INVESTIGATION OF THE INITIATION OF AN INTERELECTRODE GAP IN WATER BY THE VOLTAGE OF THE HIGH-VOLTAGE WINDING OF AN IMPULSE GENERATOR

K. A. KHOR’KOV, B. A. FRANKOVSKII, Yu. G. SHMIGIRILOV

Presented by the scientific seminar of the Department of Electrical Machines and General Electrical Engineering

Devices used for electrohydraulic excitation of seismic oscillations have capacitor banks as energy-storage units [1]. The main shortcoming of capacitor banks as sources of pulsed energy is the low energy capacity of capacitors per unit volume, which limits the power of autonomous devices. The latter reduces the effectiveness of the electrohydraulic method.

An impulse generator, being an inertial energy-storage unit, is capable of storing tens of times more energy per unit volume than a capacitor bank [2]. Designing an impulse generator to be high-voltage, with a voltage sufficient for breakdown of the interelectrode gap, and with low inherent resistance of the stator winding (the resistance of the stator winding is the principal factor limiting the amplitude of the current pulse), is achieved with large dimensions and weight of the impulse generator. Under field operating conditions, the volume and weight of the installation are strictly limited by the load capacity of motor transport.

During the formation and burning of the arc, the resistance of the arc channel decreases from thousands of ohms to fractions of an ohm [3].

Consequently, when operating into a burning arc, it is expedient to use a low-voltage impulse generator whose winding has a considerably lower resistance in comparison with a high-voltage impulse generator made with the same dimensions. Initiation of the interelectrode gap in water can be carried out by the voltage of an auxiliary high-voltage winding placed in the slots of the stator of a single-phase impulse generator that are free from the main low-voltage winding. The basic electrical circuit for connecting the windings of the impulse generator to the electrohydraulic radiator (EHR) is shown in Fig. 1. The principle of operation of the device is as follows.

Fig. 1. Basic electrical circuit for connecting the windings of the impulse generator to the EHR.

In the initial state the fast-acting switching devices K-1 and K-2 are open. The generator is excited, and emfs are induced in the generator windings. The pitch of the high-voltage winding is taken equal to 1/3 of a pole pitch in order to make fuller use of the third, fifth, and higher field harmonics. The instantaneous value of the emf of the \(\nu\)-th harmonic is determined as

\[ e_{\nu}(t)=4lW_{\mathrm{v}}K_{\mathrm{ob}\nu}f_{\nu}\tau_{\nu}B_{m\nu}\cdot \sin \nu\omega t, \tag{1} \]

where \(l\) is the length of the active part of the stator;
\(W_{\mathrm{v}}\) is the number of turns of the high-voltage winding;
\(K_{\mathrm{ob}\nu}\) is the winding factor of the \(\nu\)-th harmonic;
\(f_{\nu}\) is the frequency of the emf of the \(\nu\)-th harmonic;
\(\tau_{\nu}\) is the pole pitch of the \(\nu\)-th harmonic;
\(B_{m\nu}\) is the amplitude value of the induction of the \(\nu\)-th harmonic;
\(\omega\) is the angular frequency of the fundamental first harmonic;
\(\nu\) is the order of the higher harmonic;
\(t\) is the current time.

The resulting emf is

\[ e_{\mathrm{v}}(t)=\sum_{\nu=1}^{n} e_{\nu}(t). \tag{2} \]

The amplitude of the resulting high-voltage emf must be higher than the breakdown voltage of the interelectrode gap in water. For breakdown of interelectrode gaps of length \(0.005\)—\(0.02\) m, the breakdown voltage does not exceed 15 kV [3]. In the calculations we take the amplitude of the high-voltage emf equal to 20 kV.

When the emf on the high-voltage winding reaches the breakdown voltage, the controlled switching device K-1 connects it to the electrodes of the electrohydraulic emitter. Under the action of the applied voltage, the gap breaks down and the high-voltage winding begins to feed the plasma cord of the channel.

