International Journal of Electrical and Electronics Engineering Research (IJEEER) ISSN(P): 2250-155X; ISSN(E): 2278-943X Vol. 4, Issue 6, Dec 2014, 65-76 © TJPRC Pvt. Ltd.
MATLAB / SIMULINK IMPLEMENTATION AND COMPARATIVE ANALYSIS OF THREE PHASE SINUSOIDAL PWM AND DIRECT POWER CONTROL TECHNIQUES KAVITA NAGAR, ASHOK KUMAR SHARMA & D. K. PALWALIA Department of Electrical Engineering, University College of Engineering, Rajasthan Technical University, Kota, Rajasthan, India
ABSTRACT This paper presents the comparative analysis of sinusoidal Pulse width modulation (SPWM) technique and direct power control (DPC) Pulse width modulation technique for three-phase AC to DC converters using MATLAB/SIMULINK software. Pulse width modulation (PWM) techniques are frequently used due to improved performance such as unity power factor operation with reduced total harmonic distortion (THD) at ac mains. In this paper simulation models for both PWM techniques are simulated with closed loop at rated load condition and then comparative analysis has been done in terms of input current THD and power factor. DPC is the efficient technique because of the better performance.
KEYWORDS: Direct Power Control, Pulse Width Modulation, Sinusoidal PWM, THD, Unity Power Factor INTRODUCTION The AC/DC power converters are extensively used in various applications like household electric appliances, power conversion, dc motor drives, adjustable-speed ac drives, power supplies like SMPS and UPS and so on. The main problems faced by the power electronic design engineers are about the reduction of harmonic content in low or medium power applications. Normally the input voltage to an AC-to-DC converter is sinusoidal but the input current is non-sinusoidal i.e. harmonic currents are present in the ac lines. The harmonic content of the input current is dependent on the size and type of the line filter, switching frequency, selected control and modulation schemes and the waveform of the line voltage. Harmonics have a negative effect on the operation of the electrical system and the power factor as well therefore; an increasing attention is paid to their generation and control. . Unity power factor with lower harmonic current or low input current total harmonic distortion (THD) and fixed DC output voltage with minimum ripple are the important parameters in rectifier. A pulse width modulation (PWM) approach serves all these purposes. The PWM is a very advance and useful technique in which width of the gate pulses are controlled by various mechanisms. PWM shift the frequency of the dominant harmonics to a higher value, so that they can easily filter harmonics by employing a small passive filter [1]-[8]. Most commonly used PWM technique is SPWM in which a triangular carrier wave is compared with sinusoidal wave to generate PWM switching pulses [9]. Recently, however, new control approaches such as direct power control (DPC) based PWM technique have also emerged to implement a high-performance. In DPC the control signal is based on instantaneous active and reactive power. The instantaneous active and reactive power is calculated through input parameters, DC link voltage and switching signal. The switching sequences are selected from switching table by sector number and digital form of active and reactive power. By using such advance PWM control technique the input current can be made nearly sinusoidal with minimum THD and unity power factor operation can also be achieved [14].
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Kavita Nagar, Ashok Kumar Sharma & D. K. Palwalia
SINUSOIDAL PWM (SPWM) In sine-triangle PWM, three phase sinusoidal reference modulating signals are compared against a common triangular carrier to generate PWM switching gate triggering pulses for the three phases. The converter switching frequency is governed by the frequency of the triangular waveform and this carrier frequency is very high compared to the frequency of modulating signal. The frequency of reference signal controls the modulation index m, rms voltage Vrms and output voltage Vo. The number of pulses per half cycle depends on carrier frequency. The triangle waveform frequency or switching frequency controls the speed at which the switches are turned off and on. The magnitude and frequencies of the fundamental component in the line side are controlled by changing the magnitude and frequency of the modulating signal. It is simple and linear between 0% and 78.5% of six step voltage values, which results in poor voltage utilization [10]-[13]. Figure 1 shows block diagram of sinusoidal PWM converter. Generally, the control structure of a three-phase six-switch PWM boost converter consists of double close loop with an inner current control loop and an outer voltage control loop. The line inductors provide energy storage and allow the rectifier to operate in a boost configuration. The switching pulses are generated by current mode control scheme which is shown in Figure 2.
