Optimization via Statistical Emulation and Uncertainty Quantification: Hosting Capacity Analysis of Distribution Networks

In power systems modelling, optimization methods based on certain objective function(s) are widely used to provide solutions for decision makers. For complex high-dimensional problems, such as network hosting capacity evaluation of intermittent renewables, simplifications are often used which can lead to the ‘optimal’ solution being suboptimal or nonoptimal. Even where the optimization problem is resolved, it would still be valuable to introduce some diversity to the solution for long-term planning purposes. This paper introduces a general framework for solving optimization for power systems that treats an optimization problem as a history match problem which is resolved via statistical emulation and uncertainty quantification. Emulation constructs fast statistical approximations to the complex computer simulation model in order to identify appropriate choices of candidate solutions for given objective function(s). Uncertainty quantification is adopted to capture multiple sources of uncertainty attached to each candidate solution and is conducted via Bayes linear analysis. It is demonstrated through a hosting capacity case study involving variable wind generation and active network management. The proposed method effectively identified not only the maximum connectable capacities but also a diverse set of near-optimal solutions, and so provided flexible guides for using the existing network to maximize the benefits of renewable generation.