PV-Battery, Residential, Calculation of LCOE

How is the LCOE calculated? or how do the buying and selling prices (electricity rates) affect the calculation of LCOE?
I am using Net Billing method and I know that the LCOE is 
Equity / Lifetime Electricity Generation
Assuming no taxes and no losses or degradation, no inflation or annual costs, etc..
Assume a system with equity of 2168$ generating 2000kWh annually, assuming no inflation and so on:
Lifetime output = 2011.23 * 25 (kWh)
With electricity rates both zero
LCOE = 2168$  / 2011.23 * 25 (kWh) = 4.3117 ct/kWh

However when there are electricity rates, the LCOE becomes different, it seems to have the following equation
LCOE =  Equity / Lifetime Electricity Generation + X * C_buy - Y * C_sell
C_buy, C_sell are electricity rates by the grid, and X and Y are constants, that I am not sure what they represent. I have tried to go through some definitions of LCOE and LCOSS through the internet but haven't been very successful. Would really appreciate any help or leads.

Thank you

Hi Mustafa,

You can find a detailed description of SAM's LCOE calculations in Help.

The LCOE accounts for the cost of the system, but not for its value, so the electricity rates for a behind-the-meter project (including Residential) do not affect the LCOE.

Best regards,
Paul.

Hi Paul,

I have read the description of SAM's LCOE calculation in Help. Of course according to the definition there, the electricity rates have no effect.

However I change them, the LCOE changes and the difference is proportional to the changes. Here is an example with the same settings as before:

Net Billing

buy ($/kWh)	sell ($/kWh)	LCOE (ct/kWh)	Difference / (price_sell or price_buy)
0	0	4.31173
1	0	4.44457	0.13284
10	0	5.64012	0.13284
0	1	3.61287	0.69886
0	10	-2.67685	-0.69886

I made the buying and selling prices from the grid extreme for demonstration, and the only change was the price rates.

The equations used in SAM help are the same ones used in the Excel spreadsheets, if I was to export the Cash flow results to excel with equation, the LCOE becomes just like described in Help. But in data tables single values and in summary it is clearly different.

So I wonder where that comes from. I tried moving the changes to the numerator of the LCOE equation assuming the values in (kWh) but got the following values: 265.47 kWh and -1396 kWh, I assumed the rates were multiplied with some energy but the values also do not represent anything.

I would really appreciate any help  

Best regards,
Mustafa.

Hi Mustafa,

Attached is a .sam file with a parametric simulation set up to do the comparison you describe below. Here are results from that file showing that the LCOE remains constant over the range of buy and sell rates while the NPV and annual bill savings change:



Click Parametrics under the Simulate button to see how I set up that analysis.

The electricity bill calculations are not replicated in the Excel file that SAM uses for "Send Excel to Equations" because those calculations happen on a time-step-by-time-step basis and are too complex to replicate in Excel for each of the billing options.

Best regards,
Paul.

Hi Paul,

thanks for the quick response, I reckon that the simulation you have used is PVWatts, Commercial, however I am interested in PV-Battery-Residential.

I have run the simulation for PVWatts-Battery, Residential and here is the result:



The LCOE for zero electricity rates is 3.78219, when the buying price becomes 1$ the LCOE becomes 8.60424, the difference is 4.82205.

Now for buying price of 10$ the LCOE becomes 3.78219 + 4.82205 * 10$ = 52.0027 exactly as in SAM.

The same happens for the selling price, there is a linear dependency.

Now here is for my original question for PV-Battery, Residential:

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Hi Mustafa,

Thank you for the clarification.

For behind-the-meter systems with batteries, SAM accounts for the cost of charging the battery in the LCOE calculation. This is explained in the description of LCOE in Help:



This approach ensures that comparing the LCOE for projects with and without storage is meaningful.

The note later in the topic that says "For distributed behind-the-meter projects, the retail electricity prices from the Electricity Rates page do not affect the LCOE." is misleading. That is only true for projects with no storage. I will revise that for the next update to SAM.

You can see the calculation in the C++ source code here. The CF_parasitic_cost variable represents the cost of charging the battery:

github.com/NREL/ssc/blob/ca964fc280268b4e4efe686dc66c3c01ad555430/ssc/cmod_cashloan.cpp#L1141

Best regards,
Paul.