Three-Level Inverter-Based Shunt Active Power Filterin Three-Phase Three-Wire and Four-Wire Systems
1
2
Oleg Vodyakho, Member, IEEE, and Chris C. Mi, Senior Member, IEEE3
Abstract—This paper presents a direct current-space-vector4control of an active power filter (APF) based on a three-level5neutral-point-clamped (NPC) voltage-source inverter. The pro-6posed method indirectly generates the compensation current ref-7erence by using an equivalent conductance of the fundamental8component using APF’s dc-link voltage control. The proposed con-9trol can selectively choose harmonic current components by real-10time fast Fourier transform to generate the compensation current.11The compensation current is represented in a rotating coordinate12system with chosen switching states from a switching table imple-13mented in a field-programmable gate array. In addition, a three-14phase four-wire APF based on a three-level neutral-point-clamped15inverter is also presented. The proposed APF eliminates harmon-16ics in all three phases as well as the neutral current. A three-phase17three-wire NPC inverter system can be used as a three-phase four-18wire system since the split dc capacitors provide a neutral connec-19tion. To regulate and balance the split dc-capacitor voltages, a new20control method using a sign cubical hysteresis controller is pro-21posed. The characteristics of the APF system with an LCL-ripple22filter are investigated and compared with traditional current con-23trol strategies to evaluate the inherent advantages. The simulation24and experimental results validated the feasibility of the proposed25APF.26
Index Terms—Direct current control (DCC), multilevel invert-27ers, neutral clamped, power factor correction, power filter, reactive28power compensation, shunt active filter, space vector, three-phase29four-wire system, voltage-source inverter (VSI).30
I. INTRODUCTION31
A LARGE portion of the total electrical energy produced in32
the world supplies different types of nonlinear loads, such33
as variable-frequency drives and electronic ballasts. These loads34
are typically composed of odd harmonic currents, which are35
multiples of the fundamental frequency. The harmonic currents36
cannot contribute to active power and need to be eliminated37
to enhance power quality [1]. Active power filters (APFs) are38
designed for this purpose.39
APFs in three-phase three-wire systems can be based on sev-40
eral control methods [2]– [9]. Typically, current control is per-41
formed either by pulsewidth modulation (PWM) [3], [4], [7]42
or by direct current control [9], [10]. For detection of unde-43
lators [4], [7] or integrating oscillators [3] can be implemented.45
However, these methods result in phase shifts, which reduce46
Manuscript received November 27, 2008; revised February 14, 2009. Rec-ommended for publication by Associate Editor J. H. R. Enslin.
O. Vodyakho is with the Department of Electrical and Computer En-gineering, Florida State University, Tallahassee, FL 32310 USA (e-mail:[email protected]).
C. C. Mi is with the Department of Electrical and Computer Engineering, Uni-versity of Michigan, Dearborn, MI 48128 USA (e-mail: [email protected]).
Digital Object Identifier 10.1109/TPEL.2009.2016663
the filtering performance. A better approach is to use Fourier 47
transformation to determine individual harmonics that need to 48
be eliminated. The APF control proposed in this paper is based 49
on the Fourier transformation approach. 50
Most APFs use a standard two-level voltage-source inverter 51
(VSI) [6], [7]. However, for medium-voltage applications, three- 52
level VSIs have been proven to be more advantageous [3], [8], 53
[9]. A three-level neutral-point-clamped (NPC) inverter can be 54
employed in three-phase three-wire systems, as well as three- 55
phase four-wire systems [10], [11]. In a three-level NPC inverter, 56
the splitting dc-capacitor voltage has to be maintained as half of 57
the dc-link voltage. 58
The advantages of three-level VSIs include lower harmonic 59
distortion, lower switching frequency, and lower power loss. 60
APFs based on three-level inverters are generally more expen- 61
sive but can be compensated by using smaller filter inductors, 62
assuming the same switching frequency. However, the control 63
of a three-level inverter is more complicated than a two-level in- 64
verter because of the large number of inverter switching states. 65
Therefore, there is greater difficulty in synthesizing the volt- 66
age reference vector [12]. Typical current control strategy for 67
the space vector PWM (SVPWM) control is based on station- 68
ary αβ-coordinates [12]. In this paper, a new current control, 69
based on SV current control, is compared with the stationary 70
αβ-coordinates based control. The proposed SV current con- 71
troller (SVCC) [9] in the rotating coordinates uses five-level 72
hysteresis CC (HCC), with sector selection strategy providing 73
grid-voltage vector information, to decrease current ripple and 74
number of switching. Although HCC-based SVCC for a three- 75
level inverter has not been used for APF control, it is widely 76
used in two-level VSI for motor drives [13]. 77
The electric power distribution systems are inherently un- 78
