Direct current systems usually consist of two or three wires. Although
such distribution systems are no longer employed, except in
very special instances, older ones now exist and will continue to exist
for some time. Direct current systems are essentially the same as singlephase
ac systems of two or three wires; the same discussion for those
systems also applies to dc systems.
Alternating Current Single-Phase Systems
Two-wire Systems
The simplest and oldest circuit consists of two conductors between
which a relatively constant voltage is maintained, with the load connected
between the two conductors; refer to Figure 2-1.
In almost all cases, one conductor is grounded. The grounding of
one conductor, usually called the neutral, is basically a safety measure.
Should the live conductor come in contact accidentally with the neutral
conductor, the voltage of the live conductor will be dissipated through-
out a relatively large body of earth and thereby rendered harmless.
In calculating power (I2R) losses in the conductors, the resistance of
the conductors must be considered. In the case of the neutral conductor,
because the ground, in parallel with the conductor, reduces the effective
resistance, the “return” current will divide between the conductor and
ground in inverse proportion to their resistances. Thus the I2R loss in the
neutral conductor will be lower than that in the live conductor; the I2R
loss in the earth may, for practical purposes, be disregarded.
In calculating voltage drop in the circuits, both the resistance and
reactance of the two conductors must be considered. (In dc circuits, reactance
does not exist during normal flow of current.) This combination
of reactance and resistance, known as impedance, is measured in ohms
(μ). Because the current in the grounded neutral conductor may be less
than the current in the live conductor, the voltage drop in the neutral
conductor may also be less.
Three-wire Systems
Essentially the three-wire system is a combination of two two-wire
systems with a single wire serving as the neutral of each of the two-wire
systems. At a given instant, if one of the live conductors is E volts (say
120 V) “above” the neutral, the other live conductor will be E volts (120
V) “below” the neutral, and the voltage between the two live (or outside)
conductors will be 2E (240 V).
If the load is balanced between the two (two-wire) systems, the
common neutral conductor carries no current and the system acts as
a two-wire system at twice the voltage of the component system; each
unit of load (such as a lamp) of one component system is in series with
a similar unit of the other system. If the load is not balanced, the neutral
conductor carries a current equal to the difference between the currents
in the outside conductors. Here again, the neutral conductor is usually
connected to ground.
For a balanced system, power loss and voltage drop are determined
in the same way as for a two-wire circuit consisting of the outside
conductors; the neutral is neglected.
Where the loads on the two portions of the three-wire circuit are
unbalanced, voltages at the utilization or receiving ends may be different.
These are shown schematically in Figure 2-3. Let the distance
between the dashed lines represent the voltage. There will be a voltage
drop, with reference to the neutral, in each of the conductors 1 and 2.
The neutral conductor will carry the difference in currents, that is, I2 – I1,
or In. This current in the neutral conductor will produce a voltage drop
in that conductor, as indicated in Figure 2-3. The result will be a much
larger drop in voltage between conductor 2 and neutral than between
conductor 1 and neutral. If the unbalance is so large that In is greater
than I1, the receiving end voltage ER1 will be greater than the sending
end voltage ES1, and there will be an actual rise in voltage across that
side.
The limiting case occurs when I1 = 0 and In = I2. In that case, all
the load is carried on side 2; the rise in voltage on side 1 will be half as
much as the drop in voltage on the loaded side 2. However, if an equal
load is now added to side 1, the loads in both parts of the circuit will
be balanced and In will equal 0. The drop in voltage between conductor
2 and the neutral will be reduced to half that obtained with the load on
side 2 only, although the load now supplied is doubled.
Voltage drops in the conductors will depend on the currents flowing
in them and their impedances. The power loss in each conductor
(I2R) will depend on the current flowing in it and its resistance.
In all of this discussion, the size of the neutral has been assumed
to be the same as the live or outside conductors.
Series Systems
The series type of circuit is used chiefly for street lighting and,
although being rapidly replaced by multiple-circuit lighting, nevertheless
still exists in substantial numbers. It consists of a single-conductor
loop in which the current is maintained at a constant value, the loads
connected in series; see Figure 2-4. The voltage between the conductors
at the source or at any other point depends on the amount of load connected
beyond that point. The voltage at the source is equal to the vectorial
sum of the voltages across the various loads and the voltage drop in
the conductor.
