The combined power the induction motor and the load pload

Solved Step by Step With Explanation- Power System Operation Review

Questions

Task A2 Review of power system operation Fig. 1 One-line diagram of a 3-phase power system Consider the power system shown in Fig. 1, where "G" is generator, "T1, T2, T3, T4" are transformers, "M" is induction motor and "Load" is a load. Let the total generated power be Pgen, the total system load (i.e. the combined power of the induction motor and the load) be Pload, and total power loss in the system be Ploss. Answer the following questions.

Answers

S4 = V4 * conj(I4

Where:

We can express the current I4 in terms of the voltages and impedances using Kirchhoff's current law. Assuming purely resistive line impedances, we have:

I4 = (V4 - V3) / R34 + (V4 - V5) / R45

V5: Complex voltage at Bus 5

Step 3: Simplifying the Expression for Current I4

S4 = V4 * conj((V4 - V3) / R34 + (V4 - V5) / R45)

Step 5: Simplifying the Expression for S4

Substitute the given values for Pgen, Ploss, and Pload:

S4 = 1200 kW + j300 kVAR - (20 kW + j5 kVAR) - (1400 kW + j295 kVAR) = -220 kW - j20 kVA

|V4| = sqrt(P4^2 + Q4^2) / |S4|

theta4 = atan(Q4 / P4)

Calculation process demonstrates how to use power flow equations, Kirchhoff's current law, and complex arithmetic to find the voltage at Bus 4 in a power system. The calculations involve complex power, current, and voltage, as well as assumptions about resistive line impedances. The final result is the voltage magnitude and phase angle at Bus 4, indicating the system's behavior under specified conditions.