$NABCEP PV Associate Workbook Study Guide cover$

About the Author

$David N. Jones$

Renewable Energy Technologist

David N. Jones

College lecturer, global subject matter expert, energy consultant, inventor, and CEO of Lumena Energy.

David N. Jones works at the intersection of renewable energy, electrical systems, workforce development, software, and distributed-energy innovation. His work is centered on one goal: making advanced energy systems understandable, practical, and deployable for the communities, institutions, utilities, and governments that need them.

As CEO of Lumena Energy, he has built an integrated clean-energy platform spanning technical consulting, solar education, workforce development, software, distributed-energy strategy, and Virtual Power Plant architecture.

College LecturerTranslates complex energy engineering into rigorous, accessible instruction.

Global Subject Matter ExpertAdvises across renewable energy, VPPs, microgrids, distributed resources, and grid modernization.

Government Energy ConsultantSupports public-sector leaders evaluating clean-energy infrastructure, workforce, and technology strategy.

Renewable Energy TechnologistDesigns systems that connect energy hardware, software, data, people, and markets.

About the Author

Advancing the State of the Art in Virtual Power Plants

David's work treats the Virtual Power Plant not as a single software product, but as a coordinated energy system that joins distributed assets, controls, markets, communications, cybersecurity, and human operators.

Distributed AssetsSolar, batteries, EVs, flexible buildings, generators, microgrids, and controllable loads

Energy IntelligenceForecasting, optimization, dispatch logic, telemetry, and measurement

Grid CoordinationDemand response, capacity, resilience, energy-market participation, and utility operations

Human InfrastructureTraining, field procedures, technician development, and community participation

Selected Leadership and Innovation

Founder and CEO of Lumena Energy, developing integrated approaches to Energy-as-a-Service and distributed-energy coordination.
Architect of Virtual Power Plant, microgrid, smart-grid, and distributed-energy concepts designed to bridge technical systems with real-world deployment.
Developer of interactive renewable-energy training platforms that combine visual learning, simulation, field practice, and rigorous technical calculations.
2019 Google Innovation Award recipient.
Entrepreneur in Residence at the University of Chicago.
Executive board member of Local #944 and developer of clean-energy workforce and apprenticeship pathways.
Advisor to public-sector and institutional stakeholders on renewable-energy infrastructure, workforce strategy, and emerging grid technologies.

His teaching philosophy: A student should leave the classroom able to explain the system, calculate the system, test the system, and work safely around the system.

About the Author

A Note from David

Solar energy is not only a technology. It is an electrical discipline, a construction trade, an economic tool, a workforce pathway, and a foundation for the modern distributed grid.

I created this workbook because students deserve more than a collection of facts to memorize. They deserve to understand why a system behaves the way it does, how each calculation connects to equipment in the field, and how safe work practices protect both the technician and the public.

My goal is to help you build confidence. That confidence must be earned through practice, careful measurement, disciplined calculations, collaboration, and respect for the hazards present in electrical and construction work.

Use this workbook actively. Write in it. Highlight it. Challenge the examples. Repeat the calculations. Ask questions. Most importantly, connect every lesson to the real equipment and people who make the energy transition possible.

David N. Jones

CEO, Lumena Energy
Renewable Energy Technologist and Educator

Course Introduction

Lumena Energy Academy

Your Path to NABCEP PV Associate Readiness

This workbook is designed to be taught, written in, highlighted, discussed, and revisited. It converts the core ideas in Solar Photovoltaic Basics into original Lumena lessons, guided calculations, jobsite scenarios, and exam practice.

How to Use It

Enter your name in the toolbar.
Select text and choose Highlight.
Use the notes panel on every page.
Your work saves automatically in this browser.
Export a backup file before changing devices or clearing browser data.

Course Standard

Understand the concept, practice the calculation, connect it to field work, then answer the exam-style question.

Workbook Units

1Safety First

2Electricity Fundamentals

3Solar Fundamentals

4PV Systems & Design

5Installation, Commissioning & Maintenance

6NABCEP Master Review

Course Introduction

Learning Contract

Technical confidence comes from repetition, careful units, safe habits, and asking good questions.

My reason for earning the NABCEP PV Associate credential: The technical topic I most want to master: One habit I will use when solving calculations:

Student name

Date

Unit 1: Safety First

PV Industry and System Applications

Before working safely around a PV system, identify what kind of system you are approaching and where energy can originate.

Grid-Tied

PV array and inverter operate in parallel with the utility. Standard utility-interactive systems stop exporting during a utility outage through anti-islanding protection.

Stand-Alone

Operates independently from the utility. Common components include PV modules, charge controller, battery bank, inverter, and loads.

Hybrid

Combines PV with another energy source such as a generator, wind turbine, or micro-hydro resource.

Multimodal

Can operate grid-connected and transition to a protected stand-alone mode for selected loads.

Direct-Coupled

PV powers a load directly, commonly a motor or pump. Output changes with available sunlight.

Field Question

A homeowner says, “I have solar, so my entire house will operate during an outage.” What information must you verify before answering?

Unit 1: Safety First

Safety Authority and Responsibility

OSHA

Establishes workplace safety requirements. State plans may be more protective than federal rules, but not less protective.

NEC / NFPA

The National Electrical Code provides requirements intended to protect people and property from electrical hazards.

AHJ

The Authority Having Jurisdiction interprets and enforces the adopted rules for the project.

