IMPROVING THE EFFICIENCY OF USING SHOCK GENERATORS FOR SUPPLYING AN ARC LOAD

G. A. SIPAILOV, A. V. LOOS, E. I. SOBKO

(Presented by the scientific seminar of the Departments of Electrical Machines and General Electrical Engineering)

To supply pulsed pumping lamps of optical quantum generators—lasers—as well as installations that use the electrohydraulic effect (installations for exciting seismic oscillations in geological exploration, for destroying hard rocks, etc.), pulsed power sources are required that ensure the release in the consumer’s arc gap, over a time of several milliseconds, of energy on the order of 10–100 MJ [1].

As a rule, at present, to supply the above-mentioned consumers, capacitor banks are used as storage devices and energy sources. The accumulation of energy in capacitors is advantageous from the standpoint of minimum losses; however, on the other hand, the electrical method of storage is the most expensive and cumbersome in volume, and does not allow the indicated amounts of energy to be accumulated.

Inductive storage devices, despite their significantly high energy capacity, have low economy because of large energy losses and require a powerful charging device. The problem of commutating energy from an inductive storage device to the load also remains unsolved.

An analysis of existing trends in solving the problem of supplying pulsed arcs shows that one of the most promising pulsed energy sources is the synchronous shock generator [2]. In this connection, the task arises of studying the possibilities of shock generators and increasing the efficiency of their use in supplying an arc load.

The electromechanical transient processes occurring in a shock generator are described most fully by a system of differential and algebraic equations [3].

A pulsed arc is dynamic. In it there is no single-valued dependence of voltage on current. As the current increases, this dependence differs from that when it decreases. In addition, the volt-ampere characteristics of the devices described above, which are based on the use of a pulsed arc, are determined by their design and may have different forms. To clarify the qualitative picture, a simplified approximation of the arc volt-ampere characteristic by a hyperbola was adopted, known in the literature as Ayrton’s equation:

\[ U_{\text{d}} = K_1 + \frac{K_2}{i}, \tag{1} \]

The solution of the nonlinear system of differential and algebraic equations describing the processes taking place is impossible in general form; therefore, in order to carry out a large program of investigations using the complete system of equations, a mathematical model was created on the basis of an MN-14 analog computer.

One of the main tasks of the investigations is to determine the optimum value of the arc-burning voltage at which the maximum energy is released in the arc gap. As the investigations showed, the value of the optimum arc-burning voltage depends almost not at all on the parameters of the shock generator, but depends substantially on the arc-initiation angle \(\alpha\). As the angle \(\alpha\) is increased up to certain limits, the matched arc-burning voltage and the amount of energy released in the arc gap increase, while the duration of its input \(t_{\text{д}}\) into the arc gap is simultaneously reduced, which is very favorable for the consumers indicated above.

In this connection we proposed the following method for supplying consumers whose operation is based on a pulsed arc. The operating diagram of the generator is shown in Fig. 1, where \(X_c, X_{\text{в}}, X_{Dd}, X_{Dq}\) are the inductive resistances of the generator circuits, respectively, of the stator, the field winding, and the damper windings along the \(d\) and \(q\) axes; \(r_c, r_{\text{в}}, r_{Dd}, r_{Dq}\) are the active resistances of the circuits; K-1, K-2 are switching devices;

Fig. 1. Operating diagram of the generator for an arc gap

DP is the arc gap, short-circuited at the initial instant of time by an initiating wire.

The method of supplying pulsed arcs using a shock generator as the energy source can be clarified by considering the operation of the circuit shown in Fig. 1. In the initial state the shock generator operates at no load, contact device K-1 is open, and K-2 is closed.

At the instant when the generator EMF passes through zero (Fig. 2), the switching device K-1 is closed. The generator enters a sudden short-circuit mode, and the current \(i_c\) grows rapidly. At the same time, energy is accumulated in the leakage fields of the generator. The generator current \(i_c\) is distributed between two parallel branches: the contacts of apparatus K-2 and the closed initiating wire of the arc gap DG, in inverse proportion to their resistances.

When a definite arc-initiation angle \(\alpha\) is reached, after some amount of energy has been accumulated in the generator inductance, the contact apparatus K-2, which shunts the arc gap, is opened. Transfer of the current from contacts K-2 into the circuit of the arc gap is feasible, since the burnout time of the initiating wire can easily be selected to be somewhat greater than the opening time of contacts K-2. The initiating wire burns out, and an arc arises in the arc gap. The subsequent change in the current in the arc and the transfer of energy to it are determined by the reserve of electromagnetic energy in the generator inductance and by the phase angle of the generator voltage at which arc initiation occurred. In this process, energy is transferred to the arc simultaneously from the leakage fields of the generator and from the flywheel masses of the generator. At the instant when the stator current \(i_c\) passes through zero, K-1 is opened.

