DETERMINING HIGH VOLTAGE CABLE CONDUCTOR TEMPERATURES. Guy Van der Veken.

Euromold, Belgium.

INTRODUCTION.

INVESTIGATIONS.

Type tests on MV cable accessories are described in CENELEC HD628 and HD629 documents. Some of the tests described require elevated conductor temperatures within strict limits (e.g. 5K to 10K above the maximum permissible operating temperature of the extruded cable insulation).

Following points have been evaluated: 1) Validity of the methods as described. 2) Uncertainty of the results obtained. 3) Comparison of the two methods.

To accomplish this, over the allowed range of ambiant temperatures, the heating current is to be regulated. Due to the presence of high test-voltages across the cable’s insulation, the on-line measurement of the conductor temperature on the tested cable is not possible using standard measuring techniques. 3 methods for determining the cable temperature are given in the document HD628: 1) Method 1 using the relationship between the conductor temperature, the heating current and the ambiant temperature. 2) Method 2 using the relationship between the conductor temperature, the heating current and the cable-jacket temperature. (These two methods require a preceding calibration of the cable, to establish these relationships.) 3) Method 3 using a parallel loop of same cable in the same environment that is heated with the same current, but is not carrying high voltage.

For this purpose, following variables have been examined: a) Thermocouple materials. b) Thermocouple execution. c) Thermocouple placement. d) Effect of conductor cross-section. e) Number of thermocouples used. Uncertainty factors evaluated include: a) Uncertainty of the measuring equipments. b) Uncertainty of the measurements. c) Uncertainty of the calculated temperature.

RESULT

Evaluation of the data leads to following conclusions: 1) The method 2, using jacket temperature measurement, results in the lowest deviation. 2) Uncertainty of the temperature determined (± 3K for small crossections to ± 5K for large crosssections) is found to be high when compared to the temperature range given (5K).

Fast transients and their effect on transformer insulation : simulation and measurements 1

1

2

2

2

H De Herdt , J Declercq , T Sels , T Van Craenenbroeck , D Van Dommelen

1

Pauwels Trafo Belgium N.V., Belgium - 2Katholieke Universiteit Leuven, Belgium

ABSTRACT

An increasing number of unusual transformer failures caused by high frequency overvoltages was reported in medium voltage networks. An investigation was started to get a better understanding of these fast transient phenomena. Two major steps in this research project are described here. First, a numerical model is built to compute the occurring overvoltage phenomena. In the second part the material behaviour at highfrequencies is investigated, in order to determine the allowable voltages across the internal transformer insulation.

INTRODUCTION

The growing recognition of Power Quality issues in general, and high frequency phenomena in particular, has aroused more and more interest in transient overvoltage problems, both in industrial environments and distribution systems. For distribution transformers in particular, it has been shown by Van Craenenbroeck et al. (1) that present impulse and switching overvoltage tests do not fully cover the transient behaviour of transformers in their electrical environment. The insufficient knowledge of system and material behaviour at higher frequencies (e.g. between 10 and 200 kHz) explains the lack of standards on this subject, and vice versa. The limited interest in high frequency transients can be explained by a number of reasons : • the technical difficulty of the combined highfrequency / high-voltage measurements ; • the practical difficulty of on-site measurements in critical or afflicted systems ; • the limited practical knowledge of material and system characteristics ; • the small number of faults actually recognized as transient overvoltage problems. To get a better understanding of the origin and the consequences of high-frequency transients, two major questions need to be answered : (i) which voltage levels can be expected across the internal transformer insulation during a specific external

transient ? and (ii) which overvoltage level can be allowed across the insulation during this event ?

TRANSFORMER MODELS

High-Frequency Transformer Models

To get a detailed view on the behaviour of a distribution transformer, detailed high-frequency transformer models are required. Most of the manufacturers already have these models available for impulse voltage calculations. Some of the models even allow calculations on a turn-toturn basis, thus enabling the prediction of the voltage in every turn of the winding.

