Investigation of Forced Self-Excitation of an Impact Generator

V. S. Baklin, V. I. Popov, K. A. Khorkov

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

In recent years, autonomous high-power pulsed sources have begun to be developed and used, employing special electrical machines—impact generators—as accumulators and sources of pulsed energy. Pulsed sources, as a rule, operate on a single-phase load. This makes it possible, in a three-phase impact generator, to use the free phase for supplementary excitation of the generator. In the case of a single-phase design of an impact generator (as a rule, the single-phase stator winding occupies no more than \(2/3\) of the pole pitch of the machine), a special winding for supplementary excitation of the generator may be placed in the free stator slots.

The use of stepped excitation—pre-excitation from a low-power energy source and forced self-excitation—is applicable in those cases when, first, no more than one current pulse is required from the impact generator during an operating cycle, and, second, it is impossible or for some reason impractical to have a powerful excitation unit (limitations on installation weight, absence of a network of the required power, etc.).

Forced self-excitation of an impact generator is carried out at the expense of the excess kinetic energy of the rotating rotor. It is known that during one current pulse an impact generator can convert into electromagnetic energy and deliver to the load only some fraction of the kinetic energy stored in the rotor. For example, the Kapitsa–Kostenko impact generator [5] delivers 20% of the stored kinetic energy of the rotor to a matched inductive load, while the impact generator of the CEM firm (France) [6] delivers 23.4%.

An analysis of various self-excitation circuits of synchronous generators is given in [2, 3] and other literature sources; however, in the aspect in which the question of forced self-excitation of an impact generator must be considered, the problem has not been solved.

The present work is devoted to determining the self-excitation time of an impact generator and to constructing curves of the rise of the voltage at the machine terminals and of the excitation current under forced self-excitation from different initial flux levels.

The basic circuit of the installation is shown in Fig. 1. The following designations are adopted in the figure:

\(a, b, c\) — phases of the stator winding of the impact generator,

\(VU\) — controlled rectifier device,

OB — excitation winding,
DO — damping winding,
A — storage battery,
\(K_1\) — contactor for initial excitation (pre-excitation).

Fig. 1. Schematic diagram of the installation

The generator is excited from the storage battery up to a certain specified pre-excitation voltage. The minimum value of the pre-excitation voltage must be sufficient to overcome the threshold voltage of the rectifier device and the voltage drop under the brushes.

The time of self-excitation and the rate of increase of the excitation current depend to a greater extent on the magnitude of the initial flux of the machine, which is important to know when selecting the elements of the rectifier device.

When a control signal is applied to the rectifier device, the voltage of phase “b” is applied to the excitation winding of the generator. The self-excitation process is described by the following equation:

\[ \Psi_{1\omega}=i_{\mathrm{v}}r_{\mathrm{e}}+k\frac{d\Psi_1}{dt}, \tag{1} \]

where

\[ \Psi_{1\omega} \]
— the emf induced in the stator winding by the excitation flux;

\[ \omega \]
— angular velocity of rotation of the rotor;

\[ r_{\mathrm{e}} \]
— equivalent active resistance of the rotor circuits, taking into account the resistance of the rectifier device;

\[ k \]
— coefficient for reducing the flux linkage of the excitation winding to the flux linkage of the phase of the stator winding.

To simplify the solution, we neglect the active and inductive resistances of the phase, which are considerably smaller than the equivalent active and inductive resistances of the rotor. The influence of the armature reaction of the phase on the self-excitation process is not taken into account. The nonlinearity of the magnetization curve of the machine is taken into account by approximating the theoretical or experimental magnetization curve according to Froelich, analogously to [1].

