Power electronic converters are a family of electrical circuits which convert electrical energy from one level of voltage/current/frequency to another using semiconductor-based electronic switch. The essential characteristic of these types of circuits is that the switches are operated only in one of two states - either fully ON or fully OFF - unlike other types of electrical circuits where the control elements are operated in a (near) linear active region. As the power electronics industry has developed, various families of power electronic converters have evolved, often linked by power level, switching devices, and topological origins. The process of switching the electronic devices in a power electronic converter from one state to another is called modulation, Each family of power converters has preferred modulation strategies associated with it that aim to optimize the circuit operation for the target criteria most appropriate for that family. Parameters such as switching frequency, distortion, losses, harmonic generation, and speed of response are typical of the issues which must be considered when developing modulation strategies for a particular family of converters. 
Application areas of power converters got huge improvements in semiconductor technology, which offer higher voltage and current ratings as well as better switching characteristics. On the other hand, the main advantages of modem power electronic converters, such as high efficiency, low weight, small dimensions, fast operation, and high power densities, are being achieved through the use of switch mode operation, in which power semiconductor devices are controlled in ON~OFF fashion (no operation in the active region). This leads to different types of pulse width modulation (PWM), which is a basic energy processing technique applied in power converter systems. In modern converters, PWM is a high- speed process ranging depending on the rated power from a few kilohertz (motor control) up to several megahertz (resonant converters for power supply).therefore firstly we discuss about the principle and different topologies regarding PWM.
PULSE WIDTH MODULATION:
The most widely used control technique in power electronics is
Pulse width modulated (PWM) inverters are among the most used power-electronic circuits in practical applications. These inverters are capable of producing ac voltages of variable magnitude as well as variable frequency. The quality of output voltage can also be greatly enhanced, when compared with those of square wave inverters The PWM inverters are very commonly used in adjustable speed ac motor drive loads where one needs to feed the motor with variable voltage, variable frequency supply. For wide variation in drive speed, the frequency of the applied ac voltage needs to be varied over a wide range. The applied voltage also needs to vary almost linearly with the frequency. PWM inverters can be of
Single phase as well as three phase types. Their principle of operation remains similar. 
Principle of Pulse Width Modulation (PWM):
The dc input to the inverter is chopped by switching devices in the inverter. The amplitude and harmonic content of the ac waveform is controlled by the duty cycle of the switches. The fundamental voltage v1 has max. Amplitude = 4Vd/p for a square wave output but by creating notches, the amplitude of v1 is reduced (see next slide).
Usually, the on- and off-states of the power switches in one inverter leg are always opposite. Therefore, the inverter circuit can be simplified into three 2-position switches. Either the positive or the negative dc bus voltage is applied to one of the motor phases for a short time. Pulse width modulation (PWM) is a method whereby the switched voltage pulses are produced for different output frequencies and voltages. A typical modulator produces an average voltage value, equal to the reference voltage within each PWM period. Considering a very short PWM period, the reference voltage is reflected by the fundamental of the switched pulse pattern. 
There are several different PWM techniques, differing in their methods of implementation. However in all these techniques the aim is to generate an output voltage, which after some filtering, would result in a good quality sinusoidal voltage waveform of desired fundamental frequency and magnitude. For the inverter topology considered here, it may not be possible to reduce the overall voltage distortion due to harmonics but by proper switching control the magnitudes of lower order harmonic voltages can be reduced, often at the cost of increasing the magnitudes of higher order harmonic voltages. Such a situation is acceptable in most cases as the harmonic voltages of higher frequencies can be satisfactorily filtered using lower sizes of filter chokes and capacitors. Many of the loads, like motor loads have an inherent quality to suppress high frequency harmonic currents and hence an external filter may not be necessary. To judge the quality of voltage produced by a PWM inverter, a detailed harmonic analysis of the voltage waveform needs to be done.
