Alternative approach for efficient OPF calculations in hybrid AC/DC power grids with VSC-HVDC systems based on shift factors

Abstract

This paper introduces a novel approach for optimal power flows (OPF) in VSC-HVDC power grids based on shift factors. The optimum solution is calculated using a global equality constraint (generation minus losses equals system load) plus those related to the power set points of the VSC units. Indeed, the shift factors enable the enforcement of the VSC power flow constraints. This is the hallmark of this method which features a considerable reduction of the model complexity and the computational burden because the system nodal equations are not explicitly represented. This lies in sharp contrast with existing OPF approaches whose model complexity is inevitably increased as is the computing requirements to its solution.Three variants of the proposed OPF model are described: (i) quadratic generation cost curves with quadratic AC/DC transmission losses; (ii) quadratic generation cost curves with power losses considered by piecewise linear equations; (iii) generation cost curves and transmission losses approximated by piecewise linear functions. The effectiveness of the developed approach is assessed using three AC/DC test systems formed by three, four and six VSC stations, respectively. The results are compared against those calculated by a conventional Sequential Quadratic Programming formulation using a full, nonlinear power grid model. It is demonstrated that the optimal solutions concur very well between each other since errors inferior to 5% are obtained for the generation dispatch and nodal energy prices. Equally important is the fact that this novel approach reduces the computational time by more than 70% on average.