Value of Energy Efficiency in Stand Alone PV Systems:
Their Approach / Figuring
it the Hard Way
Because PVs have high capital costs and lower operating costs, corporate financial analysts must find a way to compare the initial capital cost of the PV system to the monthly expense of a utility bill. Their method is complicated and requires some representation of the time value of money, or “discount rate”. Based on the discount rate, the future costs of electricity, adjusted for projected increases and reduced to a “Net Present Value” or NPV are compared to the capital cost of the PV system. While this is old hat for corporate accountants, it often doesn’t seem meaningful to the average homeowner. Corporations often choose the interest rate on their loans as a discount rate. But if you can’t get a bank to finance an off-grid home, then there is not interest rate to use.
Our Approach / The Easy
The Cost of Generating
The cost of the PV system will be divided into two parts, the initial investment and operating costs. The initial costs will include PV panels, mounting hardware, original battery set etc. Operating costs will include battery replacement and the cost of backup generator power during the winter months. The system is sized so that it can provide 1 KWH/day of AC power with 4.2 hours of insolation, the average yearly insolation for Arcata, a Northern California coastal town. (Insolation is the average amount of usable sunlight available to a non-tracking solar system). It will be assumed that the system is being increased in size and that the inverter, charge controller, load center, and battery housing are large enough to handle the increase in size.
Cost per KWH – A Minimum Value
The following table summarizes the assumptions made in calculating
the initial capital costs and the operating costs of the PV system.
The Cost Of A KWH/day Over The Life Of A PV System (24 yrs.):
Modifying this approach to your Personal
You can also modify our results to fit your personal situation. For example, if you live in the Southwest and receive 20% more sunlight you could reduce the cost of producing a KWH by about 20%, or you may choose to do your own installation and deduct that cost from you solar investment. As for rebates, we have found that unfortunately they are seldom applicable to stand alone systems.
The investment for increasing the capacity of the system by 1 AC KWH/day is $5606.00: $3406.00 for the initial cost of the equipment and $2200.00 for the operating costs. If you include the cost of all the equipment to set up a system, the inverter, load center, charge controller, and battery housing add about $1000.00, the total cost to produce 1KWH/day is $6600.00.
Conservation will be a good investment if you can purchase a device that can save 1KWH/day for less than $5606.00. If the device will last less than 24 years, its replacement cost should be considered. If you spend $1000.00 on an energy-saving device that saves 1KWH/day and lasts 12 years, you’ll buy 2 over the life of your PV system and you’re investing $2000.00 that will save you $3606.00.
Battery Mismatch Losses
Unfortunately, a 1 KW solar array sitting in direct sun for one hour will not produce 1 KWH of useable AC power. There are a number of ways energy is lost in this system. A major loss occurs because the panels produce their peak rated power at 17 Volts and most of the energy input into the battery occurs at a voltage closer to 13 volts. The energy is then taken out at about 12.4 Volts. The voltage mismatch alone results in a loss of over 25%. When analyzing battery powered PV systems, it is relatively easy to take these mismatches into consideration by using a current-based analysis. With this type of analysis voltage mismatches are automatically taken into account. To get a quantitative picture of the losses in a stand-alone system, let’s calculate the size array necessary to produce 1KWH with one hour of full sun. In a loss-less system, it would of course take a 1000-watt array to produce 1000 watts AC power. In a real system there will be a number of losses along the way. The input to the inverter will have to be about 1100 watts due to the inefficiency of the inverter. If this power is supplied at an average voltage of 12.4 Volts, then the batteries must supply 1100 watts/12.4 volts or 88.7 amps. For the inverter to produce 1 KWH the batteries must then supply or 88.7 amps for one hour or 88.7 amp hrs. (An amp hour is a unit of energy like a KWH). Assuming a 10% loss in the batteries the PV panels will have to supply an additional 10% more energy or 97.6 amp/hrs. To produce 1KWH with 1 hour of insolation will then require a 97.6 amp solar array. For each 17 watts of solar panels the panel will produce one amp; i.e., a 34-watt panel will produce 2 amps. The energy required to produce 1KWH of AC power with 1 hour of direct sun then be 17 watts/amp X 97.6 amps or 1659 watts which is a lot more than the 1000 watt array required in a loss less situation. These large losses make stand-alone power more expensive than a grid-tied system. In a grid-tied system the inverter loads the panels so that they are putting out their peak power. In addition, there are no battery losses and no backup system required during cloudy winter months.
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