Question

With a bank of two single phase transformers connected in V - V fashion supplying a balanced three phase load with cos θ  as power factor. The power factor of the two transformers is given by:
1. cos (30 - θ), cos (30 + θ)
2. coscθ, cos θ
3. cos θ, cos (30 - θ)
4. cos θ, cos(30 + θ)

Answer 1

Correct Answer - Option 1 : cos (30 - θ), cos (30 + θ)
V-V connection:

• An open delta connection transformer uses two single-phase transformers to provide a three-phase supply to the load.
• An open delta connection system is also called a V-V system.
• Open delta connection systems are usually only used in emergency conditions when one of the transformers in the Delta-Delta system is damaged, and removed from service.    
• Efficiency for the operation of open delta connection is low as compared to delta-delta systems which are used during standard operations.

By applying the two-wattmeter method at lagging load, 

The reading of first wattmeter (W1) = V_L I_L cos (30 + ϕ)

The reading of second wattmeter (W2) = V_L I_L cos (30 - ϕ)

Total power in the circuit (P) = W₁ + W₂ 

Application:

Given,

power factor of the load is given by Cosθ 

The power factor of the first Transformer by observing the first wattmeter is given by cos (30 + θ)

The power factor of the second Transformer by observing the second wattmeter is given by cos (30 - θ)