Ultrasaturation Phenomenon in Power Transformers ... - IEEE Xplore

IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 23, NO. 3, JULY 2008

1327

Ultrasaturation Phenomenon in Power Transformers—Myths and Reality Andrzej Wiszniewski, Waldemar Rebizant, Senior Member, IEEE, Daniel Bejmert, and Ludwig Schiel

Abstract—In this paper, the ultrasaturation phenomenon of power transformers during their energization is studied. It is shown that under special conditions, the currents observed after transformer switching on do not contain enough restraining information (e.g., second harmonic), which may lead to protection maloperation. This paper concentrates on a thorough explanation of the problem and possible causes of ultrasaturation. Theoretical investigations are supported and illustrated with simulation studies performed both with MATLAB and Electromagnetic Transients Program–Alternative Transients Program. The outcomes of this research can further be used as hints for substation operation personnel as well as for the development of new protection stabilization criteria, which is not discussed further in this paper.

Fig. 1. Single-phase unloaded transformer equivalent circuit.

Index Terms—Harmonic restraint, transformer protection, transient analysis, ultrasaturation.

I. INTRODUCTION

S

ATURATION of power transformer magnetic cores during a sudden jump of the terminal voltages is a well-known and thoroughly studied phenomenon. It occurs either during energization of the transformer or after clearing of a nearby short circuit. In both cases, it may generate high and comparatively slowly decaying inrush currents which may be several times higher than the rated ones. In case of a single-phase transformer (Fig. 1), the inrush current waveshape contains a large and decaying dc component; however, it is always smaller than the ac component (Fig. 2). The waveshape shows flat regions—which correspond to the time span when the core is not saturated. As a result, there is always a substantial second harmonic in the current which, even in cases of very heavy saturation, when the residual flux in the core has the same polarity as the dc flux caused by the voltage jump, does not fall below approximately 15% of the fundamental one. Therefore, the presence of the second harmonic became a restraining criterion in differential relays. If the relay detects the second harmonic, which is higher than 15–20% of the fundamental component, the operation of the relay is blocked. Today, this method became standard and is effective in most cases [1], [2].

Manuscript received January 29, 2007; revised May 15, 2007. Paper no. TPWRD-00033-2007. A. Wiszniewski, W. Rebizant, and D. Bejmert are with the Wroclaw University of Technology, Wroclaw 50370, Poland (e-mail: andrzej. [email protected]; [email protected]; daniel.bejmert@ pwr.wroc.pl). L. Schiel is with the Siemens AG, PTD EA, Berlin 13629, Germany (e-mail: [email protected]). Digital Object Identifier 10.1109/TPWRD.2007.909211

Fig. 2. Typical waveshapes of flux and magnetizing current during inrush after transformer energization (transformer unloaded).

Fig. 3. Energization of a loaded transformer.

However, there are situations—although very rare—of inadvertent operation of differential relays under inrush conditions and, as a consequence, tripping of healthy transformers. Therefore, one may suspect that the restraining second harmonic was smaller than the relay setting [3]. A study of this phenomenon has been presented in [3]. The authors observed that energization of a loaded transformer (Fig. 3) may lead to the situation—called ultrasaturation—when the dc flux in the core in the initial stage of the process increases instead of decaying (Fig. 4). As a result, the distortion of the current waveshape becomes smaller, and the percentage of the second harmonic falls below the relay restraining level. In fact, there may be extreme situations (which we call excessive

0885-8977/$25.00 © 2007 IEEE .

1328


Fig. 4. Energization with flux increase after the transformer switching on.

Fig. 5. Excessive ultrasaturation after the transformer switching on.

ultrasaturation) when the magnetic flux in the core for several periods is higher than the saturation level. As a consequence, the current ac waveshape is almost undistorted and the level of the second harmonic is negligible (Fig. 5). This paper presents conditions which must be met to make ultrasaturation and excessive ultrasaturation possible. They are derived on the ground of a simplified equivalent circuit but afterwards they are confirmed by means of simulation of the nonlinear circuit of the transformer. The results prove that ultrasaturation is sometimes possible if there is a case of sudden voltage jump on the terminals of a transformer which are either loaded (Fig. 3) or connected to the primary impedance (Fig. 20). It also shows that excessive ultrasaturation is a very rare but likely phenomenon. A simulation example of the ultrasaturation case for a threephase unloaded transformer is presented in Fig. 6. One can observe that the waveshapes of transformer terminal currents consist of the purely sinusoidal component plus a dc component. Their amplitudes and level of dc components initially rise during the first five cycles and then begin to decay; however, they have .

