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newSchoolWorks.com › VoTechWorks › Building & Construction › Solar / PV Installation › Electrical Fundamentals for PV Systems › Lesson 3
BLD-SOLA09-03 · Lesson 3 · 10 clock hours · theory

AC Circuits, Waveforms, and the Role of the Inverter

Objective. Students will explain the difference between DC and single-phase AC electricity, define RMS voltage, frequency, and power factor, and describe the function of a string inverter in converting PV DC to grid-compatible AC.

⚠ 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.

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AC vs. DC: Two Kinds of Electrical Flow

Every PV cell produces direct current (DC) — electrons flow in one direction only, from the negative terminal to the positive terminal. If you plotted DC voltage on a graph over time, you would see a flat, horizontal line. That steady, unchanging characteristic makes DC ideal for charging batteries and for the internal workings of electronics, but the power grid runs on something different.

Alternating current (AC) reverses direction periodically. In the United States, the grid operates at 60 Hz, meaning the current completes 60 full cycles every second. On a graph, AC voltage traces a smooth sine wave — it rises to a positive peak, falls back through zero, drops to a negative peak, then returns to zero. One full trip from zero up, across, and back to zero is called one cycle. The time it takes to complete one cycle is the period (T), measured in seconds. Period and frequency are inversely related: T = 1 ÷ f. At 60 Hz, the period is approximately 16.7 milliseconds.

RMS Voltage: The Effective Value

Because AC voltage swings continuously between positive and negative peaks, quoting the peak value alone is not very useful for calculating real power. Engineers use root mean square (RMS) voltage, sometimes called the effective voltage, because it represents the equivalent DC voltage that would deliver the same power to a resistive load.

For a pure sine wave, the relationship between peak voltage and RMS voltage is:

> V_RMS = V_peak ÷ √2 ≈ V_peak × 0.707

US residential service is commonly described as 120 V AC. That figure is an RMS value. The actual peak voltage is approximately 170 V, and the swing from negative peak to positive peak (peak-to-peak) is about 340 V. When you work with inverter datasheets and utility interconnection requirements, RMS values are always the reference unless a document specifically states otherwise.

Frequency

Frequency is how many complete cycles occur per second, measured in hertz (Hz). North American grids are standardized at 60 Hz. Many other countries use 50 Hz. An inverter connected to the US grid must output AC at exactly 60 Hz. If the frequency drifts outside the grid's tolerance, protective relays and the inverter's own anti-islanding circuitry will disconnect the system — intentionally and quickly — to protect utility workers and equipment.

Power Factor

Power factor (PF) describes how effectively current is being used to do real work. It is the ratio of real power (watts) to apparent power (volt-amperes). A power factor of 1.0 means all the current is doing useful work. Inductive loads such as motors cause the current waveform to lag behind the voltage waveform, reducing power factor below 1.0. Grid-tied inverters are designed to operate at or very near unity (1.0) power factor, and some advanced inverters can actively supply reactive power to help support grid voltage. For most PV installation work, you will see power factor listed on inverter spec sheets as a value between 0.99 and 1.0 at rated output.

The String Inverter: Gateway Between PV and the Grid

A string inverter is the most common inverter type for residential and small commercial PV systems. It receives high-voltage DC from a series string of PV modules and converts that DC into grid-compatible AC. The main stages inside a string inverter are:

1. DC input filtering and protection — capacitors smooth the incoming DC; fuses or DC disconnect switches protect against overcurrent and ground faults. A ground fault protection device (GFPD) monitors for unintended current paths to ground and shuts the inverter down if one is detected.

2. DC-to-AC conversion — power transistors (typically IGBTs) switch the DC on and off at very high speed in a pattern that synthesizes a sine wave.

3. Output filtering — inductors and capacitors clean up the synthesized waveform so it closely matches the smooth utility sine wave.

4. Grid synchronization — the inverter constantly samples the utility voltage to match its output frequency and phase before allowing current to flow.

5. Display and communications — a screen or indicator lights show operating status, and many inverters include a data port or wireless interface for monitoring.

String inverters have clearly labeled DC input terminals (usually marked + and −, with the acceptable voltage range stamped nearby) and AC output terminals (usually marked L1, L2/N, and Ground for split-phase residential service). Never reverse these connections.

Why Grid Matching Matters

The utility grid is an enormous shared resource. For a PV system to feed power into it safely, the inverter's AC output must match the grid in three ways: voltage level (e.g., 240 V RMS for US split-phase residential), frequency (60 Hz), and phase angle. If any of these are mismatched, the inverter cannot synchronize and will not export power. More importantly, a mis-synchronized inverter could damage loads and create safety hazards for utility workers. This is why inverters include anti-islanding protection — they shut down automatically when the grid is de-energized, preventing the inverter from energizing a line that a lineworker believes is dead.

Safety Reminder

When examining any inverter — even a demonstration or cutaway unit — verify that lockout/tagout (LOTO) procedures have been completed and confirmed before touching internal components. DC input terminals on a string inverter may carry voltages exceeding 600 V from the PV array even when the inverter AC disconnect is open, because the array generates voltage whenever light is present. Wear appropriate PPE and treat all conductors as energized until proven otherwise with a calibrated meter.