balanced due to untransposed distribution lines and unbalanced 79
loads. Therefore, maintaining the distribution voltage within 80
certain limits of a perfectly balanced waveform is very difficult. 81
In addition, if the phases are unequally loaded, they produce un- 82
desired negative and zero-sequence currents. Under nonlinear 83
voltage and current, the harmonic current will generate power 84
losses. The negative sequence will cause excessive heating in 85
machines and generate low-frequency ripples in rectifiers. The 86
zero-sequence currents not only cause excessive power losses in 87
neutral lines, but also degrade the circuit protection. For the neu- 88
tral current (zero-sequence current) reduction, a zig–zag trans- 89
former is often employed, and the performance can be improved 90
by using a zero-blocking transformer [14]. Unfortunately, this 91
method has several disadvantages: 1) zero-sequence impedance 92
of the zig–zag transformer must be low, thus requiring spe- 93
cial design; 2) the effectiveness of the zig–zag transformer to 94
Fig. 1. Three-level VSI-based APF in (a) three-phase three-wire systems, and (b) three-phase four-wire systems.
divert the third harmonic current is highly dependent on the95
distribution system impedance, and in most cases, only 50% re-96
duction can be guaranteed; 3) a lower zero-sequence impedance97
increases the single-phase fault current level; therefore, fusing98
and circuit breaker resizing may be necessary; and 4) due to99
the reasons mentioned earlier, the passive zig–zag transformer100
approach is larger in size and weight. A better solution to reduce101
the neutral current is to utilize an APF in a four-wire system.102
Since a three-level VSI is used as an APF for a three-phase four-103
wire system, a strategy to balance the dc-link capacitor voltages104
is necessary [15]. This paper presents a new control strategy to105
balance the dc-link capacitor voltages by utilizing an opposite106
sign of the middle point current based on a three-level HCC [11].107
The main focus of this paper is to study the performance108
of the SV current controls in a three-phase three-wire system109
with an LCL filter. The two SV current controls, one based on110
the stationary αβ- and the other on rotating xy-coordinates, are111
compared in order to analyze the influence of the LCL filter on112
the APF system in a three-phase three-wire system. In addition,113
the APF system in a four-wire system with and without an LCL114
filter is also analyzed.115
II. COMPENSATOR CONTROL STRATEGY116
A. Calculation of APF Reference Current117
An APF is considered as a controlled current source. Fig. 1118
shows the configuration of an NPC three-level VSI for the ap-119
plication of an APF in three-phase three- and four-wire systems120
with an LCL-ripple filter. As illustrated in Fig. 1, the APF is121
connected in parallel with a nonlinear load to produce reactive122
and harmonic currents opposed to those of the nonlinear loads123
to cancel the harmonic currents.124
It is assumed that the upper-leg and lower-leg capacitor volt-125
ages are identical, which is Udc/2. In the proposed control126
method, harmonics are decomposed by FFT. The FFT algorithm127
core implemented in the proposed APF uses the Cooley–Tukey128
algorithm [16] for digital computations. Nonsinusoidal period- 129
ical waves are analyzed to extract the fundamental component 130
from the harmonics. The resultant FFT computations yield the 131
amplitude and frequency of each harmonic component. Then, 132
each harmonic is multiplied by the compensation factor. There- 133
fore, only critical harmonics can be compensated and an APF 134
does not need to cover all harmonic power. 135
The synchronous-reference-frame-based method has been 136
widely used for most of the recent APFs. Synchronous fun- 137
damental xy-frame is derived from the SV transformation of 138
the abc-coordinates. The detection of the harmonics is based 139
on removing the dc-signal using a high-pass filter [7]. The 140
synchronous harmonic xy-frame is similar to the fundamen- 141
tal xy-frame in principle. One difference is that the harmonic 142
xy-coordinate frame rotates with a frequency the same as the 143
selected harmonic. Thus, in the harmonic xy-frame, only the 144
specific harmonic will be a dc-signal and all other frequencies 145
including the fundamental will be ac-components [7]. One of 146
the practical problems for this method is the implementation 147
of the filters because of the software complexity. Those two 148
methods require additional coordinate transformation from xy- 149
to abc-coordinates for the PWM strategy. 150
The basic structure of the compensation in a three-wire sys- 151
tem is based on the method described in [8]. The strategy based 152
on the αβ-coordinates avoids instability problem in the case 153
of regeneration. As illustrated in Fig. 2(a), the measured grid 154
voltages (egrida b c) and load currents (iLOADa b c
) are inputs of 155
the FFT algorithm to extract only fundamental component (for 156
grid voltages) and to select undesired harmonic current (for 157
the load currents to provide flexibility to eliminate selected 158
harmonics). The fundamental component of the grid voltage 159
