COMPENSATION METHODS FOR MEASURING THE FORM FACTOR OF CURRENT AND VOLTAGE CURVES

I. G. Leshchenko, A. N. Obergan, V. I. Panov

(Recommended by the First Scientific and Technical Conference of the Tomsk Institute of Radio Electronics and Electronic Engineering)

To study the influence of the higher harmonics of the load current on the shape and amplitude of the voltage of generators, transformers, and other devices [1], it is necessary to have instruments for measuring the form factor of the current curve with the required accuracy and measurement ranges.

An analysis of possible [2, 3, 4] methods, and of methods investigated by the authors [5, 6], for measuring the form factor of current and voltage curves \((K_\phi)\) showed that it is expedient to develop and improve the indicated instruments according to a block diagram (Fig. 1) that combines methods for measuring \(K_\phi\) based on a null comparison of the rms and mean values of current.

Fig. 1

The block diagram contains the following converters:

MP — a scale converter, consisting of a voltage divider and an alternating-current amplifier without distortion of the waveform of the measured signal;

PD — a converter of the rms value of current;

PSr — a converter of the mean value of current, consisting of a rectifier and a magnetoelectric measuring mechanism or a galvanometric compensator;

S × Ssr — a circuit for comparing electrical signals proportional to the rms and mean values of current or voltage;

OU — a readout device for the value of the form factor;

S × URT — a circuit for setting the operating current in the circuit of the rms-current converter.

In Fig. 2a, b, c are shown the basic circuits for measuring \(K_\phi\), in which the rms-current converter is connected in series ...

…additionally into the circuit of the average-value converter. Such a connection makes it possible to reduce the error in measuring \(K_{\phi}\) due to the nonlinearity of the volt-ampere characteristic of the rectifier.

According to the circuit of Fig. 2, a, for a specified value of the current \(I_{\text{d}}\) or of the input voltage \(U_{\text{in}}\), the potentiometer \(R\) balances the emf of the vacuum thermoconverter with the drop of the average voltage, i.e.,

\[ k \cdot I_{\text{d}}^{2} = r \cdot I_{\text{av}} . \]

Fig. 2

Hence

\[ K_{\phi}=\frac{I_{\text{d}}}{I_{\text{av}}}=\frac{r}{k \cdot I_{\text{d}}}=C \cdot r, \]

where \(C\) is the instrument constant;
\(r\) is the resistance of the potentiometer, graduated in values of \(K_{\phi}\).

The scale of the \(K_{\phi}\)-meter is uniform. The measurement accuracy is determined by the sensitivity of the galvanometer, by the setting of the specified input voltage \(U_{\text{in}}\), and by the instability of the characteristics of the circuit elements. However, as investigations have shown, the principal measurement error of the circuit is caused by the inaccuracy in setting the rms value of the current, since the characteristic of the thermal emf is nonlinear (Fig. 3). When the current is changed by an amount \(\Delta I_{\text{d}}\), the emf of a thermoconverter possessing practically…

Fig. 3

with a quadratic characteristic, will change by \(\Delta E_{\text{tp}} = 2k \cdot I_{\text{d}} \cdot \Delta I_{\text{d}}\), and the average value of the voltage by \(\Delta U_{\text{av}} = r \cdot \Delta I_{\text{av}}\).

It is not difficult to show that the error in measuring \(K_{\phi}\) under a new balancing of the system will be directly proportional to the relative change in the rms value of the current, i.e., will be determined by the error in setting the operating current.

The circuits of instruments with a heated thermoresistance (Fig. 2, b) or a photoelectric converter (Fig. 2, c) make it possible to use a panel microammeter in the comparison circuit instead of a galvanometer, which is very convenient for creating portable \(K_{\phi}\)-meters of increased accuracy. In these circuits it is not difficult to obtain increased sensitivity, especially with the photoresistance–lamp converter. However, the measurement error will be determined mainly by the instability of the operating current and of the auxiliary power supply (a stabilized power supply is required). With correctly chosen parameters of the comparison circuit, the measured current form factor can be read directly by the microammeter. When a specified resistance \(r\) is set, the instrument can be graduated only in values of the increment \(\Delta K_{\phi}\) from a specified form, for example, a sinusoid, i.e. \(1.11 \pm \Delta K_{\phi}\).

