Cost Allocation for Inertia and Frequency Response Ancillary Services

TL;DR

The paper addresses allocating the costs of frequency-containment AS in low-inertia grids by formulating a frequency-secured MISOC unit commitment and pricing inertia, EFR, and PFR via dual variables. It proposes three allocation rules—proportional, Shapley value, and nucleolus—and proves that proportional allocation can cause cross-subsidies, while Shapley value and nucleolus are efficient and coalitionally rational, with nucleolus additionally guaranteeing consistency. A GB case study demonstrates how the AS market would be triggered by large contingencies and how costs distribute across nuclear, offshore wind, and storage technologies, showing nucleolus as the preferred method due to its consistency. The results highlight practical market design implications for incentivizing investments in inertia and FR while maintaining fairness and social welfare in decarbonized power systems.

Abstract

The reduction in system inertia is creating an important market for frequency-containment Ancillary Services (AS) such as enhanced frequency response (e.g.,~provided by battery storage), traditional primary frequency response and inertia itself. This market presents an important difference with the energy-only market: while the need for energy production is driven by the demand from consumers, frequency-containment AS are procured because of the need to deal with the largest generation/demand loss in the system (or smaller losses that could potentially compromise frequency stability). Thus, a question that arises is: who should pay for frequency-containment AS? In this work, we propose a cost-allocation methodology based on the nucleolus concept, in order to distribute the total payments for frequency-containment AS among all generators or loads that create the need for these services. It is shown that this method complies with necessary properties for the AS market, such as avoidance of cross-subsidies and maintaining players in this cooperative game. Finally, we demonstrate its practical applicability through a case study for the Great Britain power system, while comparing its performance with two alternative mechanisms, namely proportional and Shapley value cost allocation.

Figures (6)

• Figure 1: Schematic of system frequency following three different generator contingencies of varying sizes.
• Figure 2: AS cost allocation methodology. Set $\mathcal{N}_t = \{1, 2,..., n-1, n\}$ represents the subset of $\mathcal{G} \cup \mathcal{R} \cup \mathcal{S}$ that is dispatched (discharging in the case of storage units) at hour $t$.
• Figure 3: Energy price ($\lambda^{E}_t$) and AS prices ($\lambda_t^{\textrm{H}}, \lambda^{PFR}_t, \lambda^{EFR}_t$).
• Figure 4: AS market and cost allocation (CA) per technology (on top). Energy and AS markets, fuel costs and cost allocation per technology (bottom).
• Figure 5: Dispatch ($P_{g,t}, P_{r,t}, P_{s,t}^\textrm{cha}, P_{s,t}^\textrm{dis}$, on top) and AS market size ($\Omega^\textrm{Loss}_t$, bottom) per unit.