A 3-phase delta connected load consumes a power of 60kW taking a lagging current of 200 A at a line voltage of 400V, 50 Hz. Find the parameters of each phase. What would be the power consumed if the load where connected in star.
Question
A 3-phase delta connected load consumes a power of 60kW taking a lagging current of 200 A at a line voltage of 400V, 50 Hz. Find the parameters of each phase. What would be the power consumed if the load where connected in star.
Solution
The given parameters are:
- Power consumed, P = 60 kW
- Line current, I_L = 200 A
- Line voltage, V_L = 400 V
- Frequency, f = 50 Hz
Step 1: Calculate the power factor (cos θ)
The power factor can be calculated using the formula P = √3 * V_L * I_L * cos θ. Rearranging for cos θ gives us:
cos θ = P / (√3 * V_L * I_L) = 60,000 / (√3 * 400 * 200) = 0.433
Step 2: Calculate the phase current (I_ph)
For a delta connection, the phase current is given by I_ph = I_L / √3 = 200 / √3 = 115.47 A
Step 3: Calculate the phase voltage (V_ph)
For a delta connection, the phase voltage is equal to the line voltage, V_ph = V_L = 400 V
Step 4: Calculate the impedance (Z)
The impedance can be calculated using Ohm's law, Z = V_ph / I_ph = 400 / 115.47 = 3.46 Ω
Step 5: Calculate the power consumed in star connection
In a star connection, the line current is equal to the phase current and the line voltage is √3 times the phase voltage. Therefore, the power consumed in a star connection can be calculated using the formula P = √3 * V_L * I_L * cos θ = √3 * 400 * 115.47 * 0.433 = 36.05 kW
So, the parameters for each phase in the delta connection are:
- Power factor = 0.433
- Phase current = 115.47 A
- Phase voltage = 400 V
- Impedance = 3.46 Ω
And the power consumed if the load were connected in star would be 36.05 kW.
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