STUDY OF THE TECHNICAL-ECONOMIC PARAMETERS OF CONSTRUCTED HIGH-VOLTAGE PULSE GENERATORS

I. I. Kalyatskii

(Presented by the scientific seminar on dielectrics of TPI)

Introduction

The principle of obtaining high, short-duration voltages (voltage pulses) using spark gaps as switching elements was proposed in 1914 by Prof. V. K. Arkad’ev and was practically implemented by Eng. N. V. Baklin, who for the first time built the so-called “spark capacitor transformer” [4]. The basic part of such a “transformer” consists of capacitors charged in parallel, through sufficiently large resistances, from a source of direct or alternating voltage. When the spark gaps break down, all the capacitors are connected in series, and the voltage at the generator output increases, in the ideal case, by a factor of \(n\), where \(n\) is the transformation coefficient, equal to the number of capacitor groups charged in parallel.

Already in the 1920s, technical installations appeared for obtaining high voltage based on the use of the principle proposed by Prof. V. K. Arkad’ev; these became known as “lightning generators,” “pulse generators,” “high-voltage pulse generators,” etc.

In the first years after its creation, the pulse generator was intended for research and testing of electrical insulation as an installation imitating the effect of overvoltages during the discharge of atmospheric electricity in the form of lightning. Such pulse tests, introduced in 1930 for the insulation of high-voltage transformers, led to improvements in transformer designs and to a sharp reduction in accident rates on high-voltage transmission lines.

For example, in one power system, over the period from 1931 to 1944, on average 15% of transformers were damaged annually. In 1947, of 500 tested, 10% were damaged. In 1949, of 1000 tested, only 3% were damaged [33].

The further development of high-voltage technology led to an expansion of the field of application of high-voltage pulse generators. At present they are used in physics laboratories in the study of the physics of the atomic nucleus, in medical laboratories for therapeutic purposes, in the petroleum industry for removing certain petroleum emulsions, in magnetic flaw detection for pulse magnetization, in pulse radiography, in radar installations, in installations for obtaining pulsed light, and in other special-purpose devices.

Over the thirty years since the start of the design of technical installations for impulse voltage, dozens of generators have been created with voltage-pulse amplitudes of several million volts. The growth in pulse amplitude is clearly illustrated by the following example: the first impulse generator, built by engineer Baklin, could produce a spark 15 cm long, whereas modern generators produce a powerful spark up to 2000 cm long.

Fig. 1. Comparison of the largest constructed generators by maximum voltage-pulse amplitude.

The successes of domestic high-voltage apparatus construction and capacitor construction made it possible in our country, even before the war, to create a whole series of unique impulse generators with voltages of several million volts. From Figs. 1 and 2 it can be seen that generators built in the USSR have the highest electrical characteristics. The largest installation, producing a pulse amplitude of 8.4 million V with respect to ground [2], was built in 1940 at the Kharkov Electrotechnical Institute (KhETI).

Fig. 2. Comparison of the largest constructed generators by stored-energy value.

The principal studies in the field of high-voltage pulse generators are devoted to analyzing the influence of the parameters of the generator discharge circuit \(R\), \(L\), and \(C\) on the shape of the voltage-pulse wave and are connected with obtaining standard impulses for insulation testing. It may be noted that, despite the large amount of data on constructed pulse generators, at present there is not only no engineering calculation that links the electrical calculation with the design of the generator, but there are also no systematic studies summarizing the results of generator design. The technical literature contains only descriptions of individual constructed installations and their components. The purpose of the present work is to analyze the designs of the largest generators built both in our country and in other countries, and it is the first step toward clarifying the technical and economic conditions for rational generator design. An analysis of technical and economic characteristics also seems timely in connection with the field of application of high impulse-voltage generators, which is expanding every year. Table 1 below brings together the principal published data on the largest pulse installations built in recent years.

Principal electrical parameters of a pulse generator

The principal electrical parameters of a high-voltage pulse generator are the following quantities:

1. The maximum amplitude of the voltage pulse, determined by

\[ U_{\max}=U_0 \cdot n_0 \cdot \eta, \]

where \(U_0\) is the voltage to which the capacitor group is charged, in \((\mathrm{kV})\),

\(n_0\) is the number of capacitor groups,

\(\eta\) is the utilization factor.

