The rising penetration of vapor compression air conditioning systems in Australian dwellings has raised the peak power demand. Consequently, the electrical infrastructure requires significant, costly upgrades that is invariably passed on to all end-users. Electricity network charges account for about half the cost of an average household electricity bill, causing electricity prices to reach some of the highest levels in the developed world. Standalone solar air conditioning systems offer a radical demand side energy management solution, but have drawn criticism due to the initial high capital investment of the required components. This paper combines simulations and optimization techniques to correctly size an inverter-driven reverse cycle vapor compression air conditioner, with photovoltaic panels and battery bank to form a cost effective standalone solar air conditioning system, for a typical Australian two-story house, in three vastly different Australian climate zones. TRNSYS is used to configure these components and perform dynamic simulations, whilst GenOpt is used to carry out the optimization. Probability in yearly hours loss of load expectation is used for sizing and system life cycle cost is used for the economic assessment. It has been found that the life cycle cost of most optimized complete component configurations is AU$ 49,160 in Brisbane, AU$ 80,085 in Adelaide, and AU$ 114,906 in Melbourne. The cost of the standalone photovoltaic system alone was higher than that of an air conditioner powered by grid electricity, and the payback period exceed 20 years in the three locations. The levelized cost of electricity for the photovoltaic systems to power the air conditioner is 2.45 in Brisbane, 1.5 in Adelaide, and 1.48 AU$/kWh in Melbourne respectively which is far higher than current fixed tariff.