Case Eric is thinking about installing solar panels on his house to reduce his electricity usage and his carbon footprint Cost of Electricity Austin Energy uses the five-tier rale schedule shown below: Electricity Rate Schdule Usage (kWh) Cost ($/kWh) From Jun-Sep Oct-May 0 500 0.033 0.018 501 1000 0.080 0.056 1001 1500 0.091 0.072 1501 2500 0.110 0.084 2501 999999 0.114 0.096 Suppose Eric uses 1250 kWh of electrical energy during the month of June. The charge is then 500*10.033)+500 (0.080)+250 (0.091)=$79.25. In addition, Austin Energy charges a "fuel charge" of $0.0365/kW-h, a "regulatory charge" of $0.00728/kW-h, and a "community benefit charge of $0.00554/kW-h on all the kW-h. Also, Austin Energy charges $10/month to have an electrical hook-up. Eric believes all these costs are likely to increase in real terms at 0.5% per year. Just apply the same percentage increase to all these costs. Investment Details He has an offer from an Austin-based solar company for two different systems. The details are provided below. These costs below already include sales tax. Table 1: System Specifications and Cost Sharp 224W Sharp 175W Power (W) 224 175 Number 14 30 Efficiency 13.74% 13.45% Array Area (m 2) Power (kW) 22.82 3.14 39.03 5.25 Cost $10,990 $18,375 The solar system will be tied to the electricity grid and will not include storage. If Eric needs additional power he can purchase it from the grid. 7/28/2021 1 of 8 ME 353 H009 The city of Austin is offering a rebate equal to $1.50 per installed watt, adjusted for inverter efficiency, which is assumed to be 95.5% for this rebate. Thus, if Eric installed 3.14 kW he would receive a rebate of 3140 955 * 1,5 - $4,498 In addition, the federal government is offering a tax credit of 30%, which means Eric will get 30% of the net purchase price back when he files his 2021 tax return. The net price is the cost of the system after applying the Austin rebale. To keep things simple, assume that Eric receives this credit at the time of purchase. In addition, to keep things simple, assume that solar system would be installed at the end of 2021. The benefit of the solar panels is two-fold. First, they would allow Eric to lower the amount of electricity that he buys from the grid (from Austin Energy). Second, they would reduce the amount of greenhouse gases (GHG) that Eric is responsible for (reduce his carbon footprint). Eric's real MARR is 7%. All the dollars discussed in this case are in real terms. Electric Bill with Solar Austin Energy determines Eric's bill as follows. First, they assume Eric does not have solar and charge him according to the schedule above. They then give Eric a credit for any solar he produces at the rate of $0.128 per kW-h. However, Eric cannot have a negative bill in any year. That is, i value of his solar credit exceeds his yearly bill, Austin Energy only gives him credit for his electricity bill, not the value of all the solar Eric's real MARR is 7%. All the dollars discussed in this case are in real terms. Electric Bill with Solar Austin Energy determines Eric's bill as follows. First, they assume Eric does not have solar and charge him according to the schedule above. They then give Eric a credit for any solar he produces at the rate of $0.128 per kW-h. However, Eric cannot have a negative bill in any year. That is, if value of his solar credit exceeds his yearly bill, Austin Energy only gives him credit for his electricity bill, not the value of all the solar, Systems Specifications Unfortunately, solar panels cannot produce more power than they receive from the Sun. Eric used a system called PVWatts (http://rredcnrel.gov/solar/codes_algs/PVWATTS/versionl/), which is based on field data, to estimate the average solar flux for his system (this is the 24- hour, around the clock, and across the month, average solar flux). These results are based on the exposure of Eric's roof (170) and its slope (40%). Note: in the drawings below, it says Eric's roof is at 30, but this is incorrect. Month January February March April May June July August September October November December Solar Flux (W/m2) 187 210 223 220 214 227 240 240 246 235 238 198 172 Unfortunately, solar cells are not 100% efficient. In fact Sharp estimates that the initial efficiency is 13.74% for the 224 W module and 13.45% for the 175 W module (see Table 1 and the spec sheets at the end of this document). In addition, solar cells degrade with time and Eric estimates that the initial efficiency could decline by 1.0% per year. These changes are percentage changes so that in the base case the efficiency for the 224 W module in year I will be 13.74% *(1 - 1%)^(1-1). We subtract 1 since we assume they do not degrade the first year. In addition, the AC/DC inverter is only 95.5% efficient. To find the efficiency of the system you should multiply the collector efficiency by the inverter efficiency. The