Real-power economic dispatch of AC/DC power transmission systems comprising multiple VSC-HVDC equipment

This paper presents a practical approach for the real-power economic dispatch of AC/DC power transmission systems formed by VSC-HVDC equipment. It uses the Lagrange multipliers method combined with a comprehensive representation of the AC/DC power system. The power losses of the AC systems, DC grid and power converters are considered in this novel formulation by using incremental transmission loss factors. For realistic solutions, the different control strategies of the power converters forming any VSC-based power grid are considered. Interestingly, this approach permits to conclude that the AC grids coupled to converters charged with DC voltage control define the nodal marginal prices in the DC network, and in turn, the energy prices in the VSC-connected passive grids are inherited from the DC network. Overall, this modelling approach yields great flexibility to model any arbitrary VSC-based HVDC power grid interconnecting various AC systems. The developed method has been validated using a two-terminal VSC-HVDC network interconnecting two otherwise independent AC grids. Its results are compared against those obtained by the sequential quadratic programming method available in the optimisation toolbox of Matlab©, with both solutions exhibiting differences inferior to 0.30% in the total generation costs, therefore concurring very well between each other. The practicality of this approach is also demonstrated by carrying out the real-power economic dispatch of an AC/DC transmission system comprising seven VSC units which give rise to a thirteen-node DC grid.