## How to Calculate Your Solar Power System

The essential parts of a solar power system are:

1. Solar Panels

2. Backup Batteries

3. Charge controller

4. Inverter

5. Wiring and small accessories

Using 6 types of configuration models for Solar Systems.

1. Day use only system no battery only DC Load.

2. Off grid system only DC Load with battery.

3. Off grid system with battery AC-DC Load connected.

4. Hybrid system.

5. On grid system.

6. On grid system with battery back-up.

The most unpredictable of all solar power systems is the availability of the source itself which is the sun’s energy. There are so many different variables that one cannot depend on one fix value formula to rely on.

Variables like Climate, Weather condition, Cloudy areas, Misty areas, Air density, Geographical position, buildings, trees, mountains, Seasons, snow, tilt, temperature and others … will affect the production of your Solar Power System.

The first variable to consider when planning your solar renewable system is the sunlight. How much sunlight you have and how much energy it will produce in a worst case scenario.

In countries where this is permissible, the on grid solar Power system is the most simple one to accomplish. You can build progressively starting with some panels and add more panels over time. You don’t need battery back-up only if you decide to provide for energy in case of utility outages.

We choose the off grid system with battery backup to demonstrate one way to perform the calculations for our solar system.

Ok, here is how we approach Solar Power calculation

1. Reduce Energy Consumption. This will lower the cost of your solar inversion considerably.

a. Keep focus all the time on your new living lifestyle ’energy efficient’.

b. Select the devices to be powered by the Solar Power System.

c. Do some clean up of old appliances that are not energy efficient. (as soon as possible)

d. Shift loads of high consumption like heaters, to other form of energy transfer methods. For example electric water heaters to solar thermal heating, electric clothes dryers to gas.

e. Replace incandescent light bulbs for CFL or Led lighting.

2. Calculate your energy consumption for a day.

3. Calculate the size of your battery bank back up power.

4. Calculate how many panels you need in the array of your Solar Power System.

5. Define your Charge Controller.

6. Define your Inverter.

7. Wire your components according your selected solar power system type.

Here is how we are going to calculate and define the energy consumption. You can find your monthly energy consumption on your electricity bill in kWh (kiloWatthour). Take your last 12 bills and add each monthly kWh total to get the year kWh total. Divide this year kWh total by 365 to obtain an average daily electrical energy usage. If you compare the energy usage after you have done step 1, you will see big differences with previous months. You will notice how much money you would have saved doing only this first step.

A more precise way to define your energy usage is to make a list of all the devices that will be powered by your renewable solar power system with their accompanying Watt values. You can find this on the appliance itself whether in Watt or Amp. If it is stated in Amps you simply multiply the Amps with the value of your line voltage and you will get its Watt value. Watt = Amp x Volt. If there is nothing you can find on the appliance you have to use an Amp meter or a Kill-A-Watt meter to read the Amp drawn and then multiply this reading with your line voltage to get its wattage.

Record all the data in a table list, like Table 1.1 below. In the fourth column "Usage” fill in how much time you use the appliance in hours per day. This is for the case you don’t remember how you end up with some figures of the next column "Hour per day". Next you’ll record for each appliance, the amount of time (in hour) it is used per day in the column "Hour per day". For example if you use it 6 hours a day, you fill in 6 in this column and if you use it 15 minutes a day, you record 0.25 (15/60). And 30 minutes per week you’ll fill in 0.071 in the "Hour per day" column, this is (30/60)/7 hour per day. And 30 minutes a month would be (30/60)/30 = 0.017 hour per day…..etc.

Next you’ll multiply the two values of the columns "Ratings" and "Hour per day" to obtain the values in the column "Daily Wh". This value in the "Daily Wh" column times 7 will give you the "Weekly Wh". And the value in "Daily Wh" times 30 result in the "Monthly Wh", this can be used for comparison, but we don't need it in our calculations. In case you use an appliance once a month or once a week, you calculate backwards your daily usage. The following list is filled with our values, but you will use your specific values.

Our Energy Consumption Table in Watthour per day for our solar power system.

