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

Abstract

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.

Application of the Level Method for Computing Locational Convex Hull Prices

“…However, our experiments in [16] reveal that each iterate of the algorithm is costly, as it requires not only to solve the problems (2) for each generator to optimality, but to enumerate all the optimal solutions. Unlike these two memoryless schemes, the Analytic Center Cutting Plane Method (ACCPM, see [14], [38] for the theory and [37], [39] for its application to CHPs) is based on the principle of iteratively reducing the search domain: the price domain is initially limited to a box and, at each iterate, the supergradient is used for generating a cut, which shrinks the search domain. The next testing point is chosen as the analytical center of the updated domain.…”

Computation of Convex Hull Prices in Electricity Markets with Non-Convexities using Dantzig-Wolfe Decomposition

“…Several works have attempted to overcome the computational difficulties by relying on two main approaches. An early approach applied sub-gradient methods [18]- [21], whereas a later and methods focused on identifying the CH of individual generators through convex primal formulations [22] -also including an AC Optimal Power Flow setting [23], extended formulations [24]- [26], a network reformulation [27], and Benders decomposition leveraging advances in thermal generator CH formulations [28]. Despite the aforementioned efforts, two important barriers to CH price implementation remain: (i) computational challenges, and (ii) opacity of their properties [13].…”