Market design for ancillary service provisions of inertia and frequency response via virtual power plants: A non-convex bi-level optimisation approach

The Great Britain (GB) government is paving the path to decarbonisation by actively promoting the integration of wind power into its generation mix. This sharp transition to renewable energy, however, introduces specific challenges. The characteristics of non-synchronous wind turbines have the potential to impact grid stability and frequency security due to the reduction in system inertia. In response to these challenges, the deployment of virtual power plants (VPPs) is envisioned in deregulated power systems, which allow for the aggregation and coordinated control of diverse distributed energy resources, enhancing grid flexibility, reliability, and efficiency. Moreover, VPPs offer the provision of system inertia and frequency response services at the national level. This study drops this assumption and leverages the localised flexibility inherent in VPPs to meet the ancillary service requirements of the low-carbon power system. The formulated problem is constructed as a non-convex bi-level optimisation problem, where the upper-level problem represents the operation of a frequency-constrained unit commitment model, and the lower-level problem embodies the energy dispatches and frequency responses of a group of VPPs, guided by the dual price signals of cleared energy and ancillary services. To address the non-convex nature of the unit commitment problem, a two-fold approach is employed. First, binary commitment status decision variables are relaxed to continuous versions. Subsequently, the duality gap between the original non-convex unit commitment problem and its relaxed dual form is minimised, yielding a solution closely approximating the optimal solution of the original problem. Second, the relaxed bi-level optimisation problem is transformed into a single-level mathematical programs with equilibrium constraints by replacing the lower-level VPP problems with their equivalent Karush-Kuhn–Tucker optimality conditions. The case studies conducted in this work encompass a comprehensive scope. Initially, the study evaluates the effectiveness of VPPs in delivering ancillary services within the projected context of the GB power system for 2030. The findings reveal a substantial 28.28% decrease in system operation costs when compared to the benchmark case lacking VPP flexibility. Additionally, the integration of VPPs leads to significantly lower price signals for inertia, primary frequency response, and enhanced frequency response, reduced by 81.21%, 79.13%, and 86.27%, respectively, in contrast to the benchmark case. The analysis then delves into a sensitivity exploration, investigating the inherent flexibility of VPPs. The profit of local VPPs is expected to increase with VPP flexibility. Finally, the study illustrates how VPPs can adapt to and derive benefits from an increasing level of wind power penetration by providing a higher amount of frequency response.