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Zigzag transformer - some new applications with a note to energy efficiency
Article in International Journal of Power and Energy Conversion · January 2015
DOI: 10.1504/IJPEC.2015.070473
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Int. J. Power and Energy Conversion, Vol. 6, No. 3, 2015
Zigzag transformer – some new applications with a
note to energy efficiency
Kartik P. Basu* and Naeem M. Hanoon
Faculty of Engineering,
Multimedia University,
63100 Cyberjaya, Malaysia
Email: kartik.basu@mmu.edu.my
Email: naeem@mmu.edu.my
*Corresponding author
Abstract: Zigzag transformer is only used as a grounding transformer in a
three-phase delta connected power supply system. Equal DC current flowing
through the windings of a zigzag transformer does not produce any core
saturation and it may be used as an interfacing device for AC supply with DC
in a power system. This property of the transformer may be used to transmit
DC and AC power simultaneously through the same transmission line. It may
also be used to get three-phase voltage from three-wire, two-phase supply and
may be used to maintain three-phase load voltage when any one phase of the
three-phase supply line trips. This paper emphasises the role of zigzag
transformer as a common interfacing device in all these new applications with
some comments on the change of energy efficiency of the power system.
Keywords: zigzag transformer; EHV transmission line; HVDC transmission;
voltage sag; short-term power interruption; STPI; single-pole auto reclosing;
SPAR.
Reference to this paper should be made as follows: Basu, K.P. and
Hanoon, N.M. (2015) ‘Zigzag transformer – some new applications with a note
to energy efficiency’, Int. J. Power and Energy Conversion, Vol. 6, No. 3,
pp.267–280.
Biographical notes: Kartik P. Basu received his BEE, MEE and PhD (Eng.)
degrees from the Jadavpur University, Kolkata, India, in 1961, 1967 and 1974,
respectively. His research interests include power system operation, control,
protection and electric drives. He has authored and co-authored more than 100
journal and conference papers. Presently, he is working as a Professor in the
Multimedia University, Malaysia.
Naeem M. Hanoon has obtained his BSc with Distinction in Electrical
Engineering in 1994, MSc degree from the University Putra Malaysia in 1999
and PhD degree from Multimedia University in 2010. His research interests are
AI control of power system, protection and FACTS devices. He has published
some papers in international journals and conferences.
Copyright © 2015 Inderscience Enterprises Ltd.
267
268
1
K.P. Basu and N.M. Hanoon
Introduction
Zigzag transformer possesses two important properties, namely, no saturation with DC
current and very low zero sequence impedance along with very high positive and
negative sequence impedances.
It is commonly used as a grounding transformer in a delta connected power supply
system. The zigzag transformer may also be used for some new applications.
It can be used to interface three-phase AC with DC supply for simultaneous AC-DC
transmission through the same three-phase single or double circuit transmission line. The
scheme claims the same advantages of parallel AC-DC transmission with only one
transmission line. It may be recognised as a new type of FACTS controller.
Three-phase, four wire distribution line is commonly used to supply single and
three-phase loads. If anyone phase of the supply line trips, then the system reduces to
three-wire, two-phase system. The zigzag transformer regenerates three phase supply
from two-phase, three wire input. This property of the zigzag transformer may be used
for mitigating single phase voltage sags, running three-phase induction motors under
single-phasing condition without overheating and maintaining three-phase voltage in
distribution systems during single-pole auto reclosing.
Only one application of the zigzag transformer as a grounding transformer in a
delta-connected power supply system is mentioned in books and published papers (ABB,
1997; Shen et al., 2008).
This paper emphasises the possible new applications of zigzag transformer as a
versatile interfacing device to interface HVDC with EHVAC system as well as
two-phase, three-wire system with three-phase four-wire distribution system. The energy
efficiency of the power system changes in all these applications. Simple laboratory
experiments presented at the end verify the theories presented.
2
Zigzag transformer
Figure 1 shows the winding connection of a zigzag transformer in detail on the limbs of
its core.
Figure 1
Zigzag transformer winding connection
Zigzag transformer
269
Fluxes produced by the currents Ia, Ib, and Ic are φa, φb, and φc, respectively. In each limb
of the core the fluxes produced by the two windings, having equal number of turns,
oppose each other.
