**2. Description of the hybrid system**

The increasing energy demand and environmental concerns aroused considerable interest in hybrid renewable energy systems and its subsequent development.

The generation of both wind power and solar power is very dependent on the weather conditions. Thus, no single source of energy is capable of supplying cost-effective and reliable power. The combined use of multiple power resources can be a viable way to achieve trade-off solutions. With combine of the renewable systems, it is possible that power fluctuations will be incurred. To mitigate or even cancel out the fluctuations, energy storage technologies, such as storage batteries (SBs) can be employed [Wang et al., 2009].

The proper size of storage system is site specific and depends on the amount of renewable generation and the load. The needed storage capacity can be reduced to a minimum when a proper combination of wind and solar generation is used for a given site [Kellogg, 1996]. The hybrid system is shown in Fig. 2. In the following sections, the model of components is discussed.

Fig. 2. Block diagram of a hybrid wind/photovoltaic generation unit

#### **2.1 The wind turbine**

Choosing a suitable model is very important for wind turbine power output simulations. The most simplified model to simulate the power output of a wind turbine could be calculated from its power-speed curve. This curve is given by manufacturer and usually describes the real power transferred from WG to DC bus.

The model of WG is considered BWC Excel-R/48 (see Fig. 3) [Hakimi et al., 2009]. It has a rated capacity of 7.5 kW and provides 48 V dc as output. The power of wind turbine is described in terms of the wind speed according to Eq. 1.

$$P\_{\mathcal{V}} = \begin{cases} 0 & \boldsymbol{\upsilon}\_{\mathcal{W}} \le \boldsymbol{\upsilon}\_{ci}, \boldsymbol{\upsilon}\_{\mathcal{W}} \ge \boldsymbol{\upsilon}\_{co} \\ P\_{\mathcal{W}\_{\max}} \times \left(\frac{\boldsymbol{\upsilon}\_{\mathcal{W}} - \boldsymbol{\upsilon}\_{ci}}{\boldsymbol{\upsilon}\_{r} - \boldsymbol{\upsilon}\_{ci}}\right)^{m} & \boldsymbol{\upsilon}\_{ci} \le \boldsymbol{\upsilon}\_{\mathcal{W}} \le \boldsymbol{\upsilon}\_{r} \\\\ P\_{\mathcal{V}\_{\max}} + \frac{P\_{f} - P\_{\mathcal{W}\_{\max}}}{\boldsymbol{\upsilon}\_{co} - \boldsymbol{\upsilon}\_{r}} \times \left(\boldsymbol{\upsilon}\_{\mathcal{W}} - \boldsymbol{\upsilon}\_{r}\right) & \boldsymbol{\upsilon}\_{r} \le \boldsymbol{\upsilon}\_{\mathcal{W}} \le \boldsymbol{\upsilon}\_{f} \end{cases} \tag{1}$$

Choosing a suitable model is very important for wind turbine power output simulations. The most simplified model to simulate the power output of a wind turbine could be calculated from its power-speed curve. This curve is given by manufacturer and usually

The model of WG is considered BWC Excel-R/48 (see Fig. 3) [Hakimi et al., 2009]. It has a rated capacity of 7.5 kW and provides 48 V dc as output. The power of wind turbine is

Fig. 3. Power output characteristic of BWC Excel R/48 versus wind speed [Hakimi, 2009].

*m*

*v v P P vv v*

*W W ci W r*

max

*W ci*

*r ci f W*

*v v P P*

*co r*

*v v*

*W W r r W f*

*P v v vv v*

0 , *W ci W co*

*v vv v*

(1)

Fig. 2. Block diagram of a hybrid wind/photovoltaic generation unit

describes the real power transferred from WG to DC bus.

described in terms of the wind speed according to Eq. 1.

max

max

**2.1 The wind turbine** 

where *WG*max *P* , *Pf* are WG output power at rated and cut-out speeds, respectively. Also, *<sup>r</sup> v* , *ci v* , *co v* are rated, cut-in and cut-out wind speeds, respectively. In this study, the exponent *m* is considered 3. In the above equation, *vW* refers to wind speed at the height of WG's hub. Since, *vW* almost is measured at any height (here, 40 m), not in height of WGs hub, is used Eq. (2) to convert wind speed to installation height through power law [Borowy et al., 1996]:

$$w\_{\rm PV} = v\_{\rm PV}^{\rm measure} \times \left(\frac{h\_{\rm hub}}{h\_{\rm measure}}\right)^{\alpha} \tag{2}$$

where α is the exponent law coefficient. α varies with such parameters as elevation, time of day, season, nature of terrain, wind speed, temperature, and various thermal and mechanical mixing parameters. The determination of α becomes very important. The value of 0.14 is usually taken when there is no specific site data (as here) [Yang et al., 2007].

