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

Concept Flow - Total Harmonic Distortion (THD)

Start with signal

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Measure fundamental frequency amplitude

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Measure harmonic frequencies amplitudes

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Calculate RMS of harmonics

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

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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.