AUTONOMOUS SOURCE OF PULSE POWER WITH A SYNCHRONOUS GENERATOR

G. A. Sipailov, A. V. Loos, Yu. A. Romanov, F. P. Zverev

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

A known method for obtaining current and voltage pulses with the necessary parameters is their direct generation by means of special electrical machines—synchronous impact generators. As a rule, this method of obtaining pulse power is the most economically advantageous when large energies are transferred to the load (from 10 MJ and above) [1].

However, the use of a synchronous impact generator sometimes proves effective even for relatively small transferred energies, on the order of several hundred joules, for example, in autonomous pulse-power sources.

The principal advantage of a supply circuit with an impact synchronous generator is its structural simplicity, which eliminates a whole series of intermediate transmission elements and, consequently, provides higher reliability and, in a number of cases, lower system weight in comparison with circuits using energy storage in capacitor banks.

The transient processes that occur when an impact generator is connected to a load are described by a system of differential equations of emf equilibrium, written for each of the windings [2].

Analytical investigations of the complete system of differential equations, owing to the presence of a large number of variable coefficients, present great difficulty and do not yield a solution in general form.

In the present case it is advisable to use, for investigations, the method of physical and mathematical modeling with the application of analog computing machines.

To simplify the analysis, let us consider the operation of an impact synchronous generator on an active load (the most frequently encountered type of load for autonomous pulse systems of low power).

One of the tasks in studying the operation of an impact generator on an active load is to determine the matched load resistance at which the maximum energy will be released in it. Figure 1 presents the results of calculations on an MN-14 analog computer of the dependence of the energy in the active load on the magnitude of its resistance for various leakage inductances.

Fig. 1. Dependence of the energy in the load on the value of its resistance for various leakage inductances of the stator

stator winding. The remaining parameters of the generator in this case remained constant and were equal to (in relative units):

\[ X_{ad}=1;\quad X_{\sigma r}=0.01;\quad R_r=0;\quad R_s=0. \]

Curves 1, 2, 3, shown in Fig. 1, are given for subtransient resistances \(x''_d=0.03;\ 0.05;\ 0.07\), respectively. As is seen from the curves, the maximum value of the energy in the load corresponds to \(R_H\) somewhat smaller than \(x''_d\). It follows from this that the value of the matched load resistance is different in the case of its active and inductive character. Moreover, the deviation of the resistance has an especially strong effect on the value of the transmitted energy at small leakages of the stator winding, i.e., for large machines.

To simplify the analysis, we use the known equivalent circuit of a surge generator in the form of a sinusoidal e.m.f. and the series-connected inductance \(L_r\) and active resistance \(r_r\) [1]. The transient process in the generator stator circuit when switching on an active load can be described, in accordance with the adopted equivalent circuit, by the equation:

\[ E_m \sin \omega t = L_r \frac{di_H}{dt} + i_H(R_H+r_r), \tag{1} \]

where

\[ \begin{aligned} E_m &\text{— amplitude of the generator e.m.f.,}\\ \omega &\text{— angular frequency,}\\ L_r,\ r_r &\text{— inductance and active resistance of the generator,}\\ R_H &\text{— active resistance of the load.} \end{aligned} \]

The solution of equation (1) has the form:

\[ i_H = \frac{E_m}{\sqrt{(\omega L_r)^2+(r_r+R_H)^2}} \left[ \sin(\omega t-\varphi)+\sin\varphi \cdot e^{-\frac{t(R_H+r_r)}{L_r}} \right], \tag{2} \]

where

\[ \varphi=\operatorname{arc\,tg}\frac{\omega L_r}{r_r+R_H}, \]

Investigation of the maximum of the expression for the power in the load \(i_H^2R_H\) as a function of \(R_H\), under the condition of neglecting the exponential component-

of the current component gives the value \(R_{\mathrm{n}}\) at which the maximum power is released in the active load:

\[ R_{\mathrm{n}}=\sqrt{r_{\mathrm{g}}^{2}+(\omega L_{\mathrm{g}})^{2}} . \tag{3} \]

The actual value of the resistance of the matched load will be somewhat smaller. However, for small machines, which as a rule have \(x''_{d}>0.07\) and relatively larger values of the active resistances of the windings, one may take

\[ R_{\mathrm{n}}\approx \sqrt{r_{\mathrm{g}}^{2}+(\omega L_{\mathrm{g}})^{2}} . \]

The same conclusion also follows from the results of studies on an analog computer.