#### **2.2 The photovoltaic arrays (PVs)**

Solar energy is one of the most significant renewable energy sources that world needs. The major applications of solar energy can be classified into two categories: solar thermal system, which converts solar energy to thermal energy, and photovoltaic (PV) system, which converts solar energy to electrical energy. In the following, the modeling of PV arrays is described.

For calculating the output electric power of PVs, perpendicular radiation is needed. When the hourly horizontal and vertical solar radiation is available (as this study), perpendicular radiation can be calculated by Eq. (3):

$$\mathbf{G}\left(t,\theta\_{PV}\right) = \mathbf{G}\_V\left(t\right) \times \cos\left(\theta\_{PV}\right) + \mathbf{G}\_H\left(t\right) \times \sin\left(\theta\_{PV}\right) \tag{3}$$

where, *G t <sup>V</sup>* and *G t <sup>H</sup>* are the rate of vertical and horizontal radiations in the *tth* steptime (W/m2), respectively. The radiated solar power on the surface of each PV array can be calculated by Eq. (4):

$$P\_{pv} = \frac{G}{1000} \times P\_{pv,rated} \times \eta\_{MPPT} \tag{4}$$

where, *G* is perpendicular radiation at the arrays' surface (W/m2). *Ppv rated* , is rated power of each PV array at <sup>2</sup> *G Wm* 1000( / ) and *MPPT* is the efficiency of PV's DC/DC converter and Maximum Power Point Tracking (MPPT).

#### **2.3 The storage batteries**

Since both wind and PVs are intermediate sources of power, it is highly desirable to incorporate energy storage into such hybrid power systems. Energy storage can smooth out the fluctuation of wind and solar power and improve the load availability [Borowy et al., 1996].

When the power generated by WGs and PVs are greater than the load demand, the surplus power will be stored in the storage batteries for future use. On the contrary, when there is any deficiency in the power generation of renewable sources, the stored power will be used to supply the load. This will enhance the system reliability.

In the state of charge, amount of energy that will be stored in batteries at time step of *t* is calculated:

$$E\_B\left(t\right) = E\_B\left(t - 1\right) + \left(\left(P\_w + P\_{pv}\right)\left(t\right) - P\_{Load}\left(t\right) / \eta\_{inv.}\right)\eta\_{Bat} \tag{5}$$

In addition, Eq. 6 will calculate the state of battery discharge at time step of *t*:

$$E\_B\left(t\right) = E\_B\left(t - 1\right) + \left(P\_{Land}\left(t\right) / \eta\_{mv.} - \left(P\_w + P\_{pv}\right)\left(t\right)\right)\eta\_{Rat} \tag{6}$$

where, *E t <sup>B</sup>* , *E t <sup>B</sup>* 1 are the stored energy of battery in time step of *t* and *(t-1)*. *Pw* , *Ppv* are the generated power by wind turbines and PV arrays, *P t Load* is the load demand at time step of *t* and *Bat* is the efficiency of storage batteries.

#### **2.4 The power inverter**

The power electronic circuit (inverter) used to convert DC into AC form at the desired frequency of the load. The DC input to the inverter can be from any of the following sources: 1. DC output of the variable speed wind power system

2. DC output of the PV power system

In this study, supposed the inverter's efficiency is constant for whole working range of inverter (here 0.9).

#### **3. The reliability assessment**

A widely accepted definition of reliability is as follows [Billinton, 1992]: "Reliability is the probability of a device performing its purpose adequately for the period of time intended under the operating conditions encountered". In the following sections, reliability indices and reliability model that is used in this study is described.

