Efficient two-level interior point method for optimal pumped hydrostorage scheduling exploiting the nonsparse matrix structure

The primal-dual interior point method (PDIPM) has proven to be an efficient tool for power system optimisation problems. Its computational efficiency heavily relies on sparsity techniques. Hence, when optimisation problems cannot be formulated into sparse form, PDIPM then may not be the right choice for these problems, because the computational efficiency drops significantly in factorisation of a dense matrix. A nonsparse power-system optimisation problem containing either-or constraints, pumped hydrostorage (PHS) scheduling, is presented and a two-level predictor-corrector version of PDIPM (PCPDIPM) is proposed to cope with this nonsparse and NP hard problem. To overcome the difficulty associated with the dense matrix structure, a special data transformation is proposed. By further exploiting the dense matrix structure, the performance of PCPDIPM is not deteriorated by the nonsparse structure. On the contrary, the computational efficiency is dramatically improved due to exploiting this structure. Moreover, to solve the difficulty associated with either-or constraints. An effective two-level LP procedure is proposed. To illustrate the performance of the proposed methodology, numerical results are carried out on two test cases. These results show that the presented two-level PCPDIPM solves the PHS scheduling effectively