## Simple Payback

A simple payback calculation can provide a preliminary judgment of economic feasibility. The difference is usually around 3-7 % between borrowing money for a system and lost interest if you have enough money to pay for the system. In 2003 and again in 2008, the lost interest rate was very low. The easiest calculation is cost of the system divided by cost displaced per year, and assuming that operation and maintenance is minimal and will be done by the owner.

where SP = simple payback, years; IC = initial cost of installation, \$; AKWH = annual energy production, kWh/year; and \$/kWh = price of energy displaced.

### EXAMPLE 12.2

You purchase a 300 W wind turbine for battery charging. Installed cost = \$850, produces 220 kWh/year at \$0.50/kWh (the estimated cost for remote electricity).

SP = \$900/(220 kWh/year * 0.50 \$/kWh) SP = 900/110 = 8 years

The next calculation would include the value of money, borrowed or lost interest, and annual operation and maintenance costs:

where FCR = fixed charge rate, per year, and AOM = annual operation and maintenance cost, \$/year.

EXAMPLE 12.3

You purchase a 3.5 kW wind turbine with inverter to connect to the grid, IC = \$14,000, produces 6,000

kWh/year. You are losing interest at 4% on the installed cost. Retail rate of electricity is \$0.11/kWh.

SP = 14,000/(6,000 * 0.11 - 14,000 * 0.04) = 14,000/(660 - 560) = 140 years

You would think twice before purchasing this system on an economic basis. And no O&M was included.

The FCR could be the interest paid on a loan or the value of interest that would have been received from displaced money from savings. An average value for a number of years (5) will have to be assumed for \$/kWh for electricity displaced, as future costs of electricity from the utility company may be difficult to estimate. In general, electric rates do not fluctuate much and do not increase rapidly. The one change with deregulation is that the fuel adjustment cost can change quickly.

### EXAMPLE 12.4

You purchase a 50 kW wind turbine, IC = \$120,000, produces 120,000 kWh/year, AOM = 0.01 * IC = \$1,200/year, FCR = 0.07. Retail rate of electricity is \$0.11/kWh.

SP = 120,000/(120,000 * 0.11 - 120,000 * 0.07 - 1,200) = 120,000/(13,200 - 8400 - 1200) SP = 33 years

Equation 12.2 involves several assumptions: the same kilowatt-hours are produced each year, the value of the electricity is constant, and there is no inflation. More sophisticated analysis would include details such as escalating fuel costs of conventional electricity and depreciation. In general, these factors might reduce the payback.

### 12.3.2 Cost of Energy

The cost of energy (value of the energy produced by the wind turbine) gives a levelized value over the life of the system (assumed to be 20 to 25 years). The cost of energy (COE) is primarily driven by the installed cost and the annual energy production.

The COE is one measure of economic feasibility, and is compared to the price of electricity from other sources (primarily the utility company) or the price for which wind-generated energy can be sold. If purchasing a wind turbine for displacing electricity on site, the COE should be compared with an estimated average cost of electricity from the utility company over the next 10 years. The cost of energy for small systems is higher than for wind farms, with some economies of scale for larger size of small wind turbines (Table 12.1). In general, the AOM is around \$0.005/ kWh. In Equation 12.3, major replacement costs are included in the annual operation and maintenance costs.

EXAMPLE 12.5

Use same input data as Example 12.4, except FCR = 0.08 and AOM = 3% * IC.

A sensitivity analysis (Figure 12.1) shows how the different factors in Equation 12.3 affect the cost of energy. The most important factors are installed cost and annual energy production.

The cost of energy formula from Electric Power Research Institute (EPRI), tag-supply method [2], is similar to Equation 12.3. There is the addition of levelized replacement costs (major repairs)

## Renewable Energy 101

Renewable energy is energy that is generated from sunlight, rain, tides, geothermal heat and wind. These sources are naturally and constantly replenished, which is why they are deemed as renewable. The usage of renewable energy sources is very important when considering the sustainability of the existing energy usage of the world. While there is currently an abundance of non-renewable energy sources, such as nuclear fuels, these energy sources are depleting. In addition to being a non-renewable supply, the non-renewable energy sources release emissions into the air, which has an adverse effect on the environment.

Get My Free Ebook