1. INTRODUCTION - UniMAP Portalportal.unimap.edu.my/portal/page/portal30/Lecturer Notes... · Generation & Measurement of High Voltages & High Current MEP 1632 1 1. INTRODUCTION In

Generation & Measurement of High Voltages & High Current MEP 1632

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1. INTRODUCTION In the fields of electrical engineering and applied physics, high voltages of all types, namely, d.c., a.c., and impulse are required for several applications. The generation of high voltages and high current in a high voltage laboratory is required for the purpose of testing various types of power system equipment. High voltage tests need to be done to determine the insulation strength of the equipment when subjected to different types of voltage stresses such as the power frequency and high frequency voltages, lightning impulse, and switching impulse. Examples of high voltage usage in industrial applications include electron microscopes and x-ray units which require dc high voltages of the order of 100 kV or more. Electrostatic precipitators, particle accelerators in nuclear physics, etc. require dc high voltage of several kilovolts and even megavolts. Ac high voltages of one million volts or even more are required for testing power apparatus rate for extra high transmission voltages (400 kV system and above). Normally in high voltage testing, the current under conditions of failure is limited to a small value (less than an ampere in the case of dc or ac voltages and few amperes in the case of impulse or transient voltages). But in certain cases, like the testing of surge arresters or the short circuit testing of switchgear, high current testing with several hundreds of amperes is of importance.


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2. GENERATION OF HIGH A.C. VOLTAGES High a.c. voltages are required in laboratories for experiments and a.c. tests as well as for most of the circuits for the generation of high d.c. and impulse voltages. Test transformers generally used for this purpose have considerably lower power rating and frequently much larger transformer ratios than power transformers. The primary current is usually supplied by regulating transformers fed from the mains supply. The impedance of the transformer should be generally less than 5% and must be capable of giving the short circuit current for one minute or more depending on the design. The most common method of high a.c. voltage generation is by using step-up test transformers. The test transformers are mainly used to provide high a.c. voltages for various a.c. tests such as withstand, flashover as well as partial discharge tests. Another method of high a.c. voltage generation is by using the resonant method. This method is particularly suitable for testing high voltage apparatus such as high voltage cables where the resonant system has more advantages as compared to the pure step-up transformer circuits. 2.1 Test Transformer Circuit Figure 2.1.1 shows two basic circuits for test transformers. Transformers for generating high a.c. test voltages usually have one end of the high-voltage winding earthed. For numerous circuits for the generation of high d.c. and impulse voltages, however, transformer with completely isolated windings are required. Single transformer test units are made for high alternating voltages up to about 200 kV. However, to reduce the cost (insulation cost increases rapidly with voltage) and make transportation easier, a cascade arrangement of several transformers is used. 2.2 Cascade Transformer Circuit To generate voltages above a few hundred kV single-stage transformers according to Fig. 2.1.1 are now rarely used; for economical and technical reasons one employs instead a series connection of the high-voltage windings of several transformers. In such a cascade arrangement, an example of which is shown in Fig. 2.1.2, the individual transformers must be insulated for voltages


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corresponding to those of the lower stages. The excitation windings of the transformers of all stages except the lowest will operate at high potential. Test transformers in cascade connection have already been produced for voltages above 2MV.

a) Single pole isolated b) Fully isolated

Figure 2.1.1 Basic circuits for test transformers E – Excitation winding, H – High voltage winding, F – Iron core

Figure 2.1.2 Cascade transformer circuit


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2.3 Construction and Performance of Test Transformers For rating of not more than a few kVA, inductive voltage transformers can be used to generate high a.c. voltages. Low power test transformers are also similar in construction to voltage transformers with the same test voltage. Fig. 2.3.1 shows an example of the transformer construction.

1. High voltage winding 2. Low voltage winding 3. Iron core 4. Base 5. High voltage terminal 6. Insulation

Figure 2.3.1 An example of test transformer construction

For approximate analysis of the working performance of test transformers, the equivalent circuit shown in Fig. 2.3.2 is well suited. It comprises a series circuit of the short-circuit impedance (RK + jωLK) and the total capacitance C = Ci + Ca on the high-voltage side, where Ci is the self-capacitance of the high-voltage winding and Ca the external load capacitance. Since as a rule R << ωL and the secondary voltage U2 is then almost in phase with the primary voltage U1, we have:

(1 - ω2LKC) is always less than unity; thus series resonance leads to a capacitive enhancement of the secondary voltage.