Figure 3 presents the change in the maximum amplitude of the voltage pulse according to the years in which the generators were built.

1. The discharge capacitance of the generator, or the capacitance per shot, determined by

\[ C_{\mathrm{ud}}=\frac{C_0}{n_0}, \]

where \(C_0\) is the capacitance of one capacitor group (in picofarads),

\(n_0\) is the number of capacitor groups.

Figure 4 shows the change in capacitance per shot at the maximum amplitude of the voltage pulse for constructed generators, according to published data. The principal generators have a capacitance per shot on the order of several thousand picofarads. As the maximum amplitude increases, the capacitance per shot decreases, since the capacitance and operating voltage of a single capacitor are limited, while increasing the impulse amplitude is associated with increasing the number of capacitors connected in series during the discharge of the generator. Generators having a higher capacitance per shot make it possible to carry out tests with a standard wave on the insulation of large high-voltage installations, which represent a heavy load for the generator.

1. The amount of energy stored in the generator,

\[ W_{\Gamma}=\frac{C_{\mathrm{ud}}\,U_{\max}^{2}}{2}, \]

Fig. 3. Change in the maximum amplitude of the voltage pulse by year of construction for constructed pulse generators.

Legend within the figure:

• △ — cascade generators
• □ — stage generators
• ○ — column-type generators

Axes:

• \(U, \text{kV}\)
• year of construction

Fig. 4. Change in capacitance in the discharge as a function of generator voltage.

Axes:

• \(C_k \times 10^4 \, \mu\text{F}\)
• \(U, \text{MV}\)

Legend:

• \(*\) — USSR
• \(+\) — USA
• \(○\) — Germany
• \(□\) — England
• \(\small\triangleleft\) — Japan
• \(\odot\) — Sweden
• \(\triangle\) — France
• \(×\) — Italy
• [[unclear: symbol]] — Holland
• \(\Delta\) — Switzerland

where \(C_{ud}\) is the generator capacitance per stage, in \(\mu\mathrm{F}\).

\(U_{\max}\) is the maximum amplitude of the voltage pulse, in kV. Fig. 2 gives the energy values at discharge for the largest constructed pulse generators.

The values of the indicated electrical parameters (the amplitude of the voltage pulse, the capacitance per stage, and the stored energy) are determined by the field of application of the pulse generator.

Specific Technical-and-Economic Characteristics

The construction of any installation must be justified not only technically, but also economically; therefore it is expedient to relate the electrical parameters of the generator to its construction data: the volume, height, and built-up area, which determine the costs of construction of the generator, premises, and operation of the installation. The introduction of such characteristics will make possible a more complete analysis and comparison of various designs of pulse generators and will help indicate ways of creating new small-size generators with high electrical parameters. The following specific conventional quantities are proposed as characteristics.

Fig. 5. Change in specific energy in \(\mathrm{kW}\cdot\mathrm{sec}/\mathrm{m}^3\) as a function of year of construction.

1. Specific energy

The degree of technical perfection of a capacitor is characterized by the magnitude of the energy stored per unit volume; since the principal part of a generator consists of capacitors, it is expedient to apply to it the concept of specific energy, measured in \(\mathrm{kW}\cdot\mathrm{sec}/\mathrm{m}^3\),

\[ K_1=\frac{W_\Gamma}{V_\Gamma}, \]

where \(W_\Gamma\) is the energy stored by the generator, in \(\mathrm{kW}\cdot\mathrm{sec}\),

\(V_\Gamma\) is the construction volume of the generator, in \(\mathrm{m}^3\).

Fig. 5 presents the variation of the coefficient \(K_1\) as a function of the year of construction of the generators.

2. Average voltage gradient over the construction height of the generator

The design of a pulse generator may also be characterized by the average voltage gradient over the height of the generator. In order that, during generator operation, the spark should not pass along an arbitrary path, it is necessary that the average gradient during discharge be lower than the discharge gradient in air at pulse voltage. The magnitude of the average voltage gradient over the construction height of the generator will determine the degree of utilization of the air insulation, and will also depend on the design and arrangement of the capacitors. The average gradient is determined as

\[ K_2=\frac{U_{\max}}{H_\Gamma}, \]

where \(U_{\max}\) is the maximum amplitude of the voltage pulse, in kV,
\(H_{\mathrm{G}}\) is the structural height of the generator, in m.

