This paper determines the optimal capacities of wind turbine and battery energy storage for grid-connected households in South Australia. The current market price of the system components, electricity rates (retail price and feed-in-tariff), and hourly one-year real data of load demand and wind speed are carefully incorporated into the optimization process. Net present cost in 20-year time span is considered as the objective function. A rule-based energy management strategy of the household is proposed. Two configurations of integrating the wind turbine (with and without battery energy storage) are considered. Each configuration is analysed for three different scenarios based on the capital expenditure limitations. The optimised system is compared with a zero-net energy home in South Australia. The effect of the optimised system on the load duration curve in South Australian electricity market is investigated. Annual operational results for the optimal system are presented and discussed. The payback period of different wind turbine capacities is provided. It is found that the payback period of the optimized wind turbine (6 kW) is 13 years and it works better than the capacity for a zero net home energy (3 kW) in terms of the cost reduction.