Symmetrical Components 3n3z2g
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SYMMETRICAL COMPONENTS
SUMIT K RATHORE EE DEPT, GCET
Content
Synthesis of Unsymmetrical phasors from their symmetrical components Power in of symmetrical components Sequence circuits of Y and Δ impedances Sequence circuits of a symmetrical transmission line Sequence circuits of the synchronous machine Sequence circuits of a Y- Δ transformer Unsymmetrical series impedances Sequence networks
2
Instruction Objective of lesson
Normal types of fault are:
Fault due to lightning Tree limbs falling on the line Wind damage Insulation deterioration Vandalism
4
Types of fault Symmetrical fault : Usually three phase to ground fault Unsymmetrical fault The fault is unbalanced in nature
5
Sources of Asymmetrical fault are (cont.) One phase open circuit
6
Sources of Asymmetrical fault are (cont.) One phase open circuit
7
Sources of Asymmetrical fault are (cont.) SLG fault
8
Need for fault analysis Design of protection system requires the knowledge of fault current. The information obtained from the fault studies are used: to select the sizes of circuit breaker, fuse and characteristic, setting of relay.
9
Instruction Objective of lesson
Upunitl now we have studied faults that are symmetrical (all the three lines are shorted) but this kind of fault rare in system, and unsymmetrical faults are major and to study them or analyze them we need a simple technique this is called symmetrical component analysis discovered by C L Fortescue.
SYNTHESIS OF UNSYMMETRICAL PHASOR FROM THEIR SYMMETRICAL COMPONENT
CL Fortescue suggested that n related unbalanced phasors can be resolved into n system of balanced phasors called the symmetrical components of the original phasors. The n phasors of each set of components are equal in magnitude(length) and the angle between adjacent phasors of the set are equal. This method is applicable to any unbalanced systems we will confine attention to three phase system.
SYNTHESIS OF UNSYMMETRICAL PHASOR FROM THEIR SYMMETRICAL COMPONENT
According to CL Fortescue unbalanced phasors of three phase system can be resolved into three balanced systems of phasors. The balanced sets of components are : 1. positive sequence component consisting of three phasors equal in magnitude, displaced from each other by 120 in phase and having same phase sequence as the original phasor. 2. negative sequence components are consisting of three phasors equal in magnitude, displaced from each other by 120 in phase and having phase sequence opposite to that of original phasor. 3. zero sequence components consisting of three phasors equal in magnitude and with zero phase displacement from each other.
SYNTHESIS OF UNSYMMETRICAL PHASOR FROM THEIR SYMMETRICAL COMPONENT
SYNTHESIS OF UNSYMMETRICAL PHASOR FROM THEIR SYMMETRICAL COMPONENT
It is customary when solving problem by symmetrical components to designate the three phases of system as a, b and c of the voltages and currents of sequence of positive sequence components of unbalanced phasors is abc, negative sequence as acb. If original voltage sequence is Va, Vb, and Vc then positive sequence sets of symmetrical components are designated by subscript 1, that becomes Va1, Vb1, Vc1. Similarly negative sequence components are Va2, Vb2, Vc2 and the zero sequence components are Va0, Vb0 and Vc0. And phasor representing currents are represented by I followed by subscripts
SYNTHESIS OF UNSYMMETRICAL PHASOR FROM THEIR SYMMETRICAL COMPONENT Since each of the original unbalanced phasors is the sum of its components, the original phasors expressed in of their components are
Synthesis of set of three unbalanced phasors from the three sets of symmetrical components is show in figure (next slide)
SYNTHESIS OF UNSYMMETRICAL PHASOR FROM THEIR SYMMETRICAL COMPONENT
The advantages of analysis by symmetrical components will become apparent as we apply the method to study unsymmetrical faults on otherwise symmetrical systems. Method consist of finding symmetrical components of current at fault Then value of current and voltages at various points in the system can be found. The method is simple and leads to accurate prediction of system behavior
OPERATORS
Because of phase displacement in phase components of sysmmetrical components of voltage and currents in three phase system it is convenient to have short hand method to represent the rotation of phasor through 120 degree. Result of multiplication of two complex number is the product of their magnitudes and sum of their angles. If complex number expressing a phasor is multiplied by a complex number of unit magnitude and angle theta the resulting complex number represent a phasor equal to the original phasor displaced by the angle theta. The complex number of unit magnitude and associated angle theta is an operator that rotates the phasor on which it operates through the angle theta.Z
OPERATORS
Operator j which causes the rotation through 90 and operator -1 which causes rotation through 180. Two successive applications of operator j causes rotation through 90+90 which leads up to the conclusion that j*j causes rotation through 180 and thus we recognize to the conclusion that j2 =-1 the letter a is commonly used to designate the operator that cause a rotation of 120 in counter clock wise direction. Such an operator is a complex number of unit magnitude and with angle of 120 and defined by
=1ej2л/3= -0.5+j0.866
OPERATORS
If operator is applied twice in succession the phasor is rotated through 240 and three succession a2= 1/_240o=-0.5-j0.866 And a3=1/_360o=1/_0o=1 An important difference must be noted between uses of operators j and a. the operator j is unit magnitude at 90 and –j means that complex number j is changed by an angle of 180 to give unit magnitude at 270 thus -j j=1/_90 and –j=1/_270=1/_-90 Hence it is said sometimes that +j indicate rotation through 90 and –j indicate rotation through -90 statement is correct but a similar statement does not apply to operator a since A=1/_120
OPERATORS
-a=1/_120 x 1/-180 = 1/_ -60 -a2
a
1 a3
-1 -a3
a2
-a
SYMMETRICAL COMPONENT OF UNSYMMETRICAL PHASORS Lets see how to solve unsymmetrical phasors into their symmetrical components. Synthesis of three unsymmetrical phasors form three sets of symmetrical phasors done by use of equation as below
Now lets examine how to resolve three unsymmetrical phasors into their symmetrical components.
SYMMETRICAL COMPONENT OF UNSYMMETRICAL PHASORS
We have seen that Number of unknown quantity can be reduced by expressing each component of Vb and Vc as the product of some function of the operator α and component a of Va.
SYMMETRICAL COMPONENT OF UNSYMMETRICAL PHASORS Substituting values yield the
Or in matrix form
SYMMETRICAL COMPONENT OF UNSYMMETRICAL PHASORS For convenience we let
Then as
Rearrange the equation we ll obtain
SYMMETRICAL COMPONENT OF UNSYMMETRICAL PHASORS Which shows us how to resolve three unsymmetrical phasors into their symmetrical components. So separate equation in ordinary form
Similarly if we require to find out components Vbo. Vb1, Vb2, Vco. Vc1, and Vc2, can be found out.
