Insights from Game Theory into the Impact of Smart Balancing on Power System Stability

TL;DR

The paper addresses how smart balancing actions by balance responsible parties can influence power-system stability within a dynamic control-area framework. It formulates a 2x2 game to model BRP decisions and analyzes Nash equilibria, equilibrium selection, and Experience-weighted Attraction learning to assess stability risks. A key finding is that overreactions—where combined smart balancing overshoots the baseline disturbance—can persist in equilibrium and arise transiently during learning, signaling inherent stability risks of smart balancing. The study offers design-guidance, such as increasing the combined stakes $g+l$, enlarging the relative losses $l-g$, encouraging early ISP participation with fast assets, and considering pricing/dataPublication strategies to reduce overreactions, while noting that complete elimination of risk is unlikely.

Abstract

Smart balancing, also called passive balancing, is the intentional introduction of active power schedule deviations by balance responsible parties (BRPs) to receive a remuneration through the imbalance settlement mechanism. From a system perspective, smart balancing is meant to reduce the need for, and costs of, frequency restoration reserves (FRR), but it can also cause large oscillations in the FRR and jeopardize the system stability. Using a dynamic control area model, this work defines a 2x2 game in which two BRPs can choose to perform smart balancing. We study the impact of time delay, ramp rates, and pricing mechanisms on Nash equilibria and Experience-weighted Attraction (EWA) learning. It is found that, even in an idealized setting, a significant fraction of games in a learned equilibrium results in an overreaction relative to the baseline disturbance, creating an imbalance in the opposite direction. This suggests that the system stability risks are inherent to smart balancing and not a question of implementation. Recommendations are given for implementation choices that can reduce (but not eliminate) the risk of overreactions.

Figures (6)

• Figure 1: Single busbar model of a control area/control block.
• Figure 2: Disturbance $P_d$ due to a power plant outage at time $t=\qty{0}{min}$ and smart balancing reaction $P_b$ for $T_\mathrm{game} = 1, 5, \qty{10}{min}$ with fast and slow assets and $P_{b, \mathrm{max}} = \qty{150}{MW}$.
• Figure 3: Effect of smart balancing by one ($\sum S_b = 1$) or both ($\sum S_b = 2$) BRPs on the power for symmetric scenarios, as defined in \ref{['fig:setupScenarios']}.
• Figure 4: Exemplary EWA learning dynamics with $(\delta, \alpha, \kappa, \beta) = (0.25, 0.05, 1, 1)$ for DE-pricing: (top) probability for smart balancing by BRP $b$, (bottom) probability of overreactions caused by smart balancing.
• Figure 5: Exemplary EWA learning dynamics with $(\delta, \alpha, \kappa, \beta) = (0.25, 0.05, 1, 1)$ for NL-pricing: (top) probability for smart balancing by BRP $b$, (bottom) probability of overreactions caused by smart balancing.