perspective in [6].

It is worth noting the routed OCDM/WDM networks brings a new combination of challenges with the power control, like amplified spans, multiple links, accumulation, and self-generation of the optical spontaneous noise power (ASE) noise, as well as the MAI generated by the OCPs. On the other hand, the dispersive effects, such as chromatic or group velocity dispersion (GVD) and polarization mode dispersion (PMD), are signal degradation mechanisms that sig‐ nificantly affect the overall performance of optical communication systems [6, 18-21].

In this chapter, optimization procedures based on PSO are investigated in details, aiming to efficiently solve the optimal resource allocation for SNIR optimization of OCPs from OCDM/WDM networks under QoS restrictions and energy efficiency constraint problem, considering imperfections on physical constraints. Herein, the adopted SNIR model consid‐ ers the MAI between the OCP based on 2-D codes (time/wavelength) [22, 23], ASE at cascad‐ ed amplified spans, and GVD and PMD dispersion effects.

The optimization method based on the heuristic PSO approach is attractive due to its perform‐ ance-complexity tradeoff and fairness features regarding the optimization methods that de‐ ploy matrix inversion, purely numerical procedures and other heuristic approaches [9][17].

The chapter is organized in the following manner: in Section 2 the optical transport (OCDM/ WDM) is described, while in Section 3 the SNIR optimization for the OCPs based on particle swarm intelligence is described in order to solve the resource allocation problem. In the net‐ work optimization context, figures of merit are presented and the PSO is developed in Sec‐ tion 4, with emphasis on its input parameters optimal choice and the network performance. Afterward, numerical results are discussed for realistic networks operation scenarios. Final‐ ly, the main conclusions are offered in Section 5.

Electrical Domain

**2.2. OCDMA codes**

Edge

Access Network

**Figure 1.** OCDM/WDM routed network architecture.

Optical Domain

The OCDMA can be divided into a) non-coherent unipolar systems, based only on optical power intensity modulation [20], and b) coherent bipolar systems, based on amplitude and phase modulation [26]. As expected, the performance of coherent codes is higher than that of non-coherent ones when analyzing the SNIR [27]. This effect occurs, because the bipolar code is true-orthogonal, and the unipolar code is pseudo-orthogonal. However, the main drawback to the coherent OCDMA lies in the technical implementation difficulties, concom‐ itant with the utilization of phase-shifted optical signals [20],[27]. In this work we adopt non-coherent codes because their technological maturity and implementation easiness when compared with coherent codes [28]. The non-coherent codes can be classified into one-di‐ mensional (1-D) and two-dimensional (2-D) codes. In the 1-D codes, the bits are subdivided in time into many short chips with a designated chip pattern representing a user code. On the other hand, in the 2-D codes, the bits are subdivided into individual time chips, and each chip is assigned to an independent wavelength out of a discrete set of wavelengths. The 2-D codes have better performance than the 1-D codes, and they can significantly enhance the number of active users [29]. Besides, the 2-D codes have been applied only in access net‐ works [2]; in this way, recently the utilization of the 2-D codes to obtain optical code path routed networks was proposed, which performance evaluated by simulation, considering

coding, topology, load condition, and physical impairment [2][6][20][21][22].

The 2-D codes can be represented by *Nλ* × *NT* matrices, where *N<sup>λ</sup>* is the number of rows, that is equal to the number of available wavelengths, and *NT* is the number of columns, that is equal to the code length. The code length is determined by the bit period *TB* which is subdi‐ vided into small units namely chips, each of duration *Tc* = *TB*/ *NT*, as show Fig. 2(a). In each code, there are *w* short pulses of different wavelength, where *w* is called the weight of the code. An (*Nλ* × *NT*, *w*, *λa*, *λc*) code is the collection of binary *Nλ* × *NT* matrices each of code weight *w*; the parameters *λa* and *λc* are nonnegative integers and represent the constraints

Router Edge

Core Network

Core Router

Code Path1

Code Path2

Electrical Domain

Router

http://dx.doi.org/10.5772/52225

147

Optical Network Optimization Based on Particle Swarm Intelligence

Access Network

## **2. Network architecture**

## **2.1. OCDM/WDM transport network**

The transport network considered in this work is formed by nodes that have optical core routers interconnected by OCDM/WDM links with optical code paths defined by patterns of short pulses in wavelengths, such as shown in Fig. 1. The links are composed by sequences of span and each span consists of optical fiber and optical amplifier. The transmitting and receiving nodes create virtual path based on the code and the total link length is given by *dij* <sup>=</sup>∑ *i di tx* + ∑ *j dj rx* , where *di tx* is the span length from the transmitting node to the optical router and *dj rx* is the span between optical routers in the OCP route and the receiving node. The received power at the *j-*th node is given by*Pr* =*astar pi Gamp*exp( −*α<sup>f</sup> dij* ), where *pi* is the transmitted power by the *i-*th transmitter node, α*<sup>f</sup>* is the fiber attenuation (km-1) and *astar* is the star coupler attenuation (linear units), and *Gamp* is the total gain at the route. Considering decibel units,*astar* =10log(*K*)− 10log2 (*K*)log10*δ* , where, δ is the excess loss ratio [6]. A typical distance between optical amplifiers is about 60 km [20].

The optical core router consists of code converter routers in parallel forming a two-dimension‐ al router node [23] and each group of code converters in parallel is pre-connected to a specific output performing routing by selecting a specific code from the incoming broadcasting traffic. This kind of router does not require light sources or optical-electrical-optical conversion and can be scaled by adding new modules [22]. This code is transmitted and its route in the network is determined by a particular code sequence. For viability characteristics, we consider network equipment, such as code-processing devices (encoders and decoders at the transmitter and re‐ ceiver), star coupler, optical routers could be made using robust, lightweight, and low-cost technology platforms with commercial-off-the-shelf technologies [23-24]. For more details about transport networks the references [19],[25] should be consulted.

**Figure 1.** OCDM/WDM routed network architecture.

#### **2.2. OCDMA codes**

considering imperfections on physical constraints. Herein, the adopted SNIR model consid‐ ers the MAI between the OCP based on 2-D codes (time/wavelength) [22, 23], ASE at cascad‐

The optimization method based on the heuristic PSO approach is attractive due to its perform‐ ance-complexity tradeoff and fairness features regarding the optimization methods that de‐ ploy matrix inversion, purely numerical procedures and other heuristic approaches [9][17].

The chapter is organized in the following manner: in Section 2 the optical transport (OCDM/ WDM) is described, while in Section 3 the SNIR optimization for the OCPs based on particle swarm intelligence is described in order to solve the resource allocation problem. In the net‐ work optimization context, figures of merit are presented and the PSO is developed in Sec‐ tion 4, with emphasis on its input parameters optimal choice and the network performance. Afterward, numerical results are discussed for realistic networks operation scenarios. Final‐

The transport network considered in this work is formed by nodes that have optical core routers interconnected by OCDM/WDM links with optical code paths defined by patterns of short pulses in wavelengths, such as shown in Fig. 1. The links are composed by sequences of span and each span consists of optical fiber and optical amplifier. The transmitting and receiving nodes create virtual path based on the code and the total link length is given by

the star coupler attenuation (linear units), and *Gamp* is the total gain at the route. Considering

The optical core router consists of code converter routers in parallel forming a two-dimension‐ al router node [23] and each group of code converters in parallel is pre-connected to a specific output performing routing by selecting a specific code from the incoming broadcasting traffic. This kind of router does not require light sources or optical-electrical-optical conversion and can be scaled by adding new modules [22]. This code is transmitted and its route in the network is determined by a particular code sequence. For viability characteristics, we consider network equipment, such as code-processing devices (encoders and decoders at the transmitter and re‐ ceiver), star coupler, optical routers could be made using robust, lightweight, and low-cost technology platforms with commercial-off-the-shelf technologies [23-24]. For more details

is the span length from the transmitting node to the optical

*Gamp*exp( −*α<sup>f</sup> dij*

(*K*)log10*δ* , where, δ is the excess loss ratio [6]. A typical

is the fiber attenuation (km-1) and *astar* is

), where *pi*

is the

is the span between optical routers in the OCP route and the receiving node.

ed amplified spans, and GVD and PMD dispersion effects.

ly, the main conclusions are offered in Section 5.

**2. Network architecture**

146 Search Algorithms for Engineering Optimization

*dij* <sup>=</sup>∑ *i di tx* + ∑ *j dj rx*

router and *dj*

*rx*

decibel units,*astar* =10log(*K*)− 10log2

**2.1. OCDM/WDM transport network**

, where *di*

*tx*

The received power at the *j-*th node is given by*Pr* =*astar pi*

transmitted power by the *i-*th transmitter node, α*<sup>f</sup>*

distance between optical amplifiers is about 60 km [20].

about transport networks the references [19],[25] should be consulted.

The OCDMA can be divided into a) non-coherent unipolar systems, based only on optical power intensity modulation [20], and b) coherent bipolar systems, based on amplitude and phase modulation [26]. As expected, the performance of coherent codes is higher than that of non-coherent ones when analyzing the SNIR [27]. This effect occurs, because the bipolar code is true-orthogonal, and the unipolar code is pseudo-orthogonal. However, the main drawback to the coherent OCDMA lies in the technical implementation difficulties, concom‐ itant with the utilization of phase-shifted optical signals [20],[27]. In this work we adopt non-coherent codes because their technological maturity and implementation easiness when compared with coherent codes [28]. The non-coherent codes can be classified into one-di‐ mensional (1-D) and two-dimensional (2-D) codes. In the 1-D codes, the bits are subdivided in time into many short chips with a designated chip pattern representing a user code. On the other hand, in the 2-D codes, the bits are subdivided into individual time chips, and each chip is assigned to an independent wavelength out of a discrete set of wavelengths. The 2-D codes have better performance than the 1-D codes, and they can significantly enhance the number of active users [29]. Besides, the 2-D codes have been applied only in access net‐ works [2]; in this way, recently the utilization of the 2-D codes to obtain optical code path routed networks was proposed, which performance evaluated by simulation, considering coding, topology, load condition, and physical impairment [2][6][20][21][22].

The 2-D codes can be represented by *Nλ* × *NT* matrices, where *N<sup>λ</sup>* is the number of rows, that is equal to the number of available wavelengths, and *NT* is the number of columns, that is equal to the code length. The code length is determined by the bit period *TB* which is subdi‐ vided into small units namely chips, each of duration *Tc* = *TB*/ *NT*, as show Fig. 2(a). In each code, there are *w* short pulses of different wavelength, where *w* is called the weight of the code. An (*Nλ* × *NT*, *w*, *λa*, *λc*) code is the collection of binary *Nλ* × *NT* matrices each of code weight *w*; the parameters *λa* and *λc* are nonnegative integers and represent the constraints on the 2-D codes autocorrelation and cross-correlation, respectively [3]. The 2-D code design and selection is very important for good system performance and high network scalability with low bit error rate (BER). In [3] and [28] is presented an extensive list of code construc‐ tion techniques, as well as their technological characteristics are discussed.

( )

*K K*

:

*subject to*

same route, *Gamp* is the total gain at the OCP, *Nsp*

*Nsp eq* / *Gii*

each OCP, considering the 2-D codes, is given by [6, 8],

g

=

2

s

*i K*

ized interference matrix, which elements evaluated by *Hij* =*Gij* / *Gii*

notations, (1) can be written as *Ι***-***Γ* **\***

**=** *Ι***-***Γ* **\***

*H* **-1**

where 1*<sup>T</sup>* = [1,..., 1] and *Γ* \*

other case, thus *ui* <sup>=</sup>*<sup>Γ</sup>* \*

inversion *p* **\***

*γ<sup>i</sup>* ≈(*NT* / *σ*)2*Γ<sup>i</sup>*

sented by *σ* <sup>2</sup>

[3].

and *pj*

( )

*G pG*

*i*

G = ³ G

*ii i amp D*

*amp ij j sp j ji i*

£ £ "= ³ >

*G Gp N*

*p*

1, min max min max

= ¹

å

0,

of the OCP taking into account the power loss between the nodes, according to network top‐ ology, while *Gij* corresponds to the attenuation factor for the interfering OCP signals at the

each polarization at cascaded amplified spans [29], *pi* is the transmitted power for the *i-*OCP

Substituting inequality by equality, the optimized power vector solution through the matrix

ized power control, i.e. the existence of a central node in power control. The central node stores information about all physical network architecture, such as fiber length between no‐ des, amplifier position and regular update for the OCP establishment, and traffic dynamics. These observations justify the need for on-line SNIR optimization algorithms, which have

The SNIR and the carrier to interference ratio in eq. (1) are related to the factor*NT* / *σ*, i. e.,

Gaussian approximation is adopted, and the signal-to-noise plus interference ratio (SNIR) at

( ) <sup>2</sup>

*T ii i amp D*

*G Gp N*

*amp ij j sp j ji*

å <sup>+</sup>

where the average variance of the Hamming aperiodic cross-correlation amplitude is repre‐

1,

= ¹

*N G pG*

. The bit error probability (BER) is given by *Pb*(*i*)=*erfc*( *γ<sup>i</sup>* / 2) / 2, when the

2

s

*eq*

provable convergence properties for general network configurations [6, 16, 29].

*eq*

 is the transmitted power for the interfering OCP; *σD* is the pulse spreading due to the combined effects of the GVD and the first-order PMD for Gaussian pulses [30]. Using matrix

*P P*

min min min ,

ÎÎ Î ++ + =

**p p** ¡¡ ¡ **p 1p**

= =

*i K*

*P p*

*T*

*J p*

K

å

i 1

s

+

*i*

2

*i KP*

0

\*

Optical Network Optimization Based on Particle Swarm Intelligence

http://dx.doi.org/10.5772/52225

(1)

149

(2)

1,..

is the minimum CIR to achieve a desired QoS; *Gii* is the attenuation

*eq*

,

,

*H p* ≥*u*, where I is the identity matrix, H is the normal‐

, where there is a scaled version of the noise power.

*u* could be obtained. The matrix inversion is equivalent to central‐

is the spontaneous noise power (ASE) for

for *i* ≠ *j* and zero for an‐

The OCDMA 2-D encoder creates a combination of two patterns: a wavelength-hopping pat‐ tern and a time-spreading pattern. The common technology applied for code encoders/ decoders fiber Bragg gratings (FBGs), as show Fig. 2(b). The losses associated with the en‐ coders/ decoders are given by *CBragg*(*dB*)= *NλaBragg* + *aCirculator* [22], where *aBragg* is the FBG loss and *aCirculator* is the circulator loss. The usual value of losses for these equipments are *aBragg* = 0.5 dB and *aCirculator* = 3dB.

**Figure 2.** a) Representation of optical OCDMA codes. (b) Schematic of 2-D encoders/decoders based on fiber Bragg gratings (FBGs).

## **3. SNIR optimization procedures**

In the present approach, the SNIR optimization is based on the definition of the minimum pow‐ er constraint (also called sensitivity level) assuring that the optical signal can be detected by all optical devices. The maximum power constraint guarantees the minimization of nonlinear physical impairments, because it makes the aggregate power on a link to be limited to a maxi‐ mum value. The power control in optical networks appears to be an optimization problem.

## **3.1. Problem description**

Denoting Γ*<sup>i</sup>* the carrier-to-interference ratio (CIR) at the required decoder input, in order to get a certain maximum bit error rate (BER) tolerated by the *i*-*th* optical node, and defining the *K*-dimensional column vector of the transmitted optical power p = [*p*1*, p*2*,…, pK*] *T,* the op‐ tical power control problem consists in finding the optical power vector p that minimizes the cost function *J*(*p*) can be formulated as [6],[8] :

$$\begin{aligned} \min\_{\mathbf{p} \in \mathbb{R}\_+^k} J(\mathbf{p}) &= \min\_{\mathbf{p} \in \mathbb{R}\_+^k} \mathbf{1}^T \mathbf{p} = \min\_{p\_i \in \mathbb{R}\_+} \sum\_{i=1}^K p\_{i'} \\ \text{subject to } & \boldsymbol{\Gamma}\_i = \frac{\left(G\_{ii} p\_i G\_{amp}\right) / \sigma\_D}{G\_{amp} \sum\_{j=1, j \neq i}^K G\_{ij} p\_j + 2N\_{sp}^{eq}} \ge \boldsymbol{\Gamma}^\* \\ & P\_{\min} \le p\_i \le P\_{\max} \; \forall i = 1, \dots, K, \\ & P\_{\min} \ge 0, \quad P\_{\max} > 0 \end{aligned} \tag{1}$$

where 1*<sup>T</sup>* = [1,..., 1] and *Γ* \* is the minimum CIR to achieve a desired QoS; *Gii* is the attenuation of the OCP taking into account the power loss between the nodes, according to network top‐ ology, while *Gij* corresponds to the attenuation factor for the interfering OCP signals at the same route, *Gamp* is the total gain at the OCP, *Nsp eq* is the spontaneous noise power (ASE) for each polarization at cascaded amplified spans [29], *pi* is the transmitted power for the *i-*OCP and *pj* is the transmitted power for the interfering OCP; *σD* is the pulse spreading due to the combined effects of the GVD and the first-order PMD for Gaussian pulses [30]. Using matrix notations, (1) can be written as *Ι***-***Γ* **\*** *H p* ≥*u*, where I is the identity matrix, H is the normal‐ ized interference matrix, which elements evaluated by *Hij* =*Gij* / *Gii* for *i* ≠ *j* and zero for an‐ other case, thus *ui* <sup>=</sup>*<sup>Γ</sup>* \* *Nsp eq* / *Gii* , where there is a scaled version of the noise power. Substituting inequality by equality, the optimized power vector solution through the matrix inversion *p* **\* =** *Ι***-***Γ* **\*** *H* **-1** *u* could be obtained. The matrix inversion is equivalent to central‐ ized power control, i.e. the existence of a central node in power control. The central node stores information about all physical network architecture, such as fiber length between no‐ des, amplifier position and regular update for the OCP establishment, and traffic dynamics. These observations justify the need for on-line SNIR optimization algorithms, which have provable convergence properties for general network configurations [6, 16, 29].

on the 2-D codes autocorrelation and cross-correlation, respectively [3]. The 2-D code design and selection is very important for good system performance and high network scalability with low bit error rate (BER). In [3] and [28] is presented an extensive list of code construc‐

The OCDMA 2-D encoder creates a combination of two patterns: a wavelength-hopping pat‐ tern and a time-spreading pattern. The common technology applied for code encoders/ decoders fiber Bragg gratings (FBGs), as show Fig. 2(b). The losses associated with the en‐

and *aCirculator* is the circulator loss. The usual value of losses for these equipments are *aBragg* =

Time

**Figure 2.** a) Representation of optical OCDMA codes. (b) Schematic of 2-D encoders/decoders based on fiber Bragg

In the present approach, the SNIR optimization is based on the definition of the minimum pow‐ er constraint (also called sensitivity level) assuring that the optical signal can be detected by all optical devices. The maximum power constraint guarantees the minimization of nonlinear physical impairments, because it makes the aggregate power on a link to be limited to a maxi‐ mum value. The power control in optical networks appears to be an optimization problem.

get a certain maximum bit error rate (BER) tolerated by the *i*-*th* optical node, and defining

tical power control problem consists in finding the optical power vector p that minimizes

the *K*-dimensional column vector of the transmitted optical power p = [*p*1*, p*2*,…, pK*]

the carrier-to-interference ratio (CIR) at the required decoder input, in order to

(a) (b)

+ *aCirculator* [22], where *aBragg* is the FBG loss

*T,* the op‐

tion techniques, as well as their technological characteristics are discussed.

TC

coders/ decoders are given by *CBragg*(*dB*)= *NλaBragg*

1 2 Nt

TB

the cost function *J*(*p*) can be formulated as [6],[8] :

**3. SNIR optimization procedures**

0.5 dB and *aCirculator* = 3dB.

148 Search Algorithms for Engineering Optimization

Wavelength

1 2

**3.1. Problem description**

Denoting Γ*<sup>i</sup>*

gratings (FBGs).

 

N

The SNIR and the carrier to interference ratio in eq. (1) are related to the factor*NT* / *σ*, i. e., *γ<sup>i</sup>* ≈(*NT* / *σ*)2*Γ<sup>i</sup>* . The bit error probability (BER) is given by *Pb*(*i*)=*erfc*( *γ<sup>i</sup>* / 2) / 2, when the Gaussian approximation is adopted, and the signal-to-noise plus interference ratio (SNIR) at each OCP, considering the 2-D codes, is given by [6, 8],

$$\gamma\_i = \frac{N\_T \, ^2 \Big(G\_{ii} p\_i G\_{amp} \Big) \Big/ \sigma\_D}{\sigma^2 G\_{amp} \sum\_{j=1, j \neq i}^K G\_{ij} p\_j + 2N\_{sp}^{eq}} \tag{2}$$

where the average variance of the Hamming aperiodic cross-correlation amplitude is repre‐ sented by *σ* <sup>2</sup> [3].

#### **3.2. Physical restrictions**

The physical impairments are signal degradation mechanisms that significantly affect the overall performance of optical communication systems [6]. For the data that are transmitted through a transparent optical network, degradation effects may accumulate over a large dis‐ tance. The major linear physical impairments are group velocity dispersion (GVD), polariza‐ tion mode dispersion (PMD), and amplifier spontaneous emission (ASE) noise [24]. On the other hand, the major nonlinear physical impairments are self phase modulation (SPM), crossphase modulation (XPM), and four wave mixing (FWM), stimulated Brillouin scattering (SBS), and Raman scattering (SRS). The nonlinear physical impairments are excited with high power level [24]. However, the maximum power constraint guarantees the minimization of nonlinear physical impairments, because it makes the aggregate power on a link to be limited to a maxi‐ mum value [6]. In the currently technology stage, besides GVD, the main linear impairment is the PMD, that must be considered in high capacity optical networks. Differently from GVD, PMD is usually difficult to accurately determine and compensate due to its dynamic nature and its fluctuations induced by external stress/strain applied to the fiber after installation [5] [21][22]. As a result, the signals quality in an OCDM/WDM network can be quickly evaluated by analyzing the GVD, PMD and MAI restrictions. PMD impairment establishes an upper bound on the length of the optical segment due to fiber dispersion which causes the temporal spreading of optical pulses. On the other hand, due to the advances in the fiber manufacturing process with a continuous reduction of the PMD parameter, the deleterious effect of PMD will not be an issue for 10 Gbps or lower bit rates, for future small and medium-sized networks [20] [21]. In this context, the dominant impairment in SNIR will be given by i) ASE noise accumula‐ tion in chains of optical amplifiers for future optical networks [29] and ii) ASE, GVD and PMD for currently stage of optical networks.

and *dij* is the link length. Although there is a difference in the GVD for each wavelength, re‐ sulting from time skewing between the wavelengths, the consideration of the same GVD value for the entire transmission window is reasonable for a small number of wavelengths, as for the present code [27], [28]. On the other hand, this approximation is utilized to obtain an analytical treatment of the GVD and the PMD, in the same and less complex formalism,

) at the cascaded amplified spans is given by the model presented in Fig. 3

Pre-amplifier

Optical Network Optimization Based on Particle Swarm Intelligence

http://dx.doi.org/10.5772/52225

151

be the amplifier gain, *i.* e. *Nsp*-i will be its spontaneous


factor, one can find the noise at the cascading amplifiers. The

is the

G<sup>2</sup> G<sup>1</sup> G<sup>0</sup> R<sup>X</sup>

NSP-2 NSP-1 NSP-0

This model considers that the receiver gets the signal from a link with cascading amplifiers, numbered as 1, 2,.., starting from the receiver. The pre-amplifier can be contemplated as the

emission factor. The span between the i-*th* and the (*i − 1)*-*th* amplifier has the attenuation *Gii*. Let *Pti* be the mark power at the *i-th* amplifier input. The equivalent spontaneous emission

( ) ( ) 11 0 00

1 1 1

1 0

noise for i-*th* amplifier is given by *Nsp*−*<sup>i</sup>* =2*nsphf* (*Gi* −1)*B*0, which take into account the two polarization mode presented in a single mode fiber [24]. Where *nSP* is the spontaneous emis‐ sion factor, typically around 2 *−* 5, *h* is Planck's constant, *f* is the carrier frequency, *Gi*

amplifier gain and *Bo* is the optical bandwidth. Ideally, to reduce the ASE noise power, the optical bandwidth can be set to a minimum of *Bo* = 2*R*, where *R* is the bit rate. Without loss of generality, all employed optical amplifiers provide a uniform gain, setting the maximum obtainable Erbium-doped fiber amplifier (EDFA) to 20 dB across the transmission window. This is a reasonable assumption for the reduced number of wavelengths in the code trans‐ mission window (4 wavelengths), considering the optical amplifier gain profile, where the

*ii*

*N G GG N G*

*GGG*

*eq sp ii sp*

rather than to apply a formalism based on numerical methods [6].

