Key Takeaways & Executive Findings
- •• • The tri-layer model discretizes charging into 15-minute intervals, enabling CPLEX to solve the microgrid mixed-integer linear program while the antelope optimization algorithm handles the BSS-truck subproblem; this decomposition matters industrially because monolithic stochastic formulations for coupled vehicle-grid systems typically exceed tractable solve times beyond 96 intervals. • • Service fee adjustment is the sole control lever for reshaping truck arrival rates; the BSS layer optimizes charging power to track renewable output and balance supply-demand, then translates that schedule into a fee signal. This indirect mechanism avoids direct command-and-control over drivers, a critical design constraint for commercial fleet operations where driver autonomy is contractually protected. • • The objective function F1 maximizes net revenue by subtracting eight cost terms—operation and maintenance, gas turbine start-stop, fuel, grid purchase, battery degradation, waiting compensation, environmental, and communication—from BSS revenue. The explicit inclusion of waiting compensation cost (Cd,i) ties driver inconvenience to system economics, a parameter absent from prior BSS dispatch models that treated queue time as exogenous. • • The framework assumes uniform battery specifications across trucks and station inventory, constant charging power, and fixed cost parameters over the optimization horizon. These simplifications enable deterministic solution but exclude battery degradation heterogeneity and market price volatility; industrial deployment would require receding-horizon updates to cost coefficients at minimum daily frequency.
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Abstract
The integration of electric heavy-duty truck battery swap stations (BSSs) into microgrids introduces a bidirectional coupling between renewable generation volatility and swap demand that existing dispatch frameworks fail to capture. This study formulates a tri-layer collaborative optimal scheduling model spanning the microgrid, the battery swap station, and the heavy-duty truck fleet. The microgrid layer maximizes daily revenue by co-optimizing microgas turbine, battery storage, wind, and photovoltaic outputs, with CPLEX resolving the mixed-integer linear program. The BSS layer adjusts service fees to influence truck arrival rates, thereby reshaping the station load profile to track renewable generation. The truck layer responds to fee signals by autonomously selecting swap times, with a 15-minute discretization interval. An antelope optimization algorithm solves the BSS-truck subproblem, and the two layers iterate until convergence. The framework is validated against a case study, demonstrating that fee-mediated demand response reduces curtailment and improves supply-demand balance. The model addresses a critical gap: prior BSS scheduling treated arrival rates as exogenous and ignored renewable fluctuations, while truck swap decisions ignored station service capacity. By internalizing both signals, the proposed architecture achieves coordinated optimization without centralized control over vehicle behavior.
1. Introduction
Heavy-duty truck electrification confronts a fundamental mismatch: battery swap stations (BSSs) schedule charging based on historical arrival rates, while microgrid operators dispatch renewable generation without visibility into swap demand. Prior work optimized microgrid scheduling with cost and emissions objectives, and separately optimized BSS peak-shaving under service capacity constraints, but no framework closed the loop between renewable volatility and truck swap timing. The consequence is predictable—curtailment during high-wind or high-solar periods coinciding with low swap demand, and grid purchases during peak periods when trucks arrive en masse.
This study introduces a tri-layer collaborative architecture where the microgrid broadcasts renewable generation forecasts to the BSS, the BSS translates those forecasts into service fee adjustments, and trucks respond by shifting swap times. The BSS-truck subproblem iterates until convergence, with the BSS recalculating charging power after each truck arrival update. CPLEX solves the microgrid layer, and an antelope optimization algorithm solves the BSS-truck layer. The protocol specifically addresses the bottleneck of exogenous arrival rates by making truck behavior endogenous to renewable availability, without requiring direct control over vehicle movements.
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ZHAO Wenfei, YU Guochen, LAN Tianxiao, LI Chunyu, FU Jiajia, QI Zhiyuan (2026). Collaborative Optimal Scheduling of Microgrids Incorporating Electric Heavy-Duty Truck Battery Swap Stations. Acta Energiae Solaris Sinica. https://doi.org/10.19912/j.0254-0096.tynxb.202608_9710
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Frequently Asked Questions
What prevents the service fee mechanism from creating oscillatory arrival rates that destabilize the BSS-truck iteration?
The model iterates between the BSS charging power optimization and truck arrival rate updates until a termination condition is met. Oscillation risk depends on the fee elasticity of truck arrival rates, which is not parameterized in the extracted text. In practice, convergence requires that the fee adjustment step be bounded and that truck response exhibit diminishing sensitivity as fees deviate from a reference level. The 15-minute discretization limits the number of decision points per day to 96, which caps the iteration space and reduces the likelihood of limit cycles. Industrial deployment would require real-time monitoring of arrival rate variance and adaptive damping of fee adjustments if variance exceeds a threshold.
How does the model handle the case where a truck arrives at the BSS but no charged battery is available due to renewable-driven charging delays?
The extracted text does not specify a battery inventory constraint or a service-level guarantee. The waiting compensation cost Cd,i(t) is included in the microgrid objective, which implies that truck waiting time is penalized economically. However, the model assumes uniform battery specifications and constant charging power, which simplifies inventory dynamics. A real system would require a minimum state-of-charge inventory constraint to prevent service failures. The absence of this constraint in the extracted formulation suggests the model assumes sufficient battery inventory or that waiting compensation is sufficient to deter arrivals during low-inventory periods.
What is the computational burden of solving the microgrid MILP with CPLEX at 15-minute resolution over a 24-hour horizon?
The extracted text does not report solve times or problem dimensions. The microgrid layer includes binary variables for gas turbine start-stop decisions and continuous variables for battery, wind, photovoltaic, and grid power. At 96 time steps, the MILP size is moderate—likely solvable within minutes on standard hardware. The BSS-truck layer uses an antelope optimization algorithm, a metaheuristic that may require multiple iterations. The critical computational risk is the outer iteration between layers, which multiplies solve time by the number of convergence rounds. For industrial deployment, a rolling horizon with warm-start initialization would be necessary to meet real-time dispatch requirements.
How sensitive is the revenue maximization to the waiting compensation cost coefficient, and what happens if drivers value time nonlinearly?
The extracted text states that waiting compensation cost is solely a function of waiting time, implying a linear relationship. If drivers value time nonlinearly—for example, with a threshold beyond which dissatisfaction spikes—the linear model would underestimate the fee adjustment needed to shift arrivals. The objective function F1 subtracts Cd,i(t) from revenue, so underestimating compensation cost would lead to overestimating net revenue and under-adjusting fees. Industrial validation would require discrete-choice experiments to estimate the actual utility function of truck drivers, which may vary by fleet operator and route type.
What is the failure mode when renewable generation forecast error exceeds the BSS load flexibility?
The model assumes renewable generation is known and broadcasts it to the BSS. If forecast error is large, the BSS may adjust fees to attract or defer trucks, but truck arrival rates cannot change instantaneously—drivers have schedules and route constraints. The extracted text does not include a forecast error scenario or a robustness constraint. In practice, when forecast error exceeds the BSS load flexibility, the microgrid must fall back on battery storage and gas turbine generation, increasing cost and emissions. The model's deterministic formulation would need stochastic or robust optimization extensions to quantify this failure mode.
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