Assignment #1_ Basic Energy and Project Economics Calculations
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School
Yorkville University *
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Course
3503
Subject
Industrial Engineering
Date
Apr 3, 2024
Type
docx
Pages
7
Uploaded by 534056kp
Question 1
1GJ=1*10^9 Joule
1 Joule = 1 watt * Hour
1Joule = (KW/1000) * (Hour/3600)
1Joule=2.7777* 10^-7 kWh
1GJ=1x10^-9x2.7777x10^-7 kWh
1GJ = 277.777kWh
1kWh = (1/277.777)GJ
500kWh = 500 (1/277.777) GJ
Therefore,
500kWh = 1.8GJ
Question 2
Given:
P=12KW
Run timings, from 8:00 a.m. to 8:00 p.m.
With this we can say that,
In 1 week, the motor works 5 days from Monday thrusday Friday.
The motor works 12 hours * 5days = 60 hours in every week
In 1 month the motor works = 60 * 4weeks = 240 Hours
In 1 year the motor works = 240 hours * 12months = 2880 Hours
The energy consumed annually by the motor is 12 KW = 2880H
34560 kWh of electricity does the motor consume annually
Question 3
Motor consumes an average of =12 KW (Given) ------> A
Efficiency=75%
Poutput = B
Efficiency= A /B * 100%
I solved for B
B = Efficiency x A /100
B = (75x12KW)/100
B = 9 KW
Question 4
a)KWh consumed daily :
Sum of all powers consumed daily:
1+1+1+2+3+5+3+2+2+4+2+3+3+3+3+2+2= 42 KWh
b)
Peak demand is 5 KW at the 6th hour interval.
Question 5
Plant operates at = 50 MW = 50 * 10
6
W
Average loading = 75%
Total number of hours in a year = 24 * 365= 8760 hours
Loading percent = 75%
So, Total loading time = 0.75 * 8760 = 6570 hours
Total seconds = 6570 * 60 * 60 = 23652000
Total Kwh Does the plant supply to the grid = 50 * 10
6
*6570 * 60 * 60/1000 = 1182600 kwh
Question 6
To calculate the average cost per kWh or MWh for the power produced by the natural gas power plant, we need to consider both the initial capital cost and the annual operating cost over the plant's estimated life.
Given:
●
Initial capital cost = $175,000,000
●
Annual operating cost = $20,000,000
●
Estimated plant life = 20 years
●
Discount rate = 5%
We can use the Net Present Value (NPV) formula to calculate the present value of the total cost
over the plant's life, and then divide it by the total energy produced to find the average cost per kWh.
NPV=175,000,000+20,000,000(1+0.05)1+20,000,000(1+0.05)2+...+20,000,000(1+0.05)20
NPV=175,000,000+
NPV≈175,000,000+19,047,619+18,140,103+...+5,134,000
NPV≈175,000,000+19,047,619+18,140,103+...+5,134,000
NPV≈175,000,000+19,047,619+18,140,103+...+5,134,000
NPV≈175,000,000+19,047,619+18,140,103+...+5,134,000
NPV≈303,515,189
NPV≈303,515,189
Now, we divide the NPV by the total energy produced over the plant's life to find the average cost per kWh:
Average Cost per kWh=NPVTotal Energy Produced
Average Cost per kWh=
Total Energy Produced/NPV
Average Cost per kWh=303,515,189328,500,000
Average Cost per kWh=
328,500,000
303,515,189
Average Cost per kWh≈$0.9244/��ℎ
Average Cost per kWh≈$0.9244/kWh
Therefore, the average cost per kWh for the power produced by the natural gas power plant is approximately $0.9244/kWh.
Question 7
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To determine the minimum number of 10kW solar panels needed to supply 50% of the company's energy, we first need to calculate the total energy consumption of the company and then determine how much energy needs to be supplied by solar panels.
