How to disable second display when physical device (HDMI projector) turned off?

Hi,

I have an Epson 3020 HD projector permanently connected to iMac (later 2013) via an HDMI-to-Thunderbolt adapter. It shows as a second display in Mac OS.

For Mac OS, the second display stays connected, even when the projector is switched to "off" (standby). This is problematic as often apps/docs end up on the second display, which is not actually running/visible.

How can I (can I?) set things up in a way that when the projector is switched off, Mac OS stops seeing it as a second display (automatically, without physically unplugging or changing settings each time)?

Thank you!