Voltage-Dependent Load Models in Unbalanced Optimal Power Flow Using Power Cones

Mathematical models representing the behavior of electrical loads are an important part of any optimal power flow problem. The current state-of-the-art in unbalanced optimal power flow mostly considers wye-connected, constant power loads. However, for applications such as conservation voltage reduction, it is crucial to model how the consumption of the loads depends on the voltage of the network. This article develops a unified framework to handle a wide variety of load types: delta- or wye-connected, constant power, constant current and exponential load models. Furthermore, it proposes a novel convex relaxation for the exponential model, using power cones, that is intersected next with a well-known semi-definite relaxation of unbalanced OPF. Finally, numerical results on the LVTestCase feeder are included for both the exact, non-linear equations and the convex relaxation, which show how considering the voltage sensitivity and connection type can lead to different objective values and voltage profiles. Additional results for 128 low-voltage networks, examine the quality of the solutions obtained with the proposed relaxation.