[Paper Review] Demand Response in the Smart Grid: the Impact of Consumers Temporal Preferences

Paulin Jacquot, Olivier Beaude+2 more|arXiv (Cornell University)|Nov 30, 2017

Smart Grid Energy ManagementEngineering22 references18 citations

TL;DR

This paper models residential demand response as a game-theoretic framework where consumers incur discomfort costs for deviating from preferred load schedules. It shows that hourly proportional pricing consistently outperforms daily proportional pricing in minimizing system costs and inefficiency (Price of Anarchy), even as consumer preference for temporal scheduling varies, with the hourly mechanism maintaining PoA below 1.0015 and PoE significantly lower across all preference levels.

ABSTRACT

In Demand Response programs, price incentives might not be sufficient to modify residential consumers load profile. Here, we consider that each consumer has a preferred profile and a discomfort cost when deviating from it. Consumers can value this discomfort at a varying level that we take as a parameter. This work analyses Demand Response as a game theoretic environment. We study the equilibria of the game between consumers with preferences within two different dynamic pricing mechanisms, respectively the daily proportional mechanism introduced by Mohsenian-Rad et al, and an hourly proportional mechanism. We give new results about equilibria as functions of the preference level in the case of quadratic system costs and prove that, whatever the preference level, system costs are smaller with the hourly mechanism. We simulate the Demand Response environment using real consumption data from PecanStreet database. While the Price of Anarchy remains always close to one up to 0.1% with the hourly mechanism, it can be more than 10% bigger with the daily mechanism.

Motivation & Objective

• To analyze how consumers' temporal preferences affect equilibrium outcomes in demand response programs.
• To compare the efficiency of two dynamic pricing mechanisms—daily proportional and hourly proportional—under varying levels of consumer discomfort for schedule deviation.
• To evaluate system performance using metrics like social cost, system cost, Price of Anarchy (PoA), and Price of Efficiency (PoE).
• To validate theoretical findings using real residential load data from the PecanStreet database.
• To demonstrate the robustness of the hourly pricing mechanism in maintaining low inefficiency and system costs despite variations in consumer preferences.

Proposed method

• Formulates a game-theoretic model where each consumer's cost includes a quadratic discomfort term based on deviation from a preferred load profile.
• Introduces a parameter α to represent the weight of temporal preference in the consumer's cost function, allowing analysis of varying preference levels.
• Defines system cost as a quadratic function of total load, and social cost as the sum of system cost and consumer discomfort costs.
• Uses the Price of Anarchy (PoA) and a novel Price of Efficiency (PoE) to measure inefficiency and provider cost inefficiency, respectively.
• Employs best-response dynamics (BRD) with 150 iterations to compute Nash equilibria for each α value across 31 days of real data.
• Solves the resulting quadratic optimization problems using CPLEX 12.6, with simulations run on an 8-thread Intel Xeon system.

Experimental results

Research questions

• RQ1 How does the level of consumer preference for temporal scheduling affect the efficiency of demand response equilibria?
• RQ2 Which dynamic pricing mechanism—daily or hourly proportional—yields lower system costs and lower inefficiency (PoA) across varying preference levels?
• RQ3 How does the Price of Efficiency (PoE) vary with consumer preferences, and what does this imply for the provider’s cost?
• RQ4 To what extent do theoretical results from a simplified model hold in a realistic setting with real residential load data?
• RQ5 Is the hourly proportional mechanism robust to changes in consumer preferences, particularly in terms of maintaining low inefficiency and system cost?

Key findings

• The Price of Anarchy (PoA) for the hourly proportional (HP) mechanism remains below 1.0015 across all preference levels α, indicating near-optimal efficiency.
• In contrast, the PoA for the daily proportional (DP) mechanism peaks at 1.122 when α ≈ 0.06, indicating a 12.2% inefficiency relative to the optimal social cost.
• The Price of Efficiency (PoE) for the HP mechanism is significantly lower than for DP across a wide range of α, with the curves intersecting only at α ≈ 3×10⁻⁴.
• When α > 3×10⁻⁴, the HP mechanism results in lower system costs for the provider than the DP mechanism, making it more efficient from the operator’s perspective.
• Aggregated load profiles at equilibrium shift by over 15% when α changes from 0 to 1, demonstrating strong sensitivity to preference levels in the DP mechanism.
• As α → 1, equilibrium load profiles for both mechanisms converge to the preferred load profile (ˆℓ), confirming the model’s consistency with theoretical expectations.