(i) The bus voltages of the distribution networks at any time instant must be within the minimum (Vmin) and maximum (Vmax) voltage level as in(1.24)The placement of RDGs and the shunt capacitors may increase the bus voltage beyond the limit at low voltage level and decrease the bus voltage at high load level. Therefore, bus voltages are kept within the prescribed limit by introducing the penalty function defined as(1.25)

       (ii) The active and reactive power generation of the DGs should be within the specified limit given as(1.26)where are the minimum and the maximum limit of the active power injection of the DGs and are the minimum and the maximum limit of the reactive power injection of the DGs which are to be maintained at any time instant. These inequalities are maintained by introducing the penalty function as below(1.27)

       (iii) The total active and reactive power injections by the RDGs and shunt capacitors at any time instant should be less than the total active and reactive power load demand of the distribution network at the same instant. This inequality constraint is defined as(1.28)These inequality constraints are considered by introducing the two penalty functions as(1.29)

       (iv) Branch currents, after the placement of DGs and shunt capacitors, should be within the maximum allowable level to maintain the feeder thermal limit. The branch current limit should be(1.30)This limit is considered in the objective function with the help of a penalty function described as(1.31)After considering all the penalty functions, the objective function, to be minimized, is(1.32)The values of the penalty factors τfeed are to be selected as very high value for a minimization problem. In this book chapter, the penalty values are selected as 1016 [68]. If any of the inequality constraints violates then the corresponding penalty function adds a very high value to the objective function.