In Part 2, we discussed how to measure hot water consumption and hot water energy use in a mid-sized hotel.  We looked at what the data meant regarding the energy saving potential of a solar thermal water heating system.  This particular hotel uses about 572,500 BTU per day and spends an estimated $6,070 per year on propane to heat water.

In this post, we’ll go through the financial analysis for a solar thermal system for this hotel.  We’ll discuss the various tax incentives involved and figure out how to calculate the Annualized Life-Cycle Savings (ALCS) for the system.  After we have a solid method for estimating the ALCS for any given system, we’ll determine the system design parameters that maximize the life-cycle savings.

Financial Analysis

Available Tax Incentives

Anyone who’s interested in the finances involved in a renewable energy project should familiarize himself/herself with the DSIRE website.  DSIRE stands for Database of State Incentives for Renewables and Efficiency, which is “a comprehensive source of information on state, local, utility and federal incentives and policies that promote renewable energy and energy efficiency.”  This site summarizes all the available incentives for each state.  It also includes federal incentives.

The US federal government offers a Business Energy Investment Tax Credit (ITC), which is “equal to 30% of expenditures,” meaning the owner of the system can deduct 30% of the installed system cost from his or her taxes owed to the federal government.  A hotel owner certainly pays more than that in taxes each year, so he or she will recoup 30% of the system cost in its first year of operation.

Similarly, the state of North Carolina offers a Renewable Energy Tax Credit (Corporate) “equal to 35% of the cost of eligible renewable energy property constructed, purchased or leased by a taxpayer and placed into service in North Carolina during the taxable year.”  The  credit can be up to $2.5 million, but “may not exceed 50% of a taxpayer’s state tax liability for the year.”  But once again, 35% of the system cost will  not exceed even close to half of the owner’s tax liability, so the owner can, in effect, recoup an additional 35% of the cost within the first year.  Also, if 35% of the cost does happen to exceed half of the owner’s tax liability, the credit can be taken over 5 years in equal installments.  This is good news for smaller hotels with smaller tax liability.

Finally, there’s the Modified Accelerated Cost-Recovery System (MACRS) + Bonus Depreciation (2008-2012).  This modified depreciation schedule allows the entire solar thermal system to be depreciated in the first year of operation if the system is installed before December 31, 2011.  This generally amounts to another 30% of recouped cost in the first year.

Taking all of these incentives collectively drives the simple payback period for a solar thermal system down to about 4-6 years.

Renewable Energy Certificates/Credits (RECs)

A majority of states have some sort of Renewable Portfolio Standard (RPS) which requires a certain percentage of power distributed by its state’s utilities to be generated by renewable methods.  If the utility does not have any renewable production means, it can purchase the “renewable attribute” of electricity generated (or sometimes offset) by another party. Each REC represents the renewable attribute of 1 MWh of renewably-generated power.  For example, if a business owns a large rooftop photovoltaic system, it can sell the RECs to a local electric company.  The electric company can then claim, for each REC it owns, 1 MWh of its electricity to have been generated renewably.  RECs are bought and sold in the market similar to the way stocks are traded on Wall Street.  And, fortunately for would-be solar thermal system owners, some companies, such as Duke Energy in North Carolina, offer a higher price for RECs produced by solar means, including solar thermal water heating systems.

Annualized Life-Cycle Savings (ALCS) Calculation

This section goes into the calculation of the Annualized Life-Cycle Savings, which was the primary metric used to optimize the system design parameters.  The ALCS, or the life-cycle savings divided by the number of years of service, was calculated with an Excel spreadsheet.  To calculate the life-cycle savings, some assumptions need to made about the future:

The useful lifespan of a solar thermal system was assumed to be 20 years, although analyses by other researchers often use a lifespan of 30 years.  I simply wanted to err on the side of caution.

To determine the future cost of propane (the fuel used for water-heating at this hotel), I fit a line to the cost of propane from 1990 through 2010, then extended the line through 2030.  This forecast is very conservative, because the cost of propane has been rising faster than linearly over the past decade.  This table shows the propane price estimates for 2011 through 2030:

Year Cost of Propane ($/gallon)
2011 2.515
2012 2.612
2013 2.709
2014 2.806
2015 2.903
2016 3.000
2017 3.098
2018 3.195
2019 3.292
2020 3.389
2021 3.486
2022 3.583
2023 3.680
2024 3.777
2025 3.874
2026 3.971
2027 4.068
2028 4.165
2029 4.262
2030 4.359

REC prices were taken from Duke Energy’s Standard Purchase Offer for Renewable Energy Certificates.  Prices in years beyond those listed were assumed to increase 2.5% per year, as is the case for the years listed.