Before Work Begins

Identify all possible energy sources.
Review plans, labels, one-line diagrams, and equipment documentation.
Perform a job hazard analysis.
Confirm required PPE and fall protection.
Establish communication and emergency procedures.

Common mistake: Treating a disconnect handle as proof that every conductor is de-energized. PV conductors can remain energized whenever illuminated.

Unit 1: Safety First

Ladder and Fall Protection

Extension Ladder Setup

Use an extension ladder for roof access.
Set the ladder at approximately a 1:4 ratio.
Extend the rails at least 3 feet above the landing surface.
Secure the ladder and maintain three points of contact.
Use fiberglass ladders near electrical hazards.

Personal Fall Arrest System

Full-body harness
Connector or shock-absorbing lanyard
Lifeline where applicable
Rated anchorage
Rescue planning

41

Hazard Spotting

Why must skylights be treated as fall hazards even when they appear solid?

Unit 1: Safety First

Electrical Hazards, Arc Faults and OCPD

Arcing

An arc can occur when current crosses an unintended air gap. DC arcs may persist because direct current does not pass through a natural zero crossing like AC.

Arc Flash

An arc flash is a high-energy event that can produce extreme heat, pressure, molten material, and sound. The hazard level depends on available fault current, clearing time, distance, and equipment conditions.

Overcurrent Protection

Fuses and circuit breakers protect conductors and equipment from excessive current. Module labels commonly state a maximum series fuse rating.

Field rule: Never replace an overcurrent device with a larger rating merely to stop nuisance operation. Find the cause.

Match the Protection to the Hazard

Hazard	Primary Control
Unexpected energization	Lockout/Tagout and verification
Falling from elevation	Guardrails, safety nets, or PFAS
Excess current	Fuse or circuit breaker
Flying debris or battery electrolyte	Eye and face protection

Unit 1: Safety First

Lockout/Tagout and Verification

1Identify every energy source

2Notify affected workers

3Shut down equipment normally

4Isolate and apply locks/tags

5Release stored energy

6Verify absence of voltage

Live-dead-live: Prove the meter on a known live source, test the circuit, then prove the meter again.

Scenario

You open an AC disconnect and the inverter display goes dark. The PV array is in full sunlight. Which parts of the system may still be energized, and what is your next safe action?

Unit 1: Safety First

Unit 1 Knowledge Check

1. What is the proper extension ladder setup ratio?

1:2 1:4 4:1

2. Which action provides the best evidence that a conductor is de-energized?

The inverter screen is dark The disconnect handle is OFF A properly verified meter test

3. Which device protects conductors from excessive current?

Pyranometer Fuse or circuit breaker Inclinometer

Unit 2: Electricity Fundamentals

Electrical Quantities

V

Voltage

Electrical potential difference, often compared to pressure.

volts

I

Current

Rate of charge flow through a circuit.

amperes

R

Resistance

Opposition to current flow.

ohms

P

Power

Rate at which energy is transferred.

watts

E

Energy

Power used or produced over time.

Wh or kWh

P = V × I

E = P × t

V = I × R

Common mistake: kW measures power. kWh measures energy. “kW per hour” is usually not the correct unit for ordinary energy use.

Unit 2: Electricity Fundamentals

Power and Energy Calculations

Worked Example

A 24 V DC fan draws 3 A and operates for 5 hours.

Power: 24 V × 3 A = 72 W
Energy: 72 W × 5 h = 360 Wh
Convert: 360 Wh ÷ 1000 = 0.36 kWh

Your Turn

Voltage (V) Current (A) Hours

Explain why the answer should be in Wh rather than W:

Unit 2: Electricity Fundamentals

Ohm's Law

V

I

R

V = I × R

I = V ÷ R

R = V ÷ I

Worked Example

A 120 V load draws 0.75 A. Find resistance.

R = V ÷ I = 120 V ÷ 0.75 A = 160 Ω

Practice

Known	Find	Equation	Answer
48 V, 12 Ω	Current
8 A, 3 Ω	Voltage
24 V, 2 A	Resistance

Unit 2: Electricity Fundamentals

Series and Parallel Circuits

Series

Voltages add
Current remains limited by the series path

Parallel

Currents add
Voltage remains the branch voltage

Array Math

Four identical modules each have Vmp = 40 V and Imp = 10 A. They are wired as two modules in series, with two identical strings in parallel. Find array Vmp, Imp, and Pmp.

Unit 2: Electricity Fundamentals

Battery Capacity

Example

A 12 V battery rated at 100 Ah stores a nominal:

12 V × 100 Ah = 1,200 Wh = 1.2 kWh

Nominal energy is not the same as recommended usable energy. Allowable depth of discharge, temperature, battery chemistry, discharge rate, and system losses all affect usable capacity.

Practice

A 48 V battery bank is rated at 200 Ah. Find nominal kWh. If only 80% is intended to be used, estimate usable kWh before other losses.

Common mistake: Adding amp-hour ratings from batteries wired in series. Series increases voltage; parallel increases amp-hour capacity.

Unit 3: Solar Fundamentals

Solar Power, Solar Energy and STC

Irradiance

Instantaneous solar power received per unit area, commonly W/m².

Insolation

Solar energy received over time, often represented as peak sun hours per day.

Peak Sun Hour

Equivalent to one hour at 1,000 W/m², or 1 kWh/m².

Standard Test Conditions

1,000 W/m² irradiance
25°C cell temperature
Air mass 1.5

Important: Actual operating conditions rarely equal STC. Module output changes with irradiance, cell temperature, shading, soiling, and electrical losses.

