ELEC3575

Electric Power Systems

Coursework 2, December 2024

Software/Calculator instructions:

· You are allowed to use MATLAB, calculator or a computer calculator in this assessment.

Dictionary instructions:

· You are allowed to use your own dictionary in this assessment and/or the Spell Checker facility on your computer. You are not marked on spelling, punctuation or grammar in this assessment.

Assessment Information:

· There are 9 pages and 16 questions to this online assessment.

· You will have 7 days to complete the assessment.

· You are recommended to take a maximum of 5 hours within the time available to complete the assessment.

· This assessment is worth 70% of the overall module mark.

· The deadline for submission of your assessment is 14:00, UK time, 13/12/2024.

· Please submit your assessment to the ‘Submit Your Work’ area in the module’s Minerva page.

· Please include your Student Identification Number (SID) in the title of your submission.

· Please include your Student ID Number and the Module Code at the top of each page of your submission.

· If there is anything that needs clarification or you have any problems, please email [email protected] and copy in [email protected] and we will respond to you as quickly as possible within normal working hours UK time (9:00-17:00 hours, Monday-Friday).

· You must not discuss or share the content of or answers to this assessment, with any fellow students, any staff or other contacts outside the school or the University’s professional services. School contacts available to you will be detailed in the bullet point above.

Submission instructions:

· You must submit your assignment no later than the submission deadline of 14:00, UK time, 13 of December 2024.

· Your work should be submitted using the Turnitin link within the Minerva Module Page.

· You should receive an e-mail receipt from the Turnitin system to confirm that your work has been properly submitted.

This coursework has three main parts (Parts A, B and C) and a total of 16 Questions. You will need to carry out Tasks A1-A6 for answering Questions 1-5. Tasks B1-B4 must be carried out for answering Questions 6-10. These tasks are just enabling steps you need to take and there is no need for you to show or explain how you conducted the tasks. Question 11-16 are fundamental questions aimed at assessing what you have learned in ELEC3575 about electric power systems. You must submit your answers to Questions 1-16 in one single document via the link provided on the module’s Minerva page.

In summary, what you are expected to do for this coursework is:

Part A: Run AC power flow on a power system modelled in MATLAB/Simulink and discuss the results. Answer Questions 1-5.

Part B: Perform. DC power flow on this power system in MATLAB/M-file and compare the results with the AC power flow results. Answer Questions 6-10.

Part C: Answer some fundamental questions (Questions 11-16) about electric power systems based on what we have discussed in the lectures, screencasts and the handouts given to you.

Important: You have the option of not running AC and DC power flow studies yourself, in which case you must use the power flow results and network data provided in the "NoPowerFlow.doc" document. However, this option will result in a loss of 26 marks, as you will not be able to answer Questions 3, 4, 9, and 10, which require additional power flow studies. Please write N/A in front of these questions in your solution sheets, if you choose this option.

Preamble: In this coursework, the active power of load at bus 1 depends on your student ID number. In Parts A and B, P_L1 is set to be 40+XX/5 where XX are the last two digits of your student ID number. You should round the value of P_L1 to the

Your own P_L1 value: P_L1=40+XX/5=

closest integer number.

For example, if your student ID number is 200123065, you must use the following P_L1 value to attempt this exam:

P_L1= 40+XX/5= 53 MW (rounded to the closest integer)

Part A: AC Power Flow

For Part A you have two options. You can run an AC power flow on the power system shown in Figure 1 (as per Tasks A1-A7) and answer Questions 1-5.

Otherwise, you may decide to use the results provided in "NoPowerFlow.doc". If you choose this option, you must mention this at the beginning of your solution sheet and enter N/A in front of Questions 3 and 4, as you will not be able to answer these questions without running the power flow of your own.

Tasks A1-A7 and Questions 1-5

Task A1: Download the “ELEC3575_Power_Systems_Coursework2.slx” file from Minerva and save it on your local PC.

Task A2: You can read Power Flow-Matlab.docx document provided on how to open/run the file using an installed or online MATLAB. Then find “MATLAB” in the program manager of Windows and start it (or use the online version as explained).

