- Problem Statement Suppose You Want To Install A Home Solar System They Are All The Rage After All There Are A Number 1 (51.48 KiB) Viewed 39 times
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The reason we care about these intermediate steps, is that with each energy transformation, we incur losses due to some inefficiency, so we cannot assume we'll be able to use all of the energy we get from the sun. In general, those inefficiencies can be described with the following equation: E= A = H = Energy (kWh) Total solar panel Area (m²) Solar radiation hitting the panels (kWh/m²) r= solar panel yield or efficiency(%) PR = Performance ratio (efficiency of the system of controller, inverter, and connecting cables) The problem is, we know many of these values will change radically with time. Solar radiation (H) will obviously change throughout the day, and by season as well. Additionally, the solar panel yield (r) will vary with air temperature. It usually hovers around 15% but will decrease if the panels get too hot. E = A *H*r* PR (Equation 1: Solar panel usable energy output) Because of this, it would be incredibly helpful to have some time series data to make calculations, maybe even a few years' worth, to be able to capture the effect of the seasons. Fortunately, we have data for that! Methods: Data Collection (Already done by instructors): For this problem, we've aggregated 3 years' worth of hourly data on 3 parameters we need to solve this problem. 1. The solar energy/solar flux hitting our home (H). This is actual data provided by MSU's enviroweather station in East Lansing. Our thanks to Steve Marquie and the team at Enviroweather. 2. Air temperature also via Enviroweather. 3. Standard home energy use data in the Lansing area. Data courtesy of the National Renewable Energy Laboratory via Open El. These datasets have been aggregated into a single mat file for you to load into Matlab. The variable names and units are listed below. Value Home Energy Use Air Temperature Solar Flux Time Name HomeUse atmp srad Time Unit kWh Deg C W/m² Watch those units! Matlab Datetime Format
To move the project forward, we will make a few assumptions about constant values. These are listed below: Variable/Constant Value Note Array Area (A) 40 m^2 0.86 PR r_baseline 15% 14 kWh Battery Capacity Price of Electricity Total System Cost $0.16/kWh $20,000 Approximately 40 rooftop pannels Accounts for invertor and line losses Baseline efficiency, we'll need to adjust for temp to find the true "r" at each time Based on Tesla home battery Current average residential price in Michigan Rough estimate. Includes all components and installation fees Calculations & Coding Based off all of these assumptions and research we would like you to make the following calculations using a Matlab Script. Step 1: Load in the raw data Simply load in the given mat file. This should load the 4 variables listed in table 1. Step 2: Calculate "r" at each time This will require a simple algorithm to be applied. Most r values will be equal to r_baseline (Table 2). However, if the air temperature is above 25 °C you need to apply the following equation: r=r_baseline-(atmp-25)*.0038 (Equation 2: Finding temperature adjusted r values) Step 3: Calculate & plot the Energy output "E" of the system at each time After you've calculated r for each time-step, this can be calculated using equation 1. Step 4: Calculate & plot the amount of energy in the system's battery in each time step This will require you to create your own algorithm to determine what will happen to battery storage at each time step. Will it increase because you have surplus energy being produced? Will it be depleted because you aren't producing enough energy for your home? I would recommend charting this out using a logic diagram before coding. Any such diagram would be a HIGHLY encouraged addition to your report.
Step 4: Calculate & plot the amount of energy in the system's battery in each time step This will require you to create your own algorithm to determine what will happen to battery storage at each time step. Will it increase because you have surplus energy being produced? Will it be depleted because you aren't producing enough energy for your home? I would recommend charting this out using a logic diagram before coding. Any such diagram would be a HIGHLY encouraged addition to your report. Step 5: Calculate & plot how much energy you will need to get from the energy company to keep your house running at each time step. It's very possible at some times you won't have enough energy from your battery and solar panels combined to run your home. In this case, you'll need to buy some from the power company. Calculate at each time step if you need to buy electricity and if so, how much. Hint: this will likely require another (simple) algorithm. Step 6: Calculate how much money you would save over the hypothetical 3-year period by having the solar panels. For this piece we will assume that total energy costs are just the sum of all energy purchases (in kWh) multiplied by the assumed 16 cents/kWh value given in table 2. Do this for your solar panel scenario you've just built as well as a scenario in which you just bought all of your electricity from the grid. Step 7: Make a final determination as to how long it would take to pay off your initial investment in solar panels. This will just be a simple payback period calculation. Total investment divided by money saved per year.
HomeUse 26304x1 double 1 2 3 4 5 сл 6 7 8 x atmpx srad 9 10 11 12 13 14 15 16 17 18 19 1 0.9850 0.9621 0.9741 0.9886 1.0382 1.2322 1.4232 1.3407 1.2135 1.2232 1.1404 1.0855 1.0383 1.0111 1.0342 1.1286 1.3672 1.4395 1.5723 2 Time 3
HomeUse 26304x1 double 1 2 3 4 5 6 7 8 9 10 x atmpx srad x Time 11 12 13 14 15 16 17 18 19 1 -5.2000 -5.8000 -6.2000 -6.7000 -7.4000 -7.7000 -8.0000 -7.4000 -5.4000 -3.1000 -1.6000 -0.2000 0.2000 1.2000 2.2000 2.6000 3.5000 3.3000 3.1000 2 3
HomeUse x atmp 26304x1 double 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 1 0 0 0 0 0 0 0.1667 45.1111 201.6111 376.5278 512.4444 618.6667 698.1111 790.2222 752.4167 698.5278 583 390.8889 210.4167 srad x Time 2 3 4 5 6 O
Home Use atmp 31 26304x1 datetime 1 srad 9 10 1 08-Apr-2018 01:00:00 2 08-Apr-2018 01:59:59 3 08-Apr-2018 03:00:00 4 08-Apr-2018 04:00:00 5 08-Apr-2018 04:59:59 08-Apr-2018 06:00:00 6 7 08-Apr-2018 07:00:00 8 08-Apr-2018 07:59:59 08-Apr-2018 09:00:00 08-Apr-2018 10:00:00 11 08-Apr-2018 10:59:59 12 08-Apr-2018 12:00:00 13 08-Apr-2018 13:00:00 14 08-Apr-2018 13:59:59 15 08-Apr-2018 15:00:00 16 08-Apr-2018 16:00:00 17 08-Apr-2018 16:59:59 18 08-Apr-2018 18:00:00 19 08-Apr-2018 19:00:00 Time x 2 3