Distribution system and power quality

Cal Poly Pomona ECE 5750 Distribution system and power quality – Instructor Dr. Ha Thu Le

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California State Polytechnic University Pomona Department of Electrical and Computer Engineering

ECE 5750 Distribution system and power quality – Spring 2020

Homework 4 Distribution feeder analysis

Problem 1 Consider the feeder in the following figure.

The substation transformer is connected to an infinite bus. The infinite bus voltages (i.e. the substation primary voltages) are balanced and being held at 69 kV for all power-flow problems. The substation transformer ratings are:

5000 kVA, 69 kV delta – 13.8 kV grounded Y, Z = 1.7 + j8.5 %

The phase impedance matrix for a four-wire wye line between Node 2-3 is

The four-wire wye feeder between Node 2-3 is 0.75 miles long. An unbalanced wye-connected load is located at node 3 and has the following values:

Phase a: 650 kVA at 0.85 lagging power factor Phase b: 500 kVA at 0.90 lagging power factor Phase c: 950 kVA at 0.95 lagging power factor

Assuming that the regulators are in the neutral position:

Cal Poly Pomona ECE 5750 Distribution system and power quality – Instructor Dr. Ha Thu Le

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1) Determine the forward and backward sweep matrices for the substation transformer and the line segment.

2) Use the modified ladder technique to determine the line-to-ground voltages at all nodes. Use a tolerance of 0.0001 per unit.

3) Calculate all node voltages in actual values in volts and on a 120-V base. Problem 2 Three type B step-voltage regulators are installed in a wye connection at the substation in order to hold the load voltages (node 3) at a voltage level of 121 V and a bandwidth of 2 V.

1) Compute the actual equivalent line impedance between nodes 2 and 3.

2) Determine a potential transformer ratio and current transformer ratio given that the compensator circuit ratings are 120V and 5A. Determine the R and X compensator settings calibrated in volts and Ohms. The settings must be the same for all three regulators.

3) For the load conditions of Problem 1 with the regulators in the neutral position, compute the voltages across the voltage relays in the compensator circuits.

4) Determine the appropriate tap settings for the three regulators to hold the node 3 voltages at 121 V in a bandwidth of 2 V.

5) With the regulators taps set, compute the actual load voltages in volts and in per unit.