Unit-3 Of Hve

High Voltage Engineering UnitUnit-III

UNIT-III GENERATION OF HV AC DC IMPULSE VOLTAGE & CURRENT 22. INTRODUCTION A fundamental knowledge about generators and circuits which are in use for the generation of high voltages belongs to the background of work on H.V. technology. Generally commercially available H.V. generators are applied in routine testing laboratories; they are used for testing equipment such as transformers, bushings, cables, capacitors, switchgear, etc. The tests should confirm the efficiency and reliability of the products and therefore the H.V. testing equipment is required to study the insulation behavior under all conditions which the apparatus is likely to encounter. The amplitudes and types of the test voltages, which are always higher than the normal or rated voltages of the apparatus under test, are in general prescribed by national or international standards or recommendations, and therefore there is not much freedom in the selection of the H.V. testing equipment. Quite often, however, routine testing laboratories are also used for the development of new products. Then even higher voltages might be necessary to determine the factor of safety over the prospective working conditions and to ensure that the working margin is neither too high nor too low. Most of the H.V. generator circuits can be changed to increase the output voltage levels, if the original circuit was properly designed. Therefore, even the selection of routine testing equipment should always consider a future extension of the testing capabilities. The work carried out in research laboratories varies considerably from one establishment to another, and the type of equipment needed varies accordingly. As there are always some interactions between the H.V. generating circuits used and the test results, the layout of these circuits has to be done very carefully. The classes of tests may differ from the routine tests, and therefore specially designed circuits are often necessary for such laboratories. The knowledge about some fundamental circuits treated in this chapter will also support the development of new test circuits. Finally, high voltages are used in many branches of natural sciences or other technical applications. The generating circuits are often the same or similar to those treated in the following sections. It is not the aim, however, of this introductory text to treat the broad variations of possible circuits, due to space limitation. Not taken into account are also the

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High Voltage Engineering UnitUnit-III differing problems of electrical power generation and transmission with high voltages of A.C. or D.C., or the pure testing technique of H.V. equipment, the procedures of which may be found in relevant standards of the individual equipment. Power generation and transmission problems are treated in many modern books, some of which are listed within the bibliography of an earlier report. This chapter discusses the generation of the following main classes of voltages: direct voltages, alternating voltages, and transient voltages.

REFERENCE: •

HVE FUNDAMENTALS: KUFFEL, ZAENGL & KUFFEL: P-8-9

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23. DIRECT VOLTAGES In H.V. technology direct voltages are mainly used for pure scientific research work and for testing equipment related to HVDC transmission systems. There is still a main application in tests on HVAC power cables of long length, as the large capacitance of those cables would take too large a current if tested with A.C. voltages Although such D.C. tests on A.C. cables are more economical and convenient, the validity of this test suffers from the experimentally obtained stress distribution within the insulating material, which may considerably be different from the normal working conditions where the cable is transmitting power at low-frequency alternating voltages. For the testing of polyethylene H.V. cables, in use now for some time, D.C. tests are no longer used, as such tests may not confirm the quality of the insulation. High D.C. voltages are even more extensively used in applied physics (accelerators, electron microscopy, etc.), electro-medical equipment (X-rays), industrial applications (precipitation and filtering of exhaust gases in thermal power stations and the cement industry; electrostatic painting and powder coating, etc.), or communications electronics (TV, broadcasting stations). Therefore, the requirements on voltage shape, voltage level, and current rating, short- or long-term stability for every HVDC generating system may differ strongly from each other. With the knowledge of the fundamental generating principles it will be possible, however, to select proper circuits for a special application. In the International Standard IEC 60-1 or IEEE Standard 4-1995 the value of a direct test voltage is defined by its arithmetic mean value, which will be designated as V . Therefore, this value may be derived from: T

V =

1 V (t )dt T ∫0

2.1

Where T equals a certain period of time if the voltage V (t) is not constant, but periodically oscillating with a frequency of f = 1/T. Test voltages as applied to test objects then deviate periodically from the mean value. This means that a ripple is present. The amplitude of the ripple, δV, is defined as half the difference between the maximum and minimum values, or δV = 0.5(Vmax -Vmin)

2.2

The ripple factor is the ratio of the ripple amplitude to the arithmetic mean value, or δV/V . For test voltages this ripple factor should not exceed 3 percent unless otherwise specified by the appropriate apparatus standard or be necessary for fundamental investigations. The D.C.

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High Voltage Engineering UnitUnit-III voltages are generally obtained by means of rectifying circuits applied to A.C. voltages or by electrostatic generation. A treatment of the generation principles according to this subdivision is appropriate.

REFERENCE: •

HVE FUNDAMENTALS: KUFFEL, ZAENGL & KUFFEL: 2.1 P-9-10.

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24. HVAC HV TRANSFORMER Most of the present day transmission and distribution networks are operating on A.C. voltages and hence most of the testing equipments relate to high A.C. voltages. Even though most of the equipments on the system are 3-phase systems, a single phase transformer operating at power frequency is the most common from of HVAC testing equipment. Test transformers normally used for the purpose have low power rating but high voltage ratings. These transformers are mainly used for short time tests on high voltage equipments. The currents required for these tests on various equipments are given below: Insulators, C.B., bushings, Instrument transformers Power transformers, h.v. capacitors. Cables

= = =

0.1– 0.5 A 0.5–1 A 1 A and above

The design of a test transformer is similar to a potential transformer used for the measurement of voltage and power in transmission lines. The flux density chosen is low so that it does not draw large magnetizing current which would otherwise saturate the core and produce higher harmonics.