#### **3.1 Reliability indices**

Several reliability indices are introduced in literature [Billinton, 1994, XU et al., 2005]. Some of the most common used indices in the reliability evaluation of generating systems are Loss of Load Expected (LOLE), Loss of Energy Expected (LOEE) or Expected Energy not Supplied (EENS), Loss of Power Supply Probability (LPSP) and Equivalent Loss Factor (ELF).

In this study, ELF is chosen as the main reliability index. On the other word, the ELF index is chosen as a constraint that must be satisfied but it could be possible to calculate the other indexes as is done in this study (such as EENS, LOLE and LOEE indexes).

ELF is ratio of effective load outage hours to the total number of hours. It contains information about both the number and magnitude of outages. In the rural areas and standalone applications (as this study), ELF<0.01 is acceptable. Electricity supplier aim at 0.0001 in developed countries [Garcia et al., 2006]:

$$ELF = \frac{1}{H} \sum\_{h=1}^{H} \frac{E(Q(h))}{D(h)}\tag{7}$$

where, *Q(h)* and *D(h)* are the amount of load that is not satisfied and demand power in *hth* step, respectively and *H* is the number of time steps (here H=8760).

In this study, the reliability index is calculated from component's failure, that is concluding of wind turbine, PV array, and inverter failure.

#### **3.2 System's reliability model**

236 Renewable Energy – Trends and Applications

In the state of charge, amount of energy that will be stored in batteries at time step of *t* is

*Et Et P P t P t BB w* 1 / *pv Load inv Bat*

where, *E t <sup>B</sup>* , *E t <sup>B</sup>* 1 are the stored energy of battery in time step of *t* and *(t-1)*. *Pw* , *Ppv* are the generated power by wind turbines and PV arrays, *P t Load* is the load demand at

The power electronic circuit (inverter) used to convert DC into AC form at the desired frequency of the load. The DC input to the inverter can be from any of the following sources:

In this study, supposed the inverter's efficiency is constant for whole working range of

A widely accepted definition of reliability is as follows [Billinton, 1992]: "Reliability is the probability of a device performing its purpose adequately for the period of time intended under the operating conditions encountered". In the following sections, reliability indices

Several reliability indices are introduced in literature [Billinton, 1994, XU et al., 2005]. Some of the most common used indices in the reliability evaluation of generating systems are Loss of Load Expected (LOLE), Loss of Energy Expected (LOEE) or Expected Energy not Supplied

In this study, ELF is chosen as the main reliability index. On the other word, the ELF index is chosen as a constraint that must be satisfied but it could be possible to calculate the other

ELF is ratio of effective load outage hours to the total number of hours. It contains information about both the number and magnitude of outages. In the rural areas and standalone applications (as this study), ELF<0.01 is acceptable. Electricity supplier aim at 0.0001

> 1 1 ( ( )) ( )

(7)

*H*

*h EQh ELF H Dh*

where, *Q(h)* and *D(h)* are the amount of load that is not satisfied and demand power in *hth*

(EENS), Loss of Power Supply Probability (LPSP) and Equivalent Loss Factor (ELF).

indexes as is done in this study (such as EENS, LOLE and LOEE indexes).

step, respectively and *H* is the number of time steps (here H=8760).

In addition, Eq. 6 will calculate the state of battery discharge at time step of *t*:

*Bat* is the efficiency of storage batteries.

*Et Et P t P P t B B* 1 / *Load inv w*

1. DC output of the variable speed wind power system

and reliability model that is used in this study is described.

 .

. *pv Bat*

(5)

(6)

calculated:

time step of *t* and

inverter (here 0.9).

**3.1 Reliability indices** 

**2.4 The power inverter** 

2. DC output of the PV power system

in developed countries [Garcia et al., 2006]:

**3. The reliability assessment** 

As mentioned, outages of PV arrays, wind turbine generators, and DC/AC converter are taken into consideration. Forced outage rate (FOR) of PVs and WGs is assumed to be 4% [Karki et al., 2001]. So, these components will be available with a probability of 96%. Probability of encountering each state is calculated by binomial distribution function [Nomura 2005].

