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Three Phase system: theory of Normal, Inverse, Homopolar voltage, systems with asymmetric load

Get insight into the differences between currents, voltages and power influenced by the voltage system (Normal, Inverse, Homopolar) with the help of a special Ti84 program. This is important for electric engineering. Before you continue, it is advised that you study the three-phases asymmetric load theory first. 
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On the page 3 phases asymmetric load, it became clear that a floating point voltage arises if the load of the 3 phases differ. Calculations were done with a normal voltage system, which means that voltage vectors of the three phases turn clockwise, as is usually the case in practice.

It is also known that if two of the three phases are exchanged, an inverse voltage system arises. In practice, this means that the direction of rotation of a 3 phase motor changes, which is important to know for electrical engineers.

It is often unknown that the magnitude and phase of the floating point voltage depends on whether we have a Normal or Inverse system. We will illustrate this by examples.


Besides the Normal and Inverse voltage system, it is possible to have a homopolar system which means that all the three sources of the three-phase system have the same magnitude and phase.

It can be shown from the theory that a three-phase system with each phase a different amplitude and phase can be built up with the sum of a Normal, Inverse and Homopolar system. 

Definitions of Normal, Invers and homopolar system

The examples

Definitions of Normal, invers and homopolar systemNIHsysv2.JPG

Example of an Normal voltage system 

Three-phase system with an asymmetric load with an impedance Zo = ∞ Ω which indicates a floating star point of the load

3 fase scheme with asymmetric load and grounded star of the load

Results for a normal Voltage system (clockwise). Urms=120 V, asymmetric load, floating star. 

Examole of a normal source system with asymmetric load and floating pointvoltage
Multisim simulation of normal system with asymmetric load

Check with Multisim of Uzo and currents I1, I2, I3 calculated with the Ti program. Results Ti84 agree with Multisim results. Besides that, the Ti program calculates all voltages, supply powers and load powers which would cost a lot of effort to achieve that with Multisim. 

Example of an Inverse Voltage system 

For the same asymmetric load and supply voltage levels as above but with an inverse voltage system, the floating point voltage and currents are calculated. At the start of this new program, one must indicate whether there is a Normal voltage system (N=1)or an Inverse voltage system (I=-1) or a Homopolar voltage system (H=0). As you can see, the results for the Inverse system differ totally from the results of the Normal system. The floating voltage is 160.43 V for the Inverse system and 125.73V for the Normal voltage system. Also, the source currents differ considerably. To check the results, a Multisim analysis has been added. Not shown here is, that all voltages and powers are also calculated as shown on the page: three phase asymmetric load.

Inverse source voltage system with asymmetric load and floating pointanticlockwise.JPG
Multisim system of inverse voltage system and asymmetric load
Floating voltage Inverse system differs from normal systemInverse system has

Example of homopolar voltage system

For a homopolar voltage system, it yields that each source has the same magnitude and phase. If the star points are not connected, then there will no current flow and the floating point voltage will equal the homopolar voltage of 120V.

If you have installed the program, take for example Zo= (1+j) Ohm. The other impedances remain the same as in the other examples. Then the result for the floating voltage equals 40.84V

To get the free program, send a mail to or chat where you tell which program you want making sure to include your email address.

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