A power system consists of 4 buses. Bus 1 is the Slack bus with voltage 1.04 pu.

ID: 1715811 • Letter: A

Question

A power system consists of 4 buses. Bus 1 is the Slack bus with voltage 1.04 pu. The bus admittance matrix of the system is as follows:

41.2670 -86.5983i -20.0000 +40.0000i -5.8824 +23.5294i -15.3846 +23.0769i

-20.0000 +40.0000i 33.3333 -66.6602i 0.0000 + 0.0000i -13.3333 +26.6667i

-5.8824 +23.5294i 0.0000 + 0.0000i 6.2822 -43.5204i -0.3998 +19.9920i

-15.3846 +23.0769i -13.3333 +26.6667i -0.3998 +19.9920i 29.1178-69.7261i

After the power flow, system voltages are found to be as follows:

V1 = 1.04 pu

V2 = 0.9435 pu with angle -3.5568 degrees

V3 = 0.9585 pu with -6.2345 degrees

V4 = 1.0200 pu with angle -2.2396 degrees

Find the active and reactive power injected by the Slack bus to the system (There is no load connected to the Slack bus).

Power Injected by the slack bus to the system= (Voltage of the slack bus)*(Conjugate of Current injected to the slack bus)

so Total current I injected into the slack bus= sum of curents in all shunt branches connected to bus 2 3 4

i.e. I= I12 ( cureent between slack bus and second bus)+I13+ I14+I11

I= Y11V1+ (V1-V2)Y12+ (V1-V3)*Y13+(V1-V4)*Y14

Solve the current by putting the values.

then calculate V1* (conjugate of I)

YOu will get the total active andreactive powerinjected by slack bus into the system

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