Figure 1: Block Diagram of Three-Phase Sinusoidal PWM Boost Converter
Figure 2: Control Circuit of Current Mode Control Scheme for SPWM Converter
Impact Factor (JCC): 5.9638
Index Copernicus Value (ICV): 3.0
MATLAB / SIMULINK Implementation and Comparative Analysis of Three Phase Sinusoidal PWM and Direct Power Control Techniques
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A current-mode control scheme is required for the line currents. The DC bus voltage is controlled by comparing of measured DC voltage to the reference DC voltage. This error signal is passed through a PI controller which then forms the current amplitude reference required for all three inner current control loops. The current controller senses the input current and compares it with sinusoidal reference currents. The current amplitude reference is multiplied by three sinusoidal templates each with a 120° phase apart to form the true current references. For unity power factor operation it is required that each sinusoidal reference is in phase with the respective supply phase voltage. The inductor current is measured and compared to a reference signal. The error is passed through a proportional and integral (PI) controller providing high gain at low frequencies, but having a filtering effect on the high-frequency ripple current. The constants of the PI controllers are set by hit and trial method to produce a stable system with good response. Now, this signal is compared to a triangular carrier wave to generate the required PWM signal to control the switches. This technique has excellent features, like real-time control and easily obtained drive signals. Merits are simple to implement, easy to control etc. Demerits are dc link voltage ripple introduces additional output ripple, high THD, low input power factor at low and medium power applications.
DIRECT POWER CONTROL (DPC) From the energy point of view, when AC voltage is given, if the instantaneous power of PWM rectifier is controlled within the allowable range, the instantaneous current within the allowable range can be controlled indirectly, and such control technique is known as the direct power control (DPC). The DPC technique for PWM converter was proposed by the inventors of the direct torque control (DTC). DPC is based on the direct control of the instantaneous active and reactive power in a manner analogous to the torque and the flux control of the DTC. In DPC, instantaneous active and reactive powers are estimated based on line voltage. It does not produce sinusoidal current when the line voltage is distorted. Similar to the DTC, there are neither internal current control loops nor pulse width modulator block with fixed switching frequency, because the converter switching states are appropriately selected by using a switching table and hysteresis comparators for the instantaneous errors between reference and estimated values of the active and reactive power. The accurate and fast estimation of the active and the reactive power is of primary importance in the DPC. Structure of DPC rectifier system contains the DC voltage outer loop and power control inner loop, and it selects switches in the switching table according to the AC-side instantaneous power to achieve low total harmonic distortion (THD) and high power factor at low power ratings applications also [14]-[15]. Applications including wind mill and micro turbine driven generators, solar arrays and fuel cells as primary energy sources are already or will in the near future be at commercial stage. A block diagram for DPC is shown in Figure 3. This block diagram has three main blocks; power estimator, sector estimator and switching table. The output voltage is compared with reference voltage in the PI controller (Im). The power estimator block has two inputs (input supply & Im) and it estimates Vα and Vβ. The 12 sector are calculated from estimated Vα and Vβ. These reference currents are wished to be the actual currents in the next switching period. DPC block calculate the instantaneous real power, reactive power and Vα and Vβ. The real power trigger is compared between instantaneous real-power calculated from dc side. As similarly, reactive power trigger are compared between instantaneous reactive power and null because of set to obtain unity power factor. Finally firing pulses are selected through sector number, and digital form of real power trigger and reactive power trigger.
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Kavita Nagar, Ashok Kumar Sharma & D. K. Palwalia
Figure 3: Block Diagram of Direct Power Control PWM Converter [14] The instantaneous active and the reactive power are estimated by [15], [16].
