ELECTROMECHANICAL EQUIVALENT OF AUTONOMOUS ENERGY SOURCES

M. V. LUKYANENKO, A. N. LOVCHIKOV, V. V. KHRAMOVA

(Presented by the scientific seminar of the Department of Electrical Machines)

In developing power-supply system (PSS) circuits for autonomous objects operating underwater, in space, in thermal, radiation, and other chambers, whose main energy sources are thermoelectric, thermionic, photoelectric, isotope, nuclear, and other converters, the performance of laboratory experiments is difficult, and sometimes practically impossible. The use of energy-source equivalents greatly simplifies this task [1].

The functional diagram of the equivalent is shown in Fig. 1. The operation of the equivalent is carried out as follows. The required external characteristic of the energy source is formed with the aid of the functional converter FP(1), made on diode elements. When the load resistance changes, the voltage taken from the measuring device IU(6) changes; through the feedback amplifier UOS(8) it is applied to the input of FP(1). From the output of FP(1) a reference voltage is taken, which corresponds to the actual voltage at the output of the real energy source for the given load current. The reference voltage is compared with the feedback voltage, proportional to the actual voltage at the load. The mismatch signal \(\Delta U\) changes the voltage at the load until the difference between the reference voltage and the load voltage becomes equal to zero. Thus, with a sufficient degree of accuracy, the equivalent reproduces the external characteristic of the real energy source.

Fig. 1. Functional diagram of the equivalent of autonomous energy sources

Strict requirements are imposed on the equivalent with respect to ensuring the static and dynamic properties of the real energy source. The dynamic characteristics of the equivalent depend mainly on the dynamics of the power amplifier. In the present work an equivalent is considered in which an electromechanical amplifier (EMA) is used as the power amplifier. The static accuracy of reproducing the external characteristic is determined by the error:

\[ \delta = \delta_1 + \delta_2 + \delta_3, \tag{1} \]

where \(\delta_1\) is the error in reproducing the curve by the functional converter,
\(\delta_2\) is the error in tracking the reference voltage by the control system,
\(\delta_3\) is the error due to heating of the EMA.

By careful selection of the elements of the functional converter, the error \(\delta_1\) can be reduced to a minimum. Therefore the accuracy is determined mainly by the errors \(\delta_2\), which depends on the static gain of the open loop of the control system, and \(\delta_3\).

\[ \delta_2 = \frac{1}{1 + k_1}, \tag{2} \]

\[ k_1 = k_{y1} k_{\mathrm{EMA}}, \tag{3} \]

where

\(k_{y1}\) is the gain of the additional amplifiers;
\(k_{\mathrm{EMA}}\) is the gain of the EMA.

The static gain and frequency characteristics of the EMA depend to a considerable degree on the magnitude of the load, since the load resistance enters into its transfer function [2]. In addition, the gain is not a single-valued quantity because of the hysteresis characteristic of the EMA.

To stabilize the characteristics, rigid negative feedback was introduced (Fig. 2), which significantly improves the static and dynamic characteristics of the electromechanical equivalent.

Fig. 2. Circuit for eliminating instability of the parameters of the electromechanical equivalent

During prolonged operation of the EMA in the nominal mode, its windings heat up and, consequently, their resistance increases. Changes in the resistance of the control winding, the winding of the additional poles, and the armature-circuit winding have practically no effect on the operation of the circuit. The error \(\delta_3\) is determined mainly by heating of the compensating winding.

It has been established experimentally, during operation on the EMU-71A, that already after half an hour of operation of the equivalent in the rated mode, the increase in the resistance of the compensating winding is 8%. Let us estimate what the error \(\delta_3\) will be in this case. It is seen from Fig. 2 that an increase in the resistance of the compensating winding is equivalent to an increase in the gain of amplifier UN\(_2\), since a voltage proportional to the load current is taken from the compensating winding and is amplified by amplifier UN\(_2\). For this reason, the voltage and load current of the equivalent, with the load resistance unchanged, will decrease. If the gain of the FP over a certain section of the characteristic is regarded as constant, then the law of formation of the reference voltage can be written in simplified form as:

\[ U_{\mathrm{e}} = U_{\mathrm{xx}} - I_{\mathrm{n}} R_{\mathrm{k}} k_{\mathrm{u}_2} k_{\mathrm{fp}}, \tag{4} \]

