POWER SYSTEM ANALYSIS EET 3083 1 EET 308

POWER SYSTEM ANALYSIS EET 308/3 1 EET 308 POWER SYSTEM ANALYSIS

CHAPTER 4 SYMMETRICA L FAULT 2 EET 308 POWER SYSTEM ANALYSIS

On completion of this lesson, a student should be able to: Ability to analyze fault current in Symmetrical Fault 3 EET 308 POWER SYSTEM ANALYSIS

TOPIC OUTLINE 4. 1 Introduction 4. 2 Balance Three-phase Fault 4. 3 Short-circuit Capacity 4. 4 Systematic Fault Analysis Using Bus Impedance Matrix 4. 5 Selection of Circuit Breaker 4 EET 308 POWER SYSTEM ANALYSIS

4. 1 INTRODUCTION Faults in power systems are divided into three-phase balanced fault and unbalanced faults. The information from fault studies are used for proper relay setting and coordination. Three-phase balanced fault – the information is used to select and set phase relay. Fault analysis also used to determine the rating of protective switchgear. The magnitude of the fault current depends on the internal impedance of the generator and the network. 5 EET 308 POWER SYSTEM ANALYSIS

4. 2 BALANCED THREE-PHASE FAULT Xd” – subtransient reactance Xd’ – transient reactance Xd – synchronous reactance Generally, subtransient reactance is used for determining the interrupting capacity of the circuit breakers. While transient reactance is used for relay setting and coordination. If the fault impedance is zero, the fault is referred as the bolted fault or the solid fault. Since the impedance of a new path is usually low, an excessive current may flow. 6 EET 308 POWER SYSTEM ANALYSIS

4. 2 BALANCED THREE-PHASE FAULT Symmetrical AC component of the fault current: 1) Subtransient: first cycle or so after the fault – AC current is very large and falls rapidly; 2) Transient: current falls at a slower rate; 3) Steady-state: current gets back to normal. 7 EET 308 POWER SYSTEM ANALYSIS

ASSUMPTION BEEN MADE Load current is neglected (no load condition) All prefault bus voltages are assumed to be equal to 1. 0 per unit. Shunt capacitances are neglected Resistances are neglected All generators are running at their rated voltage and rated frequency with their emf in phase. 8 EET 102 ELECTRIC CIRCUIT II

EXAMPLE 4. 1 The one line diagram of a simple three-bus power system is shown in the Figure 4. 1. Each generator is represented by an emf behind the transient reactance. All impedances are expressed in per unit in a common 100 MVA base, and for simplicity, resistances are neglected. The following assumption are made: shunt capacitances are neglected and the system is considered on no load. all generators are running at their rated voltage and rated frequency with their emf in phase Determine the fault current, the bus voltages and the line currents during the fault when a balanced three-phase fault with a fault impedance Zf = j 0. 16 p. u. fault occurs on a) bus 3 b) bus 2 c) bus 1 9 EET 308 POWER SYSTEM ANALYSIS

EXAMPLE 4. 1 j 0. 1. j 0. 2 j 0. 1 j 0. 2 j 0. 8 1 2 j 0. 4 Figure 4. 1 One-line diagram of a simple power system 3 10 EET 308 POWER SYSTEM ANALYSIS

SOLUTION (a) Fault on bus 3 j 0. 2 j 0. 8 1 j 0. 4 Impedance network with fault at bus 3 j 0. 4 2 j 0. 4 3 Zf = j 0. 16 11 EET 308 POWER SYSTEM ANALYSIS

SOLUTION Thevenin’s theorem states that the changes in the network voltages caused by the added branch (the fault impedance) is equivalent to those caused by the added voltage V 3(0) with all other sources short-circuited. j 0. 2 j 0. 8 1 2 j 0. 4 All prefault voltages are assumed to be equal to 1. 0 per unit: V 1(0) = V 2(0) = V 3(0) = 1. 0 pu 12 EET 308 POWER SYSTEM ANALYSIS j 0. 4 3 Vth = V 3(0) I 3(F) Zf = j 0. 16 Thevenin’s equivalent network

SOLUTION using ∆ to Y transformation j 0. 2 j 0. 4 1 2 j 0. 1 3 Vth I 3(F) 13 EET 308 POWER SYSTEM ANALYSIS j 0. 16

SOLUTION combining the parallel branches, Thevenin impedance is j 0. 24 j 0. 1 3 Vth Z 33 is the Thevenin impedance viewed From the faulted bus. 14 EET 308 POWER SYSTEM ANALYSIS I 3(F) j 0. 16

SOLUTION From figure, the fault current is: Z 33 = j 0. 34 3 Vth I 3(F) 15 EET 308 POWER SYSTEM ANALYSIS j 0. 16

SOLUTION The current division between the two generators are The bus voltage changes 16 EET 308 POWER SYSTEM ANALYSIS

SOLUTION The bus voltages during the fault The short circuit line current are 17 EET 308 POWER SYSTEM ANALYSIS

SOLUTION (b) Fault on bus 2 j 0. 4 j 0. 8 1 2 j 0. 4 18 j 0. 4 3 EET 308 POWER SYSTEM ANALYSIS Zf = j 0. 16 Impedance network with fault at bus 2

SOLUTION j 0. 2 j 0. 4 j 0. 8 1 2 Vth j 0. 4 I 2(F) Thevenin’s equivalent network 19 EET 308 POWER SYSTEM ANALYSIS 3 Zf = j 0. 16

SOLUTION The equivalent impedance between bus 1 and 2 j 0. 4 2 1 Vth Zf = j 0. 16 20 EET 308 POWER SYSTEM ANALYSIS I 2(F)

SOLUTION Combining parallel branches from ground to bus 2 results The fault current is Z 22 = j 0. 24 2 Vth Zf = j 0. 16 21 EET 308 POWER SYSTEM ANALYSIS I 2(F)

SOLUTION The current division between the two generators are The bus voltage changes 22 EET 308 POWER SYSTEM ANALYSIS

SOLUTION The bus voltages during the fault The short circuit-current in the line are 23 EET 308 POWER SYSTEM ANALYSIS

SOLUTION (c) Fault on bus 1 j 0. 2 j 0. 4 j 0. 8 2 1 Zf = j 0. 16 j 0. 4 3 24 EET 308 POWER SYSTEM ANALYSIS Impedance network with fault at bus 1

SOLUTION j 0. 2 j 0. 4 j 0. 8 1 2 Vth j 0. 4 I 1(F) j 0. 4 Zf = j 0. 16 3 Thevenin’s equivalent network 25 EET 308 POWER SYSTEM ANALYSIS

SOLUTION Combining parallel branches between bus 1 and 2 j 0. 4 1 2 Vth I 1(F) 26 EET 308 POWER SYSTEM ANALYSIS j 0. 4 Zf = j 0. 16

SOLUTION Combining parallel branches from ground to bus 1 results Z 11 = j 0. 16 The fault current is 1 Vth I 1(F) 27 EET 308 POWER SYSTEM ANALYSIS Zf = j 0. 16

SOLUTION The current division between the two generators are The bus voltage changes 28 EET 308 POWER SYSTEM ANALYSIS

SOLUTION The bus voltages during the fault The short circuit-current in the line are 29 EET 308 POWER SYSTEM ANALYSIS

For More Accurate Calculation Pre fault bus voltages can be obtained from the power flow solution. Include the load currents into fault analysis where loads are expressed by a constant impedance evaluated at the pre fault bus voltages. 30 EET 102 ELECTRIC CIRCUIT II