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 = 0.91     Q  = 0.4 (oveTexcited)     Et   = 1.0∠330            Eb  = 0.991∠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.

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 including the following

Department/School:

Programme title:

Module title:

Title of submission:

Name and ID:

Date of submission:

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)

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.