To find the angle by which the third harmonic current will lead or lag the third harmonic output voltage in a single-phase full-bridge inverter with an RLC load, we need to determine the impedance of the RLC circuit at the third harmonic frequency.

1. Determine the Third Harmonic Frequency:

The fundamental frequency is 50 Hz, so the third harmonic frequency, ( f_h ), is:

[

f_h = 3 times 50 , text{Hz} = 150 , text{Hz}

]

2. Calculate the Reactance:

– Inductive reactance ( X_L ):

[

X_L = 2 pi f_h L = 2 pi times 150 times 35 times 10^{-3} approx 31.42 , Omega

]

– Capacitive reactance ( X_C ):

[

X_C = frac{1}{2 pi f_h C} = frac{1}{2 pi times 150 times 155 times 10^{-6}} approx 10.25 , Omega

]

3. Calculate the Total Impedance ( Z ):

The total impedance ( Z ) of the RLC circuit is given by:

[

Z = R + j(X_L – X_C) = 4

To find the expression for the load voltage of a single-phase full bridge inverter with an RLC load, we can utilize Fourier series expansion to account for the fundamental frequency and the higher harmonics up to the fifth harmonic.

1. DC Input Voltage (V_dc): 230 V
2. Output Frequency (f): 50 Hz
3. Angular Frequency (ω): ( omega = 2pi f = 2pi times 50 = 100pi ) rad/s
4. Harmonics: The harmonics for a full bridge inverter can be expressed as ( n times f ) where ( n ) is an integer.

The fundamental (first) harmonic and its higher harmonics up to the fifth can be expressed as:

– Voltage waveforms:

– Fundamental (1st harmonic): ( V_1(t) = frac{2V_{dc}}{pi} sin(100pi t) )

– 3rd harmonic: ( V_3(t) = frac{2V_{dc}}{3pi} sin(300pi t) )

– 5th harmonic: ( V_5(t) = frac{2V_{dc}}{5pi} sin(500pi t) )

Overall Load Voltage Expression:

The overall load voltage ( V_{load}(t)