(jump directly to calculation tables)

We want to look at a very simple model of economic efficiency where are we interested in the annual return on investment. A project involving a solar photovoltaic installation requires certain amount of capital to be built and will expect certain amount of annual revenue. The simple indicator of efficiency that we want to study is this annual return on invested capital.

There are more complex models that also include the cost of capital. In a model that studies the cost of the electricity produced for example the cost of capital and factored in return for the investor could be very important factors. Cost of capital on its own can be a complex concept too. Whether the capital is borrowed and the cost will be defined by the interest rate of the loan or is cash participation from the investor and the cost will be defined by other opportunities the investor has to invest in (including risk free investments) or the combination of the two, cost of capital is very significant factor in such models.

We simplify our model to the level of looking at potential return from invested amount of capital. Further investment efficiency study and study on the cost of production of electricity should involve cost of capital.

We will also try to come to tables of calculated efficiency depending on different factors but not the size of the installation. The size of the installation definitely impacts the efficiency of a project. This is the traditional concept of economy if scales. A larger project will be expected to be more efficient over all because of the spread fixed expenses that the project has. But we will be building our model around the idea of dollar per watt, dollar per watt peak, so that it is applicable to different. The efficiency that comes from scale can be reflected in the factors going in to our model – specifically cost to build.

Another factor not included in our model is the maintenance cost of the solar installation. We are hoping that the reader can find resources which will indicate dollar per watt peak what the expected cost to maintain the station are.

The factors that expect to influence our model are: cost to build the power installation, insolation at the geographic location, electricity market price.

The cost to build the power installation includes:

• the price of the core photovoltaic components employed: modules, panels, arrays (what exactly list of such components we deal with depends on the design and configuration of the installation),
• the price of the mounting equipment (trackers and, or positioning frames) and wiring;
• price of inverters and grid connection equipment
• service and labor cost to assemble
• management and administration costs and costs of permits

The insolation at the geographic location. The insolation is the amount of solar light energy falling on the surface of the earth at a given geographic location per certain amount of area in the span of certain unit of time. More specifically the unit of measure used is watt per square meter (W/m²) or also kilowatt hour per square meter per day (kWh/m²/day). Insolation in Europe, just for reference purposes, approximately, ranges between 1,000 to 2,000 kWh per year per installed kWp, in the continental US – between 800 to 2,100 kWh per year per installed kWp for different regions. Exact numbers can be found in different reference tables and insolation maps on the internet and elsewhere.

In the photovoltaic industry a measure of insolation is employed which helps us more directly figure out how much electricity in kilowatt hours (kWh) we can produced annually from an installed nominal watt (Wp) – that is kilowatt hours annually per installed kWp (kWh/kWp/y).

The market price of the electricity produced. Since we are trying to figure out economic efficiency – annual return on investment we need to involve in the model:

• the price of the electricity we produce and sell to the grid

or conversely

• the price of the amount of electricity we offset that we were otherwise going to pay for at such market price.

In many places in the world – by country or by specific territory (state, other subdivision) there are financial incentives for investors in photovoltaic power stations in the way of a special feed-in-tariff. These usually are higher price the grid pays to energy producers who utilize photovoltaic power stations. If we have to give some examples these countries have the following feed-in-tariffs (unit of measure is Euros per kWh since classically many of the notable incentives started in Europe and that is the currency used there): Austria 0.57 – 0.59, Germany 0.52 – 0.57, Italy, 0.36 – 0.49, France 0.30 – 0.55, Spain 0.19 – 0.44, Switzerland 0.10 – 0.50, Israel 0.14 – 0.16, Bulgaria 0.40.

The formula.

The annual return on investment in a solar power station will be the annual income from sold (or offset electricity) divided by the amount of the investment.

Annual return on investment = annual income ($) / investment amount ($).

The annual income is the market price of the electricity in dollar ($) per kilowatt hour (kWh) times the amount of energy produced in an year in kilowatt hours (kWh).

Annual income ($) = production per year (kWh) x market price ($/kWh)

The production per year is the solar insolation in kilowatt hours per year per kilowatt peak installed times the installed capacity/power in kilowatt peak (kWp).

