EE 340 – Test # 3, Spring 2011
Name:…………………………………
Consider the 9-bus electrical distribution system attached.
• The distribution substation is served by a 138 kV transmission system whose fault duty
is 1,000 MVA with an X/R ratio of 100. Then the Thevenin source impedance is 0.190 +
j19.043Ω.
• The substation transformer is OA/FA/FOA that is rated at 20 MVA, with a series
impedance of 10% and X/R ratio of 22.25. Thus, the transformer series impedance is
0.0045 +j0.0999 p.u.
• The distribution feeder is of composed of AAC 1-954 MCM cable (Goldenrod) Each
line segment is 2 miles long and has a GMD of 3.4 feet. The series impedance of each
segment is Z = 0.2 + j1.1 Ω and shunt admittance Y = 0.00001575 S.
• Each specified load is considered of constant power type.
Let 100 MVA as the system apparent power base, and 13.8 kV as the base voltage on the
distribution side of the transformer (hence, the base voltage on the high voltage side is 138 kV).
1. Use the above common base to compute the p.u. value of the source impedance,
transformer impedance, series impedance and shunt admittance of each line segment.
Source impedance: …………….…..…..
Transformer impedance: ………………
Line segment series impedance: …….………
Line segment shunt admittance: ……………..
2. Fill in the elements of the bus admittance matrix of the system. Note that the real part
(i.e., resistance) of each of the above impedances is too small compared to the imaginary
part (i.e., reactance). Furthermore the shunt admittance of each line segment is also too
small due to the short line length. Hence, you may neglect all these terms when
computing the Y-Bus elements.
3. The power flow solution of the bus voltages is as follows:
⎡V 1 ⎤ ⎡1∠0.0
⎤
⎢V 2⎥ ⎢0.975∠ − 2.3 ⎥
⎢ ⎥ ⎢
⎥
⎢V 3 ⎥ ⎢0.948∠ − 4.3 ⎥
⎢ ⎥ ⎢
⎥
⎢V 4⎥ ⎢0.935∠ − 5.3 ⎥
⎢V 5 ⎥ = ⎢0.926∠ − 6.0 ⎥
⎢ ⎥ ⎢
⎥
⎢V 6 ⎥ ⎢0.922∠ − 6.3 ⎥
⎢V 7 ⎥ ⎢0.944∠ − 4.6⎥
⎢ ⎥ ⎢
⎥
⎢V 8 ⎥ ⎢0.940∠ − 5.0 ⎥
⎢V 9 ⎥ ⎢0.935∠ − 5.3 ⎥
⎣ ⎦ ⎣
⎦
Compute the resulting p.u. value of the source current injected at bus 1. Then determine the
MWs and MVARs injected at that bus.
I1 = …………. p.u.
P = …………… MW
Q = ………….. MVAR
Take – home part of the test:
4. Perform a power flow study on the above distribution system. Identify the buses that are
experiencing low voltages. Display the results. Also compute the system efficiency.
5. Assume that the transformer taps are adjustable in increments of 0.625% on the
distribution side. Determine the minimum tap position that is required in order to bring
all the bus voltages at the minimum allowable value of 0.95 pu. Display the results.
Compute the new system efficiency.
6. Now suppose that the load at bus 6 is increased to 5 MW and 2.5 MVAR. Will raising
the tap position to its maximum value of +10% results in satisfactory voltage levels? If
not determine, the shunt capacitor size (in increments of 300 kVAR) that is needed at
bus 6, and tap transformer position to solve this voltage regulation problem.