EE6501_Power_System_Analysis_2_Marks_wit.docx

**EE6501 Power System Analysis** **2 Marks with Answers** **Regulation 2013 Anna University** **UNIT I INTRODUCTION** Need for system planning and operational studies -- basic components of a power system.-Introduction to restructuring - Single line diagram -- per phase and per unit analysis --...

**EE6501 Power System Analysis** **2 Marks with Answers** **Regulation 2013 Anna University** **UNIT I INTRODUCTION** Need for system planning and operational studies -- basic components of a power system.-Introduction to restructuring - Single line diagram -- per phase and per unit analysis -- Generator - transformer -- transmission line and load representation for different power system studies.- Primitive network - construction of Y-bus using inspection and singular transformation methods -- z-bus. 1. **What are the main divisions of power system? (NOV DEC 2014)** - Generating Station - Transmission System - Distribution System - Utilization System 2. **What is the need for per unit value? (NOV DEC 2014)** **In an electric power systems, different voltage levels and power levels are connected together through a step-up or step-down transformer or different power equipments. The varying voltages and power levels are present in the power systems. These causes problems in finding out the current at different points in the network. To avoid this problem, all the system quantities are converted to a uniform normalized platform called as per unit representation.** 3. **Draw the impedance diagram for the given single line representation of the power system.(MAY JUN 2014)** 4. **What are the types of load modelling? (MAY JUN 2014)** **How are loads represented in impedance and reactance diagram? (NOV DEC 2011)** **[Impedance diagram: ]** **Static Loads:**  **Rotational Load:** **[Reactance diagram: ]** **Rotational Load:**  5. **What are the functions of modern power system? (NOV DEC 2013)** - To provide quality power - To provide uninterrupted power supply - To provide power at low cost - To produce power using renewable source of energy than nonrenewable source of energy. - To reduce the losses in the transmission line due to various factors. - To increase the power transfer capacity of the transmission line. - T increase the power generation. 6. **Name the diagonal and off - diagonal elements of bus impedance matrix. (NOV DEC 2013)** \ [\$\$\\mathbf{Z}\_{\\mathbf{\\text{BUS}}}\\mathbf{= \\ }\\begin{bmatrix} \\mathbf{Z}\_{\\mathbf{11}} & \\mathbf{Z}\_{\\mathbf{12}} & \\mathbf{Z}\_{\\mathbf{13}} \\\\ \\mathbf{Z}\_{\\mathbf{21}} & \\mathbf{Z}\_{\\mathbf{22}} & \\mathbf{Z}\_{\\mathbf{23}} \\\\ \\mathbf{Z}\_{\\mathbf{31}} & \\mathbf{Z}\_{\\mathbf{32}} & \\mathbf{Z}\_{\\mathbf{33}} \\\\ \\end{bmatrix}\$\$]{.math.display}\ \ [**Z**~**11**~ **,**  **Z**~**22**~**,**  **Z**~**33**~ **=**Diagonal Elements]{.math.display}\ \ [**Z**~**12**~**,**  **Z**~**13**~**,**  **Z**~**21** ~**,**  **Z**~**23**~**,**  **Z**~**31**~**,**  **Z**~**32**~**=**Off**−**Diagonal Elements]{.math.display}\ 7. **What is meant by percentage reactance? (MAY JUN 2013)** \ [\$\$\\%\\ X = \\ \\frac{\\text{IX}}{V}\\ \\times 100\$\$]{.math.display}\ Alternatively it can also be expressed in terms of KVA and KV \ [\$\$\\%\\ X = X\\text{.\\ \\ }\\frac{\\text{KVA}}{10\\ \\left( \\text{KV} \\right)\^{2}}\$\$]{.math.display}\ 8. **Draw the equivalent circuit of a 3 winding transformer. (NOV DEC 2012) (MAY JUN 2013)** 9. **What are the components of power system? (MAY JUN 2012)** 10. **If the reactance in ohms is 15 ohms, find the p.u value for a base of 15 KVA and 10 KV(MAY JUN 2012)** [Solution]: Actual reactance=15Ώ \ [\$\$Base\\ impedance = \\ \\frac{{(\\text{KV}\_{b})}\^{2}}{\\text{MVA}\_{b,new}}\$\$]{.math.display}\ \ [\$\$Base\\ impedance\\ = \\ \\frac{(10\^{2})}{15/1000}\\ = 6666.7\\ \\mathrm{\\Omega}\$\$]{.math.display}\ 11. **What is single line diagram? (NOV DEC 