Solar Array Circuits Study Guide

Design, Analysis, and Implementation of Photovoltaic Array Circuits for Efficient Solar Energy Systems

PV Source Circuits
String & Array Design
Circuit Protection
NEC Compliance

Table of Contents

Navigate through this comprehensive guide to solar array circuit fundamentals and design principles.

Module 1: Solar Array Fundamentals

Basic concepts and components of PV arrays

Module 2: PV Module Electrical Characteristics

Understanding I-V curves and specifications

Module 3: Series & Parallel Connections

String and array configuration strategies

Module 4: Array Circuit Design

Sizing, calculations, and optimization

Module 5: Protection & Safety Systems

Overcurrent, fault, and rapid shutdown

Module 6: Wiring & Installation

NEC requirements and best practices

Module 7: Performance & Troubleshooting

Monitoring, maintenance, and fault finding

Appendix: Reference Tables

Quick reference for calculations and standards

1 Solar Array Fundamentals

What is a Solar Array Circuit?

A solar array circuit is the complete electrical pathway from the photovoltaic modules to the common connection point (usually a combiner box). According to NEC Article 690, a PV source circuit includes conductors between modules and from modules to the common connection point of the DC system.

Key Terminology

PV Module: A complete, environmentally protected unit consisting of solar cells, optics, and other components.
PV String: A circuit in which PV modules are connected in series to increase voltage.
PV Array: A complete system of PV modules, support structure, and other components.
PV Source Circuit: Conductors between modules and from modules to the common connection point.
PV Output Circuit: Circuit conductors between the PV source circuit and the inverter or charge controller.

Basic Components of a Solar Array Circuit

PV
PV Module
Converts sunlight to DC power
W
Wiring
PV wire or USE-2
CB
Combiner Box
Parallel connection point
OCPD
Overcurrent Protection
Fuses or breakers
DIS
Disconnect
DC disconnect switch

Types of Solar Array Configurations

Configuration Description Advantages Disadvantages Best For
Series String Modules connected positive to negative to increase voltage Simpler wiring, lower current, reduced wire costs Shading affects entire string, requires same orientation Unshaded areas, uniform orientation
Parallel Strings Multiple series strings connected positive-to-positive, negative-to-negative Higher current, shading affects only one string Higher current requires larger conductors, more fusing Partially shaded areas, different orientations
Series-Parallel Multiple modules in series forming strings, then strings in parallel Balances voltage and current, most common configuration More complex design, requires careful matching Most commercial and residential installations
Microinverter Systems Each module has its own inverter, AC output combined Maximum power per module, shading tolerance, safety Higher cost per watt, more components to fail Complex roofs, heavy shading, safety-critical apps
DC Optimizer Systems Power optimizers at each module, DC output to string inverter Module-level MPPT, rapid shutdown, monitoring Added cost, complexity, potential failure points Mixed orientations, partial shading, NEC 690.12 compliance

2 PV Module Electrical Characteristics

Understanding the I-V Curve

The current-voltage (I-V) curve is the fundamental characteristic of a PV module. It shows the relationship between current and voltage at a given irradiance and temperature.

Typical PV Module I-V Curve
[Visualization of I-V curve with key points marked]
Voc
Open-Circuit Voltage
Vmp
Maximum Power Voltage
Isc
Short-Circuit Current
Imp
Maximum Power Current

Key Electrical Parameters

Standard Test Conditions (STC)

All module ratings are specified at STC: 1000W/m² irradiance, 25°C cell temperature, AM 1.5 spectrum.

Pmax
Maximum Power
300W - 450W
Voc
Open-Circuit Voltage
40V - 50V
Isc
Short-Circuit Current
9A - 12A
Vmp
Maximum Power Voltage
32V - 40V

Temperature Effects on PV Modules

Temperature significantly affects PV module voltage and power output. As temperature increases, voltage decreases.

Voc(temp) = Voc(STC) × [1 + βVoc × (Tcell - 25°C)]
Vmp(temp) = Vmp(STC) × [1 + βVmp × (Tcell - 25°C)]
Temperature Coefficients

Voltage Temperature Coefficient (βVoc): Typically -0.3% to -0.5% per °C
Power Temperature Coefficient (γ): Typically -0.4% to -0.5% per °C
Current Temperature Coefficient (α): Typically +0.04% to +0.1% per °C (minor effect)

Example: A module with Voc = 45V and βVoc = -0.35%/°C at 65°C cell temperature:
Voc = 45V × [1 + (-0.0035) × (65-25)] = 45V × 0.86 = 38.7V

Cold Temperature Voltage Rise

In cold climates, PV module voltage increases significantly. This must be accounted for in system design to avoid exceeding inverter maximum voltage limits. NEC 690.7 requires calculating maximum system voltage using the lowest expected ambient temperature.

