Q5. slide 1 main ideas
- difference with diode rectifiers
- output voltage in thyristor converter
- firing angle
- circuit example
- thyristor operation
difference between diode rectifiers and thyristor converters
Average output voltage of thyristor converter can be controlled by delaying the instant at which gate pulse is applied
Firing angle definition
- instant at which gate pulse is applied from the instant wt=0
Q5. slide 1 explain circuit operation
- firing angle can range between wt=0 up to wt=pi, when thyristor is forward biased
- after the gate pulse is applied thyristor starts conducting and output voltage is equal to input voltage, behaves like a diode
Q5. slide 2 main ideas
- Introduce figure
- Two modes of operation
- Condition for CCM and DCM
- Infinite inductance assumption
- describe waveforms: input source I, phase lag of I, output voltage
- average output voltage calculation
Q5. slide 2 describe circuit and modes of operation
- single-phase full wave PCR with RL load
- this circuit has two modes of operation: CCM and DCM
- mode of operation depends on time constant L/R
- If time constant is large output I never goes to zero and converter operates in CCM
- If L is assumed infinite, the rectified load I can be replaced by constant I source
Q5. slide 2 describe voltage and I waveforms
- For a given firing angle
- magnitude of input I is constant and + when T1 and T2 are conducting and negative when T3 and T4 conduct.
- Input I lags input voltage by phase angle equal to firing angle.
- Output voltage is negative of input voltage in the interval wt=0 to alpha, since T3 and T4 are conducting
- Output voltage is equal to input voltage after firing angle.
Q5. slide 2 how to calculate average output voltage
- integrate sinusoidal wave from alpha to pi+alpha, and divide by period pi.
- average output voltage is a function of alpha and can take negative values
Q5. slide 3 main ideas
- firing angle will reduce average output voltage compared to diode rectifier
- if firing angle is below 90° output voltage will be positive
- if firing angle is higher than 90° output voltage will be negative
- THD calculation
Q5. slide 3 how to calculate THD for PCR with infinite inductive load
- we have to find total rms of input I and rms of fundamental component
- rms of input I is equal to output I
- by Fourier analysis we can obtain rms value of fundamental component of I current as 0.9 times output I
- we obtain a THD of 48.43%
Q5. slide 4 main ideas
- calculate P as Vs*Is1 times cosine of firing angle, considering that power consumed by the load is caused by fundamental component of I
- Calculate reactive power due to fundamental component of I
- Calculate aparent power using fundamental component of I
- calculate PF as P/S1
- calculated total aparent power and distorted PF
- we can see PF will be maximum when firing angle is 0 or 180°, and zero when firing angle is 90°
Why only fundamental component of I is used for power calculation
- Because product of sinusoidal waveforms of different frequencies has zero average value, therefore P delivered to load is due to only fundamental component of I
Q5. slide 5 main ideas
- Main effect of Ls
- Operation during interval 0 to alpha
- Operation during alpha to alpha + u
main effect of Ls in PCR
current commutation between two pair of thyristors takes a finite commutation time u
Q5. slide 5 explain commutation process in the interval 0, alpha
- between wt=0 to alpha, T3 ad T4 are conducting
- voltage across Ls is zero
- output voltage is equal to negative of input voltage.
- Input I is the negative of output I
Q5. slide 5 explain commutation process in the interval alpha, alpha+u
- At wt=alpha, gate signal is applied to T1 and T1, and they start conducting.
- Input I doesn’t change from -Io to Io instantaneously due to Ls.
- During this interval all thyristors are conducting and output voltage is zero
- I through T3 and T4 decreases from Io to 0.
- I through T1 and T2 increases from 0 to Io.
Explain operation in the interval wt>alpha+u
- when commutation interval finishes T3 and T4 turns off and T1 and T2 remain on
- output voltage equals input voltage and input I equals output I until the next cycle at t=pi+alpha
How to calculate commutation interval in PCR circuit
- we use equation of voltage across source L
- it is equal to input voltage during commutation interval
- we integrate left side of this equation from alpha to alpha+u, and right side from -Io to Io
- obtain the expression and solve for commutation time
How to calculate average output voltage in PCR with source inductance
- Use the average output voltage for the case when Ls was zero
- then substract the area Au that is lost due to commutation time
- divide by the period pi
