Data for Multistage Day-Ahead Scheduling of Energy and Reserves

In order to obtain the ex-ante least-cost schedule of energy generation and reserves for online generating units, the system operator addresses a dynamic decision-making process known as the economic dispatch (ED) problem. Current industry practice involves adopting a deterministic two-stage optimization framework that relies on a one-day-ahead horizon and a forecast of uncertain parameters. The optimal solution to the resulting problem thus yields a generation schedule for the entire day ahead.

In real-time, however, actual generation and load typically deviate from what was scheduled in the previous day. Moreover, the presently large-scale integration of renewable energy resources has led to a significant increase in the stochasticity of nodal injections. Thus, since the currently used two-stage model lacks flexibility with respect to uncertainties, it may give rise to non-implementable day-ahead dispatch decisions and over-scheduling of reserves to guarantee that nodal demands are fully met.

In this paper, we propose two new ED models for the day-ahead scheduling of energy and reserves under uncertainty. We focus on the benefits of adopting more flexible and adaptive scheduling models compared to the current two-stage approach. To that end, we propose considering a multistage stochastic framework whereby generation schedules are dynamically updated according to observed new information about uncertainty. First, a full multistage model is formulated to provide a one-hour-ahead implementable energy and reserve scheduling. Subsequently, we present an alternative model in which the energy scheduling is kept static for the day ahead, whereas reserves are allocated in a multistage manner.

The proposed multistage stochastic models offer more flexibility for scheduling decisions. However, these benefits come at the expense of solving much larger and more complex optimization problems. Hence, due to the curse of dimensionality featured by classical methods for multistage stochastic programming, such as those relying on scenario trees, and the very restrictive hypotheses of stochastic dual dynamic programming, we propose the application of the regularized linear decision rules (LDR) technique. The LDR framework allows formulating multistage stochastic linear problems as two-stage linear models with multiple periods, thus reducing the computational complexity. Furthermore, we adopt the regularization method to prevent the in-sample overfitting issue and the poor out-of-sample performance, both due to the large number of parameters that must be estimated when using LDR. Numerical results from a case study based on an IEEE test system show that the proposed multistage LDR-based stochastic models yield more cost-effective decisions than the current two-stage benchmark.