Task A3: Open the downloaded “.slx” file with MATLAB.

Task A4: Now you should see a network in the Simulink workspace. The network represents the 110-kV system shown in Figure 1.

Task A5: Double click on the lines to check if they are set with the parameters listed in Table 1.

Task A6: Ensure the demand and generation at all buses match those listed in Table 2. You must replace the active power of load at bus 1 with P_L1 you calculated based on your student ID. In the opened dialogue box, you may check the bus type in tab “load flow”.

Figure 1. 110 kV power system under study.

Figure 2. Simulink schematic of the power system under study.

Table 1: Line characteristics.

Line	Length [km]	Resistance (R′) [Ω/km]	Inductance (L′) [mH/km]	Capacitance (C′) [µF/km]
Line 1-2	160	0.016	1.30	0.009
Line 1-3	150
Line 1-4	100
Line 2-3	110
Line 3-4	75

Table 2: Load and generation data.

Bus No.	Load		Generation	Bus Type
	P (MW)	Q (MVAR)	P (MW)
1	PL1*	18	**	Slack bus
2	90	20	120 ***	PV
3	40	18	0	PQ
4	40	10	0	PQ

* The value of P_L1 is student specific and is calculated as explained in the Preamble section on page 2.

** Note that the exact amount of P for the slack generator is determined by AC power flow.

*** Bus 2 is a PV bus, and the generator at that bus is set to maintain the voltage of bus 2 at 0.98 pu (V₂= 0.98 pu).

Task A7: To run a load flow for the system, double-click on the box “powergui” and then go into tab “Apps” and select “Load Flow Alalyzer”. A window for the power flow results will pop-up, then click on the button “Compute”. The power flow results are shown in the last five columns of the window, similar to what you can see in Figure 3.

Figure 3. Sample power flow results shown in the dialogue box.

Note: Sample results shown in Figure 3 are inaccurate and are used to give you an idea of what to expect to achieve after running Task A7.

Questions 1-5 (26 Marks Overall)

Question 1 State what your own P_L1 is and check if the voltage magnitudes at different buses are within the acceptable range (i.e., 5% of the nominal voltage).   [4 marks]

Question 2 Manually calculate the active and reactive power flows through each line in MW/MVar. As you know, the power flows from the sending- and receiving- end of each line are not necessarily identical and are to be calculated and reported.

We model each transmission line simply by a series reactance. In this way, the active/reactive power flow from bus i to bus j can be approximated by

where Vi is the voltage phasor of bus i in kV, Xij is the reactance of the line connecting bus i to bus j in Ohms.

To calculate these, you may import the required data into an m-file and calculate active and reactive power transferred through each line using a code you write. Note that you will need these power flows through lines for comparison studies later in Question 8.   [5 marks]

Question 3 What is the sum of the active powers generated by G1 and G2 and is this sum greater than, equal to or smaller than the sum of active powers consumed by the loads? Explain what this difference implies. [4 marks]

Question 4 Double-click on generator G2, go into the tab “load flow”. Set the “Active power generation P(W)” to 150 MW (i.e. 150e6). Run a load flow and evaluate the load flow results. Why have the generated active and reactive power by G1 (as well as the reactive power by G2) also changed? [7 marks]

Question 5 Based on our discussion in ELEC3575, name two options as the initial guess for solving the AC power flow problem using iterative methods such as Newton-Raphson. Based on what we have discussed in the lectures, explain why these options can be considered appropriate.  [6 marks]

Part B: DC Power Flow

For this part, you must use the data listed in Tables 1 and 2. You are recommended to write an m-file code for DC power flow calculations. Please reset the load and generation values to match those in Table 2. Note that you have modified the generation of G2 in Question 4, so make sure to revert that change in particular.

Otherwise, you may decide to use the results provided in "NoPowerFlow.doc". If you choose this option, you must mention this at the beginning of your solution sheet and enter N/A in front of Questions 9 and 10, as you will not be able to answer these questions without running the power flow of your own.

