**2. Wind-diesel power system with hydrogen storage**

The structures of Hybrid Power System (HPS) can be classified into two categories: AC cou‐ pled and DC-coupled (T. Zhou, 2009).

In an AC-coupled HPS, all sources are connected to a main AC-bus before being connected to the grid. In AC-coupled structure, different sources can be located anywhere in the micro‐ grid with a long distance from each other. However, the voltage and the frequency of the main AC bus should be well controlled in order to ensure the stability of the system and the compatibility with the utility network.

In a DC-coupled HPS, all sources are connected to a main DC-bus before being connected to the grid through a main inverter. In a DC-coupled structure, the voltage and the frequency of the grid are independent from those of each source.

However, not all HPSs can be classified into AC or DC-coupled system, since it is possible to have both coupling methods, then a Mixed HPS is obtained. In this case, some advantages can be taken from both structures.

The wind-diesel HPS configuration studied in this work is represented in Fig. 1.

### **2.1. Wind turbine**

native in areas with appropriate wind speeds. Since 2000, cumulative installed capacity has grown at an average rate of around 30% per year. In 2008, more than 27 GW of capacity were installed in more than 50 countries, bringing global capacity onshore and offshore to 121 GW. Wind energy in 2008 was estimated by the Global Wind Energy Council to have generated some 260 million megawatt hours of electricity. Applications for generation of electricity are divided into the following categories: utility-scale wind farms and small wind

Currently, for remote communities and rural industry the standard is diesel generators. Re‐ mote electric power is estimated at over 11 GW, with 150,000 diesel gensets, ranging in size from 5 to 1,000 kW. In Canada, there are more than 800 diesel gensets, with a combined in‐ stalled rating of over 500 MW in more than 300 remote communities (Vaughn Nelson, 2009). Diesel generators are inexpensive to install; however, they are expensive to operate and maintain, and major maintenance is needed from every 2,000 to 20,000 hours, depending on

Wind–diesel is considered because of the high costs for generating power in isolated sys‐ tems. In near future, the market of wind–diesel systems will grow up because of the high cost of diesel fuel. Wind–diesel power systems can vary from simple designs in which wind turbines are connected directly to the diesel grid, with a minimum of additional features, to

There are a number of problems in integrating a wind turbine to an existing diesel genset: voltage and frequency control, frequent stop–starts of the diesel, utilization of surplus ener‐ gy, and the use and operation of a new technology. These problems vary by the amount of penetration. Wind turbines at low penetration can be added to existing diesel power with‐ out many problems, as it is primarily a fuel saver. However, for high wind penetration, stor‐ age is needed. Moreover, one of the major drawbacks of wind energy is its unpredictability and intermittency. So, to supply better consumers' energy needs, wind systems have to op‐ erate with storage devices. Several energy storage methods have been in development over the past several years. This includes compressed air, pumped hydro, flow battery flywheel, hydrogen storage, etc. It has been proved (E.I. Zoulias, N. Lymberopoulos, 2008; Nelson et al., 2006) that hydrogen can be effectively used as storage medium for intermittent renewa‐ ble energy sources (RES)-based autonomous power systems. More specifically, excess of RES energy produced from such systems at periods of low demand can be stored in the form of hydrogen, which will be used upon demand during periods when the wind energy

For many years, Hydrogen Research Institute (HRI) has developed a renewable photovolta‐ ic/wind energy system based on hydrogen storage(M. L. Doumbiaet al., 2009; K. Agbossou et al., 2004). The system consists of a 10 kW wind turbine generator (WTG) and a 1 kW solar photovoltaic (PV) array as primary energy sources, a battery bank, an 5 kW electrolyzer, a 5 kW fuel cell stack, different power electronics interfaces for control and voltage adaptation purposes, a measurement and monitoring system. This renewable energy system is scaled for residential applications size and can be operated in stand-alone or grid-connected mode

turbines (less than 100 kW).

366 New Developments in Renewable Energy

the size of the diesel genset.

more complex systems.

is not available.

and different control strategies can be developed.

Wind turbines come in different sizes and types, depending on power generating capaci‐ ty and the rotor design deployed. Small wind turbines with output capacities below 10 kW are used primarily for residences, telecommunications dishes, and irrigation water pumping applications. Utility-scale wind turbines have high power ratings ranging from 100 kW to 5 MW. Current wind farms with large capacity wind turbine installations are capable of generating electricity in excess of 500M MW for utility companies (Vaughn Nelson, 2009).

*r w R v*

The maximum power coefficient *Cp* is determined by Betz as follows (S. Heier, 1998):

max <sup>16</sup> ( , ) 0.593 <sup>27</sup>

Hence, even if power extraction without any losses were possible, only 59% of the wind

In our study, the mathematical representation of the power coefficient used for a wind tur‐

( 3) 0.398.sin 0.00394( 2) 15 0.3

b

In the aim to extract the maximum active power, the speed of the wind turbine must be adjusted to achieve the optimal value of the tip speed ratio. The block diagram of Fig. 3 shows the Maxi‐ mum Power Point Tracking (MPPT) technique applied to the generator to produce maximum

l

æ ö - = -- ç ÷ è ø - (4)

 b

p l

<sup>W</sup><sup>=</sup> (2)

Wind Diesel Hybrid Power System with Hydrogen Storage

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369

= » (3)

l

*Ωr* represents the rotational speed of the wind turbine in *rad/sec*.

*Cp*

The power coefficient versus the ratio speed as shown in Fig. 2.

power could be utilized by a wind turbine.

**Figure 2.** Coefficient of power versus ratio of speed

*Cp*

bine is given by:

l b

Modern wind turbines are classified into two configurations: horizontal-axis wind turbines (HAWTs) and vertical-axis wind turbines (VAWTs), depending on rotor operating princi‐ ples. The VAWT configuration employs the Darrieus model named for the famous French inventor.

**Figure 1.** Wind-diesel Hybrid Power System with hydrogen production

HAWTs with two or three blades are the most common. Wind blowing over the propeller blades causes the blades to "lift" and rotate at low speeds. Wind turbines using three blades are operated "upwind" with rotor blades facing into the wind. The tapering of rotor blades is selected to maximize the kinetic energy from the wind. Optimum wind turbine perform‐ ance is strictly dependent on blade taper angle and the installation height of the turbine on the tower (Vaughn Nelson, 2009).

According to Albert Betz, the mechanical power *Pm* captured by the turbine from the wind for a given wind speed *vw* is computed by the following expression (I. Munteanu et al., 2008; N.M. Miller et al., 2008).

$$P\_m = \frac{1}{2} \rho A \mathcal{C}\_p(\mathcal{X}, \mathcal{Y}) v\_w^3 \tag{1}$$

*ρ*is the air density in *kg/m3 ; A=πR<sup>2</sup>* is the area in *m2* swept by the blade; *R*is the radius of the blade in *m*.