P<sup>2</sup> P<sup>1</sup> P<sup>0</sup>

The ASE (*Nsp*

[29].

*eq*

**Figure 3.** Cascading amplifiers.

factor is given by [24], [29]

Calculating recursively the *Nsp*

number 0 cascade amplifier. Let *Gi*

*sp*

*eq*

*N*

The dispersive effects, such as chromatic or group velocity dispersion (GVD) and polariza‐ tion mode dispersion (PMD) constitute degradation mechanisms of the optical signal that significantly affect the overall performance of optical communication systems [21]. Current‐ ly, the PMD effect appears to be the only major physical impairment that must be consid‐ ered in high capacity optical networks, which can hardly be controlled due to its dynamic and stochastic nature [5][21-22]. On the other hand, the GVD causes the temporal spreading of optical pulses that limits the product line rate and link length [6-30]. The pulse spreading effect due to the combined effects of the GVD and the first-order PMD for Gaussian pulses can be calculated as [30]:

$$\sigma\_D = \left| \left( 1 + \frac{\mathbb{C}\_p \beta\_2 d\_{ij}}{2\pi\_0^2} \right) + \left( \frac{\beta\_2 d\_{ij}}{2\pi\_0^2} \right) + \chi - \left( \frac{1}{2\left[ 1 + \mathbb{C}\_p \right]^2} \times \sqrt{1 + \frac{4}{3} \left( 1 + \mathbb{C}\_p^2 \right)} \chi - 1 \right) \right|^{1/2} \tag{3}$$

where *Cp* is the chirp parameter, *τ*<sup>0</sup> <sup>=</sup> *TC* 2 2ln2 is the RMS pulse width, *Tc* is the chip period at half maximum, *β*<sup>2</sup> = −*Dλ*<sup>0</sup> <sup>2</sup> / 2*πc* is the GVD factor, *D* is the dispersion parameter, *c* is the speed of light in the vacuum, *<sup>x</sup>* <sup>=</sup>*Δτ* <sup>2</sup> / <sup>4</sup>*τ*<sup>0</sup> 2 and *Δτ* =*DPMD dij* , *DPMD* is the PMD parameter, and *dij* is the link length. Although there is a difference in the GVD for each wavelength, re‐ sulting from time skewing between the wavelengths, the consideration of the same GVD value for the entire transmission window is reasonable for a small number of wavelengths, as for the present code [27], [28]. On the other hand, this approximation is utilized to obtain an analytical treatment of the GVD and the PMD, in the same and less complex formalism, rather than to apply a formalism based on numerical methods [6].

The ASE (*Nsp eq* ) at the cascaded amplified spans is given by the model presented in Fig. 3 [29].

**Figure 3.** Cascading amplifiers.

**3.2. Physical restrictions**

150 Search Algorithms for Engineering Optimization

for currently stage of optical networks.

can be calculated as [30]:

*σ<sup>D</sup>* ={(1 +

half maximum, *β*<sup>2</sup> = −*Dλ*<sup>0</sup>

*Cpβ*2*dij* 2*τ*<sup>0</sup>

where *Cp* is the chirp parameter, *τ*<sup>0</sup> <sup>=</sup> *TC*

speed of light in the vacuum, *<sup>x</sup>* <sup>=</sup>*Δτ* <sup>2</sup> / <sup>4</sup>*τ*<sup>0</sup>

<sup>2</sup> ) <sup>+</sup> ( *<sup>β</sup>*2*dij* 2*τ*<sup>0</sup>

<sup>2</sup> ) <sup>+</sup> *<sup>x</sup>* <sup>−</sup>( <sup>1</sup>

2 2ln2

2

2(1 + *Cp* 2 ) <sup>×</sup> <sup>1</sup> <sup>+</sup> 4 <sup>3</sup> (1 <sup>+</sup> *Cp* 2 )*x* −1)}

<sup>2</sup> / 2*πc* is the GVD factor, *D* is the dispersion parameter, *c* is the

and *Δτ* =*DPMD dij*

1/2

, *DPMD* is the PMD parameter,

is the RMS pulse width, *Tc* is the chip period at

(3)

The physical impairments are signal degradation mechanisms that significantly affect the overall performance of optical communication systems [6]. For the data that are transmitted through a transparent optical network, degradation effects may accumulate over a large dis‐ tance. The major linear physical impairments are group velocity dispersion (GVD), polariza‐ tion mode dispersion (PMD), and amplifier spontaneous emission (ASE) noise [24]. On the other hand, the major nonlinear physical impairments are self phase modulation (SPM), crossphase modulation (XPM), and four wave mixing (FWM), stimulated Brillouin scattering (SBS), and Raman scattering (SRS). The nonlinear physical impairments are excited with high power level [24]. However, the maximum power constraint guarantees the minimization of nonlinear physical impairments, because it makes the aggregate power on a link to be limited to a maxi‐ mum value [6]. In the currently technology stage, besides GVD, the main linear impairment is the PMD, that must be considered in high capacity optical networks. Differently from GVD, PMD is usually difficult to accurately determine and compensate due to its dynamic nature and its fluctuations induced by external stress/strain applied to the fiber after installation [5] [21][22]. As a result, the signals quality in an OCDM/WDM network can be quickly evaluated by analyzing the GVD, PMD and MAI restrictions. PMD impairment establishes an upper bound on the length of the optical segment due to fiber dispersion which causes the temporal spreading of optical pulses. On the other hand, due to the advances in the fiber manufacturing process with a continuous reduction of the PMD parameter, the deleterious effect of PMD will not be an issue for 10 Gbps or lower bit rates, for future small and medium-sized networks [20] [21]. In this context, the dominant impairment in SNIR will be given by i) ASE noise accumula‐ tion in chains of optical amplifiers for future optical networks [29] and ii) ASE, GVD and PMD

The dispersive effects, such as chromatic or group velocity dispersion (GVD) and polariza‐ tion mode dispersion (PMD) constitute degradation mechanisms of the optical signal that significantly affect the overall performance of optical communication systems [21]. Current‐ ly, the PMD effect appears to be the only major physical impairment that must be consid‐ ered in high capacity optical networks, which can hardly be controlled due to its dynamic and stochastic nature [5][21-22]. On the other hand, the GVD causes the temporal spreading of optical pulses that limits the product line rate and link length [6-30]. The pulse spreading effect due to the combined effects of the GVD and the first-order PMD for Gaussian pulses This model considers that the receiver gets the signal from a link with cascading amplifiers, numbered as 1, 2,.., starting from the receiver. The pre-amplifier can be contemplated as the number 0 cascade amplifier. Let *Gi* be the amplifier gain, *i.* e. *Nsp*-i will be its spontaneous emission factor. The span between the i-*th* and the (*i − 1)*-*th* amplifier has the attenuation *Gii*. Let *Pti* be the mark power at the *i-th* amplifier input. The equivalent spontaneous emission factor is given by [24], [29]

$$N\_{sp}^{eq} = \frac{N\_{sp-1} \left(G\_1 - 1\right) G\_{ii} G\_0 + N\_{sp-0} \left(G\_0 - 1\right)}{G\_1 G\_{ii} G\_0 - 1} \tag{4}$$

Calculating recursively the *Nsp eq* factor, one can find the noise at the cascading amplifiers. The noise for i-*th* amplifier is given by *Nsp*−*<sup>i</sup>* =2*nsphf* (*Gi* −1)*B*0, which take into account the two polarization mode presented in a single mode fiber [24]. Where *nSP* is the spontaneous emis‐ sion factor, typically around 2 *−* 5, *h* is Planck's constant, *f* is the carrier frequency, *Gi* is the amplifier gain and *Bo* is the optical bandwidth. Ideally, to reduce the ASE noise power, the optical bandwidth can be set to a minimum of *Bo* = 2*R*, where *R* is the bit rate. Without loss of generality, all employed optical amplifiers provide a uniform gain, setting the maximum obtainable Erbium-doped fiber amplifier (EDFA) to 20 dB across the transmission window. This is a reasonable assumption for the reduced number of wavelengths in the code trans‐ mission window (4 wavelengths), considering the optical amplifier gain profile, where the maximum difference of this gain is 0.4 dB for the wavelength, which is the most distant one from the central wavelength (1550 nm), with spectral spacing of 100 GHz [6][17].

where *ω t* is the inertia weight of the previous velocity in the present speed calculation, the

**U***p*<sup>2</sup> *t* with dimension *K* have their elements as random variables with uniform distribution

best global vector-position and the best local vector-position found until the *tth* iteration, re‐ spectively; *C*1 and *C*2 are acceleration coefficients regarding the best particles and the best global positions influences in the velocity updating, respectively. The *pth* particle's position

where P is the population size. In order to reduce the likelihood that the particle might leave the search universe, maximum velocity factor *Vmax* factor is added to the PSO model, which will be responsible for limiting the velocity to the range ±*V max* . Hence, the adjustment of velocity allows the particle to move in a continuous but constrained subspace, been simply

each of *K*-dimension is clamped to a maximum magnitude *Vmax*. Besides, if the search space could be defined by the bounds *Pmin*; *Pmax* , then the value of *Vmax* typically is set so that *Vmax* =*τ*(*Pmax* - *Pmin*), where 0.1≤*τ* ≤1.0; please refer to Chapter 1 within the definition of

In order to elaborate further about the inertia weight it can be noted that a relatively larger value of *ω* is helpful for global optimum, and lesser influenced by the best global and local positions, while a relatively smaller value for *ω* is helpful for convergence, i.e., smaller iner‐ tial weight encourages the local exploration as the particles are more attracted towards **b***<sup>p</sup>*

ties, a linear inertia weight decreasing with the algorithm convergence evolving was adopt‐ ed, which has demonstrated good global search capability at beginning and good local

*<sup>ω</sup> <sup>t</sup>* =(*ωinitial* - *<sup>ω</sup> final*)∙( <sup>G</sup> - *<sup>t</sup>*

[31, 32]. Hence, in order to achieve a balance between global and local search abili‐

<sup>G</sup> )*<sup>m</sup>*

*<sup>t</sup>* … <sup>v</sup>*p*<sup>K</sup>

**b***<sup>p</sup> t* + 1 = **b***<sup>p</sup> t* + **v***<sup>p</sup> t* + 1 , *p* =1, …, P (6)

*<sup>t</sup>* }}, *k* =1, …, *K*; *p* =1, …, P (7)

*<sup>t</sup>* | exceeds a positive constant value *Vmax* specified by the user,

*<sup>t</sup> <sup>T</sup>* ; the diagonal matrices **U***p*<sup>1</sup> *<sup>t</sup>* and

Optical Network Optimization Based on Particle Swarm Intelligence

*best <sup>t</sup>* and **b***<sup>p</sup>*

*<sup>t</sup>* <sup>b</sup>*p*<sup>2</sup>

*<sup>t</sup>* )*Vmax*, i.e. particles velocity on

+ *ω final* (8)

*<sup>t</sup>* … <sup>b</sup>*p*<sup>K</sup>

http://dx.doi.org/10.5772/52225

*best t* are the

153

*<sup>t</sup> <sup>T</sup>* . The

*best*

*<sup>t</sup>* <sup>v</sup>*p*<sup>2</sup>

*∼ U ∈* [0, 1], generated for the *p*th particle at iteration *t* = 1, 2,..., G; **b***<sup>g</sup>*

at the *t*th iteration is defined by the power candidate-vector **b***<sup>p</sup> t* = b*p*<sup>1</sup>

position of each particle is updated using the new velocity vector for that particle,

velocity-vector has K dimension **v***<sup>p</sup> t* = v*p*<sup>1</sup>

accomplished by:

reference [35].

and **b***<sup>g</sup> best* v*pk*

From (7) it's clear that if |v*pk*

search capability latter iterations:

*<sup>t</sup>* =min {*Vmax*;max {-*Vmax*; <sup>v</sup>*pk*

the *p*th particle' velocity of *k*th user is assigned to be sign(v*pk*

## **3.3. Particle swarm optimization**

## *3.3.1. PSO description*

Particle Swarm Optimization (PSO) is a population-based stochastic optimization algorithm for global optimization that was presented first in 1995 [31]. It is based on the behavior of social groups like fish schools or bird flocks and it differs from other well-known Evolution‐ ary Algorithms (EA). As in EA, a population of potential solutions is used to probe the search space, but no operators, inspired by evolution procedures, are applied on the popula‐ tion to generate new promising solutions [32]. The fact which is recursively exploited is that an improved performance can be gained by interactions between individuals, or more spe‐ cifically by imitation of successful individuals. In a PSO system, particles fly around in mul‐ tidimensional search space. During the flight, each particle adjusts its position according to its own experience, and the experience of neighboring particles, making use of the best posi‐ tion encountered by itself and its neighbors. The swarm direction of a particle is defined by the set of particles neighboring the particle and its history experience. Although PSO does not rely on the survival of the fittest principle, it is often classified as an evolutionary algo‐ rithm (EA) because the update equations, which control the movement of individuals, are similar to the evolutionary operators used in EAs.

In general, the PSO performance for resource allocation problem can guarantee fast conver‐ gence and fairness within fewer iterations regarding the genetic algorithm-based [16]. It is well known in the literature that the PSO performance for resource allocation problem is highly dependent on its control parameters and that recommended parameter settings from the literature often do not lead to reliable and fast convergence behavior for the considered optimization problem [33], [34], [35].

In the PSO process, each particle keeps track of its coordinates in the space of interest, which are associated with the best solution (fitness) it has achieved so far. Another best value tracked by the global version of the particle swarm optimizer is the overall best value, and its location, obtained so far by any particle in the population. At each time iteration step, the PSO concept consists of velocity changes of each particle toward local and global locations. Acceleration is weighted by a random term, with separate random numbers being generated for acceleration toward local and global locations. Let *bp* and *vp* denote a particle coordinates (position) and its corresponding flight speed (velocity) in a search space, respectively. In this strategy, each power-vector candidate **b***<sup>p</sup> t* , with dimension *K* x 1, is used for the velocityvector calculation of the next iteration [33]:

$$\mathbf{v}\_p[t+1] = \omega[t] \bullet \mathbf{v}\_p[t] + \mathbf{C}\_1 \bullet \mathbf{U}\_p[t] \mathbf{b}\_p^{\mathrm{best}}[t] \bullet \mathbf{b}\_p[t] + \mathbf{C}\_2 \bullet \mathbf{U}\_p[t] \mathbf{b}\_p^{\mathrm{best}}[t] \bullet \mathbf{b}\_p[t] \tag{5}$$

where *ω t* is the inertia weight of the previous velocity in the present speed calculation, the velocity-vector has K dimension **v***<sup>p</sup> t* = v*p*<sup>1</sup> *<sup>t</sup>* <sup>v</sup>*p*<sup>2</sup> *<sup>t</sup>* … <sup>v</sup>*p*<sup>K</sup> *<sup>t</sup> <sup>T</sup>* ; the diagonal matrices **U***p*<sup>1</sup> *<sup>t</sup>* and **U***p*<sup>2</sup> *t* with dimension *K* have their elements as random variables with uniform distribution *∼ U ∈* [0, 1], generated for the *p*th particle at iteration *t* = 1, 2,..., G; **b***<sup>g</sup> best <sup>t</sup>* and **b***<sup>p</sup> best t* are the best global vector-position and the best local vector-position found until the *tth* iteration, re‐ spectively; *C*1 and *C*2 are acceleration coefficients regarding the best particles and the best global positions influences in the velocity updating, respectively. The *pth* particle's position at the *t*th iteration is defined by the power candidate-vector **b***<sup>p</sup> t* = b*p*<sup>1</sup> *<sup>t</sup>* <sup>b</sup>*p*<sup>2</sup> *<sup>t</sup>* … <sup>b</sup>*p*<sup>K</sup> *<sup>t</sup> <sup>T</sup>* . The position of each particle is updated using the new velocity vector for that particle,

maximum difference of this gain is 0.4 dB for the wavelength, which is the most distant one

Particle Swarm Optimization (PSO) is a population-based stochastic optimization algorithm for global optimization that was presented first in 1995 [31]. It is based on the behavior of social groups like fish schools or bird flocks and it differs from other well-known Evolution‐ ary Algorithms (EA). As in EA, a population of potential solutions is used to probe the search space, but no operators, inspired by evolution procedures, are applied on the popula‐ tion to generate new promising solutions [32]. The fact which is recursively exploited is that an improved performance can be gained by interactions between individuals, or more spe‐ cifically by imitation of successful individuals. In a PSO system, particles fly around in mul‐ tidimensional search space. During the flight, each particle adjusts its position according to its own experience, and the experience of neighboring particles, making use of the best posi‐ tion encountered by itself and its neighbors. The swarm direction of a particle is defined by the set of particles neighboring the particle and its history experience. Although PSO does not rely on the survival of the fittest principle, it is often classified as an evolutionary algo‐ rithm (EA) because the update equations, which control the movement of individuals, are

In general, the PSO performance for resource allocation problem can guarantee fast conver‐ gence and fairness within fewer iterations regarding the genetic algorithm-based [16]. It is well known in the literature that the PSO performance for resource allocation problem is highly dependent on its control parameters and that recommended parameter settings from the literature often do not lead to reliable and fast convergence behavior for the considered

In the PSO process, each particle keeps track of its coordinates in the space of interest, which are associated with the best solution (fitness) it has achieved so far. Another best value tracked by the global version of the particle swarm optimizer is the overall best value, and its location, obtained so far by any particle in the population. At each time iteration step, the PSO concept consists of velocity changes of each particle toward local and global locations. Acceleration is weighted by a random term, with separate random numbers being generated for acceleration toward local and global locations. Let *bp* and *vp* denote a particle coordinates (position) and its corresponding flight speed (velocity) in a search space, respectively. In this strategy, each power-vector candidate **b***<sup>p</sup> t* , with dimension *K* x 1, is used for the velocity-

*best <sup>t</sup>* - **<sup>b</sup>***<sup>p</sup> <sup>t</sup>* ) <sup>+</sup> *<sup>C</sup>*<sup>2</sup> <sup>∙</sup>**U***p*<sup>2</sup> *<sup>t</sup>* (**b***<sup>g</sup>*

*best <sup>t</sup>* - **<sup>b</sup>***<sup>p</sup> <sup>t</sup>* ) (5)

from the central wavelength (1550 nm), with spectral spacing of 100 GHz [6][17].

**3.3. Particle swarm optimization**

152 Search Algorithms for Engineering Optimization

similar to the evolutionary operators used in EAs.

optimization problem [33], [34], [35].

vector calculation of the next iteration [33]:

**v***<sup>p</sup> t* + 1 = *ω t* ∙**v***<sup>p</sup> t* + *C*1∙**U***p*<sup>1</sup> *t* (**b***<sup>p</sup>*

*3.3.1. PSO description*

$$\mathbf{b}\_p \mathbf{\sf f} t + 1 \mathbf{\sf f} = \mathbf{b}\_p \mathbf{\sf f} t + \mathbf{v}\_p \mathbf{\sf f} t + 1 \mathbf{\sf f}, \quad p = 1, \ldots, \mathbf{\sf P} \tag{6}$$

where P is the population size. In order to reduce the likelihood that the particle might leave the search universe, maximum velocity factor *Vmax* factor is added to the PSO model, which will be responsible for limiting the velocity to the range ±*V max* . Hence, the adjustment of velocity allows the particle to move in a continuous but constrained subspace, been simply accomplished by:

$$\mathbf{v}\_{pk}^{l} = \min \left\{ V\_{\max}; \max \left\| \mathbf{-} V\_{\max}; \ \mathbf{v}\_{pk}^{l} \right\| \right\}, \quad k = 1, \ldots, K; \quad p = 1, \ldots, \mathbf{P} \tag{7}$$

From (7) it's clear that if |v*pk <sup>t</sup>* | exceeds a positive constant value *Vmax* specified by the user, the *p*th particle' velocity of *k*th user is assigned to be sign(v*pk <sup>t</sup>* )*Vmax*, i.e. particles velocity on each of *K*-dimension is clamped to a maximum magnitude *Vmax*. Besides, if the search space could be defined by the bounds *Pmin*; *Pmax* , then the value of *Vmax* typically is set so that *Vmax* =*τ*(*Pmax* - *Pmin*), where 0.1≤*τ* ≤1.0; please refer to Chapter 1 within the definition of reference [35].

In order to elaborate further about the inertia weight it can be noted that a relatively larger value of *ω* is helpful for global optimum, and lesser influenced by the best global and local positions, while a relatively smaller value for *ω* is helpful for convergence, i.e., smaller iner‐ tial weight encourages the local exploration as the particles are more attracted towards **b***<sup>p</sup> best* and **b***<sup>g</sup> best* [31, 32]. Hence, in order to achieve a balance between global and local search abili‐ ties, a linear inertia weight decreasing with the algorithm convergence evolving was adopt‐ ed, which has demonstrated good global search capability at beginning and good local search capability latter iterations:

$$
\omega \mathbf{f} \mathbf{f} = \begin{pmatrix} \omega\_{initial} \ - & \omega\_{final} \end{pmatrix} \bullet \begin{pmatrix} \frac{\mathbf{G} \cdot \mathbf{t}}{\mathbf{G}} \end{pmatrix}^{m} + \begin{pmatrix} \omega\_{final} \end{pmatrix} \tag{8}
$$

where *ωinitial* and *ω final* is the initial and final weight inertia, respectively, *ωinitial* >*ω final* , G is the maximum number of iterations, and *m* ∈ 0.6; 1.4 is the nonlinear index [36].

#### *3.3.2. Optical code path resource allocation optimization*

The following maximization cost function could be employed as an alternative to OCP re‐ source allocation optimization [33]. This single-objective function was modified in order to incorporate the near-far effect [37], [38]

$$\begin{aligned} \mathcal{I}\_{1}(\mathbf{p}) &= \max \frac{\frac{1}{K} \sum\_{k=1}^{K} \mathsf{F}\_{k}^{th} \left( 1 - \frac{p\_{k}}{P\_{\max}} \right) + \frac{\rho}{\sigma\_{\eta}}}{\mathcal{V}\_{k} \geq \mathcal{V}\_{k'}^{\*} \quad 0 < p\_{k}^{l} \leq P\_{\max}, \quad \mathcal{R}^{l} = \mathcal{R}\_{\min}^{l} \; \forall \; k \in \mathcal{K}\_{l'} \; and \; \forall \; l = 1, 2, \dots, L \end{aligned} \tag{9}$$

where *L* is the number of different group of information rates allowing in the system, and *Kl* is the number of user in the *l*th rate group with minimum rate given by *R*min *<sup>l</sup>* . Important to say, the second term in eq. (9) gives credit to the solutions with small standard deviation of the normalized (by the inverse of rate factor, *F <sup>l</sup>* ) received power distribution:

$$\sigma\_{rp}^{2} = \text{var}\left(F^{1}p\_{1}G\_{11r} \; F^{1}p\_{2}G\_{22r} \; \dots \; \text{.} \; F^{1}p\_{k}G\_{kk'} \; \dots \; \text{.} \; F^{L} \; p\_{k}G\_{kk}\right) \tag{10}$$

i.e. the more close the normalized received power values are with other (small variance of normalized received power vector), the bigger contribution of the term *<sup>ρ</sup> σrp* . For single-rate systems, *F* <sup>1</sup> = … = *F <sup>l</sup>* = … = *F <sup>L</sup>* . It is worth to note that since the variance of the normalized received power vector, *σrp* <sup>2</sup> , normally assumes very small values, the coefficient *ρ* just also take very small values in order to the ratio *<sup>ρ</sup> σrp* achieves a similar order of magnitude of the first term in (9), been determined as a function of the number of users, *K*. Hence, the term *ρ σrp* has an effective influence in minimizing the near-far effect on OCDM/WDM systems, and at the same time it has a non-zero value for all swarm particles [33]. Finally, the thresh‐ old function in (9) is simply defined as:

$$\mathsf{F}\_{k}^{th} = \begin{cases} 1, & \boldsymbol{\gamma}\_{k} \ge \boldsymbol{\gamma}^\* \\ 0, & \text{otherwise} \end{cases} \tag{11}$$

The quality of solution achieved by any iterative resource allocation procedure could be measured by how close to the optimum solution is the found solution, and can be quantified by the normalized mean squared error (NMSE) when equilibrium is reached. For power al‐

denotes the squared Euclidean distance to the origin, and E ∙ the expectation

**<sup>p</sup>**\* <sup>2</sup> (12)

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155

*NMSE <sup>t</sup>* <sup>=</sup> <sup>E</sup> **<sup>p</sup>** *<sup>t</sup>* - **p**\* <sup>2</sup>

location problem, the NSE definition is given by,

where ∙ <sup>2</sup>

operator.

where the SNIR for the *k*th user, *γ<sup>k</sup>* , is given by (2). The term 1 - *pk Pmax* gives credit to those solutions with minimum power and punishes others using high power levels [33].

