Total Harmonic Distortion (THD) in Power Electronics - Step-by-Step Execution

Concept Flow - Total Harmonic Distortion (THD)

Start with signal

↓

Measure fundamental frequency amplitude

↓

Measure harmonic frequencies amplitudes

↓

Calculate RMS of harmonics

↓

Calculate THD = (RMS harmonics / fundamental) * 100%

↓

Interpret THD value

The flow shows measuring the main signal and its harmonics, then calculating THD as a percentage of distortion.

Execution Sample

Power Electronics

Fundamental = 100
Harmonics = [10, 5, 3]
THD = sqrt(10**2 + 5**2 + 3**2) / Fundamental * 100  # Result in percentage

Calculates THD by finding the root mean square of harmonic voltages divided by the fundamental voltage.

Analysis Table

Step	Action	Calculation	Result
1	Identify fundamental amplitude	Fundamental = 100V	100V
2	List harmonic amplitudes	Harmonics = 10V, 5V, 3V	[10, 5, 3] V
3	Square each harmonic	10^2=100, 5^2=25, 3^2=9	[100, 25, 9]
4	Sum squares	100 + 25 + 9	134
5	Calculate RMS of harmonics	sqrt(134)	11.57V
6	Calculate THD	(11.57 / 100) * 100%	11.57%

💡 THD calculation complete as 11.57%, representing distortion level.

State Tracker

Variable	Start	After Step 3	After Step 5	Final
Fundamental	0	100	100	100
Harmonics	[]	[10,5,3]	[10,5,3]	[10,5,3]
Harmonics Squared	[]	[100,25,9]	[100,25,9]	[100,25,9]
Sum Squares	0	0	134	134
RMS Harmonics	0	0	11.57	11.57
THD (%)	0	0	0	11.57

Key Insights - 3 Insights

Why do we square the harmonic amplitudes before summing?

Squaring ensures all values are positive and reflects power contribution of each harmonic, as shown in step 3 of the execution_table.

Why do we divide by the fundamental amplitude in the THD formula?

Dividing by the fundamental amplitude normalizes the distortion relative to the main signal size, as seen in step 6.

What does a higher THD percentage mean?

A higher THD means more distortion in the signal, indicating more unwanted harmonics compared to the fundamental.

Visual Quiz - 3 Questions

Look at the execution_table at step 5, what is the RMS of harmonics calculated?

A 100V

B 134V

C 11.57V

D 10V

💡 Hint

Check the 'Result' column at step 5 in the execution_table.

At which step does the calculation sum the squares of harmonic amplitudes?

A Step 4

B Step 2

C Step 3

D Step 6

💡 Hint

Look for the step where individual squares are added together in the execution_table.

If the fundamental amplitude was 200V instead of 100V, how would the final THD percentage change?

A It would double

B It would halve

C It would stay the same

D It would become zero

💡 Hint

Refer to the THD formula in the execution_sample and how fundamental amplitude affects the division.

Concept Snapshot

Total Harmonic Distortion (THD) measures signal distortion.
Calculate by: 1) Square each harmonic amplitude.
2) Sum these squares.
3) Take square root (RMS) of sum.
4) Divide by fundamental amplitude.
5) Multiply by 100% for percentage.

Full Transcript

Total Harmonic Distortion (THD) quantifies how much a signal is distorted by harmonics. We start by measuring the fundamental frequency amplitude and the amplitudes of harmonic frequencies. Each harmonic amplitude is squared to reflect its power contribution, then all are summed. The square root of this sum gives the RMS value of harmonics. Dividing this RMS by the fundamental amplitude and multiplying by 100% yields the THD percentage. A higher THD means more distortion. For example, with a fundamental of 100 volts and harmonics of 10, 5, and 3 volts, the THD is about 11.57%. This process helps engineers understand and control signal quality in power electronics.

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