The aerodynamic model of a wind turbine can be determined by the Cp(λ,β) curves. *Cp* is the power coefficient, which is function of both tip speed ratio λ and the blade pitch angle β. The tip speed ratio is given by:

Wind Diesel Hybrid Power System with Hydrogen Storage http://dx.doi.org/10.5772/52341 369

$$
\lambda = \frac{\Omega\_r R}{v\_w} \tag{2}
$$

*Ωr* represents the rotational speed of the wind turbine in *rad/sec*.

capable of generating electricity in excess of 500M MW for utility companies (Vaughn

Modern wind turbines are classified into two configurations: horizontal-axis wind turbines (HAWTs) and vertical-axis wind turbines (VAWTs), depending on rotor operating princi‐ ples. The VAWT configuration employs the Darrieus model named for the famous French

HAWTs with two or three blades are the most common. Wind blowing over the propeller blades causes the blades to "lift" and rotate at low speeds. Wind turbines using three blades are operated "upwind" with rotor blades facing into the wind. The tapering of rotor blades is selected to maximize the kinetic energy from the wind. Optimum wind turbine perform‐ ance is strictly dependent on blade taper angle and the installation height of the turbine on

According to Albert Betz, the mechanical power *Pm* captured by the turbine from the wind for a given wind speed *vw* is computed by the following expression (I. Munteanu et al., 2008;

> <sup>1</sup> <sup>3</sup> (,) <sup>2</sup> *m pw P AC v* <sup>=</sup> r

is the area in *m2*

 lb

The aerodynamic model of a wind turbine can be determined by the Cp(λ,β) curves. *Cp* is the power coefficient, which is function of both tip speed ratio λ and the blade pitch angle β.

(1)

swept by the blade; *R*is the radius of the

**Figure 1.** Wind-diesel Hybrid Power System with hydrogen production

*; A=πR<sup>2</sup>*

the tower (Vaughn Nelson, 2009).

N.M. Miller et al., 2008).

*ρ*is the air density in *kg/m3*

The tip speed ratio is given by:

blade in *m*.

Nelson, 2009).

368 New Developments in Renewable Energy

inventor.

The maximum power coefficient *Cp* is determined by Betz as follows (S. Heier, 1998):

$$\mathbf{C}\_p^{\text{max}}(\mathbb{A}, \boldsymbol{\beta}) = \frac{16}{27} \approx 0.593\tag{3}$$

Hence, even if power extraction without any losses were possible, only 59% of the wind power could be utilized by a wind turbine.

The power coefficient versus the ratio speed as shown in Fig. 2.

**Figure 2.** Coefficient of power versus ratio of speed

In our study, the mathematical representation of the power coefficient used for a wind tur‐ bine is given by:

$$C\_p = 0.398. \sin\left(\frac{\pi(\lambda - 3)}{15 - 0.3\beta}\right) - 0.00394(\lambda - 2)\beta\tag{4}$$

In the aim to extract the maximum active power, the speed of the wind turbine must be adjusted to achieve the optimal value of the tip speed ratio. The block diagram of Fig. 3 shows the Maxi‐ mum Power Point Tracking (MPPT) technique applied to the generator to produce maximum power. If the wind speed is below the rated value, the WTG operates in the variable speed mode, and *Cp* is keep at its maximum value. In this operating mode, the pitch control is deactivated. When the wind speed is above the rated value, the pitch control is activated, in the aim to reduce the generated mechanical power (W. Qiao, W. Zhou et al., 2008).

condition of the drive, power is fed into or out of the rotor: in an oversynchronous mode, it flows from the rotor via the converter to the grid, whereas it flows in the opposite direction in a sub‐ synchronous mode. In both cases – subsynchronous and oversynchronous – the stator feeds en‐

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371

The stator and rotor voltages of the DFIG are given by the following expression (Y. Ren, H.

*ds ds s ds s qs*

w l

w l

w l (5)

(6)

w l

*dt d*

l

l

*dt*

*<sup>d</sup> v ri*

ï =+ -

<sup>ï</sup> =+ + <sup>ï</sup>

<sup>ï</sup> =+ - <sup>ï</sup>

<sup>ï</sup> =+ + ïî

*<sup>d</sup> v ri*

*v ri*

ì

ï ï

í

ï

*v ri*

l

l

l

í

l

*L <sup>m</sup>* is the mutual inductance between the stator and the rotor windings.

The electromagnetic torque of the DFIG can be expressed as follow:

*qs qs s qs s ds*

*dr dr r dr r qr*

*dt d*

l

l

*dt*

*qr qr r qr r dr*

*rs* and *rr* are respectively the resistance of the stator and rotor windings, and *ωs* is the rota‐

*ds s ds m dr qs s qs m qr dr r dr m ds qr r qr m qs*

<sup>ì</sup> = + <sup>ï</sup> = + ï

= + ï <sup>ï</sup> = + <sup>î</sup>

*Li L i Li L i Li L i Li L i*

*L <sup>s</sup>*and*L <sup>r</sup>*represent respectively the self-inductance of the stator and the rotor windings, and

ergy into the grid (T. Ackermann, 2005).

**Figure 4.** Structure of the DFIG based wind system

Li and J. Zhou, 2009; R. G. De Almeida et al., 2004).

tional speed of the synchronous reference frame.

**Figure 3.** Block diagram of the control of the velocity of the DFIG with MPPT

### **2.2. Doubly-fed induction generator and its control**

### **a.** Doubly-Fed induction Generator

Today, the wind turbines on the market mix and match a variety of innovative concepts with proven technologies both for generators and for power electronics. Wind turbines can operate either with a fixed speed or a variable speed. Most commonly used types of wind turbines gen‐ erators are asynchronous (induction) and synchronous generators. Among these technologies, asynchronous Doubly Fed Induction Generator (DFIG) has received much attention as one of preferred technology for wind power generation (Fig.4). The DFIG consists of a Wound Rotor Induction Generator (WRIG) with the stator windings directly connected to the constant-fre‐ quency three-phase grid and with the rotor windings mounted to a bidirectional back-to-back IGBT voltage source converter.The converter compensates the difference between the mechani‐ cal and electrical frequency by injecting a rotor current with a variable frequency.The power converter consists of two converters, the rotor-side converter and grid-side converter, which are controlled independently of each other.The main idea is that the rotor-side converter controls the active and reactive power by controlling the rotor current components, while the line-side converter controls the DC-link voltage and ensures a converter operation at unity power factor (i.e. zero reactive power). Compared to a full rated converter system, the use of DFIG in a wind turbine offers many advantages, such as reduction of inverter cost, the potential to control tor‐ que and a slight increase in efficiency of wind energy extraction. Depending on the operating condition of the drive, power is fed into or out of the rotor: in an oversynchronous mode, it flows from the rotor via the converter to the grid, whereas it flows in the opposite direction in a sub‐ synchronous mode. In both cases – subsynchronous and oversynchronous – the stator feeds en‐ ergy into the grid (T. Ackermann, 2005).

