Modeling and Design of $df/dt$ -Based Inertia Control for Power Converters

Abstract

Power systems with high penetration rates of inverter-based generation units exhibit reduced system inertia. Faults like plant outages or fault-induced system splits then cause an increased rate of change of frequency and may lead to frequency instability. One of the proposed schemes to provide synthetic inertia with power electronic converters is the frequency-derivative-based ( $df/dt$ ) approach. Converters with this method inject an active current that is proportional to the derivative of the grid frequency to mimic the inertia of synchronous plants. Specification of synthetic inertia is currently being discussed for future grid codes. In this paper, we show that the frequency derivative in the $df/dt$ controller is subject to a severe bandwidth limitation. Considerable low-pass filtering is indispensable to avoid instability due to the excitation of local oscillation modes in the harmonic frequency range. We have found a first-order lag with a time constant around 1 s to be required for a robustly stable system with common parameters. A new discrete-time linear model that accurately represents sampling effects is introduced and comprehensively described. A $df/dt$ control design is proposed that leads to a robustly stable system. Model and control design are validated by laboratory experiments, especially regarding mechanisms of instability. The main finding of this paper—applying a $df/dt$ controller harbors the risk of merely shifting the initial danger of system-wide frequency instability to local stability problems—is important for power plant manufacturers as well as system operators.