Our choice is Lead Acid Battery which is the most common used when deep cycling. When we calculate our Lead Acid Battery Bank we have to take the following into account: 1. That we don't discharge a battery below 30% of its capacity. To prolong the life of our batteries we discharge our batteries to only 50%. (the lesser the better). 2. For how many days the battery bank must supply power in case of no sunshine or cloudy days. In our case we will take 2 days of no sunshine. 3. The ambient temperature of the battery bank. A temperature of 77 to 80 degrees Fahrenheit is about normal for the battery bank. Higher temperature will shorten the battery life and colder temperature will reduce its capacity.

Battery bank capacity:

Our average daily use in the above table is 7572 Wh.

Two days of no sunshine will add 2 x 7572 = 15144 Wh.

Discharging to 50 percent will add 15144 / 0.5 = 30288 Wh.

(In case we want to discharge only 40% of the battery capacity, we divide by 0.4 and the battery charge will stay at 60% of its capacity).

We add a factor of 10% to compensate for temperature variations.

This add 10% or 3029 Wh to our subtotal to bring our total to 30288 + 3029 = 33317 Wh.

Now we have to choose our battery size and puzzle out how to connect the batteries in our battery bank. With batteries it is always better to avoid parallel connections, but in most cases this is not possible, always try to maintain the least possible parallel strings of batteries and not going beyond 3 strings.

If we use a 12V system our battery bank will need a capacity of 33317 / 12 = 2775 Ah. If we make 3 strings, one string must deliver 2775 / 3 = 925 Ah. We end up with more than 3 strings of batteries. Not practical. Not recommended. If we use a 24V system our battery bank will need a capacity of 33317 / 24 = 1389 Ah. With 3 strings, one string delivers 1389 / 3 = 463 Ah. We still end up with more than 3 strings.

From the above results we see that lower voltage solar power systems will need larger capacity per battery, you will need more than recommended parallel strings and it will produce larger amounts of currents and consequently need larger wire dimensions and will be more costly. This is not practical.

So we will choose for a 48V solar power system and our battery bank will need a capacity of 33317 / 48 = 695 Ah.

Each of 3 parallel strings need to provide 695 / 3 = 232 Ah.

Choose batteries you can find with 232 Ah or the closest you can get.

To provide for the voltage of 48V while you choose for batteries of 12Volts you will need 48 / 12 = 4 batteries in series for each string. With 3 strings you will need 3 x 4 = 12 batteries in your battery bank.

The reason why to avoid parallel battery connection is that not all the batteries are exactly equal with reference to voltage, charge and internal resistance. And connecting them in parallel will meant that one can act like a load for the other and produce an unbalance charging for the battery bank. And so reduce the life of the batteries.

First we have to find out how much sunshine we dispose of in the worst case per day. The further away you live from the equator. The less sunshine you will have per day in the winter season. The less energy will your solar panels produce, the more panels you will need to meet your energy needs.

Go to the Solar Radiation Monitoring Laboratory of the University of Oregon’s Websitehttp://solardat.uoregon.edu/SunChartProgram.php , enter your Longtitude and Latitude and you will produce a Sun Chart for your location that covers a whole year and which is printable. You will get the Sun’s path, the elevation angle and azimuth angle. From this chart you can read the total hours of sun per day you have for your specific location. Use the worst case scenario (the days of least sunshine).

Or you can go to web site: http://rredc.nrel.gov/solar/old_data/nsrdb/1961-1990/redbook/atlas/Table.html

In our case we can count with 7 hours of sunshine per day worst case scenario.

In those 7 hours the array must produce at least 7572 Watthour of energy.

The Array size in Watt must be this amount of energy divided by the amount of hours.

Energy = Watthour = (Watt x hour) = (Volt x Amp) x hour.

Array Power or size in Watt is 7572 / 7 = 1081 Watt of Solar Array.

This will be the Array Power divided by the Power of one panel.

