Overview – This calculator is designed to output various forms of ROI (Return on Investment), payback time, cost savings, etc., resulting from installing green or “clean” electricity generators, such as solar PV (photo-voltaic), wind turbines and energy conservation measures (solar water heaters and energy-efficient appliances). But contrary to standard mortgage calculators, which start with a given term to pay back a bank loan, this calculator assumes that the generated average annual “clean” electricity reduces the electricity bill of the consumer or generator owner, and that this dollar amount, calculated for the first year, is equal to the “fixed,” annual loan-repayment thereafter. All costs are based on actual, rather than constant 2010 dollars, i.e. the effect of inflation is not explicitly included, but the interest on the bank loan is one of the inputs. In its revised version, this Calculator now accounts for inputs of electricity price escalation rates and bank loan compounding frequency.
All these and other needed Calculator inputs are detailed in the Appendix. Some illustrative Calculator results are described further down. Click here to launch the Calculator. The default values listed under “Calculator Inputs” correspond to the author’s home PV system, installed in Kona, Hawaii, Nov. 2009. After entering the desired inputs and pressing the “Calculate” button, the new outputs appear on the right side of Table 1. The Calculator can “Memorize inputs,” so that after the user presses that button, that set of inputs can later be retrieved by pressing the ”Reset inputs” button, after running different scenarios.
- Electricity Credits – Can get credit for all of the electricity produced by the green generator (such as solar PV, wind, etc), at a $/kWh rate or cost entered as input, and corresponding to the one the user would pay if the investment in clean or conservation energy had not been made. This version of the Calculator provides no means to account for excess electricity generated beyond what is consumed, which would be subject to provisions stated in the FIT (Feed-in-Tariff) or NEM (Net Energy Metering) agreement with the local utility. The Calculator does account for the Minimum Monthly Charge (MMC) some NEM agreements impose when the net electricity used from the grid is or approaches zero.
- Capacity Factor – Knows the value of the local wind or solar capacity (or use) factor, F. In the case of PVs, F can be calculated from average daily insolation, x, in cal/cm2/day: F = x*4.184/360/24*100 in % or from average daily peak sun hours, H, in h/d (hours/day): F = H/24*100 in %. For wind generators, and depending on location and altitude, F can range from 10 to 50%. For energy conservation based on installing higher efficiency appliances such as a window air conditioners,, the ~1000 annual hours of power-saving operation would be represented by F = 1000/8760 = 11.41%.
- Installation – In the case of PVs, the panels are not shaded by trees or other buildings. In the case of wind generators, the higher the elevation of a wind generator, the higher will be the local capacity factor.
- Tax Credits – Knows how much tax credit to enter as input, e.g. for PVs: Federal: 30% with 0 $ cap, and Hawaii State: 35% with a cap of $5000, or refundable credit of 24.5%, in case of insufficient tax liability. If a tax credit exceeds a cap, the Calculator adjsts the % input for state refund. The percentages for wind or for “conservation” generators are different.
- Return on Investment (ROI) – Wants to compare the rewards from investing in clean or conservation energy with those from placing funds into a savings account. The Calculator therefore calculates “fixed” bank-loan repayments with interest during the payback period, as described above, and outputs:
Max state tax credit/refund 35 % or 5000 $ (cap)
Crude oil cost 80 $/barrel
Now we can consider the effect of the following input variations, relative to those above:
This link opens a new window and takes the reader directly to the Calculator. Its Table 1 lists its input parameters on the left columns and its output parameters on the right side, while allowing the reader to toggle back to this text for instructions. These consist of detailed descriptions of all input and output parameters located below in the Appendix, including the used formulas.
Future Features – Clean or green energy from variable sources such as wind, solar PV of wave power need to be coupled to energy storage and stand-by generators in order for the utility to be able to continue to provide reliably constant grid voltage and frequency. As technology progresses, not only can distributed clean energy sources help the utility to smooth out some of that variability, but even further help could be provided by distributed storage equipment. In their quest for reliability, utilities may implement time-of-day or grid-load-based electricity rates. Therefore, future analyses and/or additions to this Calculator, may include:
 U. Bonne, “Study of a Newly Installed Home Solar PV System: Actual and Calculated Outputs,” at http://friendsofnelha.org/study-of-a-newly-installed-home-solar-pv-system-actual-and-calculated-outputs/, 6 Dec. 2009
One can now also enter the relevant cap and then let the Calculator determine the lesser of the two inputs
The input of an MMC escalation, dCu, gives the user a tool to account for annual escalation due to inflation, f, and/or discount future MMC payments according to the cost of money (=loan interest rate, r):
— To ignore escalation or discount by inputting dCu = 0.– To simultaneously account for inflationary escalation and for the “lower present value” of future (discounted) MMCs by inputting dCu = f – r, which would typically be a negative number, which results in Calculator outputs (e.g. E2 in $/kWh, below) representing “net present” values. Or– To only consider inflation, just input dCu = f, such as 1 or 2 %. The Calculator outputs then represent average values for the period L. But note that the above dCu values need to be consistent with the input chosen for dE1. Because kWh-energy is not subject to inflationary or discounting effects, E2 would not be affected by changes in dE1, if payback time were not. However, the Calculator displays two payback results: The first represents (minimum) payback time resulting from paying down the loan with all profits as they typically increase each year. The second represents the payback resulting from fixing the annual loan repayment at the profit made and amount paid in the first year. All ROIs are based on the former (maximum rate of loan repayment).
t = (LOG(Sc) – LOG(Sc-C*(r/100))) / LOG(1+(r/100)), if dE1=0 and n=1. To avoid escalation of the mortgage as the electricity rate escalates, we chose the mortgage payments to remain “fixed” to the amounts paid during the first year. However, daily compounding complicates the above equation a bit, to become: t = ((LOG((W*F/100*L*8760-Cmu*12)/n) – LOG((W*F/100*E1*8760-Cmu*12)/n-C*((r+0.00001)/n/100))) / LOG(1+((r+0.00001)/n/100)))/n. Depending on whether to escalate or not the loan payments as energy cost savings escalate with escalating electricity rates, we get:
Ulrich Bonne, Kailua-Kona, Hawaii