It Is Frequently Useful To Determine The Average Cost Of Energy Generated By Renewable Energy Systems

Net-Zero Energy Building Design and Economics

Introduction In the U.S., the residential and commercial buildings consume about 38% of all primary energy, about 84% of which comes from non-renewable fossil fuels (Annual Energy Review 2008, Energy Information Agency, U.S. Department of Energy). The demand for non-renewable fossil fuel energy could be significantly reduced by making buildings more energy efficient and powering them with onsite renewable energy.

Net-zero energy buildings use a combination of energy efficiency and renewable energy technologies so that the building sells back as much energy as it purchases over the course of a year; hence on a net basis the building consumes zero off-site energy. The concept of net-zero energy buildings in consistent with the larger concept of sustainability because net-zero energy buildings function within natural steady-state energy flows without borrowing energy resources from the future. In addition, generating energy onsite eliminates energy transmission and distribution losses and reduces the land required for renewable energy technologies. Many important organizations have established goals for net-zero energy or net-zero carbon emission buildings including:

 American Institute of Architects (AIA) Sustainability 2030

o Renovate new buildings for 50% CO2 reduction

o 50% CO2 reduction in new buildings by 2010

o Additional 10% reduction every 5 years until net-zero C02 by 2030.  U.S. Green Building Council LEED Certification: o 50% reduction in site energy use for base LEED o 65% Silver o 80% Gold o 100% Platinum  ASHRAE o Standard 90.1-2010: 30% less energy than 90.1-2004 o Standard 90.1-2020: guidance for net zero site energy use  U.S. Department of Energy o All commercial buildings are net zero energy by 2025

The fundamental approach to designing net-zero energy buildings is to minimize energy demand through energy efficiency, and then add sufficient on-site renewable energy technologies (i.e. solar photovoltaic system, solar thermal system, wind energy system, etc.) to satisfy that demand. To cost-effectively design net-zero energy buildings, the costs of energy-efficiency and renewable-energy options can be compared to determine the least-cost set of options for achieving net-zero energy. The levelized cost of energy provides an accurate measure of the cost of an energy option, and hence is an excellent

1 vehicle for prioritizing energy options in pursuit of net-zero energy. This chapter describes how to use solar energy simulation software and levelized cost of energy to cost-effectively design net-zero energy buildings.

Levelized Cost of Energy The levelized cost of energy (LCE) represents the total cost of an energy resource per unit of energy. Key inputs to LCE include energy output, capital costs, fuel costs, operations and maintenance costs, and financing costs. LCE enables the cost effectiveness of different types of energy options, including energy efficiency, renewable energy and purchased energy, to be compared. As such, it can be used as a guide for prioritizing energy efficiency and renewable energy options in net-zero energy buildings.

Fundamentally, LCE is the annualized total cost (ATC) of an energy project divided by the annual energy output (AEO) of the project over the project lifetime.

Levelized Cost of Energy = Annualized Total Cost / Annual Energy Output LCE = ATC / AEO

Calculation of LCE begins by determining the expected annual energy output (AEO) of a project and the expected project lifetime (n). Next, the annualized total cost of the project is determined by calculating the present value of all costs (including capital costs, fuel costs, operations and maintenance costs, and financing costs), then annualizing these costs over the expected project lifetime. In practice, some project costs occur in the future; use time-value of money relations to calculate the present values of these future costs, then sum the present values of all costs to calculate the total present value of a project (Pt). To calculate the annualized total cost (ATC) of an energy project, find the annualized value of Pt over the project life time using time value of money relations. This method accurately calculates the levelized cost of energy even when the financing period and project lifetime are different.

The two most important relations for calculating the present value (P) of a future amount (F) or series of future annual amounts (A) are the present worth factor (PWF) and the series present worth factor (SPWF). Both PWF and SPWF are functions of the discount rate (i) and the number of years into the future (n) that F or A occur. The discount rate (i) is the rate of return that could be generated by an alternative investment; in many cases the best value to use for discount rate is the annual interest rate of a loan to finance the project.

