Abstract: Controllable variable inertia water storage system for heating and/or cooling, comprising: a plurality of water storage volumes for storing and heating water, these being either a vessel comprising sub-volumes or independent multiple vessels, said volumes being interconnected in series; a water inlet and outlet connect to the interconnected volumes; an independent water heater and/or cooler for each volume. Method for operating said system comprising: defining target sub-temperatures for each volume, wherein said target sub-temperatures are sequentially higher for each volume, in the direction of the water flow from inlet to outlet; increasing the target sub-temperatures in periods of forecasted higher demand, and, inversely, decreasing the target sub-temperatures in periods of forecasted lower demand; heating the volumes up to the target sub-temperatures, when the user indicates so or when a source of heat is available.