**Figure 4.** Structure of the DFIG based wind system

power. If the wind speed is below the rated value, the WTG operates in the variable speed mode, and *Cp* is keep at its maximum value. In this operating mode, the pitch control is deactivated. When the wind speed is above the rated value, the pitch control is activated, in the aim to reduce

Today, the wind turbines on the market mix and match a variety of innovative concepts with proven technologies both for generators and for power electronics. Wind turbines can operate either with a fixed speed or a variable speed. Most commonly used types of wind turbines gen‐ erators are asynchronous (induction) and synchronous generators. Among these technologies, asynchronous Doubly Fed Induction Generator (DFIG) has received much attention as one of preferred technology for wind power generation (Fig.4). The DFIG consists of a Wound Rotor Induction Generator (WRIG) with the stator windings directly connected to the constant-fre‐ quency three-phase grid and with the rotor windings mounted to a bidirectional back-to-back IGBT voltage source converter.The converter compensates the difference between the mechani‐ cal and electrical frequency by injecting a rotor current with a variable frequency.The power converter consists of two converters, the rotor-side converter and grid-side converter, which are controlled independently of each other.The main idea is that the rotor-side converter controls the active and reactive power by controlling the rotor current components, while the line-side converter controls the DC-link voltage and ensures a converter operation at unity power factor (i.e. zero reactive power). Compared to a full rated converter system, the use of DFIG in a wind turbine offers many advantages, such as reduction of inverter cost, the potential to control tor‐ que and a slight increase in efficiency of wind energy extraction. Depending on the operating

the generated mechanical power (W. Qiao, W. Zhou et al., 2008).

370 New Developments in Renewable Energy

**Figure 3.** Block diagram of the control of the velocity of the DFIG with MPPT

**2.2. Doubly-fed induction generator and its control**

**a.** Doubly-Fed induction Generator

The stator and rotor voltages of the DFIG are given by the following expression (Y. Ren, H. Li and J. Zhou, 2009; R. G. De Almeida et al., 2004).

$$\begin{cases} \boldsymbol{\upsilon}\_{\rm ds} = \boldsymbol{r}\_{s}\dot{\mathbf{i}}\_{\rm ds} + \frac{d\boldsymbol{\lambda}\_{\rm ds}}{dt} - \boldsymbol{\alpha}\_{s}\boldsymbol{\lambda}\_{\rm qs} \\\\ \boldsymbol{\upsilon}\_{\rm qs} = \boldsymbol{r}\_{s}\dot{\mathbf{i}}\_{\rm qs} + \frac{d\boldsymbol{\lambda}\_{\rm qs}}{dt} + \boldsymbol{\alpha}\_{s}\boldsymbol{\lambda}\_{\rm ds} \\\\ \boldsymbol{\upsilon}\_{dr} = \boldsymbol{r}\_{r}\dot{\mathbf{i}}\_{dr} + \frac{d\boldsymbol{\lambda}\_{dr}}{dt} - \boldsymbol{\alpha}\_{r}\boldsymbol{\lambda}\_{\rm qr} \\\\ \boldsymbol{\upsilon}\_{qr} = \boldsymbol{r}\_{r}\dot{\mathbf{i}}\_{qr} + \frac{d\boldsymbol{\lambda}\_{qr}}{dt} + \boldsymbol{\alpha}\_{r}\boldsymbol{\lambda}\_{dr} \end{cases} \tag{5}$$

*rs* and *rr* are respectively the resistance of the stator and rotor windings, and *ωs* is the rota‐ tional speed of the synchronous reference frame.

$$\begin{cases} \dot{\mathcal{\lambda}}\_{ds} = L\_s \dot{\mathbf{i}}\_{ds} + L\_m \dot{\mathbf{i}}\_{dr} \\ \dot{\mathcal{\lambda}}\_{qs} = L\_s \dot{\mathbf{i}}\_{qs} + L\_m \dot{\mathbf{i}}\_{qr} \\ \dot{\mathcal{\lambda}}\_{dr} = L\_r \dot{\mathbf{i}}\_{dr} + L\_m \dot{\mathbf{i}}\_{ds} \\ \dot{\mathcal{\lambda}}\_{qr} = L\_r \dot{\mathbf{i}}\_{qr} + L\_m \dot{\mathbf{i}}\_{qs} \end{cases} \tag{6}$$

*L <sup>s</sup>*and*L <sup>r</sup>*represent respectively the self-inductance of the stator and the rotor windings, and *L <sup>m</sup>* is the mutual inductance between the stator and the rotor windings.

The electromagnetic torque of the DFIG can be expressed as follow:

$$T\_{em} = P(\mathcal{A}\_{ds}\mathbf{i}\_{qs} - \mathcal{A}\_{qs}\mathbf{i}\_{ds}) \tag{7}$$

2 2

*m dr m*

*L dt L*

w

*s s*

2 2

*m dr m*

*L dt L L L di v ri L L iL*

*s s*

w

*qr r qr r r r dr r m*

ï æöæö F = +- + - + ç÷ç÷ ï ïî èøèø

2 2

w

*ωr*and *ωs* are respectively rotor and stator parameters frequencies; *s*is the machine's slip.

*r s* w w= *s*

2 2

w

*m dr m*

*L dt L L L di v ri L s L i gL L dt <sup>L</sup> <sup>L</sup>*

*dr r dr r s r qr*

= +- + - + ç÷ ç÷ ï ïî èø èø

*L di <sup>L</sup> v ri L sL i*

<sup>ì</sup> æö æö <sup>ï</sup> = +- - - ç÷ ç÷ ïï èø èø <sup>í</sup>

From vector control conditions, the stator voltage can be expressed as:

Then, the final vector control equations of the rotor's voltage are:

2 2

w

*qr r qr r s r dr s m*

. *Vs ss* = F w

2 2

*m dr m*

*L dt L*

*s s*

w

*dr r dr r s r qr*

= +- + - + ç÷ ç÷ ï ïî èø èø

*L di <sup>L</sup> v ri L sL i*

<sup>ì</sup> æö æö <sup>ï</sup> = +- - - ç÷ ç÷ ïï èø èø <sup>í</sup> æö æö <sup>ï</sup>

*qr r qr r s r dr s*

*<sup>L</sup> di L LV v ri L sL is*

2 2

w

*m qr m m s*

*s s s s*

*L dt L L*

ï æö æö F

*m ms qr*

*s ss*

*s s*

*qr r qr r r r dr r m r dr*

*v ri L Li L i*

*dr r dr r r r qr r qr*

*dr r dr r r r qr*

*L di <sup>L</sup> v ri L L i*

<sup>ì</sup> æöæö <sup>ï</sup> = +- - - ç÷ç÷ ïï èøèø <sup>í</sup>

As

**2.** DFIG's Control

*L di <sup>L</sup> v ri L Li i*

ï æ ö F = +- + + - ç ÷ <sup>ï</sup> ç ÷ ïî è ø

<sup>ì</sup> æ ö <sup>ï</sup> = +- - - ç ÷ ç ÷ ïï è ø <sup>í</sup>

2 2

 w

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 w

> w

 w

w

(16)

(13)

373

(14)

(15)

(17)

 w

*m qr s m*

*L dt L L*

*L L di*

ww

*s s s*

*m ms qr*

*s ss*

*L dt L L*

*P* is the number of pole pairs.

To achieve independent control of the stator active power and stator reactive power, a vec‐ tor-control approach is used. *d-q* axis connected to the stator's rotating field is chosen and quadratic component of the stator flux is set to zero. The power control is performed through the back to back converter connected to the rotor. Then, the stator voltages can be given according the rotor currents as (D. Aouzellag et al. 2006).

