Thermal energy storage apparatus, controllers and thermal energy storage control methods are described. According to one aspect, a thermal energy storage apparatus controller includes processing circuitry configured to access first information which is indicative of surpluses and deficiencies of electrical energy upon an electrical power system at a plurality of moments in time, access second information which is indicative of temperature of a thermal energy storage medium at a plurality of moments in time, and use the first and second information to control an amount of electrical energy which is utilized by a heating element to heat the thermal energy storage medium at a plurality of moments in time.