The PSO algorithm consists of repeated application of the updating velocity and position, eq. (5) and (6), respectively. The pseudo-code for the single-objective continuous PSO power allocation problem is presented in Algorithm 1.

where *ωinitial*

*J*1

(**p**)=max

and *ω final* is the initial and final weight inertia, respectively, *ωinitial* >*ω final*

The following maximization cost function could be employed as an alternative to OCP re‐ source allocation optimization [33]. This single-objective function was modified in order to

= *R*min

where *L* is the number of different group of information rates allowing in the system, and *Kl*

say, the second term in eq. (9) gives credit to the solutions with small standard deviation of

i.e. the more close the normalized received power values are with other (small variance of

*σrp*

*th* <sup>=</sup> {1, *<sup>γ</sup><sup>k</sup>* <sup>≥</sup> *<sup>γ</sup>* \* 0, *otherwise*

solutions with minimum power and punishes others using high power levels [33].

The PSO algorithm consists of repeated application of the updating velocity and position, eq. (5) and (6), respectively. The pseudo-code for the single-objective continuous PSO power

first term in (9), been determined as a function of the number of users, *K*. Hence, the term

 has an effective influence in minimizing the near-far effect on OCDM/WDM systems, and at the same time it has a non-zero value for all swarm particles [33]. Finally, the thresh‐

*<sup>l</sup>* <sup>∀</sup>*<sup>k</sup>* <sup>∈</sup> *Kl*

, *and* ∀*l* =1,2, …, *L*

*pkGkk* , …, *<sup>F</sup> <sup>L</sup> pkGkk* ) (10)

achieves a similar order of magnitude of the

*σrp*

) received power distribution:

= … = *F <sup>L</sup>* . It is worth to note that since the variance of the normalized

<sup>2</sup> , normally assumes very small values, the coefficient *ρ* just also

the maximum number of iterations, and *m* ∈ 0.6; 1.4 is the nonlinear index [36].

*3.3.2. Optical code path resource allocation optimization*

*th* (1 - *pk Pmax* ) <sup>+</sup> *<sup>ρ</sup> σrp*

<sup>≤</sup> *<sup>P</sup>*max, *<sup>R</sup> <sup>l</sup>*

is the number of user in the *l*th rate group with minimum rate given by *R*min

normalized received power vector), the bigger contribution of the term *<sup>ρ</sup>*

F*k*

where the SNIR for the *k*th user, *γ<sup>k</sup>* , is given by (2). The term 1 - *pk*

<sup>2</sup> =var (*<sup>F</sup>* <sup>1</sup> *<sup>p</sup>*1*G*11, *<sup>F</sup>* <sup>1</sup> *<sup>p</sup>*2*G*22, …, *<sup>F</sup> <sup>l</sup>*

incorporate the near-far effect [37], [38]

*γ<sup>k</sup>* ≥ *γ<sup>k</sup>* \* , 0< *pk l*

the normalized (by the inverse of rate factor, *F <sup>l</sup>*

take very small values in order to the ratio *<sup>ρ</sup>*

allocation problem is presented in Algorithm 1.

old function in (9) is simply defined as:

1 *<sup>K</sup>* ∑ *k*=1 *K* F*k*

154 Search Algorithms for Engineering Optimization

*σrp*

systems, *F* <sup>1</sup> = … = *F <sup>l</sup>*

*ρ σrp*

received power vector, *σrp*

, G is

(9)

*<sup>l</sup>* . Important to

. For single-rate

(11)

*Pmax* gives credit to those

The quality of solution achieved by any iterative resource allocation procedure could be measured by how close to the optimum solution is the found solution, and can be quantified by the normalized mean squared error (NMSE) when equilibrium is reached. For power al‐ location problem, the NSE definition is given by,

$$\mathbb{E}\left[\text{NMSE}\left[t\right]\right] = \mathbb{E}\left[\frac{\|\left[\mathbf{f}\left[t\right]\cdot\mathbf{p}^\*\right]\|^2}{\|\mathbf{f}\left[t\right]\|^2}\right] \tag{12}$$

where ∙ <sup>2</sup> denotes the squared Euclidean distance to the origin, and E ∙ the expectation operator.

#### *3.3.3. Energy efficiency optimization in OCPs*

Recent studies have showed the importance of the consideration of energy consumption in optical communications design [39], considering the transmission infrastructure (transmit‐ ters, receivers, fibers and amplifiers) [40] and network infrastructure (switchers and rout‐ ers) [41] aspects. Researches in a global scale network have indicated that the energy consumption of the switching infrastructure is larger than the energy consumption of the transport infrastructure [39-41]. In this context, it is necessary to improving the energy ef‐ ficiency of switching and optimizing the network design in order to reduce the quantity of switching and overheads. The energy necessary for 1 bit transmission on each OCP can be expressed as [40],

$$E\_i = p\_i T\_{bit} \qquad \left[\text{J/bit}\right], i = 1, \dots, K \tag{13}$$

( ) ( ) <sup>2</sup> , 1,.., *<sup>i</sup> <sup>i</sup> i i*

( ) ( ) , ..,0 1, *<sup>i</sup>*

*i K <sup>g</sup>*

To satisfy (17) it is necessary that the received node achieves the target SNIR, namely*γ<sup>i</sup>*

this context, we propose the utilization of PSO power allocation algorithm in order to estab‐ lish the lower energy per bit according to the OCDM/WDM network QoS requirements.

For all simulations, it is considered the transmission over a nonzero-dispersion shifted fiber (NFD)-ITU G.655 with fiber attenuation (α) of 0.2 dB/km, non-linear parameter (Γ) of 2 (W.km)-1, zero-dispersion wavelength (λ0) of 1550 nm, dispersion slope (S0) of 0.07 ps/

\*

**4.1. PSO parameters optimization for resource allocation problem**

.km). The signal is placed at λ0 and its peak power is P. Note that the nonlinear length [24] LNL= 1/(ΓP) is limited to 500 km, which is much longer than the considered fiber lengths; besides self-phase modulation (SPM) should not seriously affect the system performance. Furthermore, the threshold power for stimulated Brillouin scattering (SBS) is below a few mW; as a result, SBS should also not interfere in our results. Similarly, for these considera‐ tions, the physical impairments, such as stimulated Raman scattering (SRS) should not be relevant [24]. Typical parameter values for the noise power in all optical amplifiers were as‐ sumed [21]. So, it was adopted *nSP=* 2*, h=*6*.*63 *×* 10*−*34 (J/Hz), *f=*193*.*1 (THz), *G=*20 (dB) and *Bo*=30 (GHz). Herein, it was considered an amplifier gain of 20 dB with a minimum spacing of 60 km, *DPMD=*0*.*1*ps* / *km*, and *D*=15 ps/nm/km. Losses for encoder/decoder and router ar‐ chitecture of 5 dB and 20 dB, respectively, were included in the power losses model [22-24]. The parameters are code weight of 4 and code length of 101, thus the code is characterized

=20dB was adopted.

For power resource allocation problem, simulation experiments were carried out in order to determine the suitable values for the PSO input parameters, such as acceleration coefficients, *C*1 and *C*2, maximal velocity factor, *Vmax*, weight inertia, *ω*, and population size, P, regarding

The continuous optimization for resource allocation problem was investigated in [33], [34], it indicates that after an enough number of iterations (G) for convergence, the maximization of

g

g

¶ æ ö ¶ <sup>=</sup> ç ÷ - <sup>=</sup> ¶ ¶ è ø

*<sup>R</sup> <sup>g</sup> gi K*

 g

> 0, the necessary condition to maximize the energy efficiency is

Optical Network Optimization Based on Particle Swarm Intelligence

<sup>=</sup> ¶ - = (17)

(16)

157

http://dx.doi.org/10.5772/52225

\* . In

*i i i*

g

*i i i*

 ¶g

g

*g*

 g

*p p* h

g

From (16) we observe, for *pi*

**4. Numerical results**

by (*4 × 101, 4, 1,0*) and the target SNIR *γ<sup>i</sup>*

the power optimization problem.

(nm2

where *Tbit* =1/*R* is the time to transmit one bit over the network, with *R* is the bit rate. In our analysis, to determinate the energy is necessary define the individual OCPs transmitted power (*pi* ). The *pi* is obtained by power control PSO algorithm given in Algorithm 1 and may be associated to a specific QoS, SNIR and maximum BER tolerated by the *i*-th optical node. In a power control situation, each optical node adjusts its transmitter power in an attempt to maximize the number of transmitted bits with minimum consumption of energy. This con‐ cept is formulated by the energy efficiency [42]:

$$\eta\_i = \frac{\mathcal{R} \cdot \mathcal{g}\left(\boldsymbol{\gamma}\_i\right)}{p\_i}, \quad i = 1, \ldots, K \tag{14}$$

where *g*(*γ<sup>i</sup>* ) =1− *BERi* is the efficiency function, which represents the number of correct packets received for the for the *i-*th node, given a SNIR *γ<sup>i</sup>* . In the same way this concept is used in a metric called *utility* that is the number of bits received per energy expended or the relation of the throughput and power dissipation [41].

For each *i-*th OCP, the maximum number of transmitted bits occurs at power level for which the partial derivative of energy efficiency function in (14) with respect to *pi* is zero ∂*η<sup>i</sup>* / ∂ *pi* =0. Considering a SNIR general formula for CDMA networks, given by [6]

$$\gamma\_i = \frac{h\_{ii} p\_i}{I\_i + N\_i}, \text{ i = 1,...,K} \tag{15}$$

where *hij* are the total loss in the path that connects *i-*th transmitter node to *j-*th receiver node, *I1* is the interference from the others transmitters nodes and *Ni* is the receiver noise. We can obtain the derivative of energy efficiency referring to efficiency function and (15),

$$\frac{\partial \eta\_i}{\partial p\_i} = \frac{R}{p\_i^2} \left( \gamma\_i \frac{\partial g\left(\boldsymbol{\gamma}\_i\right)}{\partial \boldsymbol{\gamma}\_i} - g\left(\boldsymbol{\gamma}\_i\right) \right) / i = \ 1, \ldots, K \tag{16}$$

From (16) we observe, for *pi* > 0, the necessary condition to maximize the energy efficiency is

$$\text{reg}\_i \frac{\partial g\left(\boldsymbol{\gamma}\_i\right)}{\partial \boldsymbol{\gamma}\_i} - g\left(\boldsymbol{\gamma}\_i\right) = 0,\\ i = 1, \ldots, K \tag{17}$$

To satisfy (17) it is necessary that the received node achieves the target SNIR, namely*γ<sup>i</sup>* \* . In this context, we propose the utilization of PSO power allocation algorithm in order to estab‐ lish the lower energy per bit according to the OCDM/WDM network QoS requirements.

## **4. Numerical results**

*3.3.3. Energy efficiency optimization in OCPs*

156 Search Algorithms for Engineering Optimization

cept is formulated by the energy efficiency [42]:

*i*

h

packets received for the for the *i-*th node, given a SNIR *γ<sup>i</sup>*

*i*

g

relation of the throughput and power dissipation [41].

expressed as [40],

power (*pi*

where *g*(*γ<sup>i</sup>*

) =1− *BERi*

Recent studies have showed the importance of the consideration of energy consumption in optical communications design [39], considering the transmission infrastructure (transmit‐ ters, receivers, fibers and amplifiers) [40] and network infrastructure (switchers and rout‐ ers) [41] aspects. Researches in a global scale network have indicated that the energy consumption of the switching infrastructure is larger than the energy consumption of the transport infrastructure [39-41]. In this context, it is necessary to improving the energy ef‐ ficiency of switching and optimizing the network design in order to reduce the quantity of switching and overheads. The energy necessary for 1 bit transmission on each OCP can be

, 1,.., *i i bit E p T J bit i K* = é ù

where *Tbit* =1/*R* is the time to transmit one bit over the network, with *R* is the bit rate. In our analysis, to determinate the energy is necessary define the individual OCPs transmitted

be associated to a specific QoS, SNIR and maximum BER tolerated by the *i*-th optical node. In a power control situation, each optical node adjusts its transmitter power in an attempt to maximize the number of transmitted bits with minimum consumption of energy. This con‐

( ) , 1,.., *<sup>i</sup>*

used in a metric called *utility* that is the number of bits received per energy expended or the

For each *i-*th OCP, the maximum number of transmitted bits occurs at power level for which

, 1,.., *ii i*

where *hij* are the total loss in the path that connects *i-*th transmitter node to *j-*th receiver node, *I1* is the interference from the others transmitters nodes and *Ni* is the receiver noise. We can obtain the derivative of energy efficiency referring to efficiency function and (15),

*i K*

the partial derivative of energy efficiency function in (14) with respect to *pi*

∂*η<sup>i</sup>* / ∂ *pi* =0. Considering a SNIR general formula for CDMA networks, given by [6]

*i i h p I N*

*R g i K*

*i*

*p* g

). The *pi* is obtained by power control PSO algorithm given in Algorithm 1 and may

ë û = (13)

<sup>=</sup> <sup>×</sup> <sup>=</sup> (14)

<sup>+</sup> == (15)

. In the same way this concept is

is zero

is the efficiency function, which represents the number of correct

For all simulations, it is considered the transmission over a nonzero-dispersion shifted fiber (NFD)-ITU G.655 with fiber attenuation (α) of 0.2 dB/km, non-linear parameter (Γ) of 2 (W.km)-1, zero-dispersion wavelength (λ0) of 1550 nm, dispersion slope (S0) of 0.07 ps/ (nm2 .km). The signal is placed at λ0 and its peak power is P. Note that the nonlinear length [24] LNL= 1/(ΓP) is limited to 500 km, which is much longer than the considered fiber lengths; besides self-phase modulation (SPM) should not seriously affect the system performance. Furthermore, the threshold power for stimulated Brillouin scattering (SBS) is below a few mW; as a result, SBS should also not interfere in our results. Similarly, for these considera‐ tions, the physical impairments, such as stimulated Raman scattering (SRS) should not be relevant [24]. Typical parameter values for the noise power in all optical amplifiers were as‐ sumed [21]. So, it was adopted *nSP=* 2*, h=*6*.*63 *×* 10*−*34 (J/Hz), *f=*193*.*1 (THz), *G=*20 (dB) and *Bo*=30 (GHz). Herein, it was considered an amplifier gain of 20 dB with a minimum spacing of 60 km, *DPMD=*0*.*1*ps* / *km*, and *D*=15 ps/nm/km. Losses for encoder/decoder and router ar‐ chitecture of 5 dB and 20 dB, respectively, were included in the power losses model [22-24]. The parameters are code weight of 4 and code length of 101, thus the code is characterized by (*4 × 101, 4, 1,0*) and the target SNIR *γ<sup>i</sup>* \* =20dB was adopted.

#### **4.1. PSO parameters optimization for resource allocation problem**

For power resource allocation problem, simulation experiments were carried out in order to determine the suitable values for the PSO input parameters, such as acceleration coefficients, *C*1 and *C*2, maximal velocity factor, *Vmax*, weight inertia, *ω*, and population size, P, regarding the power optimization problem.

The continuous optimization for resource allocation problem was investigated in [33], [34], it indicates that after an enough number of iterations (G) for convergence, the maximization of cost function were obtained within low values for both acceleration coefficients. The *Vmax* factor is then optimized. The diversity increases as the particle velocity crosses the limits es‐ tablished by ±*V max* . The range of *Vmax* determines the maximum change one particle can take during iteration. With no influence of inertial weight (*ω* =1), it was obtained that the maximum allowed velocity *Vmax* is best set around 10 to 20% of the dynamic range of each particle dimension [33]. The appropriate choose of *Vmax* avoids particles flying out of mean‐ ingful solution space. Herein, for OCP power allocation problem, similar to the problem solved in [33], the better performance *versus* complexity trade-off was obtained setting the maximal velocity factor value as *Vmax* =0.2 (*Pmax* - *Pmin*). For the inertial weight, *ω*, simula‐ tion results has confirmed that high values imply in fast convergence, but this means a lack of search diversity, and the algorithm can easily be trapped in some local optimum, whereas a small value for *ω* results in a slow convergence due to excessive changes around a very small search space. In this work, it was adopted a variable *ω*, as described in (8), but with *m* = 1, and initial and final weight inertia setting up to *ωinitial* = 1 and *ω final* = 0.01. Hence, the initial and final maximal velocity excursion values were bounded through the initial and fi‐ nal linear inertia weight multiplied by *Vmax*, adopted as a percentage of the maximal and minimal power difference values [33],

$$
\omega\_{\text{initial}} \bullet V\_{\text{max}} = 0.2 \left( P\_{\text{max}} - P\_{\text{min}} \right) \omega\_{\text{final}} \bullet V\_{\text{max}} = 0.002 \left( P\_{\text{max}} - P\_{\text{min}} \right) \tag{18}
$$

Finally, stopping criterion can be the maximum number of iterations G (velocity changes al‐ lowed for each particle) combined with the minimum error threshold:

$$\left| \frac{\|\mathbf{f}\| \cdot \|\mathbf{f}\|}{\|\mathbf{f}\|} \right| < \epsilon\_{stop} \tag{19}$$

problem through non-exhaustive search [33]. The swarm population size was set by

Optical Network Optimization Based on Particle Swarm Intelligence

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159

In power resource allocation problem for access network systems the parameters optimiza‐ tion, mainly acceleration coefficients *C1* and *C2*, depend on the number of simultaneous transmitted users [16], [33]. In the case of realistic OCDM/WDM routed networks, the num‐ ber of simultaneous transmitted OCPs is low, generally around or less than 10 [2], [5], [6], [25]. Fast convergence without losing certain exploration and exploitation capabilities could be obtained with optimization of acceleration parameters in relation to the standard values adopted in the literature [16]. Previous works have shown that the best convergence *versus* solution quality trade-off was achieved with *C1* = 1 and *C2* = 2 for number of codes less than 10 [16], [33]. On the other hand, the classical value adopted are *C1* = *C2* = 2 [32-35]. In this context, simulation experiments were carried out in order to determine the good choice for acceleration coefficients *C1* and *C2* regarding the power optimization problem. Fig. 4 illus‐ trates different solution qualities in terms of the normalized mean squared error (NMSE), when different values for *C1* combining with *C2* = 2 in a system with number of OCPs equal to 7, considering 1 span. Previous simulations have shown the non poor convergence for dif‐ ferent value of *C2* [33].The lengths of OCPs are uniformly distributed between 2 and 100 km. The NMSE values where taken as the average over T *=* 100 trials. Besides, the NMSE conver‐

(1 , 2) (1.4 , 2) (1.6 , 2) (1.8 , 2) (2 , 2) (2.2 , 2) (2.4 , 2)

(c1 , c2 )

**Figure 4.** Normalized mean squared error (NMSE) for different values for *C1* combining with *C2* = 2 in a system with

P= *K* + 2.

gence values were taken after G = 800 iterations.

1E-8 1E-7 1E-6 1E-5 1E-4 1E-3 0,01 0,1 1 10 100 1000 10000 100000

number of OCPs equal to 7, considering 1 span.

NMSE

where typically ∊*stop* ∈ 0.001;0.01 . Alternately, the convergence test can be evaluated through the computation of the average percent of success, taken over T runs to achieve the global optimum, and considering a fixed number of iterations G. A convergence test is con‐ sidered 100% successful if the following relation holds:

$$\|\cdot\|\:\|\mathbf{G}^\*-\cdot\|\:\mathbf{p}^\*\|\:\|\le\_1\|\mathbf{f}\mathbf{p}^\*\|+\,\_2\tag{20}$$

where, *J* |**p***\**| is the global optimum of the objective function under consideration, *J* |G| is the optimum of the objective function obtained by the algorithm after G iterations, and ∊<sup>1</sup> , <sup>∊</sup>2 are accuracy coefficients, usually in the range 10-6 ;10-2 . In this study it was assumed that T = 100 trials and ∊<sup>1</sup> <sup>=</sup> <sup>∊</sup><sup>2</sup> <sup>=</sup> <sup>10</sup>-2 .

The parameter *ρ* in cost function (9), was set as a function of the number of users OCPs (*K*), such that *ρ* = *K ×* 10*<sup>−</sup>*19. This relation was adapted from [38] for the power-rate allocation problem through non-exhaustive search [33]. The swarm population size was set by P= *K* + 2.

cost function were obtained within low values for both acceleration coefficients. The *Vmax* factor is then optimized. The diversity increases as the particle velocity crosses the limits es‐ tablished by ±*V max* . The range of *Vmax* determines the maximum change one particle can take during iteration. With no influence of inertial weight (*ω* =1), it was obtained that the maximum allowed velocity *Vmax* is best set around 10 to 20% of the dynamic range of each particle dimension [33]. The appropriate choose of *Vmax* avoids particles flying out of mean‐ ingful solution space. Herein, for OCP power allocation problem, similar to the problem solved in [33], the better performance *versus* complexity trade-off was obtained setting the maximal velocity factor value as *Vmax* =0.2 (*Pmax* - *Pmin*). For the inertial weight, *ω*, simula‐ tion results has confirmed that high values imply in fast convergence, but this means a lack of search diversity, and the algorithm can easily be trapped in some local optimum, whereas a small value for *ω* results in a slow convergence due to excessive changes around a very small search space. In this work, it was adopted a variable *ω*, as described in (8), but with *m*

initial and final maximal velocity excursion values were bounded through the initial and fi‐ nal linear inertia weight multiplied by *Vmax*, adopted as a percentage of the maximal and

Finally, stopping criterion can be the maximum number of iterations G (velocity changes al‐

where typically ∊*stop* ∈ 0.001;0.01 . Alternately, the convergence test can be evaluated through the computation of the average percent of success, taken over T runs to achieve the global optimum, and considering a fixed number of iterations G. A convergence test is con‐

where, *J* |**p***\**| is the global optimum of the objective function under consideration, *J* |G| is the optimum of the objective function obtained by the algorithm after G iterations, and ∊<sup>1</sup> ,

The parameter *ρ* in cost function (9), was set as a function of the number of users OCPs (*K*), such that *ρ* = *K ×* 10*<sup>−</sup>*19. This relation was adapted from [38] for the power-rate allocation

*ωinitial* ∙*Vmax* =0.2 (*Pmax* - *Pmin*) *ω final* ∙*Vmax* =0.002 (*Pmax* - *Pmin*) (18)

= 1 and *ω final* = 0.01. Hence, the


;10-2 . In this study it was assumed


= 1, and initial and final weight inertia setting up to *ωinitial*

lowed for each particle) combined with the minimum error threshold:

sidered 100% successful if the following relation holds:

<sup>∊</sup>2 are accuracy coefficients, usually in the range 10-6

.

that T = 100 trials and ∊<sup>1</sup> <sup>=</sup> <sup>∊</sup><sup>2</sup> <sup>=</sup> <sup>10</sup>-2


minimal power difference values [33],

158 Search Algorithms for Engineering Optimization

In power resource allocation problem for access network systems the parameters optimiza‐ tion, mainly acceleration coefficients *C1* and *C2*, depend on the number of simultaneous transmitted users [16], [33]. In the case of realistic OCDM/WDM routed networks, the num‐ ber of simultaneous transmitted OCPs is low, generally around or less than 10 [2], [5], [6], [25]. Fast convergence without losing certain exploration and exploitation capabilities could be obtained with optimization of acceleration parameters in relation to the standard values adopted in the literature [16]. Previous works have shown that the best convergence *versus* solution quality trade-off was achieved with *C1* = 1 and *C2* = 2 for number of codes less than 10 [16], [33]. On the other hand, the classical value adopted are *C1* = *C2* = 2 [32-35]. In this context, simulation experiments were carried out in order to determine the good choice for acceleration coefficients *C1* and *C2* regarding the power optimization problem. Fig. 4 illus‐ trates different solution qualities in terms of the normalized mean squared error (NMSE), when different values for *C1* combining with *C2* = 2 in a system with number of OCPs equal to 7, considering 1 span. Previous simulations have shown the non poor convergence for dif‐ ferent value of *C2* [33].The lengths of OCPs are uniformly distributed between 2 and 100 km. The NMSE values where taken as the average over T *=* 100 trials. Besides, the NMSE conver‐ gence values were taken after G = 800 iterations.

**Figure 4.** Normalized mean squared error (NMSE) for different values for *C1* combining with *C2* = 2 in a system with number of OCPs equal to 7, considering 1 span.

