7.2 Consider the following power system network. Both generators are at 30 MW output and both loads are consuming 30 MW. Bus 1 is the reference bus.
The data for this network is as follows:
From Bus To Bus x MW Limit
1 2 0.20 35.0
1 3 0.30 35.0
1 4 0.30 25.0
2 3 0.30 40.0
3 4 0.40 25.0
The initial power flows are calculated with a DC power flow and result in the following base flows. The line flow limits are also shown with the percent loading:
BASE TRANSMISSION LOADING
Path From To Low Flow High Percent Loading
1 1 2 -35.0 -8.87 35.0 25.4
2 1 3 -35.0 15.21 35.0 43.5
3 1 4 -25.0 23.66 25.0 94.6
4 2 3 -40.0 21.13 40.0 52.8
5 3 4 -25.0 6.34 25.0 25.4
The PTDF factors and the LODF factors for this system are as follows:
POWER TRANSFER DISTRIBUTION FACTOR (PTDF) MATRIX
Monitored Transaction
Line From(Sell) - To(Buy)
1 to 3 1 to 4 2 to 3 2 to 4
1 to 2 0.2958 0.1268 -0.4225 -0.5915
1 to 3 0.4930 0.2113 0.2958 0.0141
1 to 4 0.2113 0.6620 0.1268 0.5775
2 to 3 0.2958 0.1268 0.5775 0.4085
3 to 4 -0.2113 0.3380 -0.1268 0.4225
LINE OUTAGE DISTRIBUTION FACTOR (LODF) MATRIX
Monitored Line Outage of one circuit From - To
1 to 2 1 to 3 1 to 4 2 to 3 3 to 4
1 to 2 0.0000 0.5833 0.3750 -1.0000 -0.3750
1 to 3 0.7000 0.0000 0.6250 0.7000 -0.6250
1 to 4 0.3000 0.4167 0.0000 0.3000 1.0000
2 to 3 -1.0000 0.5833 0.3750 0.0000 -0.3750
3 to 4 -0.3000 -0.4167 1.0000 -0.3000 0.0000
a. In this problem we are only concerned with outages on lines 1-2, 1-3, and 1-4. Do any of these outages, taken one outage at a time, result in overloads? If so, how much and what lines are overloaded?
b. The generator at bus 1 is going to reduce its output and at the same time the load at bus 4 is going to reduce its load until there are no overloads due to the lines listed in part (a). How much should the load on bus 4 and the generation on bus 1 be reduced to eliminate all overloads?