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For LCD screens, you can make a screensaver, that shows white color instead of black. LCD works in that way, that power is needed to make black color. White is the natural state of the screen, so it only uses power for backlight. And if you turn of the screen light, then it saves power completely. Try white color with a voltmeter.
With plasma and CRT screens black is the natural state of them, so showing black should save power. But those screens are eating more of it naturally.