University of Michigan
Department of Electrical Engineering and Computer Science
EECS 463 – Power System Design and Operation Fall 2020
Project #1
Distributed: Monday, October 26, 2020
Due: Tuesday, December 8, 2020 (Midnight Ann Arbor time.)
The project consists of Design Project 1 from Glover, Overbye and Sarma, 6th Edition. A copy of the project details is attached, and the required PowerWorld files are provided on the Canvas website.
Comments:
1. It is stated in the “Simplifying Assumptions” that changes in load and losses are picked up by the system slack bus. This is not necessarily true as it depends on the program settings. To ensure all generators, other than the slack, maintain constant active power output, go to the PowerWorld “Simulator Options” and click the box labelled “Disable Automatic Generation Control (AGC)”. Everybody should do this to ensure consistency of results.
2. The project requires computation of line R, X and B parameter values. Details are provided in the following section.
Transmission parameter calculations
Transmission lines are typically represented by the π-model of Figure 1, where R is the line resistance, X is the line inductive reactance and B is the line capacitive susceptance. To add new lines into the power flow representation of the grid, it is necessary to determine their R, X and B parameters. The conductor characteristics given in Table A.4 will be used to determine those parameters.
R + jX
jB 22
Figure 1: Transmission line π-model. 1
jB
The following steps should be followed:
1. Use the resistance values corresponding to 50◦C and 60 Hz.
2. Line reactance and susceptance values should be computed using the “geometric mean distance” (GMD) values given in the “Transmission Lines” information provided as part of the project description, i.e., GMD = 2 metres for 69 kV lines and GMD = 4 metres for 138 kV lines.
3. Line reactance X is computed using the formula,
La = 2 × 10−7lnGMD H/m, (1)
GMR
where the “geometric mean radius” (GMR) for the various types of conductors is given in Table A.4. (This formula assumes, of course, that GMD and GMR have the same units.) After scaling by the line length, the line reactance is given by X = ωL ohms.
4. Line susceptance B is computed using the formula,
Can = 2πε F/m, (2)
ln(GMD/r)
where the permittivity ε = 8.854 × 10−12 F/m, and r is the conductor radius which can be found in Table A.4 for the various conductors. (It is different to GMR.) Again, GMD and r must have the same units, of course. After scaling by the line length, the line susceptance is given by B = ωC siemens.
5. Be very careful with units. Table A.4 uses inches, feet and miles for various quantities. The formulae (1),(2) give inductance and capacitance per metre, and the right-of-way lengths are given in kilometres. Ultimately, the values of R, X and B must be converted to per unit.
The right-most two columns of Table A.4 provide per mile values for X and B for GMD = 1 foot. Those values may be helpful in checking your use of the formulae.
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