Posted on 23rd Nov 2024 10:39:52 PM ETE
ABSTRCT
A novel single phase to single phase matrix converter is proposed in this work which can be applied for multiple application. The matrix converter is developed with only four RB-IGBTs and four diodes. This design makes it thinner in size and decrease the gate driving complexity, reduce the total equipment costs and enhance the energy conversion efficiency with minimized losses. The proposed modulation scheme can improve the power factor. In addition, the single phase matrix converter presented is applicable in various fields, including electric traction as a velocity controller, induction heating, variable power supplies for AC and DC, etc., which represent the expertise of this converter in energy conversion devices. However with regard to the number of parts, equipment prices, gate driving complexity, and application areas, a comparative study of the offered converter with the current AC-AC converters is also presented in this article. In this article, the simulation-based findings performed in MATLAB/Simulink are described and evaluated with proper explanations in order to determine the efficiency of the proposed single phase matrix converter. The output results are analyzed for each of the application. The power loss is minimized for the proposed converter and the comparison of THD for different modulation is given to understand the effect. THD is compensated around 20-30% for based on the conversion.
CHAPTER 1: INTRODUCTION
1.1 Introduction
Solid-state AC–AC converters are widely used in a number of applications such as adjustable speed drives, AC–AC transmission, uninterruptible power supplies (UPS) aircraft converter[1, 2] systems and renewable energy conversion systems[3]. An important area of AC–AC conversion concerns variable speed drive systems for induction motors which currently account for about 50% of electricity consumption[4]. Generally, the frequency converter (frequency converters) converts AC electrical power of one frequency into AC electrical power of another frequency. Typically, such units are used to convert between 50/60Hz source frequencies into 0–800Hz on the load side.
The most attractive features of frequency converters include the ability to produce arbitrary amplitude and frequency load voltages (also with greater amplitude than source voltage amplitude), sinusoidal source and load currents and waveform voltage, the ability to provide any load with a unity power factor, and finally, a simple and compact power circuit[5]. Additionally, the frequency converter was developed with a transistor inverter. There are two implementation types of the DC link: a voltage DC connection with a capacitor CDC as a DC electrical energy storage component (with voltage source inverter VSI) and a current DC connection with an inductor L as a DC electrical energy storage component .Factor (inverter CSI with current source)[6].In the case of the DC voltage connection, it is implemented on the rectifier side by a diode bridge in the simplest unidirectional case. In recent years, there have been developments in control semi-conductor switches [7]. The development of many AC-AC converter devices without DC electrical energy storage components, known as direct energy storage devices[8]. Power Frequency Converters (DPFC) or Static Power Frequency Converters (SPFC). The DPFC consists effectively of a set of static power switches attached to the source and load terminals[9]. Electrolytic capacitors or dc reactors used in these circuits reduce the life expectancy of the unit. Other disadvantages can be summarized as follows:
• poor total input power factor,
• rich in input current harmonics,
• large input and output filters must be used for harmonic reduction,
• one-directional power transfer (non-regenerative),
• costly and bulky large electrolytic capacitors at dc-link. This results in the increase of system’s size, weight, cost and losses,
• it is impossible to acquire high power density and the multi stages will certainly decrease the reliability of systems,
• the dc-link slows down the dynamic response of the circuit.
1.2 Single Phase Matrix Converter Topology
As seen in Figure 1, the SPMC consists of a matrix of four bidirectional transition input and output lines linking the single-phase input to the single-phase output at intersections. The bi-directional switch module is shown in Figure 2 using a typical antiparallel IGBT emitter with a diode pair switch-cell to allow current flow in both directions while blocking voltage at the same time.
Figure 1.1: The Single Phase Matrix Converter Topology [15]
1.2.1 Topologies of Bi-Directional Switches
The Single-phase MC topology is constructed using 4 bi-directional switches arranged in a matrix, which are capable of conducting currents and blocking voltages of both polarities[24]. There are four main topologies for bi-directional switches, which are shown in Fig1.2.