SYMMETRICAL COMPONENT OF UNSYMMETRICAL PHASORS This shows that no zero sequence component exist if the sum of the unbalanced phasors is zero. Since the sum of the line to line voltage phasors in a three phase system is always zero, zero sequence components are never present in the line voltages, regardless of the amount of unbalance. The sum of three line to neutral voltage phasor is not necessarily zero and voltages to neutral may contains zero sequence component.
SYMMETRICAL COMPONENT OF UNSYMMETRICAL PHASORS Preceding equation could have been written for any set of related phasors and we might have written them for currents instead of for voltages. They may be solved either analytically or graphically . Because some of the preceding equations are so fundamental they are summarized for currents
SYMMETRICAL COMPONENT OF UNSYMMETRICAL PHASORS In three phase system sum of line currents is equal to the currents In in the return path through the neutral Ia+Ib+Ic=In If currents are equal then In=3Iao In the absence of path through the neutral of three phase system In is zero and the line currents contain no zero sequence components A delta connected load provides no path for neutral current and line currents flowing to a delta connected load can contain no zero sequence components.
Visualization of Symmetrical Components
Visualization of Symmetrical Components
POWER IN OF SYMMETRICAL COMPONENT If the symmetrical components of current and voltage are known the power expended in three phase circuit can be computed directly from the components.
POWER IN OF SYMMETRICAL COMPONENT
Which shows complex power can be computed from symmetrical components of voltage and currents of unbalanced three phase circuit.
PHASE SHIFT OF SYMMETRICAL COMPONENT IN STARDETLA TRANSFORMER BANK Before we learn phase shift let us examine standard method of marking transformer terminals. Primary and secondary is wound on core as in figure. High voltage winding marked by H1, H2 and low tension winding is marked as X1, X2. Current flowing from H1 to H2 produces flux in common core in the same directions current flowing from X1 to X2. Transformer theory shows that current must flow out at terminal X1 when current is flowing into terminal H1 with magnetizing current neglected for the magneto motive forces produced by the currents in two coils must cancel each other all times. The flux common to both the coil is due to magnetizing current alone.
PHASE SHIFT OF SYMMETRICAL COMPONENT IN STARDETLA TRANSFORMER BANK For that we have to mark the terminal by dot that indicate direction of current flow from the terminals whether the current Ip and Is are in phase or out of phase by 180 degree. The direction of arrow and dot marked on winding terminal H1 and X1 are positive at the same time with respect to H2 and X2 if dot is on upper side in both winding that is called in phase If on low tension side dot is on bottom of winding that indicate both current are out of phase by 180degree.
PHASE SHIFT OF SYMMETRICAL COMPONENT IN STARDETLA TRANSFORMER BANK For three phase transformer high tension terminals are marked H1, H2 and H3 & for low tension terminals are marked X1, X2 and X3. For the figure YY or ∆ ∆ transformers the markings are such that voltages to neutral from terminals H1, H2 and H3 are in phase with the voltages to neutral from terminals X1, X2 and X3 respectively .
PHASE SHIFT OF SYMMETRICAL COMPONENT IN STARDETLA TRANSFORMER BANK High tension terminals H1, H2, H3 are connected to termoinals A,B,C respectively and phase sequence is ABC similarly for low tension winding X1,X2,X3. Now carefully see winding AN of Y connected side which is linked magnetically with phase winding bc on ∆ connected side. Location of dots on windings shows that VAN is in phase with Vbc
PHASE SHIFT OF SYMMETRICAL COMPONENT IN STARDETLA TRANSFORMER BANK American standard for designating terminals H1 and X1 on Y- ∆ transformer requires that positive sequence voltage drop from H1 to neutral lead the positive sequence voltage drop from X1 to neutral by 30 degree regardless of whether Y or ∆ winding is on high tension side. Similarly voltage from H2 to neutral leads the voltage from X2 to neutral by 30 and voltage from H3 to neutral leads the voltage from X3 to neutral by 30 degree. VA1 leads Vb1 by 30degree which enables us to determine that terminal to which phase b is connected should be labeled X1.
PHASE SHIFT OF SYMMETRICAL COMPONENT IN STARDETLA TRANSFORMER BANK
PHASE SHIFT OF SYMMETRICAL COMPONENT IN STARDETLA TRANSFORMER BANK
PHASE SHIFT OF SYMMETRICAL COMPONENT IN STARDETLA TRANSFORMER BANK
Van
Vbc
PHASE SHIFT OF SYMMETRICAL COMPONENT IN STARDETLA TRANSFORMER BANK Figure(b) shows that normal designation of winding terminals by which we normally designate the transformer winding but figure (a) shows nomenclature is most convenient for computations in former case we need to exchange a for b, b for c and c for a.
PHASE SHIFT OF SYMMETRICAL COMPONENT IN STARDETLA TRANSFORMER BANK Inspection of positive and negative sequence phasor diagram shows that Va1 leads VA1 by 90 and Va2 lags VA2 by 90. The diagram shows VA1 and VA2 in phase which is not necessarily ture but phase shift between VA1 and VA2 does not alter the 90 relation between VA1 and Va1 or between VA2 and Va2.
PHASE SHIFT OF SYMMETRICAL COMPONENT IN STARDETLA TRANSFORMER BANK
UNSYMMETRICAL SERIES IMPEDANCE System becomes unbalanced only upon the occurrence of unsymmetrical fault. Let see the system which having unequal impedance.(We should reach to conclusion that is important in analysis by symmetrical components) Figure shows unequal impedances Za, Zb, Zc. If we assume no mutual coupling or (mutual inductance ) the voltage drop across the part of the system given by matrix equation
UNSYMMETRICAL SERIES IMPEDANCE
And in of symmetrical components of voltage and current
Pre multiplying by equation A-1 gives the result
If all impedances are equal
UNSYMMETRICAL SERIES IMPEDANCE
UNSYMMETRICAL SERIES IMPEDANCE Thus we conclude that symmetrical components of unbalanced currents flowing in balanced series impedances produce voltage drop of like sequence only condition is that no coupling between phases. If coupling is exist so square matrix will have some off diagonal elements . In transmission line system assumption of transposition yields equal series impedances.
