Calculating Motor Impedance/Phase in a 3-Phase Delta Connection

When working with 3-phase delta-connected motors, understanding how to calculate the phase impedance is crucial for ensuring optimal performance and safety. This article delves into the process of determining motor phase impedance in a delta configuration, clarifying common misconceptions along the way.

Understanding Delta Connection

A delta connection is a method of connecting the phases of a 3-phase motor in a triangular configuration, where each phase is connected to the next, forming a closed triangle. In this setup, the phase voltages are equal to the line voltages, and the phase currents are related to the line currents. This configuration is often used in industrial applications due to its simplicity and efficiency.

Formula for Impedance per Phase

Calculating the phase impedance is similar to calculating phase resistance, but it includes both resistance and reactance. Here are the steps to determine the phase impedance:

Identify Parameters

To calculate the phase impedance, you need to know the total power (P), voltage (V), and current (I) of the motor. Additionally, you will need to calculate the phase voltage and phase current from these parameters.

Calculate Phase Voltage

In a delta connection, the phase voltage is equal to the line voltage. This can be expressed as:

[V_{ph} V_{L}]

Where:

(V_{ph}) is the phase voltage.

(V_{L}) is the line voltage.

Calculate Line Current and Phase Current

The line current is related to the phase current by:

[I_{ph} frac{I_{L}}{sqrt{3}}]

Calculate Impedance per Phase

The impedance per phase can be calculated using Ohm's Law:

[Z_{ph} frac{V_{ph}}{I_{ph}}]

Where:

(Z_{ph}) is the phase impedance.

(V_{ph}) is the phase voltage.

(I_{ph}) is the phase current.

Example Calculation

Let's consider the following motor specifications:

Line Voltage (V_{L} 400 V)

Line Current (I_{L} 10 A)

Calculate the phase voltage:

[V_{ph} 400 V]

Calculate the phase current:

[I_{ph} frac{10 A}{sqrt{3}} approx 5.77 A]

Calculate the phase impedance:

[Z_{ph} frac{400 V}{5.77 A} approx 69.3 Omega]

Conclusion

To accurately calculate the phase impedance in a 3-phase delta connection, you need to determine the phase voltage and phase current from the line voltage and line current. Understanding these calculations is essential for the proper operation and maintenance of 3-phase delta-connected motors. Always ensure you have the correct parameters to perform the calculations correctly.

Note that when dealing with large horsepower motors that can be started in a wye (Y) connection and then run in a delta (Δ) configuration, the motor typically has six terminals. To measure the phase winding resistance, isolate each phase coil, and use an ohmmeter. This ensures accurate measurements and helps in identifying any potential issues before they become critical.

It's important to clarify that impedance, not just resistance, is what is being measured in such calculations. Regardless of whether the power is presented in a delta or wye configuration, the impedance seen by the load remains the same.