The present value P of a future amount F is:

P = F PWF (i,n) where PWF = (1 + i)-n

2 The present value P of a series of annual amounts A is: P = A SPWF (i,n) where SPWF =

The total present value of a project (Pt) is the sum of all present costs:

Pt =  Pi

The annualized total cost (ATC) over the project life time is:

ATC = Pt / SPWF (i,n)

Example: Calculate the levelized cost of energy for the following project. The project is expected to save 2,000 kWh/yr over a 10 year period. The initial cost of the project is $1,000 to be financed with loan with 5% annual interest. Recycling the equipment at the end of the project lifetime will cost $200.

Solution: The annual energy output is given as AEO = 2,000 kWh/yr and project lifetime is given as n = 10 years. Assume the discount rate is the annual interest rate i = 5%. The initial cost is given as IC = $1,000 and the recycling cost after n years is given as RC= $200. The present value of the recycling cost, Pr, is the recycling cost, RC, multiplied by the present worth factor, PWF. The present value of all costs, Pt, is the sum of the initial cost, IC, and the present value of the recycling cost, Pr. The annualized total cost, ATC, is Pt annualize over the project lifetime using the series present worth factor (SPWF). The levelized cost of energy, LCE, is annual total cost, ATC, divided by annual energy output, AEO.

Input Data Annual energy output: AEO (kWh/yr) 2,000 Project life: n (years) 10 Initial Cost: IC ($) 1,000 Discount rate: i 0.05 Recycle Cost: RC ($) 200

Calculations PWF = (1+i)^(-n) 0.614 Present value of recycle cost: Pr ($) = RC PWF 123 Pt ($) = IC + Pr 1,123 SPWF(i,n) = (1-(1+i)^(-n))/i 7.722 ATC ($/yr) = Pt / SPWF 145 LCE ($/kWh) = ATC / AEO 0.073

The use of the levelized cost of energy for evaluating options for net-zero energy building design is demonstrated in the sections that follow.

3 Levelized Cost of Energy Efficiency The first step in net-zero energy building design is to make the building as energy efficient as is economically feasible. This typically involves choosing between multiple energy-efficiency measures. Calculating the LCE of energy-efficiency measures enables the cost effectiveness of these measures to be compared and prioritized.

Example: Consider a building heated by an electric heat pump and in Dayton, Ohio whose energy use is well described by the following ESim building energy simulation model. Calculate the levelized cost of energy saved from increasing ceiling insulation from R = 27 to R = 52 (hr-ft2-F/Btu) if the cost of the additional insulation is $1,000. Assume a project lifetime of 30 years and a loan rate of 5%.

Solution: Energy savings can be estimated by comparing simulated whole building electricity use from the baseline building with R = 27 (hr-ft2-F/Btu) insulation to a building with R = 52 (hr-ft2-F/Btu) insulation using the ESim software. ESim simulations from the baseline building and the building with additional ceiling insulation are shown below.

4 Based on these simulations, the annual energy output (savings) are:

AEO = Esav = E,sim,baseline – E,sim,energyefficient AEO = Esav = 18,131 kWh/yr – 17,646 kWh/yr = 485 kWh/yr

The series present worth factor is:

SPWF = = = 15.372

The annualized total cost of the additional insulation is:

ATC = Pt / SPWF = $1,000 / 15.372 = $65 /yr

Thus, the levelized cost of the energy saved by adding insulation is:

LCE = AEO / ATC = ($65 /yr) / (485 kWh/yr) = $0.134 /kWh

This approach can be used to quantify the levelized cost of energy efficiency for multiple measures and to compare the relative cost effectiveness of each measure. For example, the table below shows a list of energy efficiency options with the levelized cost of each option determined using this method. Note that each measure should be evaluated using the appropriate lifetime. For example, if the expected lifetime of an

5 Energy Star refrigerator is 12 years, then the SPWF should be computed with n = 12 years. The list is then sorted from lowest to highest levelized cost, and can be used to select the most cost-effective measures.

