Multistage Mixed-Integer Robust Optimization for Power Grid Scheduling: An Efficient Reformulation Algorithm

The penetration of renewables into power systems is gradually increasing, but its inherent uncertainty poses tremendous challenges to the coordinated operation of power grids. To overcome the demerits of canonical two-stage mixed-integer robust optimization (RO) method that neglects the nonanticipativity requirement and the computational burden in engineering applications, this paper offers a reformulated multistage mixed-integer RO method for regional power grid scheduling. Firstly, a multistage mixed-integer RO scheduling model is established considering the scheduling requests in real-world projects. The scheduling plans under the nominal scenario are determined ahead of uncertainty in the first-stage optimization, and the multistage max-min optimization with binary recourse variables is then executed for feasibility-checking with respect to the nonanticipative realization of uncertainty. Secondly, a dedicated reformulation algorithm is proposed for this intractable multistage mixed-integer RO model. Based on the implicit affine strategy, the multistage max-min optimization is equivalently encapsulated to a single-stage max-min problem, and the dual Fourier-Motzkin elimination is put forward to eliminate both continuous and binary recourse variables in the resulting feasibility-checking optimization. Therefore, the original multistage mixed-integer RO is finally recast as a mixed-integer linear programming that can be solved directly. Numerical tests on an actual 16-bus grid, the IEEE 118-bus system and the 319-bus provincial grid verify the superiority and applicability of the proposed reformulated mixed-integer RO scheduling method, which is of great significance in guiding system operations.