Aggregator of Electric Vehicles Bidding in Nordic FCR-D Markets: A Chance-Constrained Program

TL;DR

The study develops a joint chance-constrained bidding framework for EV aggregators to participate in Nordic FCR-D markets under Energinet's P90 reliability requirement and the limited-energy reservoir constraint. It solves the resulting problem with two scalable sample-based methods, ALSO-X and CVaR, and evaluates performance using minute-level flexibility data from 1400 Danish EVs. Results show potential annual bill savings of 6–10% for EV owners and a pronounced synergy effect when aggregating more vehicles, with ALSO-X achieving higher profits but greater risk of overbidding relative to the CVaR approach. The findings highlight the trade-off between market liquidity and reliability, and suggest directions for improving forecasting, exploring less restrictive LER criteria, and extending the framework to additional technologies and distributionally robust formulations.

Abstract

The Danish system operator, Energinet, has recently introduced an innovative grid code called the P90 requirement, which allows stochastic flexible resources to bid their flexibility in Nordic ancillary service markets, contingent upon a minimum 90\% probability of successfully realizing the reserve capacity bid. For limited-energy resources, Energinet imposes additional requirements for participation in these markets. Given these requirements, this paper presents a chance-constrained optimization model designed for aggregators of electric vehicles, aiming to optimally place reserve capacity bids in the Nordic Frequency Containment Reserve for Disturbances (FCR-D) market while accounting for uncertainty in future consumption baselines. We analyze both FCR-D up and down markets, reformulating and solving the proposed joint chance-constrained model using two sample-based methods. Using real data from 1400 charging stations in Denmark from March 2022 to March 2023, we demonstrate the out-of-sample profit potential. Our findings indicate that vehicle owners could save between 6\% and 10\% on their annual electricity bills by providing FCR-D services. Additionally, we observed a synergy effect, where having more vehicles in a single portfolio enables larger bids per vehicle compared to a collective bid from multiple portfolios with the same total number of vehicles.

Figures (8)

• Figure 1: Prices for the FCR-D up ($\uparrow$) and down ($\downarrow$) markets in Denmark from January $1$, $2022$, to October $1$, $2024$EnergiDataServiceFCRNDK2. The maximum price reached €$2215$/MW. In our case study, we focus on the time period highlighted in grey.
• Figure 2: Timeline of FCR-D up and down markets in Denmark. We focus on the early FCR-D market only. The optimization variables are denoted by lower-case letters, while upper-case and Greek letters are used for parameters.
• Figure 3: The historical consumption level (baseline) and the available capacity for upwards and downwards flexibility in a random hour for one or the aggregation of $1400$ EVs with and without the implementation of the $\rm{LER}$ requirement.
• Figure 4: Conditional cumulative distribution function (CCDF) of available flexibility for a portfolio of $1400$ EVs from March $24$, $2022$, to March $21$, $2023$.
• Figure 5: The mean profit (DKK/hour) of the aggregator is shown on the y-axis. On the x-axis, the first case represents the scenario where the $1400$ EVs are divided into $70$ portfolios of $20$ EVs each (i.e., the aggregator bids for each portfolio separately), while the last case corresponds to the largest portfolio where the aggregator bids the flexibility of all $1400$ EVs together. The profit for each method (oracle, ALSO-X, and CVaR) is calculated out-of-sample as per \ref{['eq:obj']}, following the $3$-fold cross-validation process described in Section \ref{['cross']}.

Theorems & Definitions (2)

• Definition 1: The $\rm{P90}$ requirement
• Definition 2: The $\rm{LER}$ requirement