low-voltage-side current-surge phenomena in single-phase distribution transformer systems

IEEE Transactions on Power Delivery, Vol. 3, No. 2, April 1988 63 7

LOW-VOLTAGE-SIDE CURRENT-SURGE PHENOMENA IN SINGLE-PHASE DISTRIBUTION TRANSFORMER SYSTEMS

Roger C. Dugan Stephen D. Smith

Canonsburg, PA Zanesville, OH

McGraw-Edison Power Systems Division Cooper Industries, Inc.

Senior Member, IEEE Member, IEEE

Abstract

L igh tn ing c u r r e n t s u r g e s en ter ing t h e secondary windings of distribution transformers can be a cause of t r a n s f o r m e r failure. Proposed solutions have included i n t e r l a c i n g t h e s e c o n d a r y windings and a p p l y i n g low-voltage arresters. Tes ts have been proposed t o verify t h e abil i ty of a transformer t o withstand these surges. Th i s paper shows t h a t t h e amount of cur ren t varies s i g n i f i c a n t l y f o r d i f f e r e n t s i z e s and des igns of transformers, loads, and secondary cables. I t is also shown that t h e en t i re secondary c i rcu i t must be treated as a sys t em. Measures taken t o p r o t e c t t h e t ransformer generally increase t h e surge voltage s t r e s s 011 t h e load equipment. The source of t h e problem is t h e voltage drop along the secondary cable. Minimizing that voltage can e f fec t ive ly alleviate t h e problem at both t h e transformer and load. These f a c t s must be taken in to consideration before developing transformer tes t standards to address t h e low-voltage-side current surge problem.

INTRODUCTION

The coupling of l ightning surge c u r r e n t s d i rec t ly in to t h e secondary c i rcu i t of a distribution transformer through t h e grounding leads has been recognized for many y e a r s [ 1 , 2 1 . More recently, repor t s on t h e suscepti- bi l i ty of distribution transformers t o these surges have b e e n p u b l i s h e d wi th t h e c o n c l u s i o n t h a t f a i l u r e s a s s o c i a t e d wi th t h e s e s u r g e s can be minimized by i n t e r l a c i n g t h e s e c o n d a r y windings o r by app ly ing low-vol t a g e a r r e s t e r s [ 3 , 4 1 . Subsequently, t e s t s have b e e n p r o p o s e d t o e v a l u a t e t h e s u s c e p t i b i l i t y of distribution transformers t o these surges.

One proposed tes t is t o in jec t a 5 k A cur ren t surge in to t h e midpoint of t h e secondary of t h e distribution t ransformer , result ing in 2 . 5 k A in each half of t h e winding. After conducting several of these tes t s , i t w a s obse rved t h a t t h e r e is a l a r g e d i f f e r e n c e in impedance between d i f fe ren t designs of transformers. In par t icu lar , transformers with non-in t er lac ed secondaries o f f e r several times more impedance t o surge cur ren ts t han d o t ransformers with interlaced secondaries and transformers pro tec ted by low-voltage arresters. Also, there were significant differences in impedances between d i f f e r e n t ratings of transformers. Because t h e higher impedance transformers required an unusually high surge genera tor voltage t o obtain a 5 k A cur ren t surge, i t was suspected tha t they would see much less surge cur ren t in normal service. Therefore, a study was undertaken t o analyze t h e typical distribution transformer system and d e t e r m i n e r easonab le s u r g e c u r r e n t leve ls for each transformer. The resu l t s of this analysis a r e presented in this paper.

86 T&D 553-2 A p a p e r recommended and a p p r o v e d hy t h e I E E Z T r a n s f o r m e r s Commit tee o f t h e I E E F Power E n g i n e e r i n g S o c i e t v f o r p r e s e n t a t i o n at t h e IF:E‘?/PFS 1986 T r a n s m i s s i o n a n d D i s t r i h u t i o n C o n f e r e n c e , ,Anaheim, C a l . i f o r n i a , S e p t e m h e r 14 - 19, 1936. ! lanuscr ip t s u h m i t t e d ‘larch 2 1 , 1986; made a v a i l a h l e f o r p r i n t i n g June 18, 1986.

T h e distribution transformer system is a Complex, t ightly coupled system with respect t o low-voltage-side cur ren t surges. That is, changes in one component in t h e sys tem can have a s i g n i f i c a n t effect on t h e o ther componen t s . T h e c i r c u i t must be considered as an i n t e r c o n n e c t e d s y s t e m o f e l e m e n t s i n which t h e distribution transformer is only one part. In f a c t , t h e s e c o n d a r y cable is, perhaps, more influential in this c i rcu i t than t h e transformer. Any proposed distribution transformer t e s t standard must recognize t h i s si tuation.

The model f o r t h e simulation is presented f i r s t , f o l l o w e d by a d i s c u s s i o n of t h e r e s u l t s of t h e simulations and their consequences.

Fig. 1. Single-phase overhead transformer installation . THE SYSTEM

The system under consideration is shown in Figure 1. Lightning surge cur ren ts can enter t h e secondary c i rcu i t through either strokes t o t h e primary l ine o r strokes d i rec t ly t o t h e secondary circuit . For strokes t o t h e primary, t h e cur ren t is conducted t o t h e secondary as shown in Figure 2.

LIGHTNING PRIMARY L I N E ,I,

3 LOAD

TRANSFORMER SECONDARY x i C A B L E

1’ GROUND

‘I

GROUND 1 - HOUSE

Fig. 2. Surge cur ren t entering secondary c i rcu i t due to l ightning s t r i k e t o primary.

0885-8977/88/0400-0637$01 .WO 1988 IEEE

638

The bulk o f t he current is conducted through the surge a r r e s t e r t o the junction of t he pole ground lead, t h e X2 bush ing on t h e t ransformer, and the neutral on the secondary cable. Some of t h e current is conducted on the primary line. The current reaching the junction of t he g r o u n d s a t t h e top of t he pole divides between the various paths according t o the impedances.

As shown, some of t he current will flow into the transformer secondary and, also, into the load. This is t h e c u r r e n t t h a t c a u s e s t h e t r a n s f o r m e r v o l t a g e s described by McMillen, et. al. [31. I t a lso causes high vol tage s t r e s s across t h e load and, presumably, fa i lures of secondary load equipment. However, t he authors a r e not aware of any work tha t has been done t o co r re l a t e l i g h t n i n g f a i l u r e s of customer appliances with these surge phenomena.

Essentially the same phenomena occur for s t rokes t o the secondary circui t as shown in Figure 3. The exact current division is dependent on t h e s t roke location.

H 2 L - ---A

HOUSE - GROUND G R O U N [

Fig. 3. Surge current entering secondary circui t due t o l ightning s t r ike to secondary cable.

In t h i s a n a l y s i s , b o t h t y p e s of s t r o k e s were simulated. However, most of t he work was done with the s t roke t o t h e primary and t h e resul ts reported here come from tha t work. It is believed that this is the more common way fo r low-voltage-side current surges t o occur.

SYSTEM MODEL

The model for t he system is shown in Figure 4. This sys t em was r e p r e s e n t e d on t h e METAP program, a g e n e r a l - p u r p o s e p r o g r a m f o r t h e s i m u l a t i o n of e l e c t r o m a g n e t i c t r ans i en t s [51. A description of t h e model of each element of t he system follows.

