Load Shifting Versus Manual Frequency Reserve: Which One is More Appealing to Flexible Loads?

TL;DR

The paper analyzes demand-side flexibility from thermostatically controlled loads by comparing load shifting with mFRR provision for a supermarket freezer using a validated second-order grey-box model. It formulates a two-stage stochastic MILP to maximize the monetary value of flexibility under price and activation uncertainty, and introduces a linear bidding policy with McCormick relaxation plus ADMM-based scenario decomposition for computational tractability. Ex-post results on 2022 Danish price data show load shifting can be more profitable than mFRR, but at the cost of larger temperature deviations, suggesting regulatory incentives may be needed to keep mFRR attractive for grid stability. The findings have practical implications for market design, flexibility aggregation, and policy initiatives to balance economic gains with system reliability and food-temperature risk.

Abstract

This paper investigates how a thermostatically controlled load can deliver flexibility either in form of manual frequency restoration reserves (mFRR) or load shifting, and which one is financially more appealing to such a load. A supermarket freezer is considered as a representative flexible load, and a grey-box model describing its temperature dynamics is developed using real data from a supermarket in Denmark. Taking into account price and activation uncertainties, a two-stage stochastic mixed-integer linear program is formulated to maximize the flexibility value from the freezer. For practical reasons, we propose a linear policy to determine regulating power bids, and then linearize the mFRR activation conditions through the McCormick relaxation approach. For computational ease, we develop a decomposition technique, splitting the problem to a set of smaller subproblems, one per scenario. Examined on an out-of-sample simulation based on real Danish spot and balancing market prices in 2022, load shifting shows to be more profitable than mFRR provision, but is also more consequential for temperature deviations in the freezer.

Figures (8)

• Figure 1: Top: temperature of a single freezer in a supermarket. Middle: opening degree (OD) of the freezer expansion valve. Bottom: electric power of the compressor rack feeding a single freezer.
• Figure 2: Validation of the state-space model in (\ref{['eq:2ndFreezerStateSpace']}). Left: auto-correlation function (acf) of the residuals. Right: cumulated periodogram of the residuals.
• Figure 3: Left: Simulation of food and air temperatures using (\ref{['eq:2ndFreezerStateSpace']}) with parameters in Table \ref{['tab:parameter_estimates']}, and its comparison to the measured air temperature. Right: Simulation where power is turned off for two hours with a subsequent rebound at the nominal power until the food temperature is back to its normal value.
• Figure 4: Decision-making timeline and variables for the TCL when providing flexibility either in the form of mFRR services (green boxes) or load shifting (blue box).
• Figure 5: Out-of-sample cumulative operational cost for the freezer during the first nine months of 2022.