Figure 1.2: Different forms to coordinate bi-directional switches [16]
The most simple switch cell is a single-phase diode bridge with an IGBT connected at the center in fig 1.2(c)The main advantage of this switch is that only one active device is needed. This approach reduces the cost of the power circuit and the complexity of the control. In fig1.2 (a) only one transistor gate drive circuit is needed for each switch cell. The disadvantage is that the conduction losses are relatively high. During the conduction stage, the three devices are conducted (two diodes and IGBT transistor). Moreover, the direction of current through the switch cell cannot be controlled. The two most commonly used configurations of switch cell are named the common emitter anti paralleled IGBT configuration. And the common collector anti-paralleled IGBT configuration1.2 (d). The diodes are included to provide reverse blocking capability, whereas, the IGBTs enable the independent control of the current direction. Finally, in fig1.2(b)the switch cell is the anti-paralleled reverse blocking IGBTs (RB-IGBT)[25]
The main feature of the RB-IGBT is its reverse voltage blocking capability, which eliminates the use of diodes. For this reason there is a reduction in the number of discrete devices and conduction losses. At any instant, there is only one device conducting current in any direction.
1.3 Conclusion
Synthesis of the load voltage waveforms and source current waveforms is the fundamental operating theory. There are several direct power frequency converter topologies. The matrix converter is the most common (MC).Some advantages of the matrix converters are:
• Adjustable input power factor regardless of the load, generally with unity power factor.
• bilateral transformation of energy,
• elimination of energy storage components,
• high-efficiency and fast-response,
• reduction of installation area and integration of more complex silicon structures in power modules,
• higher controllability,
• the number of phases on input and output sides are independent of each other,
• the waveform and the frequency on both sides are independent of each other,
• a matrix converter can reproduce any waveform without using any additional power hardware,
• it can be used as a full four-quadrant power supply without any additional power hardware,
• Elimination of temperature sensitive electrolytic dc-link capacitors, which results in higher reliability and higher operating temperature.
CHAPTER 2: LITERATURE REVIEW
2.1 Introduction
There are many types of work in Matrix converter including the power factor improvement with various control strategies for both of the single phase matrix converter and the three phase matrix converter. The modulation strategies are mainly focused in some of the recent article and there is a poor amount of article where modified topology of the matrix converter depends on the switch reduction.
2.2 Literature Review
In 1980, Venturini and Alesina published the first analysis of MCs. The authors presented the basic structure of a power circuit as an a matrix of bidirectional power switches connecting each load phase to each source phase, introduced the matrix converter term, and presented the first principle of control named Venturinimethod or improved Venturini[10]. In both Venturini modulation methods, also known as the direct transfer function approach, the output voltages are obtained by the multiplication of the modulation matrix using the input voltages. The key downside of the matrix is the voltage transmission factor of less than one. Transform the low voltage transfer ratio issue has prompted laborious studies focusing on the production of new controls over the past few years. [11]Strategies that increase the range of load voltages. In 1983, Rodriguez suggested a new control strategy that was based on a hypothetical DC bus solution. In this modulation, the input voltages are first rectified and then reversed to a fictitious DC bus. In a series of papers in which the concepts of space-vector modulation were generalized to a matrix converter, the space vector modulation (SVM) technique was first exploited by Huber et al[12]. Instantaneous space-vector representation of input and output voltages and currents is the basis of the SVM method. In matrix control with direct and indirect methods, the SVM method was successively developed and is the most common one. In addition to those mentioned above from the more widely known matrix converter control strategies, there are a few less well-known ones in the technological literature, e.g.: sliding mode control, carrier-based PWM control and the very famous predictive control in recent times[4]. It should be noted that the maximum voltage transfer ratio is provided in the presented control strategies. Concurrent commutation of controlled bidirectional switches is another major problem in matrix converters. Without creating overcurrent or overvoltage surges that can destroy the power semiconductors, switching is very difficult to achieve. Fortunately, with the implementation of many multistep commutation techniques that allowed the switches to function safely, this issue was solved[13]. The matrix converter can be used for single phase and the three phase matrix converter. The 3 phase matrix converter needs to implement nine bidirectional switches and the single phase needs the 4 bidirectional switches[14]. The single phase matrix converter is first implemented in the article of Z.Idris which was illustrated the switching modulation of SPWM[15].Also, single-phase ac/ac converter has other applications such as variable frequency speed control of single-phase induction motors, single-phase induction heating system, and low power equipment such as switching mode power supplies[16].