Tasks B1-B5 and Questions 6-10

For your convenience, the line parameters are already saved in a matrix named “Line_Data.mat”. You are supposed to add your code to this m-file such that it does the DC power flow calculations on the power system under study. Your m-file must contain the sections as explained in Task B1 to Task B4.

Task B1: Calculate the line reactance in Ohms. Ignore R′ and C′, and G′ of the lines and compute the series reactance of the line considering their “length”, per unit length “inductance”, and the system nominal frequency (50 Hz).

Task B2: Calculate the line reactance in pu. Use a base voltage (110 kV) and a base apparent power (100 MVA) to calculate the base impedance, then convert the line reactances to their per-unit values.

Task B3: Form. the nodal admittance matrix including all transmission lines. You may find useful guidance in the lecture notes about this. Eliminate the row and column corresponding to bus 1.

Task B4: Form. the vector of net active power injections. The required data are included in Table 2. Do not forget to convert Active Power generations to per-unit values. Do not forget that you need to eliminate the reference bus from this vector.

Questions 6-10 (32 Marks Overall)

Question 6 Manually calculate the phase angles of all buses.

Hint: You should do this by multiplying the inverse of the reduced nodal admittance matrix by the vector of net active power injections (. Note that phase angles calculated from this will be in radians.  [6 marks]

Question 7 Using the formulas below, calculate the active power flows through the lines (from sending end and receiving ends of each line).

Hint: The active power flow from bus i to bus j can be approximated as follows in DC power flow calculations:

where is the voltage phase angle at bus i in radians, and Xij is the reactance of the line connecting bus i to bus j in Ohms.   [5 marks]

Question 8 Compare the DC power flow result with that of AC power flow. You need to compare voltage phase angles of all buses and the active power flow of all lines obtained by DC power flow with your findings in Part A (AC power flow results). Explain the reason for their difference. Which one is more reliable, and why?   [6 marks]

Question 9 Double click on load L3 at bus 3 and set its “Inductive reactive power QL” to 100 MVAR (i.e. 100e6). Then, run an AC power flow and examine whether the power calculation converges. Does DC power flow calculation change for this new condition?  Compare DC power flow result with that of AC power flow. Is DC power flow still accurate and acceptable? Why?   [7 marks]

Question 10 Double click on load L3 at bus 3 and set its “Inductive reactive power QL” to 200 MVAR (i.e. 200e6). Then, run an AC power flow. Does the power calculation converge? Can you rely on DC power flow results in this case? Why?

Hint: You will need to use the concept of P-V curves to justify your answer to the “why” part of this question.   [8 marks]

Part C: Fundamental Questions

Questions 11-16 (42 Marks Overall)

Question 11 Based on our discussions in ELEC3575, explain the main advantage of using the per-unit system when it comes to power transformers. Is achieving this advantage conditional or always guaranteed? Explain why. [6 marks]

Question 12 Explain the “N-1” security criterion. Detail how you can check the N-1 security criterion for the power system shown in Figure 1, based on the assumptions we made in ELEC3575 regarding power systems. To this end, you need to state what study is required to be carried out and for how many times. Which variables will you need to check every time this study is performed? [6 marks]

Question 13 Based on the discussions we have had over the course of ELEC3575, why should the base power in the per-unit system be maintained constant in the entire system irrespective of the voltage level? [6 marks]

Question 14 Based on the discussions we have had over the course of ELEC3575, what is the main difference between the power flow study and solving a large linear circuit with lumped elements? [6 marks]

Question 15 Discuss how operating the system closer to its boundaries (e.g. steady-state stability margin and permissible voltage limits) will affect the accuracy of DC power flow. [9 marks]

Question 16 Assume that the DC power flow has been carried out for a power system (with several lines and buses) where bus 1 is taken as the slack bus. Using the solution of the DC power flow, parametrically calculate the reactive power at the sending-end and receiving-end of the line connecting bus k and bus m in this system and see what conclusion can be drawn. The line connecting these two buses is simply modelled by the series reactance X_km. [9 marks]