Abstract -- This paper investigates a virtual flux control for reducing the number of sensors in the direct power control of a three phase ac-dc voltage source converter. The usage of input ac voltage sensors to determine the grid voltage angle for synchronization and estimation of the instantaneous active and reactive powers, are avoided by applying a virtual flux concept in the control scheme. The virtual flux control technique is used to extract the grid voltage from the converter switching states, dc output voltage, and line currents. An improved virtual flux direct power control utilizing the new switching table has been proposed in this work. The switching table is developed based on the instantaneous power derivative method which relies on the sign and magnitude of the change in instantaneous active and reactive powers. The steady state as well as dynamic performances of the proposed system are presented and analyzed by means of Matlab simulation and experimental verification.
Index Terms--virtual flux control, direct power control, ac-dc converter, instantaneous active and reactive power, switching table.
I. INTRODUCTION The increasing usage of power diode and thyristor
rectifiers for ac to dc conversion is becoming a problem in transmission and distribution lines due to the harmonic and reactive currents they inject into the system. The non-sinusoidal shape of the input current drawn by the conventional ac-dc converter (rectifier) generates significant harmonic components which will result in increasing the volt-ampere rating of the utility equipment such as generators, transmission lines and transformers. International technical organizations and government agencies have introduced standards and regulations such as IEEE 519 and IEC 61000, to maintain the voltage and current quality of utility grids at accepted levels [1]. Therefore, front-end three phase bidirectional ac-dc converters are becoming more and more attractive in utility-interfaced applications such as high performance adjustable speed drives due to the numerous advantages. They provide low harmonic content in line currents which leads to the achievement of almost sinusoidal input currents, controllable power factor and dc-link voltage, regeneration capability, and excellent steady state and dynamic performances. The converter must be controlled properly in order to achieve proper power flow regulation in the power conversion system. Various control strategies have been proposed in recent years on the ac-dc converter. The
control strategies include the phase and amplitude control (PAC) [2], hysteresis current control (HCC), voltage-oriented control (VOC) [3], predictive control [4-5], and direct power control (DPC) [6-8] methods.
In general, the conventional control techniques of an ac-dc converter require three types of sensors such as three current sensors to measure 3-phase input currents, three voltage sensors to measure 3-phase input voltages and a dc voltage sensor to measure the dc-link output voltage. Using all of these sensors will cause the system to be bulky and expensive. In addition, the sensing signal is usually subject to high frequency noise and interference. Any incidental misreading of a signal caused by a failed sensor may decrease the system reliability and performance. Therefore, it is desirable to reduce the number of sensors to the minimum possible.
In reference [9] the authors eliminate the employment of ac input voltage sensors by estimating the three-phase grid voltage through the computation of the time derivative of measured currents. The authors combined the input voltage source estimation method with the DPC strategy to operate the three-phase ac-dc converter. The basic idea of DPC is a direct control of active and reactive powers without any internal current control loop and pulse width modulator. The switching states are selected via a switching table. The states are chosen based on the instantaneous error between the estimation and the desired active and reactive power. The accurate and fast estimation of the active and reactive power is required in the DPC scheme to achieve satisfactory performance. The computation of the time derivative of measured currents may become noisy especially if the calculation was made at the instant of power semiconductor devices changing their switching states. As a result, large errors in the calculation of both instantaneous active and reactive power will occur.
A virtual flux control concept is introduced in [10] to estimate both the three phase grid voltage and the input instantaneous active and reactive powers. The estimation procedures are much more reliable, since no differential operations are involved. Subsequently, a lower sampling frequency can be used during real-time implementation. The authors propose to combine the grid virtual control concept with the DPC scheme to operate the ac-dc converter. The key to a successful operation of the DPC utilizing a virtual flux
control is dependent on the effectiveness of the virtual flux estimation procedure and the selection of the converter switching states. However, no further explanation is given by the authors regarding the development of any switching look-up table.
