PULSED OPERATING MODE OF AN ASYNCHRONOUS GENERATOR WITH AN ACTIVE LOAD

Yu. A. Romanov, G. A. Sipailov, A. V. Loos, V. F. Sergeev

With the emergence of a need for small-size sources of pulsed power, broad possibilities are revealed for the effective use of asynchronous generators with relatively high maximum power.

Asynchronous generators (AG) with a squirrel-cage rotor possess a number of advantages that may prove decisive in the selection of economical sources for small-size autonomous power-supply units. Sources of this kind are required to have high operational reliability, low specific weight, and high density of energy stored in flywheel masses [1, 2]. Having no rotating windings, magnets, valves, or exciters, these machines are the simplest and most reliable and can operate at high rotational speeds.

In a number of special installations, the universality of asynchronous machines proves useful. By feeding an AG from an external source, it is possible to set in rotation mechanisms coupled to it and, if necessary, to operate in generator mode, converting the energy of the flywheel masses into electromagnetic energy. A special electromechanical accumulator used in space research operates in such a mode [2]. The advantages of an AG as a source of pulsed power manifest themselves in the development of new technology.

However, the development of the theory of operation of an asynchronous generator in pulsed mode with an active load has not yet received sufficient attention. In particular, the influence of individual rotor and stator parameters on the magnitude of the energy transferred to the load is unknown; there are no calculation relations for selecting the matched load resistance; the armature reaction of an asynchronous impact generator has not been investigated, etc.

The purpose of the present work is to study the pulsed operating mode of an asynchronous generator with an active load.

Mathematical Modeling of Transient Processes in an AG

The complete system of equations of a single-phase asynchronous generator in the axes $\alpha$, $\beta$, operating with an active load, has the following form [3]:

voltage equations

\[ p\Psi_a=-i_a R_a-U_c; \]

\[ p\Psi_{\alpha r}=-i_{\alpha r}R_r-\omega_r\Psi_{\beta r}; \]

\[ p\Psi_{\beta r}=-i_{\beta r}R_r+\omega_r\Psi_{\alpha r}; \]

\[ pU_c=x_c i_c; \]

current equations

\[ i_a=\frac{1}{x_{ad}}\left(\Psi_{\delta a}+\Delta\Psi_{\delta a}\right)-i_{\alpha r}; \]

\[ i_{\alpha r}=\frac{1}{x_{\sigma r}}\left(\Psi_{\alpha r}-\Psi_{\delta a}\right); \]

\[ i_{\beta r}=\frac{1}{x_{ad}}\left(\Psi_{\delta\beta}+\Delta\Psi_{\delta\beta}\right); \]

\[ i_c=i_a-i_{\mathrm{n}}; \]

\[ i_{\mathrm{n}}=\frac{U_c}{R_{\mathrm{n}}}; \]

flux-linkage equations

\[ \Psi_{\delta a}=\Psi_a-x_{\sigma s}\cdot i_a; \]

\[ \Psi_{\delta\beta}=\Psi_{\beta r}-x_{\sigma r}\cdot i_{\beta r}; \]

\[ \Psi_{\delta}=\sqrt{\Psi_{\delta a}^{2}+\Psi_{\delta\beta}^{2}}; \]

rotor equation of motion

\[ p\omega_r=\frac{1}{H_j}\left(M_m-i_a\Psi_{\delta\beta}\right). \]

The equations are written in per-unit form; the notation corresponds to that adopted in [4]. The nominal phase values of the generator current and voltage and the synchronous speed are taken as the base quantities.

The block diagram for solving the system of differential equations is given in Fig. 1.

In this case the following parameter values, in per units, were taken as the initial data:

\[ x_{ad}=1;\qquad x_{\sigma s}=0.04;\qquad x_{\sigma r}=0.01;\qquad x_c=0.4; \]

\[ R_a=0.005;\qquad R_r=0.005;\qquad \omega_r=1. \]

At the first stage of generator operation, self-excitation takes place. In an actual installation this occurs when the capacitor is connected; in the mathematical model, it occurs by issuing the “start” command for the selected initial generator parameters and with \(R_{\mathrm{n}}=\infty\). The calculations were performed on an MN-14 computer.

The excitation process, both in the block diagram and in the experimental generator installation, is recorded visually on the oscilloscope screen. The increase in magnetic flux is monitored at the output of functional block 1BN. When the resultant flux in the air gap (according to the block diagram) reaches the nominal value \(\Psi_\delta=1\), the load is switched on at the instant when the voltage across the capacitor is equal to zero.

Research Results

Investigations using the structural diagram of a single-phase machine were carried out with nonzero initial values on the integrators, corresponding to the excited state of the physical model at the moment of load connection.