Consequently, for the most acceptable circuit parameters,

\[ \operatorname{arc\,tg}\frac{\omega L_{\mathrm{g}}}{r_{\mathrm{g}}+R_{\mathrm{n}}}\approx 45^\circ;\qquad \frac{L_{\mathrm{g}}}{R_{\mathrm{n}}+r_{\mathrm{g}}}\approx \frac{T}{2\pi}. \]

Here \(T\) is the period of the generator emf. With such values of the circuit parameters, the exponential component of the current decays practically within a half-period of the supply voltage. Thus, the surge value of the current is determined by the amplitude of the periodic component, and the duration of the current pulse is equal to \(\approx 0.6T\).

The energy transferred to the load during the current pulse is

\[ Q_{\mathrm{n}}=\int\limits_{0}^{\frac{\pi+\varphi}{\omega}} i_{\mathrm{n}}^{2} R_{\mathrm{n}}\,dt . \tag{4} \]

To simplify the analysis of relation (4), we approximate the expression for the current (2) as follows:

\[ i_{\mathrm{n}}= \frac{E_{\mathrm{m}}}{\sqrt{(\omega L_{\mathrm{g}})^{2}+(R_{\mathrm{n}}+r_{\mathrm{g}})^{2}}}\, \sin 0.855\omega t . \tag{5} \]

Substituting (5) into (4), we obtain

\[ Q_{\mathrm{n}}= \frac{E_{\mathrm{m}}^{2}R_{\mathrm{n}}}{(\omega L_{\mathrm{g}})^{2}+(R_{\mathrm{n}}+r_{\mathrm{g}})^{2}} \cdot \frac{0.6\pi}{\omega}. \tag{6} \]

In the case of a sudden short circuit at the terminals, the electromagnetic energy of the surge generator is equal to [3]:

\[ Q_{\mathrm{em}}=\frac{2}{\omega}\, \frac{E_{\mathrm{m}}^{2}}{\omega L_{\mathrm{g}}}\, K_{\mathrm{z}}K_{\mathrm{e}}, \tag{7} \]

where \(K_{\mathrm{z}}\) is the current damping coefficient,

\(K_{\mathrm{e}}\) is the emf damping coefficient.

We determine the part of the short-circuit energy at the terminals that is transferred to the load:

\[ K_{\mathrm{n}}=\frac{Q_{\mathrm{n}}}{Q_{\mathrm{em}}} \approx \frac{R_{\mathrm{n}}\omega L_{\mathrm{g}}}{(\omega L_{\mathrm{g}})^{2}+(R_{\mathrm{n}}+r_{\mathrm{g}})^{2}} \cdot \frac{0.3\pi}{K_{\mathrm{z}}K_{\mathrm{e}}}. \tag{8} \]

As analysis of expression (8) shows, possible values of \(K_{\mathrm{n}}\) lie within the range \(0.5\text{--}0.75\).

In the case of an inductive load, the value of \(K_{\mathrm{n}}\) does not exceed \(0.25\). Thus, with an active load, utilization of the generator is 2–3 times greater than with an inductive load.

This is explained by the fact that, when the load resistance is increased in the case of its active character, the increase in the total complex resistance of the stator circuit occurs more slowly than in the case of an inductive load.

With changes in the rotational speed, as follows from expression (6), the magnitude of the energy transferred to the load changes insignifi-

... If \(r_{\mathrm{g}}\) is neglected, then under a matched load the quantity \(Q_{\mathrm{n}}=\mathrm{const}\).

