# 7308ELEM Power Systems Modelling and Analysis

Date: May 2022
Time Allowed: 3 Hours
Instructions to candidates:
This paper consists of a single part. Answer all four (4) questions.
Each question carries the same total mark.
The majority of marks are awarded for method and so all calculation steps should be shown.

Reminder of exam regulations:
Any form of communication with other candidates is strictly prohibited.
The following materials are provided: N/A
Examiners: Emil Levi and Martin Jones

Q1. A load of 5 MW, with power factor 0.6 lagging, is supplied at the voltage level of 6.3 kV. The transmission line between the point of common
coupling (PCC) and the load connection point is 50 km long, with parameters r = 0.012 Ω/km and x = 0.03 Ω/km. Power factor of the load is further improved to 0.98 (leading) by adding the reactive power compensator at the load connection point.
a) Determine the parallel constant impedance representation of the load at the PCC before and after reactive power compensation. [5 marks]
b) Calculate the impedance drop, voltage drop and voltage regulation at the load connection point before power factor compensation. Draw the corresponding phasor diagram. [10 marks]
c) Determine the impedance drop, voltage drop and voltage regulation after power factor correction. Draw the corresponding phasor diagram. [10 marks]

Q2. The reactances xd and xq of a salient pole synchronous generator are 1 per unit and 0.6 per unit, respectively. Resistance can be neglected. The generator delivers rated apparent power at 0.9 power factor lagging, at rated terminal voltage.
a) Compute the induced emf and the load angle, and draw the phasor diagram for the specified operating conditions. [10 marks]
b) Find the maximum active power that the generator can deliver with this excitation, as well as the corresponding load angle. [10 marks]
c) Sketch the power/load angle characteristic of the generator and label the two operating points analysed in parts a) and b). [5 marks]

Q3. A 180 km three-phase line has the following parameters R =10 Ω, X = 40 Ω, B = 2×10-3 S. At the receiving end the voltage is 100 kV and the load is 18 MVA at 0.85 lagging power factor. The sending end voltage is constant for all operating conditions. Using nominal Tcircuit representation calculate:
a) A, B, C, D constants of the line and the sending end voltage. [12 marks]
b) The sending end current, voltage, power factor and efficiency of transmission. [8 marks]
c) Determine the voltage drop and voltage regulation. [5 marks]

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