Heat can be collected from local energy sources and concentrated into a relatively small volume, and at a useful working temperature, by using a heat pump as the concentrator. That heat can be stored and utilized at a later date for applications like space heating. The process is doing two things at the same time: storing heat and shifting the power demand. The concentration step can be done at night when there is normally a surplus of power and its timing can be directly controlled by the power grid operator to ensure that the power consumption occurs only when adequate power is available. The sources of heat can be the summer air, the heat extracted from buildings by their cooling systems, natural heat from the ground or solar heat, all of which are free, abundant and readily accessible. Such systems can meet the thermal needs of buildings while at the same time stabilizing the grid power demand, thus reducing the need for using fossil-fuelled peaking power generators. The heat pump maintains the temperature of the periphery at the ambient ground temperature so very little energy is lost during storage.