Stochastic programming for hydro-thermal unit commitment

Abstract

In recent years the deregulation of energy markets and expansion of volatile renewable energy supplies has triggered an increased interest in stochastic optimization models for thermal and hydro-thermal scheduling. Several studies have modelled this as stochastic linear or mixed-integer optimization problems. Although a variety of efficient solution techniques have been developed for these models, little is published about the added value of stochastic models over deterministic ones. In the context of day-ahead and intraday unit commitment under wind uncertainty, we compare two-stage and multi-stage stochastic models to deterministic ones and quantify their added value. We show that stochastic optimization models achieve minimal operational cost without having to tune reserve margins in advance, and that their superiority over deterministic models grows with the amount of uncertainty in the relevant wind forecasts. We present a modification of the WILMAR scenario generation technique designed to match the properties of the errors in our wind forcasts, and show that this is needed to make the stochastic approach worthwhile. Our evaluation is done in a rolling horizon fashion over the course of two years, using a 2020 central scheduling model of the British National Grid with transmission constraints and a detailed model of pump storage operation and system-wide reserve and response provision. Solving stochastic problems directly is computationally intractable for large instances, and alternative approaches are required. In this study we use a Dantzig-Wolfe reformulation to decompose the problem by scenarios. We derive and implement a column generation method with dual stabilisation and novel primal and dual initialisation techniques. A fast, novel schedule combination heuristic is used to construct an optimal primal solution, and numerical results show that knowing this solution from the start also improves the convergence of the lower bound in the column generation method significantly. We test this method on instances of our British model and illustrate that convergence to within 0.1% of optimality can be achieved quickly.