2.1 Low zero sequence and high positive and negative sequence impedance
For positive sequence currents
φa = aφ b = a 2 φc
(1)
And, for negative sequence currents
φa = a 2 φ b = aφc
(2)
But for zero sequence currents
φa = φ b = φc
(3)
where a = ej2π/3; a2 = e–j2π/3
Thus, the magnitude of the net flux in each limb of the core, a result of both positive
and negative sequence current, is √3φa. But for zero sequence current its value is zero.
Hence, the zigzag winding offers very high (no load magnetising) impedance to both
positive and negative sequence currents, but very low impedance (leakage reactance) to
zero sequence current.
2.2 No saturation of core with DC current
If Ia = Ib = Ic = Idc / 3, where, Idc is DC current, then there is no DC saturation of the core
as the net DC flux in any limb of the core becomes zero due to cancellation of fluxes
produced by each half of the winding in any limb.
2.3 Building up of open phase voltage
A three-phase, four-wire supply is connected across a zigzag transformer as shown in
Figure 2. One contact Ta of the CB opens for LG fault or for any voltage sag/swell in
A-phase. Contact Tn of the circuit breaker (CBN) connected to neutral is instantaneously
closed to connect the zigzag transformer neutral to the neutral of power supply through
the ground.
Two healthy phases B and C in conjunction with the ground wire connected to the
zigzag transformer now supplies a two-phase voltage to the transformer. Assuming
ground resistance to be zero the voltages across each half of phase windings of the zigzag
transformer with the opening of phase ‘A’ are shown in Figure 2. The phases to neutral
voltages are shown as VAN, VBN, and VCN.
270
K.P. Basu and N.M. Hanoon
Figure 2
Induced voltages across half of each phase windings
From Figure 2, we get the following equations:
VBN = VE − VD ; VCN = VF − VE
(4)
It is also observed that the voltage across A1 to neutral is:
VA1N = VD − VF = − ( VBN + VCN )
(5)
Source voltages, having positive and negative sequence component of voltages E+ and E–
respectively, are:
VAN = E + + E − , VBN = a 2 E + + aE − , and VCN = aE + + a 2 E −
(6)
From equations (5) and (6)
VA1N = VAN
(7)
Thus, we may conclude that at no load the voltage across the phase, which is opened,
builds up to the pre-fault voltage of that phase, even with unbalanced three-phase source
voltage.
Current distribution in the transformer and the load under single phasing condition is
shown in Figure 3.
Figure 3
Current distribution in transformer and load during single phasing condition
Zigzag transformer
271
From Figure 3:
I A = 0; IB = Ib − Ia ; IC = Ic − Ia ; Ia + I b + Ic
(8)
I N = I n − 3Ia
(9)
Ia, Ib, Ic are load currents per phase and In is neutral current of load.
For balanced load
ZA = ZB = ZC ; and I n = 0, I N = −3Ia ; and I B = IC = √ 3Ia
(10)
Opening of any one phase increases the neutral current, IN. As a consequence voltage
drop in the open phase becomes higher.
The zigzag transformer offers a very low zero sequence impedance. Under normal
operating condition, even the presence of small zero sequence voltage in the supply,
produces large current through the zigzag transformer. Therefore, under normal operating
condition the neutral of zigzag transformer is kept disconnected from the supply neutral.
3
New applications of zigzag transformer
3.1 Combined AC-DC power flow through one transmission line (Basu and
Khan, 2001; Rahman and Khan, 2004, 2007, 2006; Basu and Rahman,
2005)
To keep a power system stable during transient disturbances long EHV AC lines are
loaded much below their thermal limit. They may be loaded to a very high value if DC
current superimposed with AC current flows through the same conductor. The added DC
power flow does not cause any transient instability.
Figure 4 shows the schematic diagram for the combined AC-DC power
transmission through the same transmission line. At the sending end a delta-zigzag-star
transformer is used to supply the power to a three-phase single circuit transmission
line. The receiving end load is connected through a zigzag-deltastar transformer.
