I'm going to use fairly round numbers to keep this simple. The numbers are also intended to be optimistic, as well. At the current time, need to about double the cost to match reality.

Assume renewable energy has only the capital cost, and that is 10% per year of the installed cost of $1/watt. 10% cost implies some combination of maintenance, replacement and return of capital, summing to 10% of the invested cost per year. Might be 20 year life and 5% return on capital, for example. Assume that the capacity factor is .25, so cost per kWh of direct renewable energy is:

Cost per kWh = Installed cost *.1/(capacity factor*hours in a year)

= (1000 watts/kW)*1 * .1/(.25*365*24)

= $0.045 per kWh

This of course ignores several factors. The power distribution network adds to this cost, and that something else needs to provide power for much of the time, and if we generate more than a certain amount of renewable power we will start increasing the costs of the other power source, and if we generate more than the load we start needing to waste power. All of which suggest that while the first kWh might cost $0.045, once we get to 20% of load the cost will have risen. For example, suppose the other power source is natural gas, and assume the cost of generation is 2/3 fuel, 1/3 capital. Note that to the extent that renewable power is correlated with the peaks in energy use, it is at worst a straight displacement, and may actually improve the capacity factor of the rest of the system, which would under fair accounting slightly lower the cost of renewable energy. As more renewable energy is generated beyond this correlation, the fraction of capital cost for the other power source rises as it depends on the capacity factor:

Cost per kWh (natural gas, no renewables) = fuel cost + capital cost

= $0.06 + installed cost/(capacity factor * hours in a year)

= $0.06 +0.03

= $0.09

Assume the first 10% is no net change in gas generation capacity factor, and the second 10% is reduced capacity factor:

Cost per kWh (natural gas, 20% renewables) = fuel cost + capital cost

= $0.06 + $0.03/(reduced capacity factor)

= $0.06 + $0.03/(0.9)

= $0.06 + $0.033

As this is a cost associated with increasing renewable power, fair accounting would move this cost to the cost of the renewable power:

Cost per kWh(renewable @20% of load) = $0.045 per kWh + $0.003333/(fraction of renewable power)

= $0.045 per kWh + $0.003333/.2

= $0.045 per kWh + $0.016

= $0.061 per kWh

At 30% renewable, a choice. Add batteries, or shut down some renewable generation at peak times, or perhaps both? At the peak, there will be more renewable generation than load, so something has to change.

Shutting down some generation will increase the cost, as we are reducing capacity factor to improve availability. Batteries will increase cost, and they will not improve the capacity factor much as we are not yet wasting much renewable power, by shutting it down. Keeping phase stability (far beyond the level of this discussion) might require adding batteries even though the cost is higher.

If we shutdown renewable on the peaks as we are generating more than the load, the capacity lost is a little less than 1% using a fairly simplistic capacity and load model.

Cost per kWh = Installed cost *.1/(capacity factor*hours in a year)

= (1000 watts/kW)*1 * .1/(.24*365*24)

= $0.0476 per kWh

Again, adjust for the reduction in capacity factor on the fossil fuel source:

Cost per kWh(renewable 30% of load) = $0.0476 per kWh + $(0.03/.8-0.03)/(fraction of renewable power)

= $0.0476 per kWh + $0.0075/.3

= $0.0476 per kWh + $0.025

= $0.073 per kWh

As the amount of renewables increases, some will need to be shutdown at times to prevent producing more. This will further increase the cost of renewable power. So as costs are rising, we need to find an alternative "other" source.

So lets add some batteries to the mix. Assume batteries are 100% efficient, and last a long time, and the cost is 10% per year of the installed cost of $50 per kWh of storage (much less than the cost of BOB in Texas, the largest battery in the US. At this cost, a Leaf battery + charger + inverter would be $1,200). So how many batteries to we add to the mix?

Suppose we add 4 hours worth of batteries. The average capacity factor over a year isn't constant. We have a sunny, windy days, that might reach closer to 75% or more, and cloudy, windless days, that might be very close to zero. So on the best days, we might provide 100%, and on the worst days, zero. So what is the cost of renewable power? It is getting more complex, of course, as there are lot of questions that aren't that easy to answer exactly. How high of fraction of the load can the renewables supply? How will this combination realistically impact the other power source?

If more power is generated than can be used on the peak days, improving availability at the cost of capacity factor, then we might get close to 80% of the load supplied by renewable power. See:

http://www.reiner-lemoine-institut.de/s ... l_proc.pdf

Based on the above source, average load for that system is about 1.58MW and the average amount of wasted power is about 1MW. This works out to about a 60% reduction in the renewable capacity factor. (but an improved availability) The above source (Scenario A) has about 3.5 hours of battery.

Cost per kWh = Installed cost *.1/(.6*capacity factor*hours in a year) + battery cost

= $0.075 + 4 hoursStorage@$50/kWh *.1 / 365

= $0.075 per kWh + 4 hours * 50/kWh * .1 /365

= $0.075 per kWh + $0.054

= $0.129 per kWh

Ah, but what will that do to the cost of the other power (assumed to be natural gas)? First, we reduce the capacity factor for the other power from the original, by about 80%, but then we let the other power run at a higher capacity factor, by using the battery to level daily peaks. The first factor would increase the capital cost by about 5x.

Cost per kWh (natural gas, 80% renewables) = fuel cost + capital cost

= $0.06 + $0.03/(reduced capacity factor)

= $0.06 + $0.03/(0.2)

= $0.06 + $0.15

= $0.21

Again, fair accounting would add the excess cost ($0.12) across the renewable power

Renewable cost = $0.129 per kWh + $0.12/fraction renewable

= $0.129 per kWh + $0.12/5

= $0.129 per kWh + $0.024 per kWh

= $0.153 per kWh

Now, if you are still reading, and I've not made any major mistakes (and these estimates, again, are optimistic, and don't include network operation cost):

0% renewable Power rate will be $0.090 per kWh

10% renewable costs $0.045 per kWh Power rate will be $0.086 per kWh

20% renewable costs $0.061 per kWh Power rate will be $0.084 per kWh

30% renewable costs $0.073 per kWh Power rate will be $0.085 per kWh

80% renewable costs $0.153 per kWh Power rate will be $0.140 per kWh

When I hear a cost for renewable power, I ask, which price is being discussed? 10% of load, or 80% of load? 100% of load is rather more complex, and I'm going to avoid that for a bit. But notice that the price rises as the share of the renewable energy increases.

(edit 12/4/2013) added blended power rate, totaled "other" fossil fuel cost.

(edit 12/4/2013) Added 30% renewable, corrected typo)