3 Series & Parallel Connections

Series Connections (Strings)

When PV modules are connected in series, voltages add while current remains constant (limited by the lowest current module).

Series Connection Calculations
Vstring = Vmodule1 + Vmodule2 + ... + VmoduleN
Istring = Imodule(min) (current limited by lowest module)
Pstring = Vstring × Istring
Example: Series String

5 identical modules with Vmp = 40V, Imp = 10A connected in series:

Vstring = 40V × 5 = 200V
Istring = 10A (same as single module)
Pstring = 200V × 10A = 2000W

Mismatch Losses in Series Strings

When modules with different I-V characteristics are connected in series, the string current is limited by the weakest module. This is particularly problematic with partial shading or module degradation. Bypass diodes help mitigate this by allowing current to bypass shaded cells.

Parallel Connections

When PV strings are connected in parallel, currents add while voltage remains constant (determined by each string).

Parallel Connection Calculations
Varray = Vstring (same for all parallel strings)
Iarray = Istring1 + Istring2 + ... + IstringN
Parray = Varray × Iarray
Example: Parallel Strings

4 identical strings with Vstring = 200V, Istring = 10A connected in parallel:

Varray = 200V (same as each string)
Iarray = 10A × 4 = 40A
Parray = 200V × 40A = 8000W

String Sizing Considerations

Inverter Voltage Window

Ensure string voltage remains within inverter minimum and maximum MPPT voltage range under all temperature conditions. Account for both cold temperature voltage rise and hot temperature voltage drop.

Maximum System Voltage

Calculate maximum voltage per NEC 690.7 using coldest expected temperature. This determines required component voltage ratings (wiring, disconnects, overcurrent devices).

Minimum String Voltage

Ensure string voltage at highest expected temperature exceeds inverter minimum MPPT voltage. Hot climates can significantly reduce module voltage.

Current Matching

When connecting strings in parallel, ensure they have similar I-V characteristics. Mismatched strings can lead to significant power losses.

Bypass Diodes and Blocking Diodes

Diode Type Purpose Location Operation Importance
Bypass Diode Prevents hot spots in shaded cells Across substrings within module junction box Conducts when cell substring is reverse-biased Critical for module safety and performance
Blocking Diode Prevents reverse current flow at night In series with each string (less common today) Blocks current from batteries flowing back to array Most modern inverters have this function built-in

4 Array Circuit Design

Design Process for Solar Array Circuits

Determine System Requirements

Calculate energy needs, available space, budget, and performance goals. Consider local climate, shading, and orientation constraints.

Select Module and Inverter

Choose compatible components. Consider module voltage, current, temperature coefficients, and inverter voltage/current ranges.

Calculate String Size

Determine number of modules per string based on temperature-adjusted voltage calculations. Ensure operation within inverter MPPT range.

Determine Number of Strings

Calculate number of parallel strings needed to meet system power requirements. Consider current limitations of inverters and conductors.

Design Protection System

Size overcurrent protection, select disconnect locations, plan rapid shutdown implementation per NEC 690.12.

Select Conductors and Components

Size conductors per NEC 690.8, select combiner boxes, disconnects, and monitoring equipment.

Voltage Calculations for String Sizing

Maximum Voltage Calculation (Cold Conditions)
Vmax = Voc(STC) × [1 + (Tmin - 25) × βVoc] × Nseries
Example Calculation

Module: Voc = 45V, βVoc = -0.35%/°C = -0.0035/°C
Coldest temp: Tmin = -10°C
Modules in series: N = 10

Vmax = 45V × [1 + (-10 - 25) × (-0.0035)] × 10
= 45V × [1 + (-35) × (-0.0035)] × 10
= 45V × [1 + 0.1225] × 10
= 45V × 1.1225 × 10 = 505.1V

Conclusion: All system components must be rated for at least 505.1V.

