ERGY8070. Week 7: Sample Problems

Week 7 ERGY8070 1. If an Ontario home consumes the following amount of electricity during June, would it be better for them to pay by time-of-use or by tiered billing? • 380 kWh off-peak • 190 kWh mid-peak • 120 kWh on-peak 2. If a company pays $215 for their electricity bill for a total electricity usage of 1,279.07 kWh, what is their blended rate? 3. In Ontario, are residential and small business electricity bills similar? 4. What is typically the most expensive charge on a Class B large business customer’s electricity bill? 5. Both Company A and Company B use the same amount of electricity, but with a different peak demand. If the electricity rate is $0.0428/kWh and the demand rate is $2.68/kW, company will have a higher bill? HINT: make sure to add both the electricity cost and peak demand cost. Note that 1 MW =1,000 kW • • Company A runs a 50 MW load continuously for 100 hours Company B runs a 5 MW load continuously for 1000 hours 6. What is the load factor of a facility that used 90,220 kWh in May (31 days) with a peak demand of 160 kW? Week 7 ERGY8070 7. Is the calculation of simple payback period the only financial consideration that should be given for ALL energy projects? 8. If a lighting retrofit costs $44,600 to implement and results in 98,110 kWh in energy savings, what is the simple payback in (years) if the blended electricity rate is 11¢/kWh? 9. An elementary school currently has one hundred (100) 30 W florescent light fixtures in their hallways that operate from 7 AM to 7 PM year-round. Assume a blended rate of $0.13/kWh. a. What is the annual energy costs to operate the current lights? b. If they replaced the fixtures with 15 W LED lights, what would be the annual energy savings in kWh and dollars ($). c. What is the simple payback period for the lighting replacement if the lights cost $9.97/light? 