Transient Transformer Model

Though general high-frequency models are very accurate and detailed, they are usually too large to be incorporated in a general system model. In order to describe the high frequency behaviour of a transformer in its electrical environment, a reduced model is required. This model can be derived from the general high-frequency models, or built as a separate model. In this project the second option was selected for reasons of efficiency and flexibility : a simplified model was chosen as a compromise between simulation time and accuracy in predicting the first transformer resonances, as they are excited by typical transient network disturbances.

Different modelling techniques can be used. The five main streams in this field of modelling are based on self and mutual inductances, on leakage inductances, on the principle of duality, on measurements and on electromagnetic field calculations. The duality based model, introduced by Cherry (2), represents the leakage fluxes by an inductive polygon. The elements of this polygon can be derived from the corresponding short-circuit inductances, that can be obtained both numerically as well as experimentally. This approach was

chosen by Van Craenenbroeck et al. (3), since it is flexible, reasonably simple and has already proven to represent the essential transformer resonances (Adielson et al. (4)). In the model, the high voltage layer winding is broken up into smaller segments. Depending on the desired accuracy, this can be done on a per turn basis, on a per layer basis, or with any segmentation in between. Fig.1 shows the principle of the modelling technique. For sake of clarity the high voltage winding in the figure is only broken up in 3 segments, which is of course inadequate for determining the high-frequency behaviour of the transformer.

LV

The whole modelling process has been integrated in an ATP preprocessing program. The inputs are the geometric and material properties of the transformer; the output is an ATP-inputfile to be used in transient runs or frequency scans. Extra options are available to investigate the influence of connected cables and RC surge protection devices.

First Results

It is proven that all resonances below 100 kHz can be adequately calculated with the model described above. A first example shows the results for a transformer with a purely resistive load.

HV1 3 .5

3

HV2

2.5

2

HV3

V [p u ] 1 .5

1

0.5

Fig.1 : Transient model with 4 winding segments

0 20 25 30 35

The model is built around a leakage inductance polygon, describing the leakage field of the transformer. The actual winding segments are connected to this polygon by means of ideal transformers, in order to allow the inductive elements to be on a common voltage level, preferable the voltage level of an (arbitrarily chosen) reference winding segment. The leakage inductances are calculated in a fourstep process. The first step consists in the calculation of the short-circuit reactances Xij. Therefore, the differential equation describing the axisymmetric magnetostatic field is analytically solved using Rabins’ procedure (5). In a second step the busimpedance matrix ZBUS is determined. The corresponding admittance matrix YBUS is then obtained by inversion, and finally the leakage inductances are calculated. The non-linear magnetizing inductance is connected at the terminals of the inner low voltage winding. A parallel resistance is included here as well, in order to represent the frequencydependent core losses. The model is finally completed with a series resistance, to account for the copper losses in each winding segment, with series capacitances for each winding segment, and shunt capacitances between adjacent winding segments.

0

40 5

45

f [k H z ]

50

10

55

15

60

R [O h m ]

20

65 70

Fig.2 : Internal voltage vs. Load/Frequency

In Fig.2 the relative voltage transfer of the loaded transformer is shown, as calculated in an internal node at 60% of the total HV winding length. The frequency of the excitation source and the value of a low voltage resistive load are chosen as parameters. Under no-load conditions only one resonance frequency can be observed around 54 kHz. With a short-circuited low-voltage winding, two resonance frequencies appear at 30 and 56 kHz respectively. Rated load approximately corresponds to this situation. A second example shows the results for a typical underground cable system feeding a transformer. The voltage transfer at an internal node is presented in Fig.3 as a function of frequency f and cable length l. It is shown that the cable characteristics have a significant influence on the internal voltages in the transformer. When the first resonance frequency of the cable approaches one of the transformer’s resonance frequencies, a strong amplification of the voltage occurs.

Model Enhancement

18 16 14

Though the model seems to compute the resonance frequencies fairly accurately, the accuracy of the voltage excitation peaks was unsatisfactory, especially at resonance conditions. Therefore the model needs to be enhanced : • by subdividing the model in smaller winding parts (addition of more nodes) ; • by adding frequency dependent characteristics.