UNSYMMETRICAL SERIES IMPEDANCE Thus component currents of any one sequence produce voltage drop of like sequence only in transmission line that is positive sequence current produces positive sequence voltage drops only, negative sequence produces negative sequence voltage drops and zero sequence currents produces zero sequence voltage drop only. We could study variation of these equation for special cases such as single phase loads where Zb=Zc=0.
SEQUENCE IMPEDANCE AND SEQUENCE NETWORK The single-phase equivalent circuit consisting of the impedances to currents of any one sequence only is called the sequence network of that particular sequence. Thus, the sequence network corresponding to positive-sequence current is called the positive-sequence network. Similarly, the sequence network corresponding to negative-sequence current is called negative-sequence network, and that corresponding to zero-sequence current is calledzero-sequence network. The sequence networks are interconnected in a particular way to represent various unsymmetrical fault conditions. Therefore, to calculate the effect of a fault by the method of symmetrical components, it is required to determine the sequence networks.
SEQUENCE IMPEDANCE AND SEQUENCE NETWORK In the method of symmetrical components, to calculate the effect of a fault on a power system, the sequence networks are developed corresponding to the fault condition. These networks are then interconnected depending on the type of fault. The resulting network is then analyzed to find the fault current and other parameters. The positive-sequence network is obtained by determining all the positive-sequence voltages and positive-sequence impedances of individual elements, and connecting them according to the SLD. All the generated emfs are positive-sequence voltages. Hence all the per unit reactance/impedance diagrams obtained in the earlier chapters are positive-sequence networks. The negative-sequence generated emfs are not present. Hence, the negative-sequence network for a power system is obtained by omitting all the generated emfs and replacing all impedances by negative-sequence impedances from the positivesequence networks.
SEQUENCE IMPEDANCE AND SEQUENCE NETWORK Since all the neutral points of a symmetrical three-phase system are at the same potential when balanced currents are flowing, the neutral of a symmetrical three-phase system is the logical reference point. It is therefore taken as the reference bus for the positive- and negative-sequence networks. Impedances connected between the neutral of the machine and ground is not a part of either the positive- or negativesequence networks because neither positive- nor negativesequence currents can flow in such impedances. Impedance of symmetrical component depends on type of power system equipment i.e generator, transformer, or transmission line. Zero sequence impedance of over head line depends on presence of ground wires, tower footing resistance and grounding.
SEQUENCE IMPEDANCE AND SEQUENCE NETWORK Line capacitance of over head lines is ignored in SC calculations. While estimating sequence impedances of power system components is one problem constructing zero, positive and negative sequence impedance network is the first step for unsymmetrical fault current calculations The sequence network are constructed as viewed from the fault point which can be defined as point at which unbalance occurs in a system i.e fault point or unbalance load. The voltages for sequence network are taken as line to neutral voltages
SEQUENCE IMPEDANCE AND SEQUENCE NETWORK Only active network contains voltage source is positive sequence networks Sequence networks have per phase impedance values Normally sequence networks are constructed on the basis of per unit values on common MVAbase and 100 MVA is in common use. Since the component current of one phase sequence cause voltage drop of like sequence only and are independent of current of other sequence. The single phase equivalent circuit composed of impedance to current of any one sequence only is called the sequence network for that particular sequence.
SEQUENCE NETWORK OF UNLOADED GENERATOR An unloaded generator, grounded through a reactor. When fault occurs at terminal of generator current Ia, Ib and Ic flows in a lines. If fault involves ground the current flowing into the neutral of generator is designated by In One or two of the line currents may be zero but the current can resolved into their symmetrical components regardless of how unbalanced they may be.
SEQUENCE NETWORK OF UNLOADED GENERATOR Drawing sequence networks is very simple. The generated voltages are of positive sequence only(and as reference) since generator is designed to supply balanced three phase voltages. Therefore positive sequence network is composed of an emf in series with the positive sequence impedance of the generator. The negative and zero sequence network contains no emf but include the impedances of the generator to negative and zero sequence respectively , Current are flowing through impedance of their own sequence only.
SEQUENCE NETWORK OF UNLOADED GENERATOR The generated emf in the positive sequence network is the no load terminal voltage to neutral which is also equal to voltages behind transient and sub transient, transient or synchronous reactance since the generator is not loaded. The reactance in the positive sequence network is sub transient, transient or synchronous reactance depending on whether sub transient, transient or steady state conditions are being studied.
SEQUENCE NETWORK OF UNLOADED GENERATOR The reference bus for the positive and negative sequence networks is the neutral of the generator. So far as positive negative sequence components are concerned the neutral of generator is at ground potential since only zero sequence current flows in the impedance between neutral and ground. There reference bus for zero sequence network is the ground at generator.
SEQUENCE NETWORK OF UNLOADED GENERATOR The current flowing in the impedance Zn between neutral and ground is 3Iao. Voltage drop of zero sequence from point a to ground it 3IaoZn +IaoZgo where Zgo is zero sequence impedance per phase of the generator. The zero sequence network which is single phase circuit assumed to carry only the zero sequence current of one phase must therefore have an impedance of 3Zn+Zgo The total zero sequence impedance through which Iao flows is Zo=3Zn+Zgo
SEQUENCE IMPDEANCES OF CIRCUIT ELEMENTS
For obtaining the sequence networks, the component voltages/ currents and the component impedances of all the elements of the network are to be determined. The usual elements of a power system are: ive loads, rotating machines (generators/ motors), transmission lines and transformers. The positiveand negative-sequence impedances of linear, symmetrical, static circuits are identical. The sequence impedances of rotating machines will generally differ from one another. This is due to the different conditions that exist when the sequence currents flow. The flux due to negative-sequence currents rotates at double the speed of rotor while that due to positive-sequence currents is stationary with respect to the rotor. The resultant flux due to zero-sequence currents is ideally zero as these flux components add up to zero, and hence the zero-sequence reactance is only due to the leakage flux. Thus, the zero-sequence impedance of these machines is smaller than positive- and negative-sequence impedances.
The positive- and negative-sequence impedances of a transmission line are identical, while the zerosequence impedance differs from these. The positive- and negative-sequence impedances are identical as the transposed transmission lines are balanced linear circuits. The zero-sequence impedance is higher due to magnetic field set up by the zero-sequence currents is very different from that of the positive- or negative-sequence currents. The zero-sequence reactance is generally 2 to 3.5 times greater than the positive- sequence reactance. It is customary to take all the sequence impedances of a transformer to be identical, although the zero-sequence impedance slightly differs with respect to the other two.