(egrid(1)a b c) is extracted by the FFT for the disturbance-free 160
identification/measurement. The fundamental grid voltages are 161
transformed to αβ-coordinates (egrid(1)αβ ) and the position of 162
the grid-voltage vector is identified (γ) to be used for the sec- 163
tor selection. The dc-voltage controller output signal (iaL α β) is 164
IEEE
Proo
f
VODYAKHO AND MI: THREE-LEVEL INVERTER-BASED SHUNT APF IN THREE-PHASE THREE-WIRE AND FOUR-WIRE SYSTEMS 3
Fig. 2. Reference current calculation in (a) three-wire systems, and (b) four-wire systems.
added to the reference current in the αβ-coordinates (iαβ ) to165
generate the reference compensation current (iCα β), which is166
the input of the current controller.167
In a three-phase four-wire system, due to the presence of168
the neutral current, the reference current can be calculated, as169
presented in [10] and [11].170
The basic structure of compensation in a four-wire system is171
shown in Fig. 2(b). The configuration of the controls for the APF172
in a four-wire system is very similar to that of the three-level173
VSI shown in Fig. 2(a) except a few components. The dc-voltage174
controller output signal (iaL ) is added to the reference current175
of the four-wire system to generate the reference compensation176
current (icabcn ), which is the input of the current controller.177
The PI controller for the dc-link voltage sets the amplitude178
of the active current of the APF inverter to regulate the dc-link179
voltage based on its reference value covering the inverter losses.180
The amplitude is multiplied by a line-voltage function derived181
from the line-voltage fundamental vector, which is obtained by182
the FFT, thus yielding the instantaneous line-current reference.183
Subtracting the measured load current, the reference value of184
the APF current is obtained.185
The dc-link capacitor will be charged or discharged by the186
difference of the active load current and grid current, forcing187
the PI controller to change its output correspondingly, until both188
active currents are equal. In this way, the APF will compensate189
all nonactive components of the load current (so-called real-time190
mode) and regulate the dc-link voltage of the APF.191
If cost of the system is of concern, then compensating only192
load-current harmonics not including the fundamental reactive193
current will be appropriate. In addition, as an extension of the194
scheme in [17], the fundamental component of the load current195
is identified by the FFT algorithm and subtracted from the actual196
load current fed back (negative) to the summing point behind the197
multiplier (switch is closed in this case). Then, the fundamental198
component will not appear in the APF current reference any199
more (selective mode). Similarly, additional harmonics can be200
detected by the FFT algorithm and the compensation of these201
components can be attenuated by an on-demand selective factor.202
This is advantageous if these harmonics can be regarded as 203
uncritical, not exciting grid resonances. Then, the whole APF- 204
rated power can be applied to the compensation only for the most 205
disturbing or dangerous load current harmonics. The current 206
controller block can be implemented in the stationary abc-, 207
αβ-, or rotating xy-coordinate system with either a three-wire 208
or a four-wire system and will be explained in the following 209
section. 210
B. Current Control of the APF With a Three-Level VSI 211
The configuration of the current control of a three-level VSI- 212
based APF is shown in Fig. 3(a), which is based on a grid-voltage 213
rotating synchronous xy-coordinate. The proposed method on 214
the rotating xy-coordinates, which is synchronized with the grid 215
voltage, is based on a five-level hysteresis comparator. Five- 216
level hysteresis comparator allows the precise selection of 27 217
output-voltage space vectors for three-level VSI. It compares 218
the actual phase-current error in the rotating xy-coordinates with 219
tolerance bands around the reference current, which are defined 220
as dx and dy , as shown in Fig. 3(a), by means of a lookup ta- 221
ble implemented in the FPGA. To find the relationship between 222
the xy-current error components and the three-level inverter’s 223
output-voltage SC Uk represented in the αβ-plane, it is nec- 224
essary to detect the position of the rotating xy-coordinates in 225
relation with the αβ-plane, which is divided into 12 sectors, as 226
shown in [8]. This sector information is delivered to the switch- 227
ing table. 228
For the sector selection, only the fundamental component of 229
the grid voltage is extracted by FFT for stable and disturbance- 230
free identification. 231
The transformation angular position γ is calculated as 232
γ = arctan(
uβ
uα
). (1)
The space-vector position angle γ of the grid voltage obtained 233
from (1) is transformed to a new signal, γn , by a lookup table 234
implemented in the FPGA. The digitized variables dx, dy and the 235
space-vector position angle of the grid voltage γn determine the 236
IEEE
Proo
f
4 IEEE TRANSACTIONS ON POWER ELECTRONICS
Fig. 3. Control block diagrams for the three-level VSI-based APF based on (a) the rotating xy-coordinates, and (b) stationary αβ-coordinates.