Therefore, the objective of the proposed paper is to bridge that gap by introducing a systematic approach to the development of a new switching look-up table for virtual flux control of the active and reactive powers. This is obtained by differentiating the active and reactive power equations. In this way, the switching table is able to choose the best converter voltage vector in order to ensure smooth control of instantaneous active and reactive powers. In addition, this paper introduces a method to compensate for the magnitude and phase errors of the virtual flux estimation procedure which is done by using a low pass filter. Those errors are undesirable since they can generate an incorrect selection of the voltage vectors from the switching look-up table.
II. MODELLING OF THE THREE PHASE AC-DC CONVERTER
The topology of the three phase bidirectional ac-dc voltage source converter is shown in Fig. 1. The converter is connected to the three phase ac power supply via a smoothing inductor L and internal resistance R for each phase. The inductance acts as a line filter for smoothing the line current with minimum ripples. Insulated gate bipolar transistors (IGBTs) are used as the converter bidirectional switches. The latch-less IGBT switches have features of high power rating, simple gate drives requirement and suitability for high frequency switching applications. It is assumed that a pure resistive load RL is connected across the dc-link capacitor C.
By assuming a balanced three phase and three wires system, the voltage and current equations of the PWM controlled rectifier can be described by equations (1) and (2):
(1)
(2)
where is the three phase voltage supply, is the three phase line current, is the three phase converter pole voltage, Sa,b,c is the switching state of the converter and, Vdc is the dc-link output voltage. The phase voltages at the poles of the converter are equal to: (3)
(4)
(5)
Any three phase electrical quantities in abc-coordinates which are defined by can further be transformed into stationary αβ -coordinates by using the transformation matrix given in equation (6):
(6)
III. DIRECT POWER CONTROL BASED ON GRID VIRTUAL FLUX ESTIMATION
A. The concept of virtual flux The concept is based on the assumption that both the utility
grid and the converter line filters behave as a virtual ac machine [10]. Therefore, the resistance and the inductance of the line filter are equivalent to the phase resistance and the leakage inductance of the machine. Meanwhile, the grid phase voltage would be induced by a virtual air gap flux in the machine. The grid virtual flux vector in a stationary reference frame is defined as the integration of the grid voltage vector :
(7) Applying the definition of virtual flux of equation (7) to the voltage loop equation of (1), the grid virtual flux vector can be estimated as shown in equation (8):
(8)
where and are the converter pole voltage vector and the line current vector, respectively in stationary reference frames. In practice, the value of internal line filter resistance R can be neglected since its value is much smaller than the value of the line inductance impedance ZL. Therefore, the equation (8) can be rewritten in the stationary coordinates for acquiring the magnitude of grid virtual flux at both real and complex axes such as:
(9)
LaRa
LbRb
LcRc
Sa Sb Sc
C
n
Vconv,aVconv,b
Vconv,c
Sa’ Sb’ Sc’
Eg,a
Eg,b
Eg,c
+ Vdc
Fig.1: A topology of 3-phase bidirectional ac-dc voltage source converter
B. Grid virtual flux and instantaneous power estimation The ideal integration that is used to calculate the grid
virtual flux as shown in equation (9) might saturate due to dc offsets present in the sensed current or voltage. Therefore, a low-pass filter is selected to replace the pure integrator. However, a simple low-pass filter reduces the system performance because it produces errors in phase and magnitude of the virtual flux components.
In order to minimize these errors, phase and magnitude compensation, as developed by [11] is analyzed and adopted in the virtual flux estimation procedure. The estimation procedure provides a low-pass filter characteristic at all frequencies, except at the operating frequency (grid voltage frequency), thus the integration drift problem can be avoided while at the same time, good system performance is maintained. The α and β components of the actual converter virtual flux , are calculated based on the operating frequency e, the low-pass filter cutoff frequency c and the estimate of converter pole flux vector . Those components can be written as: (10)
(11)
Equations (10) and (11) are used in the virtual grid flux estimation procedure as illustrated in Fig. 2.