POSITIVE AND NEGATIVE SEQUENCE NETWORK Obtaining the values of sequence impedances of power system is to enable us to construct the sequence network for the complete system. The network of particular sequence shows all the paths for the flow of current of that sequence in system. Three phase synchronous generator and motors have internal voltages of positive sequence only since they are designed to generate balance voltages. Since the positive and negative sequence impedances are same in static symmetrical system. conversion of positive sequence network to negative sequence network is accomplished by changing if necessary only the impedances that represents rotating machinery and by omitting the emfs Electromagnetic forces are omitted on assumption of balanced generated voltages and the absence of negative sequence voltages induces from outside sources
POSITIVE AND NEGATIVE SEQUENCE NETWORK Since all the neutral points of symmetrical three phase system are at the same potential when balanced three phase curents are flowing, all the neutral points must be at same potential for either positive or negative sequence currents Therefore neutral of symmetrical three phase system is the logical reference potential for specifying positive and negative sequence voltage drop and is the reference bus for positive and negative sequence network. Impedance connected between neutral of machine and ground is not a part of either the positive or negative sequence network because neither positive nor negative sequence current can flow in impedance so connected.
ZERO SEQUENCE NETWORK Zero sequence currents are same in magnitude and phase at any point in all the phases of system Therefore zero sequence current will flow only if return path exists through which a completed circuit is provided. The reference for zero sequence voltages is potential of the ground at the point in the system at which any particular voltage is specified. Since zero sequence current may be flowing in ground, the ground is not necessarily at same potential at all points and the reference bus of zero sequence network does not represent a ground of uniform potential.
ZERO SEQUENCE NETWORK The zero-sequence components are the same both in magnitude and in phase. Thus, it is equivalent to a single-phase system and hence, zerosequence currents will flow only if a return path exists. The reference point for this network is the ground. If a circuit is Y-connected, with no connection from the neutral to ground or to another neutral point in the circuit, no zero-sequence currents can flow, and hence the impedance to zero-sequence current is infinite. This is represented by an open circuit between the neutral of the Y-connected circuit and the reference bus,
ZERO SEQUENCE NETWORK if the neutral of the Y-connected circuit is grounded through zero impedance, a zero-impedance path (short circuit) is connected between the neutral point and the reference bus.
If an impedance Zn is connected between the neutral and the ground of a Y-connected circuit, an impedance of 3Zn must be connected between the neutral and the reference bus (because, all the three zero-sequence currents (3Ia0) flows through this impedance to cause a voltage drop of 3Ia0 Z0 )
ZERO SEQUENCE NETWORK
A ∆-connected circuit can provide no return path; its impedance to zero-sequence line currents is therefore infinite. Thus, the zero-sequence network is open at the ∆ -connected circuit, as shown in the figure Zero-sequence equivalent networks of ∆ connected load. However zero-sequence currents can circulate inside the ∆ -connected circuit.
ZERO SEQUENCE NETWORK TRANSFORMER
ZERO SEQUENCE NETWORK The zero-sequence equivalent circuits of three-phase transformers deserve special attention. The different possible combinations of the primary and the secondary windings in Y and ∆ alter the zero-sequence network. The possible connections of two-winding transformers and their equivalent zero-sequence networks are shown in the above figure. The networks are drawn ing that there will be no primary current when there is no secondary current, neglecting the noload component. The arrows on the connection diagram show the possible paths for the zero-sequence current. Absence of an arrow indicates that the connection is such that zerosequence currents cannot flow. The letters P and Q identify the corresponding points on the connection diagram and equivalent circuit.
ZERO SEQUENCE NETWORK
Case 1: Y-Y Bank with one neutral grounded: If either one of the neutrals of a Y-Y bank is ungrounded, zero-sequence current cannot flow in either winding ( as the absence of a path through one winding prevents current in the other). An open circuit exists for zero-sequence current between two parts of the system connected by the transformer bank. Case 2: Y-Y Bank with both neutral grounded: In this case, a path through transformer exists for the zero-sequence current. Hence zero-sequence current can flow in both sides of the transformer provided there is closed path for it to flow. Hence the points on the two sides of the transformer are connected by the zero-sequence impedance of the transformer. Case 3: Y- ∆ Bank with grounded Y: In this case, there is path for zero-sequence current to ground through the Y as the corresponding induced current can circulate in the ∆. The equivalent circuit must provide for a path from lines on the Y side through zero-sequence impedance of the transformer to the reference bus. However, an open circuit must exist between line and the reference bus on the ∆ side. If there is an impedance Zn between neutral and ground, then the zerosequence impedance must include 3Zn along with zero-sequence impedance of the transformer. Case 4: Y- ∆ Bank with ungrounded Y: In this case, there is no path for zero-sequence current. The zero-sequence impedance is infinite and is shown by an open circuit.
Case 5: ∆ -∆ Bank: In this case, there is no return path for zero-sequence current. The zerosequence current cannot flow in lines although it can circulate in the ∆ windings.
ZERO SEQUENCE NETWORK
Conclusion
The sequence networks are three separate networks which are the singlephase equivalent of the corresponding symmetrical sequence systems. These networks can be drawn as follows: For the given condition (steady state, transient, or subtransient), draw the reactance diagram (selecting proper base values and converting all the per unit values to the selected base, if necessary). This will correspond to the positive-sequence network. Determine the per unit negative-sequence impedances of all elements (if the values of negative sequence is not given to any element, it can approximately be taken as equal to the positive-sequence impedance). Draw the negative-sequence network by replacing all emf sources by short circuit and all impedances by corresponding negative-sequence impedances in the positive-sequence network. Determine the per unit zero-sequence impedances of all the elements and draw the zero-sequence network corresponding to the grounding conditions of different elements.
