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In Japan, it is expected to establish the smart grid as a power system into which a large amount of generation from renewable energy sources such as wind power generation and photovoltaic generation can be installed. A large penetration of these renewable energy sources causes some problems in power systems, e.g. distribution voltage rise and frequency fluctuation. Our research group has developed a supplementary Load Frequency Control (LFC) method by use of Heat Pump Water Heaters (HPWHs) as controllable loads. Such control methods are developed and tested in general based on numerical simulations. This paper proposes a lumped HPWH model for simplifying such numerical simulation which is statistically designed taking into account customers' convenience and uncertainty. The model can approximate well the behavior of a number of HPWHs. The effectiveness of the frequency control method by the HPWHs is also evaluated by simulations based on the proposed lumped model.