Unit 3: Solar Fundamentals

Sun Path, Tilt, Azimuth and Shading

Orientation

Azimuth describes compass direction. In the northern hemisphere, south-facing arrays often maximize annual production, but east and west orientations may better match load profiles or time-of-use rates.

Tilt

Tilt influences annual output, seasonal output, self-cleaning, row spacing, wind loading, and snow behavior.

Shading

Shade can reduce current and may affect an entire series string. Bypass diodes limit damage and reduce the effect of partial shading, but do not eliminate production loss.

Evaluate shade during the hours and seasons that matter, not only at the moment of the site visit.

Describe one reason a southwest-facing array could be preferred over a south-facing array:

Unit 3: Solar Fundamentals

PV Cells, Modules, Strings and Arrays

CellSemiconductor device

→

ModuleInterconnected cells in a protected assembly

→

StringModules connected in series

→

ArrayAll interconnected PV source circuits

Silicon Module Families

Type	Typical Visual Clue	General Note
Monocrystalline	Uniform dark cells, historically rounded corners	High efficiency and broad market use
Multicrystalline	Blue, crystalline texture	Historically lower cost
Thin-film	Uniform surface, fewer visible cell boundaries	Different voltage/current characteristics and area needs

Vocabulary

Why is “module” more precise than “panel” on technical documents?

Unit 3: Solar Fundamentals

Reading a Module Nameplate

Example PV Module

Pmax400 W

Vmp37.2 V

Imp10.76 A

Voc45.1 V

Isc11.35 A

Max series fuse20 A

Temp. coefficient Voc-0.28%/°C

Interpretation

Voc is open-circuit voltage and is used for cold maximum-voltage string checks.
Vmp is voltage at maximum power and is used for operating-voltage checks.
Isc is short-circuit current.
Imp is current at maximum power.
Pmax should approximately equal Vmp × Imp.

Verify Pmax using Vmp and Imp:

Unit 4: PV Systems & Design

PV System Components

PV Array

DC

Combiner / OCPD

DC

Inverter

AC

Service / Loads / Utility

Inverter

Converts DC to AC and may provide MPPT, monitoring, protection, and grid synchronization.

Charge Controller

Controls charging from PV into a battery system. MPPT controllers optimize the PV operating point.

Disconnect

Provides a means to isolate equipment or conductors. It is not automatically proof of de-energization.

Combiner

Combines multiple source circuits and may contain fuses or breakers.

Rapid Shutdown

Reduces controlled conductor voltage in or on buildings according to applicable code requirements.

Monitoring

Tracks power, energy, voltage, current, faults, and sometimes environmental conditions.

Unit 4: PV Systems & Design

Grid-Tied System Sizing

Worked Example

A 6 kW system receives 4.5 peak sun hours per day and has a total derate factor of 0.82.

Daily energy = 6 × 4.5 × 0.82 = 22.14 kWh/day

Annual energy ≈ 22.14 × 365 = 8,081 kWh/year

Primary Sizing Constraints

Available area and structural suitability
Annual energy goal
Budget and incentives
Utility interconnection rules
Inverter operating limits
Shade, orientation, tilt, temperature, and system losses

Estimate annual production for 10 kW, 4.2 PSH, and 14% total losses:

Unit 4: PV Systems & Design

Stand-Alone Load Analysis

Off-grid design begins with loads, not with the number of modules.

Load	Qty	Watts each	Hours/day	Wh/day

Design Questions

What is the critical design month?
How many days of autonomy are required?
What loads can be reduced before adding equipment?
What depth of discharge is appropriate?
What surge power must the inverter support?

Unit 4: PV Systems & Design

Cold-Temperature String Sizing

1ΔT = minimum temperature - 25°C

2Multiply ΔT by Voc temperature coefficient

3Apply the voltage increase to module Voc

4Inverter max DC voltage ÷ corrected Voc

5Round down

Example

Minimum temperature = -15°C, Voc = 45.1 V, coefficient = -0.28%/°C, inverter maximum = 600 V.

ΔT = -15 - 25 = -40°C
-40 × -0.28% = 11.2% increase
Corrected Voc = 45.1 × 1.112 = 50.15 V
600 ÷ 50.15 = 11.96
Maximum = 11 modules in series

Cold rule: Use Voc and round down. Exceeding the inverter maximum voltage can damage equipment and violate listing limits.

Unit 4: PV Systems & Design

Hot-Temperature Operating Voltage

At high cell temperature, module voltage decreases. The string must remain above the inverter's minimum MPPT or operating voltage.

1ΔT = hot cell temperature - 25°C

2Apply Vmp temperature coefficient

3Find corrected hot Vmp

4Minimum inverter voltage ÷ hot Vmp

5Round up

Hot rule: Use Vmp and round up. A string that is too short may fail to start or may drop out of the MPPT window.

Why is rounding direction different for cold and hot calculations?

Unit 4: PV Systems & Design

Electrical Design Essentials

Conductors

Ampacity
Temperature correction
Conduit fill
Terminal ratings
Voltage drop
Environmental rating

Protection and Control

Source-circuit and output-circuit OCPD
DC and AC disconnecting means
Ground-fault and arc-fault functions
Equipment grounding and bonding
Labels and directories
Rapid shutdown where required

Design principle: Equipment ratings, conductor ratings, overcurrent protection, and environmental conditions must agree as a system.

