Calculation Design of Solar Photovoltaic Modules Array
The power required by our daily loads range in several watts or sometimes in kilo-Watts. A single solar cell cannot produce enough power to fulfill such a load demand, it can hardly produce power in a range from 0.1 to 3 watts depending on the cell area. In the case of grid-connected and industrial power plants, we require power in the range of Mega-watts or even Giga-watts.
Thus, a single PV cell is not capable of such high demand. So, to meet these high demands solar cells are arranged and electrically connected. Such a connection and arrangement of solar cells are called PV modules. These PV modules make it possible to supply larger demand than what a single cell could supply.
When solar radiation falls on a single solar cell potential is produced across it two terminals anode and the cathode (i.e. anode is the positive terminal and cathode is the negative terminal). To increase the potential for the required power N-number of cells are connected in series. The negative terminal of one cell is connected to the positive terminal of the other cell as shown in figure below.
When we connect N-number of solar cells in series then we get two terminals and the voltage across these two terminals is the sum of the voltages of the cells connected in series. For example, if the of a single cell is 0.3 V and 10 such cells are connected in series than the total voltage across the string will be 0.3 V × 10 = 3 Volts.
If 40 cells of 0.6 V are connected in series than the total voltage would be 0.6 V × 40 = 24 Volts. It is important to note that when the cells are connected in series the voltage gets added while the current remains the same.
Similarly, when the cells are connected in parallel the current of the individual cells is added. The anode terminal of one cell is connected to the anode terminal of the next cell and similarly, the cathode terminal is connected to the cathode terminal of the next cell as shown in figure 2.
Unlike the series connection, the total voltage of the string in parallel connection remains unchanged. For example, if a cell has a current producing capacity of 2 A and 5 such solar cells are connected in parallel. Then the total current producing capacity of the cell will be 2 A × 5 = 10 A.
The PV module parameters are mentioned by the manufacturers under the Standard Test Condition (STC) i.e. temperature of 25 °C and radiation of 1000 W/m 2. In most of the time and locations, the conditions specified under STC does not occur. This happens because the solar radiation is always less than 1000 W/m 2 and the cell operating temperature is higher than 25 °C, this uncertainty results in reduced output power of the PV module.
As we discussed before that the PV module is made up of the number of solar cells, hence its parameters and factors affecting the generation of electricity are similar to that of the solar cell which we have already covered up in our previous article. So we won’t be covering that part here again.
Determining the Number of Cells in a Module
One of the basic requirements of the PV module is to provide sufficient voltage to charge the batteries of the different voltage levels under daily solar radiation. This implies that the module voltage should be higher to charge the batteries during the low solar radiation and high temperatures.
The PV modules are designed to provide the voltages in the multiple of 12 V battery level that is 12 V, 24 V, 36 V, 48 V, and so on. To charge a 12 V battery through a PV module we need a module having VM of 15 V and for 24 V battery we need a module with VM of 30 V and so on. Other devices used in the PV system are made compatible to be work with a battery voltage level.
To provide the required voltage level we need to connect cells in series. Depending on the different technologies used in the PV cell, the number of cells required to be connected in series will differ. The number of cells to be connected in series depends on the voltage at maximum power point i.e. VM of the individual cell and the voltage drop that occurs due to an increase in the temperature of the cell above STC.
Example:
Let us understand this with an example, a PV module is to be designed with solar cells to charge a battery of 12 V. The open-circuit voltage VOC of the cell is 0.89 V and the voltage at maximum power point VM is 0.79 V.
The cells operating temperature is 60 °C and there is a decrease in voltage by 2 mV for per degree Celsius rise in temperature. How many cells are required to be connected in series to charge the battery?
Step 1: Find the voltage at maximum power point VM = 0.79 V.
If VM is not specified then take VM as 80 to 85% of VOC.
Step 2: Find the loss of voltage under operating temperature i.e. at 60 °C.
Rise in temperature above STC = Operating temperature – Temperature at STC.
Rise in temperature above STC = 60 °C – 25 °C = 35 °C
Therefore, loss of voltage due to rise in temperature above STC:
Loss of Voltage = 35 °C × 0.002 V = 0.07 V
Step 3: Determining the voltage at the operating condition.
The voltage at the operating condition = Voltage at STC (VM) – loss of voltage due to a rise in temperature above STC.
Therefore, Voltage at the operating condition = 0.79 V – 0.07 V = 0.72 V
Step 4: Determine the required PV module voltage to charge the battery.
To charge a battery of 12 V we need module voltage to be around 15 V.
Step 5: Determine the number of cells to be connected in series.
The number of series-connected cells = PV module voltage / Voltage at the operating condition.
