IMPROVING THE ENERGY PERFORMANCE OF IMPACT GENERATORS OPERATING INTO A PULSED LOAD

G. A. Simailov, A. I. Verkhoturov, V. F. Kulakov

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

An impact-power generator is one of the promising sources of large energies and may find wide application in various branches of experimental physics.

The development and prospects for the application of impact generators are closely connected with the refinement and improvement of their energy performance: reduction of energy losses per stator current pulse, increase in the pulse repetition frequency, and increase in impact power.

One of the principal factors determining the impact power and pulse repetition frequency of impact generators is the electromagnetic no-load losses. Impact generators have higher electromagnetic no-load losses in comparison with turbogenerators of the same overall power rating. A high level of no-load losses limits the effective utilization of the generator over time.

For a given duration of the pauses between pulses, the no-load losses of an impact generator can be substantially reduced, and the impact power increased, if an intermittent excitation regime is used, with forced buildup of the magnetic flux before each connection of the generator to the load and subsequent extinction of the magnetic field during the currentless pause. It is therefore important to evaluate the possibilities of intermittent forced excitation both from the standpoint of reducing the energy losses per stator current pulse and increasing the pulse repetition frequency, and for the purpose of increasing the pulse power of the impact generator, as well as to establish the limits within which it is expedient to use intermittent forced excitation in comparison with constant excitation.

The operating cycle of an impact generator into a pulsed load can be divided into three stages:

a) buildup of the voltage from zero to the specified value,

b) connection of the impact generator to the load,

c) de-excitation of the generator after the stator current pulse.

The first and third stages proceed with the stator winding open and constitute the generator’s no-load operating cycle.

In [1], dependences were obtained for the energy of losses in the steel of the machine and in the rotor windings at no load over the operating cycle of an impact generator for any forcing coefficient \(k\).

For the steel,

\[ Q_{\mathrm{st}}=P_0'T\left(k^2\ln\frac{k+1}{k-0.95}-1.95\,k+0.05\right). \tag{1} \]

For the excitation winding,

\[ Q_{\mathrm{ew}}=\frac{U_2^2}{r_2}\,T\left(k^2\ln\frac{k+1}{k-0.95}-4Bk+2B^2k\right). \tag{2} \]

For the excitation and damping windings,

\[ Q_{\mathrm{mc}}=\frac{U_2^2}{r_2}\,T\left[k^2\ln\frac{k+1}{k-0.95}+B(0.05-1.95k)\right]. \tag{3} \]

where \(k\) is the ratio of the voltage applied to the excitation winding to the nominal voltage,

\(P_0'\) are the losses in the steel of the machine at no load,

\(T=T_2+T_3\) is the total time constant of the excitation and damping windings,

\(u_2\) is the voltage at the terminals of the excitation winding,

\(r_2\) is the active resistance of the excitation winding,

\[ B=\frac{T_2}{T} \]

is the ratio of the time constant of the excitation winding to the total time constant of the rotor circuits.

The dependence of the total electromagnetic energy of the no-load losses on the forcing factor can be obtained by adding the right-hand sides of equations (1) and (3):

\[ Q_{\Sigma k}=\frac{U_2^2}{r_2}\,Tk\left[(k_0+1)k\ln\frac{k+1}{k-1}-2(k_0+B)\right], \tag{4} \]

where

\[ k_0=\frac{P_0'r_2}{u_2^2} \]

is the ratio of the electromagnetic no-load losses in the steel to the losses in the excitation winding.

