Model Predictive Control (MPC) for Microgrids

The defining mechanism of MPC. At each control interval, the optimizer computes an optimal dispatch trajectory for a finite prediction horizon (e.g., 24 hours), but only the first control action is executed. The horizon then shifts forward one step and the optimization is repeated. This provides inherent feedback to correct for forecast errors in solar irradiance or load demand, preventing open-loop drift.

Unlike heuristic controllers, MPC systematically enforces hard operational limits as mathematical constraints within the optimization problem:

• State of Charge (SoC) limits: Prevents battery over-charge or deep discharge
• Power ramp rates: Respects inverter slew-rate limitations
• Transformer thermal limits: Avoids overload at the point of common coupling
• Voltage bounds: Maintains ANSI C84.1 Range A compliance

MPC requires a mathematical representation of the microgrid's temporal behavior. This model captures:

• Battery energy storage dynamics: Coulomb counting and charge/discharge efficiency
• Thermal inertia of buildings: Time constants for HVAC load shifting
• Generator fuel consumption curves: Non-linear efficiency maps This model is the controller's 'digital twin,' enabling it to predict the future consequences of current decisions.

The optimizer minimizes a weighted sum of competing objectives, formalized as a scalar cost function. Typical terms include:

• Energy cost: Minimize time-of-use ($/kWh) charges
• Demand charge penalty: Suppress peak 15-minute interval power
• Battery degradation cost: Penalize cycling to extend asset life
• Emissions penalty: Minimize diesel generator runtime The weighting factors are tuned to reflect the operator's specific economic priorities.

MPC explicitly incorporates forecasted disturbances into its prediction model, enabling proactive rather than reactive control. Key feed-forward signals include:

• Photovoltaic generation forecast: Anticipates a mid-day surplus to pre-charge storage
• Load prediction: Pre-cools a building before a predicted occupancy peak
• Electricity price schedule: Schedules arbitrage based on day-ahead market prices This anticipatory action is a primary advantage over feedback-only controllers.

To handle discrete decisions, microgrid MPC is often formulated as a Mixed-Integer Linear Program (MILP) . Binary variables represent:

• Generator on/off commitment status
• Battery charging vs. discharging mode (prevents simultaneous charging)
• Connection to or islanding from the main grid Commercial solvers like Gurobi or CPLEX are used to find the globally optimal solution to this NP-hard problem within the required control interval.