We are going to check for 3 sizes of panels, 75Watt, 100Watt and 250Watt. Why? You can choose whatever size of panel you want. The choice depends on the available space you have for installing them, to compare the cost of them. The one that best fit will get the credit.

With 75W panels we need a total of (Array size divided by panel size) = 1081/75 = 14.42 = 15 panels.

With 100W panels the total will be 1081/100 = 10.81 = 11 panels.

With 250W panels this is 1081/250 = 4.33 = 5 panels.

We can see a huge difference between 15 and 5 panels. Ok, this difference will also reflect in the prices of the panels, the time needed for installing the system, and the bottom line your budget. Here you have some thinking to do in making your best choice.

In our case we choose 16 panels of 75 Watt each, so we can make 4 strings of 4 panels in series to match our 48 Volt system. We have the space for them, we have plenty of time to install them, and they will satisfy our budget. May be this is not equal in your specific case, where the factors may not be the same like in ours. You will need to adapt the above calculations for your case.

The Array Short Circuit Current and the System Voltage are the factors for defining our Charge Controller. When making your own panel array you have to determine its Short circuit current. This is the current when no load is connected and sunshine is at it maximum, so the panels production is also at its maximum. When you buy a custom made panel this information is labeled on the back of the panel or in the specification sheets. Indicated by Ioc and Voc.

There are so many types of Charge Controller you can get on the market. For small projects it does not matter to choose from any standard one. But we will concentrate on the most sophisticated and reliable Standard PWM charge controller and the MPPT charge controller to protect our costly inversion.

The Pulse Width Modulated and the Maximum Power Point Tracking.

The PWM controller like the MPPT regulates Voltage and Current from the Array to the Battery Bank. The use of the one or the other depends on the system size and its cost. The MPPT is more sophisticated, more efficient and more costly and mostly used in large systems.

When using a PWM, the rated voltage of the Charge Controller must match the array voltage and the battery bank voltage. In our case this is 48 Volt. Other solar power system voltages may be 12 and 24 Volts.

The other factor to consider is the nominal current. This is the highest current the controller can handle. Currents higher and voltages higher than the nominal will destroy the device. For custom made panels we add up the short circuit currents of the parallel strings of the array.

Once the short circuit current (Ioc) of the array is determined, you can find the Amp rating for the Charge Controller, using the formula for Power. Power (Watt) = Volt x Amps.

Solar array is 1081 Watt and the System Voltage is 48 Volt.

Using the Power formula Power = VoIt x Amp we can calculate the Amp of the solar array. This is 1081/48 = 22.52 Amp. We add 25% safety factor for uncommon fluctuation in current variations and end up with a total of 28.15 Amp. On this subtotal we add an additional 25% (continues use) according the National Electric Code (NEC). This is 28.15 + 7.04 = 35.19 Amps Total. Look for a Charge Controller rated higher than 35.19 Amp. A 40 Amp Charge Controller will do the job. A larger sized controller will do no harm.

An MPPT solar charge controller is a smart PWM controller. It has a more extensive range of charging capabilities. You can use lower battery voltage than the array voltage. It is a more efficient charge controller and an expensive one. It’s features are better served in colder countries. If you want to have a more extensive knowledge about the MPPT and if it is adequate for your specific use, you better consult the dealer for your unit.

When determining the Inverter we have to match the input voltage (in our case 48V DC), the output voltage (we choose 120V AC) but you can choose whatever AC voltage applied in your country, different countries have different voltages. And the Inverter must support the load of all the appliances that will be on simultaneously.

We made a list of possible moments the appliances will be ‘on’ for our particular case.

The peak load is between 7 and 8pm in our case and is 1747 Watt.

So we need an Inverter with a Nominal Watt of greater than 1747 Watt. The most common is 2000 Watt.

There are inverters on the market with build in charge controller. You will have to ask your supplier for one that suits your needs or modify your setup to match those needs. Those modifications involve primarily the voltage of the Solar Power System.

1. Solar Panels

2. Backup Batteries

3. Charge controller

4. Inverter

5. Wiring and small accessories

Using 6 types of configuration models for Solar Systems.