panels will last for 25 years. Design A is shown below. Components + Design Sharp 224 Watt SMA 583000US Location SYSTEM SPECIFICATIONS 3.13 and Tied PV System 14 Sharp NO 220W Modules I Sunny 3000 Inverter 170 Design B is shown below. Components Design + SMA SBSOODUS Location _SYSTEM SPECIFICATIONS 5.25W Grid Tied PV System 30 Sharp NT 175W Modules 1 Sunny 500w inverter 170 FAQs About the Sun and the Earth Why is the solar flux an average? What does that mean? Well, let's see. What is the solar flux at night? Zero. What is it at noon? Much higher, maybe 1500 W/m^2. Can't you give us an equation that gives the flux at any instant of time? Sure! But you would then have to integrate that. What do you mean this is an average across the month? Well, the average flux on March 1 is not the same as March 31. The Earth orbits the Sun. As it does this, because the Earth is titled 23 on FAQs About the sun and the Farih Why is the solar flux an average? What does that mean? Well, let's see. What is the solar flux at night? Zero, What is it at noon? Much higher, maybe 1500 W/m^2. Can't you give us an equation that gives the flux at any instant of time? Sure! But you would then have to integrate that. What do you mean this is an average across the month? Well, the average flux March 1 is not the same as March 31. The Earth orbits the Sun. As it does this, because the Earth is titled 23 on its axis, the angle of incidence of sunlight at any location changes, as does the length of the day. So, the average flux on March 1 will be less than the average flux on March 31. If these concepts are new to you, I suggest you read up on the Earth and its place in the solar system. This is good stuff to know! Especially for an engineer from a top-program! What is Energy? This question always comes up: How do you go from solar flux to electrical energy produced? This is such a basic mechanical engineering question, that you need to figure it out. Flux is in watts per square meter. A watt is measure of power. Electrical energy is measured in watt- hours. Electricity Usage Eric has tracked his monthly electricity usage over the last thirteen years (seriously, he has done this). Based on this data he has provided the following monthly energy usage per square foot. Month January February March April May June July August September October November December Energy Usage (kW-h/ft^2) 0.3067 0.2638 0.3227 0.3177 0.4026 0.4951 0.5526 0.6591 0.6345 0.4963 0.3285 0.2929 Eric's current estate is 3200 ft2. This home is more efficient that his past homes and therefore Eric thinks his usage per square foot is likely to be lower. He estimates that his new home 10% more efficient Eric is concerned that once the solar panels are installed his family will not be as careful with their electricity use. For example, his wife has already commented that "Once we get the solar panels you won't be able to badger me about leaving the outdoor lights on all night." (Editorial comment: How funny is that?!). He believes that his family's electricity usage will rise 15% once the panels are installed. Salvage Value One thing Eric is worried about is that he may not be in his home for the entire life of solar panels, which is 25 years. His best estimate is that he will be in the home 10 more years. If Eric is not in his home for 25 years he will lose the value of solar provided electricity In addition, he is also worried that the solar panels will decrease the value of his home. Eric thinks about this and decides to divide this cost into two components: (1) the present value of the remaining electricity that solar panels would provide a positive) and (2) a change in the value of the home for purely esthetic reasons (possibly a negative). (1) Eric thinks that a future buyer will be willing to pay an extra amount for his house that is proportional to the present value of the remaining solar energy at the time of the sale. Salvage Value One thing Eric is worried about is that he may not be in his home for the entire life of solar panels, which is 25 years. His best estimate is that he will be in the home 10 more years. If Eric is not in his home for 25 years he will lose the value of solar provided electricity. In addition, he is also worried that the solar panels will decrease the value of his home. Eric thinks about this and decides to divide this cost into two components: (1) the present value of the remaining electricity that solar panels would provide a positive) and (2) a change in the value of the home for purely esthetic reasons (possibly a negative). (1) Eric thinks that a future buyer will be willing to pay an extra amount for his house that is proportional to the present value of the remaining solar energy at the time of the sale. For example, if Eric sells his home in year 10 he estimates that the new home buyers would be willing to pay some fraction of the present