Multi-stage robust transmission constrained unit commitment: A decomposition framework with implicit decision rules.

Highlights • A multi-stage robust optimization-based formulation is proposed to model the TCUC problem with uncertainty. • Non-anticipativity of the ED decisions and multi-stage robustness of the UC decisions are guaranteed. • A decomposition framework with implicit decision rules is proposed and the formulation scale is small. • Subproblems in the decomposition framework have a time-decoupled structure and are easy to solve. • A numerical example is given to clarify the difference between two-stage robustness and multi-stage robustness. Abstract With the integration of large-scale renewable energy sources to power systems, many optimization methods have been applied to solve the stochastic/uncertain transmission-constrained unit commitment problem. Among all methods, two-stage and multi-stage robust optimization-based methods are the most widely adopted ones. In the two-stage methods, non-anticipativity of economic dispatch (ED) decisions are not considered. While in multi-stage methods, explicit decision rules (like affine decision rules) are adopted to guarantee non-anticipativity of ED decisions, the computational burden can be heavy and the optimality of the solution is affected. In this paper, a multi-stage robust TCUC formulation with implicit decision rules is proposed, as well as a decomposition framework to solve it. The solutions are proved to be multi-stage robust and non-anticipativity of ED decisions is guaranteed. Meanwhile, a computationally efficient time-decoupled solution method for the feasibility check subproblems is also proposed, such that the method is suitable for large-scale TCUC problems with uncertain power injections. Numerical tests are conducted on IEEE 118-bus system and Polish 2383-bus system. The proposed method outperforms the multi-stage robust method with explicit decision rules in solution's economic performances, and is more computationally efficient than the all-scenario-feasible method. The effectiveness of time-decoupled solution method is also verified. [ABSTRACT FROM AUTHOR]