SYNCHRONOUS PULSE GENERATOR WITH A HIGH PULSE REPETITION FREQUENCY

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

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

At present, a large number of types and designs of pulsed electromechanical sources have been developed, and they have found wide industrial application owing to their relatively low cost and ease of maintenance [1, 2]. Increasing the pulse power of electromechanical pulse generators, as well as the permissible pulse repetition frequency, is a topical problem, since their increase leads to an improvement in the weight-and-size and energy characteristics of the pulsed system.

The existing progress in the field of semiconductor devices (the appearance of power diodes, thyristors, triacs, etc., varied in their operating parameters) creates the prerequisites for developing new design and circuit solutions for increasing the pulse power of electromechanical generators.

This paper considers a synchronous pulse generator in which a semiconductor switching device is connected into the circuit of the damper winding along the transverse axis. The inclusion of semiconductor valves in the circuit of the damper winding along the transverse axis in single-phase synchronous generators operating in steady-state mode is known and makes it possible to use the counter-rotating field for excitation of the machine [3]. Let us consider the operation of such a generator in pulsed mode.

Figure 1a shows the schematic circuit diagram of a pulsed synchronous generator, into the damper winding along the \(q\)-axis of which a switching apparatus has been introduced.

Here \(C\), \(f\), \(D_d\), \(D_q\) are the generator windings—respectively, the stator winding, the field winding, and the damper windings along the \(d\)- and \(q\)-axes;

\(L_n\) is the generator load;

\(K\text{-}1\), \(K\text{-}2\) are switching devices.

Figure 1b shows the curves of the generator e.m.f. \(l_1\), the current \(i_c\) in the stator winding \(C\), the current \(i_{Dq}\), and the flux linkage \(\Psi_{Dq}\) in the damper winding along the \(q\)-axis.

In the initial state the generator rotor rotates with angular velocity \(\omega\), while possessing a certain reserve of kinetic energy. The field winding, supplied with direct current \(i_{f0}\), creates an initial magnetic flux which, during rotation, induces a sinusoidal e.m.f. in the stator winding. The switching devices \(K\text{-}1\), \(K\text{-}2\) are open.

Fig. 1. Schematic circuit of a synchronous pulse generator and calculated curves of the currents in its windings

At the moment when the stator-winding emf passes through zero \(t_0\) (Fig. 1, b), the generator is switched onto the load \(L_{\mathrm{n}}\). The current in the stator winding begins to increase slowly, tending to preserve the initial magnetic flux linked with the stator winding. Since the commutating device \(K\text{-}2\) is open (along the \(q\)-axis there is, as it were, no damper winding), the current of the stator winding \(C\), up to the instant

\[ t_1 \simeq \frac{\pi}{2\omega}, \]

increases only slightly, because only a small magnetomotive force is required to maintain the magnetic flux linked with the stator winding. From time \(t_1\) there is a rapid increase in the stator current \(i_c\), since the magnetic permeance for the armature-reaction flux begins to decrease as a result of its increasing shielding by the rotor contours along the longitudinal axis.

The currents \(i_c\), \(i_f\), \(i_{D d}\) create the resultant magnetomotive force \(\overline{F}_{\mathrm{res}}\) (Fig. 1, a), which creates the resultant magnetic flux of the machine; the flux linkage of this flux with the winding \(D_q\) reaches its maximum value at an angle \(180^\circ > \omega t > 90^\circ\).

Let us determine an expression for the flux linkage of the damper winding along the transverse axis \(q\), under the condition that the active resistances of the windings are equal to zero. In this case the currents of all circuits of the machine can be determined from the condition of constancy of flux linkages, which makes it possible to pass from a system of differential equations to algebraic equations [4]. In deriving the calculated expressions we shall assume that the winding \(D_d\) along the \(d\)-axis is absent. Such a simplification does not disturb the qualitative picture of the processes. For the adopted initial conditions

\[ \Psi_c(0)=i_{f0}x_a,\qquad \Psi_f(0)=i_{f0}x_f,\qquad \Psi_{Dq}(0)=0, \]

the expression for the current \(i_c\) has the form

\[ i_c=\frac{2i_{f0}x_a(1-\cos\gamma)} {(x'_d+x_c)+(x'_d-x_c)\cos 2\gamma}, \tag{1} \]

where \(X'_d\) is the transient inductive reactance of the generator,

\[ \gamma=\int_0^t \omega\,dt \]

is the angle of rotation of the rotor.

The flux linkage of the damper winding \(\Psi_{Dq}\) along the \(q\)-axis is

\[ \Psi_{Dq}=i_c x_a\sin\gamma= \frac{2x_a^2 i_{f0}(1-\cos\gamma)\sin\gamma} {(x'_d+x_c)+(x'_d-x_c)\cos 2\gamma}. \tag{2} \]

Analysis of expression (2) shows that the flux linkage \(\Psi_{Dq}\) (Fig. 1, b), depending on the parameters, can exceed the maximum value of the no-load flux linkage \(i_{f0}X_a\) by a factor of 2–4 and reach its maximum value at \(\gamma\) somewhat less than \(180^\circ\).

At the instant \(t_2\), corresponding to the maximum value of the flux linked with winding \(D_q\), the switching apparatus K-2 closes (Fig. 1, a).

Thus, the magnetic flux is captured by the damper winding \(D_q\) and, with further rotation of the rotor, remains constant by virtue of the law of conservation of constancy of flux linkages. On the rotor, systems of circuits along the longitudinal and transverse axes are formed, which create the resultant rotor flux, exceeding the no-load flux of the machine.