List three reasons an undersized conductor may reduce performance or create a hazard:

Unit 4: PV Systems & Design

Mechanical Design Essentials

Roof Condition

Evaluate remaining roof life, material, slope, drainage, and safe access.

Structure

Account for dead load, live load, snow, wind uplift, attachment spacing, and load paths.

Waterproofing

Use compatible flashings and sealants according to roof and racking manufacturer instructions.

Thermal Movement

Allow for expansion and contraction of rails, conductors, and equipment.

Array Layout

Maintain access pathways, setbacks, equipment clearances, and fire-service needs.

Ballasted Systems

Low-slope arrays may avoid penetrations but require careful structural and wind analysis.

Scenario

A low-slope roof can physically fit 80 modules, but the structural review only supports 60 in the proposed layout. What should the design team do?

Unit 5: Installation, Commissioning & Maintenance

Installation Sequence and Quality Control

1Preconstruction review

2Layout and attachment verification

3Racking and bonding

4Module placement

5Wire management and terminations

6Equipment installation and labeling

7Inspection and commissioning

Quality Records

Torque values recorded
Photos of concealed work retained
Polarity and voltage checks documented
Labels compared with plans
As-built changes recorded

Common mistake: Using “tight enough” as a torque specification. Use calibrated tools and manufacturer values.

Unit 5: Installation, Commissioning & Maintenance

Commissioning

Commissioning verifies that the installed system is safe, documented, functional, and performing reasonably under the conditions present.

Before Energization

Visual inspection
Mechanical completion
Torque verification
Polarity checks
Grounding and bonding checks
Disconnect and OCPD verification

Operational Checks

String open-circuit voltage comparison
Operating current comparison
Inverter startup and status
Monitoring communication
AC voltage and frequency
Production reasonableness

A system does not need to produce nameplate power at every startup. Compare output with irradiance, cell temperature, orientation, and expected system losses.

Unit 5: Installation, Commissioning & Maintenance

Troubleshooting Method

1Stay safe and define the complaint

2Review monitoring, plans, alarms, and history

3Inspect before measuring

4Isolate the system or subsystem

5Verify the meter and take reproducible measurements

6Correct only after identifying the cause

7Retest and document

Symptom-to-Cause Practice

Symptom	Likely checks
System drops out on very hot afternoons	Hot string voltage, inverter MPPT window, conductor voltage drop
One string current is much lower	Shade, open connector, blown fuse, damaged module, mismatch
Winter production suddenly declines	Snow, weather, shading change, monitoring fault
Dry-season output gradually declines	Soiling, vegetation, airflow and temperature

Unit 5: Installation, Commissioning & Maintenance

Battery Maintenance

All Battery Systems

Follow chemistry-specific manufacturer instructions
Inspect terminals, conductors, fuses, and disconnects
Check ventilation and enclosure condition
Record voltage, temperature, alarms, and state-of-charge data
Use appropriate PPE and insulated tools

Flooded Lead-Acid

Check electrolyte levels
Add distilled water only as instructed
Measure specific gravity when appropriate
Control ignition sources and ventilation
Use equalization only when required by the manufacturer

Never generalize: Maintenance practices appropriate for flooded lead-acid batteries may be wrong or dangerous for sealed lead-acid, lithium-ion, or other chemistries.

Unit 6: NABCEP Master Review

NABCEP Formula Sheet

P = V × IPower

E = P × tEnergy

V = I × ROhm's law

Wh = V × AhBattery energy

Array power = module power × quantityDC nameplate

Series voltage = sum of module voltagesCurrent unchanged

Parallel current = sum of branch currentsVoltage unchanged

Production ≈ kW × PSH × derate × daysEnergy estimate

Cold string max = inverter max V ÷ corrected VocRound down

Hot string min = inverter min V ÷ corrected VmpRound up

My three formulas to practice most:

Unit 6: NABCEP Master Review

Exam Strategy

Read the final sentence first when a problem contains extra information.
Write the units on every line of math.
Estimate the expected range before calculating.
Eliminate answers with impossible units or wrong direction.
For cold voltage, expect voltage to rise. For hot voltage, expect voltage to fall.
Do not let one difficult problem consume the exam.
Return to flagged questions with fresh attention.
Practice calculations rather than only rereading them.

My Exam Plan

Unit 6: NABCEP Master Review

Final Mixed Knowledge Check

Course Completion

Course Reflection

The concept I understand best: The calculation I need to practice: The safety behavior I will carry into every jobsite: My next step in the solar industry:

This workbook belongs to

NABCEP PV Associate Workbook Study Guide

Glossary of Terms

AC-coupled system

A system in which energy sources or storage devices are interconnected on the alternating-current side through one or more inverters.

Alternating current (AC)

Electric current that periodically reverses direction. Utility power is commonly supplied as AC.

Ambient temperature

The temperature of the air surrounding equipment or conductors.

Ampacity

The maximum current a conductor can carry continuously under specified conditions without exceeding its temperature rating.

Ampere (A)

The unit used to measure electric current.

Amp-hour (Ah)

A unit of electric charge commonly used to describe battery capacity. One amp-hour represents one ampere flowing for one hour.

Anti-islanding

A protective function that causes a utility-interactive inverter to stop energizing the grid when acceptable utility voltage or frequency is absent.

Array

A mechanically and electrically integrated assembly of PV modules and related components.