Given:
●
Company's annual energy consumption = 2,000 MWh
●
Energy produced by one 10kW solar panel per year = 12,000 kWh
●
Desired percentage of energy supplied by solar panels = 50%
First, convert the company's annual energy consumption from MWh to kWh:
2,000 MWh×1,000 kWh/MWh=2,000,000 kWh/year
2,000MWh×1,000kWh/MWh=2,000,000kWh/year
Next, determine the total energy needed from solar panels to supply 50% of the company's energy:
Total energy needed from solar panels=0.5×2,000,000 kWh/year=1,000,000 kWh/year
Total energy needed from solar panels=0.5×2,000,000kWh/year=1,000,000kWh/year
Now, calculate the number of 10kW solar panels needed to produce 1,000,000 kWh/year:
Number of solar panels=Total energy neededEnergy produced by one solar panel
Number of solar panels=
Energy produced by one solar panel
Total energy needed
Number of solar panels=1,000,000 kWh/year12,000 kWh/year per panel
Number of solar panels=
12,000kWh/year per panel
1,000,000kWh/year
Number of solar panels=83.33
Number of solar panels=83.33
Since we can't have a fraction of a solar panel, we need to round up to the nearest whole number.
Therefore, the minimum number of 10kW solar panels the company would need to install to supply 50% of its energy is 84 panels.
Question 8
To calculate the simple payback for the solar panel project, we need to consider the initial investment and the annual savings generated by the solar panels.
Given:
●
Installed cost of each solar panel = $25,000
●
Cost of purchasing power from the utility = $0.14/kWh
●
Negligible annual maintenance costs
●
Number of solar panels = 84 (as calculated)
●
Energy produced by one 10kW solar panel per year = 12,000 kWh
First, calculate the total installed cost of the solar panels:
Total installed cost=Cost per panel×Number of panels
Total installed cost=$25,000×84=$2,100,000
Next, calculate the annual savings generated by the solar panels:
Annual savings=Total energy produced by all panels×Cost of purchasing power from the utility
Annual savings=1,000,000kWh/year×$0.14/kWh=$140,000/year
Now, calculate the simple payback period:
Simple payback period=Total installed costAnnual savings
Simple payback period=
Annual savings
Total installed cost
Simple payback period=$2,100,000$140,000/year
Simple payback period=
$140,000/year
$2,100,000
Simple payback period≈15 years
Simple payback period≈15years
Therefore, the simple payback for the solar panel project, assuming negligible annual maintenance costs, is approximately 15 years.
Question 9
For Questions 7 and 8, we have already calculated the average cost per kWh for the power produced by the solar panel system. We'll reuse the calculations from those questions:
●
Average cost per kWh for solar panel system = $0.14/kWh
Now, let's calculate the average cost per kWh for the power produced by the solar panel system
over its estimated 20-year life span.
Average cost per kWh=Total installed costTotal energy produced over 20 years
Average cost per kWh=
Total energy produced over 20 years
Total installed cost
Average cost per kWh=$2,100,00020 years×1,000,000 kWh/year
Average cost per kWh=
20years×1,000,000kWh/year
$2,100,000
Average cost per kWh=$2,100,00020,000,000 kWh
Average cost per kWh=
20,000,000kWh
$2,100,000
Average cost per kWh=$0.105/kWh
Question 10
To compare the average cost per MWh between the natural gas system and the solar panel system, we need to convert the cost per kWh to cost per MWh for both systems.
For the natural gas system (Question 6):
●
Average cost per kWh = $0.9244/kWh
For the solar panel system:
Average cost per MWh for solar panel system=$0.105/MWh
Now, we can compare the average cost per MWh between the natural gas system and the solar panel system:
Natural Gas System: $0.9244/MWh
Solar Panel System: $0.105/MWh
Comparing the two, we see that the natural gas system has a significantly higher average cost per MWh compared to the solar panel system.
Potential Solutions to Improve Solar Panel Project Economics:
Increase Energy Efficiency: Implementing energy efficiency measures within the company's operations can reduce overall energy consumption, thereby decreasing the amount of energy required to be generated by the solar panels. This would lead to lower
costs and potentially shorter payback periods.
Utilize Incentives and Rebates: Governments and utility companies often offer incentives, rebates, or tax credits for renewable energy projects like solar panel
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installations. Taking advantage of these incentives can significantly reduce the upfront costs and improve the financial viability of the project.
Explore Financing Options: Financing options such as loans, leases, or power purchase
agreements (PPAs) can help spread out the initial investment cost over time, making the project more financially feasible. PPAs, in particular, allow companies to purchase solar power at a predetermined rate, often lower than utility rates, without bearing the upfront costs of equipment installation.
Optimize Solar Panel Placement: Ensuring optimal placement and orientation of solar panels can maximize energy generation and efficiency, thus improving the overall economic performance of the project. This may involve conducting a thorough site analysis and considering factors such as shading, roof angle, and sun exposure.