2011)** 12. **Draw a simple per-phase model for a cylindrical rotor synchronous machine. (APR MAY 2011)** \ [**E** = **V** + IZ]{.math.display}\ 13. **What are the advantages of per unit system? (APR MAY 2011)** Per unit data representation yields valuable relative magnitude information. - Circuit analysis of systems containing transformers of various transformation ratios is greatly simplified. - The p.u systems are ideal for the computerized analysis and simulation of complex power system problems. - Manufacturers usually specify the impedance values of equivalent in per unit of the equipment's rating. If the any data is not available, it is easier to assume it's per unit value than its numerical value. **SIXTEEN MARKS** 1. **Using the method of bus building algorithm find the bus impedance matrix for the network shown in fig.** 2. **Draw the structure of an electrical power system and describe the components of the system with typical values.** 3. **Obtain the per unit impedance diagram of the power system of fig shown below :** 4. For a three bus network fig shown below, obtain Zbus by bus building algorithm. **(NOV DEC 2014)** 5. **The single line diagram of a power system is shown in figure along with components data. Determine the new per unit values and draw the reactance diagram. Assume 25 MVA, and 20KV as new base on generator G1 (MAY JUN 2014)** 6. **Describe the Zbus building algorithms in detail by using a three bus system. (MAY JUN 2014)** 7. **A 90 MVA 11 KV 3 phase generator has a reactance of 25%. The generator supplies two motors through transformer and transmission line as shown in figure. The transformer T1 is a 3 -- phase transformer, 100 MVA, 10/132 KV, 6% reactance. The transformer T2 is composed of 3 single phase units each rated, 300 MVA, 66110KV, with 5% reactance. The connection of T1 & T2 are shown. The motors are rated at 50 MVA 10 KV and 20 % reactance. Taking the generator rating as base, draw reactance diagram and indicate the reactance in per unit. The reactance of line is 100 ohms. (NOV DEC 2013)** 8. **Determine Y~bus~ for the 3 - bus system shown in figure. Neglect the shunt capacitance of the lines.(NOV DEC 2013)**  9. **For the system shown in figure, determine the generator voltage. Take a base of 100 MVA and 210 KV in the transmission line. (MAY JUN 2013)** 10. Form the bus impedance matrix for the network shown in fig. by bus building algorithm. 11. **Draw the reactance diagram using a base of 100 MVA, 220 KV in 50 ohm line.** 12. **Determine Y~BUS~ for the four bus network shown in Fig. consider bus 4 as reference bus. (MAY JUNE 2012)** 13. **The parameters of a 4 bus system are as follows** **Bus Code** **Line Impedance (p.u)** **Charging Admittance (p.u)** -------------- -------------------------- ------------------------------- **1-2** **0.2+j0.8** **j0.02** **2-3** **0.3+j0.9** **j0.03** **2-4** **0.25+j1** **j0.04** **3-4** **0.2+j0.8** **j0.02** **1-3** **0.1+j0.4** **j0.01** 14. **Determine the Z bus for the system whose reactance diagram is shown in the Fig. where the impedance is given in p.u** 15. **Explain the modeling of generator, load, transmission line and transformer for power flow, short circuit and stability studies. (NOV DEC 2008) (NOV DEC 2012, 2007 reg)** **UNIT II POWER FLOW ANALYSIS** Importance of power flow analysis in planning and operation of power systems - statement of power flow problem - classification of buses - development of power flow model in complex variables form - iterative solution using Gauss-Seidel method - Q-limit check for voltage controlled buses -- power flow model in polar form - iterative solution using Newton-Raphson method. TWO MARKS ========= 1. **Compare Gauss Seidal and Newton Raphson methods. (MAY JUN 2012)(APR MAY 2015)** **S.No** **Factor** **Gauss Seidal** **Newton Raphson** ---------- --------------------------------- ------------------------ --------------------------- **1** **Reliability** **Reliable** **More reliable** **2** **Convergence characteristics** **Linear convergence** **Quadratic convergence** **3** **Simplicity in programming** **Easy** **More complex** **4** **Memory requirement** **Less memory** **More memory** 2. **What is load flow and power flow study? (NOV DEC 2014)** **Power flow analysis is also known as load flow analysis in power engineering. It is an important tool involving numerical analysis which is applied to a power system.