Dynamic Dimensioning of Frequency Containment Reserves: The Case of the Nordic Grid

TL;DR

The paper tackles the problem of dynamically dimensioning FCR-N in the Nordic grid by embedding FCR activation into a diffusion-driven frequency model with a state-dependent mean-reversion drift. It derives closed-form exceedance probabilities and calibrates the model with extensive Nordic data, then proposes and evaluates several dynamic heuristics that adjust hourly FCR-N volumes while preserving the total annual budget. The results show that dynamic dimensioning can substantially reduce the risk of frequency excursions beyond ±0.1 Hz (up to about 37% under budget neutrality) compared to the current static approach, and that even conservative schemes can achieve meaningful risk reductions. The work offers practical pathways for TSO operators to improve grid security in low-inertia, high-renewables settings and points to further integration with markets and predictive analytics.

Abstract

One of the main responsibilities of a Transmission System Operator (TSO) operating an electric grid is to maintain a designated frequency (e.g., 50 Hz in Europe). To achieve this, TSOs have created several products called frequency-supporting ancillary services. The Frequency Containment Reserve (FCR) is one of these ancillary service products. This article focuses on the TSO problem of determining the volume procured for FCR. Specifically, we investigate the potential benefits and impact on grid security when transitioning from a traditionally \textit{static} procurement method to a \textit{dynamic} strategy for FCR volume. We take the Nordic synchronous area in Europe as a case study and use a diffusion model to capture its frequency development. We introduce a controlled mean reversal parameter to assess changes in FCR obligations, in particular for the Nordic FCR-N ancillary service product. We establish closed-form expressions for exceedance probabilities and use historical frequency data as input to calibrate the model. We show that a dynamic dimensioning approach for FCR has the potential to significantly reduce the exceedance probabilities (up to $37\%$) while maintaining the total yearly procured FCR volume equal to that of the current static approach. Alternatively, a dynamic dimensioning approach could significantly increase security at limited extra cost.

Figures (12)

• Figure 1: Activation times of ancillary services in Nordic synchronous area. Figure is borrowed from EnerginetOutlook.
• Figure 2: Graphic illustration of mean reversal function $\alpha(r_N;x_D, F)$, representing the activation of FCR-N and FCR-D according to formula \ref{['Alpha']}.
• Figure 3: Random trajectory of the shifted frequency process $F(t)$ as prescribed by an Ornstein-Uhlenbeck process with state-dependent drift.
• Figure 4: Increasing hourly FCR-N volumes $r_N$ (in GW), are required to make sure that $2p_2\leq 2\%$, (i.e., to stay within the +/- 100 mHz band $98\%$ of the time) for increasing $\sigma$.
• Figure 5: Required hourly FCR-N volumes $r_N$ (in GW) to stay within $98\%, 97\%$ and $96\%$ safety limits (i.e., required $r_N$ to make sure $2p_2 \leq 2\%$ or $2p_2 \leq 3\%$ or $2p_2 \leq 4\%$ holds, respectively) for varying $\sigma$.

Theorems & Definitions (2)

• Theorem 1
• proof