Number of series connected cells = 15 V / 0.72 V = 20.83 or about 21 cells
Thus, we need 21 series-connected cells to charge a 12V battery. It is important to note that for different solar cell technologies we will need a different number of cells in series for the same output voltage. An actual photo of the PV module which consists of N-number of electrically connected cells is shown in figure 3 below.
Measuring Module Parameters
For the measurement of module parameters like VOC, ISC, VM, and IM we need voltmeter and ammeter or multimeter, rheostat, and connecting wires.
Measurement of Open Circuit Voltage (VOC):
While measuring the VOC, no-load should be connected across the two terminals of the module. To find the open circuit voltage of a photovoltaic module via multimer, follow the simple following steps.
- Set the multimeter knob to DC voltage measurement and select the range for the voltage measurement accordingly i.e. 6 V, 12 V, 24 V, etc.
- Make sure that the one probe is connected to the COM port of multimeter and another to the voltage measuring port.
- After selecting the mode and range, connect the probes of the multimeter to the two terminals of the PV module and observe the reading on the display.
- Make sure that the positive probe (voltage measuring port) is connected to the positive terminal and negative probe (COM port) to the negative terminal. If the probes are connected vice versa it will give a negative reading.
- The reading on the display of the multimeter is the open-circuit voltage VOC of the PV module.
Measurement of Short circuit current (ISC):
While measuring the ISC, no-load should be connected across the two terminals of the module.
To find the short circuit current of a photovoltaic module via multimer, follow the simple following steps.
- Set the multimeter knob to current measurement and select the range for the current measurement accordingly i.e. typically between 0.1 to 10 A.
- Make sure that one probe is connected to the COM port of multimeter and another to the current measuring port.
- After selecting the mode and range connect the probes of the multimeter to the two terminals of the PV module and observe the reading on the display.
- Make sure that the positive probe is connected to the positive terminal (current measuring port) and negative probe (COM port) to the negative terminal. If the probes are connected vice versa it will give a negative reading.
- The reading observed on the display of the multimeter is the short circuit current ISC of the PV module.
Measuring the I-V Curve:
For measuring the I-V curve, the solar PV module must be connected in series with the variable resistor as shown in figure below.
The negative terminal of the module is connected to the positive terminal of the ammeter and the voltmeter is directly connected across the PV module as shown in figure 4.
If unknowingly the connections are done vice versa then the reading obtained will have a negative sign, reconnect the meters to obtain correct values. Once done properly adjust the variable resistor (rheostat) on one side so that the voltage will be maximum and the current is minimum.
Note down the values of current and voltage at this position of the rheostat. Now slowly slide the rheostat to the other side and note down the readings for every slide adjustment until the rheostat is completely shorted. Calculate the power for every value of voltage and current by using the equation below.
Thus, by using these measured values all the other parameters of the PV module can be obtained.
Costs
The Costs table includes the initial Capital cost and Replacement cost per kilowatt of the PV system, as well as annual operation and maintenance (OM) costs per kilowatt.
When specifying the capital and replacement costs, be sure to account for all costs associated with the PV system, which may include:
You can include the costs of the power electronics in the capital cost, or account for them separately in the MPPT or Inverter tab.
Note: The capital cost is the initial purchase price, the replacement cost is the cost of replacing the PV system at the end of its lifetime, and the OM cost is the annual cost of operating and maintaining the PV system.
Cost Curve
In the Costs table, enter the PV cost curve, meaning the way the cost varies with size. Typically this requires only a single row because analysts often assume that PV costs vary linearly with size. In the sample above, the capital cost of PV panels is specified at 3,000/kW and the replacement cost is specified at 5000,500/kW. The operating and maintenance (OM) cost is specified as 0.
If the cost of the PV subsystem was not linear with size, you can enter multiple rows of data in the Cost table. For example, if the marginal capital and replacement costs dropped to 5000,500/kW and 5000,100/kW, respectively, for quantities above 2 kW, fill in the Cost table as follows:
If HOMER then simulates a system with a PV array size of 0.1 kW, it would extrapolate from the 1 kW and 2 kW costs, giving a capital cost of 300. For a PV array size of 2.5 kW, HOMER would interpolate between the 2 kW costs and the 3 kW costs, giving a capital cost of 7,250. For a PV array size of 6 kW, HOMER would extrapolate from the 2 kW and 3 kW costs, giving a capital cost of 16,000.
Note: The capital cost is the initial purchase price, the replacement cost is the cost of replacing the PV panels at the end of their lifetime, and the OM cost is the annual cost of operating and maintaining the PV array.