CLω - 11 U U

K2

'2 1=


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Figure 2.3.2 Transformer equivalent circuit a) circuit diagram b) equivalent circuit c) phasor diagram

2.4 HV Generation with Resonant Circuits Fig. 2.3.2 demonstrates the possibility of a very considerable voltage enhancement on the secondary side of a test transformer by series resonance with a capacitive load. This effect can be used for the generation of high a.c. test voltages; to extend the tuning range, the short-circuit inductance of the test transformer is then augmented by a separate high-voltage inductor. The series resonant circuit formed by the inductance and the capacitance of the test object may be excited by a transformer of relatively low secondary voltage. Resonant circuits are particularly advantageous when the test object has a high capacitance, for instance, a high-voltage cable. The special advantage of such a circuit is that the output voltage deviates little from a sinusoid and that, due to the characteristics of the series resonant circuit, almost complete compensation of the reactive power required for the test object follows. A simplified diagram of the series resonance test system is given in Fig. 2.4.1 and that of the parallel resonant test system in 2.4.2.


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Figure 2.4.1a) Series resonant circuit

Figure 2.4.1b) Parallel resonant circuit The Tesla transformer, named after its inventor, also belongs to the class of resonant circuits. The circuit comprises a primary and a secondary oscillatory circuit in loose magnetic coupling. Periodic discharges of the primary capacitor via a spark gap will excite high frequency oscillations, typically in the frequency range104 to 105 Hz. Depending upon the chosen circuit data and the transformation ratio


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of secondary to primary winding, voltages of more than 1 MV have been generated with Tesla transformers. Most tests and experiments with high voltages require precise knowledge of the value of the voltage. This demand can normally only be fulfilled by measurements on the high-voltage side of the supply; various techniques for the measurement of high voltages have been devised for this purpose.


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3. MEASUREMENTS OF A.C. HIGH VOLTAGES There are several methods available for measuring high a.c. voltages. The incorporation of an oscilloscope in some of the measurement techniques makes it possible to view the waveshapes or oscillograms. 3.1 Measurement using Series Impedance Voltmeters For power frequency a.c. measurements the series impedance may be a pure resistance or a reactance. Since resistances involve power losses, often a capacitor is preferred as a series reactance. Moreover, for high resistances, the variation of resistance with temperature is a problem, and the residual inductance of the resistance gives rise to an impedance different from its ohmic resistance. High resistance units for high voltages have stray capacitances and hence a unit resistance will have an equivalent circuit as shown in Fig. 3.1.1.

Figure 3.1.1 Equivalent circuit of a high voltage resistor

To avoid the problems associated with a resistive element under a.c. voltages, a series capacitor is used instead of a resistor for a.c. high voltage measurements. The schematic diagram is shown in Fig. 3.1.2. The current through the meter is:

Ic = jωCV where C = capacitance of the series capacitor,

ω= angular frequency, and V = applied a.c. voltage

This method is not recommended when a.c. voltages are not pure sinusoidal waves but contain considerable harmonics.


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Figure 3.1.2 Measurement using series impedance voltmeter

3.2 Measurement with Capacitive Dividers The errors due to harmonics voltages can be eliminated by the use of capacitive voltage dividers with an electrostatic voltmeter or a high impedance meter such as an oscilloscope. If the meter is connected through a long cable, its capacitance has to be taken into account in calibration. Refering to Fig. 3.2.1 the applied voltage V1 is given by

where Cm is the capacitance of the meter and the connecting cable and the leads and V2 is the meter reading.

Fig. 3.2.1 Measurement using capacitive divider

⎟⎟⎠

⎞⎜⎜⎝

⎛ ++=

1

m2121 C

C C C VV


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3.3 Peak Value Measurements In some occasions, the peak value of an a.c. waveform is more important. This is necessary to obtain the maximum dielectric strength of insulating solids, etc. When the waveform is not sinusoidal, rms value of the voltage multiplied by √2 is not correct. Hence a separate peak value instrument is desirable in high voltage applications. Examples of the circuits used are shown in Figs. 3.3.1.

a) Peak voltmeter with a capacitive potential divider and electrostatic voltmeter

b) Peak voltmeter as modified by Haefely


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c) Peak voltmeter with equalizing branch as designed by Rabus

Fig. 3.3.1 High a.c. voltage peak value measurements 3.4 Peak Voltage Measurement with Sphere Gaps Breakdown of a spark gap occurs within a few µs once the applied voltage exceeds the ‘static breakdown discharge voltage’. Over such a short period the peak value of a power frequency voltage can be considered to be constant. Breakdown in gases will therefore always occur on the peak of low frequency a.c. voltages. Figure 3.4.1 shows the two basic arrangements of sphere gaps for measuring purposes. The published specifications (IEC-Publ. 52-1960, BS 358) prescribe minimum clearances from objects disturbing the electric field and tabulate breakdown voltages for standard conditions (b=1013mbar, T = 20°C) and various sphere diameters as a function of the gap spacing s as shown in Fig. 3.4.2.


