Modeling and Simulation of Three-phase acdc Converter-Fed dc Drive Systems with Uniform Pulse-Width Modulation Control

A three-phase ac-dc GTO (gate turn off) thyristor converter-fed dc motor is studied employing uniform pulse-width modulation (UPWM) scheme, and verified by computer simulation. It is found to offer good performance. It offers only two-quadrant operation because of the unidirectional current conduction nature of GTO’s. A four-quadrant converter that employs a single six-GTO bridge converter and four thyristors serving as a reversing switch is described. The four-quadrant dc drive employing the proposed converter and the control structure including speed and current control loop is also presented. Simulation results with a separately excited dc motor are given for steady-state and transient responses of the drive.


Introduction
Three-Phase ac-to-dc converters are severally applied to speed control of dc motors.They are ideal electronic actuators for DC drives because of their virtually unlimited output power and excellent controllability (Leonhard, 1997;Kazmierkowski and Tunia, 1994).The thyristor converters employing phase control have disadvantages of having harmonics in the source current and poor power factor, particularly at low-output voltages.When they are used for dc motor control, the armature current ripple increases losses, derates the motor, and causes discontinuous conduction, which increases speed regulation and slows down the transient response at light loads (Mohan and al;2003).Forced-commutated converters with pulse width modulation (PWM) control have been developed and offer considerable performance improvement over phase-controlled converters.It makes the fundamental power factor unity the ripple of the load current and the zone of discontinuous conduction operation are reduced when compared to conventional converters (Sato and al;1998;Wernekinck, 1991).
The increasing availability and power capability of controlled-on and controlled-off power switching devices, such as gate turn-off thyristors (GTO's), insulated gate bipolar transistors (IGBT's), and MOS-controlled thyristors (MCT's), are expected to reinforce self-commutated ac-dc converters with PWM control strategy to replace the conventional phase-controlled converters within the available power ratings (Zhou and Rouaud, 1999).
The flexibility to operate with variable chopping frequency is an additional merit of self-commutated PWM converters (Hamad, 1997;Trzynadlowski, 1998).
A three-phase PWM GTO converter-fed dc motor drive offers only two-quadrant operation because of the unidirectional current conduction nature of GTO's.A dual-converter is realized by employing two converters connected in antiparallel across the load, Allows operation in all four quadrants (Leonhard, 1997).
The present paper describes a four-quadrant converter that employs a single six-GTO bridge converter and four thyristors serving as a reversing switch.This allows substantial reduction in cost because GTO's are quite expensive compared to thyristors.The reduction in cost, however, is obtained at the expense of increase in losses and lower efficiency due to two extra devices in armature circuit at all times (Mohan and al;2003;Kenjo, 1990).
We analyse the performance characteristics of an ac-dc GTO thyristor converter, employing uniform pulse width modulated (UPWM).This control strategy is employed in the normal operation of the converter either as a rectifier or an inverter.A four-quadrant dc drive employing the proposed converter and closed-loop speed control with inner current control loop is also presented.Simulation results with a separately excited dc motor are given for steady-state and transient responses of the drive.The simulation results are shown to be in good agreement with the theory.

Operation principle
The power circuit configuration of a three phase ac-dc converter supplying an active load such as a dc motor is showed in Figure1.The source impedance is neglected.The power semiconductor switches, operating in chopping mode, are used to vary amplitude of the average output voltage.If thyristors were employed, they must be force commutated.On the other hand, if power transistors, MOSFET's, IGBT's, IGCT'or GTO's were employed; they are self-commutated without any need for forced commutation (Mohan and al;2003;Khan and al;1991).Although a GTO thyristor is employed, as seen in Figure1, UPWM control strategy is used in order to control the output voltage.The Principe of this control strategy is explained in Figure 2. The carrier wave V cr is compared with a variable time independent dc control voltage V m to generate the drive signal V g of the switching devices.The supply source is connected to the load during the interval when V m is greater than V cr .The frequency f p of the carrier signal depends on the number of desired output voltage pulses P in one cycle of the ac supply voltage.The switching-on and switching-off times of the switching devices for the K th pulse are given by the following expressions: (2. 1 ) 2 The output period of the carrier wave is given by: 2 1 Where: The mean output voltage of the converter is determined by the modulation index m, which for the UPWM control strategy, is varied by the control scheme in the range (0 m 1), with the index m given by: Where V mm = peak of modulated signal, V; V crm = peak of carrier signal, V.
The expressions for the corresponding modulating signal, switching-on angles α's and switching-off angles β's for the K th pulse in a supply cycle are given by: (2 1 )

Output voltage
According to Figure 2, the expression for the average output voltage V av for a number P of pulses is given by (Khan and al;1991): Where V av =mean dc voltage,V; V s =RMS amplitude of the line voltage,V; θ r =phase angle corresponding to ith pulse, rad; ω =supply frequency, rad/s.