10. A housing company in Toronto is trialing a net-zero home by using PV arrays to offset 100% of their electricity consumption. They want to install an 11 kW solar system that will get an estimated 1,300 hours of full-sun per year. What is the simple payback if the PV panels cost $2.5/Watt? 11. A natural-gas fired domestic hot water heater consumes 20 m3 of natural gas each month. If an electric hot water heater is installed as a replacement, what would be the difference in monthly cost? Assume: a. 100% efficiency b. $0.12/kWh of electricity c. $0.4/m3 of gas d. 1 m3 of gas = 10.5 kWh Week 7 ERGY8070 ANSWERS 1. If a home consumes the following amount of electricity during June, would it be better for them to pay by time-of-use or by tiered billing? • 380 kWh off-peak • 190 kWh mid-peak • 120 kWh on-peak $0.082 ∗ 380 𝑘𝑊ℎ 𝑘𝑊ℎ 𝑂𝑓𝑓 − 𝑃𝑒𝑎𝑘 𝐶𝑜𝑠𝑡𝑠 = $31.16 $0.113 𝑀𝑖𝑑 − 𝑃𝑒𝑎𝑘 𝐶𝑜𝑠𝑡𝑠 = ∗ 190 𝑘𝑊ℎ 𝑘𝑊ℎ 𝑂𝑓𝑓 − 𝑃𝑒𝑎𝑘 𝐶𝑜𝑠𝑡𝑠 = $21.47 $0.17 𝑂𝑛 − 𝑃𝑒𝑎𝑘 𝐶𝑜𝑠𝑡𝑠 = ∗ 120 𝑘𝑊ℎ 𝑘𝑊ℎ 𝑂𝑓𝑓 − 𝑃𝑒𝑎𝑘 𝐶𝑜𝑠𝑡𝑠 = $20.40 𝑂𝑓𝑓 − 𝑃𝑒𝑎𝑘 𝐶𝑜𝑠𝑡𝑠 = 𝑇𝑖𝑚𝑒 𝑜𝑓 𝑈𝑠𝑒 𝑇𝑜𝑡𝑎𝑙 𝐶𝑜𝑠𝑡 = $31.16 + $21.47 + $20.4 = $73.03 𝑇𝑜𝑡𝑎𝑙 𝑘𝑊ℎ 𝐶𝑜𝑛𝑠𝑢𝑚𝑝𝑡𝑖𝑜𝑛 = 380 𝑘𝑊ℎ + 190 𝑘𝑊ℎ + 120 𝑘𝑊ℎ = 690 𝑘𝑊ℎ $0.098 𝑘𝑊ℎ 𝐹𝑖𝑟𝑠𝑡 600 𝑘𝑊ℎ 𝐶𝑜𝑠𝑡 = $58.80 $0.115 𝐴𝑏𝑜𝑣𝑒 600 𝑘𝑊ℎ 𝐶𝑜𝑠𝑡 = 90 𝑘𝑊ℎ ∗ 𝑘𝑊ℎ 𝐹𝑖𝑟𝑠𝑡 600 𝑘𝑊ℎ 𝐶𝑜𝑠𝑡 = $10.35 𝐹𝑖𝑟𝑠𝑡 600 𝑘𝑊ℎ 𝐶𝑜𝑠𝑡 = 600 𝑘𝑊ℎ ∗ 𝑇𝑖𝑒𝑟𝑒𝑑 𝑇𝑜𝑡𝑎𝑙 𝐶𝑜𝑠𝑡 = $58.80 + $10.35 = $69.15 Therefore, it would be cheaper for them to use tiered billing. 2. If a company pays $215 for their electricity bill for a total electricity usage of 1,279.07 kWh, what is their blended rate? 𝑇𝑜𝑡𝑎𝑙 𝐸𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑖𝑡𝑦 𝐵𝑖𝑙𝑙 𝐶𝑜𝑠𝑡 𝑇𝑜𝑡𝑎𝑙 𝐸𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑖𝑡𝑦 𝐶𝑜𝑛𝑠𝑢𝑚𝑝𝑡𝑖𝑜𝑛 $215 𝐵𝑙𝑒𝑛𝑑𝑒𝑑 𝑅𝑎𝑡𝑒 = = $0.168/𝑘𝑊ℎ 1279.07 𝑘𝑊ℎ 𝐵𝑙𝑒𝑛𝑑𝑒𝑑 𝑅𝑎𝑡𝑒 = Week 7 ERGY8070 3. In Ontario, are residential and small business electricity bills similar? Yes. While they are not exactly the same, they are quite similar, as described in class. 4. What is typically the most expensive charge on a Class B large business customer’s electricity bill? Global Adjustment charge, as shown in slide 38. 5. Both Company A and Company B use the same amount of electricity, but with a different peak demand. If the electricity rate is $0.0428/kWh and the demand rate is $2.68/kW, company will have a higher bill? HINT: make sure to add both the electricity cost and peak demand cost. Note that 1 MW =1,000 kW • • Company A runs