**2.1 Standard Optimal Power Flow formulation**

34 Electrical Generation and Distribution Systems and Power Quality Disturbances

contributions in this area. (Chiang, 2005) presents an improved genetic algorithm for power economic dispatch of units with valve-point effects and multiple fuels. (Chien, 2008) present a novel string structure for solving the economic dispatch through genetic algorithm (GA). To accelerate the search process (Pothiya et al., 2008) proposed a multiple tabu search algorithm (MTS) to solve the dynamic economic dispatch (ED) problem with generator constraints, simulation results prove that this approach is able to reduce the computational time compared to the conventional approaches. (Gaing, 2003) present an efficient particle swarm optimization to solving the economic dispatch with consideration of practical generator constraints, the proposed algorithm applied with success to many standard networks. Based on experience and simulation results, these classes of methods do not always guarantee global best solutions. Differential evolution (DE) is one of the most prominent new generation EAs, proposed by Storn and Price (Storn et al., 1995), to exhibit consistent and reliable performance in nonlinear and multimodal environment (price et al., 2005) and proven effective for constrained optimization problems. The main advantages of DE are: simple to program, few control parameters, high convergence characteristics. In power system field DE has received great attention in solving economic power dispatch

The third category includes, a variety of combined methods based conventional (mathematical methods) and global optimization techniques like (GA-QP), artificial techniques with metaheuristic mehtods, like 'Fuzzy-GA', 'ANN-GA', 'Fuzzy-PSO'. Many modified DE have been proposed to enhance the optimal solution, (Coelho et al., 2009) present a hybrid method which combines the differential evolution (DE) and Evolutionary algorithms (EAs), with cultural algorithm (CA) to solve the economic dispatch problems associated with the valve-point effect. Very recently, a new optimization concept, based on Biogeography, has been proposed by Dan Simon (Simon, D., 2008), Biogeography describes how species migrate from one island to another, how new species arise, and how species

To overcome the drawbacks of the conventional methods related to the form of the cost function, and to reduce the computational time related to the large space search required by many methaheuristic methods, like GA, (Mahdad, B. et al., 2010) proposed an efficient decomposed GA for the solution of large-scale OPF with consideration of shunt FACTS devices under severe loading conditions, (Mahdad, B. et al., 2009) present a parallel PSO based decomposed network to solve the ED with consideration of practical generators

This chapter presents a hybrid controller model based wind source and dynamic shunt FACTS devices (STATCOM Controller) to improve the power system operation and control. Choosing the type of FACTS devices and deciding the installation location and control of multi shunt FACTS coordinated with multi wind source is a vital research area. A simple algorithm based differential evolution (DE) proposed to find the optimal reactive power exchanged between shunt FACTS devices and the network in the presence of multi wind source. The minimum fuel cost, system loadability and loss minimization are considered as a measure of power system quality. The proposed methodology is verified on many practical electrical network at normal and at critical situations (sever loading conditions, contingency). Simulation results show that the optimal coordination operating points of shunt FACTS (STATCOM) devices and wind source enhance the

(EPD) problems with consideration of discontinuous fuel cost functions.

become extinct.

constraints.

power system security.

The OPF problem is considered as a general minimization problem with constraints, and can be written in the following form:

$$\text{Min } f(\mathbf{x}, \boldsymbol{\mu}) \tag{1}$$

$$\text{Subject to: } \mathcal{g}(\mathbf{x}, \boldsymbol{\mu}) = \mathbf{0} \tag{2}$$

$$h(\mathbf{x}, \mu) \le 0 \tag{3}$$

$$
\mathfrak{X}\_{\text{min}} \le \mathfrak{X} \le \mathfrak{X}\_{\text{max}} \tag{4}
$$

$$
\mu\_{\min} \le \mu \le \mu\_{\max} \tag{5}
$$

Where; *f* (,) *x u* is the objective function, *gxu* (,) and *hxu* (,) are respectively the set of equality and inequality constraints. The vector of state and control variables are denoted by x and u respectively.

