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Efficient Scenario Generation for Chance-constrained Economic Dispatch Considering Ambient Wind Conditions

Qian Zhang, Apurv Shukla, Le Xie

TL;DR

The paper tackles the challenge of efficiently generating scenarios for chance-constrained economic dispatch under ambient wind conditions. It introduces a correlation-based ambient-wind environment filter to obtain scenarios that better reflect the conditional wind forecast error, and an incremental risk-tuning framework to meet a target risk with minimal data. Case studies on modified 24-bus and 118-bus networks using real ERCOT wind data demonstrate reduced data requirements, lower violation probabilities, and lower dispatch costs when sampling from similar environments. The approach improves risk guarantees and computational efficiency, offering practical benefits for real-time dispatch and outlining future extensions to multi-stage settings and discrete decision problems.

Abstract

Scenario generation is an effective data-driven method for solving chance-constrained optimization while ensuring desired risk guarantees with a finite number of samples. Crucial challenges in deploying this technique in the real world arise due to the absence of appropriate risk-tuning models tailored for the desired application. In this paper, we focus on designing efficient scenario generation schemes for economic dispatch in power systems. We propose a novel scenario generation method based on filtering scenarios using ambient wind conditions. These filtered scenarios are deployed incrementally in order to meet desired risk levels while using minimum resources. In order to study the performance of the proposed scheme, we illustrate the procedure on case studies performed for both 24-bus and 118-bus systems with real-world wind power forecasting data. Numerical results suggest that the proposed filter-and-increment scenario generation model leads to a precise and efficient solution for the chance-constrained economic dispatch problem.

Efficient Scenario Generation for Chance-constrained Economic Dispatch Considering Ambient Wind Conditions

TL;DR

The paper tackles the challenge of efficiently generating scenarios for chance-constrained economic dispatch under ambient wind conditions. It introduces a correlation-based ambient-wind environment filter to obtain scenarios that better reflect the conditional wind forecast error, and an incremental risk-tuning framework to meet a target risk with minimal data. Case studies on modified 24-bus and 118-bus networks using real ERCOT wind data demonstrate reduced data requirements, lower violation probabilities, and lower dispatch costs when sampling from similar environments. The approach improves risk guarantees and computational efficiency, offering practical benefits for real-time dispatch and outlining future extensions to multi-stage settings and discrete decision problems.

Abstract

Scenario generation is an effective data-driven method for solving chance-constrained optimization while ensuring desired risk guarantees with a finite number of samples. Crucial challenges in deploying this technique in the real world arise due to the absence of appropriate risk-tuning models tailored for the desired application. In this paper, we focus on designing efficient scenario generation schemes for economic dispatch in power systems. We propose a novel scenario generation method based on filtering scenarios using ambient wind conditions. These filtered scenarios are deployed incrementally in order to meet desired risk levels while using minimum resources. In order to study the performance of the proposed scheme, we illustrate the procedure on case studies performed for both 24-bus and 118-bus systems with real-world wind power forecasting data. Numerical results suggest that the proposed filter-and-increment scenario generation model leads to a precise and efficient solution for the chance-constrained economic dispatch problem.
Paper Structure (17 sections, 2 theorems, 7 equations, 14 figures, 4 tables, 3 algorithms)

This paper contains 17 sections, 2 theorems, 7 equations, 14 figures, 4 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Problem Statements
  3. Chance-Constrained Economic Dispatch
  4. Conditional Wind Power Forecast Error
  5. Method
  6. Scenario Approach
  7. Sampling Scenarios from Parameter Space
  8. Main Result I: Correlation-Based Scenario Generation
  9. Main Result II: Incremental Scenario Optimization
  10. Discussion
  11. Identical Distribution
  12. Independent Random Variables
  13. Case Study
  14. Conditional Wind Forecasting Error
  15. 24-bus System
  16. ...and 2 more sections

Key Result

Theorem 1

Under the assumptions of nondegeneracy and feasibility of the optimization problem, the deepest results show that the distribution of $\mathbb{V}_{\tilde{w}}(g^*,\eta^*)$ is dominated by a Beta distribution, namely:

Figures (14)

  • Figure 1: The comparison of the conventional scenario approach (left) and the proposed scenario generation model (right)
  • Figure 2: The wind forecasting region in ERCOT
  • Figure 3: The scatter plot (left) and density function (right) of forecasting error under different wind power forecasting value
  • Figure 4: The density function of forecasting error under different wind power ramping rate
  • Figure 5: The density function of forecasting error under different temperatures and relative humidity
  • ...and 9 more figures

Theorems & Definitions (8)

  • Definition 1: Violation Probability
  • Definition 2: Support Constraint
  • Definition 3: Sample Complexity
  • Definition 4: Helly's Dimension
  • Theorem 1: Exact Feasibility campi2008exactcampi2018general
  • Theorem 2: Property for Convex Problem campi2008exact
  • Definition 5: Parameter Space for Wind Power Forecasting Error
  • Definition 6: Probability Distribution Over Parameter Space