Probabilistic Behavioral Aggregation: A Case Study on the Nordic Power Grid

TL;DR

This work addresses rising power-grid complexity from high RES penetration by applying Probabilistic Behavioral Tuning (ProBeTune) to aggregate the Nordic5 (N5) grid into a swing-equation specification. By defining a probabilistic distance $d^{\rho}$ between full and reduced models and optimizing both the system parameters $p$ and the specification parameters $q$ against an output metric $o(p,q)$, the authors demonstrate effective reduction while preserving transient behavior. Across random-mode and realistic-demand scenarios, the tuned specification closely matches the full system (low $d^{\rho}$) and yields substantial simulation speed-ups (approximately 6–23×), with no overfitting as shown by resampling. The results lay a foundation for treating large interconnected grids as single dynamic actors and motivate extending ProBeTune to microgrids and other sub-systems for scalable, accurate stability analysis in increasingly complex power networks.

Abstract

This study applies the Probabilistic Behavioral Tuning (ProBeTune) framework to transient power grid simulations to address challenges posed by increasing grid complexity. ProBeTune offers a probabilistic approach to model aggregation, using a behavioral distance measure to quantify and minimize discrepancies between a full-scale system and a simplified model. We demonstrate the effectiveness of ProBeTune on the Nordic5 (N5) test case, a model representing the Nordic power grid with complex nodal dynamics and a high share of RESs. We substantially reduce the complexity of the dynamics by tuning the system to align with a reduced swing-equation model. We confirm the validity of the swing equation with tailored controllers and parameter distributions for capturing the essential dynamics of the Nordic region. This reduction could allow interconnected systems like the Central European power grid to treat the Nordic grid as a single dynamic actor, facilitating more manageable stability assessments. The findings lay the groundwork for future research on applying ProBeTune to microgrids and other complex sub-systems, aiming to enhance scalability and accuracy in power grid modeling amidst rising complexity.

Figures (7)

• Figure 1: Network structure of the N5 system. Each bus consists of a load, a controller, and additional energy sources. Bus 1 connects the N5 to central Europe via an HVDV link. The goal is to reduce the entire N5 system to the specification shown in orange.
• Figure 2: Two realizations of the random modes and the demand fluctuations.
• Figure 3: Comparison between the behavioral distances at the different steps in the tuning pipeline for the random mode fluctuations.
• Figure 4: Comparison between the system and the specification behavior. The upper figures always show system and specification at the initial distance $d^{\rho}_{init}$, and the lower figure shows them at the distance $d^{\rho}_{end}$ after tuning.
• Figure 5: Comparison between the behavioral distances at the different steps in the tuning pipeline for the realistic demand fluctuations.