IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 19, NO. 4, OCTOBER 2004 1819 Propagation of Asymmetrical Sags and the Influence of Boundary Crossing Lines on Voltage Sag Prediction Myo Thu Aung, Jovica V. Milanovic ´ , Senior Member, IEEE, and C. P. Gupta, Member, IEEE Abstract—This paper analyzes the influence of modeling of fault distribution along the boundary crossing lines of the area of vul- nerability on the stochastic prediction of voltage sags and their characteristics. The study was performed on a generic distribu- tion network, and all types of faults were simulated throughout the network. Two buses from the 11-kV distribution system were ran- domly selected and the areas of vulnerability due to each type of fault for specific sensitive equipment at the selected buses were de- termined. These areas were determined by assessing voltage sag performance at each phase separately. Finally, the influence of dif- ferent fault distributions along the vulnerability area boundary crossing lines was considered. It was shown that the fault distri- bution along those lines influences strongly the number and char- acteristics of voltage sags at the customer connection point. Index Terms—Area of vulnerability, boundary crossing lines, fault distribution, power quality, stochastic assessment, voltage sags. I. INTRODUCTION A. Causes, Consequences, and Characteristics of Voltage Sags In recent years, serious concerns over power-quality prob- lems associated with voltage sags have been raised by utility and customers due to the intensive use of sensitive electronic equipment in process automation [1]. If the magnitude and du- ration of a voltage sag exceed the sensitivity threshold of the equipment in a customer’s plant, the equipment may fail to op- erate, thus causing production stops with noticeable associated costs [1]. A voltage sag is defined as a decrease in the root-mean-square (rms) value of an ac voltage between 0.1 and 0.9 p.u. at power frequency for a duration from 0.5 cycles to 1 min. [2]–[4]. The magnitude and the duration of a sag have been used for the de- velopment of equipment compatibility charts and indices, and they are the main characteristics of a voltage sag. Other voltage sag characteristics (i.e., phase-angle jump, three-phase unbal- ance, and point on wave of sag initiation and recovery, are also very important for assessing equipment sensitivity to voltage Manuscript received February 20, 2003; revised July 1, 2003. Paper no. TPWRD-00062-2003. 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 Development Association (U.K.), and in part by Electrotek Concepts Inc. (U.S.). The authors are with the Department of Electrical Engineering and Electronics, University of Manchester Institute of Science and Technology (UMIST), Manchester M60 1QD, U.K. Digital Object Identifier 10.1109/TPWRD.2004.835427 sags [1]. Voltage sag duration is defined as the time interval be- tween the point on wave of sag initiation and recovery [5]. In most cases, duration of the sag is determined by fault clearing time, which highly depends on protective devices used by the utility in the power system. Different protective devices have different fault clearing times. The introduction of an intentional time delay is common, causing actual sag duration to be longer than fault clearing time. Typically, a voltage sag is divided into three categories namely instantaneous sag, momentary sag, and temporary sag, according to its duration [2]. The phase-angle jump is defined as the phase angle difference between voltages before the fault and during the fault. It may be positive or neg- ative. Positive phase-angle jump means that during the fault voltage is lagging the prefault voltage. With respect to conti- nuity of the power supply, voltage sags differ from the inter- ruptions. An interruption is a complete loss of voltage at the equipment terminals. A protective device will totally isolate the load from the power supply when interruptions occur [3], [6]. The load remains connected to the supply, however, during the voltage sag at the equipment terminals. The customer’s only concern, however, is whether the equipment in the plant trips or not, irrespectively of the type of the disturbance at the equip- ment terminals. Voltage sags are mainly caused by power system faults on the transmission or distribution system. Faults on the transmission system can affect more customers (even those who are hundreds of miles away from the fault location) than faults on the distri- bution system. In the power system, there-phase faults, which result in severe sags, are very rare. Single line-to-ground faults that typically cause shallow sags, on the other hand, are very common. Faults within the industrial facility or starting of large induction motors can also cause voltage sags. Voltage varia- tions caused by frequent motor starting (often referred to as voltage flicker or temporary undervoltages) usually do not lead to equipment misoperation [6]. Motor reacceleration after the fault clearing, however, may result in low-voltage magnitudes for up to several seconds [7]. Faults in the power system are mainly the result of adverse weather conditions, contamination of insulators, animal contact, and accidents involving construction or transportation activities. The most common cause of faults on overhead lines on the trans- mission and distribution network is lightning [8]. The lightning is highly dependent on the weather conditions and geographical regions. A strong correlation has been established between sag incident rate and flash density [9]. 0885-8977/04$20.00 © 2004 IEEE