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

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**Power System Operation and Control: 2 ^{nd} Assignment **

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__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 r__a__ted LT bus voltage and frequency are 24kV and

额定电压

60Hz, respectively. The network reactance shown in the figure are in per unit on

电抗

2220MVA, 24kV bases (refer to the LT side of the step-up transformer). Resistances

^{⼭}端 升压变压__器__

are neglected. 标⺓值基准 : 2220MVA , 24kV

稳态

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

故障__后__系统状况

2220MVA, 24kV base is:

𝑃 = 0.9 𝑄 = 0.3 (𝑜𝑣𝑒𝑟𝑒𝑥𝑐𝑖𝑡𝑒𝑑) 𝐸_{𝑡 }= 1.0∠36^{0} 𝐸_{𝐵 }= 0.995∠0^{0}

单⽵效发电机

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:

𝑋_{𝑑}^{′ }= 0.2 𝐻 = 3.5𝑀𝑊 ∙ 𝑠/𝑀𝑉𝐴

可效电路^{模型} 故障后稳态条件

(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

故障后系统的线性化⽅程 programme to determine the eigenvalues, damped frequency of oscillation in

特征值 振荡阻尼频率

Hz, damping ratio and undamped natural frequency for each of the following

_{阻}尼_{⽐}_{ }⽆阻尼固有频率 values of damping coefficient:

阻尼系数

(𝑖)𝐾_{𝐷 }= 0 (𝑖𝑖)𝐾_{𝐷 }= −10 (𝑖𝑖𝑖)𝐾_{𝐷 }= 10

- Plot the change of eigenvalues as the damping coefficient 𝐾
_{𝐷}changes from -10 to 10 using MATLAB.

1 0 10

- For the case with 𝐾
_{𝐷 }= 10, plot the change of eigenvalues as*H*changes from

Fig. 1 Two-bus system

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

- Cover page (Please use the cover page template available on Canvas and complete all sections on the cover page)
- Table of content
- Introduction
- Theory on small-signal stability analysis (necessary equations and diagrams);
- Results and Discussions
- Conclusions
- References (
*IEEE format should be used*)

IEEE reference format: __https://www.ieee-pes.org/part-4-preparation-of-a-formatted-technical-work-for-theieee-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:

- Introduction – a general description of the problem to be solved (10%).
- Methodology – how the problems are solved (20%).
- Results and discussion & MATLAB code (40%).
- Conclusions (10%).
- Use of references (5%)
- Overall report quality and structure (15%)

**Plagiarism**: __Plagiarism will not be tolerated__. It is the act of a Student claiming as their own, intentionally or by omission, work which was not done by that Student. Plagiarism also includes a Student deliberately claiming to have done work submitted by the Student for assessment which was never undertaken by that Student, including self-plagiarism and the other breaches. Sanctions of a plagiarism include the Student failing the Programme of study.

The **report** as well as the **MATLAB code** will need to be submitted via the Canvas (two separate files). Please do not submit *.zip* files. Submit *.pdf* or *word* file for the **report**, and *.m* file for **MATLAB code**.