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Figure 3.4.1 Two basic arrangements of shpere gaps for measurement

Figure 3.4.2 Breakdown voltage as a function gap spacing s, for various sphere diameters

Since the breakdown voltage Ud is proportional to the relative air density d in the range 0.9 … 1.1, the actual breakdown voltage Ud at air density d may be found from the tabulated value Udo by applying the following formula:


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with b and T in mbar and °C respectively. Even under apparently ideal conditions, a measuring uncertainty of 3% remains. Continuous voltage measurement is obviously impossible with sphere gaps. Since the voltage source is short-circuited at the instant of measurement. In-spite of their disadvantages, sphere gaps can be useful and versatile devices in a high-voltage laboratory. Apart from voltage measurement, they can also be used as voltage limiters, as voltage-dependent switches, as pulse sharpening gaps and as variable high-voltage capacitors, etc. 3.5 Measurement by means of Electrostatic Voltmeters When a voltage u(t) is applied to an electrode arrangement, such as the one shown in Fig. 3.5.1, for example, the electric field produces a force F(t) which tends to reduce the spacing s of the electrodes. This attractive force can be calculated from the change of energy of the electric field:

W(t) = ½ C u2(t) The capacitance C of the arrangement depends on the spacing s. The mean value of the force F(t) is found to be linearly related to the square of the rms value of the applied voltage and hence an rms voltage can be measured. Electrostatic voltmeters are characterised by their very high internal resistance and very small capacitance; they are thus useful for the direct measurement of high-frequency high voltages extending to the MHz region.

dododod UT273

b 0.289 UT27320273

1013b UU

+=

++

=≈


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1. Movable electrode segment. 2. Axis of rotation 3. Mirror 4. Light source 5. Scale

Fig. 3.5.1 Electrostatic voltmeters for high voltages

a) Using spherical electrodes b) Using movable electrode segment

3.6 Measurements with Voltage Transformers High a.c. voltages can be measured extremely accurately with voltage transformers. Although these devices are widely used in power supply networks, they are rarely used in laboratories for measurements of voltage above 100kV. The basic circuits of single pole isolated inductive and capacitive voltage transformers, for the measurement of voltage with respect to earth are shown in Fig 3.6.1.


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Fig. 3.6.1 Basic circuits of voltage transformers a) Inductive voltage transformer b) Capacitive voltage transformer

L – Resonant inductor W – Matching transformer


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4. GENERATION OF D.C. HIGH VOLTAGE Generation of high d.c. voltages is required in research work in the areas of pure and applied physics, insulation tests on a.c. cables and capacitors, and charging units for impulse generators. Technical uses include the generation of x-rays, precipitators, paint spraying, powder coating and in communication electronics (TV; broadcasting stations). Because of the diversity in the application of d.c. high voltages, ranging from basic physics experiments to industrial applications, the requirements on the output voltage will vary accordingly. Among the important characteristics are voltage shape, voltage level, current rating, and short- or long-term stability. With the knowledge of the fundamental generating principles it will be possible to select proper circuits for a special application. The voltages are generally obtained by means of rectifying circuits applied to a.c. voltages or by electrostatic generation. In this course, a detailed understanding of various types of generating circuits based on the a.c. to d.c. conversion is emphasised. The rectification of alternating currents is the most efficient means of obtaining high voltage d.c. supplies. Most of the rectifier diodes used adopt the Si-type, and though the peak reverse voltage is limited to less than about 2500V, rectifying diode units up to tenth and hundredths of a kV can be made by series connection if appropriate means are applied to provide equal voltage distribution during the non-conducting period. 4.1 Characteristic Parameters of D.C. High Voltages The d.c. test voltage is defined as the arithmetic mean value between the highest and lowest level within a period [Publ. 60-1, 1989]:

Periodic fluctuations of the direct voltage between the peak value Umax and the minimum value Umin are given in terms of ripple amplitude:

δU = ½ (Umax –Umin) The ripple is influenced by the load current, frequency and the smoothing capacitance.

∫=T

0

^dt u(t)

T1 U


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4.2 Properties of High Voltage Rectifiers Rectifiers in laboratory circuits for the generation of high d.c. voltages are usually series connected stacks of semiconductor diodes or previously, vacuum valves. In contrast to high vacuum rectifiers, semiconductor diodes are not true valves since they allow a small but finite current flow in the blocked condition. More commonly used semiconductor rectifiers are of the type silicon, selenium and germanium diodes. 4.3 Half Wave Rectifier Figure 4.3.1 shows a single-phase half-wave rectifier with smoothing capacitance C. From the circuit, it is obvious that the diode D must be dimensioned to withstand a peak reverse voltage of 2Vmax.

Fig. 4.3.1 Half-wave rectifier For high voltage test circuits, a sudden voltage breakdown at the load (RL nearing to 0) must always be taken into account. The rectifiers should be able to carry either the excessive currents, which can be limited by fast, electronically controlled switching devices at the transformer input, or they can be protected by an additional resistance inserted in the high voltage circuit. 4.4 Full Wave Rectifier A full wave rectifier circuit is shown in Figure 4.4.1. In the positive half cycle, the rectifier A conducts and charges the capacitor C, while in the negative half cycle the rectifier B conducts and charges the capacitor. The source transformer requires a centre tapped secondary


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with a rating of 2V. Fig 4.4.2 show the waveforms for both half and full wave rectifiers.