In relative units,

\[ E=\Psi=\frac{a i_{\mathrm{v}}}{1+b\cdot i_{\mathrm{v}}}, \tag{2} \]

where \(a\) and \(b\) are approximation coefficients, with

\[ b=a-1. \]

For highly saturated machines, which include impact generators, it is impossible to select a value of \(a\) that would be valid for all sections of the magnetization curve. Therefore, we divide the magnetization characteristic into several sections. For the initial, first section of the magnetization curve, the value \(a=r_{\mathrm{cr}}\), where \(r_{\mathrm{cr}}\) is the resistance determined by the tangent to the magnetization characteristic from the point \(i_{\mathrm{v}}=0\). For the subsequent sections (the knee of the magnetization curve, the saturated part), the value of \(a\) differs substantially from \(r_{\mathrm{cr}}\).

Let us represent the machine parameters in relative units. The established values of the generator voltage and flux linkage are determined by the point of intersection of the machine magnetization curve with the volt-ampere characteristic of the excitation circuit.

The flux linkage \(\Psi_{\mathrm{op}}\), corresponding to the rated emf in the generator no-load mode, is taken as unity.

Denote by

\[ \Psi_n^*=\frac{\Psi_n}{\Psi_{\mathrm{v}}} \]

the relative instantaneous flux linkage;

\[ \Psi_{\mathrm{init}}^*=\frac{\Psi_{\mathrm{init}}}{\Psi_{\mathrm{v}}} \]

the relative value of the initial flux linkage;

\[ r_{\mathrm{e}}^*=\frac{r_{\mathrm{e}}}{r_{\mathrm{b}}\cdot a_n} \]

the relative active resistance of the excitation circuit, taking into account the rectifier device;

\(a_n\) is the value of the approximation coefficient for the given section of the magnetization curve;

\(r_{\mathrm{b}}\) is the base resistance, equal to the ratio of the rated generator voltage in the no-load mode to the rated excitation current.

The solution of equation (1) with respect to time has the form

\[ t^*=\sum_{n=1}^{k}\frac{r_{\mathrm{e}n}^*}{1-r_{\mathrm{e}n}^*}\ln\frac{1-\Psi_{n-1}^*}{1-\Psi_n^*} +\frac{1}{1-r_{\mathrm{e}n}^*}\ln\frac{\Psi_n^*}{\Psi_{n-1}^*}, \tag{3} \]

where

\(k\) is the number of sections of approximation of the magnetization characteristic;

\(\Psi_{n-1}^*\) are the initial values of the flux linkage on the approximation section. For \(n=1\),

\[ \Psi_{n-1}^*=\Psi_{\mathrm{init}}^*; \]

\(t^*\) is the relative self-excitation time.

The self-excitation time in seconds is

\[ t=t^*\cdot T_{\mathrm{v}}, \tag{4} \]

where

\(T_{\mathrm{v}}\) is the time constant of the excitation circuit, characterized by the parameters of the steady-state mode.

The agreement of the results of calculating the self-excitation time with the actual picture was checked on a model impact generator having the following excitation-circuit parameters:

\[ r_2=3.2\ \Omega \]

active resistance of the excitation winding;

\[ r_{\mathrm{d}}=8.3\ \Omega \]

active resistance of the damper winding, referred to the excitation winding;

\[ r_{\mathrm{add}}=2\ \Omega \]

additional active resistance introduced into the excitation-winding circuit;

\(T_{\mathrm{v}} = 0{,}043\) s — time constant of the excitation circuit;
\(i_{\mathrm{vn}} = 6\) A — rated excitation current;
\(E = \Psi_{\mathrm{on}} = 95\) V — rated voltage at the terminals of the generator phase.

The magnetization characteristic (Fig. 2) was divided into two sections: section I from \(\Psi = 0\) to \(0{,}6\Psi_{\mathrm{on}}\); section II from \(\Psi = 0{,}6\) to \(\Psi_{\mathrm{y}}\). These sections correspond to the approximating coefficients: \(a_{\mathrm{I}} = r_{\mathrm{kr}} = 1{,}8\); \(b_{\mathrm{I}} = 0{,}8\); \(a_{\mathrm{II}} = 2{,}8\); \(b_{\mathrm{II}} = 1{,}8\).

