Increased production of renewable energy as wind energy will give a fluctuating production which requires flexible energy storages. Heat capacity in single-family houses with electrical heating using heat pumps represents a storage which can be used to balance the electricity supply. It is assumed that electricity prices will reflect surplus or deficiency in production. A performance function describing cost of electricity combined hour by hour with user comfort is formulated. Minimization of this performance will balance the grid by pushing consumption towards hour with surplus production capacity. The minimization results in a power consumption schedule and a temperature schedule for each house. A number of control structures are described aiming to obtain this optimum by communicating references to either house temperature or heat pump power or by offering the consumer an hour by hour price. By simulation the schemes are compared by there ability to time shift consumption and to avoid consumer discomfort. Additionally the necessary information exchange for the schemes is discussed. Comparisons indicate that it is possible to use heat pump heated private houses to move power consumption within a time interval without loss of consumer comfort. However the full potential of the storage capacity can only be achieved in the schemes which combine feedback with an optimizing solution.