A Data-Driven Sparse Polynomial Chaos Expansion Method to Assess Probabilistic Total Transfer Capability for Power Systems With Renewables

Wang, Xiaoting; Wang, Xiaozhe; Sheng, Hao; Lin, Xi

doi:10.1109/tpwrs.2020.3034520

Cited by 37 publications

(23 citation statements)

References 29 publications

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“…where Z could be volatile renewables (e.g., wind speed), load variations, etc. The system response Y is also a random variable (e.g., voltage variation in [5], [13], [14], probabilistic total transfer capability (PTTC) in [15], [16]). Covariance-based sensitivity indices can be utilized arXiv:2307.07080v1 [eess.SP] 13 Jul 2023 to quantify how the variation in Zj affects the variance of the system response Y .…”

Section: The Polynomial Chaos Expansion-based Global Sensitivity Anal...mentioning

confidence: 99%

A Comparative Study of Polynomial Chaos Expansion-Based Methods for Global Sensitivity Analysis in Power System Uncertainty Control

Wang¹,

Liu²,

Wang³

et al. 2024

IEEE Trans. Circuits Syst. II

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In this letter, we compare three polynomial chaos expansion (PCE)-based methods for ANCOVA (ANalysis of CO-VAriance) indices based global sensitivity analysis for correlated random inputs in two power system applications. Surprisingly, the PCE-based models built with independent inputs after decorrelation may not give the most accurate ANCOVA indices, though this approach seems to be the most correct one and was applied in [1] in the field of civil engineering. In contrast, the PCE model built using correlated random inputs directly yields the most accurate ANCOVA indices for global sensitivity analysis. Analysis and discussions about the errors of different PCE-based models will also be presented. These results provide important guidance for uncertainty management and control in power system operation and security assessment.

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Section: The Polynomial Chaos Expansion-based Global Sensitivity Anal...mentioning

confidence: 99%

A Comparative Study of Polynomial Chaos Expansion-Based Methods for Global Sensitivity Analysis in Power System Uncertainty Control

Wang¹,

Liu²,

Wang³

et al. 2024

IEEE Trans. Circuits Syst. II

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“…One such method to quantify the Uncertainty in modern power systems is using Monte Carlo simulations, which are computationally expensive. As measurement devices such as phasor measurement units are prevalent in the network, various data-driven methods have gained growing attention in the literature (see, Wang (2020), Wang et al (2021)).…”

Section: Case Study 3: Stochastic Power Flowmentioning

confidence: 99%

“…Such large deviations from the assumptions will result in strongly biased hyperparameter estimates if non-robust estimation methods are applied which eventually affects the resulting uncertainty quantification. Consequently, data-driven models are popular in these areas (see, Wang et al (2020)).…”

Section: Introductionmentioning

confidence: 99%

Robust Hyperparameter Estimation in Gaussian Process Regression Model

Algikar

Mili

2023

Preprint

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A stochastic process mathematically models the random behavior of systems and naturally occurring phenomena. A popular process is a Gaussian process which assumes a multivariate Gaussian distribution for the response variables. The predictive distributions of target variables can be explicitly obtained by using conditioning and inference techniques. The mean function and covariance function of the predictive distributions are parameterized whose estimates can be obtained by maximizing the marginal likelihood of the training responses or their posterior distribution. Unfortunately, these estimates are not robust to outliers that are often present in the observational training data sets. To overcome this problem, we develop a robust data-driven process based on the Schweppe-type Huber-generalized maximum likelihood (SHGM) estimator to bound the influence of all types of outliers on the estimates while exhibiting a high statistical efficiency at the Gaussian and thick-tail distributions. The weights utilized by the SHGM estimator are calculated using projection statistics, which are robust distances of the data points determined by the row vectors of the design matrix. These weights make the estimator robust to both vertical outliers and bad leverage points while not downweighting good leverage points. We show that the proposed robust model is able to handle up to 25 percent of outliers among the data set. The proposed method is illustrated by two real-world examples in which the performance of the proposed method is assessed against the standard Gaussian process regression.

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“…This paper finds that installing PST in the grid can increase the TTC of the grid while increasing the wind power consumption. However, wind power's uncertainty will greatly affect TTC's calculation (Wang et al, 2021), so the traditional TTC calculation method (Verboomen et al, 2008) is no longer applicable. This paper proposes a method to calculate the TTC of grids with PST and wind power.…”

Section: Introductionmentioning

confidence: 99%

Optimal allocation of phase shifting transformer with uncertain wind power based on dynamic programming

Zhang²,

Li³

et al. 2023

Front. Energy Res.

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Phase Shifting Transformer (PST) can help improve the power flow distribution of the transmission section, which can increase the wind power consumption of the grid. In order to adapt the PST allocation to the grid evolution, this paper presents a dynamic programming method to allocate PST in each planning stage of the grid optimally. The optimal allocation model of PST under a single grid seeks to maximize the wind power consumption and the Total Transfer Capacity (TTC) between areas. A calculation method for TTC of grids containing PST and wind power is proposed. The Non-Dominated Sorting Genetic Algorithm II (NSGA2) is used to solve the Pareto sets under each planning stage of the grid. Then, the optimal planning path of PST is derived based on dynamic programming. The superiority of the proposed method is demonstrated by comparing the IEEE-118 system results of dynamic and static programming.

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A Data-Driven Sparse Polynomial Chaos Expansion Method to Assess Probabilistic Total Transfer Capability for Power Systems With Renewables

Cited by 37 publications

References 29 publications

A Comparative Study of Polynomial Chaos Expansion-Based Methods for Global Sensitivity Analysis in Power System Uncertainty Control

A Comparative Study of Polynomial Chaos Expansion-Based Methods for Global Sensitivity Analysis in Power System Uncertainty Control

Robust Hyperparameter Estimation in Gaussian Process Regression Model

Optimal allocation of phase shifting transformer with uncertain wind power based on dynamic programming

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