Total Harmonic Distortion (THD) in Power Electronics - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is Total Harmonic Distortion (THD)?

THD is a measure of how much a signal is distorted by harmonics compared to its fundamental frequency. It shows the amount of unwanted frequencies mixed with the original signal.

beginner

Why is THD important in power electronics?

THD helps us understand the quality of electrical power. High THD means more distortion, which can cause equipment to heat up, malfunction, or become less efficient.

intermediate

How is THD calculated?

THD is calculated by dividing the square root of the sum of the squares of all harmonic voltages or currents by the fundamental frequency voltage or current, then multiplying by 100 to get a percentage.

beginner

What are harmonics in electrical signals?

Harmonics are frequencies that are multiples of the fundamental frequency. For example, if the main frequency is 50 Hz, harmonics could be 100 Hz, 150 Hz, and so on.

intermediate

What can cause high THD in a power system?

Non-linear loads like computers, LED lights, and variable speed drives can create harmonics, increasing THD and causing distortion in the power system.

What does a high THD value indicate in a power system?

A Higher fundamental frequency

B Better power quality

C Lower voltage levels

D More distortion and unwanted harmonics

High THD means there are more unwanted harmonic frequencies causing distortion in the power system.

Which of the following is NOT a harmonic frequency if the fundamental frequency is 60 Hz?

A 90 Hz

B 180 Hz

C 120 Hz

D 240 Hz

Harmonics are multiples of the fundamental frequency. 90 Hz is not a multiple of 60 Hz.

How is THD usually expressed?

A In volts

B As a percentage

C In hertz

D In watts

THD is expressed as a percentage showing the ratio of harmonic distortion to the fundamental frequency.

Which device is likely to increase THD in a power system?

A LED light with driver

B Resistive heater

C Incandescent bulb

D Transformer

LED lights with electronic drivers are non-linear loads that can create harmonics and increase THD.

What is the fundamental frequency in a power system?

A The highest frequency present

B The lowest frequency present

C The main frequency of the power supply

D The frequency of the harmonics

The fundamental frequency is the main frequency of the power supply, like 50 Hz or 60 Hz.

Explain what Total Harmonic Distortion (THD) is and why it matters in electrical power systems.

Think about how unwanted frequencies affect the original signal and devices.

Describe how THD is calculated and what information it gives about a signal.

Consider the relationship between the fundamental and harmonic components.

Practice

1. What does Total Harmonic Distortion (THD) measure in an electrical signal?

easy

A. The total voltage of the main signal only

B. The amount of unwanted harmonic frequencies compared to the main signal

C. The frequency of the main signal

D. The power consumption of the device

Solution

1. Step 1: Understand the definition of THD

   THD measures how much extra unwanted signals (harmonics) are present compared to the main signal.

2. Step 2: Compare options with the definition

   Only the option describing the amount of unwanted harmonic frequencies compared to the main signal matches the definition of THD.

3. Final Answer:

   The amount of unwanted harmonic frequencies compared to the main signal -> Option B

4. Quick Check:

   THD = unwanted harmonics / main signal [OK]

Hint: THD shows extra unwanted signals vs main signal [OK]

Common Mistakes:

• Confusing THD with total voltage
• Thinking THD measures frequency only
• Mixing THD with power consumption

2. Which formula correctly represents Total Harmonic Distortion (THD)?

easy

A. THD = V1 x (V2 + V3 + ... + Vn)

B. THD = V1 / (V2 + V3 + ... + Vn)

C. THD = V1 + V2 + V3 + ... + Vn

D. THD = √(V2² + V3² + ... + Vn²) / V1

Solution

1. Step 1: Recall the THD formula

   THD is calculated as the square root of the sum of squares of harmonic voltages divided by the fundamental voltage (V1).

2. Step 2: Match formula to options

   THD = √(V2² + V3² + ... + Vn²) / V1 matches the correct formula: THD = √(V2² + V3² + ... + Vn²) / V1.

3. Final Answer:

   THD = √(V2² + V3² + ... + Vn²) / V1 -> Option D

4. Quick Check:

   THD formula uses root sum squares over fundamental [OK]

Hint: THD = root sum squares of harmonics over main voltage [OK]

Common Mistakes:

• Using addition instead of root sum squares
• Dividing fundamental by harmonics instead of reverse
• Multiplying voltages instead of dividing

3. Given harmonic voltages V2 = 3V, V3 = 4V, and fundamental voltage V1 = 10V, what is the THD value?

medium

A. 0.5

B. 0.25

C. 0.7

D. 0.1

Solution

1. Step 1: Calculate root sum squares of harmonics

   √(3² + 4²) = √(9 + 16) = √25 = 5 volts.

2. Step 2: Divide by fundamental voltage

   THD = 5 / 10 = 0.5.

3. Final Answer:

   0.5 -> Option A

4. Quick Check:

   THD = 5/10 = 0.5 [OK]

Hint: Use Pythagoras for harmonics, then divide by main voltage [OK]

Common Mistakes:

• Adding harmonic voltages instead of root sum squares
• Dividing fundamental by harmonics
• Mixing up voltage values

4. A student calculates THD using THD = (V2 + V3 + ... + Vn) / V1 instead of the correct formula. What is the main error?

medium

A. They calculated THD correctly

B. They used the fundamental voltage incorrectly

C. They forgot to square the harmonic voltages before summing

D. They used the wrong units for voltage

Solution

1. Step 1: Identify the correct THD calculation method

   THD requires squaring each harmonic voltage, summing, then taking the square root before dividing by fundamental voltage.

2. Step 2: Analyze the student's formula

   The student summed harmonic voltages directly without squaring, which underestimates the distortion.

3. Final Answer:

   They forgot to square the harmonic voltages before summing -> Option C

4. Quick Check:

   THD needs squares of harmonics, not simple sums [OK]

Hint: Always square harmonics before summing for THD [OK]

Common Mistakes:

• Summing harmonics directly without squares
• Ignoring square root step
• Mixing voltage units

5. If a power system has a fundamental voltage of 120V and harmonic voltages of 12V, 9V, and 5V, what is the approximate THD percentage? (Use THD = √(V2² + V3² + V4²) / V1 x 100%)

hard

A. 13.5%

B. 10.5%

C. 15.0%

D. 20.0%

Solution

1. Step 1: Calculate root sum squares of harmonic voltages

   √(12² + 9² + 5²) = √(144 + 81 + 25) = √250 ≈ 15.81 volts.

2. Step 2: Calculate THD percentage

   THD = (15.81 / 120) x 100% ≈ 13.18%.

3. Step 3: Choose closest option

   13.5% is the closest approximate value among the options.

4. Final Answer:

   13.5% -> Option A

5. Quick Check:

   THD ≈ 13.2% closest to 13.5% [OK]

Hint: Calculate root sum squares, divide by fundamental, multiply by 100% [OK]

Common Mistakes:

• Forgetting to multiply by 100 for percentage
• Adding harmonics instead of root sum squares
• Rounding errors without checking options