Power Factor with Two Transformers in 3-Phase Open-Delta Configuration
The power factor of a typical T/F is 0.866, so the max output (KVA) of a T/F will be 86.6% of its rated capacity. Suppose we have three transformers each having the same rating (50 KVA). Then the total capacity is equal to 150 * 0.866=130 KVA and not 150 KVA. (The factor 0.866 is called the Utility Factor.)
If one transformer is removed, the total output of two T/Fs will be 100 * 0.866=86.6 KVA. From this calculation, we see that output capacity is reduced when a Delta-Delta configuration is operated as an Open-Delta connection, i.e. with one T/F removed.
Let say the two T/Fs of Open-Delta configuration are supplying 3-phase power to a load having power factor Cosα. The power factor of one T/F is Cos(30-α) and the other is Cos(30+α).
Power (T/F1)=KVA Cos(30-α) and Power(T/F2)= KVACos(30+α)
- Case (i): When phase angle (α=0) is zero, mean load p.f=1 - each transformer has power factor = Cos30 = 0.866
- Case (ii):When phase angle is 30(α=30), mean load p.f=0.866, one T/F will have p.f of cos(30-30) = Cos0 = 1 and the other will be operating at p.f of Cos(30+30) = Cos60 = 0.866
- Case(iii):When phase angle is 60 (α=60), mean load p.f=0.5, then one T/F will have p.f of Cos(30-60) = 0.866 and other will have a p.f of Cos(30+60) = Cos90 = 0.
From the third scenario we conclude that if we have a transformer Open-Delta configuration in which one T/F is transferring power to an entire load at a p.f of 0.866, then the other one will not provide any load.
Applications of Open-Delta configurations
- Widely used for small 3-phase loads.
- Used in applications where the current load is less, and may increase in future.
- There is no relative shift in output, so can be used for unbalanced loads and where harmonics are involved.
Author's own experience
Electrical Technology By A.K Theraja and B.L Theraja.
Electric Machinery Fundamentals by Stephen J.Chapman 3rd Ed.