Fig. 6. Transformer energization with ultrasaturation (system scheme and conditions as for Fig. 21): (a) HV terminal currents. (b) Second harmonic ratio.

the same polarity for a comparatively long time. In the case shown in Fig. 6(b), the level of the Ih2/Ih1 ratio measured is extremely low, falling down to even less than 5% for the current in phase L1 (A). This would cause relay inadvertent operation (overfunction) since the harmonic stabilization is not sufficient enough to prevent tripping. The 100-Hz restraint ratio is low not only for phase currents but also in the zero-sequence current, thus also making this signal useless for transformer protection stabilization. The research performed was divided into three parts. The theoretical approach presented in [3] was analyzed and verified in Section II. The new theoretical approach to the problem is presented in Section III. It is followed by both Matlab and EMTP–ATP simulations (Section IV). Final conclusions are proposed in Section V. II. ANALYSIS OF THE CASES REPORTED IN THE LITERATURE The ultrasaturation phenomenon is characterized by the fact that after switching on the loaded transformer, the amplitudes of

WISZNIEWSKI et al.: ULTRASATURATION PHENOMENON IN POWER TRANSFORMERS

1329

Fig. 7. Simplified circuit of the transformer for ultrasaturation studies [3]. Fig. 8. Basic circuit of the loaded transformer for ultrasaturation studies.

the magnetic flux increase. In some cases, the fluxes oscillate in the saturated region during a considerable period of time, which is called excessive ultrasaturation. The possibility of such an event has already been reported in the literature [3]; however, the explanation that is found is not sufficient. In this paper [3], the authors suggest that the mechanism of ultrasaturation phenomenon can be explained when the transformer under study, together with the primary feeding system and load, is represented by the following simplified single-phase circuit. The main assumption here was that the secondary side of the transformer be fully resistive and that the magnetizing inbe constant. ductance For the simplified transformer model from Fig. 7, the following relationship for the main flux after switching on the transformer with the sinusoidal supply with the amplitude can be derived: (1) where the amplitude and phase of the fundamental component of the flux are given by the formulae (2a)

(2b) the initial value of the component decaying with the time constant is equal to

and

(6) where (7) The analysis of the previously cited equations (5) and (6) leads to the conclusions that the excessive ultrasaturation is hardly possible in real cases of power transformers with purely resistive loads. One ought to bear in mind that the load resistance must not be too small when compared with the source reactance. Otherwise, it would lead to the power system voltage instability. III. NEW APPROACH TO THE ULTRASATURATION PROBLEM Theoretical analyses of the possible transformer ultrasaturation have been performed now for the system as shown in Fig. 8. The most important differences with respect to the study preis negligible sented in [3] are that the magnetizing current , by with almost compared with (i.e., infinite or at least much higher than the impedance ), and that the secondary side reactance is considered. The extreme cases of inrush may be expected if the supplying voltage is (8)

(3) with and being the remanent flux level. The initial value of the component decaying with time conamounts to stant

which causes the current that can be expressed as (9) ,

where

, and (4) . with The time constants of decaying components are defined as

Therefore, the voltage

. (Fig. 8) becomes

(10) (5) .

where

and

.

1330


, Bearing in mind that , , and and sub, one may write the formula, stituting that into (14) for which determines the maximum value of the dc flux increase (16) Therefore, the maximum value of the total flux in the core becomes (17) At the time when the dc flux component is maximum, the total and . The latter is flux oscillates between the

X = 1, X = 2, R = 0:1, V=!Z

Fig. 9. Flux waveshape according to (11), for or 0.5, (flux values relative to ).

