Let's make our homework at what it would take to convert Australia to 100% renewable energy.* Not to make the exercise extremely complex, let's simplify it a bit by using only solar photo-voltaic (PV) in our calculations.
According to the IEA (International Energy Agency) Australia's electrical energy supply in 2013 was 228,152 GWh. To convert this to average power consumption we divide it by 365 and then by 24 to arrive at a figure of ~26 GW average power consumption.
If we consider that the capacity factor (CF) of solar PV in Australia is 20%, then the solar PV capacity that needs to be installed is:
26GW / 0.20 = 130 GW. At $2 dollars per watt that would add up to $260 billion dollars (~$11,000 per person).
Let's also consider that at peak hours, Australia actually consumes 50% more than the average power and thus their typical peak consumption would be 26 GW x 1.50 = 39GW.
This means that, say, at noon in central Australia, we would have a surplus of 130 - 39 = 91 GW.
Thus, at many instances during the year most of the solar capacity would have to be disconnected to prevent destroying the electrical grid. This would mean that the effective capacity factor of solar would be considerably lower than 20% and thus more capacity would need to be installed but this would make the excessive production at many instances during the year even more problematic.
On the other hand and obviously, during the night there would be no energy production.
So, OK, by themselves the solar panels would not be able to supply the energy Australia requires but we can always use storage to smooth the power delivered.
Considering that in winter days are shorter let's add enough storage for 14 hours of the average consumption. That would be 14 x 26 GW = 364 GWh.
Considering Tesla S grade batteries for the above, a total of approximately 2,330,000 tons of batteries would be required. The above would represent ~100 kgs per person. Sure, lithium batteries are among the lowest weight technology, other chemistries would be heavier.
According to IEA's latest electric vehicle report, the cost of this type of battery could reach ~$200 dollars per kWh by 2020. That would represent a total cost of ~$73 billion dollars. Sure, other chemistries might be less expensive. This would represent ~ $3,100 dollars per person.
Adding the panels ($11,000) plus the storage ($3,100) gives a total of $14,100 per person. Sure, this is only the upfront investment. Every so many years the batteries would have to be replaced, as well as the panels.
However, the above system wouldn't provide reliable electricity on an annual basis, as we know the insolation in Australia is relatively low from April to August. More storage would make it somewhat more reliable but the total cost would increase.
Feel free to make your own calculations and share your comments if you get different numbers.
* We are considering only electricity which is a fraction of Australia's total energy consumption that includes fuel for transportation, for industrial processes, etc.
http://www.gaisma.com/en/location/sydney-au.html (data for individual cities).