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EE655: Computer Aided Power System Analysis

Autumn semester 2010

1. Show all the calculations and steps clearly. This is not a programming assignment.

2. But you may use your own computer programs for solving parts of the problem. In which case

you are instructed to also explain the logic used in the program.

Tutorial 4 : Optimal Power Flow

Problem 1 :

Obtain optimal dispatch solution by formulating an OPF problem for following 3 bus system. Your 

objective is to minimize the total cost of generation.

Line data: All lines (1-2, 1-3 and 2-3 with r = 0.005 pu, x = 0.03 pu, b/2 = 0.2 pu).Bus data: Generators at buses 1 and 3, Load at bus 2 with active power load = 3.5 pu

The cost characteristics areC1 = 9.2 + 3.9 PG1 + 1.2 PG1

2 pu

C2 = 7.6 + 3.0 PG2 + 0.8 PG22 pu

Where PGi is the power generated at bus i.

Make following assumptions

1) The voltage magnitudes at all the buses are held at 1.0 pu by appropriate reactive support2) The generators and lines have very large capacity and hence they do not form a constraint

3) Use PG1 = 1.5 pu as initial value

Identify control variables, state variables, formulate the OPF problem and solve one iteration.

Problem 2 :

For a 3 bus system bus data is:Bus 1 : Ref. Bus (Generator)

Bus 2 : P2 = 2.0 pu (Generator) (active power generation is fixed at P2 = 2.0 pu)

Bus 3 : P3 = 3.3 pu (Load), Q3 = 1.2 pu (Load)Line data:

Line Yij

2 – 3 3 – j 10

1 – 3 4 – j 5

Formulate OPF problem to minimize total active power loss of system.

Complete one iteration. Assume initial values of V1 and V2 as 0.97 and 0.97.(Hint : Active power loss minimization is same as minimizing swing bus power. Take V1 and

V2 as control variables)

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Problem 3 :

Consider the following four-bus and five-line system. All the line impedances are shown in per unit.There are two generators, say G1 and G2, connected at Buses 1 and 4, respectively. The cost functions

of these generators are shown below. The total load on the system is 300 MW which is distributed in

5:1 ratio over Buses 2 and 3. The capacity of Line 1-4 is given as 40 MW and the capacities of other lines are large enough not to bind the generation scheduling. By using the DC power flow

approximation, find out the optimal generation schedules respecting the line flow limits. Now

determine the optimal generation schedules without considering any network limit. Compare the tworesults. Also determine the line flows for both the cases. In any case, you need not to worry about the

upper and lower limits of the power outputs of generators.

Cost functions:

C1(PG1) = 0.004 PG12 + 8 PG1 + 40

C2(PG2) = 0.0048 PG22 + 6.4 PG2 + 50

= End of Tutorial =

 Four-bus and five-line system