Power electronics converters are a family of electrical circuits which converts 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 [1,2].

The process of switching the electronic devices in a power electronic converter from one state to another is called modulation, and the development of optimum strategies to implement this process has been the subject of intensive international research efforts for at least 30 years. Each family of power converters has performed 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.

The conversion of DC power to three-phase AC power is exclusively performed in the switched mode. Power semiconductor switches effectuate temporary connections at high repetition rates between the two dc terminals and three phases of the ac drive motor. The actual power flow in each motor phase is controlled by the on/off ratio, dutycycle, of the respective switches. The desired sinusoidal wave form of the currents is achieved by varying the dutycycles sinusoidal with time, employing techniques of pulse width modulation (PWM). Three-phase electronic converters controlled by pulse width modulation have a wide range of applications for DC-AC power supplies and AC machine drives [3,5].

The three-phase two level VSI consists of six active switches. The basic topology of the inverter is shown in Figure1. The converter consists of the three legs with IGBT transistors, or (in the case of high power) GTO thyristors and free-wheeling diodes. The inverter is supplied by a voltage source composed of a diode rectifier with a C filter in the dc-link. The capacitor C is typically large enough to obtain adequately low voltage source impedance for the alternating current component in the dc-link [6,7].

Figure 1. Voltage Source Inverter

The self-commutated frequency converters generate th rectangular waveshapes that contain substantial 5 and th 7 harmonic voltages and currents. When the harmonic currents flow in the motor windings, they produce torque pulsations that are superimposed on the main driving torque. The frequency of the torque pulsation is six times that of the fundamental frequency.

For example, suppose the drive involves in a 4-pole induction motor. When the frequency of the rectangular wave is 60Hz,the synchronous speed is 1800 r/min and corresponding torque pulsation is 60x6=360Hz.On the other hand, when the frequency of 1.5Hz is applied to the stator, the synchronous speed is 45r/min and the associated torque vibration is 1.5x6=9Hz.

Torque pulsations, such as 360Hz, are damped out at moderate and high speeds, due to mechanical inetia. However, at low speeds (such as 45r/min), a 9 Hz vibration is very noticeable. Such torque fluctuations are unacceptable in some industrial applications, where fine speed control down to zero speed is required. Under these circumstances, instead of using rectangular wave shapes, the motor is driven by pulse width modulation techniques [8,9].

In the voltage source inverter conversion of dc power to three-phase ac power is performed in the switched mode. This mode consists in power semiconductor switches are controlled in an on-off fashion. The actual power flow in each motor phase is controlled by the duty cycle of the respective switches. To obtain a suitable duty cycle for each switches technique pulse width modulation is used. Many different methods were proposed and development of it is still in progress [10-17].

The modulation method is an important part of the control structure. It should provide features like:

• Wide range of linear operation
• Low content of higher harmonics in voltage and current
• Low frequency harmonics
• Operation in over modulation
• Reduction of common mode voltage
• Minimal number of switching to decrease switching losses in the power components

The most widely used method of pulse width modulations are carrier based. This method is also known as the sinusoidal (SPWM), triangulation, subharmonic, or suboscillation method [1,16, 18-19]. All PWM methods have specific features. However, there is not just one PWM method which satisfies all requirements in the whole operating region. Therefore, in the literature are proposed modulators, which contain from several modulation methods. For example, space vector pulse width modulation (SVPWM) [1,10,20-22], which provides the following features:

• Full control range including over modulation and sixstep mode, achieved by the use of three different modulation algorithms
• Reduction of switching losses thanks to an instantaneous tracking peak value of the phase current

The content of the higher harmonics voltage (current) and electromagnetic interference generated in the inverter fed drive depends on the modulation technique.

