Bilevel Optimization for Improved Flexibility Aggregation Models of Electric Vehicle Fleets

TL;DR

This work addresses the challenge of accurately representing the flexibility potential of large and heterogeneous EV fleets in power system planning. It introduces a bilevel aggregation framework in which the outer level minimizes scheduling deviations between an aggregated EV unit (AEV) and reference individual EV units, while the inner level optimizes the AEV unit’s profits, parameterized by hourly-to-daily scaling mappings. By reformulating the bilevel problem into a single MILP via KKT conditions and big-$M$ disjunctive constraints, the approach enables tractable computation and high-fidelity representations of fleet flexibility. Case studies show the bilevel method achieving up to a 78% reduction in charging-power RMSE relative to simple aggregation, with finer temporal mappings yielding the closest match to reference schedules and offering a foundation for future extensions such as vehicle-to-grid integration and more varied user behaviors.

Abstract

Electric vehicle (EV) fleets are expected to become an increasingly important source of flexibility for power system operations. However, accurately capturing the flexibility potential of numerous and heterogeneous EVs remains a significant challenge. We propose a bilevel optimization formulation to enhance flexibility aggregations of electric vehicle fleets. The outer level minimizes scheduling deviations between the aggregated and reference EV units, while the inner level maximizes the aggregated unit's profits. Our approach introduces hourly to daily scaling factor mappings to parameterize the aggregated EV units. Compared to simple aggregation methods, the proposed framework reduces the root-mean-square error of charging power by 78~per cent, providing more accurate flexibility representations. The proposed framework also provides a foundation for several potential extensions in future work.

Figures (7)

• Figure 1: Monthly distributions of hourly power consumption for electric vehicles, heat pumps, and household loads in Germany under a net-neutral scenario. Boxplots show the inter-quartile range, with whiskers extending to the 2.5 % and 97.5 % percentiles.
• Figure 2: Schematic overview of the bilevel optimization problem structure.
• Figure 3: Profile generation based on driving behavior, available charging and discharging power, and state-of-charge (SOC) limits, resulting in two EV fleet strategies: uncontrolled behavior and optimized fleet scheduling.
• Figure 4: Electricity price, resulting Aggregated Electric Vehicle (AEV) and Simple Aggregation (SA) profiles compared to the reference EV profiles for state-of-charge (SOC) and charging power scheduling decisions during the considered three-week planning horizon.
• Figure 5: Comparison of optimized scaling factors for maximum charging power availability and minimum/maximum SOC profiles for all considered scaling factor mappings and each weekday. Note that in order to obtain the final aggregated profiles shown in Figs. \ref{['fig:charge_individual']} and \ref{['fig:soc_individual']}, the factors need to be applied to the corresponding aggregated profiles $\overline{X}^{\text{C}}_{v,t}$, $\overline{X}^{\text{S}}_{v,t}$ and $\underline{X}^{\text{S}}_{v,t}$.