In fact, after removing 3rd and multiples of 3rd harmonics from the pole voltage waveform one obtains the corresponding load phase voltage waveform. The pole voltage waveforms of 3-phase inverter are simpler to visualize and analyze and hence the harmonic analysis of load phase and line voltage waveforms is done via the harmonic analysis of the pole voltages. It is implicit that the load phase and line voltages will not be affected by the 3rd and multiples of 3rd harmonic components that may be present in the pole voltage waveforms.
Nature of Pole Voltage Waveforms Output By PWM Inverters:
Unlike in square wave inverters the switches of PWM inverters are turned on and off at significantly higher frequencies than the fundamental frequency of the output voltage waveform. The typical pole voltage waveform of a PWM inverter is shown in Fig. 1 over one cycle of output voltage. In a three-phase inverter the other two pole voltages have identical shapes but they are displaced in time by one third of an output cycle. Pole voltage waveform of the PWM inverter changes polarity several times during each half cycle. The time instances at which the voltage polarities reverse have been referred here as notch angles. It may be noted that the instantaneous magnitude of pole voltage waveform remains fixed at half the input dc voltage (Edc). When upper switch (SU), connected to the positive dc bus is on, the pole voltage is + 0.5 Edc and when the lower switch (SL), connected to the negative dc bus, is on the instantaneous pole voltage is - 0.5 Edc. The switching transition time has been neglected in accordance with the assumption of ideal switches. It is to be remembered that in voltage source inverters, meant to feed an inductive type load, the upper and lower switches of the inverter pole conduct in a complementary manner. That is, when upper switch is on the lower is off and vice-versa. Both upper and lower switches
should not remain on simultaneously as this will cause short circuit across the dc bus. On the other hand one of these two switches in each pole (leg) must always conduct to provide continuity of current through inductive loads. A sudden disruption in inductive load current will cause a large voltage spike that may damage the inverter circuit and the load.
Harmonic Analysis of Pole Voltage Waveform:
The pole voltage waveform shown in Fig. 1 has half wave odd symmetry and quarter-wave mirror symmetry. The half wave odd symmetry of any repetitive waveform f (?t), repeating after every 2?/? duration, is defined by f (?t) = - f (?+?t). Such symmetry in the waveform amounts to absence of dc and even harmonic components from the waveform. All inverter output voltages maintain half wave odd symmetry to eliminate the unwanted dc voltage and the even harmonics. The half wave odd symmetry followed by quarter wave mirror symmetry, defined by f (?t) = - f (?+?t), results in presence of only sine components in the Fourier series representation of the waveform. It may be verified that quarter wave symmetry may not hold good once the time origin is shifted arbitrarily. However the half-wave odd symmetry is maintained in spite of shifting of time origin. This is quite expected, as by just shifting the time origin new (even) harmonic frequencies will not creep up in the voltage waveform, whereas by shifting time origin the sine wave may become cosine or may have some other phase-shift. The quarter wave symmetry talked above is not necessary for improvement of the output waveform quality; it merely simplifies the Fourier analysis of the pole voltage waveform. It may also be noted that the quarter wave symmetry is not achieved at the cost of compromising the inverter's output capability (in terms of magnitude and quality of achievable output voltage).
With the assumed quarter wave mirror symmetry and half wave odd symmetry the waveform shown in Fig. 1 may be decomposed in terms of its Fourier components as below:
Where VA0 is the instantaneous magnitude of the pole voltage shown in Fig. 1 and is the peak magnitude of its nth harmonic component. Because of the half wave and quarter wave symmetry of the waveform, mentioned before, the pole voltage has only odd harmonics and has only sinusoidal components in the Fourier expansion. Thus the pole voltage will have fundamental, third, fifth, seventh, ninth, eleventh and other odd harmonics. The peak magnitude of nth harmonic voltage is given as:
Where ?1, ?2, ?3 and ?4 are the four notch angles in the quarter cycle (0 = ?t = ?/2) of the waveform.
