Power Electronics Dr - Philadelphia University...Power Electronics Dr.Mohammed Tawfeeq Tutorial Sheet No. 7 Single-phase AC-AC Converter with Resistive Load 1.An a.c./a.c. converter,

Power Electronics Dr. Al-Zuhairi Mohammed Tawfeeq

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Power Electronics Dr.Mohammed Tawfeeq

7 Tutorial Sheet No.

AC Converter with Resistive Load-AC phase-Single

1.An a.c./a.c. converter, using back—to—back (inverse—parallel) thyristors, is used

to control the power supplied to a 20 ohm resistive load from a single-phase, 230 V,

50 Hz supply. When the triggering angle is 60 degrees the measured r.m.s load

current and. voltage are 10.3.A and 200 V respectively. Determine the ideal

theoretical values for the r.m.s current and voltage and suggest reasons for any

difference

( Ans: 10.34 A, 207 V)

2. Derive an expression for the r.m.s. load voltage in a single-phase resistive circuit

where load voltage is varied by firing-angle adjustment of a pair of SCRs connected

in inverse-parallel. If v = 100 sinωt and R = 50 ohms, what is the r.m.s. load voltage

at α = 30°, 60°, 120° ?

( Ans: 70V,63.64V,31.82V)

3.An ideal voltage supply v = Vm sin ωt provides a power to a single-phase load R by

symmetrical phase-angle triggering of a pair of inverse-parallel connected SCRs in

the supply lines. Sketch the load voltage waveform for firing-angle α = 90° and also

sketch the corresponding fundamental component of the load current. Derive, from

first principles, an expression for the r.m.s. load current IL at any arbitrary angle α, in

terms of Vm, R and α. Use IL, or otherwise, to calculate the per-unit average power

dissipated in the load at α = 80°.

(Ans:0.6 p.u.)

4. A single – phase resistive heating load is to be controlled from a single – phase ,

50 Hz ,AC supply by means of an inverse – parallel pair of thyristors .What will be

the firing angle of the thyristors when a load of 60% of its maximum value?

( α = 81° )

5. The circuit arrangement shown in Fig. 1 is used to vary the current in resistor RB.

The two thyristors are triggered at identical points of their respective anode voltage

waves so as to produce a periodic load voltage with identical positive and negative

alternations.


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(a) Sketch the waveform of current in resistor RB if the thyristor

firing angle α is 90°. Assume that v = Vm sin ωt.

b) Show that the Fourier coefficients for the fundamental component )

of current are given by:

Calculate the value of the fundamental current IB1 in resistor RB when RA = RB = l0Ω,

Vm = 100V and α = π/2.

Also calculate the phase-angle of the fundamental current IB1 with respect to the

supply voltage. Does this value of phase-angle suggest a power factor other than

unity? If so, what happens to the fundamental reactive power?

6. An ideal single-phase supply e = Em sin ωt provides power to a resistive load

R = 100 using the circuit of Fig. 2. The SCRs of the inverse-parallel pair are gated to

provide symmetrical phase-angle triggering.

(a) Sketch compatible waveforms, for two cycles, of the supply voltage, supply

current and load current.

(b) Derive an expression for the load power dissipation in terms of Em, R and α.

Calculate the power at α = 60° if Em = 340 V.

Fig.2


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(c) If diode D1, in Fig. 2 fails to an open circuit, sketch the waveform of the resulting

load current. What effect does the failure of D1 have on the load power dissipation?

(Ans: (b) 465W, (c) Power is halved)

7. The power flow to a resistive load R from an ideal sinusoidal single-phase supply

e(ωt) = Em sin ωt is controlled by a pair of SCRs connected in inverse-parallel. These

are gated to produce symmetrical angle triggering of the current waveform.

(a) Derive an expression for the load power dissipation P in terms of Em, R and α . If

the r.m.s. supply voltage is 240 V and R =25Ω, what is the power dissipation at

α = 90 degrees?

(b) The fundamental component of the current at α = 90° can be described by the

expression

Calculate the displacement factor, distortion factor and hence power factor of the

circuit at = 90°.

(Ans: (a) 1152W,(b) displacement

factor = 0.843,distortion factor = 0.834, PF=0.707.)

8.A pair of thyristors connected in inverse-paralle, Figure2 , is used to supply

adjustable current to a resistive load. If the supply voltage is e = Em sin ωt and the thyristors are each triggered at an angle α after their respective anode voltage zeros, sketch the load current waveform for α = 60° and a) Obtain an expression for the r.m.s. value IL of the load current in terms of Em, R

and α b) calculate the value of IL for α = 60° compared with the value for sinusoidal

operation.

c) If one of the thyristors is replaced by a diode, what effect would this have on the

order of the harmonic components of the load current at α = 60°.

Fig. 2


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9-A pair of thyristors connected in inverse-parallel, Figure2 , is used to supply

adjustable current to a resistive load of R = 10 Ω. If the supply voltage is v = √2 x220

sin ωt and the thyristors are each triggered at an angle α after their respective anode

voltage zeros, sketch the load current waveform for α = 30° and

(a) Prove that the r.m.s. value Vo of the load current is given by

(b) Calculate the value of Vo for α = 30 ° and sketch its waveform.

(c) Calculate the r.m.s. value Io of the load current and the power delivered to the

load.

10-A single-phase a.c. voltage controller has a 120 V r.m.s. 50 Hz source. The load

resistance is 15 Ω.. (a). Prove that the r.m.s. load voltage is given by

. b). Determine the delay angle required to deliver 500 W )

(c). Calculate the r.m.s. source current and the r.m.s. and average current in the

SCRs.

Note that

and the relation between the normalized r.m.s. load voltage and the delay angle

a for a single-phase a.c. voltage controller with a resistive load is given in Fig.3.


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Power Electronics Dr - Philadelphia University...Power Electronics Dr.Mohammed Tawfeeq Tutorial Sheet No. 7 Single-phase AC-AC Converter with Resistive Load 1.An a.c./a.c. converter,