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Chance-Constrained Economic Dispatch with Flexible Loads and RES

Tian Liu, Bo Sun, Danny H. K. Tsang

TL;DR

This paper addresses the challenge of integrating wind-uncertainty in power systems by incorporating multi-dimensional load flexibility (MDF) into the day-ahead market. It introduces a virtual-battery representation for MDF, a parametric MDF bidding mechanism, and a chance-constrained economic dispatch (CEDP) framework that captures wind deviations via an affine control policy and probabilistic constraints, reformulated as an SOCP for efficiency. The key contributions are a unified MDF market design that supports partial bid acceptance, a tractable SOCP formulation, and demonstrative case studies showing MDF reduces LMP volatility and informs MDF market design. The approach enables demand-side resources to participate in security-constrained markets with measurable value, enhancing reliability and economic efficiency under renewable intermittency.

Abstract

With the increasing penetration of intermittent renewable energy sources (RESs), it becomes increasingly challenging to maintain the supply-demand balance of power systems by solely relying on the generation side. To combat the volatility led by the uncertain RESs, demand-side management by leveraging the multi-dimensional flexibility (MDF) has been recognized as an economic and efficient approach. Thus, it is important to integrate MDF into existing power systems. In this paper, we propose an enhanced day-ahead energy market, where the MDFs of aggregate loads are traded to minimize the generation cost and mitigate the volatility of locational marginal prices (LMPs) in the transmission network. We first explicitly capture the negative impact of the uncertainty from RESs on the day-ahead market by a chance-constrained economic dispatch problem (CEDP). Then, we propose a bidding mechanism for the MDF of the aggregate loads and combine this mechanism into the CEDP for the day-ahead market. Through multiple case studies, we show that MDF from load aggregators can reduce the volatility of LMPs. In addition, we identify the values of the different flexibilities in the MDF bids, which provide useful insights into the design of more complex MDF markets.

Chance-Constrained Economic Dispatch with Flexible Loads and RES

TL;DR

This paper addresses the challenge of integrating wind-uncertainty in power systems by incorporating multi-dimensional load flexibility (MDF) into the day-ahead market. It introduces a virtual-battery representation for MDF, a parametric MDF bidding mechanism, and a chance-constrained economic dispatch (CEDP) framework that captures wind deviations via an affine control policy and probabilistic constraints, reformulated as an SOCP for efficiency. The key contributions are a unified MDF market design that supports partial bid acceptance, a tractable SOCP formulation, and demonstrative case studies showing MDF reduces LMP volatility and informs MDF market design. The approach enables demand-side resources to participate in security-constrained markets with measurable value, enhancing reliability and economic efficiency under renewable intermittency.

Abstract

With the increasing penetration of intermittent renewable energy sources (RESs), it becomes increasingly challenging to maintain the supply-demand balance of power systems by solely relying on the generation side. To combat the volatility led by the uncertain RESs, demand-side management by leveraging the multi-dimensional flexibility (MDF) has been recognized as an economic and efficient approach. Thus, it is important to integrate MDF into existing power systems. In this paper, we propose an enhanced day-ahead energy market, where the MDFs of aggregate loads are traded to minimize the generation cost and mitigate the volatility of locational marginal prices (LMPs) in the transmission network. We first explicitly capture the negative impact of the uncertainty from RESs on the day-ahead market by a chance-constrained economic dispatch problem (CEDP). Then, we propose a bidding mechanism for the MDF of the aggregate loads and combine this mechanism into the CEDP for the day-ahead market. Through multiple case studies, we show that MDF from load aggregators can reduce the volatility of LMPs. In addition, we identify the values of the different flexibilities in the MDF bids, which provide useful insights into the design of more complex MDF markets.
Paper Structure (13 sections, 24 equations, 7 figures, 5 tables)

This paper contains 13 sections, 24 equations, 7 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Chance-constrained ED Problem
  3. Wind Uncertainty Model and Affine Control Policy
  4. CEDP for Incorporating Uncertain Generation
  5. Market Clearing Problem for MDF Services
  6. MDF Bidding for Incorporating Controllable Loads
  7. Market Clearing Problem by the CEDP with MDF Bidding
  8. SOCP Reformulation of the Market Clearing Problem
  9. Case Studies
  10. Improving LMP Profiles by MDF Bidding
  11. Nine-bus System
  12. Beyond the Normal Wind Forecast Errors
  13. Conclusions

Figures (7)

  • Figure 1: Q-Q plots for hourly forecast errors of wind power output in August from 2011 to 2017.
  • Figure 2: Six-bus transmission network.
  • Figure 3: Total hourly net load over 24-hour horizon.
  • Figure 4: LMPs for load buses in three cases.
  • Figure 5: Nine-bus transmission network.
  • ...and 2 more figures