A Comparison Study of Sinusoidal PWM and Space Vector PWM Techniques for Voltage Source Inverter

In this paper, the methods used to control voltage source inverters, which have been intensively investigated in recent years, are compared. Although the most efficient result is obtained with the least number of switching elements in the inverter topologies, the method used in the switching is at least as effective as the topology. Besides, the selected switching method to control the inverter will play an effective role in suppressing harmonic components while producing the ideal output voltage. There are many derivatives of pulse width modulation techniques that are commonly used to control voltage source inverters. Some of widespread methods are sinusoidal pulse width modulation and space vector pulse width modulation techniques. These modulation techniques used for generating variable frequency and amplitude output voltage in voltage source inverters, have been simulated by using MATLAB/SIMULINK. In addition, the total harmonic distortions of the output voltages are compared. As a result of simulation studies, sinusoidal pulse width modulation has been found to have more total harmonic distortion in output voltages of voltage source inverters in the simulation. Space vector pulse width modulation has been shown to produce a more efficient output voltage with less total harmonic distortion.


Introduction
DC-AC converters are known as inverters.The function of an inverter is to convert the DC input voltage to a symmetrical AC output voltage of the desired amplitude and frequency.One of the most common problems in the power electronics industry is low-order harmonics, which cause distortions in voltage and current (Kumar, Michael, John, & Kumar, 2010).One solution to reduce low-level harmonics in high-power converters is to use PWM control techniques.There are many studies about PWM control techniques in the last decades (Ashish & Sanjiv, 2012;Colak & Kabalci, 2016;Durgasukumar & Pathak, 2012;Jesmin F. Khan, 2013;Vural, 2016;Guoqiang, Jianli, & Junwei, 2013;Wanchai, 2016;Gopalakrishnan & Narayanan, 2014;Oka & Matsuse, 2011).As can be seen from these studies; the point of density of the studies is low-order harmonics, which is a common problem.In this study, SPWM and SVPWM techniques, which are the most common PWM techniques, have been studied in detail and the six-pulse inverter circuit is simulated with the help of MATLAB / Simulink and the controls that are controlled by these two methods are examined for harmonics.
This paper is therefore organized as follows: An overview of inverter structure and its circuit are presented in the next section.The most common used PWM techniques which SPWM and SVPWM are presented in Section 2. The simulation results and discussions are presented in Section 3. Finally, the main concluding remarks of the paper are presented in the conclusions section.

Inverter Structure
The three-phase voltage source inverter (VSI) topology is presented in Figure 1.The output voltage can be obtained by changing the DC input voltage and holding the inverter gain constant.On the other hand, if the DC input voltage is fixed and cannot be controlled, the gain of the inverter can be varied to obtain a variable output voltage.This is accomplished by pulse width modulation (PWM) in the inverter (Bedford & Hoft, 1964;Rashid, 2003).Among PWM techniques, sinusoidal pulse width modulation (SPWM) and space vector pulse width modulation (SVPWM) are the most widely used techniques (Vural, 2016;Guoqiang, Jianli, & Junwei, 2013;Durgasukumar & Pathak, 2012;Wanchai, 2016;Colak & Kabalci, 2016;Gopalakrishnan & Narayanan, 2014;Jesmin F. Khan, 2013;Oka & Matsuse, 2011.However, in the SPWM technique, the peak voltage of the output voltage cannot exceed the DC supply voltage without operating in the over-modulation region.The SVPWM is more flexible and can be programmed to synthesize the output voltage with a numerical application.(Nandhakumar & Jeevananthan, 2007).By comparing the carrier signal to the reference signals, the switch states G1, G2, G3, G4, G5 and G6 shown in Fig. 2. The switching elements G1 and G4, G3 and G6, G5 and G2 are not open or closed at the same time.To explain the Figure 2, if the Vcr>Vra, G1 is off and G4 is on state, Vcr<Vra, G1 is on and G4 off state, Vcr>Vrb, G3 is off and G6 is on state, Vcr<Vra, G3 is on and G6 off state, the other rule is Vcr>Vrc, G2 is off and G5 is on state, Vcr<Vrc, G2 is on and G5 off state.To determine the reference voltages, The signals can be regulated by the equation (1.1) Where A is the magnitude of the signal, o To determine the reference voltages for V(a-b-c) the following equations are used; Figure 2. Sinusoidal PWM for three phase VSIs (Rashid, 2003) The frequency of the output voltage is determined by the frequency of the reference signal.The amplitude of the reference signal determines the modulation index and in turn determines the rms value of the output voltage.The change of the rms value of the output voltage is possible by changing the modulation index (Zhenyu, Arefeen, & Issa, 1997).
The simulated SPWM circuit in MATLAB/Simulink is shown in below Figure 3. Space vector PWM avoids unnecessary switching.This leads to excellent output performance, high efficiency and reliability compared to similar inverters with conventional pulse width modulators (Ashish & Sanjiv, 2012).In the SVPWM method, the reference signals in the abc coordinates are transformed to the normalized reference vector in the coordinates by the following transformation matrix, which is generated by the order of application and the application period of the vectors occurring in the switching states of the inverter.
Synthesis of voltage in Space Vector PWM applications; First, the transformation from a, b, c to α-β is done.
The magnitude of the reference voltage The angle between α-β is determined by the following equation.
The period of the vectors occurring in the switching states of the inverter is shown as a Clarke matrix (Tabc-αβ) which is determined by the given equations ((2.1) and (2.2)).
In the inverter topology shown in Figure 1, if the switching elements G1 and G4, G3 and G6, G5 and G2 are not open or closed at the same time, eight different switching state vectors are generated.These switching vectors and the output voltages generated in these switching states are given in Table I at abc coordinates and normalized values in co-ordinates.
The simulated SVPWM circuit in MATLAB/Simulink is shown in below Figure 4.The representation of the vectors occurring in the switch cases at the coordinates is shown in Figure 5.Among the space vectors that occur in switching states, there are six regions called sectors.

