ELECTRIC MACHINE PULSED ENERGY SOURCE

A. V. LOOS, G. A. SHIPAILOV, A. A. SHCHEGOLEV

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

Existing solutions for increasing the pulsed power of shock generators, based on the use of special circuits, have a significant drawback, since they require the presence of an auxiliary energy storage device—a capacitor bank [1, 2]. Increasing the pulsed power by exciting a shock generator to a voltage higher than the nominal value and using forced excitation modes leads to considerable energy losses and requires a powerful excitation source [3].

In the electric-machine energy source under consideration, it is possible to increase the pulsed power and, consequently, the energy transmitted to the load during one half-wave of the emf without the use of auxiliary energy storage devices and excitation sources.

The increase in pulsed power is achieved by using the known effect of voltage rise that occurs during a two-phase short circuit of a synchronous machine with an asymmetrical rotor, with the remaining third stator phase open [4]. The total voltage of the open phase \(e_a\) consists of the sum of the no-load voltage \(e_{a0}\) and the additional voltage \(\Delta e_{a\max}\):

\[ e_a = e_{a0} + \Delta e_{a\max} = \left( 2 \frac{x''_q}{x''_d} - 1 \right)e_{a0}, \tag{1} \]

As follows from expression (1), the maximum value of the voltage on the open phase depends strongly on the ratio of the machine parameters along the direct and quadrature axes, \(x''_d\) and \(x''_q\).

The electric-machine pulsed energy source under consideration contains a shock synchronous generator consisting of a stator and a rotor, and switching devices K-1 and K-2 (Fig. 1). On the stator there is a two-phase winding consisting of two magnetically uncoupled parts displaced relative to one another by 90 electrical degrees.

One of them, the auxiliary winding A, can be short-circuited through switching device K-1; the other, the working winding B, can be connected to the load through switching device K-2. On the rotor are located the excitation winding \(f\), supplied from a voltage source, and damper windings \(D_d\) and \(D_q\). The damper winding \(D_d\), along the axis coinciding with the axis of the excitation winding, is made more powerful than the damper winding \(D_q\).

Fig. 1. Schematic diagram of an electric-machine pulse source.

In the initial position, the contacts of the switching devices K-1 and K-2 are open; the generator is operating at no load. In stator windings A and B, emfs \(e_A\) and \(e_B\) are induced, shifted relative to each other by 90 degrees (Fig. 2).

At the instant \(t_1\), when the emf of the auxiliary winding \(e_A\) passes through zero, the contacts of switching device K-1 are closed. The generator enters a short-circuit mode; in this process the kinetic energy of the rotor is converted into electromagnetic energy of the fields linked with the stator and rotor windings. The nature of the currents in windings A, f, Dd, and Dq is shown in Fig. 2.

All rotor windings have magnetic coupling with working winding B of the stator; therefore, the magnitude and character of the currents in them determine its emf. If the damper system is symmetrical, then the resultant action of the transient currents in the rotor windings does not lead to an increase in the emf in working winding B. In our case the damper system is asymmetrical: damper winding Dq has a greater total resistance than winding Dd; consequently, the current \(i_{Dq}\) will be smaller than the current \(i_{Dd}\). It may be assumed that the main influence on the emf in winding B will be exerted by windings f and Dd. As can be seen from Figs. 1 and 2, the currents in windings f and Dd magnetize the machine along the pole axis in the same direction and, consequently, the main magnetic flux increases substantially. This increase in magnetic flux leads to a substantial increase of the emf in working winding B.

At the instant \(t_2\), corresponding to the beginning of the working half-wave of emf in winding B, K-2 is closed. In this case, owing to the increase of the emf, the pulse power of the ge-

Fig. 2. Curves of EMF and currents in the windings of the pulse source

of the generator and the fraction of the rotor’s kinetic energy converted into electromagnetic energy and delivered to the load.

At the moments when the currents $i_A$ and $i_B$ pass through zero, the contacts of the switching devices K-1 and K-2 open. Experimental investigations of the pulse-power source under consideration confirmed the correctness of the principles on which it is based (Fig. 3).

Fig. 3. Oscillogram of the EMF $e_B$ and currents $i_A$ and $i_B$ of the experimental pulse source

More detailed investigations of an electric-machine source are most expediently carried out using the complete system of differential equations of electromagnetic transients. An electric-machine pulse-power source is an electric machine with stator and rotor asymmetry. It is known that the use of coordinate-transformation methods for the differential equations of synchronous machines with limiting asymmetry does not make it possible to eliminate variable coefficients. The need to take into account saturation of the magnetic circuit along the path of the main magnetic flux complicates the original system of equations to an even greater degree and makes its analytical investigation impossible. In this connection it becomes necessary to use computers for the investigations. Analog computers possess great capabilities in analyzing transient processes by differential equations.