R = 0:5

(18) Substituting (16) into (18) yields (19)

The flux in the transformer core is then given as (11a)

The excessive ultrasaturation takes place if the flux ceeds the saturation level , that is, when

ex-

(20) with

The flux increase the dc component

Substituting (19) into (20), one obtains the condition of excessive ultrasaturation

consists of the ac component . The former is

(11b)

(21)

and

There are two special cases which ought to be considered. The first one, which represents the predominantly reactive load , , of the transformer, is the following: . For these parameters, the condition of excessive and saturation becomes

(12) while the dc flux increase becomes

(22)

(13) or

The condition (21) in some rare cases may be met; therefore, the excessive ultrasaturation is possible. The second case represents the purely active load of the transformer, that is, when , , and . Then, the condition takes the form (23)

(14) Analysis of (13) indicates that the dc flux component increases with time only if (15) The formula (15) presents the condition of ultrasaturation. Only when it is satisfied, does the aperiodic flux component start to rise; otherwise, it decays, as presented in Fig. 9.

Since the left-hand side of (22) is very small, in this case, the excessive ultrasaturation is practically impossible. IV. SIMULATION STUDIES WITH EMTP–ATP All the above considerations assumed that the magnetizing inis much greater then the source inductance even ductance if the magnetic core is fully saturated. However, this is seldom the case, and often the magnetizing inductance of the saturated


1331

Fig. 10. Flux and magnetizing current waveshapes for the condition of exces, ) and sive ultrasaturation met tangentially ( .

5

Fig. 11. Flux and magnetizing current waveshapes for the condition of excessive ultrasaturation met tangentially ( , ) and .

X =

Fig. 13. Maximum and minimum values of the steady-state flux as a function of ( , , , , , ). and

transformer is comparable with the source inductance. This affects the inrush phenomenon and conditions of ultrasaturation. The simulation studies have been performed with the EMTP–ATP package, first for a single-phase transformer with the system structure as shown in Fig. 8. The transformer and system parameters were first chosen in such a way that the condition of excessive ultrasaturation was met just tangentially, ( , , , that is, for , , ). It has been verified how the may influence the possibility value of saturation reactance of excessive ultrasaturation occurrence. In Figs. 10–12, the obtained waveshapes of flux and magnetizing current are shown for three chosen values of the transformer saturation reactance (1000, 50, and 5 ), respectively. From Fig. 10, it can be seen that for a high saturation reactance value , the magnetizing current is very small; however, the excessive

ultrasaturation takes place, confirming the analysis presented in Section III. are lower, what If reactances of the saturated transformer is more realistic, the magnetizing current must not be neglected. As a result, the magnetizing flux is not in the saturated region curve all of the time. Since the waveshapes of the of the magnetizing current show flat regions in every cycle (Fig. 12), it means that with the saturation reactance of the transformer decreasing, the probability of excessive ultrasaturation also decreases. , the However, even in cases of very small values of amount of the second harmonic in the magnetizing currents is very low (see Figs. 13 and 14). Another set of simulations was performed for the conditions leading to distinct excessive ultrasaturation (Figs. 15 and 16, parameters under the figures). Under such conditions, the second

X = 4:3 X = 10

1000

X = 4:3 X = 10

50

.

X =

Fig. 12. Flux and magnetizing current waveshapes for the condition of exces, ) and sive ultrasaturation met tangentially ( .

X = 4:3 X = 10

X =

X X = 4:3 X = 10 R = 0:01 R = 1 9 = 0:79 V=! = 1:09

1332


Fig. 14. Maximum values of the magnetizing current and second harmonic ( , , , ratio as a function of , and ). ,

Fig. 16. Maximum values of the magnetizing current and second harmonic

X X = 4:3 X = 10 R = 0:01 ratio as a function of X (X = 10 , X = 10 , R = 0:01 , R = 1 , V=! = 1:09 R = 1 9 = 0:79 9 = 0:79 , V=! = 0:89 ).