The stator's flux and current equations are:

$$\begin{cases} \mathcal{J}\_{ds} = L\_s \dot{i}\_{ds} + L\_m \dot{i}\_{dr} = \Phi\_s\\ \mathcal{J}\_{qs} = L\_s \dot{i}\_{qs} + L\_m \dot{i}\_{qr} = 0 \end{cases} \tag{8}$$

$$\begin{cases} \dot{\mathbf{i}}\_{ds} = \frac{\Phi\_s}{L\_s} - \frac{L\_m}{L\_s} \dot{\mathbf{i}}\_{dr} \\ \dot{\mathbf{i}}\_{qs} = -\frac{L\_m}{L\_s} \dot{\mathbf{i}}\_{qr} \end{cases} \tag{9}$$

Fom equations (5) et (6), rotor's voltages can be rewritten as:

$$\begin{cases} \upsilon\_{dr} = r\_r \dot{i}\_{dr} + \frac{d\left(L\_r \dot{i}\_{dr} + L\_m \dot{i}\_{ds}\right)}{dt} - \alpha\_r \left(L\_r \dot{i}\_{qr} + L\_m \dot{i}\_{qs}\right) \\ \upsilon\_{qr} = r\_r \dot{i}\_{qr} + \frac{d\left(L\_r \dot{i}\_{qr} + L\_m \dot{i}\_{qs}\right)}{dt} + \alpha\_r \left(L\_r \dot{i}\_{dr} + L\_m \dot{i}\_{ds}\right) \end{cases} \tag{10}$$

$$\begin{cases} \boldsymbol{\upsilon}\_{dr} = \boldsymbol{r}\_{r}\mathbf{i}\_{dr} + \mathbf{L}\_{r}\frac{d\mathbf{i}\_{dr}}{dt} + \mathbf{L}\_{m}\frac{d\mathbf{i}\_{ds}}{dt} - \boldsymbol{\alpha}\_{r}\mathbf{L}\_{r}\mathbf{i}\_{qr} + \boldsymbol{\alpha}\_{r}\mathbf{L}\_{m}\mathbf{i}\_{qs} \\ \boldsymbol{\upsilon}\_{qr} = \boldsymbol{r}\_{r}\mathbf{i}\_{qr} + \mathbf{L}\_{r}\frac{d\mathbf{i}\_{qs}}{dt} + \mathbf{L}\_{m}\frac{d\mathbf{i}\_{qs}}{dt} + \boldsymbol{\alpha}\_{r}\mathbf{L}\_{r}\mathbf{i}\_{dr} + \boldsymbol{\alpha}\_{r}\mathbf{L}\_{m}\mathbf{i}\_{ds} \end{cases} \tag{11}$$

$$\begin{cases} \upsilon\_{dr} = r\_r \dot{\mathbf{i}}\_{dr} + \mathbf{L}\_r \frac{d\dot{\mathbf{i}}\_{dr}}{dt} - \mathbf{L}\_m \frac{\mathbf{L}\_m d\dot{\mathbf{i}}\_{dr}}{\mathbf{L}\_s dt} - \alpha\_r \mathbf{L}\_r \dot{\mathbf{i}}\_{qr} - \alpha\_r \mathbf{L}\_m \frac{\mathbf{L}\_m}{\mathbf{L}\_s} \dot{\mathbf{i}}\_{qr} \\\\ \upsilon\_{qr} = r\_r \dot{\mathbf{i}}\_{qr} + \mathbf{L}\_r \frac{d\dot{\mathbf{i}}\_{qr}}{dt} - \mathbf{L}\_m \frac{\mathbf{L}\_m d\dot{\mathbf{i}}\_{qr}}{\mathbf{L}\_s dt} + \alpha\_r \mathbf{L}\_r \dot{\mathbf{i}}\_{dr} + \alpha\_r \mathbf{L}\_m \frac{\mathbf{\Phi}\_s}{\mathbf{L}\_s} - \alpha\_r \mathbf{L}\_m \frac{\mathbf{L}\_m}{\mathbf{L}\_s} \dot{\mathbf{i}}\_{dr} \end{cases} \tag{12}$$

#### Wind Diesel Hybrid Power System with Hydrogen Storage http://dx.doi.org/10.5772/52341 373

$$\begin{cases} \boldsymbol{\upsilon}\_{dr} = \boldsymbol{r}\_{r}\dot{\mathbf{i}}\_{dr} + \left(\boldsymbol{L}\_{r} - \frac{\boldsymbol{L}\_{m}}{\boldsymbol{L}\_{s}}\right)\frac{d\dot{\mathbf{i}}\_{dr}}{dt} - \boldsymbol{\alpha}\_{r}\boldsymbol{L}\_{r}\,\dot{\mathbf{i}}\_{qr} - \boldsymbol{\alpha}\_{r}\frac{\boldsymbol{L}\_{m}}{\boldsymbol{L}\_{s}}\,\dot{\mathbf{i}}\_{qr} \\\\ \boldsymbol{\upsilon}\_{qr} = \boldsymbol{r}\_{r}\dot{\mathbf{i}}\_{qr} + \left(\boldsymbol{L}\_{r} - \frac{\boldsymbol{L}\_{m}}{\boldsymbol{L}\_{s}}\right)\frac{d\dot{\mathbf{i}}\_{qr}}{dt} + \boldsymbol{\alpha}\_{r}\boldsymbol{L}\_{r}\,\dot{\mathbf{i}}\_{dr} + \boldsymbol{\alpha}\_{r}\boldsymbol{L}\_{m}\,\frac{\boldsymbol{\Phi}\_{s}}{\boldsymbol{L}\_{s}} - \boldsymbol{\alpha}\_{r}\frac{\boldsymbol{L}\_{m}}{\boldsymbol{L}\_{s}}\,\dot{\mathbf{i}}\_{dr} \end{cases} \tag{13}$$

$$\begin{cases} \upsilon\_{dr} = r\_r \dot{i}\_{dr} + \left(L\_r - \frac{L\_m}{L\_s}\right) \frac{d\dot{i}\_{dr}}{dt} - \alpha \rho \left(L\_r - \frac{L\_m}{L\_s}\right) \dot{i}\_{qr} \\ \upsilon\_{qr} = r\_r \dot{i}\_{qr} + \left(L\_r - \frac{L\_m}{L\_s}\right) \frac{d\dot{i}\_{qr}}{dt} + \alpha \rho \left(L\_r - \frac{L\_m}{L\_s}\right) \dot{i}\_{dr} + \alpha \rho \left. L\_m \frac{\Phi\_s}{L\_s} \right. \end{cases} \tag{14}$$

*ωr*and *ωs* are respectively rotor and stator parameters frequencies; *s*is the machine's slip.

As

( ) *em ds qs qs ds T Pi i* = l

given according the rotor currents as (D. Aouzellag et al. 2006).

l

l

í <sup>ï</sup> = - <sup>ï</sup> î

Fom equations (5) et (6), rotor's voltages can be rewritten as:

ï +

The stator's flux and current equations are:

í

ì

í

ì

ï í

î

*P* is the number of pole pairs.