From then many research article improve power quality and the switch reduction for improving THD and for the lower cost. The single phase Matrix Converter will execute all the functions of a simplified single phase power converter by adjusting the input parameters. The use of pulse width modulation (PWM) operated safe-commutation switches will greatly boost the efficiency of ac/ac converters. This has, this has a number of scientific papers[17] were published in which numerous ac/ac converters were suggested. However the AC output voltage cannot surpass the AC input voltage in the traditional single-phase matrix converter. In addition, both bidirectional switches of either step leg can never be switched on at the same time; otherwise the switches would be killed by current spikes caused in this way. Using the Z-source inverter will solve these limitations. In view of the Z-source converter topologies, it is found that they may be specifically generalized or derived from the well-understood topology of the Z-source inverter[17]. There are very poor studies on the cost reducing technique with switch reduction. In order to achieve a high step-up AC-DC converter with low voltage ripple and variable voltage. There are many problems caused by the unwanted current harmonics, such as heating and life loss in transformers and induction drives and system voltage waveform decay. In numerous research studies, the MCs have been extensively studied, covering several aspects such as modulation and control systems[18], ac drive implementations, and circuit progress[19]. For this MC converter the step up and step down frequency operations are discussed with the safe commutation strategy[20]. .The sinusoidal pulse width modulation ,the staircase modulation[21] and other modulation schemes are simulated and experimented for improving the power quality. This functionality of the Matrix Converter simplifies the need for modern hardware converters. This potential use of the Matrix Converter eliminates the need to understand many different converter topologies. The single phase Matrix Converter will execute all the functions of a simplified single phase power converter by adjusting the input parameters[22]. Nowadays, some of the research articles represented the modified single phase matrix converter with reduced number of switch for AC-DC conversion[23] and the high frequency buck converter.
2.2.1 Review of The Current Single Phase Matrix Converter
This single phase to single phase matrix converter is used for the recent years for the purpose of step up and step down frequency operation. This converter is composed of 8 semiconductor soft switches and 8 diodes. The switch can be MOSFET or IGBT. The switches are operated as the matrix for getting any negative and positive output waveform. But using the more switches for the step up and down operation causes the switching complexity and increases the cost.
Figure 2.2.1: Single Phase Matrix converter Topology[15]
2.2.2 Definition Dilemma OF Current SWITCHING SCHEMES
The switching difficulties of the existing modulation scheme are addressed in this section. In the recent publications used Sinusoidal PWM(SPWM), harmonic injected PWM(THPWM), trapezoidal PWM(TRPWM), third harmonic trapezoidal PWM (THTRPWM), fifth harmonic trapezoidal PWM (FHTRPWM).staircase modulation, space vector modulation, Delta sigma modulation. These systems introduce harmonic injection issues into the converters output power and place excess dv/dt stress on switching components. As a result, it raises the cumulative loss of the converter. If the power, which includes the converter's higher harmonics, is inserted into the load, the quality of the power system decreases. The Sinusoidal Pulse width modulation depicts here.
Figure 2.2.2: The Sinusoidal Pulse Width Modulation [17]
Figure 2.1 depicts the sinusoidal pulse width modulation technique. When the reference signal is higher than the carrier signal then the output is high, otherwise low. This modulation has a problem of higher third order harmonics and the inter-harmonics component. The DC component is also presented here. Which is not desirable in the AC conversion technique.
2.3 Conclusion
There are very poor work in this field of single phase matrix converter of cost reduction technique by reducing switch. The existing modulation schemes produce high amount of THD that is not tolerable. The cost and complexity of typical single or three phase matrix converter design and implementation are so much that local production of it is about impossible .This obstacle for this field is overlooked. The cost effective configuration for the lower and middle level industrial application is not proposed anywhere in the existing article. There is no comparison of THD for different modulation schemes in the single phase matrix converter.
CHAPTER 3: PROPOSED TOPOLOGY AND SWITCHING SCHEME
3.1 Introduction
The proposed single phase matrix converter is more relevant than any other matrix converter topology is examined before. This converter can be used as a multi-operational matrix converter giving single phase AC voltage as input and varying the switching pattern. This SPMC is cost effective and can be used with the less switching complexity.
The proposed switching scheme is also very effective to reduce total harmonic distortion (THD) and increase the lifetime of the converter.
3.2 Objectives
• To develop a single phase matrix converter with less harmonics with developed modulation scheme and appropriate RMS value using simple switching arrangement.
• To develop a single phase matrix converter configuration which will be cost effective and for lower and middle level industrial application.
• To reduce the cost of production and complexity of design thus local production can be possible.
3.3 Theory
The single phase matrix converter converts the AC voltage and it can be operated as the step up SPMC, step down SPMC, AC voltage regulator and controlled rectifier. Based on the form of active energy conversion modes, including step-down SPMC, step-up SPMC, AC voltage regulator, and regulated rectifier, the operating theory of the proposed SPMC is explained. The operating modes can be developed by the following matrix.
