ASHRAE Journal - November 2010 - 51

Solar ZEB ProjEct
OSB (oriented strand boards) that are each 7/16 in. (11 mm) thick. The green line shows the total SIPs cost that includes sealants, adhesives, fasteners, design services, taxes, shipping, etc. The slope of the panel cost lines is the primary factor of interest, as it provides the cost per insulation value information. The intercept values represent fixed costs (such as design services, cost of OSB panels, etc.) that do not vary with panel thickness. These fixed costs do not impact the optimal choice of an insulation system. Finally, the red line indicates the cost of additional lumber needed for SIP installation, but is a very small percentage of cost. Overall, this information indicates that the EPS insulation in this SIPs panel system costs $0.35 to $0.39 per inch thickness per square foot panel area. The labor to install the panels is assumed to be a fixed cost that is relatively independent of thickness and comes to roughly $2/ft2 to $3/ft2 ($22/m2 to $32/m2). For the energy cost, our installed cost for solar PV was $4.45/W, or $3.12/W after applying the 30% federal tax credit. We spent $29,000 for the 8,200 W array’s solar panels, inverters, wire, and panel supports; $2,500 for ground-mount support steel and aluminum; $1,000 for trenching, post holes and concrete in post holes; and $4,000 for labor at $30 per hour for a total of $36,500. With the U.S. federal tax credit of 30%, the system cost is $25,500. The solar panels are warranted for 20 years (the inverters for 10 years). So, on the same simple basis as we’ve been using, if the panels provide 10,000 kWh per year for 20 years of maintenancefree operation (Yes, we know. That’s not a good assumption, but all the numbers are here, so you can add your own maintenance and replacement factors.), with an installed cost of $25,500, we have an energy cost of $0.128 per kWh. At the end of 20 years, as the infrastructure for recycling solar panels and inverters matures, and the technology and manufacturing advances continue, your next system may cost even less in today’s dollars. With the insulation and energy cost information, we can move on to the optimization calculations. Minimization of the life-cycle cost for the wall or roof thickness results in the following relation: Optimal Wall or Roof Thickness (inches) = square root [(DDh + DDc) × Years × E$/(11.9 × R × COP × I$)] where DDh = Annual heating degree-days (F-day) DDc = Annual cooling degree-days (F-day) Years = House lifetime (100 years from our viewpoint) E$ = Energy cost per kWh (solar electricity ~$0.125 to $0.15 per kWh) R = Thermal resistance value per inch thickness (e.g., R=3.5 per inch for EPS) COP = Ratio of comfort conditioning energy required to electrical energy for maintaining comfort (assume something in the 1 to 5 range, equivalent to SEER and HPSF range of 3.4 to 20) I$ = Insulation cost per volume ($4/ft3 to $5/ft3 [$141/ m3 to $177/m3] for EPS SIPs from Figure 2) 11.9 = A number for all the unit conversions
November 2010

In central Illinois, we have approximately 5,000 F-days for heating and about 1,000 F-days for cooling. This is a pretty mushy number because super-insulating the house shifts the “no load” reference temperature built into the simple degreeday parameter. Figure 3 shows the trends in optimal insulation thickness based on the dimensional parameter ratio from the above relation versus total degree-days. The optimal insulation thickness for Equinox house is in the range of 11 in. to 13 in. (275 mm to 325 mm). The parameter ratio used for Figure 3 shows the significance of each of the factors in the optimal thickness relation. When varying parameters, an increase in the parameter ratio results in an increase in the optimal thickness. The sensitivity to the choice of insulation thickness is shown in Figure 4 in which the total cost of wall insulation and lifetime energy (100 years of energy based on a solar system with a 20-year lifetime) is plotted versus the wall thickness. Equinox has a wall and roof surface area of 4,400 ft2 (410 m2), which coupled with the parameters assumed for the optimal wall and roof thickness results in the lifetime cost shown in Figure 4. For Equinox, the lifetime cost of the wall and roof and the energy to keep the space conditioned due to the wall and roof is $42,000. Figure 4 also shows that the minimum cost solution for walls and roof is not very sensitive to insulation thickness. That is,

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ASHRAE Journal

ASHRAE Journal - November 2010

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