Massachusetts Institute of Technology
Department of Electrical Engineering and Computer Science
6.691 Seminar in Advanced Electric Power Systems
Problem Set 2
Issued February 26, 2006
Due March 15, 2006
This problem set involves the example power system which was presented in class on class on
February 20, reproduced in Figure 1. We are going to do a few things with this example system,
so save your notes.
1. Re-draw the system diagram with all impedances and loads translated to per-unit. Assume
that the transformers between 69 and 161 kV buses 15 and 16 at one substation and between
buses 9 and 17 at another substation are rated at 150 MVA and that their voltage ratings
correspond with the nominal system voltages. You may represent them as purely reactive with
xt = 8% on their own base. For your per-unit normalization use a system base of 100 MVA
and the nominal system voltages (161 and 69 kV). Note, of course, that power called out at
each bus is MW+j*MVAR and that voltages are line-line, RMS.
2. Find a ’load flow’ solution which includes bus voltages (magnitudes and angles) and line
flows. Assume the power plants connected to buses 2 and 3 are producing 220 MW and
70 MVAR (each). Assume that the power plant connected to Bus 1 is providing whatever
real and reactive power is required to maintain the system at constant frequency and the
voltage at Bus 1 at rated (161 kV). As we will discuss in class, there are multiple ways of
computing this load flow. I would suggest doing the calculation using both Gauss-Seidel and
Newton-Raphson and comparing the solutions.
1
Loads MW + j MVAR
Impedances in Ohms R + jX
161 kV
69 kV
1
14
1
3.629+j20.53
35+j10
2
3
4.718+j26.70
17
5
9
3.085+j17.47
11
3.085+j17.47
10+j5
2
4
75+j15
2.774+j15.66
6
17
8
7
2.411+j13.69
2.618+j14.78
2.514+j14.18
3.433+j11.49
4
60+j10
5
10
1.529+j6.3
15+j10
10
1.089+j4.48
3.033+j10.15
40+j5
20
1.996+j8.17
1.270+j7.13
11
80+j15
90+j20
6
1.866+j10.63
15
3.551+j20.09
14
10+j0
4.642+j15.54
19
30+j10
13
3.551+j20.09
12 1.97+j8.09
16
13
12
100+j30
18
7
40+j15
8
9
16
15
3.003+j17.16
Figure 1: Example Power System
2
3