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Towards Stochastic (N-1)-Secure Redispatch

Oleksii Molodchyk, Hendrik Drögehorn, Martin Lindner, Mario Kendziorski, Timm Faulwasser

TL;DR

The paper tackles uncertainty in renewable generation and the need for $N-1$-secure redispatch by proposing a polynomialChaos Expansion (PCE)-based stochastic OPF framework. The method minimizes the expected redispatch cost while enforcing equality constraints on PCE coefficients and incorporating chance constraints for line flows, using an epsilon-CBCO-driven constraint-generation loop to guarantee feasibility under outages. Key contributions include a dedicated stochastic redispatch formulation, an epsilon-CBCO extension for probabilistic outages, and a Beta-distribution-based RES forecast basis with a structured PCE. Numerical results on the IEEE 118-bus test system show that the PCE approach achieves comparable accuracy to Monte Carlo with substantially lower computation time, and offers interpretability through its PCE coefficients. This work advances uncertainty-aware planning for transmission operators and points to future enhancements such as stochastic unit commitment and copula-based dependency modeling for RES forecasts.

Abstract

The intermittent nature of renewable power availability is one of the major sources of uncertainty in power systems. While markets can guarantee that the demand is covered by the available generation, transmission system operators have to often intervene via economic redispatch to ensure that the physical constraints of the network are satisfied. To account for uncertainty, the underlying optimal power flow (OPF) routines have to be modified. Recently, polynomial chaos expansion (PCE) has been suggested in the literature as a tool for stochastic OPF problems. However, the usage of PCE-based methods in security-constrained OPF for (N-1)-secure operations has not yet been explored. In this paper, we propose a procedure that iteratively solves a PCE-overloaded stochastic OPF problem by including line outage constraints until an (N-1)-secure solution is achieved. We demonstrate the efficacy of our method by comparing it with a Monte-Carlo simulation on a 118-bus example system.

Towards Stochastic (N-1)-Secure Redispatch

TL;DR

The paper tackles uncertainty in renewable generation and the need for -secure redispatch by proposing a polynomialChaos Expansion (PCE)-based stochastic OPF framework. The method minimizes the expected redispatch cost while enforcing equality constraints on PCE coefficients and incorporating chance constraints for line flows, using an epsilon-CBCO-driven constraint-generation loop to guarantee feasibility under outages. Key contributions include a dedicated stochastic redispatch formulation, an epsilon-CBCO extension for probabilistic outages, and a Beta-distribution-based RES forecast basis with a structured PCE. Numerical results on the IEEE 118-bus test system show that the PCE approach achieves comparable accuracy to Monte Carlo with substantially lower computation time, and offers interpretability through its PCE coefficients. This work advances uncertainty-aware planning for transmission operators and points to future enhancements such as stochastic unit commitment and copula-based dependency modeling for RES forecasts.

Abstract

The intermittent nature of renewable power availability is one of the major sources of uncertainty in power systems. While markets can guarantee that the demand is covered by the available generation, transmission system operators have to often intervene via economic redispatch to ensure that the physical constraints of the network are satisfied. To account for uncertainty, the underlying optimal power flow (OPF) routines have to be modified. Recently, polynomial chaos expansion (PCE) has been suggested in the literature as a tool for stochastic OPF problems. However, the usage of PCE-based methods in security-constrained OPF for (N-1)-secure operations has not yet been explored. In this paper, we propose a procedure that iteratively solves a PCE-overloaded stochastic OPF problem by including line outage constraints until an (N-1)-secure solution is achieved. We demonstrate the efficacy of our method by comparing it with a Monte-Carlo simulation on a 118-bus example system.

Paper Structure

This paper contains 10 sections, 22 equations, 1 figure, 2 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. The Redispatch Problem and (N-1)-Security
  4. Polynomial Chaos Expansions
  5. Stochastic Redispatch
  6. Proposed Approach For (N-1)-Secure Stochastic OPF
  7. PCE-based (N-1)-Secure Redispatch
  8. Polynomial Basis for RES Generation Forecasts
  9. Numerical Example
  10. Conclusions and Outlook

Figures (1)

  • Figure 1: Density functions of generator setpoints computed via PCE (green) and MC-based (red) (N-1)-secure redispatch.

Theorems & Definitions (4)

  • Definition 1: (N-1)-Security endrenyiBulkPowerSystemReliability1988
  • Definition 2: CBCO and CBCO Analysis
  • Definition 3: $\epsilon$-CBCO and $\epsilon$-CBCO Analysis
  • Remark 1: Forecast dependencies