Fig. 4.4.1 Full-wave rectifier

Fig 4.4.2 Input and output waveforms of half and full wave rectifiers a) Input sine wave b) Output with half wave rectifier and capacitor filter c) Output with full wave rectifier and capacitor filter d) Vmax, Vmean and ripple voltage and δV with capacitor filter of a

full wave rectifier.


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4.5 Voltage Doubler 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 a voltage doubler is given in Figure 4.5.1.

Fig. 4.5.1 Voltage doubler In the voltage doubler circuit shown, the capacitor C1 is charged through rectifier R1 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. Thus, the capacitor C2 in turn is charged through R2 to 2Vmax. Cascade voltage doublers are used when larger output voltages are needed without changing the input transformer voltage level. A typical cascaded voltage doubler is shown in Figure 4.5.2.


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Fig. 4.5.2 Cascade voltage doubler

4.6 Voltage Multiplier Cascaded voltage multiplier circuits for higher voltages are cumbersome and require too many supply and isolating transformers. It is possible to generate very high d.c. voltages from single supply transformers by extending the simple voltage doubler circuits. Voltage multiplier circuit using the Cockcroft-Walton principle is shown in Fig. 4.6.1. The first stage, i.e. D1, D2, C1, C2, and the transformer T are identical as in the voltage doubler shown in Fig. 4.5.1.


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Fig. 4.6.1 Cockroft-Walton Voltage multiplier

Fig. 4.6.2 Voltage waveform across the first and the last capacitors of the cascaded voltage multiplier circuit shown in Fig. 4.6.1.


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For higher output voltage of up to 2n of the input voltage V, the circuit is repeated with cascade or series connection. Thus, the capacitor C4 is charged to 4Vmax and C2n to 2nVmax above the earth potential. But the volt across any individual capacitor or rectifier is only 2Vmax.


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5. MEASUREMENT OF D.C. HIGH VOLTAGES Measurement of high d.c. voltages as in low voltage measurements, is generally accomplished by extension of meter range with a large series resistance. The net current in the meter is usually limited to one to ten microamperes for full-scale deflection. For very high voltages (1000kV or more) problems arise due to large power dissipation, leakage currents and limitation of voltage stress per unit length, change in resistance due to temperature variations, etc. Hence, a resistance potential divider with an electrostatic voltmeters is sometimes better when high precision is needed. But potential dividers also suffer from the disadvantages stated above. Both series resistance meters and potential dividers cause current drain from the source. 5.1 Measurement with High Ohmic Resistors with

Microammeter High d.c. voltages are usually measured by connecting a very high resistance (few hundreds of megaohms) in series with a microammeter as shown in Fig. 5.1.1.

Fig. 5.1.1 High resistance in series with a microammeter

Only the current I flowing through the large calibrated resistance R is measured by the moving coil microammeter. The voltage of the source is given by

V = IR The ohmic value of the series resistance R is chosen such that a current of one to ten microamperes is allowed for full-scale deflection.


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The resistance is constructed from a large number of wire wound resistors in series. The voltage drop in each resistor element is chosen to avoid surface flashovers and discharges. A value of less than 5kV/cm in air or less than 20kV/cm in good oil is permissible. The resistor chain is provided with corona free terminations. The material for resistive elements is usually a carbon-alloy with temperature coefficient less than 10-4/°C. Carbon and other metallic film resistors are also used. Series resistance meters are built for 500kV d.c. with an accuracy better than 0.2%. 5.2 Measurement with Resistive Voltage Dividers A resistance voltage divider with an electrostatic or high impedance voltmeter is shown in Fig. 5.2.1. The influence of temperature and voltage on the elements is eliminated in the voltage divider arrangement. The high voltage magnitude is given by

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21hv v .

RR R V +

=

where v2 is the d.c. voltage across the low voltage arm R2.

Fig. 5.2.1 Resistance potential divider with an electrostatic voltmeter P – Protective device ESV – Electrostatic voltmeter


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Fig. 5.2.2 Series resistor with parallel capacitors for potential linearization for transient voltages

With sudden changes in voltage, such as switching operations, flashover of the test objects, or source short circuits, flashover or damage may occur to the divider elements due to the stray capacitance across the elements and due to the ground capacitances. To avoid these transient voltages, voltage controlling capacitors are connected across the elements. Potential dividers are made with 0.05% accuracy up to 100kV, with 0.1% accuracy up to 300kV, and with better than 0.5% accuracy for 500kV.

5.3 Measurement with Electrostatic Voltmeters As may be seen from the description, in section 3.5, of the working principle of electrostatic voltmeters, this type of instrument can also be used for d.c. high voltages. Electrostatic voltmeters do in fact represent the best way of measuring d.c. high voltages directly. In this method, voltage measurement is reduced to measurement of a field strength at an electrode, which is particularly illustrated by the arrangement indicated in Fig. 3.5.1.