** **The power flow analysis is applied to steady state performance of the power system. This analysis involves for specified terminal or bus conditions calculation of power flows and voltages of a transmission network.** 3. **Define voltage controlled bus. (NOV DEC 2014)** **This bus is also called generator bus. Here the voltage magnitude corresponding to the generator voltage and real power generation corresponding to its ratings are specified. Hence it is required to determine the reactive power generation and the phase angle of the voltage.** 4. **What is the role of swing bus in power flow study? (MAY JUN 2014)** A bus is called swing bus when the magnitude and phase of the bus voltage are specified for it. The swing bus is the reference bus for load flow solution and it is required for accounting line losses. Usually one of the generator bus is selected as swing bus. 5. **At what condition generator bus is treated as load bus? (MAY JUN 2014)** **When will the generator bus be treated as load bus? (NOV DEC 2013)** 6. **Why do Y~bus~ used in load flow study instead of Z~bus~? (NOV DEC 2013)** 7. **What is the necessity for slack bus? (MAY JUN 2013)** **What is the need for slack bus? (APR MAY 2011)** 8. **What is meant by acceleration factor? (MAY JUN 2013)** **What is meant by acceleration factor in load flow studies? (NOV DEC 2012)** 9. **What are the data required for a load flow study? (NOV DEC 2012)** 10. **What are the information's that are obtained from a power flow study? (MAY JUN 2012)** 11. **What are the different types of buses in a power system? What are the quantities specified in each bus? (NOV DEC 2011)** -- -- -- -- -- -- 12. **How are the disadvantages of Newton Raphson method overcome? (NOV DEC 2011)** 13. **What is Jacobian matrix? (APR MAY 2011)** 14. **What is the need for load flow study? (MAY JUNE 2006)** 15. **What is bus admittance matrix? (MAY JUNE 2006)** 16. **What is PQ bus(load bus)? (APRMAY 2005)** 17. **What are the works involved in a load flow study? (NOV DEC 2004)** The following has to be performed for a load flow study. - **Representation of the system by single line diagram.** - **Formation of impedance diagram using the information in single line diagram.** - **Formulation of network equations** - **Solution of network equations.** 18. **Discuss the effect of acceleration factor in the load flow solution algorithm. (APR MAY 2004)** **SIXTEEN MARKS** 1. **Fig shows the one line diagram of a simple three bus power system with generation at buses 1 and 2. The voltage at bus 1 is V=1+j0.0 V per unit. Voltage magnitude at bus 2 is fixed at 1.05 p.u with a real power generation of 400 MW. A load consisting of 500 MW and 400 MVAR is taken from bus 3. Line admittances are marked in per unit on a 100 MVA base. For the hand calculation, line resistances and line charging succeptance are neglected.** 2. **In a power network shown in fig, bus 1 is a slack bus with V1=1.0+j0.0 per unit and bus 2 is a load bus with S~2~=280 MW+j60 MVAr. The line impedance on a base of 100 MVA is Z=0.02+0.04j per unit. Using Gauss Seidal method, determine V~2~. Use an initial estimate of** [*V*~2~^0^ = 1.0 + *j*0.0]{.math.inline} **and perform four iterations. Also find S1 and real, reactive power loss in the line, assuming the bus voltages have converged. (APR MAY 2015)** 3. **Fig shown below a three bus power system** 4. **With a neat flow chart, explain the computational procedure for load flow solution using Newton Raphson iterative method when the system contains all types of buses.