1. Day use only system no battery only DC Load.

2. Off grid system only DC Load with battery.

3. Off grid system with battery AC-DC Load connected.

4. Hybrid system.

5. On grid system.

6. On grid system with battery back-up.

The most unpredictable of all solar power systems is the availability of the source itself which is the sun’s energy. There are so many different variables that one cannot depend on one fix value formula to rely on.

Variables like Climate, Weather condition, Cloudy areas, Misty areas, Air density, Geographical position, buildings, trees, mountains, Seasons, snow, tilt, temperature and others … will affect the production of your Solar Power System.

The first variable to consider when planning your solar renewable system is the sunlight. How much sunlight you have and how much energy it will produce in a worst case scenario.

In countries where this is permissible, the on grid solar Power system is the most simple one to accomplish. You can build progressively starting with some panels and add more panels over time. You don’t need battery back-up only if you decide to provide for energy in case of utility outages.

We choose the off grid system with battery backup to demonstrate one way to perform the calculations for our solar system.

Ok, here is how we approach Solar Power calculation

1. Reduce Energy Consumption. This will lower the cost of your solar inversion considerably.

a. Keep focus all the time on your new living lifestyle ’energy efficient’.

b. Select the devices to be powered by the Solar Power System.

c. Do some clean up of old appliances that are not energy efficient. (as soon as possible)

d. Shift loads of high consumption like heaters, to other form of energy transfer methods. For example electric water heaters to solar thermal heating, electric clothes dryers to gas.

e. Replace incandescent light bulbs for CFL or Led lighting.

2. Calculate your energy consumption for a day.

3. Calculate the size of your battery bank back up power.

4. Calculate how many panels you need in the array of your Solar Power System.

5. Define your Charge Controller.

6. Define your Inverter.

7. Wire your components according your selected solar power system type.

**Step 1. Let’s assume you have done step 1****Step 2. Calculate your energy consumption per day**Here is how we are going to calculate and define the energy consumption. You can find your monthly energy consumption on your electricity bill in kWh (kiloWatthour). Take your last 12 bills and add each monthly kWh total to get the year kWh total. Divide this year kWh total by 365 to obtain an average daily electrical energy usage. If you compare the energy usage after you have done step 1, you will see big differences with previous months. You will notice how much money you would have saved doing only this first step.

A more precise way to define your energy usage is to make a list of all the devices that will be powered by your renewable solar power system with their accompanying Watt values. You can find this on the appliance itself whether in Watt or Amp. If it is stated in Amps you simply multiply the Amps with the value of your line voltage and you will get its Watt value. Watt = Amp x Volt. If there is nothing you can find on the appliance you have to use an Amp meter or a Kill-A-Watt meter to read the Amp drawn and then multiply this reading with your line voltage to get its wattage.

Record all the data in a table list, like Table 1.1 below. In the fourth column "Usage” fill in how much time you use the appliance in hours per day. This is for the case you don’t remember how you end up with some figures of the next column "Hour per day". Next you’ll record for each appliance, the amount of time (in hour) it is used per day in the column "Hour per day". For example if you use it 6 hours a day, you fill in 6 in this column and if you use it 15 minutes a day, you record 0.25 (15/60). And 30 minutes per week you’ll fill in 0.071 in the "Hour per day" column, this is (30/60)/7 hour per day. And 30 minutes a month would be (30/60)/30 = 0.017 hour per day…..etc.

Next you’ll multiply the two values of the columns "Ratings" and "Hour per day" to obtain the values in the column "Daily Wh". This value in the "Daily Wh" column times 7 will give you the "Weekly Wh". And the value in "Daily Wh" times 30 result in the "Monthly Wh", this can be used for comparison, but we don't need it in our calculations. In case you use an appliance once a month or once a week, you calculate backwards your daily usage. The following list is filled with our values, but you will use your specific values.

Our Energy Consumption Table in Watthour per day for our solar power system.

