Unsymmetrical Series Impedances:

1
Unsymmetrical Series Impedances Consider
a portion of transmission system Assume no
coupling between the 3 impedances
2
The voltage drops between two ends In terms of
sym components
3
Premultiplying both sides by A-1 Vaa1
1/3 Ia1 (Za Zb Zc) 1/3 Ia2
(Za a2 Zb a Zc) 1/3 Ia0 (Za a Zb
a2 Zc) Vaa2 1/3 Ia1 (Za a Zb a2
Zc) 1/3 Ia2 (Za Zb Zc)
1/3 Ia0 (Za a2 Zb a Zc)
4
Vaa0 1/3 Ia1 (Za a2 Zb a Zc)
1/3 Ia2 (Za a Zb a2 Zc) 1/3 Ia0
(Za Zb Zc) If Za Zb Zc, Above
Eqs. reduces to Vaa0 Za Ia0 Vaa1 Za Ia1
Vaa2 Za Ia2
5
Sequence Impedances In an uncoupled balanced
Y-load, Sym comps of unsymmetrical currents cause
voltage drops of like sequence only. The voltage
drop caused by current of a certain sequence at
any part of the system, depends on the impedance
of that part to current of that sequence. The
impedance of any part to current of one sequence
may be different from impedance to current of
another seq.
6
Definition Impedance of a network when
positive-sequence currents are alone flowing is
called the impedance to positive-sequence current
or positive-sequence impedance (Z1)
7
Definition Impedance of a network when
negative-sequence currents are alone flowing is
called the impedance to negative-sequence current
or negative-sequence impedance (Z2).
8
Definition Impedance of a network when
zero-sequence currents are alone flowing is
called the impedance to zero-sequence current
or zero-sequence impedance (Z0).
9

• Sequence Networks
• For balanced impedance systems, the voltage drop
  of a particular sequence is independent of
  other sequence currents.
• In other words, we can represent the 3 sequence
  systems by 3 independent 1-ph equivalent
  circuits.
• In each such circuit, voltages, currents and
  impedances of only one sequence is present.

10
Definition The 1-ph equivalent circuit composed
of the impedances to currents of any one sequence
is called the sequence network for that
particular sequence. The sequence networks
consists of any generated voltage, and impedance
of like sequences such that the currents of that
sequence only flows.
11
Definition The positive-sequence network is a
single-phase equivalent circuit consisting of
generated emf, if any, and impedances of
positive-sequence only.
12
Definition The negative-sequence network is a
single-phase circuit consisting of generated emf,
if any, and impedances of negative-sequence only.
13
Definition The zero-sequence network is a
single-phase circuit consisting of generated emf,
if any, and impedances of zero-sequence only.
14
Seq. Imp. of balanced Y-load Vag ZYIa
Zn In ZYIa Zn(Ia Ib Ic)
Vag (ZyZn)Ia ZnIb ZnIc
Similarly, Vbg ZnIa (ZyZn)Ib
ZnIc Vcg ZnIa ZnIb (ZyZn)Ic
15
In matrix form, Vph Zph Iph In terms of
sym components,
16
Vph Zph Iph A Vs Zph A Is Vs A-1
Zph A Is Vs Zs Is where Zs
A-1 Zph A
17
Simplifying A-1 Zph A or
where Z0 ZY3Zn
Z1 ZY
Z2 ZY
18
If neutral is grounded through Zn Z0 ZY 3
Zn If neutral is solidly grounded, i.e., Zn 0
Z0 ZY If neutral is not grounded, i.e.,
Zn 8 Z0 ZY 8 8 i.e., open circuit Thus
zero-sequence currents cannot flow if neutral to
ground connection is absent
19

20
Sequence Impedance of balanced ?-load
21
Numerical Example A Y-connected source with
phase voltages Vag 277lt00, Vbg 260lt-1200 and
Vcg 295lt1150 is applied to a balanced ? load of
30lt400 O/phase through a line of impedance 1lt850
O. The neutral of the source is solidly grounded.
Draw the sequence networks of the system and find
source currents.
22
Solution
23
Solution Va0 15.91lt62.110 V Va1 277.1lt-1.70
V Va2 9.22lt216.70 V Y eq. of ? load 10lt400
O/phase Zline 1lt850 O. Zneutral 8 (since
delta load neutral is not connected to the
ground)
24

