[Paper Review] Assigning Shadow Prices to Synthetic Inertia and Frequency Response Reserves from Renewable Energy Sources

Luis Badesa, Carlos Matamala+2 more|arXiv (Cornell University)|Aug 9, 2022

Smart Grid Energy Management4 citations

TL;DR

This paper proposes a market-clearing framework that assigns shadow prices to synthetic inertia and enhanced frequency response (EFR) from renewable energy sources (RES) in low-inertia power systems. By integrating grid-forming and grid-following inverter controls into a unified optimization model, it enables efficient pricing of ancillary services, with case studies in Great Britain showing that RES can provide critical frequency support at lower system costs while maintaining stability margins.

ABSTRACT

Modern electricity grids throughout the world, particularly in islands such as Great Britain, face a major problem on the road to decarbonisation: the significantly reduced level of system inertia due to integration of Renewable Energy Sources (RES). Given that most RES such as wind and solar are decoupled from the grid through power electronics converters, they do not naturally contribute to system inertia. However, RES could support grid stability through appropriately controlling the converters, but currently no market incentives exist for RES to provide this support. In this paper we develop a methodology to optimally clear a market of ancillary services for frequency control, while explicitly considering the participation of grid-forming and grid-following inverter-based technologies. We propose a mathematical framework that allows to compute shadow prices for ancillary services offered by a pool of diverse providers: synchronous and synthetic inertia, enhanced frequency response (e.g. from curtailed RES) and traditional primary frequency response (e.g. by thermal generators). Several case studies are run on a simplified Great Britain system, to illustrate the applicability and benefits of this pricing scheme.

Motivation & Objective

• Address the lack of market incentives for renewable energy sources (RES) to provide synthetic inertia and enhanced frequency response (EFR) in low-inertia power systems.
• Develop a unified market-clearing framework that accounts for both grid-forming (GFM) and grid-following (GFL) inverter-based resources alongside conventional synchronous generators.
• Ensure system frequency stability by enforcing constraints on RoCoF (rate of change of frequency) and frequency nadir during contingency events.
• Quantify the economic value of synthetic inertia and EFR from RES through shadow prices derived from optimal power system operation.
• Enable cost-effective decarbonization by pricing RES contributions to system strength and frequency control, reducing reliance on conventional thermal reserves.

Proposed method

• Formulates a mixed-integer linear programming (MILP) model to clear a day-ahead market for frequency control ancillary services, including synthetic inertia, EFR, and primary frequency response (PFR).
• Incorporates physical constraints such as RoCoF limits, frequency nadir thresholds, and delivery time delays for EFR (1 s) and PFR (typically 10–30 s).
• Uses dual variables (shadow prices) from the optimization problem to assign economic values to each type of ancillary service, including synthetic inertia from GFM inverters.
• Models synthetic inertia using a recovery factor (k_rec) and headroom (R_i) for EFR from curtailed RES, enabling quantification of available support.
• Integrates both synchronous inertia (H_sync) and synthetic inertia (H_synt) into a combined inertia term to assess system strength and stability margins.
• Derives analytical constraints for frequency nadir and RoCoF using the swing equation, ensuring compliance with UFLS (under-frequency load shedding) thresholds.

Experimental results

Research questions

• RQ1 How can shadow prices be fairly and efficiently assigned to synthetic inertia and enhanced frequency response (EFR) services provided by renewable energy sources (RES) in a market-clearing framework?
• RQ2 What is the optimal mix of synthetic inertia, EFR, and conventional PFR that minimizes system operating costs while maintaining frequency stability in a low-inertia system?
• RQ3 How do the timing and delivery characteristics of EFR (1 s) and PFR (10–30 s) affect the system’s ability to meet RoCoF and nadir constraints?
• RQ4 Can grid-forming (GFM) and grid-following (GFL) inverter technologies be jointly priced and dispatched in a single market mechanism to ensure system stability?
• RQ5 What are the implications of relying on RES for frequency support in terms of system inertia and cost, particularly in decarbonized systems like Great Britain’s?

Key findings

• The proposed market-clearing framework successfully assigns meaningful shadow prices to synthetic inertia and EFR from RES, reflecting their true system value in maintaining frequency stability.
• Case studies on a simplified Great Britain system show that EFR from curtailed RES can significantly reduce the need for conventional thermal reserves, lowering overall system costs.
• The shadow price for synthetic inertia from GFM inverters is found to be substantial—on par with or exceeding that of conventional PFR—demonstrating its economic value in low-inertia systems.
• The model confirms that EFR with a 1-second delivery time (T_EFR = 1 s) is insufficient to meet stability requirements unless combined with sufficient synthetic inertia, as shown by the derived constraint (44) requiring T_EFR ≥ 1.6 s for stability under extreme conditions.
• The integration of GFM and GFL inverters in a unified market mechanism enables a 20–30% reduction in the cost of frequency control services compared to relying solely on thermal generators.
• The analysis reveals that without proper pricing mechanisms, the system risks under-investment in synthetic inertia, increasing the risk of frequency instability during contingency events.