Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Robust Optimal Operation of Virtual Power Plants Under Decision-Dependent Uncertainty of Price Elasticity

Tao Tan, Rui Xie, Meng Yang, Yue Chen

Abstract

The rapid deployment of distributed energy resources (DERs) is one of the essential efforts to mitigate global climate change. However, a vast number of small-scale DERs are difficult to manage individually, motivating the introduction of virtual power plants (VPPs). A VPP operator coordinates a group of DERs by setting suitable prices, and aggregates them for interaction with the power grid. In this context, optimal pricing plays a critical role in VPP operation. This paper proposes a robust optimal operation model for VPPs that considers uncertainty in the price elasticity of demand. Specifically, the demand elasticity is found to be influenced by the pricing decision, giving rise to decision-dependent uncertainty (DDU). An improved column-and-constraint (C&CG) algorithm, together with tailored transformation and reformulation techniques, is developed to solve the robust model with DDU efficiently. Case studies based on actual electricity consumption data of London households demonstrate the effectiveness of the proposed model and algorithm.

Robust Optimal Operation of Virtual Power Plants Under Decision-Dependent Uncertainty of Price Elasticity

Abstract

The rapid deployment of distributed energy resources (DERs) is one of the essential efforts to mitigate global climate change. However, a vast number of small-scale DERs are difficult to manage individually, motivating the introduction of virtual power plants (VPPs). A VPP operator coordinates a group of DERs by setting suitable prices, and aggregates them for interaction with the power grid. In this context, optimal pricing plays a critical role in VPP operation. This paper proposes a robust optimal operation model for VPPs that considers uncertainty in the price elasticity of demand. Specifically, the demand elasticity is found to be influenced by the pricing decision, giving rise to decision-dependent uncertainty (DDU). An improved column-and-constraint (C&CG) algorithm, together with tailored transformation and reformulation techniques, is developed to solve the robust model with DDU efficiently. Case studies based on actual electricity consumption data of London households demonstrate the effectiveness of the proposed model and algorithm.

Paper Structure

This paper contains 23 sections, 1 theorem, 24 equations, 9 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Robust Optimal Operation Model of Virtual Power Plants
  3. First-Stage Constraints
  4. Decision-Dependent Uncertainty Set
  5. Second-Stage Constraints
  6. Overall Robust Optimal Operation Model
  7. Solution Method
  8. Linearization of Quadratic Constraints
  9. Uncertainty Set Reformulation
  10. Improved C&CG Algorithm
  11. Feasibility Check Problem and Subproblem
  12. Representation of Worst-Case Scenario
  13. Master Problem
  14. Overall algorithm
  15. Numerical Experiments
  16. ...and 8 more sections

Key Result

Proposition 1

Let $\overline{N} = 2^{I T} + 1$, where $I$ is the number of nodes and $T$ is the number of periods. If error tolerance $\tau = 0$, then Algorithm 1 converges within $\overline{N}$ iterations and outputs the optimal solution of problem compact.

Figures (9)

  • Figure 1: The overview of the VPP system.
  • Figure 2: The basic idea of inner approximation.
  • Figure 3: Up: High-sensitive user distribution at electricity price ratio 0.3; Middle: Medium-sensitive user distribution at electricity price ratio 3; Down: Low-sensitive user distribution at electricity price ratio 16.
  • Figure 4: The topology of the IEEE-33 bus system.
  • Figure 5: Change of UB and LB during the iterations of Algorithm 1.
  • ...and 4 more figures

Theorems & Definitions (1)

  • Proposition 1