Numerical results have shown the solution quality for different values of acceleration coeffi‐ cient *C1* and it was found *C*1 = 1.8 presents the lower NMSE for the number of OCPs < 10. Hence, the best solution quality was achieved with *C*<sup>1</sup> = 1.8 and *C*<sup>2</sup> = 2. Fig. 5 shows the sum of power for the evolution through the *t=*1,…, 800 iterations for 7 OCPs under different ac‐ celeration value of *C1* and *C2* = 2, considering 1 span.

2 4 6 8 10 12

Number of OCPs

**Figure 6.** Normalized mean squared error (NMSE) for the number of OCPs for (*C1* = 1.8 and *C2* = 2.0) and (*C1* = 2.0 and

The OCPs increasing affects the solution quality. This effect is directly related to the MAI rising which increases with the number of OCPs, i.e., the MAI effects are strongly influenced by the increase of the active OCPs; an error occurs when cross-correlational pulses from the (*K* – 1) interfering optical code paths built up to a level higher than the autocorrelation peak,

In conclusion, our numerical results for the power minimization problem have revealed for low system loading that the best acceleration coefficient values lie on *C*<sup>1</sup> = 1.8 and *C*2 = 2.0, in terms solution quality trade-off. This result was compared with *C*<sup>1</sup> = 2.0 and *C*<sup>2</sup> = 2.0 previ‐

The solution quality *versus* convergence trade-off analysis presented in Figs. 4, 5 and 6 for the PSO's acceleration coefficients optimization in the case of OCDM/WDM networks with 1 span should be extended taking into account the use of more spans. The state-of-art for the number of spans without electronic regeneration is around 4 considering the ASE effect lim‐ iting applying fibers with low PMD effects for bit rate of 10 Gbps (lower than 40 Gbps) [29]. In Fig. 7 the analysis of subsection 4.1 is extended until 8 spans, showing the influence of the number of spans on the NMSE for 7 OCPs and the same parameters values optimized in

1E-19 1E-17 1E-15 1E-13 1E-11 1E-9 1E-7 1E-5 1E-3 0,1 10

C1

C1

= 1.8 C2

= 2.0 C2

= 2.0

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= 2.0

NMSE

*C2* = 2.0), considering 1 span.

changing a bit zero to a bit one.

**4.2. PSO optimization for OCPs**

that subsection.

ously reported in the literature [32]-[35].

**Figure 5.** Sum of power for power vector evolution through the 800 iterations for 7 OCPs under different acceleration value of *C1* and *C2* = 2 for 1 spans.

The algorithm reaches convergence for *C1* = 1.4, 1.6, 1.8, 2, 2.2 and 2.4, however it doesn't reach acceptable convergence for *C1* = 1. Simulations revealed that increasing parameter *C1* results in a slower convergence with approximately 320, 343, 373, 639, 659 and 713, itera‐ tions, respectively. However, NMSE for faster convergence is higher than for the slower con‐ vergence parameters with minimum value for *C1* = 1.8, as indicated in Fig. 4. In this context, the best convergence *versus* solution quality trade-off was achieved with *C*<sup>1</sup> = 1.8 and *C*2 = 2 for number of OCPs of 7.

It is worth to expand this analysis to other number of OCPs that are generally between 4 and 8 OCPs. For this purpose, Fig 6 shows the NMSE for the number of OCPs regarding two combination of acceleration coefficient: i) optimized herein (*C1* = 1.8 and *C2* = 2.0) and report‐ ed in the literature (*C1* = 2.0 and *C2* = 2.0).

**Figure 6.** Normalized mean squared error (NMSE) for the number of OCPs for (*C1* = 1.8 and *C2* = 2.0) and (*C1* = 2.0 and *C2* = 2.0), considering 1 span.

The OCPs increasing affects the solution quality. This effect is directly related to the MAI rising which increases with the number of OCPs, i.e., the MAI effects are strongly influenced by the increase of the active OCPs; an error occurs when cross-correlational pulses from the (*K* – 1) interfering optical code paths built up to a level higher than the autocorrelation peak, changing a bit zero to a bit one.

In conclusion, our numerical results for the power minimization problem have revealed for low system loading that the best acceleration coefficient values lie on *C*<sup>1</sup> = 1.8 and *C*2 = 2.0, in terms solution quality trade-off. This result was compared with *C*<sup>1</sup> = 2.0 and *C*<sup>2</sup> = 2.0 previ‐ ously reported in the literature [32]-[35].

#### **4.2. PSO optimization for OCPs**

Numerical results have shown the solution quality for different values of acceleration coeffi‐ cient *C1* and it was found *C*1 = 1.8 presents the lower NMSE for the number of OCPs < 10. Hence, the best solution quality was achieved with *C*<sup>1</sup> = 1.8 and *C*<sup>2</sup> = 2. Fig. 5 shows the sum of power for the evolution through the *t=*1,…, 800 iterations for 7 OCPs under different ac‐

Popt

0 100 200 300 400 500 600 700 800

 c1 = 1; c2

c1

c1

c1

 c1 = 2; c2 = 2

c1

c1

= 2

= 2

= 2

= 2

= 2

= 2

= 1.4; c2

= 1.6; c2

= 1.8; c2

= 2.2; c2

= 2.4; c2

Number of iterations

**Figure 5.** Sum of power for power vector evolution through the 800 iterations for 7 OCPs under different acceleration

The algorithm reaches convergence for *C1* = 1.4, 1.6, 1.8, 2, 2.2 and 2.4, however it doesn't reach acceptable convergence for *C1* = 1. Simulations revealed that increasing parameter *C1* results in a slower convergence with approximately 320, 343, 373, 639, 659 and 713, itera‐ tions, respectively. However, NMSE for faster convergence is higher than for the slower con‐ vergence parameters with minimum value for *C1* = 1.8, as indicated in Fig. 4. In this context, the best convergence *versus* solution quality trade-off was achieved with *C*<sup>1</sup> = 1.8 and *C*2 = 2

It is worth to expand this analysis to other number of OCPs that are generally between 4 and 8 OCPs. For this purpose, Fig 6 shows the NMSE for the number of OCPs regarding two combination of acceleration coefficient: i) optimized herein (*C1* = 1.8 and *C2* = 2.0) and report‐

celeration value of *C1* and *C2* = 2, considering 1 span.

1E-5

value of *C1* and *C2* = 2 for 1 spans.

for number of OCPs of 7.

ed in the literature (*C1* = 2.0 and *C2* = 2.0).

1E-4

1E-3

Sum Power (W)

0,01

0,1

1

160 Search Algorithms for Engineering Optimization

The solution quality *versus* convergence trade-off analysis presented in Figs. 4, 5 and 6 for the PSO's acceleration coefficients optimization in the case of OCDM/WDM networks with 1 span should be extended taking into account the use of more spans. The state-of-art for the number of spans without electronic regeneration is around 4 considering the ASE effect lim‐ iting applying fibers with low PMD effects for bit rate of 10 Gbps (lower than 40 Gbps) [29]. In Fig. 7 the analysis of subsection 4.1 is extended until 8 spans, showing the influence of the number of spans on the NMSE for 7 OCPs and the same parameters values optimized in that subsection.

The reader interested in quality of solution metrics, a similar definition for RC and another

Number of spans:

0 100 200 300 400 500 600 700 800

(b)

Iterations

**Figure 8.** Rate of convergence versus the number of iterations for 1 until 6 spans for (a) 4 OCPs and (b) 8 OCPs.

Fig. 8 (a) and (b) shows the convergence rate of the sum of power for vector evolution through the 800 iterations for 4 a 8 OCPs, respectively, considering 1 until 6 spans. The re‐ sults have shown that increasing span number results in a faster convergence. This fact oc‐ curs because until 6 spans the increase of the number of span increases the contribution of

0 100 200 300 400 500 600 700 800

(a)

...

EDFA

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Fiber Span

0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0

Rate of convergence

0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0

Rate of convergence

figure of merit for the PSO, namely success cost, are presented in [35].

**Figure 7.** NMSE for the number of spans for 7 OCPs.

The results show that NMSE decreases when the number of spans increases until 6 spans, after this number of spans the NMSE alters the tendency and increases. This behavior shows the limitation of PSO convergence when the ASE increases. After 6 spans the PSO algorithm does not reach the total convergence. This fact occurs, directly by the limita‐ tions generate with the increase of the ASE. In other sense, the transmitted power needed to reach the target SNIR will overcome the maximum allowed transmitted power. The average number of spans increases slightly as *K* increases, as longer OCP routes become available. This increase is, however, not very significant, and on average, the path lengths are around four spans [22].

The convergence quality of the PSO algorithm presents variation with the increase in the number of spans. The figure of merit utilized as tool to this analysis is the rate of conver‐ gence (RC), which can be described as the ratio of PSO solution after the *t*-th iteration divid‐ ed by the PSO solution after total convergence, which in this optimization context is given by the matrix inversion solution, as discussed in Section 3.1. Recalling eq. (19), the RC can be expressed in term of ∊*stop* as:

$$RC\mathbf{f}[t] = 1 - \left|\frac{\eta \mathbf{f}[\mathbf{f}] \cdot \eta \mathbf{f}\_P \mathbf{f}}{\eta \mathbf{f}\_P \mathbf{f}}\right|\tag{21}$$

The reader interested in quality of solution metrics, a similar definition for RC and another figure of merit for the PSO, namely success cost, are presented in [35].

1 2 3 4 5 6 7 8

Number of spans

The results show that NMSE decreases when the number of spans increases until 6 spans, after this number of spans the NMSE alters the tendency and increases. This behavior shows the limitation of PSO convergence when the ASE increases. After 6 spans the PSO algorithm does not reach the total convergence. This fact occurs, directly by the limita‐ tions generate with the increase of the ASE. In other sense, the transmitted power needed to reach the target SNIR will overcome the maximum allowed transmitted power. The average number of spans increases slightly as *K* increases, as longer OCP routes become available. This increase is, however, not very significant, and on average, the path lengths

The convergence quality of the PSO algorithm presents variation with the increase in the number of spans. The figure of merit utilized as tool to this analysis is the rate of conver‐ gence (RC), which can be described as the ratio of PSO solution after the *t*-th iteration divid‐ ed by the PSO solution after total convergence, which in this optimization context is given by the matrix inversion solution, as discussed in Section 3.1. Recalling eq. (19), the RC can be

*RC <sup>t</sup>* =1 - <sup>|</sup> *<sup>J</sup> <sup>t</sup>* - *<sup>J</sup>* **<sup>p</sup>**\*

*<sup>J</sup>* **<sup>p</sup>**\* <sup>|</sup> (21)

...

EDFA

Fiber Span

1E-12 1E-11 1E-10 1E-9 1E-8 1E-7 1E-6 1E-5 1E-4 1E-3 0,01 0,1 1 10

**Figure 7.** NMSE for the number of spans for 7 OCPs.

are around four spans [22].

expressed in term of ∊*stop* as:

NMSE

162 Search Algorithms for Engineering Optimization

**Figure 8.** Rate of convergence versus the number of iterations for 1 until 6 spans for (a) 4 OCPs and (b) 8 OCPs.

Fig. 8 (a) and (b) shows the convergence rate of the sum of power for vector evolution through the 800 iterations for 4 a 8 OCPs, respectively, considering 1 until 6 spans. The re‐ sults have shown that increasing span number results in a faster convergence. This fact oc‐ curs because until 6 spans the increase of the number of span increases the contribution of the amplifier with signal, besides for more than 6 spans the contribution of the amplifier is for the ASE noise. On the other hand, the increase in the number of OCPs results in a slow convergence that results from the MAI between the OCPs.

In summary, our numerical results for the power minimization problem considering differ‐ ent number of spans have revealed the viability of the PSO algorithm deployment to solve a power allocation in OCPs with until 6 spans in order to guarantee the solution quality in terms of NMSE. Furthermore, the numerical results revealed that increasing the number of spans results in a faster convergence. In this context, the PSO algorithm is quite suitable to solve a power allocation in OCPs that presents an average of 4 spans as reported in the liter‐ ature [22].

In order to evaluate the impact of physical restrictions on the OCM/WDM network, further numerical results presented in Fig. 9 shows the sum power evolution of the PSO algorithm with respect to the number of iterations, considering a) 4 OCPs, and b) 8 OCPs. One span was considered as reference for bit rate of 10 Gbps taking into account two situations: i) with only ASE effects, ii) with ASE, GVD and PMD effects.

The target SNIR established for all the nodes is equal, and if the perfect power balancing with ideal physical layer (no physical impairments) is assumed, it could be demonstrated that the maximum SNIR and the transmitted power are defined by the number of OCPs in the same route. However, when the ASE, GVD and PMD effects are considered, there is a penalty. This penalty represents the received power reduction due to temporal spreading. Fig. 9 shows that when ASE, GVD and PMD effects are considered there is a power penalty of 3 decades compared with the situation where only ASE is considered (fibers with low PMD). Comparing Figs. 9(a) and 9(b), it could be noticed that the convergence velocity de‐ pends on the number of OCPs. The increase of OCPs from 4 to 8 affects the convergence ve‐ locity, from ≈200 to ≈500 iterations, respectively. This effect is directly related to the MAI increasing, which increases with the number of OCPs. The MAI effects are strongly influ‐ enced by the increase of the active number of OCPs; as explained before, an error occurs when cross-correlational pulses from the (*K* – 1) interfering optical code paths built up to a level higher than the autocorrelation peak, changing a bit zero to a bit one. The PMD effects degrade the performance when the link length and bit rate increase. This effect occurs be‐ cause PMD impairment establishes an upper bound on the link length, which causes the temporal spreading of optical pulses. The upper bound for link distance depends on the chip-rate distance product (*d.R.NT )*, where *d* is the link length, *R* is the bit rate, and *NT* is the code length. The analysis of code parameters, MAI and PMD effects for 2D-based OCPs was previously reported in [20].

0 100 200 300 400 500 600 700 800

(b)

Iterations

**Figure 9.** PSO sum power evolution for a) 4 OCPs; b) 8 OCPs. One span as reference, with R=10 Gbps. Two situations: i)

The results in Table I show the necessary values for transmitted power, as well as the solu‐ tion quality evaluation in terms of NMSE. The increase in the target SNIR results in the in‐ crease of the transmitted power, which is major for more OCPs. On the other hand, the solution quality (NMSE) decreases with the increase of SNIR target, since the number of the

0 100 200 300 400 500 600 700 800

ASE

ASE + GVD + PMD

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(a)

Popt

1E-8

ASE effects, ii) ASE, GVD and PMD effects.

PSO iterations is fixed.

1E-7

1E-6

1E-5

1E-4

Sum power (W)

1E-3

0,01

0,1

1

1E-8

1E-7

1E-6

1E-5

1E-4

Sum power (W)

1E-3

0,01

0,1

1

In OCDM/WDM networks, the OCPs with various classes of QoS are obtained with trans‐ mission of different power levels. Distinct power levels are obtained with adjustable trans‐ mitters and it does not cause the change of the bit rate. The intensity of the transmitted optical signal is directly adjusted from the laser source with respect to the target SNIR by PSO algorithm. Table 1 shows the optimization aspects of QoS regarding different levels of SNIR considering sum power and NMSE for 4 and 8 OCPs with 1 span.

the amplifier with signal, besides for more than 6 spans the contribution of the amplifier is for the ASE noise. On the other hand, the increase in the number of OCPs results in a slow

In summary, our numerical results for the power minimization problem considering differ‐ ent number of spans have revealed the viability of the PSO algorithm deployment to solve a power allocation in OCPs with until 6 spans in order to guarantee the solution quality in terms of NMSE. Furthermore, the numerical results revealed that increasing the number of spans results in a faster convergence. In this context, the PSO algorithm is quite suitable to solve a power allocation in OCPs that presents an average of 4 spans as reported in the liter‐

In order to evaluate the impact of physical restrictions on the OCM/WDM network, further numerical results presented in Fig. 9 shows the sum power evolution of the PSO algorithm with respect to the number of iterations, considering a) 4 OCPs, and b) 8 OCPs. One span was considered as reference for bit rate of 10 Gbps taking into account two situations: i) with

The target SNIR established for all the nodes is equal, and if the perfect power balancing with ideal physical layer (no physical impairments) is assumed, it could be demonstrated that the maximum SNIR and the transmitted power are defined by the number of OCPs in the same route. However, when the ASE, GVD and PMD effects are considered, there is a penalty. This penalty represents the received power reduction due to temporal spreading. Fig. 9 shows that when ASE, GVD and PMD effects are considered there is a power penalty of 3 decades compared with the situation where only ASE is considered (fibers with low PMD). Comparing Figs. 9(a) and 9(b), it could be noticed that the convergence velocity de‐ pends on the number of OCPs. The increase of OCPs from 4 to 8 affects the convergence ve‐ locity, from ≈200 to ≈500 iterations, respectively. This effect is directly related to the MAI increasing, which increases with the number of OCPs. The MAI effects are strongly influ‐ enced by the increase of the active number of OCPs; as explained before, an error occurs when cross-correlational pulses from the (*K* – 1) interfering optical code paths built up to a level higher than the autocorrelation peak, changing a bit zero to a bit one. The PMD effects degrade the performance when the link length and bit rate increase. This effect occurs be‐ cause PMD impairment establishes an upper bound on the link length, which causes the temporal spreading of optical pulses. The upper bound for link distance depends on the chip-rate distance product (*d.R.NT )*, where *d* is the link length, *R* is the bit rate, and *NT* is the code length. The analysis of code parameters, MAI and PMD effects for 2D-based OCPs was

In OCDM/WDM networks, the OCPs with various classes of QoS are obtained with trans‐ mission of different power levels. Distinct power levels are obtained with adjustable trans‐ mitters and it does not cause the change of the bit rate. The intensity of the transmitted optical signal is directly adjusted from the laser source with respect to the target SNIR by PSO algorithm. Table 1 shows the optimization aspects of QoS regarding different levels of

SNIR considering sum power and NMSE for 4 and 8 OCPs with 1 span.

convergence that results from the MAI between the OCPs.

164 Search Algorithms for Engineering Optimization

only ASE effects, ii) with ASE, GVD and PMD effects.

ature [22].

previously reported in [20].

**Figure 9.** PSO sum power evolution for a) 4 OCPs; b) 8 OCPs. One span as reference, with R=10 Gbps. Two situations: i) ASE effects, ii) ASE, GVD and PMD effects.

The results in Table I show the necessary values for transmitted power, as well as the solu‐ tion quality evaluation in terms of NMSE. The increase in the target SNIR results in the in‐ crease of the transmitted power, which is major for more OCPs. On the other hand, the solution quality (NMSE) decreases with the increase of SNIR target, since the number of the PSO iterations is fixed.


**Table 1.** The optimization aspects of QoS.

#### **4.3. PSO optimization for energy efficiency in OCPs**

An efficient resource allocation algorithm is needed to overcome the problem of energy effi‐ ciency and to enhance the performance and QoS of the optical network. This could be ach‐ ieved via signal-to-noise plus interference (SNIR) PSO optimization.

**Figure 10.** Energy per bit sum of the OCPs as a function of the rate of convergence using PSO algorithm. Three differ‐ ent SNIRs target of 17, 20 and 22 dB; a) 4 OCPs and b) 8 OCPs.

5

Fig. 10 shows the sum of energy per bit as a function of the rate of convergence of eq. (21) for the PSO optimization with different QoS requirements represented by SNIR target of 17, 20 and 22 dB, considering a) 4 OCPs and b) 8 OCPs, i.e., same scenario presented in the pre‐ vious subsection. One can see when rate of convergence evolving, the energy per bit solu‐ tion offered by the PSO algorithm convergences to the best lower values as predicted in (17).

It can be seen from Fig. 10 the impact of the PSO power allocation optimization procedure (in terms of transmitted energy per bit) on the energy efficiency improvement. The deploy‐ ment of PSO with 100% of rate of convergence results in an enormous saving of energy. In‐ deed, with very low number of PSO iterations, rate of convergence is poor (*RC* <0.03), the transmitted energy per bit is high because the MAI are strongly influenced by near-far ef‐ fects. As expected, the increase of the active OCPs from 4 to 8, results in the increase of the transmitted energy per bit to reach the SNIR target. Furthermore, one can analyze the varia‐ tion of saving energy for different levels of convergence rate; for instance, the variation of saving energy regarding the rate convergence in the range *RC* ∈ 0.5;1.0 remains in approx‐ imately from 40 to 60 % for different SNIR target and number of OCPs, as presented in Fig. 10. In this context, aiming to analyze the effect of the number of spans in the transmitted energy per bit for 4 and 8 OCPs, Table 2 presents the sum energy per bit considering SNIR

**4 OCPs 8 OCPs**

**Σ energy (pJ) RC=0.5**

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**Σ energy (pJ) RC=1.0**

**Σ energy (pJ) RC=1.0**

2 0.0135 0.0120 0.3145 0.1100 4 1.0545 1.0108 2.2295 1.8199

The results show the impact of the number of spans in the transmitted energy per bit for the variation of rate convergence of 0.5 and 1. As expected, the increase in the number of spans and the number of OCPs results in the increase of the transmitted energy per bit. Besides, the sum energy per bit variation, regarding the RC from 0.5 to 1.0, declines with the increase of the number of spans from 2 to 4. This results agree with the previous results illustrated in

In this chapter, optimization procedures based on particle swarm intelligence are investigat‐ ed in details, aiming to efficiently solve the optimal resource allocation for signal-to-noise plus interference ratio (SNIR) optimization of optical code paths (OCPs) from OCDM/WDM networks under quality of service (QoS) restrictions and energy efficiency constraint prob‐

target of 20 dB and rate of convergence of 0.5 and 1.0, for 2 and 4 spans.

Fig. 8, meaning the increase of the number of spans accelerate the RC.

**Σ energy (pJ) RC=0.5**

**Table 2.** Sum energy per bit in [pJ] for SNIR target of 20 dB.

**Number of spans**

**5. Conclusions**

Fig. 10 shows the sum of energy per bit as a function of the rate of convergence of eq. (21) for the PSO optimization with different QoS requirements represented by SNIR target of 17, 20 and 22 dB, considering a) 4 OCPs and b) 8 OCPs, i.e., same scenario presented in the pre‐ vious subsection. One can see when rate of convergence evolving, the energy per bit solu‐ tion offered by the PSO algorithm convergences to the best lower values as predicted in (17).

It can be seen from Fig. 10 the impact of the PSO power allocation optimization procedure (in terms of transmitted energy per bit) on the energy efficiency improvement. The deploy‐ ment of PSO with 100% of rate of convergence results in an enormous saving of energy. In‐ deed, with very low number of PSO iterations, rate of convergence is poor (*RC* <0.03), the transmitted energy per bit is high because the MAI are strongly influenced by near-far ef‐ fects. As expected, the increase of the active OCPs from 4 to 8, results in the increase of the transmitted energy per bit to reach the SNIR target. Furthermore, one can analyze the varia‐ tion of saving energy for different levels of convergence rate; for instance, the variation of saving energy regarding the rate convergence in the range *RC* ∈ 0.5;1.0 remains in approx‐ imately from 40 to 60 % for different SNIR target and number of OCPs, as presented in Fig. 10. In this context, aiming to analyze the effect of the number of spans in the transmitted energy per bit for 4 and 8 OCPs, Table 2 presents the sum energy per bit considering SNIR target of 20 dB and rate of convergence of 0.5 and 1.0, for 2 and 4 spans.


**Table 2.** Sum energy per bit in [pJ] for SNIR target of 20 dB.

The results show the impact of the number of spans in the transmitted energy per bit for the variation of rate convergence of 0.5 and 1. As expected, the increase in the number of spans and the number of OCPs results in the increase of the transmitted energy per bit. Besides, the sum energy per bit variation, regarding the RC from 0.5 to 1.0, declines with the increase of the number of spans from 2 to 4. This results agree with the previous results illustrated in Fig. 8, meaning the increase of the number of spans accelerate the RC.

## **5. Conclusions**

5

**4 OCPs 8 OCPs**

**NMSE Sum power**

**(W)**

SNIR (dB): 17 20 22

**NMSE**

**SNIR (dB) BER Sum power**

**4.3. PSO optimization for energy efficiency in OCPs**

ieved via signal-to-noise plus interference (SNIR) PSO optimization.

**Table 1.** The optimization aspects of QoS.

166 Search Algorithms for Engineering Optimization

1E-3

ent SNIRs target of 17, 20 and 22 dB; a) 4 OCPs and b) 8 OCPs.

