A Mixed-integer Linear Programming Model for Defining Customer Export Limit in PV-rich Low-voltage Distribution Networks

A photovoltaic (PV)-rich low-voltage (LV) distribution network poses a limit on the export power of PVs due to the voltage magnitude constraints. By defining a customer export limit, switching off the PV inverters can be avoided, and thus reducing power curtailment. Based on this, this paper proposes a mixed-integer nonlinear programming (MINLP) model to define such optimal customer export. The MINLP model aims to minimize the total PV power curtailment while considering the technical operation of the distribution network. First, a nonlinear mathematical formulation is presented. Then, a new set of linearizations approximating the Euclidean norm is introduced to turn the MINLP model into an MILP formulation that can be solved with reasonable computational effort. An extension to consider multiple stochastic scenarios is also presented. The proposed model has been tested in a real LV distribution network using smart meter measurements and irradiance profiles from a case study in the Netherlands. To assess the quality of the solution provided by the proposed MILP model, Monte Carlo simulations are executed in OpenDSS, while an error assessment between the original MINLP and the approximated MILP model has been conducted.