Solar photovoltaic (PV) systems are capable of generating large amounts of electrical power by interconnecting smaller solar modules (also called panels) in series and parallel. Modules are often rated to produce power on the order of hundreds of Watts during typical midday sunlight conditions in the United States. Arrays, large collections of solar modules, may use hundreds of thousands of modules.
Up-Close Photo of Solar Modules Mounted on a Typical Utility-Scale Foundation
The block diagram below is a high level representation of a solar power plant. Modules are wired in series to form "strings". Strings are combined in parallel before entering an inverter. The inverter converts DC power to AC power through the use of switching electronics. Inverters may operate in a variety of different ways, but they all generally attempt to extract as much power as possible without exceeding the inverters' ratings.
Solar PV Block Diagram
To ensure any solar PV plant will be safe, whether a small rooftop project or a large-utility scale farm, it is necessary to know the maximum voltage and current that can be expected from the modules. Wiring modules in series increases the system voltage, but keeps the output current of the string the same. This means that for a given voltage limit, say 600V, as limited for on-building applications by the NEC, maximizing the number of modules wired in series will minimize the amount of output wiring required to get from the modules to the inverter.
Open Circuit Voltage - Modules produce their maximum voltage in the open circuit condition. In other words, when the module is disconnected from the inverter (or when the inverter is off), modules will produce their maximum voltage. Modules produce higher voltages at colder temperatures. The maximum open circuit voltage to be expected can be computed as follows:
V' = V (1 + B (TL - 25°C) )
Where:
V' is the module open circuit voltage in Volts after temperature correction
V is the module open circuit voltage at Standard Test Conditions (STC), a value provided by manufacturers
B is the open circuit voltage temperature correction factor in %/°C, a value provided by manufacturers
TL is the project site's average annual minimum temperature in °C
Once the value of V' is known, the maximum string length can be calculated as follows:
N = VS / V'
Where:
N is the maximum number of modules that can be wired in series safely
VS is the maximum allowable system voltage in Volts. This is typically either 600V or 1500V depending on the project type.
The calculated value of N will need to be rounded down to the nearest integer. So, for example, if N = 28.65 for a particular module, then only 28 modules can be wired in series safely.
Short Circuit Current - Modules produce their maximum current under short circuit conditions. Although actual short circuit conditions are rare for an inverter-connected PV plant, operating currents may come very close to short circuit currents on hot days. This causes a unique problem: overcurrent devices will have problems clearing some kinds of faults since the operating current is so close to the short circuit current. Because of this, conductors need to have sufficient ampacity to carry the worst-case short circuit current of the modules without overheating. In short, determining the maximum short circuit current is critical for both safety and effective operation of the power plant. Fortunately, determining the maximum short circuit current is simple:
I' = 1.25 I
Where:
I' is the worst-case short circuit current in Amperes
I is the short circuit current of the module (or string) at Standard Test Conditions, a value provided by the manufacturer.
The value of I should be adjusted to account for bifacial gain when bifacial modules are used. For larger projects, a detailed analysis of expected irradiance can be used to determine the maximum short circuit current by evaluating the anticipated irradiance based on mounting configurations and site-specific data.
Inverters - The maximum output current and voltage of inverters are values that will be provided by the manufacturer. Inverters should be selected based on the project requirements, including grid voltage, output power needs, and constructability. Inverters are almost always smart devices with a significant amount of monitoring built-in.
Conductor Ampacity - Conductors need to have an ampacity, A' greater than 125% of the maximum output current of the inverter or modules.
This means that, for solar modules, an additional 1.25 multiplication factor is required on top of the 1.25 multiplier already applied. The original 1.25 multiplier on the module short circuit current was to capture the effect of increased irradiance leading to higher currents under typical operation. The second multiplier of 1.25 is required to provide margin for overcurrent protection coordination.
Example: Consider a monofacial PV module with a short circuit current at STC of I = 10A and an open circuit voltage at STC of V = 40V. The conductors are routed in conduit aboveground in a with no more than 2 current-carrying conductors bundled. The maximum ambient temperature is 40°C and the minimum ambient temperature is 0°C. The module's temperature correction coefficient B = -.25% / °C. The system will be mounted on a building.
How many modules can be wired in series to form a string?
What minimum conductor size is required for the output of the string if 60°C conductors are used?
Solution: Start by drawing a picture to understand the problem.
The number of modules that we can wire in series is determined by calculating the temperature-corrected open circuit voltage for worst-case conditions. Open circuit voltage is highest in cold conditions:
V' = V (1 + B (TL - 25°C) ) = 40 (1 - .0025 (0 - 25) ) = 42.5V
The number of modules that can be connected in series is limited by the system voltage. For systems mounted on buildings, the voltage can be no higher than 600V. Using this information, we can calculate the maximum number of modules in series:
N = VS / V' = 600 / 42.5 =14.12
The number of modules that can be placed in series must be rounded down to avoid overvoltage. This means that no more than 14 modules can be placed in a string.
Determining the conductor size requires us to first determine the maximum expected output current. The worst-case current is calculated as:
I' = 1.25 I = 1.25 * 10 = 12.5A
Conductors must have an ampacity of 125% of the worst-case current, so the conductors must be able to carry before any derating factors.:
1.25 * 12.5 = 15.625A
With the load current now known, the conductor ampacity must be determined to find a suitable conductor type. For low voltage systems routed in conduit, NEC 310.16 is applicable. For a system this small, we are likely to be limited to 60°C termination temperature ratings.
Derating factors must be calculated. Burial depth derating is not applicable since the system is routed aboveground. Bundling derating is not relevant since no more than 2 current-carrying conductors will be bundled. Ambient temperature derating is applicable, since the ambient temperature is higher than the 30°C value reference for NEC 310.16. The ambient temperature correction factor, y, can be calculated:
y = √( (60°C - 40°C) / (60°C - 30°C) ) = .816
Using NEC Table 310.16's 60°C column, a 12 AWG CU conductor is suitable for 20A. Derating this value for ambient temperature:
20 * .816 = 16.32A
Since 16.32A is greater than the 15.625A required for the load current, 12 AWG CU will be the minimum conductor size required.
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