Conclusion Unbalanced voltage and currents can be resolved into their symmetrical components. Problem are solved by treating each set of components separately and super imposing the results In balanced network having no coupling between phases the currents of one phase sequence induces voltage drop of like sequence only Knowledge of positive sequence is necessary for load flow studies on power system Fault calculation and stability studies that involves unsymmetrical faults that needed negative and zero sequence components also. Synthesis of zero sequence network requires particular care because the zero sequence network may differ from others considerably
Reference
Elements of power system analysis by Willian D Stevenson Jr. International student edition Power system analysis by JB Gupta
http://elearning.vtu.ac.in/P2/EE61/Ch03/html/0019.htm http://nptel.iitm.ac.in/courses/Webcourse-contents/IIT-KANPUR/power-system/chapter_8/8_5.html
THANK YOU
SUMIT K RATHORE EE DEPT, GCET
Content
Synthesis of Unsymmetrical phasors from their symmetrical components Power in of symmetrical components Sequence circuits of Y and Δ impedances Sequence circuits of a symmetrical transmission line Sequence circuits of the synchronous machine Sequence circuits of a Y- Δ transformer Unsymmetrical series impedances Sequence networks
2
Instruction Objective of lesson
Normal types of fault are:
Fault due to lightning Tree limbs falling on the line Wind damage Insulation deterioration Vandalism
4
Types of fault Symmetrical fault : Usually three phase to ground fault Unsymmetrical fault The fault is unbalanced in nature
5
Sources of Asymmetrical fault are (cont.) One phase open circuit
6
Sources of Asymmetrical fault are (cont.) One phase open circuit
7
Sources of Asymmetrical fault are (cont.) SLG fault
8
Need for fault analysis Design of protection system requires the knowledge of fault current. The information obtained from the fault studies are used: to select the sizes of circuit breaker, fuse and characteristic, setting of relay.
9
Instruction Objective of lesson
Upunitl now we have studied faults that are symmetrical (all the three lines are shorted) but this kind of fault rare in system, and unsymmetrical faults are major and to study them or analyze them we need a simple technique this is called symmetrical component analysis discovered by C L Fortescue.
SYNTHESIS OF UNSYMMETRICAL PHASOR FROM THEIR SYMMETRICAL COMPONENT
CL Fortescue suggested that n related unbalanced phasors can be resolved into n system of balanced phasors called the symmetrical components of the original phasors. The n phasors of each set of components are equal in magnitude(length) and the angle between adjacent phasors of the set are equal. This method is applicable to any unbalanced systems we will confine attention to three phase system.
SYNTHESIS OF UNSYMMETRICAL PHASOR FROM THEIR SYMMETRICAL COMPONENT
According to CL Fortescue unbalanced phasors of three phase system can be resolved into three balanced systems of phasors. The balanced sets of components are : 1. positive sequence component consisting of three phasors equal in magnitude, displaced from each other by 120 in phase and having same phase sequence as the original phasor. 2. negative sequence components are consisting of three phasors equal in magnitude, displaced from each other by 120 in phase and having phase sequence opposite to that of original phasor. 3. zero sequence components consisting of three phasors equal in magnitude and with zero phase displacement from each other.
SYNTHESIS OF UNSYMMETRICAL PHASOR FROM THEIR SYMMETRICAL COMPONENT
SYNTHESIS OF UNSYMMETRICAL PHASOR FROM THEIR SYMMETRICAL COMPONENT
It is customary when solving problem by symmetrical components to designate the three phases of system as a, b and c of the voltages and currents of sequence of positive sequence components of unbalanced phasors is abc, negative sequence as acb. If original voltage sequence is Va, Vb, and Vc then positive sequence sets of symmetrical components are designated by subscript 1, that becomes Va1, Vb1, Vc1. Similarly negative sequence components are Va2, Vb2, Vc2 and the zero sequence components are Va0, Vb0 and Vc0. And phasor representing currents are represented by I followed by subscripts
SYNTHESIS OF UNSYMMETRICAL PHASOR FROM THEIR SYMMETRICAL COMPONENT Since each of the original unbalanced phasors is the sum of its components, the original phasors expressed in of their components are
Synthesis of set of three unbalanced phasors from the three sets of symmetrical components is show in figure (next slide)
SYNTHESIS OF UNSYMMETRICAL PHASOR FROM THEIR SYMMETRICAL COMPONENT
The advantages of analysis by symmetrical components will become apparent as we apply the method to study unsymmetrical faults on otherwise symmetrical systems. Method consist of finding symmetrical components of current at fault Then value of current and voltages at various points in the system can be found. The method is simple and leads to accurate prediction of system behavior
OPERATORS
Because of phase displacement in phase components of sysmmetrical components of voltage and currents in three phase system it is convenient to have short hand method to represent the rotation of phasor through 120 degree. Result of multiplication of two complex number is the product of their magnitudes and sum of their angles. If complex number expressing a phasor is multiplied by a complex number of unit magnitude and angle theta the resulting complex number represent a phasor equal to the original phasor displaced by the angle theta. The complex number of unit magnitude and associated angle theta is an operator that rotates the phasor on which it operates through the angle theta.Z
OPERATORS
Operator j which causes the rotation through 90 and operator -1 which causes rotation through 180. Two successive applications of operator j causes rotation through 90+90 which leads up to the conclusion that j*j causes rotation through 180 and thus we recognize to the conclusion that j2 =-1 the letter a is commonly used to designate the operator that cause a rotation of 120 in counter clock wise direction. Such an operator is a complex number of unit magnitude and with angle of 120 and defined by
=1ej2л/3= -0.5+j0.866
OPERATORS
If operator is applied twice in succession the phasor is rotated through 240 and three succession a2= 1/_240o=-0.5-j0.866 And a3=1/_360o=1/_0o=1 An important difference must be noted between uses of operators j and a. the operator j is unit magnitude at 90 and –j means that complex number j is changed by an angle of 180 to give unit magnitude at 270 thus -j j=1/_90 and –j=1/_270=1/_-90 Hence it is said sometimes that +j indicate rotation through 90 and –j indicate rotation through -90 statement is correct but a similar statement does not apply to operator a since A=1/_120
OPERATORS
-a=1/_120 x 1/-180 = 1/_ -60 -a2
a
1 a3
-1 -a3
a2
-a
SYMMETRICAL COMPONENT OF UNSYMMETRICAL PHASORS Lets see how to solve unsymmetrical phasors into their symmetrical components. Synthesis of three unsymmetrical phasors form three sets of symmetrical phasors done by use of equation as below
Now lets examine how to resolve three unsymmetrical phasors into their symmetrical components.
SYMMETRICAL COMPONENT OF UNSYMMETRICAL PHASORS
We have seen that Number of unknown quantity can be reduced by expressing each component of Vb and Vc as the product of some function of the operator α and component a of Va.
SYMMETRICAL COMPONENT OF UNSYMMETRICAL PHASORS Substituting values yield the
Or in matrix form
SYMMETRICAL COMPONENT OF UNSYMMETRICAL PHASORS For convenience we let
Then as
Rearrange the equation we ll obtain
SYMMETRICAL COMPONENT OF UNSYMMETRICAL PHASORS Which shows us how to resolve three unsymmetrical phasors into their symmetrical components. So separate equation in ordinary form
Similarly if we require to find out components Vbo. Vb1, Vb2, Vco. Vc1, and Vc2, can be found out.