LIGHTNING CURRENT SOURCE (8 x 20) SECONDARY

SURGE (See Fig. 6) (See Fig

ARRESTER

POLE GROUND L E A D

POLE GROUND RESISTANCE

HOUSE GROUND

HOUSE GROUND

RES I STANCE

Fig. 4. System model fo r simulations

Transformer Model

T h r e e d i f f e r e n t s i z e s o f t r a n s f o r m e r s w e r e simulated: 10, 25, and 50 kVA, al l rated 7200/12470Y - 120/240 volts. So tha t t h e voltage distribution within t h e t r a n s f o r m e r cou ld be observed, t he transformer windings were broken into ei ther 9 o r 1 0 groups o f winding layers and represented as coupled inductors. The capaci tances between the primary winding layers were a l s o represented. A sensit ivity analysis showed that t he capacitances in t he secondary had minimal e f f ec t on the waveforms for low-voltage-side current surges and these capacitances were neglected. Figure 5 shows the cross sect ion of t he construct ion of t h e t ransformers and Figure 6 shows the typical model schematic.

CORE

P * P R I M A R Y WINDING S1 = SECONDARY WINDING 1 52 = SECONDARY WINDING 2

Fig. 5. Cross-section of shel l - type distribution transformer construct ion.

x2'

Fig. 6. Model of transformer used in this s tudy; non- inter laced con nec t ion shown.

Because of limited space, we will present only the 10-kVA model here. The problem is more pronounced with t h i s s i ze of t r a n s f o r m e r and t h e general principles apply t o the other sizes as well. The primary winding was broken i n t o 10 winding g roups . Each 120-vol t secondary winding was broken into two pa r t s so that interlacing could be represented simply by al ter ing the connections of t h e terminals.

Brief ly , t h e general procedure for developing the coupled inductance model is as follows:

1. Compute t h e short c i r cu i t ( leakage) reactance, Xs,, between each pair of winding groups (45 different values for 1 0 winding groups).

2. Choose one winding group a5 a reference and build the so-called "Zbus" matrix [SI, which we wil l ca l l x b because i t is purely react ive in this case. If winding group one is chosen as a reference, t h e elements of t he matrix can be determined as follows:

Diagonal elements:

N = number of groups

Subscripts on X S c refer t o winding group.

639

3 .

O f f-di agonal el emen t s:

X b i j = L 2 (Xbii + X b , j - x ~ C i + l , j + l )

Convert the x b matrix to nodal admit tance form for use in general-purpose transients program. T h i s i s d o n e by a s imple power- invar ian t transformation of reference frame [61.

i * J

The & matrix will be of order N-1 while the nodal admit tance form will be of order N . One must be careful t o compensate for tu rns ratios throughout this process. The authors prefer t o build x b in per unit quantit ies and then compensate each element of t he nodal admit tance form.

The gamma m a t r i x , which is t h e inverse of the inductance matrix, for the 1 0 kVA transformer model is given in the appendix. This can be used in a general- purpose electromagnetic transients program t o allow the interested reader t o dupl icate the si mulat ions presented in this paper.

The i n d u c t a n c e s and capac i tances determined by conventional transformer design formulae were found to be q u i t e a c c u r a t e for the type of transient analysis performed. However, the apparent winding resistance at the transformer's natural frequency must be determined e m p i r i c a l l y . This was done by comparing surge tes t r e s u l t s with c a l c u l a t e d r e s u l t s and a d j u s t i n g t h e resistance for t he best match. The model verification fo r the 10-kVA transformer was performed using the tes t c i r c u i t shown i n F i g u r e 7 , which r e s u l t e d i n t h e transient voltages shown i n Figure 8a. The best match was obtained with approximately 6000 ohms of resistance in the primary winding. The result ing waveform is shown i n Figure 8b. As can be seen, t he model very accurately d u p l i c a t e s t he measured t r a n s i e n t response of t he t r a n s f o r m e r . T h e o n l y e x c e p t i o n s a r e the minor o s c i l l a t i o n s i n t h e f i r s t p a r t of t h e low-vol tage winding waveform. These o s c i l l a t i o n s a r e due t o capaci tances i n the secondary windings or in t he surge tes t generator, which were not modeled.

ziaJ--

I I TEST WAVEFORM 1 AMPERE

Fig. 7. Test c i rcu i t for transformer verification.

Secondary Cable Model

B o t h t h e c o n s t r u c t i o n and t h e l e n g t h of t he secondary cable were found to have significant influence on the results. Only the series impedance of the cables was found to be important. Our investigations did not show any significant influence of the cable capaci tance and, therefore, it was neglected.

Perhaps, t he two most common types of secondary cable used in overhead transformer installations a re the t r i p l e xed c a b l e and the v e r t i c a l 1 y-spaced open-wir e types shown in Figure 9. Both of these types were modeled using a coupled se t of three lossy inductors. The impedances were computed in the same manner as a t h r e e - p h a s e t ransmiss ion l ine with earth return [71. R e s i s t a n c e and inductance matrices for two types of cable used with 10-kVA transformers a re given in the appendix.

In addition. a shielded cable was investieated. I t was assumed t h a t t he c a b l e would have ympedance c h a r a c t e r i s t i c s similar t o the triplexed cable except that the se l f inductance of the neutral , or shield, would be equal t o t h e mutual inductance between each phase conductor and shield.

48 MIDPOINT OF PRIMARY WINDING

Ai P -X3 TERMINAL

1 3 . 8 VOLTS -ku 1 I 1 0 2 5 50 75

Y S

(a) Measured transformer response.

I -I 0 2 5 50 7 5

JJS

(b) Computed response of the model.

Fig. 8. Comparison of measured and computed wavefom for t he t e s t c i rcu i t in Figure 7.

0 -+ 2 T R I P L E X E D CABLE V E R T I C AL LY -SPAC E D

OPEN-WIRE CABLE

Fig. 9. Two types of secondary cable considered in this study.

Load Model

The load was assumed to be 50 percent motor load and 50 percent resistive load connected as shown in Figure 10. The motor load was represented as an inductance in series w i t h a resistance. At the frequency of in te res t , t h e inductance dominates the impedance and is such a high value w i t h respect t o the other inductances in the c i r c u i t t h a t i t e f fec t ive ly blocks the flow of surge currents. The to ta l load was varied from 1 0 percent t o 100 percent of t he transformer's rating. At times, the load was assumed t o be shor t circuited by insulation flashover.

1 L t t I 120VI

2 4 0 V 120vi RES1 STlVE MOTOR

RESISTIVE MOTOR LOAD LOAD

Fig. 10. Load model used in this study.

640

Other Models

T h e g r o u n d l e a d s were r e p r e s e n t e d as lossy inductors, having an inductance of 0.4 microhenries per foot and a resistance of 260 micro-ohms per foot. A 15 f t (4.6 m ) pole ground lead and a 5 f t (1.7 m ) house ground lead were assumed.

'The grounding resistances at the pole and the house were both assumed t o be 25 ohms for most of the investigations.

The surge arrester was assumed to have a discharge vol tage of 39 k V and was represented by a simple, two - s 1 ope v o 1 t age cu r r en t characteristic. The primary distribution line was represented by a surge impedance of 400 ohms. A mid-line stroke was assumed, which would see this impedance in both directions. Hence, a 200-ohm value was used in the simulations. The results were not very sensitive to variations in the surge arrester and line models, but both models should be present in some form t o provide a path for the small amount of current t ha t f lows i n t he transformer primary winding as a result of sl ight mismatches in the ampere-turn balance i n t he secondary windings. Also, the surge arrester discharge voltage biases the voltage across the primary winding layers so that the ground-end layer is stressed higher than the line-end layer in transformers without inter laced secondaries.