Fig. 1. Structural diagram for solving the system of differential equations

of load connection. The following quantities were adopted as base units:
\(I_{\mathrm{в}}\) — the value of the excitation current of the stator winding at which the resultant magnetic flux in the air gap of the asynchronous generator reaches its rated value;

\[ W_{\delta}=0.5U_{\delta}I_{\delta}\Delta t \]

is the base energy corresponding to the rated power of the generator over the time \(\Delta t=\pi\).

The maximum energy transmitted to the load in one pulse was calculated by the formula

\[ W_{\mathrm{н}}=\frac{0.5U_{mi}I_{mi}\Delta t}{W_{\delta}}=I_m^2R_{\mathrm{н}}. \]

1. Generator with a superconducting rotor winding and stator active resistance equal to zero

The study of such a generator, possessing a purely inductive supertransient reactance, is mainly of theoretical interest. These studies make it possible to reveal the qualitative picture of the influence of the nature of the load on the matched operating mode of the generator, i.e., to determine the value of the load resistance at which the generator transfers the maximum energy.

Figure 2a presents the results of calculations, using the complete system of equations, of the dependence of the energy in an active load on the magnitude of its resistance for various supertransient reactances of the generator. All other generator parameters in this case remained constant and were equal to (in relative units)

\[ x_{ad}=1;\quad x_{\sigma r}=0.01;\quad R_r=0;\quad R_a=0;\quad C=0. \]

Curves 1, 2, 3, shown in Fig. 2a, are given for the supertransient reactances \(x'_{\alpha}=0.03;\ 0.05;\ 0.07\), respectively. As follows from the calculations, the maximum value of the energy in the load corresponds to \(R_{\mathrm{н}}\) somewhat smaller than \(x^1_{\alpha}\). Consequently, the value of the matched load is different for active and inductive resistances. Moreover, the deviation of the resistance has an especially strong effect on the amount of transmitted energy at small supertransient reactances, i.e., for large machines.

2. Influence of the active resistance of the rotor on the magnitude of the energy transmitted to the load

The active resistance of the stator in this case is taken to be constant and equal to \(R_a=0.005\). Figure 2b shows the dependences of the load energy on the magnitude of its resistance for various active resistances of the rotor circuits (curve 1 — \(R_r=0\), 2 — \(R_r=0.01\), 3 — \(R_r=0.02\), 4 — \(R_r=0.04\)) for the generator parameters \(x_{ss}=0.04,\ x_{sr}=0.01\).

Comparing the results in Fig. 2a (curve 2) and Fig. 2b (curve 1), it may be noted that, in the absence of the influence of armature reaction, the appearance of an active component of the stator resistance \(R_a=0.1|x'_{\alpha}|\), and hence of a new energy consumer, reduces the maximum energy in the load by 10%; no appreciable increase in the matched resistance is observed. A decrease in the time constant of the rotor winding naturally leads to a reduction in the maximum energy transferred to the load. Thus, when the rotor time constants are changed to \(T_r=100,\ 50\) rad (curves 2 and 3), the decrease in the energy in the load is of the order of 20 and 40%, respectively, relative to the generator with \(R_r=0\). Such a noticeable influence of \(T_r\) on the dependence \(W_{\mathrm{н}}=f(R_{\mathrm{н}})\) is explained, on the one hand, by the demagnetizing action of the armature reaction, and on the other by the character of the variation of the variables participating in the transient process. By their nature all the variables—flux linkages, currents in all circuits, and voltages—have no forced component, i.e., the process is free and all variables decay. In practice this is confirmed by the fact that, when the load is connected, the generator is not capable of self-excitation.

As follows from Fig. 2b, for small machines the value of the matched load approaches the values of the transient resistance of the asynchronous generator; this simplifies the choice of the optimum resistance

Fig. 2

without taking capacitance into account. For parameter values \(x_a = 1.04\); \(R_a = 0.005\); \(T_r = (50\text{–}100)\) rad; \(x'_a = 0.05\), the load resistance values \(R_{\mathrm{н}} = (0.04\text{–}0.06)\) may be recommended for selection.

3. Determination of the Influence of the Active and Inductive Leakage Resistance of the Stator Winding on the Energy-

… characteristics of the generator. The initial parameters of the generator are \(x_{\delta s}=0.04;\ x_{jr}=0.01;\ R_r=0.005\).

Fig. 3

An increase in the active resistance of the stator leads to an overall increase in the resistance of the generator–load circuit. At the same time, the fraction of energy expended on losses increases.