Denote by

\[ k_1=\frac{Q_{\Sigma k}}{Q_{\Sigma 1}}, \]

where \(Q_{\Sigma 1}\) is the total no-load loss per cycle at \(k=1\); then

\[ k_1= \frac{ k\left[(k_0+1)k\ln\frac{k+1}{k-0.95}-2(k_0+B)\right] }{ 3.69+1.09k_0-2B }. \tag{5} \]

The results of calculation by (5) are presented in Fig. 1 for \(k_0=6\), with \(\frac{T_3}{T_2}\) varying from 0.4 to unity. It is evident from the figure that there is such a forcing factor at which the no-load energy losses per operating cycle are minimal. The value of \(k\) at which the losses are minimal can be found from the condition that the first derivative of \(Q_{\Sigma k}\) with respect to \(k\) be equal to zero:

\[ k\ln\frac{k+1}{k-1}-\frac{k^2}{k^2-1}-\frac{k_0+B}{k_0+1}=0. \tag{6} \]

The results of solving equation (6) are presented in Fig. 2 for \(\frac{T_3}{T_2}\) varying from 0.2 to unity, for \(k_0=4\div10\).

The presence of a minimum in the total electromagnetic energy losses per operating cycle at a certain forcing factor is explained—

In the figure: vertical axis \(K_2\); horizontal axis \(K\); \(K_0=6\); curve parameter \(\dfrac{T_3}{T_2}-1\) with values \(0.8\), \(0.6\), \(0.4\).

Fig. 1. For comparing the total electromagnetic no-load losses over the operating cycle for any \(K\) with the losses at \(K=1\)

In the figure: vertical axis \(K_{\mathrm{op}}\); horizontal axis \(\dfrac{T_3}{T_2}\); curves \(K_0=10\), \(K=8\), \(K_0=6\), \(K_0=4\).

Fig. 2. For calculating the optimal forcing coefficients over the operating cycle

is explained by the fact that the losses in the machine steel and in the rotor windings behave differently as \(k\) changes: with increasing \(k\), the losses in the steel decrease sharply, whereas in the rotor windings they first decrease, reach a minimum, and then increase sharply.

By the same principle one can find the minimum of the total no-load electromagnetic losses in the rotor for a certain air gap between rotor and stator, since the losses in the excitation winding increase as the gap increases, while the additional losses in the rotor steel decrease.

Calculations show that the gap chosen from the condition of minimum no-load losses in the rotor conditionally satisfies the requirement of mechanical strength, but its value is approximately 1.5 times greater than in existing pulse- and impact-power generators.

In the intermittent mode, the excitation winding is in the most unfavorable thermal conditions, since it is additionally loaded by the currents of the damping system.

Therefore, the minimum duration of the pauses between pulses should be determined from the condition of the permissible thermal loading of the excitation winding:

\[ (k^2 - 1)\ln \frac{k + 1}{k - 1} - 2Bk(2 - B) = 0 . \tag{7} \]

Solving equation (7) approximately, one can find \(k\) for the given ratio

\[ \frac{T_3}{T_2} \]

and compute the minimum pause duration

\[ t_{\mathrm{p}} = T \ln \frac{k + 1}{k - 1}. \tag{8} \]

The investigations performed show that for existing impact generators \(t_{\mathrm{p}} \approx T\).

Thus, in machines with a damping winding on the rotor, there exists a forcing coefficient at which the voltage rise from zero to a specified value and the de-excitation of the machine occur with the smallest no-load losses.

The use of intermittent excitation with the optimal forcing coefficient makes it possible to reduce the energy of the no-load electromagnetic losses by almost a factor of 2 compared with constant excitation over the same time, and by a factor of 5–7 compared with intermittent excitation at \(k = 1\).

If it is assumed that, under intermittent excitation with the optimal forcing coefficient, the same amount of losses is released in the rotor as at \(k = 1\), then, when operating with the optimal forcing coefficient, the machine can be excited to a higher voltage than at \(k = 1\), thereby significantly increasing the impact power of the generator, which depends on the square of the voltage.

The use of intermittent excitation becomes especially effective when the duration of the pauses between pulses is greater than the total time constant of the rotor circuits.

References

1. G. A. Sipaylov, A. I. Verkhoturov. Experimental study of intermittent excitation on a model of an impact generator. Izvestiya TPI, vol. 162, 1966.