Authority Having Jurisdiction (AHJ)

The organization or official responsible for interpreting and enforcing adopted codes, standards, and permitting requirements.

Autonomy

The amount of time a battery-based system can serve loads without additional charging.

Available fault current

The maximum current that can flow at a point in a circuit during a fault.

Azimuth

The compass direction an array faces, expressed as an angle.

Backfed breaker

A circuit breaker supplied from its load terminals, commonly used for a load-side PV interconnection.

Balance of system (BOS)

All PV system components other than the modules, including wiring, racking, inverters, disconnects, and protection.

Ballasted mounting system

A mounting system held in place primarily by weight rather than roof penetrations.

Battery

An electrochemical device that stores and releases electrical energy.

Battery bank

Two or more batteries interconnected to provide a required system voltage and capacity.

Battery-based system

A PV system that includes electrochemical energy storage.

Glossary of Terms

Bifacial module

A PV module designed to convert light received on both its front and rear surfaces.

Bimodal system

A system capable of operating both utility-interactive and stand-alone, also called multimodal.

Bonding

The permanent joining of conductive parts to establish electrical continuity and an effective fault-current path.

Branch circuit

Circuit conductors between the final overcurrent device and the load or outlet.

Building-integrated photovoltaics (BIPV)

PV materials that also serve as part of the building envelope, such as roof tiles, glazing, or facade elements.

Bypass diode

A diode connected across groups of cells to reduce hot-spot risk and limit the effect of partial shading.

Capacity factor

Actual energy produced over a period divided by the energy that would have been produced at continuous rated power.

Cell

The smallest semiconductor device in a PV module that directly converts light into electricity.

Cell temperature

The operating temperature of a PV cell, which can be substantially higher than ambient air temperature.

Central inverter

A large inverter that serves many PV source circuits or subarrays.

Charge controller

A device that controls current and voltage from an energy source into a battery.

Circuit

A complete conductive path through which current can flow.

Circuit breaker

A resettable overcurrent protection device that opens a circuit when current exceeds its rating under specified conditions.

Clipping

Loss of potential PV power when array output exceeds the inverter's maximum conversion capability.

Combiner box

An enclosure that combines multiple PV source circuits into one output circuit and may contain fuses, breakers, monitoring, or disconnects.

Commissioning

The documented process of verifying that an installed system is safe, complete, functional, and performing reasonably.

Conductor

A material or wire that allows electric current to flow.

Conduit

A raceway used to route and protect conductors.

Glossary of Terms

Continuity

The presence of a complete electrical path.

Critical design month

The month with the most demanding combination of load and solar resource for stand-alone system design.

Current

The rate of electric charge flow, measured in amperes.

Current-voltage curve (I-V curve)

A graph showing the relationship between PV current and voltage under specified conditions.

DC-coupled system

A system in which PV, storage, or other components are interconnected on the direct-current side.

Dead load

A permanent load on a structure, including the PV array and mounting system.

Demand charge

A utility charge based on a customer's highest measured power demand during a billing interval.

Demand response

A change in electricity consumption or generation in response to grid, utility, or market signals.

Depth of discharge (DOD)

The percentage of a battery's rated capacity that has been removed.

Derate factor

A multiplier below 1.0 used to account for expected system losses or operating conditions.

Direct-coupled PV system

A simple system in which a PV source directly powers a DC load without energy storage.

Direct current (DC)

Electric current that flows in one direction.

Disconnect

A device that provides a means to isolate conductors or equipment from a source of power.

Distributed energy resource (DER)

A small or modular resource connected to a distribution system, including PV, storage, generators, EVs, and flexible loads.

Distributed generation (DG)

Electric generation located near the point of use or connected to the distribution grid.

Duty cycle

The fraction of time a load or device operates during a defined period.

Efficiency

Useful output divided by total input, usually expressed as a percentage.

Electrical load

A device or system that consumes electric power.

Glossary of Terms

Electrical potential

The ability of electric charge to perform work because of a voltage difference.

Electromagnetic induction

The production of voltage by changing magnetic flux through a conductor.

Energy

Power produced or consumed over time, commonly measured in Wh or kWh.

Energy audit

A systematic evaluation of energy use and opportunities to reduce consumption.

Energy storage system (ESS)

One or more devices and controls that store energy for later use.

Equipment grounding conductor (EGC)

A conductive path that connects exposed metal equipment to the grounding system for fault-current protection.

Fall arrest system

Equipment designed to stop a worker after a fall begins.

Fall restraint

A system that prevents a worker from reaching a fall hazard.

Feed-in tariff

A policy that compensates renewable generation at a specified rate for energy delivered to the grid.

Flash test

A controlled light test used by manufacturers to characterize module electrical output.

Frequency

The number of AC cycles per second, measured in hertz.

Full-body harness

Personal fall protection equipment that distributes arrest forces across the body.

Fuse

A one-time overcurrent device that opens when its element melts from excessive current.

Generator

A machine that converts mechanical energy into electrical energy.

Grid-direct system

A utility-interactive PV system without battery storage.

Grid parity

The point at which PV electricity is economically competitive with conventional utility electricity.

Grid-tied system

A PV system designed to operate in parallel with the utility grid.

Ground fault

An unintended electrical connection between an energized conductor and ground or grounded conductive material.

Glossary of Terms

Ground-fault protection device (GFPD)

A device that detects ground-fault current and initiates protective action.

Grounded conductor

A current-carrying conductor intentionally connected to ground at one point.