Fig. 3. Optimal power flow (OPF) strategy

In general, the state vector includes bus voltage angles δ , load bus voltage magnitudes*VL* , slack bus real power generation *Pg*, *slack* and generator reactive power *Qg* . Fig. 3 shows the optimal power flow strategy. The problem of optimal power flow can be decomposed in two coordinated sub problemes:

#### **a. Active Power Planning**

The main role of economic dispatch is to minimize the total generation cost of the power system but still satisfying specified constraints (generators constraints and security constraints).

$$\sum\_{i=1}^{N\_{\text{fl}}} P\_{\text{S}} = P\_{\text{D}} + P\_{\text{loss}} \tag{6}$$

Optimal Location and Control of

limits.

• Upper transmission line loadings.

follows (Mahdad et al, 2010):

at specified buses and lines.

*0.9 pu* 

*-0.5pu 0.95 pu* 

adjust dynamically the voltage at specified buses.

dynamically the transit power at specified lines.

Fig. 4. Vector control structure based DE for reactive power planning

Multi Hybrid Model Based Wind-Shunt FACTS to Enhance Power Quality 37

• Parameters of shunt FACTS Controllers must be restricted within their upper and lower

• Upper and lower limits on voltage magnitude at loading buses (PQ buses)

1 11 ,..., , ,..., , ,..., *NPV Nt Nsvc V V n nQ Q g g t t svc svc* ⎡ ⎤ ⎣ ⎦

Fig. 5 shows the strategy of FACTS controllers integrated in power system to improve the power quality. In general these FACTS devices are classified in three large categories as

1. Shunts FACTS Controllers (SVC, STATCOM): Principally designed and integrated to

0 *des V V*− =*i* (17)

2. Series FACTS Controllers (TCSC, SSSC): Principally designed and integrated to adjust

 (18) 3. Hybrid FACTS Controllers (UPFC): Principally designed and integrated to adjust dynamically and simultaneously the voltage, the active power, and the reactive power

*des*

*V V P P Q Q*

 − = − = − =

*des ij ij des ij ij* 0 0 0

*i*

max , 1,2, , *S S i NPQ li li* ≤ = (14)

min max , 1,2, , *V V V i NPQ Li Li Li* ≤≤ = (15)

min max *XX X* ≤ ≤ *FACTS* (16)

*1.1pu 1.1pu 0.5pu* 

*Length of Vector Control* 

(19)

For optimal active power dispatch, the simple objective function *f* is the total generation cost expressed as follows:

*i*

$$\text{Min } f = \sum\_{i=1}^{N\_\xi} \left( a\_i + b\_i P\_{g^i} + c\_i P\_{g^i}^2 \right) \tag{7}$$

where *Ng* is the number of thermal units, *Pgi* is the active power generation at unit *i* and *<sup>i</sup> a* , *<sup>i</sup> b* and *<sup>i</sup> c* are the cost coefficients of the *th i* generator.

In the power balance criterion, the equality constraint related to the active power balance with consideration of wind power should be satisfied expressed as follow:

$$\sum\_{i=1}^{N\_R^c} P\_{g^i} + \sum\_{i=1}^{N \wedge V} P\_{wi} - P\_D - P\_{loss} = 0 \tag{8}$$

Where; *Ng* represents the total number of generators, *NW* the number of wind source integrated into the system, *Pwi* represents the active power of wind units, *PD* is the total active power demand, *Ploss* represent the transmission losses.

The inequality constraints to be satisfied for this stage are given as follows:

• Upper and lower limits on the active power generations:

$$P\_{g^i}^{\text{min}} \le P\_{g^i} \le P\_{g^i}^{\text{max}} \tag{9}$$

• Wind power availability: the total wind power generated, is limited by the available amount from the wind park *av Pw* ,

$$P\_{loss} + P\_D - \sum\_{i=1}^{N\_S} P\_{g^i} \le P\_w^{av} \tag{10}$$

#### **b. Reactive Power Planning**

The main role of reactive power planning is to adjust dynamically the control variables to minimize the total power loss, transit power, voltages profiles, and voltage stability, individually or simultaneously, but still satisfying specified constraints (generators constraints and security constraints). Fig. 4 shows the structure of the control variable to be optimized using DE.

