## We have discussed in the lecture that the optimal solution for economic dispatch with power grid constraint is to solve an optimization problem with constraints.

### engineering

##### Description

1 Problem definition

We have discussed in the lecture that the optimal solution for economic dispatch with power grid constraint is to solve an optimization problem with constraints. Here we will study three nodes case as in Figure 1 where each node is numbered from 1 to 3. We assume that power transfers on lines are unconstrained and constrained.

1. Busbar 1 has PD1 = 2000KW of demand. Assume that the demand is inelastic and not changed by prices.

2. Busbar 2 generation PG2 has maximum generation capacity of 500KW. The cost of production is c(PG2 ) = 10 × PG2 + 0.005 × P 2 G2 USD.

3. Busbar 3 generation PG3 has maximum generation capacity of 1500KW. The cost of production is c(PG3 ) = 13 × PG3 + 0.01 × P 2 G3 USD.

2 Problem solution Employ the information that was given to you in Section 1 and execute the following tasks with a Matlab script that you develop. 1

1. With assumption that generation and power lines are unconstrained, find the cost of generation by Lagrange multipliers and confirm your results with previous laboratory results.

2. With assumption that lines are constrained with the load equations given below and generation limits ignored,