Fundamentals of State-Space Based Load Flow Calculation of Modern Energy Systems

Our current energy landscape is ever-changing, resulting from the ongoing energy transition and introducing a massive expansion of volatile generation feed-in and energy consumption (due to electrification). In turn, the energy supply’s requirements are also being affected. In this context, the energy system’s optimisation across all sectors will only grow in significance, especially in terms of future developments. Facilitating and researching methods for carrying out the aforementioned optimisation creates new demands pertaining to load flow simulation programmes. The volatility of specific participants and their interactions within existing power grids must be evaluated, wherefore the consideration of a large number of time steps but also dynamic simulations becomes inevitable. Carrying out such simulations is possible but very time-consuming. This article compared a variety of conventional load flow simulations such as the current iteration and Newton–Raphson methods and also introduced a novel, state-space based calculation approach, which boasts the potential of structurally increasing simulation speeds. Each of the method’s underlying principles, requirements, and mathematical correlations will be discussed and explained. In the second part of this article, the most important state-space equivalent circuit models of critical operating equipment are introduced. These models are essential for carrying out load flow simulation tests for an exemplary test network but could also be used for dynamic purposes. The previously showcased load flow methods were applied to a test network, with which the simulation methods should be validated. The results show that the state-space simulation has high accuracy while also being very flexible. All in all, the load flow calculation in state-space offers many advantages that could be an interesting alternative to conventional load flow simulations, especially for the analysis of complex, time series-based, and intelligently controlled smart grid power systems. In this context, the direct application of system theoretical methods for stability calculations, controllability, and dynamic system studies is to be mentioned. Optimisation options regarding the processes within the state-space calculation software still promise further significant increases in performance.