As the rotor turns, the current \(i_c\) increases further, reaching its maximum value at the instant when the stator-winding axis and the axis of the resultant rotor flux coincide.

Let us determine expressions for the currents \(i_c\) and \(iD_q\), beginning from the instant \(t_2\), when the switching apparatus K-2 closes. At the instant \(t_2\) the \(d\)-axis will be displaced relative to phase \(C\) by the angle \(\omega t_2\). Under the initial conditions

\[ \Psi_c(t_2)=i_{f0}x_a,\qquad \Psi_f(t_2)=i_{f0}x_f,\qquad \Psi_{Dq}=\Psi_{Dq}(t_2), \]

the expressions for the currents \(i_c\) and \(iD_q\), beginning from the instant \(t_2\), have the form:

\[ i_c= \frac{i_{f0}x_a x_f^2(1-\cos\gamma)-\Psi_{Dq}(t_2)\cdot x_f x_a\cdot \sin\gamma} {x'_d x_f^2}, \tag{3} \]

\[ D_q= \frac{ \frac{\Psi_{Dq}(t_2)}{2}\left[(x_c+x'_d)+(x'_d-x_c)\cos 2\gamma\right] +i_{f0}x_a^2(\sin\gamma\cos\gamma-\sin\gamma) } {x_f x'_d}. \tag{4} \]

Expressions (1–4) were used to calculate the curves (Fig. 1, b) for the following generator parameters:

\[ x_a=1.0,\qquad x_c=1.05, \]

\[ x_f=x_{Dq}=1.05,\qquad L_n=0,\qquad r_c=r_f=r_{Dq}=0. \]

With further rotation of the rotor, the current $i_c$ decreases, and at the instant when it passes through zero, $t_3$, the switching device K-1 is opened. Through winding $D_q$, beginning at time $t_2$, there flows a current of such magnitude as is necessary to keep its flux linkage constant.

After the switching device K-1 is opened ($t_3$), the magnitude of the current $i_{Dq}$ is small, since the reluctance of the magnetic circuit is low for the magnetic flux produced by it.

After the current pulse $i_c$, the magnitude of the emf in the stator winding is determined by the total magnetic flux created by the currents in the rotor windings $f$, $D_q$, and, consequently, is greater than the emf of the generator at no load.

Thus, after the current pulse, demagnetization of the machine does not occur and, consequently, it is possible to reconnect the generator to the load.

The highest pulse repetition frequency can be ensured if the generator is connected to the load at time $t_4$, the beginning of the first positive half-wave of the emf after the pulse, by closing K-1. Beginning at time $t_4$, the current $i_c$ increases and $i_{Dq}$ decreases.

At the instant $t_5$ when the current $i_{Dq}$ passes through zero, K-2 is opened. Thereafter the processes in the circuit repeat. The amplitude of the second current pulse $i_c$, like that of the first, is determined by the magnitude of the resultant magnetic flux of the rotor, produced by the system of circuits along the direct and quadrature axes after K-2 is closed at time $t_6$, and is equal to the amplitude of the first pulse.

The unipolar character of the current $i_{Dq}$ makes it possible to use, as the switching device K-2, an uncontrolled semiconductor valve. Experimental verification of the operability of a synchronous pulse generator with a high pulse repetition frequency was carried out on a mock-up model made on the basis of a standard AK-51-4 motor. As the switching device K-1, a PTL-150-8 thyristor was used; as the switching device K-2, a VK-50-8 diode was used. When the damper winding $D_q$ is short-circuited, the generator circuit assumes the usual form [4]. This makes it possible to perform an experimental comparison of the effectiveness of using the generator circuits under consideration.

Figure 2a shows oscillograms of the emf and currents in the stator winding with the damper winding short-circuited along the quadrature axis.

a)

b)

c)

Fig. 2. Experimental results

Figure 2b shows an oscillogram of the e.m.f. and of the currents in the stator winding and in the damper winding along the \(q\)-axis of a synchronous generator with a switching device in the circuit of the damper winding \(D_q\). A comparison of the amplitudes of the stator current in Figs. 2a and 2b shows that the synchronous generator with a switching device in the rotor circuit has a significantly greater pulse power. At the same time, the demagnetizing effect of the armature reaction, manifested in a decrease of the e.m.f. after the current pulse in the generator with a symmetrical damper winding (Fig. 2a), is absent in the generator under consideration (Fig. 2b). After the current pulse, even some increase in the e.m.f. takes place (Fig. 2b). This makes it possible to achieve the maximum possible pulse repetition frequency and to feed the load with a series of pulses of equal power (Fig. 2c).

Thus, the inclusion of a switching device in the circuit of the damper winding along the \(q\)-axis makes it possible, without the use of additional energy sources, to perform a kind of forcing of the generator directly at the beginning of each current pulse.

The pulse synchronous generator considered has significant advantages in comparison with ordinary generators having a symmetrical damper system. Its use in pulsed power-supply systems substantially expands the possibilities of electric-machine sources of pulsed power.

REFERENCES

1. Pulsed electric power engineering. Collection of articles, Kazan, 1970.

2. A. L. Livshits, I. S. Rogachev, M. G. Otto. Pulse generators. “Energiya,” 1970.

3. S. Nonaka. Analysis of the Self-Excited Salient-Pole Type Single-Phase Synchronous Machine, I. Inst. Electr. Engs. Japan, 1961, 81, No. 3.

4. G. A. Sipailov, A. V. Loos, E. I. Sobko. Mathematical modeling of a single-phase synchronous generator. “Elektrotekhnika,” 1972, No. 10.