Fig. 4. Derivation of the current error vectors.
addresses of the main lookup table, which is also implemented237
in the FPGA [9].238
The line current error ic is influenced by the output voltage,239
grid voltage, and derivative of the commanded current. If the240
current error is zero (ic =icomp ), the desired output voltage241
vector, udo = sk · (Udc/2), will be defined as242
udo = Ldicdt
+ e. (2)
Otherwise, the desired output voltage vector udo will be rep-243
resented by the space vector Un and the line-current error as244
follows:245
Ldiedt
= udo − Un . (3)
Fig. 4 illustrates an example of proper switching vector se-246
lection with the proposed method. The proposed control, which247
is based on the xy-coordinates with the grid vector informa-248
tion (sector 3 for this case), can select switching vectors among249
U1 ∼ U8 . In this case, the length between udo and a switch-250
ing vector is proportional to the amount of the current varia-251
tion. As an example, the length between U3 and udo is propor-252
tional to d ie3/dt as specified in Fig. 4. If the ud0 is in sector 3,253
the proposed control will select inverter-voltage space vectors254
among U3 , U4 , and U7/U8 (U7 or U8). However, the conven- 255
tional methods, without the direct grid voltage information in 256
xy-coordinates, would select the voltage vector, Uk in Fig. 4. 257
In addition, the conventional methods, without utilizing the xy- 258
coordinates and lacking grid voltage information, can select 259
the voltage vectors, U2 , U3 , and U4 more frequently than xy- 260
coordinates control, as shown in Fig. 5(a). In both cases, diek/dt 261
will be much greater than that of the proposed method. On the 262
other hand, the proposed method utilizes the detected position of 263
the rotating coordinates to estimate the grid voltage vector based 264
on the 12 sectors. The selected switching vectors (Uk= (0.27) in 265
Fig. 4), with the proposed method, are presented in Fig. 5(b). In 266
this case, the switching vectors causing higher current variation, 267
such as U2 and U3 , are rarely selected. The simulation results 268
verified the examples of the current error shown in Fig. 4. As a 269
result, current control using the xy-coordinates (rotating coordi- 270
nates) has less current ripple, as shown in Fig. 5(b). 271
The proposed control integrates the gird-voltage vector to es- 272
timate the position of the vector. Based on the position, the con- 273
trol chooses the minimal value of the line-current error ie . The 274
proposed control significantly reduces the number of switch- 275
ings compared with the control in the stationary coordinates 276
as it processes the information about the actual position of the 277
grid-voltage space vector. 278
The configuration of the controls for an APF on the stationary 279
αβ-coordinates is very similar to that of a three-level VSI shown 280
in Fig. 3(a), except a few components, as shown in Fig. 3(b). 281
The current control of an APF in a four-wire system is based 282
on the dual-current hysteresis control. The significant advan- 283
tages of this control are the simplicity and better dynamic re- 284
sponse. One disadvantage of the hysteresis control is that there 285
is no limit to the switching frequency, but additional circuitry 286
can be used to limit the maximum switching frequency. 287
Three-level hysteresis comparators with upper and lower 288
commutation bands are used. The band change can be obtained 289
by a simple logic when two slightly shifted bands are employed. 290
The decision of the commutation band change depends on the 291
phase voltage, eL , current reference, iref , and line inductance, 292
Lk . Since a three-level VSI is implemented as an APF instead 293
of a two-level VSI, a modification of the conventional three- 294
IEEE
Proo
f
VODYAKHO AND MI: THREE-LEVEL INVERTER-BASED SHUNT APF IN THREE-PHASE THREE-WIRE AND FOUR-WIRE SYSTEMS 5
Fig. 5. Switching vector selection example: (a) phase current (top) and space vectors (bottom) using the stationary coordinate control, (b) phase current (top),space vectors (middle), and selected sector (grid-voltage position, bottom) using the proposed control.