SYMMETRICAL COMPONENT OF UNSYMMETRICAL PHASORS This shows that no zero sequence component exist if the sum of the unbalanced phasors is zero. Since the sum of the line to line voltage phasors in a three phase system is always zero, zero sequence components are never present in the line voltages, regardless of the amount of unbalance. The sum of three line to neutral voltage phasor is not necessarily zero and voltages to neutral may contains zero sequence component.
SYMMETRICAL COMPONENT OF UNSYMMETRICAL PHASORS Preceding equation could have been written for any set of related phasors and we might have written them for currents instead of for voltages. They may be solved either analytically or graphically . Because some of the preceding equations are so fundamental they are summarized for currents
SYMMETRICAL COMPONENT OF UNSYMMETRICAL PHASORS In three phase system sum of line currents is equal to the currents In in the return path through the neutral Ia+Ib+Ic=In If currents are equal then In=3Iao In the absence of path through the neutral of three phase system In is zero and the line currents contain no zero sequence components A delta connected load provides no path for neutral current and line currents flowing to a delta connected load can contain no zero sequence components.
Visualization of Symmetrical Components
Visualization of Symmetrical Components
POWER IN OF SYMMETRICAL COMPONENT If the symmetrical components of current and voltage are known the power expended in three phase circuit can be computed directly from the components.
POWER IN OF SYMMETRICAL COMPONENT
Which shows complex power can be computed from symmetrical components of voltage and currents of unbalanced three phase circuit.
PHASE SHIFT OF SYMMETRICAL COMPONENT IN STARDETLA TRANSFORMER BANK Before we learn phase shift let us examine standard method of marking transformer terminals. Primary and secondary is wound on core as in figure. High voltage winding marked by H1, H2 and low tension winding is marked as X1, X2. Current flowing from H1 to H2 produces flux in common core in the same directions current flowing from X1 to X2. Transformer theory shows that current must flow out at terminal X1 when current is flowing into terminal H1 with magnetizing current neglected for the magneto motive forces produced by the currents in two coils must cancel each other all times. The flux common to both the coil is due to magnetizing current alone.
PHASE SHIFT OF SYMMETRICAL COMPONENT IN STARDETLA TRANSFORMER BANK For that we have to mark the terminal by dot that indicate direction of current flow from the terminals whether the current Ip and Is are in phase or out of phase by 180 degree. The direction of arrow and dot marked on winding terminal H1 and X1 are positive at the same time with respect to H2 and X2 if dot is on upper side in both winding that is called in phase If on low tension side dot is on bottom of winding that indicate both current are out of phase by 180degree.
PHASE SHIFT OF SYMMETRICAL COMPONENT IN STARDETLA TRANSFORMER BANK For three phase transformer high tension terminals are marked H1, H2 and H3 & for low tension terminals are marked X1, X2 and X3. For the figure YY or ∆ ∆ transformers the markings are such that voltages to neutral from terminals H1, H2 and H3 are in phase with the voltages to neutral from terminals X1, X2 and X3 respectively .
PHASE SHIFT OF SYMMETRICAL COMPONENT IN STARDETLA TRANSFORMER BANK High tension terminals H1, H2, H3 are connected to termoinals A,B,C respectively and phase sequence is ABC similarly for low tension winding X1,X2,X3. Now carefully see winding AN of Y connected side which is linked magnetically with phase winding bc on ∆ connected side. Location of dots on windings shows that VAN is in phase with Vbc
PHASE SHIFT OF SYMMETRICAL COMPONENT IN STARDETLA TRANSFORMER BANK American standard for designating terminals H1 and X1 on Y- ∆ transformer requires that positive sequence voltage drop from H1 to neutral lead the positive sequence voltage drop from X1 to neutral by 30 degree regardless of whether Y or ∆ winding is on high tension side. Similarly voltage from H2 to neutral leads the voltage from X2 to neutral by 30 and voltage from H3 to neutral leads the voltage from X3 to neutral by 30 degree. VA1 leads Vb1 by 30degree which enables us to determine that terminal to which phase b is connected should be labeled X1.
PHASE SHIFT OF SYMMETRICAL COMPONENT IN STARDETLA TRANSFORMER BANK
PHASE SHIFT OF SYMMETRICAL COMPONENT IN STARDETLA TRANSFORMER BANK
PHASE SHIFT OF SYMMETRICAL COMPONENT IN STARDETLA TRANSFORMER BANK
Van
Vbc
PHASE SHIFT OF SYMMETRICAL COMPONENT IN STARDETLA TRANSFORMER BANK Figure(b) shows that normal designation of winding terminals by which we normally designate the transformer winding but figure (a) shows nomenclature is most convenient for computations in former case we need to exchange a for b, b for c and c for a.
PHASE SHIFT OF SYMMETRICAL COMPONENT IN STARDETLA TRANSFORMER BANK Inspection of positive and negative sequence phasor diagram shows that Va1 leads VA1 by 90 and Va2 lags VA2 by 90. The diagram shows VA1 and VA2 in phase which is not necessarily ture but phase shift between VA1 and VA2 does not alter the 90 relation between VA1 and Va1 or between VA2 and Va2.
PHASE SHIFT OF SYMMETRICAL COMPONENT IN STARDETLA TRANSFORMER BANK
UNSYMMETRICAL SERIES IMPEDANCE System becomes unbalanced only upon the occurrence of unsymmetrical fault. Let see the system which having unequal impedance.(We should reach to conclusion that is important in analysis by symmetrical components) Figure shows unequal impedances Za, Zb, Zc. If we assume no mutual coupling or (mutual inductance ) the voltage drop across the part of the system given by matrix equation
UNSYMMETRICAL SERIES IMPEDANCE
And in of symmetrical components of voltage and current
Pre multiplying by equation A-1 gives the result
If all impedances are equal
UNSYMMETRICAL SERIES IMPEDANCE
UNSYMMETRICAL SERIES IMPEDANCE Thus we conclude that symmetrical components of unbalanced currents flowing in balanced series impedances produce voltage drop of like sequence only condition is that no coupling between phases. If coupling is exist so square matrix will have some off diagonal elements . In transmission line system assumption of transposition yields equal series impedances.
