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Implement two-quadrant single-phase rectifier DC drive
The high-level schematic shown below is built from five main blocks. The DC motor, the single-phase full converter, and the bridge firing unit are provided with the SimPowerSystems™ library. More details are available in the reference pages for these blocks. The two other blocks are specific to the Electric Drives library. These blocks are the speed controller and the current controller. They allow speed or torque regulation. A "regulation switch" block allows you to toggle from one type of regulation to the other. During torque regulation the speed controller is disabled. It is possible to use a simplified version of the drive containing an average-value model of the single-phase converter and allowing faster simulation.
The speed regulator in the following figure uses a PI controller. The controller outputs the armature current reference (in pu) used by the current controller in order to obtain the electromagnetic torque needed to reach the desired speed. During torque regulation, the speed controller is disabled.
The controller takes the speed reference (in rpm) and the rotor speed of the DC machine as inputs. The speed reference change rate will follow user-defined acceleration and deceleration ramps in order to avoid sudden reference changes that could cause armature over-current and destabilize the system. The speed measurement is filtered by a first-order low-pass filter.
The current reference output is limited between 0 pu and an upper limit defined by the user.
The armature current regulator in the following figure is based on a second PI controller. The regulator controls the armature current by computing the appropriate thyristor firing angle. This generates the rectifier output voltage needed to obtain the desired armature current and thus the desired electromagnetic torque.
The controller takes the current reference (in pu) and the armature current flowing through the motor as inputs. The current reference is either provided by the speed controller during speed regulation or computed from the torque reference provided by the user during torque regulation. This is managed by the "regulation switch" block.
The armature current input is filtered by a first-order low-pass filter. An arccosine function is used to linearize the control system during continuous conduction. To compensate nonlinearities appearing during discontinuous conduction, a feedforward term is added to the firing angle. This improves the system's response time. The firing angle can vary between 0 and 180 degrees. You can limit the lower and upper limits to intermediate values.
The average-value converter is shown in the following figure.
It is composed of one controlled current source on the AC side and one controlled voltage source on the DC side. The AC current source allows the representation of the fundamental single-phase current behavior following the next equation:
$${I}_{a}=\sqrt{2}{I}_{d}\mathrm{sin}\left(2\pi ft+\alpha +{\alpha}_{0}\right),$$
with α being the firing angle value, α_{0} the phase angle of the AC side, f the AC frequency and I_{d} the rectified output current value. The DC voltage source represents the average voltage value of the rectified voltage waveform following the next equation:
$${V}_{d}=\frac{2\sqrt{2}}{\pi}{V}_{\text{rms}}\mathrm{cos}\alpha -4fL{I}_{d},$$
with V_{rms} being the input RMS voltage value and L being the source inductance value.
The bridge firing unit converts the firing angle, provided by the current controller, to four pulses applied to the thyristor gates. The bridge firing unit block contains a band-pass filter on voltage measurement to remove voltage harmonics. The discrete synchronized pulse generator block generates the pulses. Its architecture is based on the Discrete Synchronized 6-Pulse Generator block. Refer to the Synchronized 6-Pulse Generator for more information on this block. When using the average-value converter the bridge firing unit simply outputs the firing angle value needed by the converter.
The machine is separately excited with a constant DC field voltage source. There is thus no field voltage control. By default, the field current is set to its steady-state value when a simulation is started.
The armature voltage is provided by a single-phase rectifier controlled by two PI regulators. Armature current oscillations are reduced by a smoothing inductance connected in series with the armature circuit.
The average-value converter represents the average behavior of a single-phase rectifier for continuous armature current. This model is thus not suitable for simulating DC drives under discontinuous armature current conditions.The converter outputs a continuous voltage value equal to the average-value of the real-life rectified voltage. The armature voltage, armature current and electromagnetic torque ripples are thus not represented. The input currents have the frequency and amplitude of the fundamental current component of the real-life input currents.
The model is discrete. Good simulation results have been obtained with a 25 µs time step. The control system (speed and current controllers) samples data following a user-defined sample time in order to simulate a digital controller device. Keep in mind that this sampling time has to be a multiple of the simulation time step.
The average-value converter allows the use of bigger simulation time steps since it does not generate small time constants (due to the RC snubbers) inherent to the detailed converter. For a controller sampling time of 100 µs good simulation results have been obtained for a simulation time step of 100 µs. This time step can of course not be higher than the controller time step.
The DC Machine tab displays the parameters of the DC Machine block of the powerlib library.
Select how the output variables are organized. If you select Multiple output buses, the block has three separate output buses for motor, converter, and controller variables. If you select Single output bus, all variables output on a single bus.
Select between the detailed and the average-value inverter.
Select between the load torque, the motor speed and the mechanical rotational port as mechanical input. If you select and apply a load torque, the output is the motor speed according to the following differential equation that describes the mechanical system dynamics:
$${T}_{e}=J\frac{d}{dt}{\omega}_{r}+F{\omega}_{r}+{T}_{m}$$
This mechanical system is included in the motor model.
If you select the motor speed as mechanical input, then you get the electromagnetic torque as output, allowing you to represent externally the mechanical system dynamics. The internal mechanical system is not used with this mechanical input selection and the inertia and viscous friction parameters are not displayed.
For the mechanical rotational port, the connection port S counts for the mechanical input and output. It allows a direct connection to the Simscape™ environment. The mechanical system of the motor is also included in the drive and is based on the same differential equation.
