Calculation Example of Small Photovoltaic (PV) Residential Stand-Alone System
2kW Solar PV Array on Campus Crossings at Briarcliff (photo by Soenso Energy)
Example
– Array Size: 10, 12-volt, 51-watt modules; Isc= 3.25 amps, Voc= 20.7 volts – Batteries: 800 amp-hours at 12 volts – Loads: 5 amps DC and 500-watt inverterwith 90% efficiency.
Description
The PV modules are mounted on the roof. Single-conductor cables are used to connect the modules to a roof-mounted junction box. Potential reverse fault currents indicate that a PV combiner be used with a series fuse for each PV module.
UF two-conductor sheathed cable is used from the roof to the control center.
Physical protection (wood barriers or conduit) for the UF cable is used where required. The control center, diagrammed in Figure 1, contains disconnect and overcurrent devices for the PV array, the batteries, the inverter, and the charge-controller.
Figure 1 – Small Residential Stand-Alone System
Calculations
– The moduleshort-circuit current is 3.25 amps. – CONTINUOUS CURRENT: 1.25 x 3.25 = 4.06 amps – 80% OPERATION: 1.25 x 4.06 = 5.08 amps per module
The maximum estimated moduleoperating temperature is 68°C.
From NECTable 310.17:
The derating factor for USE-2 cable is 0.58 at 61-70°C.
Cable 14 AWG has an ampacity at 68°C of 20.3 amps (0.58 x 35) (max fuse is 15 amps).
Cable 12 AWG has an ampacity at 68°C of 23.2 amps (0.58 x 40) (max fuse is 20 amps).
Cable 10 AWG has an ampacity at 68°C of 31.9 amps (0.58 x 55) (max fuse is 30 amps).
Cable 8 AWG has an ampacityat 68°C of 46.4 amps (0.58 x 80)
The array is divided into two five-module sub-arrays.
The modules in each sub-array are wired from module junction box to the PV combiner for that sub-array and then to the array junction box. Cable size 10 AWG USE-2 is selected for this wiring, because it has an ampacityof 31.9 amps under these conditions, and the requirement for each sub-array is 5 x 4.06 = 20.3 amps.
Evaluated with 75°C insulation, a 10 AWG cable has an ampacity of 35 amps at 30°C, which is greater than the actual requirement of 20.3 amps (5 x 4.06).
In the array junction box on the roof, two 30-amp fuse sin pullout holders are used to provide overcurrent protection for the 10 AWG conductors. These fuses meet the requirement of 25.4 amps (125% of 20.3) and have a rating less than the derated cable ampacity.
!!! In this junction box, the two sub-arrays are combined into an array output. The ampacity requirement is 40.6 amps (10 x 4.06). A 4 AWG UF cable (4-2 w/gnd) is selected for the run to the control box. It operates in an ambient temperature of 40°C and has a temperature-corrected ampacity of 86 amps (95 x 0.91). This is a 60°C cable with 90°C conductors and the final ampacity must be restricted to the 60°C value of 70 amps, which is suitable in this example.
Appropriately derated cables must be used when connecting to fusesthat are rated for use only with 75°C conductors. A 60-amp circuit breaker in the control box serves as the PV disconnect switch and overcurrent protectionfor the UF cable.
The minimum rating would be 10 x 3.25 x 1.56 = 51 amps.
The NEC allows the next larger size; in this case, 60 amps, which will protect the 70 amp rated cable. Two single-pole, pullout fuse holders are used for the battery disconnect. The charge circuit fuse is a 60-amp RK-5 type.
The inverter has a continuous rating of 500 watts at the lowest operating voltage of 10.75 volts and an efficiency of 90% at this power level. The continuous current calculation for the input circuit is 64.6 amps ((500 / 10.75 / 0.90) x 1.25).
The cables from the battery to the control center must meet the inverter requirements of 64.6 amps plus the DC load requirements of 6.25 amps (1.25 x 5).
A 4 AWG THHN has an ampacityof 85 amps when placed in conduit and evaluated with 75°C insulation. This exceeds the requirements of 71 amps (64.6 + 6.25). This cable can be used in the custom power center and be run from the batteries to the inverter.
The discharge-circuit fuse must be rated at least 71 amps. An 80-amp fuse should be used, which is less than the cable ampacity.
!!! The DC load circuit is wired with 10 AWG NM cable (ampacityof 30 amps) and protected with a 15-amp circuit breaker.
The grounding electrode conductor is 4 AWG and is sized to match the largest conductor in the system, which is the array-to-controlcenter wiring. This size would be appropriate for a concrete-encased grounding electrode. Equipment-grounding conductors for the array and the charge circuit can be 10 AWG based on the 60-amp overcurrent devices.
The equipment ground for the inverter mustbe an 8 AWG conductor based on the 80-amp overcurrent device. All components should have at least a DC voltage rating of 1.25 x 20.7 = 26 volts.
Reference: Photovoltaic Power Systems And the 2005 National Electrical Code – John Wiles Southwest Technology Development Institute New Mexico State University