SIMULATION RESULTS

Effects of Interlacing Transformer Secondaries

Figure 11 shows a comparison of voltage and current w a v e f o r m s c o m p u t e d f o r b o t h i n t e r l a c e d and non-interlaced transformers. The transformer was rated 1 0 k V A and was f u l l y loaded using the load model previously described. A 10-kA 8 X 20 microsecond l igh tn ing s t roke current was applied to the primary circuit. Note that the peak current in the interlaced t r a n s f o r m e r i s m o r e t h a n t w i c e t h a t i n t h e non- in te r laced transformer. For this particular case, the non-interlaced transformer would be expected to see approximately th ree percent of the lightning stroke current i n each half of the secondary winding.

VOLTS QROUNO-END FIRST LAYER FLTAQE

-MEMACE0 WlNDlNQ

VOLTS LOAD VOLTAQE

NoN-.NlERLAcED WINDING

SECONDARY CURRENT

INTERLACED WINDING

Fig. 11. Comparison of computed voltage and current waveforms for interlaced and non-interlaced secondary

windings for a 10-kVA transformer, 10-kA 8x20 surge; 65-ft. triplexed cable, 100 percent load.

TRANSFORMER SECONDARY WIND IN G INTERLACED

131rH

NON-INTERLACE0 170pH

SECONDARY CABLE 90-250pH

LOAD 5-50 OHMS

90-250pH !5 OHMS 25 OHMS

Pig. 12. Redrawn equivalent circuit showing the surge current paths more clearly.

This is a typical resul t of comparisons between inter 1 aced and non- inter 1 aced t r an sf or mew. The current division dur ing the cr i t ical part of the transient is governed by t h e inductances of the circuit and the differences in response of the two types of transformers can be easily explained in terms of these inductances. The circuit is redrawn in Figure 1 2 t o help visualize the phenomena. The l ightning surge current flowing toward the house ground in this problem sees three parallel paths: the secondary cable neutral and the two paths through the transformer secondary and load. Note the polarity of the transformer windings with respect t o the direction of current flow. The bulk of the current flows in the secondary cable neutral, causing a large vol tage drop across the length of the cable neutral conductor. This voltage is the determining factor in the amount of current that flows through the other two paths (Figure 13). The inductances limiting the currents in t h e s e two p a t h s a r e t h e secondary- to-secondary inductance of t he t ransformer , the secondary cable inductance, and the back emf due t o the mutual coupling of the phases of the secondary cable with the neutral. Note that i f the secondary cable is short , or that i f the mutua l ly coupled voltage is nearly equal t o the vol tage drop in the neutral, l i t t l e current will flow through the transformer and load.

I I

CURRENT PATH

WINDING 1 , $t7 WINDING CURRENT CURRENT

x 1 x 3 I * I I

THROUGH TRANS FORMER

AND LOAD

1 LOA0

I

Fig. 13. Detail of the boxed area in Figure 12, showing how the secondary cable voltage drop

determines the amount of current in the transformer and load.

64 1

r h e s e c o n d a r y - t o - s e c o n d a r y i n d u c t a n c e of t h e non-interlaced transformer is on the same order as t he secondary cable inductances, while t he inductance of t h e i n t e r l a c e d t r a n s f o r m e r is approximately an order of m a g n i t u d e l e s s . T h e r e f o r e , t h e c o m b i n a t i o n o f n o n - i n t e r l a c e d t r a n s f o r m e r a n d c a b l e o f f e r s a p p r o x i m a t e l y tw ice t h e inductance to the l ightning s u r g e c u r r e n t a s does the combination of interlaced transformer and cable. When high cu r ren t s can flow, due t o e i t h e r h i g h l o a d o r s e c o n d a r y f l a s h o v e r , t h e interlaced connection will typically allow twice as m u c h current t o flow.

The c u r r e n t s i n t h e secondary windings a re not perfect ly balanced because of differences in impedances o f the secondary windings. The interlaced transformer has more nearly balanced secondary winding impedances than does the non-interlaced transformer. Differences in the ampere turns between the secondary windings a r e made up in t he primary winding.

As e x p e c t e d , t h e vol tage s t r e s s across the f i r s t l a y e r ( g r o u n d e d end) of t he primary winding of t he i n t e r l a c e d t r a n s f o r m e r is much lower t h a n i n t h e n o n - i n t e r l a c e d transformer. I t is proportional t o the primary arrester discharge voltage by the rat io of t he t u r n s i n t h e f i r s t l a y e r t o t h e t o t a l turns on the winding. The voltage in the non-interlaced transformer osci l la tes a t the natural frequency of t h e transformer and se t t l e s out a t a value proportional t o t h e arrester d i s c h a r g e v o l t a g e ( s e e F i g u r e 11). No te tha t t h e a r r e s t e r discharge voltage adds t o the induced transient voltage at t he end of the winding shown, which is the grounded end. The transient layer-to-layer voltage a t the l ine end of t he winding is in t he opposite polarity with respect t o the arrester discharge voltage, w h i c h r e s u l t s i n somewhat lower voltages. This may help explain w h y failures due t o this surge phenomenon a r e f o u n d more f r e q u e n t l y a t t h e grounded end of the winding.

The vol tage across the load is proportional t o the surge current flowing into the load and is higher when the transformer has in t er 1 aced secondary win din gs.

E f f e c t of Low-Voltage Arresters

The simulations show that placing a r r e s t e r s across the s e c o n d a r y winding is e f f e c t i v e i n l imi t ing the vol tage within the transformer fo r this type of surge. The voltages induced in t h e primary a re approximately p r o p o r t i o n a l , by the turns ra t io , t o t h e low-voltage a r r e s t e r d r o p and would n o t be e x p e c t e d t o va ry s ignif icant ly for reasonable increases in surge current magn i tudes . Thus , i t would appea r t h a t this is an effect ive al ternat ive t o inter lacing secondary windings where abnorma l ly high secondary surge cu r ren t s a r e expected.

However , t h e l o w - v o l t a g e a r r e s t e r s o f f e r no protect ion for t he load. In f ac t , arresters applied t o non-inter laced transformers will actual ly increase the voltage s t r e s s on the load t o approximately t h e same level as would an interlaced transformer. This may not be intuit ively obvious because the arresters would seem t o be close enough t o the load t o protect it as well as t he transformer from t h e surges that a r e character is t ic of this problem. However, t h e arrester is not connected across the load, but is actual ly in series with the load and the surge current path. This may be seen by adding a r r e s t e r s t o the redrawn circui t diagram as shown i n Figure 14. The arresters simply bypass the transformer, removing i ts impedance from t h e current path. Thus, more c u r r e n t can f low t h r o u g h t h e l o a d because o f t he reduction in c i rcui t impedance.

In s h o r t , add ing low-vo l t age a r r e s t e r s t o t h e circui t has approximately the same a f f ec t on the system as interlacing the transformer secondary windings.