Fig. 15. Maximum and minimum values of the steady-state flux as a function ( , , , , , of ). and

X X = 10 X = 10 R = 0:01 R = 1 9 = 0:79 V=! = 0:89

harmonic ratio becomes negligible when the excessive ultrasaturation takes place, which is the case for higher than some 25 (see Fig. 16). By studying the plots presented in Figs. 13 and 15, one may observe that a good correlation of analytical formulae and sim(19) inulation results may be obtained, while calculating and , one uses corrected values and stead of

Fig. 17. Approximation error of minimum flux in relation to values obtained from simulation ( , , , , , ).

X = 4:3 X = 10 R = 0:01 R = 1

9 = 0:79 V=! = 1:09 This yields

(27)

(24) (25) where (26)

obtained from simA comparison of the minimum flux ulation runs and calculated with the formula (27) is shown in Figs. 17 and 18 for both cases presented in Figs. 13 and 15, being equal to 4.3 and 10.0 ). The respectively (i.e., with values of corrective coefficient for both cases are given graphically in Fig. 19. One may observe that the flux approximation . quality is very good in the wide range of


1333

Fig. 20. Alternative system configuration for EMTP–ATP studies.

Fig. 18. Approximation error of minimum flux in relation to values obtained , , , , from simulation ( , ).

X = 10 X = 10 R = 0:01 R = 1

9 = 0:79 V=! = 0:89

Fig. 21. Flux waveshape and transformer input current (primary), for , and

0:5X , X = 0:5X , R = 0:1X , X = 2X , V = V 0:79 .

Fig. 19. Corrective coefficient . reactance

X

X = 9 =

k according to (26) for two chosen values of the

The approximation formulae for fluxes , , and can be easily derived, analogously as for . Analyses have indicated that the accuracy of such equations is similar to (27). Further simulation studies have been performed for a three, , phase power transformer ( YNd11 connection, , , five-leg core) and two structures of the system, namely: 1) basic structure, as given in Fig. 8 (supplying system, transformer, load); 2) alternative structure, as presented in Fig. 20 (supplying system, transformer—unloaded or loaded, additional line, or load from the supplying side). The system shown in Fig. 20 is highly unfavorable, since particularly in such a configuration, the ultrasaturation may appear, during voltage jumps caused by disconnection of a nearby short circuit.

Fig. 22. Flux waveshape and transformer input current (primary), for X = 0:5X , X = 0:5X , R = 0:1X , X = 2X , V = 1:2V , 9 = 0:79 .

Several cases of transformer energization were simulated for and , residual fluxes , saturated various impedances , and system voltages . An extransformer reactances ample is presented in Fig. 21 and it is a case of excessive ultrasaturation. One may note that in the time span between 0.05 and 0.3 s, the transformer inrush current (dashed curve) has a very low second-harmonic component. Therefore, the differential relay operation is not blocked by the second harmonic restraint. The situation is even worse if, for some reason (e.g., emergency excitation buildup in the generator during a fault), the supplying voltage is higher than nominal. In such a case increased by 20%), the flux induced after trans(Fig. 22, former energization is much higher and the resulting inrush current contains almost no second harmonic at all.

1334


V. CONCLUSION Ultrasaturation poses a great problem for protective relaying of power transformers. The work presented here concentrates on the phenomenon itself, trying to explain when excessive flux without zero crossing may appear. Knowing why and when the ultrasaturation may occur, one may better understand the possible cases of the differential protection maloperation. The outcomes of this paper may be also treated as hints for substation personnel, defining the system configurations, and parameters that should be avoided in order to be on the safe side should unfavorable energization occur. It is clear that the explanation of the ultrasaturation and excessive ultrasaturation phenomena is only the first step toward developing new ideas and criteria for more reliable transformer protection that would better handle such unusual cases than currently employed relaying equipment. It seems that improvement of the protection operation would be possible with the introduction of new, modified, or extended criteria. The protection criteria should, on one hand, carry enough information on the event to be distinguished and, on the other hand, ensure appropriate stabilization for other events for which protection operation is undesirable. Certain proposals of such new criteria can be found in the literature, such as a complex second harmonic restraint [5], flux restraint (estimated on basis of voltages) [6], or current waveshape analysis [7]; others still wait for their inventors. It is believed that a lot of improvement can be reached with the introduction of adaptivity in the differential protection, a simple example of which is to use adaptive thresholds as well as adaptive measurement procedures. It has also been proved that considerable improvement of the operation and quite simple achievement of adaptive features of protection functions may be obtained with the use of various artificial-intelligence techniques. An example of using a fuzzy-logic technique for the realization of fuzzy differential protection is given in [8]. There is hope that an appropriate combination of classical and intelligent techniques should bring additional benefits; therefore, further investigations on the subject are desirable.