a 50 MW load continuously for 100 hours Company B runs a 5 MW load continuously for 1000 hours 50 MW = 50MW x 1000kW/MW = 50,000 kW 5MW = 5MW x 1000kW/MW = 5,000 kW 𝑇𝑜𝑡𝑎𝑙 𝐸𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑖𝑡𝑦 𝐶𝑜𝑠𝑡 = (𝑇𝑜𝑡𝑎𝑙 𝐶𝑜𝑛𝑠𝑢𝑚𝑝𝑡𝑖𝑜𝑛 𝑘𝑊ℎ ∗ 𝑒𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑖𝑡𝑦 𝑟𝑎𝑡𝑒) + (𝑝𝑒𝑎𝑘 𝑑𝑒𝑚𝑎𝑛𝑑 𝑘𝑊 ∗ 𝑑𝑒𝑚𝑎𝑛𝑑 𝑟𝑎𝑡𝑒) 𝐶𝑜𝑚𝑝𝑎𝑛𝑦 𝐴 𝑐𝑜𝑠𝑡 = (50,000 𝑘𝑊 ∗ 100 ℎ𝑟𝑠 ∗ $0.0428) + (50,000 𝑘𝑊 ∗ 𝐶𝑜𝑚𝑝𝑎𝑛𝑦 𝐴 𝑐𝑜𝑠𝑡 = $348,000 𝐶𝑜𝑚𝑝𝑎𝑛𝑦 𝐵 𝑐𝑜𝑠𝑡 = (5,000 𝑘𝑊 ∗ 1000 ℎ𝑟𝑠 ∗ $0.0428) + (5,000 𝑘𝑊 ∗ 𝐶𝑜𝑚𝑝𝑎𝑛𝑦 𝐵 𝑐𝑜𝑠𝑡 = $227,400 $2.68 ) 𝑘𝑊 $2.68 ) 𝑘𝑊 Even though both companies use the same amount of kWh, Company A’s electricity bill is much higher, because it has higher peak demand costs (both Company A and Company B have the same electricity cost). 6. What is the load factor of a facility that used 90,220 kWh in May (31 days) with a peak demand of 160 kW? 𝐿𝑜𝑎𝑑 𝐹𝑎𝑐𝑡𝑜𝑟 = 𝑇𝑜𝑡𝑎𝑙 𝐵𝑖𝑙𝑙𝑒𝑑 𝑘𝑊ℎ 𝑃𝑒𝑎𝑘 𝐷𝑒𝑚𝑎𝑛𝑑 ∗ 𝐷𝑎𝑦𝑠 𝑖𝑛 𝐵𝑖𝑙𝑙𝑖𝑛𝑔 𝑃𝑒𝑟𝑖𝑜𝑑 ∗ 24 ℎ𝑟𝑠 Week 7 ERGY8070 90,220 𝑘𝑊ℎ 160 𝑘𝑊 ∗ 31 𝑑𝑎𝑦𝑠 ∗ 24 ℎ𝑟𝑠/𝑑𝑎𝑦 𝐿𝑜𝑎𝑑 𝐹𝑎𝑐𝑡𝑜𝑟 = 0.758 𝐿𝑜𝑎𝑑 𝐹𝑎𝑐𝑡𝑜𝑟 = 7. Is the calculation of simple payback period the only financial consideration that should be given for ALL energy projects? No! As discussed in class, simple payback can sometimes be “good enough” for projects with fast (typically 1 -2 years or less) payback periods. Some projects can still be cost-effective even with longer payback periods, though additional financial analysis is required to demonstrate this (note that this additional analysis is outside the scope of ERGY1010). 8. If a lighting retrofit costs $44,600 to implement and results in 98,110 kWh in energy savings, what is the simple payback in years with a blended electricity rate of 11¢/kWh? 𝐶𝑜𝑠𝑡 𝑜𝑓 𝑁𝑒𝑤 𝑆𝑦𝑠𝑡𝑒𝑚 𝐴𝑛𝑛𝑢𝑎𝑙 𝐸𝑛𝑒𝑟𝑔𝑦 𝐶𝑜𝑠𝑡 𝑆𝑎𝑣𝑖𝑛𝑔𝑠 𝑑𝑢𝑒 𝑡𝑜 𝑁𝑒𝑤 𝑆𝑦𝑠𝑡𝑒𝑚 $44,600 𝑆𝑖𝑚𝑝𝑙𝑒 𝑃𝑎𝑦𝑏𝑎𝑐𝑘 𝑃𝑒𝑟𝑖𝑜𝑑 = = 4.13 𝑦𝑒𝑎𝑟𝑠 98,110 𝑘𝑊ℎ ∗ $0.11/𝑘𝑊ℎ 𝑆𝑖𝑚𝑝𝑙𝑒 𝑃𝑎𝑦𝑏𝑎𝑐𝑘 𝑃𝑒𝑟𝑖𝑜𝑑 = 9. An elementary school currently has one hundred 32 W florescent light fixtures in their hallways that operate from 7 AM to 7 PM year-round. Assume a blended rate of $0.13/kWh. a. What is the annual energy costs to operate the current lights? 