** 5. **Describe the step by step procedure for load flow solution from GaussSeidal method, if PV and PQ buses are present along with slack bus (MAY JUNE 2014)** 6. **A three bus power system is shown in figure. The relevant per unit line admittance on 100MVA base are indicated on the diagram and bus data are given in table. Form Ybus and determine the voltages at bus 2 and bus 3 after first iteration using Gauss Seidal method. Take theacceleration factor a = 1.6 (NOV DEC 2013)** Bus Number Type Generation Load Bus Voltage ------------ ------- ------------ ------ ------------- ------ ------ --- P~G~ Q~G~ P~L~ Q~L~ V ᵟ 1 Slack 0 0 1.02 0 2 PQ 25 15 50 25 3 PV 0 0 60 30 7. **Consider the power system with the following data:** \ [\$\$Y\_{\\text{BUS}} = \\ \\begin{pmatrix} - j12 & j8 & j4 \\\\ j8 & - j12 & j4 \\\\ j4 & j4 & - j8 \\\\ \\end{pmatrix}\$\$]{.math.display}\ Bus Number Type Generation Load Bus Voltage ------------ ------- ------------ ------ ------------- ------ ------ --- P~G~ Q~G~ P~L~ Q~L~ V ᵟ 1 Slack 0 0 1.02 0 2 PQ 25 15 50 25 3 PV 0 0 60 30 8. **Derive load flow algorithm using Gauss -- Seidal method with flow chart and discuss the disadvantages of the method (NOV DEC 2009) (APR MAY 2011) (MAY JUNE 2006) (MAY JUNE 2013)** 9. **The one line diagram of three bus power system is shown in given figure.** Carry out one iteration of load flow solution by Gauss-Seidel method. Take Q limits of generator 2 as 0 ≤ Q ≤ 4. 10. **With a neat flow chart explain the computational procedure for load flow solution using fast decoupled method when the system contains all types of buses.** **III FAULT ANALYSIS -- BALANCED FAULTS** Importance of short circuit analysis - assumptions in fault analysis - analysis using Thevenin's theorem - Z-bus building algorithm - fault analysis using Z-bus -- computations of short circuit capacity, post fault voltage and currents. TWO MARKS ========= 1. **What for short circuit capacity (SCC) should be known at any bus. Write down the expression for SCC.** \ [SCC = \|*V*~TH~\|\|*I*~*F*~\|]{.math.display}\ 2. 3. **What is symmetrical fault? (NOV DEC 2014)** This type of fault is defined as the simultaneous short circuit across all the three phases. It occurs infrequently, but it is the most severe type of fault encountered. Because the network is balanced, it is solved by per phase basis using Thevenin's theorem or bus impedance matrix or KVL, KCL laws. 4. **Give the frequency of various faults occurrence in ascending order. (MAY JUN 2014)** **Types of fault** **Relative frequency of occurrence of fault** -------------------- ----------------------------------------------- 5. **Define bolted fault or solid fault. (MAY JUN 2014)** 6. **What are the characteristics of shunt and series faults? (NOV DEC 2013)** 7. **Distinguish symmetrical and unsymmetrical faults. (NOV DEC 2012) (MAY JUN 2013)** S.No Symmetrical Fault Unsymmetrical Fault ------ ------------------------------------------------------------------------------ ----------------------------------------------------------------------------------------------------------- 1 Balanced currents in all the three phases Unbalanced currents in all the three phases 2 Three phase fault is a symmetrical fault Single line to ground fault, Line to line fault, Double line to ground fault are the unsymmetrical faults 3 It can be solved using Thevenin's method, KVL, KCL laws and impedance matrix It can be solved using impedance matrix 4 It is the most severe fault and less occurrence fault It is highly prone to fault with less severity 8. 