The subgradient-simplex based cutting plane method for convex hull pricing

In current deregulated power markets, prices are determined in the economic dispatch problem with fixed unit commitment decisions. Start-up and no-load costs are not included in the prices and significant uplift payments have to be paid to generators. The convex hull pricing model was developed to include the fixed costs in setting prices by solving the dual of the unit commitment and economic dispatch problem. The optimal multipliers are the convex hull prices, and the prices minimize the uplift payments. The optimal multipliers can be obtained by using cutting plane methods that iteratively shrink the feasible polyhedron in the dual space to the optimal point. The calculation of query points is a key step for cutting plane methods and centers such as center of gravity and analytic center are reported as the query point. To calculate the convex hull prices in a more efficient way, this paper develops a subgradient-simplex based cutting plane method to find a query point along the subgradient. When the query point is not deep inside, a sphere inscribed in a corner or the Chebyshev center is calculated by the use of simplex tableaus to ensure the query point is always deep inside. Redundant constraints are also pruned based on the tableaus.