The voltage drop in each section of the conductor depends on the
current flowing in it (which is constant in value) and the impedance of
that section of the conductor.
The power supplied the circuit equals the sum of the power for the
individual units of load and the line losses. Power loss in each section of
the conductor will depend on the current (squared) and the resistance of
that section of the conductor.
Alternating Current Two-phase Systems
Two-phase systems are rapidly becoming obsolete, but a good
number of them exist and may continue to exist for some time.
Four-wire Systems
The four-wire system consists of two single-phase two-wire systems
in which the voltage in one system is 90° out of phase with the voltage
in the other system, both usually supplied from the same generator.
Refer to Figure 2-5.
In determining the power, power loss, and voltage drops in such a
system, the values are calculated as for two separate single-phase twowire
systems.
Three-wire Systems
The three-wire system is equivalent to a four-wire two-phase system,
with one wire (the neutral) made common to both phases; refer to
Figure 2-6. The current in the outside or phase wires is the same as in the
four-wire system; the current in the common wire is the vector sum of
these currents but opposite in phase. When the load is exactly balanced
in the two phases, these currents are equal and 90° out of phase with
each other and the resultant neutral current is equal to √2 or 1.41 times
the phase current.
The voltage between phase wires and common wire is the normal
phase voltage, and, neglecting the difference in neutral IR drop, the
same as in the four-wire system. The voltage between phase wires is
equal to √2 or 1.41 times that voltage.
The power delivered is equal to the sum of the powers delivered
by the two phases. The power loss is equal to the sum of the power
losses in each of the three wires.
The voltage drop is affected by the distortion of the phase relation
caused by the larger current in the third or common wire. In Figure
2-6, E1 and E2 are the phase voltages at the source and I1 and I2, the
corresponding phase currents (assuming balanced loading), I3 is the
current in the common wire. The voltage (IZ) drops in the two conductors,
subtracted vectorially from the source voltages E1 and E2, give the
resultant voltages at the receiver of AB for phase 1 and AC for phase 2.
The voltage drop numerically is equal to E1 – AB for phase 1, and E2
– AC for phase 2. It is apparent that these voltage drops are unequal
and that the action of the current in the common wire is to distort the
relations between the voltages and currents—the effect shown in Figure
2-6 is exaggerated for illustration.
Five-wire Systems
The five-wire system is equivalent to a two-phase four-wire system
with the midpoint of both phases brought out and joined in a fifth wire.
The voltage is of the same value from any phase wire to the common
neutral, or fifth, wire. The value may be in the nature of 120 V, which
is used for lighting and small motor loads, while the voltage between
opposite pairs of phase wires, E, may be 240 V, used for larger-power
loads. The voltage between adjacent phase wires is √2, or 1.41, times 120
V (about 170 V).
If the load is exactly balanced on all four phase wires, the common
or neutral wire carries no current. If it is not balanced, the neutral
conductor carries the vector sum of the unbalanced currents in the two
phases.
Alternating Current Three-phase Systems
Four-wire Systems
The three-phase four-wire system is perhaps the most widely used.
It is equivalent to three single-phase two-wire systems supplied from the
same generator. The voltage of each phase is 120° out of phase with the
voltages of the other two phases, but one conductor is used as a common
conductor for all of the system. The current In in that common or neutral
conductor is equal to the vector sum of the currents in the three phases,
but opposite in phase, as shown in Figure 2-8.
If these three currents are nearly equal, the neutral current will be
small, since these phase currents are 120° out of phase with each other.
The neutral is usually grounded. Single-phase loads may be connected
between one phase wire and the neutral, but may also be connected
between phase wires if desired. In this latter instance, the voltage is √3
or 1.73 times the line-to-neutral voltage E. Three-phase loads may have
each of the separate phases connected to the three phase conductors and
the neutral, or the separate phases may be connected to the three phase
conductors only.
Power delivered is equal to the sum of the powers in each of the
three phases. Power loss is equal to the sum of the I2R losses in all four
wires.
The voltage drop in each phase is affected by the distortion of the
phase relations due to voltage drop caused by the current in the neutral
conductor. This is not so, however, when the neutral conductor is
grounded at both the sending and receiving ends, in which case the neutral
drop is theoretically zero, the current returning through ground.
