AbstractâThis paper presents the state of the art in the field of three-phase voltage source PWM rectifier with reduced input harmonics and unity power factor.
Modeling and Control of Three-phase Voltage Source PWM Rectifier Yao Chen, XinMin Jin School of Electrical Engineering, Beijing Jiaotong University, Beijing, China
Abstract—This paper presents the state of the art in the field of three-phase voltage source PWM rectifier with reduced input harmonics and unity power factor. The working principle, modeling procedure, corresponding control strategy as well as typical waveforms are introduced in detail which can provide some guidelines for engineers to analyze, design and implement. Keywords-modeling; control strategy; unity power factor; PWM rectifier; power electronics
I.
INTRODUCTION
The ac/dc conversion is used increasingly in a wide diversity of applications such as power supplies for microelectronics, battery management, motor drives, etc. The simplest rectifier uses diodes to transform the electrical energy from ac to dc side. And then thyristors are used to control the energy flow. However these linecommutated rectifiers generate large amount of harmonics and reactive power which can serious pollute the power grid. Although multipulse connections or passive power filters can reduce grid current harmonics to some extent, these methods will greatly increase the volume and the cost which are not desired [1]. Another conceptually different way of harmonics reduction is to adopt new topologies which naturally possess the function of power factor correction. PWM rectifier is one of the most popular topologies which can obtain unity power factor or any active-reactive power combination. PWM rectifiers can be classified as singlephase, three-phase, voltage source and current source rectifier. In recent years, three-phase voltage source PWM rectifier obtained widely application in machine drives and power generation [2]-[4]. This paper is dedicated to this special type of rectifier. Working principle, modeling procedure, corresponding control strategy as well as typical waveforms are introduced in detail which can give some guidelines for engineers to analyze, design and implement three-phase voltage source PWM rectifier. II.
POWER CIRCUIT AND WORKING PRINCIPLE
The power circuit of three-phase voltage-source PWM rectifier (VSR) is showed in Fig. 1 where L is the value of the inductors, R their equivalent resistance and C the value of the dc-side capacitor. Inductances are inserted between
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Figure 1. Power circuit of three-phase voltage source PWM rectifier.
grid and converter and insulated gate bipolar transistors (IGBTs) are adopted as the controlled power switches, which are the major differences compared with traditional rectifiers. The basic operation principle of VSR is to keep the load dc-link voltage Vdc at a reference value Vdc* meanwhile obtain desired grid side power factor. This reference dclink voltage value has to be high enough to keep the diodes of the converter blocked, e.g., in three-phase 380V system, Vdc* must be higher than 2 × 380V = 537V . Once this condition is satisfied, the dc-link voltage is measured and compared with the reference. The error signal generated from this comparison is used to switch ON and OFF the valves of the VSR. When the dc load current io is positive during rectifier operation, the capacitor C is being discharged, and the error signal becomes positive. Under this condition, the control block takes power from the supply by generating the appropriate PWM signals for the six power switches of the VSR. In this way, current flows from the ac to the dc side, and the capacitor voltage is recovered. Inversely, when io becomes negative during inverter operation, the capacitor C is overcharged, and the error signal requires the control block to discharge the capacitor by returning power to the ac mains. To make the rectifier work properly, the frequency of fundamental of converter side voltage ux must be the same with the power source ex, x=a,b,c. Changing the amplitude of this fundamental, and its phase shift with respect to the mains, the rectifier can be controlled to obtain any activereactive power combination. There are mainly four kinds
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of operate modes: unity power factor rectifier, unity power factor inverter, capacity operation at zero power factor and inductor operation at zero power factor [5]. The corresponding waveforms and phasor diagrams are showed in Fig. 2. Obviously, the inductance L plays an extremely importance role in every operation mode. First, the induced voltage it generates allows the VSR working in boost style, which makes dc-link voltage higher than the magnitude of the main so as to block the diodes and working properly. Second, the inductance also works as a filter, which can maintain ac current almost sinusoidal, reducing harmonic contamination to the power supply. III.
SYSTEM MODELING
Considering the displayed variables on the circuit of Fig.1, applying Kirchhoff laws, the following differential equations of the VSR in the three-phase reference frame can be obtained [6]:
R 1 1 dia dt = − L ia − L u a + L ea R 1 1 dib = − ib − ub + eb dt L L L dic R 1 1 dt = − L ic − L uc + L ec
(1)
By transforming three-phase grid voltage and current of VSR into d-q rotating reference frame synchronized with K the main and aligning the d axis on grid voltage vector E , we can obtain the time-invariant model of VSR as follow,
where ed=E, eq=0 and hence be omitted in the equations.