12

V [pu]

10 8 6 4 2

25

f [kHz]

35

45

55

1

15

65

l [km]

0

5

2

0

Fig.3 : Internal voltage vs. cable length/Frequency

The cable has a first resonance frequency at

fr =

1

(I)

4l L’ C ’

MATERIAL TESTING

with L’ and C’ the direct sequence inductance and capacitance per unit cable length, and l the total cable length. This resonance frequency is typically around 30 to 50 kHz/km. As Fig.3 points out, cable resonances with long cable lengths are less harmful since damping is proportional to e the propagation constant γ defined as

The addition of the frequency dependent capacitances, inductances and resistances requires an extensive experimental evaluation and tuning process. Especially the calculation of the losses as function of frequency needs a detailed consideration.

−γl

with

γ = Z ’.Y ’

(II)

Z’ = R’ + jωL’  Y ’ = jωC’

(III)

with R’ the resistance per unit cable length. In these calculations the frequency dependence of the cable parameters must be taken into account. The internal flux linkages decrease rapidly with frequency in the range up to 10 kHz. Therefore, the value of the cable inductance may be computed somewhere between 10 and 100 kHz, as the variation of the cable inductance in this frequency range is rather limited. The value of the resistance however increases drastically with frequency (first quadratically and then slowly shifting to a square-root dependency at higher frequencies) and a correct assessment is thus necessary for an adequate representation of the cable damping. As a result of this frequency dependence of the losses, higher order resonances are very unlikely.

Tesla Transformer Setup

As was shown by former studies, e.g. by Tsuneharu et al (6), the ageing of insulating materials, such as oil impregnated paper and enamel, may be accelerated by high-frequency pulses. Therefore a research project was set up in order to study the effects of repetitive pulses on the transformer winding insulation. To investigate these effects, a complete test system has been developed by Sels et al. (7). This system enables the generation of high-frequency high-voltage pulses superimposed on a 50 Hz mains waveform. After applying a series of pulses to the test object, the possible degradation of the test object insulation can be checked by measuring the Partial Discharge (PD) level. The test system was based on a Tesla Transformer set-up as described by Hardt and Koenig (8) and by Heise (9). The full test circuit is shown in Fig.4. The concept of the Tesla Transformer principle is based on the energy transmission between two coupled resonating circuits (8). The first circuit consists of C1 and L1, where L1 is air-coupled with L2. The second resonating circuit is formed by L2 and the overall capacity Ctot of the measurement circuit (Cd1, Cd2 and CPD), the coupling capacitor C3 and the capacity of the test object C2. The two circuits are theoretically tuned when

L1 ⋅ C1 = L2 ⋅ C tot

(IV)

The resonance frequency f2 of the secondary circuit is then :

RDC

R1

TT

R2 CPD

VDC

C1

L2

Cd1

L1

RCd PD

S

C2

C3

TH

Cd2

R3 Driver

Measurements T2

VAC

Fig.4 : Test circuit

Material Testing Procedure

f2 =

1 1 − 2 π L2 C tot

R 22 4 L22

(V)

A single-phase transformer T2, applies the mains voltage to the test object. Precautions need to be taken for the coupling of this transformer to the circuit. This coupling is carried out through a coupling capacitor C3 which acts like a short-circuit for the HF pulses and like an open circuit for the 50 Hz mains voltage. Also, in the case of a shortcircuit at C2, capacitor C3 collaborates with R3 to limit the current through transformer T2. The primary of T2 is supplied by an auto-transformer which is protected against overcurrents and will shut down the system if necessary. Also the coupling of the equipment for measuring PD with the test circuit needs to be performed carefully. The used PD measuring instruments are not compatible with the high peak voltages. Therefore, a switch S will be closed when the high frequency pulses are fired to the test object, and S will be opened when it is save to measure PD’s. When S is opened, high frequency pulse trains are blocked by the ’driver’, which mainly has two functions: the first one is producing a pulse train to fire the thyristor, and the second one is improving the safety conditions of the test circuit. The resistor RDC ensures that the current flowing through L1 and the thyristor TH drops below the hold-current of the thyristor. Due to this, the thyristor is allowed to extinguish in a natural way.