Key terms9

Direct Current (DC)Electric current that flows continuously in one direction; produced by PV cells and batteries.
Alternating Current (AC)Electric current that reverses direction periodically, tracing a sine wave; the North American grid operates at 60 Hz.
RMS VoltageRoot mean square voltage — the effective value of an AC voltage, equal to the equivalent DC voltage that delivers the same power to a resistive load. For a sine wave, V_RMS = V_peak ÷ √2.
FrequencyThe number of complete AC cycles per second, measured in hertz (Hz); the US grid standard is 60 Hz.
PeriodThe time required to complete one full AC cycle; the inverse of frequency (T = 1 ÷ f). At 60 Hz, the period is approximately 16.7 ms.
Power Factor (PF)The ratio of real power (watts) to apparent power (volt-amperes); a value of 1.0 means all current is doing useful work. Grid-tied inverters aim for unity or near-unity power factor.
String InverterA type of inverter that converts the combined DC output of a series string of PV modules into grid-compatible AC; the most common inverter type for residential and small commercial systems.
Anti-Islanding ProtectionA required inverter safety function that automatically disconnects the inverter from the grid when utility power is lost, preventing the inverter from energizing conductors that utility workers may assume are de-energized.
Ground Fault Protection Device (GFPD)A device built into inverters that detects unintended current paths from PV conductors to ground and shuts the system down to prevent fire and shock hazards.

Worked examples4

1. A string inverter datasheet states the AC output voltage is 240 V RMS (single-phase, split-phase). What is the peak voltage of the AC sine wave at this output?
  1. Recall the relationship: V_peak = V_RMS × √2
  2. Substitute the known value: V_peak = 240 V × 1.4142
  3. Calculate: V_peak = 339.4 V, which is commonly rounded to approximately 339 V
Answer: The peak voltage is approximately 339 V.
2. The US grid frequency is 60 Hz. What is the period (T) of one AC cycle, expressed in milliseconds?
  1. Recall the relationship: T = 1 ÷ f
  2. Substitute: T = 1 ÷ 60 = 0.01667 seconds
  3. Convert to milliseconds: 0.01667 s × 1000 ms/s = 16.67 ms
Answer: The period is approximately 16.7 milliseconds.
3. An inverter datasheet lists output apparent power as 5000 VA and real power output as 4950 W at full load. What is the power factor?
  1. Recall the formula: PF = Real Power (W) ÷ Apparent Power (VA)
  2. Substitute: PF = 4950 W ÷ 5000 VA
  3. Calculate: PF = 0.99
Answer: The power factor is 0.99, which is very close to unity, as expected for a grid-tied PV inverter.
4. An oscilloscope shows an AC sine wave with a peak-to-peak voltage of 678 V. What is the RMS voltage?
  1. Find the peak voltage from peak-to-peak: V_peak = 678 V ÷ 2 = 339 V
  2. Apply the RMS formula: V_RMS = V_peak ÷ √2 = 339 V ÷ 1.4142
  3. Calculate: V_RMS = 239.7 V, approximately 240 V RMS
Answer: The RMS voltage is approximately 240 V, consistent with standard US split-phase residential service.

The math in this lesson3

Learners compute power factor as real power divided by apparent power.
6.RP.3N-RN.2F-TF.5
Brush up in the math halls at newSchoolWorks.com:
In class: Oscilloscope or simulation software (e.g., PhET Circuit Construction Kit) demonstration: instructor displays a DC flat line and a 60 Hz AC sine wave side by side; students sketch both waveforms and label peak voltage, RMS voltage, and period. · Inverter teardown or cutaway model review: students examine a small string inverter (de-energized and LOTO-verified), identify the DC input terminals, AC output terminals, ground fault protection device, and display panel, then match each to a labeled diagram. · Think-pair-share: pairs read a short excerpt from an inverter manufacturer datasheet listing input DC voltage range, output AC voltage, frequency, and efficiency; they explain in writing why the AC voltage and frequency must match the utility grid.
Materials: Oscilloscope or laptop with PhET simulation, string inverter cutaway or non-energized demonstration unit, manufacturer datasheet (e.g., SMA or Enphase publicly available spec sheet), student workbook Chapter 3, whiteboard.
Check: Exit ticket: 5 short-answer questions on AC vs. DC characteristics and inverter function; pass mark 80%; instructor collects and reviews before next lesson.

Practice check8

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

Electrical Fundamentals
1. Which statement best describes the difference between DC and AC electricity as they relate to PV systems?
Electrical Fundamentals
2. A sine wave has a peak voltage of 170 V. What is its RMS voltage, rounded to the nearest volt?
Electrical Fundamentals
3. The period of the US grid AC waveform is closest to which value?
Electrical Fundamentals
4. Power factor is defined as the ratio of:
PV System Components
5. Which component inside a string inverter is specifically designed to detect unintended current paths from PV conductors to ground?
Safety and Codes
6. Anti-islanding protection in a grid-tied inverter is primarily intended to:
Safety and Codes
7. A student is about to examine the internal components of a de-energized string inverter for a lab exercise. Which action is most important before touching any internal terminals?
Electrical Fundamentals
8. An inverter datasheet shows an AC output of 240 V RMS at 60 Hz. A technician measures the peak-to-peak voltage with an oscilloscope. Which result is consistent with the datasheet?
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