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5.4 Voltmeter and Field Strength Meter Based upon the

Generator Principle Consider the electrode arrangement shown in Fig. 5.4.1a, where a measuring electrode of area A, assumed to be at earth potential, has constant surface charge density εoE produced by the steady field strength E. The total charge on the measuring electrode is given by:

AEεdA Eε q o(A)

o == ∫

Fig. 5.4.1 Voltmeter and field strength meter (a) Schematic measuring arrangement (b) Charge and current curves

The charge q is now allowed to vary between the values Qmax and Qmin as shown in Fig. 5.4.1b, this being done by periodic covering and uncovering of a portion of the measuring electrode by an earthed plate. An alternating current I(t) = dq/dt then flows in the earth lead. It follows that the arithmetic mean value I taken over a period T is found to be given by

AEε T2 q

T2 I omax ==

Thus, I is proportional to the field strength and can be used to measure the latter.


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5.5 Other Methods for the Measurement of High D.C. Voltages The method of measuring a.c. high voltages using sphere gaps, described in 3.4, is also suitable for the determination of the peak value U of d.c. high voltages.


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6. GENERATION OF HIGH IMPULSE VOLTAGES Impulse voltages are required in high-voltage tests to simulate the stresses due to external and internal overvoltages, and also for fundamental investigations of the breakdown mechanisms. They are usually generated by discharging high voltage capacitors through switching gaps onto a network of resistors and capacitors, whereby voltage multiplier circuits are often used. The peak value of impulse voltages can be determined with the aid of measuring gaps, or better, be measured by electronic circuits combined with voltage dividers. The most important measuring device for impulse voltage is, however, the cathode ray oscilloscope, which allows the complete time characteristic of the voltage to be determined by means of voltage dividers. 6.1 Characteristic Parameters of Impulse Voltages In high voltage technology a single, unipolar voltage pulse is termed an impulse voltage; three important examples are shown in Fig. 6.1.1, with reference to possible characteristic parameters. The time dependence, as well as the duration of the impulse voltage, depends upon the method of generation. For basic experiments, rectangular impulse voltages are often used which rise abruptly to an almost constant value, as well as wedge-shaped impulse voltages characterised by a rise which is as linear as possible up to breakdown, and described simply by the steepness S.

Fig. 6.1.1 Characteristic parameters - three important examples a) Rectangular impulse voltage b) Wedge-shaped impulse voltage c) Double exponential impulse voltage

For testing purposes, double exponential impulse voltages have been standardised; without appreciable oscillation these rapidly reach a maximum, the peak value U, and finally drop less abruptly to zero. If


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an intentional breakdown or unintentional breakdown occurs in the high voltage circuit during the impulse, leading to a sudden collapse of the voltage, this is then called a chopped impulse voltage. The chopping can occur on the front, at the peak or in the tail section of the impulse voltage. For overvoltages following lightning strokes, the time required to reach the peak value is of the order of 1µs; they are named atmospheric or external overvoltages. Voltages generated in a laboratory to simulate these are called lightning impulse voltages. For internal overvoltages, occurring as a consequence of switching operations in high voltage networks, the time taken to reach the peak value is at least about 100µs. Their reproduction in the laboratory is effected by switching impulse voltages; these are of approximately the same shape as lightning impulse voltages, but last considerably longer. In the case of impulse voltages for testing purposes the shape of the voltage is determined by certain time parameters for the front and tail, as shown in Fig. 6.1.2 (IEC Publ. 60-1 (1989). Since the true shape of the front of lightning impulse voltages is often difficult to measure, the straight line O1S1 through the points A and B is introduced as an auxiliary construction on the front, to characterise the latter. Then the time Ts to front, as well as the time Tr to half-value, being the time from O1 to the point C, are also determined. In general, lightning impulse voltages of shape 1.2/50 are used, which means an impulse voltage with Ts = 1.2 µs ± 30% and Tr = 50µs ± 20%. On the other hand, recording the much slower switching impulse voltage presents no difficulties; hence the true origin O and the true peak S can be utilised for standardisation. For tests with switching impulse voltages the shape 250/2500 is often used, which corresponds to Tcr = 250 µs ± 20% and Th = 2500 µs ± 60% (Tcr = time to crest, Th = time to half value)


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Fig. 6.1.2 Front and tail times definition

6.2 Capacitive Circuits for Impulse Voltage Generation Fig. 6.2.1 shows the two most important basic circuits, denoted ‘circuit a’ and ‘circuit b’, used for the generation of impulse voltages. The impulse capacitor Cs is charged via a high charging resistance to the d.c. high voltage Uo and then discharged by ignition of the switching gap F. The desired impulse voltage u(t) appears across the load capacitor Cb. The circuits a and b differ from one another in that, in the one case, the discharge resistor Re is connected in front of, and in the other, behind the damping resistor Rd.