Figure 3.3: Switching Matix of the proposed SPMC
The 2*2 matrix is demonstrated here. Here S1 & S3 are operated simultaneously. Moreover, S2 & S4 are operated simultaneously for obtaining the desired application and follow the matrix rule as illustrated in Figure 3.1.Thus, and only four common modes offer any type of energy conversion from AC-AC.
3.3.1 Proposed Single Phase Matrix Converter for different operation
Figure 3.3.1: A Novel Matrix Converter with Switch Reduction Count
Figure 3.3 illustrates the proposed topology of SPMC with reduced switch count. Only four soft silicon switches(e.g.-IGBT) and are used. Here two unidirectional switches S1 and S3 are the MOSFET & two anti-paralleled reverse blocking switch cells (RB-IGBT) are used to perform the suitable operation and two switches are alleviated from the conventional one. With less gate driver sophistication, the proposed converter can be used as a multi converter since the switches can be operated according to the desired function. Hence, the benefits of a power MOSFET are higher switching speed and better performance at low voltages during service. Moreover, it can sustain a high blocking voltage and retain a high current. Therefore the proposed converter is simultaneously lightweight, cost-efficient, and effective.
3.4 Nature of Operating Modes
Mode-1: Switch S1 & S3 is on for getting the same polarity of output voltage when input is positive .But here D1&D4 are conducted simultaneously. They then include the direction of conduction for the current to pass through the load seen in the figure-3.2(a)
V_o=V_i 1
Mode-2: S2 & S4 are turned on together for getting the negative voltage output when input is positive. Here, D1&D4 are conducted simultaneously .These two switches produced path to flow current through the load that is illustrated in figure-3.2(b)
V_o=〖-V〗_i 2
Mode-3: In such a mode, the S2 & S4 are turned on simultaneously and D2&D3 for obtaining equivalent output voltage as the input is negative. The conduction path is depicted with these two switches shown in figure-3.2(c)
V_o=〖-V〗_i 3
Mode-4: S1 & S3 on during this mode. Moreover, D2&D3 is on at that instant and create the current conducting path through the load for acquiring the output voltage which is 180° out of phase from the negative input voltage depictured in figure-3.2(d).
V_o=V_i 4
Figure 3.4:Working modes of the SPMC. Here(a)mode-1, (b)mode-2, (c)mode-3, (d)mode-4
Table3.4: Switching Matrix Converter States for Multiple Forms of Energy Transformation.
Energy conversion modes Output frequency in hertz Switching states (ON=1,OFF=0) Output Voltage(Vout) Ranges of Angle(θ)
D1 D2 D3 D4 S1 S2 S3 S4
Step-up Matrix Converter 100 1 0 0 1 1 0 1 0 VmSinθ 0 ≤ θ <π/4
1 0 0 1 0 1 0 1 -VmSinθ π/4≤ θ <π/2
0 1 1 0 1 0 1 0 VmSinθ π/2≤ θ < 3π/4
0 1 1 0 0 1 0 1 -VmSinθ 3π/4≤ θ ≤ π
150 1 0 0 1 1 0 1 0 VmSinθ (0 ≤ θ ≤ π/6),( π/3≤ θ ≤ π/2)
1 0 0 1 0 1 0 1 -VmSinθ π/6≤ θ ≤ π/3
1 0 0 1 1 0 1 0 -VmSinθ ( π/2≤ θ ≤ 2π/3), ( 5π/6≤ θ ≤ π)
0 1 1 0 1 0 1 0 VmSinθ 2 π/3≤ θ ≤ 5π/6
200 1 0 0 1 1 0 1 0 VmSinθ (0 ≤ θ ≤ π/8),( π/4≤ θ ≤ 3π/8)
1 0 0 1 0 1 0 1 -VmSinθ (π/8≤ θ ≤ π/4),( 3π/8≤ θ ≤ π/2)
0 1 1 0 1 0 1 0 VmSinθ (π/2≤ θ ≤ 5π/8),( 3π/4≤ θ ≤ 7π/8)
0 1 1 0 0 1 0 1 -VmSinθ (5π/8≤ θ ≤ 3π/4),( 7π/8≤ θ ≤ π)
Step-down Matrix Converter 25 1 0 0 1 1 0 1 0 VmSinθ 0 ≤ θ ≤ π/2
0 1 1 0 1 0 1 0 VmSinθ π/2≤ θ ≤ π
1 0 0 1 0 1 0 1 -VmSinθ π/≤ θ ≤ 3π/2
0 1 1 0 0 1 0 1 -VmSinθ 3π/2≤ θ ≤ 2π
Regulated Rectifier 0 1 0 0 1 1 0 1 0 VmSinθ α≤ θ ≤ π/2
0 1 1 0 1 0 1 0 VmSinθ (π/2)+α ≤ θ ≤ π
Regulator of AC voltage 50 1 0 0 1 1 0 1 0 VmSinθ α≤ θ ≤ π/2
0 1 1 0 0 1 0 1 -VmSinθ (π/2)+α ≤ θ ≤ π
3.5 The desired Scheme of Switching