Fig. 6. Control block diagram for the APF in four-wire system.
level hysteresis current controller is required due the neutral-295
point potential control, as described in [11]. The structure of the296
three-phase four-wire APF control system is shown in Fig. 6. A297
traditional proportional–integral (PI) controller is used in order298
to control the dc-link voltage. The PI controller for the dc-link299
voltage sets the amplitude of the active current of the APF300
inverter to regulate the dc-link voltage based on its reference301
value. The amplitude is multiplied with the line-voltage funda-302
mental component, which is obtained by the FFT, yielding the303
instantaneous line-current reference. The dc-link neutral-point304
voltage is controlled by adjusting the hysteresis band positions,305
with respect to the initial situation. When zero voltage is applied306
to any phase, the summation of the currents flowing through the307
clamping diodes, id0 , produces the unbalanced charging of the 308
dc-link capacitors. In this case, a positive current of the id0 309
charges the dc-link capacitor C2 , and a negative current dis- 310
charges it. To control the dc-link neutral voltage, the durations 311
of the charging and discharging need to be regulated. Subtract- 312
ing the measured load current, the reference value of the APF’s 313
current is obtained. The current control is based on a three-level 314
hysteresis comparator, comparing the actual phase-current error 315
with tolerance bands around the reference current by means of a 316
lookup switching table implemented in the FPGA. The current 317
controller generates the insulated-gate bipolar transistor (IGBT) 318
firing pulses depending on the sign of dc-link current id0 and the 319
sign of the phase-current error so termed “sign cubical hysteresis 320
IEEE
Proo
f
6 IEEE TRANSACTIONS ON POWER ELECTRONICS
controller” will be appropriate to be used for the implemented321
control.322
C. Design of the LCL-Ripple Filter323
The compensation current of an APF usually contains high-324
frequency components caused by switching actions, which can325
disturb other EMI-sensitive loads on the common utility grid326
[18]. Typically, only series inductors are used as a filter, which327
interface the PWM-inverter and the power grid. In this case,328
the size of the inductor for optimal switching frequency should329
be chosen appropriately to reduce the current ripple (harmon-330
ics) around the switching frequency [19]. As the inverter ripple331
current with a hysteresis of 14 A is rather big in comparison332
to the rated current of 32 A (rms), a second-order line-ripple333
filter has been inserted between the APF filter and the grid,334
with grid-side inductors of the same size as those of the filter335
and capacitive-resistive branches between the lines (Fig. 1). The336
LCL-filters give advantages in costs and dynamic performance337
since smaller inductors can be used compared to L-filters in338
order to achieve the necessary damping of the switching har-339
monics. However, LCL-filter design is complex and needs to340
consider many constraints, such as the current ripple through341
inductors, total impedance of the filter, resonance phenomenon,342
reactive power absorbed by filter capacitors, etc. In addition,343
the LCL-filters may cause steady-state and transient distortion344
in the output current due to resonances. This distortion can be345
reduced but not solved in PWM converters if the main reso-346
nance frequency is selected in a range where no harmonics of347
the output current exist. With this filter, the switching frequency348
of the converter has to be high enough to obtain sufficient har-349
monic attenuation. In the existing controls, this approach can-350
not be considered since the switching harmonic spectrum is not351
clearly defined due to the variable switching frequency. This is352
in contrast to PWM, where the resonance frequency can be cho-353
sen easily with frequency lower than the definable lowest pulse354
frequency, which is roughly twice the switching frequency in355
the case of a three-level inverter. The LCL-filter design in case356
of PWM will affect the size and cost as shown in Section III357
compared to the existing controls.358
To analyze the filtering characteristics in a three-phase three-359
wire system, one single phase is considered, as shown in Fig. 7.360
In this case, it should be noted that CY = 3 · Cfilt and RY =361
1/3 · Rfilt , where Rfilt and Cfilt are parameters for each phase.362
Resistor RY , shown in Fig. 7, is utilized to limit the ripple363
current in order to protect capacitor CY .364
The transfer function of the LCL-filter can be defined as365
GuV S I→Ig r id =Igrid(s)UVSI(s)
= − 1sL
·1 + s
Q f i l t ·ω f i l t
1 + sQ f i l t ·ω f i l t
+ s2
ω 2f i l t
. (4)
The resonance frequency ωfilt and quality factor Qfilt are366
given by367
ωfilt = 2 · πffilt =1√
3 · Cfilt · Lg r id ·L f i l tL
(5)
Fig. 7. LCL-filter: single-phase case.