Fig. 6.2.1 Two important impulse voltage circuits

The value of the circuit elements determines the curve shape of the impulse voltage. The basic working principle of both circuits can be readily understood from the following simple considerations. The short time to front requires rapid charging of Cb to the peak value U, and the long time to tail, slow discharge. This is achieved by Re >> Rd. Immediately after ignition of F at t=0, almost the full charging voltage


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Uo appears across the series combination of Rd and Cb in both circuits. The smaller the value of the expression RdCb, the faster is the rate at which the voltage u(t) reaches its peak value. The peak value U cannot be greater than is determined by distribution of the initially available charge UoCs onto Cs + Cb. For the utilisation factor η therefore we have:

bs

s

o C CC

UU η

+≤=

ˆ

Since for a given charging voltage U should generally be as high as possible, one will choose Cs >> Cb. The exponential decay of the impulse voltage on the tail would then, in circuit a, occur with the time constant Cs(Rd + Re), and in circuit b with the time constant CsRe. The impulse energy transformed during a discharge is then:

W = ½ CsUo2

For given d.c. charging voltage, to obtain impulse voltages with as high a peak value as possible, the multiplier circuit proposed by E. Marx in 1923 is commonly used. Several identical impulse capacitors are charged in parallel and then discharged in series, obtaining in this way a multiplied total charging voltage, corresponding to the number of stages. The mechanism of the Marx circuit will be explained with the aid of the impulse generator shown in Fig. 6.2.2, with n = 3 stages in circuit b connection. The impulse capacitors of the stages Cs’ are charged to the stage charging voltage Uo’, via the high charging resistors RL’ in parallel. When all the switching gaps F break down, the capacitors Cs’ will be connected in series, so that Cb is charged via the series connection of all the damping resistors Rd’; finally all Cs’ and Cb will discharge again via resistors Re’ and Rd’. It is expedient to choose RL’ >> Re’. The n-stage circuit can be reduced to a single stage equivalent circuit, such as circuit b, where the following relationships are valid:

Uo = nUo’ Rd = nRd’

Cs = 1/n Cs’ Re = nRe’


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Fig. 6.2.2 Modified Marx impulse generator circuit If, in the circuit shown in Fig. 6.2.2, the discharge resistors Re’ in each stage are connected in parallel to the series combination of Rd’, F and Cs’, an impulse generator of type circuit a is obtained. Impulse voltage generators have already been built for voltages of the order of few MV and for impulse energies of a few hundred kWs, where the charging voltages per stage are usually of the order of 100 … 300kV. The utilisation factor η depends on the shape of the impulse voltage to be generated and generally lies between 0.6 and 0.9. It is also principally higher for circuit b than for circuit a, especially for impulse voltage with comparatively shorter time to tail. 6.3 Calculation of Single Stage Impulse Voltage Circuits For the design of impulse voltage circuits it is necessary to establish relationships between the value of the circuit element and the


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characteristics of the voltage shape. Because of the higher utilisation factor, impulse generators are built predominantly in the basic circuit b connection. For the impulse voltage curve the solution is:

⎟⎟⎠

⎞⎜⎜⎝

⎛−

−= 21 T

tT

t-

21

21

bd

o ee TT

TT

CRU u(t)

It is seen that the impulse voltage is given by the difference of two exponentially decaying functions with time constants T1 and T2. Fig. 6.3.1 shows the curve which reaches the peak value Up at time Tf. With the usually satisfied approximation,

ReCs >> RdCb the following simple expressions are obtained for circuit b:

T1 ≈ Re(Cs + Cb)

bs

bsd2 C C

CC R T+

≈

bs

s

C CC η+

≈


34

Fig. 6.3.1 Calculation of double exponential impulse voltages

The above simplified calculation of T1 and T2 is satisfied if T1 >> T2. The time constants T1 and T2 are then linked with the characteristics of lightning impulse voltages by factors which depend upon the ratio Tf/Tt as follows:

Tf = k2T2’ Tt = k1T1.

The values of these proportionality factors for the more important standard forms are as in Table 6.3.1.

Tf/Tt 1.2/5 1.2/50 1.2/200 k1 1.44 0.73 0.70 k2 1.49 2.96 3.15

The shape of the voltage for lightning impulse voltages often deviates considerably from that calculated theoretically, particularly on the front and at the peak. This is caused by the inevitable inductance of the circuit elements and of the spatial setup.


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6.4 Further Means of Generating Impulse Voltages Short rectangular impulse voltages can be generated quite well with energy storage devices of the transmission line type. In a much used setup, a high-voltage cable is charged to a d.c. voltage Uo via a high resistance and then discharged through a sphere gap into an initially uncharged cable, at the end of which the test object is connected.


