Joint Price and Power MPC for Peak Power Reduction at Workplace EV Charging Stations

1. Problem Statement

The paper addresses the high operational costs faced by commercial Electric Vehicle (EV) charging station operators, specifically demand charges. Demand charges are utility fees based on the highest power consumption (peak load) during a billing cycle, often accounting for 30% to 70% of total electricity costs.

• The Challenge: EV charging arrivals are stochastic. A single poorly timed arrival can push the station's load above the current running peak, triggering a significant increase in demand charges.
• Limitations of Existing Work:
  • Prior optimization strategies often focus solely on power scheduling (offline or non-anticipatory) without considering user behavior.
  • Some joint price-power formulations exist but lack anticipatory capabilities. They fail to account for the fact that early morning control decisions (e.g., 8 AM) significantly influence peak loads later in the day (e.g., 2 PM).
  • Existing methods often control only ongoing sessions, missing the opportunity to shape the load profile for the entire day based on early indicators.

2. Methodology

The authors propose a Joint Price and Power Optimization framework enhanced by Model Predictive Control (MPC) and time-series forecasting.

A. Benchmark Optimization Problem

The baseline is a station-level optimization solved upon every new user arrival.

• User Choices: Users are presented with two prices: $z_{sch}$ (Scheduled) and $z_{reg}$ (Regular). They choose between:
  1. Regular: Uncontrollable, maximum power charging.
  2. Scheduled: Controllable power profile, guaranteed energy delivery by departure.
  3. Leave: User departs if prices are too high.
• Objective: Maximize expected profit by optimizing the price menu and power profiles for scheduled users.
• Behavioral Model: A two-step discrete choice model estimates the probability of users selecting an option based on the price difference between Scheduled and Regular.

B. Proposed Controllers for Peak Reduction

To overcome the limitations of the benchmark, the authors introduce three specific modifications:

1. Iterative Hard Thresholding:

   • Adds a hard constraint ($G_\tau \le M$) to the station load, where $M$ is initialized at the current running peak.
   • If the problem is infeasible, $M$ is iteratively increased until a solution is found. This strictly caps peak growth but may limit flexibility.

2. Softplus Demand Charge Penalty:

   • Replaces the linear demand charge term with a convex softplus function ($\log(1+e^x)$).
   • This creates a smooth, increasing penalty as the optimized load approaches the running peak, encouraging the controller to avoid the "danger zone" before a peak is actually broken.

3. Forecast-Enabled Model Predictive Control (MPC):

   • Core Innovation: Incorporates a time-series forecast of future station power into the demand charge calculation.
   • Mechanism: Instead of optimizing only for the current state, the cost function anticipates future arrivals and load spikes. The demand charge term is modified to consider the maximum of the forecasted load and the current running peak.
   • Forecasting Models: Three types were tested:
     • Naive: Assumes no new arrivals; sums previous optimal profiles with the new user's profile.
     • Linear: Elastic Net regression.
     • XGBoost: Gradient boosting.
   • Features: Historical power, planned profiles, session counts, and temporal encodings (time of day, day of week).

3. Key Contributions

1. Anticipatory Control: The first application of MPC with time-series forecasting specifically for workplace EV charging to anticipate demand spikes and adjust pricing/power schedules proactively.
2. Load Flexibility via Dynamic Pricing: Demonstrates how dynamic pricing can incentivize users to select "Scheduled" (controllable) charging, thereby increasing the controller's flexibility to shave peaks.
3. Superior Performance: Proves that the proposed MPC approach outperforms state-of-the-art benchmark optimization (non-anticipatory) and other non-MPC reformulations in reducing both demand charges and total operator costs.
4. Insight on Forecasting: Reveals that minimizing standard forecast error (RMSE) does not strictly correlate with better MPC performance; the structure of the forecast relative to the control loop is more critical.

4. Results

The methods were validated using a Monte Carlo simulation replaying 2,274 real-world charging sessions from the Smart Learning Pilot for EV Charging Stations (SlrpEV) over 12 months.

• Cost Reduction:
  • The MPC (Naive) scheme achieved the best results, reducing Demand Charges by 16.9% and Total Operator Costs by 4.6% compared to the benchmark.
  • All MPC variants reduced Demand Charges by approximately 15% and TOU (Time-of-Use) energy costs by ~1%.
  • Non-MPC controllers (Threshold and Softplus) failed to significantly reduce total costs.
• Peak Power Management:
  • The MPC controller shifted charging to off-peak hours by anticipating busy days, whereas the benchmark waited for the cheapest energy (super off-peak) only after the day started, leading to higher peaks.
  • Pricing Strategy: MPC sets high prices for "Regular" charging during peak hours but offers significant discounts for "Scheduled" charging early in the morning (6–8 AM). This builds a base of controllable load early, allowing the system to maintain lower prices later in the day.
• Forecasting Nuance:
  • Surprisingly, the Naive model (highest RMSE) outperformed the Linear and XGBoost models (lower RMSE) in peak reduction.
  • Reason: The advanced models were trained on historical data controlled by a different algorithm (benchmark), creating a distribution mismatch. The Naive model, based on the MPC's own previous outputs, was more consistent with the optimization loop's reality.

5. Significance and Limitations

Significance:

• Economic Impact: The approach offers a viable path for operators to reduce costs by ~5%, which can be passed to consumers as lower prices or retained as profit.
• Scalability: While tested on a small station (8 chargers), the authors argue the approach would perform even better at larger sites due to the Law of Large Numbers smoothing load curves.
• Feasibility: The computational complexity is low (runs in fractions of a second on a laptop), making real-time deployment feasible.

Limitations & Future Work:

• Simulation Constraints: The Monte Carlo simulation assumed users had already decided to charge (no "Leave" option in the simulation data), which may skew profit calculations.
• Self-Referential Problem: Retraining forecast models on data generated by the MPC itself would improve accuracy but creates a circular dependency (forecasts depend on MPC outputs, which depend on forecasts).
• Data Size: The study used a dataset from a small station (8 chargers). Future work is needed to validate scalability across hundreds of chargers.

In conclusion, the paper demonstrates that joint price and power optimization, when combined with anticipatory MPC, is a highly effective strategy for mitigating demand charges in workplace EV charging, outperforming traditional static or non-anticipatory optimization methods.