In my work, the offered modulation scheme is unipolar fifth harmonics injected and ninth harmonics rejected trapezoidal Pulse Width Modulation (UFNTPWM). By specifically reducing the influence of the third harmonic and the inter-harmonic elements, the suggested switching scheme gives a greater use of the AC power supply. There is no Dc component too. So it is effective for the AC-AC conversion technique. The following figure depicts the proposed modulation scheme in the terms of modulating signal and the carrier signal. The proposed UFNTPWM modulation scheme can be mathematically expressed as,
m=M+Bsin(5ωt)-Csin(9ωt) 5
Where, M=A sin^(-1){sin(ωt) }
=0.98A(When M>0.98A)
=-0.98A(When M<0.98A)
6
Figure 3.5: The UFNT Pulse Width Modulation
3.6 Conclusion
The technique of proposed matrix converter is more effective for reducing cost and the complexity of switching. There is used only 4 semiconductor soft switches (RB-IGBT) and 4 diode only for implementing the single phase matrix converter. The modulation technique is new and it is very effective for reducing the voltage THD comparing to the SPWM .The conduction mode is shown in the Fig.3.4 and there is the smart option for reverse blocking.
CHAPTER 4: SIMULATION RESULTS
4.1 Introduction
The simulation and circuit implementation is conducted in the MATLAB 2018a platform. The circuit is same for getting any output such as step up, step down, ac voltage regulator and the regulated converter. In the step up/down converter there can be obtained any of the frequency by adjusting the switching time only.
4.2 50Hz-25 Hz Down-Converter
The down converter of output 12.5 Hz is obtained from the modified single phase matrix converter with changing its switching pattern depending the mode-1, mode-2, mode-3 and mode-4 and the simulated output is as shown in the following figure.
4.2.1 Switching Pattern
The S1&S3 go in conduction for 0 to 0.02 times and S2&S4 go in conduction form 0.02 to 0.04 times.
Figure 4.2.1:Switching pattern for the 25 Hz output
4.2.2 Output Figure
The output figure is shown below. It is shown for the one cycle of the 25Hz signal.
Figure 4.2.2: The Down-converter output frequency is 25Hz
4.3 50Hz-12.5 Hz Down-Converter
The down converter of output 12.5 Hz is obtained from the modified single phase matrix converter with changing its switching pattern depending the mode-1, mode-2, mode-3 and mode-4 and the simulated output is as shown in the following figure.
4.3.1 Switching Pattern
The output figure is shown below. It is shown for the one cycle of the 12.5Hz signal.
Fig.4.3.1:Switching pattern for the 12.5 Hz output
4.3.2 Output Figure
The output figure is shown below. It is shown for the one cycle of the 25Hz signal.
Figure 4.3.2: The Down-converter output frequency is 12.5Hz
4.4 50Hz-100 Hz Up-Converter
When we want to get the output of the 100hz frequency from a 50hz fundamental frequency as a up converter, then half of the positive input is positive which is mode-1 and other half is negative that is mode-2. In the negative portion of the output the mode-4 which makes the positive from output and the mode-3 is other half of negative portion of input that remains in the same polarity.
4.4.1 Switching Pattern
The output figure is shown below. It is shown for the one cycle of the 100 Hz signal.
Figure 4.4.1: Switching pattern for the 100 Hz output
4.4.2 Output Figure
The output figure is shown below. It is shown for the one cycle of the 100 Hz signal.
Figure 4.4.2: The Up-converter output frequency is 100Hz
4.5 50Hz-150Hz Up-Converter
The mode sequence here is mode-1, mode-2, mode-1, mode-3, mode-4 and mode-3. For the input positive half cycle the output should be divided into three parts and the first and third parts are positive and the second part is negative. Moreover, for the negative half cycle at the input the output is negative, positive, negative sequentially.