𝑑𝑎𝑦𝑠 𝑊 ℎ𝑟𝑠 ∗ 12 ∗ 365 𝑦𝑒𝑎𝑟 𝑓𝑖𝑥𝑡𝑢𝑟𝑒 𝑑𝑎𝑦 𝐵𝑎𝑠𝑒𝑙𝑖𝑛𝑒 𝐸𝑛𝑒𝑟𝑔𝑦 = = 13,140 𝑘𝑊ℎ 1000 𝑊/𝑘𝑊 $0.13 𝐵𝑎𝑠𝑒𝑙𝑖𝑛𝑒 𝐸𝑛𝑒𝑟𝑔𝑦 𝐶𝑜𝑠𝑡𝑠 = 13,140 𝑘𝑊ℎ ∗ = $1,708.2 𝑘𝑊ℎ 100 𝑓𝑖𝑥𝑡𝑢𝑟𝑒𝑠 ∗ 30 b. If they replaced the fixtures with 15 W LED lights, what would be the annual energy savings in kWh and dollars ($). 𝑑𝑎𝑦𝑠 𝑊 ℎ𝑟𝑠 ∗ 12 ∗ 365 𝑦𝑒𝑎𝑟 𝑓𝑖𝑥𝑡𝑢𝑟𝑒 𝑑𝑎𝑦 1000 𝑊/𝑘𝑊 100 𝑓𝑖𝑥𝑡𝑢𝑟𝑒𝑠 ∗ 15 𝑃𝑜𝑠𝑡 − 𝐼𝑛𝑠𝑡𝑎𝑙𝑙𝑎𝑡𝑖𝑜𝑛 𝐸𝑛𝑒𝑟𝑔𝑦 = = 6,570 𝑘𝑊ℎ Week 7 ERGY8070 𝐵𝑎𝑠𝑒𝑙𝑖𝑛𝑒 𝐸𝑛𝑒𝑟𝑔𝑦 𝐶𝑜𝑠𝑡𝑠 = 6,570 𝑘𝑊ℎ ∗ $0.13 = $854.10 𝑘𝑊ℎ 𝐴𝑛𝑛𝑢𝑎𝑙 𝐸𝑛𝑒𝑟𝑔𝑦 𝑆𝑎𝑣𝑖𝑛𝑔𝑠 [𝑘𝑊ℎ] = 13,140 𝑘𝑊ℎ − 6,570 𝑘𝑊ℎ = 6,570 $0.13 𝐴𝑛𝑛𝑢𝑎𝑙 𝐸𝑛𝑒𝑟𝑔𝑦 𝑆𝑎𝑣𝑖𝑛𝑔𝑠 [$] = 6,570 𝑘𝑊ℎ ∗ = $854.10 𝑘𝑊ℎ c. What is the simple payback period for the lighting replacement if the lights cost $9.97/light? $9.97 ∗ 100 𝑙𝑖𝑔ℎ𝑡𝑠 𝑙𝑖𝑔ℎ𝑡 𝑆𝑖𝑚𝑝𝑙𝑒 𝑃𝑎𝑦𝑏𝑎𝑐𝑘 𝑃𝑒𝑟𝑖𝑜𝑑 = = 1.17 𝑦𝑒𝑎𝑟𝑠 $854 10. A housing company in Toronto is trialing a net-zero home by using PV arrays to offset 100% of their electricity consumption. They want to install an 11 kW solar system that will get an estimated 1,300 hours of full-sun per year. What is the simple payback if the PV panels cost $2.5/Watt and the blended rate of electricity is 15 cents/kWh? 𝐶𝑜𝑠𝑡 𝑜𝑓 𝑆𝑜𝑙𝑎𝑟 = $2.5 1000𝑊 ∗ 11𝑘𝑊 ∗ = $27,500 𝑊 1𝑘𝑊 𝐴𝑛𝑛𝑢𝑎𝑙 𝐺𝑒𝑛𝑒𝑟𝑎𝑡𝑖𝑜𝑛 = 11 𝑘𝑊 ∗ 1,300 ℎ𝑜𝑢𝑟𝑠 = 14,300 𝑘𝑊ℎ $0.15 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝐴𝑛𝑛𝑢𝑎𝑙 𝐺𝑒𝑛𝑒𝑟𝑎𝑡𝑖𝑜𝑛 = 14,300 𝑘𝑊ℎ ∗ = $2,145 𝑘𝑊ℎ $27,500 𝑆𝑖𝑚𝑝𝑙𝑒 𝑃𝑎𝑦𝑏𝑎𝑐𝑘 𝑃𝑒𝑟𝑖𝑜𝑑 = = 12.82 𝑦𝑒𝑎𝑟𝑠 $2,145 11. A natural-gas fired domestic hot water heater consumes 20 m3 of natural gas each month. If an electric hot water heater is installed as a replacement, what would be the difference in monthly cost? Assume: a. 100% efficiency b. $0.12/kWh of electricity c. $0.4/m3 of gas d. 1 m3 of gas = 10.5 kWh Natural gas costs = 20 m3 x $0.4/m3 = $8 Electricity costs = 20 m3 x 10.5 kWh/m3 x $0.12/kWh = $25.2 Note that the above comparison is oversimplified. Natural gas water heaters have burners that are less than 100% efficient. Water heaters that use electric resistance have heaters that are 100% efficient. Another variable is tank losses. The more insulation a water tank Week 7 ERGY8070 has, the less heat loss it will have to the environment when hot water is not being used (regardless of fuel type).