Joined Probabilistic Load Flow and Sensitivity Analysis of Distribution Networks Based on Polynomial Chaos Method

Abstract

Due to the statistical uncertainty of loads and power sources found in smart grids, effective computational tools for probabilistic load flow analysis and planning are now becoming indispensable. In this research, we describe a unified simulation framework that allows quantifying the probability distributions of a set of observation variables as well as evaluating their sensitivity to potential variations in the power demands. The proposed probabilistic technique relies on the generalized Polynomial Chaos algorithm and on a region-wise aggregation/description of the time-varying load profiles. It is shown how detailed statistical distributions of some important figures of merit, which includes voltage unbalance factor in distribution networks, can be calculated with a two-orders of magnitude acceleration compared to standard Monte Carlo analysis. In addition, it is highlighted how the associated sensitivity analysis is of guidance for the optimal allocation and planning of new loads.

A Framework for Analytical Power Flow Solution Using Gaussian Process Learning

“…Yet, they are time consuming as the accuracy directly depends upon the number of samples used MCS and every sample requires a multiiteration NRLF. The methods to calculate VP, other than MCS, are built with the information of uncertainty distribution type and parameters [43]. Obtaining the uncertainty information is becoming increasingly challenging due to overlapping of EVs and RESs uncertainties in ADN net-load.…”

“…The proposed CFPF approximation can work with any distribution like MCS and have reduced computational burden like polynomial chaos expansion [43]. The analytical function ( 7)-( 9) can estimate the VP for various input distribution without retraining of the model.…”

Piece-Wise Linear (PWL) Probabilistic Analysis of Power Grid with High Penetration PV Integration

“…Stochastic Response Surface Methods (SRSM) or techniques based on generalized Polynomial Chaos (gPC) adopt series expansions of multi-variate polynomial basis functions spanning the whole statistical/parameter space to approximate y j ( x) [17][18][19]. The success of such techniques in PLF analysis relies on the fact that load-flow-established relationships y j ( x) are commonly almost linear and thus they can be accurately approximated by series expansions of low order (commonly order ≤ 2) polynomials.…”

“…Several probabilistic acceleration techniques have be proposed that approximate the input-output relationship between PV injected powers and node voltages variations. Many of such techniques rely on polynomial chaos expansions [17][18][19] and have been proved to supply excellent results. Unfortunately, they suffer of the curse of dimensionality and loose much of their effectiveness when the number of statistical parameters involved grows to much [20].…”

“…In the second experiment, we compare the PWL method to another state-of-the art ¾ technique employed in probability load flow problems. The technique relies on Copula ¾ method [28] for modeling correlated PV sources combined with generalized-Polynomial-¾ Chaos (gPC) approximation [17], [18], [19]. Fig.…”