R 1 1 did dt = − L id + ωiq − L u d + L ed (2) diq = − R i − ωi − 1 u q d q dt L L Considering a symmetrical three-phase system, the transform matrix can be defined as follow where the voltage and current variables are represented by v and θ=ω t is the angle between a-axis and d-axis. 0 v sin θ 1 1 2 a (3) cos θ vb 3 3 The relationship among stationary and rotating reference frames is showed in Fig. 3 where ds-qs represents bi-phase stationary reference frame. According to (2), we can obtain the equivalent circuits of the VSR in d-q vector space showed respectively in Fig. 4 (a)and (b) where ωLid and ωLiq can be regarded as the additional voltage due to axis transformation. v d cos θ = v q − sin θ
IV.
CONTROL SCHEME AND TYPICAL WAVEFORMS
In the steady state, id and iq are constant components so their derivatives equal to zero. Ignore the equivalent resistance R which is always small, we can obtain the steady state control function according to (2):
a)
Figure 3. Relationship among stationary and rotating reference frames.
b)
a) c)
d)
b)
Figure 2. Four modes of operation of the three-phase voltage source PWM rectifier. (a) Unity power factor rectifier. (b) Unity power factor inverter. (c) Capacity operation at zero power factor. (d) Inductor operation at zero power factor.
Figure 4. Equivalent circuits in d-q vector space. (a) d-axis equivalent circuit. (b) q-axis equivalent circuit.
u d = ed + ωLi q u q = −ωLid
(4)
Feedback control components should be added into (4) in order to keep dc-link voltage and ac current at the desired value. Linear control technique such as the PIbased method has been widely applied to both of them. The PI-based control structure is showed in Fig. 5
a unity power factor rectifier. Fig. 7 represents the grid side voltage and current waveforms when VSR is operating as a unity power factor inverter. Fig. 8 shows the voltage waveforms on grid side inductance and Fig. 9 shows the waveform of converter side line voltage uab. Waveforms of three-phase upper valves’ switching signals generated by SVPWM with lower-pass filter are showed in Fig 10, which can be used to verify the correctness of SVPWM module.
where id* and iq* are the reference current components in d-q frame. This control structure is defined as ‘cascade’ because the dc voltage controller in outer loop calculates the reference value id* for the d-axis current controller and in the inner loop id is controlled to perform the dc-link voltage regulation while iq is controlled to obtain a desired power factor. For unity power factor application
iq* should be set to zero. SVPWM can be applied directly to generate ON and OFF switching signals right after we obtain the value of u d and u q . Hence the total control equations can be obtained as follow. k vp , k vi , k ip and k ii are proportional and integral gains of voltage and current loop respectively. These parameters can significantly influent the system stability as well as dynamic performance. Generally, the voltage loop parameters are selected according to ‘symmetrical optimum’ criterion to obtain optimum regulation and stability while the current loop parameters are selected according to ‘technical optimum’ criterion provides a good control of the overshot to the step change of the reference [7], [8].
i * = k (V * − V ) + k (V * − V ) dt vp dc dc vi dc dc d i * = 0 q (5) * * u d = ed + ωLi q − k ip (id − id ) − kii (id − id ) dt u q = −ωLid − k ip (iq* − iq ) − k ii (iq* − iq ) dt Some typical waveforms obtained by simulations and experiments are given respectively. The grid-side line voltage rms is 380V, dc-link voltage is 700V and the power stage is 5KW. Fig. 6 represents the grid side voltage and current waveforms when VSR is operating as
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V.
This paper has reviewed the state of the art in the field of three-phase voltage source PWM rectifier. The working principle, modeling procedure, control scheme and typical waveforms have been completely introduced to provide some guidelines for the analysis and design. With the sustained theoretical and technological development, three-phase voltage source PWM rectifier will be even widely accepted in industry. REFERENCES [1]
Figure 5. PI-based control structure with d-q axis oriented cascade control of three-phase voltage source PWM rectifier
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CONTROL SCHEME AND TYPICAL WAVEFORMS
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a) Voltage: 100V/div; Current: 10A/div
a) Voltage: 200V/div
b) Voltage: 100V/div; Current: 10A/div; Time: 5ms/div
b) Voltage: 200V/div; Time: 2.5ms/div
Figure 6. Grid side voltage and current waveforms at rectification state. (a) Simulation waveform. (b) Experiment waveform.
a) Voltage: 100V/div; Current: 10A/div
b) Voltage: 100V/div; Current: 10A/div; Time: 5ms/div Figure 7. Grid side voltage and current waveforms at inversion state. (a) Simulation waveform. (b) Experiment waveform.
Figure 8. Voltage waveforms on grid side inductance. (a) Simulation waveform. (b) Experiment waveform.
Figure 9. Waveform of converter side line voltage. Voltage: 500V/div; Time: 5ms/div
Figure 10. Three-phase upper valves’ switching signals generated by SVPWM with low-pass filter. Time: 10ms/div
