I believe the "Green Plug" is probably a power factor controller. They're specifically for induction motors and this one might be specifically for the induction motor in a refrigeration compressor. The rationale behind the device is that motors have to be designed to start up and run on the lowest expected supply voltage. At nominal or greater voltage, the motor is over-driven. The back-EMF is limited by the RPM, which can't increase very much because an induction motor requires some "slip" to produce torque. The excess supply voltage therefore appears across the motor's equivalent load inductance and therefore contributes reactive current - hence the increasing phase lag and lower power factor. The extra current is not purely reactive, however, because it also increases the copper and iron core losses, so power consumption is increased. Reducing the supply voltage to not much more than necessary to run the motor thus improves efficiency.
I had a device about 30 years ago called the "Watt Wizard" which I used on my refrigerator. It was damaged by an electrical storm (which also took out a lot of other electronics in my apartment), and when I opened it up to repair it I found the markings on an IC had been removed. I wound up tracing out the circuit to identify its function (it was a quad op-amp). It had a manual adjustment to tweak it for whatever motor it was powering. Without the Watt Wizard, I could hear a whine from the compressor - sounded to me like 360 Hz (I'm in the land of 60 Hz power) but I never confirmed that. With the Watt Wizard operating, that whine disappeared. The device monitored the phase lag of the load current and reduced the RMS voltage by delaying the triggering of a Triac until the phase lag relative to the applied voltage was reduced to match the manual adjustment. If the phase lag decreased rapidly (due to e.g. increasing mechanical load), the unit would immediately apply full voltage to prevent stalling. This would happen when I opened the refrigerator door and the incandescent lamp lit. It can only control a single motor properly - fortunately the small fan motor could run just fine on lower voltage than the compressor could.
As you would expect from the above, the Watt Wizard did nothing to reduce the startup current. It did reduce the running current. I believe, however, that the startup current could be reduced substantially by using a voltage/frequency controller. The start winding would probably have to be supplied a controlled current at 90 degree leading phase angle. This would also eliminate the start capacitor and thermistor. Without matching the voltage and frequency of the supply to the speed of the motor as it's starting up, the motor is terribly inefficient during startup.
It must be noted that the mechanical load on the compressor increases rapidly as the refrigerant is compressed. This may limit the startup current reduction which can be achieved.
