Multi-stage siting and sizing of PV stations under long-term carbon price: a branch-and-bound embedded progressive hedging approach

Abstract

Reasonable programming of photovoltaic (PV) site selection and sizing is essential for boosting renewable energy penetration and power system carbon emission reduction, thereby mitigating future electricity procurement cost risks under dynamic carbon pricing. However, the problem of optimal PV siting and sizing with integer decision variables is complicated by the long-term uncertainty of carbon prices. To address the above issue, this paper proposes a PV site selection and capacity determination mixed integer multi-stage stochastic programming model considering the long-term uncertainty of carbon prices, and designs a collaborative solution framework of the Progressive Hedging (PH) algorithm and Branch-and-Bound (BB) to optimize the low-carbon and economic performance of the system. Firstly, a multi-stage stochastic programming model for PV siting and sizing is constructed, employing scenario trees based on an enhanced binomial tree model to depict the stochastic evolution of carbon prices over the long term. Secondly, the PH algorithm solves the subproblems for individual scenarios and refines the solutions through interaction to meet the nonanticipativity constraints in carbon prices. Finally, the PH algorithm is embedded within the BB framework to optimize the integer decisions related to PV siting locations. Case studies on the IEEE 33-bus system demonstrate the effectiveness of the framework in identifying adaptive PV deployment strategies under long-term carbon price uncertainty. A 10% decrease or increase in carbon prices changes the expected final-stage PV capacity by approximately -11.2% and +10.7%. These results highlight the capability of the framework to capture the impacts of carbon price uncertainty on PV investment decisions.