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BLD-SOLA09-10 · Lesson 2 · 16 clock hours · theory

Domain Deep-Dive: System Design, Sizing, Electrical Theory, and NEC 690 Code Review

Objective. The learner will accurately solve PV system sizing calculations (array voltage, current, conductor ampacity, overcurrent protection, string configuration) and correctly apply NEC Article 690 rules and electrical theory concepts in timed practice-question sets, scoring at least 75% on each domain sub-quiz.

⚠ Pending professional review

This lesson, its worked examples and its practice questions has not yet been verified by a licensed professional engineer or master tradesperson or by a certification or approval body. It is a study draft and may contain errors. Do not use it as instructions for work on a job site or on live equipment. Always follow your instructor, your supervising professional, and current official references and regulations.

VoTechWorks program approval and accreditation are still in progress. Credentials are issued only by the certifying bodies named in each program, after their own exams.

Why This Domain Matters on NABCEP Exams

System design, sizing, electrical theory, and NEC Article 690 code compliance make up a substantial portion of both the NABCEP PV Associate and PV Installation Professional exams. You will not pass by memorizing vocabulary alone. You must be able to set up and solve calculations under time pressure, cite code provisions accurately, and connect electrical theory to real system behavior. This lesson walks you through the core calculation types, the key Article 690 rules, and the electrical theory fundamentals you need to hit the 75% threshold on every domain sub-quiz.

Electrical Theory Fundamentals

PV system math is built on Ohm's Law (V = I × R), the power equation (P = V × I), and the relationships among series and parallel circuits.

In a PV array, modules wired in series form a string. The string voltage equals the sum of individual module voltages. Strings wired in parallel share the same voltage; their currents add together. Understanding this lets you size conductors, overcurrent devices, and inverter inputs correctly.

Temperature affects module output significantly:

Always use the temperature coefficients printed on the module datasheet and the extreme temperatures for the installation site when calculating worst-case voltage and current.

Voc and Vmp Temperature Correction

The standard formula for correcting Voc for a string of modules is:

Voc_corrected = Voc_STC × [1 + (γ × ΔT)] × N_series

Where:

The result must not exceed the inverter's maximum DC input voltage or the voltage rating of any system component, including conductors and overcurrent devices.

Apply the same structure to Vmp correction when sizing for the inverter's MPPT voltage window.

Array Current and the 125% Continuous Load Rule

The array short-circuit current (Isc) is the starting point for sizing DC conductors and overcurrent protective devices (OCPDs). Because PV sources are treated as continuous loads under the NEC, you apply a 125% multiplier:

Minimum conductor ampacity = Isc × 1.25 × N_parallel

Minimum OCPD rating = Isc × 1.25 × N_parallel

OCPD ratings must then be rounded up to the next standard fuse or breaker size. Conductors must also meet the ampacity requirements after applying any required correction factors for temperature and conduit fill (NEC Chapter 3 tables).

String Configuration

To determine how many modules go in series, divide the inverter's maximum DC input voltage by the corrected Voc per module (rounding down to stay within limits). To confirm MPPT compatibility, check that the resulting string Vmp falls within the inverter's MPPT voltage range.

To determine how many strings go in parallel, divide the desired array power by the string power, or size to the inverter's maximum input current rating.

NEC Article 690 Key Provisions

Article 690 of the National Electrical Code governs photovoltaic systems specifically. Know these areas thoroughly:

When answering code questions on the exam, look for the word that changes everything: shall, shall not, listed, identified. These are precise NEC terms.

Safety Notes

Even in a classroom calculation exercise, embed safe habits. PV arrays generate voltage whenever illuminated — there is no "off" switch for the DC source. Always apply lockout/tagout (LOTO) procedures before working on any part of a live system. Use PPE rated for the arc-flash and shock hazard present (at minimum, insulated gloves rated for the DC voltage, safety glasses, and appropriate arc-rated clothing when working near energized DC conductors). Rapid shutdown exists specifically because firefighters and first responders must be able to reduce shock hazards quickly — understanding Article 690.12 is not just an exam topic, it is life safety.

Exam Strategy for This Domain

On timed exams, read the datasheet values given in the question stem carefully — do not substitute memorized typical values. Write out the formula before plugging in numbers. For code questions, eliminate answers that use absolute numbers not stated in the question; the correct answer usually references the requirement (continuous load, listed equipment, required label) rather than a specific number pulled from thin air. Track every missed item type in your domain-tracking spreadsheet and drill it the same evening.

Key terms10

Open-Circuit Voltage (Voc)The voltage across a PV module or string when no current is flowing; the highest voltage the module or string produces under a given set of conditions. It is the critical value for sizing system components against maximum voltage limits.
Temperature Coefficient (γ)A value provided on a module datasheet, expressed per degree Celsius (often as %/°C or V/°C), that describes how much a parameter such as Voc or Vmp changes with each degree of temperature change from the STC reference of 25 °C.
Standard Test Conditions (STC)The laboratory conditions under which PV module ratings are established: 1000 W/m² irradiance, 25 °C cell temperature, and AM 1.5 spectrum. Real-world performance differs from STC ratings.
Continuous LoadUnder the NEC, a load where the maximum current is expected to continue for three hours or more. PV systems are treated as continuous loads, requiring conductor ampacity and OCPD ratings to be multiplied by 125% of the calculated current.
Overcurrent Protective Device (OCPD)A fuse or circuit breaker that interrupts current when it exceeds a safe level. In PV systems, OCPDs must be rated for DC use and sized based on 125% of the PV source circuit short-circuit current.
Rapid ShutdownA requirement under NEC Article 690.12 that PV systems on buildings include a means to reduce voltage and current within the array boundary and inside the building to safer levels within a specified time when the system is shut down, primarily to protect emergency responders.
StringA series-connected group of PV modules. The string voltage equals the sum of the individual module voltages; string current equals the current of a single module.
Maximum Power Point (Vmp / Imp)The operating voltage (Vmp) and current (Imp) at which a PV module or array produces its maximum power output under given conditions. Inverter MPPT circuits track this point continuously.
NEC Article 690The section of the National Electrical Code that specifically addresses solar photovoltaic systems, covering topics including system design, conductor requirements, disconnecting means, ground-fault and arc-fault protection, rapid shutdown, and required labeling.
AmpacityThe maximum continuous current a conductor can carry under specified conditions (insulation type, ambient temperature, conduit fill) without exceeding its rated temperature. Conductors must be selected so their derated ampacity meets or exceeds the calculated load current.

Worked examples4

1. A PV module has Voc = 45.0 V at STC and a Voc temperature coefficient of −0.30%/°C. The site's record low temperature is −15 °C. How many modules can be wired in series if the inverter's maximum DC input voltage is 600 V?
  1. Step 1 – Find ΔT: ΔT = −15 °C − 25 °C = −40 °C
  2. Step 2 – Convert the temperature coefficient to decimal per °C: −0.30%/°C = −0.0030/°C
  3. Step 3 – Calculate the corrected Voc per module: Voc_corrected = 45.0 V × [1 + (−0.0030 × −40)] = 45.0 V × [1 + 0.12] = 45.0 V × 1.12 = 50.4 V per module
  4. Step 4 – Divide the inverter maximum voltage by the corrected Voc per module: 600 V ÷ 50.4 V = 11.90 modules
  5. Step 5 – Round DOWN to stay within the voltage limit: maximum 11 modules in series
  6. Step 6 – Verify: 11 × 50.4 V = 554.4 V ≤ 600 V ✓
Answer: Maximum 11 modules in series; corrected string Voc = 554.4 V
2. A PV source circuit consists of 3 strings wired in parallel. Each module has an Isc of 9.8 A (STC). What is the minimum conductor ampacity and the minimum OCPD rating for the combined circuit output, before any derating for temperature or conduit fill?
  1. Step 1 – Find total array Isc: 3 strings × 9.8 A = 29.4 A
  2. Step 2 – Apply the 125% continuous load factor for minimum conductor ampacity: 29.4 A × 1.25 = 36.75 A → conductor must have an ampacity of at least 36.75 A (select the next standard conductor size that meets or exceeds this value after derating)
  3. Step 3 – Apply the 125% factor for the minimum OCPD rating: 29.4 A × 1.25 = 36.75 A
  4. Step 4 – Round UP to the next standard OCPD size: standard sizes near 36.75 A include 40 A; select 40 A as the minimum OCPD rating
Answer: Minimum conductor ampacity: 36.75 A (before derating); minimum OCPD: 40 A (next standard size up)
3. A module datasheet shows Vmp = 38.0 V and a Vmp temperature coefficient of −0.45%/°C. At the site's highest expected cell temperature of 70 °C, what is the corrected Vmp for a single module?
  1. Step 1 – Find ΔT: ΔT = 70 °C − 25 °C = +45 °C
  2. Step 2 – Convert temperature coefficient to decimal: −0.45%/°C = −0.0045/°C
  3. Step 3 – Calculate corrected Vmp: Vmp_corrected = 38.0 V × [1 + (−0.0045 × 45)] = 38.0 V × [1 − 0.2025] = 38.0 V × 0.7975 = 30.305 V
  4. Step 4 – Round to a reasonable precision: approximately 30.3 V per module
  5. Step 5 – Confirm this value falls within the inverter's MPPT voltage window to ensure the inverter will track power at high temperatures
Answer: Corrected Vmp at 70 °C cell temperature ≈ 30.3 V per module
4. An installer must verify that a 10-module, single-string array meets the minimum MPPT voltage of an inverter at maximum expected cell temperature. Module Vmp at STC = 40.0 V; Vmp temperature coefficient = −0.40%/°C; maximum cell temperature = 65 °C; inverter minimum MPPT voltage = 200 V. Does the string meet the requirement?
  1. Step 1 – Find ΔT: ΔT = 65 °C − 25 °C = +40 °C
  2. Step 2 – Convert coefficient: −0.40%/°C = −0.0040/°C
  3. Step 3 – Corrected Vmp per module: 40.0 V × [1 + (−0.0040 × 40)] = 40.0 V × [1 − 0.16] = 40.0 V × 0.84 = 33.6 V
  4. Step 4 – String Vmp at maximum temperature: 10 × 33.6 V = 336 V
  5. Step 5 – Compare to inverter minimum MPPT voltage: 336 V ≥ 200 V ✓
Answer: Yes, the string Vmp at maximum cell temperature is 336 V, which exceeds the inverter's minimum MPPT voltage of 200 V.

The math in this lesson2

Learners apply 125% factors to parallel string Isc to size conductors and OCPD.
7.RP.3A-SSE.1
Brush up in the math halls at newSchoolWorks.com:
In class: Instructor-led worked-example sessions covering the highest-frequency calculation types on NABCEP exams: Voc temperature correction, Vmp temperature correction, array series/parallel string sizing, minimum conductor ampacity (125% continuous load rule), DC and AC disconnect sizing, and conduit fill; learners work each problem independently then compare with the instructor's solution, noting formula sources in their notes. · NEC 690 speed-drill: learners receive a 30-item fill-in-the-blank worksheet requiring them to cite the correct code provision (e.g., rapid shutdown requirements, ground-fault protection, labeling) using only a tabbed NEC; they complete it in 25 minutes, then review errors in pairs, and re-attempt any missed items. · Domain sub-quizzes: three separate 20-item timed quizzes covering (a) system design and sizing, (b) electrical theory fundamentals, and (c) NEC 690 code compliance; learners record scores in their domain-tracking spreadsheet and flag any item type missed more than once for targeted self-study that evening.
Materials: NEC (current adopted edition) with Article 690 tabbed, Photovoltaic Systems textbook, manufacturer specification sheets (sample module and inverter datasheets from prior courses), scientific calculator, domain sub-quiz packets (instructor-prepared), formula reference sheet (instructor-prepared, identical in format to any allowed reference on the actual exam), learner domain-tracking spreadsheets.
Check: Score on each of the three 20-item domain sub-quizzes recorded and reviewed; pass standard is 75% (15/20) on each. Learners scoring below 75% on any sub-quiz must complete a targeted 10-item remediation set on that domain before the next lesson and achieve 80% on the remediation set.

Practice check8

Answer each question, then check it. Nothing is recorded; this is your own practice.

System Design and Sizing
1. A PV module has a Voc of 42.0 V at STC and a Voc temperature coefficient of −0.35%/°C. At a site low temperature of −20 °C, what is the corrected Voc per module?
NEC 690 Code Compliance
2. Under the NEC, PV source circuit conductors are treated as continuous loads. What minimum ampacity must a conductor have to serve a single-string source circuit with a module Isc of 8.5 A, before applying any temperature or conduit-fill derating?
NEC 690 Code Compliance
3. Which NEC Article 690 provision specifically addresses the requirement to reduce PV system voltage to safer levels within the array boundary and inside a building when the system is shut down?
System Design and Sizing
4. An array has 4 strings in parallel, each string consisting of 10 modules with Isc = 9.0 A. What is the minimum overcurrent protective device (OCPD) rating for the combined DC output circuit, rounded up to the next standard size?
Electrical Theory Fundamentals
5. When modules are connected in series to form a string, which of the following statements is correct?
Electrical Theory Fundamentals
6. A module datasheet lists Vmp = 36.0 V and Imp = 8.0 A at STC. What is the rated maximum power output of this module?
System Design and Sizing
7. A PV module's Voc at STC is 40.0 V and its Voc temperature coefficient is −0.30%/°C. At a cell temperature of 25 °C (STC), a second module of the same model is mounted adjacent. The site record low is −10 °C. How many modules in series keeps the string Voc at or below a 480 V inverter maximum DC input limit?
NEC 690 Code Compliance
8. Which type of conductor insulation or cable type is specifically listed and acceptable for use in exposed outdoor PV source circuit wiring applications, such as on a rooftop array?
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