REFERENCE: •

HVE: C. L. WADHWA, 2.4; P-69

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25. NEED FOR CASCADE CONNECTION & WORKING OF TRANSFORMERS UNITS CONNECTED IN CASCADE For voltages higher than 400 KV, it is desired to cascade two or more transformers depending upon the voltage requirements. With this, the weight of the whole unit is subdivided into single units and, therefore, transport and erection becomes easier. Also, with this, the transformer cost for a given voltage may be reduced, since cascaded units need not individually possess the expensive and heavy insulation required in single stage transformers for high voltages exceeding 345 kV. It is found that the cost of insulation for such voltages for a single unit becomes proportional to square of operating voltage.

Fig. 2.9 shows a basic scheme for cascading three transformers. The primary of the first stage transformer is connected to a low voltage supply. A voltage is available across the secondary of this transformer. The tertiary winding (excitation winding) of first stage has the same number of turns as the primary winding, and feeds the primary of the second stage transformer. The potential of the tertiary is fixed to the potential V of the secondary winding as shown in Fig. 2.9. The secondary winding of the second stage transformer is connected in series with the secondary winding of the first stage transformer, so that a voltage of 2V is available between the ground and the terminal of secondary of the second stage transformer. Similarly, the stage-III transformer is connected in series with the second stage transformer. With this the output voltage between ground and the third stage transformer, secondary is 3V.

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High Voltage Engineering UnitUnit-III It is to be noted that the individual stages except the upper most must have three-winding transformers. The upper most, however, will be a two winding transformer. Fig. 2.9 shows metal tank construction of transformers and the secondary winding is not divided. Here the low voltage terminal of the secondary winding is connected to the tank. The tank of stage-I transformer is earthed. The tanks of stage-II and stage-III transformers have potentials of V and 2V, respectively above earth and, therefore, these must be insulated from the earth with suitable solid insulation. Through H.T. bushings, the leads from the tertiary winding and the H.V. winding are brought out to be connected to the next stage transformer. However, if the high voltage windings are of mid-point potential type, the tanks are held at 0.5 V, 1.5 V and 2.5 V, respectively. This connection results in a cheaper construction and the high voltage insulation now needs to be designed for V/2 from its tank potential. The main disadvantage of cascading the transformers is that the lower stages of the primaries of the transformers are loaded more as compared with the upper stages. The loading of various windings is indicated by P in Fig. 2.9. For the three-stage transformer, the total output VA will be 3VI = 3P and, therefore, each of the secondary winding of the transformer would carry a current of I = P/V. The primary winding of stage-III transformer is loaded with P and so also the tertiary winding of second stage transformer. Therefore, the primary of the second stage transformer would be loaded with 2P. Extending the same logic, it is found that the first stage primary would be loaded with P. Therefore, while designing the primaries and tertiaries of these transformers, this factor must be taken into consideration.

The total short circuit impedance of a cascaded transformer from data for individual stages can be obtained. The equivalent circuit of an individual stage is shown in Fig. 2.10. Here Zp, Zs, and Zt, are the impedances associated with each winding. The impedances are shown in series with an ideal 3-winding transformer with corresponding

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High Voltage Engineering UnitUnit-III number of turns Np, Ns and Nt. The impedances are obtained either from calculated or experimentally-derived results of the three short-circuit tests between any two windings taken at a time. Let

Zps = leakage impedance measured on primary side with secondary short circuited and tertiary open. Zpt = leakage impedance measured on primary side with tertiary short circuited and secondary open. Zst = leakage impedance on secondary side with tertiary short circuited and primary open.

If these measured impedances are referred to primary side then Zps = Zp + Zs, Zpt = Zp + Zt

and Zst = Zs + Zt

Solving these equations, we have 1 1 1 Z p = ( Z ps + Z pt − Z st ) , Z s = ( Z ps + Z st − Z pt ) and Z t = ( Z pt + Z st − Z ps ) 2 2 2

2.19

Assuming negligible magnetizing current, the sum of the ampere turns of all the windings must be zero. N p I p − Ns I s − Nt It = 0 Assuming lossless transformer, we have,

Zp = jXp,

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Zs = jXs,

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and

Zt = jXt

High Voltage Engineering UnitUnit-III

Also let Np = Nt for all stages, the equivalent circuit for a 3-stage transformer would be given as in Fig.2.11. Fig. 2.11 can be further reduced to a very simplified circuit as shown in Fig. 2.12. The resulting short circuit reactance Xres is obtained from the condition that the power rating of the two circuits be the same. Here currents have been shown corresponding to high voltage side.

I 2 X res = (3I ) 2 X p + (2 I ) 2 X p + I 2 X s + I 2 X s + I 2 X s + (2 I ) 2 X t + I 2 X t X res = 14 X p + 3 X s + 5 X t

2.20

Instead of 3(Xp + Xs + Xt) as might be expected. Equation (2.20) can be generalized for an nstage transformer as follows: n

Xres = ∑ [(n − i + 1) 2 X pi + X si + (i + 1) 2 X ti i =1

REFERENCE: REFERENCE: •

HVE: C. L. WADHWA, 2.4; P-69

•

HVE: C. L. WADHWA, 2.4; P-70-72

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26. SERIES RESONANT CIRCUIT (PRINCIPLE OF OPERATION AND ADVANTAGES) The equivalent circuit of a single-stage-test transformer along with its capacitive load is shown in Fig. 2.15. Here L1 represents the inductance of the voltage regulator and the transformer primary, L the exciting inductance of the transformer, L2 the inductance of the transformer secondary and C the capacitance of the load. Normally inductance L is very large as compared to L1 and L2 and hence its shunting effect can be neglected. Usually the load capacitance is variable and it is possible that for certain loading, resonance may occur in the circuit suddenly and the current will then only be limited by the resistance of the circuit and the voltage across the test specimen may go up as high as 20 to 40 times the desired value. Similarly, presence of harmonics due to saturation of iron core of transformer may also result in resonance. Third harmonic frequencies have been found to be quite disastrous. With series resonance, the resonance is controlled at fundamental frequency and hence no unwanted resonance occurs. The development of series resonance circuit for testing purpose has been very widely welcome by the cable industry as they faced resonance problem with test transformer while testing short lengths of cables. In the initial stages, it was difficult to manufacture

continuously

variable

high

voltage and high value reactors to be used in the series circuit and therefore, indirect methods to achieve this objective were employed. Fig. 2.16 shows a continuously variable reactor connected in the low voltage winding of the step up transformer whose secondary is rated for the full test voltage. C2 represents the load capacitance. If N is the transformation ratio and L is the inductance on the low voltage side of the transformer, then it is reflected with N2L value on the secondary side (load side) of the

