Symmetrical Components and Symmetrical and Unsymmetrical Faults · Power System Analysis · GATE EE
Marks 1
1
The valid positive, negative and zero sequence impedances (in p.u.), respectively, for a 220 kV, fully transported three-phase transmission line, from the given choices are
GATE EE 2022
2
The series impedance matrix of a short three-phase transmission line in phase coordinates is
$$\left[ {\matrix{
{{Z_s}} & {{Z_m}} & {{Z_m}} \cr
{{Z_m}} & {{Z_s}} & {{Z_m}} \cr
{{Z_m}} & {{Z_m}} & {{Z_s}} \cr
} } \right]$$.
If the positive sequence impedance is (1 + 𝑗 10) $$\Omega $$, and the zero sequence is (4 + 𝑗 31) $$\Omega $$, then the imaginary part of Zm (in $$\Omega $$) is ______(up to 2 decimal places).
If the positive sequence impedance is (1 + 𝑗 10) $$\Omega $$, and the zero sequence is (4 + 𝑗 31) $$\Omega $$, then the imaginary part of Zm (in $$\Omega $$) is ______(up to 2 decimal places).
GATE EE 2018
3
The positive, negative and zero sequence impedances of a 125 MVA, three-phase, 15.5 kV,
star-grounded, 50 Hz generator are 𝑗0.1 pu, j0.05 pu and j0.01 pu respectively on the
machine rating base. The machine is unloaded and working at the rated terminal voltage. If
the grounding impedance of the generator is j0.01 pu, then the magnitude of fault current
for a b-phase to ground fault (in kA) is __________ (up to 2 decimal places).
GATE EE 2018
4
For a fully transposed transmission line
GATE EE 2014 Set 3
5
A three phase star-connected load is drawing power at a voltage of 0.9 pu and 0.8 power factor lagging. The three phase base power and base current are 100 MVA and 437.38 A respectively. The line-to-line load voltage in kV is __________.
GATE EE 2014 Set 2
6
A 2-bus system and corresponding zero sequence network are shown in the figure.
The transformers T1 and T2 are connected as
GATE EE 2014 Set 1
7
Three phase to ground fault takes place at locations $${F_1}$$ and $${F_2}$$ in the system shown in the figure.
If the fault takes place at location $${F_1}$$, then the voltage and the current at bus A are $${V_F1}$$ and $${{\rm I}_{F1}}$$ respectively. If the fault takes place at location $${F_2}$$, then the voltage and the current at bus A are $${V_{F2}}$$ and $${{\rm I}_{F2}}$$ respectively.
The correct statement about voltages and currents during faults at $${F_1}$$ and $${F_2}$$ is
GATE EE 2014 Set 1
8
The sequence components of the fault current are as follows:
$${{\rm I}_{positive}} = j1.5\,pu,\,\,{{\rm I}_{negative}} = - j0.5\,\,pu,$$
$${{\rm I}_{zero}} = - j1\,\,pu.$$ The typeof fault in the system is
$${{\rm I}_{positive}} = j1.5\,pu,\,\,{{\rm I}_{negative}} = - j0.5\,\,pu,$$
$${{\rm I}_{zero}} = - j1\,\,pu.$$ The typeof fault in the system is
GATE EE 2012
9
A 3-phase transmission line is shown in figure:
Voltage drop across the transmission line is given by the following equation:
$$$\left[ {\matrix{
{\Delta {V_a}} \cr
{\Delta {V_b}} \cr
{\Delta {V_c}} \cr
} } \right] = \left[ {\matrix{
{{Z_s}} & {{Z_m}} & {{Z_m}} \cr
{{Z_m}} & {{Z_s}} & {{Z_m}} \cr
{{Z_m}} & {{Z_m}} & {{Z_s}} \cr
} } \right]\left[ {\matrix{
{{i_a}} \cr
{{i_b}} \cr
{{i_c}} \cr
} } \right]$$$
Shunt capacitance of the line can be neglect. If the line has positive sequence impedance of $$15\,\,\Omega $$ and zero sequence in impedance of $$48\,\,\Omega ,$$ then the values of $${{Z_s}}$$ and $${{Z_m}}$$ will be
GATE EE 2008
10
For a fault at the terminals of a synchronous generator, the fault current is maximum for a
GATE EE 1997
11
For an unbalanced fault, with paths for zero sequence currents, at the point of fault
GATE EE 1996
12
The positive sequence component of the voltage at the point of fault in a power system is zero for a _________fault.
