PWM symmetrical regular sampling control circuit for a two-level three phase inverter

Project Theme

Implement the control circuit for a two-level three phase inverter having the following design inputs.

1. Control Technique sinusoidal PWM – symmetrical sampling;2. Semiconductor Devices: MOSFET;

3. DC Voltage Link =300V;

4. Switching frequency of the inverter =5kHz;

5. The maximum value of the line-to-line voltage =210V at an output frequency of

100Hz, =0.9;

Task to be full field:1. Implementing the control circuit using Matlab Simulink software and comparison with

the ready to use circuit from Simulink;2. Computing the switching times;3. Simulating the inverter motor circuit using the control circuit from point 1;4. Fourier Analyze of the output waveforms;5. Switching times for 50 Hz output frequency and simulation.

Abstract

This project aims at the simulation study of three phase two level inverter. The power electronics device which converts DC power to AC power at required output voltage and frequency level is known as inverter. Inverters can be broadly classified into single level inverter and multilevel inverter. Multilevel inverter as compared to single level inverters have advantages like minimum harmonic distortion, reduced EMI/RFI generation and can operate on several voltage levels. A multi-stage inverter is being utilized for multipurpose applications, such as active power filters, static vary compensators and machine drives for sinusoidal and trapezoidal current applications. The drawbacks are the isolated power supplies required for each one of the stages of the multi-converter and it’s also lot harder to build, more expensive, harder to control in software.

Three-phase inverters are used for variable-frequency drive applications and for high power applications. A basic three-phase inverter consists of three single-phase inverter switches each connected to one of the three load terminals. For the most basic control scheme, the operation of the three switches is coordinated so that one switch operates at each 60 degree point of the fundamental output waveform. This creates a line-to-line output waveform that has six steps. The six-step waveform has a zero-voltage step between the positive and negative sections of the square-wave such that the harmonics that are multiples of three are eliminated as described above. When carrier-based PWM techniques are applied to six-step waveforms, the basic overall shape, or envelope, of the waveform is retained so that the 3rd harmonic and its multiples are cancelled.

The three-phase PWM rectifier has the characteristic of drawing nearly sinusoidal current with stable switching frequency and tight control of the position of modulation pulses. The simulation results show that the designed technique can improve three-phase PWM rectifier performance noticeably.

.

Introduction

Pulse width modulation (PWM) is the method of choice to control modern power electronics circuits. The basic idea is to control the duty cycle of a switch such that a load sees a controllable average voltage. To achieve this, the switching frequency (repetition frequency for the PWM signal) is chosen high enough that the load cannot follow the individual switching events. Switching, rather than linear operation of the power semiconductors is of course done to maximize the efficiency because the power dissipation in a switch is ideally zero in both states. In a typical case, the switching events are just a “blur” to the load, which reacts only to the average state of the switch.

PWM control is the most powerful technique that offers a simple method for controlling of analog systems with the processor’s digital output. PWM is employed in a wide variety of applications, ranging from measurement and communications to power control and conversion.

Pulse-width modulation, or pulse-duration modulation (PDM), is a commonly used technique for controlling power to inertial electrical devices, made practical by modern electronic power switches.

PWM technique is based on comparison of carrier signal with control signal. Intersection points of signals shows commutation time of semiconductor power electronic switching components. There are two PWM signals as symmetric and asymmetric. Pulses of symmetric PWM signal are always symmetric according to center of each PWM period. Pulses of asymmetric PWM signal are aligned with one side of PWM period. Symmetric PWM signals produce less output current and voltage harmonic

Basic purpose of PWM technique is to reduce inverter output harmonic level, to increase voltage magnitude, to reduce switching losses. The most important characteristic of PWM method is that as inverter input DC voltage is constant, inverter output voltage and frequency can be changed. Existence of harmonics in energy system is understood from corruptions of current and voltage waveforms that have sinusoidal form. One of the known harmonic sources is inverter too. Effects of inverter output current harmonics cause that increment of voltage droop because of current harmonic components, overheating at induction motors because of occurred oscillations, faulty measurements and decrement of life of equipments which are connected to out of inverter. So decrement of harmonics is desired. Inverter power devices are switched as on-off many times in half period to produce output voltage which has less harmonic. SPWM is used widespread from of old because of application easiness of PWM techniques. Fundamental output voltage magnitude of PWM techniques is provided by adjusting of modulation index. If modulation index is less than one, only side bands of fundamental wave frequency.

Theory

Sampling techniques

The symmetric and asymmetric PWM methods are explained with the following figure:

Figure 2. Symmetric and asymmetric PWM

In symmetric PWM, the positive (or negative) pulse of every PWM cycle is located in the middle of the cycle period, while in the asymmetric PWM, the pulses are usually aligned to the start or end of the PWM cycle.

Practically, asymmetric methods are relatively easier to realize, but symmetric methods evoke fewer harmonic interferences. Therefore, symmetric PWM should be used when possible.

a) Symmetrical regular sampling

Computation of the switching times in case of symmetrical regular sampling:

b) Asymmetrical regular sampling

Power MOSFET is a universally popular device for low-voltage, low-power, high-frequency applications, such as switching mode power supply, portable brush and brushless DC drives, has no fear of competition by other devices in the future at that power level.

