**3
Phase Power Calculation**

There
are several mathematical
3 phase power calculations that you can use to
calculate your 3
phase power distribution to make sure that your
wiring distributes your load evenly maintaining a
balanced system. These calculations are useful
for many purposes including when you have single phase
equipment and 3 phase equipment running on the same
power lines. Read more about 3
phase power calculation here.
This
article deals with the basic mathematics and
principles of three-phase
electricity. For information on where, how and why
three-phase is used, see three-phase electric power.
For information on testing three-phase kit, see
three-phase testing

In
electrical
engineering, three-phase electric power systems
have at least three conductors carrying voltage
waveforms that are 2π/3 radians (120°,1/3 of a
cycle) offset in time. In this article angles will be
measured in radians
except where otherwise stated.

**Variable
3 Phase Mathematics Setup and Basic Definitions**

Let

where
t is
time and f is frequency.

Using
x =
ft the waveforms for the three phases are

where
A is the peak voltage and the voltages on L1, L2 and
L3 are measured relative to the neutral.

## Balanced
3 Phase Power Loads

Generally,
in electric power systems the load is distributed as
evenly as practical between the phases. It is usual
practice to discuss a balanced system first and then
describe the effects of unbalanced systems as
deviations from the elementary case.

To
keep the calculations simple we shall normalize A and
R to 1 for the remainder of these calculations

**Star
Connected Systems With Neutral
**

**Constant
Power Transfer**

An
important property of three-phase power is that the
power available to a resistive load,

,
is constant at all times.

Using
R=1

Using
angle subtraction formulae

Using
the Pythagorean trigonometric identity

since
we have eliminated x we can see that the total power
does not vary with time. This is essential for keeping
large generators and motors running smoothly.

**No
Neutral Current**

The
neutral current is the sum of the phase currents.

Since
R=1

Using
angle subtraction formulae

### Star
Connected Systems Without Neutral

Since
we have shown that the neutral current is zero we can
see that removing the neutral core will have no effect
on the circuit, provided the system is balanced. In
reality such connections are generally used only when
the load on the three phases is part of the same piece
of equipment (for example a three-phase
motor), as otherwise switching loads and slight
imbalances would cause large voltage fluctuations.

## Unbalanced
3 Phase Power Systems

Practical
systems rarely have perfectly balanced loads,
currents, voltages or impedances in all three phases.
The analysis of unbalanced cases is greatly simplified
by the use of the techniques of symmetrical
components. An unbalanced system is analyzed as the
superposition of three balanced systems, each with the
positive, negative or zero sequence of balanced
voltages.

**Revolving
Magnetic Field**

Any
polyphase system, by virtue of the time displacement
of the currents in the phases, makes it possible to
generate easily a magnetic field that revolves at the
line frequency. Such a revolving magnetic field makes
polyphase induction motors possible. Indeed, where
induction motors must run on single-phase power (such
as is usually distributed in homes), the motor must
contain some measure to produce a revolving field,
otherwise the motor cannot generate any stand-still
torque and will not start. The field produced by a
single-phase winding can provide energy to a motor
already rotating, but without auxiliary functions the
motor will not accelerate from a stop when energized.

**Conversion
To Other Phase Systems**

Provided
two voltage waveforms have at least some relative
displacement on the time axis, other than a multiple
of a half-cycle, any other polyphase set of voltages
can be obtained by an array of passive transformers.
Such arrays will evenly balance the polyphase load
between the phases of the source system. For example,
balanced two-phase power can be obtained from a
three-phase network by using two specially constructed
transformers, with taps at 50% and 86.6% of the
primary voltage. This Scott
T connection produces a true two-phase system with
90° time difference between the phases. Another
example is the generation of higher-phase-order
systems for large rectifier systems, to produce a
smoother DC output and to reduce the harmonic currents
in the supply.

References:William
D. Stevenson Jr., "Elements of Power Systems
Analysis", 3rd ed. 1975, McGraw Hill, New York
USA ISBN 0070612854

**
3 Phase Power
Generators**

There are many options for 3 phase
power
generators. These range from small portable
3 phase generators to large
industrial diesel generators. There are many
different fuel options to choose from and your
application will help determine what is best for your
companies need. Propane generators and
diesel
generators are the most popular because of the
availability of these common fuels.

**3
Phase Loads**

The
most common class of 3
phase load is the 3
phase electric motor. A common 3 phase induction
motor has a simple design, inherently high starting
torque, and high efficiency. Such 3 phase motors are
applied in industry for 3
phase pumps, fans, blowers, compressors, conveyor
drives, and many other types of motor-driven
equipment. A 3 phase motor is more compact and less
costly than a 1-phase motor of the same voltage class
and rating; also 1-phase AC motors above 10 HP (7.5
kW) are not as efficient and thus not usually
manufactured.
Large
air conditioning equipment (for example, most York
air conditioning units above 2.5 tons (8.8 kW) cooling
capacity) use 3 phase motors for reasons of economy
and efficiency. Read more about 3
phase power loads here.

**3
Phase Loads Run on 3 Phase Power Generated on 1 Phase
Power**

There
are many places and instances where 1 phase power is
the only type of power that is available, or where the
power company wants to charge tens, or even hundreds
of thousands of dollars to install and supply 3 phase
power. In this situation a quality 3
phase generating phase converter is the easy
choice to be run on 1 phase to power 3 phase equipment
of any type.
Quality
3 phase converters are super efficient and a a good
choice for this use. Click here to read
more about powering
3 phase loads with 3 phase power generated from 1
phase power.

**3 Phase
Converters**

Often
the advantages of 3 phase motors, and other 3 phase
equipment, make it smart and easily worthwhile to
convert single-phase power to generate 3 phase. Small
and large customers, such as residential, rural
businesses, or farm properties may not have access to
a 3 phase supply, or may not want to pay for the extra
cost of a 3 phase service, but may still wish to use 3
phase equipment. Such 3
phase converters may also allow the frequency (see
also frequency
converters) to be varied allowing for different
equipment frequency requirements (50Hz, 60Hz, 400Hz,
etc.) and also for motor speed control (VFDs).
Some locomotives are driven by 3-phase motors with 3
phase converters converted from the incoming supply of
either DC or 1 phase AC.
The
two main types of 1 phase to 3 phase converters are Rotary
Phase Converters and Static
Phase Converters. Click here to read more
about 3
phase converters.

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