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Efficient Demand Response Location Targeting for Price Spike Mitigation by Exploiting Price-demand Relationship

Yufan Zhang, Honglin Wen, Tao Feng, Yize Chen

TL;DR

This work tackles wholesale price spikes by jointly selecting demand-response (DR) locations and reductions to steer average nodal prices toward a target. It formulates a bilevel MILP where the upper level sets DR locations and reductions and the lower level solves economic dispatch (ED); to overcome nonconvexity, it replaces the ED-based price-demand coupling with a piecewise linear mapping $\pi(\hat{l})$ derived from multiparametric quadratic programming, enabling tractable MILPs on each linear piece. The authors provide a concrete solution strategy with an LP-based feasibility check and a per-segment MILP, and an acceleration scheme to reduce computation time. Case studies on the New England 39-bus system show the method reduces average LMP more effectively and at lower cost than heuristic highest-LMP targeting, while remaining robust to parameter inaccuracies and achieving over 50% faster computation in some settings. The approach yields a practical, theoretically grounded DR targeting framework that can be extended to other DR objectives and operation problems beyond price spike mitigation, with the price-demand mapping serving as a central tool for tractable optimization.

Abstract

Demand response (DR) leverages demand-side flexibility, offering a promising approach to enhance market conditions like mitigating wholesale price spikes. However, poorly chosen DR locations can inadvertently increase electricity prices. For that, we introduce a method to rigorously select DR locations and corresponding demand reductions. We formulate a bilevel program where the upper level determines the DR locations and demand reductions while ensuring the average nodal prices meet a predetermined target. The lower level tackles an economic dispatch (ED) problem and feeds the resulting nodal prices back to the upper level based on post-DR demands. This bilevel formulation presents challenges due to the lower-level non-convexity affecting the upper-level constraints on average nodal prices. To address this, we propose to replace the lower level with a piecewise linear function representing the price-demand relationship, solving iteratively for each linear segment. This results in a tractable mixed-integer linear program. An acceleration strategy is proposed to further reduce the computation time. Numerical studies demonstrate the ability of the proposed approach to reduce prices to a desired level. Besides, we empirically show that the proposed approach is robust against inaccurate system parameters and can reduce computation time by over 50%.

Efficient Demand Response Location Targeting for Price Spike Mitigation by Exploiting Price-demand Relationship

TL;DR

This work tackles wholesale price spikes by jointly selecting demand-response (DR) locations and reductions to steer average nodal prices toward a target. It formulates a bilevel MILP where the upper level sets DR locations and reductions and the lower level solves economic dispatch (ED); to overcome nonconvexity, it replaces the ED-based price-demand coupling with a piecewise linear mapping derived from multiparametric quadratic programming, enabling tractable MILPs on each linear piece. The authors provide a concrete solution strategy with an LP-based feasibility check and a per-segment MILP, and an acceleration scheme to reduce computation time. Case studies on the New England 39-bus system show the method reduces average LMP more effectively and at lower cost than heuristic highest-LMP targeting, while remaining robust to parameter inaccuracies and achieving over 50% faster computation in some settings. The approach yields a practical, theoretically grounded DR targeting framework that can be extended to other DR objectives and operation problems beyond price spike mitigation, with the price-demand mapping serving as a central tool for tractable optimization.

Abstract

Demand response (DR) leverages demand-side flexibility, offering a promising approach to enhance market conditions like mitigating wholesale price spikes. However, poorly chosen DR locations can inadvertently increase electricity prices. For that, we introduce a method to rigorously select DR locations and corresponding demand reductions. We formulate a bilevel program where the upper level determines the DR locations and demand reductions while ensuring the average nodal prices meet a predetermined target. The lower level tackles an economic dispatch (ED) problem and feeds the resulting nodal prices back to the upper level based on post-DR demands. This bilevel formulation presents challenges due to the lower-level non-convexity affecting the upper-level constraints on average nodal prices. To address this, we propose to replace the lower level with a piecewise linear function representing the price-demand relationship, solving iteratively for each linear segment. This results in a tractable mixed-integer linear program. An acceleration strategy is proposed to further reduce the computation time. Numerical studies demonstrate the ability of the proposed approach to reduce prices to a desired level. Besides, we empirically show that the proposed approach is robust against inaccurate system parameters and can reduce computation time by over 50%.
Paper Structure (19 sections, 1 theorem, 24 equations, 7 figures, 5 tables, 2 algorithms)

This paper contains 19 sections, 1 theorem, 24 equations, 7 figures, 5 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Background and Motivation
  3. Related Works
  4. Proposed Method and Contribution
  5. Preliminaries: Economic Dispatch
  6. Methodological Components
  7. The Physical Framework for DR Targeting
  8. The Formulation of DR Targeting
  9. Price-demand Relationship Derivation via Multi-parametric Quadratic Programming
  10. An Illustrative Example
  11. The Derivation of Price-demand Relationship
  12. Solution Strategy for DR Targeting Problem
  13. Case Study
  14. Operational Advantage of the Proposed Approach
  15. Investigation on Values of Different Acceptable LMP Deviation
  16. ...and 4 more sections

Key Result

Proposition 1

Consider the QP problem 6. Let $\bm{P}^\text{g}_m(\hat{\bm{l}}),\gamma_m(\hat{\bm{l}}),\bm{\mu}_m(\hat{\bm{l}}),\bm{\psi}_m(\hat{\bm{l}})$ denote the mapping between the load $\hat{\bm{l}}$ and the optimal solutions of primal and dual variables, $\Tilde{\bm{P}^\text{g}},\Tilde{\gamma},\Tilde{\bm{\mu where $\bm{M}_0 \in \mathbb{R}^{(3|\mathcal{N}|+1+2|\mathcal{A}|)\times(3|\mathcal{N}|+1+2|\mathcal

Figures (7)

  • Figure 1: Illustration of the proposed DR targeting framework. When a DR event is triggered, TSO determines the a). targeted nodes and b). the corresponding demand reduction. The LSE connected to the targeted node (plotted in red) reduces the demand as required.
  • Figure 2: The system pattern before and after DR with improperly targeted node. Binding lines and nodes are shown in red.
  • Figure 3: The policy curve of a single bus load with two generators.
  • Figure 4: The nodal LMPs and nodal demand levels before DR, along with demand reduction upper bound.
  • Figure 5: The average LMP before and after DR in a day. Shaded regions depict DR events with price spikes, where the total demand reduction at 7 am, 8 am, 7 pm, and 8 pm are 644, 662, 655, and 641 MW, respectively.
  • ...and 2 more figures

Theorems & Definitions (5)

  • Remark 1
  • Remark 2
  • Proposition 1
  • proof
  • proof