MCQ+2 / -0.67MediumPower Flow EquationsPer-Unit System & Load FlowPower Systems
Power Systems → Per-Unit System & Load Flow → Power Flow Equations
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Question
Consider the two bus power system network with given loads as shown in the figure. All the values shown in the figure are in per unit. The reactive power supplied by generator G1 and G2 are QG1 and QG2 respectively. The per unit values of QG1,QG2, and line reactive power loss (Qloss) respectively are
Correct answer
(C) 6.34, 11.34, 2.68
Solution
1.Real Power Balance:
Net real power at Bus 1: P1=PG1−PL1=20−15=5 pu. Net real power at Bus 2: P2=PG2−PL2=15−20=−5 pu. The real power flow from Bus 1 to Bus 2 is: P12=X∣V1∣∣V2∣sin(δ1−δ2)=0.11×1sinδ=10sinδ Since P1=5, we have 10sinδ=5⟹sinδ=0.5⟹δ=30∘.
2.Reactive Power Flow:
Reactive power flow from Bus 1 to Bus 2: Q12=X∣V1∣2−X∣V1∣∣V2∣cosδ=0.112−0.11×1cos30∘=10(1−0.866)=1.34 pu. Reactive power flow from Bus 2 to Bus 1: Q21=X∣V2∣2−X∣V1∣∣V2∣cos(−δ)=0.112−0.11×1cos30∘=1.34 pu.
3.Reactive Power Loss:
Qloss=Q12+Q21=1.34+1.34=2.68 pu.
4.Generator Reactive Power:
At Bus 1: QG1−QL1=Q12⟹QG1−5=1.34⟹QG1=6.34 pu. At Bus 2: QG2−QL2=Q21⟹QG2−10=1.34⟹QG2=11.34 pu.The values are QG1=6.34,QG2=11.34,Qloss=2.68. Option (C) is correct.
