[Paper Review] Adaptive Distributionally Robust Planning for Renewable-Powered Fast Charging Stations Under Decision-Dependent EV Diffusion Uncertainty

Yujia Li, Feng Qiu+2 more|arXiv (Cornell University)|Oct 11, 2023

Electric Vehicles and InfrastructureEngineering3 citations

TL;DR

This paper proposes a two-stage decision-dependent distributionally robust fast charging station (D3R-FCSP) planning model that explicitly models electric vehicle (EV) adoption rates as decision-dependent uncertainties (DDUs) using decision-dependent ambiguity sets (DDASs). By integrating a multi-period capacitated arc cover-path cover (MCACPC) model and reformulating the problem into a single-level mixed-integer linear program via strong duality and McCormick envelopes, the model enables adaptive, cost-efficient, and secure deployment of renewable-powered FCSs while accelerating EV adoption through a positive feedback loop between FCS placement and EV diffusion.

ABSTRACT

When deploying fast charging stations (FCSs) to support long-distance trips of electric vehicles (EVs), there exist indirect network effects: while the gradual diffusion of EVs directly influences the timing and capacities of FCS allocation, the decisions for FCS allocations, in turn, impact the drivers' willingness to adopt EVs. This interplay, if neglected, can result in uncovered EVs and security issues on the grid side and even hinder the effective diffusion of EVs. In this paper, we explicitly incorporate this interdependence by quantifying EV adoption rates as decision-dependent uncertainties (DDUs) using decision-dependent ambiguity sets (DDASs). Then, a two-stage decision-dependent distributionally robust FCS planning (D$^3$R-FCSP) model is developed for adaptively deploying FCSs with on-site sources and expanding the coupled distribution network. A multi-period capacitated arc cover-path cover (MCACPC) model is incorporated to capture the EVs' recharging patterns to ensure the feasibility of FCS locations and capacities. To resolve the nonlinearity and nonconvexity, the D$^3$R-FCSP model is equivalently reformulated into a single-level mixed-integer linear programming by exploiting its strong duality and applying the McCormick envelope. Finally, case studies highlight the superior out-of-sample performances of our model in terms of security and cost-efficiency. Furthermore, the byproduct of accelerated EV adoption through an implicit positive feedback loop is highlighted.

Motivation & Objective

• To address the 'chicken-and-egg' problem in EV adoption and FCS deployment by modeling EV adoption rates as decision-dependent uncertainties.
• To enhance grid security and cost-efficiency in coupled transportation and distribution networks by integrating on-site renewable energy and energy storage.
• To develop a robust optimization framework that accounts for ambiguous probability distributions of EV adoption rates due to limited historical data.
• To ensure feasible FCS locations and capacities by modeling EV recharging patterns using a multi-period capacitated arc cover-path cover (MCACPC) model.
• To enable adaptive, out-of-sample robust planning through a single-level MILP reformulation of the original bilevel problem.

Proposed method

• The D3R-FCSP model uses decision-dependent ambiguity sets (DDASs) to represent uncertain EV adoption rates that are endogenously influenced by FCS deployment decisions.
• A multi-period capacitated arc cover-path cover (MCACPC) model is embedded to ensure that all EV trips along designated paths are covered by at least one FCS with sufficient capacity.
• The bilevel structure of the problem is reformulated into a single-level mixed-integer linear program (MILP) using strong duality and McCormick envelopes to handle bilinear terms.
• The model jointly optimizes first-stage investments in FCSs, on-site PVs, ESSs, substation capacity, and distribution line expansions.
• The objective function minimizes total cost, including investment, operation, and penalty costs for load shedding, PV curtailment, and uncovered EVs.
• The formulation incorporates power flow constraints, voltage limits, and line ratings to ensure radial distribution network security.

Experimental results

Research questions

• RQ1 How can decision-dependent uncertainties in EV adoption rates be effectively modeled in FCS planning under limited data?
• RQ2 To what extent does incorporating DDAs improve out-of-sample performance in terms of cost, security, and EV coverage?
• RQ3 Can a robust FCS planning model that accounts for ambiguous probability distributions of EV adoption outperform traditional deterministic or distributionally robust models?
• RQ4 How does the feedback loop between FCS deployment and EV adoption influence long-term diffusion rates and system performance?
• RQ5 What is the monetary value of incorporating DDUs in FCS planning under varying traffic and sensitivity conditions?

Key findings

• The proposed D3R-FCSP model achieves 25.9% and 30.3% expected cost savings under IF = 1 and IF = 2 p.u., respectively, when TF is set at 125%, demonstrating significant monetary benefits.
• The model maintains sufficient security margins and effectively prevents voltage violations and line overloads, as confirmed by voltage profiles and line rating analyses across all planning periods.
• The MCACPC model ensures that all EV trips are covered by FCSs with adequate capacity, with no uncovered EVs in the out-of-sample evaluation.
• The VD3RS metric peaks at TF = 150% under fixed IF, indicating optimal value of information under moderate traffic, but declines at higher traffic due to grid capacity constraints.
• The model accelerates EV adoption through a positive feedback loop: better FCS placement increases EV adoption, which in turn justifies further FCS investment.
• Case studies show that the proposed strategy leads to higher EV adoption rates—e.g., 30.53% by period 3 in OD pair 3-19—compared to baseline strategies, confirming the effectiveness of the feedback mechanism.