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High Voltage Engineering UnitUnit-III transformer. For certain setting of the reactor, the inductive reactance may equal the capacitive reactance of the circuit, hence resonance will take place. Thus, the reactive power requirement of the supply becomes zero and it has to supply only the losses of the circuit. However, the transformer has to carry the full load current on the high voltage side. This is a disadvantage of the method. The inductor are designed for high quality factors Q = ωL/R. The feed transformer, therefore, injects the losses of the circuit only.

It has now been possible to manufacture high voltage continuously variable reactors 300 kV per unit using a new technique with split iron core. With this, the testing step up transformer can be omitted as shown in Fig. 2.17. The inductance of these inductors can be varied over a wide range depending upon the capacitance of the load to produce resonance. Fig. 2.17 (b) represents an equivalent circuit for series resonance circuit. Here R is usually of low value. After the resonance condition is achieved, the output voltage can be increased by increasing the input voltage. The feed transformers are rated for nominal current ratings of the reactor. Under resonance, the output voltage will be V0 =

V 1 R ωC 2

Where V is the supply voltage. Since at resonance

ωL =

Therefore,

V0 =

1 ωC 2

V ωL = VQ R

Where Q is the quality factor of the inductor which usually varies between 40 and 80. This means that with Q = 40, the output voltage is 40 times the supply voltage. It also means that the reactive power requirements of the load capacitance in kVA is 40 times the power to be provided by the feed transformer in KW. This results in a relatively small power rating for the feed transformer.

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ADVANTAGES: The following are the advantages of series resonance circuit: (i). The power requirements in KW of the feed circuit are (kVA)/Q where kVA is the reactive power requirements of the load and Q is the quality factor of variable reactor usually greater than 40. Hence, the requirement is very small. (ii). The series resonance circuit suppresses harmonics and interference to a large extent. The near sinusoidal wave helps accurate partial discharge of measurements and is also desirable for measuring loss angle and capacitance of insulating materials using Schering Bridge. (iii). In case of a flashover or breakdown of a test specimen during testing on high voltage side, the resonant circuit is detuned and the test voltage collapses immediately. The short circuit current is limited by the reactance of the variable reactor. It has proved to be of great value as the weak part of the isolation of the specimen does not get destroyed. In fact, since the arc flash over has very small energy, it is easier to observe where exactly the flashover is occurring by delaying the tripping of supply and allowing the recurrence of flashover. (iv). No separate compensating reactors (just as we have in case of test transformers) are required. This results in a lower overall weight. (v). When testing SF6 switchgear, multiple breakdowns do not result in high transients. Hence, no special protection against transients is required. (vi). Series or parallel connections of several units is not at all a problem. Any number of units can be connected in series without bothering for the impedance problem which is very severely associated with a cascaded test transformer. In case the test specimen requires large current for testing, units may be connected in parallel without any problem.

REFERENCE: •

HVE: C. L. WADHWA, 2.4; P-73-76

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27. TESLA COIL High frequency high voltages are required for rectifier D.C. power supplies. Also, for testing electrical apparatus for switching surges, high frequency high voltage damped oscillations are needed which need high voltage high frequency transformers. The advantages of these high frequency transformers are: (i)

The absence of iron core in transformers and hence saving in cost and size,

(ii)

Pure sine wave output,

(iii) Slow build-up of voltage over a few cycles and hence no damage due to switching surges, and (iv) Uniform distribution of voltage across the winding coils due to subdivision of coil stack into a number of units. The commonly used high frequency resonant transformer is the Tesla coil, which is a doubly tuned resonant circuit shown schematically in Fig. 6.13a. The primary voltage rating is 10 kV and the secondary may be rated to as high as 500 to 1000 kV. The primary is fed from a D.C. or A.C. supply through the condenser C1. A spark gap G connected across the primary is triggered at the desired voltage V1 which induces a high self-excitation in the secondary. The primary and the secondary windings (L1 and L2) are wound on an insulated former with no core (air-cored) and are immersed in oil. The windings are tuned to a frequency of 10 to 100 kHz by means of the condensers C1 and C2.

Fig. 6.13 Tesla Coil equivalent circuit and its output waveform

The output voltage V2 is a function of the parameters L1, L2 C1, C2 and the mutual inductance M. usually, the winding resistances will be small and contribute only for damping of the oscillations. The analysis of the output waveform can be done in a simple manner neglecting the winding resistances. Let the condenser C1 be charged to a voltage V1 when the spark gap is

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High Voltage Engineering UnitUnit-III triggered. Let a current i1 flow through the primary winding L1 and produce a current i2 through L2 and C2. Then, t

1 di di V1 = ∫ i1dt + L1 1 + M 2 C1 0 dt dt

(6.9)

t

1 di di 0= i2 dt + L2 2 + M 1 ∫ C2 0 dt dt

And,

The Laplace transformed equations for the above are,

V1  1  =  L1s + I1 + MsI 2 s  C1s 

(6.10)