Grounding electrode

A conductive object that establishes a direct connection to earth.

Grounding electrode conductor (GEC)

The conductor connecting the grounding electrode system to the grounded conductor, equipment grounding system, or both.

Harness suspension trauma

A potentially life-threatening condition caused by prolonged suspension in a fall-arrest harness.

Hertz (Hz)

The unit of frequency equal to one cycle per second.

Hot spot

Localized overheating in a cell or module caused by mismatch, shading, damage, or reverse bias.

Hybrid system

A system using more than one energy source, such as PV and a generator.

Incentive

A financial, tax, policy, or regulatory mechanism intended to encourage an investment or behavior.

Insolation

Solar energy received over time on a surface, often represented as equivalent peak sun hours.

Insulation

Material that resists the flow of electric current.

Interconnection

The physical and contractual connection of a generating system to the utility grid.

Inverter

A power electronic device that converts DC electricity into AC electricity.

Inverter efficiency

AC output power divided by DC input power.

Irradiance

Instantaneous solar power incident on a surface, measured in W/m².

Islanding

A condition in which a portion of the grid remains energized by local generation after being separated from the utility source.

Junction box

An enclosure on a PV module or electrical system where conductors and protective components are connected.

Kilowatt (kW)

One thousand watts, a unit of power.

Glossary of Terms

Kilowatt-hour (kWh)

One thousand watt-hours, a unit of energy.

Line conductor

An energized AC conductor, commonly called hot.

Line-to-line voltage

Voltage measured between two ungrounded AC conductors.

Line-to-neutral voltage

Voltage measured between an ungrounded conductor and neutral.

Live load

A temporary structural load, such as workers, movable equipment, rain, or snow.

Load controller

A device that disconnects or regulates loads to protect a battery from excessive discharge.

Load profile

A record or pattern of electric power use over time.

Load-side connection

A PV interconnection made on the load side of the utility service disconnect.

Lockout/Tagout (LOTO)

A procedure for isolating energy sources, applying locks and tags, releasing stored energy, and verifying a safe condition.

Maximum power point (MPP)

The operating point on an I-V curve where voltage multiplied by current is greatest.

Maximum power point tracking (MPPT)

Electronic control that continuously seeks the PV operating point that produces maximum power.

Maximum series fuse rating

The largest series overcurrent device permitted by the module listing and label.

Microinverter

A small inverter typically connected to one PV module.

Module

A complete, environmentally protected assembly of interconnected PV cells.

Module mismatch

Power loss caused by electrical differences among modules or cells.

Monocrystalline silicon

PV material made from a single-crystal silicon structure.

Multicrystalline silicon

PV material formed from multiple silicon crystal grains, also called polycrystalline.

Multimodal inverter

An inverter capable of utility-interactive and stand-alone operation.

Glossary of Terms

National Electrical Code (NEC)

A U.S. electrical installation standard published by NFPA and adopted by jurisdictions.

Net metering

A billing arrangement that credits customer-generated electricity exported to the utility grid.

Neutral conductor

A grounded AC circuit conductor intended to carry current during normal operation.

Nominal operating cell temperature (NOCT)

A reference cell temperature measured under specified outdoor operating conditions.

Nominal voltage

A named system voltage used for classification rather than an exact operating value.

Occupational Safety and Health Administration (OSHA)

The U.S. agency responsible for workplace safety and health standards.

Open-circuit voltage (Voc)

The voltage of a PV source when no current is flowing.

Overcurrent

Current exceeding the rated or allowable value of conductors or equipment.

Overcurrent protection device (OCPD)

A fuse or circuit breaker intended to protect conductors and equipment from excessive current.

Parallel connection

A connection in which positive conductors join together and negative conductors join together, increasing current while voltage remains approximately unchanged.

Peak demand

The highest average power demand measured during a specified interval.

Peak sun hour (PSH)

An equivalent hour of solar irradiance at 1,000 W/m².

Performance ratio

Actual system energy divided by a reference energy based on irradiance and rated capacity.

Personal fall arrest system (PFAS)

A system including anchorage, connectors, and a full-body harness that stops a fall.

Personal protective equipment (PPE)

Wearable equipment used to reduce exposure to hazards.

Photovoltaic effect

The physical process by which light creates voltage and current in a semiconductor.

Photovoltaic output circuit

Circuit conductors between a PV source-circuit combiner and the DC utilization equipment.

Photovoltaic source circuit

Circuit conductors from modules connected in series to the common connection point.

Glossary of Terms

Point of interconnection

The location where a generating system connects to an electrical system or utility grid.

Polarity

The positive or negative electrical orientation of a DC conductor or terminal.

Polycrystalline silicon

Another term for multicrystalline silicon.

Power

The instantaneous rate of energy transfer, measured in watts.

Power factor

Real power divided by apparent power in an AC circuit.

Power purchase agreement (PPA)

A contract in which a customer purchases energy produced by a system owned by another party.

Power tolerance

The permitted range between a module's labeled power and measured power.

Pyranometer

An instrument used to measure solar irradiance.

PV panel

A term sometimes used for a group of modules, though module is the preferred technical term for one factory-assembled unit.

PV source circuit combiner

Equipment that combines multiple PV source circuits.

PV system disconnect

A disconnecting means for the PV system output from other conductors in a building or structure.

PVUSA Test Conditions (PTC)

A set of outdoor reference conditions used to estimate module or system output more realistically than STC.

Rapid shutdown

A function that reduces voltage on controlled PV conductors within a specified time after initiation.

