# THE 3 PHASE POWER RESOURCE SITE

 3 phase power is used today for many applications ranging from the above grain dryer to saw mills, conveyer belt systems, refrigeration and air conditioning, etc.
3 Phase Contents
 - 3 Phase Power Home - 3 Phase Wiring - 3 Phase Power Calculation - 3 Phase Power Converter - 3 Phase Converters   * Rotary Phase Converters   * Static Phase Converters - 3 Phase Generators - 3 Phase Transformers   * 3 Phase Isolation Transformers - 3 Phase Motors - 3 Phase Electricity - 3 Phase Power Loads - 3 Phase Frequency   * Frequency Converters - 3 Phase Distribution - 2 Phase Systems - 1 Phase Loads on 3 Phase Power - 3 Phase Loads on 1 Phase Power

# 3 Phase Power Calculation and Mathamatics

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

## 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

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.