Total Harmonic Distortion (THD) in Power Electronics - Mini Project: Build & Apply

Understanding Total Harmonic Distortion (THD)

📖 Scenario: You are working with an electrical power system that supplies alternating current (AC) to a home. The quality of this power is important because distortions can damage appliances or reduce efficiency.Total Harmonic Distortion (THD) is a measure used to understand how much the electrical signal deviates from a perfect sine wave due to harmonics.

🎯 Goal: Build a simple step-by-step understanding of how to calculate Total Harmonic Distortion (THD) using given harmonic amplitudes.You will create a data set of harmonic amplitudes, set a reference for the fundamental frequency, calculate the THD, and finalize the result for interpretation.

📋 What You'll Learn

Create a dictionary with harmonic amplitudes including the fundamental and harmonics

Define a variable for the fundamental frequency amplitude

Calculate the THD using the harmonic amplitudes and fundamental amplitude

Complete the calculation by expressing THD as a percentage

💡 Why This Matters

🌍 Real World

THD is used by electrical engineers to assess power quality and ensure electrical devices operate safely and efficiently.

💼 Career

Understanding THD is important for roles in power systems engineering, electrical maintenance, and quality control in manufacturing of electrical equipment.

1

Create harmonic amplitudes data

Create a dictionary called harmonics with these exact entries: 1: 100 (fundamental), 3: 5, 5: 3, 7: 2 representing the amplitudes of the fundamental and harmonic frequencies.

Power Electronics

# Create the harmonics dictionary with given amplitudes
# Your code here

Hint

Use a dictionary with keys as harmonic numbers and values as their amplitudes.

2

Set the fundamental amplitude variable

Create a variable called fundamental_amplitude and set it to the amplitude of the fundamental frequency from the harmonics dictionary using the key 1.

Power Electronics

harmonics = {1: 100, 3: 5, 5: 3, 7: 2}
# Set fundamental_amplitude to harmonics[1]
# Your code here

Hint

Access the dictionary value for key 1 and assign it to fundamental_amplitude.

3

Calculate the Total Harmonic Distortion (THD)

Calculate the THD by first summing the squares of all harmonic amplitudes except the fundamental. Use a variable called sum_squares for this sum. Then calculate thd_ratio as the square root of sum_squares divided by fundamental_amplitude. Use a for loop with variables harmonic and amplitude to iterate over harmonics.items().

Power Electronics

harmonics = {1: 100, 3: 5, 5: 3, 7: 2}
fundamental_amplitude = harmonics[1]
# Calculate sum_squares and thd_ratio
# Your code here

Hint

Remember to exclude the fundamental (key 1) when summing squares.

4

Express THD as a percentage

Create a variable called thd_percent and set it to thd_ratio multiplied by 100 to express the Total Harmonic Distortion as a percentage.

Power Electronics

harmonics = {1: 100, 3: 5, 5: 3, 7: 2}
fundamental_amplitude = harmonics[1]
sum_squares = 0
for harmonic, amplitude in harmonics.items():
    if harmonic != 1:
        sum_squares += amplitude ** 2
thd_ratio = (sum_squares ** 0.5) / fundamental_amplitude
# Calculate thd_percent
# Your code here

Hint

Multiply the ratio by 100 to convert it to a percentage.

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