• Upper and lower limits on the reactive power generations:

$$Q\_{\mathcal{Y}^i}^{\text{min}} \le Q\_{\mathcal{Y}^i} \le Q\_{\mathcal{Y}^i}^{\text{max}} \text{ , i = 1, 2, \dots, NPV} \tag{11}$$

• Upper and lower limits on the generator bus voltage magnitude:

$$V\_{g^{\rm i}}^{\rm min} \le V\_{g^{\rm i}} \le V\_{g^{\rm i}}^{\rm max}, \text{ i } = 1, 2, \dots, NPV \tag{12}$$

• Upper and lower limits on the transformer tap ratio (t).

$$t\_i^{\text{min}} \le t\_i \le t\_i^{\text{max}}, i = 1, 2, \dots, NT \tag{13}$$

• Upper transmission line loadings.

36 Electrical Generation and Distribution Systems and Power Quality Disturbances

*Pg P P*

For optimal active power dispatch, the simple objective function *f* is the total generation

*f a bP cP*

where *Ng* is the number of thermal units, *Pgi* is the active power generation at unit *i* and *<sup>i</sup> a* ,

*i* generator. In the power balance criterion, the equality constraint related to the active power balance

*gi wi D loss*

Where; *Ng* represents the total number of generators, *NW* the number of wind source integrated into the system, *Pwi* represents the active power of wind units, *PD* is the total

• Wind power availability: the total wind power generated, is limited by the available

1

*av*

*Ng*

*loss D gi w i P P PP* =

The main role of reactive power planning is to adjust dynamically the control variables to minimize the total power loss, transit power, voltages profiles, and voltage stability, individually or simultaneously, but still satisfying specified constraints (generators constraints and security constraints). Fig. 4 shows the structure of the control variable to be

*P P PP*

1

*i*

with consideration of wind power should be satisfied expressed as follow:

1 1

*i i*

= =

The inequality constraints to be satisfied for this stage are given as follows:

*Ng NW*

=

*Ng*

*i D loss*

*i i gi i gi*

0

+ −− = (8)

min max *P PP gi gi gi* ≤ ≤ (9)

+− ≤ (10)

min max , 1,2, , *Q Q Q i NPV gi gi gi* ≤≤ = (11)

min max , 1,2, , *V V V i NPV gi gi gi* ≤≤ = (12)

min max, 1,2,..., *i ii t t t i NT* ≤≤ = (13)

= + (6)

= ++ (7)

1

*i*

 *Min* ( ) <sup>2</sup>

active power demand, *Ploss* represent the transmission losses.

• Upper and lower limits on the active power generations:

• Upper and lower limits on the reactive power generations:

• Upper and lower limits on the transformer tap ratio (t).

• Upper and lower limits on the generator bus voltage magnitude:

cost expressed as follows:

*<sup>i</sup> b* and *<sup>i</sup> c* are the cost coefficients of the *th*

amount from the wind park *av Pw* ,

**b. Reactive Power Planning** 

optimized using DE.

=

*Ng*

$$S\_{\rm il} \le S\_{\rm il}^{\rm max}, \text{ i } = 1, 2, \dots, NPQ \tag{14}$$

• Upper and lower limits on voltage magnitude at loading buses (PQ buses)

$$V\_{\rm Li}^{\rm min} \le V\_{\rm Li} \le V\_{\rm Li}^{\rm max}, \text{ i } = 1, 2, \dots, NPQ \tag{15}$$

• Parameters of shunt FACTS Controllers must be restricted within their upper and lower limits.

$$X^{\text{min}} \le X\_{\text{FACTS}} \le X^{\text{max}} \tag{16}$$

Fig. 4. Vector control structure based DE for reactive power planning

Fig. 5 shows the strategy of FACTS controllers integrated in power system to improve the power quality. In general these FACTS devices are classified in three large categories as follows (Mahdad et al, 2010):

1. Shunts FACTS Controllers (SVC, STATCOM): Principally designed and integrated to adjust dynamically the voltage at specified buses.

$$V^{\rm abs} - V\_l = \mathbf{0} \tag{17}$$

2. Series FACTS Controllers (TCSC, SSSC): Principally designed and integrated to adjust dynamically the transit power at specified lines.