4.5.1 Switching Pattern
The output figure is shown below. It is shown for the one cycle of the 150 Hz signal.
Fig.4.5.1: Switching pattern for the 150 Hz output
4.5.2 Output Figure
The output figure is shown below. It is shown for the one cycle of the 150 Hz signal.
Figure 4.5.2: The Up-converter output frequency is 150 hz
4.6. 50Hz-200Hz Up-Converter
The 50 Hz to 200 Hz up frequency output which fourth times of the input frequency is. The on state and the off state of the s1, s2, s3 & s4 is turned off and on at a primitive measures, depending on the switching modes.
4.6.1 Switching Pattern
The output figure is shown below. It is shown for the one cycle of the 200 Hz signal.
Figure 4.6.1: Switching pattern for the 200 Hz output
4.6.2 Output Figure
The output figure is shown below. It is shown for the one cycle of the 200 Hz signal.
Figure 4.6.2: The Up-converter output frequency is 200 Hz
4.7 50Hz-1000Hz Up-Converter
Here, also the mode is calculated with either the positive is positive or negative in the output neither the negative is negative or positive at the output. The figure 4.3 represents the 1000Hz output from the input of 50Hz as a fundamental frequency.
4.7.1 Switching Pattern
The output figure is shown below. It is shown for the one cycle of the 1000 Hz signal.
Figure 4.7.1: Switching pattern for the 1000 Hz output
4.7.2 Output Figure
The output figure is shown below. It is shown for the one cycle of the 1000 Hz signal.
Figure 4.7.2: The Up-converter output frequency is 1000 Hz
4.8 Modified SPMC Used as AC Voltage Regulator
From the switching table we find the switching states of obtaining the AC voltage controller. Analyzing it with block a portion of the voltage. The blocked portion is 0.004s.
4.8.1 Switching Pattern
The output figure is shown below. It is shown for the one cycle of the AC voltage regulator signal.
Figure 4.8.1: Switching pattern for the regulated output
4.8.2 Output Figure
The output figure is shown below. It is shown for the two cycle of the regulated signal.
Figure 4.8.2: The AC Voltage Regulator
4.9 Modified SPMC Used as Controlled Rectifier
From the switching table we find the switching states of obtaining the controlled rectifier. Analyzing it with block a portion of the voltage. When the blocked portion isα= 0.004s.
4.9.1 Output Figure
The output figure is shown below. It is shown for the two cycle of the controlled rectifier signal.
Figure 4.9.1: The Controlled output of rectifier
4.10 Conclusion
All the simulation is done using the MATLAB. The output figure and the switching pattern are shown above. The output is as same as we have to get. The switching pulses are calculated for each of the output and then give the switch of the proposed converter to obtain the desired result. Any of the frequency up and down and the blocking a portion of the voltage can be possible by adjusting the switching frequency.
CHAPTER 5: RESULT AND ANALYSIS
5.1 Introduction
The simulation output is shown in the previous chapter. The development of this converter is tested with the scope of Simulink block. Moreover the THD is analyzed and the power loss calculation is another significant part of any of the conversion. The reliability and the robustness of the converter can be examined from this.
5.2 Mathematical Modeling for Different Conversion Process
It is the way to understand the result that have shown in the previous chapter. The mathematical modeling of each of the converted output can prove the outcome.
5.2.1 25 Hz Down-Converter
The mode-1 and mode-4 are operated during the one cycle of the fundamental and mode-2 and mode-3 are operated for the next 1 cycle. Thus, the respective output voltages are,
V_out=V_m sin〖θ; 0≤θ≤π〗 7
V_out=〖-V〗_m sin〖θ; π≤θ≤2π〗 8
5.2.2 12.5 Hz Down-Converter
The mode-1 and mode-4 are operated during the two cycle of the fundamental and mode-2 and mode-3 are operated for the next 2 cycle
V_out=V_m sin〖θ; 0≤θ≤2π〗 9
V_out=〖-V〗_m sin〖θ; 2 π≤θ≤4π〗 10
5.2.3 100 Hz Up-Converter
The mode-1 and mode-2 are operated during the positive half cycle of the fundamental and mode-4 and mode-3 are operated for the negative half cycle.