Output current
The expression for the armature current during the i th voltage pulse is given by: Where E a = motor back emf, V; i a = instantaneous armature current, A; L a = armature circuit inductance, H; R a = armature circuit resistance, Ω; Z = armature impedance at supply frequency=[R 2 +(Lω) 2 ] 1/2 , Ω; φ = load phase angle, rad; I αi = armature current at α i, A; I βi =armature current at β i, A; I p = peak current =√2V s /Z , A; I E = current component =E a /R a , A.

Four-quadrant converter
The converter power circuit with a dc motor load is shown in Figure 3.The GTO converter employs a six-GTO bridge converter.This two-quadrant GTO converter is operated with uniform PWM to produce 12 output voltage pulses during a cycle of the ac source voltage.The principle of armature reversal is shown in Figure 3 with the help of static reversing switch that consists of four reversing thyristors.
Thyristor pair (T 1 ,T' 1 ) continuously conduct for positive direction of motor current while the others are blocked.When zero current is reached, the opposite pair of thyristors (T 2 ,T' 2 ) can be fired in order to reverse the polarity of the armature current.

Control structure of the drive
The schematic block diagram of speed control scheme is given in Figure 4.The schematic diagram of the closed loop speed control scheme is shown in Figure 5.It employs an inner-current control loop within the speed loop.The speed controller output, which forms the current reference for the current controller, is clamped to provide a current-limiting feature.

Dc motor
The equivalent circuit of the separately excited dc motor coupled to a separately excited dc generator for the purpose of loading can be represented in a schematic form as shown in Figure 6.Assuming constant field excitation, the equations are expressed as: . .
Taking Laplace transform of ( 11) -( 14) and rearranging the terms of the equations, we obtain where S is the Laplace operator.
The dynamic system, described by equations ( 15), ( 16), ( 17), is represented by a block diagram in Figure 7.As a constant field dc generator connected to a fixed resistance forms the load on the motor shaft, the load torque varies linearly with the speed.The equation is: .

Converter
The secondary voltage of the power transformer is chosen in such a way that for the control voltage V c =0.9 V cmax , the converter voltage is equal to the rated voltage of the dc motor.
The control voltage varies from -5 to + 5V.Gain K t of the converter (including the firing circuit) is given as the ratio of the maximum value of desired output voltage to the change in control voltage V c required to vary the output voltage from 0 to V cmax .The time delay of the converter is approximated by first-order time constant T t which is equal to half the interval between two consecutive voltage pulses (Leonhard, 1997,Khan and al;1991).Thus, The transfer function of the converter can be written as:

Current transducer
A signal proportional to the armature current is obtained by using a small resistance in series with the armature circuit.
The feedback signal derived from the current transducer is applied to an RC filter with a time constant T 2 in order to reduce the ripple in the current signal.Thus, the transfer function of the current transducer with the filter is written as:

Speed transducer
A tacho-generator is used to get the speed signal.Since a 5V dc signal corresponds to the rated speed (1500 r/min).An RC filter with a time constant T 1 is used to smooth out the spikes in the speed signal.The transfer function of the speed transducer with the filter is given as:

Simulated Results and Discussions
The parameters of the used machine model are given in Table 1.The source voltage; the motor armature voltage and current waveforms for motoring and regenerating (for rectification and inversion) operation, are shown in Figure 8 and Figure 9 respectively.The waveforms of the developed torque and the motor speed for a different number of pulses P (P=6 and P=12) are shown in Figure 10, where the load is applied at t=1s.The ripples in the developed torque were observed.
There is an improvement in performance with an increase in the pulse number.Four-quadrant drive ability is demonstrated in Figure 11 and Figure 12.The former shows the speed response for a speed reversal command from +1500 to -1500 rpm.As the speed reversal is initiated, the armature current quickly reverses through the static reversing switch.The motor decelerates to standstill as the converter operates as an inverter feeding power back the ac supply.The motor is then accelerating fast in the reverse direction and the speed settles down to the desired value.
Figure 12 shows the speed response for control voltage varying from -5 to +5v, with a load torque m L =constant.The armature current reverses though the reversing switch the motor is decelerated quickly.When desired speed is reached, the current is again set back in previous direction (corresponding to the operation in a four quadrant drive).

Conclusion
The study of pulse width modulation scheme for an ac-dc PWM converter shows that the uniform pulse width modulation scheme offers good performance.Simulation results show that the control strategy can be applied to both rectifying and regenerating modes of operation.A four-quadrant dc drive employing the proposed converter and closed-loop speed control with inner current control loop has been described and verified by computer simulation.The simulation results are shown to be in good agreement with the theoretical calculations.

Figure 3 .
Figure 3. Four-quadrant operation of a DC drive

Table 1 .
Separately excited DC machine data