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Chance Constrained Optimal Power Flow: Risk-Aware Network Control under Uncertainty (1209.5779v2)

Published 25 Sep 2012 in math.OC, cs.SY, and physics.soc-ph

Abstract: When uncontrollable resources fluctuate, Optimum Power Flow (OPF), routinely used by the electric power industry to re-dispatch hourly controllable generation (coal, gas and hydro plants) over control areas of transmission networks, can result in grid instability, and, potentially, cascading outages. This risk arises because OPF dispatch is computed without awareness of major uncertainty, in particular fluctuations in renewable output. As a result, grid operation under OPF with renewable variability can lead to frequent conditions where power line flow ratings are significantly exceeded. Such a condition, which is borne by simulations of real grids, would likely resulting in automatic line tripping to protect lines from thermal stress, a risky and undesirable outcome which compromises stability. Smart grid goals include a commitment to large penetration of highly fluctuating renewables, thus calling to reconsider current practices, in particular the use of standard OPF. Our Chance Constrained (CC) OPF corrects the problem and mitigates dangerous renewable fluctuations with minimal changes in the current operational procedure. Assuming availability of a reliable wind forecast parameterizing the distribution function of the uncertain generation, our CC-OPF satisfies all the constraints with high probability while simultaneously minimizing the cost of economic re-dispatch. CC-OPF allows efficient implementation, e.g. solving a typical instance over the 2746-bus Polish network in 20 seconds on a standard laptop.

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Authors (3)
  1. Daniel Bienstock (35 papers)
  2. Michael Chertkov (151 papers)
  3. Sean Harnett (2 papers)
Citations (488)

Summary

Chance Constrained Optimal Power Flow: Risk-Aware Network Control under Uncertainty

The paper "Chance Constrained Optimal Power Flow: Risk-Aware Network Control under Uncertainty" presents an innovative approach to addressing the uncertainties inherent in power grid operations, particularly due to renewable energy sources. The authors, Bienstock, Chertkov, and Harnett, propose an optimization framework that incorporates risk-awareness into On-line Power Flow (OPF) calculations, termed Chance Constrained-Optimal Power Flow (CC-OPF).

Key Contributions

The paper's central contribution is the introduction of chance constraints into the OPF problem to better handle the stochastic nature of renewable energy sources, such as wind. Traditional OPF models do not account for the variability and unpredictability of such resources, potentially leading to grid instability and cascading outages. By contrast, CC-OPF addresses these uncertainties by ensuring that constraints are satisfied with a high probability, offering enhanced grid reliability without significantly altering existing operational procedures.

Methodology

The authors assume that wind generation is uncertain, presenting this uncertainty through Gaussian distributions for simplicity and tractability. They further incorporate an affine control law that modulates generator outputs in response to fluctuations in wind power, thereby maintaining the balance between supply and demand.

Technically, the paper derives a convex formulation of the CC-OPF problem, identifying it as a Second-Order Cone Program (SOCP). This allows the problem to be efficiently solved using modern optimization methods, even for large-scale grid models. The proposed model includes rigorous definitions of the chance constraints: the probability of line flows exceeding their limits must remain below a specified threshold, providing robust operational guarantees.

Empirical Results

Empirical analysis is conducted on several test cases, including the Polish network and the Bonneville Power Administration grid, demonstrating computational efficiency and effectiveness of the proposed model. Notably, the CC-OPF model ensures operational reliability in scenarios where traditional OPF models fail to prevent line overloads. The approach successfully maintains grid stability at a fraction of the cost associated with traditional curtailment strategies, highlighting its practical benefits.

Implications and Future Directions

The introduction of CC-OPF represents a significant step forward in integrating renewable energy into existing power grids. The research suggests that such an approach can facilitate higher penetration of renewables without necessitating substantial infrastructure investments, thereby supporting global energy transition goals.

Theoretically, this work opens avenues for further exploration in robust and stochastic optimization applied to power systems. Future research could delve into non-Gaussian distributions, multi-time scale control integration, and broader applications of CC-OPF in grid resilience planning and emergency management.

Moreover, the paper's foundational methodology allows for customization to various grid operational challenges, including dynamic load changes and fault scenarios, marking CC-OPF as a versatile tool in modernizing grid operations.

In summary, the paper articulates a sophisticated yet computationally feasible approach to managing uncertainty in power grids with growing renewable energy integration. It provides a framework that not only ensures reliability and stability but also aligns operational practices with the evolving landscape of energy production.