Inflation was assumed to be 2.99%, which was the 2010 fourth quarter annualized Consumer Price Index (CPI), not including food and energy, from the US Bureau of Labor Statistics.

The system’s operation and maintenance cost is assumed to be 3% of the total installed cost (Russo & Chvala, 2010), plus inflation, annually

The cost per installed square foot of collector area is usually between $90 and $120 (Russo & Chvala, 2010).  This cost includes all of the system equipment, such as the collectors, pump, pipes, controller, hardware, and storage tank, as well as costs associated with the installation of the system, such as labor.  For this study, the cost was assumed to be $105 per square foot because the storage tank cost was estimated separately.

This was done so the storage tank volume could be optimized.  The ALCS can be calculated for different tank sizes.  A larger tank is more expensive, but it increases the heat storage capacity of the system.  There is some tank size that maximizes the life-cycle savings of the system.  The storage tank cost per gallon was assumed to be: tank cost (USD/gallon) = 204.84*gallons-0.576. This equation was arrived at by averaging the retail prices of storage tanks of sizes ranging from 30 gallons to 120 gallons from several different tank retailers.  The following graphs show the estimates given by this equation as well as those used by Kulkarni et al., who in a recent study estimated the storage tank cost as $84.2/m2 of tank surface area, which turns out to be a much lower estimate than what is used in this study (Kulkarni, Kedare, & Bandyopadhyay, 2007).  The first graph is plotted on linear axes.  The second is plotted on logarithmic axes.  A logarithmic-axis graph is useful because it reveals patterns in data points close to the y-axis while allowing us to project trend lines to points far from the y-axis.

 

cost as a function of storage volume

 

cost as a function of storage volume

 

This table shows the cash flows for an example system (56 collectors, 8,400 gallon storage tank) before converting to Present Value dollars:

Year Year from Installation Installed Cost O&M Federal Tax Credit State Tax Credit MACRS Deduction Propane cost offset REC revenue
2011 0 ($229,767.73) ($6,893.03) $68,930.32 $16,083.74 $68,355.90 $8,208.27 $2,460.00
2012 1 $0.00 ($7,099.13) $0.00 $16,083.74 $0.00 $8,524.79 $2,521.50
2013 2 $0.00 ($7,311.40) $0.00 $16,083.74 $0.00 $8,842.18 $2,584.64
2014 3 $0.00 ($7,530.01) $0.00 $16,083.74 $0.00 $9,158.70 $2,649.42
2015 4 $0.00 ($7,755.16) $0.00 $16,083.74 $0.00 $9,475.22 $2,715.02
2016 5 $0.00 ($7,987.03) $0.00 $0.00 $0.00 $9,791.74 $2,783.08
2017 6 $0.00 ($8,225.85) $0.00 $0.00 $0.00 $10,109.13 $2,852.78
2018 7 $0.00 ($8,471.80) $0.00 $0.00 $0.00 $10,425.66 $2,924.12
2019 8 $0.00 ($8,725.11) $0.00 $0.00 $0.00 $10,742.18 $2,997.10
2020 9 $0.00 ($8,985.99) $0.00 $0.00 $0.00 $11,058.70 $3,072.54
2021 10 $0.00 ($9,254.67) $0.00 $0.00 $0.00 $11,376.09 $3,148.80
2022 11 $0.00 ($9,531.38) $0.00 $0.00 $0.00 $11,692.61 $3,227.52
2023 12 $0.00 ($9,816.37) $0.00 $0.00 $0.00 $12,009.13 $3,308.70
2024 13 $0.00 ($10,109.88) $0.00 $0.00 $0.00 $12,325.66 $3,391.52
2025 14 $0.00 ($10,412.17) $0.00 $0.00 $0.00 $12,643.05 $3,475.98
2026 15 $0.00 ($10,723.49) $0.00 $0.00 $0.00 $12,959.57 $3,562.88
2027 16 $0.00 ($11,044.12) $0.00 $0.00 $0.00 $13,276.09 $3,651.95
2028 17 $0.00 ($11,374.34) $0.00 $0.00 $0.00 $13,592.61 $3,743.25
2029 18 $0.00 ($11,714.43) $0.00 $0.00 $0.00 $13,910.00 $3,836.83
2030 19 $0.00 ($12,064.70) $0.00 $0.00 $0.00 $14,226.52 $3,932.75

 

And this table shows the Present Value of the same cash flows, which accounts for inflation:

Year Year from Installation Installed Cost NPV O&M NPV Federal Tax Credit NPV State Tax Credit NPV MACRS Deduc. NPV Propane cost offset NPV REC revenue NPV TOTAL NPV Cumulative NPV
2011 0 ($229,767.73) ($6,893.03) $68,930.32 $16,083.74 $68,355.90 $8,208.27 $2,460.00 ($72,622.54) ($72,622.54)
2012 1 $0.00 ($6,893.03) $0.00 $15,616.80 $0.00 $8,277.30 $2,448.30 $19,449.36 ($53,173.18)
2013 2 $0.00 ($6,893.03) $0.00 $15,163.41 $0.00 $8,336.22 $2,436.74 $19,043.34 ($34,129.83)
2014 3 $0.00 ($6,893.03) $0.00 $14,723.19 $0.00 $8,383.95 $2,425.30 $18,639.41 ($15,490.43)
2015 4 $0.00 ($6,893.03) $0.00 $14,295.75 $0.00 $8,421.88 $2,413.20 $18,237.79 $2,747.37
2016 5 $0.00 ($6,893.03) $0.00 $0.00 $0.00 $8,450.55 $2,401.87 $3,959.39 $6,706.76
2017 6 $0.00 ($6,893.03) $0.00 $0.00 $0.00 $8,471.17 $2,390.55 $3,968.69 $10,675.45
2018 7 $0.00 ($6,893.03) $0.00 $0.00 $0.00 $8,482.78 $2,379.19 $3,968.94 $14,644.39
2019 8 $0.00 ($6,893.03) $0.00 $0.00 $0.00 $8,486.56 $2,367.78 $3,961.31 $18,605.69
2020 9 $0.00 ($6,893.03) $0.00 $0.00 $0.00 $8,482.98 $2,356.90 $3,946.86 $22,552.55
2021 10 $0.00 ($6,893.03) $0.00 $0.00 $0.00 $8,473.10 $2,345.28 $3,925.35 $26,477.90
2022 11 $0.00 ($6,893.03) $0.00 $0.00 $0.00 $8,456.02 $2,334.12 $3,897.11 $30,375.00
2023 12 $0.00 ($6,893.03) $0.00 $0.00 $0.00 $8,432.78 $2,323.36 $3,863.11 $34,238.12
2024 13 $0.00 ($6,893.03) $0.00 $0.00 $0.00 $8,403.77 $2,312.38 $3,823.12 $38,061.24
2025 14 $0.00 ($6,893.03) $0.00 $0.00 $0.00 $8,369.91 $2,301.16 $3,778.04 $41,839.27
2026 15 $0.00 ($6,893.03) $0.00 $0.00 $0.00 $8,330.38 $2,290.21 $3,727.56 $45,566.83
2027 16 $0.00 ($6,893.03) $0.00 $0.00 $0.00 $8,286.08 $2,279.31 $3,672.36 $49,239.19
2028 17 $0.00 ($6,893.03) $0.00 $0.00 $0.00 $8,237.34 $2,268.47 $3,612.78 $52,851.97
2029 18 $0.00 ($6,893.03) $0.00 $0.00 $0.00 $8,184.95 $2,257.68 $3,549.60 $56,401.57
2030 19 $0.00 ($6,893.03) $0.00 $0.00 $0.00 $8,128.17 $2,246.93 $3,482.07 $59,883.64

 

The simple payback period is the amount of time it takes for the Cumulative Net Present Value to become positive.  In this example, it is 4.85 years.  And the life-cycle savings is the Cumulative NPV at the end of the system’s useful lifetime ($59,884).  The Annualized Life-Cycle Savings, then, is the life-cycle savings divided by the system’s lifespan, so $59,884/20 = $2,994 per year.  This means that over a 20-year period, the system saves an average of $2,994 per year.

 

System Design Optimization

Computer Simulation

Hundreds of computer simulations were run in order to determine the optimal system configuration.  The simulations were performed using TRNSYS, an energy system simulation application. It has been available commercially since 1975 and is well-established in both academia and industry.  The user constructs a virtual system from a library of components, which includes solar thermal collectors, thermal storage tanks, pumps, boilers, etc.  The user then connects the components with “wires” that indicate which variable values to pass from one component to another, and in which direction to pass them.  For example, a pump can be connected to a water storage tank such that the pump will pass to the tank information about the fluid’s temperature and flow rate at each time step during the simulation time period. Any variable can be printed to a file and/or plotted directly to a TRNSYS graph.

In this study, the main components were a water storage tank with a submersed heat exchanger, a water boiler unit, an array of solar thermal collectors, a water circulation pump, a differential controller to govern the pump, an hourly weather input file, and a component to read an external spreadsheet containing the water draw profile.  A one-hour time step was used, meaning TRNSYS calculated the value of all variables in the system every hour of the simulation time period (one year).  The system design parameters were optimized in the following order: collector tilt angle, collector flow rate, storage tank volume, collector array area.

