Flexible and low-carbon retrofit planning for wind-solar-thermal system: a distributionally robust Lipschitz dynamic programming approach

Increasing penetration of renewable energy sources poses serious issues to the power balance. Retrofitting a thermal unit effectively improves flexibility and reduces carbon emissions. However, existing two-stage retrofit planning models determined the retrofit schedules before the uncertainties were realized. To this end, this study proposes a distributionally robust multi-stage retrofit planning model where the retrofit schedules are decided, with uncertainties gradually revealed. Mixed-integer nonlinear flexibility, carbon capture and storage retrofit, and unit commitment constraints are formulated and embedded into the retrofit planning model. To consider the probability distribution uncertainties, the retrofit planning model is expanded to the multi-stage distributionally robust form, which is solved by the distributionally robust Lipschitz dynamic programming algorithm. The numerical results based on the Shantou system, IEEE 39-bus, and 118-bus test systems showed that the proposed multi-stage model outperformed the two-stage one in terms of lower cost (−9.7 %) and better out-of-sample performances. Compared with the existing solution method, the average solution time and final gap of the proposed solution method were decreased by 24.4 % and 10.1 %. The numerical results proved that the proposed approach could effectively improve system flexibility and reduce carbon emissions.