Monday, November 16, 2015

Levelised Cost of Electricity Storage

RenewEconomy had an interesting story recently by Ramez Naam about the likely decrease in costs of battery storage.  This relates particularly to the learning curve, or how quickly costs fall for every doubling of installed capacity.  Naam cites Bloomberg, the Electric Power Research Institute and a private enterprise (Applied Materials) and suggests that the learning rate for battery storage is in the range 15-21%.

I too have written about the learning curve for battery storage – see my post of April 2015 that relies on the work of two academics, Nykvist & Nilsson.  Their estimate of the learning curve is slower, about 14% for general battery storage and 8% for automotive applications.  Whatever, everyone agrees that the cost of battery storage will continue to fall for several years at least.

Note that the above discussion refers to the capital cost of installation, measured in units like $ per kWh installed capacity.

But that begs the question of the cost of battery storage in an operational sense when capital costs and operating costs need to be included.  Let me call that the Levelised Cost of Electricity Stored, LCOES.   I should note that Naam gives figures for LCOES, but does not give the methodology, and that’s the purpose for my post today.

Here’s the notation I’ll use:

P          cost of the installed system [$]
C         capacity of the installed system [kWh]
d          depth of discharge on a sustainable basis [-]
N         lifetime of battery at daily discharge d [years]
i           weighted cost of capital [-]
m         maintenance cost per year as fraction of installed cost [-]

The first thing to calculate is the capital recovery factor, R.  This is the rate at which the capital cost must be repaid over N years, given that the weighted cost of capital is i, and so that no further payments are required after N years.

The answer (see e.g. Wikipedia) is

R = i * (1+i)^N / { (1+i)^N – 1}.

Here’s an example:  suppose we wish to pay back $1,000 over 20 years given that the weighted average cost of capital is 6%.  Then the capital recovery factor is

R = 0.06 * 1.06^20 / { 1.06^20 – 1} = 0.08719 approximately.

So to pay back $1,000 over 20 years when the weighted cost of capital is 6%, the required annual payment is $1,000 * 0.08719 = $87.19, each year for 20 years.  Inflation is not included in this simplified calculation.

Let me now give the basis for estimation of Levelised Cost of Electricity Stored, LCOES.  My standard assumptions are:
  • there is no inflation,
  • taxation implications are neglected,
  • all projects have the same annual maintenance and operating costs (say 1% of the total project cost), and
  • government subsidies are neglected.

Variables will be capacity (C), price (P), weighted cost of capital (i), depth of discharge (d) and lifetime of battery (N).

Annual costs ($) are as follows:

Capital cost:              P * R
Maintenance cost:    P * m
Total cost:                  P * (R + m)

The annual output (kWh) will be

C * d * 365

Hence the Levelised Cost of Electricity Storage is

LCOES = P * (R + m) / {C * d * 365}  in $/kWh

Examples of systems at 10 kWh capacity

Pessimistic assumptions (for Australia in 2015):

P = $5,000, i = 0.10, d = 0.6, N = 10 years.
Result: $0.394 per kWh

Neutral assumptions:

P = $3,500, i = 0.08, d = 0.7, N = 12 years.
Result: $0.195 per kWh

Optimistic assumptions:

P = $2,500, i = 0.06, d = 0.8, N = 14 years.
Result: $0.101 per kWh


To install your home battery system under the neutral assumptions, your actual costs will be $0.195 per kWh.  If you are coupling your battery system with a rooftop PV system, then you would have additional costs of say $0.15 - $0.20 per kWh (and that’s taking into account the government small-scale technology certificates).  At this stage, in 2015, home battery storage is for enthusiastic early adopters, not canny investors.  I expect the results will be more favourable in a few years.

Note added (18 November 2015)

Let me make a link to a related report by Lazard on the Levelised Cost of Storage.  I should also note that I’ve assumed that charging is 100% efficient, which is not the case.  It would be simple to subtract from the annual output C*d*365 so as to account for charging inefficiency.