The rectifier bridge provides DC power, which is fed to the neutral point of the zigzag
connected secondary of sending end transformer. At receiving end the inverter bridge
reconverts DC to AC again. The zigzag winding neutral point of the receiving end
transformer is connected to the inverter bridge. Both DC and three-phase AC power
are carried by the single transmission line. AC current, Ia, per conductor along with
one third of the total DC current is carried by each conductor of the line. The DC
flows through the ground to complete its path. Cancellation of flux produced
by DC current flowing through zigzag windings at both end of transmission line avoids
saturation of transformer core. Harmonics in DC current is reduced to a great extent by
using a high value of reactor Xd.
272
K.P. Basu and N.M. Hanoon
Schematic diagram for combined AC-DC power transmission
Figure 5 shows the equivalent circuit of the combined AC-DC scheme under steady state
operating condition with assumptions of
1
constant current control of rectifier
2
constant extinction angle control of inverter.
Figure 5
Equivalent circuit for combined AC-DC transmission
The return current path of AC is shown by dotted line in Figure 5. The total DC current,
Id, returns through the ground. One third of the DC current, Id / 3, superimposed with the
AC current Ia, flows through each conductor of the line. Ia is the RMS value of AC
current. Total RMS current per conductor at any point of the line is:
I = Ia2 + ( Id 3)
And
2
(11)
273
Zigzag transformer
PL ≅ 3I 2 R
(12)
PL is the power loss of the line and R is the resistance per phase.
It is to be noted that Ia is much less than Ith, the conductor current rating indicating its
allowable temperature rise. To maintain the transient stability of the system, if Ia = x . Ith;
where x < 1, the maximum value of DC current is:
Id = 3 (1 − x 2 )I th
(13)
The conductor current, I, is asymmetrical. If (Id / 3) < √2Ia, then two zero-crossings of
current wave in each cycle are observed.
With respect to ground the peak value of each conductor voltage is:
E max = Vd + 2.E ph
(14)
where Vd = DC voltage, and Eph = RMS value of AC voltage per phase.
Electric field produced by any conductor voltage is pulsating. It has a sinusoidal AC
component with a superimposed DC component. Keeping (Vd / Eph) < √2, the electric
field intensity crosses zero twice in a cycle. It will avoid the requirement of longer creep
age distance for insulator discs used in HVDC lines.
Vd / Eph = m (assumed); combined AC-DC power transfer becomes:
⎡ m 1− x2 ⎤
Pt = Pdc + Pac = ⎢1 +
⎥ .Pac
xpf ⎦
⎣
(15)
where pf is the power factor of AC power.
If (Id / 3Ia) < √2, CBs connected at the two ends of transmission line interrupt current
at natural current zeroes and no special DC circuit breaker is required.
Assuming Vd / Eph = √2; x = 1 / √3 and pf = 1; the total power transmitted is:
Pt = 1.67Pac
(16)
Thus, an increment of 67% power flow is achieved by combining DC with AC for the
assumed values of m and x. Modulation of the DC power by fast control action of DC
regulator may maintain the transient stability and oscillations are damped out optimally.
Power losses in the combined AC-DC power transmission system through one
single-circuit three-phase AC line may be compared with a system having one
single-circuit three-phase line transmitting only AC power operating in parallel with a
mono-polar DC line transmitting DC power with ground return. For the same values of
Eph, Vd, Ia and Id in each system, Pac and Pdc remain same in both the systems. AC power
′ and PLdc in
loss (PLac = 3Ia2R) is equal in both the systems. DC power losses are PLdc
combined AC-DC and mono-polar DC line respectively.
′ = RId 2 + R G Id 2
PLdc = 3(R + 2Rz) ( Id 3) +R G Id 2 , and PLdc
2
(17)
where RZ = resistance of the zigzag transformer per phase and RG = ground resistance
offered to Id. Resistance of the DC line conductor is assumed to be equal to the resistance
′ . Thus, the
per phase of the AC line. For a long line, 2RZ < R, and PLdc is less than PLdc
combined AC-DC power flow is more energy efficient.