(18)

3. Hybrid FACTS Controllers (UPFC): Principally designed and integrated to adjust dynamically and simultaneously the voltage, the active power, and the reactive power at specified buses and lines.

$$\begin{cases} V^{des} - V\_i = 0\\ P\_{ij}^{des} - P\_{ij} = 0\\ Q\_{ij}^{des} - Q\_{ij} = 0 \end{cases} \tag{19}$$

Optimal Location and Control of

<sup>0</sup> <sup>20</sup> <sup>40</sup> <sup>60</sup> <sup>80</sup> <sup>100</sup> <sup>0</sup>

Time (s)

power flow algorithm

using the following equations:

: is the air density,

*VD* : Critical wind speed *VA* : Wind stopping speed

*V* : Wind speed

 : tip speed ratio *Rt* : is the blade length

*S* : the surface swept by the turbine

*Qt* : is the angular velocity of the turbine

references (Bent, S., 2004), (Chen et al. 2008).

**3.1 Wind energy** 

Where; ρ

λ

Wind Power

Multi Hybrid Model Based Wind-Shunt FACTS to Enhance Power Quality 39

*P*

Fig. 6. The proposed combined model based wind/STATCOM Compensators integrated in

The principle of wind energy transformation based aerodynamic power can be formulated

( ) <sup>3</sup>

≤ < <sup>=</sup>

 λβ

*SV C V V V <sup>P</sup>*

<

*N N A*

. *Q Rt t*

ν<sup>=</sup> ;

Detailed descriptions about various types of aero-generators are well presented in many

λ

*P V V V*

≤ < <sup>≥</sup>

<sup>1</sup> ... . ,

0

2

ρ

*w*

0

+P

*i* 

*Vr*

*Wind* +Q -Q

min Bmin

*D*

*V V*

*V V*

*A*

*p DN*

*P*max

ijij P + jQ *j* 

Bmax

(20)

*k* 

Fig. 5. Basic strategy of FACTS technology integrated in power system

In this study we are interested in the integration of hybrid model based shunt FACTS controller (STATCOM) and wind energy to enhance the indices of power quality at normal and at critical situations.

#### **3. Hybrid model based wind energy and shunt FACTSController**

The proposed approach requires the user to define the number of wind units to be installed, in this study voltage stability used as an index to choose the candidate buses. The differential evolution (DE) algorithm generates and optimizes combination of wind sources sizes. Minimum cost, and power losses, used as fitness functions. Wind units modelling depend on the constructive technology and their combined active and reactive power control scheme.

In this study wind has been considered as not having the capability to control voltages. Dynamic shunt compensators (STATCOM) modelled as a PV node used in coordination with wind to control the voltage by a flexible adjustment of reactive power exchanged with the network (Mahdad.b et al., 2011). Fig. 6 shows the proposed combined model based wind source and STATCOM Controller.

