Phenomenon of sympathetic interaction between transformers caused ...

Phenomenon of sympathetic interaction between transformers caused by inrush transients H. Bronzeado R. Yacamini

lndexing terms: lnrush transients, Transformers, Sympathetic interaction

Abstract: In power systems with appreciable resistance, the transformers already connected to the supply system can experience unexpected saturation during the inrush transient of an incoming transformer. This saturation, which is established by the asymmetrical voltage drop across the system resistance caused by the inrush current, demands offset magnetising currents of high magnitude in the already connected transformers. This generates a transient interaction between the transformers, a ‘sympathetic interaction’, that affects the magnitude and duration of the inrush current. As a consequence, problems in the operation of the system, such as false operation of transformer differential relays and prolonged temporary harmonic overvoltages, can occur. The sympathetic interaction between the transformers is analysed in the paper. System configurations with transformers in parallel and in series are investigated. The transformers and system models have been validated using small transformers. List of principal symbols

4ca,4 & ,+cc 4,,,, 4pab9 4pbc bsab? 4sbc 4 1 k a , f$[kb,

q$a, &,,

$lkc

&

R A , R , , R, R a , R b , Rc

1

= flux in the limbs = flux in the air

between each inner winding and its core limb = flux in the upper yolks = flux in the lower yolks = flux in the air between primary and secondary windings (the transformer leakage flux) = flux in the air, external to the windings (the core leakage flux) = resistances of primary windings = resistances of secondary windings

Introduction

Transients caused by energisation of large transformers are one of the more common problems in the operation of power systems. The challenge of predicting transformer transients, especially inrush current, has been with

0IEE, 1995 Paper 1953A (P7), first received 12th October 1994 and in revised form 10th March 1995 The authors are with the Department of Engineering, Aberdeen University, Aberdeen AB9 2UE, Scotland, United Kingdom H. Bronzeado is on leave from Companhia Hidro-Eletrica do Sao Francisco - CHESF, Brazil I E E Proc.-Sci. Meas. Technol., Vol. 142, N o . 4, July 1995

us since the last decade of the 19th century, when it was first reported. This current has received considerable attention, as protective devices must discriminate between transient inrush current and fault currents. Much research has been carried out to explain the nature of the transformer inrush phenomenon, to derive its mathematical formulations and especially to calculate the first peak of the inrush current under assumed worst conditions [1-71. However, one aspect of this transient that has largely been ignored in the relevant literature is the effect of the inrush current on the transformers that are already in operation and vice versa. The traditional method for calculating inrush current assumes that the transformer is being switched onto a system to which there are no other transformers connected. In practice, however, transformers are normally energised either in parallel or in series with other transformers that are already in operation. In power systems with appreciable resistance, such as those with long transmission lines, it has been found that the transformer inrush current lasts longer than for systems with a strong busbar. Additionally, offset magnetising currents of high magnitude arise in the transformers that are already connected to the system, indicating they also are saturated [8]. This suggests that a transient interaction between the energising and the already energised transformers takes place, developing prolonged saturation of the transformers. This phenomenon, which has been pointed out as one of the reasons for false operation of transformer differential relays and prolonged temporary harmonic overvoltages on power systems [9, lo], is examined in this paper. Cases where the transformer is energised in parallel and in series with another transformer are investigated. 2

Transformer models

The transformer models used in the simulations were developed based on a physical modelling approach that involves the decoupling and direct solution of the electric and magnetic circuits of the transformer [ l l , 121. The transformer magnetic system is not converted into its dual electrical equivalent, being treated totally on the magnetic domain. The interconnection between the magnetic system and the external electrical system is made by the transformer windings, which exhibit both electrical The authors wish to thank CHESF, CNPq (Brazil) and the British Council for the study leave and financial support granted to H. Bronzeado throughout this research. 323

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and magnetic characteristics. This is achieved by using the commercial software package SABER, which permits simultaneous simulation of both the electrical and magnetic systems. This package is available from Analogy Ltd. of Portland, Oregon, or its worldwide distributors. Fig. 1 shows the approach used in modelling a typical three-phase core-type transformer. To achieve an accur@lb

mines the value of the current that flows in the transformer windings. Any transformer core geometry or winding connection can thus be readily investigated. mp