The process of initiating the water-filled interelectrode gap is described by the nonlinear differential equation

\[ E_{m\mathrm{v}}\sin(\omega't+\psi)=L\frac{di_{\mathrm{v}}}{dt}+ri_{\mathrm{v}}+R_g(t)i_{\mathrm{v}}, \tag{3} \]

where \(L, r\) are the inductance and active resistance of the high-voltage-winding circuit of the impulse generator, equal to the corresponding parameters of the generator winding, the supply cable, and the arrester (switching device K-1);
\(R_{\mathrm{d}}(t)\) is the active resistance of the interelectrode water gap;
\(i_{\mathrm{v}}\) is the current in the high-voltage-winding circuit;
\(E_{m\mathrm{v}}\) is the amplitude of the resulting emf of the high-voltage winding;
\(\psi\) is the switching angle of the emf of the high-voltage winding;
\(\omega'\) is the equivalent circular frequency of the high-voltage emf.

The dependences for calculating the active resistance of the interelectrode water gap \(R_{\mathrm{d}}(t)\) in the leader and arc stages of the discharge are given in [4]. Equation (3) was solved numerically on a BESM-4 digital computer.

As an example, Fig. 2 shows curves of the variation of the emf of the high-voltage winding, the voltage on the arc, the current in the circuit, the active resistance of the arc channel, and the energy introduced into the arc as functions of time for the variant \(l_{\mathrm{d}}=0.02\) m, \(L_{\mathrm{v}}=0.01\) H, \(r_{\mathrm{v}}=1\ \Omega\). For other circuit parameters the curves have an identical character. The results of the computer calculations were processed and are presented in Tables 1–4. The tables present the following parameters:

$L$, $r$ — total inductance and active resistance of the high-voltage winding circuit;

$I_m$ — amplitude of the current pulse;

$R_{\mathrm{d}\min}$ — minimum resistance of the arc channel;

$\tau_{\mathrm{v}}$ — duration of arc burning;

$W(\tau_{\mathrm{v}})$ — total energy introduced into the arc channel;

$R_{\mathrm{d}}(t_{\mathrm{on}})$ — resistance of the arc channel at the assumed moment of switching on the low-voltage winding;

$t_{\mathrm{on}}$ — assumed moment of switching on the low-voltage winding by switching apparatus K-2 onto the initiated interelectrode gap.

Fig. 2. Curves of variation of the emf of the high-voltage winding of the impulse generator $e_{\mathrm{n}}$, the voltage on the arc $U_{\mathrm{d}}$, the active resistance of the arc channel $R$, and the energy introduced into the arc $W(\tau_{\mathrm{v}})$

Table 1

Interelectrode gap $l_{\mathrm{e}} = 0.005\ \mathrm{m}$

Table 2

Interelectrode gap \(l_{\mathrm{e}}=0.01\ \mathrm{m}\)

Table 3

Interelectrode gap \(l_{\mathrm{e}}=0.015\ \mathrm{m}\)

Table 4

Interelectrode gap \(l_{\mathrm{e}}=0.02\ \mathrm{m}\)

Attention is drawn to the similar values of the current amplitude in the arc for different lengths of the interelectrode gap for the same variants of the circuit parameters \((L\) and \(r)\). The constancy of \(I_m\) is determined by the larger value of the inherent resistance of the high-voltage winding in comparison with the resistance of the arc channel.

Variation of the parameters of the high-voltage-winding circuit at a constant interelectrode gap shows that the current amplitude and the energy introduced into the arc channel increase as the active and inductive resistance of the high-voltage-winding circuit decrease. Accordingly, at smaller \(L_{\mathrm{v}}, r_{\mathrm{v}}\) we obtain smaller values of the active resistance of the arc channel. It should be noted that the prolonged burning of the arc (measured in milliseconds) facilitates reliable interception of the arc by the working low-voltage winding of the impulse generator.

Prolonged maintenance of arc burning in the interelectrode gap by the high-voltage winding is a major advantage of the method of arc initiation under consideration.

REFERENCES

1. M. V. Mazov, V. M. Verevkin, V. V. Alekseev. Excitation of elastic waves in soil by means of electrical discharges in a liquid medium. Problems of Exploration Geophysics, Issue 4, “Nedra,” 1964.

2. G. A. Sipaĭlov, K. A. Khorkov. Specific energy of a shock generator. Proceedings of TPI, Vol. 132, published by TSU, Tomsk, 1965.

3. K. A. Naugol’nykh, N. A. Roi. Electrical Discharges in Water. Moscow, “Nauka,” 1971.

4. B. A. Frankovskii, K. A. Khorkov, Yu. G. Shmigirilov. Investigation of arc initiation in an interelectrode gap in water by a discharge of a high-voltage capacitor bank with arc supply from a low-voltage shock generator. Proceedings of TPI. Present collection.