Search Space
Click the MPPT or Inverter tab to see the Search Space. Enter the nominal capacity of the PV in kW, or enter several quantities for HOMER to consider in the system optimization. Include a zero if you wanat HOMER to consider systems without this PV.
Click the Star icon to enable the optimizer. The search space is replaced by a lower bound and an upper bound. With the optimizer turned on, HOMER automatically finds the best capacity for you.
See the help article about Optimization for a more detailed explanation of HOMER’s optimizer.
PV Inputs
From the main section of the PV page, you can edit the following inputs.
This determines whether the PV array produces AC or DC power. All PV cells produce DC electricity, but some PV arrays have built-in inverters to convert to AC.
The number of years before the PV panels must be replaced at the replacement cost specified in the costs table.
A scaling factor applied to the PV array power output to account for reduced output in real-world operating conditions compared to operating conditions at which the array was rated.
Note: To the right of each numerical input is a sensitivity button ( ) that allows you to do a sensitivity analysis on that variable. For more information, see Why Would I Do a Sensitivity Analysis?
Solar Voltaic Arrays
The Bryce Canyon Solar Array consists of two dual-axis trackers that perfectly follow our Sun throughout each day during every season of the year. Such telescope-like precision is required because unlike regular photovoltaic panels, Concentrating PhotoVoltaic (CPV) technology does not generate electricity from ambient light. For the Fresnel lens to concentrate sunlight and for the tiny triple-junction chips to convert it to electricity, the sun alignment has to be within 1-2 degrees.
When installed in sunny locations, CPV outperforms all other kinds of solar energy, both in sunlight conversion efficiency and energy density (kilowatts / acre). Operating at 140kW per hour and peaking at 150kW, this array generates more energy than can be easily stored in batteries, so instead, excess energy is returned to the grid. On a sunny day, the array generates more than twice the energy the Bryce Canyon Visitor Center uses, providing us with an energy credit that can then be reclaimed at night or on cloudy days.
The Photovoltaic Cell
Each tracker consists of 5,040 individual solar collection cells. Sunlight enters each cell through a Fresnel lens, (commonly used in lighthouses to FOCUS light into a beam) which concentrates sunlight through a reflecting chamber on to a tiny triple junction photovoltaic chip.
Because all photovoltaics perform better at cooler temperatures, the chip itself is mounted on a large aluminum heat-sink (similar to those used to cool computer processors) with blades that extend out of the cell, on the shaded size of the unit, where air circulation aids in further
Maximizing Solar Energy
Only half of our Sun’s energy reaches Earth’s surface. The narrow range known as optical light is what the human eye-brain combination uses. Through photosynthesis, plants convert 2-4% of solar energy into sugars. The best silicon solar panels are about 18% efficient. Concentrating PhotoVoltaics (CPV) technology focuses light onto triple-stacked photocells of different alloys. Each layer in the stack collects sunlight from a different part of the spectrum, that when added together, converts 34% of our Sun’s transmitted energy into electricity.
- When wind speeds exceed 35 mph, each tracker’s anemometer instructs it to tilt back to the horizontal wind stow position where they can survive winds speeds up to 100 mph.
- A clock drive allows the trackers to track our Sun even when cloudy. A sun-tracker in the upper center of each tracker adds precision when our Sun is out.
- A pyrheliometer independently measures sunlight intensity and our Sun’s precise position in the sky to improve efficiency.
Solar Photovoltaic Technology Basics
Solar cells, also called photovoltaic cells, convert sunlight directly into electricity.
Photovoltaics (often shortened as PV) gets its name from the process of converting light (photons) to electricity (voltage), which is called the photovoltaic effect. This phenomenon was first exploited in 1954 by scientists at Bell Laboratories who created a working solar cell made from silicon that generated an electric current when exposed to sunlight. Solar cells were soon being used to power space satellites and smaller items such as calculators and watches. Today, electricity from solar cells has become cost competitive in many regions and photovoltaic systems are being deployed at large scales to help power the electric grid.
Silicon Solar Cells
The vast majority of today’s solar cells are made from silicon and offer both reasonable and good efficiency (the rate at which the solar cell converts sunlight into electricity). These cells are usually assembled into larger modules that can be installed on the roofs of residential or commercial buildings or deployed on ground-mounted racks to create huge, utility-scale systems.
Another commonly used photovoltaic technology is known as thin-film solar cells because they are made from very thin layers of semiconductor material, such as cadmium telluride or copper indium gallium diselenide. The thickness of these cell layers is only a few micrometers—that is, several millionths of a meter.
Thin-film solar cells can be flexible and lightweight, making them ideal for portable applications—such as in a soldier’s backpack—or for use in other products like Windows that generate electricity from the sun. Some types of thin-film solar cells also benefit from manufacturing techniques that require less energy and are easier to scale-up than the manufacturing techniques required by silicon solar cells.