Ia0 0lt00 A (open ckt)
Ia1 25.82lt-45.60 A
Ia2 0.86lt172.80 A
25
IP A Is Ia 25.15lt-46.80 A Ib
25.71lt196.40 A Ic 26.62lt73.80 A
26
Unloaded Generator Consider an
unloaded generator grounded through a reactor
Let Ia, Ib and Ic are
line currents after a fault The
neutral current In flows only if fault
involves ground
27
Positive-Sequence Network Va1 Ea Z1 Ia1
28
Negative-Sequence Network Va2 Z2 Ia2
29
Zero-Sequence Network Va0 Z0 Ia0
30

• Sequence Impedances of
• Basic Elements
• Passive loads
• Positive- and negative-sequence impedances
  are equal Zero-sequence impedance depends on
  the ground connection

31

• Sequence Impedances of
• Basic Elements
• Rotating machines (generators/motors)
• Zg0, Z1, Z2 are generally different
• Take Z1 Z2 unless otherwise specified

32

• Sequence Impedances of
• Basic Elements
• Transmission lines
• Are balanced because of transposition
• Hence, Z1 Z2
• Z0 is higher --- 2 to 3.5 times Z1

33

• Sequence Impedances of
• basic Elements
• Transformers
• Although Z0 slightly differ from other two,
• it is customary to take
• Z1 Z2 Z0

34

• To calculate the effect of a fault on a power
  system corresponding to the fault condition
• Sequence networks are developed
• These networks are then properly interconnected
• The resulting network is then analyzed to find
  the fault current and other parameters.

35

• Sequence Networks of Power Systems
• The Positive-sequence Network
• Find the positive-sequence voltages and
  positive-sequence impedances of all individual
  elements, and connect them according to the SLD.
• Generated emfs are ve-seq. voltages
• All per unit reactance/impedance diagrams are
  ve-sequence networks

36

• Sequence Networks of Power Systems
• The Negative-sequence Network
• No negative-sequence generated emfs
• Thus, 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
  positive-sequence network

37

• Neutral point in Positive- and
• Negative Sequence Networks
• Neutral points of a sym. system are at the same
  potential for balanced currents
• Neutral is the logical reference point
• Hence, it is taken as the reference bus for the
  ve- and -ve-sequence networks
• Impedances between the neutral and ground is not
  a part of either the positive- or negative-
  sequence networks

38

• Sequence Networks of Power Systems
• The 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
• Hence, zero-sequence currents will flow only if a
  return path exists

39

• The Zero-sequence Network
• The reference point for this network is the
  ground
• The ground is not necessarily at the same
  potential at all points for this network
• Thus, the reference bus of zero-sequence network
  does not represent a ground of uniform potential

40

• The Zero-sequence Network
• For a Y-connected ckt, without neutral to ground
  or to another neutral point connection, Z0 is
  infinite, hence it is represented by an open
  circuit between the neutral and the reference bus

41

• The 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

42

• The Zero-sequence Network
• If the neutral of the Y-connected circuit is
  grounded through an impedance Zn, an impedance of
  3Zn is connected between the neutral point and
  the reference

43

• The Zero-sequence Network
• A ?-connected circuit can provide no return path
  its Z0 is therefore infinite. Thus,
  zero-sequence network is open at the ?-connected
  circuit. However zero-seq. currents can circulate
  inside the ?

44

• The Zero-seq Network of 3-ph Transformers
• Zero-sequence networks of 3-ph transformers
  deserve special attention
• The various Y-? combinations alter the
  zero-sequence network
• Basic concept is that no I1flows if I2 0
• Five possible combinations are shown
• Absence of arrows indicate that there is no path
  for zero-sequence current

45

• Zero-sequence Network of 3-ph Transformer
• Y-Y Bank, One neutral grounded

46

• Zero-sequence Network of 3-ph Transformer
• Y-Y Bank, Both neutrals grounded

47

• Zero-sequence Network of 3-ph Transformer
• Y-? Bank, Grounded Y

48

• Zero-sequence Network of 3-ph Transformer
• Y-? Bank, Grounded Y

49

• Zero-sequence Network of 3-ph Transformer
• ?-? Bank

50
Numerical Example For the power system shown in
the SLD, draw the sequence networks.
51

• Thank you
• Dr G.K. Purushothama
• email gkp_at_mcehassan.ac.in
• gkuttama_at_rediffmail.com
• Phone [phone]