Model Predictive Control (MPC)

MPC solves an optimization problem over a finite prediction horizon (e.g., 24 hours) but implements only the first control action. At the next time step, the horizon shifts forward and the problem is re-solved with updated state information.

• Prediction Horizon: The future window over which the controller forecasts grid load, energy prices, and EV availability
• Control Horizon: The subset of the prediction horizon where actual charging commands are executed
• Feedback Mechanism: New measurements of State of Charge (SoC) and grid conditions are fed back at each interval, creating a closed-loop system that corrects for forecast errors
• This approach makes MPC inherently robust to uncertainty in renewable generation forecasts and driver behavior

Unlike rule-based controllers, MPC systematically incorporates physical and operational constraints directly into the optimization problem as mathematical inequalities.

• Transformer Thermal Limits: Maximum kVA rating constraints prevent distribution transformer overload from coincident EV charging
• Voltage Bounds: Maintains local bus voltages within ANSI C84.1 limits (±5% of nominal)
• Battery Degradation Constraints: Limits on Depth of Discharge (DoD) and C-Rate to preserve State of Health (SoH)
• Charger Capacity: Per-EVSE maximum power limits and total site capacity constraints
• User Constraints: Minimum SoC requirements by departure time to ensure operational readiness for fleet vehicles

The MPC controller minimizes a multi-objective cost function that balances competing priorities through weighted terms.

• Energy Cost Minimization: Shifts charging to periods of low wholesale electricity prices or high renewable generation
• Demand Charge Management: Penalizes peak power draw to reduce commercial Demand Charge Management costs for fleet operators
• Battery Degradation Cost: Incorporates a Battery Degradation Model that assigns a monetary cost to capacity fade based on cycling depth and C-rate
• Fairness Terms: Ensures equitable power allocation across multiple vehicles rather than prioritizing a single EV
• Frequency Regulation Revenue: Negative cost terms can represent revenue from providing Frequency Regulation ancillary services via Vehicle-to-Grid (V2G)

MPC relies on an internal dynamic model that predicts how the system state evolves in response to control actions.

• Battery Dynamics: A simplified equivalent circuit model tracks SoC evolution: SoC(k+1) = SoC(k) + (η × P_ch × Δt) / E_max where η is charging efficiency
• Transformer Thermal Model: Predicts winding hot-spot temperature and oil temperature based on load current and ambient conditions per IEEE C57.91
• Arrival/Departure Predictions: Integrates with Fleet Energy Management System (FEMS) data to model vehicle availability windows
• Charging Load Forecasting: Uses time-series predictions of aggregate demand as a disturbance input to the model
• The model is typically linear or linearized to enable fast Mixed-Integer Linear Programming (MILP) solvers

MPC proactively compensates for measured or forecasted disturbances before they affect the system, rather than reacting after deviations occur.

• Solar Generation Forecasts: Anticipates on-site photovoltaic output to align EV charging with peak solar production
• Building Load Predictions: Incorporates forecasted facility load to avoid coincident peaks that trigger demand charges
• Grid Price Signals: Responds to day-ahead or real-time electricity price forecasts to minimize energy procurement costs
• OpenADR Integration: Receives utility Demand Response Orchestration signals as external disturbance inputs
• This feedforward capability is a key advantage over reactive controllers like PID, enabling preemptive load shifting

The optimization problem is formulated as a Mixed-Integer Linear Programming (MILP) or quadratic program and solved at each time step using specialized algorithms.

• Decision Variables: Continuous variables for charging power and binary variables for on/off status of each EVSE
• Solver Selection: Commercial solvers like Gurobi or CPLEX, or open-source alternatives like HiGHS, execute the optimization within the control interval deadline
• Decomposition Strategies: For large fleets, the problem may be decomposed using Lagrangian relaxation or distributed MPC across clusters of chargers
• Warm Start: The previous solution is used to initialize the solver, dramatically reducing solve time
• Embedded Deployment: Lightweight MPC formulations can run on edge controllers or within the Charge Point Operator (CPO) central management system

The primary state variable tracked by the MPC controller. SoC represents the current energy stored as a percentage of maximum usable capacity.

• MPC predicts SoC trajectory over the finite horizon
• Terminal constraint ensures SoC meets departure target
• Non-linear voltage characteristics require accurate SoC estimation
• Coulomb counting with voltage-based recalibration prevents drift

A real-time constraint enforcement mechanism that MPC must respect. Distributes available electrical capacity across multiple charging points to prevent circuit breaker trips and transformer overload.

• MPC receding horizon naturally handles shifting load profiles
• Phase balancing prevents neutral conductor overheating
• Infrastructure upgrade deferral is a key economic objective

The active monitoring and algorithmic control of DERs to prevent thermal overload and accelerated aging of distribution transformers. MPC incorporates transformer thermal models as dynamic constraints.

• Hot-spot temperature prediction uses IEC 60076-7 models
• Loss-of-life calculations inform penalty weights in the cost function
• Coincident EV charging is the primary stressor MPC mitigates

An empirical or physics-based representation of capacity fade and internal resistance growth incorporated into the MPC cost function. Balances charging speed against long-term battery health.

• Calendar aging and cycle aging are distinct degradation modes
• High C-rates and extreme SoC accelerate degradation
• MPC weights degradation cost against energy cost and schedule penalties

The application of time-series machine learning models to predict aggregate power demand of EV fleets hours or days in advance. These forecasts serve as the reference trajectory or disturbance input to the MPC controller.

• LSTM and Transformer architectures capture temporal dependencies
• Probabilistic forecasts provide uncertainty bounds for robust MPC
• Forecast accuracy directly impacts constraint violation frequency