EE (sorted by LCE) Base Engy Eff Esav InitCost AnnCost LevCostEngy kWh/yr kWh/yr kWh/yr $ $/yr $/kWh HW: T140 to T120 18,131 16,889 1,242 0 0 0.00 Nightsetback 22-7, 72to80sum, 72to64win 18,131 17,279 852 100 7 0.01 Comp Fluor 18,131 17,218 913 80 16 0.02 HW: ef.86 to ef.92 18,131 17,772 359 200 20 0.06 Infiltration: n.5 to n.25 18,131 17,007 1,124 1,000 65 0.06 Energy Star Refigerator 18,131 18,008 123 108 7 0.06 Infiltration+AtoAHXe.7: n=.25 effhx=.7 18,131 16,290 1,841 2,000 130 0.07 HP: SEER12 to 18, HSPF 8.3 to 10.5 18,131 16,783 1,348 2,000 133 0.10 Ceiling+Roof Insul: 27 to 52 18,131 17,646 485 1,000 65 0.13 slab: r5 to r15 floor: r2 to r7 18,131 17,823 308 800 52 0.17 Windows: 3ftover + (N40to10, S40to90, EW24to14) 18,131 17,950 181 500 33 0.18 Walls: 15 to 30 18,131 17,410 721 2,000 130 0.18 Windows: r2 to r4 18,131 17,686 445 2,000 130 0.29 Total EE 9,942 11,788

Including Interaction Effects The method described above is useful for prioritizing energy efficiency options. However, interaction effects between options can cause the overall energy savings from multiple options to be different than the sum of the savings from each option evaluated individually. For example, increasing the thermal resistance of the envelope reduces the heating load and heating energy use. Similarly, improving the efficiency of the heating system reduces heating energy use. However, when both measures are implemented simultaneously, the reduced heating load decreases the savings from improving heating system efficiency. Thus, the overall savings, including interaction effects, is less than the sum of the savings evaluated independently. To quantify interaction effects, include all of the selected energy efficiency measures in a single building energy simulation.

Example: To illustrate the importance of including interaction effects, recall that the total expected savings from each energy efficiency measure evaluated individually is 9,942 kWh/yr. In comparison, the ESim output below shows that building electricity use with all energy efficiency measures evaluated simultaneously would be 10,992 kWh/yr.

6 The total energy savings including interaction effects would be:

Esav = E,sim,baseline – E,sim,energyefficient Esav = 18,131 kWh/yr – 10,992 kWh/yr = 7,139 kWh/yr

Thus, in this example, interaction effects reduced the total expected savings by about 28%. When all energy efficiency options are combined and interaction effects included, the overall levelized cost of energy efficiency is about $0.11 /kWh.

Base Engy Eff Esav InitCost AnnCost LevCostEngy kWh/yr kWh/yr kWh/yr $ $/yr $/kWh EE with interaction 18,131 10,992 7,139 11,788 767 0.11

Levelized Cost of Solar Hot Water Systems In many buildings, hot water is required year round and the energy required to heat the water can be substantial. In many cases, solar hot water systems can preheat water at a lower levelized cost than heating the water with electricity. To determine whether solar hot water is cost effective, the solar hot water system must first be sized to meet hot water demand. This is typically done using a solar simulation program that

7 calculates savings from solar hot water systems based on system performance and design parameters and meteorological data. After the system is appropriately sized, the levelized cost of energy from system can be computed to evaluate the system’s cost effectiveness.

Sizing and Performance of Solar Hot Water Systems The thermal energy delivered by solar hot water systems varies throughout the year with incident solar radiation. Thus, sizing a solar hot water system to meet the entire hot water heating load, even during winter, means that the system will be oversized during summer. To improve cost-effectiveness, many solar hot water systems are sized to deliver 100% of the hot water heating requirements during the summer, and some fraction of the annual hot water heating requirements. The performance of solar hot water systems can be simulated using solar simulation programs such as SolarSim. The use of SolarSim to size a solar hot water system to deliver 100% of hot water requirements during the summer is shown below.

Example: Use the SolarSim software to size a solar hot water system for a house in Dayton, Ohio so that the solar system delivers about 100% of the energy needed for hot water during the summer. The collectors face south with a slope of 39.9 degrees. The system has a 227 gallon storage tank. Average hot water use is 2.5 gal/hr (60 gal/day), the hot water set point temperature is 120 F, and the backup electric hot water heater has an energy factor of 0.92. Once the system is sized, determine the annual water heating energy savings.