Optimization of Parameters

Collector Tilt Angle

The optimal collector tilt angle was found to be between 33 and 34 degrees.  The latitude in Boone, North Carolina (the location of the hotels) is 36 degrees.  Common design practice is to tilt the collectors at an angle equal to the latitude, and other software predicts the maximum performance when the tilt angle is a few degrees less than latitude, so this result is right in line with conventional solar thermal wisdom.  And, as it turns out, system performance is pretty resilient to changes in the tilt angle.  This graph shows the effect of tilt angle on the system’s ALCS.

 

Collector Flow Rate

The collector flow rate is the flow rate of the heat transfer fluid passing through the collector array.  If the flow rate is too low, the system won’t be able to take advantage of the fluid’s ability to store and move heat.  If the flow rate is too high, the fluid’s won’t get hot enough to transfer heat efficiently to the water in the storage tank.  Usually, a flow rate of 1.5 or 2 gpm per collector (0.0375 or 0.05 gpm/sq ft) is used.  This flow rate is just fine for most systems, and for all residential systems.  But for commercial systems, this may not always be the optimal flow rate to use.  In this study, I found the optimal flow-rate-to-collector-area ratio to vary with collector area.

The optimal flow rate as a function of collector area for this hotel is: flow rate (gpm/ft2) = 5.8983*collector area (ft2)-0.734.  The first graph below shows the flow rate optimization curves for different collector areas.  The second graph shows the optimal flow rates for the different collector areas fitted with a power curve.

 

ALCS-optimized flow rates for different collector areas

 

The optimal flow rate per square foot of collector area decreases as the collector area increases. The optimal flow rate for the optimal system is about 1 gpm per (4′ x 10′) collector. However, if a smaller collector area is chosen, the flow rate should be increased accordingly. The NREL-recommended residential system flow rate is for an optimal collector area (about two collectors), which is what is usually installed. In a larger system, there is more opportunity for error. It’s important to determine the optimal system parameters in order to maximize life-cycle savings.

 

Storage Tank Volume

Most residential systems use a storage volume of 1.5 gallons per square foot of collector area (a 100 sq ft collector array would require a 150-gallon storage tank); this storage volume is recommended by the National Renewable Energy Laboratory (p. 8).  Residential hot water use profiles are well-defined, with peak usage times in the morning and at night.  However, hotel hot water draw profile data is sparse and outdated.  Because the hotel’s draw profile varies drastically from day to day, a larger storage volume is needed to lessen the impact of usage rate  fluctuations.

Using the optimized collector tilt angle and collector flow rate, the storage tank volume was optimized in a similar fashion.  The optimal storage tank volume is about 4 gallons per square foot of collector area.  However, if the facility doesn’t have room for a storage tank that large, 3 gallons per square foot can be used instead, with only a small penalty to the ALCS.  This graph shows the effect of storage tank volume on the system’s ALCS:

Effect of storage tank volume on system ALCS

 

Collector Array Area

Finally, having optimized the collector tilt angle, collector flow rate, and storage volume, the collector array area was optimized. Effect of the hot water draw profile on the ALCS was also examined. The following graph shows the system ALCS as a function of collector area and average draw profile.  The table briefly describes each of the draw profiles.  “Discretionary draw” is hot water usage that is not caused by hotel guests.

Profile Description
2A measured from data
2B discretionary draw moved to morning
2C discretionary draw centered at 2:00 PM
2D discretionary draw centered at 4:00 PM
2E constant draw throughout the day
ALCS for various collector areas and draw profiles

 

As long as the storage tank volume is properly sized, the effect of the draw profile on the ALCS is very small.  For this hotel, the optimal storage volume is 6,000 gallons, and the optimal collector area is about 1,500 square feet, which corresponds to 42 4′-x-10′ flat-plate collectors.  The system will save $53,800 over its 20 years of service and will pay for itself in 4.67 years.  It will save the hotel owner an average of $2,700 per year.

To read the study in its entirety, click this link.     Hotel Solar Thermal Study [full text .pdf]

 

References

Kulkarni, G.N., Kedare, S.B., & Bandyopadhyay, S. (2007). Determination of design space and optimization of solar water heating systems. Solar Energy. 81, 958-968.

National Renewable Energy Laboratory (NREL). (2003, December). A consumer guide: heat your water with the sun. For the US Department of Energy’s Office of Energy Efficiency and Renewable Energy. Retrieved from http://www.nrel.gov/docs/fy04osti/34279

Russo, B.J., & Chvala, W.D. (2010). US Department of Energy, Pacific Northwest National Laboratory. Solar hot water application assessment for u.s. army imcom-southeast region (PNNL-19811)

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