Impact of Grey wolf optimization and modify Grey Wolf optimization on power flow have been presented [17

Impact of Grey wolf optimization and modify Grey Wolf optimization on power flow have been presented 17, 18, and 19. Moth swarm algorithm has been presented for optimum power flow 20, and 21.
Effect of DG and capacitor; Hybrid configuration of the weight improved particle swarm optimization (WIPSO) algorithm and gravitational search algorithm (GSA) called the hybrid WIPSO–GSA algorithm has been used for obtained the optimal DG and capacitor location and size considering the reduction of the total apparent power loss 22. Modified version of the teaching–learning-based optimization technique has been provided to optimize the optimal allocation of DG and capacitor considering minimization active power loss and maximizing network reliability 23. Genetic algorithm and Artificial Bee colony algorithm is used to obtained the optimal placement of capacitor and DG considering total power losses minimization 24. Genetic moth swarm algorithm (GMSA) is hybrid approach based on the genetic algorithm (GA) and moth swarm algorithm (MSA) used for reduction the electrical power loss by integrating DG and capacitor 25. New optimization algorithms, named intersect mutation differential evolution (IMDE) is presented to determine the optimally locate and the size of DGs and capacitors in distribution networks considering minimization of the power loss 26.
In this paper, the feasibility of WOA technique for the DG and capacitor optimal allocation problem is evaluated and its performance is compared with other algorithms that considering reduction of network power losses, voltage deviation, and total operating cost.
This paper is organized as follows: Section II present the formulation of the problem includes objective functions and constrains. The optimization algorithm is described in section III. The cases study and simulation results are described in section IV. Finally, the paper concludes in Section V.
The optimum placement and size of new energy sources and capacitor have been obtained by using WOA technique considering minimization of single and multi-objective (network power losses, total operating cost, and voltage deviation). This section contains two parts.
The various objective functions are explained in first part. The constraints are explained in second part.
Objective Functions
Single objective function
Minimization of power losses :
Minimizing the total electrical power losses of distribution network is an important goal from integrating DGS and capacitor, which can be formulated as follows, 27.
P_loss=?_(j=1)^nbr??(P_gnj-P_dnj-V_mj V_nj Y_nj cos??(?_(mj -) ? ?_(nj +) ?_nj )????
Minimization of voltage deviation
The voltage deviation is minimized after the integration of DG and C, which is formulated as follows, 28:
VD=?_nj^nb?(V_ni-V_rated ) (2)
Minimization of total operating cost
The total operating cost of DGs includes the cost of power supplied from the substation, which can be reduced by reducing the total power loss in the network, and the cost of real power provided by the installed DG, which is reduced by reducing the amount of real power drawn from DG. The total operating cost can be expressed as 29.
TOC=(c1P_loss )+(c2.P_DG ) (3)
multiple objective function
Minimization of total power losses, total operating cost, and voltage deviation.
Multi objective WOA algorithm is formulated with three different objective functions and is solved as a minimization problem using weighted sum method. Total network power losses, total operating cost, and voltage deviation cost are the three objectives function, which can be expressed as 15.
min?(F)=min?(?_1 ??pl?_DG+?_2 ?V_DEV+?_3 ?TOC) (4)
?pl_DG,?V_DEV,and ?TOC Value can be calculated as follows:
??pl?_DG=p_(DG,T loss)/p_(T loss) (5)
?V_DEV=max?((v_1-v_i)/v_1 ) ? i?{1,2,…,bus number} (6)
?TOC=TOC/(c_2 ?pt?_DG^max ) (7)
The optimal allocation of DG in distribution system is need to satisfy all of the operational constraints such as the limitation of active and reactive power generated, limitation of bus voltages, capacitor reactive power constraint.
Generation constraints: For stable operation, real and reactive powers supplied by DG are restricted by the lower and upper limits as follows 27:
? P?_gni^min?P_gni?P_gni^max (8)
? Q?_gni^min?Q_gni?Q_gni^max (9)
Voltage Constraint: the constraints of load buses voltage magnitudes to be restricted within their limits as follows 27:
V_i^min?V_i?V_i^max (10)
Parallel capacitor Constraint: The capacitance size at the buses should not be beyond the allowable constraint 27.
?_(i=1)^nc?Q_cni ?Q_t (7)
The mathematical model for each proposed optimization algorithm namely, Whale Optimization Algorithm (WOA) explained in this section.
Whale Optimization Algorithm
Bubble-net feeding method is the behavior of humpback whales during hunting process; this behavior is introduced by the WOA algorithm. The humpback whale went fell in water about 10-15 meter and began to produce bubbles in the spiral shape that encircled the prey and then followed the bubbles and moved up to the surface 30, 31.
The steps involved in the optimization algorithmic of the particle swarm are as follows;
Start algorithm.
read system data(bus and branch data) and define the upper and lower bounds of the variables(location and size of DG and bus voltage)
Generate the initial population for each whales (a, A, C, I, p) randomly.
Calculate fitness of objective function for each search agent(P loss*, a, A, C, l, and p)
If p


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