When these values are loaded into SolarSim, the output screen below shows that a solar hot water system with 6 m2 of collector area would supply 100% of the energy needed during July and August.

8 In addition, the output screen shows that the annual amount of electrical heating energy displaced by the solar hot water system would be 3,103 kWh/yr, which would account for 85% of the total how water heating requirement.

Levelized Cost of Energy from Solar Hot Water Systems The levelized cost of energy from solar hot water systems can be calculated from performance and cost data.

Example: Calculate the levelized cost of energy from the solar hot water system in the previous example. The solar hot water system reduced electricity use by 3,103 kWh/yr. The solar hot water system costs $2,000 plus $500 per m2 of collector area, has a lifetime of 20 years, and negligible maintenance costs. The solar system can be financed with a loan interest rate of 5% per year

Solution: The annual energy output AEO is 3,103 kWh/yr over a lifetime of n = 20 years. Assuming negligible maintenance costs, the present value of the total system is:

Pt = $2,000 + (6 m2 x $500 /m2) = $5,000

Assuming a loan interest rate of 5% per year, the series present worth factor, SPWF, is:

9 SPWF = = = 12.462

The annualized total cost of the solar hot water system is:

ATC = Pt / SPWF = $5,000 / 12.462 = $401 /yr

The levelized cost of the energy from the solar hot water system is:

LCE = AEO / ACT = $401 /yr / 3,103 kWh/yr = $0.129 /kWh

Levelized Cost of Photovoltaic Systems For a net-zero energy building, energy saved from energy-efficiency measures and energy produced by a solar hot water system reduces the energy that must be provided by a photovoltaic (PV) or other renewable energy system. After energy demand has been minimized by energy efficiency and solar thermal hot water systems, a photovoltaic system can be sized to meet the remaining energy demand. This is typically done using a solar photovoltaic system simulation program that calculates solar PV electrical output based on system and design parameters and meteorological data. After the system is appropriately sized, the levelized cost can be computed to evaluate the systems cost effectiveness.

Sizing and Performance of Solar Photovoltaic Systems The performance of solar photovoltaic systems can be simulated using solar simulation programs such as SolarSim.

Example: Use the SolarSim software to size a solar photovoltaic system for the house in Dayton, Ohio considered in previous examples so that the solar system delivers 100% of the electricity needs after energy efficiency and solar heating options have been implemented. The collectors face south with a slope of 39.9 degrees.

Solution: The building’s baseline energy use is 18,131 kWh/yr, the total expected savings from energy efficiency measures is 7,139 kWh/yr and the electrical heating energy displaced by the solar hot water system is 3,103 kWh/yr. Thus, for the building to be net-zero energy, the electrical energy required from a photovoltaic system is:

Esolar,pv = 18,131 kWh/yr – 7,139 kWh/yr - 3,103 kWh/yr = 7,889 kWh/yr

To size a solar photovoltaic system to deliver this much electrical energy, the performance specifications of the solar system and the energy requirements of the building were loaded into the solar energy simulation program SolarSim. The performance of the system in Dayton, OH was then simulated, and the size of the system was then modified until the system delivered the required amount of

10 electricity. According to SolarSim, the annual amount of electrical energy generated by a solar photovoltaic system rated at 5.4 kW with 52 m2 of collector area would be 7,891 kWh/yr.

Levelized Cost of Energy from Solar Photovoltaic Systems The levelized cost of energy from solar photovoltaic systems can be calculated from performance and cost data.

Example: Calculate the levelized cost of energy from the solar photovoltaic system in the previous example with PV output of 7,891 kWh/yr. The solar PV system costs $5,000 /kW, has a lifetime of 20 years, and incurs negligible maintenance costs. The solar system can be financed with a loan interest rate of 5% per year

Solution: The annual energy output AEO is 7,891 kWh/yr over a lifetime of n = 20 years. Assuming negligible maintenance costs, the present value of the total system is:

Pt = 5.4 kW x $5,000 /kW = $27,000

The series present worth factor, SPWF, is:

11 SPWF = = = 12.462

The annualized total cost of the solar hot water system is:

ATC = Pt / SPWF = $27,000 / 12.462 = $2,167 /yr

The levelized cost of the energy from the solar system is:

LCE = AEO / ATC = $2,167 /yr / 7,891 kWh/yr = $0.275 /kWh

Levelized Cost of Purchased Energy In many cases it is useful to compare the costs of energy-efficiency and renewable energy options to the cost of commercially-purchased energy. To do so, the cost of commercially-purchased energy over the lifetime of the energy efficiency and renewable energy technologies must be determined.

