Total Harmonic Distortion (THD) in Power Electronics - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the formula to calculate Total Harmonic Distortion (THD) given the RMS values of harmonics.

Power Electronics

THD = \frac{\sqrt{V_2^2 + V_3^2 + \cdots + V_n^2}}{V_[1]

Drag options to blanks, or click blank then click option'

AV_h

BV_0

CV_n

DV_1

Attempts:

3 left

💡 Hint

Common Mistakes

Using the total voltage instead of the fundamental voltage in the denominator.

Confusing the harmonic voltages with the fundamental voltage.

The THD formula divides the root sum square of all harmonic voltages by the fundamental voltage V₁.

2fill in blank

medium

Complete the sentence: THD is expressed as a percentage of the ratio of the harmonic content to the {{BLANK_1}}.

Power Electronics

THD (%) = \left( \frac{V_{harmonics}}{V_[1] \right) \times 100

Drag options to blanks, or click blank then click option'

Aaverage voltage

Btotal voltage

Cfundamental voltage

Dpeak voltage

Attempts:

3 left

💡 Hint

Common Mistakes

Using total voltage instead of fundamental voltage.

Confusing peak voltage with fundamental voltage.

THD is the ratio of the harmonic voltages to the fundamental voltage, expressed as a percentage.

3fill in blank

hard

Fix the error in the THD calculation formula by filling the blank correctly.

Power Electronics

THD = \frac{\sqrt{V_1^2 + V_2^2 + V_3^2}}{V_[1]

Drag options to blanks, or click blank then click option'

AV_1

BV_0

CV_2

DV_3

Attempts:

3 left

💡 Hint

Common Mistakes

Including the fundamental voltage in the numerator.

Using the wrong voltage in the denominator.

The formula incorrectly includes the fundamental voltage V₁ inside the root sum square. THD should only include harmonics in the numerator and divide by V₁.

4fill in blank

hard

Fill both blanks to complete the THD formula using RMS voltages of harmonics and fundamental.

Power Electronics

THD = \frac{\sqrt{V_[1]^2 + V_[2]^2}}{V_1}

Drag options to blanks, or click blank then click option'

A2

B3

C4

D1

Attempts:

3 left

💡 Hint

Common Mistakes

Using the fundamental voltage as a harmonic.

Repeating the same harmonic number incorrectly.

The THD numerator includes the squares of the 2nd and 3rd harmonic voltages, V₂ and V₃.

5fill in blank

hard

Fill all three blanks to complete the THD formula with harmonics 2, 3, and 4.

Power Electronics

THD = \frac{\sqrt{V_[1]^2 + V_[2]^2 + V_[3]^2}}{V_1}

Drag options to blanks, or click blank then click option'

A2

B3

C4

D1

Attempts:

3 left

💡 Hint

Common Mistakes

Including the fundamental voltage as a harmonic.

Skipping harmonic orders or repeating the same number.

The THD numerator includes the squares of the 2nd, 3rd, and 4th harmonic voltages.

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