The estimation of the input active power P and reactive power Q in a stationary reference frame is given by equations (12) and (13), respectively.
(12)
(13)
The input reactive power Q is set to zero to make the input power factor unity. In some applications however, the front-end converter is required to operate in leading power factor (pf) to compensate the motoring loads of lagging pf that are connected in a near-by utility grid.
C. Virtual flux direct power control The control structure of the virtual flux direct power
control method (VFDPC) is illustrated in Fig. 3. The VFDPC regulates the line currents and dc-link output voltage by controlling the input instantaneous active and reactive power.
The references of active power, Pref and reactive power, Qref are compared with the estimated P and Q values. The error quantities which are denoted by P and Q, are processed by two hysteresis controllers. The output of the hysteresis controllers designated by dP,Q, are used by the switching look-up table for selecting a suitable converter voltage vector. The behavior of a hysteresis controller concerning its band level can be summarized as follows:
(14)
(15)
(16)
where hP,Q is the hysteresis band for either the active or reactive power hysteresis controller. dP,Q=1 indicates that the switching table must be able to select an appropriate voltage vector to increase the active or reactive power. On the other hand, dP,Q=0 implies that the controller must be able to reduce the level of active or reactive power.
IV. DEVELOPMENT OF SWITCHING LOOK-UP TABLE FOR VIRTUAL FLUX DIRECT POWER CONTROL
In VFDPC, the switching table operates according to the position of the virtual grid flux vector which is rotating in a complex αβ-plane. Based on the estimated virtual grid flux components, the virtual grid flux vector angle, is calculated using: (17)
The αβ-plane is divided into 12 sectors. Each sector is wide as shown in Fig. 4. The sectors rotate in the anticlockwise direction and can be generally expressed as:
(18)
cs ω+
cs ω+
c
e
ωω
c
e
ωω
conv αΨ ′conv αΨ g αΨ
conv βΨ ′ conv βΨ g βΨ PI
Load
PQ Pref
Qref = 0
Vdc
++
+
--
-
Eg,a
dP
L
L
L
Eg,b
Eg,c
IGBT
dQn
PQ
N
Fig. 2: Detailed control blocks for virtual flux estimation
Fig.3: Control structure of Virtual Flux Direct Power Control
The new switching look-up table is developed based on the derivative of instantaneous active and reactive powers. The active and reactive power derivatives are calculated as:
(19)
(20)
The three phase grid voltage is assumed to be balanced. Therefore, the grid voltage in a stationary reference frame can be expressed as: (21)
Applying a definition of virtual flux into the grid voltage equations of (21), the grid flux in a stationary reference frame can be written as:
(22)
(23)
Consequently, the derivative expression of grid flux can be written as:
(24)
(25)
Based on the voltage equations of the grid connected ac-dc converter as shown in equation (1), the instantaneous current variations can be expressed as:
(26)
(27)
Substituting equations (24)-(27) into (19)-(20), and assuming that the line resistance value is negligibly small, one can
obtain the final power derivative equations as shown in equations (28)-(29):
( )( ) ( )( )
α α β β
α β α β β α
ωΨ ωΨω
ω Ψ ω Ψ Ψ Ψ
− + +=
+ − +
g g g g
g g g conv g conv
I IdPdt V V
L
(28)
( )
( )α β β α α β α
β α β
ωΨ ωΨ Ψ ωΨω
Ψ ωΨ
− + − − +=
−
g g g g g g conv
g g conv
I I VdQ Ldt
VL
(29)
The power derivatives equations in (28) and (29) are influenced by the grid voltage and current variables, the filter inductance and the converter switching states. Both equations are plotted in Figures 5 and 6 using the actual and operating parameters of the converter system. The plotted waveforms of active and reactive power derivative as shown in Fig. 5 and 6, respectively are used to study the effect of a particular converter voltage vector Vn on the behavior of instantaneous active and reactive powers. Information of the sign and magnitude of the change in active and reactive power for each sector are used in developing the switching table. For example, for the angle in the range , the application of V3, V4, V5, V6, V0 or V7 voltage vectors will generate a positive time-derivative of the active power. As a result, if any of these vectors is applied, the active power tends to increase. On the other hand, the employment of V1 leads to a negative time-derivative which will decrease the active power. The same procedure is applied for the analysis of different angles, including the reactive power characteristics. The application of V2, V3, V4, V0 or V7 voltage vectors will produce a positive time-derivative of reactive power. Therefore, if any of these vectors is applied, the reactive power tends to increase. However, the use of V1, V5 or V6 leads to a negative time-derivative which will reduce the reactive power.
