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. First part explained the various objective functions. 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)