Stochastic-Robust and Robust Programs for the Ramp-Constrained Economic Dispatch Problem with Uncertain Renewable Energy

The inherent uncertainty of renewable energy sources (RES) makes the solution to the electricity network’s associated economical dispatch (ED) problem with network constraints challenging. In particular, the uncertainty in the power output of RES requires conventional generation units to ramp up and down more frequently to maintain the power balance and the reliability of the system. Typically, the RES power output uncertainty is modeled in ED problems by considering its potential future scenarios. However, this leads to an optimization problem that is difficult to solve for real-sized networks. Here, we present two proposals for this problem.

In the first one, we consider the uncertainty of RES and the consequent ramping of conventional generation via a robust reformulation of the problem. In particular, we show that in typical instances of the ED problem, the associated deterministic formulation of the robust problem can be solved efficiently for medium scale constrained electricity networks even when the underlying uncertainty distribution is not normal. Moreover, by comparing the proposed robust solutions to the ED problem with the typical scenario optimization approach, we show that the former solutions result on dispatch solutions that require less ramping than the later solutions, with little trade-off on the long-term expected costs of the dispatch. These results also provide insights about how RES penetration affects cost and dispatch policies in the electricity network. To illustrate our results, we present relevant numerical experiments on IEEE test networks.