Device for Integral Assessment of the Degree of Asymmetry of the Operating Mode

V. V. Litvak, V. V. Prokopchik

(Presented by the scientific seminar of the departments of electric stations and electrical systems and networks)

One of the most important indicators of the quality of electric energy is the degree of voltage asymmetry. It is characterized by the voltages of the negative- and zero-sequence components. Distortion of the symmetry of a three-phase voltage system in electrical systems may lead to very serious technical and economic consequences, depending on the depth and duration of this distortion. The appearance of a negative-sequence voltage, for example, causes the appearance in the stators of rotating electrical machines of an alternating magnetic field of negative sequence, and in the rotors—currents of double frequency. This causes additional heating of the windings of rotating electrical machines. An analogous process of additional heating also occurs in transformers. As a result, it may be necessary to limit the load of rotating machines and to underutilize the capacity of transformers [1].

The sources of asymmetry in the networks of metallurgical plants are three-phase arc furnaces and single-phase electric receivers.

Existing analytical methods for determining the asymmetry of a mode make it possible to obtain approximately point values of the positive-, negative-, and zero-sequence voltages from measured values of phase and line-to-line voltages [2]. However, the quantities calculated by these methods give an idea of the mode only at a fixed instant of time for one or several realizations, and such an assessment is applicable only to networks with a sufficiently steady voltage mode.

By its nature, the degree of voltage asymmetry is an integral criterion of the quality of electric power, since the effect of load asymmetry on network elements and electric receivers is determined not by the instantaneous values of the ordinates of the negative- and zero-sequence voltages, but by individual sections of their graphs [3].

The quantities \(U_2\) and \(U_0\) change continuously with time, and the apparatus of random functions of time is most suitable for determining the laws of their distribution. It is advisable to carry out an integral assessment of the influence of voltage asymmetry on the operating mode of the network and of electric receivers according to the “residence time” of the realization of a random function above the analysis level (permissible level) and according to the amount of electric energy supplied to consumers during this time.

In accordance with this, monitoring the asymmetry of a three-phase voltage system can be carried out as follows. Voltages of the negative- or zero-sequence components are extracted by means of FNOP or FNNP filters, connected at the point of the electric network under investigation, and are fed through a rejection filter of the fundamental frequency to the measuring unit (Fig. 1). If the measured voltage \(U_2\) or \(U_0\) exceeds the setpoint voltage, then the measuring element gives a start signal to the time and energy meters. Since the random processes \(U_2(t)\) and \(U_0(t)\) are ergodic and do not have shift and daily nonstationarity [1, 4], then, by changing the setpoints of the measuring element and measuring, for each new setpoint value, the residence time and the amount of electric energy consumed during this time, one can obtain a series of points and construct from them the distribution-function curve, since there is a definite relationship between the probability distribution function of the stationary ergodic random process \(X(t)\) and the relative residence time of the realization \(x(t)\) of this process above a specified analysis level \(x\) (Fig. 2, a) [5]. The formula for estimating the complementary distribution function \(F_1(x)=P[X(t)>x]\), which establishes the indicated relationship, has the form:

Fig. 1. Block diagram of the device.
1 — FNOP or FNNP; 2 — rejection filter of the fundamental frequency; 3 — measuring unit; 4 — indication unit

\[ F_1^*(x)=\frac{1}{T}\sum_{i=1}^{n}\tau_i . \]

To reduce the investigation time, and also when investigating processes possessing weekly (daily) nonstationarity, the number of channels in the measuring unit and the indication unit must be increased. The operation of the device for such a case can be described, according to the block diagram (Fig. 1), as follows.

The measuring elements of the channels are constantly in operation and, if the measured voltage exceeds the setpoint voltage, they give a start signal to “their” electric meters and timing devices of the indication unit. Moreover, starting the time and energy meters of a channel with a lower voltage setpoint is possible only if the channel with the higher setpoint is in the non-operated state. Otherwise, an inhibit signal is applied to its measuring element. Thus, by quantizing the input voltage by levels, measurement is carried out of the residence time of the realization and of the amount of electric energy consumed during this time in each interval of analysis levels, since the channel voltage setpoints differ by a certain value \(\Delta U\). The relationship between the distribution density \(W(x)\) and the relative residence time of the realization within one interval, for example the interval \(\Delta x\) between the levels \(x_1\) and \(x_2\) (Fig. 2, b), is expressed as follows:

\[ W^*(x)=\frac{1}{T\Delta x}\left(\Delta t_1+\Delta t_3+\ldots+\Delta t_{2n+1}\right). \]

This relationship makes it possible to determine the probability distribution density for the entire range of analysis levels if the measurement data are grouped and presented in the form of a histogram.

The expected measurement errors will not substantially exceed the permissible values if the number of analysis levels, the interval width \(\Delta x\), and the duration of the study are chosen correctly. The solution of these questions is not given in the present work.

Fig. 2.

An experimental prototype of the device was developed and manufactured in which an \(R—C\) filter with imbalance compensation under temperature variation was used as the FNSF. Conventional FNSFs used in relay protection are unsuitable because of the coarse adjustment of the imbalance magnitude and the strong temperature dependence of the resistances of their elements. In the filter that was manufactured, highly stable metal-film resistors of type S2-13 were used as the active resistances, and temperature compensation was required only for the capacitive resistances included in the circuit. Since, with increasing temperature, the capacitance of metal-paper capacitors decreases and the capacitive reactance increases, to compensate for this change part of the active resistance of the circuit was made of copper, as a material with a temperature coefficient of resistance (TCR) of the same sign.

The zero-sequence voltage filter was made with three identical capacitances [6]. The difficulty consists only in selecting capacitances of equal value.

The measuring elements of the proposed device are constructed on the basis of tunnel diodes operating as amplitude selectors. The operating settings of the measuring elements can be adjusted smoothly or discretely from \(+1\%\) to \(+10\%\) relative to the nominal-

... to the nominal line voltage. The operating error of the measuring elements on the setting scale, when the ambient temperature varies from minus 20 to plus 40°C, was checked experimentally and does not exceed $\pm 0.5\%$ of the corresponding setting value.

The time counters are made on DSD60-L1 synchronous electric motors; counting mechanisms from electric meters are used to count their number of revolutions, which makes it possible to present information on residence time in continuous digital form. The continuity of digital information is preferable to discreteness, since it takes into account the duration and frequency with which the parameter deviates from its permissible value.

REFERENCES

1. D. V. Timofeev. Modes in electrical systems with traction loads. Moscow, “Energiya,” 1972.

2. N. A. Medelnikov, D. V. Timofeev. Approximate determination of operating-mode asymmetry. “Promyshlennaya energetika,” 1972, No. 4.

3. E. G. Kurennyi, A. M. Sanaev. Calculation of unbalanced loads of factory electrical networks. “Elektrichestvo,” 1971, No. 4.

4. V. P. Murav’ev, N. M. Kozlova. Voltage asymmetry in mine distribution networks. Proceedings of MEI, “In-Plant Power Supply,” 1972, issue 103.

5. G. Ya. Mirsky. Instrumental determination of the characteristics of random processes. Moscow, “Energiya,” 1972.

6. V. L. Fabrikant. Filters of symmetrical components. Moscow, Gosenergoizdat, 1962.