p = L(
q=
dia di di ia + b ib + c ic ) +Udc (Sa + Sb + Sc ) dt dt dt
1 dia dic 3L( ic − ia ) −Udc[Sa (ib −ic ) +Sb(ic −ia ) +Sc (ia −ib )] dt 3 dt
(1)
(2)
It is obvious that the first part of both equations represents the power in the line filter inductors and the last part gives the power of the rectifier. The equations can also be interpreted such that the line voltages are estimated by adding the voltage losses in the line filter inductors to the phase voltages of the rectifier bridge and then calculating the active and the reactive power from equation (1) and equation (2), respectively. The instantaneous active and reactive powers are defined by the product of the three-phase voltages and currents. The active power, p is the scalar product of the current and the voltage, whereas the reactive power, q is calculated as a vector product of them. However, once the estimated values of active and reactive power are calculated and the ac-line currents are known, the line voltages can easily be calculated as follows. Instantaneous active power of the three-phase circuit can be defined as
p = uα iα + u β i β
(3)
Similarly instantaneous reactive power can be defined as
q = uα × iβ + uβ × iα
(4)
From equation (3) and equation (4), the conventional instantaneous active power p and the instantaneous reactive power q are expressed by [17]:
p iα iβ uα = q −iβ iα uβ
(5)
The α -β voltages can be obtained from the above equation
Impact Factor (JCC): 5.9638
Index Copernicus Value (ICV): 3.0
MATLAB / SIMULINK Implementation and Comparative Analysis of Three Phase Sinusoidal PWM and Direct Power Control Techniques
uα 1 = 2 2 uβ i α + i β
iα iβ
−i β p iα q
69
(6)
Where uα, uβ are the estimated values of the three-phase voltages ua, ub and uc, in the fixed α-β reference frame. iα, iβ are the measured three-phase currents ia, ib and ic in the fixed α-β reference frame. DPC is based on the instantaneous active and reactive power control loops. The converter switching states are selected by a switching table is based on the instantaneous errors between the commanded and estimated values of active and reactive power. The commands of reactive power qref (set to zero for unity power factor) and active power pref (delivered from the outer PI dc voltage controller) are compared with the estimated q and p values, in reactive and active power hysteresis controllers, respectively. Errors between the commands and the estimated feedback power are input to the hysteresis comparators and are digitized to the signals dp and dq [14]. The digitized output signal of the reactive power controller is defined as [18], [19]: dq = 1 for q < qref – Hq
(7)
dq = 0 for q > qref + Hq
(8)
and similarly of the active power controller as dp = 1 for p < pref - Hp
(9)
dp = 0 for p > pref + Hp
(10)
Where Hq & Hp are the hysteresis bands. Also, the phase of the power-source voltage vector is converted to the digitized signal θn. For this purpose, the complex plane is divided into twelve sectors in DPC, as shown in Figure 4.
Figure 4: Sector Selection for DPC The sectors can be numerically expressed as: (n −2) π/6 ≤ θn < (n −1) π/6 Where number of sectors n = 1, 2...12 [14] [18]-[20]. It is found that twelve sector method results in a better instantaneous power tracking than the six-sector method. Moreover, usually two level hysteresis comparators are applied in DPC for both active and reactive power. By using several comparators, it is possible to specify the sector where the voltage vector exists. The digitized error signals dp and dq and digitized voltage phase θn are input to the switching table in which every switching state, SA, SB and SC, of the converter is stored, as shown in Table 1. www.tjprc.org
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Kavita Nagar, Ashok Kumar Sharma & D. K. Palwalia
Table 1: Switching Table for DPC Sp 1 1 0 0
Sq 0 1 0 1
θ1 101 111 101 100
θ2 111 111 100 110
θ3 100 000 100 110
θ4 000 000 110 010
θ5 110 111 110 010
θ6 111 111 010 011
θ7 010 000 010 011
θ8 000 000 011 001
θ9 011 111 011 001
θ10 111 111 001 101
θ11 001 000 001 101
θ12 000 000 101 100
According to the combination of the digitized input signals, using this switching table, the optimum switching state of the converter can be selected uniquely in every specific moment. The selection of the optimum switching state is performed so that the power errors can be restricted within the hysteresis bands [20]. An important point has to be noted that the sampling frequency has been about few times higher than the average switching frequency for precise control of instantaneous active and reactive power and also for limiting the errors by the hysteresis band. This technique deals with instantaneous variables, therefore, estimated values contain not only a fundamental but also harmonic components. This feature improves the total power factor. The instantaneous active and reactive power depends on position of converter voltage vector. It has indirect influence on inductance voltage as well as phase and amplitude of line current. Therefore, different pattern of switching table can be applied to DPC [14]. It influences control condition as instantaneous power and current ripple and switching frequency. For drives, there exist more switching table techniques because of wide range of output frequency and dynamic demands. The advantages and disadvantages of DPC technique are as follows:
ADVANTAGES •
No separate voltage modulation block
•
No current regulation loops
•
No coordinate transformation
•
Improved dynamics
•
Simple algorithm
•
Decoupled active and reactive power control
•
Instantaneous variables are estimated with all harmonic components (improvement of the power factor and efficiency).
DISADVANTAGES •
Variable switching frequency
•
High values of line inductance and sampling frequency are needed (because smooth shape of the current waveform is required)
•
Power and voltage estimation should be avoided at the moment of switching (it yields high errors)
•
Fast microprocessor and A/D converters required.
SIMULATION AND RESULTS The simulation has been done using MatLab/Simulink software which it is easy to implement. Impact Factor (JCC): 5.9638
Index Copernicus Value (ICV): 3.0
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MATLAB / SIMULINK Implementation and Comparative Analysis of Three Phase Sinusoidal PWM and Direct Power Control Techniques
Various Parameters Used for Simulation Study: AC input voltage (peak) = 230V Supply frequency = 50Hz Rated output power =7.5 kW (Load resistance = 40Ω, Load inductance = 2mH) DC reference voltage = 550V Sinusoidal PWM The output DC link voltage is measured from voltage and current meter block. The DC link and source side voltage and current waveforms of the SPWM for a switching frequency of 10 KHz are shown in Figure 5 and Figure 6 respectively. The input current THD is taken from POWERGUI block of SIMULINK. The FFT analysis of the source current is depicted in Figure 7. The total harmonic distortion of the source current comes out to be 3.68% so satisfied IEEE standard. The input power factor is calculated from functional block active and reactive power from the simulink model.
Figure 5: Output Voltage (V) & Output Current (A) Waveform of SPWM at Rated Load with Switching Frequency Fs=10 Khz
Figure 6: Input Voltage (V) & Input Current (A) Waveform of SPWM at Rated Load with Switching Frequency Fs=10 Khz
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Kavita Nagar, Ashok Kumar Sharma & D. K. Palwalia
Figure 7: FFT Analysis of Input Current (A) Of SPWM at Rated Load with Switching Frequency Fs=10 Khz Direct Power Control PWM Figure 8 shows the sector selector for DPC. Switching pulses are selected through the digital form of power triggers and sector number by using direct look up table in MATLAB.
1 delta Valpha 2 delta Vbeta
Scope5 atan2
floor
1 Sn
2*pi
Switch
Look-Up Table
Constant
Scope1
Scope4
Figure 8: Simulink Block Diagram of Sector Selector for DPC The output DC link voltage is measured from voltage and current meter block. The DC link and source side voltage and current waveforms of the DPC for a switching frequency of 10 KHz are shown in Figure 9 and Figure 10 respectively. The input current THD is taken from POWERGUI block of SIMULINK. The FFT analysis of the source current is depicted in Figure 11. The total harmonic distortion of the source current comes out to be 0.60% so satisfied IEEE standard. The input power factor is calculated from functional block active and reactive power from the simulink model.
Figure 9: Output Voltage (V) & Output Current (A) Waveform of DPC at Rated Load Condition Impact Factor (JCC): 5.9638
Index Copernicus Value (ICV): 3.0
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MATLAB / SIMULINK Implementation and Comparative Analysis of Three Phase Sinusoidal PWM and Direct Power Control Techniques
Figure 10: Input Voltage (V) & Input Current (A) Waveform of DPC at Rated Load Condition
Figure 11: FFT Analysis of Input Current (A) of DPC at Rated Load Condition
CONCLUSIONS The proposed work presents the comparative analysis of SPWM and DPC based three-phase AC to DC PWM converters. Both techniques are simulated using MATLAB/SIMULUINK software and their performance is compared in terms of input power factor and input current THD value at rated load condition. From the Simulation, at rated load condition, the power factor obtained for SPWM is 0.9972 and unity power factor is obtained for DPC based PWM technique. From the FFT analysis, at rated load condition, the input current THD obtained is 3.68% and 0.60% for SPWM and DPC based PWM techniques respectively. From these simulation results it is concluded that unity power factor operation with very low input current THD is obtained by DPC based PWM technique so that the improved performance is obtained in DPC technique compared to SPWM.
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Index Copernicus Value (ICV): 3.0
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