13.1 Solar Photovoltaic (PV) Systems Fundamentals & Sizing

13.1 Solar Photovoltaic (PV) Systems Fundamentals & Sizing

Quick Reference (NEC Article 690 Fundamentals & Sizing):

• Governing NEC Article: Article 690 (Solar Photovoltaic Systems).
• Maximum PV Voltage (NEC 690.7): $V_{max} = \text{Module } V_{oc} \times \text{Series Modules} \times \text{Cold Temperature Correction Factor}$.
• Dwelling Voltage Limit (NEC 690.7(C)): Maximum 600 Volts DC on or in one- and two-family dwellings.
• Maximum Circuit Current (NEC 690.8(A)(1)): $I_{max} = 1.25 \times I_{sc}$ (accounts for irradiance reflection and cloud-edge effects).
• Conductor Ampacity & OCPD Sizing (NEC 690.8(B)): Minimum ampacity before derating $= 1.25 \times I_{max} = 1.25 \times (1.25 \times I_{sc}) = 1.5625 \times I_{sc}$ (156.25% rule).
• Exposed Outdoor Array Wiring (NEC 690.31(C)): Must be listed single-conductor Type USE-2 or Photovoltaic Wire (PV Wire); PV Wire is mandatory for ungrounded (floating) DC arrays.
• Interior DC Raceways (NEC 690.31(D)): DC circuits operating over 30V inside buildings must be installed in metal raceways (EMT, IMC, RMC) or metal-clad cable (Type MC).

Solar photovoltaic (PV) electrical energy systems represent one of the fastest-growing sectors in the electrical contracting industry. Because PV modules generate direct current (DC) whenever exposed to daylight—independent of utility grid availability—they introduce distinct engineering challenges, fire hazards, and shock hazards that differ fundamentally from standard alternating-current (AC) branch circuits and services.

In the National Electrical Code (NEC), Article 690 governs the design, equipment specifications, conductor sizing, and installation of solar photovoltaic systems. On the Connecticut E-2 Unlimited Journeyperson licensing examination, Article 690 calculations frequently appear. Candidates must master maximum DC system voltage determinations under cold-weather conditions, two-stage circuit current calculations, overcurrent protective device (OCPD) sizing, and conductor selection criteria for harsh outdoor rooftop environments.

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1. PV System Architecture & Component Terminology

To apply Article 690 accurately, an electrician must understand the flow of electrical energy from the solar cell to the utility grid connection and master the defined Code terminology:

                         SOLAR PV ELECTRICAL PATHWAY
  +------------+     +------------+     +------------------+
  |  PV Module | --> | Series     | --> | DC Combiner Box  |
  | (Solar Cell|     | String     |     | (Fuses, Surge,   |
  |  Assembly) |     | (Additive  |     |  Paralleling)    |
  +------------+     |  Voltage)  |     +------------------+
                     +------------+              |
                                                 v
  +------------+     +------------+     +------------------+
  | AC Service | <-- | AC         | <-- | Interactive      |
  | Panelboard |     | Disconnect |     | Inverter (DC/AC) |
  +------------+     +------------+     +------------------+

Core System Components

• Photovoltaic Cell: The basic photovoltaic device that generates direct-current electricity when exposed to photons.
• Photovoltaic Module: A complete, environmentally protected unit consisting of interconnected solar cells encapsulated in a rigid frame (commonly 60-cell, 72-cell, or modern split-cell formats).
• PV String (PV Source Circuit): Multiple PV modules wired in series to build sufficient DC operating voltage for inverter operation. In series circuits, voltages add together while current remains constant.
• PV Output Circuit: Circuit conductors running between the combiner box (where multiple parallel strings join) and the inverter or DC disconnect equipment.
• DC Combiner Box: An outdoor-rated enclosure housing overcurrent protective devices (string fuses), surge arresters, and terminal busbars that parallel multiple PV source circuits into a single PV output circuit.
• Inverter: Equipment used to convert direct current (DC) generated by the PV array into alternating current (AC) compatible with the premises wiring system and the electric utility grid. Inverters are classified as:
  • Interactive Inverters (Grid-Tied): Inverters designed to operate in parallel with the electric utility grid, automatically ceasing power delivery when the utility grid is de-energized (anti-islanding).
  • Multimode Inverters: Hybrid units capable of operating in grid-interactive mode or islanding to provide backup power during utility outages in conjunction with energy storage systems.
  • Microinverters: Miniaturized grid-interactive inverters attached directly to individual modules or small sub-arrays on the roof, converting DC to AC at the module level.
• DC-to-DC Converters (Power Optimizers): Module-Level Power Electronics (MLPE) installed on each module that track the maximum power point (MPPT), step voltage up or down, and provide rapid shutdown capabilities while feeding a central string inverter.

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2. Maximum PV System Voltage Calculations (NEC 690.7)

Determining the maximum direct-current voltage of a PV system is one of the most critical calculations in renewable energy design. Standard electrical equipment, conductor insulation, overcurrent devices, and disconnect switches are rated for specific maximum voltages (typically 600V or 1,000V). Exceeding these dielectric thresholds leads to catastrophic insulation failure, sustained DC arc faults, and structural fire.

Temperature Physics & The Negative Temperature Coefficient

Unlike standard resistive conductors whose resistance rises with temperature, silicon semiconductor photovoltaic cells exhibit an inverse voltage-to-temperature relationship: as ambient temperature decreases, module open-circuit voltage ($V_{oc}$) increases. In freezing winter conditions, a PV array produces significantly higher open-circuit voltage than its standard test conditions (STC) nameplate rating (measured at $25^\circ\text{C}$ or $77^\circ\text{F}$).

Per NEC 690.7(A), the maximum PV system voltage for DC circuits shall be determined using one of two approved methods:

1. Manufacturer's Temperature Coefficient Method: Using the module manufacturer's certified temperature coefficient of open-circuit voltage ($%/^{\circ}\text{C}$ or $\text{mV}/^{\circ}\text{C}$) and the lowest expected ambient temperature for the geographic location.
2. Table 690.7(A) Correction Factors: Multiplying the rated module open-circuit voltage by the correction factors tabulated in NEC Table 690.7(A) for crystalline and multi-crystalline silicon modules.

The 600-Volt Residential Dwelling Threshold (NEC 690.7(C))

NEC 690.7(C) establishes a strict life-safety threshold: in one- and two-family dwellings, PV system DC circuits shall not exceed 600 volts nominal.

Commercial and industrial structures are permitted to operate at up to 1,000V or 1,500V DC where access is restricted to qualified personnel. However, on residential roofs in Connecticut, any string design whose cold-weather corrected voltage exceeds 600.0 volts constitutes a direct code violation. Designers must divide the modules into shorter series strings.

Worked Example: Connecticut Winter Sizing

An electrician in Hartford, Connecticut is designing a residential rooftop array.

• Module Specifications: $V_{oc} = 41.2\text{ V}$ at STC ($25^\circ\text{C}$).
• Series String Length: 13 modules wired in series.
• Lowest Expected Ambient Temperature: $-22^\circ\text{C}$ ($-8^\circ\text{F}$).
• Temperature Coefficient of $V_{oc}$: $-0.29%/^{\circ}\text{C}$.

                   VOLTAGE CALCULATION STEP-BY-STEP
  1. Temperature Differential:
     Delta T = Lowest Temp - STC Temp
     Delta T = -22 deg C - (+25 deg C) = -47 deg C

  2. Percentage Voltage Increase:
     Voltage Increase = -47 deg C * (-0.29 % / deg C) = +13.63 %
     Correction Factor = 1 + 0.1363 = 1.1363

  3. Corrected Open-Circuit Voltage per Module:
     Corrected Voc = 41.2 V * 1.1363 = 46.82 V

  4. Maximum PV String Voltage:
     Vmax = 13 modules * 46.82 V = 608.66 V

Evaluation: Because $608.66\text{ V} > 600\text{ V}$, this 13-module string violates NEC 690.7(C) for a residential dwelling. The string must be reconfigured into two shorter strings (e.g., one string of 7 and one of 6, or two strings of 6) to keep maximum winter voltage below 600V.

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3. Circuit Current & Conductor Sizing Rules (NEC 690.8)

Sizing PV circuit conductors and overcurrent protective devices involves a specialized two-tier calculation under NEC 690.8 to safeguard circuits against prolonged overload and thermal breakdown.

               NEC 690.8 TWO-STAGE SIZING METHODOLOGY
   
   [Module Nameplate Isc]
             |
             v  (Multiply by 125% per NEC 690.8(A)(1))
   [Maximum Circuit Current (Imax) = 1.25 * Isc]
   * Accounts for cloud-edge effect and solar irradiance > 1000 W/m2
             |
             v  (Multiply by 125% per NEC 690.8(B))
   [Required OCPD & Conductor Ampacity = 1.25 * Imax]
   * Accounts for continuous duty operation (3+ hours at max current)
             |
             v  
   [Cumulative Multiplier: 1.25 * 1.25 = 1.5625 (156.25% of Isc)]

Stage 1: Maximum Circuit Current (NEC 690.8(A)(1))

Standard PV module nameplates display the short-circuit current ($I_{sc}$) under Standard Test Conditions (irradiance of $1,000\text{ W/m}^2$). However, in the field, atmospheric conditions such as the "cloud-edge effect" (cumulus cloud lensing reflecting extra sunlight onto the array) frequently produce solar irradiances of $1,200\text{ W/m}^2$ to $1,300\text{ W/m}^2$ for sustained periods.

To account for this natural phenomena, NEC 690.8(A)(1) dictates that the maximum circuit current for a PV source or output circuit shall be calculated as: $I_{max} = 1.25 \times I_{sc}$

Where multiple parallel strings feed a DC combiner box, the maximum circuit current is the sum of the individual string maximum currents: $I_{max(\text{combiner})} = \sum (1.25 \times I_{sc}) = 1.25 \times (N_{\text{strings}} \times I_{sc})$

Stage 2: Conductor Ampacity & Overcurrent Protection (NEC 690.8(B))

Because PV systems operate at peak capacity for hours under direct sunlight, solar circuits are classified as continuous loads (loads where maximum current is sustained for 3 hours or more per NEC Article 100).

Under NEC 690.8(B), conductors and overcurrent protective devices must be sized for not less than 125 percent of the maximum circuit current determined in 690.8(A): $\text{Minimum Ampacity / OCPD} = 1.25 \times I_{max} = 1.25 \times (1.25 \times I_{sc}) = 1.5625 \times I_{sc}$

Master Electrician Rule of Thumb: When calculating the minimum overcurrent protective device rating or the minimum uncorrected conductor ampacity directly from the module nameplate short-circuit current, multiply $I_{sc}$ by 1.5625 (or 156.25%).

Adjustment and Correction Factors (NEC 310.15)

Once the minimum ampacity is established via the 156.25% rule, conductors must be evaluated under actual operating conditions using standard ampacity tables (Table 310.16) subject to:

1. Ambient Temperature Correction: Rooftop environments routinely reach $50^\circ\text{C}$ to $60^\circ\text{C}$ ($122^\circ\text{F}$ to $140^\circ\text{F}$) on hot summer afternoons, requiring severe thermal derating multipliers (e.g., 0.71 or 0.58 for $90^\circ\text{C}$ wire).
2. Conduit Fill Adjustment: When multiple PV source circuits share a common raceway, conductor ampacity must be derated according to NEC Table 310.15(C)(1) (e.g., 80% for 4–6 current-carrying conductors, 70% for 7–9 conductors).

Under NEC 690.8(B)(1), the conductor ampacity after applying all thermal and raceway adjustment factors must be equal to or greater than the maximum circuit current ($I_{max} = 1.25 \times I_{sc}$). Conductor sizing is governed by the larger of the two calculations:

• Requirement 1: $1.25 \times I_{max}$ (no derating applied).
• Requirement 2: $I_{max} / (\text{Temp Factor} \times \text{Fill Factor})$.

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4. Conductor Selection & Wiring Methods (NEC 690.31)

Conductors installed on photovoltaic arrays are subjected to environmental extremes unmatched in typical building wiring: ultraviolet (UV) radiation, severe thermal cycling, wind whipping, ice buildup, and prolonged moisture immersion.

Type USE-2 vs. Photovoltaic Wire (PV Wire)

Per NEC 690.31(C), single-conductor cable exposed to outdoor array conditions must be listed as Type USE-2 (Underground Service Entrance) or listed Photovoltaic Wire (PV Wire).

                      INSULATION DIELECTRIC BARRIER
   +-------------------------------------------------------------------------+
   | PV WIRE: Dual-layer or heavy thermoset cross-linked polyethylene (XLPE) |
   | Rated 1000V/2000V DC | VW-1 Flame Rated | Sunlight Resistant | Sub-Zero |
   +-------------------------------------------------------------------------+

Mandatory Use of PV Wire in Modern Arrays

Modern grid-interactive inverters are predominantly non-isolated (transformerless) topologies. Under NEC 690.35 / 690.41, transformerless inverters operate with ungrounded (floating) DC arrays, meaning neither the positive nor the negative conductor is solidly bonded to earth. In an ungrounded system, both DC conductors operate at high potentials to ground, and a single ground fault does not trip an overcurrent device.

Because of these elevated electrical stresses, PV Wire is mandatory on ungrounded DC arrays. Type USE-2 is strictly prohibited on floating systems because its insulation is not evaluated for continuous ungrounded DC stress or elevated operating potentials above 600V.

Interior DC Wiring Methods (NEC 690.31(D))

Where PV DC source and output circuits from a building-mounted array run inside a building, they present a fire danger because rooftop modules cannot be switched off during daylight. Under NEC 690.31(D):

• Conductors must be contained in metal raceways (Electrical Metallic Tubing [EMT], Intermediate Metal Conduit [IMC], or Rigid Metal Conduit [RMC]) or metal-clad cable (Type MC) conforming to 250.118(10).
• Flexible metal conduit (FMC) is limited to connections at equipment and cannot exceed 6 feet in length.
• The raceways must be clearly labeled every 10 feet with yellow reflective labels reading: "WARNING: PHOTOVOLTAIC POWER SOURCE" in capital letters of at least 3/8 inch height.