# Grid Connected Solar Power Model

Grid connected electric power provides opportunities for households and businesses to reduce electric power costs by both offsetting the cost of power used, and selling back electric power to the local power grid. Solar power provided by arrays of solar modules is probably the least maintenance intensive of the methods available.

The mathematical models already described on this website for solar modules and atmospheric absorption can be used to extend the simulation program developed for a remote battery backed system. The program is written in C++ for Linux using the Eclipse IDE (proejct files are included). This is currently in a rather minimal state, and is only provided as source code under the GPLv2 licence. It may later be ported to JAVA with a suitable user interface. Documentation (in OpenOffice format) on the models and program is also provided.

The extension to the models is simply to compute a value for the financial return from the system over a day.

Let P be the instantaneous generated power, PT the usage power, re the feed-in tariff, and ro the cost of power.

r = roP(1-H(P-PT)) +  roPTH(P-PT) + re(P-PT)H(P-PT)

where r is the actual return rate and H(x) is the Heaviside function, which is 0 for x<0 and 1 otherwise. The first term is the financial return rate whengenerated power is below the usage power, the second is the portion of return rate for offset to usage when generated power is above the usage power, and the last is the portion of return rate for generated power returned to the grid. This is integrated over a day and summed over a year to obtain an estimate for the annual return on investment.

For the purposes of comparison between different feed-in tarrifs, it is sufficient to compute the multipliers to the two costs re and ro rather than run the entire simulation for each tariff value.

Among the assumptions used in the simulations is included that of ignoring the effects of cloud cover. Bureaux of Meteorology provide fractional cloud cover averages for each month, but these are only of value if all cloud cover results in zero power generated. They could be used to obtain a lower bound of financial returns. A more accurate computation would use measured averages of solar irradiation over each day; such data most likely isn't available.

An example based on an actual system shows that with a capital rebate of \$8000 on a system of 24m2 of thin film amorphous Si panels at a total cost of \$15,000, a feed-in tariff of 60¢ per kWH, a usage cost of 18¢ per kWH and an average daytime usage of 0.33kW, the yearly return would be \$950 giving a rate of return of 13.5%. The effect of cloud cover would reduce this by roughly 30% giving an approximate rate of return on investment of about 10-11%. This drops to about 8% for a feed-in tariff of 44¢. For a low risk, low maintenance investment this is quite attractive.

First created 5 August 2009