**Step 3. How to calculate the size of the battery bank for our Solar Power System**Our choice is Lead Acid Battery which is the most common used when deep cycling. When we calculate our Lead Acid Battery Bank we have to take the following into account: 1. That we don't discharge a battery below 30% of its capacity. To prolong the life of our batteries we discharge our batteries to only 50%. (the lesser the better). 2. For how many days the battery bank must supply power in case of no sunshine or cloudy days. In our case we will take 2 days of no sunshine. 3. The ambient temperature of the battery bank. A temperature of 77 to 80 degrees Fahrenheit is about normal for the battery bank. Higher temperature will shorten the battery life and colder temperature will reduce its capacity.

Battery bank capacity:

Our average daily use in the above table is 7572 Wh.

Two days of no sunshine will add 2 x 7572 = 15144 Wh.

Discharging to 50 percent will add 15144 / 0.5 = 30288 Wh.

(In case we want to discharge only 40% of the battery capacity, we divide by 0.4 and the battery charge will stay at 60% of its capacity).

We add a factor of 10% to compensate for temperature variations.

This add 10% or 3029 Wh to our subtotal to bring our total to 30288 + 3029 = 33317 Wh.

Now we have to choose our battery size and puzzle out how to connect the batteries in our battery bank. With batteries it is always better to avoid parallel connections, but in most cases this is not possible, always try to maintain the least possible parallel strings of batteries and not going beyond 3 strings.

If we use a 12V system our battery bank will need a capacity of 33317 / 12 = 2775 Ah. If we make 3 strings, one string must deliver 2775 / 3 = 925 Ah. We end up with more than 3 strings of batteries. Not practical. Not recommended. If we use a 24V system our battery bank will need a capacity of 33317 / 24 = 1389 Ah. With 3 strings, one string delivers 1389 / 3 = 463 Ah. We still end up with more than 3 strings.

From the above results we see that lower voltage solar power systems will need larger capacity per battery, you will need more than recommended parallel strings and it will produce larger amounts of currents and consequently need larger wire dimensions and will be more costly. This is not practical.

So we will choose for a 48V solar power system and our battery bank will need a capacity of 33317 / 48 = 695 Ah.

Each of 3 parallel strings need to provide 695 / 3 = 232 Ah.

Choose batteries you can find with 232 Ah or the closest you can get.

To provide for the voltage of 48V while you choose for batteries of 12Volts you will need 48 / 12 = 4 batteries in series for each string. With 3 strings you will need 3 x 4 = 12 batteries in your battery bank.

The reason why to avoid parallel battery connection is that not all the batteries are exactly equal with reference to voltage, charge and internal resistance. And connecting them in parallel will meant that one can act like a load for the other and produce an unbalance charging for the battery bank. And so reduce the life of the batteries.

**Step 4. Calculate how many panels we need in the array of our Solar Power System**First we have to find out how much sunshine we dispose of in the worst case per day. The further away you live from the equator. The less sunshine you will have per day in the winter season. The less energy will your solar panels produce, the more panels you will need to meet your energy needs.

Go to the Solar Radiation Monitoring Laboratory of the University of Oregon’s Websitehttp://solardat.uoregon.edu/SunChartProgram.php , enter your Longtitude and Latitude and you will produce a Sun Chart for your location that covers a whole year and which is printable. You will get the Sun’s path, the elevation angle and azimuth angle. From this chart you can read the total hours of sun per day you have for your specific location. Use the worst case scenario (the days of least sunshine).

Or you can go to web site: http://rredc.nrel.gov/solar/old_data/nsrdb/1961-1990/redbook/atlas/Table.html

**Hours of Sun**In our case we can count with 7 hours of sunshine per day worst case scenario.

In those 7 hours the array must produce at least 7572 Watthour of energy.

The Array size in Watt must be this amount of energy divided by the amount of hours.

Energy = Watthour = (Watt x hour) = (Volt x Amp) x hour.

**Array Size**Array Power or size in Watt is 7572 / 7 = 1081 Watt of Solar Array.

**How many panels do we need**This will be the Array Power divided by the Power of one panel.

We are going to check for 3 sizes of panels, 75Watt, 100Watt and 250Watt. Why? You can choose whatever size of panel you want. The choice depends on the available space you have for installing them, to compare the cost of them. The one that best fit will get the credit.