Historically, the cost of most commercially-purchased energy has increased over time as fuel, equipment and maintenance costs increase. Residential natural gas and electricity price escalation rates, e, over various periods are shown in the tables below (Annual Energy Review 2006, Energy Information Agency, U.S. Department of Energy).

Natural Gas

Residential Residential Residential Nominal Nominal Nominal 1967-2006 1996-2006 2001-2006 Input Input Input n 39 N 10 n 5 P 1.04 P 6.34 P 9.63 F 13.76 F 13.76 F 13.76 Calculations Calculations Calculations e 0.068461 E 0.08057 e 0.073986

Electricity

Residential Residential Residential 1967-2006 1996-2006 2001-2006 Input Input Input N 39 N 10 n 5 P 2.3 P 8.36 P 8.58 F 10.4 F 10.4 F 10.4 Calculations Calculations Calculations E 0.039448 E 0.022075 e 0.039224

12 Over any period of n years, the annualized (levelized) cost of energy can be calculated by:

1) Defining the current cost of energy as A, then finding the present value P of future costs escalating at rate e with discount rate i over n years as: P = A ESPWF(i, e, n)

2) Finding the annualized (levelized) cost, A’, of the present value as: A’ = P / SPFW(i, n).

Where: SPWF(i,n) = series present worth factor = ESPWF(i,e,n) = escalating series present worth factor = if i  e = if i = e

Example:

Determine the annualized (levelized) cost of electricity if the initial cost of electricity is $0.13 /kWh and the projected electricity cost escalation rate is 4% per year. The system lifetime is 20 years and the discount rate is 5% per year.

Annualized Cost of Purchased Electricity

Inputs i = 0.05 n = 20 e = 0.04 A = Init cost elec ($/kWh) 0.13

Outputs ESPWF(i,e,n) 17.419 P = A ESPWF 2.264 SPWF(i,n) = 12.462 LCE ($/kWh) = A' = P / SPWF 0.182

Thus, in this example, investments in energy efficiency or renewable energy that have marginal costs of less than $0.182 /kWh are cost effective.

13 Summary: Evaluating Energy Options for Net-Zero Energy Buildings Net-zero energy buildings rely on both energy efficiency and renewable energy technologies to achieve net-zero energy use, and the cost-effectiveness of these measures is often assessed by comparisons with purchased energy. The levelized cost of energy method described above provides a consistent basis for evaluating the economics of both types of technologies. It also makes it possible to evaluate the overall cost effectiveness of a net-zero buildings by comparing levelized costs of energy efficiency and renewable energy to purchased energy.

Example: Sort the energy-efficiency, solar hot water and solar photovoltaic options from the previous examples according to levelized cost to prioritize measures to achieve net-zero energy according to cost.

Solution:

EE + SHW + PV (sorted by LCE) Base Engy Eff Esav InitCost AnnCost LevCostEngy kWh/yr kWh/yr kWh/yr $ $/yr $/kWh HW: T140 to T120 18,131 16,889 1,242 0 0 0.000 Nightsetback 22-7, 72to80sum, 72to64win 18,131 17,279 852 100 7 0.008 Comp Fluor 18,131 17,218 913 80 16 0.018 HW: ef.86 to ef.92 18,131 17,772 359 200 20 0.056 Infiltration: n.5 to n.25 18,131 17,007 1,124 1,000 65 0.058 Energy Star Refigerator 18,131 18,008 123 108 7 0.059 Infiltration+AtoAHXe.7: n=.25 effhx=.7 18,131 16,290 1,841 2,000 130 0.071 HP: SEER12 to 18, HSPF 8.3 to 10.5 18,131 16,783 1,348 2,000 133 0.099 Solar hot water 18,131 15,028 3,103 5,000 325 0.105 Ceiling+Roof Insul: 27 to 52 18,131 17,646 485 1,000 65 0.134 slab: r5 to r15 floor: r2 to r7 18,131 17,823 308 800 52 0.169 Windows: 3ftover + (N40to10, S40to90, EW24to14) 18,131 17,950 181 500 33 0.180 Walls: 15 to 30 18,131 17,410 721 2,000 130 0.180 Solar photovolaic electricity 18,131 10,240 7,891 27,000 2,167 0.275 Windows: r2 to r4 18,131 17,686 445 2,000 130 0.292 Total 20,936

