AIMS Energy, 2018, 6(3): 414-435. doi: 10.3934/energy.2018.3.414

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The probabilistic load flow analysis by considering uncertainty with correlated loads and photovoltaic generation using Copula theory

1 School of Electrical and Electronic Engineering, North China Electric Power University, Beijing 102206, P.R. China
2 Department of Electrical Engineering, The Superior University Lahore, Lahore 54000, Pakistan
3 Department of Electrical Engineering, Government College University Faisalabad Sahiwal Campus, Sahiwal 57000, Pakistan

In this paper, a probabilistic load flow analysis is proposed in order to deal with probabilistic problems related to the power system. Due to increasing trend of penetration of renewable energy sources in power system brought two factors: One is uncertainty, and another one is dependence. Uncertainty and dependence factor increase risk associated with power system operation and planning. In this proposed model these two factors is considered. Gaussian Copula theory is proposed to establish the probability distribution of correlated input random variables. Three sampling methods are used with Monte Carlo simulation as simple random sampling, Box-Muller sampling, and Latin hypercube sampling in order to evaluate the accuracy of the proposed method. The main advantages of this model are as: It can establish any type of correlation between input random variable with the help of Copula theory, it is free from the restrictions of Pearson coefficient of correlation, it is unconstrained by the marginal distribution of input random variables, and uncertainty is established with photovoltaic generation this is the main source of uncertainty. Additional, in order to evaluate the accuracy and efficiency of the proposed model a real load and photovoltaic generation data is adopted. For accuracy evaluation purpose two comparative test system is adopted as modified IEEE 14 and IEEE 118-bus test system.
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