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    Estimating Solar System Yields

    If all you want to do is try and estimate what your grid connect solar output should be you should check this out first (Grid Connect Solar Troubleshooting).

    What follows is a significant discussion, and will get very technical in parts. We will following the format shown below

    1. The sun, power, and energy

    2. Solar Panels and Standard Test Condition

    3. Solar energy calculations

     

    1. The sun, power, and energy

    First of all lets talk about some definitions:

    Irradiance (G):

    This is how much power the sun is delivering per second. It is measured in Watts per meter square (W/m2). On a clear day around 12 noon this is going to be around 1000W/m2

     

    Irradiation (H):

    This is how much energy has struck the ground over a period of time. There are two units commonly used for irradiation.

    Megajoules per meter square (MJ/m2)
    kilowatt hours per meter square (kWh/m2)

    Another term for irradiation is insolation; bother terms are commonly used, and they mean the same thing.

    It is really important to be able to convert between these two units:

    MJ/m2 = 3.6 x kWh/m2

    kWh/m2 = MJ/m2 / 3.6

     

    Peak Sunshine Hours (PSH)

    Peak sunshine hours is the equivalent number of hours at 1000W/m2 of irradiance it would take to reach a particular irradiation level.

    For example:

    Assume that over the period of one day there was 20MJ/m2 of solar energy delivered over 16 hours, how many peak sunshine hours is that?

    Lets firstly convert MJ/m2 to kWh/m2

    20MJ/m2 = 20/3.6 = 5.55kWh/m2

    Now 1kWh = 1000Wh, so 5.55kWh/m2 = 5550Wh/m2

    Now to find Peak Sunshine Hours we simply divide 5550Wh/m2 by 1000W/m2

    and that gives 5.55 Peak Sunshine Hours

    You will notice that once you have converted the Irradiation to kWh, it is very easy to identify the Peak Sunshine Hours.

    I guess you are wondering why we need to worry about this idea of Peak Sunshine Hours? lets take a look.

    chart showing daily irradiance and PSH relationship

    The chart above shows how the suns power changes over the day (the purple line). The blue line shows you the equivalent PSH value (5hrs @ 1000W/m2).

    If you look a little closer at the Irradiance you will notice at 10am the solar irradiance is 700W/m2, and at 12pm the irradiance is 825W/m2. The power coming from the sun is changing all the time.

    In the next section you will learn about solar module standard test conditions. A Solar panels rated electrical power output is based on the sun producing 1000W/m2, as you can see from the previous discussion this may not happen in a day, which makes it hard to estimate solar panel output. To fix the problem we convert the total energy received from the sun (in our example 20MJ/m2) into a PSH value (5.55). We can then say for 5.55hrs in the day the sun was providing 1000W/m2, and from this all of our calculations can be performed.

     

    2. Solar Panels & Standard Test Conditions (STC)

    All solar panels are test using a standard set of test conditions, this allows panels to be compared, and power calculations to be easily performed. At first glance it seems a little strange, however all panels are tested under these conditions.

    Irradiance of 1000W/m2 This is the solar irradiance hitting the module. As was mentioned in the previous section, irradiance from the sun us rarely equak to 1000W/m2, but if we convert to PSH a test value of 1000W/m2 is very useful.
    Cell Temperature of 25 deg C. The physical cell temperature is at 25 deg. C
    Atmospheric Mass of 1.5

    This is an unusual concept, but basically it refers the the amount of atmosphere the sun must travel through. A value of 1 means the sun is right above you.

    The amount of atmosphere changes the makeup of the light spectrum that actually arrives on the solar module.

    for the purposes of your calculations you can ignore this test condition.

     

    Some important notes about solar panel standard test conditions:

    - Power rating of solar module is based on irradiance of 1000W/m2, hence the need for us to use Peak Sunshine Hours (PSH)

    - Power out of module is based on a solar cell temperature of 25 deg C. However cells normally operate at 20 deg C above ambient air temperature, so power adjustments will need to be made based on temperature.

     

    3. Solar Energy Calculations

     

    We have one solar panel with a rating plate as shown below. We want to determine the expected energy yield from the solar panel in January if it were situation in Sydney. Based on solar data captured from a local weather station we know the average energy yield for january is typically 23MJ/m2 per day, and the average daily air temperature is 27 deg C.

     

    Rating Plate on Solar Panel

    Rated Max Power (Pmax) 190W
    Power Tolerance +/- 3%
    Temperature coefficient of power -0.45%/deg C
    Nominal Operating Cell Temperature(NOCT) 45
    Standard test Conditions AM=1.5, 1000W/m2, Cell Temp 25 deg C
       

    OK, lets get started.

    Step 1: Convert the average daily energy yield to Peak Sunshine Hours (PSH)

    23MJ/m2 = 23/3.6 = 6.4 kWh

    We know that 6.4kWh means there are 6.4 Peak Sunshine Hours.

     

    Step 2: Calculate the Operating Cell temperature

    Solar Panel Cell temperature formula

    Where:

    Tair : is the expected air temperature (27 deg C)

    NOCT: is the Nominal operating cell temperature (45 deg C)

    G: is the solar irradiance. Given it is January I would assume it to be 1000W/m2

     

    Tcell = 27 + (45-25)/800 x 1000 = 52 deg. C


    Step 3: Derate the Panel output power

    Firstly we derate the panel down by the manufactures tolerance of 3%
    Pmax = 190 x 0.97 = 184W

     

    Next derate the cell based on the expected cell temperature.

    According to the rating plate we loose 0.45% of our panel power for each degree rise in temperature above 25 deg C.
    percentage loss  = (52 - 25) x (0.45/100) = 0.1215

    Pmax = 184 * (1-0.1215) = 161W

     

    Now we should also derate the panel by another 5% because of dust and dirty build up that will occur once install.

    Pmax = 161 * 0.95 = 152W

     

    WOW.... we started with 190W panel, but based on all the engineering we are left with 152W for each peak sunshine hour.

     

    Step 4: Calculate Expected energy yield

     

    Energy Produced each day = 152W x 6.4PSH = 972.8Wh.

    Now January has 31 days, so the total energy produced = 972.8 x 31 = 30156Wh = 30kWh

     

    Therefore total energy produced from a 190W solar module in january is likely to be 30kWh.

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