Statistical Feasibility Robust Optimization With Polyhedron Uncertainty Set for Hydrogen-Data Center Microgrid Operations

Robust optimization (RO) has been widely used in the hydrogen-data-center microgrid (H2-DCMG) optimal operations. However, the operation results based on RO are too conservative. Statistical feasibility can be introduced into RO to reduce conservatism. Therefore, statistical feasibility-based RO is adopted in the H2-DCMG operations optimization. In this study, a data-driven statistical-feasibility-based robust rolling optimization framework is constructed for the optimal operations of the c-DCMG. In this framework, DC temperature is influenced by the uncertain outside temperature, and an uncertainty set is needed to express the uncertain outside temperature. Unfortunately, the existing studies that construct the uncertainty set satisfying statistical feasibility only constructs the ellipsoid uncertainty sets. The ellipsoid uncertainty sets will be converted into the second-order cone constraints, which will increase the complexity when solving. In this study, the Statistical-Guarantee-based Vertex Link (SGVL) algorithm is proposed to construct the polyhedron uncertainty sets, which are used to describe the uncertainty of the outside temperature. Moreover, statistical feasibility-based DC temperature bound is guaranteed by the optimal operations obtained based on these uncertainty sets. Compared with the traditional ellipsoid uncertainty set, the polyhedron uncertainty set can reduce the complexity of the optimization problem and improve the efficiency of the solution process. Case studies based on the real-world temperature dataset are processed. The results show that the introduction of statistical feasibility can reduce the total operation cost by 0.29%~0.64%. The average solving time of the optimization problems based on the polyhedron uncertainty sets constructed using the SGVL algorithm also reduces by 7%~13%. The cases also verify that other uncertainty parameters and different kinds of forecasters do not influence the performance and effectiveness of the framework. Note to Practitioners—This paper focuses on optimizing the operations of a hydrogen-data center microgrid (H2-DCMG) to minimize its operation cost in the way of statistical feasibility-based robust optimization. The statistical feasibility is introduced into the framework for the relaxation of the data center (DC) temperature bound. The Statistical-Guarantee-based Vertex Link (SGVL) algorithm is proposed to construct the uncertainty set of outside temperature that guarantees the dispatch results satisfying statistical feasibility. In practice, the settings of the framework and the data used in the SGVL are significant. Firstly, in the rolling dispatch, the length of the forecasting period needs also to be set after the trade-off between the solving efficiency, the dispatch economy and the DC temperature stability. Secondly, the pre-set DC temperature bound is advisable to be set below the maximum temperature that does not harm its normal operation. When constructing the uncertainty sets, the two parameters of the statistical feasibility need also to be set after the trade-off between the economics of dispatch results and the acceptability of constraint violations. The dataset and the actual forecasting error need to remain equally distributed to guarantee the performance of the dispatch of the proposed framework. The proposed framework can be readily implemented and integrated into the actual dispatch of H2-DCMG.