9. - Three phase fault - Single line to ground fault ,Line to line fault, Double line to ground fault 10. **[Shunt faults]**: - Line to ground fault , Line to line fault, Double line to ground fault, Three phase fault. [Series faults]: - One open conductor fault Two open conductor fault 11. **Mention the objectives of short circuit analysis. (APR MAY 2011)** - To determine the current interrupting capacity of the circuit breakers so that the faulted equipment can be isolated. - To establish the relay requirements and setting to detect the fault and cause the circuit breakers to operate when the current flowing through it exceeds the maximum value. 12. **Write the unbalanced and balanced fault in power system? (APR MAY 2011)** - Three phase fault - Single line to ground fault - Line to line fault - Double line to ground fault. 13. **Define short circuit MVA (APR MAY 2008)** \ [\$\$S.C\\ \\text{MVA} = \\ \\sqrt{3}\\left\| V\_{\\text{Pf}} \\right\|\\left\| I\_{F} \\right\|\$\$]{.math.display}\ 14. **What are the assumptions in short circuit studies? (APRMAY 2005)** - Representing each machine by its constant voltage source behind proper reactances which may be X,X',X'' - Prefault load currents are neglected. - Transformer taps are assumed to be nominal - Shunt capacitance of transmission line is ignored. **SIXTEEN MARKS** 1. **For the radial Network shown below, a three phase fault occurs at F. Determine the fault current and the line voltage at 11KV bus under fault conditions. (16) (NOV DEC 2014)** 2. **Explain the step by step procedure for systematic fault analysis using bus impedance matrix.** 3. **A 11KV, 100 MVA alternator having a sub-transient reactance of 0.25 p.u is supplying a 50 MVA motor having a sub-transient reactance of 0.2 p.u through a transmission line. The line reactance is 0.05 p.u on a base of 100 MVA. The motor is drawing 40 MW at 0.8 pf leading with a terminal voltage of 10.95 KV when a three phase fault occurs at the generator terminal. Calculate the total current in generator and motor under fault condition.** 4. **Figure shows a generating station feeding a 132 KV system. Determine the total fault current, fault level and fault current supplied by each alternator for a 3 - phase fault at the receiving end bus. The line is 200 km long. Take a base of 100MVA, 11KV for LV side and 132 KV for HT side. (NOV DEC 2011) (NOV DEC 2013)** 5. **A synchronous generator and motor are rated 30 MVA, 13.2KV and both have subtransient reactance of 20%. The line connecting them has reactance of 10% on the base of machine ratings. The motor is drawing 20,000 kW at 0.8 pf leading and terminal voltage of 12.8 KV when a symmetrical 3-¢ fault occurs at the motor terminals. Find the sub-transient current in the generator, motor and fault by using interval voltages of the machines.(MAY JUNE 2013)** 6. **For the radial Network shown below, a three phase fault occurs at F. Determine the fault current and the line voltage at 11KV bus under fault conditions. (NOV DEC 2012)** 7. **A 3 phase 5 MVA 6.6 KV alternator with a reactance of 8 % is connected to a feeder of series impedance (0.12+j0.48) ohm/phase/km through a step up transformer. The transformer is rated at 3 MVA 6.6 KV/33KV and has a reactance of 5 %. Determine the fault current supplied by the generator operating under no load with a voltage of 6.9 KV, when a 3 phase symmetrical fault occurs at a point 15 km along the feeder. (MAY JUN 2012)** 8. **The bus impedance matrix of a 4 bus system with values in p.u is given by,** \ [\$\$Z\_{\\text{BUS}} = \\ j\\begin{pmatrix} 0.15 & 0.08 & 0.04 & 0.07 \\\\ 0.08 & 0.15 & 0.06 & 0.09 \\\\ 0.04 & 0.06 & 0.13 & 0.05 \\\\ 0.07 & 0.09 & 0.05 & 0.12 \\\\ \\end{pmatrix}\$\$]{.math.display}\ 9. Two synchronous motors are connected to the bus of large system through a short transmission line shown in fig. the rating of the various components are: Motor (each) : 1MVA,440 V, 0.1 p.u transient reactance Line : 0.05Ω (reactance) Large System : short circuit MVA at its bus at 440V is 8 When the motors are operating at 440V, calculate the short circuit current (symmetrical) fed into a three phase fault at motor bus. **(APR MAY 