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# Power System - Transient StabilityTransient stability analysis of a single machine - infinite bus

system using equal area criteria and validation through step-by-step numerical integration method.   Single machine - infinite bus system:
Figure. 1 shows the considered simple single-machine infinite-bus system. A hydraulic power plant
(HPP) with four identical units (each has 20-pole, 50 Hz, 125 MVA, 15 kV generators) supplying
power to an infinite bus through two transmission circuits. In Figure.1, the network reactances
(transmission lines and transformer) are in per-unit on 100 MVA, 15 kV base (referred to the LT
side of the step-up transformer). The voltage magnitudes at BI and B3 (|VB1 | and [VB3[) are 15.75
k V and 400 k V, respectively. The fault on transmission line (either on Line-1 or Line-2) is cleared
by opening the line breakers at the same time.
B1
B2
B3
15 kV / 400 kV
line-1 (j0.08)
SM
line-2 (j0.12)
4 x 125 MVA
jo.024
Inf. Bus
P = 425 MWH&gt;
Figure.1. Single machine - infinite bus system
Classical model parameters of each machine (expressed in per-unit on 125 MVA, 15 kV base):
Xd'= 0.36 pu, H = 5s
Questions:
In the following questions, use 125 MVA power base.
Q1. Find the parameters of the reduced equivalent circuit of the system for small-signal and
transient stability analysis.
(10 marks)
Q2. Determine the frequency of machine rotor oscillations when it is subjected to a small
temporary electrical disturbance.
(5 marks) Q3. Q4. Q5. Q6. Q7. Consider the faults on line-1. For which fault location (or locations) the critical clearing time
is the smallest? Write down the reason brieﬂy (do NOT use the equation of critical clearing angle and/or time in your explanation). (10 marks) Does any fault on Line-2 result into a smaller critical clearing time compared to the Line-l
fault scenario (or scenarios) identiﬁed in Q3? For either answer (yes or no), write down the
reason brieﬂy (do NOT use the equation of critical clearing angle and/or time in your
explanation). (10 marks) Consider the fault scenario identiﬁed in Q3 (or Q4), i.e. the fault scenario results into the
smallest critical clearing time. a. Calculate the maximum power outputs of the generator before, during and after fault
Pmax, Pmaxl and me2, respectively. (5 marks) b. Plot approximately the power-angle curves of the generator before, during and after the
fault. Indicate the pre-fault, critical clearing and maximum angles, and the acceleration
and deceleration areas, (15 marks) c. Calculate the critical clearing angle and critical clearing time. (5 marks) Suppose that clearing time of the line breakers are 100ms. Write a Matlab Script that
computes the swing curve using step-by-step method. Use 10 ms time step and plot the power
swing curve for 2 s period. Is the system stable? (30 marks) If the system is stable in Q6, repeat the simulations by increasing the clearing time with 5
ms until unstable scenario is obtained. Plot the swing curves for all simulations. Is the critical
clearing time obtained in Q5.c consistent with the simulations? (10 marks)

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