Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Optimal Contract Design for Incentive-Based Demand Response

Donya G. Dobakhshari, Vijay Gupta

Abstract

We design an optimal contract between a demand response aggregator (DRA) and a customer for incentive-based demand response. We consider a setting in which the customer is asked to reduce her consumption by the DRA and she is compensated for this reduction. However, since the DRA must supply the customer with as much power as she desires, a strategic customer can temporarily increase her base load to report a larger reduction as a part of the demand response event. The DRA wishes to incentivize the customer both to make the maximal effort in reducing the load and to not falsify the base load. We model the problem of designing the contract by the DRA for the customer as a management contract design problem and present a solution. The optimal contract consists of two parts: a part that depends on (the possibly inflated) load reduction as measured and another that provides a share of the profit that ensues to the DRA through the demand response event to the customer.

Optimal Contract Design for Incentive-Based Demand Response

Abstract

We design an optimal contract between a demand response aggregator (DRA) and a customer for incentive-based demand response. We consider a setting in which the customer is asked to reduce her consumption by the DRA and she is compensated for this reduction. However, since the DRA must supply the customer with as much power as she desires, a strategic customer can temporarily increase her base load to report a larger reduction as a part of the demand response event. The DRA wishes to incentivize the customer both to make the maximal effort in reducing the load and to not falsify the base load. We model the problem of designing the contract by the DRA for the customer as a management contract design problem and present a solution. The optimal contract consists of two parts: a part that depends on (the possibly inflated) load reduction as measured and another that provides a share of the profit that ensues to the DRA through the demand response event to the customer.

Paper Structure

This paper contains 11 sections, 9 theorems, 34 equations, 2 figures.

Table of Contents

  1. INTRODUCTION
  2. Problem Statement
  3. Problem Formulation
  4. Contract Structure
  5. Optimal contract Structure
  6. Discussion of Results
  7. Form of the reporting function
  8. Optimal Compensation
  9. Impact of Estimation Error
  10. Optimal Share Allocated to the Customer
  11. CONCLUSIONS

Key Result

Lemma 1

The properties encapsulated in assumptions $\mathcal{A}_{1}$-$\mathcal{A}_{4}$ hold for the probability density function $f_{Y|A}(y|a)$ and the corresponding CDF $F_{Y|A}(y|a)$ as well.

Figures (2)

  • Figure 1: Timeline of the DR event and the proposed contract.
  • Figure 2: The form of the reporting function. There exists an $x^+$ such that $R-x>0$ for $x>x^+$ (i.e., over-reporting happens) and $R-x<0$ for $x<x^+$ (i.e., under-reporting happens). The falsification is $-\alpha$ for $x\leq\hat{x}$ and $\frac{(1-\lambda)(F-1)-\mu F_a}{f}$ for $x>\hat{x}$.

Theorems & Definitions (20)

  • Example 1
  • Example 2
  • Lemma 1
  • proof
  • Lemma 2
  • Theorem 1
  • proof
  • Definition 1
  • Theorem 2
  • proof
  • ...and 10 more