372 New Developments in Renewable Energy

 l

To achieve independent control of the stator active power and stator reactive power, a vec‐ tor-control approach is used. *d-q* axis connected to the stator's rotating field is chosen and quadratic component of the stator flux is set to zero. The power control is performed through the back to back converter connected to the rotor. Then, the stator voltages can be

> *ds s ds m dr s qs s qs m qr Li L i Li L i*

> > *s m ds dr s s m qs qr s*

*<sup>L</sup> i i L L*

*<sup>L</sup> i i L*

*r dr m ds dr r dr r r qr m qs*

*d Li L i v ri Li L i dt d Li L i v ri Li L i dt*

<sup>ì</sup> <sup>+</sup> <sup>ï</sup> =+ - + <sup>ï</sup>

<sup>ï</sup> =+ + + <sup>î</sup>

<sup>ï</sup> =+ + - + <sup>ï</sup>

<sup>ï</sup> =+ + + + ïî

*dr r dr r m r r qr r m qr*

*di L di <sup>L</sup> v ri L L Li L i*

ï F =+ - + + - <sup>ï</sup>

ï =+ - - -

*r qr m qs qr r qr r r dr m ds*

*dr ds dr r dr r m r r qr r m qs*

*di di v ri L L Li L i dt dt di di v ri L L Li L i dt dt*

*qr qs qr r qr r m r r dr r m ds*

*dr m dr m*

w

*dt L dt L di L di <sup>L</sup> v ri L L Li L L i*

*qr r qr r m r r dr r m r m dr*

<sup>ì</sup> <sup>F</sup> <sup>ï</sup> = - <sup>ï</sup>

ìï = + =F <sup>í</sup> =+ = ïî

0

( ) ( )

w

( ) ( )

w

w

w

*s s qr m qr s m*

*dt L dt L L*

ww

*s s s*

 w  w

 w

> w

(7)

(8)

(9)

(10)

(11)

(12)

$$o\sigma\_r = so\_s$$

$$\begin{cases} \upsilon\_{dr} = r\_r i\_{dr} + \left(L\_r - \frac{L\_m}{L\_s}\right) \frac{di\_{dr}}{dt} - so\_s \left(L\_r - \frac{L\_m}{L\_s}\right) i\_{qr} \\ \upsilon\_{qr} = r\_r i\_{qr} + \left(L\_r - \frac{L\_m}{L\_s}\right) \frac{di\_{qr}}{dt} + so\_s \left(L\_r - \frac{L\_m}{L\_s}\right) i\_{dr} + go\_s L\_m \frac{\Phi\_s}{L\_s} \end{cases} \tag{15}$$

From vector control conditions, the stator voltage can be expressed as:

$$V\_s = \alpha\_s, \Phi\_s \tag{16}$$

Then, the final vector control equations of the rotor's voltage are:

$$\begin{cases} \upsilon\_{dr} = r\_r \dot{i}\_{dr} + \left(L\_r - \frac{L\_m}{L\_s}\right) \frac{d\dot{i}\_{dr}}{dt} - s o\_s \left(L\_r - \frac{L\_m}{L\_s}\right) \dot{i}\_{qr} \\ \upsilon\_{qr} = r\_r \dot{i}\_{qr} + \left(L\_r - \frac{L\_m}{L\_s}\right) \frac{d\dot{i}\_{qr}}{dt} + s o\_s \left(L\_r - \frac{L\_m}{L\_s}\right) \dot{i}\_{dr} + s o\_s \frac{L\_m V\_s}{o\_s L\_s} \end{cases} \tag{17}$$

**2.** DFIG's Control

The Rotor Side Converter (RSC) is used to control both active and reactive powers provided by the stator of the DFIG. The control strategy of the RSC is based on the power vector con‐ trol of the DFIG, and the principle of this control is illustrated by Fig. 5. Different controllers can be used for this purpose.

**Figure 5.** Scheme of the power control vector of the DFIG

The Grid Side Converter (GSC) is used to regulate the DC-link voltage and to adjust the power factor. The GSC is a bidirectional converter which operates as a rectifier when the slip (g) is positive (subsynchronous mode) and as an inverter when the slip is negative (oversyn‐ chronous mode).

The active and reactive powers on the grid side are written respectively as follows (X. Yao et al. 2008):

$$\begin{cases} P = \frac{\mathfrak{D}}{2} V\_m \dot{\mathfrak{a}}\_d \\ Q = -\frac{\mathfrak{D}}{2} V\_m \dot{\mathfrak{a}}\_q \end{cases} \tag{18}$$

**Figure 6.** Scheme of the GSC converter control

sented with gain *K2* and delay *τ*2(R. Dettmer, 1990).

**Controller** 

The diesel ge4narator is composed of the diesel engine and Wound Rotor Synchronous Gen‐

The model of the diesel engine is shown in Fig. 7 (R. Dettmer, 1990; R. Pena et al., 2002; S. Roy et al., 1993). The dynamic of the actuator is modeled by a first order model with time constant *τ*1and gain *K1* (R. Pena et al., 2008; S. Roy et al., 1993). The combustion bloc is repre‐

**Bloc Actuator** 

**- -**

**Mechanical Torque ion +**

**Speed** W

**Combustion** 

**SynchronousGenerator Torque (eq. 33)** 

*mes*

+ *DMs* 1

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375

**2.3. Diesel generator modelling**

erator (WRSG).

**a.** Diesel Engine

*ref* W

**+**

**Figure 7.** Block diagram of diesel generator model

*Vm*isthe magnitude of voltage of the grid. The principle of control of GSC is illustrated by Fig. 6.

**Figure 6.** Scheme of the GSC converter control

#### **2.3. Diesel generator modelling**

The diesel ge4narator is composed of the diesel engine and Wound Rotor Synchronous Gen‐ erator (WRSG).

#### **a.** Diesel Engine

The Rotor Side Converter (RSC) is used to control both active and reactive powers provided by the stator of the DFIG. The control strategy of the RSC is based on the power vector con‐ trol of the DFIG, and the principle of this control is illustrated by Fig. 5. Different controllers

The Grid Side Converter (GSC) is used to regulate the DC-link voltage and to adjust the power factor. The GSC is a bidirectional converter which operates as a rectifier when the slip (g) is positive (subsynchronous mode) and as an inverter when the slip is negative (oversyn‐

The active and reactive powers on the grid side are written respectively as follows (X. Yao et

3 . 2

*P Vi*

ì = ïï í <sup>ï</sup> = - ïî

*Q Vi*

3 . 2

*Vm*isthe magnitude of voltage of the grid. The principle of control of GSC is illustrated by

*m q*

(18)

*m d*

can be used for this purpose.

374 New Developments in Renewable Energy

**Figure 5.** Scheme of the power control vector of the DFIG

chronous mode).

al. 2008):

Fig. 6.

The model of the diesel engine is shown in Fig. 7 (R. Dettmer, 1990; R. Pena et al., 2002; S. Roy et al., 1993). The dynamic of the actuator is modeled by a first order model with time constant *τ*1and gain *K1* (R. Pena et al., 2008; S. Roy et al., 1993). The combustion bloc is repre‐ sented with gain *K2* and delay *τ*2(R. Dettmer, 1990).

