Region of Attraction for Power Systems using Gaussian Process and Converse Lyapunov Function -- Part I: Theoretical Framework and Off-line Study

Zhai, Chao; Nguyen, Hung D.

doi:10.48550/arxiv.1906.03590

Cited by 7 publications

(18 citation statements)

References 30 publications

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“…Proof. The proof follows Theorem 6 in [18] and Theorem 1 in [16]. The result on regret bound, after N GP-UCB sampling points for training, provides the relation as [18]:…”

Section: A Main Resultsmentioning

confidence: 76%

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Non-parametric Probabilistic Load Flow using Gaussian Process Learning

Pareek¹,

Wang²,

Nguyen³

2019

Preprint

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In this paper, we propose a non-parametric probabilistic load flow (NP-PLF) technique based on Gaussian process (GP) learning. The technique can provide "semi-explicit" power flow solutions by implementing learning step and testing step. The proposed NP-PLF leverages upon GP upper confidence bound (GP-UCB) sampling algorithm. The salient features of this NP-PLF method are: i) applicable for power flow problem having power injection uncertainty with unknown class of distribution; ii) providing probabilistic learning bound (PLB) provides control over the error and convergence; iii) capable of handling intermittent distributed generation as well as load uncertainties; and iv) applicable to both balanced and unbalanced power flow with different type and size of systems. The simulation results performed on IEEE 30-bus and IEEE 118-bus system show that the proposed method is able to learn the state variable function in the input subspace using a small number of training samples. Further, the testing with different distributions indicates that more complete statistical information can be obtained for the probabilistic power flow problem.

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“…Proof. The proof follows Theorem 6 in [18] and Theorem 1 in [16]. The result on regret bound, after N GP-UCB sampling points for training, provides the relation as [18]:…”

Section: A Main Resultsmentioning

confidence: 76%

“…In power systems, various forecasting applications for wind power [12], [13], solar power [14], and electricity demand [15] used GP. Other than these forecasting works, the idea of using GP to learn the dynamics and stability index behavior has been explored recently in [16], [17].…”

Section: A Gp Regressionmentioning

confidence: 99%

Non-parametric Probabilistic Load Flow using Gaussian Process Learning

Pareek¹,

Wang²,

Nguyen³

2019

Preprint

Self Cite

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“…It follows from the non-singularity of the matrix ∂ g/∂ y in (3) that δ y goes to 0 as well. This implies that the operating point (x 0 , y 0 ) is asymptotically stable, which enables us to estimate the ROA of power grids by constructing converse Lyapunov function [6].…”

Section: The Roa Of Dae Systemmentioning

confidence: 99%

“…This advantage enables us to obtain a better ROA by collecting more sampling points in order to enlarge the level sets. In practice, the converse Lyapunov function V (x) proposed in Proposition 1 can be estimated by [6] V…”

Section: The Roa Of Dae Systemmentioning

confidence: 99%

“…Thus, this paper centers on the online security assessment of power systems with limited sampling data using the online GP approach. Compared with existing work [6]- [9], the key contributions of this work lie in 1) Construct the region of attraction for a general differential-algebraic equation (DAE) system with the converse Lyapunov function. 2) Develop an online GP approach for the dynamic security assessment of power systems with limited sampling data in a finite time window.…”

Section: Introductionmentioning

confidence: 99%

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Dynamic Security Assessment of Small-Signal Stability for Power Systems using Windowed Online Gaussian Process

Zhai

2019

Preprint

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Due to the evolving nature of power grids and model uncertainty, the online stability assessment of electrical power systems is always a challenging problem. This paper aims to provide a theoretical framework for estimating the region of attraction for power systems in real time. By analyzing and learning the measurement data in a given time duration, a windowed online Gaussian process (GP) approach is developed to provide the real-time security assessment and quantify the uncertainty caused by measurement errors and dynamic evolution of power systems. In addition, the theoretical analysis is conducted to ensure the conference level of the estimated region of attraction. Finally, numerical simulations are implemented on a microgrid model with 9 buses and 3 generators to validate the proposed approach. The proposed online assessment approach contributes to improving the situational awareness of human operators, thereby taking remedial actions before the emergency.

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Probabilistic robust small-signal stability framework using gaussian process learning

Pareek

Nguyen

2020

Electric Power Systems Research

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Region of Attraction for Power Systems using Gaussian Process and Converse Lyapunov Function -- Part I: Theoretical Framework and Off-line Study

Abstract: σ i (x) standard deviation of a Gaussian process at the i-th iteration • 2-norm in Euclidean space • k induced RKHS norm with the kernel k(x, x )

Cited by 7 publications

References 30 publications

Non-parametric Probabilistic Load Flow using Gaussian Process Learning

Non-parametric Probabilistic Load Flow using Gaussian Process Learning

Dynamic Security Assessment of Small-Signal Stability for Power Systems using Windowed Online Gaussian Process

Probabilistic robust small-signal stability framework using gaussian process learning

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