In regards to your query 'heating a tank from cold would take more power than just keeping a warm tank topped up'.
An important part of this management is stratification control; Within the same hot water cylinder it is possible to have both hot and cooler water.
The hot water will sit on top of the cooler water without it mixing. Cold water enters into the bottom of the cylinder and rises as a layer while hot water
is drawn off the top. Traditional style heating of the water will decrease and eventually destroy this stratification, unless you have a Smart Controller which will manage this heating to your advantage.
The Smart Controller knows where this stratification line is (the technical term is a thermocline), and to what degree the different water volumes might need heating to be useful for you. Only when absolutely necessary will it heat, and not before and even then use just enough energy to ensure you never run of hot water. So no waste of energy usuage.
This way a lot less heat (and money) is lost through the cylinder walls compared to keeping fully heated water in the entire cylinder. This can be quite substantial as testimonials from our customers confirm.
There are other methods of using stratification control with an iSmart Hot Water Controller for even greater savings if you are using, or intend to use, special energy sources such as a solar pv or solar thermal.
The idea is you only heat the hot water when you need it. With the iSmart Controller set your Profile Settings for the time when you want hot water available.
My power bill before the iSmart Controller
June to July - 667kW/month
July to Aug - 580kW/month
Aug to Sept - 321kW/month ( installed iSmart)
Sept to Oct - 325kW/month
Oct to Nov - 437kW/month
Here is a video link about the iSmart Hot Water Controller.
I've been in the home energy industry for over 20 years and my business partners have been in the hot water management industry for about 25 years. So together for the last two years we have been developing this technology, to help reduce the biggest hungry power device in peoples households.