Performance Parameters of Rectifiers (Input AC side)

Consider the waveforms in Figure. v_s is the sinusoidal input voltage, i_s the instantaneous input current, i_s1 is the fundamental component of i_s

The displacement angle Φ is the angle between fundamental components of input current and voltage. The displacement factor (DF) or Displacement Power Factor (DPF) is defined as

$DF = \cos \phi$

The harmonic factor (HF) also known as total harmonic distortion (THD) is a measure of the distortion of a waveform. The harmonic factor of the input current is given as

$HF = {\left( {\frac{{I_S^2 - I_{S1}^2}}{{I_{S1}^2}}} \right)^{\frac{1}{2}}}$

Where both currents are recorded as rms values

The crest factor (CF) is a comparison of the peak input current to its rms value. It is given as

$CF = \frac{{{I_{S(peak)}}}}{{{I_S}}}$
For a pure sinusoidal input current and voltage, power factor is defined as the cosine of the load angle Φ

$PF = \frac{{{\rm{Real Power}}}}{{{\rm{Apparent Power}}}} = \frac{{{P_R}}}{{{P_{RMS}}}} = \frac{{{V_S}{I_S}\cos \phi }}{{{V_S}{I_S}}} = \cos \phi$
where the voltages and currents are stated in rms values and VA is

$VA = \sqrt {P_R^2 + P_Q^2}$
For a rectifier circuit, the input power factor is given by

$PF = \frac{{{\rm{RealPower}}}}{{{\rm{ApparentPower}}}} = \frac{{{V_{Fund}}{I_{Fund}}\cos {\phi _1}}}{{{V_{RMS}}{I_{RMS}}}}$ $= \frac{{{V_{Fund}}}}{{{V_{RMS}}}}\frac{{{I_{Fund}}}}{{{I_{RMS}}}}\cos {\phi _1}$
Power factor in rectifier circuits is related to harmonic voltages and currents given in the diagrams
Where,
${I_{Har}} = \sqrt {\sum\nolimits_{n = 2}^\infty {I_n^2} }$
${V_{Har}} = \sqrt {\sum\nolimits_{n = 2}^\infty {V_n^2} }$
${V_{RMS}} = \sqrt {V_{Fund}^2 + V_{Har}^2}$
${I_{RMS}} = \sqrt {I_{Fund}^2 + I_{Har}^2}$
$PF = \sqrt {1 - {{\left( {\frac{{{V_{Har}}}}{{{V_{RMS}}}}} \right)}^2}} \sqrt {1 - {{\left( {\frac{{{I_{Har}}}}{{{I_{RMS}}}}} \right)}^2}} \cos {\phi _1}$
$Hence,{\rm{ }}PF = \cos {\phi _2}\cos {\phi _3}\cos {\phi _1}$
An ideal rectifier should have η = 100%, V_ac = 0, RF = 0, TUF = 1, HF = THD = 0, and PF = PDF = 1.
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Power, Electronic Systems, Applications and Resources on Electrical and Electronic Project-Thesis

Performance Parameters of Rectifiers (Input AC side)

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