368
Qfilt =
√Lfilt · Lgrid
(Lfilt + Lgrid) · Cfilt·√
3Rfilt
(6)
where L is the line inductor (L = Lfilt + Lgrid = 2 · Lfilt), 369
Uvsi(s) is the inverter output voltage, and Igrid is the grid-side 370
current. Qfilt is not high (for the proposed control, Qfilt ≈ 1.4) 371
because of the filter size and costs. LCL-filter gets the max- 372
imum attenuation when the inverter-side inductance is equal 373
to the grid-side inductance, as shown in [20]. The frequency 374
responses of the L- and LCL-filters are shown in Fig. 8. 375
However, systems incorporating LCL-filters are of second or- 376
der, and there exists a peak amplitude response at the resonant 377
frequency of the LCL-filter. This requires more careful design of 378
the LCL-filter parameters and current control strategy to main- 379
tain system stability since the filters tend to oscillate with the 380
filter resonance frequency. 381
The most popular method is to insert a damping resistor in the 382
capacitor shunt branch of the LCL-filter, as shown in Fig. 1. The 383
frequency response of the LCL-filter with a damping resistor is 384
shown in Fig. 9. As shown in Fig. 9, the damped filter has more 385
attenuation on the resonant frequency, but has less attenuation 386
in the high-frequency region than that of the nondamped filter. 387
In addition, this approach causes considerable power losses. 388
Fig. 10 shows hysteresis current through the LCL-filter resis- 389
tor. From Fig. 10, the power losses can be calculated as 390
Another approach is to actively damp the resonance by con- 392
trol algorithms without increased power losses. The approaches 393
presented in the literature differ in signals used for the con- 394
trol, number of sensors, control complexity, and performance. 395
In [20], an additional feedback of the filter capacitor current 396
is used for damping the resonance to enhance the control 397
performance. 398
From an industrial point of view, it is desirable to have a 399
minimum number of sensors. Therefore, these approaches are 400
not further considered in this paper since the simulation and 401
experimental results show good performance for the proposed 402
filter, and the cost of the inverter system will not be increased. 403
An effect of the active damping control loop is the reduction 404
of the harmonic currents that are present in the LCL-filter reso- 405
nance range. However, the reduction of these harmonic currents 406
IEEE
Proo
f
VODYAKHO AND MI: THREE-LEVEL INVERTER-BASED SHUNT APF IN THREE-PHASE THREE-WIRE AND FOUR-WIRE SYSTEMS 7
Fig. 8. Transfer functions of an L-filter and an LCL-filter with two different filter capacitances. (a) L-filter, (b) LCL filter.
Fig. 9. Transfer functions of an LCL-filter with damping resistor and with twodifferent filter capacitances.
Fig. 10. Current through resistor Rfi lt .