The voltage drop may be obtained vectorially by applying the impedance
drop of each phase to its voltage. The neutral point is shifted from O to
A by the voltage drop in the neutral conductor and the resulting voltages
at the receiver are shown by E1R, E2R, and E3R. The voltage drops
in each phase are numerically equal to the difference in length between
E1S and E1R, E2S and E2R, and E3S and E3R. The effects of the distortion
due to voltage drop in the neutral conductors are exaggerated in Figure
2-8 for illustration.
Three-wire Systems
If the load is equally balanced on the three phases of a four-wire
system, the neutral carries no current and hence could be removed, making a three-wire system. It is not necessary, however, that the load be
exactly balanced on a three-wire system.
Considering balanced loads, on a three-phase three-wire system, a
three-phase load may be connected with each phase connected between
two phase wires—a delta (Δ) connection—or with each phase between
one phase wire and a common neutral point—the star or wye (Y) connection,
as shown in Figure 2-9.
The voltage between line conductors is the delta voltage EΔ while
the line current is the wye current IY. The relations in magnitude and
phase between the various delta and wye voltages and currents for the
same load are shown in Figure 2-9. For the delta connection, IY is equal
to the vector difference between the adjacent delta currents; hence:
IY = √3 (or 1.73) times I
and
EΔ = √3 (or 1.73) times EY
Power delivered, when balanced loads are considered, is equal to
3 times the power delivered by one phase. Power loss is equal to the
sum of the losses in each phase, or when balanced conditions exist, it is
3 times the power loss in any one phase.
The voltage drop in each phase, referred to the wye (Y) voltages,
may be determined by adding the impedance drop in one
conductor vectorially to EY, when balanced loads are considered.
The same thing is done in determining voltages where unbalanced
loads are considered. If EM is the voltage between phases
at the source and EΔS the phase-to-neutral voltage, the drop due
to conductor impedance, IZ, is subtracted vectorially from EYS for
each of the three phases, and the resulting voltages between phases
at the receiving end (EΔR) are obtained. The effects shown in the
vector diagram of Figure 2-9 are exaggerated for illustration.
Alternating Current Six-phase Systems
Six-wire Systems
Six-phase systems consist essentially of two three-phase systems
connected so that each phase of one system will be displaced 1800 with
reference to the same phase of the other system. These may consist of
two banks of three transformers connected separately with the polarity
of one bank reversed with reference to the second bank; or one bank of
transformers may be employed, with the secondary windings divided
into two equal parts and both ends of each winding part brought out to
separate terminals (for a total of 12 terminals).
The windings may be connected in a double-delta fashion as
shown in Figure 2-10a, or in a double-wye arrangement as shown in
Figure 2-10b. The associated vector diagrams of the voltage relationships
are also indicated.
In the double-wye connection, it is not necessary to have the windings
brought out to 12 terminals; the neutral connection may be made
by connecting together the mid tap from each of the three secondary
windings.
Such systems are almost exclusively used in supplying rectifiers or
synchronous converters to serve direct current loads; the synchronous
converter also aids in improving power factor on the alternating current
supply system.
Seven-wire Systems
A seventh, or neutral, wire may be brought out from the common
junction of the double-wye connection, as indicated by the dashed line
in Figure 2-106.
The seven-wire system may be used for distribution purposes, with
the neutral connected to other common neutral systems. The disadvantage
of the additional conductor is balanced against two major advantages:
1. The ability to serve single-phase loads from a source of higher voltage,
i.e., twice the line-to-neutral voltage, compared with 1.73 times
the line-to-neutral voltage in a three-phase system.
2. Reduction in overall line losses, as each conductor will carry only
one-sixth of the load, compared with one-third in a three-phase
system—only half the load per conductor in a three-phase system.
The losses, therefore, will be one-quarter those in a three-phase
(three- or four-wire balanced) system.
The overall savings in fuel costs for supplying the lesser losses may
exceed the increased carrying charges associated with the additional conductors.
The improved voltage in supplying three-phase delta (power)
loads from such a system also contributes to its acceptability. As fuel and
operating costs increase, such systems may find wider application.
Comparison between Alternating Current Systems
A comparison of efficiencies for the several alternating current
systems, assuming the same (balanced) loads, the same voltage between
conductors, and the same conductor size is summarized in Table 2-1,
which uses a single-phase two-wire circuit as a basis for comparison.
