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

Abstract

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.

Probabilistic available transfer capability assessment in power systems with wind power integration

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“…The canonical decompositions are typically used to compress and extract information of a tensor and have been used in a broad range of fields, like signal processing and data mining [28][29][30]. Recently, it also attracts interest in the probabilistic power flow problem [31]. The number of coefficients in canonical decompositions grows linearly rather than exponentially with the input dimension [32], making LRA more powerful in dealing with high-dimensional problems.…”

Compressed Machine Learning Models for the Uncertainty Quantification of Power Distribution Networks

“…Specifically, a beta distribution with parameters α = 0.90 and β = 0.85 is considered here. In turn, the active power P pv of the PV generator is expressed as a function of the solar radiation r as discussed in [48]. The rated power of each PV is 100 kVA.…”

“…The rated power of each PV is 100 kVA. The PV generators are assumed to be operating at a unitary power factor [48], and therefore their reactive power is considered to be zero in this study, with a capacity penetration level of 17.5%.…”

Wind speed estimation based on a novel multivariate Weibull distribution

“…Since the wind stream applied to the wind turbine have impacts on both node voltage and branch power of microgrid, so the prediction of microgrid power flow is much needed to provide information for the energy management system of microgrid [31]. Probabilistic power flow (PPF) can be used to obtain the probability distributions of microgrid variables, that are functions of load variation, and generation uncertainties (load forecast error, generator failure and stochastic of renewable energy sources) [31][32][33][34][35][36]. Probabilistic measurements based on PPF are more reliable than deterministic values [35], because of the instantaneous…”