Jehum Cho

A Novel Practical Stochastic Pricing Model for Multi-Interval Real-Time Markets Practical implementations of economic dispatch with associated pricing systems are crucial for operating electricity markets. Because of the high volatility caused by the increasing integration of renewable energy, consideration of the underlying stochastic problem is becoming more important than ever. It is a challenge to incorporate the uncertain nature of real-time operations into an already complex multi-interval dynamic problem with intertemporal constraints. Because solving a standard multi-stage stochastic programming problem is too burdensome in terms of calculation time for real-time markets, it has been standard practice in electricity markets to use a deterministic approximation with varying degrees of look-ahead. Cho and Papavasiliou, in their article “Pricing Under Uncertainty in Multi-Interval Real-Time Markets”, introduced a practical alternative method for pricing under uncertainty in multi-interval real-time markets. Using slightly different stochastic formulations, these authors propose an approach that preserves the attractive features from both the deterministic formulation (simpler calculation) and the standard stochastic formulation (better performance).

An exact algorithm is developed for the chance-constrained multi-area reserve sizing problem in the presence of transmission network constraints. The problem can be cast as a two-stage stochastic mixed integer linear program using sample approximation. Due to the complicated structure of the problem, existing methods attempt to find a feasible solution based on heuristics. Existing mixed-integer algorithms that can be applied directly to a two-stage stochastic program can only address small-scale problems that are not practical. We have found a minimal description of the projection of our problem onto the space of the first-stage variables. This enables us to directly apply more general Integer Programming techniques for mixing sets, that arise in chance-constrained problems. Combining the advantages of the minimal projection and the strengthening reformulation from IP techniques, our method can tackle real-world problems. We specifically consider a case study of the 10-zone Nordic network with 100,000 scenarios where the optimal solution can be found in approximately 5 minutes.