Plotting the data makes it easier to visualize the relationship between levelized cost and energy output.

14 The levelized cost of energy method makes it possible to combine all of the energy efficiency and renewable energy options needed to achieve net-zero energy into a single levelized cost. This cost can be comparted to the levelized cost of purchased energy to evaluate the overall cost effectiveness of the energy measures.

Example: Calculate the levelized costs of energy efficiency combined, solar hot water and solar photovoltaic electricity individually and as a group. Compare the overall levelized cost to the levelized cost of purchased energy.

Solution: The list of energy efficiency, solar hot water and solar photovoltaic energy options sorted by levelized cost is shown below.

EE(with interaction) + SHW + PV (sorted by LCE) Base Engy Eff Esav InitCost AnnCost LevCostEngy kWh/yr kWh/yr kWh/yr $ $/yr $/kWh EE with interaction 18,131 10,992 7,139 11,788 767 0.11 Solar hot water 18,131 15,028 3,103 5,000 401 0.13 Solar photovolaic electricity 18,131 10,240 7,891 27,000 2,167 0.27 Total 18,133 43,788 3,335 0.18

A plot of cumulative savings versus cumulative levelized cost is shown below.

15 In summary, in this example, the additional energy efficiency and renewable energy measures considered here would increase the cost of the building by $43,788, which would increase the annual mortgage cost by $3,335 per year. However, annual energy costs would be negligible. The fraction of total energy demand met by energy efficiency is 39%; 17% is met by solar hot water and 44% is met by solar photovoltaic system. The overall cost of all energy efficiency, solar thermal and solar photovoltaic measures is $0.18 /kWh. This is comparable to the average cost of purchased energy of $0.18 /kWh when projected energy escalation costs are included. Thus, over a 30- year lifetime, the owning and operating cost of this net-zero energy building is about the same as a traditional building.

Leasing Solar Collectors In many parts of the country, leasing provides a maintenance-free alternative to purchasing a solar system. In most cases, the leasing company owns the system. Systems are financed over 20 years and offer lower net monthly costs than purchasing electricity from the utility. Total cost savings would be greater if the customer purchased the PV system. However, the combination of guaranteed savings and maintenance with no/low first cost is attractive. In some states, such as California, leased systems account for the small PV system sales.

Annual deployment of residential scale (<10 kW) PV in California. (Rutberg, M., Bouza, A., “Leasing Residential PV Systems”, ASHRAE Journal, December 2013)

16 For example, the pictures below show a solar photovoltaic system on a house in Agua Dulce, California, about 45 minutes north of Los Angeles in the high desert mountains. The system was installed in two half days.

A solar company owns the system and is responsible for its maintenance. In this example, the homeowner used about 19,000 kWh/yr at an average unit cost of about $0.174 /kWh for an annual cost of about $3,300 /yr. The PV system is guaranteed to produce 11,639 kWh/yr. If the system doesn’t produce the expected electricity, the company washes or replaces the panels. In this example, the homeowner would still have to pay for 7,361 kWh per year, but at a reduced maximum rate of about $0.12 /kWh for a total cost of about $888 /yr. In addition, the homeowner would pay the solar company $2,735 per year. Thus, the total cost for the home owner would be the sum of $888 /yr and $2,735 /yr or about $3,623 /yr. This is only slightly more than the $3,300 /yr the homeowner currently pays for electricity. But the homeowner has the satisfaction of knowing that its electricity is carbon free and that the system may actually reduce total costs in the future if purchased electricity rates increase.

Net-Zero Energy Buildings

U.D. partner Melink Corporation’s headquarters in Milford, Ohio is a net zero energy facility.