PRIMARY VOLTAGE ARRESTER - I 1

- >OLE GROUND

ARRESTERS BYPASS SURGE CURRENTS AROUND TRANSFORMER'S IMPEDANCE

3 +HOUSE GROUND

Fig. 14. The e f f ec t of low-voltage a r r e s t e r s on t h e secondary dis t r ibut ion system for low-voltage s ide

current surges.

E f fec t s of Load

As shown in Figure 2 , the current that flows through the transformer secondary must a lso flow through the load . Therefore, t he load magnitude is a determining f a c t o r in the amount of current that can flow. Figure 15 shows how the peak current i n t he transformer varies as a function of load. A 10-kVA transformer with a 65 f t ( 2 0 m ) tr iplexed secondary cable, consisting of a 50 f t span and 15 f t lead, was assumed for developing this curve. The load was assumed t o be 50 percent resist ive and 5 0 percent motor load as described previously.

0.0 0.2 0.3 0.4 0.8 1.0

L O A D , PER UNIT

Fig. 15. cu r ren t as a function of load, 10-kVA transformer,

Variation of peak transformer secondary

65-f t. t riplexed cable.

642

The peak voltage s t ress in t he primary windings of t he n o n - i n t e r l a c e d t r a n s f o r m e r w i l l g e n e r a l l y b e p r o p o r t i o n a l t o t h e cur ren t , although there is some decrease in the proportion as t he load increases due t o c h a n g i n g r a t e s - o f - r i s e i n t h e c i r c u i t . The primary winding l a y e r s t ress in the interlaced transformer is relatively insensitive t o the change in current because the discharge voltage of t he primary a r res te r reflected t h r o u g h the winding is much larger than the voltage induced from the secondary surge current ( a t least for l ightning strokes in t he 10-15 k A range).

The limiting values of current in this case occur when the load is short-circuited. They a re 4.6 percent i n e a c h half of t h e winding for the non-interlaced t r a n s f o r m e r a n d 1 2 p e r c e n t f o r t h e i n t e r l a c e d transformer. These limiting values a re sensitive t o the secondary cable length, as described in t he next section o f this paper.

The peak voltage across the load corresponding to the current variation of Figure 15 is shown in Figure 16. A s expected, t h e use of the interlaced transformer r e s u l t s i n s u b s t a n t i a l l y higher voltage s t r e s s across t h e l o a d f o r most of the load range. Both curves a p p r o a c h t h e same o p e n - c i r c u i t va lue as t h e load approaches zero.

The open-circuit (no load) voltage is t he voltage drop across the secondary cable neutral less t he voltage induced i n t he phase conductors by mutual coupling. The induced voltage i n t he secondary cable is substantial and the mutual coupling must be represented for accura te simulations of this phenomenon.

From t h e s e two c h a r t s , i t is observed that the transformer is more at risk when the load is high, or when the secondary flashes over, and the load appliances a r e more at risk when the to t a l resistive load is small.

E f f e c t s of Secondary Cable Length

The real cu lpr i t i n t he system with respect t o this surge problem is not the transformer, and i t s design, nor t he load magnitude, but the secondary cable. The amount of current that flows through the transformer and load is dependent on t h e net voltage drop across the secondary cable.

1.4

I- z 0.6 a 0

w

E ti O.€ c) z o I-

0.4

a K

*

L 2

0.2

0.0 0.0 0.2 0.4 0.6 0.8 1.0

LOAD, PER UNIT

Pig. 16. Variation of peak load voltages as a funct ion of load, 10-kVA transformer, 65-ft. tr iplexed cable.

Of course, this drop across the secondary cable is a f u n c t i o n of length . To study the e f f ec t s of cable length, a short-circuited load was assumed because this yields the worst case in terms of current magnitude i n t he s e c o n d a r y . Of par t icu lar interest here a re the c u r r e n t m a g n i t u d e , t o w h i c h t h e l o a d s t r e s s is proportional, a n d the voltage across the f i rs t layer o f the primary transformer winding. Figure 17 and 18 show the results for t he 1 0 - k V A non-interlaced transformer considered throughout this paper.

9.0

LENGTH, FT

Fig. 17. Variation of maximum transformer secondary current as a funct ion of secondary cable length;

non-interlaced 10-kVA transformer.

3.0

5 K

0 W

5 2.5

P ti 2.0 (3 L I-

f 1.5

IL

5

1;

1.0 W

0.5

0.0 0.0 200.0 400.0 600.0 81 b.0 1000.0

LENGTH. FT

Fig. 18. Variation of t he peak vol tage across the f i r s t grounded-end layer of a 10-kVA transformer primary winding, as a funct ion of cable length.

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w o u l d r e d u c e t h e t r a n s i e n t v o l t a g e s on b o t h t h e transformer and load simultaneously. Surrounding the two phase conductors w i t h the ground conductor w i l l provide very c lose mutual coupling between the ground and phase conductors. Therefore, t he induced voltage in t he phase c o n d u c t o r s is approximately equal t o the i n d u c t i v e d r o p i n t h e n e u t r a l . The net d i f fe ren t ia l voltage forcing current through the transformer and load is the resistive voltage drop, which should be much lesy than with either triplexed o r open-wire cable. I n t e r e s t i n g l y , t h i s is one of t h e s o l u t i o n s t o the problem of secondary surge cur ren ts proposed by Bryant and Newman in 1 9 4 2 [21.

Effec t s of Multiple Customers

The general e f fec t of having more than one customer on the same transformer is t o reduce the s t ress on both the transformer and the loads. Consider t he case of two houses on one transformer and compare it t o t he case of one house per transformer. Assuming equal grounding r e s i s t an ce s t h rough out t he ci r c u i t , ap p r ox i mat el y 3 3 percent of t he lightning surge current w i l l travel in each of the three available paths: the pole ground and the two house grounds. In cont ras t , 50 percent of the current flows in each path when there is only one house per transformer. Therefore, having multiple houses on a t r a n s f o r m e r r e s u l t s i n l e s s vol tage drop across the secondary cables because the surge current is dispersed. This , i n t u r n , r e s u l t s i n l e s s current being forced through the transformer secondary than for t he case with only one house per transformer.

Tne current magnitude increases somewhat less than linearly for the first 400 feet , and then approaches a limiting value. The transformer voltage also increases, b u t is l e s s than p r o p o r t i o n a l t o t h e i n c r e a s e i n cur ren t , and eventually begins to decrease as t he cable ge ts longer. Although more current is being forced into the transformer secondary by the longer cable, t he s lope of the current is modified by the different inductance- to-resistance ratios of t he to t a l system at each cable length, result ing in less induced voltage than might be ex pec t ed.

Assuming equal ground resistance at the pole and at the house, i t appears that this particular transformer sees no more than about 6.8 percent of t he lightning s t roke current in each half of the secondary winding. In the same c i rcu i t , the interlaced connection of this transformer sees up t o about 16 percent of the stroke c u r r e n t i n e a c h h a l f , which is approximately equal sharing of current between the three paths leading to the house.

E f fec t s of Secondary Cable Type

F i g u r e 19 shows t h e ne t v o l t a g e d r o p i n t h e secondary cable c i rcu i t ( i .e. , t he open-circuit voltage across the load) for th ree types of cable. The resultant secondary surge current and primary winding voltage for 100 percent load a re also shown.