0.01

0.1

Ebit (pJ)

1

1E-3

0.01

0.1

Ebit (pJ)

1

10

**(W)**

17 7.2 × 10-13 3.3 × 10-8 3.0 × 10-18 1.2 × 10-7 2.3 × 10-8 20 7.6 × 10-24 6.0 × 10-8 6.2 × 10-16 2.8 × 10-7 1.2 × 10-3 22 1.2 × 10-36 9.5 × 10-8 3.8 × 10-16 4.3 × 10-7 1.0 × 10-1

An efficient resource allocation algorithm is needed to overcome the problem of energy effi‐ ciency and to enhance the performance and QoS of the optical network. This could be ach‐

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Rate of convergence

**Figure 10.** Energy per bit sum of the OCPs as a function of the rate of convergence using PSO algorithm. Three differ‐

100.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

In this chapter, optimization procedures based on particle swarm intelligence are investigat‐ ed in details, aiming to efficiently solve the optimal resource allocation for signal-to-noise plus interference ratio (SNIR) optimization of optical code paths (OCPs) from OCDM/WDM networks under quality of service (QoS) restrictions and energy efficiency constraint prob‐ lem, considering imperfections on physical constraints. The SNIR model considers multiple access interference (MAI) between the OCP based on 2-D codes (time/wavelength), amplifi‐ er spontaneous emission (ASE) at cascaded amplified spans, and group velocity dispersion (GVD) and polarization mode dispersion (PMD) dispersion effects. The characteristic of the particle swarm optimization (PSO) is attractive due their performance-complexity tradeoff and fairness regarding the optimization methods that use numerical methods, matrix inver‐ sion and other heuristics. The resource allocation optimization based on PSO strategy allows the regulation of the transmitted power and the number of active OCPs in order to maxi‐ mize the aggregate throughput of the OCDM/WDM networks considering QoS and energy efficiency constraint. For the network optimization context, system model was described, figures of merit were presented and a suitable model of PSO was developed, with emphasis in the optimization of input parameters and network performance. Afterward, extensive nu‐ merical results for the optimization problem are discussed taking into account realistic net‐ works operation scenarios.

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nications Surveys & Tutorials, ACCEPTED FOR PUBLICATION

In order determine the suitable values for the PSO input parameters, such as acceleration co‐ efficients, *C*1 and *C*2, maximal velocity factor, *Vmax*, weight inertia, *ω*, and population size, P, simulation experiments were carried out in regarding the power optimization problem for OCDM/WDM networks. In these networks, the number of simultaneous transmitted OCPs is low, generally around or less than 10. For our specific problem, the optimized input pa‐ rameters are different from the reported in the literature for similar problems. The numeri‐ cal results considering the number of spans have revealed the viability of the PSO algorithm deployment in order to solve a power allocation in OCPs with until 6 spans to guarantee the solution quality and convergence. This result is adequate considering the average of 4 spans without electronic regeneration presented for this kind of network. Besides, the numerical results have shown a penalty when the ASE, GVD and PMD effects are considered. This penalty represents the received power reduction due to temporal spreading. Indeed, when ASE, GVD and PMD effects are considered there is a power penalty of 3 decades compared with the situation where only ASE is considered (fibers with low PMD). Finally, our numeri‐ cal results reveal considerable variation of transmitted energy for different levels of conver‐ gence rate of PSO algorithm, in which the maximum energy efficiency is reached when the convergence of PSO algorithm is total. Interesting, even with only 10%-20% of the total PSO convergence, the network is able to operate within a remarkable energy efficiency gain re‐ gion compared to network operation without power allocation policy.

## **Author details**

Fábio Renan Durand1 , Larissa Melo1 , Lucas Ricken Garcia1 , Alysson José dos Santos2 and Taufik Abrão2

1 Federal University of Technology, Parana, Campo Mourão, Brazil

2 State University of Londrina – Electrical Engineering Department, Brazil

## **References**

lem, considering imperfections on physical constraints. The SNIR model considers multiple access interference (MAI) between the OCP based on 2-D codes (time/wavelength), amplifi‐ er spontaneous emission (ASE) at cascaded amplified spans, and group velocity dispersion (GVD) and polarization mode dispersion (PMD) dispersion effects. The characteristic of the particle swarm optimization (PSO) is attractive due their performance-complexity tradeoff and fairness regarding the optimization methods that use numerical methods, matrix inver‐ sion and other heuristics. The resource allocation optimization based on PSO strategy allows the regulation of the transmitted power and the number of active OCPs in order to maxi‐ mize the aggregate throughput of the OCDM/WDM networks considering QoS and energy efficiency constraint. For the network optimization context, system model was described, figures of merit were presented and a suitable model of PSO was developed, with emphasis in the optimization of input parameters and network performance. Afterward, extensive nu‐ merical results for the optimization problem are discussed taking into account realistic net‐

In order determine the suitable values for the PSO input parameters, such as acceleration co‐ efficients, *C*1 and *C*2, maximal velocity factor, *Vmax*, weight inertia, *ω*, and population size, P, simulation experiments were carried out in regarding the power optimization problem for OCDM/WDM networks. In these networks, the number of simultaneous transmitted OCPs is low, generally around or less than 10. For our specific problem, the optimized input pa‐ rameters are different from the reported in the literature for similar problems. The numeri‐ cal results considering the number of spans have revealed the viability of the PSO algorithm deployment in order to solve a power allocation in OCPs with until 6 spans to guarantee the solution quality and convergence. This result is adequate considering the average of 4 spans without electronic regeneration presented for this kind of network. Besides, the numerical results have shown a penalty when the ASE, GVD and PMD effects are considered. This penalty represents the received power reduction due to temporal spreading. Indeed, when ASE, GVD and PMD effects are considered there is a power penalty of 3 decades compared with the situation where only ASE is considered (fibers with low PMD). Finally, our numeri‐ cal results reveal considerable variation of transmitted energy for different levels of conver‐ gence rate of PSO algorithm, in which the maximum energy efficiency is reached when the convergence of PSO algorithm is total. Interesting, even with only 10%-20% of the total PSO convergence, the network is able to operate within a remarkable energy efficiency gain re‐

, Lucas Ricken Garcia1

, Alysson José dos Santos2

and

gion compared to network operation without power allocation policy.

1 Federal University of Technology, Parana, Campo Mourão, Brazil

2 State University of Londrina – Electrical Engineering Department, Brazil

, Larissa Melo1

works operation scenarios.

168 Search Algorithms for Engineering Optimization

**Author details**

Taufik Abrão2

Fábio Renan Durand1


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**Section 3**

**Power Systems and Industrial Processes**

**Applications**


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**Chapter 7**

**Provisional chapter**

**An Adaptive Neuro-Fuzzy Strategy for a Wireless**

**Coded Power Control in Doubly-Fed Induction**

**An Adaptive Neuro-Fuzzy Strategy for a Wireless**

Renewable energy systems and specially wind energy have attracted governmental interests in opposition to energy sources that increase CO2 emissions and cause enormous environmental impact. Recently, the concept of smart grid has been applied to power plants to enable and optimize the generation of energy by efficiently combining wind, solar and tidal. Moreover, the efforts for consolidation and implementation of this new concept through wind energy systems have attracted great interest from the technical community

Smart grids are an evolution of conventional power grids to optimally manage the relationship between energy supply and demand in electrical systems to overcome the actual problem of contingency of energy of the modern world. They employ an interactive framework composed by integrated communication networks with real time monitoring, control and automatic intervention capability to use more efficiently the infrastructure of

Advances in wind power technology have greatly improved its system integration with smart grid, however, there are still some unsolved challenges in expanding its use. Due to the usual variations of the wind speed, its utilization entails undesirable fluctuations in the generated power that, if not compensated in real time, can lead to frequency imbalance and disturbance in the stability of the electrical system. Although smart grid can minimize this problem through a more precise demand response for load control and dispatch of other generation

> ©2012 Casella et al., licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2013 Casella et al.; licensee InTech. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

© 2013 Casella et al., licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

distribution, and reproduction in any medium, provided the original work is properly cited.

**Coded Power Control in Doubly-Fed Induction**

I. R. S. Casella, A. J. Sguarezi Filho, C. E. Capovilla,

and has been the focus of several recent scientific works [1–3].

generation, transmission and distribution of energy.

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

**Aerogenerators**

**Aerogenerators**

J. L. Azcue and E. Ruppert

I. R. S. Casella, A. J. Sguarezi Filho ,

C. E. Capovilla , J. L. Azcue and E. Ruppert

http://dx.doi.org/10.5772/52090

10.5772/52090 ima running title

**1. Introduction**

**Provisional chapter**

## **An Adaptive Neuro-Fuzzy Strategy for a Wireless Coded Power Control in Doubly-Fed Induction Aerogenerators An Adaptive Neuro-Fuzzy Strategy for a Wireless Coded Power Control in Doubly-Fed Induction Aerogenerators**

I. R. S. Casella, A. J. Sguarezi Filho, C. E. Capovilla, J. L. Azcue and E. Ruppert I. R. S. Casella, A. J. Sguarezi Filho , C. E. Capovilla , J. L. Azcue and E. Ruppert

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/52090 10.5772/52090 ima running title

## **1. Introduction**

Renewable energy systems and specially wind energy have attracted governmental interests in opposition to energy sources that increase CO2 emissions and cause enormous environmental impact. Recently, the concept of smart grid has been applied to power plants to enable and optimize the generation of energy by efficiently combining wind, solar and tidal. Moreover, the efforts for consolidation and implementation of this new concept through wind energy systems have attracted great interest from the technical community and has been the focus of several recent scientific works [1–3].

Smart grids are an evolution of conventional power grids to optimally manage the relationship between energy supply and demand in electrical systems to overcome the actual problem of contingency of energy of the modern world. They employ an interactive framework composed by integrated communication networks with real time monitoring, control and automatic intervention capability to use more efficiently the infrastructure of generation, transmission and distribution of energy.

Advances in wind power technology have greatly improved its system integration with smart grid, however, there are still some unsolved challenges in expanding its use. Due to the usual variations of the wind speed, its utilization entails undesirable fluctuations in the generated power that, if not compensated in real time, can lead to frequency imbalance and disturbance in the stability of the electrical system. Although smart grid can minimize this problem through a more precise demand response for load control and dispatch of other generation

©2012 Casella et al., licensee InTech. This is an open access chapter distributed under the terms of the Creative

resources, it is still necessary to employ variable speed aerogenerators and a precise power control system to guarantee stability and maximum power generation.

10.5772/52090 ima running title

http://dx.doi.org/10.5772/52090

177

these systems yet, making it difficult to estimate the real impact of its use or its advantages

An Adaptive Neuro-Fuzzy Strategy for a Wireless Coded Power Control in Doubly-Fed Induction Aerogenerators

Grid

Converter and Controller

Modern wireless digital communication techniques can be used to improve the robustness of the power control system and to minimize the mentioned problems through the application of Forward Error Correction (FEC) [14]. FEC is a coding technique used in all current digital wireless systems and it is essential to ensure the integrity of information, reducing significantly the Bit Error Rate (BER) and the latency of the information by adding controlled redundancy to the transmitted information [15]. In theory, the appropriate use of coding

There are currently several different schemes of FEC that are used in commercial wireless communication systems [17], [18], [19–21]. Among them, LDPC is the one that presents the best performance and shows an excellent compromise between decoding complexity and performance [22, 23].The LDPC coding has recently been added to the IEEE 802.16e Standard, commonly known as Worldwide Interoperability for Microwave Access (WiMAX) for mobile

In this context, this chapter will analyze the performance of a new wireless coded adaptive neuro-fuzzy power control system for variable speed wind DFIG, presented in Fig. 1. The system is based on a discrete dynamic mathematical model of the generator and uses the vector control technique to independently control the active and reactive power. The proposed adaptive neuro-fuzzy system is designed from an input and output data set collected from a DFIG with a deadbeat controller [25] operating at different conditions and considering the rotor current error as input. The wireless communication system, employed

technology can offer the same reliability obtained by using fiber optic cables [16].

(Remote Control Central)

Communication System

Communication System

> Smart Grid Operator

*Wireless Communication Channel*

Wind Turbine

DFIG n1 n2

and difficulties.

**Figure 1.** Wireless System Control Schematic.

applications [24].

Among the existing aerogenerators, Doubly-Fed Induction Generators (DFIG) are the most widely employed in wind power systems [4] due to their interesting main characteristics as, for instance, the ability to operate at variable speed and the capacity to control the active and reactive power into four quadrants by means of field orientation [5, 6]. The precise power control of the aerogenerators is essential to maximize the generated power. The conventional Proportional-Integral (PI) [7] and Proportional-Integral-Derivative (PID) [8, 9] have been widely used as the core of different power control systems due to their simplicity of implementation. However, the design of these fixed gain control systems is very cumbersome, since it depends on the exact mathematical model of the generator. Also, they are very sensitive to disturbances, parameter variations and system nonlinearities.

On the other hand, the design of intelligent control systems based on Computational Intelligence (CI) does not require the exact mathematical model of the generator. Among of the CI techniques, Fuzzy Logic (FL) and Artificial Neural Networks (ANN) appear as powerful options for identification and control of nonlinear dynamic systems as power control systems. However, each of these intelligent techniques has its own drawbacks which restrict its use. For instance, FL suffers from some limitations as the appropriate selection of Membership Functions (MF), the adequate selection of fuzzy rules and, furthermore, how to adjust both of them to achieve the best performance. ANN have also some limitations as their black-box nature, the selection of the best structure and size, and the considerable training time to solve a specific problem. In order to overcome these problems, it is possible to use a hybrid neuro-fuzzy system [10] that can combine the learning capability of ANN with the knowledge representation of FL based on rules. One of the most widely used neuro-fuzzy system is the Adaptive Neural Fuzzy Inference System (ANFIS), proposed by [11]. It can use a hybrid learning procedure to construct an input-output mapping based on both human-knowledge as fuzzy rules and approximate MF from the corresponding input-output data pairs as ANN learning.

Another very important issue in the deployment of smart grids is the application of a modern telecommunications system to guarantee an effective monitoring and control of the grid. Nevertheless, its development and operability require a fairly complex infrastructure and present several non-trivial questions due to the convergence of different areas of knowledge and design aspects. In this way, the wireless transmission appears as an interesting solution for presenting many benefits such as low cost of development, expansion facilities, possibility of using the technologies currently applied in mobile telephone systems, flexibility of use, and distributed management. However, the employment of wireless technologies for transmitting power control signals may cause apprehension due to the possibility of the occurrence of errors in the transmission process that can cause serious problems to the generators and, consequentially, to the energy system. Such behavior is different from what usually happens in telecommunications systems designed to voice and data transmissions, where small errors can be detected, initiate requests for retransmission (generating delays) or even, in some cases, be ignored without any significant impact to the network. It is worth noting that there are some works in the scientific literature referencing the application of wireless technology for monitoring wind energy systems [12, 13], but there has not been presented any deep research about the use of wireless technology for control applications in these systems yet, making it difficult to estimate the real impact of its use or its advantages and difficulties.

**Figure 1.** Wireless System Control Schematic.

2 Search Algorithms

data pairs as ANN learning.

resources, it is still necessary to employ variable speed aerogenerators and a precise power

Among the existing aerogenerators, Doubly-Fed Induction Generators (DFIG) are the most widely employed in wind power systems [4] due to their interesting main characteristics as, for instance, the ability to operate at variable speed and the capacity to control the active and reactive power into four quadrants by means of field orientation [5, 6]. The precise power control of the aerogenerators is essential to maximize the generated power. The conventional Proportional-Integral (PI) [7] and Proportional-Integral-Derivative (PID) [8, 9] have been widely used as the core of different power control systems due to their simplicity of implementation. However, the design of these fixed gain control systems is very cumbersome, since it depends on the exact mathematical model of the generator. Also, they are very sensitive to disturbances, parameter variations and system nonlinearities.

On the other hand, the design of intelligent control systems based on Computational Intelligence (CI) does not require the exact mathematical model of the generator. Among of the CI techniques, Fuzzy Logic (FL) and Artificial Neural Networks (ANN) appear as powerful options for identification and control of nonlinear dynamic systems as power control systems. However, each of these intelligent techniques has its own drawbacks which restrict its use. For instance, FL suffers from some limitations as the appropriate selection of Membership Functions (MF), the adequate selection of fuzzy rules and, furthermore, how to adjust both of them to achieve the best performance. ANN have also some limitations as their black-box nature, the selection of the best structure and size, and the considerable training time to solve a specific problem. In order to overcome these problems, it is possible to use a hybrid neuro-fuzzy system [10] that can combine the learning capability of ANN with the knowledge representation of FL based on rules. One of the most widely used neuro-fuzzy system is the Adaptive Neural Fuzzy Inference System (ANFIS), proposed by [11]. It can use a hybrid learning procedure to construct an input-output mapping based on both human-knowledge as fuzzy rules and approximate MF from the corresponding input-output

Another very important issue in the deployment of smart grids is the application of a modern telecommunications system to guarantee an effective monitoring and control of the grid. Nevertheless, its development and operability require a fairly complex infrastructure and present several non-trivial questions due to the convergence of different areas of knowledge and design aspects. In this way, the wireless transmission appears as an interesting solution for presenting many benefits such as low cost of development, expansion facilities, possibility of using the technologies currently applied in mobile telephone systems, flexibility of use, and distributed management. However, the employment of wireless technologies for transmitting power control signals may cause apprehension due to the possibility of the occurrence of errors in the transmission process that can cause serious problems to the generators and, consequentially, to the energy system. Such behavior is different from what usually happens in telecommunications systems designed to voice and data transmissions, where small errors can be detected, initiate requests for retransmission (generating delays) or even, in some cases, be ignored without any significant impact to the network. It is worth noting that there are some works in the scientific literature referencing the application of wireless technology for monitoring wind energy systems [12, 13], but there has not been presented any deep research about the use of wireless technology for control applications in

control system to guarantee stability and maximum power generation.

Modern wireless digital communication techniques can be used to improve the robustness of the power control system and to minimize the mentioned problems through the application of Forward Error Correction (FEC) [14]. FEC is a coding technique used in all current digital wireless systems and it is essential to ensure the integrity of information, reducing significantly the Bit Error Rate (BER) and the latency of the information by adding controlled redundancy to the transmitted information [15]. In theory, the appropriate use of coding technology can offer the same reliability obtained by using fiber optic cables [16].

There are currently several different schemes of FEC that are used in commercial wireless communication systems [17], [18], [19–21]. Among them, LDPC is the one that presents the best performance and shows an excellent compromise between decoding complexity and performance [22, 23].The LDPC coding has recently been added to the IEEE 802.16e Standard, commonly known as Worldwide Interoperability for Microwave Access (WiMAX) for mobile applications [24].

In this context, this chapter will analyze the performance of a new wireless coded adaptive neuro-fuzzy power control system for variable speed wind DFIG, presented in Fig. 1. The system is based on a discrete dynamic mathematical model of the generator and uses the vector control technique to independently control the active and reactive power. The proposed adaptive neuro-fuzzy system is designed from an input and output data set collected from a DFIG with a deadbeat controller [25] operating at different conditions and considering the rotor current error as input. The wireless communication system, employed to send the power reference signals to the DFIG controller, uses LDPC coding to reduce the transmission errors and the overall latency of the system. The performance of the system is investigated in a frequency flat fading scenario, to evaluate the real impact of the wireless transmission in the wind energy control system. It is noteworthy that the errors generated in the wireless transmission cannot be easily removed without using advanced FEC coding techniques similar to those presented in this work.

## **2. Doubly-Fed Induction Generator model**

The DFIG model in synchronous *dq* reference frame can be mathematically represented by [26]:

$$
\vec{\sigma}\_{1dq} = R\_1 \vec{i}\_{1dq} + \frac{d\vec{\lambda}\_{1dq}}{dt} + j\omega\_1 \vec{\lambda}\_{1dq} \tag{1}
$$

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179

*i*2*<sup>d</sup>* (7)

*i*2*<sup>q</sup>* (8)

*i*2*<sup>q</sup>* (9)

(10)

of each individual rotor current. Using stator flux orientation, that decouples the *dq* axis, it

An Adaptive Neuro-Fuzzy Strategy for a Wireless Coded Power Control in Doubly-Fed Induction Aerogenerators

− *LM L*1

*<sup>λ</sup>*1*dq*|, thus, the equation (3) becomes:

*<sup>i</sup>*1*<sup>d</sup>* <sup>=</sup> *<sup>λ</sup>*<sup>1</sup> *L*1

*<sup>P</sup>* <sup>=</sup> <sup>−</sup><sup>3</sup> 2 *v*1 *LM L*1

*<sup>Q</sup>* <sup>=</sup> <sup>3</sup> 2 *v*1 *λ*<sup>1</sup> *L*1

*<sup>i</sup>*1*<sup>q</sup>* <sup>=</sup> <sup>−</sup> *LM L*1

Similarly, using stator flux oriented, the stator voltage becomes *<sup>v</sup>*1*<sup>d</sup>* = 0 and *<sup>v</sup>*1*<sup>q</sup>* = *<sup>v</sup>*<sup>1</sup> = |*<sup>v</sup>*1*dq*|. Hence, the active (5) and reactive (6) powers can be calculated by using equations (7) and (8):

Thus, the rotor currents will reflect on the stator currents and on the active and reactive power of the stator, respectively. Consequently, this principle can be used to control the

Thus, the rotor currents will reflect on the stator currents and the active and reactive power of the stator, respectively. Therefore, this principle can be used to control the active and

As mentioned before, an accurate power control system of the aerogenerators connected to the grid is essential to guarantee stability and maximum energy generation. In this way, ANFIS has been shown a powerful technique to control the nonlinear dynamic behavior of aerogenerators. Usually, it can use a hybrid learning procedure to construct an input-output mapping based on both human-knowledge as fuzzy rules and approximate MF from the stipulated input-output data pairs as ANN learning to precisely control the power

An ANFIS is an adaptive network architecture whose overall input-output behavior is determined by the values of a collection of modifiable parameters [11, 27]. More specifically, the configuration of an adaptive network is composed by a set of nodes connected through directed links, where each node is a process unit that performs a static node function on its

− *LM L*1 *i*2*d* 

has that *<sup>λ</sup>*1*<sup>d</sup>* = *<sup>λ</sup>*<sup>1</sup> = |

active and reactive power of the DFIG stator.

**3. Adaptive Neuro-Fuzzy Power Control**

reactive power of the DFIG.

generation.

**3.1. ANFIS overview**

$$\vec{v}\_{2dq} = R\_2 \vec{i}\_{2dq} + \frac{d\vec{\lambda}\_{2dq}}{dt} + j\left(\omega\_1 - N\_P \omega\_{mc}\right) \vec{\lambda}\_{2dq} \tag{2}$$

and the relationships between fluxes and currents are:

$$
\vec{\lambda}\_{1dq} = L\_1 \vec{i}\_{1dq} + L\_M \vec{i}\_{2dq} \tag{3}
$$

$$
\vec{\lambda}\_{2dq} = L\_M \vec{i}\_{1dq} + L\_2 \vec{i}\_{2dq} \tag{4}
$$

so, the active and reactive power are given by:

$$P = \frac{3}{2} \left( v\_{1d} i\_{1d} + v\_{1q} i\_{1q} \right) \tag{5}$$

$$Q = \frac{3}{2} \left( v\_{1q} i\_{1d} - v\_{1d} i\_{1q} \right) \tag{6}$$

The subscripts 1 and 2 represent the stator and rotor parameters, respectively; *ω*<sup>1</sup> represents the synchronous speed, *ωmec* represents machine speed, *R* represents winding per phase electrical resistance, *L* and *LM* represent the proper and the mutual inductances of windings, *<sup>v</sup>* represents voltage vector, and *NP* represents the machine number of pair of poles.

The DFIG power control aims independent stator active *P* and reactive *Q* power control by means of a rotor current regulation. For this purpose, *P* and *Q* are represented as functions of each individual rotor current. Using stator flux orientation, that decouples the *dq* axis, it has that *<sup>λ</sup>*1*<sup>d</sup>* = *<sup>λ</sup>*<sup>1</sup> = | *<sup>λ</sup>*1*dq*|, thus, the equation (3) becomes:

$$i\_{1d} = \frac{\lambda\_1}{L\_1} - \frac{L\_M}{L\_1} i\_{2d} \tag{7}$$

$$\dot{\mathbf{u}}\_{1q} = -\frac{L\_M}{L\_1}\dot{\mathbf{u}}\_{2q} \tag{8}$$

Similarly, using stator flux oriented, the stator voltage becomes *<sup>v</sup>*1*<sup>d</sup>* = 0 and *<sup>v</sup>*1*<sup>q</sup>* = *<sup>v</sup>*<sup>1</sup> = |*<sup>v</sup>*1*dq*|. Hence, the active (5) and reactive (6) powers can be calculated by using equations (7) and (8):

$$P = -\frac{3}{2} v\_1 \frac{L\_M}{L\_1} i\_{2q} \tag{9}$$

$$Q = \frac{3}{2} v\_1 \left(\frac{\lambda\_1}{L\_1} - \frac{L\_M}{L\_1} i\_{2d}\right) \tag{10}$$

Thus, the rotor currents will reflect on the stator currents and on the active and reactive power of the stator, respectively. Consequently, this principle can be used to control the active and reactive power of the DFIG stator.