GATE EE 1995
Marks 2
1
The two-bus power system shown in figure (i) has one alternator supplying a synchronous motor load through a Y-$$\Delta$$ transformer. The positive, negative and zero-sequence diagrams of the system are shown in figures (ii), (iii) and (iv), respectively. All reactances in the sequence diagrams are in p.u. For a bolted line-to-line fault (fault impedance = zero) between phases 'b' and 'c' at bus 1, neglecting all pre-fault currents, the magnitude of the fault current (from phase 'b' to 'c') in p.u. is ____________ (Round off to 2 decimal places).
GATE EE 2023
2
The positive, negative and zero sequence impedances of a three phase generator are Z1, Z2
and Z0 respectively. For a line-to-line fault with fault impedance Zf, the fault current
is If1 = kIf, where If is the fault current with zero fault impedance. The relation between
Zf and k is
GATE EE 2018
3
The positive, negative and zero sequence reactances of a wye-connected synchronous generator are 0.2 pu, 0.2 pu, and 0.1 pu, respectively. The generator is on open circuit with a terminal voltage of 1 pu. The minimum value of the inductive reactance, in pu, required to be connected between neutral and ground so that the fault current does not exceed 3.75 pu if a single line to ground fault occurs at the terminals is _______ (assume fault impedance to be zero). (Give the answer up to one decimal place)
GATE EE 2017 Set 1
4
A 30 MVA, 3-phase, 50Hz, 13.8 kV, star-connected synchronous generator has positive, negative and zero sequence reactances, 15%, 15% and 5% respectively. A reactance (Xn) is connected between the neutral of the generator and ground. A double line to ground fault takes place involving phases ‘b’ and ‘c’, with a fault impedance of j0.1 p.u. The value of Xn (in p.u.) that will limit the positive sequence generator current to 4270 A is __________.
GATE EE 2016 Set 1
5
A sustained three phase fault occurs in the power system shown in the figure. The current and voltage phasors during the fault (on a common reference), after the natural transients have died down, are also shown. Where is the fault located?
GATE EE 2015 Set 1
6
A three phase, $$100$$ $$MVA,$$ $$25$$ $$kV$$ generator has solidly grounded neutral. The positive, negative, and the zero sequence reactance's of the generator are $$0.2$$ $$pu$$, $$0.2$$ $$pu$$, and 0.05 $$pu,$$ respectively, at the machine base quantities. If a bolted single phase to ground fault occurs at the terminal of the unloaded generator, the fault current in amperes immediately after the fault is __________
GATE EE 2014 Set 2
7
In an unbalanced three phase system phase current $${{\rm I}_a} = 1\angle \left( { - {{90}^0}} \right)\,\,pu,\,\,$$ negative sequence current $$\,{{\rm I}_{b2}} = 4\angle \left( { - {{150}^0}} \right)\,\,pu,\,\,$$ zero sequence current $$\,\,{{\rm I}_{c0}} = 3\angle {90^0}\,\,pu.\,\,\,$$ The magnitude of phase current $${{\rm I}_b}$$ in $$pu$ is
GATE EE 2014 Set 1
8
The zero-sequence circuit of the three phase transformer shown in the figure is
GATE EE 2010
9
Given that: $$\,{V_{s1}} = {V_{s2}} = 1 + j0\,\,p.u,\,\, + ve\,\,$$ sequence impedance are $$\,{Z_{s1}} = {Z_{s2}} = 0.001 + j0.01\,\,p.u\,\,$$ and $${Z_L} = 0.006 + j\,0.06\,\,p.u,\,\,3\phi .\,\,\,$$ Base $$MVA=100,$$ voltage base $$=400$$ $$kV(L-L).$$
