Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Optimal Bidding Strategies in Network-Constrained Demand Response: A Distributed Aggregative Game Theoretic Approach

Xiupeng Chen, Jacquelien M. A. Scherpen, Nima Monshizadeh

TL;DR

The paper addresses demand-response bidding in a distribution network with a deficit, modeling aggregators as players in a network-constrained aggregative game. It proposes a fully distributed generalized Nash equilibrium seeking algorithm that relies on local neighbor communication and partial information exchange, using a forward-backward splitting framework to ensure convergence to a v-GNE without requiring a central coordinator. Theoretical results establish cocoercivity, averagedness, and step-size conditions that guarantee convergence, supported by a case study on a modified IEEE 33-bus network where bids, estimates, and multipliers converge within a finite number of iterations. The approach enables scalable, privacy-preserving coordination of prosumer groups under power-flow constraints, with potential applicability to real-world demand-response schemes and renewable integration. Future work includes accommodating more general cost functions and more accurate network models.

Abstract

Demand response has been a promising solution for accommodating renewable energy in power systems. In this study, we consider a demand response scheme within a distribution network facing an energy supply deficit. The utility company incentivizes load aggregators to adjust their pre-scheduled energy consumption and generation to match the supply. Each aggregator, which represents a group of prosumers, aims to maximize its revenue by bidding strategically in the demand response scheme. Since aggregators act in their own self-interest and their revenues and feasible bids influence one another, we model their competition as a network-constrained aggregative game. This model incorporates power flow constraints to prevent potential line congestion. Given that there are no coordinators and aggregators can only communicate with their neighbours, we introduce a fully distributed generalized Nash equilibrium seeking algorithm to determine the optimal bidding strategies for aggregators in this game. Within this algorithm, only estimates of the aggregate and certain auxiliary variables are communicated among neighbouring aggregators. We demonstrate the convergence of this algorithm by constructing an equivalent iteration using the forward-backward splitting technique.

Optimal Bidding Strategies in Network-Constrained Demand Response: A Distributed Aggregative Game Theoretic Approach

TL;DR

The paper addresses demand-response bidding in a distribution network with a deficit, modeling aggregators as players in a network-constrained aggregative game. It proposes a fully distributed generalized Nash equilibrium seeking algorithm that relies on local neighbor communication and partial information exchange, using a forward-backward splitting framework to ensure convergence to a v-GNE without requiring a central coordinator. Theoretical results establish cocoercivity, averagedness, and step-size conditions that guarantee convergence, supported by a case study on a modified IEEE 33-bus network where bids, estimates, and multipliers converge within a finite number of iterations. The approach enables scalable, privacy-preserving coordination of prosumer groups under power-flow constraints, with potential applicability to real-world demand-response schemes and renewable integration. Future work includes accommodating more general cost functions and more accurate network models.

Abstract

Demand response has been a promising solution for accommodating renewable energy in power systems. In this study, we consider a demand response scheme within a distribution network facing an energy supply deficit. The utility company incentivizes load aggregators to adjust their pre-scheduled energy consumption and generation to match the supply. Each aggregator, which represents a group of prosumers, aims to maximize its revenue by bidding strategically in the demand response scheme. Since aggregators act in their own self-interest and their revenues and feasible bids influence one another, we model their competition as a network-constrained aggregative game. This model incorporates power flow constraints to prevent potential line congestion. Given that there are no coordinators and aggregators can only communicate with their neighbours, we introduce a fully distributed generalized Nash equilibrium seeking algorithm to determine the optimal bidding strategies for aggregators in this game. Within this algorithm, only estimates of the aggregate and certain auxiliary variables are communicated among neighbouring aggregators. We demonstrate the convergence of this algorithm by constructing an equivalent iteration using the forward-backward splitting technique.
Paper Structure (11 sections, 4 theorems, 64 equations, 3 figures, 1 table, 1 algorithm)

This paper contains 11 sections, 4 theorems, 64 equations, 3 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Notation
  3. Operator theory
  4. Problem Statement
  5. Game formulation
  6. Algorithm design
  7. Algorithm description
  8. Steady-state analysis
  9. Convergence analysis
  10. Case study
  11. Conclusion

Key Result

Theorem 1

Assume that the matrix $\Phi$ is positive definite. Then, the dynamics eq_compact is equivalent to the forward-backward iteration eq_iteration; in particular, the steady state $\omega^*=(\beta^*,\psi^*,\sigma^*,z^*,\lambda^*)$ of eq_compact coincides with a fixed point of iteration eq_iteration and

Figures (3)

  • Figure 1: Physical network and communication network among aggragators
  • Figure 2: The evolution of $\beta$ and $\sigma$
  • Figure 3: The evolution of $\lambda$ and $x$

Theorems & Definitions (11)

  • Theorem 1
  • proof
  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • Theorem 2
  • proof
  • proof : Proof of Theorem \ref{['proposition_steady']}
  • proof : Proof of Lemma \ref{['lemma_tilde_A']}
  • ...and 1 more