 1  0 = [Ms ]I 2 +  L2 s + I2 C2 s  

And,

Where I1 & I2 are the Laplace transformed values, of i1 and i2. The output voltage V2 across the condenser C2 is t

V2 =

1 i2 dt ; C2 ∫0

V2 (s ) =

Or its transformed equation is

1 C2 s

(6.11)

Where V2(s) is the Laplace transform of V2. The solution for V2 from the above equations will be V2 =

MV1 1 [cos γ 1t − cos γ 2t ] 2 σL1 L2C1 γ 2 − γ 12

σ 2 =1−

Where,

(6.12)

M2 = 1− K 2 L1 L2

K = coefficient of coupling between the windings L1 and L2

γ 1, 2 = ω1 =

ω12 + ω22 2 1 L1C1

 ω 2 + ω22   − ω12ω22 1 − K 2 ±  1 2  

(

And

ω2 =

)

1 L2C2

The output waveform is shown in Fig. 6.13(b). The peak amplitude of the secondary voltage V2 can be expressed as,

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V2 max = V1e

Where,

e=

L2 L1

(6.13)

2 (1 − σ ) (1 + a ) 2 − 4σa

L2C2 W12 a= = L1C1 W22 A more simplified analysis for the Tesla coil may be presented by considering that the energy stored in the primary circuit in the capacitance C1 is transferred to C2 via the magnetic coupling. If W1 is the energy stored in C1 and W2 is the energy transferred to C2 and if the efficiency of the transformer is η, then 1 1  W1 = ηC1V12 =  C2V22  2 2  From which

V2 = V1 η

C1 C2

(6.14)

(6.14a)

It can be shown that if the coefficient of coupling K is large the oscillation frequency is less, and for large values of the winding resistances and AT, the waveform may become a unidirectional impulse. This is shown in the next sections while dealing with the generation of switching surges.

REFERENCE: •

HVE: KAMARAJU NAIDU; 6.2.3; P-126-128

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28. HVDC- VOLTAGE DOUBLER CIRCUIT

Both full wave and half wave rectifier circuits produce a D.C. voltage less than the A.C. maximum voltage. When higher D.C. voltages are needed, a voltage doubler or cascaded rectifier doubler circuits are used. The schematic diagram of voltage doublers are given in Figs. 6.3a and b. In voltage doubler circuit shown in Fig. 6.3a, the condenser C1 is charged through rectifier R to a voltage of +Vmax with polarity as shown in the figure during the negative half cycle. As the voltage of the transformer rises to positive Vmax during the next half cycle, the potential of the other terminal of C1 rises to a voltage of +2Vmax.

Fig. 6.2 Input and output waveforms of half and full wave rectifiers (a) Input sine wave (b) Output with half wave rectifier and condenser filter (c) Output with full wave rectifier and condenser filter (d) Vmax, Vmean and ripple voltage and 8V with condenser filter of a full wave rectifier

Thus, the condenser C2 in turn is charged through R2 to 2Vmax. Normally the D.C. output voltage on load will be less than 2Vmax, depending on the time constant C2RL and the forward charging time constants. The ripple voltage of these circuits will be about 2% for RL/r ≤ 10 and X/r ≤ 0.25, where X and r are the reactance and resistance of the input transformer. The rectifiers are rated to a peak inverse voltage of 2Vmax, and the condensers C1 and C2 must also have the same rating. If the load current is large, the ripple also is more.

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High Voltage Engineering UnitUnit-III Cascaded voltage doublers are used when larger output voltages are needed without changing the input transformer voltage level. A typical voltage doubler is shown in Fig. 6.3b and its input and output waveforms are shown in Fig. 6.3(c). The rectifiersR1 and R2 with transformer T1 and condensers C1 and C2 produce an output voltage of 2V in the same way as described above. This circuit is duplicated and connected in series or cascade to obtain a further voltage doubling to 4V. T is an isolating transformer to give insulation for 2Vmax since the transformer T2 is at a potential of 2Vmax above the ground. The voltage distribution along the rectifier string R1, R2, R3 and R4 is made uniform by having condensers C1, C2, C3 and C4 of equal values. The arrangement may be extended to give 6V, 8V, and so on by repeating further stages with suitable isolating transformers. In all the voltage doubler circuits, if valves are used, the filament transformers have to be suitably designed and insulated, as all the cathodes will not be at the same potential from ground. The arrangement becomes cumbersome if more than 4V is needed with cascaded steps.

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(1) A.C. input voltage waveform, (2) A.C. output voltage waveform without condenser filter, (3) A.C. output voltage waveform with condenser filter Fig. 6.3 Voltage doubler circuits R1, R2, R3, R4 - rectifiers; T1, T2 - H.V. transformers; C1, C2, C3- condensers; RL - Load resistance; T- Isolating transformer

REFERENCE: •

HVE: KAMARAJU NAIDU; 6.1.2; P-106-108

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29. COCK CROFT- WALTON TYPE HIGH VOLTAGE DC SET In 1932, Cockroft and Walton suggested an improvement over the circuit developed by Greinacher for producing high D.C. voltages. Fig. 2.3 shows a multistage single phase cascade circuit of the Cockroft-Walton type.

