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Optimizing Flexibility in Power Systems by Maximizing the Region of Manageable Uncertainties

Aron Zingler, Stephane Fliscounakis, Patrick Panciatici, Alexander Mitsos

TL;DR

This work introduces a rigorous framework to maximize the region of manageable uncertainty in power systems under worst-case conditions using a DC power-flow model. It casts the problem as an existence-constrained semi-infinite program (ESIP) and solves it via a specialized discretization algorithm, enabling two-stage decisions with preventive actions and real-time controls. Two interpretable uncertainty-region parametrizations are proposed: an inner hyperbox approximation and a maximal available power-transfer capacity, each yielding actionable insight into grid robustness and flexibility. Numerical experiments on small and medium-scale grids demonstrate the method's feasibility and highlight its sensitivity to algorithmic parameters, while pointing to practical applicability for improving grid reliability and planning under uncertainty.

Abstract

Motivated by the increasing need to hedge against load and generation uncertainty in the operation of power grids, we propose flexibility maximization during operation. We consider flexibility explicitly as the amount of uncertainty that can be handled while still ensuring nominal grid operation in the worst-case. We apply the proposed flexibility optimization in the context of a DC flow approximation. By using a corresponding parameterization, we can find the maximal range of uncertainty and a range for the manageable power transfer between two parts of a network subject to uncertainty. We formulate the corresponding optimization problem as an (existence-constrained) semi-infinite optimization problem and specialize an existing algorithm for its solution.

Optimizing Flexibility in Power Systems by Maximizing the Region of Manageable Uncertainties

TL;DR

This work introduces a rigorous framework to maximize the region of manageable uncertainty in power systems under worst-case conditions using a DC power-flow model. It casts the problem as an existence-constrained semi-infinite program (ESIP) and solves it via a specialized discretization algorithm, enabling two-stage decisions with preventive actions and real-time controls. Two interpretable uncertainty-region parametrizations are proposed: an inner hyperbox approximation and a maximal available power-transfer capacity, each yielding actionable insight into grid robustness and flexibility. Numerical experiments on small and medium-scale grids demonstrate the method's feasibility and highlight its sensitivity to algorithmic parameters, while pointing to practical applicability for improving grid reliability and planning under uncertainty.

Abstract

Motivated by the increasing need to hedge against load and generation uncertainty in the operation of power grids, we propose flexibility maximization during operation. We consider flexibility explicitly as the amount of uncertainty that can be handled while still ensuring nominal grid operation in the worst-case. We apply the proposed flexibility optimization in the context of a DC flow approximation. By using a corresponding parameterization, we can find the maximal range of uncertainty and a range for the manageable power transfer between two parts of a network subject to uncertainty. We formulate the corresponding optimization problem as an (existence-constrained) semi-infinite optimization problem and specialize an existing algorithm for its solution.

Paper Structure

This paper contains 33 sections, 1 theorem, 21 equations, 6 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Motivating example
  3. Literature review
  4. Problem Formulation and Solution
  5. Model equations
  6. Notation
  7. Summary of the model
  8. Components
  9. Edges
  10. Nodes
  11. Algorithm
  12. Reformulation to an existence constrained semi-infinite optimization problem
  13. Algorithmic steps
  14. Specialization
  15. Dropping redundant discretization points
  16. ...and 18 more sections

Key Result

Proposition 1

Assume that the uncertainty domain is defined by a continuous function $h$ in the form $\mathcal{T}(\boldsymbol{x},\delta) := \{\boldsymbol{y}\in \bar{\mathcal{Y}}| h(\boldsymbol{x},\boldsymbol{y}) \le \delta\}$ with a given host set for the uncertain values $\bar{\mathcal{Y}}$. We can exactly refor with for any arbitrarily chosen but fixed scaling constant $\alpha \in \mathbb{R}^+$.

Figures (6)

  • Figure 1: Motivating power grid instance with two generators and two uncertain loads.
  • Figure 2: Illustration of the behavior of phase shifters.
  • Figure 3: Illustration of the behavior of generator $g$.
  • Figure 4: Illustration of the behavior of the algorithm with and without transformation in a fictitious example. $\mathcal{Y}^*(x)$ denotes the set of all uncertainty values $\boldsymbol{y}$ that can be handled with the preventive actions $\boldsymbol{x}$. None of the preventive actions $\boldsymbol{x}^A,\boldsymbol{x}^B,\boldsymbol{x}^C$ can handle the discretization point $\boldsymbol{y}^1$.
  • Figure 5: Visualization of the result from the motivating example for the final preventive actions. The optimized region of manageable uncertainties is valid and optimal for the chosen parameterization.
  • ...and 1 more figures

Theorems & Definitions (2)

  • Proposition 1
  • proof