3. Coefficient — \(K_3\)

For an approximate estimate of the change in generator volume with an increase in the maximum amplitude of the voltage pulse, it is necessary to introduce a specific quantity equal to the number of kV of voltage amplitude per unit structural volume of the generator,

\[ K_3=\frac{U_{\max}}{V_{\mathrm{G}}}. \]

4. Coefficient of utilization of the generator’s structural volume — \(K_4\)

This quantity characterizes the compactness of the entire installation and the degree of utilization of the structural volume; it is equal to the ratio of the specific energies of the generator and the capacitor and expresses what part of the entire structural volume of the generator is occupied by the total volume of the capacitors,

\[ K_4=\frac{K_1}{K_0}\cdot 100\%, \]

where \(K_1\) is the specific energy of the generator, in kW·s/m\(^3\);
\(K_0\) is the specific energy of one capacitor group, in kW·s/m\(^3\).

Since

\[ K_0=\frac{C_0 U_0^2}{2}\cdot \frac{1}{V_0}, \]

where \(C_0, V_0, U_0\) refer to a capacitor group,

then

\[ K_4=\frac{C_{\mathrm{u}} U_{\max}^2}{2}\cdot \frac{2V_0}{C_0 U_0^2} =\frac{C_0 U_0^2 n_0^2 \eta^2 V_0}{n_0 C_0 U_0^2 V_{\mathrm{G}}}\cdot 100\% \]

or finally

\[ K_4=\frac{V_0 n_0}{V_{\mathrm{G}}}\cdot \eta^2 \cdot 100\%. \]

Figure 6 presents the variation, over the years, of the coefficient of utilization of structural volume for generators of various designs. It should be emphasized that each parameter of a pulse generator characterizes the installation from only one aspect; only comparison and analysis of all the parameters and proposed specific characteristics gives a complete picture of the installation.

Study of the Designs of Pulse Generators

In terms of structural design, high-voltage pulse generators are very simple and may be classified as follows:

a) single-capacitor generators,
b) ladder-type generators,
c) multideck-type generators,
d) column-type generators.

In addition, all generators may be divided into stationary and mobile units, and into installations built for operation in enclosed premises

and in the open air. Each pulse generator can be characterized by the number of voltage-multiplication stages and by the type of capacitor used. For pulse generators, two types of capacitors are used mainly: (a) with a metal casing and bushing, (b) with an insulating cylindrical casing.

Fig. 6. Change in the coefficient of utilization of building volume by year of construction for certain constructed pulse generators.

Sometimes coils of high-voltage cable are used as capacitors; their use was first proposed by Prof. A. M. Zalesskii.

1. Single-capacitor generators

The principal elements in the design of a pulse generator are capacitors, resistors, and spark gaps. The simplest generator (Fig. 7) consists of a capacitor \(C\), supplied from a charging transformer \(T\) through a protective resistor \(R_z\) and a rectifier \(B\). When the spark gap \(S\) breaks down, the capacitor discharges into the resistor \(R\).

The single-capacitor generator circuit is distinguished by the simplicity of regulating the amplitude and shape of the voltage pulse, and by the small values of the parasitic capacitance and external inductance of the circuit. The amplitude of the voltage pulse in such a circuit is limited by the operating voltage of the capacitor and usually does not exceed \(300\text{–}400\ \mathrm{kV}\). Owing to these qualities, this very simple generator design is made portable, collapsible, and is used for research on breakdown of gases, liquids, and samples of solid dielectric, as well as for other laboratory purposes.

2. Ladder-Type Generators

Ladder-type generators consist of a wooden or wood-and-metal stepped frame with porcelain insulation between the steps and the ground. Capacitors are placed on the steps of the frame, usually in two rows, and sometimes in parallel groups of several units. The ladder structure may be single-flight, two-flight, or three-flight. Installations operating in the open air usually have one flight, while installations operating inside a building have 2–3 flights, since the floor area in the high-voltage hall is limited.