Nominal system frequency $$= 50$$ $$Hz.$$ The reference voltage for phase $$'a'$$ is defined as $$\,\,V\left( t \right) = {V_m}\,\cos \left( {\omega t} \right).\,\,\,$$ A symmetrical $$3\phi $$ fault occurs at centre of the line, i.e., at point $$'F'$$ at time 'to' the $$+ve$$ sequence impedance from source $${S_1}$$ to point $$'F'$$ equals $$(0.004 + j \,\,0.04)$$ $$p.u.$$ The wave form corresponding to phase $$'a'$$ fault current from bus $$X$$ reveals that decaying $$d.c.$$ offset current is $$-ve$$ and in magnitude at its maximum initial value. Assume that the negative sequence are equal to $$+ve$$ sequence impedances and the zero sequence $$(Z)$$ are $$3$$ times $$+ve$$ sequence $$(Z).$$
Nominal system frequency $$= 50$$ $$Hz.$$ The reference voltage for phase $$'a'$$ is defined as $$\,\,V\left( t \right) = {V_m}\,\cos \left( {\omega t} \right).\,\,\,$$ A symmetrical $$3\phi $$ fault occurs at centre of the line, i.e., at point $$'F'$$ at time 'to' the $$+ve$$ sequence impedance from source $${S_1}$$ to point $$'F'$$ equals $$(0.004 + j \,\,0.04)$$ $$p.u.$$ The wave form corresponding to phase $$'a'$$ fault current from bus $$X$$ reveals that decaying $$d.c.$$ offset current is $$-ve$$ and in magnitude at its maximum initial value. Assume that the negative sequence are equal to $$+ve$$ sequence impedances and the zero sequence $$(Z)$$ are $$3$$ times $$+ve$$ sequence $$(Z).$$
The $$rms$$ value of the ac component of fault current $$\,\left( {{{\rm I}_x}} \right)$$ will be
GATE EE 2008
10
Given that: $$\,{V_{s1}} = {V_{s2}} = 1 + j0\,\,p.u,\,\, + ve\,\,$$ sequence impedance are $$\,{Z_{s1}} = {Z_{s2}} = 0.001 + j0.01\,\,p.u\,\,$$ and $${Z_L} = 0.006 + j\,0.06\,\,p.u,\,\,3\phi .\,\,\,$$ Base $$MVA=100,$$ voltage base $$=400$$ $$kV(L-L).$$
Nominal system frequency $$= 50$$ $$Hz.$$ The reference voltage for phase $$'a'$$ is defined as $$\,\,V\left( t \right) = {V_m}\,\cos \left( {\omega t} \right).\,\,\,$$ A symmetrical $$3\phi $$ fault occurs at centre of the line, i.e., at point $$'F'$$ at time 'to' the $$+ve$$ sequence impedance from source $${S_1}$$ to point $$'F'$$ equals $$(0.004 + j \,\,0.04)$$ $$p.u.$$ The wave form corresponding to phase $$'a'$$ fault current from bus $$X$$ reveals that decaying $$d.c.$$ offset current is $$-ve$$ and in magnitude at its maximum initial value. Assume that the negative sequence are equal to $$+ve$$ sequence impedances and the zero sequence $$(Z)$$ are $$3$$ times $$+ve$$ sequence $$(Z).$$
Nominal system frequency $$= 50$$ $$Hz.$$ The reference voltage for phase $$'a'$$ is defined as $$\,\,V\left( t \right) = {V_m}\,\cos \left( {\omega t} \right).\,\,\,$$ A symmetrical $$3\phi $$ fault occurs at centre of the line, i.e., at point $$'F'$$ at time 'to' the $$+ve$$ sequence impedance from source $${S_1}$$ to point $$'F'$$ equals $$(0.004 + j \,\,0.04)$$ $$p.u.$$ The wave form corresponding to phase $$'a'$$ fault current from bus $$X$$ reveals that decaying $$d.c.$$ offset current is $$-ve$$ and in magnitude at its maximum initial value. Assume that the negative sequence are equal to $$+ve$$ sequence impedances and the zero sequence $$(Z)$$ are $$3$$ times $$+ve$$ sequence $$(Z).$$
The instant $$\,\left( {{t_0}} \right)\,\,$$ of the fault will be
GATE EE 2008
11
Given that: $$\,{V_{s1}} = {V_{s2}} = 1 + j0\,\,p.u,\,\, + ve\,\,$$ sequence impedance are $$\,{Z_{s1}} = {Z_{s2}} = 0.001 + j0.01\,\,p.u\,\,$$ and $${Z_L} = 0.006 + j\,0.06\,\,p.u,\,\,3\phi .\,\,\,$$ Base $$MVA=100,$$ voltage base $$=400$$ $$kV(L-L).$$