Racking

The structural framework used to support and secure PV modules.

Raceway

An enclosed channel designed to hold and protect conductors.

Real power

The portion of AC power that performs useful work, measured in watts.

Resistance

Opposition to current flow, measured in ohms.

Return on investment (ROI)

Net financial gain divided by investment cost.

Glossary of Terms

Roof attachment

Hardware that transfers array loads into the building structure.

Series connection

A connection in which components are connected end-to-end, increasing voltage while current remains limited by the series path.

Series fuse

A fuse installed in series with a source circuit to protect it from reverse current from parallel sources.

Service equipment

The main control and disconnecting equipment for utility-supplied electricity at a building.

Shading

Obstruction of solar radiation reaching a PV array.

Short-circuit current (Isc)

The current of a PV source when its output terminals are directly connected through negligible resistance.

Silicon

A semiconductor material widely used in PV cells.

Single-axis tracker

A mounting system that rotates an array around one axis to follow the sun.

Soiling

Accumulation of dust, dirt, pollen, bird droppings, or other material on module surfaces.

Solar access

The availability of unobstructed sunlight at a site during relevant hours and seasons.

Solar altitude

The sun's angular height above the horizon.

Solar azimuth

The compass direction from an observer to the sun.

Solar resource

The amount and pattern of solar energy available at a location.

Stand-alone system

A system that operates independently from the utility grid.

Standard Test Conditions (STC)

Module rating conditions of 1,000 W/m² irradiance, 25°C cell temperature, and air mass 1.5.

State of charge (SOC)

The percentage of a battery's usable capacity remaining.

String

A group of PV modules connected in series.

String inverter

An inverter connected to one or more series strings of modules.

Glossary of Terms

Supply-side connection

A generation interconnection made on the supply side of the service disconnect.

Surge power

Short-duration power required by certain loads during startup.

Temperature coefficient

The rate at which an electrical parameter changes with temperature.

Thin-film PV

PV technology made by depositing very thin semiconductor layers onto a substrate.

Tilt angle

The angle between a module surface and the horizontal plane.

Time-of-use rate (TOU)

An electricity tariff in which prices vary by time of day or season.

Torque

Rotational force applied to a fastener or terminal.

Transformer

A device that changes AC voltage and current levels through electromagnetic induction.

Ungrounded conductor

A current-carrying conductor not intentionally connected to ground.

Utility-interactive inverter

An inverter listed to operate in parallel with and synchronize to the utility grid.

Virtual Power Plant (VPP)

A coordinated network of distributed energy resources operated through communications, controls, forecasting, and optimization to provide grid or market services.

Voltage

Electric potential difference between two points, measured in volts.

Voltage drop

Reduction in voltage caused by current flowing through conductor impedance.

Volt-ampere (VA)

Apparent power in an AC circuit, equal to RMS voltage multiplied by RMS current.

Watt (W)

The unit of power equal to one joule per second.

Watt-hour (Wh)

A unit of energy equal to one watt sustained for one hour.

Wind uplift

Upward structural force caused by wind acting on an array or building surface.

Wire management

The support, routing, protection, and securing of conductors and connectors.

Glossary of Terms

Work clearance

Required unobstructed space around electrical equipment for safe access and servicing.

Glossary of Equations

Write units on every line. Confirm that the final unit matches the quantity requested.

Power

P = V × I

P in watts, V in volts, I in amperes.

Voltage from power

V = P ÷ I

Use when power and current are known.

Current from power

I = P ÷ V

Use when power and voltage are known.

Ohm's Law

V = I × R

Relationship among voltage, current, and resistance.

Current from Ohm's Law

I = V ÷ R

Current equals voltage divided by resistance.

Resistance from Ohm's Law

R = V ÷ I

Resistance equals voltage divided by current.

Power using current and resistance

P = I² × R

Useful when current and resistance are known.

Power using voltage and resistance

P = V² ÷ R

Useful when voltage and resistance are known.

Energy

E = P × t

Energy equals power multiplied by time.

Power from energy

P = E ÷ t

Average power equals energy divided by time.

Time from energy

t = E ÷ P

Operating time equals energy divided by power.

Watt-hours to kilowatt-hours

kWh = Wh ÷ 1,000

Move to the larger unit by dividing by 1,000.

Kilowatt-hours to watt-hours

Wh = kWh × 1,000

Move to the smaller unit by multiplying by 1,000.

Kilowatts to watts

W = kW × 1,000

Metric conversion.

Glossary of Equations

Write units on every line. Confirm that the final unit matches the quantity requested.

Megawatts to kilowatts

kW = MW × 1,000

Metric conversion.

Gigawatts to megawatts

MW = GW × 1,000

Metric conversion.

Horsepower to watts

W = hp × 746

Approximate mechanical-to-electrical power conversion.

Battery nominal energy

Wh = V × Ah

Nominal battery energy.

Battery amp-hours

Ah = Wh ÷ V

Required amp-hour capacity at a selected nominal voltage.

Amp-hour use

Ah = A × h

Charge removed at a constant current.

Usable battery energy

Usable Wh = Nominal Wh × allowable DOD

Before efficiency and temperature adjustments.

Battery bank series voltage

Vbank = Vbattery × number in series

Amp-hour rating remains approximately that of one series string.

Battery bank parallel capacity

Ahbank = Ahstring × number of parallel strings

Voltage remains approximately that of one string.

