322 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 21, NO. 1,JANUARY 2006 Stochastic Prediction of Voltage Sags by Considering the Probability of the Failure of the Protection System Myo Thu Aung, Student Member, IEEE, and Jovica V. Milanovic ´ , Senior Member, IEEE Abstract—This paper presents a comprehensive method for sto- chastic prediction of the number and characteristics of voltage sags in large distribution networks. The novelty of the proposed ap- proach is in probabilistic modeling of the failure of the protection system. The probability of the failure of the protection system is de- termined using a straightforward, decision tree based method. The paper highlights the effects of the protection system failure on the number and characteristics of voltage sags. The method proposed and its capabilities are demonstrated on the realistic size generic distribution system. The results presented in the paper show that the proposed method is superior to the traditional techniques used for the assessment of voltage sags as it results in higher accuracy of the prediction of the number and characteristics of voltage sags. Index Terms—Fault tree method, power system protection, sto- chastic assessment, voltage sags. I. INTRODUCTION S ERIOUS concerns related to financial losses due to voltage sags have been raised recently by utilities and industries. Those losses are mainly the consequence of the intensive use of sensitive electronic equipment in process automation. When the magnitude and the duration of voltage disturbance exceed the sensitivity threshold of the equipment in the customer’s facility, the equipment may malfunction, thus causing an interruption of the production process resulting in substantial financial losses [1]. It is necessary therefore, to be able to predict as accurately as possible the voltage sag performance at power system buses and at the equipment’s terminals as this will ultimately lead to more accurate assessment of potential production losses. The voltage sag’s performance can be assessed either by long term monitoring of voltages at various buses in the network or by a stochastic approach. The monitoring of voltages at power system buses is the best way to quantify and understand the voltage sag performance. However, it may take quite a long time, typically several years, if a higher accuracy and reliability of the monitoring data is required [2]. The other possibility is to use a stochastic approach based on computer simulations. This is generally the most suitable technique a) to assess voltage sags during the power system planning stage when the actual system (or part of it) may not exist yet or b) to assess the system sag Manuscript received July 22, 2004; revised December 15, 2004. This work was supported in part by the Electrical and Physical Sciences Research Council (EPSRC) under Grant GR/R40265/01, in part by the Copper Develop- ment Association (UK), and in part by Electrotek Concepts Inc. Paper no. TPWRD-00342–2004. M. T. Aung is with MottMacDonald, Glasgow G2 8JB, U.K. J. V. Milanovic ´ with the School of Electrical and Electronic Engineering, University of Manchester, Manchester, M60 1QD U.K. (e-mail: milanovic@ manchester.ac.uk). Digital Object Identifier 10.1109/TPWRD.2005.852385 performance for different operating scenarios and/or different loading conditions. Moreover, computer simulation based on the stochastic ap- proach does not take many years of monitoring to obtain the required accuracy of the results. (The results are as accurate as the input data and models used.) These are clearly advantages of the stochastic approach compared to the monitoring based approach. In the stochastic approach, traditionally the performance of voltage sags is predicted by assuming that all faults in the power systems are cleared by the primary protection system. Several authors [3]–[6] including Bollen [7], [8] and Olguin [9], [10] have discussed a straightforward technique for the prediction of voltage sags. In the method, faults are applied at every fault location in an attempt to obtain the remaining voltage magni- tude and angles during the faulted conditions. The duration of voltage sags is determined by the typical fault clearing times of the primary protection systems for buses or lines. In other words, the voltage sag performance is predicted assuming that the faults last a certain amount of time at each fault location and that they are subsequently removed by the operation of pri- mary protection systems. In fact, it is almost impossible to have 100% reliable protection system in reality, so it may sometimes fail to operate. In [11] Topham addressed the issue of protec- tion systems and their effects on the quality of power supply. The paper however, primarily focuses on the discussion of the effects of the speed of the protection system on the performance of voltage sags. Rombouts [12] modeled the effects of the failure of protective relays in the voltage sag prediction study by set- ting the fault clearing time of ever-relay up to infinity. In re- ality however, ever-protective relay may not fail to respond to the faults, and the probability of their failure should be taken into account in a stochastic way. When the primary protective relay or system fails, the backup protection system will respond to the faults, and consequently it will lead to longer duration of voltage sags. This longer duration voltage sags will almost cer- tainly trip the sensitive equipment in the customer’s facility even though this equipment may have been capable of riding-through the voltage sags related to the primary protection system (short duration voltage sags). Since the voltage sags are mainly caused by the faults in the power system, the failure of the primary pro- tection system and the effects of its failure on the number and characteristics of voltage sags ought to be considered in a sto- chastic manner. In this study, protection systems and their effects on the duration of voltage sags are firstly discussed. The paper further reveals a method that can be used for determining the prob- ability of the failure of the primary protection system. This 0885-8977/$20.00 © 2006 IEEE