Nominal system frequency $$= 50$$ $$Hz.$$ The reference voltage for phase $$'a'$$ is defined as $$\,\,V\left( t \right) = {V_m}\,\cos \left( {\omega t} \right).\,\,\,$$ A symmetrical $$3\phi $$ fault occurs at centre of the line, i.e., at point $$'F'$$ at time 'to' the $$+ve$$ sequence impedance from source $${S_1}$$ to point $$'F'$$ equals $$(0.004 + j \,\,0.04)$$ $$p.u.$$ The wave form corresponding to phase $$'a'$$ fault current from bus $$X$$ reveals that decaying $$d.c.$$ offset current is $$-ve$$ and in magnitude at its maximum initial value. Assume that the negative sequence are equal to $$+ve$$ sequence impedances and the zero sequence $$(Z)$$ are $$3$$ times $$+ve$$ sequence $$(Z).$$
Nominal system frequency $$= 50$$ $$Hz.$$ The reference voltage for phase $$'a'$$ is defined as $$\,\,V\left( t \right) = {V_m}\,\cos \left( {\omega t} \right).\,\,\,$$ A symmetrical $$3\phi $$ fault occurs at centre of the line, i.e., at point $$'F'$$ at time 'to' the $$+ve$$ sequence impedance from source $${S_1}$$ to point $$'F'$$ equals $$(0.004 + j \,\,0.04)$$ $$p.u.$$ The wave form corresponding to phase $$'a'$$ fault current from bus $$X$$ reveals that decaying $$d.c.$$ offset current is $$-ve$$ and in magnitude at its maximum initial value. Assume that the negative sequence are equal to $$+ve$$ sequence impedances and the zero sequence $$(Z)$$ are $$3$$ times $$+ve$$ sequence $$(Z).$$
Instead of the three phase fault, if a single line to ground fault occurs on phase $$' a '$$ at point $$' F '$$ with zero fault impedance, then the $$rms$$ of the ac component of fault current $$\left( {{{\rm I}_x}} \right)$$ for phase $$'a'$$ will be
GATE EE 2008
12
Suppose we define a sequence transformation between ''a-b-c'' and ''p-n-0''' variables as follows:
$$\left[ {\matrix{ {{f_a}} \cr {{f_b}} \cr {{f_c}} \cr } } \right] = k\left[ {\matrix{ 1 & 1 & 1 \cr {{\alpha ^2}} & \alpha & 1 \cr \alpha & {{\alpha ^2}} & 1 \cr } } \right]\left[ {\matrix{ {{f_p}} \cr {{f_n}} \cr {{f_o}} \cr } } \right]$$ where $$\,\alpha = {e^{j{{2\pi } \over 3}}}\,\,$$ and $$k$$ is a constant
Now, if it is given that:
$$\left[ {\matrix{ {{V_p}} \cr {{V_n}} \cr {{V_o}} \cr } } \right] = k\left[ {\matrix{ {0.5} & 0 & 0 \cr 0 & {0.5} & 0 \cr 0 & 0 & {2.0} \cr } } \right]\left[ {\matrix{ {{i_p}} \cr {{I_n}} \cr {{i_o}} \cr } } \right]\,\,$$ and $$\left[ {\matrix{ {{V_a}} \cr {{V_b}} \cr {{V_c}} \cr } } \right] = z\left[ {\matrix{ {{i_a}} \cr {{I_b}} \cr {{i_c}} \cr } } \right]\,\,$$ then,
$$\left[ {\matrix{ {{f_a}} \cr {{f_b}} \cr {{f_c}} \cr } } \right] = k\left[ {\matrix{ 1 & 1 & 1 \cr {{\alpha ^2}} & \alpha & 1 \cr \alpha & {{\alpha ^2}} & 1 \cr } } \right]\left[ {\matrix{ {{f_p}} \cr {{f_n}} \cr {{f_o}} \cr } } \right]$$ where $$\,\alpha = {e^{j{{2\pi } \over 3}}}\,\,$$ and $$k$$ is a constant
Now, if it is given that:
$$\left[ {\matrix{ {{V_p}} \cr {{V_n}} \cr {{V_o}} \cr } } \right] = k\left[ {\matrix{ {0.5} & 0 & 0 \cr 0 & {0.5} & 0 \cr 0 & 0 & {2.0} \cr } } \right]\left[ {\matrix{ {{i_p}} \cr {{I_n}} \cr {{i_o}} \cr } } \right]\,\,$$ and $$\left[ {\matrix{ {{V_a}} \cr {{V_b}} \cr {{V_c}} \cr } } \right] = z\left[ {\matrix{ {{i_a}} \cr {{I_b}} \cr {{i_c}} \cr } } \right]\,\,$$ then,
GATE EE 2007
13
Three identical star connected resistors of $$1.0$$ $$p.u$$ are connected to an unbalanced $$3$$ phase supply. The load neutral is isolated. The symmetrical components of the line voltages in $$p.u.$$ calculations are with the respective base values, the phase to neutral sequence voltages are