NET DIFFERENTIAL VOLTAGE IN SECONDARY CABLE

TRIPLEX

SHIELDED

SURGE CURRENT IN SECONDARY WINDINGS ( EACH HALF)

15

k V

VOLTAGE ACROSS FIRST LAYER OF PRIMARY WINDING

PRIMARY ARRESTER (REFLECTED TO DISCHARGE FIRST LAYER ) VOLTAGE

Effec ts of Grounding Resistance

The fundamenta l d iv is ion of the lightning surge c u r r e n t s i n t h e c i rcu i t is determined by the ground res i s tance at the various grounding points. There a re s o m e c h a n g e s i n w a v e f o r m f o r d i f f e r e n t g round r e s i s t a n c e s , b u t , i n g e n e r a l , t h e c u r r e n t i n t h e secondary cables can be accurately determined by direct p r o p o r t i o n based on grounding resistance differences from a known case.

The better t he pole ground with respect t o the house ground, the more protected a re the transformer and load. Ideally, the pole ground should be much be t te r than the house ground and divert most of t he surge current away from the load. Of course, this is not always achievable and, in f a c t , nearly the opposite occurs in some cases. In some areas it is d i f f icu l t t o achieve pole grounds t h a t a r e s i g n i f i c a n t l y b e t t e r than house g r o u n d , especially when the house ground is also at tached t o the municipal water system or a deep water well. I n such cases, much of the lightning current is diverted t o the house ground, imposing greater voltage stresses on the transformer and load. It would seem tha t t he homeowner would be well-advised t o ins ta l l a low-voltage a r res te r a t the service entrance.

CON CLUS IONS Fig. 19. Comparison of th ree secondary cable types, 10-kVA transformer, 10-kA 8x20 surge, 65-ft. cable,

100 percent load.

The open-wire secondary cable develops more net voltage and allows more surge current t o flow i n the t ransformer and load than the same length of triplexed cable. This is due to the higher inductance that results from greater spacing between conductors and the lower mutual coupling between wires.

The shielded cable develops a small net voltage, which is e s s e n t i a l l y t h e r e s i s t i ve d r o p a c r o s s t h e neut ra l conductor . Not only is the current that resu l t s from this voltage smaller than either of t he other two t y p e s , bu t t he r a t e - o f - r i s e is dramatically reduced, r e s u l t i n g i n a s imi la r r e d u c t i o n of induced voltage within the transformer. Thus, the use of shielded cable

C o n c e r n i n g p roposed t e s t levels for low-voltage c u r r e n t s u r g e s i n distribution transformers, it would appear t o be inappropriate t o specify a single current magn i tude for a l l transformers. The amount of surge c u r r e n t t h a t passes t h r o u g h t h e t ransformer varies s i g n i f i c a n t l y with the design and k V A rating of t he transformer. The current tha t flows is not a cons tan t , but is determined, primarily, b y the net differential mode voltage drop across the secondary cable and, also, by the impedances of t he transformer, cable, load, and ground.

Sm a1 l e r - s i z ed t r a n s f o r m e r s w i t h i n t e r1 a c e d secondaries or low-voltage a r res te rs will typically pass t w i c e a s much s u r g e c u r r e n t as c o n v e n t i o n a l , non-interlaced designs of the same rating. The 10-kVA transformer described i n this paper would typically see

644

less than 7 percent of t h e l ightning s t roke cur ren t in each half of t h e secondary winding (14 percent t o t a l in t h e s e c o n d a r y ) when t h e secondary windings a r e not i n t e r l a c e d . I n t h e i n t e r l a c e d c o n n e c t i o n , t h e same transformer would be expected t o see nearly 16 percent of t h e l ightning s t roke cur ren t in each half (33 percent t o t a l ) . The l a t t e r f i g u r e is t h e theore t ica l limiting value assuming equal division of t h e s t roke cur ren t in t h e secondary cable and between pole and house grounds.

2 5- k V A and 5 0- k V A non- inter 1 aced transformers w i 11 a l l o w m o r e c u r r e n t t o f l o w t h a n t h e 10-kVA n o n - i n t e r l a c e d t r a n s f o r m e r because of t h e i r l ower i m p e d a n c e s . In f a c t , t h e impedance of a 50-kVA transformer is relatively insignificant when compared t o t h e c a b l e impedance and t h e s u r g e c u r r e n t i n t h e t r a n s f o r m e r a p p r o a c h e s t h e t h e o r e t i c a l limit. This f a c t , in combination with different distributions of t h e t u r n s i n larger-kVA t r a n s f o r m e r s may e x p l a i n why r e s e a r c h e r s have reported tha t transformers tha t a r e 50-kVA, o r l a r g e r , a r e essentially immune t o fa i lure from low-voltage-side current surge phenomena. Another f a c t o r might be tha t these transformers a r e generally connected t o more than one secondary load, which our s t u d i e s i n d i c a t e would decrease t h e voltages induced within t h e transformers.

T h e s y s t e m c o n s i s t i n g o f t h e d i s t r i b u t i o n transformer and load has a complex response t o l ightning s u r g e s a n d is v e r y s e n s i t i v e t o c h a n g e s i n t h e charac te r i s t ics of t h e components of t h e system. Changes t o t h e transformer cannot be considered without also considering t h e e f fec ts of t h e changes on t h e rest of t h e sys t em. F o r example, p ro tec t ing t h e transformer insulation by interlacing t h e transformer secondaries o r by a p p l y i n g low-vol t a g e a r res te rs will approximately double t h e voltage s t r e s s on t h e load for t h e smaller t r a n s f o r m e r s i z e s . The o n l y s o l u t i o n found t h a t minimizes t h e problem in a l l areas of t h e system is t o use shielded secondary cable tha t has adequate mutual coupling between t h e neut ra l and phase conductors. This minimizes t h e s u r g e c u r r e n t s by r e d u c i n g t h e n e t d i f f e r e n t i a l v o l t a g e induced by t h e l ightning surge cur ren ts flowing in t h e cable neutral.

Other general trends found in this analysis include:

1. The transformer is more susceptible t o fa i lure when t h e load is high, o r is shor t circuited, than a t low load.

2. The load is more suscept ib le t o fa i lure a t low load levels.

3. T o m i n i m i z e p r o b l e m s t o b o t h l o a d a n d transformer f o r low-voltage-side cur ren t surges,

a. Secondary cables should be kept as shor t as poss ib l e ( a sh i e lded s e c o n d a r y c a b l e is desirable).

b. Every a t tempt should be made t o achieve a be t te r pole ground than house ground.

c. Having multiple houses fed from t h e same t r a n s f o r m e r helps by fur ther diluting t h e 1 i gh tn ing s u r g e cu r ren t in t h e secondary cab 1 es.

d. W h e r e t h e s e c o n d i t i o n s c a n n o t b e prac t ica l ly achieved, protection of t h e load wi th low-vo l t age a r res te rs would a l so be advisable.

The distribution transformer is only one element in a complex system consisting of transformers, a r res te rs , s e c o n d a r y c a b l e s , po le grounds , house grounds, and l o a d s . Transformer t e s t standards must recognize this fac t .

REFERENCES

1. K . D. Beardsley, W. A. McMorris, H. C. Stewart , "Voltage Stresses in Distribution Transformers Due t o Lightning Curren ts in Low-Voltage Circuits," AIEE Transact ions, Volume 67, 1948, pp 1632-1635.

2. J . M. Bryant, V. Newman, "Abnormal Curren ts in Distribution Transformers Due t o Lightning," AIEE Transactions, Volume 61, 1942, pp 564-8.