274
Figure 6
K.P. Basu and N.M. Hanoon
Schematic diagram of combined AC-DC transmission through converted double circuit
ac line
The idea of combined AC-DC power transmission may also be extended to double circuit
EHV AC transmission line. The DC current flows from sending to receiving end from
one line and returns back through the other line. The drawback of ground return of DC
current in single circuit AC line is eliminated. The basic scheme of double circuit AC-DC
transmission with double circuit AC line is shown in Figure 6. All the four transformers
connected to the two transmission lines at the sending and receiving ends have zigzag
windings to interface DC power supply with AC power line.
Power losses in the combined AC-DC power transmission system through
double-circuit three-phase AC line may be compared with a system having a
double-circuit three-phase line transmitting only AC power operating in parallel with a
bi-polar DC line having grounded mid-point and transmitting DC power. AC power loss
remains equal in both the systems. DC power losses are:
275
Zigzag transformer
′ = 2RId 2
PLdc = 6 ( R + 2Rz ) ( Id 3) , and PLdc
2
(18)
Thus, the combined AC-DC power flow is more energy efficient for long lines.
3.2 Mitigation of single-phase power supply disturbance to loads (Basu and
Mukerji, 2004; Basu and Hafidz, 2008; Basu et al., 2011)
It has been pointed out earlier that a zigzag transformer may transform two-phase supply
having a neutral wire to three-phase supply. This characteristic of a zigzag transformer
may be used to transfer power from the opened phase of a three-phase power supply
system to the connected phases as shown in Figure 7. A switch, having three closed (Ta)
and one open (Tn) contacts, is used for fast transfer of load.
Figure 7
Zigzag transformer with fast switching arrangement for power transfer
With no disturbance in the system the loads get the three-phase supply directly from the
source. The neutral point of zigzag transformer is kept open.
LG fault may cause power interruption or voltage sag in any one phase. Sensing low
voltage at any one phase, a voltage sensitive relay may be programmed to open the
supply of the faulty phase by opening the corresponding ‘Ta’ contact and simultaneously
closing the ‘Tn’ contact (refer Figure 7). So, the zigzag transformer is now connected
across a two-phase supply and rebuilds the three-phase voltage across the load. As the
zero sequence impedance of the zigzag transformer is very low the magnitude of open
phase voltage does not differ too much from that of the healthy phases particularly with
low values of ground resistance. Approximately balanced three-phase supply is available
across the adjustable speed drive (ASD). Rated power of the zigzag transformer is same
as that of the three-phase load. It has very short time rating as the voltage disturbance
persists for a short period. So, the transformer cost becomes low.
A static switching device is used to open contact ‘Ta’ and to close contact ‘Tn’. Thus,
the power failure time is reduced to 0.02 second or only one cycle.
276
K.P. Basu and N.M. Hanoon
The capacitors across the DC load and the inverter of the ASD must have the ride
through capability to maintain the voltage for 0.02 sec. For any single-phase AC load
there will be a power failure of 0.02 second only.
When phase ‘A’ opens, currents in phases ‘B’ and ‘C’ become √3 times (each) of the
normal. The voltage disturbance period is very short and the system is expected to carry
this current without excessive overheating.
3.3 Medium voltage distribution system: maintenance of three-phase voltage
during single-pole auto reclosing (Basu et al., 2013; Basu and Moleykutty,
2011)
Figure 8 barring block A, depicts a common medium voltage (MV) radial distribution
system with overhead distribution lines indicated as L1, L2 and L3. The transmission
voltage levels are usually 132 kV, 230 kV or 500 kV and the distribution line is
commonly rated for 33 kV or 11 kV. The power supply transformer TRS is generally
connected in star-delta with the neutral point of the star grounded. The low voltage
distribution lines are generally rated for a line voltage of 400 V, having three phase wires
and one neutral wire, to supply both three-phase and one-phase loads. TR1, TR2 and TR3
are distribution transformers, each having delta primary connected to MV bus and
grounded star secondary connected to 400 V line. The delta connected power supply
system needs ground fault protection. A grounding transformer TRG1, having zigzag
winding and connected to Bus1, serves this purpose. Delta-star connection of distribution
transformers effectively change the low voltage loads as delta connected loads to the MV
system. Initiation of a line to ground (LG) fault in L1 trips circuit breaker CB1. If single
pole auto reclosing (SPAR) with CB1 is used to remove this temporary fault, the line
voltages across the primary windings of TR1, TR2 and TR3 during the reclosure dead
time become VBC = 1 pu, VAB = –0.5 pu, and VCA = –0.5 pu. So, the star side phase
voltages become vb = 1 pu, va = –0.5 pu and vc = –0.5 pu.
