Nikola Tesla “discovered” that efficiencies changed with applied frequency, although for him, there was no simple way to change the frequency without changing the generator. His first AC motors on pumps powered off of Niagara Falls were 25Hz because he experimented and found that to be the ideal frequency for motor efficiency. The pumps that were keeping New Orleans dry were still 25Hz up until hurricane Katrina (which was part of the problem getting them back on line after the generators were flooded). We later settled on 50 or 60Hz for lighting to avoid detectable flicker, so once that became the distribution standard, motor design standards were made to match.
Variable speed of AC motors was “invented” in 1921 at Westinghouse by Benjamin Lamme, the engineer who implemented Tesla’s generators at Niagara, using a motor-generator set. That technology was used extensively until solid state electronics came along. This later became what was known as a “Ward-Leonard Drive” system, very common for hoists and ship cranes. After WWII, there were so many Ward-Leonard drives taken off of Navy and Merchant Marine ships and given to industry for virtually no cost, that they remained a dominant type of variable speed control for decades.
The first solid state variable frequency drive was made in 1958 at GE using thyristors, a type of SCR, which were the dominant form of VFD for years because transistors were not yet reliable. These eventually morphed into what were called “Current Source Inverters” and were very bulletproof, but the thyristor firing was dependent on the motor circuit, so had to be “tuned” to each motor in the initial setup, then re-tuned if the motor changed. These were still being used right up into the 1990s when PWM drives made it unnecessary to tune the drive to the motor.
The first PWM transistor drives were invented in 1960 by Martti Harmoinen at Stromberg in Finland, but it was for large motors used in traction drives on streetcar systems. Stromberg later was merged with Asea and a Swiss company called Brown Boveri to become ABB.
The first commercially available small packaged PWM VFD as we know them today was developed and released by Yaskawa in 1974, but we didn’t start seeing widespread adoption of that technology until the late 1980s - early 1990s in the US. The big explosion in PWM VFD use happened when transistor technology changed radically with MOSFET type transistors that were smaller-cheaper-faster, slowing them to be miniaturized because they gave off less heat and thus able to become hyper efficient (by comparison). That really took off in the late 90s, early 2000s.
So the concept itself is as old as the AC motor, but the ease of implementation was only facilitated recently (comparatively) with the advancement of technology.