Fig. 2. No-load characteristic of the generator

The results of calculating the self-excitation time at various levels of the initial flux, with an additional resistance in the excitation circuit and without it, are presented in Tables 1 and 2. Experimental—

Table 1

Table 2

The experimental check was carried out by oscillographing the excitation current and the voltage at the machine terminals during self-excitation. Typical oscillograms are presented in Fig. 3. The time marks on the oscillograms correspond to intervals of 0.02 sec. The results of processing the oscillograms obtained are plotted on the calculated curves with the symbol \((x)\), Fig. 4. Curve 1 corresponds to the self-excitation time when an additional resistance is present in the excitation circuit. The index “C” denotes the experimental point at the initial flux linkage \(\Psi_{\mathrm{in}}=0.26\Psi_{\mathrm{on}}\). Curve 2 corresponds to the self-excitation time without additional resistance.

Fig. 3. Oscillograms of the excitation current and voltage (flux linkage) at the generator terminals
a) with additional resistance in the generator excitation circuit and \(\Psi_{\mathrm{in}}=0.26\Psi_{\mathrm{on}}\)
b) without additional resistance in the generator excitation circuit and \(\Psi_{\mathrm{in}}=0.43\Psi_{\mathrm{on}}\)

The index “K” denotes the experimental point at the initial flux linkage \(\Psi_{\mathrm{in}}=0.43\Psi_{\mathrm{on}}\). The oscillograms in Fig. 3 correspond to these points. Comparison of the calculated and experimental data shows good agreement between the experimental and calculated self-excitation time of the generator.

Fig. 4. Dependence of the generator self-excitation time on the level of flux linkage of the pre-excitation

The calculation of the increase in flux linkage (generator emf as a function of time) is carried out using expression (3).

Table 3 gives the calculated and experimental values of \(\Psi(E)\) in the presence of additional resistance in the field-winding circuit and at \(\Psi_{nch}=0{,}26\Psi_{on}\). Table 4 gives the calculated and experimental values of \(\Psi(E)\) without additional resistance in the field-winding circuit and at \(\Psi_{nch}=0{,}43\Psi_{on}\). The experimental values of the flux linkages were obtained by processing the oscillograms of Fig. 3.

Table 3

Table 4

These flux linkages are presented in Fig. 5. In the same figure, curves of the increase in the field current, obtained from the magnetization characteristic, are plotted. The experimentally found values \(\Psi_k\), \(\Psi_s\), and \(i_{vk}\), \(i_{vs}\) are indicated by the sign \((x)\).

The discrepancy between the calculated and experimental values of the flux linkages and field currents is insignificant.

Thus, the considered method for calculating the self-excitation time of an impact generator from different levels of the initial pre-excitation current gives good agreement between the calculations and experiment. The method presented makes it possible to construct curves of the increase in flux linkage (generator emf) and field current as functions of time, which is necessary for the correct choice of the beginning of field forcing (self-excitation) and for the selection of semiconductor elements of the controlled rectifier device.

Fig. 5. Curves of the variation of voltage (flux linkage) and excitation current over time

REFERENCES

1. A. I. Vazhnov. Electrical Machines. “Energiya,” 1969.

2. I. A. Glebov. Basic directions of work in the field of excitation systems for synchronous machines. In: Calculation and Study of Excitation Systems of Synchronous Machines. Publishing House of the USSR Academy of Sciences, Moscow–Leningrad, 1963.

3. A. G. Zdrok, A. A. Salyutin. Self-Excitation Systems of Synchronous Generators with Magnetic Amplifiers. “Energiya,” 1968.

4. R. Ryudenberg. Transient Processes in Electrical Systems. IL, 1955.

5. M. B. Kostenko. Electrical Machines (Special Part). GEI, 1949.

6. Energy storage in rotating electrical machines. Express information “Electrical Machines and Apparatus,” 1970, No. 36.