Convex Flexible Branch Model (CFBM): Convex model for solving AC/DC hybrid networks optimal power flows

Abstract

Transmission technologies such as VSC-High-Voltage DC (HVDC) transmission and Multi Terminal DC (MTDC) grids are becoming more common due to their advantages for bulk transmission and their ability to provide coupling conditions for RES-based generation. Generally, the Optimal Power Flow (OPF) analysis is used for modelling power systems, but in its standard form, it is computationally difficult to solve because it is non-linear and non-convex and may not be sufficient for modelling new power system paradigms. This work proposes a convex branch model for the OPF solution of AC/DC hybrid networks. The convex formulation is based on the non-ideal transformer model with additional shunt elements in the standard π branch model. Then, convex relaxations are applied to exploit their mathematical advantages over a non-convex non-linear formulation of the OPF. With this convex framework, it is possible to model different electrical devices, including VSCs terminals for HVDCs and MTDCs. The model is implemented in the CVX optimisation package for MATLAB. Simulations show that this convex framework can obtain comparable, if not identical, results as those obtained from other non-convex non-linear models for solving hybrid networks. Moreover, a benchmark test using different network sizes is carried out, and the results indicate that the convex model maintains a small gap in objective function values and is solved several times faster than the non-linear model.

Keywords

• Convex optimal power flow
• Flexible model
• Hybrid AC/DC networks
• AC/DC converter modelling