    19 th International Conference on Electricity Distribution Vienna, 21-24 May 2007 Paper 0157- CIRED2007 Session 2 Paper No 0157 Page 1 / 4 STATISTICAL ANALYSIS OF VOLTAGE SAGS IN DISTRIBUTION NETWORK ACCORDING TO EN 50160 STANDARD – CASE STUDY Zvonimir KLAIC Srete NIKOLOVSKI Zoran BAUS Faculty of Electrical Engineering Faculty of Electrical Engineering Siemens – Croatia Osijek – Croatia Osijek – Croatia klaic@etfos.hr srete@etfos.hr zoran.baus@siemens.com ABSTRACT Voltage events introduce considerable economic losses and have the high impact on consumers. From an economic point of view the frequency and duration of voltage sags are very important because they can cause huge damage in industrial processes. This paper presents results of voltage dips measurements in several transformer stations in eastern Croatia. Power network analysers (LEM MEMOBOX 800, LEM MEMOBOX 808 and LEM TOPAS 1000, supported by powerful mathematical software) were used for measurements and analysis. The paper presents voltage dip probability functions calculated from the actual measurement data. The intention of the authors is to show a statistical method which could be useful for assessing the total annual event. INTRODUCTION Voltage dips are the most frequent cause of power quality problems. They introduce considerable economic losses and have the high impact on industry and other consumers. The most sensitive applications are continuous production lines, lighting and safety systems and computer equipment. From an economic point of view the dip frequency, i.e. the annual number of dips, is very important [1]. When assessing the total annual dip related cost one has to find out how many dips are expected. Some rough estimation can be acquired from measurement over a shorter period. Another approach is to use stochastic mathematical methods for assessing more precise figures. Measurements of voltage events for a number of domestic transformer stations using LEM MEMOBOX 800, LEM MEMOBOX 808 and LEM TOPAS 1000 power quality analyzers were performed, which enabled the detailed statistical analysis and derivation of probability density functions. Furthermore, a hill climbing algorithm used for minimizing the chi squared criterion and the best probability distributions used for fitting the measured data are presented in the paper. PROBABILITY DISTRIBUTION FUNCTIONS Probability distribution functions are mathematical equations allowing a large amount of information, characteristics and behaviour to be described by a small number of parameters [2]. A probability distribution function has an associated density function, f(x), that represents the likelihood that a random variable x will be a particular value. In this paper, lognormal and Weibull probability functions are used for describing voltage dip distributions. FITTING CURVES TO MEASURED DATA When probability distribution curves are used to represent empirical data, the information associated with thousands of data points can be modeled with one or two parameters. Chi Squared Criterion Chi squared criterion (χ 2 ) indicates how well a model matches the data that is supposed to represent [2]. It is based on density functions and data bin densities: ( 29 2 2 . . . bins Observed Freq in Bin Expected Freq in Bin Expected Freq in Bin χ - =  . Number of Samples in Bin Observed Freq in Bin Total Number of Samples = . () () () b a Expected Freq in Bin f x dx Fb Fa = = -  Bin a x b = ≤ < A hill climbing algorithm is used for minimizing the chi squared error of a curve fit. This algorithm guarantee that the parameters are locally optimal. VOLTAGE EVENTS ANALYSIS Measurements were performed on several (13) LV transformer stations with domestic consumers. A measurement period used for each consumer was one week, according to the European standard EN 50160. According to EN 50160, a voltage dip is a sudden reduction of the voltage supply to a value between 90% and 1% of the nominal voltage, with duration between 10 ms and 1 minute [3]. Table 1 represents summed voltage events for domestic transformer station measurements. Figure 1 (3D view) which derives from Table 1, shows that most voltage dips are found in two depth categories: 10 – 15 % U n and 15 – 30 % U n . Table 1. Voltage events for domestic transformer stations