Abstract
This paper presents a cumulant-based method for probabilistic load flow (PLF) analysis which incorporates correlation between input random variables. Our approach can approximate non-Gaussian variables of all kinds (e.g. different load profiles or renewable power injections) accurately using the Gaussian mixture model (GMM), which also facilitates the computation of cumulants in a straightforward numerical way. Multiple correlations can be easily handled by transforming correlated variables into a combination of uncorrelated ones. To reduce the deviations introduced by traditional series expansions such as Edgeworth or Cornish-Fisher series, we use C-type Gram-Charlier series instead, which can better predict the probabilistic tail regions and have good convergence property as well. The good performance of the proposed method is verified using the IEEE 30 test system in terms of accuracy and efficiency.DOI: http://dx.doi.org/10.5755/j01.eie.24.3.20980
Highlights
A surge of grid complexity associated with increasing level of uncertainties, such as high penetration of weather-dependent renewable energies (REs) and plug-in hybrid electric vehicles (PEVs) has brought crucial challenges to system planning and operation [1]–[3]
The average root mean square (ARMS) deviations with the proposed method are comparatively smaller, most of which are less than 1 %, even for the maximum values, showing large improvement compared with original cumulant method (CM)
It is concluded that both the proposed method and original CM can significantly reduce the computational burden in probabilistic load flow (PLF) analysis compared with Monte Carlo simulation (MCS), while their execution time goes up steadily as the size of network grows
Summary
A surge of grid complexity associated with increasing level of uncertainties, such as high penetration of weather-dependent renewable energies (REs) and plug-in hybrid electric vehicles (PEVs) has brought crucial challenges to system planning and operation [1]–[3]. The use of different series expansions (e.g. Edgeworth series, Cornish-Fisher series) show satisfactory performance when input variables are Gaussian or near-Gaussian, they may have serious convergence problems and large deviations for non-Gaussian distributions [16] Another prevalent proposal is the point estimate method (PEM), which selects a set of quadrature points to estimate the moments of output variables [17], [18]. The main contribution of the paper is to develop an improved CM for PLF studies, which can conveniently handle the correlated variables It has made big progress by solving the subsequent problems in original CM, such as a) calculating the cumulants for non-Gaussian variables, b) considering the dependency without sacrificing computation speed, c) accelerating convergence rate, and d) avoiding negative PDF values.
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