where

\[ \begin{aligned} U_{\mathrm{e}}&\text{ is the reference voltage at the FP output;}\\ I_{\mathrm{n}}&\text{ is the load current;}\\ R_{\mathrm{k}}&\text{ is the total resistance of the compensating winding and shunt;}\\ k_{\mathrm{u}_2}&\text{ is the gain of amplifier UN}_2;\\ k_{\mathrm{fp}}&\text{ is the gain of the FP;}\\ U_{\mathrm{xx}}&\text{ is the no-load voltage of the equivalent.} \end{aligned} \]

The load voltage and the reference voltage are related by the ratio:

\[ U_{\mathrm{n}} = U_{\mathrm{e}} k_2, \tag{5} \]

where \(k_2\) is the transmission coefficient of the closed loop.

On the basis of the foregoing, one may write:

\[ U_{\mathrm{e}} - \Delta U_{\mathrm{e}} = U_{\mathrm{xx}} - (I_{\mathrm{n}} - \Delta I_{\mathrm{n}}) (R_{\mathrm{k}} + \Delta R_{\mathrm{k}}) k_{\mathrm{u}_2} k_{\mathrm{fp}}, \tag{6} \]

\[ U_{\mathrm{n}} + \Delta U_{\mathrm{n}} = (U_{\mathrm{e}} + \Delta U_{\mathrm{e}}) k_2. \tag{7} \]

Neglecting quantities of the second order of smallness, we obtain an equation in deviations:

\[ \Delta U_{\mathrm{n}} = - \Delta I_{\mathrm{n}} R_{\mathrm{k}} k_{\mathrm{u}_2} k_{\mathrm{fp}} k_2 + \Delta R_{\mathrm{k}} I_{\mathrm{n}} k_{\mathrm{u}_2} k_{\mathrm{fp}} k_2 . \tag{8} \]

From equation (8) we determine the error \(\delta_3\):

\[ \delta_3 = \frac{\Delta U_{\mathrm{n}}}{U_{\mathrm{n}}} = \frac{\Delta I_{\mathrm{n}}}{I_{\mathrm{n}}} = \frac{R_{\mathrm{k}} k_{\mathrm{u}_2} k_{\mathrm{fp}} k_2} {R_{\mathrm{n}} + R_{\mathrm{k}} k_{\mathrm{u}_2} k_{\mathrm{fp}} k_2} \cdot \frac{\Delta R_{\mathrm{k}}}{R_{\mathrm{k}}}. \tag{9} \]

From the resulting equation (9) it is seen that, when \(R_{\mathrm{k}}\) changes as a result of heating, the relative change in the load voltage and current is the greater, the more heavily the system is loaded.

In the case of operation of the equivalent in the rated mode, when the resistance of the compensating winding changes by 8%, the relative change in voltage and current is about 4.5%.

To compensate this phenomenon, a correction was introduced, consisting of a voltage divider, taken from the compensating winding, in one arm of which a thermistor is included (Fig. 2). The thermistor is inserted inside the EMU in the region of the brush contacts.

The principle of operation of the correction is analogous to the operation of a transistor with temperature stabilization. The introduction of the thermistor made it possible to achieve an accuracy of reproduction of the external characteristic, taking into account the errors \(\delta_1\) and \(\delta_2\), on the order of 1%. The best results were obtained by using a TVR thermistor.

Thus, elimination of the above-mentioned phenomena and the corresponding correction of the dynamic characteristics make it possible to construct an electric-machine equivalent of autonomous power sources that satisfies the requirements imposed upon it.

References

1. M. V. Lukyanenko, V. F. Trefilov, E. A. Mizrakh, N. B. Kobelev. A method of physical modeling of the volt-ampere characteristics of autonomous power sources. Proceedings of the 11th Regional Conference Dedicated to Radio Day, Institute of Physics, Siberian Branch, USSR Academy of Sciences, Krasnoyarsk, 1971.

2. E. S. Bleiz, Yu. N. Semenov, B. K. Chemodanov, P. M. Yakimenko. Dynamics of Electric-Machine Tracking Systems. Moscow, “Energiya,” 1967.