Reduced voltage stresses across power transformer winding sections provided with metal oxide surge absorbers.

Ansari, Mohd. Zahed Ahmed ; Gurumurthy, G.R. ; Amarnath, J. 等

Introduction

Power transformers in service experience different types of transient overvoltages. One of them is effects of lightning. Lightning overvoltages are characterized by very steep initial rate of rise of voltage and relatively slower rate of fall of voltage with respect to time. Surge voltages with steep front time are most important type of transient overvoltages which can cause damage to insulation of transformer windings. The practice of design and construction of HV transformer windings to withstand effects of surge voltages with steep fronts appearing at its line terminal has been to provide a surge voltage distribution controlling ring at line end which is also called as static end ring. Other method of improving the steep front surge voltage withstand performance of power transformer HV windings is to increase the series capacitance between turns of sections or discs of winding known as interleaving [1-3].

MOA blocks have been known to be able to provide very good surge protection to equipments used in electrical power stations and substations for more than a decade. Their technology has advanced to highly satisfactory levels as to be able to provide surge absorbers having required type of characteristics to suit different applications [4, 6, 7]. The voltage V relating to current I through a surge absorber block is given by the equation V = K[I.sup.[beta]] (K and [beta] are constants for the MOA blocks).

Computer simulations carried out on HV windings of power transformers provided without and with suitable MOA blocks to investigate behavior of these windings due to appearance of very fast rise time transient voltage at its line terminal are reported in this paper. The values of [alpha] considered for study are 6, 12 and 18. Extensive investigations have shown that it is essential to provide MOA blocks of appropriate characteristics (i.e., [beta] and K values) across all sections of winding referring to entire HV winding length if it is desired to reduce the voltage stresses enormously. However, it may be noted here that by providing suitable MOA blocks across 50% of winding length only, voltage stresses across sections can be reduced to some extent. All the simulation investigations reported in this paper have been carried out using PSpice software version 10.

Simulation

Model winding and analysis

The HV winding has been represented by a single layer coil wound on an insulating former of mean diameter 20.1cms and coil consisting of 8 sections, each coil section constituted 60 turns. Thus, the HV winding equivalent circuit consists of sections incorporating series inductance L, series capacitance Cs and ground capacitance Cg, which represent inductance due to turns of coil sections, capacitance between terminals of coil sections and capacitance of coil sections to ground. In the present investigations mutual inductance between coil sections [M.sub.12], [M.sub.21].... [M.sub.18], [M.sub.81].... etc have also been considered in the simulations.

Initial Voltage distribution without surge absorber block

HV windings of power transformer can be represented by equivalent circuit network for analysis of surge behavior as shown in Fig. 1 [1-3]. Although close coupling of all turns do exist in power transformer windings, for investigation of behavior of windings for fast front surge voltages (near step voltages) appearing at line terminal, effect of inductance can be ignored for analysis of initial voltage distribution [1-3]. Therefore, the equivalent network for study of behavior for initial voltage distribution is as shown in Fig. 2.

[FIGURE 1 OMITTED]

The initial voltage distribution for a equal to 6, 12 and 18 for step voltage input at line terminal with neutral end of winding grounded is obtained using the equation [1]:

[[epsilon].sub.x] = E Sinh ([alpha]x) / Sinh [alpha](1)

[alpha] = (n)[square root of [C.sub.g] / [C.sub.s]] (2)

[FIGURE 2 OMITTED]

E = Magnitude of input step voltage

n = number of sections in transformer winding equivalent network

x = fraction of winding length from neutral end (in present study referring to node position)

[e.sub.x] = voltage at fraction of winding length with respect to neutral

Initial voltage distribution with surge absorber blocks

Equivalent circuit representation of transformer HV winding for analysis of surge behavior with surge absorber block provided across 25% of winding portion is shown in Fig. 3.