value of the remaining 15 years of solar energy. He estimates this value is 25%. (2) Eric thinks that new home buyers are likely to decrease how much they are willing to pay for the house because they don't like the way solar panels look. He estimates that they will pay $8000 less for his home (this is a future value, that is constant no matter when he sells his home-since it is in real terms). The Social Cost of Carbon Electricity production from fossil fuels (coal, natural gas, oil) emits CO2, which is a greenhouse gas (GHG). The emission of CO2 is believed to be warming the planet, which will result in future damages to society. This means that when we burn coal, for example, we are imposing a cost on society that is not reflected in the price. This is called an "externality." In order to make better choices we need an estimate for the "social cost of carbon," which is the present value of the damages done by emitting one more metric ton (MT) of CO2 into the atmosphere. William Nordhaus, a professor at Yale University, has estimated that this social cost is currently $40 per metric ton (MT) of CO2 and is increasing at about 3% per year in real terms. Eric wants his investment decision to include this cost, even though he may never personally have to pay it. Now, to use this information, you will need to convert the damages from $ per MT of CO2 to $ per kW-h. The carbon intensity of coal is 1000 kW-h per MT of CO2. That is, for every 1 MT of CO2 emissions we get 1000 kW-h of electricity. The carbon intensity of natural gas is 1700 kWh per MT of CO2. Based on Austin Energy's generation portfolio, Eric believes his carbon intensity is 1400 kW-h per MT of CO2. How do you use this information? Well, you need to calculate the how much CO2 is saved by using solar and multiply it by the social cost of CO2. Is it really that simple? Yes. Analysis As you can see, this is a complicated investment and Eric has many questions. These are divided into questions regarding the social value of solar energy and the direct benefit to him. Eric's Value Is this a good investment from Eric's perspective? Which system is best and why? In this section, you should assume Eric may not be in the house for 25 years (as detailed above). Here are some questions Eric is interested in: . Will he still have to purchase electricity from Austin Energy or will the solar panels supply all his energy needs? What fraction of his energy needs will the panels cover? How much of a cost is Eric imposing on society through the use of electricity? Based on media reports and actions taken by the Austin City Council, he believes this cost must be very high What are the present value, payback, AEC, and IRR of the two solar systems? What is the breakeven social cost of carbon (such that the PV = $0 or the IRR = MARR) from Eric's perspective? Just find the initial cost. That is instead of $8/MT of CO2 find the amount that results in a PV of $0. Assume that this initial amount grows at the rate listed in the case. What is the breakeven cost of the system in terms of $ per installed Watt? Value to Society Are Eric's solar panels a good investment from society's perspective? The panels will last for 25 years, even it Eric sells the home to someone else and they will offset the amount of electricity purchased from the grid. However, society does not reap the benefit of the rebates and tax credits since society is paying these. Thus, you should assume that society pays the full cost of the system. Society does benefit however from a reduction in the use of GHG's, which should be valued at the social cost of carbon. Of course, society also gets the value of the produced electricity. Assume that society's MARR is 7%, like Eric's. This calculation is no different than assuming Eric is in the house for 25 years and gets no tax breaks-so analyze it by assuming there are no tax breaks and the panels are used for 25 years. Here are some questions Eric is interested in from Society's perspective: . What are the present value, payback, AEC, and IRR of the two solar systems? What is the breakeven social cost of carbon (such that the PV = $0)? Just find the initial cost. That is instead of $8/MT of CO2 find the amount that results in a PV of $0. Assume that this initial amount grows at the rate listed in the case. How much is society paying per kW-h for solar? Compare this to the existing cost of electricity What is the breakeven cost of the system in terms of $ per installed Watt? . Conclusions What do you think about this investment from society's perspective? Are the rebates a good use of taxpayer money? The Austin Energy rebate comes from the citizens of Austin. Can you think of anything else that the city could do with the money that might be a better investment? What about the Federal Tax Credit? Is this a good use of taxpayer funds? Explain your position on these issues. Case