Leveraging P90 Requirement: Flexible Resources Bidding in Nordic Ancillary Service Markets

TL;DR

This work addresses the challenge of integrating stochastic flexible resources into Nordic ancillary service markets under Energinet's $P90$ reliability rule. It develops a distributionally robust joint chance-constrained bidding framework (DRJCCP) with a Wasserstein ambiguity set, giving a tractable MILP reformulation for aggregators to decide reserve capacity bids. A bi-level structure captures the TSO-aggregator interaction, with a grid-search heuristic to tune the $\epsilon$ (shortfall probability) and $\theta$ (conservativeness), demonstrated on an electric-vehicle portfolio. The results show that appropriate conservativeness is essential in non-stationary environments to maintain $P90$ compliance while enabling meaningful reserve procurement, highlighting practical implications for market design and portfolio bidding.

Abstract

The P90 requirement of the Danish transmission system operator, Energinet, incentivizes flexible resources with stochastic power consumption/production baseline to bid in Nordic ancillary service markets with the minimum reliability of 90%, i.e., letting them cause reserve shortfall with the probability of up to 10%. Leveraging this requirement, we develop a distributionally robust joint chance-constrained optimization model for aggregators of flexible resources to optimize their volume of reserve capacity to be offered. Having an aggregator of electric vehicles as a case study, we show how distributional robustness is key for the aggregator when making bidding decisions in a non-stationary uncertain environment. We also develop a heuristic based on a grid search for the system operator to adjust the P90 requirement and the level of conservativeness, aiming to procure the maximum reserve capacity from stochastic resources with least expected shortfall.

Figures (3)

• Figure 1: Input data: Simulation of EV power consumption for 90 days. First day is a burn-in period, green is the in-sample period (constructing the empirical distribution), and yellow is the out-of-sample period.
• Figure 2: As input data, the blue curve shows the stochastic consumption of the portfolio on 20 EVs over a day, representing the mean (dark blue) and 10-90% quantiles (light blue). The left plot shows the in-sample historical consumption data which are already represented in the green area of Fig. \ref{['fig:drjcc_raw']}. The right plot includes the out-of-sample consumption data coming from the yellow part of that figure. As outputs of model \ref{['P90:General:DRJCC-tract']} given in-sample data, the three dashed line curves (identical in both plots) show the optimal reserve capacity bids for three values of $\theta = \{0.01, 0.1, 0.35\}$ representing different levels of conservativeness.
• Figure 3: Total reserve capacity procurement of the TSO over a day from the aggregator of 20 EVs for different values of $\epsilon$ and $\theta$. Each $(\epsilon, \theta)$ has been solved using \ref{['P90:TSO']} using a grid search on in-sample data. The optimal value obtained by this grid search heuristic is $(\epsilon, \theta) = (0.11, 0.2)$.

Theorems & Definitions (1)

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