[FIGURE 3 OMITTED]

[Z.sub.B]: Metal oxide surge absorber block

[V.sub.A]: Voltage across [Z.sub.B] when passing surge current [I.sub.A]

[C.sub.eq]: Equivalent capacitance across terminal 'p' and ground due to chain of [C.sub.g] and [C.sub.s]

Referring to Fig.3, the voltage appearing across the capacitive network of transformer winding portion after the surge absorber block can be written as:

[V.sub.p] = E - [V.sub.A] (3)

[V.sub.p] = Voltage across equivalent capacitance [C.sub.eq] (across point p and ground as shown in Fig.3)

Relation between voltage and current for MOA block [4, 5] is:

[I.sub.A] = [KV.sub.[beta]] (4)

K and [beta] are constants. Value of [beta] is in range of 25 to 30

Referring to Fig.3, [I.sub.A] is also the current entering to the capacitance network at point p with equivalent capacitance [C.sub.eq]. Therefore, for extremely short time duration after appearance of step voltage E at line terminal, we can write

d[V.sub.p] / dt = [I.sub.A] / [C.sub.eq](5)

From (2) and (3) we can write after integration:

[V.sub.p] = [I.sub.A] / [C.sub.eq] t + D (6)

D = constant of integration.

We have the initial conditions that IA = 0 at t = 0. Therefore value of constant D = 0 in (4)

Thus, during the initial time period after appearance of step voltage, we have

[V.sub.p] = [I.sub.A] / [C.sub.eq] t (7)

The MOA block has a highly non linear voltage current relationship and for surge current magnitudes [I.sub.A] in the range of few hundred amperes to few thousand amperes, the voltage across it does not change appreciably. Also, the resistance offered by metal oxide surge absorber block is a low value for flow of large surge currents through it and the equivalent capacitance [C.sub.eq] (capacitance between points p and ground in Fig. 3 gets charged up to the maximum value in very quick time (in the order of small fraction of microsecond). This situation can be considered as though a step voltage of magnitude (E-VA) appears across [C.sub.eq], which is the capacitance equivalent network representing the portion of the HV transformer winding connected to the end of the metal oxide surge absorber block. Thus, the initial voltage distribution referring to remaining transformer winding portion is calculated considering as though a step voltage of magnitude (E-[V.sub.A]) appears at point p and ground in Fig. 3 applying same method as detailed in previous section.

Discussions and comparison

The initial voltage distributions along winding length for values of [alpha] equal to 6, 12 and 18 are shown in Fig. 4 considering magnitude of input step voltage E as 1.0 pu.

The voltage stress across the winding insulation near the line end can be observed to be very much higher as compared to uniform stress distribution. Also, voltage stress at line end portion of winding can be observed to increase considerably with increase in [alpha] value from 6 to 18.

[FIGURE 4 OMITTED]

When a MOA block is provided across 25% of winding length at line terminal which develops a constant voltage of 0.25 pu (approx.) during flow of surge currents through it, the altered surge voltage initial distributions are as shown in Fig. 5. The input surge voltage magnitude considered in this case also is same as 1.0 pu step voltage at line terminal. The values of maximum voltage stresses developed in the transformer HV winding due to presence of metal oxide surge absorbers are reduced considerably. Calculations of these values have shown that for HV winding with [alpha] = 6, the maximum stress is reduced by 22.7%. The reduction in stress for winding with [alpha] = 18 is 20.3%.

The non-uniform initial voltage distribution is due to effect of capacitive network which is made up of [C.sub.s] and [C.sub.g]. The initial voltage distribution arising due to capacitive network does not exist for longer duration of time. Subsequent to charging of capacitive network in the initial short duration of time, currents start flowing through the inductive network and finally after sufficient duration of time uniform voltage distribution due to inductive effects of network will be reached. The transition from non-uniform initial voltage distribution to final uniform distribution takes place through a series of damped oscillations between capacitive and inductive networks. The initial voltage distribution represents envelope of maximum possible transient voltage zero current phase. With the introduction of MOA blocks, analysis in earlier sections has shown that maximum voltage stresses across coils of HV transformer windings due to initial voltage distribution are considerably reduced. From these considerations, the maximum voltages that can be developed in the windings during transition from initial voltage distribution due to appearance of a series of damped oscillations will also be reduced appreciably when MOA blocks are provided across the portion of windings at line end (in this case across 25% of winding length).