The test object C2 consists of two wound layers of round magnet wire, separated by an insulating layer of paper. This type of test objects allows the determination the effect of the High-Frequency High-Voltage (HF-HV) pulses on the material properties of a typical distribution transformer insulation structure. A number of different test objects, with different insulating materials and insulating distances can be tested in this way. After the detection the PD inception and extinction voltage, the test object will be subjected to the HFHV pulses. The 50 Hz mains can be set at the rated voltage of the double layer or can be increased to the calculated maximum partial discharge free voltage level. After applying a large number of pulses (e.g. 500.000), a new examination is carried out on the PD inception and extinction voltage. This test cycle is then repeated until breakdown of the insulation, or until the PD inception voltage decreases below the rated voltage. Other test cycles can be taken into consideration : • Increasing the peak to peak voltage levels of the HF-HV pulses, with constant pulse frequency (frequency of the damped oscillation) ; • Increasing the 50 Hz mains voltage, with a constant pulse frequency ; • Increasing the pulse frequency at a constant 50 Hz and pulse voltage level ; • Decreasing the pulse repetition time (between two consecutive pulses).

CONCLUSION

REFERENCES

A reduced numerical distribution transformer model has been built and will be improved in the future. The main objective is to combine simplicity of the model with a reasonable accuracy. The model is integrated in an ATP preprocessing program, which allows to add a model of the electrical environment of the transformer.

1. Van Craenenbroeck T, De Herdt H, De Ceuster J, Marly J P, Van Dommelen D, Belmans R, 1999, "Detailed Study of Fast Transient Phenomena in Transformers and Substations Leading to an Improved System Design", th Proc. 15 CIRED, pp. 1.12.1-6

A material testing set-up has been designed, built and tested. A full test program has been prepared, and the results will lead to a better understanding of the behaviour of the typical insulation structure in distribution transformers. This knowledge can then be incorporated into the distribution transformer model. The combination of both studies will eventually help to understand and predict the behaviour of a distribution transformer in its network environment. The new model will be able to simulate the transient behaviour of a transformer in its environment, and evaluate the effects on the material life expectancy. This will result in new design guidelines extending the reliability of the transformer even in a disturbed environment. However, this approach will require a close cooperation between the transformer manufacturer and the customer, in order to allow an optimized and tuned design of the transformer as part of the surrounding system.

2. Cherry E C, 1949, "The Duality between Interlinked Electric and Magnetic Circuits and the Formation of Transformer Equivalent Circuits", Proc. of the Phys. Soc., Vol. (B) 62, pp.101-111 3. Van Craenenbroeck T, De Ceuster J, Marly J P, De Herdt H, Brouwers B, Van Dommelen D, 2000, "Experimental and Numerical Analysis of Fast Transient Phenomena in Distribution Transformers", Proc. IEEE/PES Winter Meeting, Singapore, CD-ROM (6P) 4. Adielson T, Carlson A, Margolis H B, Halladay J H, “Resonant Overvoltages in EHV Transformers - Modelling and Application”, 1981, IEEE Trans. on Power App. and Syst., Vol. PAS-100 No. 7, pp. 3563-3572 5. Rabins L, 1956, "Transformer Reactance Calculations with Digital Computers", AIEE Trans. 75, pp.261-267 6. Tsuneharu T, Toshiyuki Y, Masaki H, Tamotsu I, 1984, "Dielectric Strength of Transformer Insulation Against Oscillatory Impulse Voltages", Electr. Eng. in Japan, Vol. 104B No. 1, pp. 66-73 7. Sels T, Van Craenenbroeck T, Brouwers B, Van Dommelen D, De Ceuster J, 2000, "Simulation of Transformer Behaviour Subject to Fast Transients th Using a Tesla Transformer", 8 Int. Conf. DMMA 8. Hardt N, Koenig D, 1998, "Testing of Insulating Materials at High Frequencies and High Voltage Based on the Tesla Transformer Principle", Conf. Rec. of IEEE Int. Symp. on Electr. Ins., 517-520 9. Heise W, 1964, "Tesla-Transformatoren", Elektr. Zeitschrift, 85 Jahrgang, 1-8