Thus, three-phase induction motors connected to 400 V supply receive a highly
unbalanced voltage, and negative sequence current causes severe heating. The
overheating becomes more severe with higher values of reclosure dead time.
Three-phase voltage with minimum unbalancing should be restored to the loads at the
earliest (≤ 0.1 second) during SPAR of any CB, when one pole opens.
Block A, having a zigzag grounding transformer TRG2 connected to load BUS4, is
now included in the distribution system shown in Figure 8. The neutral of TRG2 is
grounded through a circuit breaker, CBN, which is normally kept open.
All the circuit breakers are interconnected with a communication link. Opening of
one pole of CB1 during SPAR clears any single phase fault in L1. A command signal is
sent from a relay connected to CB1 to instantaneously trip CB2 and for a delayed closure
of CBN after 0.1 sec. As a consequence Load1 is disconnected from both sides, but the
voltage building up process of TRG2 provides three-phase voltage across Load2 and
Load3 after 0.1 sec. To avoid the feeding of fault current by TRG2, delayed closure of
CBN by 0.1 sec is done intentionally to trip CB1 and CB2 first to isolate the fault. After
the auto-reclosure dead time CB1is reclosed. Multi-shot auto-reclosing with longer dead
time may also be used. CB2 may be reclosed with the availability of sustained
three-phase voltage from L1 side. Then, a relay connected to CB2 sends a command
signal to trip CBN and the pre-fault condition is restored. Similar sequence of operation
may be carried out for any LG fault in L2 and L3.
Zigzag transformer
Figure 8
277
MV distribution system
It is meaningless to compare the energy efficiency for short-term power interruption
(STPI) in any one phase, with and without mitigation using zigzag transformer, when the
period of interruption is few seconds or minutes. But for long-term power interruptions
(LTPI) in any one phase, comparison of energy efficiency should be carried out for
two-phase, three-wire system with the converted three-phase, four-wire system using
zigzag transformer. The resistance of each phase conductor as well as the neutral wire is
assumed to be R the load is assumed to be balanced.
VAN = VBN = VCN = Vph ,
Ia = I b = Ic = I ph and load power factor = cosφ
(19)
When power interruption occurs in one phase, the current in two healthy phases become
Iph (each) and the neutral current is also Iph.
Output power = 2Vph I ph cosφ; Input power = 2Vph I ph cosφ + 3I ph 2 R
(20)
In the converted three-phase, four-wire system (refer Figure 3),
I A = 0, I B = IC = √ 3I ph and I N = 3I ph
Output power = 3Vph I ph cos φ; Input power = 3Vph I ph cos φ + 6I ph 2 R
+9I ph ( R+R Z )
(21)
(22)
Therefore, the energy efficiency of the converted system is less than that of the two-phase
system for any load during LTPI.
278
4
K.P. Basu and N.M. Hanoon
Experimental verification
Simple laboratory experiments were conducted in a power system lab to verify the
validity of the simultaneous AC-DC power transmission and maintenance of three-phase
voltage during the interruption of power in any one phase of three-phase supply.
4.1 Experiment 1: Simultaneous AC-DC power transmission
Figure 9 shows the experimental setup for simultaneous AC-DC power transmission.
Figure 9
Experimental setup for simultaneous AC-DC power transmission
Notes: Ratings: supply (G) – three-phase, 400 V, 50 Hz; transformers (TR1, TR2)
each – three-phase, 1.5 kVA, 400 V/400 V, delta-zigzag, 50 Hz; transmission
line (represented by reactance X) – three-phase, 400 V, 20 mH/phase;
load – three-phase induction motor – star connected, 400 V, 50 Hz, 1.17 A,
0.37 kW, 1,400 rpm; DC supply – 120 V battery; DC load – 100 Ω resistor;
DC reactor – XD – 100 mH.