UNSYMMETRICAL SERIES IMPEDANCE Thus component currents of any one sequence produce voltage drop of like sequence only in transmission line that is positive sequence current produces positive sequence voltage drops only, negative sequence produces negative sequence voltage drops and zero sequence currents produces zero sequence voltage drop only. We could study variation of these equation for special cases such as single phase loads where Zb=Zc=0.
SEQUENCE IMPEDANCE AND SEQUENCE NETWORK The single-phase equivalent circuit consisting of the impedances to currents of any one sequence only is called the sequence network of that particular sequence. Thus, the sequence network corresponding to positive-sequence current is called the positive-sequence network. Similarly, the sequence network corresponding to negative-sequence current is called negative-sequence network, and that corresponding to zero-sequence current is calledzero-sequence network. The sequence networks are interconnected in a particular way to represent various unsymmetrical fault conditions. Therefore, to calculate the effect of a fault by the method of symmetrical components, it is required to determine the sequence networks.
SEQUENCE IMPEDANCE AND SEQUENCE NETWORK In the method of symmetrical components, to calculate the effect of a fault on a power system, the sequence networks are developed corresponding to the fault condition. These networks are then interconnected depending on the type of fault. The resulting network is then analyzed to find the fault current and other parameters. The positive-sequence network is obtained by determining all the positive-sequence voltages and positive-sequence impedances of individual elements, and connecting them according to the SLD. All the generated emfs are positive-sequence voltages. Hence all the per unit reactance/impedance diagrams obtained in the earlier chapters are positive-sequence networks. The negative-sequence generated emfs are not present. Hence, the negative-sequence network for a power system is obtained by omitting all the generated emfs and replacing all impedances by negative-sequence impedances from the positivesequence networks.
SEQUENCE IMPEDANCE AND SEQUENCE NETWORK Since all the neutral points of a symmetrical three-phase system are at the same potential when balanced currents are flowing, the neutral of a symmetrical three-phase system is the logical reference point. It is therefore taken as the reference bus for the positive- and negative-sequence networks. Impedances connected between the neutral of the machine and ground is not a part of either the positive- or negativesequence networks because neither positive- nor negativesequence currents can flow in such impedances. Impedance of symmetrical component depends on type of power system equipment i.e generator, transformer, or transmission line. Zero sequence impedance of over head line depends on presence of ground wires, tower footing resistance and grounding.
SEQUENCE IMPEDANCE AND SEQUENCE NETWORK Line capacitance of over head lines is ignored in SC calculations. While estimating sequence impedances of power system components is one problem constructing zero, positive and negative sequence impedance network is the first step for unsymmetrical fault current calculations The sequence network are constructed as viewed from the fault point which can be defined as point at which unbalance occurs in a system i.e fault point or unbalance load. The voltages for sequence network are taken as line to neutral voltages
SEQUENCE IMPEDANCE AND SEQUENCE NETWORK Only active network contains voltage source is positive sequence networks Sequence networks have per phase impedance values Normally sequence networks are constructed on the basis of per unit values on common MVAbase and 100 MVA is in common use. Since the component current of one phase sequence cause voltage drop of like sequence only and are independent of current of other sequence. The single phase equivalent circuit composed of impedance to current of any one sequence only is called the sequence network for that particular sequence.
SEQUENCE NETWORK OF UNLOADED GENERATOR An unloaded generator, grounded through a reactor. When fault occurs at terminal of generator current Ia, Ib and Ic flows in a lines. If fault involves ground the current flowing into the neutral of generator is designated by In One or two of the line currents may be zero but the current can resolved into their symmetrical components regardless of how unbalanced they may be.
SEQUENCE NETWORK OF UNLOADED GENERATOR Drawing sequence networks is very simple. The generated voltages are of positive sequence only(and as reference) since generator is designed to supply balanced three phase voltages. Therefore positive sequence network is composed of an emf in series with the positive sequence impedance of the generator. The negative and zero sequence network contains no emf but include the impedances of the generator to negative and zero sequence respectively , Current are flowing through impedance of their own sequence only.
SEQUENCE NETWORK OF UNLOADED GENERATOR The generated emf in the positive sequence network is the no load terminal voltage to neutral which is also equal to voltages behind transient and sub transient, transient or synchronous reactance since the generator is not loaded. The reactance in the positive sequence network is sub transient, transient or synchronous reactance depending on whether sub transient, transient or steady state conditions are being studied.
SEQUENCE NETWORK OF UNLOADED GENERATOR The reference bus for the positive and negative sequence networks is the neutral of the generator. So far as positive negative sequence components are concerned the neutral of generator is at ground potential since only zero sequence current flows in the impedance between neutral and ground. There reference bus for zero sequence network is the ground at generator.
SEQUENCE NETWORK OF UNLOADED GENERATOR The current flowing in the impedance Zn between neutral and ground is 3Iao. Voltage drop of zero sequence from point a to ground it 3IaoZn +IaoZgo where Zgo is zero sequence impedance per phase of the generator. The zero sequence network which is single phase circuit assumed to carry only the zero sequence current of one phase must therefore have an impedance of 3Zn+Zgo The total zero sequence impedance through which Iao flows is Zo=3Zn+Zgo
SEQUENCE IMPDEANCES OF CIRCUIT ELEMENTS
For obtaining the sequence networks, the component voltages/ currents and the component impedances of all the elements of the network are to be determined. The usual elements of a power system are: ive loads, rotating machines (generators/ motors), transmission lines and transformers. The positiveand negative-sequence impedances of linear, symmetrical, static circuits are identical. The sequence impedances of rotating machines will generally differ from one another. This is due to the different conditions that exist when the sequence currents flow. The flux due to negative-sequence currents rotates at double the speed of rotor while that due to positive-sequence currents is stationary with respect to the rotor. The resultant flux due to zero-sequence currents is ideally zero as these flux components add up to zero, and hence the zero-sequence reactance is only due to the leakage flux. Thus, the zero-sequence impedance of these machines is smaller than positive- and negative-sequence impedances.
The positive- and negative-sequence impedances of a transmission line are identical, while the zerosequence impedance differs from these. The positive- and negative-sequence impedances are identical as the transposed transmission lines are balanced linear circuits. The zero-sequence impedance is higher due to magnetic field set up by the zero-sequence currents is very different from that of the positive- or negative-sequence currents. The zero-sequence reactance is generally 2 to 3.5 times greater than the positive- sequence reactance. It is customary to take all the sequence impedances of a transformer to be identical, although the zero-sequence impedance slightly differs with respect to the other two.