No Load Operation: The portion ABM′MA is exactly indentical to Greinarcher voltage doubler circuit and the voltage across C becomes 2Vmax when M attains a voltage 2Vmax. During the next half cycle when B becomes positive with respect to A, potential of M falls and, therefore, potential of N also falls becoming less than potential at

M′

hence C2 is charged through D2. Finally all the capacitors C′1, C′2, C′3, C1, C2, and C3 are charged. The voltage across the column of capacitors consisting of C1, C2, C3, keeps on oscillating as the supply voltage alternates. This column, therefore, is known as oscillating column. However, the voltage across the capacitances C′1, C′2, C′3, remains constant and is known as smoothening column. The voltages at M′, N′, and O′ are 2Vmax, 4Vmax and 6Vmax. Therefore, voltage across all the capacitors is 2Vmax except for C1 where it is Vmax only. The total output voltage is 2nVmax where n is the number of stages. Thus, the use of multistages arranged in the manner shown enables very high voltage to be obtained. The equal stress of the elements (both capacitors and diodes) used is very helpful and promotes a modular design of such generators. Generator

Loaded:

When

the

generator is loaded, the output voltage will

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High Voltage Engineering UnitUnit-III never reach the value 2nVmax. Also, the output wave will consist of ripples on the voltage. Thus, we have to deal with two quantities, the voltage drop ∆V and the ripple δV. Suppose a charge q is transferred to the load per cycle. This charge is q = 1/f = 1T. The charge comes from the smoothening column, the series connection of C′1, C′2, and C′3. If no charge were transferred during T from this stack via D1, D2, D3, to the oscillating column, the peak to peak ripple would merely be n

1 n = 0 Ci '

2δV = 1T ∑

(2.6)

But in practice charges are transferred. Cascade generators of Cockcroft – Walton type are used and manufactured today worldwide. The D.C. voltages produced with this circuit may range from some 10 kV up to more than 2 MV, with current ratings from some 10 µA up to some 100 mA. Supply frequencies of 50/60 Hz are heavily limiting the efficiency, and therefore higher frequencies up to about 1000 Hz (produced by single-phase alternators) or some 10 kHz (produced by electronic circuits) are dominating.

REFERENCE: •

HVE: C L WADHWA; 2.2; P-59-60

•

HVE FUNDAMENTALS: KUFFEL, ZAENGL & KUFFEL; P-19

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30. INTRODUCTION TO STANDARD LIGHTNING AND SWITCHING IMPULSE VOLTAGES Disturbances of electric power transmission and distribution systems are frequently caused by two kinds of transient voltages whose amplitudes may greatly exceed the peak values of the normal A.C. operating voltage. The first kind is lightning overvoltages, originated by lightning strokes hitting the phase wires of overhead lines or the busbars of outdoor substations. The amplitudes are very high, usually in the order of 1000 kV or more, as every stroke may inject lightning currents up to about 100 kA and even more into the transmission line; each stroke is then followed by traveling waves, whose amplitude is often limited by the maximum insulation strength of the overhead line. The rate of voltage rise of such a traveling wave is at its origin directly proportional to the steepness of the lightning current, which may exceed 100 kA/µsec, and the voltage levels may simply be calculated by the current multiplied by the effective surge impedance of the line. Too high voltage levels are immediately chopped by the breakdown of the insulation and therefore traveling waves with steep wave fronts and even steeper wave tails may stress the insulation of power transformers or other H.V. equipment severely. Lightning protection systems, surge arresters and the different kinds of losses will damp and distort the traveling waves, and therefore lightning overvoltages with very different waveshapes are present within the transmission system. The second kind is caused by switching phenomena. Their amplitudes are always related to the operating voltage and the shape is influenced by the impedances of the system as well as by the switching conditions. The rate of voltage rise is usually slower, but it is well known that the waveshape can also be very dangerous to different

insulation

systems,

especially

to

atmospheric air insulation in transmission systems with voltage levels higher than 245 kV.

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High Voltage Engineering UnitUnit-III Both types of overvoltages are also effective in the L.V. distribution systems, where they are either produced by the usual, sometimes current-limiting, switches or where they have been transmitted from the H.V. distribution systems. Here they may often cause a breakdown of electronic equipment, as they can reach amplitudes of several kilovolts, and it should be mentioned that the testing of certain L.V. apparatus with transient voltages or currents is a need today.

REFERENCE: •

HVE FUNDAMENTALS: KUFFEL, ZAENGL & KUFFEL; P-48-51

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31. ANALYSIS OF SINGLE STAGE IMPULSE GENERATOR EXPRESSION FOR OUTPUT IMPULSE VOLTAGE Two basic circuits for single-stage impulse generators are shown in Fig. 2.25. The capacitor C1 is slowly charged from a D.C. source until the spark gap G breaks down. This spark gap acts as a voltage-limiting and voltage-sensitive switch, whose ignition time (time to voltage breakdown) is very short in comparison to T1.

As such single-stage generators may be used for charging voltages from some kV up to about 1MV; the sphere gaps will offer proper operating conditions. An economic limit of the charging voltage V0 is, however, a value of about 200 to 250 kV, as too large diameters of the spheres would otherwise be required to avoid excessive inhomogeneous field distributions between the spheres. The resistors R1, R2 and the capacitance C2 form the wave shaping network. R1 will primarily damp the circuit and control the front time T1. R2 will discharge the capacitors and therefore essentially control the wave tail. The capacitance C2 represents the full load, i.e. the object under test as well as all other capacitive elements which are in parallel to the test object (measuring devices; additional load capacitor to avoid large variations of T1/T2, if the test objects are changed). No inductances are assumed so far,

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High Voltage Engineering UnitUnit-III and are neglected in the first fundamental analysis, which is also necessary to understand multistage generators. In general this approximation is permissible, as the inductance of all circuit elements has to be kept as low as possible. Before starting the analysis, we should mention the most significant parameter of impulse generators. This is the maximum stored energy: W=

1 C1 (V0 MAX ) 2 2

(2.22)

Within the ‘discharge’ capacitance C1.As C1 is always much larger than C2, this figure determines mainly the cost of a generator. For the analysis we may use the Laplace transform circuit sketched in Fig. 2.25(c), which simulates the boundary condition, that for t ≤ 0, C1 is charged to V0 and for t> 0 this capacitor is directly connected to the wave-shaping network. For the circuit Fig. 2.25(a) the output voltage is thus given by the expression

V ( s) = Where

By Substitution we find

Where

V0 Z 2 , s Z1 + Z 2

Z1 =

1 + R1 ; C1 s

Z2 =

R2 / C 2 s . R2 + 1 / C 2 s

V ( s) =

V0 1 2 k s + as + b

 1 1 1 a =  + +  R1C1 R1C 2 R2 C 2

(2.23)

 ; 

  1 ; b =  R R C C  1 2 1 2

k = R1C 2 .

