Applying Polynomial Chaos Expansion to Assess Probabilistic Available Delivery Capability for Distribution Networks With Renewables

Sheng, Hao; Wang, Xiaozhe

doi:10.1109/tpwrs.2018.2825657

Cited by 43 publications

(21 citation statements)

References 43 publications

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“…One can notice that the gPCC and the proposed aPCW methods yield similar performance in this test where the marginal CDF of uncertain parameters are known. These results imply that the accuracy of the marginal CDF of uncertain parameters has the effects on the PCE‐based methods as mentioned in Sheng and Wang and Eldred…”

Section: Numerical Experimentsmentioning

confidence: 65%

“…Only four uncertain parameters are considered. The Pearson correlation coefficient between S1‐W1, S1‐P1, S1‐Q1, W1‐P1, W1‐Q1, and P1‐Q1 are 0.0103, 0.1006, 0.1654, 0.3293, −0.2827, and 0.9014, respectively.…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…To address these issues, Sun et al and Sheng and Wang have proposed the application of gPCE to solve the PPF problem by using a sparse scheme and the copula theory. The sparse scheme is used to overcome the high dimensional calculation by fitting the sparsity gPCE model using small number of samples.…”

Section: Introductionmentioning

confidence: 99%

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Probabilistic power flow analysis based on arbitrary polynomial chaos expansion of bus voltage phasor

Laowanitwattana

Uatrongjit

2020

Int Trans Electr Energ Syst

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Summary An increasing penetration of renewable energy sources, such as solar farms and wind farms, necessitates a usage of statistical analysis and modeling for efficient operation and planning of the power systems. The probabilistic power flow (PPF) analysis based on the generalized polynomial chaos expansion (gPCE) technique has been applied to investigate the effects of random parameters in the power system network. Nevertheless, the gPCE‐based methods can be applied to the systems whose random parameters belong to specific probability distributions. If there exists a correlation among random parameters, then a decorrelation technique, for example, a copula function, is required. In this paper, a new approach for PPF analysis based on the arbitrary polynomial chaos expansion (aPCE) has been proposed. A set of basic polynomial functions used in this method is constructed using the recorded dataset of random parameters. The dependency of these uncertain parameters is decoupled by the whitening transformation. Instead of applying the aPCE to the required power system responses such as active power flow, current magnitude, etc, the proposed method uses the aPCE to construct a surrogate model of each bus voltage phasor. The bus voltage phasor model can then be employed to compute other power system responses without performing power flow analysis of the original power system. The proposed technique has been implemented and demonstrated in a MATLAB environment. On the basis of the numerical experiments with the modified IEEE 14‐bus and 118‐bus systems, the results indicate that the proposed method can achieve better accuracy and use less computation time than the techniques based on the gPCE with Gaussian copula function.

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Section: Numerical Experimentsmentioning

confidence: 65%

Section: Numerical Experimentsmentioning

confidence: 99%

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Probabilistic power flow analysis based on arbitrary polynomial chaos expansion of bus voltage phasor

Laowanitwattana

Uatrongjit

2020

Int Trans Electr Energ Syst

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“…The stochastic modeling for the wind speed is implemented as described in Section II-B and the parameters derived from real measurements [17] are c = 3.36, k = 1.51, α w = 0.2575/3600( 1 /s), β w = √ 2α w . Stochastic solar irradiance trajectories are generated according to Section II-C and the associated parameters are p = 1.11, q = 0.73 [18], α s = 0.2231/3600( 1 /s) [23], β s = √ 2α s , r c = 150W/m 2 , r std = 1000W/m 2 [5].…”

Section: B Impact Of Stochastic Load and Renewable Generation Variatmentioning

confidence: 99%

The Effect of the Uncertainty of Load and Renewable Generation on the Dynamic Voltage Stability Margin

Pierrou

Wang

2019

2019 IEEE PES Innovative Smart Grid Technologies Europe (ISGT-Europe)

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In this paper, the impact of stochastic load and renewable generation uncertainty on the dynamic voltage stability margin is studied. Stochastic trajectories describing the uncertainty of load, wind and solar generation have been incorporated in the power system model as a set of Stochastic Differential-Algebraic Equations (SDAEs). A systematic study of Monte Carlo dynamic simulations on the IEEE 39-Bus system has been conducted to compute the stochastic load margin with all dynamic components active. Numerical results show that the uncertainty of both demand and generation may lead to a decrease on the size of the dynamic voltage stability margin, yet the variability of renewable generators may play a more significant role. Given that the integration of renewable energy will continue growing, it is of paramount importance to apply stochastic and dynamic approaches in the voltage stability study.Index Terms-dynamic voltage stability, power systems dynamics, stochastic differential equations, voltage stability margin

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“…Particularly, the polynomial chaos expansion (PCE) is the most popular one because (i) it has strong mathematical basis; (ii) it works with deterministic tools in a non-intrusive fashion; (iii) it can provide accurate and comprehensive statistical properties of responses with low computational effort. The PCE method has been applied in the context of power systems to study the probabilistic power flow [11], [12], the load margin problem [13], and the available delivery capability problem [14].…”

Section: Introductionmentioning

confidence: 99%

Probabilistic Power Flow Calculation Using Non-Intrusive Low-Rank Approximation Method

Sheng

Wang

2019

IEEE Trans. Power Syst.

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In this paper, a novel non-intrusive probabilistic power flow (PPF) analysis method based on the low-rank approximation (LRA) is proposed, which can accurately and efficiently estimate the probabilistic characteristics (e.g., mean, variance, probability density function) of the PPF solutions. This method aims at building up a statistically-equivalent surrogate for the PPF solutions through a small number of power flow evaluations. By exploiting the retained tensor-product form of the univariate polynomial basis, a sequential correction-updating scheme is applied, making the total number of unknowns to be linear rather than exponential to the number of random inputs. Consequently, the LRA method is particularly promising for dealing with high-dimensional problems with a large number of random inputs. Numerical studies on the IEEE 39-bus, 118bus, and 1354-bus systems show that the proposed method can achieve accurate probabilistic characteristics of the PPF solutions with much less computational effort compared to the Monte Carlo simulations. Even compared to the polynomial chaos expansion method, the LRA method can achieve comparable accuracy, while the LRA method is more capable of handling higher-dimensional problems. Moreover, numerical results reveal that the randomness brought about by the renewable energy resources and loads may inevitably affect the feasibility of dispatch/planning schemes.

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Applying Polynomial Chaos Expansion to Assess Probabilistic Available Delivery Capability for Distribution Networks With Renewables

Cited by 43 publications

References 43 publications

Probabilistic power flow analysis based on arbitrary polynomial chaos expansion of bus voltage phasor

Probabilistic power flow analysis based on arbitrary polynomial chaos expansion of bus voltage phasor

The Effect of the Uncertainty of Load and Renewable Generation on the Dynamic Voltage Stability Margin

Probabilistic Power Flow Calculation Using Non-Intrusive Low-Rank Approximation Method

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