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DEPARTMENT OF ELECTRONIC, ELECTRICAL AND SYSTEMS ENGINEERING

MSc in Electrical Power Systems

Power System Operation and Control: 2nd Assignment

Small-signal stability of a single-machine infinite bus system

Introduction: This assignment tests the student’s ability of carrying out small-signal stability analysis of single-machine infinite bus system.

Consider a single-machine infinite bus system shown in Fig.1. The total generating capacity is 2220MVA and the rated LT bus voltage and frequency are 24kV and 60Hz, respectively. The network reactance shown in the figure are in per unit on 2220MVA, 24kV bases (refer to the LT side of the step-up transformer). Resistances are neglected.

The small-signal stability of the system at the steady state condition following the loss of circuit 2 needs to be analysed. The post fault system condition in per unit on the 2220MVA, 24kV base is:

P = 0.9     Q  = 0.3 (overexcited)     Et  =  1.0∠360            Eb  = 0.995∠00

The generators are to be modelled as a single equivalent generator represented by the classical model with the following parameters expressed in per unit on 2220MVA, 24kV base:

xd(′)  = 0.21                               H  = 4.0 MW ∙ S/MVA

(1) Draw  the  equivalent  circuit  model  representing  the  post  fault  steady  state condition with all parameters expressed in per unit on 2220MVA base.

(2) Write  the  linearized  equations  of  the  post  fault  system.  Using  MATLAB programme to determine the eigenvalues, damped frequency of oscillation in Hz, damping ratio and undamped natural frequency for each of the following values of damping coefficient:

(i)KD  = 0                          (ii)KD  = −10                       (iii)KD  = 10

(3) Plot the change of eigenvalues as the damping coefficient KD  value changes from -10 to 10 using MATLAB.

(4) For the case with KD   =  10, plot the change of eigenvalues as H changes from 2 to 10  MW ∙ S/MVA using MATLAB.

Fig. 1 SMIB system

Report Structure: Based on the above assignment, you are asked to prepare a report of around 15 pages including the following sections:

1. Cover page (Please use the cover page template available on Canvas)

2. Table of content

3. Introduction

4. Theory on small-signal stability analysis (necessary equations and diagrams);

5. Results and Discussions

5. Conclusions

6. References (IEEE format should be used)

7. Appendix

IEEE reference format:

https://www.ieee-pes.org/part-4-preparation-of-a-formatted-technical-work-for-the- ieee-power-energy-society

Report Layout: Page numbers should be inserted at the bottom centre of each page except the cover page. Report should be typed on A4 paper, spaced 1.5 with margins as follows: Top-2.54cm, bottom-2.54cm, left-2.54cm, right-2.54cm. Font size of 11 or 12 can be used.

Report Writing: The style of writing should be formal and precise with no more words than needed to make the meaning clear. Every statement must be justified, and nothing that is written should be vague.  Tables and diagrams should be used wherever appropriate. A specific point that must be made is that the report should be written in the third person. For example, ‘this was carried out’ should be used rather than ‘I did this’ .

MATLAB code: MATLAB code should be put in a separate *.m file where necessary comments in your computer code to explain your calculations should be included.

Marking Criteria: The following is the marking criteria for this assignment:

(1) Introduction - a general description of the problem to be solved (10%).

(2) Methodology – how the problems are solved (20%).

(3) Results and discussion & MATLAB code (40%).

(4) Conclusions (10%).

(5) Use of references (5%)

(6) Overall report quality and structure (15%)

Note: English Language Proficiency

Pass and above:

The work is written / spoken to an acceptable standard of English

Spelling, punctuation, vocabulary, sentence construction, and textual coherence is of an acceptable standard.

Fail:

Poor standard of written / spoken English, making it difficult to understand the points being made.

Weaknesses of writing / speaking are so frequent or serious that they impede communication.

Statement for Use of Generative AI in the coursework

Please put the following Statement between the Conclusion part and References part:

“I do not use generative AI tools such as ChatGPT (or any equivalent alternative) in the preparation of the submission. ”

or

“I have used generative AI tools such as ChatGPT (or any equivalent alternative) in the preparation of the submission. ”

If you have used generative AI, the use of generative AI  should be referenced using an appropriate method such as suggested in this example: https://apastyle.apa.org/blog/how-to- cite-chatgpt