[FIGURE 5 OMITTED]

The general construction practices over past few decades for transformer HV windings to withstand effects of surge voltage initial distribution have been to provide static end ring at line terminal [1-3], providing increased insulation size for conductors near line terminal and adopt interleaved type of construction for coils. By providing metal oxide surge absorber blocks as detailed above, it is possible to overcome these special constructional requirements for making HV winding of transformer withstand effects of steep front surge voltages. It may be noted here that providing metal oxide surge absorber as described above reduces the energy in the incoming surge voltage wave to the extent of energy dissipation in the surge absorber block. Thus, the surge voltage energy which can cause damage to transformer HV winding can also be reduced considerably.

Voltage distributions with MOA blocks across 50% of winding from line end

The equivalent circuit for analysis of surge behavior of HV windings of power transformer MOA blocks across 50% of winding from line end is shown in Fig. 6 [1-3].

[FIGURE 6 OMITTED]

Fig. 7 and 8 show simulated voltages to ground at different points of HV winding when the first 50% of HV winding are provided with MOA blocks [Z.sub.B] (Fig. 6) for values of [alpha] equal to 6 and 18 respectively (neutral grounded). We observe from these figures that maximum voltage is appearing across last section of the winding although the surge voltage magnitude across 50% of the winding which are provided with MOA blocks are considerably reduced. Further we observe that the time instance of appearance of maximum surge voltage across last section of winding is increasing with increasing [alpha] value of windings.

Further we observe that the time instance of appearance of maximum surge voltage across last section of winding is increasing with increasing [alpha] value of windings. For comparison, surge responses of HV winding without presence of MOA blocks at different nodes are shown in Fig. 9.

[FIGURE 7 OMITTED]

[FIGURE 8 OMITTED]

[FIGURE 9 OMITTED]

This figure shows that there are possibilities of occurrence of very large voltages across sections of winding due to voltage oscillations caused by appearance of unit step voltage at line terminal. These voltage oscillations are due to natural frequencies of winding which consists of capacitances and inductances. Such enormous voltage oscillations with respect to the time are considerably reduced (see Fig. 7 and 8) even when MOA blocks are provided across 50% of winding only from the line end. This suggests that enormous magnitude high voltages appearing across sections of HV winding can be reduced to certain extent by providing suitable MOA blocks across first few sections of the HV winding. However the maximum value of surge voltage can be between 35% to 45% of the surge magnitude that appears at line terminal. Other important aspect we can observe from this investigation is the appearance of negative voltages with respect to ground. The magnitudes of negative voltages to ground for case in which MOA blocks are provided across 50% of winding are very much smaller as compared to the values that can be present in the winding without the MOA blocks. It may also be noted from these figures that for the case of windings with MOA blocks across 50% of winding, the magnitude of positive node voltages does not exceed the input surge voltage magnitude which is 1.0 pu. Also, we observe that the positive node voltage magnitude for case without MOA blocks can be higher than input surge magnitude by approximately 25% due to voltage oscillations.

Voltage distributions with MOA blocks across all sections of HV winding

Fig. 10 and 11 show voltage distribution across sections of winding when 100% of winding are provided with suitable MOA blocks. We observe from these figures that there are no oscillations on waveform of voltage to ground at different node positions of the winding. Also, these figures indicate that the maximum surge voltage to ground does not exceed the magnitude of the input step voltage. Further there are no voltage reversals at any node position on the winding. The maximum value of surge voltage across any section of the winding in this case is approximately 23.5% for all the three [alpha] values. The behavior of HV winding when all sections of the winding are provided with suitably designed MOA blocks can be explained as follows:

When a steep front HV surge appears at terminal of winding, till sufficient magnitude current flows through the nonlinear blocks, the voltage distribution is governed mainly by the effect of series capacitance across sections and shunt capacitances to ground (in less than small fraction of micro second time). Once sufficient current (approximately few milliamperes) is established through highly non linear resistance path of MOA blocks, the voltage distribution across winding sections is completely decided by the V-I characteristics of the MOA blocks. The MOA blocks not only serve to reduce surge voltage across winding sections but also dissipate surge energy and thus prevent possibility of winding failures.

