Question

3) Solve the following Economic Dispatch problem using Dynamic Programming to find total minimum cost and P, P2, Ps, for load 300 MW? (25 points) 0 50 75 100 125 800 850 975 1000 1000 1250 1400 500 600 700

Answer 1

A dynamic programming method is an iterative method. So, steps for this method only are described below:

STEP-1: First it is necessary to describe the costs characteristics of each generator in form of

To do so, the values given in table can be used.

C is the cost in $/hr and P_G is MW generation. There are three unknowns x, y and z. Three equations can be formed through table to find these unknowns for each generator.

STEP-2: Incremental fuel cost $\lambda$ is given as $\lambda \, = \,x{P_G}\, + \,y$ .

So, P_G is given by ${P_G}\, = \,(\lambda \, - \,y)/x$ ------------------------------------------------------------------------(Eq - 1)

STEP-3: Take an initial random value of $\lambda$ .

STEP-4: Solve Eq (1) for each generator.

STEP-5: Calculate, Total power generation = sum of all individual generation

STEP-6: Check whether Total power - Load demand < tolerance

if yes, calculated power generation is the correct answer and stop.

If no, go to step-7.

STEP-7: Check Total power - Load demand > 0

If yes, get new value of $\lambda$ by $\lambda \, = \,\lambda \, - \,\Delta \lambda$ and repeat from step-4.

If no, get new value of $\lambda$ by $\lambda \, = \,\lambda \, + \,\Delta \lambda$ and repeat from step-4.