V_out=V_m sin〖θ; 0≤θ≤π⁄2〗 11
V_out=〖-V〗_m sin〖θ; π⁄2≤θ≤π〗 12
V_out=V_m sin〖θ; π≤θ≤3π⁄2〗 13
V_out=〖-V〗_m sin〖θ; 3π⁄2≤θ≤2〗 π 14
5.2.4 150 Hz Up-Converter
The mode-1, mode-2, mode-1 are operated during the positive half cycle of the fundamental and mode-3, mode-4, mode-3 are operated for the negative half cycle.
V_out=V_m sin〖θ; 0 ≤ θ ≤π/6;〗 15
V_out=-V_m sin〖θ; π/6≤ θ ≤π/3;〗 16
V_out=V_m sin〖θ; π/3≤ θ ≤π/2;〗 17
V_out=-V_m sin〖θ; π/2≤ θ ≤2π/3;〗 18
V_out=V_m sin〖θ; 2π/3≤ θ ≤5π/6;〗 19
V_out=-V_m sin〖θ; 5π/6≤ θ ≤π;〗 20
5.2.5 200 Hz Up-Converter
The mode-1, mode-2, mode-1, mode-2 are operated during the positive half cycle of the fundamental and mode-3,mode-4, mode-3,mode-4 are operated for the negative half cycle.
V_out=V_m sin〖θ; (0 ≤ θ ≤ π/8),( π/4≤ θ ≤ 3π/8);〗 21
V_out=〖-V〗_m sin〖θ; (π/8≤ θ ≤ π/4),( 3π/8≤ θ ≤ π/2);〗 22
V_out=V_m sin〖θ; (π/2≤ θ ≤ 5π/8),( 3π/4≤ θ ≤ 7π/8);〗 23
V_out=〖-V〗_m sin〖θ; (5π/8≤ θ ≤ 3π/4),( 7π/8≤ θ ≤ π);〗 24
5.2.6 Controlled Rectifier
For the following result the α portion of the rectifier output is blocked and the equation will be
V_out=V_m sin〖θ; α≤ θ ≤π/2;〗 25
V_out=V_m sin〖θ; π/2+α≤ θ ≤ π;〗 26
5.2.7 AC Voltage Regulator
For the following result the α portion of the rectifier output is blocked and the equation will be
V_out=V_m sin〖θ; α≤ θ ≤π/2;〗 27
V_out=〖-V〗_m sin〖θ; π/2+α≤ θ ≤ π;〗 28
5.3 Total Harmonic Distortion Analysis
The THD is analyzed with the help of MATLAB Simulink. The graph of the magnitude of THD vs. frequency is generated for each of the conversion. THD graphs are shown below.
Figure 5.3: THD graph of 100 Hz and 25 Hz frequency converter.
The comparison table of the up converter and down converter based on THD between the conventional and proposed is shown below.
Table 5.3: Table of Voltage THD differences of SPWM & UFNTWM
Frequency THD of SPWM THD of Proposed Modulation Technique
12.5 85.91% 73.51%
25 91.74% 65.79%
100 104.93% 67.52%
150 60.93% 45.54%
200 67.74% 47.09%
1000 345.80% 53.09%
5.4 Power Loss Calculation
Three types of losses, including conduction loss (PC) and switching loss (PS), are primarily introduced by the proposed matrix converter. The key causes of power losses are then estimated in the following subsections, including conduction losses and switching losses. The conduction losses are analyzed both the switch and the diode. The operation is executed in this section for any of the output waveform.
The conduction losses within a device are caused by the circuit elements' transient impedances, including the switches (Rsw_on) and the diodes (RD_on) internal on-state resistances. The conduction losses incurred by the switch and diode transient resistances can therefore be determined using the following equations.
P_CS=V_SO.I_SA+R_SO.I_SR^2 29
P_CD=V_DO.I_DA+R_DO.I_DR^2 30
Here, in this following equation the P_CS means the switch conduction loss and the P_CDis the diode conduction loss.R_SO,R_DO are the RB-IGBT and the diode on resistance. The I_SA,I_DA represents the switch and diode average current and .I_SR,I_DR is the rms current. The V_SO and V_DO defines the voltage at the saturated states of the switch and diode sequentially.
5.4.1 Step Down Matrix-Converter
From the fundamental 50 hz frequency the output of the converter is 12.5 hz. The pair of diodes and switches are conducted 8 times for completing an entire cycle. So for this the conduction loss will be as in the following equation,
P_(CL_12.5 )=16P_CS+16P_CD 31
Here the P_CS and the P_CD are from equation (25)and (26). The P_(CL_12.5 )represents the conduction loss of the 50-12.5 Hz step down single phase matrix converter.
