Two-stage robust optimal scheduling with price-based demand response

With the rapid development of the electricity spot market, the price of electricity is changing all the time based on supply and demand, and the user will also adjust the way of electricity consumption under the influence of electricity price, which are collectively referred to as price-based demand response (PBDR) load. However, the price elasticity of the real -time market is not exactly known in advance, which provides a challenge for power system scheduling. To accommodate the uncertainty of PBDR load, we adopt a budget uncertainty set to describe the stochastic variability of PBDR load. Additional variables are introduced to flexibly adjust the temporal and spatial conservatism. We develop a robust optimization (RO) approach to derive an optimal decision for power system scheduling, with the objective of maximizing total social welfare under the worst PBDR scenario. The problem is formulated as a two-stage robust mixed-integer programming problem. An exact solution approach leveraging Column and Constraint Generation (C &CG) algorithm and strong duality theory is developed to decompose the original problem into a master problem (MP) and a subproblem (SP), solving them alternately to obtain the optimal solution of the original problem. Finally, we test the performance of the proposed approach using case study based on an improved IEEE 30-node system. The results verify that our proposed approach can effectively accommodate the uncertainty of PBDR.