(2.24)

For circuit Fig. 2.25(b) one finds the same general expression (eqn (2.23)), with the following constants; however,

 1 1 1  ; a =  + +  R1C1 R1C 2 R2 C1   1 b =   R1 R2 C1C 2 k = R1C 2

Deependra Singh

 ;  as Above  

(2.25)

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High Voltage Engineering UnitUnit-III For both circuits, therefore, we obtain from the transform tables the same expression in the time domain:

V (t ) =

V0 1 [exp(−α1t ) − exp(−α 2 t ] k (α 1 +α 2 )

(2.26)

Where α1 and α2 are the roots of the equation s2+ab+b = 0, or 2

a a α1 ,α 2 = m   − b 2 2

(2.27)

The output voltage V(t) is therefore the superposition of two exponential functions of different signs. According to eqn (2.27), the negative root leads to a larger time constant 1/ α1 than the positive one, which are 1/ α2. A graph of the expression (eqn (2.26)) is shown in Fig. 2.26, and a comparison with Figs 2.23 and 2.24 demonstrates the possibility to generate both types of impulse voltages with these circuits.

REFERENCE: •

HVE FUNDAMENTALS: KUFFEL, ZAENGL & KUFFEL; 2.3.1; P-52-55

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32. MULTISTAGE IMPULSE GENERATOR COMPONENTS OF MULTISTAGE IMPULSE GENERATOR In order to obtain higher and higher impulse voltage, a single stage circuit is inconvenient for the following reasons: (i). The physical size of the circuit elements becomes very large. (ii). High D.C. charging voltage is required. (iii). Suppression of corona discharges from the structure and leads during the charging period is difficult. (iv). Switching of vary high voltages with spark gaps is difficult. In 1923 E. Marx suggested a multiplier circuit which is commonly used to obtain impulse voltages with as high a peak value as possible for a given D.C. charging voltage. Depending upon the charging voltage available and the output voltage required a number of identical impulse capacitors are charged in parallel and then discharged in series, thus obtaining a multiplied total charging voltage corresponding to the number of stages. Fig. 3.7 shows a 3-stage impulse generator circuit due to Marx employing ‘b’ circuit connections. The impulse capacitors C1 are charged to the charging voltage V0 through the high charging resistors RC in parallel. When all the gaps G break down, the C1′ capacitances are connected in series so that C2 is charged through the series connection of all the wave front resistances R1′ and finally all C1′ and C2 will discharge through the resistors R2′ and R1′. Usually RC >> R2 >> R1. If in Fig. 3.7 the wave tail resistors R2′ in each stage are connected in parallel to the series combination of R1′, G and C1′, an impulse generator of type circuit ‘a’ is obtained.

In order that the Marx circuit operates consistently it is essential to adjust the distances between various sphere gaps such that the first gap G1 is only slightly less than that of G2 and so on. If is also necessary that the axes of the gaps G be in the same vertical plane

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High Voltage Engineering UnitUnit-III so that the ultraviolet radiations due to spark in the first gap G, will irradiate the other gaps. This ensures a supply of electrons released from the gap electrons to initiate breakdown during the short period when the gaps are subjected to overvoltages. The wave front control resistance can have three possible locations (i) entirely within the generator (ii) entirely outside the generator (iii) partly within and partly outside the generator. The first arrangement is unsatisfactory as the inductance and capacitance of the external leads and the load form an oscillatory circuit which requires to be damped by an external resistance. The second arrangement is also unsatisfactory as a single external front resistance will have to withstand, even though for a very short time, the full rated voltage and therefore, will turn out to be inconveniently long and would occupy much space. A compromise between the two is the third arrangement as shown in Fig. 3.7 and thus both the “space economy” and damping of oscillations are taken care of. It can be seen that Fig. 3.7 can be reduced to the single stage impulse generator of Fig. 3.4 (b). After the generator has fired, the total discharge capacitance C1 may be given as: 1 n 1 ∑C ' C1 1 n

the equivalent front resistance

R1 = ∑ R1 '+ R1" n

and the equivalent tail control resistance

R2 = ∑ R2 '

where n is the number of stages.

CONSTRUCTION OF IMPULSE GENERATOR: An impulse generator requires a D.C. power supply for charging the impulse capacitance C1 of the generator. The supply consists of a step-up transformer and rectifier. The charging times should not be less than 3 to 10 seconds as every application of voltage will leave behind pre-ionizing effects, so a time should be allowed between two successive applications so that the pre-stressing effects within the insulations do not influence the breakdown strength. These days thyristor controlled D.C. supply for charging is available. The resistors may be made up of wire, liquid or composite (carbon etc.) resistive materials. The liquid and carbon resistors even though have high heat capacity, these are

