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

Abstract

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.

Data‐driven modeling for fatigue loads of large‐scale wind turbines under active power regulation

“…The aPCE formulates a stochastic component fatigue load output DEL ( ξ ), dependent on a vector independent stochastic input variables ξ = [ P set , V ] ( P set is the WT active power setting and V is the mean wind speed) with the probability space of event Ω, σ ‐algebra Λ, and probability measure Γ, 40 as a linear combination of p stochastic multivariate orthogonal polynomials Ψ i ( ξ ) and deterministic coefficients c i . 24 where the coefficients c i of aPCE is obtained using orthonormal property, 24 and the number of m of terms in the expansion depends on the total number of input parameters n and on the order p of the expansion, according to the formula m = ( n + p ) ! /( n !…”

“…where the coefficients c i of aPCE is obtained using orthonormal property, 24 and the number of m of terms in the expansion depends on the total number of input parameters n and on the order p of the expansion, according to the formula m = (n+p) ! /(n !…”

“…Many surrogate models are available to express the relationship between fatigue load of WT and its influential factors. The arbitrary polynomial chaos expansion (aPCE) can achieve better accuracy and is robust than the other methods (e.g., polynomial chaos expansion, quadratic response surface, universal kriging, importance sampling, and nearest‐neighbor interpolation) 14,24 . The support vector regression (SVR) performs well in data‐driven modeling, which is suitable for a finite sample regression and has good generalization ability for the regression 25 .…”

“…The arbitrary polynomial chaos expansion (aPCE) can achieve better accuracy and is robust than the other methods (e.g., polynomial chaos expansion, quadratic response surface, universal kriging, importance sampling, and nearest-neighbor interpolation). 14,24 The support vector regression (SVR) performs well in data-driven modeling, which is suitable for a finite sample regression and has good generalization ability for the regression. 25 Inspired by the strong nonlinear capabilities of aPCE and SVR, it would be a good idea to choose a DEL data model suitable for coordinative optimization by comparing the accuracy, complexity and calculation time of these two methods.…”

Scrutiny of power grids by penetrating PV energy in wind farms: a case study of the wind corridor of Jhampir, Pakistan

“…For the energy industry to have a sustainable future, it is essential to integrate renewable energy sources into organised environments, such as solar systems. As a result, photovoltaic systems have seen a sharp surge in their use recently (Lampropoulos et al, 2020;Laowanitwattana and Uatrongjit, 2020;Lin, 2022;Stecanella et al, 2020). Global energy demand is expected to rise by more than 30% by 2040, according to the International Energy Agency (Vainio et al, 2020).…”