Eric is thinking about installing solar panels on his house to reduce his electricity usage and his carbon footprint Cost of Electricity Austin Energy uses the five-tier rale schedule shown below: Electricity Rate Schdule Usage (kWh) Cost ($/kWh) From Jun-Sep Oct-May 0 500 0.033 0.018 501 1000 0.080 0.056 1001 1500 0.091 0.072 1501 2500 0.110 0.084 2501 999999 0.114 0.096 Suppose Eric uses 1250 kWh of electrical energy during the month of June. The charge is then 500*10.033)+500 (0.080)+250 (0.091)=$79.25. In addition, Austin Energy charges a "fuel charge" of $0.0365/kW-h, a "regulatory charge" of $0.00728/kW-h, and a "community benefit charge of $0.00554/kW-h on all the kW-h. Also, Austin Energy charges $10/month to have an electrical hook-up. Eric believes all these costs are likely to increase in real terms at 0.5% per year. Just apply the same percentage increase to all these costs. Investment Details He has an offer from an Austin-based solar company for two different systems. The details are provided below. These costs below already include sales tax. Table 1: System Specifications and Cost Sharp 224W Sharp 175W Power (W) 224 175 Number 14 30 Efficiency 13.74% 13.45% Array Area (m 2) Power (kW) 22.82 3.14 39.03 5.25 Cost $10,990 $18,375 The solar system will be tied to the electricity grid and will not include storage. If Eric needs additional power he can purchase it from the grid. 7/28/2021 1 of 8 ME 353 H009 The city of Austin is offering a rebate equal to $1.50 per installed watt, adjusted for inverter efficiency, which is assumed to be 95.5% for this rebate. Thus, if Eric installed 3.14 kW he would receive a rebate of 3140 955 * 1,5 - $4,498 In addition, the federal government is offering a tax credit of 30%, which means Eric will get 30% of the net purchase price back when he files his 2021 tax return. The net price is the cost of the system after applying the Austin rebale. To keep things simple, assume that Eric receives this credit at the time of purchase. In addition, to keep things simple, assume that solar system would be installed at the end of 2021. The benefit of the solar panels is two-fold. First, they would allow Eric to lower the amount of electricity that he buys from the grid (from Austin Energy). Second, they would reduce the amount of greenhouse gases (GHG) that Eric is responsible for (reduce his carbon footprint). Eric's real MARR is 7%. All the dollars discussed in this case are in real terms. Electric Bill with Solar Austin Energy determines Eric's bill as follows. First, they assume Eric does not have solar and charge him according to the schedule above. They then give Eric a credit for any solar he produces at the rate of $0.128 per kW-h. However, Eric cannot have a negative bill in any year. That is, i value of his solar credit exceeds his yearly bill, Austin Energy only gives him credit for his electricity bill, not the value of all the solar Eric's real MARR is 7%. All the dollars discussed in this case are in real terms. Electric Bill with Solar Austin Energy determines Eric's bill as follows. First, they assume Eric does not have solar and charge him according to the schedule above. They then give Eric a credit for any solar he produces at the rate of $0.128 per kW-h. However, Eric cannot have a negative bill in any year. That is, if value of his solar credit exceeds his yearly bill, Austin Energy only gives him credit for his electricity bill, not the value of all the solar, Systems Specifications Unfortunately, solar panels cannot produce more power than they receive from the Sun. Eric used a system called PVWatts (http://rredcnrel.gov/solar/codes_algs/PVWATTS/versionl/), which is based on field data, to estimate the average solar flux for his system (this is the 24- hour, around the clock, and across the month, average solar flux). These results are based on the exposure of Eric's roof (170) and its slope (40%). Note: in the drawings below, it says Eric's roof is at 30, but this is incorrect. Month January February March April May June July August September October November December Solar Flux (W/m2) 187 210 223 220 214 227 240 240 246 235 238 198 172 Unfortunately, solar cells are not 100% efficient. In fact Sharp estimates that the initial efficiency is 13.74% for the 224 W module and 13.45% for the 175 W module (see Table 1 and the spec sheets at the end of this document). In addition, solar cells degrade with time and Eric estimates that the initial efficiency could decline by 1.0% per year. These changes are percentage changes so that in the base case the efficiency for the 224 W module in year I will be 13.74% *(1 - 1%)^(1-1). We subtract 1 since we assume they do not degrade the first year. In addition, the AC/DC inverter is only 95.5% efficient. To find the efficiency of the system you should multiply the collector efficiency by the inverter efficiency. The