[6] Y. C. Kang et al., “Transformer protection relay based on the increment of the flux linkages,” presented at the CIGRE Study Committee B5 Colloq., Calgary, AB, Canada, Sep. 2005, paper 108. [7] B. Kasztenny, E. Rosolowski, M. M. Saha, and B. Hillstrom, “A comparative analysis of protection principles for multi-criteria power transformer relaying,” in Proc. 12th Power Systems Computation Conf., Dresden, Germany, Aug. 19–23, 1996, pp. 107–113. [8] B. Kasztenny, E. Rosolowski, M. M. Saha, and B. Hillstrom, “A selforganizing fuzzy logic based protective relay—An application to power transformer protection,” IEEE Trans. Power Del., vol. 12, no. 3, pp. 1119–1127, Jul. 1997. Andrzej Wiszniewski received the Ph.D. and D.Sc. degrees and the professorship in Electrical Engineering from the Wroclaw University of Technology, Wroclaw, Poland, in 1961, 1967, and 1972, respectively. He has worked in the field of power apparatus and systems as a specialist in the protection and control of power systems. He is an author of nine books and more than 130 scientific publications. He was Rector of the university for two terms (from 1990 to 1996). He was Minister for Science for four years, beginning in 1997. Prof. Wiszniewski is a Distinguished Member of CIGRE and Honorary Member of the Polish Institution of Electrical Engineers.

Waldemar Rebizant (M’00–SM’05) was born in Wroclaw, Poland, in 1966. He received the M.Sc., Ph.D., and D.Sc. degrees from the Wroclaw University of Technology (WUT), Wroclaw, in 1991, 1995, and 2004, respectively. Since 1991, he has been a faculty member with the Electrical Engineering Faculty at the WUT and is currently Assistant Professor and Vice Dean for Faculty Development and International Cooperation. His research interests are digital signal processing and AI techniques for power system protection purposes.

Daniel Bejmert was born in 1979 in Walbrzych, Poland. He graduated from the Electrical Engineering Faculty of Wroclaw University of Technology, Wroclaw, Poland, in 2004, where he is currently pursuing the Ph.D. degree at the Institute of Electrical Power Engineering. His research interests include application of intelligent algorithms in digital protection and control systems.

REFERENCES [1] A. Wiszniewski, H. Ungrad, and W. Winkler, Protection Techniques in Electrical Energy Systems. New York: Marcel Dekker, 1995. [2] “Numerical Differential Protection Relay for Transformers, Generators, Motors and Mini Busbars,” SIEMENS AG, 2006, 7UT613/63x V.4.06 Instruction Manual, Order . C53000-G1176-C160-2. [3] X. N. Lin and P. Liu, “The ultra-saturation phenomenon of loaded transformer energization and its impacts on differential protection,” IEEE Trans. Power Del., vol. 20, no. 2, pt. 2, pp. 1265–1272, Apr. 2005. [4] “EMTP-ATP Manuals,” EEUG, 2001. [5] B. Kasztenny and A. Kulidjian, “An improved transformer inrush restraint algorithm increases security while maintaining fault response performance,” presented at the 53rd Annu. Conf. Protective Relay Engineers, College Station, TX, Apr. 11–13, 2000.

.

Ludwig Schiel was born in Weimar, Germany, in 1957. He received the Dipl.-Ing. and Dr.-Ing. degrees from the Institute of Technology Zittau, Zittau, Germany, in 1984 and 1991, respectively. In the 1991, he joined the Department of Power Transmission and Distribution, Energy Automation, Siemens AG, Berlin, Germany. He is Project Manager of transformer differential protection systems.