The synchronization of the VFDPC with the virtual grid flux vector causes a shift of the space vectors with respect to the line voltage vector. Therefore, a sector which represents an angle range between in Fig. 5 and Fig. 6, is compatible to sector 1. The sector 1 is located in an angle between in the αβ-plane as shown in Fig. 4. The same procedure is applied for the other sectors. Table 1 shows the new switching look-up table for VFDPC.
Table 1: New switching table for the front-end ac-dc converter
Power error status
Sector position ( ) and converter voltage vector (
dp dq 0 0
0 1 1 0
1 1
Fig. 4: Sector location for the virtual grid flux vector
V. SIMULATION RESULTS The entire rectifier system is simulated in the
Matlab/Simulink environment to study its performance under steady state and transient conditions. The main parameters used in the simulation are tabulated in Table 2.
Table 2: Electrical Parameters of Power Circuit
Eg
fVdc,ref
RL
CRL
fs
Fig. 7 represents balanced three phase line current
waveforms. A VFDPC scheme utilizing the new switching table is able to produce almost sinusoidal line currents with unity power factor (pf). An insight of the line current performance during the steady state and unity pf operation is given by Figs. 8 and 9, respectively. The total harmonic distortion (THD) of the line current is 4.79% which fulfills the standard requirement of less than 6%. Note that the harmonic frequency spectrum of line current as shown in Fig. 9, generates variable switching frequency with the current harmonics spread over a wide range of frequency.
The VFDPC is able to adjust the power factor of the rectifier system. In this study, the reference reactive power Q* is changed to +50 var in order to demonstrate leading power factor operation as illustrated by Fig. 10.
Fig. 11 shows transient responses when the dc voltage reference changes from 150 V to 180 V at 2s and back to 150 V at 4s. With the estimated quantities of the dc-link voltage PI regulator, the control performance is satisfactory.
Fig. 12 shows transient responses during a load variation. The load variation is performed by connecting abruptly a 100
resistor in parallel with the existing resistor across the dc-link at a time of 2s, to cause a sudden disturbance in the load current. The line current and estimated active power, immediately follow the change on the active power reference. The response occurs very quickly without any undesirable overshoot and oscillation. Forced by the voltage PI regulator, the dc output voltage recovers to the original value of 150 V after experiencing a small dip.