causes an increase in the low-order harmonics that are present407
in the capacitor current, and consequently, results in a reduc-408
tion in the quality of the output current waveforms. This effect409
occurs because not only the resonance frequencies are used in410
the active damping controller, but also all the other harmonics 411
in the capacitor current are included in the active and reactive 412
power references [20]. 413
In addition, an LCL-filter is considered and designed for a 414
three-phase four-wire system. The proposed four-wire system 415
LCL-filter has a star connection, as shown in Fig. 1(b). In this 416
case, it should be noted that Cy = Cfilt , Ry = Rfilt , and the 417
other filtering characteristics remain the same. 418
The inherent advantages and drawbacks of the designed LCL- 419
filter with different control algorithms are presented and dis- 420
cussed in Section III. 421
III. SIMULATION RESULTS 422
Simulation is performed to evaluate and compare the two 423
direct current-space-vector control (DCSVC) control methods 424
in a three-wire system with the same current hysteresis band of 425
± 7 A. 426
The major parameters of the APF system are as follows: 427
dc-link voltage is 700 V, dc-link capacitor size is 4.4 mF, in- 428
ductor (Lfilt) size is 150 µH, inductor (Lgrid ) size is 150 µH, 429
LCL-filter capacitor (Cfilt) is 10 µF, LCL-filter damping resis- 430
tor Rfilt = 3.4 Ω, and inverter power rating is 30 kVA. Fig. 11 431
shows the simulated APF system currents with the three-level 432
VSI in a three-wire system based on the control in stationary 433
αβ-coordinates and rotating xy-coordinates. 434
Fig. 12 shows simulation results of the load current of a 435
thyristor bridge with a very large smoothing inductance. 436
To compare the two controls, a simulation is conducted re- 437
garding the total harmonic distortion (THD) and the number 438
of switching times (WdcΣ ) during two cycles with the same 439
hysteresis band. The result is illustrated in Tables I and II, re- 440
spectively, for the three-level VSI in a three-wire system. 441
It should be noted that the DCSVC control with an LCL- 442
filter caused the switching frequency to increase, as shown in 443
Table II, and as result, a higher power loss and a higher inverter 444
temperature, as shown in Section IV. 445
In addition, the DCSVC method on rotating xy-coordinates is 446
compared with a conventional PWM-based control for perfor- 447
mance monitoring. The conventional PWM modulator uses two 448
IEEE
Proo
f
8 IEEE TRANSACTIONS ON POWER ELECTRONICS
Fig. 11. Simulation results with the three-level VSI (A) based on the control in the stationary αβ-coordinates, and (B) based on the rotating xy-coordinates,where (a) load current, (b) compensation current, (c) grid current without ripple filter, and (d) grid current with ripple filter.
Fig. 12. Simulation results with the three-level VSI based on the control of the rotating xy-coordinates with different load: (a) load current, (b) compensationcurrent, (c) grid current without ripple filter, and (d) grid current with ripple filter.
TABLE ICURRENT HARMONIC SPECTRA DEPENDING ON LCL-FILTER PARAMETERS (RELATIVE TO FUNDAMENTAL)
IEEE
Proo
f
VODYAKHO AND MI: THREE-LEVEL INVERTER-BASED SHUNT APF IN THREE-PHASE THREE-WIRE AND FOUR-WIRE SYSTEMS 9
TABLE IINUMBER OF SWITCHING DEPENDING ON LCL-FILTER PARAMETERS
Fig. 13. Three-level PWM strategy. (a) reference signal and triangular carriers, and (b) PWM pulse.
depth M = 0.8), which have opposite phases (one positive and450
one negative, offset by ± 0.5) as shown in Fig. 13. Each phase451
reference voltage is compared with each of the triangle carriers.452
The frequency of the carriers is the switching frequency, and453
their amplitude is related to the dc-link voltage [9].454
For the comparison, control parameters for both methods are455
adjusted to have almost same THD results. At those conditions,456
which generate almost same THDs, the total number of switch-457
ing for both methods is compared in [9]. However, since the458
proposed method’s switching frequency is not fixed like the459
PWM-based controller, the performance with a line-ripple filter460
should be evaluated with regard to filter size and THD results. In461
this paper, the comparison regarding the filter size is presented462
and shown in Table III.463
Since the resonance frequency of the PWM control can be464
chosen easily with lower frequency than the definable lowest465
pulse frequency, the size of the LCL-filter in case of PWM466
control is bigger (Lfiltpwm = 1.4 · LfiltDCSVC ), as shown in467
Table III.468
Fig. 14 illustrates the nonlinear load current, compensation469
current, and grid current using the proposed control strategy on470
a three-phase four-wire APF. Fig. 15 depicts the neutral load471
(a), compensation (b), and grid (c) currents.472
As shown in Fig. 14, the varying switching frequency in 473
case of the three-level hysteresis current control in a four-wire 474
system complicates the LCL-filter design and decreases the per- 475
formance of the designed LCL-filter. 476
Based on the simulation results, the optimal filter size is se- 477
lected regarding the costs, switching frequency, and THD, as 478
shown in Table IV. The experimental results are presented in 479
Section IV. 480
IV. EXPERIMENTAL RESULTS 481
To validate the performance of the proposed method, a pro- 482
totype test bed has been built for the 400-V, three-phase utility. 483
Table IV shows the experimental parameters in absolute and 484
per unit values for the three-wire and four-wire systems. For 485
the proposed control, a control board is designed and built. The 486
control board includes voltage and current acquisition circuit 487
and an FPGA. The grid and dc link voltages are measured by 488
VS750B (ABB) transducers and the nonlinear load and inverter 489
currents are measured by ES300C (ABB) transducers. The con- 490
trol board also includes two A/D converters for load current 491
acquisition (LTC-1851, 8-channel, 10 bit, 1.25 MSPS), and for 492
high-frequency inverter current sampling (AD-9201, 2-channel, 493
10 bit, 20 MSPS). For isolation/protection, fiber optic transmit- 494
IEEE
Proo
f
10 IEEE TRANSACTIONS ON POWER ELECTRONICS
Fig. 14. Simulation results: (a) load current, (b) compensation current without ripple filter, (c) compensation current with ripple filter, and (d) grid current withoutripple filter.