GATE EE 2006
14
The parameters of transposed overhead transmission line are given as: self reactance $${X_s} = 0.4\,\,\Omega /km$$ and Mutual reactance $$\,{X_m} = 0.1\,\,\Omega /km.\,\,$$ The positive sequence reactance $${X_1}$$ and zero sequence reactance $${X_0}$$ respectively in $$\Omega /km$$ are
GATE EE 2005
15
At a $$220$$ kV substation of a power system, it is given that the three-phase fault level is $$4000$$ MVA and single-line to ground fault level is $$5000$$ MVA. Neglecting the resistance and the shunt susceptances of the system.
The positive sequence driving point reactance at the bus is
GATE EE 2005
16
At a $$220$$ kV substation of a power system, it is given that the three-phase fault level is $$4000$$ MVA and single-line to ground fault level is $$5000$$ MVA. Neglecting the resistance and the shunt susceptances of the system.
The zero sequence driving point reactance at the bus is
GATE EE 2005
17
A $$3$$-phase generator rated at $$110$$ MVA, $$11$$ kV is connected through circuit breakers to a transformer. The generator is having direct axis sub-transient reactance $$X'{'_d} = 19\% ,\,\,$$ transient reactance $$X{'_d} = 26\% \,\,$$ and synchronous reactance $$=130$$%. The generator is operating at no load and rated voltage when a three phase short circuit fault occurs between the breakers and the transformer. The magnitude of initial symmetrical rims current in the breakers will be
GATE EE 2004
18
A 3-phase transmission line supplies $$\Delta - $$ connected load Z. The conductor $$'c'$$ of the line develops an open circuit fault as shown in figure. The currents in the lines are as shown on the diagram. The +ve sequence current component in line 'a' will be
GATE EE 2004
19
A 500 MVA, 50 Hz, 3-phase turbo-generator produces power at 22 kV. Generator is Y-connected and its neutral is solidly grounded. Its sequence reactances are X1 = X2 = 0.15 and X0 = 0.05 pu. it is operating at rated voltage and disconnected from the rest of the system (no load). The magnitude of the sub-transient line current for single line ground fault at the generator terminal in pu will be
GATE EE 2004
20
A three-phase alternator generating unbalanced voltages is connected to an unbalanced load through a 3-phase transmission line as shown in figure. The neutral of the alternator and the star point of the load are solidly grounded. The phase voltages of the alternator are
$${E_a} = 10\angle {0^ \circ }V,\,\,\,{E_b} = 10\angle - {90^ \circ }V,\,\,{E_c} = 10\angle {120^ \circ }\,\,V.\,\,\,\,$$ The positive sequence component of the load current is
$${E_a} = 10\angle {0^ \circ }V,\,\,\,{E_b} = 10\angle - {90^ \circ }V,\,\,{E_c} = 10\angle {120^ \circ }\,\,V.\,\,\,\,$$ The positive sequence component of the load current is
GATE EE 2003
21
A 20-MVA, 6.6-kV, 3-phase alternator is connected to a 3-phase transmission line. The per unit positive sequence, negative sequence and zero sequence impedance of the alternator are j0.1, and j0.04 respectively. The neutral of the alternator is connected to ground through an inductive reactor of j0.05 p.u. The per unit positive, negative and zero sequence impedances of the transmission line are j0.1 and j0.3 respectively. All per unit values are based on the machine ratings. A solid ground fault occurs at one phase of the far end of the transmission line. The voltage of the alternator neutral with respect to ground
