Following requirements must be satisfied in order for a set of 3 sinusoidal variables (usually voltages or currents) to be a "balanced 3phase set"
Following requirements must be satisfied in order for a 3phase system or circuit to be balanced.
Advantages of 3 Phase Circuits:
Three Phase Circuit Connections: There are two basic schemes for connecting a load or generator in a threephase circuit.
Star or “Y” (also known as the “T”) configuration:
Delta, or Δ (also known as the “Pi,” or π) configuration:
Balanced Three‐Phase Connections: Four possible connections between source and load.
Wye‐Delta transformation
Transformations
Note: Both Star Delta Transformation and Delta Star Transformation allows us to convert one type of circuit connection into another type in order for us to easily analyse the circuit. These transformation techniques can be used to good effect for either star or delta circuits containing resistances or impedances.
Example1: Compute the total resistance between A and B terminals in the following network circuit.
Using the Delta to star transformation, the following network in between 1,2,and 3 points converted.
Delta to star transformation equations:
(i) R_{1} = R_{12}R_{31} / (R_{12}+R_{23}+R_{31})
R_{1} = (3*6)/ (3+6+9) = 1Ω
(ii) R_{2} = R_{23}R_{12} / (R_{12}+R_{23}+R_{31})
R_{2} = (9*3)/18 = 1.5Ω
(iii) R_{3} = R_{31}R_{23} / (R_{12}+R_{23}+R_{31})
R_{3} = (6*9)/18 = 3Ω
Now, it is easy to compute the total resistance between points A and B.
R_{AB} = (7Ω+3Ω) + (8.5Ω+1.5Ω) + 1Ω = 6Ω.
Example2: Compute the total resistance between A and B terminals in the following network circuit.
Solution: In the above circuit, identify the star connections (Y) which is shown with circles in the following circuits.
Star to Delta Transformation
Similarly other circle can also be converted from star to delta as included in the following circuit.
It is simple to convert two parallel connections of above circuit into the below circuit.
R_{AB} = {[(7+5)  8  8] + 5}  8  4 R_{AB} = (3 + 5)  8  4 R_{AB} = 4  4 R_{AB} = 2Ω
DeltaStar and StarDelta Transformation
Note: Both Star Delta Transformation and Delta Star Transformation allows us to convert one type of circuit connection into another type in order for us to easily analyse the circuit. These transformation techniques can be used to good effect for either star or delta circuits containing resistances or impedances.
Three Phase Power:
If line values of voltage and current are known, the power (watts) of a pure resistive load is:
If the phase values of voltage and current are known, the apparent power is:
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