## Thursday, October 26, 2017

### Three power calculations from single phase and three phase loads

Three phase power calculations when you have Both Single and Three Phase loads in System:-
While calculating three phase loads where  there are both single phase and three phase loads there are so many confusions arises such as how single phase and three phase loads comes at same platform while calculating total load.

This is can be simplified in below stated article:-

In electrical systems power is always additive i.e. if we have connected load in each single phase of 20 KW then total three phase power requirement will be 60 KW. There is often confusion arises while studying that if you have Three phase power of 90 KW then it means power will be 90 KW in each phase but same is not true as it means power will be 30 KW in each phase.
This can be illustrated by doing calculations in reverse order also:-

Three Phase Power calculations for Line to Line Voltage:-
Three phase power(KW) = 3 × PF × I(A) × VL-L (V) / 1000
Where PF= Power Factor
I(A)= Phase current in Amperes
VL-L= Line to Line RMS Voltage

Three Phase Power calculations for Line to Neutral Voltage:-
Three phase power(KW) = 3 × PF × I(A) × VL-N (V) / 1000
Power factor is usually taken as 1 for Resistive loads
Power factor is usually taken as 0.85 for Induction motors at full loads and 0.35 for no loads.
Now lets take three phase load of 90 KW, now if you consider this load to be equal to 90 KW in each phase then current in each phase will be= 90000/(1.732 X230X0.8)= 282 A
So every-time if you have to calculate total power then  just add single phase load and three phase load then cumulative will be your three phase load requirement.
In a balanced power system if there is total P having power factor pf and line to line voltage as VL

Then single phase power will be P(Single Phase)= P/3

Single Phase apparent power will =P/(3Xpf)
Phase current= Apparent Power
VLN
Then Phase current(A) =
1.732=  which comes as VLN=VL/

While doing above calculations efficiency must also be taken care.

These calculations given above are done considering three phase balanced load, which means that there will be same current and power consumption in each phase.  This is mostly applicable for electrical motors and transmission lines but in domestic loads where most of load is single phase this may not be effective. But above calculations will hold good for any industry.

This can be further simplified by assuming three motor of 90 KW. Now if you assume that there is 90KW load in each phase then you will get 270 KW overall load (Adding 90 KW of each phase) then you will pay for only 90 KW electricity charges then this will be huge savings as by withdrawal of 270 KW you have to pay only for 90 KW.
This means if you have a motor which is consuming a given KW then KW per winding is to be divided by 3 which are similar for three phase transformers where transformer is supplying given KVA then KVA in each winding will be third of total power.

Advantages of Three Phase power Over single phase power
There are following advantages of three phase power above single phase power:-
1.     When we use three phase power than frame size of required machine of same rating get reduce in comparison to when we use single phase power. It means frame size of machine get reduced.
2.     Single phase motors are not self-starting and required auxiliary means of starting the same but three phase motors are self-starting.
3.     Three phase motors have higher power factor and higher efficiency in comparison to single phase motors.
4.     Three phase motors of same rating as of single phase motors are smaller in size which will leads to lower cost , lighter in weight, lower in maintenance cost.
5.     Even in transmission lines for same amount of power at same voltage three phase transmission line requires lesser conductor material in comparison to single phase transmission lines. Thus three phase transmission system becomes cheaper. This will also leads to reduction in cross-sectional area of conductor. Thus leads to lower installation cost.
6.     Single phase motors have pulsating torque whereas polyphase system has uniform torque.

7.       It is quite easier to have parallel operation of three phase generators in comparison to single phase system.