III-V Solar Cells
A third type of photovoltaic technology is named after the elements that compose them. III-V solar cells are mainly constructed from elements in Group III—e.g., gallium and indium—and Group V—e.g., arsenic and antimony—of the periodic table. These solar cells are generally much more expensive to manufacture than other technologies. But they convert sunlight into electricity at much higher efficiencies. Because of this, these solar cells are often used on satellites, unmanned aerial vehicles, and other applications that require a high ratio of power-to-weight.
Solar cell researchers at NREL and elsewhere are also pursuing many new photovoltaic technologies—such as solar cells made from organic materials, quantum dots, and hybrid organic-inorganic materials (also known as perovskites). These next-generation technologies may offer lower costs, greater ease of manufacture, or other benefits. Further research will see if these promises can be realized.
Reliability and Grid Integration Research
Photovoltaic research is more than just making a high-efficiency, low-cost solar cell. Homeowners and businesses must be confident that the solar panels they install will not degrade in performance and will continue to reliably generate electricity for many years. Utilities and government regulators want to know how to add solar PV systems to the electric grid without destabilizing the careful balancing act between electricity supply and demand.
Materials scientists, economic analysts, electrical engineers, and many others at NREL are working to address these concerns and ensure solar photovoltaics are a clean and reliable source of energy.
What Is a Solar Array?
An array of anything is an ordered arrangement of objects. Solar panels happen to be objects, and therefore, solar arrays are groups of solar panels. They should probably be more commonly called “solar panel arrays.”
Because it takes a number of solar panels to produce enough power for a home, if you’re installing a solar system, you will definitely want an array. If, however, you’re thinking about installing a small auxiliary solar system for something like an RV, you might get away without using an array, and instead just use a single solar panel.
How Big Is a Solar Array?
Solar arrays can be custom designed in a number of different configurations to fit the space where they’ll be installed. This means that any number of solar panels might be involved, from just a few to hundreds or thousands, in the case of solar farms.
For a residential home, you’re more likely to see groupings of solar panels between about 16 and 26, depending on where you live and how much sun your panels can collect. For example, in the western part of the country, where the peak sun hours average almost seven hours per day, a smaller system can get just as much done as a larger system in the northeast, where average daily peak sun hours average just over four hours.
A typical 60-cell monocrystalline solar panel measures about 5.5 feet by 3.25 feet, and weighs about 40 pounds. Depending on the arrangement of your panels, 16 panels arranged in an array that’s four panels wide and four panels tall would be about 22 feet long and 13 feet wide, but they can be configured in a wide range of shapes beyond simple rectangles. Sixteen of these panels add about 640 pounds of weight to your home’s roof, distributed across that array.
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How Does a Solar Array Work?
At the heart of every solar array are the solar panels. These are based on photovoltaic (PV) solar cells, each measuring about six inches square and generally arranged in groupings of either 60 or 72, depending on the wattage of the panel.
When sunlight strikes these solar cells, electrons in the silicon wafers inside come loose from their bonds and begin to flow in a single direction, due to how the solar cell is made. This flow creates an electrical current that’s contained and controlled, making it possible to harness efficiently.
Once the juice is flowing, as it were, metal plates on the sides of the solar cells collect the charged electrons and transfer them to wiring within the panels connected within the solar array. This then feeds them into a power inverter that further transforms the direct current (DC) that’s been produced into alternating current (AC) that you can use in your home.
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What Are the Components of a Solar Array System?
If you’re considering installing a solar array on your home, you’ll need more than just solar panels and some wire. Solar array systems that are directly tied to the electricity grid need additional equipment, including a power inverter and a net meter, to make the electricity you produce usable in homes and transferable to the grid.
Grid-tied systems are fairly simple, feeding the items in your home that are drawing electricity in that moment first, then pushing the excess electricity out of your home and into the grid. The net meter will track how much electricity goes out as well as what you draw back in, like on days that are dark or rainy, when it’s hard for your panels to produce a lot of power.
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Hybrid systems, which are grid-tied, have the ability to store some power for later, because they include battery banks. Depending on how many batteries are in your bank, you may be able to ride out a storm that knocks out the electricity for a few hours, or a few days, on the power you’ve generated yourself.
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THIS IS AN ADVERTISEMENT AND NOT EDITORIAL CONTENT. Please note that we do receive compensation for any products you buy or sign up to via this advertisement, and that compensation impacts the ranking and placement of any offers listed herein. We do not present information about every offer available. The information and savings numbers depicted above are for demonstration purposes only, and your results may vary.