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.
- REVIEW:
- 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).
- Split-phase AC sources can be easily
created by center-tapping the coil windings of transformers or
alternators.
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