Now, as described in the beginning of this lesson, the third and multiples of third harmonics do not show up in the load phase and line voltage waveforms of a balanced 3-phase load. Most of the three phase loads of interest are of balanced type and for such loads one need not worry about triplen (3rd and multiples of 3rd) harmonic distortion of the pole voltages. The peak magnitudes of fundamental (b1) and three other lowest order harmonic voltages that matter most to the load can be written as:
It can be seen that the 3rd and 9th harmonics have been not considered, as they will not appear in the load side phase and line voltages. Most of the industrial loads are inductive in nature with an inherent quality to attenuate currents due to higher order harmonic voltages. Thus after fundamental voltages, the other significant voltages for the load are 5th, 7th and 11th etc.
Generally, only the fundamental frequency component in the output voltage is of interest and all other harmonic voltages are undesirable. As such one would like to eliminate as many low order harmonics as possible. Accordingly the fundamental voltage magnitude (b1) may be set at the desired value and the magnitudes of fifth (b5), seventh (b7) and eleventh (b11) harmonics may be set to zero. These voltage magnitudes when substituted in the expressions given by Eqn. 3 to Eqn.6 will lead to the solutions of the notch angles. One may like to eliminate many more unwanted harmonic frequencies from the load voltage waveform but this will require introduction of more notch angles per quarter cycle of the pole voltage. In fact if there are 'k' notch angles per quarter cycle, 'k' number of equations may be written each of which determines the magnitude of a particular harmonic voltage. Now, each time a notch angle is encountered in the pole voltage waveform, the top and bottom switches of that particular pole undergo a switching transition (on to off or vice versa). The switching frequency (f sw) of the inverter switches can be equated to
where one turn-on and one turn-off has been taken as one switching cycle, ‘k' is the number of notches per quarter cycle and f1 is the frequency of fundamental component in the output voltage. Thus it can be seen that a better quality output waveform (in terms of elimination of more numbers of unwanted harmonic voltages) comes at the cost of increasing the switching frequency of the inverter. The switching frequency is directly proportional to the switching losses in the inverter switches. Also, the switch must be capable of being switched on and off at the required frequency. The IGBT switches used in medium power inverters are generally switched at a frequency of 20 kHz or more. With a switching frequency of 20 kHz and the output (fundamental) frequency of 50 Hz there will be up to 200 notches per quarter cycle of the output waveform. The load voltage can thus be made virtually free of low order harmonics and the load current (for an inductive load) can be expected to have a good quality sinusoidal waveform. The switching frequency of 20 kHz is important in another sense too. The range of audible noise for human beings extends from few Hertz to 20 kHz. Thus if the switching frequency is 20 kHz or beyond, the switching frequency related audible noise will not be present when the inverter operates. The inverter operation can then be very quite. If the inverter operates at low frequency, the connecting wires to the switches etc. also carry low frequency current producing low frequency vibrations (due to interaction of current with the stray magnetic field produced by other conductors etc.) and result in audible noise. Similarly low frequency current through inductors and transformers also produce audible noise. The humming or whistling type noise due to low switching frequency may at times be too annoying and unacceptable.
Description of Some Popular PWM Techniques:
The schematic PWM waveform shown in Fig. 1 is only representative in nature. The logic described to select notch angles is also specific to one particular PWM technique that is known as selective harmonic elimination technique. There are several other PWM techniques, the
important ones are:-
- SINUSOIDAL PULSE WIDTH MODULATION
- SPACE VECTOR PULSE WIDTH MODULATION
Sinusoidal pulse width modulation:
The most common PWM approach is sinusoidal PWM and Sinusoidal Pulse Width Modulation (SPWM), also called Sine coded Pulse Width Modulation, is used to control the inverter output voltage. In this method a triangular wave is compared to a sinusoidal wave of the desired frequency and the relative levels of the two waves is used to control the switching of devices in each phase leg of the inverter. The three phase implementation of sinusoidal pulse width modulation is shown below
mf should be an odd integer
- if mf is not an integer, there may exist sub harmonics at output voltage
- if mf is not odd, DC component may exist and even harmonics are present at output voltage
mf should be a multiple of 3 for three-phase PWM inverter
An odd multiple of 3 and even harmonics are suppressed
SPACE VECTOR PULSE WIDTH MODULATION:
A three phase balanced vectors can be represented using a single vector called space vector
Space Vector PWM (SVM) is a more sophisticated technique for generating a fundamental sine wave that provides a higher voltage to the motor and lower total harmonic distortion.