Fig. 6. The proposed combined model based wind/STATCOM Compensators integrated in power flow algorithm

#### **3.1 Wind energy**

38 Electrical Generation and Distribution Systems and Power Quality Disturbances

ij <sup>−</sup><sup>P</sup>

max

In this study we are interested in the integration of hybrid model based shunt FACTS controller (STATCOM) and wind energy to enhance the indices of power quality at normal

The proposed approach requires the user to define the number of wind units to be installed, in this study voltage stability used as an index to choose the candidate buses. The differential evolution (DE) algorithm generates and optimizes combination of wind sources sizes. Minimum cost, and power losses, used as fitness functions. Wind units modelling depend on the constructive technology and their combined active and reactive power

In this study wind has been considered as not having the capability to control voltages. Dynamic shunt compensators (STATCOM) modelled as a PV node used in coordination with wind to control the voltage by a flexible adjustment of reactive power exchanged with the network (Mahdad.b et al., 2011). Fig. 6 shows the proposed combined model based wind

*Flexible Control: Voltage, Active Power and Reactive Power*

*ij <sup>t</sup>* max <sup>≤</sup> *PP ijij*

⊕Q

*B*max

*B*min

*B*max

i j *Pij*

*Qij Qi*

Load

**G1** 

and at critical situations.

control scheme.

source and STATCOM Controller.

MinPgi, Qgi min

Max Pgi, Qgi

<sup>i</sup> ⊕P

−Q

*ij t*

Fig. 5. Basic strategy of FACTS technology integrated in power system

**3. Hybrid model based wind energy and shunt FACTSController** 

The principle of wind energy transformation based aerodynamic power can be formulated using the following equations:

$$P\_w = \begin{cases} 0 & V < V\_D \\ \frac{1}{2} \cdot \mathcal{P}.S.V.^3.\mathcal{C}\_p\left(\mathcal{A}, \mathcal{B}\right) & V\_D \le V < V\_N \\ P\_N & V\_N \le V < V\_A \\ 0 & V \ge V\_A \end{cases} \tag{20}$$

Where;


$$\mathcal{A} = \frac{Q\_r.\mathcal{R}\_r}{\nu};$$


Detailed descriptions about various types of aero-generators are well presented in many references (Bent, S., 2004), (Chen et al. 2008).

Optimal Location and Control of

Fig. 9. STATCOM equivalent circuit

formulated as follows:

Where,

follows:

as follows:

**3.2.2 STATCOM modelling based power flow** 

reactive power (absorbed or generated) with the network.

~

*Y G jB ss s* = + ; is the equivalent admittance of the STATCOM;

)(*Ys <sup>V</sup>* <sup>∠</sup>θ*ss*

Multi Hybrid Model Based Wind-Shunt FACTS to Enhance Power Quality 41

In the literature many STATCOM models have been developed and integrated within the load flow program based modified Newton-Raphson, the model proposed by (Acha, et al, 2004), is one of the based and efficient models largely used by researchers. Fig. 9 shows the equivalent circuit of STATCOM, the STATCOM has the ability to exchange dynamically

Based on the simplified equivalent circuit presented in Fig. 9, the following equation can be

The active and reactive power exchanged with the network at a specified bus expressed as

{ () ()} <sup>2</sup> *P V G VV G s s s sk s s k s s k* = − cos

θθ

{ () ()} <sup>2</sup>

θθ

*Q V B VV G s s s sk s s k s s k* =− − sin

The modified power flow equations with consideration of STATCOM at bus k are expressed

. . cos

. . sin

*k s ki k i k i ki*

Differential Evolution (DE) is a new branch of EA proposed by (Storn and Price, 1995). DE has proven to be promising candidate to solve real and practical optimization problem. The strategy of DE is based on stochastic searches, in which function parameters are encoded as floating point variables. The key idea behind differential evolution approach is a new mechanism introduced for generating trial parameter vectors. In each step DE mutates

*k s ki k i k i ki*

After performing complex transformations; the following equations are deduced:

1

*N*

1

*i Q Q Y VV*

**4. Overview of Differential Evolution technique** 

=

*i P P Y VV*

=

*N*

*Bus K* 

*I YV V s ss k* = − .( ) ; (21)

( ) \* \*\* \* . .. *S VI VY V V s ss s s s k* == − ; (22)

 θθ

> θθ

( )

( )

= + − − (25)

= + − − (26)

θ θθ

θ θθ

−+ − *B* sin (23)

−− − *B* sin (24)

*V* ∠θ*kk*

*s I*