Fig. 7. Circuit of the simplest impulse generator.

Ladder-type generators, in the first years of construction of impulse installations, were the most frequently used design and were built up to 1940. From Fig. 3 it can be seen that the principal ladder-type installations were built in the period from 1930 to 1940, including seven generators rated at 3 million volts and one at 8.4 million volts, with the greatest energy released during discharge.

The value of the specific energy for ladder-type generators is comparatively small and ranges from 0.01 to 0.5 kW·s/m³. The small magnitude of the specific energy is due to the degree of utilization of the construction volume, the large “under-stair” volume. The coefficient of utilization of the construction volume is small and amounts to 1.6–2.8%.

Figure 8 presents a graph of the variation of the coefficient \(K_3\), in kV/m³, with increasing amplitude of the impulse voltage for constructed generators of various types. The decrease of \(K_3\) with increasing \(U_{\max}\) shows that the volume of a ladder-type generator increases not in proportion to the amplitude of the impulse, but much more rapidly. The degree of increase of the volume can be expressed by the empirical dependence \(K_3 = A - B U_{\max}\), or, since \(K_3 = \dfrac{U_{\max}}{V_g}\), one may write that

\[ V_g = \frac{U_{\max}}{A - B U_{\max}}, \]

where \(A = 30,\quad B = 0.002,\quad U_{\max}\) is in kV.

Figure 9 presents the variation of the coefficient \(K_2\), in kV/m—the average voltage gradient over the construction height of the generator—with increasing amplitude of the impulse voltage for constructed generators. The high gradient values, up to 600 kV/m, for ladder-type generators are due to the good utilization of air insulation, since, unlike other designs, the total construction height of the ladder-type ge-

Fig. 8. Variation of the coefficient \(K_3\), \(\mathrm{kV}/\mathrm{m}^3\), as a function of the voltage-pulse amplitude for constructed pulse generators.

Legend:
\(\square\) — floor-type generators
\(\triangle\) — ladder-type generators
\(\circ\) — column-type generators

Fig. 9. Variation of the coefficient \(K_2\), \(\mathrm{kV}/\mathrm{m}\), as a function of the voltage-pulse amplitude for constructed pulse generators.

Legend:
\(\triangle\) — ladder-type generators
\(\square\) — floor-type generators
\(\circ\) — column-type generators

generator does not include the sum of the heights of each capacitor. The external inductance, owing to the considerable length of the discharge path, is of the order of hundreds of microhenries.

The parasitic capacitance between stages is small in comparison with the capacitance of the stages to ground.

At present, ladder-type generators for operation in enclosed premises are no longer being built, because of their considerable dimensions and low specific characteristics; they have been replaced by designs of the shelf and column types.

For creating an outdoor installation of ultrahigh voltage and large energy, however, the ladder design may still be used, since it has greater mechanical stability in comparison with shelf-type generators and a greater impulse capacitance in comparison with column-type generators.

3. Shelf-Type Generators

Generators of the shelf, or tower, type have a frame in the form of a stack of shelves on which the capacitors are placed. The frame is made of wooden or metal frames separated by porcelain support insulators. The capacitors are arranged one above another or along a helical line. In the latter case the constructional height of the generator is lower. The number of shelves may amount to dozens and is limited by mechanical stability and by the height of the room, since shelf-type generators are mainly built for operation indoors. Shelf-type generators began to be built later than ladder-type generators (Fig. 3). The largest shelf-type generator was built in 1940 at the Leningrad Polytechnic Institute—amplitude 4.3 million volts and discharge energy 155 kW·sec.