Thus, the rotor currents will reflect on the stator currents and the active and reactive power of the stator, respectively. Therefore, this principle can be used to control the active and reactive power of the DFIG.

## **3. Adaptive Neuro-Fuzzy Power Control**

As mentioned before, an accurate power control system of the aerogenerators connected to the grid is essential to guarantee stability and maximum energy generation. In this way, ANFIS has been shown a powerful technique to control the nonlinear dynamic behavior of aerogenerators. Usually, it can use a hybrid learning procedure to construct an input-output mapping based on both human-knowledge as fuzzy rules and approximate MF from the stipulated input-output data pairs as ANN learning to precisely control the power generation.

#### **3.1. ANFIS overview**

4 Search Algorithms

by [26]:

to send the power reference signals to the DFIG controller, uses LDPC coding to reduce the transmission errors and the overall latency of the system. The performance of the system is investigated in a frequency flat fading scenario, to evaluate the real impact of the wireless transmission in the wind energy control system. It is noteworthy that the errors generated in the wireless transmission cannot be easily removed without using advanced FEC coding

The DFIG model in synchronous *dq* reference frame can be mathematically represented

*d λ*1*dq dt* <sup>+</sup> *<sup>j</sup>ω*<sup>1</sup>

*dt* <sup>+</sup> *<sup>j</sup>*(*ω*<sup>1</sup> <sup>−</sup> *NPωmec*)

*λ*1*dq* (1)

*<sup>i</sup>*1*dq* <sup>+</sup> *LM<sup>i</sup>*2*dq* (3)

*<sup>i</sup>*2*dq* (4)

(5)

(6)

*λ*2*dq* (2)

*<sup>i</sup>*1*dq* <sup>+</sup>

*d λ*2*dq*

techniques similar to those presented in this work.

**2. Doubly-Fed Induction Generator model**

*<sup>v</sup>*2*dq* <sup>=</sup> *<sup>R</sup>*<sup>2</sup>

and the relationships between fluxes and currents are:

so, the active and reactive power are given by:

*<sup>v</sup>*1*dq* <sup>=</sup> *<sup>R</sup>*<sup>1</sup>

*<sup>i</sup>*2*dq* <sup>+</sup>

 *λ*1*dq* = *L*<sup>1</sup>

*<sup>P</sup>* <sup>=</sup> <sup>3</sup> 2 

*<sup>Q</sup>* <sup>=</sup> <sup>3</sup> 2 

*<sup>λ</sup>*2*dq* <sup>=</sup> *LM<sup>i</sup>*1*dq* <sup>+</sup> *<sup>L</sup>*<sup>2</sup>

*v*1*di*1*<sup>d</sup>* + *v*1*qi*1*<sup>q</sup>*

*<sup>v</sup>*1*qi*1*<sup>d</sup>* − *<sup>v</sup>*1*di*1*<sup>q</sup>*

The subscripts 1 and 2 represent the stator and rotor parameters, respectively; *ω*<sup>1</sup> represents the synchronous speed, *ωmec* represents machine speed, *R* represents winding per phase electrical resistance, *L* and *LM* represent the proper and the mutual inductances of windings,

The DFIG power control aims independent stator active *P* and reactive *Q* power control by means of a rotor current regulation. For this purpose, *P* and *Q* are represented as functions

*<sup>v</sup>* represents voltage vector, and *NP* represents the machine number of pair of poles.

An ANFIS is an adaptive network architecture whose overall input-output behavior is determined by the values of a collection of modifiable parameters [11, 27]. More specifically, the configuration of an adaptive network is composed by a set of nodes connected through directed links, where each node is a process unit that performs a static node function on its incoming signals to generate a single node output and each link specifies the direction of the signal flow from one node to another.

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181

*O*1,*<sup>i</sup>* = *µAi*

*O*2,*<sup>i</sup>* = *wi* = *µAi*

*<sup>O</sup>*3,*<sup>i</sup>* <sup>=</sup> *<sup>w</sup>*¯*<sup>i</sup>* <sup>=</sup> *wi*

called consequent parameters and the nodes outputs are expressed by:

where *µAi*

are defined by the following product:

results into a crisp value, as expressed by:

*3.1.2. Hybrid Learning Algorithm*

nonlinear input MF parameters [30].

(*x*1), for *i* = 1, 2 or

(*x*1) and *µBi*<sup>−</sup><sup>2</sup> (*x*2) are, respectively, the MF for the inputs *x*<sup>1</sup> and *x*2. • Layer 2: Each node in this layer, denoted as Π, is a non-adaptive node. This layer receives the input values *x*<sup>1</sup> and *x*<sup>2</sup> from the first layer and acts as a MF to represent the fuzzy sets of the respective input variables. Further, it computes the membership values that specify the degree to which the input values belongs to the fuzzy set. The nodes outputs

An Adaptive Neuro-Fuzzy Strategy for a Wireless Coded Power Control in Doubly-Fed Induction Aerogenerators

(*x*1) · *<sup>µ</sup>Bi*

• Layer 3: Each node in this layer, denoted as *N*, is a non-adaptive node that normalizes the weight functions obtained from layer Π. This layer is usually called as the rule layer since it determines the activation level of each rule. The nodes outputs are given by:

*w*<sup>1</sup> + *w*<sup>2</sup>

*O*4,*<sup>i</sup>* = *w*¯*<sup>i</sup> fi* = *w*¯*i*(*pix*<sup>1</sup> + *qix*<sup>2</sup> + *ri*), for *i* = 1, 2 (16)

*<sup>w</sup>*¯*<sup>i</sup> fi* <sup>=</sup> <sup>∑</sup>*<sup>i</sup> wi fi* ∑*<sup>i</sup> wi*

• Layer 4: Every node *i* in this layer is an adaptive node. The parameters of this layer are

where *w*¯*<sup>i</sup>* is the output of layer 3 and {*pi*, *qi*,*ri*} are the consequent parameters set. • Layer 5: This layer, denoted by Σ, is non-adaptive and produces the output function by adding all inputs from the previous layers and transforming the fuzzy classification

The learning process can update the MF parameters by a hybrid learning procedure [29] composed by the Least Squares (LS) method, which is applied for tuning the linear output MF parameters, and the Backpropagation (BP) method, which is employed for tuning the

In the forward pass, LS estimates the consequent parameters, keeping the premise parameter fixed, and in the backward pass, the premise parameters are obtained by BP, keeping the

*O*5,1 = ∑ *i*

*O*1,*<sup>i</sup>* = *µBi*<sup>−</sup><sup>2</sup> (*x*2), for *i* = 3, 4 (13)

(*x*2), for *i* = 1, 2 (14)

, for *i* = 1, 2 (15)

(17)

The parameters of an adaptive network are distributed into the network nodes, so each node has a local parameter set. The union of these local parameter sets forms the network overall parameter set. If a node parameter set is non-empty, then its node function depends on the parameter values, and it is used a square to represent this kind of adaptive node. On the other hand, if a node has an empty parameter set, then its function is fixed and it is used a circle to denote this type of fixed node [11].

This technique offers a method for learning information about a given data set during the fuzzy modeling procedure in order to adjust the MF parameters that best control the associated fuzzy inference system (FIS) to obtain the desired behavior.

#### *3.1.1. ANFIS Architecture*

In order to describe the ANFIS architecture in more detail, it is considered in the following, without loss of generality, a system with two inputs *x*<sup>1</sup> and *x*<sup>2</sup> and one output *y*, based on a first-order Takagi-Sugeno fuzzy model [28] with the fuzzy rules expressed as:

Rule 1 : If *x*<sup>1</sup> is *A*<sup>1</sup> and *x*<sup>2</sup> is *B*<sup>1</sup> then *f*<sup>1</sup> = *p*1*x*<sup>1</sup> + *q*1*x*<sup>2</sup> + *r*<sup>1</sup> (11)

$$\text{Rule 2}: \text{ If } \mathbf{x}\_1 \text{ is } A\_2 \text{ and } \mathbf{x}\_2 \text{ is } B\_2 \text{ then } f\_2 = p\_2\mathbf{x}\_1 + q\_2\mathbf{x}\_2 + r\_2 \tag{12}$$

The ANFIS network structure is composed by a set of units and connections arranged into five layers [11, 27, 29], as shown in Fig. 2, where the output of the *i th* node of the *l th* layer is denoted as *Ol*,*i*.

**Figure 2.** ANFIS Structure [11]

• Layer 1: Nodes in this layer are adaptive nodes and represent the membership grade of the inputs *x*<sup>1</sup> and *x*2. Here, triangular or bell shaped MF [11] can be used. The parameters of this layer are called premise parameters and the nodes outputs are represented by:

.

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$$\begin{aligned} \mathcal{O}\_{1,i} &= \mu\_{A\_i}(\mathbf{x}\_1), \text{ for } i = 1,2 \text{ or } \\ \mathcal{O}\_{1,i} &= \mu\_{B\_{i-2}}(\mathbf{x}\_2), \text{ for } i = 3,4 \end{aligned} \tag{13}$$

where *µAi* (*x*1) and *µBi*<sup>−</sup><sup>2</sup> (*x*2) are, respectively, the MF for the inputs *x*<sup>1</sup> and *x*2.

• Layer 2: Each node in this layer, denoted as Π, is a non-adaptive node. This layer receives the input values *x*<sup>1</sup> and *x*<sup>2</sup> from the first layer and acts as a MF to represent the fuzzy sets of the respective input variables. Further, it computes the membership values that specify the degree to which the input values belongs to the fuzzy set. The nodes outputs are defined by the following product:

$$\mathcal{O}\_{2,i} = w\_i = \mu\_{A\_i}(\mathbf{x}\_1) \cdot \mu\_{B\_i}(\mathbf{x}\_2), \text{ for } i = 1, 2 \tag{14}$$

• Layer 3: Each node in this layer, denoted as *N*, is a non-adaptive node that normalizes the weight functions obtained from layer Π. This layer is usually called as the rule layer since it determines the activation level of each rule. The nodes outputs are given by:

$$\mathcal{O}\_{3,i} = \vec{w}\_i = \frac{w\_i}{w\_1 + w\_2}, \text{ for } i = 1, 2 \tag{15}$$

• Layer 4: Every node *i* in this layer is an adaptive node. The parameters of this layer are called consequent parameters and the nodes outputs are expressed by:

$$O\_{4,i} = \overline{w}\_i f\_i = \overline{w}\_i (p\_i \mathbf{x}\_1 + q\_i \mathbf{x}\_2 + r\_i)\_\prime \text{ for } i = 1, 2 \tag{16}$$

where *w*¯*<sup>i</sup>* is the output of layer 3 and {*pi*, *qi*,*ri*} are the consequent parameters set.

• Layer 5: This layer, denoted by Σ, is non-adaptive and produces the output function by adding all inputs from the previous layers and transforming the fuzzy classification results into a crisp value, as expressed by:

$$O\_{5,1} = \sum\_{i} \bar{w}\_{i} f\_{i} = \frac{\sum\_{i} w\_{i} f\_{i}}{\sum\_{i} w\_{i}} \tag{17}$$

#### *3.1.2. Hybrid Learning Algorithm*

6 Search Algorithms

signal flow from one node to another.

circle to denote this type of fixed node [11].

*3.1.1. ANFIS Architecture*

denoted as *Ol*,*i*.

*x*1

*A*1

*A*2

*B*1

*B*2

*x*2

**Figure 2.** ANFIS Structure [11]

incoming signals to generate a single node output and each link specifies the direction of the

The parameters of an adaptive network are distributed into the network nodes, so each node has a local parameter set. The union of these local parameter sets forms the network overall parameter set. If a node parameter set is non-empty, then its node function depends on the parameter values, and it is used a square to represent this kind of adaptive node. On the other hand, if a node has an empty parameter set, then its function is fixed and it is used a

This technique offers a method for learning information about a given data set during the fuzzy modeling procedure in order to adjust the MF parameters that best control the

In order to describe the ANFIS architecture in more detail, it is considered in the following, without loss of generality, a system with two inputs *x*<sup>1</sup> and *x*<sup>2</sup> and one output *y*, based on a

The ANFIS network structure is composed by a set of units and connections arranged into

*N*

Layer 1 Layer 2 Layer 3 Layer 4 Layer 5

.

• Layer 1: Nodes in this layer are adaptive nodes and represent the membership grade of the inputs *x*<sup>1</sup> and *x*2. Here, triangular or bell shaped MF [11] can be used. The parameters of this layer are called premise parameters and the nodes outputs are represented by:

Rule 1 : If *x*<sup>1</sup> is *A*<sup>1</sup> and *x*<sup>2</sup> is *B*<sup>1</sup> then *f*<sup>1</sup> = *p*1*x*<sup>1</sup> + *q*1*x*<sup>2</sup> + *r*<sup>1</sup> (11) Rule 2 : If *x*<sup>1</sup> is *A*<sup>2</sup> and *x*<sup>2</sup> is *B*<sup>2</sup> then *f*<sup>2</sup> = *p*2*x*<sup>1</sup> + *q*2*x*<sup>2</sup> + *r*<sup>2</sup> (12)

*x*1

*x*2

*x*1

*<sup>N</sup> <sup>w</sup>*<sup>1</sup> *<sup>w</sup>*¯ <sup>1</sup> *<sup>w</sup>*¯ <sup>1</sup> *<sup>f</sup>*<sup>1</sup>

*w*<sup>2</sup> *w*¯ <sup>2</sup> *w*¯ <sup>2</sup> *f*<sup>2</sup>

*x*2

*th* node of the *l*

*th* layer is

∑ *<sup>y</sup>*

associated fuzzy inference system (FIS) to obtain the desired behavior.

five layers [11, 27, 29], as shown in Fig. 2, where the output of the *i*

∏

∏

first-order Takagi-Sugeno fuzzy model [28] with the fuzzy rules expressed as:

The learning process can update the MF parameters by a hybrid learning procedure [29] composed by the Least Squares (LS) method, which is applied for tuning the linear output MF parameters, and the Backpropagation (BP) method, which is employed for tuning the nonlinear input MF parameters [30].

In the forward pass, LS estimates the consequent parameters, keeping the premise parameter fixed, and in the backward pass, the premise parameters are obtained by BP, keeping the consequent parameter fixed. When the values of the premise parameters are fixed, the overall output can be expressed as a linear combination of the consequent parameters.

Thus, considering the general LS approach, the output *y* of a given system to an input **x** can be represented by the following linearly parameterized equation:

$$y = \theta\_1 f\_1(\mathbf{x}) + \theta\_2 f\_2(\mathbf{x}) + \dots + \theta\_{N\_l} f\_{N\_l}(\mathbf{x}) \tag{18}$$

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(23)

= **e***<sup>T</sup>* × **e** (25)

**A** × θ + **e** = **v** (24)

*<sup>m</sup>* is the *<sup>m</sup>th* row vector of **<sup>A</sup>**, **<sup>e</sup>** = **<sup>v</sup>** − **<sup>A</sup>** × <sup>θ</sup> is the error

× θ = **A***<sup>T</sup>* × **v** (26)

× **A***<sup>T</sup>* × **v** (27)

*th* layer, the output *Ol*,*<sup>i</sup>* of the *i*

*th* node

**v** =

Whose solution θ = θˆ is obtained by minimizing the sum of the squared error:

�

*vm* − **a***<sup>T</sup>*

The squared error in equation (25) is minimized when θ = θˆ, where θˆ is obtained through a

�−<sup>1</sup>

The LS solution is computationally very expensive, mainly for vectorial inputs, since it requires matrix inversion. Moreover, it can become ill-conditioned if **A***<sup>T</sup>* × **A** becomes singular. Thus, in practice, a recursive LS (RLS) algorithm can usually be employed [11,

In the backward pass, the premise parameters are estimated iteratively by a modified BP procedure that employs the Gradient Descent (GD) algorithm along with the chain rule to find the minimum of the error function in the weight space [29]. Considering a feed-forward

*<sup>i</sup>* nodes in the *l*

× **A***<sup>T</sup>* is the pseudo-inverse of **A** [30] and ()−<sup>1</sup> is the inverse operation.

*<sup>m</sup>* × <sup>θ</sup> �2

*Nm* ∑ *m*=1

vector produced by a specific choice of θ and ()*<sup>T</sup>* is the transpose operation.

� **A***T* × **A** �

θˆ = � **A***T* × **A**

If **A***<sup>T</sup>* × **A** is non-singular, the LS solution θˆ can be obtained by:

vector **e** is introduced, resulting in the following equation:

ℓ(θ) =

LS estimator that satisfies the following normal equation:

where ℓ(θ) is the objective function, **a***<sup>T</sup>*

where �

29, 30].

of the *l*

**A***T* × **A**

�−<sup>1</sup>

adaptive network with *NL* layers and *N<sup>l</sup>*

*th* layer can be represented by:

 

Usually, *Nm* > *Ni* and, instead of directly obtaining a solution for equation (20), an error

*v*1 . . . *vNm*

An Adaptive Neuro-Fuzzy Strategy for a Wireless Coded Power Control in Doubly-Fed Induction Aerogenerators

 

where **x** is the input vector of the model with dimension *Nx*, *fi* are known functions of **x**, *θ<sup>i</sup>* are the unknown parameters to be optimized and *i* = 1, ··· , *Ni*.

Usually, to identify the unknown parameters, a training set of data pairs (**u***m*, *vm*) is employed, where **u** is a vector with dimension *Nx* and *m* = 1, ··· , *Nm*. Substituting each data pair into equation (18) yields the following set of *Nm* linear equations:

$$f\_1(\mathbf{u}\_1)\theta\_1 + f\_2(\mathbf{u}\_1)\theta\_2 + \dots + f\_{N\_l}(\mathbf{u}\_1)\theta\_{N\_l} = \mathbf{v}\_1$$

$$\begin{bmatrix} \vdots & \vdots & \vdots & \vdots\\ f\_1(\mathbf{u}\_{N\_m})\theta\_1 + f\_2(\mathbf{u}\_{N\_m})\theta\_2 + \dots + f\_{N\_l}(\mathbf{u}\_{N\_m})\theta\_{N\_l} = \mathbf{v}\_{N\_m} \end{bmatrix}$$

These equations can also be expressed through the following vector representation:

$$\mathbf{A} \times \boldsymbol{\theta} = \mathbf{v} \tag{20}$$

where **A** is a (*Nm*) by (*Ni*) matrix:

$$\mathbf{A} = \begin{bmatrix} f\_1(\mathbf{u}\_1) & \cdots & f\_{N\_l}(\mathbf{u}\_1) \\ \vdots & \ddots & \vdots \\ f\_1(\mathbf{u}\_{N\_m}) & \cdots & f\_{N\_l}(\mathbf{u}\_{N\_m}) \end{bmatrix} \tag{21}$$

θ is the (*Ni*) by (1) vector of unknown parameter:

$$\boldsymbol{\theta} = \begin{bmatrix} \theta\_1 \\ \vdots \\ \theta\_{N\_i} \end{bmatrix} \tag{22}$$

and **v** is the (*Nm*) by (1) output vector:

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$$\mathbf{v} = \begin{bmatrix} v\_1 \\ \vdots \\ v\_{N\_{\text{fw}}} \end{bmatrix} \tag{23}$$

Usually, *Nm* > *Ni* and, instead of directly obtaining a solution for equation (20), an error vector **e** is introduced, resulting in the following equation:

$$\mathbf{A} \times \mathbf{\theta} + \mathbf{e} = \mathbf{v} \tag{24}$$

Whose solution θ = θˆ is obtained by minimizing the sum of the squared error:

8 Search Algorithms

consequent parameter fixed. When the values of the premise parameters are fixed, the overall

Thus, considering the general LS approach, the output *y* of a given system to an input **x** can

*<sup>y</sup>* = *<sup>θ</sup>*<sup>1</sup> *<sup>f</sup>*1(**x**) + *<sup>θ</sup>*<sup>2</sup> *<sup>f</sup>*2(**x**) + ··· + *<sup>θ</sup>Ni fNi*

where **x** is the input vector of the model with dimension *Nx*, *fi* are known functions of **x**, *θ<sup>i</sup>*

Usually, to identify the unknown parameters, a training set of data pairs (**u***m*, *vm*) is employed, where **u** is a vector with dimension *Nx* and *m* = 1, ··· , *Nm*. Substituting each

. .

*<sup>f</sup>*1(**u**1) ··· *fNi*

*<sup>f</sup>*1(**u***Nm* ) ··· *fNi*

 

*θ*1 . . . *θNi*  

. ... .

. .

θ =

(**x**) (18)

(19)

(**u**1)*θNi* = *<sup>v</sup>*<sup>1</sup>

. .

(**u***Nm* )*θNi* = *vNm*

**A** × θ = **v** (20)

(21)

(22)

. .

.

(**u**1)

 

(**u***Nm* )

. .

output can be expressed as a linear combination of the consequent parameters.

be represented by the following linearly parameterized equation:

are the unknown parameters to be optimized and *i* = 1, ··· , *Ni*.

. .

**A** =

 

. .

θ is the (*Ni*) by (1) vector of unknown parameter:

and **v** is the (*Nm*) by (1) output vector:

where **A** is a (*Nm*) by (*Ni*) matrix:

data pair into equation (18) yields the following set of *Nm* linear equations:

*<sup>f</sup>*1(**u**1)*θ*<sup>1</sup> + *<sup>f</sup>*2(**u**1)*θ*<sup>2</sup> + ··· + *fNi*

.

*<sup>f</sup>*1(**u***Nm* )*θ*<sup>1</sup> + *<sup>f</sup>*2(**u***Nm* )*θ*<sup>2</sup> + ··· + *fNi*

These equations can also be expressed through the following vector representation:

$$\ell(\boldsymbol{\theta}) = \sum\_{m=1}^{N\_m} \left( v\_m - \mathbf{a}\_m^T \times \boldsymbol{\theta} \right)^2 = \mathbf{e}^T \times \mathbf{e} \tag{25}$$

where ℓ(θ) is the objective function, **a***<sup>T</sup> <sup>m</sup>* is the *<sup>m</sup>th* row vector of **<sup>A</sup>**, **<sup>e</sup>** = **<sup>v</sup>** − **<sup>A</sup>** × <sup>θ</sup> is the error vector produced by a specific choice of θ and ()*<sup>T</sup>* is the transpose operation.

The squared error in equation (25) is minimized when θ = θˆ, where θˆ is obtained through a LS estimator that satisfies the following normal equation:

$$\left(\mathbf{A}^T \times \mathbf{A}\right) \times \boldsymbol{\theta} = \mathbf{A}^T \times \mathbf{v} \tag{26}$$

If **A***<sup>T</sup>* × **A** is non-singular, the LS solution θˆ can be obtained by:

$$\hat{\boldsymbol{\theta}} = \left(\mathbf{A}^T \times \mathbf{A}\right)^{-1} \times \mathbf{A}^T \times \mathbf{v} \tag{27}$$

where � **A***T* × **A** �−<sup>1</sup> × **A***<sup>T</sup>* is the pseudo-inverse of **A** [30] and ()−<sup>1</sup> is the inverse operation.

The LS solution is computationally very expensive, mainly for vectorial inputs, since it requires matrix inversion. Moreover, it can become ill-conditioned if **A***<sup>T</sup>* × **A** becomes singular. Thus, in practice, a recursive LS (RLS) algorithm can usually be employed [11, 29, 30].

In the backward pass, the premise parameters are estimated iteratively by a modified BP procedure that employs the Gradient Descent (GD) algorithm along with the chain rule to find the minimum of the error function in the weight space [29]. Considering a feed-forward adaptive network with *NL* layers and *N<sup>l</sup> <sup>i</sup>* nodes in the *l th* layer, the output *Ol*,*<sup>i</sup>* of the *i th* node of the *l th* layer can be represented by:

$$\mathcal{O}\_{l,i} = f\_{l,i} \left( \mathcal{O}\_{l-1,1\prime} \cdots \mathcal{O}\_{l-1,N\_l^{l-1}\prime} \mathbb{E}\_{l,i\prime}^1 \mathbb{E}\_{l,i\prime}^2 \cdots \cdot \mathbb{E}\_{l,i}^{N\_{\xi}} \right) \tag{28}$$

where *fl*,*i*() is the node function of the *i th* node of the *l th* layer and *ξ*<sup>1</sup> *l*,*i* , *ξ*<sup>2</sup> *l*,*i* , ··· , *ξ Nξ <sup>l</sup>*,*<sup>i</sup>* are the parameters associated with this specific node.