Space Vector Modulation (SVM) This technique involves synthesis of required voltage vector from a number of voltage vectors corresponding to switching states. Nearest three vectors (NTV) algorithm synthesizes voltage vector from nearest three vectors and is found to be the optimal solution in synthesis of required voltage vector and excellent spectral quality. Non-nearest three and four vector algorithm is an important extension to NTV proposed to avoid narrow pulse formation at low modulation index.
The circuit model of a typical three-phase voltage source PWM inverter is shown in Fig. 3. S1 to S6 are the six power switches that shape the output, which are controlled by the switching variables a, a', b, b', c and c'. When an upper transistor is switched on, i.e., when a, b or c is 1, the corresponding lower transistor is switched off, i.e., the corresponding a', b' or c' is 0.Therefore, the on and off states of the upper transistors S1, S3 and S5 can be used to determine the output voltage
As illustrated in Fig. 3, there are eight possible combinations of on and off patterns for the three upper power switches. The on and off states of the lower power devices are opposite to the upper one and so are easily determined once the states of the upper power transistors are determined. According to equations (8) and (9), the eight switching vectors, output line to neutral voltage (phase voltage), and output line-to-line voltages in terms of DC-link Vdc, are given in Table1 and Fig. 4 shows the eight inverter voltage vectors (V0 to V7).
Space Vector PWM (SVPWM) refers to a special switching sequence of the upper three power transistors of a three-phase power inverter. It has been shown to generate less harmonic distortion in the output voltages and or currents applied to the phases of an AC motor and to provide more efficient use of supply voltage compared with sinusoidal modulation technique as shown in Fig.5
As described in Fig.6, this transformation is equivalent to an orthogonal projection of [a, b, c]t onto the two-dimensional perpendicular to the vector [1, 1, 1]t (the equivalent d-q plane) in a three-dimensional coordinate system. As a result, six non-zero vectors and two zero vectors are possible. Six nonzero vectors (V1 - V6) shape the axes of a hexagonal as depicted in Fig. 7, and feed electric power to the load. The angle between any adjacent two non-zero vectors is 60 degrees. Meanwhile, two zero vectors (V0 and V7) are at the origin and apply zero voltage to the load. The eight vectors are called the basic space vectors and are denoted by V0, V1, V2, V3, V4, V5, V6, and V7. The same transformation can be applied to the desired output voltage to get the desired reference voltage vector Vref in the d-q plane. The objective of space vector PWM technique is to approximate the reference voltage vector Vref using the eight switching patterns. One simple method of approximation is to generate the average output of the inverter in a small period, T to be the same as that of Vref in the same period
The emergence of multilevel inverters has been in increase since the last decade. These new types of converters are suitable for high voltage and high power application due to their ability to synthesize waveforms with better harmonic spectrum. Numerous topologies have been introduced and widely studied for utility and drive applications.
The multilevel voltage source inverters unique structure allows them to reach high voltages with low harmonics without the use of transformers or series connected synchronized switching devices, a benefit that many contributors have been trying to appropriate for high voltage, high power applications.
The general structure of the multilevel converter which has a multiple of the usual six switches found in a three-phase inverter is to synthesize a sinusoidal voltage from several levels of voltages, typically obtained from capacitor voltage sources The main motivation for such converters is that current is shared among these multiple switches, allowing a high converter power rating than the individual switch VA rating would otherwise allow with low harmonics. As the number of levels increases, the synthesized output waveform, a staircase wave like, approaches a desired waveform with decreasing harmonic distortion, approaching zero as the number of levels increases
There are roughly three main types of transform less multilevel inverter topologies, which have been studied and received considerable interest from high power inverter system manufacturers: