Test: Effect of Source Impedence on the Performance of Converters

Effect of source inductance on 1ϕ full controlled rectifier:
For 1ϕ full wave converter, the average reduction in dc output voltage due to source inductance is:

where, Δ V_o =  Average reduction in dc output voltage
V_m = Maximum value of source voltage
α = Firing angle
μ = Overlap angle
L_S = Source inductance

• If f ↑ , L_s ↑, I_o ↑, without changing the Vm and α, then μ also increases.
• If V_m ↑ , without changing f, L_s, I_o, and α, then μ decreases.

Hence, option 4 is correct.

Concept-
If a gate signal is applied to the SCR at ωt = α, where α is the delay (firing or triggering) angle. The average (dc) voltage across the load resistor is

The rms voltage Across the Resistor is

FORM factor for Rectifier is given by


Given:
α = π/3

Concept:
The average output voltage of a three-phase bridge rectifier is given by

Maximum possible output voltage 

Calculation:
Given that, line voltage (V_L) = 420 V
Maximum line voltage = 420 × √2 V
Maximum possible output voltage
Maximum possible output voltage 

Concept:
In a single-phase full wave rectifier with source inductance is given by,

Average output current 


Where, V_m is the maximum value of supply voltage
α is the firing angle
μ is the overlapping angle
L_s is the source inductance
R is the load resistance

Calculation:
Given that, supply voltage (V_rms) = 230 V
Firing angle (α) = 45°
Source inductance (L_s) = 2.28 mH
Load resistance (R) = 10 Ω
Frequency (f) = 50 Hz
The average output voltage is

⇒ I₀ = 14.003 A

⇒ μ = 4.8°

Concept:
The small inductance connected with supply work as a source inductance Due to this inductance, there will be overlapping takes place between two diodes. As a result, this will cause an overlap angle 'μ'.
During overlap period, both diode D₁ & D₂ will conduct.

Calculation:
The output voltage (V₀) & current waveform is shown below,

Output voltage in terms of load current is given by,

For diode α = 0°,

⇒ V₀ = 170.06 V
In terms of overlap angle,

Since, for an overlap angle of μ, all four diodes conduct & each diodes conducts for (180 + μ) degree.
So,
conduction angle (γ) = 180 + μ = 180 + 44.17
γ = 224.17°

Concept:
Effect of source inductance: The presence of source inductance affects the rectifier output voltage
V₀ = Vd₀ cos α – ΔVd₀  

μ is the overlap angle


Also, ΔV_d0 = f Ls I₀ (1 pulse)
= 4 f Ls I₀ (2 pulse)
= 3 f L_s I₀ (3 pulse)
= 6 f L_s I₀ (6 pulse)

Calculation:
V₀ = -E₀ + I₀ R
V_d0 cos α – 3 f L_s I₀ = -200 + (20)(2)


On solving we get cos α = - 0.57
⇒ α = 124.76°
For three pulse converters:

On solving the above equation for overlap angle (μ) we get
cos (α + μ) = -0.6145
μ = 3.15° 

Concept:
Ripple Frequency: Ripple frequency is the output frequency of a converter which is some integral multiple of the supply frequency.
f_ripple= n × f_s
f_ripple= Ripple frequency
f_s = Supply frequency
n = No. of pulses in the time period

Calculation:
The 3ϕ full converter has 6 no. of pulses in the time period of the output waveform.
f_s = 50 Hz
f_ripple = 6 × 50
f_ripple = 300 Hz

Concept:
Source inductance effect of single-phase full-wave rectifier:
By considering the source inductance effect the average output voltage of a single-phase full-wave converter is given by


Where,
α = firing angle, ω = 2πf = angular frequency of supply
μ = overlap angle, I₀ = load current
Inductive voltage regulation of single-phase full-wave rectifier is given by

Application:
From equation (1), we can observe that
As frequency (ω) of supply increases the cos (α + μ) term decreases. Hence the value of the overlap angle inceases.
Now from equation (2),
As value of overalp angle increases cosμ decreses. Hence the inductive volatge regulation increses.

The average output voltage of a 1-ϕ full converter with RLE loads for continuous conduction.

V₀ = 146.42 V
V₀ = E + I₀R

I₀ = 12.50 A

The frequency of ripple in the output voltage of a three-phase controlled bridge rectifier depends on the supply frequency. The output frequency is
f₀ = n f_S
Where n is the number of pulses in the output of the converter and f_s is the supply frequency
Note: Ripple factor depends on the firing angle, load inductance, and resistance.