The Rectifier section of the Converter tab displays the parameters of the Universal Bridge block of the powerlib library. Refer to the Universal Bridge for more information on the Universal Bridge block parameters.
The DC motor field voltage value (V).
RMS voltage of the single-phase voltage source connected to the A+,A- terminals of the drive (V). This parameter is not used when using the detailed rectifier.
Frequency of the single-phase voltage source connected to the A+,A- terminals of the drive (Hz). This parameter is not used when using the detailed rectifier.
Source inductance of the single-phase voltage source connected to the A+,A- terminals of the drive (H). This parameter is not used when using the detailed rectifier.
Phase angle of the single-phase voltage source connected to the A+,A- terminals of the drive (deg.). This parameter is not used when using the detailed rectifier.
When you press this button, a diagram illustrating the speed and current controllers schematics appears.
This pop-up menu allows you to choose between speed and torque regulation.
The controller (speed and current) sampling time (s). The sampling time has to be a multiple of the simulation time step.
The nominal speed value of the DC motor (rpm). This value is used to convert motor speed from rpm to pu (per unit).
The initial speed reference value (rpm). This value allows the user to start a simulation with a speed reference other than 0 rpm.
Cutoff frequency of the low-pass filter used to filter the motor speed measurement (Hz).
The proportional gain of the PI speed controller.
The integral gain of the PI speed controller.
The maximum change of speed allowed during motor acceleration (rpm/s). Too great a value can cause armature over-current.
The maximum change of speed allowed during motor deceleration (rpm/s). Too great a value can cause armature over-current.
The DC motor nominal power (W) and voltage (V) values. These values are used to convert armature current values from amperes to pu (per unit).
The proportional gain of the PI current controller.
The integral gain of the PI current controller.
Cutoff frequency of the low-pass filter used to filter the armature current measurement (Hz).
Maximum current reference value (pu). 1.5 pu is a common value.
Minimum firing angle value (deg.). 20 degrees is a common value.
Maximum firing angle value (deg.). 160 degrees is a common value.
Frequency of the synchronization voltages used by the discrete synchronized pulse generator block (Hz). This frequency is equal to the line frequency of the single-phase power line. This parameter is not used when using the average-value converter.
The width of the pulses applied to the four thyristor gates (deg.). This parameter is not used when using the average-value converter.
The speed or torque set point. The speed set point can be a step function, but the speed change rate will follow the acceleration / deceleration ramps. If the load torque and the speed have opposite signs, the accelerating torque will be the sum of the electromagnetic and load torques.
The mechanical input: load torque (Tm) or motor speed (Wm). For the mechanical rotational port (S), this input is deleted.
The single-phase electric connections. The applied voltage must be adequate for the motor size.
The mechanical output: motor speed (Wm), electromagnetic torque (Te) or mechanical rotational port (S).
When the Output bus mode parameter is set to Multiple output buses, the block has the following three output buses:
The motor measurement vector. This vector is composed of two elements:
The armature voltage
The DC motor measurement vector (containing the speed, armature current, field current, and electromagnetic torque values). Note that the speed signal is converted from rad/s to rpm before output.
The single-phase converter measurement vector. It includes the converter output voltage. The output current is not included since it is equal to the DC motor armature current.
Note that all current and voltage values of the bridges can be visualized with the Multimeter block.
The controller measurement vector. This vector contains:
The armature current reference
The firing angle computed by the current controller
The speed or torque error (difference between the speed reference ramp and actual speed or between the torque reference and actual torque)
The speed reference ramp or torque reference
When the Output bus mode parameter is set to Single output bus, the block groups the Motor, Conv, and Ctrl outputs into a single bus output.
The library contains a 5 hp drive parameter set. The specifications of the 5 hp drive are shown in the following table.
5 HP Drive Specifications
Drive Input Voltage | ||
---|---|---|
Amplitude | 320 V | |
Frequency | 50 Hz | |
Motor Nominal Values | ||
Power | 5 hp | |
Speed | 1750 rpm | |
Voltage | 240 V |
The dc1_example example illustrates the single-phase rectifier drive used with the 5 hp drive parameter set during speed regulation.
The rectifier is fed by a 220 V AC 50 Hz voltage source followed by a linear transformer to boost the voltage to a sufficient value.
The speed reference is set at 1750 rpm at t = 0 s. Initial load torque is 15 N.m.
Observe that the motor speed follows the reference ramp accurately (+250 rpm/s) and reaches steady state around t = 8.5 s.
The armature current follows the current reference very well, and the firing angle stays below 90 degrees, the converter being in rectifier mode (first quadrant operating mode). The lower limit of the firing angle has been set to 20 degrees.
At t = 8.75 s, the load torque passes from 15 N.m to 20 N.m. The motor speed recovers fast and is back at 1750 rpm at t = 10 s. The current reference rises to about 17.5 A to generate a higher electromagnetic torque to maintain the needed speed. As observed before, the armature current follows its reference perfectly.
The following figure illustrates the results obtained respectively with the detailed and the average-value converters. Average voltage, current, torque and speed values are identical for both models. The average firing angle values however are slightly different. Notice that the higher frequency signal components are not represented with the average-value converter.
DC1 Example Waveforms (Blue: Detailed Converter, Red: Average-Value Converter)