panels will last for 25 years. Design A is shown below. Components + Design Sharp 224 Watt SMA 583000US Location SYSTEM SPECIFICATIONS 3.13 and Tied PV System 14 Sharp NO 220W Modules I Sunny 3000 Inverter 170 Design B is shown below. Components Design + SMA SBSOODUS Location _SYSTEM SPECIFICATIONS 5.25W Grid Tied PV System 30 Sharp NT 175W Modules 1 Sunny 500w inverter 170 FAQs About the Sun and the Earth Why is the solar flux an average? What does that mean? Well, let's see. What is the solar flux at night? Zero. What is it at noon? Much higher, maybe 1500 W/m^2. Can't you give us an equation that gives the flux at any instant of time? Sure! But you would then have to integrate that. What do you mean this is an average across the month? Well, the average flux on March 1 is not the same as March 31. The Earth orbits the Sun. As it does this, because the Earth is titled 23 on FAQs About the sun and the Farih Why is the solar flux an average? What does that mean? Well, let's see. What is the solar flux at night? Zero, What is it at noon? Much higher, maybe 1500 W/m^2. Can't you give us an equation that gives the flux at any instant of time? Sure! But you would then have to integrate that. What do you mean this is an average across the month? Well, the average flux March 1 is not the same as March 31. The Earth orbits the Sun. As it does this, because the Earth is titled 23 on its axis, the angle of incidence of sunlight at any location changes, as does the length of the day. So, the average flux on March 1 will be less than the average flux on March 31. If these concepts are new to you, I suggest you read up on the Earth and its place in the solar system. This is good stuff to know! Especially for an engineer from a top-program! What is Energy? This question always comes up: How do you go from solar flux to electrical energy produced? This is such a basic mechanical engineering question, that you need to figure it out. Flux is in watts per square meter. A watt is measure of power. Electrical energy is measured in watt- hours. Electricity Usage Eric has tracked his monthly electricity usage over the last thirteen years (seriously, he has done this). Based on this data he has provided the following monthly energy usage per square foot. Month January February March April May June July August September October November December Energy Usage (kW-h/ft^2) 0.3067 0.2638 0.3227 0.3177 0.4026 0.4951 0.5526 0.6591 0.6345 0.4963 0.3285 0.2929 Eric's current estate is 3200 ft2. This home is more efficient that his past homes and therefore Eric thinks his usage per square foot is likely to be lower. He estimates that his new home 10% more efficient Eric is concerned that once the solar panels are installed his family will not be as careful with their electricity use. For example, his wife has already commented that "Once we get the solar panels you won't be able to badger me about leaving the outdoor lights on all night." (Editorial comment: How funny is that?!). He believes that his family's electricity usage will rise 15% once the panels are installed. Salvage Value One thing Eric is worried about is that he may not be in his home for the entire life of solar panels, which is 25 years. His best estimate is that he will be in the home 10 more years. If Eric is not in his home for 25 years he will lose the value of solar provided electricity In addition, he is also worried that the solar panels will decrease the value of his home. Eric thinks about this and decides to divide this cost into two components: (1) the present value of the remaining electricity that solar panels would provide a positive) and (2) a change in the value of the home for purely esthetic reasons (possibly a negative). (1) Eric thinks that a future buyer will be willing to pay an extra amount for his house that is proportional to the present value of the remaining solar energy at the time of the sale. Salvage Value One thing Eric is worried about is that he may not be in his home for the entire life of solar panels, which is 25 years. His best estimate is that he will be in the home 10 more years. If Eric is not in his home for 25 years he will lose the value of solar provided electricity. In addition, he is also worried that the solar panels will decrease the value of his home. Eric thinks about this and decides to divide this cost into two components: (1) the present value of the remaining electricity that solar panels would provide a positive) and (2) a change in the value of the home for purely esthetic reasons (possibly a negative). (1) Eric thinks that a future buyer will be willing to pay an extra amount for his house that is proportional to the present value of the remaining solar energy at the time of the sale. For example, if Eric sells his home in year 10 he estimates that the new home buyers would be willing to pay some fraction of the present