The specific energy in shelf-type generators has higher values than in ladder-type generators and lies within the range from 0.2 to 1.2 kW·sec/m³. The utilization coefficient of the constructional volume of shelf-type generators is higher than that of ladder-type generators and reaches 4–7%. The volume of the generator increases nonproportionally with increasing impulse amplitude. The empirical expression relating the generator volume to the maximum impulse amplitude has the same form as for ladder-type generators:

\[ V=\frac{U_{\max}}{A-BU_{\max}}, \]

where \(A=110\), \(B=0.025\), where the volume is in m³ and the voltage amplitude in kV. The low values of the average voltage gradient over the constructional height of the generator, equal to 250–350 kV/m (Fig. 9), are due to the fact that the constructional height includes the total height of the capacitors:

\[ H_{\Gamma}=\Sigma h_{\mathrm{iz}}+\Sigma h_k, \]

where \(h_{\mathrm{iz}}\) is the height of the intercapacitor space,
\(h_k\) is the height of a capacitor lying on a shelf,
\(H_{\Gamma}\) is the constructional height of the generator,

and also to the considerable nonuniformity of the electric field in the intercapacitor space. The external inductance of the largest generator itself (LPI at 4.3 million V) is 170 microhenries, and the parasitic capacitance is 250 pF.

It may be noted that impulse generators of the shelf type are the most widespread stationary installations for ra-

tests in enclosed spaces at pulse amplitudes of up to 1–2 million V. The generator design is simple and can be used for temporary pulse installations when an increase in capacitance in the discharge is required at the expense of reducing the voltage-pulse amplitude. Equalizing the electric field between the capacitors makes it possible to reduce the overall dimensions of the installation.

4. Column-Type Generators

The increasing requirements imposed on pulse generators with respect to their high structural and electrical characteristics led to the creation of column-type generators. The simplest design of such a generator is a single-column pulse generator consisting of paper and porcelain cylinders placed one on top of another. Inside the cylinders, filled with oil, are flat capacitor elements connected into parallel and series groups.

Operational inconveniences—the difficulty of repair and of routine inspection of the capacitors—led to the creation of 2-, 3-, 4-, and 6-column generators. In multicolumn generators the capacitor elements form an independent unit and are arranged one above another, separated by insulating cylinders of the same diameter as the capacitors. The cylinders are made either of varnished pressed paper or of porcelain. Porcelain cylinders may be made approximately 15% shorter than paper ones for the same voltage, but the manufacturing technology for porcelain is much more complicated. For compactness and uniform appearance, the elements of the charging device, the filament transformers of the rectifiers, and certain other elements are also placed inside the oil-filled cylinders.

Column-type generators began to be built in the second half of the 1930s (Fig. 3). Many generators for voltages of 2–3 million volts were built already in the postwar period. The largest column-type generator was built in 1939 and has a pulse amplitude of 5.1 million volts with respect to ground, and, when the capacitors are charged to the test voltage, 7.5 million volts. The specific energy of the generators has values approaching the specific energy of the capacitors and is equal to 1–3 kW·s/m³. The high values of the utilization coefficient of the structural volume also testify to the considerable perfection of column-type designs. For built generators it reaches 25% (Fig. 6). The variation of volume with increasing voltage-pulse amplitude can be described by the empirical formula characteristic of all types of pulse generators:

\[ V=\frac{U_{\max}}{A-BU_{\max}}, \]

where \(A=180\), \(B=0.025\), \(V\) is in m³, and \(U_{\max}\) is in kV.

The values of the voltage gradient along the structural height of the generator lie within the range 300–500 kV/m and indicate effective use of the insulating surface of the supporting cylinders. The parasitic capacitance of each stage with respect to ground is small. The external inductance is also smaller for column-type designs owing to the short discharge path, and depends on the arrangement of the columns within the overall volume of the hall and on the number of stages in the columns.

Column-type generators are at present the most advanced design. All modern pulse generators with pulse amplitudes above one million volts are built as column-type generators. The compactness of the generators makes it possible to use them both for stationary

operation in enclosed rooms, as well as for operation in the open air as mobile installations.

General Remarks and Conclusions

The technical level of high-voltage capacitor engineering determines the perfection of the designs of pulse-voltage generators, since high-voltage capacitors are their principal component.

The first pulse generators of all designs had poor characteristics, since they were built on the basis of cosine capacitors—there were as yet no special capacitors for high-voltage pulse circuits at that time. As the quality of high-voltage capacitors improved (with an increase in specific energy per unit volume, an increase in operating gradients, the development of special design types, etc.), the designs of pulse generators improved sharply. An increase in the operating voltage of capacitors led to an increase in the charging voltage of a generator stage. Modern generators have a stage charging voltage reaching 400 kV (Table 1). The increase in charging voltage leads to a reduction in the number of stages, and the latter is associated with a decrease in the inductance of the circuit and an increase in the capacitance in the pulse—both of which are desirable.