**Figure 7.** Block diagram of diesel generator model

The actuator is modelled as:

$$\frac{K\_1}{1 + s\tau\_1} \tag{19}$$

Rotor armature winding voltage is

Damper windings are characterized by

0

ì

í

î

which is supplied by the synchronous generator.

Where

[X]=[idiq if

iDiQ]

*d*

*q*

*di*

*di*

T and [B]=[0 0 0 vf

0

*f d D*

*f d D*

*dt dt dt*

=- - + + (24)

Wind Diesel Hybrid Power System with Hydrogen Storage

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(25)

377

(26)

(28)

*dt dt dt*

*f f f d f md di di di v Ri L L L*

*D D md md D*

*di di di Ri L L L*

*Q Q mq Q*

<sup>ï</sup> =- + + <sup>ï</sup>

*Ri L L*

<sup>ï</sup> =- + <sup>ï</sup>

ì

í

*q Q*

To eliminate *vd* and *vq* in the expression of the stator voltages, we introduced the *RcLc* load

*d d cd c cq*

w

w

*X*˙ = *A* . *X* + *B* . *U* (27)

b

c

w

*di v Ri L Li dt di v Ri L Li dt*

<sup>ï</sup> =+ - <sup>ï</sup>

<sup>ï</sup> =+ + ïî

*A* : State matrix; *X* : State vector; *B* : Control matrix; *U* : Control vector.

( )( ) <sup>1</sup>

*c f f D D mq Q*

 b

 c

*L R i Ri L i*

( )( ) <sup>1</sup> *d c d s c q md f*

æ öç ÷ <sup>=</sup> ç ÷

*mq*

*L*

*L*

*Q*

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

æ öæ ö ç ÷ç ÷ -+ + + + +

1

*L Li R Ri L i*

æ ö - + -+ + +

è ø

w

*s cd q cq f*

*R Ri L Li V*

*md*

*D*

 w

*L*

0 0]T

*dt L*

w

*dt L L i Ri*

è ø + -

g w b

c

*c md D Q Q*

ab

> c

a

*q q cq c cd*

By using the equations above, the state space model of the Wound Rotor Synchronous Gen‐ erator (WRSG) can be written as follow (Belmokhtar et al., 2012a, Belmokhtar et al., 2012b)):

*di di*

*dt dt*

The model of the combustion bloc is given by:

$$K\_2 e^{-s\tau\_2} \tag{20}$$

The delay can be expressed as (R. Pena et al., 2002; R. Pena et al., 2008):j

$$
\pi\_2 = \frac{60h}{2N\nu\_c} + \frac{60}{4N} \tag{21}
$$

*h* represents the strokes number, *nc* the number of cylinders and *N* the speed of diesel gener‐ ator (rpm), Φ is the fuel consumption rate (kg/sec) (F. Jurado and J. R. Saenz, 2002). In the order to maintain constant the frequency of the grid (AC-bus), the speed of the diesel engine must be kept constant when the load varies.

#### **2.** Synchronous Generator

The simplified model of the Wound RotorSynchronous Generator (WRSG) can be obtained in *dq* frame (conversion between *abc* and *dq* can be realized by means of the Park Transform) (T. Burton et al., 2001).

The stator armature windings voltages are:

$$\begin{cases} \upsilon\_d = -R\_s i\_d + \frac{d\lambda\_d}{dt} - \alpha \varkappa\_q \\ \upsilon\_q = -R\_s i\_q + \frac{d\lambda\_q}{dt} + \alpha \lambda\_d \end{cases} \tag{22}$$

*Rs*is the stator winding resistance

The stator fluxes are

$$\begin{cases} \mathcal{k}\_d = -L\_d \dot{\mathbf{i}}\_d + L\_{md} \left( \dot{\mathbf{i}}\_f + \dot{\mathbf{i}}\_D \right) \\ \mathcal{k}\_q = -L\_q \dot{\mathbf{i}}\_q + L\_{mq} \dot{\mathbf{i}}\_Q \end{cases} \tag{23}$$

Rotor armature winding voltage is

The actuator is modelled as:

376 New Developments in Renewable Energy

The model of the combustion bloc is given by:

must be kept constant when the load varies.

The stator armature windings voltages are:

*Rs*is the stator winding resistance

The stator fluxes are

**2.** Synchronous Generator

(T. Burton et al., 2001).

1 <sup>1</sup> 1 *K* + *s*t

2 2 *<sup>s</sup> K e* t

60 60 2 4 *<sup>c</sup> h Nn N*

*h* represents the strokes number, *nc* the number of cylinders and *N* the speed of diesel gener‐ ator (rpm), Φ is the fuel consumption rate (kg/sec) (F. Jurado and J. R. Saenz, 2002). In the order to maintain constant the frequency of the grid (AC-bus), the speed of the diesel engine

The simplified model of the Wound RotorSynchronous Generator (WRSG) can be obtained in *dq* frame (conversion between *abc* and *dq* can be realized by means of the Park Transform)

> *d d sd q*

wl

wl

l

*dt d*

l

*dt*

*d d d md f D* ( )

*Li L i i*

*q q q mq Q*

<sup>ï</sup> =- + <sup>î</sup>

<sup>ì</sup> =- + + <sup>ï</sup>

*Li L i*

*<sup>d</sup> v Ri*

<sup>ï</sup> =- + - <sup>ï</sup>

<sup>ï</sup> =- + + ïî

*v Ri*

ì

í

l

l

í

*q q sq d*

The delay can be expressed as (R. Pena et al., 2002; R. Pena et al., 2008):j

2

t

(19)

(20)

= + (21)

$$
\sigma v\_f = -\mathbf{R}\_f i\_f - \mathbf{L}\_d \frac{d\dot{\mathbf{i}}\_d}{dt} + \mathbf{L}\_f \frac{d\dot{\mathbf{i}}\_f}{dt} + \mathbf{L}\_{md} \frac{d\dot{\mathbf{i}}\_D}{dt} \tag{24}
$$

Damper windings are characterized by

$$\begin{cases} 0 = R\_D i\_D - L\_{md} \frac{di\_d}{dt} + L\_{md} \frac{di\_f}{dt} + L\_D \frac{di\_D}{dt} \\ 0 = R\_Q i\_Q - L\_{mq} \frac{di\_q}{dt} + L\_Q \frac{di\_Q}{dt} \end{cases} \tag{25}$$

To eliminate *vd* and *vq* in the expression of the stator voltages, we introduced the *RcLc* load which is supplied by the synchronous generator.

$$\begin{cases} \boldsymbol{\upsilon}\_{d} = \boldsymbol{R}\_{c}\dot{\boldsymbol{i}}\_{d} + \boldsymbol{L}\_{c}\frac{d\dot{\boldsymbol{i}}\_{d}}{dt} - \alpha \boldsymbol{L}\_{c}\dot{\boldsymbol{i}}\_{q} \\ \boldsymbol{\upsilon}\_{q} = \boldsymbol{R}\_{c}\dot{\boldsymbol{i}}\_{q} + \boldsymbol{L}\_{c}\frac{d\dot{\boldsymbol{i}}\_{q}}{dt} + \alpha \boldsymbol{L}\_{c}\dot{\boldsymbol{i}}\_{d} \end{cases} \tag{26}$$