Assuming that the training data set has *Nm* terms, a measure of error at the output layer *L* corresponding to the *mth* term of the training set, where 1 ≤ *m* ≤ *Nm*, can be defined as [11, 27, 29]:

$$\ell\_m = \sum\_{i=1}^{N\_l^L} \left( v\_m^i - O\_{L,i}^m \right)^2 \tag{29}$$

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*th* node of 1*st* layer are given

(33)

185

(34)

(35)

(36)

(37)

*e m <sup>l</sup>*,*<sup>i</sup>* =

where 1 ≤ *l* ≤ *NL* − 1 and *NL* = 5 for the considered ANFIS model.

layer *ς*1,*i*. The gradient vector elements corresponding to the *i*

by:

= *Nl*+<sup>1</sup> *i* ∑ *m*=1 *e m l*+1,*i*

*∂*+ℓ*<sup>m</sup> ∂ς*1,*i*

The derivative of the total error measure ℓ*total* with respect to *<sup>ς</sup>*1,*<sup>i</sup>* is given by:

*<sup>∂</sup>*+ℓ*total ∂ς*1,*i*

Accordingly, the parameter *ς*1,*<sup>i</sup>* can be updated using the following expression:

where *η* is the learning rate [11, 29].

∆*ς*1,*<sup>i</sup>* = −*η*

The parameter *ς*1,*<sup>i</sup>* can be updated employing the following recursive expression:

= *ς*old 1,*<sup>i</sup>* <sup>−</sup> *<sup>η</sup>*

*ς*new 1,*<sup>i</sup>* <sup>=</sup> *<sup>ς</sup>*old

*Nl*+<sup>1</sup> *i* ∑ *m*=1

*∂*+ℓ*<sup>m</sup> ∂O<sup>m</sup> l*+1,*i*

An Adaptive Neuro-Fuzzy Strategy for a Wireless Coded Power Control in Doubly-Fed Induction Aerogenerators

As the consequent parameters are fixed in the backward pass, the gradient vector can be defined as the derivative of the error measure with respect to the node parameters of the first

> <sup>=</sup> *<sup>∂</sup>*+ℓ*<sup>m</sup> ∂v*1,*<sup>i</sup>*

= *e*1,*<sup>i</sup>*

= *Nm* ∑ *m*=1 *∂ f*1,*<sup>i</sup> ∂ς*1,*i*

*∂*+ℓ*<sup>m</sup> ∂ς*1,*i*

*<sup>∂</sup>*+ℓ*total ∂ς*1,*i*

1,*<sup>i</sup>* + ∆*ς*1,*<sup>i</sup>*

*<sup>∂</sup>*+ℓ*total ∂ς*1,*i*

*∂ f*1,*<sup>i</sup> ∂ς*1,*i*

*∂ fl*<sup>+</sup>1,*<sup>m</sup> ∂O<sup>m</sup> l*,*i*

*∂ fl*<sup>+</sup>1,*<sup>m</sup> ∂O<sup>m</sup> l*,*i*

where *v<sup>i</sup> <sup>m</sup>* is the *mth* desired output for the *i th* node of the output layer (*Lth* layer) and *O<sup>m</sup> <sup>L</sup>*,*<sup>i</sup>* is the actual output of the *i th* node of the output layer produced by applying the *mth* training input vector to the network.

In this way, the main task of this step is to employ the GD algorithm to minimize the total measure of error defined as:

$$\ell\_{total} = \sum\_{m=1}^{N\_m} \ell\_m \tag{30}$$

In order to compute the gradient vector of the parameters, a form of the derivative information has to be passed backward, layer by layer, from the output layer to the input layer. This procedure is called BP because the gradient is obtained sequentially from the output layer to the input layer.

The corresponding error signal *el*,*<sup>i</sup>* can be defined by the ordered derivative [31] of ℓ*<sup>m</sup>* with respect to the output of the *i th* node of the *l th* layer:

$$e\_{l,i}^{m} = \frac{\partial^{+} \ell\_m}{\partial \mathcal{O}\_{l,i}^{m}}\tag{31}$$

Particularly, for the output layer *L*, the error signal can be represented by the following simplified expression:

$$\boldsymbol{e}\_{\rm L,i}^{m} = -2\left(\boldsymbol{v}\_{m}^{i} - \boldsymbol{O}\_{\rm L,i}^{m}\right) \tag{32}$$

For the internal *i th* node at the *l th* layer, the error signal can be derived iteratively by the following chain rule [11, 29]:

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$$c\_{l,i}^m = \sum\_{m=1}^{N\_l^{l+1}} \frac{\partial^+ \ell\_m}{\partial O\_{I+1,i}^m} \frac{\partial f\_{l+1,m}}{\partial O\_{l,i}^m}$$

$$= \sum\_{m=1}^{N\_l^{l+1}} c\_{l+1,i}^m \frac{\partial f\_{l+1,m}}{\partial O\_{l,i}^m} \tag{33}$$

where 1 ≤ *l* ≤ *NL* − 1 and *NL* = 5 for the considered ANFIS model.

As the consequent parameters are fixed in the backward pass, the gradient vector can be defined as the derivative of the error measure with respect to the node parameters of the first layer *ς*1,*i*. The gradient vector elements corresponding to the *i th* node of 1*st* layer are given by:

$$\frac{\partial^+ \ell\_m}{\partial \zeta\_{1,i}} = \frac{\partial^+ \ell\_m}{\partial v\_{1,i}} \frac{\partial f\_{1,i}}{\partial \zeta\_{1,i}}$$

$$= e\_{1,i} \frac{\partial f\_{1,i}}{\partial \zeta\_{1,i}}\tag{34}$$

The derivative of the total error measure ℓ*total* with respect to *<sup>ς</sup>*1,*<sup>i</sup>* is given by:

$$\frac{\partial^+ \ell\_{total}}{\partial \zeta\_{1,i}} = \sum\_{m=1}^{N\_{\rm u}} \frac{\partial^+ \ell\_m}{\partial \zeta\_{1,i}} \tag{35}$$

Accordingly, the parameter *ς*1,*<sup>i</sup>* can be updated using the following expression:

$$
\Delta \xi\_{1,i} = -\eta \frac{\partial^+ \ell\_{total}}{\partial \xi\_{1,i}} \tag{36}
$$

where *η* is the learning rate [11, 29].

10 Search Algorithms

as [11, 27, 29]:

where *v<sup>i</sup>*

the actual output of the *i*

input vector to the network.

measure of error defined as:

output layer to the input layer.

respect to the output of the *i*

simplified expression:

For the internal *i*

following chain rule [11, 29]:

*Ol*,*<sup>i</sup>* = *fl*,*<sup>i</sup>*

*<sup>m</sup>* is the *mth* desired output for the *i*

where *fl*,*i*() is the node function of the *i*

parameters associated with this specific node.

*Ol*−1,1, ··· ,*Ol*<sup>−</sup>1,*Nl*−<sup>1</sup>

ℓ*<sup>m</sup>* =

*N<sup>L</sup> i* ∑ *i*=1 *vi <sup>m</sup>* − *<sup>O</sup><sup>m</sup> L*,*i* 2

*i* , *ξ*1 *l*,*i* , *ξ*2 *l*,*i* , ··· , *ξ Nξ l*,*i* 

*th* layer and *ξ*<sup>1</sup>

*th* node of the output layer (*Lth* layer) and *O<sup>m</sup>*

ℓ*<sup>m</sup>* (30)

*th* node of the output layer produced by applying the *mth* training

*l*,*i* , *ξ*<sup>2</sup> *l*,*i* , ··· , *ξ Nξ <sup>l</sup>*,*<sup>i</sup>* are the

*th* node of the *l*

Assuming that the training data set has *Nm* terms, a measure of error at the output layer *L* corresponding to the *mth* term of the training set, where 1 ≤ *m* ≤ *Nm*, can be defined

In this way, the main task of this step is to employ the GD algorithm to minimize the total

In order to compute the gradient vector of the parameters, a form of the derivative information has to be passed backward, layer by layer, from the output layer to the input layer. This procedure is called BP because the gradient is obtained sequentially from the

The corresponding error signal *el*,*<sup>i</sup>* can be defined by the ordered derivative [31] of ℓ*<sup>m</sup>* with

Particularly, for the output layer *L*, the error signal can be represented by the following

 *vi <sup>m</sup>* − *<sup>O</sup><sup>m</sup> L*,*i* 

*th* layer, the error signal can be derived iteratively by the

*th* layer:

*th* node of the *l*

*e m <sup>L</sup>*,*<sup>i</sup>* <sup>=</sup> <sup>−</sup><sup>2</sup>

*th* node at the *l*

*e m <sup>l</sup>*,*<sup>i</sup>* <sup>=</sup> *<sup>∂</sup>*+ℓ*<sup>m</sup> ∂O<sup>m</sup> l*,*i*

*Nm* ∑ *m*=1

ℓ*total* =

(28)

(29)

*<sup>L</sup>*,*<sup>i</sup>* is

(31)

(32)

The parameter *ς*1,*<sup>i</sup>* can be updated employing the following recursive expression:

$$
\xi\_{1,i}^{\text{new}} = \xi\_{1,i}^{\text{old}} + \Delta \xi\_{1,i}
$$

$$
= \xi\_{1,i}^{\text{old}} - \eta \frac{\partial^+ \ell\_{total}}{\partial \xi\_{1,i}} \tag{37}
$$

In this type of learning procedure, the MF update occurs only after the whole set of training data pair is introduced. This process of introduction of the whole set of training data pairs is called epoch.

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187

*<sup>a</sup>* <sup>|</sup>2*<sup>b</sup>* (38)

*dt* (39)

*ωsldt* (41)

(40)

• Operation at different wind speed profiles;

• Operation during voltage sag conditions.

where, the parameter *b* is usually positive.

and angle between stator and rotor flux.

**4. Flux estimation**

The stator flux

• Operation at different ramp increments in wind speed; • Operation at different step increments in wind speed;

parameters *a*, *b*, *c*, besides the input *u*, has been considered:

MF and then use *b* to control the slopes at the crossover points [27].

switching signals for the rotor side using either space vector modulation.

 *λ*1*αβ* =

The stator flux position can be obtained by using equation (39) as:

And the angle between stator and rotor flux is given by:

The grid partition method is chosen to design the fuzzy controller structure, which usually involves just some few state variables as inputs to the controller. A generalized bell MF with

An Adaptive Neuro-Fuzzy Strategy for a Wireless Coded Power Control in Doubly-Fed Induction Aerogenerators

The desired generalized bell MF can be obtained by a proper selection of the parameter set {*a*, *b*, *c*}. Specifically, we can adjust *c* and *a* to vary, respectively, the center and width of the

To calculate the numerical value resulting from the activated rules, it was used the weighted average method for defuzzification. Thus, if the *direct* and *quadrature* voltage components are calculated according to the ANFIS controller and are applied to the generator, then the active and reactive power convergence to their respective commanded values will occur in a few sampling intervals. The desired rotor voltage in the rotor reference frame (*δ<sup>s</sup>* − *δr*) generates

For work properly, the ANFIS controller requires the estimation of stator flux, stator position

*<sup>v</sup>*1*αβ* <sup>−</sup> *<sup>R</sup>*<sup>1</sup>

*<sup>δ</sup><sup>s</sup>* <sup>=</sup> arctan *<sup>λ</sup>*1*<sup>β</sup>*

*δ<sup>s</sup>* − *δ<sup>r</sup>* =

*<sup>i</sup>*1*αβ*

*λ*1*<sup>α</sup>*

*λ*1*αβ* in stationary reference frame can be estimated by:

<sup>1</sup> + | *<sup>u</sup>*−*<sup>c</sup>*

*bell*(*u*, *<sup>a</sup>*, *<sup>b</sup>*, *<sup>c</sup>*) = <sup>1</sup>

#### **3.2. Proposed Adaptive Neuro-Fuzzy Power Control**

The proposed adaptive neuro-fuzzy power control system, shown in Fig. 3, is composed by two ANFIS controllers based on a first-order Takagi-Sugeno fuzzy model [28] with one input and one output. The first controller has *ε*2*<sup>q</sup>* as input and *v*2*<sup>q</sup>* as output, and the second controller has *<sup>ε</sup>*2*<sup>d</sup>* and *<sup>v</sup>*2*<sup>d</sup>* as input and output, respectively, where *<sup>ε</sup>*2*<sup>q</sup>* = *<sup>i</sup>*2*qref* − *<sup>i</sup>*2*<sup>q</sup>* and *<sup>ε</sup>*2*<sup>d</sup>* <sup>=</sup> *<sup>i</sup>*2*dref* <sup>−</sup> *<sup>i</sup>*2*d*.

**Figure 3.** Neuro-Fuzzy DFIG Power Control.

Differently from what has been presented in the literature [10], the ANFIS controller employs just the rotor current error as input and it is designed from an input and output data set collected from a DFIG with a deadbeat controller [25] operating at different conditions.

In Fig. 4, it is shown a simplified representation of the substitution that was made in this work with the purpose of illustrating that the designed ANFIS presents the same behavior of a deadbeat controller.

**Figure 4.** ANFIS Controller.

The tests used in this work for collect data set training are similar to the ones used in [10]:

• Operation at different wind speed profiles;

12 Search Algorithms

is called epoch.

*<sup>ε</sup>*2*<sup>d</sup>* <sup>=</sup> *<sup>i</sup>*2*dref* <sup>−</sup> *<sup>i</sup>*2*d*.

**Figure 3.** Neuro-Fuzzy DFIG Power Control.

of a deadbeat controller.

**Figure 4.** ANFIS Controller.

In this type of learning procedure, the MF update occurs only after the whole set of training data pair is introduced. This process of introduction of the whole set of training data pairs

The proposed adaptive neuro-fuzzy power control system, shown in Fig. 3, is composed by two ANFIS controllers based on a first-order Takagi-Sugeno fuzzy model [28] with one input and one output. The first controller has *ε*2*<sup>q</sup>* as input and *v*2*<sup>q</sup>* as output, and the second controller has *<sup>ε</sup>*2*<sup>d</sup>* and *<sup>v</sup>*2*<sup>d</sup>* as input and output, respectively, where *<sup>ε</sup>*2*<sup>q</sup>* = *<sup>i</sup>*2*qref* − *<sup>i</sup>*2*<sup>q</sup>* and

Differently from what has been presented in the literature [10], the ANFIS controller employs just the rotor current error as input and it is designed from an input and output data set collected from a DFIG with a deadbeat controller [25] operating at different conditions.

In Fig. 4, it is shown a simplified representation of the substitution that was made in this work with the purpose of illustrating that the designed ANFIS presents the same behavior

*v*2*<sup>q</sup> v*2*<sup>q</sup>*

−

+

*v*2*<sup>d</sup> v*2*<sup>d</sup>*

−

+

ANFIS

ANFIS

*i*2*<sup>q</sup> i*2*<sup>q</sup>*

*i*2*<sup>d</sup> i*2*<sup>d</sup>*

The tests used in this work for collect data set training are similar to the ones used in [10]:

*i*2*qref i*2*qref*

Deadbeat

*i*2*dref i*2*dref*

Deadbeat

+

−

+

−

**3.2. Proposed Adaptive Neuro-Fuzzy Power Control**


The grid partition method is chosen to design the fuzzy controller structure, which usually involves just some few state variables as inputs to the controller. A generalized bell MF with parameters *a*, *b*, *c*, besides the input *u*, has been considered:

$$bell(u, a, b, c) = \frac{1}{1 + |\frac{u - c}{a}|^{2b}}\tag{38}$$

where, the parameter *b* is usually positive.

The desired generalized bell MF can be obtained by a proper selection of the parameter set {*a*, *b*, *c*}. Specifically, we can adjust *c* and *a* to vary, respectively, the center and width of the MF and then use *b* to control the slopes at the crossover points [27].

To calculate the numerical value resulting from the activated rules, it was used the weighted average method for defuzzification. Thus, if the *direct* and *quadrature* voltage components are calculated according to the ANFIS controller and are applied to the generator, then the active and reactive power convergence to their respective commanded values will occur in a few sampling intervals. The desired rotor voltage in the rotor reference frame (*δ<sup>s</sup>* − *δr*) generates switching signals for the rotor side using either space vector modulation.

## **4. Flux estimation**

For work properly, the ANFIS controller requires the estimation of stator flux, stator position and angle between stator and rotor flux.

The stator flux *λ*1*αβ* in stationary reference frame can be estimated by:

$$
\vec{\lambda}\_{1a\beta} = \int \left( \vec{v}\_{1a\beta} - R\_1 \vec{i}\_{1a\beta} \right) dt \tag{39}
$$

The stator flux position can be obtained by using equation (39) as:

$$\delta\_s = \arctan\left(\frac{\lambda\_{1\beta}}{\lambda\_{1a}}\right) \tag{40}$$

And the angle between stator and rotor flux is given by:

$$
\delta\_{\rm s} - \delta\_{r} = \int \omega\_{\rm sl} dt \tag{41}
$$

## **5. Wireless Coded Communication System**

The wireless communication system, shown in Fig. 5, is responsible for transmitting the power references from the remote control unit to the ANFIS controller and it uses Quaternary Phase Shift Keying (QPSK) modulation and LDPC coding [18, 32, 33] to improve system performance and reliability.

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<sup>1</sup> and then differentially

(44)

189

**G** = [**I Ψ**] (43)

<sup>2</sup> , ()−*<sup>T</sup>* is the inverse transpose operation, and

where **I** is the identity matrix, **Ψ** = **H***<sup>T</sup>*

<sup>2</sup> is the upper triangular matrix given by:

*qb*,1 ··· *qb*,*Nb*

Gaussian random variables with autocorrelation function [15, 40]:

**H**−*<sup>T</sup>*

vector **<sup>q</sup>***<sup>b</sup>* = �

*<sup>s</sup>*<sup>1</sup> ··· *sNs*

the parity bits.

*qc*,1 ··· *qc*,*Nc*

can be represented by [15]:

*<sup>r</sup>*<sup>1</sup> ··· *rNs*

complex coefficients of the channel and **n** = �

�*T*

**q***<sup>c</sup>* = �

**s** = �

spread.

where **r** = �

<sup>1</sup> <sup>×</sup> **<sup>H</sup>**−*<sup>T</sup>*

 

The encoding process can be accomplished by first multiplying the control information

encoding this partial result to obtain the parity bits. The systematic codeword vector

In the transmission process, for each transmitted frame, the codeword vector is interleaved and mapped to QPSK symbols by using Gray coding [15], resulting in the symbol vector

the coded symbols are filtered, upconverted and transmitted by the wireless fading channel. Assuming that the channel variations are slow enough that intersymbol interferences (ISI) can be neglect, the fading channel can be modeled as a sequence of zero-mean complex

where *J*0() is the *zeroth* order Bessel function, *Ts* is the signaling time and *fD* is the Doppler

Thus, in the receive process, the complex low-pass equivalent discrete-time received signal

�*<sup>T</sup>* is the received signal vector, <sup>γ</sup> = �

*<sup>n</sup>*<sup>1</sup> ··· *nNs*

�*<sup>T</sup>* by the sparse matrix **H***<sup>T</sup>*

111 ··· 1 1 1 1 ··· 1 1 1 11 ... . . . . . . 1 1 1

An Adaptive Neuro-Fuzzy Strategy for a Wireless Coded Power Control in Doubly-Fed Induction Aerogenerators

 

�*<sup>T</sup>* can be simply obtained by combining the control information and

, where *Ns* is the number of transmitted coded control symbols. Afterward,

*Rh* (*τ*) = *J*<sup>0</sup> (2*π fDTs*) (45)

**r** = γ · **s** + **n** (46)

*<sup>γ</sup>*<sup>1</sup> ··· *<sup>γ</sup>Ns*

�*<sup>T</sup>* is the Additive White Gaussian

�*<sup>T</sup>* is the vector of

**H**−*<sup>T</sup>* <sup>2</sup> =

**Figure 5.** Wireless Coding Communication Diagram.

LDPC are (*Nc*, *Nb*) binary linear block codes that have a sparse parity-check matrix **H** that can be described in terms of a Tanner graph [34], where each bit in the codeword corresponds to a variable node and each parity-check equation corresponds to a check node. A check node *j* is connected to a variable node *k* whenever the element *hj*,*<sup>k</sup>* in **H** is equal to 1 [18, 34].

Extended Irregular Repeat Accumulate (eIRA) codes [35–39] are a special subclass of LDPC codes that improve the systematic encoding process and generate good irregular LDPC codes for high code rate applications. The eIRA parity-check matrix can be represented by **H** = [**H**<sup>1</sup> **H**2], where **H**<sup>1</sup> is a sparse (*Nz*) by (*Nc*) matrix, that can be constructed irregularly by density evolution according to optimal weight distribution [38], and **H**<sup>2</sup> is the (*Nz*) by (*Nz*) dual-diagonal square matrix given by:

$$\mathbf{H}\_2 = \begin{bmatrix} 1 \\ 1 \ 1 \\ \vdots \\ 1 \ \vdots \\ \vdots \\ 1 \ 1 \end{bmatrix} \tag{42}$$

where *Nb* is the number of control bits, *Nc* is the number of coded bits and *Nz* is the number of parity bits.

Given the constraint imposed on the **H** matrix, the generator matrix can be represented in the systematic form by the (*Nb*) by (*Nc*) matrix:

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$$\mathbf{G} = \begin{bmatrix} \mathbf{I} & \mathbf{\varPsi} \end{bmatrix} \tag{43}$$

where **I** is the identity matrix, **Ψ** = **H***<sup>T</sup>* <sup>1</sup> <sup>×</sup> **<sup>H</sup>**−*<sup>T</sup>* <sup>2</sup> , ()−*<sup>T</sup>* is the inverse transpose operation, and **H**−*<sup>T</sup>* <sup>2</sup> is the upper triangular matrix given by:

14 Search Algorithms

performance and reliability.

Power

Pref Qref

**5. Wireless Coded Communication System**

QPSK

**Figure 5.** Wireless Coding Communication Diagram.

dual-diagonal square matrix given by:

the systematic form by the (*Nb*) by (*Nc*) matrix:

of parity bits.

ADC & Mux

Demodulation Deinterleaving Decoding

q qc <sup>b</sup> r

**H**<sup>2</sup> =

 

where *Nb* is the number of control bits, *Nc* is the number of coded bits and *Nz* is the number

Given the constraint imposed on the **H** matrix, the generator matrix can be represented in

 

The wireless communication system, shown in Fig. 5, is responsible for transmitting the power references from the remote control unit to the ANFIS controller and it uses Quaternary Phase Shift Keying (QPSK) modulation and LDPC coding [18, 32, 33] to improve system

References qb qc s

**n**

LDPC are (*Nc*, *Nb*) binary linear block codes that have a sparse parity-check matrix **H** that can be described in terms of a Tanner graph [34], where each bit in the codeword corresponds to a variable node and each parity-check equation corresponds to a check node. A check node *j* is connected to a variable node *k* whenever the element *hj*,*<sup>k</sup>* in **H** is equal to 1 [18, 34].

Extended Irregular Repeat Accumulate (eIRA) codes [35–39] are a special subclass of LDPC codes that improve the systematic encoding process and generate good irregular LDPC codes for high code rate applications. The eIRA parity-check matrix can be represented by **H** = [**H**<sup>1</sup> **H**2], where **H**<sup>1</sup> is a sparse (*Nz*) by (*Nc*) matrix, that can be constructed irregularly by density evolution according to optimal weight distribution [38], and **H**<sup>2</sup> is the (*Nz*) by (*Nz*)

Modulation Coding Interleaving

QPSK

DAC & Demux

Pref Qref

(42)

Recovered Power References

$$\mathbf{H}\_2^{-T} = \begin{bmatrix} 1 \ 1 \ 1 \ \cdots \ 1 \ 1 \\ 1 \ 1 \ \cdots \ 1 \ 1 \\ 1 \ \cdots \ 1 \ 1 \\ \vdots \ \ddots \ \vdots \ \vdots \\ 1 \ 1 \\ 1 \end{bmatrix} \tag{44}$$

The encoding process can be accomplished by first multiplying the control information vector **<sup>q</sup>***<sup>b</sup>* = � *qb*,1 ··· *qb*,*Nb* �*<sup>T</sup>* by the sparse matrix **H***<sup>T</sup>* <sup>1</sup> and then differentially encoding this partial result to obtain the parity bits. The systematic codeword vector **q***<sup>c</sup>* = � *qc*,1 ··· *qc*,*Nc* �*<sup>T</sup>* can be simply obtained by combining the control information and the parity bits.

