alt Hacker NewsSo this is specifically about Toyota's hybrid engines (which is very different from e.g. Honda's engine, not to mention plug-in hybrids or "mild hybrids"). The explanation of the mechanics starts around the 36 minute mark.
I always found most explanations of Toyota's Power Split Device too abstract, until I found this page where you can play with the sliders to see how the power is actually split between the ICE and the MG1/MG2 electric generators: https://eahart.com/prius/psd/
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Note that Ford's plugin hybrids (using the same 2.5L engine as the full hybrids) also use the same technology (due to them having a cooperation and patent sharing agreement with Toyota) though they do differ a tiny bit due to the engine.
The tool is interesting though the Ford system can run independently on MG2/MG1 alone up to about 130kph (~80mph) depending on requested torque and load.
Only thing Ford screwed up is the battery (or Samsung since this time it's the cells).
Fun story: I used to own a Prius, and it turns out they expose the speeds and torque values of MG1, MG2, and the engine independently on the OBDII port.
What this means it that you can set up an app like Torque[0] and add widgets that show you how fast each of the motors are spinning, live, and watch what happens when e.g. the engine starts: MG1 and MG2 both torque the engine forward, MG2 just enough to stop the car from attempting to roll backward in response to MG1's torque through the planetary gearset, and then MG1 spins up with the engine and then stops torquing it once the engine reaches idle.
Battery charging while idling is similar: MG1 turns itself into a generator, fighting the engine and generating electricity in the process. The throttle opens considerably, as if you'd pressed the accelerator halfway to the floor, but MG1 and the engine work together to keep the engine's RPM around ~1,200 so you'd never know it - it's as if you're driving up a really steep hill that stops you from accelerating even though you have the gas pressed halfway down. And then MG2 torques backward to stop the car from rolling forward any more than the Prius's normal "simulate a normal gas car's tendency to roll forward when the user lets their foot off the brake" would have it do.
It was fascinating to watch, and I kind of regret not building an app similar to the parent comment's link that showed what my car was doing in real time with the gears drawn out like that.
[0]: https://torque-bhp.com/