**7. Simulation results**

The first goal of each planning in electrical network is that the system meets the demand. For satisfying this goal, the cost of costumer's dissatisfaction is considered as well as the other costs. Flowchart of the proposed optimization methodology is shown in Fig. 4. The hourly data of wind speed, vertical and horizontal solar radiation and residential load during a year is plotted in Fig. 5, Fig. 6 and Fig. 7, respectively. The data that used in this study is the data of Ardebil convince that is located in the North West of Iran (latitude: 38°17´, longitude: 48°15´, altitude: 1345 m). The peak load is considered as 50 kW. In table 1, data that used in the simulation are listed.

Fig. 4. Flowchart of the proposed optimization methodology.

where *c1* and *c2* are acceleration constants and *r1* and *r2* are random real numbers drawn from [0,1]. Thus the particle flies trough potential solutions toward ( ) *P t <sup>i</sup>* and *G t*( ) in a navigated way while still exploring new areas by the stochastic mechanism to escape from

Since there was no actual mechanism for controlling the velocity of a particle, it was necessary to impose a maximum value *Vmax*, which controls the maximum travel distance in each iteration to avoid this particle flying past good solutions. Also after updating the positions, it must be checked that no particle violates the boundaries of search space. If a particle has violated the boundaries, it will be set at boundary of search space [Jahanbani et

the current one and is extremely important to ensure convergent behavior. It is exposed

The first goal of each planning in electrical network is that the system meets the demand. For satisfying this goal, the cost of costumer's dissatisfaction is considered as well as the other costs. Flowchart of the proposed optimization methodology is shown in Fig. 4. The hourly data of wind speed, vertical and horizontal solar radiation and residential load during a year is plotted in Fig. 5, Fig. 6 and Fig. 7, respectively. The data that used in this study is the data of Ardebil convince that is located in the North West of Iran (latitude: 38°17´, longitude: 48°15´, altitude: 1345 m). The peak load is considered as 50 kW. In table 1,

is constriction factor which is used to limit velocity, here

( )*t* is employed to control the impact of the previous history of velocities on

( )*t* is the constriction coefficient, which is used to

(18)

(19)

0.7 .

1 1 2 2 ( 1) ( ) ( ) ( ( ) ( )) ( ( ) ( )) *i i ii v t tv t cr P t X t cr Gt Xt*

( 1) ( ) ( 1) *Xt Xt vt i ii*

local optima.

al., 2008]. In Eq. (20),

restrain velocity.

**7. Simulation results** 

completely in the following section.

data that used in the simulation are listed.

Fig. 4. Flowchart of the proposed optimization methodology.


Table 1. Data used for simulation program [Tina et al., 2006, Khan et al., 2005]

Fig. 5. Hourly wind speed during a year.

Fig. 6. Hourly vertical and horizontal solar radiation during a year.

Fig. 7. Hourly residential load during a year.

It is noticeable that the technical constraint, related to system reliability, is expressed by the equivalent loss factor. The reliability index is calculated from component's failure, that includes wind turbine, PV array, battery and inverter failure. The power generated by each wind turbine and PV array can be derived by Eq. (1) and Eq. (3), respectively. The total power that can be generated with NWG wind turbines and NPV PV arrays that nWG and nPV of all wind turbines and PV arrays are out of work, respectively, will be calculated as follows:

$$P\_{ren} = \left(\mathbf{N\_{WG}} - \mathbf{n\_{WG}}\right) \times A\_{WG} \times P\_{WG} + \left(\mathbf{N\_{PV}} - \mathbf{n\_{PV}}\right) \times A\_{PV} \times P\_{PV} \tag{20}$$

Vertical Horizontal

0 1000 2000 3000 4000 5000 6000 7000 8000

Fig. 6. Hourly vertical and horizontal solar radiation during a year.

Time (hour)

0 1000 2000 3000 4000 5000 6000 7000 8000 9000

Time (hour)

It is noticeable that the technical constraint, related to system reliability, is expressed by the equivalent loss factor. The reliability index is calculated from component's failure, that includes wind turbine, PV array, battery and inverter failure. The power generated by each wind turbine and PV array can be derived by Eq. (1) and Eq. (3), respectively. The total power that can be generated with NWG wind turbines and NPV PV arrays that nWG and nPV of all wind turbines and PV arrays are out of work, respectively, will be calculated as follows:

( ) () *P N n A P N n AP ren WG WG WG WG PV PV PV PV* (20)

0

10

Fig. 7. Hourly residential load during a year.

15

20

25

30

Load power (kW)

35

40

45

50

200

400

Annual radiation (W/m2

)

600

800

1000

As previously mentioned, the reliability constraint is considered as the penalty factor in the objective function. To consider the constraint of reliability in Eq. (16), the excess amount of inequality constraint is multiplied by 1010 and then, this additional cost is added to the objective function in Eq. (15). With this method, the NPC of the system that couldn't satisfy the reliability constraint will increase, and then this system would not be chosen as the best economic system.

One of the best methods in the planning area is using scenario method. To choose the best plan (the minimum cost) different scenarios is implemented. In this study, the optimal size of components for hybrid system is calculated in three scenarios based on proposed approach. These systems are PV/battery system, wind/battery system and PV/wind/battery system. For each system the minimum cost and reliability indices is calculated. The results are shown in the following.

As mentioned before, in this study particle swarm optimization algorithm is used for optimal sizing of system's components. Each particle has 6 variables that are defined as below:


Fig. 8. A typical vector for a particle

Each population consists of 30 particles that are calculated for 120 iterations. The fitness function is defined in Eq. (15). It must be considered that if the costs of loss of load are more expensive than the cost of bigger system, the bigger system will be chosen because it is economically reasonable.