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7. Measurements of Impulse Voltages 7.1 Peak Value Measurement Using a Sphere Gap The use of sphere gaps for the measurement of the peak value of a.c. high voltages was described in section 3.4. From investigations on the breakdown of gases it is known that the development of a complete breakdown of such a system takes only a few µs at the most, if applied voltage exceeds the peak value of the breakdown voltage Ûd for a.c. voltages. However, for the case of impulse voltages, one cannot ascertain how close the peak value Û of the applied impulse voltage lies to Ûd due to the statistical scatter of the breakdown time. This can only be determined by repeated impulses. To this end the amplitude of a sequence of impulse voltages is systematically varied until about half the impulses lead to breakdown, i.e., the breakdown probability P(Û) is about 50%. For this impulse voltage we then have

Ud – 50 ≈ Ûd ≈ d Ûdo where d represents the relative air density and Ûdo is the breakdown voltage under standard conditions. The distribution function P(Û) of the breakdown voltage, shown in Fig. 7.1.1, may be determined by repeatedly stressing an electrode arrangement. It can be seen that the withstand voltage Ud – 0 and the assured breakdown voltage Ud – 100, corresponding to a breakdown probability of 0% and 100%.

Fig. 7.1.1 Distribution function of the breakdown voltage


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7.2 Circuit and Transient Response of Impulse Voltage Dividers The voltage shape of an impulse voltage is measured, using a cathode ray oscilloscope. The quantity to be measured is fed in via a coaxial measuring cable, the input end of which is connected to the secondary terminals of a voltage divider wired to the measuring point (test object). The divider leads, divider, measuring cable and the oscilloscope together constitute the measuring system. If the peak value U alone is to be measured, then a directly indicating electronic device may be connected instead of the oscilloscope. 7.3 Resistive Voltage Divider In measuring systems with resistive dividers, as in Fig. 7.3.1, it is useful for the measuring cable K to be terminated at the CRO with its surge impedance Z, thus loading the divider with an effective resistance of the same value. The most important disturbance of the ideal behaviour of the divider is brought about the earth capacitance of the high voltage branch R1, which must necessarily be long for reasons of insulation at higher voltages. The output voltage tends to the limiting value

21

212 R R

R U U+

= ∞∞

Fig. 7.3.1 Impulse voltage measuring system with resistive divider (a) circuit diagram (b) Equivalent circuit with earth capacitance


38

7.4 Capacitive Voltage Divider In measuring systems with capacitive dividers, as in Fig. 7.4.1, the measuring cable K cannot usually be terminated at the oscilloscope, since C2 would discharge too rapidly because of the usual order of magnitude of the surge impedance (Z~100 Ω). The series matching with Z indicated in the figure has the effect that only half the voltage at the divider tap enters the cable, yet this is doubled again at the open end, so that the full voltage will be measured at the oscilloscope once more. On the other hand the reflected wave may find matching at the cable input, since for very high frequencies C2 acts as a short-circuit. The transformation ratio therefore changes from the value

1

21

CCC + for very high frequencies, to the value

1

K21

CC C C ++ for lower frequencies.

However, the capacitance of the measuring cable CK can usually be neglected compared with C2.

Fig. 7.4.1 Impulse voltage measuring system with capacitive divider (a) Circuit diagram (b) Equivalent circuit with lead inductance


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8. Generation of Impulse Current Rapidly carrying transient currents of large magnitude as a rule appear in connection with high voltages, namely through the discharge of energy storing devices. They often develop as a consequence of breakdown discharge mechanisms and are frequently accompanied by large forces and high temperatures. If these currents have definite shape they are referred as impulse currents; among other things, these are required for the simulation of lightning and short circuit currents during tests on service equipment. The measurement of rapidly varying high currents is usually performed with measuring resistors, or with arrangements which exploit the inductive effect of the current to be measured. 8.1 Characteristic Parameters of Impulse Currents Impulse currents can have very different shapes, depending upon their application and occurrence. Quite often impulse currents appear as aperiodic or damped oscillatory currents, and as alternating currents with a duration of only a few half-periods. The maximum instantaneous value of the current is denoted the peak value Ip; characteristic parameters for the time dependence will be mentioned here only for impulse currents intended for testing. To simulate currents produced by lightning strokes single, uni-directional impulse currents of short duration are used, which reach a peak value Ip rapidly without appreciable oscillation and then decrease to zero. The characteristics of these double exponential impulse currents are defined in accordance with the analysis parameters for impulse voltages given in Fig. 8.1.1 (IEC Publ. 60-1 (1989)). Usual values are Tf = 4µs, Tt = 10 µs. Rectangular impulse currents appear during the discharge of long transmission lines. The duration of these impulses is the time Td during which the current stays larger than 0.9Ip (Fig. 8.1.1 b). Rectangular impulse current with Td = 2000µs are often used for testing surge arresters.


