Please do on matlab accurately and simply: E $=$ A $*$ H $*$ r $*$ PR E $=$ Energy $($kWh$)$

A $=$ Total solar panel Area $($m$2$

$)$

H $=$ Solar radiation hitting the panels $($kWh$/$m$2$

$)$

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.

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 that data for you! 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 data from the given excel file and separate the columns into relevant vectors.

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 $25$ oC you need to apply the following equation:

r $=$ r$\_$baseline$-($atmp$-25)*\mathrm{.}0038$

$($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 $1.$ Be aware, this may require some unit

conversion.

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 $19$ cents$/$kWh value given in table $2.$ Do this for your solar pan el scenario you$$ve just built as well as a scenario in

which you just bought all of your electricity from the grid.

Data Collection $($Already done by instructors$)$:

We the instructional team have aggregated $3$ years$$ worth of hourly data on $3$ parameters for you, that will be needed to solve this

problem. You$$re welcome $$

$1.$ 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 EI$.$

These datasets have been aggregated into a single excel file for you to load into Matlab. The variable names and units are listed

below.

Table $1$: Names and Units of Variables Included in the project $.$csv file

Value Name Unit

Home Energy Use HomeUse kWh

Air Temperature atmp Deg C

Solar Flux srad kJ$/$m$2$ Watch those units!

Assumptions $($Already done by instructors$)$:

To move the project forward, we will make a few assumptions about constant values. These are listed below:

Table $2$: List of pre$-$determined project assumptions with units

Variable$/$Constant Value Note

Array Area $($A$)40$ m$^2$ Approximately $40$ rooftop pannels

PR $0\mathrm{.}86$ Accounts for invertor and line losses

r$\_$baseline $15\%$ Baseline efficiency, we$$ll need to adjust for temp to find the true $$r$$ at each time

Battery Capacity $14$ kWh Based on Tesla home battery

Price of Electricity $$0\mathrm{.}19/$kWh Current average residential price in Michigan

Total System Cost $$25,000$ Rough estimate. Includes all components and installation fees