Compensation of Asymmetry in Electric Power Transmission

V. K. Shcherbakov and L. D. Mazur

1

Engineering thought encountered asymmetry in electrical systems comparatively long ago. As early as the beginning of the twentieth century, in three-phase electrical systems there arose the need to supply single-phase loads. Lighting loads in three-phase networks often led to asymmetrical operation of the network and generators. Single-phase arc furnaces, welding transformers, and other types of single-phase load often amounted to as much as 20 percent of the power taken from the power station.

Supplying an asymmetrical load over symmetrical three-phase networks from symmetrical three-phase generators (Fig. 1) is associated with additional heating of the generators and with a reduced utilization factor for the conductor cross sections in the network.

The point is that an asymmetrical three-phase system of currents (unequal loading of the phases), observed in generators, can be represented as the sum of two symmetrical three-phase systems of currents: positive sequence and negative sequence. The symmetrical system of positive-sequence currents is the ordinary system of currents. Three-phase generators are designed for this system of currents. The symmetrical system of negative-sequence currents, appearing in generators in connection with the supply of single-phase loads, creates in the generator a magnetic field of negative sequence, on account of which parasitic currents arise in the windings and closed circuits of the rotor, producing additional heating of the rotor. Thus the utilization factor of the generator is reduced, since the limiting heating temperature under these conditions is reached at incomplete loading of the generator.

Fig. 1

Wishing to avoid disturbance of the normal operating conditions of a three-phase symmetrical generator, designers proposed a number of schemes for supplying asymmetrical loads, the meaning of which was, in the main, reduced to the inclusion of such additional devices as would satisfy the load demand for negative-sequence currents. Consequently, in the final analysis, there arose here the need to produce negative-sequence currents along with positive-sequence currents.

Let us repeat once more that in all the above-mentioned cases the matter concerned the supply of an asymmetrical load through symmetrical three-phase electrical networks.

The question arose in a fundamentally new way when, in the last decade, asymmetrical power transmissions appeared in the operating practice of electrical systems and installations: lines with a grounded phase, lines with phase-by-phase switching, power transmissions with asymmetrical connection of transformers, etc. In this case the problem is the supply of a three-phase symmetrical load through asymmetrical power transmissions. Here, as before, because of asymmetry in the power transmissions, negative-sequence currents arise in the generators; but these negative-sequence currents are not needed by the load, they have not appeared as the result of demand on the part of the load; moreover, because of asymmetry in the power transmissions, parasitic negative-sequence currents appear in symmetrical receivers of electric power, reducing the efficiency of these receivers. If in the first case the problem was to find ways of satisfying the load’s demand for negative-sequence currents, then in this case, on the contrary, the problem is to seek means of combating negative-sequence currents which are needed neither by the generators nor by the load and have appeared only as a result of the presence of asymmetry in the power transmissions.

2

The degree of asymmetry in motors and generators connected with an asymmetrical power transmission can be calculated [1] and in individual cases reaches a very large value. Thus, for example, in the case of disconnection of one phase in a three-phase single-circuit transmission line, the motor load experiences current asymmetry amounting to 30 percent, provided that only 50 percent of the consumers by power remain in operation [1]. It can be shown that the utilization factor of the motor load is significantly reduced, since the negative-sequence magnetic fields induce parasitic currents in the windings and closed circuits of the motor rotors, causing additional heating of the motors. Generators are in a somewhat better position because, as a rule, symmetrical power transmissions as well as asymmetrical ones are connected to the busbars of a power station. The negative-sequence currents caused by asymmetry in the power transmissions are distributed over a large generating capacity. The case in which a generator operates only through an asymmetrical power transmission is exceptionally rare. In the overwhelming majority of cases, the power delivered through an asymmetrical power transmission will constitute only some part of the full power of the power station, and, consequently, the asymmetry in the generators caused by the asymmetrical power transmission connected to the station will be small and, apparently, most often within permissible limits. In addition, it should be taken into account that, for example, lines with phase-by-phase switching, when operating with an incomplete number of line conductors, are capable of transmitting only part of the rated power. Thus, the generators of the power station in this case are partially unloaded.

It follows from what has been said that, in the case of asymmetry under consideration, special attention must be paid to freeing the motor load from negative-sequence currents. Here it is important to note that the transmission of power through an asymmetrical power transmission, i.e., the transmission of positive-sequence currents, is possible only with the simultaneous flow through the line of negative-sequence currents as well. If the neutrals of the transformers are grounded, then the flow of positive-sequence currents will be associated with the simultaneous flow of negative- and zero-sequence currents.

Limiting the negative- or zero-sequence currents in the line will mean a simultaneous limitation of the positive-sequence current.

... in the line [1]. It would have been possible to limit the negative-sequence current in the line and thereby reduce the magnitude of this current to minimal values in the motor load by increasing the zero-sequence current. However, the flow of zero-sequence current in the line is associated with the return of this current through the earth and, consequently, with the harmful effects of current in the earth. Thus, this way of limiting the negative-sequence current does not appear expedient. What remains, as it were, the only correct solution is to permit the existence of negative-sequence currents in the line and, at the same time, not to allow these currents into the motor windings.

3

It is probably possible to block the path of negative-sequence currents to the motor load by several methods. Below, one such method is considered schematically.

As can be seen from the diagram in Fig. 2, ahead of the load an additional synchronous negative-sequence generator is inserted, with a frequency equal to the

a. Diagram of the flow of currents of different sequences in one phase of the line without insertion of an additional generator

b. Diagram of the flow of currents of different sequences in one phase of the line with an additional generator inserted

Fig. 2

frequency of the transmission current. In the absence of such a generator, the negative-sequence currents close through the load and the synchronous compensator or static capacitor, which are often installed on power...

substations or directly at the load. If the negative-sequence generator produces an electromotive force equal to the negative-sequence voltage at the load terminals, then no negative-sequence current will flow through the load; the current will close only through the synchronous compensator. The magnitude of the negative-sequence EMF should amount to several percent of the nominal voltage of the power transmission, since the voltage asymmetry usually does not exceed a few percent. Consequently, the power of the additional generator will also amount to only a few percent of the power transmitted by the electric power line.

Regulation of the magnitude and phase of the negative-sequence EMF can be accomplished by a combined field winding, which at each given moment produces the sum of two magnetic fluxes acting in mutually perpendicular planes. By changing the magnitude of one or the other component of the resultant magnetic flux of the generator rotor, it is possible to change the phase of the generator EMF. The possibility of such regulation of the phase of a generator EMF was long ago indicated in principle as applied to series compensation of the reactance of transmission lines. Subsequently, Docent G. E. Pukhov analyzed this method of regulating the EMF phase in detail in his Candidate’s dissertation [2].

The presence of a synchronous compensator or static capacitors is absolutely necessary at the substation or near the load in the event that there is no separately connected and sufficiently powerful non-motor load.

The point is that the existence of negative-sequence currents in a power-transmission line, as was shown above, is inevitable. Consequently, these currents must have a path for flow with comparatively low resistance. A non-motor load (for example, electric furnaces) can, without damage to itself, permit the flow of negative-sequence currents. In the absence of such a separately connected, sufficiently powerful non-motor load, the negative-sequence currents could close through the synchronous compensator, as shown in Fig. 2.

REFERENCES

1. V. K. Shcherbakov—Asymmetrical Electric Power Transmissions. Publishing House of the Tomsk Polytechnic Institute, 1945.

2. G. E. Pukhov—On the Question of Series Compensation of the Reactance of Electric Power-Transmission Lines. Dissertation, 1943.