Single-phase power systems
Depicted above is a very simple AC circuit.
If the load resistor's power dissipation were substantial,
we might call this a "power circuit" or "power system"
instead of regarding it as just a regular circuit. The
distinction between a "power circuit" and a "regular
circuit" may seem arbitrary, but the practical concerns are
definitely not.
One such concern is the size and cost of
wiring necessary to deliver power from the AC source to the
load. Normally, we do not give much thought to this type of
concern if we're merely analyzing a circuit for the sake of
learning about the laws of electricity. However, in the real
world it can be a major concern. If we give the source in
the above circuit a voltage value and also give power
dissipation values to the two load resistors, we can
determine the wiring needs for this particular circuit:
83.33 amps for each load resistor adds up to
166.66 amps total circuit current. This is no small amount
of current, and would necessitate copper wire conductors of
at least 1/0 gage. Such wire is well over 1/4 inch in
diameter, weighing over 300 pounds per thousand feet. Bear
in mind that copper is not cheap either! It would be in our
best interest to find ways to minimize such costs if we were
designing a power system with long conductor lengths.
One way to do this would be to increase the
voltage of the power source and use loads built to dissipate
10 kW each at this higher voltage. The loads, of course,
would have to have greater resistance values to dissipate
the same power as before (10 kW each) at a greater voltage
than before. The advantage would be less current required,
permitting the use of smaller, lighter, and cheaper wire:
Now our total circuit current is
83.33 amps, half of what it was before. We can now use
number 4 gage wire, which weighs less than half of what 1/0
gage wire does per unit length. This is a considerable
reduction in system cost with no degradation in performance.
This is why power distribution system designers elect to
transmit electric power using very high voltages (many
thousands of volts): to capitalize on the savings realized
by the use of smaller, lighter, cheaper wire.
However, this solution is not without
disadvantages. Another practical concern with power circuits
is the danger of electric shock from high voltages. Again,
this is not usually the sort of thing we concentrate on
while learning about the laws of electricity, but it is a
very valid concern in the real world, especially when large
amounts of power are being dealt with. The gain in
efficiency realized by stepping up the circuit voltage
presents us with increased danger of electric shock. Power
distribution companies tackle this problem by stringing
their power lines along high poles or towers, and insulating
the lines from the supporting structures with large,
porcelain insulators.
At the point of use (the electric power
customer), there is still the issue of what voltage to use
for powering loads. High voltage gives greater system
efficiency by means of reduced conductor current, but it
might not always be practical to keep power wiring out of
reach at the point of use the way it can be elevated out of
reach in distribution systems. This tradeoff between
efficiency and danger is one that European power system
designers have decided to risk, all their households and
appliances operating at a nominal voltage of 240 volts
instead of 120 volts as it is in North America. That is why
tourists from America visiting Europe must carry small
step-down transformers for their portable appliances, to
step the 240 VAC (volts AC) power down to a more suitable
120 VAC.
Is there any way to realize the advantages
of both increased efficiency and reduced safety hazard at
the same time? One solution would be to install step-down
transformers at the end-point of power use, just as the
American tourist must do while in Europe. However, this
would be expensive and inconvenient for anything but very
small loads (where the transformers can be built cheaply) or
very large loads (where the expense of thick copper wires
would exceed the expense of a transformer).
An alternative solution would be to use a
higher voltage supply to provide power to two lower voltage
loads in series. This approach combines the efficiency of a
high-voltage system with the safety of a low-voltage system:
Notice the polarity markings (+ and -) for
each voltage shown, as well as the unidirectional arrows for
current. For the most part, I've avoided labeling
"polarities" in the AC circuits we've been analyzing, even
though the notation is valid to provide a frame of reference
for phase. In later sections of this chapter, phase
relationships will become very important, so I'm introducing
this notation early on in the chapter for your familiarity.
The current through each load is the same as
it was in the simple 120 volt circuit, but the currents are
not additive because the loads are in series rather than
parallel. The voltage across each load is only 120 volts,
not 240, so the safety factor is better. Mind you, we still
have a full 240 volts across the power system wires, but
each load is operating at a reduced voltage. If anyone
is going to get shocked, the odds are that it will be from
coming into contact with the conductors of a particular load
rather than from contact across the main wires of a power
system.
There's only one disadvantage to this
design: the consequences of one load failing open, or being
turned off (assuming each load has a series on/off switch to
interrupt current) are not good. Being a series circuit, if
either load were to open, current would stop in the other
load as well. For this reason, we need to modify the design
a bit:
Instead of a single 240 volt power supply,
we use two 120 volt supplies (in phase with each other!) in
series to produce 240 volts, then run a third wire to the
connection point between the loads to handle the eventuality
of one load opening. This is called a split-phase
power system. Three smaller wires are still cheaper than the
two wires needed with the simple parallel design, so we're
still ahead on efficiency. The astute observer will note
that the neutral wire only has to carry the difference
of current between the two loads back to the source. In the
above case, with perfectly "balanced" loads consuming equal
amounts of power, the neutral wire carries zero current.
Notice how the neutral wire is connected to
earth ground at the power supply end. This is a common
feature in power systems containing "neutral" wires, since
grounding the neutral wire ensures the least possible
voltage at any given time between any "hot" wire and earth
ground.
An essential component to a split-phase
power system is the dual AC voltage source. Fortunately,
designing and building one is not difficult. Since most AC
systems receive their power from a step-down transformer
anyway (stepping voltage down from high distribution levels
to a user-level voltage like 120 or 240), that transformer
can be built with a center-tapped secondary winding:
If the AC power comes directly from a
generator (alternator), the coils can be similarly
center-tapped for the same effect. The extra expense to
include a center-tap connection in a transformer or
alternator winding is minimal.
Here is where the (+) and (-) polarity
markings really become important. This notation is often
used to reference the phasings of multiple AC voltage
sources, so it is clear whether they are aiding ("boosting")
each other or opposing ("bucking") each other. If not for
these polarity markings, phase relations between multiple AC
sources might be very confusing. Note that the split-phase
sources in the schematic (each one 120 volts ∠ 0o),
with polarity marks (+) to (-) just like series-aiding
batteries can alternatively be represented as such:
To mathematically calculate voltage between
"hot" wires, we must subtract voltages, because their
polarity marks show them to be opposed to each other:
If we mark the two sources' common
connection point (the neutral wire) with the same polarity
mark (-), we must express their relative phase shifts as
being 180o apart. Otherwise, we'd be denoting two
voltage sources in direct opposition with each other, which
would give 0 volts between the two "hot" conductors. Why am
I taking the time to elaborate on polarity marks and phase
angles? It will make more sense in the next section!
Power systems in American households and
light industry are most often of the split-phase variety,
providing so-called 120/240 VAC power. The term
"split-phase" merely refers to the split-voltage supply in
such a system. In a more general sense, this kind of AC
power supply is called single phase because both
voltage waveforms are in phase, or in step, with each other.
The term "single phase" is a counterpoint to
another kind of power system called "polyphase" which we are
about to investigate in detail. Apologies for the long
introduction leading up to the title-topic of this chapter.
The advantages of polyphase power systems are more obvious
if one first has a good understanding of single phase
systems.
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REVIEW:
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Single phase power systems are
defined by having an AC source with only one voltage
waveform.
-
A split-phase power system is one
with multiple (in-phase) AC voltage sources connected in
series, delivering power to loads at more than one
voltage, with more than two wires. They are used primarily
to achieve balance between system efficiency (low
conductor currents) and safety (low load voltages).
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Split-phase AC sources can be easily
created by center-tapping the coil windings of
transformers or alternators.
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