3. C. J. VcMillen, C. W. Schoendube, D. W. Caverly, " S u s c e p t i b i l i t y of D i s t r ibu t ion T r a n s f o r m e r s t o Low-Voltage S ide Lightning Surge Failure," IEEE Transactions on Power Apparatus and Systems, Vol. PAS-101, No. 9 , September 1982, pp 3457-3464.

4. Surge Charac te r i s t ics and Protection of Distribution Transformers, EPRI EL-3385, Pro jec t 1532-1, Final R e p o r t , E l e c t r i c Power Research Ins t i tu te , Palo Alto, CA, January 1984.

5. S. N . Talukdar, "METAP - A Modular and Expandable Program for Simulating Power System Transients," IEEE Transactions on Power Apparatus and Systems, Vol. PAS-95, Nov/Dec 1976, pp 1882-1891.

S tagg and El-Abiad, Computer Methods in Power System Analysis, iVlcGraw-Hill Book Company, 1968, Chaps 3 and 4.

6.

7. E l e c t r i c a l Transmission and Distribution Reference Book, Central Station Engineers of t h e Westinghouse E l e c t r i c C o r p o r a t i o n , East Pit tsburgh, P4, 1964, Chap 3.

APPEND I X

Transformer Model Data

The transformer is modeled as a couple s e t of lossy i n d u c t o r s as shown in F igu re 6. The gamma matrix ( i n v e r s e of t h e i n d u c t a n c e m a t r i x ) f o r t h e 10 kva transformer in lower tr iangular form is: -

185.0

2.388 -15 .31 1.326 ( h y - l x 1000) -233.5 517.8

- .6256 3 .811 - .9121 1.514 .06838 - .6003 .1968 -.9124 1.455

- .1358 .4417 -.0017 -.0457 .1996 - .a404 1.317 -.04450 .2499 -.0531 .2118 - .8794 1.398

- .1546 -.I3352 .0079 .0126 -.0358 .1752 - .7037 .a622 7.138 - .2519 .3003 - .2221 .0398 - .5565 1 .589 -7.100 286.0

-2.555 -16.60 .7304 - .1681 - .0057 .0970 - .3105 1 .218 -158 .8 L The sequence of windings represented by t h i s matrix

goes from l e f t t o right in t h e diagram in Figure 6. I'o match t h e damping a t t h e natural frequency, p lace about 1000 ohms resistance in each primary winding group.

The capacitances in t h e primary winding, beginning with t h e grounded end of t h e winding are:

Capacitor pf

1 1372 2 1432 3 14 96 4 1557 5 1619 6 1700

Secondary Cable Data

The s e c o n d a r y c a b l e is represented as a simple series impedance:

Z = R + jwL

645

The R and L matrices used for t h e d i f fe ren t types BIOGRAPHY of cable follow. Each cable was assumed t o consist of #2 A1 phase conductors with a #4 A1 neutral . All matrices R o g e r D. D u g a n (M’73 , S N I ’ 8 3 ) w a s b o r n in a r e symmetrical and t h e neut ra l conductor is represented McConnelsville, ohia in 1950. He obtained t h e R.S.E.E. by t h e middle row and column. The R matrix was assumed degree from Ohio University i n Athens, Ohio in 1972 and t o be t h e same f o r each type of cable: t h e M.E. d e g r e e in E l e c t r i c Power Engineering from

Rensselaer Polytechnic Ins t i tu te i n Troy, New York in 1973.

He has worked f o r t h e Systems Engineering department of McGraw-Edison Power Systems s ince graduation. He has been primarily involved with t h e computer simulation o f power sys t ems , especially with respect t o harmonics, e 1 e c t r om a g n e t i c t r a n s i e n t s , a n d distribution engineering applications. He has also done work in computer sc ience and computer graphics.

(ohms per 1000 f t )

t r a n s f o r m e r , Triplexed Cable

(microhenries per 1000 f t ) S t e D h e n S m i t h is a s t a f f E n g i n e e r in t h e

12- inch Vert ically-spaced Open Wire (Neutral on top)

Dist ribufion Transformer Product Engineering Department a t t h e McGraw-Edison Zanesville, Ohio faci l i ty . He is a 1972 graduate of Ohio S t a t e Universitv. holding both a BSEE -and MSEE in Elec t r ic Power Engineering.- Before r e jo in ing McGraw-Edison i n A p r i l , 1984, he was a

L = 525 785 (microhenries per 1000 f t ) P r o f e s s o r of E l e c t r i c a l Techno logy and Phys ics a t 525 483 772 Muskingum Area Technical College, where he had been

s ince 1980. Steve has also gained considerable experience as an Shielded Cable

e l e c t r i c a l e n g i n e e r i n g c o n s u l t a n t i n t h e a r e a s o f e l e c t r i c a l power d i s t r i b u t i o n and power transformer

(microhenries per 1000 f t ) maintenance. He is a member of IEEE and a Registered Professional Engineer in t h e S t a t e of Ohio.

1” 1

A l l R and L matrices a r e symmetrical.

Discussion D. R. Smith, T. J. Dionise, N. C. Abi-Samra, and J. Pun (Westinghouse Electric Corporation, Pittsburgh, PA and Athens, CA): The authors have done a thorough job in identifying those parameters which affect secondary winding currents and currents in the house load for lightning strokes to the primary system. They not only identify the parameters, but they show how parameter changes, such as service drop length and house load, affect winding currents. From their results, it is clear that secondary winding configuration, either interlaced or noninterlaced, can significantly affect winding currents and house load voltages for most conditions en- countered in practice. We are conducting similar studies and our results are in good agreement with those reported in the paper.

This is encouraging as their models for the transformer and service drop are different from ours. For example, they represent the secondary circuit with mutually coupled lumped inductors. In our studies the secondary is represented by positive and zero mode surge impedances and the propagation velocities for each mode. The authors’ studies used a IO-kA 8 x 20 ps lightning stroke current, whereas we are using 30 kA strokes with either 1.3 x 90 or 2.5 x 90 ps wave shapes. Our studies show that when the house load is shorted, stroke wave shape does not have a significant effect on surge current distribution, and in particular the current in terminal X2 of the transformer. It appears that any minor differences between the authors and our results are due to particulars of the systems studied and not the modeling techniques.

There are several comments and questions that we would like to address to the authors. From Figs. 1-4 in the paper it appears that the authors did not represent the neutral conductor of the primary line. When the neutral conductor is represented, the surge impedance model for the line consists of three wye-connected resistors connected between transformer terminals H1, H2, and ground, rather than one 200-ohm resistor from HI to ground as shown in the paper. Would the authors comment on the effect of omitting the representation of the primary neutral conductor?

From the open wire secondary, we have calculated the inductance values given in the Appendix to within two tenths of one percent for both the selfs and mutuals. To obtain the self-inductance values of 772 and 785 yH we had to use the conductor geometric mean radius rather than the conductor radius. It is, we believe, more accurate to use the conductor radius for these calculations as the current is on the conductor surface for lightning surges. Furthermore, to obtain the mutual inductance values given in the paper, we had to assume a spacing of 6, 6, and 12 in rather

than the 12-, 12-, and 24-in spacings given in Fig. 9 of the paper. For what spacings do these inductance values apply?