Sinusoidal modulation is based on triangular carrier signals as in Figure 2. This relatively unsophisticated method employs a triangular carrier wave modulated by a sine wave and the points of intersection determine the switching points of the power devices in the inverter. However, this method is unable to make full use of the inverter's supply voltage and the asymmetrical nature of the PWM switching characteristics produces relatively high harmonic distortion in the supply. One commonly used PWM scheme is called carrier based modulation. This uses a carrier frequency usually between 10 to 20 kHz to produce positive and negative pulses of varying frequency and varying width. The pulse widths and spacing are arranged so that their weighted average produces a sine wave. Increasing the number of pulse per half cycle reduces the frequency of the output sine wave while, increasing the pulse widths increases the amplitude. In sine-triangle PWM a triangular carrier waveform of frequency fs establishes the inverter switching frequency.

Figure 2. Single phase Sine-Triangle Modulation

This is compared with three sinusoidal control voltages that comprise the three phase system. The output of the comparators produces the switching scheme used to turn particular inverter MOSFETS on or off. These three control voltages have the same frequency as the desired output sine wave which, is commonly referred to as the modulating frequency, f1. The modulation ratio is equal to mf = f1/fs. The value of mf should be an odd integer and preferably a multiple of three in order to cancel out the most dominant harmonics as these are responsible for converter losses. One limitation of the sine triangle method is that it only allows for a limited modulation index, so it doesn't fully use the DC bus. The modulation index can be increased by using distorted wave forms that contain multiples of third harmonics [23, 26]. These form zero sequence systems where the harmonics cancel out resulting in no iron losses.

The essential parameters of the SPWM are

(1)

where,

f_r is the frequency of the reference.

f_p is the frequency of the carrying wave.

(2)

where,

A_r : Amplitude of the reference.

A_p Amplitude of the carrying wave.

Reference signals are sinusoidal signals shifted between them of 120^o and are characterized by the amplitude A_r and its frequency f.

(3)

The flux locus of SPWM is given in the Figure 3. and the harmonic content of SPWM is given in the Figure 4.

Figure 3. Flux Locus of SPWM

Figure 4. Harmonic Order of SPWM

• The index modulation is:
• The control factor in voltage is:

Space Vector PWM (SVPWM) is a more sophisticated technique for generating fundamental sine wave that provides a higher voltage to the motor and lower total harmonic distortion, it is also compatible for use in vector control (Field orientation) of AC motors. The aim of any modulation technique is to obtain variable output having a maximum fundamental content with minimum harmonics. Space vector PWM method is an advanced, computation intensive PWM method and possibly the best techniques for variable frequency drive applications [24-25,27]. A different approach to PWM modulation based on space vector representation of the voltages in the α-β plane. The α-β components are found by transformation. SVPWM increases output capability of SPWM without distorting line to line output voltage waveform. Because of its following superior performance characteristics, it has been finding widespread application in recent years.

• SVM considers interaction among the phases in three phase neutral isolated system, while SPWM does not do it.
• Waveform generation for all three phase can be achieved simultaneously, while in SPWM three different references for three phases should be compared with carrier wave.
• For any power device design heat sink is based on the power dissipation (Conduction loss and switching loss are dominating). To calculate switching loss, duty cycle/ ON time devices are important. In case of Sinusoidal PWM, finding duty cycle is very difficult. But in SVPWM, ON time and OFF time of switches during a known fraction of a complete three phase cycle is readily available and helps in revising computation of incidental dissipation and heat sink size for a given power.
• Online computation is possible by look up table.
• Extended output capability.

Space Vector PWM (SVPWM) refers to a special technique of determining the switching sequence of the upper three power transistors of a three phase voltage source inverter. It has been shown to generate less harmonic distortion in the output voltages or current in the windings of the motor load. SVPWM provides more efficient use of the dc bus voltage, in comparison with the direct sinusoidal modulation technique.

The structure of a typical three-phase voltage source inverter is shown in Figure 5. The voltages V_a, V_b, V_c are the output voltages applied to the windings of a motor.Q1 through Q6 are the six power transistors which are controlled by a, a^', b, b', c and c^' gating signals and shape , the output voltages. When an upper transistor is switched on, i.e., when a, b, and c are 1, the corresponding lower transistor is switched off, i.e., the corresponding a^', b' or c^' is 0. The ON and OFF states of upper transistor Q1, Q3 and Q5, or the states to evaluate the output voltage.

