What does your fan's on/off switch look like? Multi-position rotary switch or single "electronic" button?

smart plug can only turn the power on and off.
It can't control the device. It seems that your fan need a switch or remote controller to use it.

Here’s a quick test:- Plug in fan without module- turn on fan- unplug fan- plug in fanIf the fan is not on when you last plug it in, the module won’t work for you. The switch on most modern devices defaults to "off." A module will always turn it off, as you are removing power to the device. However, the power button must be pressed to turn on the device. Merely restoring power to the device will not turn it on. You need to press the button.

I will test the fan as indicated. The fan has a push button (single electric) and has a remote. I knew I would not be able to change fan speeds with tp-link but am disappointed that it won't turn back on.
Thanks for the feedback!