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High Voltage Engineering UnitUnit-III invariably not used especially for wave front and tail control resistances as these are highly unstable i.e. their value is not constant and may change with various factors. Therefore, noninductive wire would resistors are used for this purpose even though these are relatively costly. It is found that for most of the circuits if the time constant of those resistances is less than 0.1 micro se. they are considered quite satisfactory from the view point of oscillation in the circuit. These resistors should be placed in such a way that they can be exchanged and replaced easily as they must be charged as per the requirement of a particular wave shape. The layout of an impulse generator is mainly decided by the type of capacitors used. Oil paper insulated capacitors having low inductance and high rate of discharge are normally employed. The material oil is often replaced by special fluids which are having higher permittivity to reduce the size of the capacitor for the same capacitance. Some of the designs use oil impregnated capacitors in insulating containers. These capacitors have the dielectric assembled in an insulating cylinder of porcelain or varnished paper with plane metal plates. An advantage of this form of capacitor is that successive stages of capacitors can be built up in vertical columns, each stage being separated from the adjacent one by supports of the same form as the capacitors but without the dielectric. Recently, modular constructions with simple capacitor units within insulating cylinders or vessels or within metal tanks and bushings have been recommended are in use. These designs were made possible due to the use of high dielectric fluids (e.g. SF6) which could reduce the size of the capacitors significantly. The coupling sphere gaps are arranged one above the other on horizontal arms and the setting of the gaps is adjusted by a remotely controlled motor in conjunction with an indicator. This arrangement with mutual irradiation ensures a perfect cascading of the spark gaps. They are normally encapsulated in a chimney provided with dust free and dry air. The use of proper gas mixtures gives good switching performance. The impulse generator should have a device to earth the capacitors when it is not in operation. The D.C. capacitors can build up high voltages after a short time of short circuit due to the relaxation phenomenon. A series protective resistance should be included in this earthing device to avoid too high discharge currents. The front and tail resistors are fixed to the generator frame by means of resistor carriers of bakelized paper tubes. The charging resistors are fixed along the sphere gap column. All leads and electrodes within the generator should be dimensioned properly to avoid too heavy corona discharges during the charging period. A typical impulse generator circuit giving all details is shown in Fig. 3.9.

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High Voltage Engineering UnitUnit-III

REFERENCE: •

HVE FUNDAMENTALS: C L WADHWA; 3.5; P-94-98

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33. TRIGGERING OF IMPULSE GENERATOR BY THREE ELECTRODE GAP ARRANGEMENT Impulse generators are normally operated in conjunction with cathode ray oscillographs for measurement and for studying the effect of impulse waves on the performance of the insulations of the equipments. Since the impulse waves are of shorter duration, it is necessary that the operation of the generator and the oscillograph should be synchronised accurately and if the wave front of the wave is to be recorded accurately, the time sweep circuit of the oscillograph should be initiated at a time slightly before the impulse wave reaches the deflecting plates. If the impulse generator itself initiates the sweep circuit of the oscillograph, it is then necessary to connect a delay cable between the generator or the potential divider and the deflecting plates of the oscilloscope so that the impulse wave reaches the plates at a controlled time after the sweep has been tripped. However, the use of delay cable leads to inaccuracies in measurement. For this reason, some tripping circuits have been developed where the sweep circuit is operated first and then after a time of about 0.1 to 0.5 µ sec. the generator is triggered.

Fig. 3.11 shows a trigatron gap which is used as the first gap of the impulse generator and consists essentially of a three-electrode gap. The high voltage electrode is a sphere and the earthed electrode may be a sphere, a semi-sphere or any other configuration which gives homogeneous electric field. A small hole is drilled into the earthed electrode into which a metal rod projects. The annular gap between the rod and the surrounding hemisphere is about 1 mm. A glass tube is fitted over the rod electrode and is surrounded by a metal foil which is connected to the earthed hemisphere. The metal rod or trigger electrode forms the third electrode, being essentially at the same potential as the drilled electrode, as it is connected to

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High Voltage Engineering UnitUnit-III it through a high resistance, so that the control or tripping pulse can be applied between these two electrodes. When a tripping pulse is applied to the rod, the field is distorted in the main gap and the latter breaks down at a voltage appreciably lower than that required to cause its breakdown in the absence of the tripping pulse. The function of the glass tube is to promote corona discharge round the rod as this causes photo-ionization in the annular gap and the main gap and consequently facilitates their rapid breakdown. REFERENCE: •

HVE FUNDAMENTALS: C L WADHWA; 3.7; P-98-99

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34. TRIGGERING GAP AND OSCILLOGRAPH TIME SWEEP CIRCUITS For single stage or multi-stage impulse generators the trigatron gaps have been found quite satisfactory and these require a tripping voltage of about 5 kV of either polarity. The tripping circuits used today are commercially available and provide in general two or three tripping pulses of lower amplitudes. Fig. 3.12 shows a typical tripping circuit. The capacitor C1 is charged through a high resistance R1. As the remotely controlled switch S is closed, a pulse is applied to the sweep circuit of the oscillograph through the capacitor C3. At the same time the capacitor C2 is charged up and a triggering pulse is applied to the trigger electrode of the trigatron. The requisite delay in triggering the generator can be provided by suitably adjusting the values of R2 and C2. The residual charge on C2 can be discharged through a high resistance R3. Nowadays lasers are also used for tripping the spark gap.

The trigatron also has a phase shifting circuit associated with it so as to synchronise the initiation time with an external alternating voltage. Thus, it is possible to combine high alternating voltage tests with a superimposed impulse wave of adjustable phase angle. The trigatron is designed so as to prevent the overcharging of the impulse capacitors in case of an accidental failure of triggering. An indicating device shows whether the generator is going to fire correctly or not. An additional feedback circuit provides for a safe wave chopping and oscillograph release, independent of the emitted control pulse.

REFERENCE: •

HVE FUNDAMENTALS: C L WADHWA; 3.7; P-100

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High Voltage Engineering UnitUnit-III

35. GENERATION OF SWITCHING IMPULSE VOLTAGE

The common impulse generator circuits discussed so far are well capable of producing standard switching impulses with adequate voltage efficiency η, if the circuit is well designed and the ratio C2/C1 is kept adequately small. Other methods, however, have taken advantage of utilizing testing transformers to step up the amplitudes from impulse voltages also. One such circuit is shown in Fig. 2.31. An initially charged capacitor C1 is discharged into the waveshaping circuit R1, C2 as well as into the L.V. winding of the transformer. The elements R1 and C2 or other suitable components, in the dotted rectangle, may be used to control the waveshape. The wave tail is not only controlled by the resistive voltage divider included, but also from the main inductance of the transformer equivalent circuit. The time to crest Tp is even without R1, C2 limited by the series inductance of the transformer, LS, which forms a series resonant circuit in combination with

C1

capacitance

and

the

load

C2 .

