Superposition-based modelling of series FACTS in nonlinear mathematical optimized grid operation

Ongoing changes in electrical energy systems and increasing possibilities to control power flows increase volatility as well as flexibility and therefore complexity of their operation. Hence, systems for power flow control, system optimization, and their efficient integration in system operation and planning currently are researched. Especially for grid operation, reproducible and robust solutions are needed which can be provided by mathematical optimizations. This work describes a novel approach to flexibly and efficiently integrate different series FACTS and compensation elements with just one common equivalent circuit in a nonlinear mathematical optimization framework. The superposition-inspired modelling approach divides pi-line and series element power flows in order to easily implement series elements in the proposed power flow description. The presented implementation allows to model different elements while keeping the node-admittance matrix constant and to include equipment-specific control structures and constraints in the optimization framework. The implementation is validated compared to a detailed modelling in a reference simulation environment. In different applications of the novel modelling a reduction of losses over 14 % even in a small test system can be achieved, while a second application example highlights the importance of optimization with system-wide views compared to local set-point controls.