Figure 5. Three dimensional space vectors
The SVPWM method is applied in three basic steps; Step I: The reference voltage in the abc coordinates is converted to the space vector normalized to the DC voltage in the alpha-beta coordinates and the rotation angle in the coordinates of the reference vector is determined.
Step II: The sector in which the reference vector is located is determined and it is determined how long the vectors in the switching states must be applied in order to form the reference voltage.
Step III: Switching is performed according to the order in which the vectors in the switching states are applied.

Simulation Results
SPWM and SVPWM techniques have been applied to a three-phase VSI.Output voltage and current graphs of SPWM and SVPWM are given below in Figure 6-9.As can be seen from the graphs, the output graphs of the SPWM controlled inverter show less degraded shapes.
Total harmonic distortion values of the output voltages and currents of VSI are given in Figure 10-13 and Table 2.In Table 2, the inductive load value for the same resistive load value is increased, the resistive load value for the same inductive load value is increased, the resistive and inductive load values are increased, and the THD values of the output voltage and current are examined.As a result, the total harmonic distortion of the output current and voltage under different load conditions has been found to be higher in SVPWM than in SPWM switching technique.

Conclusion
In this study, SPWM and SVPWM techniques used to switch voltage source inverters have been simulated and compared under different types of load in MATLAB/SIMULINK.Figure 6, Figure 7, Figure 8 and Figure 9 show output voltage and current graphs of the voltage source inverter switched with SPWM and SVPWM.When the THD value of these voltages and currents are analyzed, THD value of the output voltage of the inverter which is controlled by SPWM is 8,15%, THD value of the current was 4.09%, THD value of the output voltage was 5.77% and the THD value of the current was 1.85% for the inverter controlled with SVPWM.In power systems, total harmonic distortion is an important factor in terms of power quality.In this study, the SPWM and SVPWM techniques used to switch voltage source inverters are compared in terms of THD.As a result of analysis, SVPWM technique has been found to be a more efficient switching method in terms of power quality.This study is a benchmarking in this respect.The aim of this study is to be able to transmit energy which obtain from renewable energy resources in the most efficient way possible and to choose the appropriate switching technique to minimize the harmonic rates to the lowest possible level.The next step of this study will be used the inverter controlled by the SVPWM technique with the renewable energy source for on-grid systems.

Figure 4 .
Figure 4. Simulated Space Vector PWM circuit in Matlab/Simulink

Figure 6 .
Figure 6.Output voltage of VSI switched with SPWM

Figure 10 .
Figure 10.Total Harmonic Distortion of Output Voltages of VSI switched SPWM

Table 1 .
Switching States of Space Vector Modulation