value of the remaining 15 years of solar energy. He estimates this value is 25%. (2) Eric thinks that new home buyers are likely to decrease how much they are willing to pay for the house because they don't like the way solar panels look. He estimates that they will pay $8000 less for his home (this is a future value, that is constant no matter when he sells his home-since it is in real terms). The Social Cost of Carbon Electricity production from fossil fuels (coal, natural gas, oil) emits CO2, which is a greenhouse gas (GHG). The emission of CO2 is believed to be warming the planet, which will result in future damages to society. This means that when we burn coal, for example, we are imposing a cost on society that is not reflected in the price. This is called an "externality." In order to make better choices we need an estimate for the "social cost of carbon," which is the present value of the damages done by emitting one more metric ton (MT) of CO2 into the atmosphere. William Nordhaus, a professor at Yale University, has estimated that this social cost is currently $40 per metric ton (MT) of CO2 and is increasing at about 3% per year in real terms. Eric wants his investment decision to include this cost, even though he may never personally have to pay it. Now, to use this information, you will need to convert the damages from $ per MT of CO2 to $ per kW-h. The carbon intensity of coal is 1000 kW-h per MT of CO2. That is, for every 1 MT of CO2 emissions we get 1000 kW-h of electricity. The carbon intensity of natural gas is 1700 kWh per MT of CO2. Based on Austin Energy's generation portfolio, Eric believes his carbon intensity is 1400 kW-h per MT of CO2. How do you use this information? Well, you need to calculate the how much CO2 is saved by using solar and multiply it by the social cost of CO2. Is it really that simple? Yes. Analysis As you can see, this is a complicated investment and Eric has many questions. These are divided into questions regarding the social value of solar energy and the direct benefit to him. Eric's Value Is this a good investment from Eric's perspective? Which system is best and why? In this section, you should assume Eric may not be in the house for 25 years (as detailed above). Here are some questions Eric is interested in: . Will he still have to purchase electricity from Austin Energy or will the solar panels supply all his energy needs? What fraction of his energy needs will the panels cover? How much of a cost is Eric imposing on society through the use of electricity? Based on media reports and actions taken by the Austin City Council, he believes this cost must be very high What are the present value, payback, AEC, and IRR of the two solar systems? What is the breakeven social cost of carbon (such that the PV = $0 or the IRR = MARR) from Eric's perspective? Just find the initial cost. That is instead of $8/MT of CO2 find the amount that results in a PV of $0. Assume that this initial amount grows at the rate listed in the case. What is the breakeven cost of the system in terms of $ per installed Watt? Value to Society Are Eric's solar panels a good investment from society's perspective? The panels will last for 25 years, even it Eric sells the home to someone else and they will offset the amount of electricity purchased from the grid. However, society does not reap the benefit of the rebates and tax credits since society is paying these. Thus, you should assume that society pays the full cost of the system. Society does benefit however from a reduction in the use of GHG's, which should be valued at the social cost of carbon. Of course, society also gets the value of the produced electricity. Assume that society's MARR is 7%, like Eric's. This calculation is no different than assuming Eric is in the house for 25 years and gets no tax breaks-so analyze it by assuming there are no tax breaks and the panels are used for 25 years. Here are some questions Eric is interested in from Society's perspective: . What are the present value, payback, AEC, and IRR of the two solar systems? What is the breakeven social cost of carbon (such that the PV = $0)? Just find the initial cost. That is instead of $8/MT of CO2 find the amount that results in a PV of $0. Assume that this initial amount grows at the rate listed in the case. How much is society paying per kW-h for solar? Compare this to the existing cost of electricity What is the breakeven cost of the system in terms of $ per installed Watt? . Conclusions What do you think about this investment from society's perspective? Are the rebates a good use of taxpayer money? The Austin Energy rebate comes from the citizens of Austin. Can you think of anything else that the city could do with the money that might be a better investment? What about the Federal Tax Credit? Is this a good use of taxpayer funds? Explain your position on these issues