By using the equations above, the state space model of the Wound Rotor Synchronous Gen‐ erator (WRSG) can be written as follow (Belmokhtar et al., 2012a, Belmokhtar et al., 2012b)):

$$\mathsf{L}\{\dot{X}\} = \mathsf{L}\{A\}\mathsf{L}\{X\} + \mathsf{L}\{B\}\mathsf{L}\{U\} \tag{27}$$

Where

(22)

(23)

*A* : State matrix; *X* : State vector; *B* : Control matrix; *U* : Control vector. [X]=[idiq if iDiQ] T and [B]=[0 0 0 vf 0 0]T

$$\begin{aligned} \frac{di\_d}{dt} &= \left(\frac{1}{L\_c + \left(\alpha - \frac{\alpha\beta}{\mathcal{X}}\right)}\right) \left(\frac{-(R\_s + R\_c)i\_d + o(L\_q + L\_c)i\_q + \frac{\beta}{\mathcal{X}}V\_f + }{\mathcal{X}}\right) \\\\ \frac{\beta}{\mathcal{X}} R\_f i\_f &+ \left(\frac{\beta}{\mathcal{X}} - 1\right) \frac{L\_{md}}{L\_D} R\_D i\_D - oL\_{mq}i\_Q \end{aligned} \tag{28}$$
 
$$\frac{di\_q}{dt} = \left(\frac{1}{L\_c + \gamma}\right) \left(\frac{-o(L\_d + L\_c)i\_d - (R\_s + R\_c)i\_q + o(L\_{md}i\_f + \gamma)}{oL\_{md}i\_D - L\_Q}\right)$$

$$\begin{aligned} \frac{d\dot{I}\_{f}}{dt} &= -\frac{\alpha (R\_{i} + R\_{c})}{\varkappa \delta} i\_{f\_{d}} + \frac{\alpha \alpha (L\_{i} + L\_{c})}{\varkappa \delta} i\_{f} + \left( \left( \frac{\alpha \beta}{\varkappa^{2} \delta} R\_{f} \right) + \left( \frac{R\_{f}}{\varkappa} \right) \right) i\_{f} + \\ & \left( \frac{1}{\varkappa} + \frac{\alpha \beta}{\varkappa^{2} \delta} \right) V\_{f} + \left( \left( \frac{\beta}{\varkappa} - 1 \right) \frac{\alpha}{\varkappa} + \frac{1}{\varkappa} \right) \frac{L\_{md}}{L\_{D}} R\_{D} I\_{f} - \frac{\alpha \alpha L\_{m}}{\varkappa \delta} i\_{Q} \\ \frac{d\dot{I}\_{D}}{dt} &= \frac{L\_{md} (R\_{c} + R\_{c})}{L\_{D} \delta} \bigg( \left( \frac{\alpha}{\varkappa} - 1 \right) i\_{f} + \frac{\alpha L\_{m} (L\_{q} + L\_{c})}{L\_{D} \delta} \bigg( 1 - \left( \frac{\alpha}{\varkappa} \right) \Big) i\_{q} - \\ & \frac{L\_{md} R\_{f}}{L\_{D} \delta} \bigg( 1 + \left( \frac{\alpha \beta}{\varkappa^{2} \delta} \right) + \frac{\beta}{\varkappa} \Big) i\_{f} - \frac{L\_{md}}{L\_{D}} \bigg( \frac{1}{\varkappa} + \left( \frac{\alpha \beta}{\varkappa^{2} \delta} \right) + \frac{\beta}{\varkappa^{3} \delta} \Big) V\_{f} - \\ & \left( \left( \left( \frac{\alpha}{\varkappa} - 1 \right) \left( \frac{\alpha}{\varkappa} - \frac{1}{\varkappa} \right) + \$$

( )

<sup>3</sup> . . <sup>2</sup>

*diesel d d q q*

*P vi vi*

= + ïï

<sup>ï</sup> = - ïî

*Q vi vi*

*diesel d q q d*

*Add*

ì

í

The total stator currents of the diesel generator are:

Then, (27) is expressed as follow:

**2.4. Alkaline electrolyzer**

line aqueous solution.

voltages (equation 34) (O. Ulleberg, 1998).

*Add*

<sup>3</sup> . . <sup>2</sup>

0 1 0 1 *dt d d qt q q iii iii* ìï = + <sup>í</sup> = + ïî

The diesel generator will operate with minimum load of 35% of the rated power. The alka‐ line electrolyzers are used as dump load. The electrolyzers are supplied by the surplus pow‐

The decomposition of water into hydrogen and oxygen can be obtained by passing a direct electric current (DC) between two electrodes separated by a membrane and containing an aqueous electrolyte with good ionic conductivity. The electrodes are immersed in an alka‐

The electrolyzer model is composed of several modules (F. J. Pino et al., 2011). Powered by the DC electrical sources and pure water, an electrolyzer can effectively split water into hy‐ drogen and oxygen. Since it is difficult to obtain analytically the inverse of the equation (34),

In this paper, the electrolyzer model takes into account the ohmic resistances and cell over‐

/ / log <sup>1</sup> *ele ele ele*

2

è ø

+ æ ö + + =+ + ç ÷ +

1 2 12 3

*r rT t tT tT V E Is A A*

*ele ele*

2

012 3 *ele ele s s sT sT* =+ + (35)

er, and then contribute to balance the load demand and power production.

linear models are used generally in literature (R.Takahashi et al. 2010).

0 0

*cell ele*

1 1

Wind Diesel Hybrid Power System with Hydrogen Storage

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*T p L L i i L ii L i i L i i em d q dt qt md f qt md qt D mq dt Q* =- + + - (( ) ) (33)

(31)

379

(32)

(34)

( )

*P* is the number of the poles

In order to improve the efficiency and avoid wet stacking, a minimum load of about 30% to 40% is usually recommended by the manufacturers (J. B. Andriulli et al., 1999). To achieve this goal, the values of *Rc* and *Lc* are chosen in the aim to give 35% of the rated power of the diesel generator when it is switched on. Then the partial values of the stator currents *id0* and *iq0* in the *dq* frame are calculated. The additional values of the stator currents *id1* and *iq1* are computed respectively as follow:

$$\begin{cases} \dot{\mathbf{i}}\_{d1} = \frac{\upsilon\_d \mathbf{P}\_{d\text{diesel}}^{Add} - \upsilon\_q \mathbf{Q}\_{d\text{disel}}^{Add}}{2} \\ \qquad \frac{\mathbf{3}}{2} (\upsilon\_d^2 + \upsilon\_q^2) \\ \dot{\mathbf{i}}\_{q1} = \frac{\upsilon\_q \mathbf{P}\_{d\text{disel}}^{Add} + \upsilon\_d \mathbf{Q}\_{d\text{disel}}^{Add}}{2} \\ \qquad \frac{\mathbf{3}}{2} (\upsilon\_d^2 + \upsilon\_q^2) \end{cases} \tag{30}$$

The active additional power and the reactive power of the diesel generator are expressed re‐ spectively as:

#### Wind Diesel Hybrid Power System with Hydrogen Storage http://dx.doi.org/10.5772/52341 379

$$\begin{cases} P\_{diesel}^{Add} = \frac{3}{2} \left( \upsilon\_d \dot{\imath}\_{d1} + \upsilon\_q \dot{\imath}\_{q1} \right) \\ Q\_{diesel}^{Add} = \frac{3}{2} \left( \upsilon\_d \dot{\imath}\_{q1} - \upsilon\_q \dot{\imath}\_{d1} \right) \end{cases} \tag{31}$$

The total stator currents of the diesel generator are:

$$\begin{cases} \dot{\mathbf{i}}\_{dt} = \dot{\mathbf{i}}\_{d0} + \dot{\mathbf{i}}\_{d1} \\ \dot{\mathbf{i}}\_{qt} = \dot{\mathbf{i}}\_{q0} + \dot{\mathbf{i}}\_{q1} \end{cases} \tag{32}$$

Then, (27) is expressed as follow:

2

c

*mq md mq*

 d

*L LL*

æ ö æ ö ç ÷ - ç ÷ ç ÷ è ø è ø

 w

> g

*D*

*L*

*Q*

(29)

(30)

*i*

ab

*md mq*

wa

 a

 c

cd

*L L*

c d

*d qf f*

*d q*

 b

cd

*dqf*

*i ii*

w

 w

a

cd

*i i*

*i iR i*

+ + æ ö æ ö æ ö =- + + + + ç ÷ ç ÷ ç ÷ ç ÷ ç ÷ è ø è ø è ø

> *f D D Q D*

> > 2

() () ()

1

In order to improve the efficiency and avoid wet stacking, a minimum load of about 30% to 40% is usually recommended by the manufacturers (J. B. Andriulli et al., 1999). To achieve this goal, the values of *Rc* and *Lc* are chosen in the aim to give 35% of the rated power of the diesel generator when it is switched on. Then the partial values of the stator currents *id0* and *iq0* in the *dq* frame are calculated. The additional values of the stator currents *id1* and *iq1* are

( )

*v v*

3 2

<sup>ì</sup> - <sup>ï</sup> <sup>=</sup> <sup>ï</sup> <sup>+</sup> ïï

ï +

<sup>ï</sup> <sup>+</sup> ïî

*vP vQ <sup>i</sup>*

3 2

*vP vQ <sup>i</sup>*

2 2

*d q Add Add q diesel d diesel*

*Add Add d diesel q diesel*

( )

The active additional power and the reactive power of the diesel generator are expressed re‐

*v v*

2 2

*d q*

*Q c Q c Q c*

+ + <sup>=</sup> - -++ ++ +

ab

 d

*f f*

c d

*md md D D D D D*

*L L R i L L L*

c

() ()

*di L L L L R R LL*

*dt L L L L L L*

*Q mq d c mq s c mq md*

gg

*D Q Q*

g

*T p L L ii L ii L ii L ii em d q d q md f q md q D mq d Q* =- + + - (( ) )

*i R i*

æ ö - + ç ÷ <sup>+</sup> ç ÷ <sup>+</sup> è ø

*V RI i L*

2

ab

a

*dt*

378 New Developments in Renewable Energy

c c d

c

b

c

w

*P* is the number of the poles

computed respectively as follow:

spectively as:

( ) ( )

æ ö æ ö æ ö ç ÷ + +- + - ç ÷ ç ÷ è ø è ø è ø

2 2

*D D*

*L R <sup>L</sup> i V*

wa

> a

 dc c

( ) ( ) 1 1

æ ö æ ö æ ö æ ö ç ÷ + +- + + - ç ÷ ç ÷ ç ÷ ç ÷ è ø è ø è ø è ø

2

2

1

*d*

1

ï =

*q*

í

*Q c Q c Q*

( ) ( )

*L L L L L*

*md mq mq*

*LL L*

g

*f q c f s c*

cd

w

<sup>+</sup> æö æö æ ö <sup>+</sup> æ ö <sup>=</sup> ç÷ ç÷ ç ÷ - + - - ç ÷ èø èø è ø è ø

*di R R L L R*

1 1 <sup>1</sup>

<sup>1</sup> <sup>1</sup>

 b

 d

*dt L L*

dc

*md f md*

*D D*

è ø è øè ø è ø

*L L*

w

ab

 cd

 a

 dc d c

11 1 <sup>1</sup>

æ ö æ ö æ öæ ö ç ÷ ç ÷ ç ÷ç ÷ - -+ + +

 b

*D md s c md q c*

*di LRR LLL*

a

c

cd

$$T\_{em} = p\left(\left(L\_d - L\_q\right)\dot{\mathbf{i}}\_{dt}\dot{\mathbf{i}}\_{qt} + L\_{md}\dot{\mathbf{i}}\_f\dot{\mathbf{i}}\_{qt} + L\_{md}\dot{\mathbf{i}}\_{qt}\dot{\mathbf{i}}\_D - L\_{mq}\dot{\mathbf{i}}\_{dt}\dot{\mathbf{i}}\_Q\right) \tag{33}$$

The diesel generator will operate with minimum load of 35% of the rated power. The alka‐ line electrolyzers are used as dump load. The electrolyzers are supplied by the surplus pow‐ er, and then contribute to balance the load demand and power production.

#### **2.4. Alkaline electrolyzer**

The decomposition of water into hydrogen and oxygen can be obtained by passing a direct electric current (DC) between two electrodes separated by a membrane and containing an aqueous electrolyte with good ionic conductivity. The electrodes are immersed in an alka‐ line aqueous solution.

The electrolyzer model is composed of several modules (F. J. Pino et al., 2011). Powered by the DC electrical sources and pure water, an electrolyzer can effectively split water into hy‐ drogen and oxygen. Since it is difficult to obtain analytically the inverse of the equation (34), linear models are used generally in literature (R.Takahashi et al. 2010).

In this paper, the electrolyzer model takes into account the ohmic resistances and cell over‐ voltages (equation 34) (O. Ulleberg, 1998).

$$V\_{cell} = E\_0 + \frac{r\_1 + r\_2}{A\_{ele}} I\_{ele} + s\_0 \log\left(\frac{t\_1 + t\_2 \,/\, T\_{ele} + t\_3 \,/\, T\_{ele}^2}{A\_{ele}} + 1\right) \tag{34}$$

$$\mathbf{s}\_0 = \mathbf{s}\_1 + \mathbf{s}\_2 \, T\_{ele} + \mathbf{s}\_3 \, T\_{ele}^2 \tag{35}$$

*Vrev*is the reversible voltage, *ri* , *si* and *ti* are the empirical parameters whose values are deter‐ mined from experiments (N. Gyawali and Y. Oshsawa, 2010).

The electrolyzer's voltage is expressed as:

$$\mathbf{V}\_{ele} = \mathbf{N}\_c \mathbf{V}\_{cell} \tag{36}$$

**Figure 9.** Diesel genset power

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381

**Figure 10.** Wind farm power

*Vcell* is the voltage of electrolyzer cell and *Nc* is the number of cells of the electrolyzer.