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Fig. 8.1.1 Examples of impulse current a) Double exponential impulse current b) Rectangular impulse current c) Sinusoidal impulse current with exponential decaying

dc component d) Sinusoidal impulse current without dc component


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8.2 Generation of Impulse Currents 8.2.1 Energy Storage Systems For the generation of high impulse currents the power which may be drawn from the power supply network is not normally sufficient to obtain a current of given shape and amplitude. In these cases one has to resort to energy storage systems which can be discharged with much greater power than is required to charge them. Capacitors, inductors, transmission line storages, rotating machines, accumulator batteries and even explosives are basically available as energy storage devices. 8.2.1.1 Capacitive Energy Storage The energy stored in a capacitor of capacitance C at the voltage Uo is given by:

W = ½ Cuo2. It follows that the energy density in the dielectric stressed at the field strength E is given by:

W’ = ½ εoεrE2 If one substitutes εr = 4, E = 1000kV/cm, the values achievable with oil-impregnated paper, one obtains W’ = 0.2Ws/cm3. Capacitors are energy storage devices of high quality and extremely suitable for power amplification. A capacitive energy storage device can be charged by a source of low power. The largest storage systems of this type were built for experimental investigations in plasma physics to generate high magnetic fields; their energy content is a few MWs and the charging voltage some tens of kV. When these systems discharge, currents of several tens of MA are obtained. Further fields of application are test setups for surge arresters and lightning current simulation. 8.3 Discharge Circuits for the Generation of Impulse Currents The aim of impulse current circuits is to generate a rapidly varying transient current of specified form and amplitude in a given


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arrangement. This may be needed to test the withstand capacity of operating equipment against stress by an impulse current, or to repeatedly trigger certain physical effects. The equivalent circuit of an impulse current circuit with capacitive energy storage is shown in Fig. 8.2.3. L1 and R1 represent the unavoidable inductance and ohmic resistance respectively of the impulse current circuit. The test object P consists of a resistance R2 and an inductance L2 in series. 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;

V Ri Ldidt C

i dtmm

m

t

= + + ∫1

0

Fig. 8.2.3 Basic circuit of an impulse current generator a) Equivalent circuit b) Current curves


43

In this kind of discharge circuit the impulse current is critically influenced by the test object. The highest peak value of the current is reached for the case of low damping (underdamped), i.e. when

CL2 R ⟨⟨


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9. Impulse Current Measurements 9.1 Current Measurement with Measuring Resistors A current measuring system with measuring resistor (shunt) is shown in Fig. 9.1.1. The voltage across the resistor R due to the current i(t) to be measured is fed to the oscilloscope CRO via a measuring cable K. Termination of the cable with the surge impedance Z hardly affects the measuring voltage, if the condition R << Z is satisfied. However, magnetic fields caused by the current to be measured and stray magnetic fields can induce voltages in the measuring circuit which are superimposed on the desired measuring signal iR. The following relationship is true:

dtdΦ

dtdiL iR u(t) ++=

Fig. 9.1.1 (a) Ohmic shunt (b) Equivalent circuit of the shunt Induced voltages due to stray magnetic fields phi can usually be kept low by careful screening. An arrangement of the measuring circuit with low self-inductance L requires the current path within the screening to be such that minimum magnetic flux is linked by the loop formed at the measuring tap. Various current shunt designs with reduced inductive effects are: a) Bifilar flat strip design; b) Coaxial tube design c) Coaxial squirrel cage design.


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9.2 Current Measurement Using Induction Effects If two circuits are magnetically coupled, as shown in Fig. 9.2.1, the following expression is true:

dtdidi M

dtdi

L - Ri- u 11

22222 +=

where R2 and L2 are the effective resistance and self-inductance respectively, measurable at the terminals of circuit 2; M is the mutual inductance of circuits 1 and 2. A measuring system with a high internal resistance is connected to the terminals of circuit 2 and with i2 = 0, we have:

dtdi M u 1

2 =

Fig. 9.2.1 Rogowski coil for high impulse current measurements Vi(t) – Induced voltage in coil Zo – Coaxial cable of surge impedance Zo R-C – Integrating network.

In the other arrangement of the measuring loop, often in the form of the Rogowski coil, coil 2 encircles the conductor through which the current to be measured flows, in the manner shown in Fig. 9.2.1b. From the law of induction it follows directly that, for a uniformly wound coil with N turns, winding area A and length lm

m

o

l AN µ M =

In order to obtain a parameter which is proportional to the current to be measured, the measuring voltage u2 must be integrated. This can


46

be done most easily by an RC circuit or an appropriately wired operational amplifier. 9.3 Other Methods of Measuring Rapidly Varying Transient

Currents As further means of measuring impulse currents one may mention those methods which make use of magnetic field dependent material properties. The Hall generator and magnetic optic elements are in this category. REFERENCES 1. Kind, Dieter: High-Voltage Experimental Technique, Vieweg,

1978. 2. Naidu, M.S. & Kamaraju, V.: High Voltage Engineering, 2nd edn.,

McGraw-Hill, 1995. 3. Kuffel, E & Zaengl, W.S.: High-Voltage Engineering

Fundamentals, Pergamon Press, 1984. 4. Ryan, H.M.: High Voltage Engineering and Testing, Peter

Peregrinus Ltd., 1994.

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