chapter 3 - Bentham Science

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Applications of Spreadsheets in Education The Amazing Power of a Simple Tool, 2011, 3–17 3 Fault Analysis in Power Systems Mark A. Lau ∗ and Sastry P. Kuruganty Department of Electrical and Computer Engineering Universidad del Turabo, Gurabo, Puerto Rico, USA CHAPTER 1 ∗ Address correspondence to: Dr. Mark A. Lau, Department of Electrical and Computer Engineering, Universidad del Turabo, Road 189 Km 3.3, Gurabo, Puerto Rico 00778-3030, USA; Tel: (+1) 787-743-7979, Ext. 4174; E-mail: mlau@suagm.edu Abstract: Fault analysis is an important consideration in power system planning, protection equipment selection, and overall system reliability assessment. At the heart of today’s power generation and distribution are high-voltage transmission and distribution networks. When a fault (e.g., a short circuit) occurs at some point in the network, the normal operating conditions of the system are upset; if the fault is persistent severe loss of load, property damage due to fire or explosion, and steep economic losses can arise as undesirable consequences. Therefore, the correct modeling of components and the correct fault analysis in power systems are critical to ensuring safety and reliability. In this chapter fault analysis is illustrated via spreadsheets. Spreadsheets are widely accessible and the ease of programming is the hallmark feature that renders them appealing to many users. This simple tool is employed to analyze both symmetrical and unsymmetrical faults in power systems. The determination of fault currents aids the power engineer in the selection and coordination of protective equipment to ensure the safe and reliable operation of the system. Keywords: fault analysis, symmetrical faults, unsymmetrical faults, short circuits, power systems. 1.1 Introduction The complexity of power systems demands a variety of tools for their correct modeling, analysis, and design. Classical problems such as power (load) flows, transient stability, dynamic stability, fault analysis, and economical dispatch are part of the knowledge repertoire of any practicing power engineer. This chapter discusses fault analysis in power systems utilizing spreadsheets. Fault analysis is an important aspect in power system planning, protection equipment selection, and overall system reliability. A fault is defined to be an event or condition that disrupts the normal operation of a power system. To be more specific, this chapter focuses on short circuits in three-phase power systems. Short circuits may be classified under two categories: symmetrical faults and unsymmetrical faults. Mark Lau and Stephen Sugden (Eds) All rights reserved – c○2011 Bentham Science Publishers Ltd.
4 Applications of Spreadsheets in Education The Amazing Power of a Simple Tool Lau and Kuruganty A three-phase short circuit constitutes a symmetrical fault; single line-to-ground, line-to-line, and double line-to-ground short circuits are instances of unsymmetrical faults. In decreasing order of frequency short circuits in three-phase power systems occur as follows: single line-to-ground, line-to-line, double line-to-ground, and balanced three-phase faults. While balanced three-phase faults are the least frequent, these faults will be presented first because of their conceptual simplicity. The material presented in this chapter is accessible to most undergraduatelevel students with some previous exposure to power system concepts. The presentation follows those of most textbooks [1–4]; equations are given without derivations as they can be found in standard reference books [1–4]. Instead, the emphasis is placed on the construction of spreadsheet models to analyze faults in power systems. Applications of spreadsheets in power system analysis have been reported in the literature [5–8]. It is along this line that this chapter is presented, continuing the efforts initiated by the authors in a power systems course [6, 7]. This chapter is organized as follows. Section 1.2 presents a spreadsheet implementation to analyze balanced three-phase short circuits. Spreadsheet models for analyzing unbalanced threephase faults are presented in Section 1.3. Subsequently, a discussion on the spreadsheet models and possible adaptations is given in Section 1.4. Finally, Section 1.6 gives some concluding remarks. It is pointed out that throughout this chapter, spreadsheet models are implemented in Microsoft Excel. 1.2 Symmetrical Faults A power system is normally treated as a balanced (symmetrical) three-phase network. When a fault occurs, the symmetry is oftentimes upset, resulting in unbalanced phase currents and phase voltages. A three-phase symmetrical fault is a special case because it involves all three phases equally at the fault location. Fault analysis is typically performed by examining the so called sequence networks of the system being analyzed. In fact, any system can be represented by three sequence networks: zero-, positive-, and negative-sequence networks. In the special case of a balanced three-phase short circuit, the resulting fault currents are balanced and, hence, only the positive-sequence network is considered. For more background information on symmetrical components and sequence networks, the reader may consult any of the standard books [1–4]. It turns out that fault currents resulting from symmetrical three-phase short circuits can be calculated from the one-line (or per-phase equivalent) diagram of the system and the pre-fault operating conditions. During the fault the phase current and phase voltage undergo a subtransient period, followed by a transient period, before settling down to a steady state. To simplify matters and to make the analysis amenable to spreadsheet implementation, the following assumptions are made [1–4]: 1. All system voltages are replaced by a single driving voltage at the fault location. This driving voltage is the pre-fault voltage at the fault location. Further, this pre-fault voltage is assumed to be the open-circuit voltage at that point. 2. In most applications, load currents are small in comparison to fault currents and may be neglected. 3. Transformers are represented by their leakage reactances. Winding resistances and shunt admittances are neglected.
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