Neglecting

any losses within the circuit, the voltage across the test object would therefore start with a (1-cosωt) function and as Tp ≈ T/2 = π/fr, fr being the resonance frequency, the time to crest is approximately Tcr ≅ π Ls C where, neglecting transformer ratio,

C=

C1C 2 ' C1 + C 2 '

In general, low values of Tp are difficult to achieve, as Ls is quite large and also the capacitance of the H.V. winding of the transformer contributes to the load C2. Further problems arise with transient oscillations within the transformer windings, mainly if cascaded testing transformers are used. REFERENCE: •

HVE FUNDAMENTALS: KUFFEL, ZAENGL & KUFFEL; 2.3.1; P-64-65

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36. ENERATION OF HIGH IMPULSE CURRENT

For producing impulse currents of large value, a bank of capacitors connected in parallel are charged to a specified value and are discharged through a series R-L circuit as shown in Fig. 6.20. C represents a bank of capacitors connected in parallel which are charged from a D.C. source to a voltage up to 200 kV. R represents the dynamic resistance of the test object and the resistance of the circuit and the shunt L is an air cored high current inductor, usually a spiral tube of a few turns. If the capacitor is charged to a voltage V and discharged when the spark gap is triggered, the current im will be given by the equation

t

di 1 V = Rim + L m + ∫ im dt dt C 0

(6.24)

The circuit is usually underdamped, so that R < L C 2 Hence, im is given by im =

Deependra Singh

V [exp(−αt )]sin(ωt ) ωL

90

(6.25)

High Voltage Engineering UnitUnit-III

α=

Where

R and ω = 2L

1 R2 − 2 LC 4 L

(6.25a)

The time taken for the current im to rise from zero to the first peak value is

t1 = t f =

1

ω

sin −1

ω LC

=

1

ω

tan −1

ω α

(6.26)

The duration for one half cycle of the damped oscillatory wave t2 is,

t2 =

π 1 R2 − 2 LC 4 L

(6.27)

REFERENCE: •

HVE KAMARAJU NAIDU; 6.4.2; P-145

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PROBLEMS Q. 1

Describe in brief, the generation of HVDC HVAC & Impulse voltages?

Q. 2

Explain and compare the performance of half wave rectifier and voltage doubler circuits for generation of high D.C. voltages.

Q. 3

Define ripple voltage. Show that the ripple voltage in a rectifier circuit depends upon the load current and the circuit parameters.

Q. 4

Explain with neat sketches Cockroft-Walton voltage multiplier circuit. Explain clearly its operation when the circuit is (i) unloaded (ii) loaded.

Q. 5

Derive an expression for ripple voltage of a multistage Cockroft-Walton Circuit.

Q. 6

Derive an expression for the voltage output under load condition. Hence, deduce the condition for optimal number of stage if a maximum value of output voltage is desired.

Q. 7

Describe with neat diagram the principle of operation and application of a symmetrical cascaded rectifier.

Q. 8

Explain clearly the basic principle of operation of an electrostatic generator. Describe with neat diagram the principle of operation, application and limitations of Van de Graf generator.

Q. 9

What is a cascaded transformer? Explain why cascading is done? Describe with neat diagram a three stage cascaded transformer. Label the power ratings of various stages of the transformer.

Q. 10 Draw equivalent circuit of a 3-stage cascaded transformer and determine the expression for short circuit impedance of the transformer. Hence deduce an expression for the short-circuit impedance of an n-stage cascaded transformer. Q. 11 Explain with neat diagram the basic principle of reactive power compensation is high voltage A.C. testing of insulating materials. Q. 12 Explain with neat diagram the principle of operation of (i) series (ii) parallel resonant circuits for generating high A.C. voltages. Compare their performance. Q. 13 Explain the series-parallel resonant circuit and discuss its advantages and disadvantages Q. 14 Give the principle of operation of series resonant circuit along with advantages? Q. 15 Define the terms: (i) Impulse voltages (iv) Impulse puncture voltage

Deependra Singh

(ii) Chopped wave (v)

(iii) Impulse flash over voltage

Impulse ratio for flash over (vi) Impulse ratio for puncture

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High Voltage Engineering UnitUnit-III Q. 16 Draw a neat exact equivalent circuit of an Impulse Generator and indicate the significance of each parameter being used. Q. 17 Draw and compare the two simplified equivalent circuits of the impulse generator circuits. Q. 18 Give complete analysis of circuit ‘a’ and show that the wave front and wave tail resistances are physically realizable only under certain condition. Derive the condition. Q. 19 Give complete analysis of circuit ‘b’ and derive the condition for physical realization of wave front and wave tail resistances. Q. 20 Derive an expression for voltage efficiency of a single stage impulse generator. Q. 21 Describe the construction, principle of operation and application of a multistage Marx's Surge Generator. Q. 22 Explain the Goodlet circuit of impulse voltage generation and compare its performance with that of Marx’s circuit. Q. 23 Describe the construction of various components used in the development of an impulse generator. Q. 24 Explain with neat diagram triggering and synchronization of the impulse generator with the CRO. Q. 25 Draw a typical impulse current generator circuit and explain its operation and application. Q. 26 Draw a neat diagram of a high current generator circuit (equivalent circuit) and through analysis of the circuit show how the wave form can be controlled.

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