For the development of instruments of increased accuracy, the circuit shown in Fig. 4 is recommended, in which the principle of simultaneous-comparison comparators is used [7]. When thermoconverters with identical characteristics in the range of the operating current are selected, the error due both to instability of the measured current and to instability of the direct-current source is practically eliminated.

Fig. 4

In the balanced state of the measuring circuit \(I_{\text{d}} = I\), \(I_{\text{av}} \cdot r = I \cdot R_2\),

\[ K_{\phi} = \frac{r}{R_2}, \]

i.e., it is directly proportional to the resistance \(r\) of potentiometer \(R\).

Each of the circuits studied can be used for developing \(K_{\phi}\)-meters intended for measuring the form factor of current and voltage in one or another circuit under investigation, analogously to ordinary instruments of direct evaluation.

For purposes of studying the influence of the current form factor on synchronous generators up to 5 kW, which operate into a low-ohmic load (10–15 ohms), the \(K_{\phi}\)-meter must have an input resistance on the order of hundredths of an ohm for currents up to 10 A. In view of the absence of such converters, the authors developed an instrument that is connected into the measured circuit by means of a shunt. The voltage drop across the shunt, on the order of several millivolts, is amplified by a broadband alternating-current amplifier constructed on transistors with deep negative-

...negative feedbacks. The principal characteristics of the amplifier are presented in Figs. 5 and 6 for a sinusoidal input voltage. Similar dependences were obtained for rectangular and triangular input signals.

Fig. 5

Fig. 6

From the characteristics it is evident that the dependence between \(U_{\text{out}}\) and \(f\) is linear in the frequency range from 50 to 15000 Hz, i.e., the frequency distortions in this range are practically equal to zero. The nonlinear distortions of the amplifier were measured with an INI-12 instrument; in repeated measurements, the nonlinear distortions at the output, relative to the input, did not exceed 0.5%.

Technical characteristics of the instrument

1. Measurement range for \(K_\phi\): from 1.00 to 2.00.
2. Measurement range for current: \(1 \div 10\) A.
3. Smallest limit of measured voltages — 20 mV.

1. Range of fundamental frequencies from 50 Hz to 1000 Hz.

2. Measurement accuracy \(<1\%\) when using, in the operating-current setting circuit, a null indicator with a sensitivity of \(0.5 \cdot 10^6\) divisions/A. The measurement accuracy can be substantially increased by using a more sensitive null indicator or by employing an UPT.

3. Power consumed from the measured circuit: 0.2 W at the highest measured current of 10 A.

REFERENCES

1. I. G. Leshchenko, A. N. Obergan. Scientific report on the topic: “Development and investigation of means and methods for analyzing the dependence of the voltage of alternating-current sources on distortion of the load-current waveform,” part 1, Tomsk, TPI, 1968.

2. A. Ya. Bezinkovich. Error of rectifier instruments caused by distortion of the alternating-current waveform, and methods for its determination. Electrical Measurements, Proceedings of VNIIM, issue 14 (74), p. 134, GEM, 1953.

3. D. S. Rusev. Apparatus for measuring the form factor of a periodic function. Author’s certificate No. 1004, class 21e, 36/10, Bulgaria.

4. L. Sh. Kherej. Instrument for direct measurement of the form factor of an alternating-current curve. Author’s certificate, class 21e, 36, No. 107409, 1956.

5. I. G. Leshchenko, A. N. Obergan. On measurement of the form factor of a curve. Izv. TPI, vol. 194.

6. A. N. Obergan, I. G. Leshchenko. Instrument for measuring the form factor of a voltage curve. Izv. TPI, vol. 194.

7. T. B. Rozhdestvenskaya. Electrical Comparators for Precision Measurements of Current, Voltage, and Power. Standards Publishing House, Moscow, 1964.