A Tractable Approximation Approach to Deal with the Binary Nature of Shiftable Loads in Multi-Period Optimal Power Flow

Distribution systems are currently in a transitional phase, as they transform from passive to active. In the coming years, customer participation is expected to drastically increase, as an additional option for maintaining reliable operation of distribution systems and for supporting the distribution and transmission system operators' growing needs. Amongst the available customer-side technologies, the shiftable load (SL) has one of the highest electricity demands and complexity levels; modelling its operation requires a multi-period optimal power flow (MP-OPF) approach. The SL is traditionally modelled in a mixed-integer nonlinear programming (MINLP) setting using many binary variables. However, for larger problem sizes, the MINLP approach lacks tractability. This work proposes a novel NLP approximation of the classic MINLP SL modelling that accurately mimics a SL at the optimum. The proposed approach is validated in a day-ahead deterministic multi-period OPF on two small distribution networks. It is demonstrated that when convergence is achieved, it occurs much faster than for the original formulation. The approach's sensitivity to the chosen level of accuracy and the initialization point are also explored in order to determine the best way to further complement it.