It depends if the screen is turning itself off (power options), or just displaying a screensaver.
With a screensaver it does not go black to save electricity. It goes black to stop an image being "burnt" into the screen.
If the same image is left on a computer screen for too long then it can burn a faint outline of this image into the scren.
For screensaver then If you are using Windows right click on the desktop and select Screensaver to what that is set at.
For powering itself off, open the Windows Control Panel and select Power Options and look at the power options for your screen.
Note if it is a laptop it will behave differently if it is running on batteries than if it is plugged into the mains. On batteries it may switch off quicker than when plugged into the mains.