Solving long time-horizon dynamic optimal power flow of large-scale power grids with direct solution method

Dynamic optimal power flow (DOPF) is an extension of optimal power flow for the optimal generation dispatch in a given time-horizon. The dynamic constraints bring tremendous numerical difficulties in solving this model. With particular attention to handle dynamic constraints, an efficient method has been presented for directly solving the large-scale DOPF Karush-Kuhn-Tucker (KKT) system arising from the primal-dual interior point method. First, the reduced KKT system is derived, showing that dynamic constraints lead to non-zeros in off-diagonal parts in the coefficient of KKT system. Then, the efficiency of the algorithm is improved by two measures: (i) to utilise the Cholesky factorisation algorithm, a constant diagonal perturbation is introduced in the positive-indefinite KKT coefficient and (ii) efficient reordering algorithms are identified and integrated in the sparse direct solver to improve the efficiency. Case studies on the IEEE 118-bus system over 24-96 time intervals are presented. These case studies show that the proposed method has a significant speed-up than decomposed interior point methods. The proposed method has also been successfully applied in Chinese realistic large-scale power grids. Two realistic case studies are reported. Both realistic cases have over 100 000 decision variables.