0 30 60 90 120 150 180 210 240 270 300 330330 360
0
Angle (degree)
Act
ive
Pow
er D
eriv
ativ
e (d
P/d
t)
V5V1 V2 V3 V4 V6
V0
V7
0 30 60 90 120 150 180 210 240 270 300 330 360
0
Angle (degree)
Rea
ctiv
e P
ower
Der
ivat
ive
(dQ
/dt)
V1 V2 V3 V4 V5V6
V0
V7
1.67 1.675 1.68 1.685 1.69 1.695 1.7-2
-1
0
1
2
t(s)
Pha
se c
urre
nt
2.9 2.92 2.94 2.96 2.98 3
-50
0
50
Pha
se a
vol
tage
(V)
2.9 2.92 2.94 2.96 2.98 3
4
-2
0
2
4
t(s)
Pha
se a
cur
rent
(A)
0 1000 2000 3000 4000 5000 60000
0.5
1
1.5
2
2.5
3
3.5
Frequency (Hz)
Fundamental (60Hz) = 1.533 , THD= 4.79%
Mag
(%
of F
unda
men
tal)
2.9 2.92 2.94 2.96 2.98 3
-50
0
50
Pha
se a
vol
tage
(V)
2.9 2.92 2.94 2.96 2.98 3
-4
-2
0
2
4
t(s)
Pha
se a
cur
rent
(A)
Fig. 5: Active power derivatives characteristic under different voltage vector Vn
Fig. 6: Reactive power derivatives characteristic under different voltage vector Vn
Fig. 7: 3-phase line currents
Fig. 8: Phase voltage and line current at unity pf
Fig. 9: Harmonic spectrum of the line current
Fig. 10 Voltage and current during leading pf operation
VI. EXPERIMENTAL RESULTS The system parameters used in the experiment are shown
in Table 2. The sampling time for real-time implementation has been increased to 50 because of the speed limitation of the real-time board. The development of the control algorithm is performed using Matlab/Simulink and the real-time implementation with the dSPACE (DS-1104) digital signal processor board. The experimental prototype of the ac-dc converter system has been developed in the MUN Power
Devices and System Research Laboratory to study and examine the proposed VFDPC scheme. A three phase PWM ac-dc converter has been constructed using six power IGBTs type GAPSC71K and six ultrafast high voltage diodes type HFA08TB60 from International Rectifier. The gate drive modules which act as interfaces between the gate control signals and the power switches have been developed. Each module consists of an isolated dc-dc converter, voltage regulators, dead-time control circuits and opto-coupler circuits. The experimental set-up pictures from several different view angles are shown in Fig 13.
The experimental results under unity power factor operation are shown in Fig. 14. The VFDPC with a new developed switching table is able to produce line currents that are in phase with their associated phase voltages. Fig. 15 shows the experimental waveforms of the virtual grid flux in stationary αβ -coordinates which are used to determine the sector location for the switching table and to estimate the instantaneous power. Meanwhile, Fig. 16 presents the experimental phase-a current waveform and its harmonic spectrum. The odd order harmonics are much smaller than the magnitude of the fundamental which gives the confirmation that the developed switching table is able to produce the sinusoidal current. The estimated instantaneous active power P and reactive power Q are shown in Fig. 17. It is to be noted that the reactive power Q is kept at 0 var to achieve unity power factor operation.
1.5 2 2.5 3 3.5 4 4.5 5
140
150
160
170
180
190
t(s)
Dc-
link
outp
ut v
olta
ge (
V)
1.8 1.85 1.9 1.95 2 2.05 2.1 2.15 2.2 2.25 2.3
40
0
40
Pha
se a
vol
tage
(V
)
1.8 1.85 1.9 1.95 2 2.05 2.1 2.15 2.2 2.25 2.3
-6
-4
-2
0
2
4
6
t(s)P
hase
a c
urre
nt (A
)
1.8 1.85 1.9 1.95 2 2.05 2.1 2.15 2.2 2.25 2.3
149.2
149.4149.6
149.8150
150.2
150.4150.6
150.8
t(s)
Dc-
link
outp
ut v
olta
ge (
V)
1.8 1.85 1.9 1.95 2 2.05 2.1 2.15 2.2 2.25 2.3
050
100150200250300350400450
t(s)Est
imat
ed A
ctiv
e po
wer
(W
) an
dE
stim
ated
Rea
ctiv
e P
ower
(V
ar)
Fig. 11: Transient response for the step changes of dc-link voltage
Fig. 12: Transient response for load variation from low to high current demand (a) Phase-a current and voltage (b) Dc-link voltage (c)
Estimated active and reactive power
12(a)
12(b)
12(c)
Fig. 14: Voltage (40V/div) and current (2A/div) in phase-a and phase-b at unity power factor operation