The inductance of the circuit is determined by the inductance of the capacitors, resistances, and supply leads, and may be estimated on the basis of the following formulas:

a) the inductance of two parallel conductors of length \(l\) cm, diameter \(d\) cm, and distance between axes \(D\) cm is equal to:

\[ L_1 = 0.004\, l \left( 2.303 \log \frac{2D}{d} - \frac{D}{l} + \frac{1}{4} \right)\ \mu\text{H}; \]

b) the inductance of a square with sides \(a\) cm and a square cross section of the conductor \(\alpha \times \alpha\ \text{cm}^2\) is equal to:

\[ L_1 = 8a \left( \ln \frac{a}{\alpha} + 0.447 \frac{\alpha}{a} + 0.033 \right)\cdot 10^{-3}\ \mu\text{H}; \]

c) the inductance of a single capacitor ranges from 0.01 to 3.5 \(\mu\text{H}\).

Of all the design types of pulse generators, column-type generators have received the greatest development; at present they have the highest electrical and structural characteristics. With an increase in the capacitance of capacitors in an insulating cylindrical casing—and at present the specific energy in them is lower than in capacitors with a metal casing and bushing—column generators will be the only practical design for obtaining pulse voltage of several million volts.

As a result of significant advances in capacitor engineering and apparatus engineering, it is now possible to build compact generators with various pulse amplitudes and energies. The maximum electrical parameters and dimensions of a modern very-high-voltage pulse generator may be approximately estimated as follows: the most realistic design appears to be a multi-column generator (8–10 parallel columns), since with an increase in the number of columns the mechanical strength of the generator and its capacitance in the pulse increase. Experience in operating multistage generators has shown that the maximum number of voltage-multiplication stages is limited to a figure of the order of 50. Starting from the value of the operating voltage of a modern capacitor in

Table 1

Basic data on constructed high-voltage pulse generators with pulse amplitude greater than one million volts

Continuation of Table 1

400 kV, the maximum amplitude may be approximately estimated as equal to 20 million volts relative to ground.

A capacitor with \(U = 400\) kV has a capacitance of \(0.13\ \mu\mathrm{F}\) at a height \(H = 1\ \mathrm{m}\) and diameter \(D = 0.75\ \mathrm{m}\).

Since it is desirable to have 8–10 columns, a parallel connection of two capacitors is probable, and then the capacitance in the impulse is

\[ C_{\mathrm{ud}}=\frac{0.13\cdot 2}{50}\cdot 1000=5000\ \mathrm{pF} \]

and the stored energy is

\[ W=\frac{5000\cdot 20^2}{2}=1000000\ \mathrm{W\cdot sec}. \]

Taking the average voltage gradient over the structural height as equal to \(500\ \mathrm{kV/m}\), we obtain \(H_g = 40\ \mathrm{m}\), and, taking the base to be approximately \(5 \times 5\ \mathrm{m}^2\), we obtain the generator volume \(V_g = 1000\ \mathrm{m}^3\).

With the construction of two generators of opposite polarity, it is possible to obtain an impulse voltage of 40 million volts.

Conclusions

1. High-voltage impulse generators operating by the spark method proposed by Prof. V. K. Arkad’ev are finding ever broader and more varied application in engineering with each passing year.

2. Installations built in the Soviet Union have the highest electrical parameters.

3. All structural types of impulse generators have undergone significant development, and their technical-and-economic characteristics have improved. The column-type generator has received the greatest development.

4. It is necessary to develop a special design, convenient for assembly, for a high-voltage impulse capacitor with high specific characteristics.

5. The proposed technical-and-economic specific characteristics make possible a more concrete and more complete comparison of impulse-generator designs.

6. At the present level of development of technology, it is practically possible to create a generator with a maximum voltage-impulse amplitude of 20 million volts relative to ground and with discharge energy on the order of \(1000\ \mathrm{kW\cdot sec}\).

In conclusion, I express my gratitude to Professor A. A. Vorob’ev for proposing the topic and for his guidance of the present work.

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