The experimental result showed that there was no saturation of TR1 and TR2 with the
DC current of 1.2 A flowing through the 100 Ω resistor. The induction motor current was
0.8 A/phase at no load.
4.2 Experiment 2: Maintenance of three-phase load voltage during STPI in one
phase
Figure 10 shows the connection diagram for the experimental setup.
During the experiment motors were operated at no load.
STPI in any one phase is simulated the by disconnecting that phase (A, B, or C).
Neutral point of the zigzag transformer should remain connected to the neutral point of
source throughout the experiment. Table 1shows the experimental results.
279
Zigzag transformer
Figure 10
Experimental setup for maintenance of three-phase voltage with STPI
Notes: Ratings: DC load – 165 Ω; AC load – R = 165 Ω, connected in parallel with
X = 250 Ω; C – 32 μF; induction motor – star connected, 400 V, 50 Hz, 1.17 A,
0.37 kW, 1,400 rpm; one-phase induction motor – 1 hp, 230 V, 50 Hz, 4.98 A;
zigzag transformer – 1 kVA, 400 V, 50 Hz; ZG0 = 2.5 + j3.2 Ω.
Table 1
Experimental results of STPI in one phase
Load voltage (V)
Current (amp)
Operation
VAN
VBN
VCN
Idc
Iac
I1M
I3M
230
230
230
1.25
1.7
3.0
0.8
Normal
226
230
230
1.22
1.7
3.0
0.8
A-open
230
225
230
1.25
1.65
3.0
0.8
B-open
230
230
223
1.25
1.7
2.9
0.8
C-open
where three-phase motor current per phase is printed as I3M.
The zero sequence impedance of the zigzag transformer creates voltage drop in the
opened phase.
5
Conclusions
Zigzag transformer, having very low value of zero sequence reactance, is traditionally
used as grounding transformer in a delta connected power supply system. Equal amount
of DC current flowing through each winding of a zigzag transformer does not saturate the
core due to flux cancellation. The property of no DC current saturation may be used to
superimpose DC current in EHV AC transmission line by using the zigzag transformer as
the interfacing device. Combined ACDC transmission through the same line is possible
and the advantage of AC line operating in parallel with DC transmission line is obtained.
Energy efficiency of combined AC-DC transmission is increased.
280
K.P. Basu and N.M. Hanoon
The zigzag transformer also regenerates three phase supply from a two phase supply
with neutral. Thus, the transformer may be able to maintain three phase voltage during
STPI of any one phase. In this case, the zigzag transformer is interfacing a two-phase,
three-wire supply with a three-phase, four-wire load.
Energy efficiency of the converted three-phase, four-wire system is always less than
the two-phase system during LTPI.
Simple laboratory experiments illustrate the validity of the possible new applications
of zigzag transformers.
References
ABB (1997) Electrical Transmission and Distribution Reference Book, ABB.
Basu, K.P. and Hafidz, S.A. (2008) ‘Mitigation of single-phase voltage sag and swell with zigzag
transformer’, Electric Utility Deregulation and Restructuring and Power Technologies, 2008.
DRPT 2008: Third International Conference on, 6–9 April 2008, Nanjing, China,
pp.2369–2373.
Basu, K.P. and Khan, B.H. (2001) ‘Simultaneous AC-DC power transmission’, Journal of the
Institution of Engineers (India), June, Vol 82, No. 3, pp.32–35.
Basu, K.P. and Moleykutty, G. (2011) ‘Maintenance of three-phase load voltage during single
phase auto reclosing in medium voltage distribution lines’, International Journal of Emerging
Electric Power Systems, July, Vol. 12, No. 4, pp.1–15.
Basu, K.P. and Mukerji, S.K. (2004) ‘Experimental investigation into operation under
single-phasing condition of a three-phase induction motor connected across a zigzag
transformer’, IEEE Transaction on Education, August, Vol. 47, No. 3, pp.365–368.
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transmission line for simultaneous AC-DC power transmission’, IEEE Sixth International
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December, pp.972–976.
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transmission’, IEEE Trans. Power Syst., Vol. 22, No. 1, pp.459–466.
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simulation’, Power and Energy Society General Meeting - Conversion and Delivery of
Electrical Energy in the 21st Century, pp.1–8, IEEE.
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