Minimum Voltage Calculation (Hot Conditions)
Vmin = Vmp(STC) × [1 + (Tmax - 25) × βVmp] × Nseries
Example Calculation

Module: Vmp = 37.5V, βVmp = -0.4%/°C = -0.004/°C
Hottest cell temp: Tmax = 70°C (45°C ambient + 25°C rise)
Modules in series: N = 10

Vmin = 37.5V × [1 + (70 - 25) × (-0.004)] × 10
= 37.5V × [1 + (45) × (-0.004)] × 10
= 37.5V × [1 - 0.18] × 10
= 37.5V × 0.82 × 10 = 307.5V

Conclusion: Inverter minimum MPPT voltage must be below 307.5V.

Current Calculations for Array Sizing

Maximum Circuit Current Calculation
Imax-circuit = Isc(STC) × 1.25 × 1.25

The first 1.25 factor accounts for possible current increase above Isc (NEC 690.8(A)(1)). The second 1.25 factor applies for continuous currents (3+ hours, NEC 690.8(B)(1)).

Example Calculation

Module: Isc = 10A
Strings in parallel: 4

String current: Istring = 10A × 1.25 = 12.5A
Continuous current: 12.5A × 1.25 = 15.625A per string
Array current: 15.625A × 4 = 62.5A

Conclusion: Array conductors must have ampacity ≥ 62.5A. Overcurrent device rating ≥ 62.5A (next standard size: 70A).

Voltage Drop Calculations

Excessive voltage drop reduces system efficiency and can cause inverters to operate outside optimal voltage range.

Vdrop = 2 × L × I × R / 1000

Where:
L = One-way circuit length (feet)
I = Circuit current (amps)
R = Conductor resistance (ohms per 1000 ft)

Voltage Drop Guidelines

DC Circuits: Limit voltage drop to 2% or less for optimal performance
AC Circuits: Limit voltage drop to 2% or less
Critical Systems: Consider 1% or less for maximum efficiency

Example: For 200V DC circuit, 2% = 4V drop. At 10A current, maximum allowable resistance = 4V / 10A = 0.4Ω for round trip.

A Appendix: Reference Tables & Resources

Wire Sizing for PV Systems

Application Recommended Wire Type Temperature Rating Sunlight Resistance NEC Reference
Module interconnections PV wire, USE-2, RHW-2 90°C or higher Required 690.31(B)
Within array boundary PV wire, TC-ER cable 90°C Required if exposed 690.31(C)
Inside buildings THWN-2, XHHW-2 in conduit 90°C Not required 690.31(E)
Grounding conductors Bare or insulated copper Not required 690.45

Temperature Correction Factors (NEC Table 690.7)

Ambient Temp (°C) Ambient Temp (°F) Temp Correction Factor For Crystalline Silicon
-40 to -31-40 to -241.251.25
-30 to -21-22 to -61.241.24
-20 to -11-4 to 121.231.23
-10 to -114 to 301.221.22
0 to 932 to 481.211.21
10 to 1950 to 661.191.19
20 to 2968 to 841.161.16
30 to 3986 to 1021.131.13
40 to 49104 to 1201.101.10

Common Faults and Troubleshooting

Symptom Possible Cause Diagnosis Solution
Low system output Shading, soiling, module mismatch, string failures IR thermal imaging, I-V curve tracing, string current measurements Clean modules, trim vegetation, replace faulty modules
Inverter fault - high DC voltage Cold temperature voltage rise, too many modules in series Measure string Voc at cold conditions, compare to design Reduce modules per string, install lower Voc modules
Inverter fault - low DC voltage Hot temperature voltage drop, too few modules, wiring faults Measure string Vmp at operating temperature, check connections Add modules to strings, improve ventilation, fix connections
Blown fuses in combiner Short circuit, ground fault, fuse sizing error Insulation resistance test, visual inspection, current measurements Locate and repair fault, ensure proper fuse sizing
Hot spots on modules Bypass diode failure, cell damage, partial shading IR thermal imaging during operation Replace faulty diodes or modules
Final Design Checklist

□ Maximum system voltage calculated for coldest temperature
□ Minimum string voltage exceeds inverter minimum MPPT at highest temperature
□ Conductors sized for 125% of maximum current (×1.25×1.25)
□ Overcurrent protection provided per NEC 690.9
□ Rapid shutdown system designed per NEC 690.12
□ Voltage drop limited to ≤2%
□ All equipment listed for PV system use
□ Grounding system designed per NEC 690.41-47
□ Disconnects accessible and properly rated
□ Documentation complete with drawings and calculations

Important Safety Reminder

Solar array circuits remain energized whenever exposed to light, even when disconnected from inverters or batteries. Always treat PV conductors as energized. Use proper PPE and follow lockout/tagout procedures. Never work on PV systems without proper training and equipment.