Creating the output frequency of the 25 Hz, The pair of diodes and switches and switches are conducted 4 times for completing an entire cycle. So for this the conduction loss will be as in the following equation,
P_(CL_25 )=8P_CS+8P_CD 32
Here the P_CS and the P_CD are from equation (25) and (26). The P_(CL_25 )represents the conduction loss of the 50-25 Hz step down single phase matrix converter.
5.4.2 Step Up Matrix-Converter
The up converter rises the fundamental frequency. For converting the fundamental frequency to the 100 Hz, 150Hz, 200Hz and any other increased frequency the power loss generalized equation can be obtained from the following equation as the pair of diode and switch are conducted 2 times.
P_(CL_up )=4P_CS+4P_CD 33
This conduction loss is equal to the conduction loss in down converter when we converted the fundamental to 100 Hz,150Hz,200Hz,1000Hz and any other as described before.P_(CL_up) represents the conduction loss at up converter.
Regulated Rectifier & Voltage Regulator: A pair of switch go to conduction for 2 times and four diode is conducted for this purpose. Moreover, for the regulator of AC voltage the combination of four switches and four diodes are used. Thus the conduction loss is same as the regulated rectifier. The conduction loss is calculated with the following equation,
P_(CL_RR_vc)=4P_CS+4P_CD 34
Here P_(CL_RR_vc) represents the regulated rectifier and controlled voltage conduction loss.
5.4.3 Switching Loss Calculation
Another concern for calculating the power loss is the switching loss. The soft semiconductor switch (IGBT) has a significant amount of power loss when mixing the off state voltage and current. The turn on and turn off process is not ideal. The following equation can be made for calculating these two losses.
P_l=∑_(L=1)^L▒〖P_(s_on )+P_(s_off ) 〗 35
Here, v_0 is the voltage of off state and the f_s is known as the switching frequency.
Figure 5.4: Power loss profile of The SPMC Matrix Converter.
From the above figure the Ps and Pc represents the switching loss and the conduction loss.
5.5 Conclusion
The results are analyzed based on the harmonic distortion and power loss of the converter. The harmonic distortion is much lower than that of the conventional has for each conversion. The power loss is calculated and the loss profile is shown in the previous section. The loss is also minimized.
CHAPTER 6: CONCLUSION AND FUTURE WORK
6.1 Introduction
The design and development of the single phase matrix converter is down with lower number of semiconductor switch and diode. The output waveform obtained from the scope to ensure the output. The analysis is done in the previous chapter.
In my work, a new converter topology with reduced number of semiconductor switches has been suggested that has vast application areas including electric traction, induction heating, AC and DC variable power supply, etc. In the above parts, the circuit layout, the switching scheme and the operating theory of this converter were sequentially clarified with the necessary figures.
Another part of my thesis was to improve the power quality with the new modulation technique that has represented clearly with the THD reduction basis. The new modulation reduce THD in a significant manner. It has lower cost of equipment, achieves lower losses than current topologies with increased energy transfer performance, and has a very low degree of complexity of the gate driver. It can therefore be inferred that the proposed updated matrix converter is extremely compatible with electrical traction, induction heating, variable power supplies for AC and DC, etc.
In the later sections, the performances of the presented converter have been evaluated with simulation with MATLAB 2018a.
6.2 Future Scope of Development
• The three phase matrix converter can be designed with the reduced number of switch count.
• The three to five phase converter can be generated with the lower amount of switch.
• The single phase to three phase matrix converter can be designed with reduced number of switch
• The new modulation technique can be analyzed for the reduction of THD more.
6.3 Conclusion
The modified single phase matrix converter is developed with only four switch and four diode. The converter can be more effective for lower and middle level industrial production. It will reduce the cost of implementation. Development of the modulation schemes because a vital effect of reducing THD and the power factor is improved.
REFERENCES
Author
Parag Mazumder, Roll # 1504033, Department of Electronics & Telecommunication Engineering, Rajshahi University of Engineering & Technology, Bangladesh
Thesis, Novel, Single-Phase-Ac, Ac-Matrix-Converter, Single, Phase, Matrix, Converter, Topology, Bi-Directional, Switch, AC, Voltage, Regulator, Controlled, Rectifier, Mathematical, Modeling, Different, Conversion, Process
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