With 75W panels we need a total of (Array size divided by panel size) = 1081/75 = 14.42 = 15 panels.

With 100W panels the total will be 1081/100 = 10.81 = 11 panels.

With 250W panels this is 1081/250 = 4.33 = 5 panels.

We can see a huge difference between 15 and 5 panels. Ok, this difference will also reflect in the prices of the panels, the time needed for installing the system, and the bottom line your budget. Here you have some thinking to do in making your best choice.

In our case we choose 16 panels of 75 Watt each, so we can make 4 strings of 4 panels in series to match our 48 Volt system. We have the space for them, we have plenty of time to install them, and they will satisfy our budget. May be this is not equal in your specific case, where the factors may not be the same like in ours. You will need to adapt the above calculations for your case.

**Step 5. Defining the Charge Controller for our Solar Power System**The Array Short Circuit Current and the System Voltage are the factors for defining our Charge Controller. When making your own panel array you have to determine its Short circuit current. This is the current when no load is connected and sunshine is at it maximum, so the panels production is also at its maximum. When you buy a custom made panel this information is labeled on the back of the panel or in the specification sheets. Indicated by Ioc and Voc.

There are so many types of Charge Controller you can get on the market. For small projects it does not matter to choose from any standard one. But we will concentrate on the most sophisticated and reliable Standard PWM charge controller and the MPPT charge controller to protect our costly inversion.

The Pulse Width Modulated and the Maximum Power Point Tracking.

The PWM controller like the MPPT regulates Voltage and Current from the Array to the Battery Bank. The use of the one or the other depends on the system size and its cost. The MPPT is more sophisticated, more efficient and more costly and mostly used in large systems.

**PWM charge controller**When using a PWM, the rated voltage of the Charge Controller must match the array voltage and the battery bank voltage. In our case this is 48 Volt. Other solar power system voltages may be 12 and 24 Volts.

The other factor to consider is the nominal current. This is the highest current the controller can handle. Currents higher and voltages higher than the nominal will destroy the device. For custom made panels we add up the short circuit currents of the parallel strings of the array.

Once the short circuit current (Ioc) of the array is determined, you can find the Amp rating for the Charge Controller, using the formula for Power. Power (Watt) = Volt x Amps.

Solar array is 1081 Watt and the System Voltage is 48 Volt.

Using the Power formula Power = VoIt x Amp we can calculate the Amp of the solar array. This is 1081/48 = 22.52 Amp. We add 25% safety factor for uncommon fluctuation in current variations and end up with a total of 28.15 Amp. On this subtotal we add an additional 25% (continues use) according the National Electric Code (NEC). This is 28.15 + 7.04 = 35.19 Amps Total. Look for a Charge Controller rated higher than 35.19 Amp. A 40 Amp Charge Controller will do the job. A larger sized controller will do no harm.

**MPPT solar charge controller**An MPPT solar charge controller is a smart PWM controller. It has a more extensive range of charging capabilities. You can use lower battery voltage than the array voltage. It is a more efficient charge controller and an expensive one. It’s features are better served in colder countries. If you want to have a more extensive knowledge about the MPPT and if it is adequate for your specific use, you better consult the dealer for your unit.

**Step 6. Define the Inverter**When determining the Inverter we have to match the input voltage (in our case 48V DC), the output voltage (we choose 120V AC) but you can choose whatever AC voltage applied in your country, different countries have different voltages. And the Inverter must support the load of all the appliances that will be on simultaneously.

We made a list of possible moments the appliances will be ‘on’ for our particular case.

The peak load is between 7 and 8pm in our case and is 1747 Watt.

So we need an Inverter with a Nominal Watt of greater than 1747 Watt. The most common is 2000 Watt.

There are inverters on the market with build in charge controller. You will have to ask your supplier for one that suits your needs or modify your setup to match those needs. Those modifications involve primarily the voltage of the Solar Power System.