2010)**  **UNIT IV FAULT ANALYSIS -- UNBALANCED FAULTS** Introduction to symmetrical components -- sequence impedances -- sequence circuits of synchronous machine, transformer and transmission lines - sequence networks analysis of single line to ground, line to line and double line to ground faults using Thevenin's theorem and Z-bus matrix. TWO MARKS ========= 1. **What are symmetrical components? (NOV DEC 2014)** 2. **What is sequence networks? (NOV DEC 2014)** The single phase equivalent circuit of a power system consists of impedances to current of any one sequences is called sequence network 3. **What are the features of zero sequence current? (MAY JUN 2014)** **Zero sequence currents can flow in star winding if there is a neutral connection, and corresponding zero-sequence currents flow within the delta winding. However, no zero sequence current enters or leaves the delta winding.** **Zero-sequence currents cannot enter or leave either delta winding, al-though they can circulate within the delta windings.** 4. **Write the symmetrical component currents of phase \'a\' in terms of three phase currents. (MAY JUN 2014)** I~a1~ positive sequence current I~a2~ Negative sequence current I~a0~ Zero sequence current 5. **What are the observations made from the analysis of various faults? (NOV DEC 2013)** **Single line to ground fault** \ [\$\$\\mathbf{I}\_{\\mathbf{a}\\mathbf{0}} = \\ \\mathbf{I}\_{\\mathbf{a}\\mathbf{1}} = \\ \\mathbf{I}\_{\\mathbf{a}\\mathbf{2}} = \\ \\frac{\\mathbf{I}\_{\\mathbf{a}}}{\\mathbf{3}}\$\$]{.math.display}\ **Line to line fault** \ [**I**~**a0**~ = 0]{.math.display}\ **Double line to ground fault** \ [*V*~**a1**~= **V**~**a2**~]{.math.display}\ 6. **Write the boundary conditions for single line to ground fault. (APR MAY 2005) (NOV DEC 2013)** \ [**I**~*b*~ = 0 ;  **I**~*c*~ = 0 ;  **I**~*a*~= **I**~*f*~]{.math.display}\ \ [*V*~**a**~= **Z**~*f* ~**I**~*a*~]{.math.display}\ 7. **Define negative sequence impedance. (NOV DEC 2011) (MAY JUN 2013)** 8. **Draw the sequence networks for a delta delta connected transformer.(NOV DEC 2005) (NOV DEC 2012)** 9. 10. **Write the matrix notation of the operator 'a' which relates the phasors V~a~, V~b~ and V~c~ with V~a0~, V~a1~, V~a2~ (MAY JUN 2012)** 11. **Name the fault which do not have zero sequence current flowing. (NOV DEC 2011)** Line to line fault 12. **What is sequence network? (APR MAY 2011)** 13. **Write the symmetrical components of three phase system. (APR MAY 2011)** - positive sequence components - Negative sequence components. - Zero sequence components. 14. **What is the significance of operator 'a' (NOV DEC 2007)** **'a' is the operator that causes a counter clockwise rotation of 120 degree.** 15. **Draw the equivalent sequence network for a line to line bolted fault in a power system. (MAY JUN 2007)** **SIXTEEN MARKS** 1. **Explain about the concept of symmetrical components. (NOV DEC 2014)** 2. **A 25 MVA, 13.2 KV alternator with solidly grounded neutral has a subtransient reactance of 0.25.p.u. The negative and zero sequence reactances are 0.35 and 0.01 p.u respectively. If a double line-to-ground fault occurs at the terminals of the alternator, determine the fault current and line-to-line voltages at the fault. (MAY JUN 2014)** 3. **Obtain the expression for fault current for a line to line fault taken place through an impedance Z~b~ in a power system.** 4. **Derive the expression for fault current in line to line fault on unloaded generator. Draw an equivalent network showing the inter connection of networks to simulate line to line fault** 5. **Figure shows a power system network. Draw zero sequence network for this system. The system data is as under.