Production per year (kWh) = insolation (kWh/y/kWp) x installed capacity (kWp) .

So that we can work on dollar per watt basis we will express the investment amount by the investment cost per watt.

Investment amount ($) = total cost per watt ($/Wp) x installed capacity (kWp) x 1,000

– the 1,000 factor  is to adjust the dollar per watt unit to the kWp in which we are measuring the installed power.

So the complete formula for the annual return on investment will be:

Annual return on investment = annual income ($) / investment amount ($)

If we use the formula for the annual income we get:

= production per year (kWh) x market price ($/kWh) / (total cost per watt ($/Wp) x installed capacity (kWp) x 1,000)

If we use the formula for the production per year we come to:

= insolation (kWh/y/kWp) x installed capacity (kW) x market price ($/kWh) / (total cost per watt ($/Wp) x installed capacity (kWp) x 1,000)

Here we can get rid of the installed capacity (kWp) in the numerator and denominator and get to:

Annual return on investment
= insolation (kWh/y/kWp)   x   market price ($/kWh)
/  ( total cost per watt ($/Wp)   x   1,000 )

Let’s use the formula in an example where $7 per watt were spend in the building of the station, the insolation is 1,200 kWh per installed kWp and there is a $0.52 feed-in-tariff for the electricity produced.

Annual return on investment = 1,200 x 0.52 / (7 x 1,000) = 624 / 7,000 = 8.92%.

This calculated rate now can be compared to cost of capital and maintenance cost can be factored in to look for some more complete number of real economic return.

In addition to this formula the following tables can be used to get to approximate numbers:

The first table is given for insolation of 1,000 (this can be easily factored if we know the specific insolation, i.e. for 1,500 we just have to multiply by 1.5, for 2,200 we simply multiply by 2.2, etc.)

The investment cost per watt is given in a very wide range of $3 to $10 per watt but it is not implied that these are possible, practical or easy to obtain prices in reality. Our research shows that large industrial project can reach down to $6 per watt of such cost and smaller commercial and residential projects can go up to $10 and even $15 per watt peak installed.

The price for kWh of electricity is given in a range of $0.05 to $0.60 to reflect different market prices for electric energy and all possible feed in tariffs.

Annual Return on Investment At Insolation of 1,000 kWh/kWp:

Annual Return on Investment At Insolation of  1,500 kWh/kWp:

Annual Return on Investment At Insolation of 2,000 kWh/kWp:

To factor in the cost of capital  in the numbers from these tables one needs to subtract the cost of capital as a percentage. For example if the cost of capital is 4%  that has to be subtracted from the numbers in the tables above. Similar adjustment can be made for to factor in the maintenance costs.

Configuration efficiency, (performance ratio). We do not know whether this term is discussed in other research in length but we want to mention it for this reason: projects with equal labeled peak power – watt peak (Wp), nominal power, if taken directly from the labeled peak power of the modules involved can have different overall output electricity production – kilowatt hour (kWh) per year at the same geographic location. This could be because of how different modules perform when positioned with trackers or mounted stationary, or how well they perform in different cloud conditions etc. etc. So, realistically the nominal installed power (Wp) that can be used with insolation numbers to figure out annual production can be different for different installations mainly because of the type of modules used a the specific conditions (insolation, cloudiness, positioning etc.) For the different projects this factor has to be specifically researched based on data from similar configuration used in existing projects. By information we can get to such factor can vary between 0.75 and 1.4 – i.e. the electricity produced in a year from the installation in kWh may vary from the above calculation for known insolation from –25% to +40% from the indicated.

Related Articles:

Solar Energy Land Area Efficiency or How Many Acres per MW, kWp per Acre

Can Solar Energy Completely Replace Fossil Fuel and Other Sources?

A Short Science Lesson for Journalists – Watts, Kilowatts, Megawatts, Kilowatt Hours

Lowest Solar Panel Prices Per Watt 2009-02-24

Resources:

http://en.wikipedia.org/wiki/Photovoltaic

http://en.wikipedia.org/wiki/Insolation

http://en.wikipedia.org/wiki/Feed-in_Tariff

http://en.wikipedia.org/wiki/PV_financial_incentives