For example, given *nWG* fail out of total *NWG* installed WGs, and *nPV* fail out of total *NPV* installed PV arrays are failed, the probability of encountering this state is calculated as follows:

 ,1 1 *fail fail fail fail WG WG PV WG PV PV PV WG PV fail fail fail fail N n n n N n WG ren WG WG PV PV WG PV n n fnn A A A A N N* (8)

The outage probability of other components is negligible. But, because, DC/AC converter is the only single cut-set of the system reliability diagram, the outage probability of it is taken consideration (it's FOR is considered 0.0011 [Kashefi et al., 2009]).

In [Kashefi et al., 2009] an approximate method is used that proposed all the possible states for outages of WGs and PV arrays to be modeled with an equivalent state. This idea is modeled by Eq. 7.

$$E\left[P\_{ren}\right] = N\_{\rm WG} \times P\_{\rm WG} \times A\_{\rm WG} + N\_{PV} \times P\_{PV} \times A\_{PV} \tag{9}$$

#### **4. Problem formulation**

The economical viability of a proposed plant is influence by several factors that contribute to the expected profitability. In the economical analysis, the system costs are involved as:


It is desirable that the system meets the electrical demand, the costs are minimized and the components have optimal sizes. Optimization variables are number of WGs, number of PV arrays, installation angle of PV arrays, number of storage batteries, and sizes of DC/AC converter. For calculation of system cost, the Net Present Cost (NPC) is chosen.

For optimal design of a hybrid system, total costs are defined as follow:

$$\text{NPC}\_{i} = N\_{i} \times \left( \text{CC}\_{i} + \text{RC}\_{i} \times \text{K}\_{i} + O \text{ \& } \text{MC}\_{i} \times \text{1} / \text{CRF}(ir, R) \right) \tag{10}$$

where *N* may be number (unit) or capacity (kW), *CC* is capital cost (US\$/unit), *O&MC* is annual operation and maintenance cost (US\$/unit-yr) of the component. *R* is Life span of project, *ir* is the real interest rate (6%). *CRF* and *K* are capital recovery factor and single payment present worth, respectively.

$$ir = \frac{\left(ir\_{nominal} - f\right)}{\left(1 + f\right)}\tag{11}$$

$$\text{CRF}\left(ir, R\right) = \frac{ir\left(1 + ir\right)^{R}}{\left(1 + ir\right)^{R} - 1} \tag{12}$$

$$K\_i = \sum\_{n=1}^{y\_i} \frac{1}{\left(1 + ir\right)^{n \times L\_i}} \tag{13}$$

#### **4.1 The cost of loss of load**

In this study, cost of electricity interruptions is considered. The values found for this parameter are in the range of 5-40 US\$/kWh for industrial users and 2-12 US\$/kWh for domestic users [Garcia et al., 2006]. In this study, the cost of customer's dissatisfaction, caused by loss of load, is assumed to be 5.6 US\$/kWh [Garcia et al., 2006]. Annual cost of loss of load is calculated by:

$$\text{NPC}\_{\text{loss}} = \text{LOEE} \times \text{C}\_{\text{loss}} \times \text{PVVA} \tag{14}$$

where, *Closs* is cost of costumer's dissatisfaction (in this study, US\$5.6/kWh). Now, the objective function with aim to minimize total cost of system is described:

$$\text{Cost} = \sum\_{i} \text{NPC}\_{i} + \text{NPC}\_{\text{loss}} \tag{15}$$

where *i* indicates type of the source, wind, PV, or battery. To solve the optimization problem, all the below constraints have to be considered:

$$\begin{aligned} 0 &\le N\_i < N\_{\text{max}}\\ 10 &\le H\_{\text{bub}} \le 20\\ 0 &\le \theta\_{PV\&\&\text{PVT}} \le \sqrt[\pi]{2} \\ E\_{\text{but}\_{\text{min}}} &\le E\_{\text{but}} \le E\_{\text{but}\_{\text{max}}} \\ E\left[ELF\right] &\le ELF\_{\text{max}} \end{aligned} \tag{16}$$

The last constraint is the reliability constraint. Equivalent Loss Factor is ratio of effective load outage hours to the total number of hours. In the rural areas and stand-alone applications (as this study), ELF<0.01 is acceptable [Tina, 2006]. For solving the optimization problem, particle swarm algorithm has been exploited.

#### **5. Operation strategy**

The system is simulated for each hour in period of one year. In each step time, one of the below states can occur:



By consideration these states and all the constraints, the optimal hybrid system is calculated.