[FIGURE 10 OMITTED]

[FIGURE 11 OMITTED]

The explanation for surge voltage response curves for the situation where MOA blocks are provided across 50% of winding sections is that the other 50% of winding without MOA blocks can give rise to the initial node voltage variations in time range 0 to 10 microseconds as may be observed from Fig. 7 and 8. In view of the fact that there are no enormous node voltage oscillations that is present only in case where no MOA blocks are used across sections of winding, for cases where 50% of winding or 100% of winding sections are provided with MOA blocks, the simulation results indicate (Fig. 7 and 8 & 10 and 11) that graded insulation type construction can be effectively used for HV winding.

Conclusion

Computer simulation investigations of HV windings of HV power transformers for its behavior with [alpha] values 6, 12 and 18 to appearance of very fast rise voltage surges at line terminal have indicated that:

1. The response of windings without MOA blocks consists of enormous magnitudes of voltage oscillations and magnitudes of node voltage distribution in this case can be higher than the magnitude of input surge at few nodes. Also, at few other nodes the surge magnitude can reach negative values to considerable voltage levels.

2. By providing suitable MOA blocks across sections of winding up to 50% of length of winding, the surge voltage magnitudes can be reduced to some considerable extent. In this case the surge voltage magnitude at any of the nodes is not higher than the magnitude of the input surge.

3. When all sections of entire winding are provided with suitable MOA blocks, the surge voltage distributions have no oscillations. The magnitude of surge voltage at any of nodes is less than the input surge voltage magnitude and the magnitudes of surge voltages appearing across sections of winding are reduced to larger extents.

4. For cases where 50% of winding or entire winding sections are provided with suitable MOA blocks, graded insulation type construction can be effectively used for HV winding of power transformers.

Acknowledgements

The authors would like to thank the authorities of Ghousia College of Engineering, Ramanagaram, BNM Institute of Technology, Bangalore and JNTU, Hyderabad for cooperation, encouragement and for providing facilities to publish this work.

References

[1] L. F Blume et al, Transformer engineering (John Wiley and Sons, 1952).

[2] S. B Vasutinsky, Principles, operation and design of power transformer (PSG College of Technology, Coimbatore (Book), Tamilnadu, India, 1962).

[3] B. Heller and A. Veverka, Surge phenomena in electrical machines (London, Iliffe Books Ltd., 1968).

[4] E. Kuffel, W. S. Zaengl and J. Kuffel, High voltage engineering: fundamentals (Newnes, Elsevier, 2000).

[5] Yuanfang Wen and Chengke Zhou, A novel method for predicting the life time of MOV, IEEE Trans. on Power Delivery, 19(4), 2004, 1689-1691.

[6] Yuanfang Wen and Chengke Zhou, Experimental studies on the use of MOV in transformer windings, IEEE Trans. on Power Delivery, 20(2), 2005, 1441-1446.

Mohd. Zahed Ahmed Ansari (1), G. R. Gurumurthy (2) and J. Amarnath (3)

(1) Department of Electrical & Electronics Engineering, Ghousia College of Engineering, Ramanagaram--571511, Karnataka, India Phone: +919900650035, Email: zahedansari@gmail.com (2) Department of Electrical & Electronics Engineering, BNM Institute of Technology, Banashankari, Bangalore--560070, Karnataka, India Phone: +919845038229, Email: grgurumurthy@yahoo.com (3) Department of Electrical & Electronics Engg., JNTU, Hyderabad--500085, Andhra Pradesh, India Phone: +919347277771, Email: amarnathjinka@yahoo.com