Series PV voltage

Vseries = V1 + V2 + ... + Vn

For identical modules, Vseries = n × Vmodule.

Series PV current

Iseries ≈ Imodule

Series current is limited by the lowest-current element.

Parallel PV current

Iparallel = I1 + I2 + ... + In

For identical strings, Iparallel = n × Istring.

Parallel PV voltage

Vparallel ≈ Vstring

Parallel branches operate at a common voltage.

Array nameplate power

Parray = module Pmp × module quantity

DC nameplate rating.

Glossary of Equations

Write units on every line. Confirm that the final unit matches the quantity requested.

Maximum power point

Pmp = Vmp × Imp

Power at the maximum-power operating point.

Fill factor

FF = Pmp ÷ (Voc × Isc)

A dimensionless measure of I-V curve squareness.

Module efficiency

ηmodule = Pmp ÷ (irradiance × module area)

Use consistent units.

Daily production estimate

kWh/day ≈ system kW × PSH × derate

Simplified energy estimate.

Period production estimate

Energy ≈ system kW × PSH/day × days × derate

Simplified monthly or annual production.

Loss-to-derate conversion

Derate = 1 - loss fraction

A 15% loss corresponds to 0.85.

Energy offset

Offset % = PV annual kWh ÷ annual load kWh × 100

Compares production with consumption.

Capacity factor

CF = actual kWh ÷ (rated kW × hours)

Use matching period.

Performance ratio

PR = actual energy ÷ reference energy

Reference energy accounts for irradiance and array rating.

Specific yield

Specific yield = annual kWh ÷ installed kW

Expressed as kWh/kW-year.

Voltage drop

Vdrop = I × R

Basic DC voltage-drop relationship.

Voltage-drop percentage

Vdrop % = Vdrop ÷ circuit voltage × 100

Compare drop with operating voltage.

Conductor resistance

R = ρL ÷ A

Resistance depends on resistivity, length, and cross-sectional area.

Cold temperature difference

ΔT = Tmin - 25°C

Used for cold Voc correction relative to STC.

Glossary of Equations

Write units on every line. Confirm that the final unit matches the quantity requested.

Cold voltage correction fraction

Correction = ΔT × temperature coefficient Voc

With both values negative, result is a positive increase.

Cold corrected module Voc

Voc,cold = Voc,STC × (1 + increase fraction)

Convert percent to decimal first.

Maximum modules in series

Nmax = inverter max DC voltage ÷ Voc,cold

Always round down.

Hot temperature difference

ΔT = Tcell,hot - 25°C

Used for hot Vmp correction.

Hot corrected module Vmp

Vmp,hot = Vmp,STC × (1 + coefficient × ΔT)

Coefficient is normally negative, so voltage decreases.

Minimum modules in series

Nmin = inverter minimum MPPT voltage ÷ Vmp,hot

Always round up.

Temperature conversion to Celsius

°C = (°F - 32) × 5/9

Temperature conversion.

Temperature conversion to Fahrenheit

°F = °C × 9/5 + 32

Temperature conversion.

Efficiency

η = useful output ÷ input × 100%

General efficiency relationship.

Inverter efficiency

ηinv = Pac ÷ Pdc × 100%

AC output divided by DC input.

Power factor

PF = real power W ÷ apparent power VA

For AC circuits.

Apparent power

S = Vrms × Irms

Expressed in volt-amperes.

Simple payback

Payback years = net installed cost ÷ annual savings

Does not include discounting or escalation.

Return on investment

ROI % = net gain ÷ investment cost × 100

Define net gain and period clearly.

Glossary of Equations

Write units on every line. Confirm that the final unit matches the quantity requested.

Annual electricity savings

Savings = displaced kWh × applicable energy rate

May require time-varying rates.

Demand savings

Demand savings = reduced kW × demand rate

Based on utility billing rules.

Future value with escalation

FV = PV × (1 + g)^n

Used for compounded price or cost escalation.

Present value

PV = FV ÷ (1 + r)^n

Discounts a future value to present dollars.

Net present value

NPV = Σ[Cash flow_t ÷ (1 + r)^t] - initial investment

Positive NPV indicates value above the discount rate.

Levelized cost of energy

LCOE = lifetime present-value cost ÷ lifetime present-value energy

Use consistent discount and degradation assumptions.

Annual degradation

Output_n = Output_1 × (1 - d)^(n-1)

Models compounding annual production decline.

Module quantity by power

Modules = required DC watts ÷ module watts

Round according to design constraints.

Area-limited PV capacity

PV kW ≈ area × irradiance × module efficiency ÷ 1,000

At 1,000 W/m² reference irradiance.

Ladder ratio

Horizontal distance = vertical height ÷ 4

The 1:4 extension-ladder setup rule.

Slope

Slope = rise ÷ run

May be expressed as a ratio, decimal, percent, or angle.

Percent change

Percent change = (new - original) ÷ original × 100

General comparison equation.

Availability

Availability % = available time ÷ total scheduled time × 100

Operational availability.

Trip rate

Trip rate per 1,000 h = trips ÷ operating hours × 1,000

Normalizes event frequency.

Glossary of Equations

Write units on every line. Confirm that the final unit matches the quantity requested.

System DC-to-AC ratio

DC/AC ratio = array DC nameplate kW ÷ inverter AC rated kW

Used to describe inverter loading.

Annual energy density

kWh/m²-year = annual energy ÷ occupied area

Useful for comparing land or roof utilization.