VII. CONCLUSION This paper presents a new control scheme for the pulse
width modulated three phase ac-dc voltage source converter without employing ac input voltage sensors. The control scheme employs only three ac input current sensors and a dc output voltage sensor. Hence, the size and cost of the ac-dc converter system can be reduced. The proposed control scheme of virtual flux direct power control (VFDPC) has been successfully used to estimate the grid voltage and the instantaneous active and reactive powers. Selection of a suitable converter voltage vector for switching purposes is performed by a newly designed switching look-up table. A comprehensive and systematic approach has been presented in developing the switching table. A compensation method to correct the magnitude and phase errors of the virtual flux estimation is used in this work. The proposed control scheme utilized hysteresis controllers in the inner loop and discrete PI in the outer loop for the dc-link voltage regulation. It has been successfully simulated in the Matlab/Simulink environment. The simulation results show that the proposed VFDPC is able to produce three phase input currents with
low total harmonic distortion factor, unity power factor and adjustable dc-link output voltage. The real-time implementation of the proposed ac-dc converter system incorporating the new virtual flux control techniques has been successfully tested using the DS1104 digital signal processing board. There exist close agreement between the simulated and experimental performances.
ACKNOWLEDGMENT The authors would like to thank Universiti Teknikal
Malaysia Melaka (UTeM) for providing continuous financial support that enabled the achievement of these research results.
REFERENCES [1] B. Singh, et al., "A review of three-phase improved power quality
AC-DC converters," Industrial Electronics, IEEE Transactions on, vol. 51, pp. 641-660, 2004.
[2] R. Wu, et al., "Analysis of an AC to DC voltage source converter using PWM with phase and amplitude control," in Industry Applications Society Annual Meeting, 1989., Conference Record of the 1989 IEEE, 1989, pp. 1156-1163 vol.1.
[3] V. Blasko and V. Kaura, "A new mathematical model and control of a three-phase AC-DC voltage source converter," Power Electronics, IEEE Transactions on, vol. 12, pp. 116-123, 1997.
[4] R. Wu, et al., "Analysis of a PWM AC to DC voltage source converter under the predicted current control with a fixed switching frequency," Industry Applications, IEEE Transactions on, vol. 27, pp. 756-764, 1991.
[5] A. Bouafia, et al., "Predictive Direct Power Control of Three-Phase Pulsewidth Modulation (PWM) Rectifier Using Space-Vector Modulation (SVM)," Power Electronics, IEEE Transactions on, vol. 25, pp. 228-236, 2010.
[6] J. Eloy-Garcia and R. Alves, "DSP-based Direct Power Control of a VSC with Voltage Angle Estimation," in Transmission & Distribution Conference and Exposition: Latin America, 2006. TDC '06. IEEE/PES, 2006, pp. 1-5.
[7] G. Escobar, et al., "Analysis and design of direct power control (DPC) for a three phase synchronous rectifier via output regulation subspaces," Power Electronics, IEEE Transactions on, vol. 18, pp. 823-830, 2003.
[8] M. Cirrincione, et al., "Direct power control of three-phase VSIs for the minimization of common-mode emissions in distributed generation systems," Electric Power Systems Research, vol. 81, pp. 830-839, 2011.
[9] T. Noguchi, et al., "Direct power control of PWM converter without power-source voltage sensors," Industry Applications, IEEE Transactions on, vol. 34, pp. 473-479, 1998.
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Fig. 15: (a) Virtual grid flux in stationary αβ-coordinates. (b) 12 sectors produced by the virtual grid flux vector.
Fig. 16: (a) Phase-a current (2A/div) and its frequency spectrum
Fig. 17: (a) Estimated active power P (200W/div) and reactive power Q (200var/div)
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