during the fault is
GATE EE 2003
22
A generator is connected to a transformer which feeds another transformer through a short feeder. The zero sequence impedance values are expressed in pu on a common base and are indicated in figure. The Thevenin equivalent zero sequence impedance at point B is
GATE EE 2002
23
A $$50$$ Hz alternator is rated $$500$$ $$MVA,$$ $$20$$ $$kV,$$ with $${X_d} = 1.0$$ per unit and $$X'{'_d} = 0.2$$ per unit. It supplies a purely resistive load of $$400$$ $$MW$$ at $$20$$ $$kV.$$ The load is connected directly across the generator terminals when a symmetrical fault occurs at the load terminals. The initial rms current in the generator in per units is
GATE EE 2001
24
The severity of line-to-ground and three phase faults at the terminals of an unloaded synchronous generator is to be same. If the terminal voltage is
$$1.0$$ p.u. and $${Z_1} = {Z_2} = j0.1\,\,$$ p.u.,
$$\,{Z_0} = j0.05\,\,\,\,\,$$ p.u., for the alternator, then the required inductive reacttance for neutral grounding is
$$1.0$$ p.u. and $${Z_1} = {Z_2} = j0.1\,\,$$ p.u.,
$$\,{Z_0} = j0.05\,\,\,\,\,$$ p.u., for the alternator, then the required inductive reacttance for neutral grounding is
GATE EE 2000
25
For the network shown in figure the zero sequence reactances in p.u. are indicated. The zero sequence driving point reactance of the node 3 is
GATE EE 1998
Marks 5
1
A single line-to-ground fault occurs on an unloaded generator in phase a positive, negative, and zero sequence impedances of the generator are j0.25 p.u., j0.25 p.u., and j0.15 p.u. respectively. The generator neutral is grounded through a reactance of j0.05 p.u. The prefault generator terminal voltage is 1.0 p.u.
(a) Draw the positive, negative, and zero sequence networks for the fault given.
(b) Draw the interconnection of the sequence networks for the fault analysis.
(c) Determine the fault current.
(a) Draw the positive, negative, and zero sequence networks for the fault given.
(b) Draw the interconnection of the sequence networks for the fault analysis.
(c) Determine the fault current.
GATE EE 2001
2
For the configuration shown in figure, the breaker connecting a large system to bus $$2$$ is initially open. The system $$3$$-phase fault level at bus $$3$$ under this condition is not known. After closing the system breaker, the $$3$$-phase fault level at bus $$1$$ was found to be $$5.0$$ p.u. What will be the new $$3$$-phase fault level at system bus $$3,$$ after the interconnection? All per unit values are on common base. Prefault load currents are neglected and prefault voltages are assumed to be $$1.0$$ p.u. at all buses.
GATE EE 2000
3
Determine the required MVA rating of the circuit breaker CB for the system shown in given figure. Consider the grid as infinite bus. Choose 6 MVA as base. Transformer 3-phase, 33/11 kV, 6 MVA, 0.01+j0.08 p.u. impedance. Load 3-phase 11 kV, 5800 kVA, 0.8 lag, j0.2 p.u. impedance. Impedance of each feeder 9+j 18 $$\Omega $$.
GATE EE 1999
4
Determine the magnitudes of the symmetrical components ($${{{\rm I}_{R1}},\,{{\rm I}_{R2}}\,}$$ and $${{{\rm I}_{R0}}}$$) of the currents in a three phase (RYB) three wire system, when a short circuit occurs between R and Y phase wires, the fault current being 100 A.
GATE EE 1999
5
In a power-system, the $$3$$-phase fault MVA is always higher than the single-line-ground fault MVA at a bus (State True or False)
GATE EE 1994