In the section titled, “Effects of Load,” it is stated that with 65-ft drop, IO-kVA noninterlaced unit, and the load shorted, the current in each half of the secondary winding is 4.6 percent of the stroke current. However, in Fig. 17 which applies when the load is shorted, the maximum secondary current for the IO-kVA noninterlaced transformer with the 65-ft drop is about 3.2 percent. What is the reason for this difference?

In summary, the paper shows that interlacing of secondary windings can have a significant effect on secondary winding currents and phase- to-neutral voltages at the house for lightning strokes to the primary. This is in agreement with the results of our studies.

Manuscript received October 7 , 1986

C. J. McMillen (General Electric Company, Hickory, NC) and C. W. Schoendube (Retired, Hickory, NC): This paper contributes a valuable study identifying and quantifying the system parameters influencing surge currents entering the low-voltage side of the distribution system. I t is noteworthy in that it complements our experimental work exploring the effects on the transformer of low-voltage-side surges originating at the customer’s premises [l], [2], [3].

However, there are many differences in the parameters described in this paper that account for differences from the results in our tests.

The shape of the applied current wave used in this study was 8 x 20 as. This is a good wave for obtaining reproducible discharge voltages of lightning arresters, but does not correspond to typical lightning strokes. Lightning generally has higher maximum rates of rise and much longer duration tails [4]. A 1 x 50 wave is a more appropriate wave shape. The damaging oscillatory voltages generated in the high-voltage coil are sensitive in magnitude to the rate of rise duration of the front and the tail duration of the current wave [3]. The slowfront and short tail of the 8 x 20 wave used in this study will therefore reduce the voltage developed between high-voltage layers compared to our experimental tests. It is stated that other wave shapes were investigated. What were they and what were the results?

The mutual inductance between each low-voltage coil and approximately half of the high-voltage coil is also significant. It appears from Fig.

646

8 that the mutual inductance of the IO-kVA transformers simulated was considerably lower than our transformers, thus yielding lower primary voltages. The shell-type transformer tested [l] in our scaled tests had 29 turns per 120-volt coil. The IO-kVA shell types used in our EPRI study [2], [3] had 39 turns. Figure 12 states 170 pH for the noninterlaced secondary winding and 13 pH for interlaced. Our transformers with 39 turns had 226 pH and 59 p H for noninterlaced and interlaced, respectively, utilizing the same core design and turns for both transformers. The high ratio of inductances in your simulation suggests entirely different transformers were simulated. How many turns per 120 volts were simulated in your study? The voltage developed in the high-voltage winding is proportional to the mutual inductance of the high- and low-voltage coils and therefore proportional to the product of the high- and low- voltage turns and a permeance term.

We do not agree that the model very accurately duplicates the transient response of your transformer. The measured transformer response, Fig. 8A, has a natural period of 14.6 ps while the model Fig. 8B was 22.8 ps. The model peak voltage was 6 percent higher and the response was underdamped, i.e., the second peak is 77 percent of the first peak versus 65 percent of the transformer. The natural period is determined by the square root of the product of an inductance and capacitance. The difference in natural periods indicates an average error of 56 percent in calculation of each of those components. Figure 8[b] also shows a significant negative offset in the primary voltage trace which is not present in Fig. 8[a].

Figure 6, the schematic model of the transformer in this study indicates a high-voltage coil with layers connected in what we call a crossback type coil, rather than a conventional barrel type coil. The capacitor shown connected from the H2 terminal to the start of the second layer indicates that only the first layer has a crossback since capacitors are not shown across the corresponding layers at the bottom end of the high voltage layers. We also do not understand your capacitance matrix [Appendix]. How are only six capacitors connected to 10 primary groups?

The paper stresses the magnitude of voltage impressed on the customer’s wiring and appliances, particularly in regard to the greater magnitude that interlaced transformers will allow. In reality, the meter protection [flashover at approximately 7 kV and outlet or wiring flashovers, approximately 2 to 5 kV] will limit the overvoltages impinging on susceptible appliances for currents allowed by both noninterlaced or interlaced windings. The best assurance for protection of the customer’s premises is the installation of home lightning protectors at the service entrance and spike protectors at more sensitive electronic appliances.

We also believe the study may be flawed by not incorporating the effects of the service cable capacitance and the customer’s wiring. Our scaled tests included those capacitances which tend to reduce the slope of the current waves and voltage magnitudes calculated in your study.

We do not understand the “theoretical limiting value” of current division in the second paragraph of your conclusions, nor the logic of the third sentence of the third paragraph. “This fact” referring to “fact” in the previous sentence does not logically follow as an explanation for the relative immunity to failure of 50-kVA noninterlaced transformers. The fact of having a lower mutual inductance between the low-voltage winding and half the high-voltage winding explains the induction of lower primary voltage as the kVA rating is increased, with a given magnitude of current.

Your analysis of the effect of the home load on the system response, as well as line lengths, is a significant contribution toward understand- ing the complexity of the problem. The recommendation that shielded service cable is one solution that tends to protect both the transformer and the customer is also worthy of note. However, we doubt that it will be economically acceptable by either customers or utilities when compared to the application of home lightning protectors and interlaced windings.

We do not agree with the implication that general adoption of interlaced windings in the lower kVA ratings of distribution transformers will lead to serious problems in the home. It is estimated that at least half of the distribution transformers, approximately 10 million transformers, have interlaced secondary windings, If there are serious problems, it seems that insurance companies would be advocating installation of home lightning protectors and spike protectors.

Your work is a welcome contribution in that it thoroughly explores the effects of system parameters that help initiate the commonly occur- ring failures of shell-type transformers utilizing noninterlaced low-voltage windings. This work, combined with our work which defined the transformer parameters that influence susceptibility to failure, are both milestones towards establishing suitable low-side-surge withstand requirements for distribution transformers. The need for withstand re-

quirements is amply demonstrated in [5], which documents the prevalence of distribution transformer failures attributable to this phenomenon.

References

11 ] C . J. McMillen, D. W. Caverly, and C . W. Schoendube, “Scaled Low Voltage Side Surge Current Tests on a Model Distribution System,” 86 T&D 552-4, IEEE/PES 1986 Transmission and Distribution Conference, Anaheim, CA, September 14-19, 1986. C. J. McMillen, C. W. Schoendube, and D. W. Caverly, “Suscep- tibility of Distribution Transformers to Low Voltage Side Light- ning Surge Failure,” IEEE Transactions on Power Apparatus and Systems, Vol. PAS-101, No. 9, September 1982, pp. 3457-3470. Surge Characteristics and Protection of Distribution Transformers, Electric Power Research Institute Final Report EL-3385, January, 1985. H. M. Schneider and H. R. Stilwell, “Measurement of Lightning Current Wave Shapes on Distribution Systems,” paper #A79 526-5, presented at the IEEE-PES Summer Meeting, July 15-20, 1979. W. J. Ros, “A Realistic Evaluation of Interlaced Secondary Designs,” EEI Transmission and Distribution Committee, May 15, 1986. J . D. Borst, “Susceptibility of Distribution Transformers to Low Voltage Surges,” EEI Transmission and Distribution Committee, May 15, 1986.

Manuscript received October 10, 1986.

Roger C. Dugan and Stephen D. Smith: We appreciate the discussers’ taking the time to study our work carefully and making several good, constructive comments about this very interesting problem.

First, we will address the comments of Messrs. Smith, Dionise, Abi- Samra, and Puri. It is also encouraging to us to know that our studies can be duplicated with somewhat different models and methods. We are looking forward to publication of the discussers’ results.

