An improved LHS is proposed in Section 3.
The remainder of this paper is organised as follows: Section 2 presents the modelling of probability distribution of correlated input random variables by Copula theory. The results obtained by MCILHS are compared with those got by MCSM with Copula and SRS (MCSRS) with regards to both accuracy and execution time criteria using IEEE 14-bus and IEEE 118-bus test systems. An MCSM with Copula and improved LHS (MCILHS) is proposed. An improved LHS based on discrete data is proposed. This theory not only contains the complete information of the degree of dependence and dependence structure between different input random variables, but also can deal with both linear and non-linear dependence relationships flexibly, and it is unconstrained by the marginal distribution type of input random variable. In this paper, Copula theory is adopted to establish the probability distribution of correlated input random variables. For example, the marginal distribution function of wind farm power output is hard to be obtained because it does not follow the typical marginal distribution. However, MCSM-LHS always assumes that the input random variable follows a typical marginal distribution and its CDF is known, which limits its application in some circumstances. So, MCSM with LHS (MCSM-LHS) is more computationally efficient than MCSM-SRS. Compared with simple random sampling (SRS), LHS can obtain an accurate result with a much smaller sample size. Latin hypercube sampling (LHS) is an efficient stratified sampling technique that generates random numbers according to the marginal cumulative distribution function (CDF) of input random variable. But this method requires a large computation effort. This method is commonly used as a reference to check the accuracy of other PLF methods. MCSM with simple random sampling (MCSM-SRS) can achieve a considerably high accuracy when the sample size is large enough. So it is considered to be the most accurate, flexible and robust PLF method. Once this method is converged, all the distribution functions of output random variables are simultaneously obtained. The number of simulations needed to obtain an accurate result by MCSM is independent of system size. MCSM can use the exact non-linear load flow equations and does not need miscellaneous simplifications or complicated mathematical computation. Since different degrees of dependence may have a same dependence structure, different dependence structures may have a same degree of dependence. The complete measure of dependence between input random variables should consider both the degree of dependence and dependence structure. The dependence relationships between different input random variables may be linear dependence or non-linear dependence. For example, wind power is influenced by the factors of wind direction, wind speed, power curve and control strategy of wind turbine. As a matter of fact, the input random variables in power system operation are affected by various factors.
Most of these proposed PLF methods only consider the linear dependence between input random variables and adopt Pearson's linear correlation coefficient and covariance matrix to demonstrate the degree of linear dependence between them. Some PLF methods have been proposed in the technical literature to deal with the correlated input random variables, including convolution method, Gaussian mixture model method, unscented transformation, point estimate method, cumulant method and Monte Carlo simulation method (MCSM). In order to evaluate system load flow more accurately and comprehensively, and provide system operators with more valuable information, PLF computation should consider the dependence factor. The dependence factor affects load demands, generators’ power output and operation modes of power system, and further has an important influence on system load flow.Īs one of the most commonly used tools for system load flow analysis, probabilistic load flow (PLF) can effectively assess the performance of a power network over most of its working conditions taking into account the uncertainty of input random variables, such as wind power. Power output of different neighbouring wind farms is strongly correlated. For example, a group of loads existing in the same area will tend to increase and decrease in a similar manner due to the environmental factors and social ones. Plenty of stochastic dependence between power injections exists in power system operation, including linear and non-linear dependence.