⚡ Power Supplied by a Complex Wave

Interactive demonstration of average power supplied by individual harmonics

1. Waveform Controls

Fundamental Voltage V₁ (RMS) 230 V

Fundamental Current I₁ (RMS) 5 A

3rd Harmonic V₃ (%) 15%

3rd Harmonic I₃ (%) 20%

5th Harmonic V₅ (%) 10%

5th Harmonic I₅ (%) 15%

7th Harmonic V₇ (%) 5%

7th Harmonic I₇ (%) 10%

2. Complex Voltage and Current Waveforms

v(t) = v₁(t) + v₃(t) + v₅(t) + v₇(t)
i(t) = i₁(t) + i₃(t) + i₅(t) + i₇(t)

3. Instantaneous Power

p(t) = v(t) × i(t)

The instantaneous power waveform contains a constant/average component as well as oscillating components. The average value of this waveform over one complete fundamental cycle is the real power supplied to the load.

4. Average Power of Each Harmonic

Fundamental

0 W

3rd Harmonic

0 W

5th Harmonic

0 W

7th Harmonic

0 W

Total Average Power

0 W

P_total = P₁ + P₃ + P₅ + P₇

5. Harmonic Power Contribution

6. Calculation Table

Harmonic	Voltage RMS	Current RMS	Power Factor
1st	0 V	0 A	0.90
3rd	0 V	0 A	0.85
5th	0 V	0 A	0.80
7th	0 V	0 A	0.75
Total

Important: For ideal orthogonal harmonics, the average cross-products between different harmonic orders over an integer number of fundamental cycles are zero. Therefore, under this model, the total average real power is the sum of the average powers associated with corresponding voltage/current harmonics.

How the Simulation Works

A complex periodic waveform can be represented as the sum of a fundamental component and harmonic components. In this simulation the voltage and current are represented by the 1st, 3rd, 5th and 7th harmonics. For each harmonic, the average real power is calculated using:

P_h = V_h,RMS × I_h,RMS × cos(φ_h)

The simulation then adds the individual harmonic power contributions:

P_average = P₁ + P₃ + P₅ + P₇

Notice that increasing a harmonic’s voltage or current amplitude increases its corresponding power contribution. The instantaneous power waveform may look highly distorted even though the average power can still be represented by the sum of the harmonic contributions.