** **Generator G~1~** **50 MVA** **11 KV** **X~0~ = 0.08 pu** ---------------------- ------------ --------------- -------------------- **Transformer T~1~** **50 MVA** **11/220 KV** **X~0~ = 0.1 pu** **Generator G~2~** **30 MVA** **11 KV** **X~0~ = 0.07 pu** **Transformer T~2~** **30 MVA** **11/220 KV** **X~0~ = 0.09 pu** 6. **Discuss in detail about the sequence impedances and networks of synchronous machines, transmission lines transformers and loads. (MAY JUN 2013)** 7. **A single line diagram of a power network is shown in Fig.** **Element** **Positive Sequence Reactance** **Negative Sequence Reactance** **Zero Sequence Reactance** ---------------------- --------------------------------- --------------------------------- ----------------------------- **Generator G** **0.1** **0.12** **0.05** **Motor M~1~** **0.05** **0.06** **0.025** **Motor M~2~** **0.05** **0.06** **0.025** **Transformer T~1~** **0.07** **0.07** **0.07** **Transformer T~2~** **0.08** **0.08** **0.08** **Line** **0.1** **0.1** **0.1** 8. **Derive the expression for fault current in double line to ground fault on unloaded generator. Draw an equivalent network showing the inter connection of networks to simulate double line to ground fault** 9. **Derive the expression for fault current in single line to ground fault on unloaded generator. Draw an equivalent network showing the inter connection of networks to simulate single line to ground fault** 10. A 30MVA, 11KVgenerator.has Z~1~ = Z~2~ = jO.2p.u. Z~0~ = j 0.05p.u. A line to ground fault occurs on the generator terminals. Find the fault current and line to line voltages during fault conditions. Assume that the generator neutral is solidly grounded and that the generator is operating at no-load and at rated voltage at the occurrence of fault. **(NOV DEC 2011) (MAY JUN 2012)** 11. A 50 MVA, 11KV three phase alternator was subjected to different types of faults. The magnitude of the fault currents were. Three phase fault :1870A Line to Line fault : 2590A Single Line to Ground fault : 4130A The alternator neutral is solidly grounded. Find the p.u value of three sequence reactance of the alternator. Neglected the resistance. **(MAY JUN 2012)** 12. **A 30 MVA, 11KV 3 phase synchronous generator has direct axis sub-transient reactance of 0.25 per unit. The negative and zero sequences reactance are, respectively, 0.35 and 0.1 per unit. The neutral of the generator is solidly grounded. Determine the sub transient current in the generator and line-to-line for sub transient conditions when a single line-to-ground fault occurs at the terminals of generator, assume that the generator is unloaded at rated terminal when the fault occurs. (APR MAY 2005) (MAY JUN 2012)** 13. An alternator of negligible resistance, with solidly earthed neutral, having rated voltage at no load condition is subjected to different types of fault at its terminals. The per unit values of Magnitudes of the fault currents are: Three phase fault : 4.0 p.u L-G fault : 4.2857 p.u L-L fault : 2.8868 p.u Calculate three sequence reactance **(NOV DEC 2008)** 14. **A single line to ground fault occurs at bus 4 of the system shown in fig.** **Draw sequence networks and compute fault currents** **Gen 1 and 2 : 100MVA, 20KV, X'=X"=20%; X0=4%; X~n~=5%** 15. **The unbalanced phase currents are Ia=100\|\_0, Ib= 141.4\|\_225, Ic=100\|\_90. Find the symmetrical components of the given line currents and draw phasor diagram of the positive and negative sequence line to phase currents. (NOV DEC 2007)** **UNIT V STABILITY ANALYSIS** Importance of stability analysis in power system planning and operation - classification of power system stability - angle and voltage stability -- Single Machine Infinite Bus (SMIB) system: Development of swing equation - equal area criterion - determination of critical clearing angle and time -- solution of swing equation by modified Euler method and Runge-Kutta fourth order method. TWO MARKS ========= 1. **Define critical clearing time and critical clearing angle. (NOV DEC 2014)(MAY JUN 2012)** 2. **What is steady state stability limit**? **(NOV DEC 2014)** 3. **Define dynamic stability with an example. (MAY