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5CCE2ECM 2022/2023 - Assignment 2

The assignment consists of two parts, for a total of eight (8) questions, labelled Q1 to Q8. Each question is worth 10 marks. 20 marks will be assigned based on report quality and formatting (i.e. numbering of the answers, order of the answers, quality of the graphs etc). Please ensure to include your name and ID in the report.

The page limit for the submission is five (5) pages. You don’t need to include a cover page, but if choose to add it, it will be counted in the total number of pages. If you exceed the page limit, the report will be marked as zero, even if the results are correct. This is to ensure that answers are to the points and graphs are well-formatted.

Answers should be provided with up to four (4) significant digits. It is expected that results may be slightly different between students due to rounding errors and blocks used for the calculations, and this will be taken into account when assessing the report.

You do not need to include the Simulink files in your submission, but you are required to keep the Simulink files as you may be asked to provide them upon request.

Part A

Consider the three-phase system shown in Figure 1. The line parameters are given below: Vs = 660 V, fs = 50 Hz (set all other parameters so that the source is close to ideal) Transmission line parameters: Z = 0.18 + j10 Ω

Load parameters (series load): P = 20 kW; Q = +15 kvar (all other parameters are set based on the system rated voltage and current)

Figure 1: Equivalent circuit for Part A.

Answer the questions below:

Q1: Calculate the theoretical current (in phasor form) absorbed by the load, and the load power factor. Show all steps and equations used.

[10 marks]

Q2: Verify the answers above in Simulink: plot the three-phase load current (measured at P2) and the load power factor as functions of time, and comment on the similarity with the Simulink results. Ensure that the amplitudes and labels are visible.

[10 marks]

Q3: Plot the three-phase voltage at the load terminal (P2) and compare it to the theoretical value.

[10 marks]

Q4: Calculate the theoretical line losses (using the current value you obtained in Q1). Calculate the line losses in Simulink and plot the losses as function of time. Comment on the difference between the two results. Explain how the difference in the power loss can be correlated to the difference between the theoretical and the actual current amplitude.

[10 marks]

Part B

Now, consider the modified system shown in Figure 2. The transformer primary and secondary voltages and winding connections are given below (set the remaining transformer parameters so that the transformer is close to ideal):

Transformer 1: V1 = 660 V, V2 = 33 kV; Connection: Yg-D1 Transformer 2: V1 = 33 kV, V1 = 660 V; Connection: D1-Yg

Figure 2: Equivalent circuit for Part B.

Build the model in Simulink, keeping all other components the same as in Part A. Using this new model, answer the questions below.

Q5: Plot the following graphs at the load terminal (i.e. P2): current, voltage and power factor. Comment on the difference between the simulation results here and the results in Part A. Explain the difference.

[10 marks]

Q6: Plot the current in the line. From the line current, calculate the line losses. Explain the difference between these results to those in Part A.

[10 marks]

Q7: Connect a capacitor bank in parallel to the load, with the aim of obtaining a unity power factor at point P2. Calculate the theoretical value of the capacitance (you can choose if the capacitor bank is wye- or delta- connected)

[10 marks]

Q8: Measure the voltages at P1 and P3 and the voltages at P2 and P4 after connecting the capacitor, and verify the transformer ratio. Show your calculations (you don’t need to include graphs for this question, but only the measurement results).

[10 marks]