In order to use the known form of notation for a synchronous machine in the \(d\) and \(q\) axes and methods for modeling it with allowance for saturation along the path of the main magnetic flux [5], we apply an artificial symmetrization of the generator from the stator side. For this purpose the active and inductive resistances of windings A and B of the stator are represented in the form:

\[ r_A = r + r_a , \tag{2} \]

\[ r_B = r + r_b , \tag{3} \]

\[ x_A = (x_a + x_s) + x_{sa} , \tag{4} \]

\[ x_B = (x_a + x_s) + x_{sb} , \tag{5} \]

Assigning the second terms of expressions (3) and (5) to the load \(r_n, x_n\) and considering the second terms of expressions (2) and (4) as a certain conditional load connected into winding A, we obtain a two-phase electric machine symmetrical with respect to the stator, in the phases of which different loads are connected.

Applying the known notation of the differential equations of a synchronous machine in the \(d\) and \(q\) axes with allowance for saturation along the path of the main magnetic flux and compiling the load equations in real variables, we obtain the complete system of differential equations of the generator:

\[ p\Psi_d = - U_d - r i_d + \omega \Psi_q , \tag{6} \]

\[ p\Psi_q = - U_q - r i_q - \omega \Psi_d , \tag{7} \]

\[ p\Psi_f = U_f - r_f i_f , \tag{8} \]

\[ p\Psi_{Dd} = - r_{Dd} i_{Dd} , \tag{9} \]

\[ p\Psi_{Dq} = - r_{Dq} i_{Dq} , \tag{10} \]

\[ i_d = \frac{1}{x_s}\left(\Psi_d - \Psi_{\delta d}\right), \tag{11} \]

\[ i_q = \frac{1}{x_s}\left(\Psi_q - \Psi_{\delta q}\right), \tag{12} \]

\[ i_f = \frac{1}{x_{\sigma f}}\left(\Psi_f - \Psi_{\delta d}\right), \tag{13} \]

\[ i_{Dd} = \frac{1}{x_{\sigma Dd}}\left(\Psi_{Dd} - \Psi_{\delta d}\right), \tag{14} \]

\[ i_{Dq} = \frac{1}{x_{\sigma Dq}}\left(\Psi_{Dq} - \Psi_{\delta q}\right), \tag{15} \]

\[ \Psi_{\delta d}=\eta(i_d+i_f+i_{Dd}), \tag{16} \]

\[ \Psi_{\delta q}=\eta(i_q+i_{Dq}), \tag{17} \]

\[ \eta=\Phi(\Psi_\delta), \tag{18} \]

\[ \Psi_\delta=\sqrt{\Psi_{\delta d}^{2}+\Psi_{\delta q}^{2}}, \tag{19} \]

\[ U_d=U_A\cos\Theta+U_B\sin\Theta, \tag{20} \]

\[ U_q=-U_A\sin\Theta+U_B\cos\Theta, \tag{21} \]

\[ U_A=r_a i_A+x_{\mathrm{э}a}\frac{di_A}{dt}, \tag{22} \]

\[ U_B=(r_{\mathrm{н}}+r_b)i_B+(x_{\mathrm{н}}+x_{\mathrm{э}b})\frac{di_B}{dt}, \tag{23} \]

\[ i_A=i_d\cos\Theta-i_q\sin\Theta, \tag{24} \]

\[ i_B=i_d\sin\Theta+i_q\cos\Theta. \tag{25} \]

The mathematical model of the system (6)—(25) is presented in Fig. 4. Saturation of the magnetic circuit along the path of the main magnetic flux is determined as a function of the flux linkage in the air gap, \(\psi^\delta\). With an inductive character of the generator load, the solution circuit contains two differentiating elements. With an active load, the differentiation operation can be eliminated.

Fig. 4. Mathematical model of the differential equations of the pulse source

Thus, the experimental investigation of the electromechanical source of pulsed power confirmed the correctness of the principles underlying it and the possibility of a substantial increase in the pulsed power of impact generators. The developed mathematical model of the electromechanical pulsed energy source makes it possible to carry out its investigations for any ratios of paramet-

of the windings, taking into account saturation of the magnetic circuit by the main magnetic flux.

References

1. V. V. Kaplan, V. M. Nashtatyr. Method of accumulating energy in an inductive load. Author’s Certificate No. 164640.

2. G. A. Sipailov, V. V. Ivashin, K. A. Khorkov. Method of transmitting energy to an inductive load from a shock-power generator. Author’s Certificate No. 192922.

3. A. I. Verkhoturov. Investigation of intermittent excitation modes of a shock generator. Candidate dissertation, Tomsk, 1968.

4. I. M. Postnikov. Generalized theory and transient processes of electrical machines. “Tekhnika,” 1966.

5. N. I. Sokolov. Application of analog computers in power systems. “Energiya,” 1970.