Speaker
Description
Due to the massive integration of decentralised energy resources (DER) such as photovoltaic systems, battery storage and e-charging stations, the optimal power flow (OPF) in electric distribution networks has gained significant research interest. Assuming that an active distribution network possesses a fixed topology, the equality constraints are described by the power flow equations, which must satisfy Kirchhoff’s Law and Ohm’s Law, whereas the state and control variables compose inequality constraints posed by the physical limitations of the network components. Particularly, radial low-voltage networks have the nature of simpler topology and a larger set of variables.
Given a set of linear or quadratic objectives and constraints concerned with power network security, a steady-state OPF can be formulated as a non-linear, non-convex optimisation problem. Generally, solving a large-scale, single-stage OPF is already faced with challenges including the non-convexity of the feasible set and the size of the large, sparse admittance matrix.
From there, researchers have been employing optimal control techniques to transform the time-invariant OPF into a time-varying problem on a discrete temporal domain. The discrete-time OPF can be solved progressively at each time instant, or, if forecast data are available, as a stacked model predictive control problem over a longer discretised time window. However, classical centralised Newton-type methods, such as the interior point (IP) and sequential quadratic programming (SQP), will not be suitable for large-scale online OPF regarding the computation time requirement and data privacy concerns. Consequently, the demand for distributed OPF formulations and algorithms arises.
With this background, various distributed optimisation approaches and their variants have been investigated recently to accommodate the requirements for online, time-varying OPF. Several examples of distributed OPF approaches are the projected primal-dual gradient method, the alternating direction method of multipliers (ADMM) and Augmented Lagrangian Alternating Direction Inexact Newton (ALADIN). For instance, a possibility for model reduction by condensing the variable space is implicitly contained in the OPF formulation. The implicit function theorem suffices that the control variables can be mapped to state variables by the power flow equation, if the discretised time step is small enough.
In this talk, we present recent advances in the real-time OPF formulation and online algorithms regarding their convergence properties and error estimates.
