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A Minimal Incentive-based Demand Response Program With Self Reported Baseline Mechanism

Deepan Muthirayan, Enrique Baeyens, Pratyush Chakraborty, Kameshwar Poolla, Pramod P. Khargonekar

TL;DR

The paper addresses incentive-based demand response by introducing a minimal-information mechanism in which participants self-report baselines, are randomly called with probability $p$, paid per unit reduction, and penalized for uninstructed deviations. It analyzes the two-stage consumer optimization, derives the optimal baseline report $f^*$ via the condition $\\pi_0 = M(f^*)$, and demonstrates how baseline inflation can be bounded through penalty design and the calling probability, including a deadband to guarantee individual rationality. The results show that, with negligible recruitment costs, the SO can achieve near-optimal cost while obtaining a more accurate baseline than CAISO's $m/m$ approach, and it discusses how recruitment costs alter the design and achievable performance. Overall, the work provides a theoretically grounded, information-light DR mechanism with practical implications for reducing baseline bias and system costs, along with clear comparisons to existing baseline methods.

Abstract

In this paper, we propose a novel incentive based Demand Response (DR) program with a self reported baseline mechanism. The System Operator (SO) managing the DR program recruits consumers or aggregators of DR resources. The recruited consumers are required to only report their baseline, which is the minimal information necessary for any DR program. During a DR event, a set of consumers, from this pool of recruited consumers, are randomly selected. The consumers are selected such that the required load reduction is delivered. The selected consumers, who reduce their load, are rewarded for their services and other recruited consumers, who deviate from their reported baseline, are penalized. The randomization in selection and penalty ensure that the baseline inflation is controlled. We also justify that the selection probability can be simultaneously used to control SO's cost. This allows the SO to design the mechanism such that its cost is almost optimal when there are no recruitment costs or at least significantly reduced otherwise. Finally, we also show that the proposed method of self-reported baseline outperforms other baseline estimation methods commonly used in practice.

A Minimal Incentive-based Demand Response Program With Self Reported Baseline Mechanism

TL;DR

The paper addresses incentive-based demand response by introducing a minimal-information mechanism in which participants self-report baselines, are randomly called with probability , paid per unit reduction, and penalized for uninstructed deviations. It analyzes the two-stage consumer optimization, derives the optimal baseline report via the condition , and demonstrates how baseline inflation can be bounded through penalty design and the calling probability, including a deadband to guarantee individual rationality. The results show that, with negligible recruitment costs, the SO can achieve near-optimal cost while obtaining a more accurate baseline than CAISO's approach, and it discusses how recruitment costs alter the design and achievable performance. Overall, the work provides a theoretically grounded, information-light DR mechanism with practical implications for reducing baseline bias and system costs, along with clear comparisons to existing baseline methods.

Abstract

In this paper, we propose a novel incentive based Demand Response (DR) program with a self reported baseline mechanism. The System Operator (SO) managing the DR program recruits consumers or aggregators of DR resources. The recruited consumers are required to only report their baseline, which is the minimal information necessary for any DR program. During a DR event, a set of consumers, from this pool of recruited consumers, are randomly selected. The consumers are selected such that the required load reduction is delivered. The selected consumers, who reduce their load, are rewarded for their services and other recruited consumers, who deviate from their reported baseline, are penalized. The randomization in selection and penalty ensure that the baseline inflation is controlled. We also justify that the selection probability can be simultaneously used to control SO's cost. This allows the SO to design the mechanism such that its cost is almost optimal when there are no recruitment costs or at least significantly reduced otherwise. Finally, we also show that the proposed method of self-reported baseline outperforms other baseline estimation methods commonly used in practice.

Paper Structure

This paper contains 32 sections, 7 theorems, 90 equations, 3 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Our Contribution
  3. Related Work
  4. Problem Setup
  5. Market Model
  6. Consumer Model
  7. Incentive-Based Demand Response Program
  8. Consumer Recruitment and Selection
  9. Reward and Penalty Function
  10. Consumer's Optimization Problem
  11. Optimal baseline report and inflation
  12. The Consumer's Second Stage Problem
  13. Consumer is not participating in the DR program
  14. Consumer is participating in the program but is not signaled to reduce consumption
  15. Consumer is participating in the program and is signaled to reduce consumption
  16. ...and 17 more sections

Key Result

Lemma 1

The optimal consumptions for the three cases $q^a(\theta)$, $q^b(\theta,f)$, $q^c(\theta)$ satisfy the conditions (i) $q^c < q^a$ and (ii) $q^a < q^b < f$ or $f < q^b < q^a$ for every $\theta$.

Figures (3)

  • Figure 1: Inverse Supply Curve and Threshold Market Clearing (TMC) Price $\pi^*$
  • Figure 2: Penalty function with deadband
  • Figure 3: SO cost vs $p$ when load reduction is $\Delta Q^*$ during a DR event. Top: $\pi_{\text{rec}} = \$ 2/\text{Customer}$, bottom:$\pi_{\text{rec}} = \$ 10/\text{Customer}$.

Theorems & Definitions (17)

  • Remark 1
  • Definition 1
  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • Definition 2: Consumer's Expected Marginal Utility
  • Theorem 1
  • proof
  • Theorem 2
  • ...and 7 more