Assignment 4

1. The fuel-cost function for three thermal plants in Rs./h are given byC1 = 500 + 5.3P1 + 0.004 P1

2

C2 = 400 + 5.5P2 + 0.006 P22

C3 = 200 + 5.8P3 + 0.009 P32

Where P1, P2 and P3 are in MW. The total load, PD is 800 MW. Neglecting line losses and generator limits, find the optimal dispatch and the total cost in Rs./h.(a) by analytical method.(b) by graphical demonstration.(c) by iterative technique using the gradient method.

2. Find the optimal dispatch and the total cost in Rs./h for the thermal plants of the above example, when the total load is 975 MW with the following generator limits (in MW):

200 ≤ P1 ≤ 450150 ≤ P2 ≤ 350100 ≤ P3 ≤ 225

3. The fuel-cost of three thermal plants of a power system are:C1 = 200 + 7.0 P1 + 0.008 P1

2

C2 = 180 + 6.3 P2 + 0.009 P22

C3 = 140 + 6.8 P3 + 0.007 P32

Where P1, P2 and P3 are in MW. Plant outputs are subject to the following limits (in MW)

10 ≤ P1 ≤ 8510 ≤ P2 ≤ 8010 ≤ P3 ≤ 70

For this problem, assume the real power loss is given by the simplified expression:

PL (pu) = 0.218 P12 (pu) + 0.0228 P2

2 (pu) + 0.0179 P32 (pu)

Where the loss coefficients are specified in per unit on a 100 MVA base. Determine the optimal dispatch of generation when the total system load is 150 MW.

4. Write a program in MATLAB, for n generators with all possible options of including/neglecting losses and generator limits. Program must input the coefficients of fuel-cost function of each generator and the simplified expression of real power loss (if considered).