Our choice of lightning current waveshape was somewhat arbitrary, but did correspond to the waveshape used in the full-scale tests we conducted that preceded the analysis reported in the paper. It would, perhaps, be better to assume a steeper wavefront. We also have found that the results are not as sensitive to the wavefront as one might think. We discuss this in greater detail below.

As the discussers assumed, we did not represent the primary line neutral conductor. We believe that the general effect will be to bleed off a little of the lightning current and reduce the currents flowing in the distribution circuit. The amount of current flowing into the neutral will be dependent on the local ground resistances. For resistances in the 10-25 ohm range, the effect should be slight. For higher grounding resistances, the primary neutral will be more effective in limiting the surge currents. To model the primary neutral correctly, one should represent the coupling to the phase conductor and include several pole spans. We have not yet added this degree of complexity to our models.

Regarding the inductances used in our model, we agree with the discussers that it would be more accurate to use the conductor radius instead of the GMR because of the higher frequencies involved. This will reduce the self-inductance relative to the mutual inductance and reduce the net differential voltage induced in the secondary cable loop. Thus our model as stated in the paper will predict higher than actual voltages. Our simulations to this point in time indicate that the difference is small.

As the discussers have determined, the inductance matrix for the open- wire cable given in the appendix is for 6-in spacing rather than 124x1 spacing as we had believed. An open-wire secondary with 12-in spacing will generally yield somewhat higher surge voltages throughout the system than our simulatons would indicate.

In the section titled “Effects of Load” there is indeed a typographical error. The actual maximum secondary current that we compute for a noninterlaced transformer and 65 ft of cable is 2.9 percent rather than the 4.6 percent printed. This is more apparent from Fig. 15 than from Fig. 17. In any case, it is much smaller than the proposed test values. The 4.6 percent figure applies to 165 ft of cable and was mistakenly transcribed from the wrong line of data.

Now, we will address the comments of Messrs. McMillen and Schoen- dube. A steeper wavefront than the 8 x 2 0 ps wave is probably more typical of lightning surge currents as the discussers point out. We have looked at a variety of waveshapes including 1.2 x 50 ps wave. This causes

647

It is true that the model has slightly less damping than the actual transformer. This will give voltages that are conservatively high and we feel it is better for the model to exhibit slightly lower damping for this reason. We do not feel that the difference in damping pointed out by the discussers is significant.

The negative offset questioned by the discussers is actually a transient swing due to the fact that the model has slightly less damping than the actual device. When the simulation is extended beyond 75 ps, this decays to zero.

Figure 6 has no relationship to the actual physical design of the transformer, but is intended to show only the connections of the model. The transformer is indeed a conventional design with no crossback coils. The capacitors are not intended to depict a particular design, but only nodal connections in the model. Simply stated, the model consists of a capacitor in parallel with each primary winding section. Perhaps, this can be seen better by drawing the diagram differently.

There are only six capacitors because there are only six primary groups. The transformer was broken into a total of 10 groups, four of which are secondary groups. The capacitances in the transformer secondaries were found to be of minor importance and were neglected.

We agree that home lightning protectors should be installed at the service entrance and urge the power industry to develop methods to en- courage their use.

We have investigated the effects of service cable capacitance and the capacitance of the customer’s wiring, which is assumed by the discussers in their work to be 15 nF. As of this writing, we have not found any noticeable effect of this capacitance. Perhaps it is because we inject our current from the primary h e rather than the secondary.

By “theoretical limiting value” we mean the maximum possible current that could flow in the transformer windings assuming the transformer winding impedance is zero and the load is shorted. If that were the case, the surge current would split equally between the three conductors of the secondary cable. Half of the surge current goes to the house ground in this example. Thus, 1/6 of the lightning current would flow in each wire of the cable.

The “fact” that we were referring to with respect to the 50 kVA transformers is indeed the lower impedance. However, we have found that lower impedance is not the complete story. Lower impedance means that there will be less voltage per ampere of surge current, but the 5O-kVA transformer allows more current to flow than does a IO-kVA transformer. Therefore, we often find that when the transformer is simulated in an actual circuit, the layer voltages are in the same ballpark as for IOIVA transformers. Of course, the voltage is always lower, but not by as substantial a factor as one might think. We have not completed our analysis of this, but it seems that other factors such as layer distribution, insulation thickness, wire size, and typical load application prac- tices also play significant roles in the apparent immunity of SO-kVA transformers to low-voltage-side current surges. We are studying this to gain some insight into how to improve the withstand of the smaller sizes as well.

We recognize that there are no data generally available from which we could correlate transformer winding connection with customer ap- pliance failures. It very likely makes little difference in areas where it is possible to consistently achieve good pole grounds compared to house grounds; there will be few surge problems in any case. However, in other areas it is easily shown that the use of interlaced transformers will often inject two to three times more surge current into the customer load than will noninterlaced transformers. Thus, the potential for customer load failure is greater. These are the same areas that would be expected to experience higher-than-normal incidence of lightning failures of noninterlaced transformers. Thus, we should concentrate on these areas to try to gather data on customer equipment failure due to lightning.

We will continue to work in this area to help the industry define ra- tional and realistic surge withstand requirements.

Manuscript received November 6, 1986.

an increase in the computed first layer voltage from 10 kV to 12 kV. This is, perhaps, not as much as one might expect. Early in our research, we found that the voltages were not very sensitive to lightning current waveshape. It is the current through the secondary drop neutral that is the root cause of the voltages in the transformer. Due to typical values of inductance and resistance in the secondary circuit, the front of this current always seems to be significantly slower than the front of the lightning stroke current.

Concerning the inductances of the transformer, we did use the same transformer model for both the interlaced and noninterlaced analysis and merely reconnected the secondaries. Perhaps, this transformer is built differently than the discussers’, but at this time we do not think we have made any errors in the calculation of the inductances. We broke the transformer down into 10 winding groups and calculated the short-circuit impedances between each pair of groups. Then we constructed the inductance matrix (actually, its inverse) as described in the paper. The model checks out well with respect to high-to-low short circuit impedances and the transient response is well matched. It also is possible that we are not comparing apples-to-apples with respect to the discussers’ transformer. The inductance we refer to is the short-circuit inductance from one secondary winding to the other. The number of turns per 120 V in the transformers we tested and simulated were 29 turns for the 10 kVA, 19 turns for the 25 kVA, and 15 turns for the 50 kVa. These values are typical for our shell-type, loss-evaluated designs.

The discussers point out that the simulated and measured results in Fig. 8 do not match very well. This is due to a misunderstanding with the artist who drew the figure from two plots on different scales. The time scale for Fig. 8a should be from 0 to 100 ps. The corrected figure is shown in Fig. A, included with this closure. Also, because the render- ing makes it difficult to determine time scales, we have pointed out key time points in Fig. A. As can be seen, the dominant frequencies in the two oscillograms match very well, with the model exhibiting a slightly lower frequency. We apologize for difficulties caused by this error.

4 8 V O L ~ S MIDPOINT OF PRIMARY WlNDlNQ

6.35 psec

13.8 VOLTS

0 25 5 0 75 100 Ir=

(a) Mensured transformer response.

DPOINT OF PRIMARY WINDING

1 4 . 7 VOLTS-

I 0 25 50 75

9 s (b) Computed response of the model.

Fig. A. Correction of Figure 8.