Three-phase Y and Δ configurations
Initially we explored the idea of
three-phase power systems by connecting three voltage sources together
in what is commonly known as the "Y" (or "star") configuration. This
configuration of voltage sources is characterized by a common connection
point joining one side of each source:
If we draw a circuit showing each voltage
source to be a coil of wire (alternator or transformer winding) and do
some slight rearranging, the "Y" configuration becomes more obvious:
The three conductors leading away from
the voltage sources (windings) toward a load are typically called
lines, while the windings themselves are typically called phases.
In a Y-connected system, there may or may not be a neutral wire attached
at the junction point in the middle, although it certainly helps
alleviate potential problems should one element of a three-phase load
fail open, as discussed earlier:
When we measure voltage and current in
three-phase systems, we need to be specific as to where we're
measuring. Line voltage refers to the amount of voltage measured
between any two line conductors in a balanced three-phase system. With
the above circuit, the line voltage is roughly 208 volts. Phase
voltage refers to the voltage measured across any one component
(source winding or load impedance) in a balanced three-phase source or
load. For the circuit shown above, the phase voltage is 120 volts. The
terms line current and phase current follow the same
logic: the former referring to current through any one line conductor,
and the latter to current through any one component.
Y-connected sources and loads always have
line voltages greater than phase voltages, and line currents equal to
phase currents. If the Y-connected source or load is balanced, the line
voltage will be equal to the phase voltage times the square root of 3:
However, the "Y" configuration is not the
only valid one for connecting three-phase voltage source or load
elements together. Another configuration is known as the "Delta," for
its geometric resemblance to the Greek letter of the same name (Δ). Take
close notice of the polarity for each winding in the drawing below:
At first glance it seems as though three
voltage sources like this would create a short-circuit, electrons
flowing around the triangle with nothing but the internal impedance of
the windings to hold them back. Due to the phase angles of these three
voltage sources, however, this is not the case.
One quick check of this is to use
Kirchhoff's Voltage Law to see if the three voltages around the loop add
up to zero. If they do, then there will be no voltage available to push
current around and around that loop, and consequently there will be no
circulating current. Starting with the top winding and progressing
counter-clockwise, our KVL expression looks something like this:
Indeed, if we add these three vector
quantities together, they do add up to zero. Another way to verify the
fact that these three voltage sources can be connected together in a
loop without resulting in circulating currents is to open up the loop at
one junction point and calculate voltage across the break:
Starting with the right winding (120 V ∠
120o) and progressing counter-clockwise, our KVL equation
looks like this:
Sure enough, there will be zero voltage
across the break, telling us that no current will circulate within the
triangular loop of windings when that connection is made complete.
Having established that a Δ-connected
three-phase voltage source will not burn itself to a crisp due to
circulating currents, we turn to its practical use as a source of power
in three-phase circuits. Because each pair of line conductors is
connected directly across a single winding in a Δ circuit, the line
voltage will be equal to the phase voltage. Conversely, because each
line conductor attaches at a node between two windings, the line current
will be the vector sum of the two joining phase currents. Not
surprisingly, the resulting equations for a Δ configuration are as
follows:
Let's see how this works in an example
circuit:
With each load resistance receiving 120
volts from its respective phase winding at the source, the current in
each phase of this circuit will be 83.33 amps:
So, the each line current in this
three-phase power system is equal to 144.34 amps, substantially more
than the line currents in the Y-connected system we looked at earlier.
One might wonder if we've lost all the advantages of three-phase power
here, given the fact that we have such greater conductor currents,
necessitating thicker, more costly wire. The answer is no. Although this
circuit would require three number 1 gage copper conductors (at 1000
feet of distance between source and load this equates to a little over
750 pounds of copper for the whole system), it is still less than the
1000+ pounds of copper required for a single-phase system delivering the
same power (30 kW) at the same voltage (120 volts
conductor-to-conductor).
One distinct advantage of a Δ-connected
system is its lack of a neutral wire. With a Y-connected system, a
neutral wire was needed in case one of the phase loads were to fail open
(or be turned off), in order to keep the phase voltages at the load from
changing. This is not necessary (or even possible!) in a Δ-connected
circuit. With each load phase element directly connected across a
respective source phase winding, the phase voltage will be constant
regardless of open failures in the load elements.
Perhaps the greatest advantage of the
Δ-connected source is its fault tolerance. It is possible for one of the
windings in a Δ-connected three-phase source to fail open without
affecting load voltage or current!
The only consequence of a source winding
failing open for a Δ-connected source is increased phase current in the
remaining windings. Compare this fault tolerance with a Y-connected
system suffering an open source winding:
With a Δ-connected load, two of the
resistances suffer reduced voltage while one remains at the original
line voltage, 208. A Y-connected load suffers an even worse fate with
the same winding failure in a Y-connected source:
In this case, two load resistances suffer
reduced voltage while the third loses supply voltage completely! For
this reason, Δ-connected sources are preferred for reliability. However,
if dual voltages are needed (e.g. 120/208) or preferred for lower line
currents, Y-connected systems are the configuration of choice.
- REVIEW:
- The conductors connected to the three
points of a three-phase source or load are called lines.
- The three components comprising a
three-phase source or load are called phases.
- Line voltage
is the voltage measured between any two lines in a three-phase
circuit.
- Phase voltage
is the voltage measured across a single component in a three-phase
source or load.
- Line current
is the current through any one line between a three-phase source and
load.
- Phase current
is the current through any one component comprising a three-phase
source or load.
- In balanced "Y" circuits, line voltage
is equal to phase voltage times the square root of 3, while line
current is equal to phase current.
-
- In balanced Δ circuits, line voltage
is equal to phase voltage, while line current is equal to phase
current times the square root of 3.
-
- Δ-connected three-phase voltage
sources give greater reliability in the event of winding failure than
Y-connected sources. However, Y-connected sources can deliver the same
amount of power with less line current than Δ-connected sources.
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