In Fig. 3a, calculated dependences \(W_{\text{н}} = f(R_{\text{н}})\) are given for different active stator resistances of an asynchronous generator (curve \(1\)—\(R_a = 0\), \(2\)—\(R_a = 0.005\), \(3\)—\(R_a = 0.01\), \(4\)—\(R_a = 0.02\)). Here we observe the same characteristic dependence as in Fig. 2b. As the total resistance of the generator increases, the maximum energy decreases, and the resistance of the matched load increases. For generator parameters equal to \(x_a = 1.04\), \(R_a = 0.02\), \(x'_a = 0.05\), \(T_r = 200\ \text{rad}\), the optimal load resistance may be chosen within the limits \(R_{\text{н}} = (0.04\text{–}0.07)\).

In Fig. 3b, calculated dependences \(W_{\text{н}} = f(R_{\text{н}})\) are shown for different stator leakage resistances (curve \(1\)—\(x_{ss} = 0.02\), \(2\)—\(x_{ss} = 0.04\), \(3\)—\(x_{ss} = 0.06\)) and generator parameters \(R_a = 0.005\), \(x_{\sigma r} = 0.01\), \(R_r = 0.005\). Comparing the energy characteristics of the asynchronous generator (Fig. 3b) with the characteristics of an idealized machine (Fig. 2a), one may note the following: the energy indices of an asynchronous generator with time constant \(T_r = 200\ \text{rad}\) are determined not only by the transient resistance \(x'_a\), but also by the degree of magnetization of the machine. Thus, from comparison of the indicated characteristics the following picture is revealed: when \(x'_a\) is decreased from 0.07 to 0.03, the increase in energy in the load for the idealized machine (Fig. 2a)

Fig. 4

amounts to a value on the order of 2.32 times, and for an asynchronous machine with \(T_r = 200\) rad—1.77 times.

For each value \(x'_\alpha = 0.03;\ 0.05;\ 0.07\), the reduction in the energy transferred to the load for a real asynchronous generator relative to an idealized machine is, respectively, 48, 19, and 13%. If, moreover, the presence of the active resistance of the stator in an asynchronous generator is taken into account, then it may be asserted that low-power asynchronous generators in single-phase design will have reduced energy indices (by 5–10%) relative to synchronous ones solely because of armature reaction. Increasing the exciting capacitance does not lead to a substantial reduction in armature reaction or to an increase in the energy delivered to the load.

The demagnetizing action of armature reaction depends strongly on the magnitude of the load. Figure 4 shows oscillograms of the load currents (\(i_{n1}\) and \(i_{n2}\)), the voltages across the capacitance (\(U_{c1}\) and \(U_{c2}\)), the no-load emf (\(l_{xx}\)), and the generator emf during the current pulse (\(e_1\) and \(e_2\)) for different values of \(R_n\) (curve 1—\(R_n = 0.02\), 2—\(R_n = 0.01\)) and generator parameters \(x_{ad} = 1\), \(x'_\alpha = 0.05\), \(R_\alpha = R_r = 0.005\).

As is evident from Fig. 4, with an increase in the load current the pulse duration increases, with a shift of the current maximum, which should be taken into account when determining the energy consumed by the load. The action of armature reaction is considerable and increases strongly with increasing current.

Conclusions

On the basis of the investigations carried out into the operation of an asynchronous impulse generator with an active load, the following basic conclusions may be drawn:

1. The value of the matched resistance of the active load does not coincide with the value of the supertransient resistance of the asynchronous generator. The greatest deviations occur for large machines.

2. For small-size asynchronous generators, the value of the matched load resistance approaches the value of the supertransient resistance of the asynchronous generator. This simplifies the choice of the optimum resistance and makes it possible to determine it without taking the exciting capacitance into account.

3. For small asynchronous generators, a strong influence on the magnitude of the energy in the pulse is exerted by armature reaction and by the decay of all variable quantities characteristic of the load-connection regime, which causes a decrease in the energy indices of the asynchronous generator in comparison with synchronous generators having the same parameters, by 5–10%.

4. As the active resistance of the rotor increases, the energy transferred to the load decreases, owing to the increase in the demagnetizing action of armature reaction.

5. The energy indices of an asynchronous generator are determined not only by the transient resistance \(x'_\alpha\), but also by the active resistance of the stator winding and by the degree of demagnetization of the machine.

References

1. V. I. Radin, V. A. Vinokurov, V. S. Askerenko. Application of asynchronous generators as autonomous sources of alternating current. Elektrotekhnika, 1967, No. 8.

2. John Rous. Electromechanical system of energy storage for application in outer space. Conversion of heat and chemical energy into electrical energy in rocket systems. Energiya Publishing House, Moscow, 1963.

3. Yu. A. Romanov, G. A. Sipailov. Analysis of the operation of an asynchronous impulse generator using a computer. Izvestiya TPI, vol. 212, 1970.

4. L. M. Gruzov. Methods of mathematical investigation of electrical machines. Gosenergoizdat, 1953.