Frequency Stability Using MPC-based Inverter Power Control in Low-Inertia Power Systems

The electrical grid is evolving from a network consisting of mostly synchronous machines to a mixture of synchronous machines and inverter-based resources such as wind, solar, and energy storage. This transformation has led to a decrease in mechanical inertia, which necessitate a need for the new resources to provide frequency responses through their inverter interfaces. In this paper we proposed a new strategy based on model predictive control to determine the optimal active-power set-point for inverters in the event of a disturbance in the system. Our framework explicitly takes the hard constraints in power and energy into account, and we show that it is robust to measurement noise, limited communications and delay by using an observer to estimate the model mismatches in real-time. We demonstrate the proposed controller significantly outperforms an optimally tuned virtual synchronous machine on a standard 39-bus system under a number of scenarios. In turn, this implies optimized inverter-based resources can provide better frequency responses compared to conventional synchronous machines.

💡 Research Summary

The paper addresses the growing challenge of frequency stability in low‑inertia power systems, where traditional synchronous generators are being replaced or supplemented by inverter‑based resources (IBRs) such as wind turbines, photovoltaic plants, and battery storage. The loss of mechanical inertia makes the grid more vulnerable to large frequency deviations and high rates of change of frequency (ROCOF) after disturbances. Existing control approaches for IBRs—primarily droop control and virtual synchronous machines (VSMs)—rely on a small set of tunable parameters (virtual inertia and damping) and cannot directly enforce hard power or energy limits that are intrinsic to renewable and storage devices. Moreover, VSMs suffer from an inherent trade‑off: improving one performance metric (e.g., reducing frequency deviation) typically worsens another (e.g., increasing settling time).

To overcome these limitations, the authors propose a Model Predictive Control (MPC) based strategy called MIPC (MPC‑based Inverter Power Control). At each discrete time step the controller predicts the system’s evolution over a finite horizon N, solves an optimization problem that minimizes a weighted sum of the squared frequency deviations and the squared ROCOF, and then applies only the first control action (the optimal inverter power set‑point). The decision variables are the inverter voltage angles (u_k), which are later mapped to active power outputs through the power‑flow equations. The objective function is

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