A Hierarchical Stochastic Model Predictive Control Framework for Integrated Request-aware Charge Scheduling and Service Allocation

Technical Summary: A Hierarchical Stochastic Model Predictive Control Framework for Integrated Request-aware Charge Scheduling and Service Allocation

Problem Statement
The paper addresses the operational challenges faced by Mobility-on-Demand Electric Vehicle (MoD-EV) fleets operating under a flexible A-to-B rental model. In this context, vehicles are rented from a charging station (CS) and returned to another, with trip bookings lacking precise information regarding distance or route. The fleet operator faces a complex optimization problem involving:

1. Stochastic Demand: Customer rental requests are uncertain and intermittent.
2. Dynamic Pricing: Electricity prices vary over time.
3. Nonlinear Battery Dynamics: Accurate modeling requires capturing nonlinear behaviors such as temperature effects, open-circuit voltage (OCV) variations, and capacity fading, which are often oversimplified in existing literature.
4. Scalability: Centralized optimization approaches for large fleets suffer from computational intractability due to the combinatorial nature of mixed-integer constraints and the size of the prediction horizon.

The core objective is to minimize total operational costs (electricity, switching, and battery degradation) while ensuring service reliability (meeting rental requests) under uncertainty, without compromising battery health.

Methodology
The authors propose an Integrated Charging Management and Service Allocation Mechanism (iCMS) based on a stochastic, multi-objective Model Predictive Control (MPC) framework.

1. Battery Modeling:

   • The study utilizes an enhanced Equivalent Circuit Model (ECM) to represent battery dynamics, capturing internal temperature, State of Charge (SOC), and terminal voltage.
   • To handle nonlinearity within a linear programming framework, the authors employ a piece-wise linear approximation of the battery dynamics and the capacity fading model. The SOC range is divided into mutually exclusive segments, allowing the use of Mixed-Integer Linear Programming (MILP).
   • A cyclic capacity fading model is integrated to quantify degradation based on average SOC, SOC deviation, and charge transfer amount, moving beyond simple aggregated cost models.

2. Stochastic Optimization (Chance-Constrained MPC):

   • The framework incorporates chance constraints to handle uncertain ride requests. Instead of assuming a specific parametric distribution, the model uses historical data scenarios to enforce service-level constraints probabilistically (e.g., ensuring a specific confidence level $\alpha_{CON}$ that demand is met).
   • The objective function minimizes a weighted sum of electricity costs, battery degradation costs, and charging mode switching costs.

3. Hierarchical Distributed Solution:

   • To address the computational complexity of the centralized MILP formulation, the authors develop a two-stage hierarchical distributed algorithm:
     • Upper Stage (Ride Assignment): A reduced-order model optimizes high-level service allocation and vehicle departure times ($t_{dep}$) across the fleet, satisfying chance constraints.
     • Lower Stage (Charging Scheduling): Decentralized optimization problems are solved for individual idle EVs. Each vehicle determines its detailed charging sequence (current, mode switching) based on the departure time provided by the upper stage, local battery dynamics, and electricity prices.

Key Contributions
The paper claims the following specific contributions:

• Integrated Mechanism: Development of a unified framework that simultaneously handles service allocation under stochastic requests and nonlinear battery dynamics.
• Advanced Battery Modeling: Adaptation of a parametric battery model that captures nonlinear dynamical behavior and a detailed cyclic capacity fading model, rather than relying on simplified State-of-Charge (SOC) linear models.
• Computational Efficiency: Construction of a MILP problem via piece-wise linear relaxation of nonlinear dynamics to improve decision-making efficiency.
• Discrete Mode Switching: Formulation of discrete charging operations (including V2G discharging, multiple charging modes, and OFF states) with transition automata.
• Scalable Architecture: Development of a hierarchical distributed algorithm that decomposes the centralized problem to reduce computational complexity, enabling real-time implementation for larger fleets.

Results and Evaluation
The framework was evaluated using a dataset of 300 EVs over a 24-hour horizon with Singapore wholesale electricity prices and historical demand data. The proposed methods (Centralized iCMS and Distributed iCMS) were compared against a Business-as-Usual (BAU) heuristic and a Laxity-based Charging (LC) approach.

• Cost Efficiency: The proposed iCMS approaches significantly outperformed BAU and LC. The Distributed iCMS (D-iCMS) achieved the lowest battery degradation cost ($5.2 vs. $21.04 for BAU) and near-optimal electricity costs ($138.38 vs. $193.95 for BAU).
• Load Profile: While the Centralized approach (C-iCMS) achieved the lowest electricity cost, it resulted in a higher Peak-to-Average Ratio (PAR) of 3.89 due to aggressive exploitation of low-price periods. D-iCMS offered a balanced solution with a moderate PAR of 2.33.
• Stochastic Performance: Analysis of varying confidence levels showed that higher confidence levels yield more robust solutions with smaller deviations between predicted and actual costs, though at the expense of higher resource utilization.
• Computational Scalability: Runtime analysis demonstrated that the centralized approach suffers from exponential growth in computation time as the prediction horizon and sampling interval increase. In contrast, the distributed D-iCMS approach maintained low runtimes (e.g., 1.3 seconds for a 30-minute interval) by decomposing the problem, making it suitable for real-time applications.
• Hyperparameter Sensitivity: The study analyzed the impact of switching costs and penalty factors, showing that tuning these parameters allows operators to prioritize grid smoothness (lower degradation) or operational feasibility (lower penalties).

Significance
The paper positions this work as a practical decision-support tool for fleet management. It claims that the proposed framework bridges the gap between theoretical battery modeling and operational reality by:

1. Enabling grid-responsive dispatching that mitigates peak-load impacts while leveraging price incentives.
2. Providing a mechanism to balance competing objectives (electricity cost, service reliability, and battery longevity) through tunable cost function weights.
3. Offering scalability through decentralized computation, allowing fleet operations to grow without being bottlenecked by the computational limits of centralized solvers.

The authors conclude that while 10% SOC discretization offers a robust starting point for balancing runtime and accuracy, the framework's ability to handle nonlinear dynamics and stochastic demand simultaneously represents a significant advancement over existing simplified scheduling strategies.