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VSD Motor Power, Speed & Torque – How and Why

We came across a situation recently on site where an induction motor being driven by a VSD at a reduced speed had the operators asking "Why is the motor running at the rated current but not at the rated power?"
It was actually a very good question and one that we thought we would share with you all.

First of all there are a few things to remember about a motor;

• Torque is a measurement of the amount of work the motor is doing.
  
• Power is the rate at which the work (torque) is being done. I.E. How fast the motor can deliver the torque or do the work.
• The motor’s power rating of is the maximum power that motor can deliver when it is run at the full rated speed (i.e. 50Hz).
  

The most basic method of control for an induction motor on a VSD is the Volts per Hertz (V/Hz) method, also known as open-loop or scalar control. This is where the VSD controls the motor speed by maintaining a constant ratio between motor voltage and frequency, as the frequency of the motor is reduced so is the voltage by the same ratio to maintain a constant magnetic flux.

If we have a look at the motor power formula, we see that the speed of a motor (shown as rpm) directly effects the power of a motor;

                HP = (t x rpm) / 5252               
Where;

• HP = Horsepower (1HP = 0.7457kW)
• t = Motor torque
• rpm = Motor speed
• 5252 = James Watt’s original test data of 33,000 / 2π

So the simple answer is whenever you reduce the speed of a motor below its rated speed, you also reduce the motor’s output power due to the natural relation between motor speed, power and torque.

This theory is often used for power savings in a plant or process by installing a VSD on a motor and running it at a reduced speed. Interestingly enough, if you drive a motor above its rated speed, the power remains at 100% but the torque will drop off at an approximate rate of base speed /actual speed.

Interesting Fact

The Horsepower and Torque curves for a motor
will always cross at 5,252 rpm!

If this is all too confusing and complex, think about the basic Direct Current (DC) power formula;

                P = V x I
Where;

• P = Power
• V = Voltage
• I = Current

Sure this a DC power formula and it doesn't take into consideration the power factor within an AC circuit, but the basic principle is the same. We learned above that the VSD is reducing the voltage (V) as well as the frequency to control the motor speed. So based on the formula above, the power (P) will also be reduced.

There are advantages and disadvantages to the V/Hz method of control but we will go into further detail on the various methods of VSD control in a future blog, so stay tuned!

In the meantime, here are a couple of fantastic YouTube clips on this topic that we think are worth watching.

What is Horsepower and Torque?

Motor production: Speed, Torque and Horsepower