Importance sampling approach to chance-constrained DC optimal power flow

Lukashevich, Aleksander; Gorchakov, V. V.; Vorobev, Petr; Deka, Deepjyoti; Maximov, Yury

doi:10.48550/arxiv.2111.11729

Cited by 2 publications

(4 citation statements)

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“…Scenario approximation (SA) is very attractive from the practical perspective but requires an extreme number of samples to get reasonable accuracy [13]. Importance sampling helps to reduce the SA computational burden [23]- [25] in chance-constrained optimization; however, it has not yet been studied for dynamic power flow optimization problems.…”

Section: Scenario Approximation Of Chance Constrained Controlmentioning

confidence: 99%

“…Finally, instead of using vanilla Monte-Carlo, we sample from a proxy (importance) distribution having less redundant scenarios. This approach improves the sample complexity and reliability [23].…”

Section: Scenario Approximation Of Chance Constrained Controlmentioning

confidence: 99%

“…. Such mixture has proven to be useful in approximating the distribution of interest [23], [24], [17]. For this study, we use w 1 = • • • = w |S| .…”

Section: The Exact Expression For the Density Is Fmentioning

confidence: 99%

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Power Grid Reliability Estimation via Adaptive Importance Sampling

Lukashevich

Maximov

2022

IEEE Control Syst. Lett.

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Renewable energy sources (RES) has become common in modern power systems, helping to address decarbonization and energy security goals. Despite being attractive, RES such as solar and have low inertia and high uncertainty, thus compromising power grid stability and increasing the risk of energy blackouts. Stochastic (chance-constrained) optimization and other state-of-theart algorithms to optimize and control power generation under uncertainty either explicitly assume the distribution of renewables, or use data-driven approximations. The latter becomes time-consuming and inaccurate, esp. when optimizing over multiple time steps.This paper considers a discrete-time chance-constraint direct current optimal power flow control problem for minimizing power generation costs subjected to power balance and security constraints. We propose an importancesampling-based data-driven approximation for the optimal automated generation control, which allows to improve accuracy and reduce data requirements compared to stateof-the-art methods. We support the proposed approach theoretically and empirically. The results demonstrate the approach superior performance in handling generation uncertainty, enhancing the stability of renewable-integrated power systems, and facilitating the transition to clean energy.

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Section: Scenario Approximation Of Chance Constrained Controlmentioning

confidence: 99%

Section: Scenario Approximation Of Chance Constrained Controlmentioning

confidence: 99%

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Power Grid Reliability Estimation via Adaptive Importance Sampling

Lukashevich

Maximov

2022

IEEE Control Syst. Lett.

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“…Monte Carlo scenario-based CC-OPF [7,8], with nonlinear AC-PF equations, does not computationally scale for large systems or a large number of scenarios [9]. Consequently, advanced sampling policies (importance sampling, active sampling) have been recommended to reduce the number of samples necessary [10,11,9,12,13]. In contrast, analytical approach to CC-OPF states the chance constraints using distributional information of the uncertainty and is the focus of this work.…”

Section: Introductionmentioning

confidence: 99%

Data-Driven Stochastic AC-OPF using Gaussian Processes

Mile¹,

Aleksandr²,

Vorobev³

et al. 2022

Preprint

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In recent years, electricity generation has been responsible for more than a quarter of the greenhouse gas emissions in the US. Integrating a significant amount of renewables into a power grid is probably the most accessible way to reduce carbon emissions from power grids and slow down climate change. Unfortunately, the most accessible renewable power sources, such as wind and solar, are highly fluctuating and thus bring a lot of uncertainty to power grid operations and challenge existing optimization and control policies. The chance-constrained alternating current (AC) optimal power flow (OPF) framework finds the minimum cost generation dispatch maintaining the power grid operations within security limits with a prescribed probability. Unfortunately, the AC-OPF problem's chance-constrained extension is non-convex, computationally challenging, and requires knowledge of system parameters and additional assumptions on the behavior of renewable distribution. Known linear and convex approximations to the above problems, though tractable, are too conservative for operational practice and do not consider uncertainty in system parameters. This paper presents an alternative data-driven approach based on Gaussian process (GP) regression to close this gap. The GP approach learns a simple yet non-convex data-driven approximation to the AC power flow equations that can incorporate uncertainty inputs. The latter is then used to determine the solution of CC-OPF efficiently, by accounting for both input and parameter uncertainty. The practical efficiency of the proposed approach using different approximations for GP-uncertainty propagation is illustrated over numerous IEEE test cases.

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Importance sampling approach to chance-constrained DC optimal power flow

Cited by 2 publications

References 25 publications

Power Grid Reliability Estimation via Adaptive Importance Sampling

Power Grid Reliability Estimation via Adaptive Importance Sampling

Data-Driven Stochastic AC-OPF using Gaussian Processes

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