Calculating Total Three-Phase Power for a Balanced Load Connected to a 400V 50 Hz 3-Phase Supply

When a balanced three-phase load is connected to a 400V 50 Hz 3-phase supply, the calculation of the total three-phase power involves several steps. This article will guide you through the process of determining the total three-phase power for such a balanced load with an impedance of 10 ohms per phase. We will use both the given formula and a simpler alternative method to ensure a comprehensive understanding.

Understanding the Basics

A three-phase power system is commonly used in industrial and commercial applications, featuring a balanced load where each phase is identical. The impedance of each phase is given as 10 ohms, and the supply voltage is 400V at a frequency of 50 Hz (though the latter is not required for power calculations).

Step-by-Step Calculation

Step 1: Calculate the Phase Voltage

In a Y-connected (star) configuration, the phase voltage V_p can be calculated using the following formula:

V_p frac{V_L}{sqrt{3}} frac{400}{sqrt{3}} ≈ 230.94V

Step 2: Calculate the Phase Current

The phase current I_p can be calculated using Ohm's Law:

I_p frac{V_p}{Z_p} frac{230.94V}{10Ω} ≈ 23.094A

Step 3: Calculate the Line Current

In a Y-connected configuration, the line current I_L is equal to the phase current:

I_L I_p ≈ 23.094A

Step 4: Calculate the Total Three-Phase Power

For a purely resistive load, the power factor cosφ is 1. The total three-phase power can be calculated using the formula:

P_{total} sqrt{3} times V_L times I_L times cosφ

Substituting the values:

P_{total} sqrt{3} times 400V times 23.094A times 1

P_{total} ≈ 1.732 times 400 times 23.094 ≈ 16058.7W

The total three-phase power is approximately 16.06 kW.

Alternative Method

Another way to find the total three-phase power is to use the simpler method:

Step 1: Calculate the Power in Each Phase

Using the phase voltage and phase current:

Power_{each} V_p times I_p frac{400}{sqrt{3}} times frac{40}{sqrt{3}} frac{16000}{3} VA

Step 2: Calculate the Total Power for Three Phases

The total power for three phases is:

Total Power frac{16000}{3} times 3 16000 VA or 16 kVA

Alternatively, for a purely resistive load, the total power can be calculated using:

Total Power sqrt{3} times V_L times I_L sqrt{3} times 400 times frac{40}{sqrt{3}} 16000 VA or 16 KV

Conclusion

The calculation of three-phase power for a balanced load is essential in understanding the electrical demands of industrial and commercial applications. Using the detailed steps provided above, you can ensure accurate calculations and efficient power management.