# Table 3 Optimum sizing of DGs and shunt capacitors for 51-bus system

Sensitivity analysis [22]Simultaneous optimization-based method
With upf DGs and shunt capacitorsWith 0.95 lag pf DGs OnlyWith 0.95 lag pf DGs and shunt capacitorsWith upf DGs and shunt capacitorsWith 0.95 lag pf DGs onlyWith 0.95 lag pf DGs and shunt capacitors
$${\text{P}}_{{{\text{DG}}_{ 1 6} }}$$ = 206.45$${\text{P}}_{{{\text{DG}}_{ 1 6} }}$$ = 206.45
$${\text{Q}}_{{{\text{DG}}_{ 1 6} }}$$ = 67.86
$${\text{P}}_{{{\text{DG}}_{ 1 6} }}$$ = 189.09
$${\text{Q}}_{{{\text{DG}}_{ 1 6} }}$$ = 62.15
$${\text{P}}_{{{\text{DG}}_{ 1 1} }}$$ = 488.14$${\text{P}}_{{{\text{DG}}_{ 1 4} }}$$ = 492.00
$${\text{Q}}_{{{\text{DG}}_{ 1 4} }}$$ = 161.72
$${\text{P}}_{{{\text{DG}}_{ 6} }}$$ = 490.67
$${\text{Q}}_{{{\text{DG}}_{ 6} }}$$ = 161.28
$${\text{P}}_{{{\text{DG}}_{ 1 5} }}$$ = 486.21$${\text{P}}_{{{\text{DG}}_{ 1 5} }}$$ = 486.21
$${\text{Q}}_{{{\text{DG}}_{ 1 5} }}$$ = 159.82
$${\text{P}}_{{{\text{DG}}_{ 1 5} }}$$ = 490.07
$${\text{Q}}_{{{\text{DG}}_{ 1 5} }}$$ = 161.09
$${\text{P}}_{{{\text{DG}}_{ 4 1} }}$$ = 490.07$${\text{P}}_{{{\text{DG}}_{ 4 8} }}$$ = 482.35
$${\text{Q}}_{{{\text{DG}}_{ 4 8} }}$$ = 158.55
$${\text{P}}_{{{\text{DG}}_{ 4 4} }}$$ = 488.74
$${\text{Q}}_{{{\text{DG}}_{ 4 4} }}$$ = 160.65
$${\text{P}}_{{{\text{DG}}_{ 4 5} }}$$ = 492.0$${\text{P}}_{{{\text{DG}}_{ 4 5} }}$$ = 492.00
$${\text{Q}}_{{{\text{DG}}_{ 4 5} }}$$ = 161.72
$${\text{P}}_{{{\text{DG}}_{ 4 5} }}$$ = 490.07
$${\text{Q}}_{{{\text{DG}}_{ 4 5} }}$$ = 161.09
$${\text{P}}_{{{\text{DG}}_{ 4 6} }}$$ = 484.28$${\text{P}}_{{{\text{DG}}_{ 4 2} }}$$ = 490.07
$${\text{Q}}_{{{\text{DG}}_{ 4 2} }}$$ = 161.09
$${\text{P}}_{{{\text{DG}}_{ 1 3} }}$$ = 488.01
$${\text{Q}}_{{{\text{DG}}_{ 1 3} }}$$ = 160.41
$${\text{QC}}_{ 1 5}$$ = 225.0$${\text{QC}}_{ 1 5}$$ = 125.0$${\text{QC}}_{ 1 3}$$ = 300.0$${\text{QC}}_{ 2 6}$$ = 200.00
$${\text{QC}}_{ 1 6}$$ = 150.0$${\text{QC}}_{ 1 6}$$ = 25.00$${\text{QC}}_{ 4 8}$$ = 300.0$${\text{QC}}_{ 4 1}$$ = 125.00
$${\text{QC}}_{ 1 4}$$ = 300.0$${\text{QC}}_{ 1 4}$$ = 300.0$${\text{QC}}_{ 4 1}$$ = 300.0$${\text{QC}}_{ 1 1}$$ = 250..00