There are eight possible combinations of on and off states for the three upper power transistors. The on and off states of the lower power transistors are opposite to the upper ones, so they are determined once the states of the upper transistors are known. The eight combinations are derived output line-line and phase voltages in terms of DC supply voltage V_dc, according to (1) and (2), which are shown in  Table1.

Table 1. Combinations of VSI

The relationship between the switching variable vector [a,  b, c]^T and the line to line voltage vector [V_ab, V_bc, V_ca ]^T is given by the equ. 4

(4)

In addition, phase (line-to-line) output voltage vector [V_a,V_b, V_c ]^T is given by (2)

(5)

Assuming q and d are the horizontal and vertical axes of the stator coordinate frame, the d-q transmission can transform three phase voltage vector into a vector in the d-q coordinate frame. This vector represents the spatial vector sum of the three phase voltage. The phase voltages corresponding to the eight combinations of switching patterns can be mapped into the d-q plane by the same d- q transformation. This mapping results in 6 non-zero vectors and 2 zero vectors. The non-zero vectors form the axes of a hexagonal as shown in Figure 6. The angle between any two adjacent non-zero vectors is 60^o .

Figure 5. Three Phase Voltage Source Inverter

Figure 6. Basic Switching Vectors and Sensors

The objective of the space vector PWM techniques is to approximate the reference voltage vector V_out by a combination of the eight switching patterns. One simple means of approximation is to require the average output voltage of the inverter (in small period T) to be the same as the average of V_out in the same period. This is shown in (6)  for the output voltage in the sector 0, where T₄ and T₆ are  the respective durations in time for which switching patterns are V₄ and V₆.

(6)

Where T₄ +T₆ ≤ T

Assuming the PWM period, T_ows , is small and the change of V_out is relatively slow, from (4.4), we obtain,

(7)

Where T₄ +T₆ ≤ T_pwn

Equation (4.4) shows that for every PWM period, the desired reference voltage V_out can be approximated by having the power inverter in a switching pattern of V₄ and V₆ for T₄ and T₆ periods of time, respectively. Since the sum of  T₄ and T₆ is less than or equal to T_pwm , the inverter needs to  have a 0((000)V0 or (111) V7 ) pattern for the rest of the period as shown in Figure.7. Therefore, (8) will then become

(8)

Where,

The SVPWM for three phase induction motor drive has been simulated and the results are shown in Figure 8. This simulation results show the output line-to-line and line-toneutral fundamental rms voltage in function of modulation index.

Figure 7. Timing Diagrams

Figure 8. Simulation Results of SVPWM

Figure 8. Simulation Results of SVPWM

The SVPWM generates minimum harmonic distortion of the currents in the winding of 3-phae AC motor. SV Modulation also provides a more efficient use of the supply voltage in comparison with sinusoidal modulation methods [26]. In fact, with conventional sinusoidal modulation in which the sinusoidal signals are compared with a triangular carrier, we know that the locus of the reference vector is the inside of a circle with a radius of 1/2V_DC In SV modulation it can be shown that the length of  each of the six vectors is 2/3V_DC In steady state the  reference vector magnitude might be constant. This fact makes the SV modulation reference vector locus smaller than the hexagon described above. This locus narrows itself to the circle inscribed within the hexagon, thus having a radius of 1/√ 3 V_DC . In Figure 9 the different DC reference vector loci are presented.

Figure 9. Locus Comparison of SPWM and SVPWM

Therefore, the maximum output voltage based on the Space Vector theory is 2/√3ON/OM times as large as that of the conventional sinusoidal modulation. This explains why, with SVPWM, we have a more efficient use of the supply voltage than with the sinusoidal PWM method and comparisons are given in Tables 2 and 3 applications. Its inner control system can be based on the SPWM or Space Vector PWM.

Table 2. Harmonics in output currents with SPWM & SVPWM (dB)

Table 3. Comparison of Space Vector PWM and Sinusoidal PWM

This paper presents an overview of simulation results regarding its main performance issues namely efficient use of supply voltage and harmonic distortions. These results show that there is a superior performance of SVPWM compared to the SPWM.