A

@IC

g = N.I

mn Fig. 2

Schematic diagram of the M M F source

Note that, in parallel with each nonlinear ferromagnetic reluctance, there is an air reluctance that is not generally considered in most other models of transformers. It has been found that this gives a more accurate solution, especially when the transformer is heavily saturated. For simplicity, the hysteresis and eddy current losses in the core have not been considered, as the core is heavily saturated. The piece-wise linear B-H-curve with three slopes, shown in Fig. 3, has been adopted to take into

*sab

a

Y

I

b

Fig. 1

Three-phase transformer model

a Flux distribution b Computer model

ate simulation, the ferromagnetic core and air space within the transformer have been divided into several sections that are assumed to have an approximately uniform flux density [13]. This division is particularly important when parts of the core have differing levels of saturation. As can be seen from Fig. 1, the equivalent magnetic circuit of the transformers consists of lumped linear and nonlinear reluctances having one-to-one correspondence with the flux paths in the transformers. The parameters of the model are determined from the design dimensions of the transformer windings and core and thus give a true representation of the actual transformer. The MMF sources, which represent the primary and secondary windings of the transformer, are modelled as shown schematically in Fig. 2; ep and en are the electrical nodes, and mp and mn are the magnetic nodes. The main feature of this modelling is the capacity to link the nonlinear properties of the core to the rest of the electrical circuit [14]. From the point of view of the electrical system, the magnetic circuit of the transformer provides an equivalent apparent inductance, which deter324

Fig. 3

Piece-wise linear B-H-curve

account the saturation. This results in a simple and easily analysed nonlinear model with sufficient accuracy for practical results. 3

Interaction between parallelled transformers

The circuit used to investigate the transient interaction between parallelled transformers is shown in Fig. 4. Parallel means that the transformer primaries are connected to the same busbar. The other windings of the transformer may or may not be in parallel. The parameters of the laboratory supply system were 0.1 mH and 0.1 R for the inductance and resistance, respectively. A resistance R of 0.65 R in series with the resistance of the supply system was also added for this investigation. The test consisted of closing switch S and connecting transformer T, in parallel with the unloaded transformer TI, which was already connected to the system (Fig. 4). Before each switching, the residual flux in I E E Proc.-Sci. Meas. Techno/., Vol. 142, No. 4, July I995

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were used as single-phase transformers by connecting only the windings corresponding to the central leg). The magnetising current i, in the already energised transformer T I rises abruptly after transformer T, is switched on, attaining a peak of around 30 times its steady-state value. This phenomenon, which will be discussed later, occurs owing to the saturation of T I produced by the voltage asymmetry on the system, which is caused by the inrush current i, of transformer T, . A computer simulation of this system was set up. The results (Fig. 6) show

transformer T, was reduced to zero using a variable AC source. Fig. 5 shows the currents measured in two small threephase transformers of 5 kVA rating (the transformers

m

I

40r

I

a

I

1

-L

-L

-101 0

+T2

-

1

lOOm

200m

t

TI

300m

400m

500m

300m

400m

500m

1,s

a

b

40r

Fig. 4 Electrical system used to investigate sympathetic interaction between transformers in parallel a System configuration b Schematicdiagram of the electric circuit

-1601 0

1

lOOm

200m t.5

b

Fig. 6

Currents calculated in tranSformms T, and Tz (single-phase)

a Offset magnetising current i, in transformerT, b Inrush current i, in transformer T,

-101 0

I

lOOm

1

I

200m

300m

J

4OOm

500m

1,s

a

O -40-

'

h

o

U.

-

-80

-

-120 -1601 0

1

lOOm

200m

300m

400m

500m

1,s b

Fig. 5

Currents measured in transjormers T, and T2 (single-phase)

a Offset magnetising current i, in transformer T,

b Inrush current i, in transformer T,

IEE Proc.-Sci.Meas. Technol., Vol. 142, No. 4, July I995

that the transformer model is reasonably accurate in predicting the pheomenon observed in the laboratory tests. A three-phase simulation, with two identical threephase, three-limb core-type transformers of 180 MVA, 275166 KV, in parallel, was also carried out. The winding resistances and leakage inductance of the transformer were around 0.1% and 12%, respectively, on the base of 100 MVA. The supply system was assumed to have a reactance of 10% and a series resistance of 2% (on 100 MVA base), typical values for a system with long transmission lines. Capacitances were not taken into account. These system parameters are typical of those found in systems with long transmission lines, such as in South America. The parameters used were kindly supply by CHESF. It is in systems of this type that the sympathetic inrush is not prevenant. If a stronger system of the type described by IEC 76-5 is assumed, this will give a level of initial inrush current that is twice that of the system studied here, but will also (because of the lower resistive impedance) exhibit far less sympathetic reaction. This is illustrated in Fig. 12 in the Appendix. 325

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The transformer was energised from the high-voltage side, with all poles of the switch being closed simultaneously at the instant the voltage of phase b passes through zero, going positive. The ‘knee’ of the B-H-curve has been assumed to be 125% of the nominal peak core flux density. The residual flux in the limbs corresponding to phases a, b and c has been assumed to be 8O%, 0% and - 80% of the nominal flux, respectively. Fig. 7 shows the currents of phase c in transformers T, and T, during the transient inrush of T, . The occurrence

/300 OOi

4

-1001 0

I

200m

400m

600m

800m

1

t,s

current of the transformer, being of opposite polarity to the peaks of the inrush current i,, on alternate halfcycles. 3.1 Analysis of sympathetic interaction The interaction between parallelled transformers that occurs when one is energised can be explained as follows (see Fig. 4): Before switch S is closed, only the magnetising current i, of the unloaded transformer T, flows through the system. When transformer T, is energised by the switch being closed, a transient inrush current i, is drained from the system. Owing to the almost entirely unidirectional characteristic of the current i, , the voltage drop across the total system resistance Rsys makes the voltage at the point of common coupling of the transformers asymmetrical. As the flux in a transformer is strictly proportional to the areas of the voltage waveform, the flux generated in transformer T, is asymmetrical by an amount

a

(1)

loor 0

As isys = i,

-300

then

Q.

-

1

i+zn

- 600

Abp,

-900 -1100 0

1

200m

600m

4OOm

800m

1

t,S

b

Fig. 7 Currents (phase c ) calculated during the sympathetic interaction occurring between two identical three-phase 180 M V A transformers in parallel a Offset magnetising current i, in transformer T, b Inrush current i, in transformer T,

of the sympathetic interaction can be seen clearly, with the inrush current i, decaying slower than that experienced by the ‘usual’ inrush current io (Fig. 8), which was lOOr

interaction addition

,

- - - ---_--------

=

or

t 1:;

-11001

0

1

200m

400m

600m

800m

1

t,s Fig. 8 Inrush current io calculated in the three-phase transformer of 180 M V A being energised without other transformers connected to the supply system

calculated assuming that there are no other trnasformers connected to the supply system. Note that the peaks of the offset magnetising current i,, the sympathetic magnetising current, reach values that are close to the full load

+ Rsysizl

dt

(3)

I

t+2n

Abp,

phase c

C(Rsys+ rpl)il

where Abpl. is the flux change per cycle in transformer T,, and rpl 1s the transformer winding resistance. The flux change per cycle Abpl creates an offset flux in transformer T,, which may drive it into saturation. As the flux in the transformer controls the magnetising current (via the B-H-curve), a corresponding offset magnetising current is generated that increases gradually from the steady state to a considerable magnitude when the transformer saturates fully. Note that the polarity of transformer saturation is determined by the sign of Abpl. This phenomenon, which is largely a function of the system resistance, will occur at any point in the system where the voltage exhibits some degree of asymmetry, so that any system transformer may be affected. Similarly, the flux change per cycle Abp2 in transformer T, can be given by

iz/envelope

326

+ i,

=

CRsysil + (Rsys+ rp2)i21 dt

(5)

where rp2 is the primary winding resistance of transformer T, . The effect of the flux change Ab,,, which can be seen to be a function of the resistances, IS to reduce the offset flux in the incoming transformer T, , producing the wellknown phenomenon of inrush current decay. This is because the polarity of Abp2 is opposite in sign to the initial offset flux in the transformer, which depends on the voltage switching angle and the value of the residual flux in the core at the moment of switching. From the analysis, it should be noted that the mechanism by which the magnetising current in a transformer already in operation rises gradually is analogous, but in I E E Proc.-Sci. Meas. Technol., Vol. 142, No. 4, July 1995

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the opposite direction, to the phenomenon of the transformer inrush current decay; the coupling between transformers T, and T, is established by the voltage drop across the system resistance Rsysisys,which is common in both eqns. 1 and 4. The inductance of the system appears to have no effect on the flux change per cycle and A4p2. However, this voltage drop reduces the instantaneous voltage on the busbar so that the total flux in the transformers is diminished. Consequently, both the currents i, and i, will be reduced as a second-order effect. From eqns. 3 and 5, it can be seen that, at the beginning of the transient, the flux change per cycle in both transformers T, and T, will depend mainly on the voltage drop caused by the inrush current i, as current i , is initially small and substantially symmetrical and therefore does not cause an appreciable flux change per cycle. There is a period of time, however, in which current i, begins to increase owing to the gradual saturation of transformer T I . In this period, the decay of the inrush current i, is somewhat reduced. This is because transformer T, becomes saturated with the opposite polarity to transformer T,, with the peaks of the currents i , and i, having opposite polarities, on alternate half-cycles. As a result, the voltage drop across the system resistance R,,, caused by the inrush current i, during one half-cycle is gradually cancelled by the opposite voltage drop produced by the rising offset magnetising current i, during the subsequent half-cycle. Thus, both the flux changes per cycle A4pl and AcPp2 will gradually decrease, which will cause currents i, and i, also to change slowly. The flux change per cycle becomes zero at some time. The offset magnetising current i, will then not increase further when [t+2nil dt =

-

(Rsys Rsys + rpl) [ + 2 n i 2 dt

(6)

From this point onwards, the polarity of inverts, and the offset magnetising current i, of T, begins to decay, behaving like the inrush current i, in transformer T, but with opposite polarity. Henceforth, the system resistance R,,, plays the paradoxical role of keeping both transformers saturated. The currents i, and i, will be concomitantly cause and efect of saturation in both transformers. That is, the voltage drop across the resistance Rsys produced by current i, during one half-cycle forces upwards the offset flux in transformer T, and so current i, tends to increase. In the following half-cycle, it is current i, that causes the voltage drop across Rsys,which turns up the offset flux in transformer T I ; hence, an increase in current i, is required. This sequence repeats, developing a phenomenon of ‘sympathy’ between the transformers in ‘sharing’ their saturation. This sympathetic interaction phenomenon will persist until the transformers reach their steady-state magnetising condition, which may be several seconds or perhaps even minutes later, depending upon the system parameters. It should be noted that, during this interaction, both decaying currents i, and i, have substantially the same mean value but with opposite sign. In other words, the direct component of the sympathetic current i, will balance the direct component of the inrush current i, . In this condition, the voltage on the busbar will be symmetrical, and the flux change per cycle in the transformers will depend on the effective voltage drop across the winding resistance of each transformer itself. This is IEE Proc.-Sci. Meas. Technol., Vol. 142, No. 4, July 1995

one of the reasons for finding prolonged inrush current in power systems supplying large transformers, as such transformers generally present a relatively small value of winding resistance. Typical envelopes of the sympathetic magnetising current i, and the inrush magnetising current i, are shown in Fig. 9. The inrush magnetising current i o ,

st

5)

u

t

\

inrush current 1 2 ( w i t h / sympathetic interaction) ‘-. /inrush current ig(without .---___-sympathetic interaction)

----- _ _ _ _ _ _ _

time sympathetic magnetising current

Fig. 9

* 11

Typical envelopes of transformer transient currents i o , i , and i ,

which is calculated assuming there are no other transformers connected to the supply system, is also shown for comparison purposes. 4

Interaction between transformers in series

Simulations and laboratory tests were also carried out to investigate the sympathetic interaction between transformers in series. Series here means that the primary winding of the first transformer is connected to the supply system, and its secondary winding feeds the transformer that is being energised. The transformers and the system parameters are similar to those used previously. With the unloaded transformer T, already connected to the supply system, transformer T, was energised by closing switch S connecting T, to the other winding of T , as shown in Fig. 10. Before each switching, transformer T, was demagnetised.

Fig. 10 System configuration used to investigate sympathetic interaction between transformers in series

The currents of phase c in two identical three-phase transformers of 180 MVA, 275166 kV, in series, are shown in Fig. 11. Note that transformer T, is energised from the low-voltage side. The results suggest that the interaction between series transformers is more than somewhat similar to the interaction occurring between the transformers in parallel previously discussed. Before switch S is closed (see Fig. lo), only the magnetising current i, of transformer T, is flowing through the system, i.e. isys = i,. When T, is energised, a transient inrush current i, flows through the secondary of transformer T,, producing a corresponding inrush current i; 327

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in the primary of T,. The current i; is added to current i, to yield the total current is,, which flows through the circuit formed by the supply system and the primary

The flux change per cycle A#,, will drive transformer T,, initially in the steady state, into saturation, with the offset magnetising current i, increasing gradually until the flux change per cycle A4sl becomes zero. In this condition,

i"'"

400 r

i, dt

200

-

i, dt

From this point onwards, the flux change per cycle A$,, inverts the polarity, so that the offset magnetising current i, starts to decay, developing the sympathetic interaction between transformers T I and T, . The rate of decay of the inrush current i, and, consequently, the rate of decay of the 'primary inrush current' i; are essentially determined by the flux change A$,, in transformer T, , which can be described by

0

Q .-

=

-200

-400 -600

I

i+2n

-8001 0

A4s2

I

200m

400m

600m

800m

1

t.5

(Rsys + rp1)isys + (rs1

4

2 =

~ + 2 n l ( R s y+s r p l )l'1

+ (rsl + rp2)i21 dt

-600 -1200

N ._

-1800

-3000 -2400

t /I'm

I

0

200m

J

600m

400m

+ rp2P21 dt

(11)

or

0

300r 0

Q.

=

800m

1

t,s 'b

400r

+ (Rsys + rpl)i; (12)

where r,, is the resistance of the secondary winding of T,, and rp2 is the resistance of the primary winding of T, connected to the secondary of T,. It should be observed that, when eqn. 10 is satisfied, the first two terms of eqn. 12 add to zero. In this condition, the flux change A@,, will depend basically on the voltage drop across the total resistance in the circuit formed by the secondary winding of T, and the primary winding of T, connected to T,. This indicates, paradoxically, that the total resistance in the primary side of transformer TI, i.e. R,, + r p l , does not contribute effectively to the decay of the inrush current in transformer T, during the sympathetic interaction.

200 Q.

-

c

5

0

I -2001 0

I

200m

400m

600m

8OOm

1

t ,s C

Fig. 11 Currents (phase c) calculated during sympathetic interaction occurring between two identical three-phase I80 M V A transformers in series Primary current,,i in transformer TI b Inrush current i, In transformer T, c Offset magnetising current i, in transformer T, U

winding of T,, thus

+

is, = i, i; (7) It should be noted that transformer T, sees the inrush current i, of T, as a load current. Also, note that the referred current i; is not calculated using merely the transformer ratio, as transformer T I is saturated. The flux change per cycle Absl in transformer T, can be given by AA1 =

or

328

s"iffl(Rsy,

+ ~ p l ~ ~ s dty s l

(8)

Conclusions

In this paper, the sympathetic interaction between transformers that takes place during the inrush transient has been investigated. This phenomenon is triggered by the voltage drop across the system resistance produced by the inrush current. The value of the total series resistance of the AC supply system has been found to be the determining factor in causing this interaction. This investigation has shown that, when the transformer is switched onto a system to which there are other transformers connected, the inrush current of the incoming transformer decays slower than generally expected when only one transformer is involved. Also, offset magnetising current of high magnitude in the transformers already connected to the system is generated owing to saturation. Prolonged inrush current associated with high offset magnetising current can lead to temporary harmonic overvoltages of long duration, causing serious problems to the operation of power systems. The impact and duration of sympathetic interaction will depend on the saturation levels reached by the transformers and the energy dissipation pattern in the system. This phenomenon should therefore be considered mainly when power system transients and insulation coordination are being studied. It is apparent that this interaction will become more significant as modern transformers with amorphous soft magnetic material or superconducting windings come into general use. I E E Proc.-Sci. Meas. Technol., Vol. 142, N o . 4, July 1995

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This interaction is greatly reduced if the series resistance of the supply system is small and also if the resistance of the transformer windings or that between the transformers is relatively large. The latter could represent the case where transformers are separated by an appreciable length of transmission line. 6

References

1 BLUME, L.F., CAMILLI, G., FARNHAM, S.B., and PETERSON, H.A. : ‘Transformer magnetising inrush currents and influence on system operation’, A I E E Trans., 1944,63, pp. 366-375

2 PENDLEBURY, B.: ‘Calculation of transformer inrush currents using a digital computer’, AEI Eng., 1967,7, (I), pp. 42-46 3 MACFADYEN, W.K., SIMPSON, R.R.S., SLATE, R.D., and WOOD, W.S.: ‘Method of predicting transient-current patterns in transformers’, I E E Proc, 1973, 120, (11), pp. 1393-1396 4 SONNEMAN, W.K., WAGNER, C.L., and ROCKFELLER, G.D.: ‘Magnetising inrush phenomena in transformer banks’, A I E E Trans., 1958,77, pp. 884-892 5 NAKRA, H.L., and BARTON, T.H.: ‘Three phase transformer transients’, I E E E Trans., 1974, PAS-93, pp. 1810-1819 6 STUEHM, D.L., MORK, A.B., and MAIRS, D.D.: ‘Five legged core transformer equivalent circuit’, I E E E Trans., 1989, PWRD-4, (3), pp. 1786-1793 7 GORMAN, J.M., and GRAINGE, J.J.: ‘Transformer modelling for distribution system studies, Part I : Linear modelling basics’, I E E E Trans., 1992, PWRD-7, (2), pp. 567-574 8 HAYWARD, C.D.: ‘Prolonged inrush currents with parallel transformers affect differential relaying’, A I E E Trans., 1941,60, pp. 10961101 9 PUENT, H.R., BURGES, M.L., LARSEN, E.V., and ELAHI, H.: ‘Energisation of large shunt reactors near static Var compensators and hvdc converters’, I E E E Trans., 1989, PWRD-4, (I), pp. 629-635 10 POVH, D., and SCHULTZ, W.: ‘Analysis of overvoltages caused by transformer magnetising inrush current’, I E E E Trans., 1978, PAS-97, (4), pp. 1355-1365

I E E Proc.-Sci. Meas. Technol., Vol. 142, N o . 4, July 1995

11 BRONZEADO, H.: ‘Transformer interaction caused by inrush current’. MSc Thesis, University of Aberdeen, April 1993 12 BRONZEADO, H., and YACAMINI, R.: ‘Sympathetic interaction between power transformers’. UPEC 29, Galway, 14-16th September 1994, pp. 236-239 13 ARTURI, C.M.: ‘Transient simulation and analysis of a three-phase five-limb step-up transformer following an out-of-phase synchronisation’, I E E E Trans., 1991, PWRD-6, (l), pp. 196-207 14 YACAMINI, R., and BRONZEADO, H.: ‘Transformer inrush calculations using a coupled electromagnetic model’, IEE Proc.-Sci. Meas. Technol., 1994,141, (6), pp. 491-498

7

Appendix

2000

-

1000 -

weak system inrush

A

-1 000

Fig. 12

sympathetic inrush with weak system

Sympathetic reaction

Effect of AC system strength on sympathetic reaction

329

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