7.4 Solar Fractions: Gains and Loads

Loads, Costs, and Fractions

We know that a local SECS like a Solar Hot Water system will have a certain quantity of demand from a residential family.

• Annual Loads (L) Example: In the Midwest of the USA, a residential family will consume 1.5-2 MWh of energy to heat water per year. That's an energetic load.
• Annual Costs (C) Example: In the USA, an average retail electricity cost is \$0.08/kWh, or \$80/MWh.
• Annual Solar Fraction (F): The fraction of energy provided by a SECS relative to the total energy demanded for the periodic step size (here, annual). In the solar field, we call the supplemental energy required beyond the SECS: "auxiliary" energy (even if it is a primary energy source in society).

We often design a domestic solar hot water (DSHW) system to provide an annual fraction F = 0.4-0.7 (40-70% of the total annual demand), sized for the summer loads, because the heat would be wasted/dumped in the summer. That would mean the client would be buying a bigger system that does not have utility in the summer. Better to have a less sufficient system for hot water in the winter, than for the client to pay for something they cannot use part of the year.

In our reading, we made the distinction between the annual solar fraction (uppercase F) and the monthly solar fraction (lowercase f). We can use the solar fraction as a factor in project finance to estimate an ideal array size for our client in his/her locale. Consider that a large solar fraction will entail more modules or panels, and will increase the cost for the client in the system investment (according to the unit cost). It will also increase the time to payback the investment. Our clients will no doubt have finite cash on hand to put a down payment into a SECS, and to acquire a loan for the rest of the investment. They may also require a fast payback that will influence the sizing of the system.

• An annual solar fraction of zero (F=0) is where the client opts for no installation of a new SECS.
  • $F=0$ will have the highest energy costs (fuel costs; $FC$ ) of any alternative SECS
• An annual solar fraction of one $\left(F=1\right)$ is where the client opts for a SECS that covers all energy loads for the entire year.
  • $F=1$ will have the highest solar investment costs ($C_S$), with the lowest associated annual energy costs
• We are to work with the client to find a strong solution between those two trivial extremes (a maximum return on investment), specifically a return with net positive in cumulative solar savings (Life Cycle Savings: LCS).

$$L\cdot F\cdot C_{fuel}=$$annual fuel savings (considered before discounting or fuel inflation rates)