Optimal Placement of Distributed Generations in Radial Distribution Systems Using Various PSO and DE Algorithms

Distributed generations (DGs) have been continuously integrating into the distribution systems. Size and site of distributed generations have significant impacts on the system real power losses reduction and voltage profile improvement in the radial distribution systems. In this paper, recent and more dynamic PSO as well as improved DE algorithms are used for optimum placement of distributed generations in radial distribution systems. The objective of this paper is to minimize distribution system real power losses by the least possible injected power from distributed generations. To assess different PSO and DE algorithms capabilities, simulations carried out on two IEEE 33-bus and 69-bus standard radial distribution systems. DOI: http://dx.doi.org/10.5755/j01.eee.19.10.1941


I. INTRODUCTION
Distributed Generations (DGs) are mentioned usually to the production of electricity using small generators located in power distribution systems or the power load centers.The reasons for implementation of DGs have been motivated due to the different factors such as recent advances in small and efficient generation technologies, increasing interests in the environmental issues, postponing investment on new power transmission and distribution networks, and the need for more reliable and flexible electric power systems [1]- [3].
Many potential benefits of DGs depend on the size and location of DGs.In this regard, there have been different methodologies which have been proposed for optimal placement of DGs.For solving the DG placement optimization problem, a mixed integer linear program was formulated.The objective function was to optimal determination of the DG unit mix on a network section [4].Tabu Search (TS)-based method was proposed to determine convergence properties and is principally easy to understand [12,13].In this paper, several advanced and evolved PSO and DE techniques are utilized for optimal DG allocation.
Rest of the paper is organized as follows: Section II presents problem formulation and objective function.PSO and DE Techniques for finding optimal sizes and locations of various DG sizes are included and referred in Section III.Case studies for optimum DG placement on two IEEE 33bus and 69-bus radial distribution systems are addressed in Section IV.At the end, conclusions are sum up in Section V.

II. PROBLEM FORMULATION
To solve DG placement problem, first a power flow method should be used.The goal of a power flow calculation is obtaining complete voltage angles and magnitudes information for each bus in a power system.In this paper, power flow calculation which is forward-backward (fw-bw) method is also necessary to obtain the variation of power and voltage when some DGs are installed into the system.

A. Objective Function
Mathematically, the objective function is formulated to minimize the total real power losses as , Pi and Qi are real and reactive power injection in bus i. Rij is the resistance between ith and jth bus.Vi and δi are the voltage magnitude and angle of ith bus.Vj and δj are the voltage magnitude and angle of jth bus.

B. Problem Constraints
In this paper, optimization problem is solved subject to several problem constraints which are given further.
Load balance: For each bus, to meet demand and supply the following equations should be satisfied 1 1 , Voltage limits: For each bus, there should be an upper and lower voltage bounds min max , where |Vi| min = 0.95 p.u. and |Vi| max = 1.05 p.u. Active (real) and reactive power limit of DG: To size DGs, there should be a range of available DG size:

III. OPTIMIZATION ALGORITHMS: PSO AND DE
The reason for selecting PSO as an optimization algorithm is that in PSO there is neither competition between particles nor self-adaptation of the strategic parameters.The progression towards the optimum solution is governed by the movement equation.PSO has the fast convergence ability which is a great attractive property for a large iterative and time consuming problem [14].While, the reason why we chose DE is for its good convergence properties.It has only a few control parameters kept fixed throughout the entire evolutionary process [15].

A. Standard PSO
In PSO, the optimization process begins with a randomly created population constituted by the so called particles.Each particle contains a position vector, a velocity vector and a memory vector of its previous best position.Each member of the population is moved in the search space according to three vectors called inertia (first term), memory (second term) and cooperation (third term) as ( 7)-( 9): where, ≥0 defined as inertia weight factor.

B. Various PSO Branches
So far various PSO techniques have been developed and implemented on various parts of engineering problems.Five improved PSOs are utilized in this paper for optimal placement of DGs [11].The PSO techniques used in this paper are: Adaptive Dissipative PSO (ADPSO), Escape Velocity PSO (EVPSO), PSO with Passive Congregation (PSOPC), PSO with Area Extension (AEPSO) and Dynamic Adaptation of PSO (DAPSO) [16]- [20].Figure 1 shows the computational flow chart of the PSO algorithms.