In inverter circuits, the PWM is used in order to obtain inverter output to be sinusoidal with magnitude and frequency controllable.PWM control technique is to that conclusion as the theoretical basis of the semiconductor switching devices turn on and off control, so that the output to be a series of unequal amplitude equal to the width of the pulse, with these pulses instead of sine waves or other of the required waveform. According to certain rules of each pulse-width modulated inverter circuit output voltage can change the size, but also can change the output frequency. 

Induction motor driver circuits are harmonic sources because of their semiconductor switching power components. Harmonics are provided by inverter, are inevitable, so optimization of these is made. For this purpose, more fast and had less switching losses ones of used semiconductor power switching components are preferred, also PWM (Pulse Width Modulation) techniques used in inverter are developed.

Because of advances in solid state power devices and microprocessors, switching power converters are used in more and more modern motor drivers to convert and deliver the required energy to the motor. Task of inverter is convert DC input voltage to AC voltage with desired magnitude and frequency. Output voltage regulation is made as constant or variable frequency. Variable output voltage can be obtained keeping constant inverter gain and adjusting DC input

voltage. Another method, if DC input voltage is constant and not adjustable, variable output voltage can be obtained by adjusting of inverter gain, this is provided by PWM control of inverter.

PWM signals are obtained putting related signal data to sin table at software which developed for carrier based PWM signals. For different PWM techniques, inverter output current harmonic analysis is made changing modulation index and modulation ratio with harmonic analyzer. Output current of the system which controlled according to different techniques and output current harmonics are investigated comparing each other.

PWM control technique is to that conclusion as the theoretical basis of the semiconductor switching devices turn on and off control, so that the output to be a series of unequal amplitude equal to the width of the pulse, with these pulses instead of sine waves or other of the required waveform. According to certain rules of each pulse-width modulated inverter circuit output voltage can change the size, but also can change the output frequency. 

Theoretical calculations and simulation results

In this project we use the symmetrical sampling sinusoidal PWM technique for simulating the inverter motor circuit.

Symmetrical sampling – calculationsInitial values:

;

;

;;

;.

Computing of the switching times in case of symmetrical regular sampling:

;

;

;

;;

;

;;

;

(the frequency modulation ratio);

(the amplitude modulation ratio);

;

;

;

;

;……………………………………………………….

;

;;

;

;

;

;

;

;;;

……………………………………………………...

The model simulates three phase inverter with symmetric PWM modulation in which reference is sampled at the positive peak of the carrier and is held constant till the next positive peak of the carrier appears. The model demonstrates symmetric regular sampling at positive peaks of carrier and Fourier analysis of three phase inverter with this modulation technique. Symmetric modulation can be observed on the scope used by zooming the waveforms to large scale on time axis.

1. Implementing the control circuit using Matlab Simulink software and comparison with the ready to use circuit from simulink;

The control circuit imported from Matlab Simulink:

Fig.1.1.Control Circuit for a two-level three phase inverter

Comparison our circuit with the ready to use circuit from Simulink:

Fig.1.2.Control Circuit for a two-level three phase inverter from SimulinkIn this part we implemented the universal bridge ready to use from matlab with six

mosfets, and the discrete 3-phase generator is modulating the signals internal. The comparison is used so that we can see the output waveforms are identically or approximately identical.

Short analyze about every block from this circuit:

The Repeating Sequence Stair block outputs and repeats a discrete time sequence. You can specify the stair sequence with the Vector of output values parameter.

Vector of output values

Vector containing values of the repeating stair sequence.

Sample time

Specify the time interval between samples. In our case we have 1/5000.

Output data type

Specify the output data type. At the output we have float('double') that returns a MATLAB structure that describes the data type of an IEEE double (64 total bits, 11 exponent bits).

The PWM Generator block generates pulses for carrier-based pulse width modulation (PWM) converters using two-level topology. The block can be used to fire the forced-commutated devices (FETs, GTOs, or IGBTs) of single-phase, two-phase, three-phase, two-level bridges or a combination of two three-phase bridges.

The pulses are generated by comparing a triangular carrier waveform to a reference modulating signal. The modulating signals can be generated by the PWM generator itself, or they can be a vector of external signals connected at the input of the block. One reference signal is needed to generate the pulses for a single- or a two-arm bridge, and three reference signals are needed to generate the pulses for a three-phase, single or double bridge.

The amplitude (modulation), phase, and frequency of the reference signals are set to control the output voltage (on the AC terminals) of the bridge connected to the PWM Generator block.

The metal-oxide semiconductor field-effect transistor (MOSFET) is a semiconductor device controllable by the gate signal (g > 0). The MOSFET device is connected in parallel with an internal diode that turns on when the MOSFET device is reverse biased (Vds < 0) and no gate signal is applied (g=0). The model is simulated by an ideal switch controlled by a logical signal (g > 0 or g = 0), with a diode connected in parallel.