Fig. 2. Shape of the current, voltage, and energy curves

Figure 2 shows oscillograms of the solution, on an MN-14 analog computer, of the equations of the shock generator with parameters in p.u. \(x''_d = 0.0391,\ x_{Dd} = x_{Dq} = 1.02,\ x_{\mathrm{B}} = 1.2,\ r_c = 0.00156,\ r_{\mathrm{B}} = r_{Dd} = r_{Dq} = 0.001,\ U_{\mathrm{B}} = 0.001\), with an arc-burning voltage in p.u. \(U_{\mathrm{d}} = 1\). The amplitude value of the voltage of the shock generator is taken as the unit of voltage.

Figure 3 shows the dependences of the matched arc-burning voltage \(U_{\mathrm{d}}\), the duration of energy input into the arc \(t_i\), and the coeffi-

delivery of energy to the arc, \(K_d=\dfrac{W_d}{W_{kz}}\) (\(W_{kz}\) is the short-circuit energy), and the current amplitude coefficient \(K_i=\dfrac{1}{I_{kz}}\) as functions of the arc-initiation angle \(\alpha\), calculated for a shock generator with the parameters indicated above. As can be seen from Fig. 3, as the arc-initiation angle \(\alpha\) increases, the shock generator is transformed to an ever greater extent into an inductive storage device, charged during the time in which the rotor turns through the angle \(\alpha\), and discharged during the time \(t_i\).

At the same time, if the arc is initiated at the instant when the stator current \(i_c\) reaches its maximum (shown by the dashed line in Fig. 2), then, with an infinitely large arc-burning voltage, in this case it is theoretically possible to transfer completely to the arc gap the energy of a sudden short circuit stored in the leakage fields of the generator in an infinitely short time interval. In practice this is impossible; therefore we shall limit ourselves to an arc-burning voltage in per-unit values \(U_d=1\) (i.e., equal to the amplitude value of the generator emf). In this case the coefficient of energy transfer to the arc gap will be \(K_d=0.9\), and the pulse duration

\[ t_i = 1.7 \ \text{rad} \quad (\text{at } f=50\ \text{Hz},\ t_i=5.4\ \text{ms}). \]

For engineering calculations, analytical expressions are needed for determining the current and energy in the arc. We shall determine them, adopting the following assumptions:

1. We shall regard the rotor circuits as superconducting, i.e., the flux linkages \(\psi_v\), \(\psi_{pd}\), \(\psi_{pq}\) do not change during the current pulse. The possibility of such an assumption is confirmed by oscillograms of the flux linkages of the rotor windings during operation on an arc, obtained on the MN-14 machine.

2. Since \(i_{\text{sc}}\ll U_d\), we neglect the voltage drop across the active resistance of the stator winding.

3. We take \(X''_d=X''_q\), which is quite permissible for a nonsalient-pole shock generator having a powerful damping system.

4. The voltage gradient in the arc column is constant [4]. Based on these assumptions, we obtain the expression for the current in the arc

\[ i_c=\frac{\omega}{X''_d} \left[ \psi_{co}-U_d t-\frac{E_m}{\omega}\cos(\alpha+\omega t) \right] \ \text{A}, \tag{2} \]

where \(t\) is the current time, counted from the moment of arc ignition,

\(\psi_{co}\) is the initial value of the flux linkage of the stator winding.

The energy released in the arc gap is determined by the formula

\[ W_d=U_d\int_0^{t_i} i_c\,dt, \tag{3} \]

After substituting expression (2) into formula (3), we obtain

\[ W_d=\frac{U_d\omega}{X''_d} \left\{ \psi_{co}t-\frac{t^2U_d}{2} -\frac{E_m}{\omega^2} \left[ \sin(\alpha+\omega t)+\sin\alpha \right] \right\}\ \text{J}. \tag{4} \]

The final value of the energy released in the arc during one pulse can be determined from the simpler relation

\[ W_d=\frac{2K_dE_m^2}{X''_d\omega}\ \text{J}, \tag{5} \]

where

\[ K_d=f(\alpha) \]

can be determined from Fig. 3.

Fig. 3. Energy characteristics of the generator when operating on a pulsed arc

Thus, the studies carried out showed that the matched arc-burning voltage does not depend on the parameters of the shock generator, but depends to a great extent on the angle of arc initiation. Moreover, an increase in the initiation angle leads to an increase in the utilization of the shock generator. This latter circumstance made it possible to develop a circuit for supplying a pulsed arc from a shock generator that allows a substantially larger fraction of the energy of a sudden short circuit to be transferred to the arc than when the generator is connected directly to the arc gap. At the same time, the time of energy transfer to the arc is reduced, reaching several milliseconds at a generator emf frequency of 50 Hz, which significantly broadens the areas of application of shock generators.

REFERENCES

1. S. P. Kononov, B. A. Skrebnev, “Application of pulsed electric-power systems; pulsed electric power engineering.” In: Collection of Articles. Kazan, 1970.

2. L. P. Gnedin, E. G. Kasharskii, F. G. Rutberg. “On the prospects for using turbine generators to obtain large pulsed powers in supplying powerful plasmatrons.” Elektrotekhnika, 1971, No. 3.

3. A. V. Loos, G. A. Sipailov. “Mathematical modeling of the electromagnetic processes of a shock generator.” Izv. TPI, Vol. 152, 1966.

4. L. M. Zalesskii. The Circuit-Breaker Arc. GEI, 1963.