Optimal placement of wind turbine in a radial distribution network using PSO method

Received Aug 23, 2019 Revised Nov 9, 2019 Accepted Jan 22, 2020 The aim of this article is to apply the Particle Swarm Optimization (PSO) method to find the best location for the wind turbine in the radial distribution network. The optimal location is found using the loss sensitivity factor. By respecting the constraints of the active power transmitted in the branches and the limits of the voltages modules for all the nodes. The validity of this method is tested on a 33-IEEE test network and the results obtained are compared with the results of basic load flow.

Where , and are the real and reactive power flowing out of bus ; and are the real and reactive load powers at bus 1.line section between buses and 1has resistance , and reactance , .voltage magnitude of bus is | |.for convergence of power flow ,the power balance (1)and (2) must be satisfied in addition, magnitudes of sending and receiving end bus voltages must satisfy (3). The well known generalized formulas for real and reactive power loss in the line section between buses and 1 are calculated by using the following equations.
, , , , The total active and reactive losses in the distribution network can be easily found by adding all the power losses in all branches and they are expressed as follows. Where, is the total real power loss and is the loss incurred due to reactive power throughout the network. In this study we consider wind supplying real power with unity power factor.

Electrical grid operating constraints
To ensure the stability of the network and the safety of equipment, voltage must be maintained within limits set by the rules of operation of the power grids. (8) Where and are the minimum and maximum values of bus voltage amplitudes, respectively. And the power transited in a line must not, under any circumstances, exceed the maximum limit.

And
: Maximum apparent power transited in line i -j.

WIND GENERATION SYSTEM MODELLING
The power generated by the wind turbine depends on their type and location, as well as the wind speed [7][8][9][10][11][12]. The electrical output power of a wind turbine is determined by using (11). With , , are different speeds corresponding to the wind turbine and is rated out pout power of wind turbine and it can be determined from (12).

LOSS SENSITIVITY FACTOR
The Active power losses in electrical networks are given by (12).
Where, cos sin (15) And Are the of matrix And

&
: Active and reactive power of the generator. & : Active and reactive load power The sensitivity factor of real power loss with respect to real power injection from the DG is given by The sensitivity factor is calculated for each node using the values obtained from the calculation of the basic flow. The node with the lowest loss sensitivity factor will be the best node for DG placement [13][14][15].

PARTICLE SWARM OPTIMIZATION 5.1. Introduction
The PSO algorithm is initialized by a population of random potential solutions, interpreted as particles moving in the research space. Each particle is attracted to its best position discovered in the past as well as to the best position discovered by the particles of its vicinity (or of the whole swarm, in the global version of the algorithm). The PSO algorithm includes several adjustment parameters which act on the exploration-exploitation compromise [16][17][18][19][20][21][22]. Exploration is the ability to test different regions of space in search of good candidate solutions. Exploitation is the ability to focus research around promising solutions in order to get as close to the optimum as possible. The choice of parameters remains largely empirical. A complete analysis of the algorithm was made by Kennedy In general, a PSO algorithm has three main steps:  First step: consists in authorizing all the particles arbitrarily distributed across the search space.  Second step: consists in evaluating the fitness value of the particles in order to determine the best position of each particle and to reveal the particle which has the best overall fitness value in the current swarm.  Third step: updates the speed of the particles which are then used as information to change the position of all the particles. In PSO, two different definitions are used: the individual best and the global best. As a particle moves through the search space, it compares its fitness value at the current position to the best fitness value it has ever attained previously. Adjustment of the position and speed of each particle is calculated using the current position , the best particle position so far and the best overall particle position in the population . Velocity of each particle in the next generation can be calculated as: With 1 r and 2 r are two numbers between 0 and 1 while 1 c and 2 c are positive constants, respectively. Inertia weight w is is formulated by the following expression: Where max w and min w are maximum and minimum of inertia weight, max iter and iter are maximum iteration number and current iteration, respectively.

PSO Procedure
The calculation procedure for the PSO calculation algorithm is as follows.
Step 1: Introduce data for all nodes and branches as well as the limits of nodal voltages.
Step 2: Calculating the power flow in the distribution network and determining total active losses.
Step 3: generate an initial population of particles with random positions and velocity. Set the iteration index t= 0.
Step 4: For each particle, update the bus data (for wind turbine) based on its locations and setting values, if all nodal voltages are within the permissible limits, estimate the total loss.
Step 5: Compare the fitness value of each particle with the personal best, Pbest . If the fitness value is lower than Pbest, set this value as the current Pbest, and record the particle position corresponding to this Pbest value.
Step 6: Select the minimum value of Pbest from all particles to be the current global best, Gbest , and record the particle position corresponding to this Gbest value.
Step 7: Update the velocity and position of particle. Step 8: If the maximum number of iterations is reached, the particle associated with the current Gbest is the optimal solution and then go to Step 9. Otherwise, set t=t+1 and return to Step 4.
Step 9: Displayed the best position for each particle.

RESULTS AND SIMULATIONS
Optimization of the location of the wind is done by the PSO algorithm, always programmed under MATLAB and tested on the IEEE33-bus distribution network system containing 33 buses and 32 branches as shown in Figure 3. The bus and line data are taken from [23][24]. The real and reactive power loads and voltage of radial distribution system are 3.72 , 2.3 and 12.66KV respectively. This program searches for the best wind turbine location on the network to minimize total active losses. Voltage sensitivity index was calculated at all nodes. Bus 18 was found to have the least VSI. Hence Wind Turbine was placed at this bus. The active power losses before the placement (basic calculation) of the distributed generator (wind) is 208,492 KW and the minimum voltage is 0.91075 pu at node level number 18. The first step in determining the wind power injected into the grid using the (11), with an average annual wind speed considered to be 6.02 m/s to determine the optimal location. [25].  The comparison for the real power losses in the branches is shown in Figure 6 for the initial network (with out wind) and with wind (case 1 and case 2), respectively, The power losses in almost every branch in case 2 reduced, except at 18, 19, 20, 21, 33, 34 and 35, where there was a small increase in losses.

CONCLUSION
The optimal insertion of wind turbines into the distribution network, the technique used to contribute to the management of distribution networks with the aim of minimizing total power losses by ensuring a good voltage profile, are carried out in the process of based on optimization by a meta heuristic method called pso algorithm. Many perspectives open up on the subject of the optimal insertion of decentralized production in the distribution network, in particular with regard to the types of DGs installed (photovoltaic, wind, etc.) and their maximum numbers to be installed, thus reconfiguring the distribution network taking into account other constraints such as transit limits and the assurance of continuity of service in the event of faults.