Balanced and Residual Currents and Voltages

(1) "balanced" with respect to earth as a neutral conductor or point of reference, and (2) "residual," completely unbalanced with respect to the earth, i.e., employing the metallic power-circuit conductors, as a group, for one "side" and the earth as the other side of their circuit.⁽¹⁾

To quote this committee further,

"Balanced" current components in the several conductors of a power circuit are such that at every instant their algebraic sum is zero. The algebraic sum of the total currents in the several conductors of a power circuit at any instant is the "residual" current. Similarly, the "balanced" voltages of the several conductors are such that their algebraic sum is zero at every instant, while the algebraic sum of the total voltages to ground at any instant is the "residual" voltage. [AUTHOR'S NOTE : The word algebraic as used probably implies what is usually termed a vector solution.]

As an example, a trolley circuit, consisting of an overhead trolley wire and "return" through rails and earth, is completely unbalanced with respect to earth, its total voltage and current being residual. On the other hand, a two-wire circuit having no metallic connection to earth and its two sides symmetrical with respect to the earth's surface and not in close proximity to other circuits or objects would have no residuals, the voltages to earth of the sides of the circuit being equal and opposite and the currents wholly confined to the metallic conductors and therefore equal and opposite, i.e., in both cases balanced.

This classification of the voltages and currents is of basic importance, since there is no generally applicable relation between balanced and residual components or their inductive effects, and furthermore since the remedies for induction from balanced and residual voltages or currents are often fundamentally different.⁽¹⁾

These definitions and explanations can be illustrated by the simple series of drawings of Fig. 14. In this, (a) illustrates an electric railway system employing a trolley wire. A voltmeter connected between the trolley wire and ground measures the entire system voltage. This system is accordingly entirely unbalanced with respect to the earth. Similarly, (b) represents a single-phase system which fulfils the requirements of balance as specified in the quotation given. If a voltmeter is connected between wire 1 and ground and another voltmeter is connected between wire 2 and ground, for perfect balance to ground each voltmeter will read the same. The voltages at any instant will be opposite, however, and thus the resultant voltage to ground will be zero. That is, there will be no residual voltage. If, however, either wire has an impedance to ground different from that of the other, the voltmeters will not read the same, and their vector sum will show a residual voltage to exist. For the three-phase system in (c), if the line is properly transposed and if the insulation is good, the impedance of each line wire to ground will be essentially the same, and the voltages to ground will be about equal.

Figure 14.

In a balanced three-phase system a voltage exists between each line wire and ground, and these voltages are equal and 120 degrees out of phase. These balanced components accordingly add up to zero as shown by Fig. 15(a). If, however, for any reason a balance does not exist among the voltages to ground, the triangle will not close, and a residual will be left as shown in Fig. 15(6). Although in this section only voltages were considered, similar reasoning can be applied to the currents.

Figure 15.

Those familiar with the subject of symmetrical components will recognize balanced voltages and currents as positive - or negative - sequence quantities and will recognize that the residual voltages or currents correspond to the sum of three phase quantities or to three times the zero-sequence quantities.²⁰

Causes of Residuals. Power systems use the balanced components of voltages and currents for giving electrical service. Moderate residuals are usually no great detriment to a power system, but they are very undesirable from an inductive interference standpoint. In one instance it was reported²⁵ that one ampere residual produced as much induction in a ground return communication circuit as would be produced by 40 amperes of balanced current and that one volt residual voltage produced as much induction as 110 volts of balanced voltage.

Residual voltages and currents may be caused by either the transmission line itself or the apparatus connected to the line. If, because of the configuration, the line wires do not each have the same capacitance to ground or because of poor insulation do not each have the same leakage to ground, the power line will be unbalanced and residuals will result. Capacitive unbalances to ground can in general be prevented by properly transposing the power-line conductors, and this is usually done. Unbalances caused by poor insulation can be corrected by proper line maintenance.

As would be expected, the connected loads and apparatus can cause residuals in many ways (references 9, 10, 11, 12, 20, 21, 26, and 27). Among the causes are the following:

Load Unbalances. If all the loads connected to the three phases of a power system do not have the same magnitude and phase angle, the transmission line will be unbalanced.

Generators and Transformers. The generating and transforming equipment connected to power lines is a source of residuals, as will be explained in the following sections.

(1)	Reprinted by permission, courtesy the Railroad Commission of the State of California.