Model Predictive Control

MPC solves an optimization problem over a finite future time window (the prediction horizon), but only the first computed control action is implemented. The horizon then shifts forward one time step, and the optimization is repeated. This receding horizon strategy provides inherent feedback, allowing the controller to compensate for model inaccuracies and external disturbances at each iteration.

A defining advantage of MPC is its ability to systematically incorporate hard constraints directly into the control law synthesis. These constraints can represent physical limits such as:

• Actuator saturation: Maximum generator ramp rates.
• State limits: Voltage magnitude bounds (e.g., ±5% of nominal).
• Safety margins: Minimum frequency nadir thresholds. This ensures optimal performance without violating operational limits.

Unlike single-loop PID controllers, MPC natively handles Multiple-Input Multiple-Output (MIMO) systems with complex cross-coupling. In a microgrid, a single MPC can simultaneously coordinate:

• Frequency regulation via battery active power injection.
• Voltage support via reactive power from smart inverters.
• Thermal management of transformer loading. This holistic view prevents conflicting control actions.

MPC explicitly uses a dynamic model of the plant to anticipate future behavior. By incorporating forecasts of external disturbances—such as predicted solar irradiance drops or expected load spikes—the controller can act preemptively. This feedforward capability allows it to mitigate disturbances before they manifest as significant tracking errors, rather than reacting after the fact.

The control action is determined by minimizing a cost function that mathematically defines the desired performance trade-offs. Typical terms in a microgrid MPC cost function include:

• Tracking error: Penalizing deviation from the nominal frequency (e.g., 60 Hz).
• Control effort: Penalizing aggressive battery cycling to extend lifespan.
• Economic dispatch: Minimizing the cost of imported grid power or fuel consumption.

The primary limitation of MPC is its computational footprint. Solving a constrained optimization problem (often a Quadratic Program or Mixed-Integer Linear Program) at every time step requires significant processing power. For high-speed power electronics switching in the kHz range, explicit MPC solutions or hardware-accelerated solvers are necessary to meet strict real-time execution deadlines.