A subgradient-based cutting plane method to calculate convex hull market prices

The unit commitment and economic dispatch problem in electricity markets has mixed-integer variables with piecewise linear bids. By using Lagrangian relaxation, a concave and piecewise linear dual problem is obtained. The resulting multipliers can be used to set prices in the convex hull pricing model, and this would result in the minimal uplift payment. This paper presents a subgradient-based cutting plane method to obtain the optimal multipliers in a computationally efficient way. The idea is to use subgradients to find an approximate center of the feasible polyhedron within the cutting plane framework. The time consuming process of finding centers such as analytic centers can thus be reduced. At nondifferentiable points, the cuts resulting from approximate centers may oscillate, and this difficulty is overcome by choosing a proper linear combination of these oscillating subgradients. The analytic centers are inserted as needed as spacer steps to ensure algorithm convergence. Testing results demonstrate the effectiveness of the algorithm.