POSITIVE AND NEGATIVE SEQUENCE NETWORK Obtaining the values of sequence impedances of power system is to enable us to construct the sequence network for the complete system. The network of particular sequence shows all the paths for the flow of current of that sequence in system. Three phase synchronous generator and motors have internal voltages of positive sequence only since they are designed to generate balance voltages. Since the positive and negative sequence impedances are same in static symmetrical system. conversion of positive sequence network to negative sequence network is accomplished by changing if necessary only the impedances that represents rotating machinery and by omitting the emfs Electromagnetic forces are omitted on assumption of balanced generated voltages and the absence of negative sequence voltages induces from outside sources
POSITIVE AND NEGATIVE SEQUENCE NETWORK Since all the neutral points of symmetrical three phase system are at the same potential when balanced three phase curents are flowing, all the neutral points must be at same potential for either positive or negative sequence currents Therefore neutral of symmetrical three phase system is the logical reference potential for specifying positive and negative sequence voltage drop and is the reference bus for positive and negative sequence network. Impedance connected between neutral of machine and ground is not a part of either the positive or negative sequence network because neither positive nor negative sequence current can flow in impedance so connected.
ZERO SEQUENCE NETWORK Zero sequence currents are same in magnitude and phase at any point in all the phases of system Therefore zero sequence current will flow only if return path exists through which a completed circuit is provided. The reference for zero sequence voltages is potential of the ground at the point in the system at which any particular voltage is specified. Since zero sequence current may be flowing in ground, the ground is not necessarily at same potential at all points and the reference bus of zero sequence network does not represent a ground of uniform potential.
ZERO SEQUENCE NETWORK The zero-sequence components are the same both in magnitude and in phase. Thus, it is equivalent to a single-phase system and hence, zerosequence currents will flow only if a return path exists. The reference point for this network is the ground. If a circuit is Y-connected, with no connection from the neutral to ground or to another neutral point in the circuit, no zero-sequence currents can flow, and hence the impedance to zero-sequence current is infinite. This is represented by an open circuit between the neutral of the Y-connected circuit and the reference bus,
ZERO SEQUENCE NETWORK if the neutral of the Y-connected circuit is grounded through zero impedance, a zero-impedance path (short circuit) is connected between the neutral point and the reference bus.
If an impedance Zn is connected between the neutral and the ground of a Y-connected circuit, an impedance of 3Zn must be connected between the neutral and the reference bus (because, all the three zero-sequence currents (3Ia0) flows through this impedance to cause a voltage drop of 3Ia0 Z0 )
ZERO SEQUENCE NETWORK
A ∆-connected circuit can provide no return path; its impedance to zero-sequence line currents is therefore infinite. Thus, the zero-sequence network is open at the ∆ -connected circuit, as shown in the figure Zero-sequence equivalent networks of ∆ connected load. However zero-sequence currents can circulate inside the ∆ -connected circuit.
ZERO SEQUENCE NETWORK TRANSFORMER
ZERO SEQUENCE NETWORK The zero-sequence equivalent circuits of three-phase transformers deserve special attention. The different possible combinations of the primary and the secondary windings in Y and ∆ alter the zero-sequence network. The possible connections of two-winding transformers and their equivalent zero-sequence networks are shown in the above figure. The networks are drawn ing that there will be no primary current when there is no secondary current, neglecting the noload component. The arrows on the connection diagram show the possible paths for the zero-sequence current. Absence of an arrow indicates that the connection is such that zerosequence currents cannot flow. The letters P and Q identify the corresponding points on the connection diagram and equivalent circuit.
ZERO SEQUENCE NETWORK
Case 1: Y-Y Bank with one neutral grounded: If either one of the neutrals of a Y-Y bank is ungrounded, zero-sequence current cannot flow in either winding ( as the absence of a path through one winding prevents current in the other). An open circuit exists for zero-sequence current between two parts of the system connected by the transformer bank. Case 2: Y-Y Bank with both neutral grounded: In this case, a path through transformer exists for the zero-sequence current. Hence zero-sequence current can flow in both sides of the transformer provided there is closed path for it to flow. Hence the points on the two sides of the transformer are connected by the zero-sequence impedance of the transformer. Case 3: Y- ∆ Bank with grounded Y: In this case, there is path for zero-sequence current to ground through the Y as the corresponding induced current can circulate in the ∆. The equivalent circuit must provide for a path from lines on the Y side through zero-sequence impedance of the transformer to the reference bus. However, an open circuit must exist between line and the reference bus on the ∆ side. If there is an impedance Zn between neutral and ground, then the zerosequence impedance must include 3Zn along with zero-sequence impedance of the transformer. Case 4: Y- ∆ Bank with ungrounded Y: In this case, there is no path for zero-sequence current. The zero-sequence impedance is infinite and is shown by an open circuit.
Case 5: ∆ -∆ Bank: In this case, there is no return path for zero-sequence current. The zerosequence current cannot flow in lines although it can circulate in the ∆ windings.
ZERO SEQUENCE NETWORK
Conclusion
The sequence networks are three separate networks which are the singlephase equivalent of the corresponding symmetrical sequence systems. These networks can be drawn as follows: For the given condition (steady state, transient, or subtransient), draw the reactance diagram (selecting proper base values and converting all the per unit values to the selected base, if necessary). This will correspond to the positive-sequence network. Determine the per unit negative-sequence impedances of all elements (if the values of negative sequence is not given to any element, it can approximately be taken as equal to the positive-sequence impedance). Draw the negative-sequence network by replacing all emf sources by short circuit and all impedances by corresponding negative-sequence impedances in the positive-sequence network. Determine the per unit zero-sequence impedances of all the elements and draw the zero-sequence network corresponding to the grounding conditions of different elements.
Conclusion Unbalanced voltage and currents can be resolved into their symmetrical components. Problem are solved by treating each set of components separately and super imposing the results In balanced network having no coupling between phases the currents of one phase sequence induces voltage drop of like sequence only Knowledge of positive sequence is necessary for load flow studies on power system Fault calculation and stability studies that involves unsymmetrical faults that needed negative and zero sequence components also. Synthesis of zero sequence network requires particular care because the zero sequence network may differ from others considerably
Reference
Elements of power system analysis by Willian D Stevenson Jr. International student edition Power system analysis by JB Gupta
http://elearning.vtu.ac.in/P2/EE61/Ch03/html/0019.htm http://nptel.iitm.ac.in/courses/Webcourse-contents/IIT-KANPUR/power-system/chapter_8/8_5.html
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