C. Standard DE
In general, DE algorithm has five stages.Figure 2 shows structure of the algorithm [21].
import values of population size, generation, variable number.while termination criteria is satisfied { for i=1 to NP; i++ { selection three vector from population randomly; Initialization: This algorithm is a population based algorithm, for this, initial population is produced as (10) , ( ), , to start optimization process.
Dimensions of DE algorithm depend on the size of population P, and variable V, ZL MIN and ZL MAX are lower and upper boundaries, respectively, selected based on the type of problem.rand produces a value in [0,1], randomly.Mutation: The initialized population is mutated using (11).Mutation operator helps algorithm to escape from local minima.For this, three vectors are randomly selected from initial population called Z1, Z2 and Z3.Main criterion in production of mutated matrix is scaling factor, F, which is selected from [0, 2].The impact of 2 nd and 3 rd selected vectors, Z2 and Z3, in mutation process are controlled by .
Crossover: By crossover operator, prior population (parent) is composed and then produces next population (children).Crossover operator is not applied on all population, and applying criteria is Crossover Rate, CR.This parameter has a real value in [0, 1].If crossover rate is more than a random value, vectors from mutation step are selected; otherwise, selection is performed from initial population 1 , , , , , Selection: In this stage, the algorithm uses selection operator to select optimal solution.In other words, selection operator decides between initial matrix, Zi, and crossover matrix, Zji.If related solution of crossover vector, f(Zc,i G ), is less or equal to solution corresponding to initial population, f(Zi G ), crossover vector is selected which is shows in (13) , , , , where 1,..., i P  .Termination Criteria: To terminate algorithm, there are two techniques; reaching optimal solution and finishing iteration number.In optimization problem, second criterion is used.

D. D. Various DE Branches
So far various DE techniques have been developed and improved.Three improved DEs are utilized in this paper for optimal placement of distributed generations [15], [22].The DE techniques used in this paper are Self-Adaptive DE, Opposition-based DE, BSNN DE.

IV. CASE STUDY
PSO and DE Techniques have been implemented in the MATLAB software for optimal sitting and sizing of DGs and tested on two standard IEEE 33-bus and 69-bus radial distribution systems.

A. PSO Techniques, IEEE 33-bus Radial Distribution System
The first system is a radial distribution system with the total load of 3720 kW, 2300 kVar, 33 bus and 32 branches, the real power losses in the system is 210.98 kW while the reactive power losses is at 143 kVar.The optimum results for each PSO technique are obtained with population size of 30, after 30 runs and for power factor of 0.85 lagging (Table I-Table III).For single-DG placement, it was assumed that maximum DG size is less/equal to 1250 kW (Table I).As it can be seen from results in Table I, the minimum real power loss is achieved by DAPSO algorithm.The maximum real power loss reduction by DAPSO is at 39.70 % in comparison to the case without DG installation.However, this solution does not lead to the best voltage profile because the main purpose is to minimize real power loss.AEPSO, ADPSO and DAPSO are marginally same for Min. and Mean voltage values.AEPSO has the best results for voltage profile, since it propose a DG near the lowest bus voltage (bus 18).
For double and triple-DG placement it was assumed that maximum DG size is less/equal to 2000 kW (Table II).The minimum real power loss is achieved again using DAPSO algorithm which the reduction is at 54.53 % in comparison to the case without any DG installation.It is obvious that the more the DG size and DG number, the more is the benefits.Unlike single-DG placement, in this case DAPSO not only could reach the maximum real power loss reduction, but also suggests the best voltage profiles among all PSO techniques.Studying results in Table III reveals that DAPSO and ADPSO could gain better results compared to the other techniques in real power loss reduction, by reducing real power loss to 56.13 % and 55.43 %, respectively.In addition, DAPSO could improve voltage profile better than the other techniques.It should be mentioned that the size and number of DGs are very important in power loss reduction, and in particular for voltage profile improvement.Thus, to show this fact, voltage profile is depicted in Fig. 3 only for DAPSO and ADPSO as the two best techniques for three cases.From Fig. 3, it is clear that DAPSO has better results than ADPSO and the best case is blue curve.It is interesting that DAPSO in Case-II (light green curve4) has better voltage profile than ADPSO in all cases.This fact is more obvious and attractive by considering bus-18 voltage which is the lowest voltage without DG installation and experience more improvement after installing DG units than the other buses.This phenomenon is due to the fact that DAPSO could escape local minima and seek vast search space dynamically which depends on to its structure.

B. PSO Techniques, IEEE 69-bus Radial Distribution System
The second test system is the IEEE 69-bus radial distribution system with the total load of 3.80 MW and 2.69 MVar.Data for this system are as in [23].Results are furnished in Table IV which is evaluated for three DG units placement.Table IV shows the best behavior of DAPSO in results, for the larger radial distribution system, DAPSO has better results.Voltage profile is shown in Fig. 4.

C. DE Techniques, IEEE 69-bus Radial Distribution System
Due to the space limitation and huge number of results the IEEE 69-bus test system was used for DE techniques.The optimum results for each DE technique are obtained with population size of 30, after 30 runs, CR = 0.1 and for power factor of 0.85 lagging (Table V).

TABLE I .
SINGLE DG PLACEMENT RESULTS IN IEEE 33-BUS SYSTEM.

TABLE II .
DOUBLE-DG PLACEMENT RESULTS IN IEEE 33-BUS SYSTEM.

TABLE III .
TRIPLE-DG PLACEMENT RESULTS IN IEEE 33-BUS SYSTEM.

TABLE IV .
TRIPLE-DG PLACEMENT RESULTS IN IEEE 69-BUS SYSTEM.