Class 4

We continued with the study of Lagrange duality. We introduced the concept of partial Lagrangian and demonstrated that, if strong duality holds, then complementary slackness must hold as well. Furthermore, in the case that the constraint and objective functions are differentiable, strong duality naturally leads to the KKT conditions.

We have then studied the well-known economic dispatch problem as the basis of most clearing procedures for electricity markets worldwide. We have shown, using Lagrange duality, that the solution to the economic dispatch problem is equivalent to the solutions yielded by the individual profit/utility maximization problems of the involved market agents, with the dual variable of the power balance equation being the electricity price.

We have next discussed some fundamental concepts of markets such as social welfare, market-clearing price, marginal pricing vs. pay-as-bid, revenue adequacy, non-convex costs, etc.