When the resistance \(r_{\mathrm{g}}\) is taken into account, there is some increase in the energy in the load with increasing rotational speed. However, the increase in energy with increasing rotational speed is limited by a certain limit corresponding to the value of \(Q_{\mathrm{n}}\) calculated from (6) for \(r_{\mathrm{g}}=0\). Therefore, an increase in the energy in the load with increasing rotational speed is characteristic only of small machines, for which \(r_{\mathrm{g}}\) is large.

For an experimental verification of the relations given above, a synchronous generator was built in an EMU-12PM frame.

The oscillogram of the current and emf during operation into an active load is shown in Fig. 2. As can be seen, the current in the load has a bell-shaped

Fig. 2. Oscillogram of the current and emf during operation into an active load

form, and the pulse duration is somewhat greater than a half-period of the generator emf. Investigation of the dependence of the power in the load on the value of the generator resistance showed that the maximum transmitted power corresponds to the value

\[ R_{\mathrm{n}}=\sqrt{(\omega L_{\mathrm{g}})^2+r_{\mathrm{g}}^2}=1.5\ \Omega \]

at a generator excitation current \(i_{\mathrm{vg}}=3\) A. The results of these studies at various excitation currents are presented in Fig. 3. The shift of the power maximum toward values of \(R_{\mathrm{n}}\) when the excitation current is increased is explained by saturation of the magnetic circuit and the resulting decrease in \(L_{\mathrm{g}}\). Thus, the experimental results are in agreement with the regularities obtained above.

Figure 4 presents the dependence of the energy in the load on the rotational speed for a matched load resistance and with constant excitation of the generator. Increasing the rotational speed causes an increase in the energy in the active load.

Experimental investigations of armature reaction with active and inductive loads showed that the effect of armature reaction with an active load is considerably smaller. The ratios of the amplitudes of the generator emf...

Fig. 3. Dependence of the power in the active load on the magnitude of the resistance at various excitation currents

(In the graph: \(P_{\mathrm{ud}}\) (W), \(r_{\mathrm{n}}\) (ohm); \(P_{\mathrm{ud}} = f(r_{\mathrm{n}})\), \(n = 6000\) rpm; curves for \(i_{\mathrm{v}} = 3a,\ 4a,\ 5a,\ 6a\).)

Fig. 4. Dependence of the energy in the active load on the rotational speed

(In the graph: \(Q_{\mathrm{n}}\) (J), \(n \cdot 10^3\) (rpm).)

of the rotor after the pulse to the amplitude of the no-load emf, for matched active and inductive loads, respectively, are equal to:

\[ \frac{E_{mR}}{E_m} = 0.92;\qquad \frac{E_{mL}}{E_m} = 0.74. \]

The rise of the emf after the pulse to the value of the no-load emf occurs with the combined time constant of the rotor circuits. In small machines this time constant is small and, as is seen from Fig. 2, after only \(6 \div 10\) periods the emf is restored to its maximum value and, consequently, it becomes possible to switch the generator onto the load again. The possibility

operation of the generator into an active load at such short pulse-repetition periods determines its chief advantage—the possibility of concentrating large powers and energies in the load over time. In this case, the average power in the load approaches the rated power of the generator. Thus, in order to obtain the same average power in pulse-supply circuits with storage capacitors, the required power of the charging generator, taking into account the efficiency of the circuit, exceeds the rated power of the impulse generator.

The experimental investigations carried out confirmed the theoretical conclusions made earlier and showed that a compact impulse synchronous generator is a promising power source in autonomous systems.

REFERENCES

1. G. A. Sipaylov, V. V. Ivashin, A. V. Loos, K. A. Khor'kov. Obtaining electromagnetic energies during the joint operation of an impulse generator and a capacitor bank. Elektrichestvo, No. 8, 1967.

2. A. V. Loos, G. A. Sipaylov. Mathematical modeling of electromagnetic processes in an impulse generator. Izvestiya TPI, vol. 152, 1966.

3. G. A. Sipaylov, K. A. Khor'kov. Energy and the machine constant of an impulse generator. Izvestiya TPI, vol. 132, 1965.