JUN 2014)** It is the ability of a power system to remain in synchronism after the initial swing (transient stability period) until the system has settled down to the new steady state equilibrium condition 4. **Find the frequency of oscillation for a synchronizing co-efficient of 0.6, inertia constant H = 4 and system frequency of 50 Hz. (MAY JUN 2014)** \ [\$\$\\text{Natural\\ frequency\\ of\\ oscillation\\ }\\omega\_{n} = \\ \\sqrt{\\frac{\\pi\\ f\\ P\_{s}}{H}}\\text{\\ \\ \\ \\ \\ }\\text{rad}/s\$\$]{.math.display}\ \ [\$\$\\text{Natural\\ frequency\\ of\\ oscillation\\ }\\omega\_{n} = \\ \\sqrt{\\frac{\\pi \\times 50 \\times \\ 0.6}{4}}\\frac{\\text{rad}}{s}\$\$]{.math.display}\ \ [Natural frequency of oscillation *ω*~*n*~= 4.8541 ad/*s*]{.math.display}\ \ [\$\$\\text{frequency\\ of\\ oscillation\\ }f\_{n} = \\ \\frac{\\omega\_{n}}{2\\pi} = \\frac{4.8541}{2\\pi} = 0.7726\\ \\ \\ \\ \\text{Hz}\$\$]{.math.display}\ 5. **Differentiate between voltage stability and rotor angle stability. (NOV DEC 2013)** 6. **Define swing curve? What is the use of this curve? (NOV DEC 2013)** The swing curve is the plot or graph between the power angle δ, and time, t. **[Use:]** 7. **Define infinite bus in a power system. (NOV DEC 2012) (MAY JUN 2013)** If the external power system is very large as compared to the system of any installation, disturbances within the installation do not affect the voltage and frequency of the external system. In such a situation, the external power source is known as an Infinite Bus.  8. **What is meant by power angle curve? (MAY JUN 2013)** Plotting Variation of Electrical power with the variation of power angle. 9. **Define critical clearing angle. (APR MAY 2011) (NOV DEC 2012)** 10. **What is transient stability and transient stability limit? (MAY JUN 2012)** 11. **Write swing equation. (APR MAY 2011)** \ [\$\$\\frac{\\mathbf{H}\\mathbf{\\ }}{\\mathbf{\\text{πf}}\\mathbf{\\ }}\\frac{\\mathbf{d}\^{\\mathbf{2}}\\mathbf{\\delta}}{\\mathbf{d}\\mathbf{t}\^{\\mathbf{2}}}\\mathbf{= \\ }\\mathbf{P}\_{\\mathbf{m}}\\mathbf{-}\\mathbf{\\ }\\mathbf{P}\_{\\mathbf{e}}\$\$]{.math.display}\ Where H = Inertia constant in MJ/MVA. f = Frequency in Hz. M = Inertia constant in p.u. Pm= Mechanical power input to the system (neglecting mechanical losses) in p.u. P~e~ = Electrical power output of the system (neglecting electrical losses) in p.u. 12. **State Equal Area Criterion (NOV DEC 2004) (NOV DEC 2011)** 13. **What are coherent machines? (APR MAY 2004)** **SIXTEEN MARKS** 1. **Explain the equal area criteria for the following applications:** 2. **Derive swing equation used for stability studies in power system. Why it is non-linear** 3. What are the factors affecting transient stability? Discuss the methods of improving the transient stability. **(NOV DEC 2011) (NOV DEC 2013)** 4. **Describe the equal area criterion for transient stability analysis of a system.** 5. Explain the modified Euler method of analyzing multimachine power system for stability with neat flowchart **(NOV DEC 2012)(MAY JUN 2013)** 6. **Derive the power angle equation of a single machine infinite bus system. (MAY JUN 2012)** 7. **A three phase generator delivers 1.0 PU power to an infinite bus through a transmission network when a fault occurs. The maximum power which can be transferred for pre-fault, during fault and post-fault conditions are 1.75pu, 0.4pu and 1.25pu. Find the critical clearing angle. (MAY JUN 2012)** 8. Describe the RK method of solution of swing equation for multi machine systems. **(APR MAY 2011) (NOV DEC 2011)** 9. **A generator operating at 50 Hz delivers 1 p.u power to an infinite bus through a transmission circuit in which the resistances are ignored. A fault takes place reducing maximum power to 0.5 p.u, whereas before the fault it is 2.0 p.u and after fault clearance it is 1.5 p.u. By the use of equal area criterion, determine critical clearing angle. (NOV DEC 2011)**