In the transmission process, for each transmitted frame, the codeword vector is interleaved and mapped to QPSK symbols by using Gray coding [15], resulting in the symbol vector **s** = � *<sup>s</sup>*<sup>1</sup> ··· *sNs* �*T* , where *Ns* is the number of transmitted coded control symbols. Afterward, the coded symbols are filtered, upconverted and transmitted by the wireless fading channel.

Assuming that the channel variations are slow enough that intersymbol interferences (ISI) can be neglect, the fading channel can be modeled as a sequence of zero-mean complex Gaussian random variables with autocorrelation function [15, 40]:

$$R\_h\left(\tau\right) = f\_0\left(2\pi f\_D T\_s\right) \tag{45}$$

where *J*0() is the *zeroth* order Bessel function, *Ts* is the signaling time and *fD* is the Doppler spread.

Thus, in the receive process, the complex low-pass equivalent discrete-time received signal can be represented by [15]:

$$\mathbf{r} = \gamma \cdot \mathbf{s} + \mathbf{n} \tag{46}$$

where **r** = � *<sup>r</sup>*<sup>1</sup> ··· *rNs* �*<sup>T</sup>* is the received signal vector, <sup>γ</sup> = � *<sup>γ</sup>*<sup>1</sup> ··· *<sup>γ</sup>Ns* �*<sup>T</sup>* is the vector of complex coefficients of the channel and **n** = � *<sup>n</sup>*<sup>1</sup> ··· *nNs* �*<sup>T</sup>* is the Additive White Gaussian Noise (AWGN) vector. Note that the above vector multiplication is performed element by element.

Once the transmitted vector **s** is estimated, considering perfect channel estimation, the transmitted control bits can be recovered by performing symbol demapping, code deinterleaving and bit decoding. Bit decoding can be accomplished by a message passing algorithm [23, 41–43] based on the Maximum A Posteriori (MAP) criterion [18], that exchanges soft-information iteratively between the variable and check nodes.

The exchanged messages can be represented by the following Log-Likelihood Ratio (LLR):

$$L\_{\mathbf{c}\_k} = \log \left[ \frac{p(\mathbf{q}\_{c,k} = 0 | \mathbf{d})}{p(\mathbf{q}\_{c,k} = 1 | \mathbf{d})} \right] \tag{47}$$

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**6. Performance of the Wireless Power Control System**

In the presented simulations, the sampling time is of 5 × 10<sup>−</sup>5s and the active and reactive power references are step changed, respectively, from -100 to -120 kW and from 60 to 0 kvar at 1.25s. At 1.5s, the references also are step changed from -120 to -60 kW and from 0 to -40 kvar. Again, at 1.75s, the references are step changed from -60 to -100 kW and from -40 to -60 kvar. These references are the inputs of the wireless coded power control shown in Fig. 5. The nominal power at each instant of time is calculated by means of the turbine parameters, presented in the Appendix, and the speed of the wind, monitored by the remote control unit (that can also be obtained directly from the turbine and sent to the remote control unit).

An Adaptive Neuro-Fuzzy Strategy for a Wireless Coded Power Control in Doubly-Fed Induction Aerogenerators

The wireless control system is evaluated in a frequency flat fading Rayleigh channel with a Doppler spread of 180 Hz. The employed LDPC coding scheme is the (64800, 32400) eIRA code specified in [44] and an ordinary Convolution Coding (CC) scheme with a (171, 133) generator polynomial with constrain length of 7 is used as a reference of performance [18]. Both schemes have code rate of 1/2 and employ a random interleaving of length 64,800. For simplicity, the number of iterations in the LDPC decoding is limited to 25. The bit duration is 16 × 10−<sup>5</sup> s and each transmitted frame is composed by 32,400 QPSK coded symbols.

The training process of the adaptive neuro-fuzzy power control strategy employed in this

In Fig. 6 and 7, the step response of the active and reactive power and of the rotor currents of the wireless controller using CC scheme are presented, respectively, considering an *Eb*/*N*<sup>0</sup>

**5 5.2 5.4 5.6 5.8 6**

**Q Qref**

**P Pref**

**5 5.2 5.4 5.6 5.8 6**

**Time [s]**

work considered a maximum of 5,000 epochs and an error tolerance of 0.0001.

of 10 dB.

**−20 −15 −10 −5 0 5 x 10<sup>4</sup>**

> **−2 −1 0 1 2 x 10<sup>5</sup>**

**Figure 6.** Step Response of Active and Reactive Power using CC in a Flat Fading Channel.

**Reactive Power [VAR]**

**Active Power [W]**

where, **d** is the vector of coded bits obtained by the processes of demodulation and deinterleaving.

The LLR message from the *j th* check node to the *kth* variable node is given by [37]:

$$L\_{r\_{jk}} = \text{2 } \text{atanh} \left[ \underset{k' \in \ V\_{f\_{/k}}}{\text{III}} \tanh \left( \frac{L\_{q\_{k',j}}}{2} \right) \right] \tag{48}$$

On the other hand, the LLR message from the *kth* variable node to the *j th* check node is obtained by:

$$L\_{q\_{k\boldsymbol{j}}} = L\_{\mathfrak{c}\_k} + \sum\_{\boldsymbol{j}' \in \mathfrak{C}\_{k\boldsymbol{j}}} L\_{r\_{\boldsymbol{j}',k}} \tag{49}$$

And the LLR for the *kth* code bit can be represented by:

$$L\_{\mathbb{Q}\_k} = L\_{\mathbb{C}\_k} + \sum\_{j \in \mathbb{C}\_k} L\_{r\_{jk}} \tag{50}$$

where the set *Vj* contains the variable nodes connected to the *j th* check node and the set *Ck* contains the check nodes connected to the *kth* variable node. *Vj*\*<sup>k</sup>* is the set *Vj* without the *kth* element, and *Ck*\*<sup>j</sup>* is the set *Ck* without the *j th* element.

At the end of each iteration, *LQk* provides an updated estimate of the a posteriori LLR of the transmitted coded bit *qc*,*k*. If *LQk* > 0, then *<sup>q</sup>*ˆ*c*,*<sup>k</sup>* = 1, else *<sup>q</sup>*ˆ*c*,*<sup>k</sup>* = 0.

## **6. Performance of the Wireless Power Control System**

16 Search Algorithms

element.

deinterleaving.

obtained by:

The LLR message from the *j*

Noise (AWGN) vector. Note that the above vector multiplication is performed element by

Once the transmitted vector **s** is estimated, considering perfect channel estimation, the transmitted control bits can be recovered by performing symbol demapping, code deinterleaving and bit decoding. Bit decoding can be accomplished by a message passing algorithm [23, 41–43] based on the Maximum A Posteriori (MAP) criterion [18], that

The exchanged messages can be represented by the following Log-Likelihood Ratio (LLR):

where, **d** is the vector of coded bits obtained by the processes of demodulation and

Π *k*′ ∈ *Vj*\*<sup>k</sup>*

*Lqk*,*<sup>j</sup>* = *Lck* + ∑

*LQk* = *Lck* + ∑

contains the check nodes connected to the *kth* variable node. *Vj*\*<sup>k</sup>* is the set *Vj* without the *kth*

At the end of each iteration, *LQk* provides an updated estimate of the a posteriori LLR of the

 *<sup>p</sup>*(**q***c*,*<sup>k</sup>* = <sup>0</sup>|**d**) *<sup>p</sup>*(**q***c*,*<sup>k</sup>* = <sup>1</sup>|**d**) *th* check node to the *kth* variable node is given by [37]:

 *Lqk*′,*<sup>j</sup>* 2

tanh

*j*′∈ *Ck*\*<sup>j</sup>*

*j*∈ *Ck*

*th* element.

(47)

(48)

*th* check node is

*Lrj*′,*<sup>k</sup>* (49)

*Lrj*,*<sup>k</sup>* (50)

*th* check node and the set *Ck*

exchanges soft-information iteratively between the variable and check nodes.

*Lck* = log

*Lrj*,*<sup>k</sup>* = 2 atanh

And the LLR for the *kth* code bit can be represented by:

element, and *Ck*\*<sup>j</sup>* is the set *Ck* without the *j*

where the set *Vj* contains the variable nodes connected to the *j*

transmitted coded bit *qc*,*k*. If *LQk* > 0, then *<sup>q</sup>*ˆ*c*,*<sup>k</sup>* = 1, else *<sup>q</sup>*ˆ*c*,*<sup>k</sup>* = 0.

On the other hand, the LLR message from the *kth* variable node to the *j*

In the presented simulations, the sampling time is of 5 × 10<sup>−</sup>5s and the active and reactive power references are step changed, respectively, from -100 to -120 kW and from 60 to 0 kvar at 1.25s. At 1.5s, the references also are step changed from -120 to -60 kW and from 0 to -40 kvar. Again, at 1.75s, the references are step changed from -60 to -100 kW and from -40 to -60 kvar. These references are the inputs of the wireless coded power control shown in Fig. 5. The nominal power at each instant of time is calculated by means of the turbine parameters, presented in the Appendix, and the speed of the wind, monitored by the remote control unit (that can also be obtained directly from the turbine and sent to the remote control unit).

The wireless control system is evaluated in a frequency flat fading Rayleigh channel with a Doppler spread of 180 Hz. The employed LDPC coding scheme is the (64800, 32400) eIRA code specified in [44] and an ordinary Convolution Coding (CC) scheme with a (171, 133) generator polynomial with constrain length of 7 is used as a reference of performance [18]. Both schemes have code rate of 1/2 and employ a random interleaving of length 64,800. For simplicity, the number of iterations in the LDPC decoding is limited to 25. The bit duration is 16 × 10−<sup>5</sup> s and each transmitted frame is composed by 32,400 QPSK coded symbols.

The training process of the adaptive neuro-fuzzy power control strategy employed in this work considered a maximum of 5,000 epochs and an error tolerance of 0.0001.

In Fig. 6 and 7, the step response of the active and reactive power and of the rotor currents of the wireless controller using CC scheme are presented, respectively, considering an *Eb*/*N*<sup>0</sup> of 10 dB.

**Figure 6.** Step Response of Active and Reactive Power using CC in a Flat Fading Channel.

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*dt* that can completely

**Q Qref**

**Pref P**

These errors in the control system can permanently damage the aerogenerator or even cause a loss of system efficiency, since the machine will not generate its maximum power track at that moment. Additionally, they generate undesirable harmonic components to the power grid.

An Adaptive Neuro-Fuzzy Strategy for a Wireless Coded Power Control in Doubly-Fed Induction Aerogenerators

deteriorate the Insulated Gate Bipolar Transistors (IGBTs) and, consequently, cause short

**5 5.2 5.4 5.6 5.8 6**

**5 5.2 5.4 5.6 5.8 6**

**Time [s]**

In this way, it turns out the necessity of employing a wireless coded control system capable of minimizing the occurrence of these spikes arising from errors caused by the channel distortions. With this finality, it is highlighted the proposal of using a more robust wireless

In Fig. 9 and 10, the step response of the active and reactive power and of the rotor currents of the wireless controller using the LDPC scheme are presented, respectively, considering an *Eb*/*N*<sup>0</sup> of 10 dB. The satisfactory performance of the wireless control system can be seen due to the fact the references were perfectly followed by the controller and the inexistence of destructive spikes caused by errors in the wireless transmission system. Additionally, these good functionalities are shown in Fig. 11, where the stator currents present expected

**Figure 9.** Step Response of Active and Reactive Power using LDPC in a Flat Fading Channel.

neuro-fuzzy power control system based on LDPC coding.

As shown in Fig. 8, the damages can occur due to the high values of *di*

**−15**

**−1 −0.5 0 0.5 1 x 10<sup>5</sup>**

**−10**

**Active Power [W]**

**Reactive Power [VAR]**

waveforms.

**−5 x 10<sup>4</sup>**

circuits in rotor and/or stator of the generator through the power converter.

**Figure 7.** Step Response of Rotor Current*<sup>i</sup>*2*dq* using CC in a Flat Fading Channel.

The spikes presented in the responses of the system occur due to the errors in the wireless communication caused by the fading channel, even with the use of a very efficient error correction CC scheme. It can be observed that several of these spikes, presented in the recovered reference signals, are followed by the controller.

**Figure 8.** Stator and Rotor Currents using CC in a Flat Fading Channel.

These errors in the control system can permanently damage the aerogenerator or even cause a loss of system efficiency, since the machine will not generate its maximum power track at that moment. Additionally, they generate undesirable harmonic components to the power grid. As shown in Fig. 8, the damages can occur due to the high values of *di dt* that can completely deteriorate the Insulated Gate Bipolar Transistors (IGBTs) and, consequently, cause short circuits in rotor and/or stator of the generator through the power converter.

18 Search Algorithms

**−200**

**0**

**0**

**−400 −200 0 200 400**

**500**

**−500**

**Figure 8.** Stator and Rotor Currents using CC in a Flat Fading Channel.

**0**

**Rotor current [A]**

**Stator current [A]**

**Figure 7.** Step Response of Rotor Current*<sup>i</sup>*2*dq* using CC in a Flat Fading Channel.

recovered reference signals, are followed by the controller.

**100**

**Rotor Current − i2q [A]** 

**200**

**200**

**Rotor Current − i2d [A]**

**5 5.2 5.4 5.6 5.8 6**

**i 2q i 2qref**

**i 2d i 2dref**

**5 5.2 5.4 5.6 5.8 6**

**Time [s]**

The spikes presented in the responses of the system occur due to the errors in the wireless communication caused by the fading channel, even with the use of a very efficient error correction CC scheme. It can be observed that several of these spikes, presented in the

**5 5.2 5.4 5.6 5.8 6**

**5 5.2 5.4 5.6 5.8 6**

**Time [s]**

**Figure 9.** Step Response of Active and Reactive Power using LDPC in a Flat Fading Channel.

In this way, it turns out the necessity of employing a wireless coded control system capable of minimizing the occurrence of these spikes arising from errors caused by the channel distortions. With this finality, it is highlighted the proposal of using a more robust wireless neuro-fuzzy power control system based on LDPC coding.

In Fig. 9 and 10, the step response of the active and reactive power and of the rotor currents of the wireless controller using the LDPC scheme are presented, respectively, considering an *Eb*/*N*<sup>0</sup> of 10 dB. The satisfactory performance of the wireless control system can be seen due to the fact the references were perfectly followed by the controller and the inexistence of destructive spikes caused by errors in the wireless transmission system. Additionally, these good functionalities are shown in Fig. 11, where the stator currents present expected waveforms.

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No Coding CC LDPC

LDPC is significantly superior than CC for flat fading channels. As pointed out in Fig. 12, for a BER of 10<sup>−</sup>5, the performance improvement of LDPC over CC is approximately 26.8 dB and more than 30 dB over no coding. Table 1 shows a resume of the results presented in

An Adaptive Neuro-Fuzzy Strategy for a Wireless Coded Power Control in Doubly-Fed Induction Aerogenerators

0 5 10 15 20 25 30 35

It can be seen that LDPC requires a significant lower *Eb*/*N*<sup>0</sup> to present the same order of performance of CC. It can be noted that, even for a low BER as 10<sup>−</sup>5, it can occur some changes in the active and reactive power references that can cause serious problems in the generator, and consequentially, in the energy plant. However, the use of LDPC can reduce notably this number for a typical *Eb*/*N*<sup>0</sup> value and can improve considerably the system robustness to the channel impairments. For instance, a system operating with a typical *Eb*/*N*<sup>0</sup> of 10 dB employing CC will fail dramatically, while a system using LDPC coding will

> **Coding Scheme Bit Error Rate Eb/No (dB)** CC 10−<sup>3</sup> 20.0 CC 10−<sup>4</sup> 25.5 CC 10−<sup>5</sup> 31.5 LDPC 10−<sup>3</sup> 3.20 LDPC 10−<sup>4</sup> 3.80 LDPC 10−<sup>5</sup> 4.70

**Figure 12.** Performance Comparison for Different Coding Schemes in a Flat Fading Channel.

Fig. 12.

10−7

**Table 1.** Performance Comparison for Both Coding Schemes.

be free of errors.

10−6

10−5

10−4

10−3

10−2

10−1

100

**Figure 10.** Step Response of Rotor Current*<sup>i</sup>*2*dq* using LDPC in a Flat Fading Channel.

**Figure 11.** Stator and Rotor Currents using LDPC in a Flat Fading Channel.

To complete the analysis, it is presented in Fig. 12, a comparison of the BER performance for different values of *Eb*/*N*<sup>0</sup> for the proposed wireless coded neuro-fuzzy power control system using three different schemes: No Coding, CC, and LDPC. As expected, the performance of LDPC is significantly superior than CC for flat fading channels. As pointed out in Fig. 12, for a BER of 10<sup>−</sup>5, the performance improvement of LDPC over CC is approximately 26.8 dB and more than 30 dB over no coding. Table 1 shows a resume of the results presented in Fig. 12.

20 Search Algorithms

**50**

**−400 −200 0 200 400**

**−400 −200 0 200 400**

**Figure 11.** Stator and Rotor Currents using LDPC in a Flat Fading Channel.

**Stator Current [A]**

**Rotor Current [A]**

**Figure 10.** Step Response of Rotor Current*<sup>i</sup>*2*dq* using LDPC in a Flat Fading Channel.

**100**

**150**

**Rotor Current − i2q [A]**

**Rotor Current − i2d [A]**

**200**

**5 5.2 5.4 5.6 5.8 6**

**5 5.2 5.4 5.6 5.8 6**

**i 2dref i 2d**

**i 2qref i 2q**

**Time [s]**

**5 5.2 5.4 5.6 5.8 6**

**5 5.2 5.4 5.6 5.8 6**

**Time [s]**

To complete the analysis, it is presented in Fig. 12, a comparison of the BER performance for different values of *Eb*/*N*<sup>0</sup> for the proposed wireless coded neuro-fuzzy power control system using three different schemes: No Coding, CC, and LDPC. As expected, the performance of

**Figure 12.** Performance Comparison for Different Coding Schemes in a Flat Fading Channel.

It can be seen that LDPC requires a significant lower *Eb*/*N*<sup>0</sup> to present the same order of performance of CC. It can be noted that, even for a low BER as 10<sup>−</sup>5, it can occur some changes in the active and reactive power references that can cause serious problems in the generator, and consequentially, in the energy plant. However, the use of LDPC can reduce notably this number for a typical *Eb*/*N*<sup>0</sup> value and can improve considerably the system robustness to the channel impairments. For instance, a system operating with a typical *Eb*/*N*<sup>0</sup> of 10 dB employing CC will fail dramatically, while a system using LDPC coding will be free of errors.


**Table 1.** Performance Comparison for Both Coding Schemes.

## **7. Conclusion**

In this chapter, it was introduced a new wireless coded control system based on an adaptive neuro-fuzzy inference system applied to a doubly-fed induction aerogenerator. In order to improve the performance of the controller to the nonlinear characteristics of the wind system, the proposed adaptive neuro-fuzzy system uses a different design strategy based on the input and output data set collected from a DFIG with a deadbeat controller operating at different conditions and considering as input the rotor current error. The wireless communication system, employed to send the power reference signals to the DFIG controller, uses LDPC coding to reduce the transmission errors and the overall latency of the system by mitigating the necessity of retransmissions.

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The presented analysis showed that the adaptive neuro-fuzzy strategy is a powerful technique to precisely control the dynamic nonlinear behavior of aerogenerators and to guarantee stability and maximum energy generation in smart grids applications. Furthermore, it was concluded that the use of LDPC coding can significantly improve the robustness of the wireless power control system in severe noise and fading channel conditions, being essential to maintain the integrity of the aerogenerators and to reduce the overall system response.

## **Appendix**

Doubly-fed induction generator parameters [45]:

*R*<sup>1</sup> = 24.75 *m*Ω; *R*<sup>2</sup> = 13.3 *m*Ω; *LM* = 14.25 *mH*; *Ll*<sup>1</sup> = 284 *µH*; *Ll*<sup>2</sup> = 284 *µH*; *J* = 2.6 *Kg* · *m*2; *NP* = 2; *PN* = 149.2 *kVA* and *VN* = 575 *V*.

## **Acknowledgments**

This work was partially supported by Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP), Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) and Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES).

## **Author details**

I. R. S. Casella1,<sup>⋆</sup>, A. J. Sguarezi Filho 1, C. E. Capovilla 1, J. L. Azcue <sup>2</sup> and E. Ruppert <sup>2</sup>

<sup>⋆</sup> Address all correspondence to: ivan.casella@ufabc.edu.br; alfeu.sguarezi@ufabc.edu.br; carlos.capovilla@ufabc.edu.br; jl.azcue@gmail.com; ruppert@fee.unicamp.br

1 Centro de Engenharia, Modelagem e Ciências Sociais Aplicadas - CECS, Universidade Federal do ABC - UFABC, Brazil

2 Faculdade de Engenharia Elétrica e de Computação - FEEC, Universidade de Campinas - UNICAMP, Brazil

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22 Search Algorithms

**7. Conclusion**

the necessity of retransmissions.

the overall system response.

**Acknowledgments**

**Author details**

UNICAMP, Brazil

Doubly-fed induction generator parameters [45]:

*NP* = 2; *PN* = 149.2 *kVA* and *VN* = 575 *V*.

I. R. S. Casella1,<sup>⋆</sup>, A. J. Sguarezi Filho 1,

Federal do ABC - UFABC, Brazil

C. E. Capovilla 1, J. L. Azcue <sup>2</sup> and E. Ruppert <sup>2</sup>

**Appendix**

In this chapter, it was introduced a new wireless coded control system based on an adaptive neuro-fuzzy inference system applied to a doubly-fed induction aerogenerator. In order to improve the performance of the controller to the nonlinear characteristics of the wind system, the proposed adaptive neuro-fuzzy system uses a different design strategy based on the input and output data set collected from a DFIG with a deadbeat controller operating at different conditions and considering as input the rotor current error. The wireless communication system, employed to send the power reference signals to the DFIG controller, uses LDPC coding to reduce the transmission errors and the overall latency of the system by mitigating

The presented analysis showed that the adaptive neuro-fuzzy strategy is a powerful technique to precisely control the dynamic nonlinear behavior of aerogenerators and to guarantee stability and maximum energy generation in smart grids applications. Furthermore, it was concluded that the use of LDPC coding can significantly improve the robustness of the wireless power control system in severe noise and fading channel conditions, being essential to maintain the integrity of the aerogenerators and to reduce

*R*<sup>1</sup> = 24.75 *m*Ω; *R*<sup>2</sup> = 13.3 *m*Ω; *LM* = 14.25 *mH*; *Ll*<sup>1</sup> = 284 *µH*; *Ll*<sup>2</sup> = 284 *µH*; *J* = 2.6 *Kg* · *m*2;

This work was partially supported by Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP), Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

<sup>⋆</sup> Address all correspondence to: ivan.casella@ufabc.edu.br; alfeu.sguarezi@ufabc.edu.br;

1 Centro de Engenharia, Modelagem e Ciências Sociais Aplicadas - CECS, Universidade

2 Faculdade de Engenharia Elétrica e de Computação - FEEC, Universidade de Campinas -

and Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES).

carlos.capovilla@ufabc.edu.br; jl.azcue@gmail.com; ruppert@fee.unicamp.br


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**Chapter 8**

**Application of Harmony Search Algorithm in**

**1.1. On the use of harmony search algorithm in optimal placement of FACTS devices to**

With the increasing electric power demand, power systems can face to stressed conditions, the operation of power system becomes more complex, and power system will become less secure. Moreover, because of restructuring, the problem of power system security has become a matter of concern in deregulated power industry. Better utilization of available power system capacities by Flexible AC Transmission Systems (FACTS) devices has become a major concern

FACTS devices can control power transmission parameters such as series impedance, voltage, and phase angle by their fast control characteristics and continuous compensating capability. They can reduce flow of heavily loaded lines, resulting in low system losses, improved both transient and small signal stability of network, reduced cost of production, and fulfillment of contractual requirement by controlling the power flow in the network. They can enable lines to flow the power near its nominal rating and maintain its voltage at desired level and thus, enhance power system security in contingencies [1-6]. For a meshed network, an optimal allocation of FACTS devices allows to control its power flows and thus, to improve the system

The effect of FACTS devices on power system security, reliability and loadability has been studied according to proper control objectives [4-14]. Researchers have tried to find suitable location for FACTS devices to improve power system security and loadability [13-16]. The optimal allocation of these devices in deregulated power systems has been presented in

> © 2013 Baghaee et al.; licensee InTech. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2013 Baghaee et al.; licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

H. R. Baghaee, M. Mirsalim and G. B. Gharehpetian

Additional information is available at the end of the chapter

**Power Engineering**

http://dx.doi.org/10.5772/55509

**1. Introduction**

**improve power systems**

in power systems too.

loadability and security [1].
