An intuition-based uncertain variable reduction approach for robust optimization in power systems

The two-stage robust optimization considering uncertainties from load and renewable energies is addressed. Namely, we show that it is possible to reduce a significant portion of uncertain variables in its second-stage sub-problem. Intuitively, high net load power tends to increase controllable generators’ costs. Thus for the case with a box uncertainty set, in most situations, the net load power’s worst case takes its upper bound. Consequently, the number of uncertain variables can be drastically reduced by fixing many uncertain variables at their corresponding boundaries. Nevertheless, there are counterexamples where the worst case is the opposite. We summarize the correlation between possible ranges of locational marginal price (LMP) and uncertain variables’ worst case. Thus worst-case prediction can be transformed into the well-studied LMP prediction. Accordingly, an uncertain-variable-reduction approach is proposed for the box uncertainty set. Considering general polyhedral uncertainty sets, for a given vertex, a coordinate-rotation based approach is developed to make adjacent edges of the vertex orthogonal to each other and calculate rotated LMP intervals. Subsequently, a vertex-reduction approach based on rotated LMP intervals is proposed to exclude vertices that are not the worst case. Simulations on 14-, 118- and 300-bus systems demonstrate that the proposed approach significantly improves computational efficiency.