The Asynchronous Machine block operates in either generator or motor mode. The mode of operation is dictated by the sign of the mechanical torque:

If Tm is positive, the machine acts as a motor. If Tm is negative, the machine acts as a generator.

The electrical part of the machine is represented by a fourth-order state-space model and the mechanical part by a second-order system. All electrical variables and parameters are referred to the stator. This is indicated by the prime signs in the machine equations given below. All stator and rotor quantities are in the arbitrary two-axis reference frame (dq frame).

Machine Measurement DemuxSplit measurement signal of machine models into separate signals

Output waveform:

Fig.1.3.Simulation Results for the two-level three phase inverter

The output waveform of the voltage is from -300V and 300V the same as the input of the control circuit. At the second imagine of the waveforms is stator current and the third is the rotor current.

Te is the magnetic torque and when is positive the asynchronous machine acts like a motor and when is negative acts like a generator.

The intersection of the points shows the commutation time of the semiconductors, in our case mosfet.

Vab

ir_abc

is_abc

Te

wm

Fig.1.4.Simulation Results for the two-level three phase inverter from Matlab Simulink

Here we can see the simulation from the control circuit we have made is similar with the one ready to use from matlab.

2.Fourier Analyze of the output waveforms:

Fig. 2.1. Control Circuit for a two-level three phase inverter with Fourier Analyze

Vab

ir_abc

is_abc

Te

wm

Theoretical

In mathematics, Fourier analysis is a subject area which grew from the study of Fourier series. The subject began with the study of the way general functions may be represented by sums of simpler trigonometric functions. Fourier analysis is named after Joseph Fourier, who showed that representing a function by a trigonometric series greatly simplifies the study of heat propagation. Today, the subject of Fourier analysis encompasses a vast spectrum of mathematics. In the sciences and engineering, the process of decomposing a function into simpler pieces is often called Fourier analysis, while the operation of rebuilding the function from these pieces is known as Fourier synthesis. In mathematics, the term Fourier analysis often refers to the study of both operations. The decomposition process itself is called a Fourier transform. The transform is often given a more specific name which depends upon the domain and other properties of the function being transformed. Moreover, the original concept of Fourier analysis has been extended over time to apply to more and more abstract and general situations, and the general field is often known as harmonic analysis. Each transform used for analysis (see list of Fourier-related transforms) has a corresponding inverse transform that can be used for synthesis.

We can see in this circuit that we have interrupted the A phase and measured the current for the Fourier Analyze. After we introduced a voltage measurement between phase A and B after the oscilloscope is being set tot the sample time 10e-6.

The continuous block has the FFT analyze, to see the harmonic at 50 Hz we introduced the fundamental frequency 100 Hz and the harmonic order 5000.

Fig. 2.2 Fourier Analyze of the output signal from the voltage measurement block.

Harmonic = 1200Fundamental Frequency=100Hz

Fig. 2.2 Fourier Analyze of the output signal from the current measurement block.

In signal processing, the Fourier transform often takes a time series or a function of continuous time, and maps it into a frequency spectrum. That is, it takes a function from the time domain into the frequency domain; it is a decomposition of a function into sinusoids of different frequencies; in the case of a Fourier series or discrete Fourier transform, the sinusoids are harmonics of the fundamental frequency of the function being analyzed. When the function ƒ is a function of time and represents a physical signal, the transform has a standard interpretation as the frequency spectrum of the signal. The magnitude of the resulting complex-valued function F at frequency ω represents the amplitude of a frequency component whose initial phase is given by the phase of F. Fourier transforms are not limited to functions of time, and temporal frequencies. Symmetrical PWM signal produces less harmonics of current and voltage.

5.Finally we are switching times for 50Hz output frequency and the control circuit is:

Fig. 5.1.Control Circuit for 50 Hz frequency.

In this block we have modified the switching times in the first block we had the 100 Hz frequency, here we have 50 Hz. Of course the output waveform is modified.

Output waveforms:

Fig. 5.2. Output waveform for frequency equals 50Hz

5.3.Fourier Analyze of the circuit control block with 50 Hz frequency at the output of the voltage measurement.

5.3.Fourier Analyze of the circuit control block with 50 Hz frequency at the output of current measurement.

Conclusions:

PWM control technique is to that conclusion as the theoretical basis of the semiconductor switching devices turn on and off control, so that the output to be a series of unequal amplitude equal to the width of the pulse, with these pulses instead of sine waves or other of the required waveform. According to certain rules of each pulse-width modulated inverter circuit output voltage can change the size, but also can change the output frequency.

We use the symmetrical regular sampling because we approximate the sinusoidal control voltage with constant value for the whole interval of switching time measured at the beginning of sampling interval. We compare the triangular waveforms and approximate the control function.

We have 300V DC input and with help of the MOSFET’s who simulate an ideal switch controlled and the PWM Generator block where we introduce our times switching the Asynchronous Machine transforms the DC in AC…and we visualization the waveforms of the current, torque and the couple.