Fig. 15. Simulation results: (a) neutral load current. (b) Neutral compensation current without ripple filter. (c) Neutral compensation current with ripple filter,and (c) Neutral grid current without ripple filter.
TABLE IVEXPERIMENTAL PARAMETERS
ter (HFBR-1521) and receiver (HFBR-2521) are used between495
the control board and the IGBT inverter. The proposed control496
method is fully implemented in the Xilinx FPGA VIRTEX-II497
utilizing the Xilinx’s integrated software environment (ISE).498
The FFT algorithm and the coordinate transforms are imple-499
mented using the CORDIC FPGA algorithm [16].Q1
Q2
500
The three-level inverter used in the APF system is designed 501
with IGBT power module (BSM200GB120, Siemens). The 502
measured inverter mean switching frequency is 7.2 kHz. It 503
should be, however, noted that due the proposed control (closed- 504
loop, hysteresis comparators), the switching frequency is not a 505
constant value. 506
IEEE
Proo
f
VODYAKHO AND MI: THREE-LEVEL INVERTER-BASED SHUNT APF IN THREE-PHASE THREE-WIRE AND FOUR-WIRE SYSTEMS 11
Fig. 16. Experimental results.
IEEE
Proo
f
12 IEEE TRANSACTIONS ON POWER ELECTRONICS
Fig. 16. (Continued) Experimental results.
Fig. 17. Harmonic spectrum comparison: (a) harmonic spectrum of the grid current for the proposed control [Fig. 16 (e) and (g), THD , f =2 kHz = 4.4%];(b) harmonic spectrum of the grid current for the controller in the αβ-coordinates [Fig. 16 (f) and (h), THD , f =2 kHz = 6.9%].
the line-to-line voltage of the three-level inverter with the control 513
in xy-coordinates. Fig. 16(b) shows the compensation current in 514
the case where only the harmonic components of the load cur- 515
rent are to be compensated. The transient performance of the 516
IEEE
Proo
f
VODYAKHO AND MI: THREE-LEVEL INVERTER-BASED SHUNT APF IN THREE-PHASE THREE-WIRE AND FOUR-WIRE SYSTEMS 13
proposed control is shown in Fig. 16(c) and (d), by turning ON517
and OFF the load. The grid current is regulated after an identifica-518
tion period of 20 ms as a sinusoidal waveform. The grid-current519
waveforms are shown with control in the xy-coordinates, as520
shown in Fig. 16(e) with ripple filter and Fig. 16(g) without521
ripple filter. The VSI is directly connected to the grid, and the522
grid impedance being very small, can be neglected. The grid-523
current waveforms, using control in the αβ-coordinates, with524
ripple filter and without ripple filter, are shown in Fig. 16(f) and525
(h) for comparison purpose. Fig. 16(i) shows the well-regulated526
upper and lower dc-link capacitor voltages. Fig. 16(j) shows the527
APF current waveforms to compensate both fundamental and528
harmonic components of the load current (total compensation,529
real-time mode) with a ripple filter.530
Fig. 17 illustrates the comparison of the harmonic content531
spectrum between the two different control methods. The THD532
of the inverter output current based on the rotated xy-coordinates533
is lower than that of the control method in the αβ-coordinates.534
The FFT waveforms are obtained by Tektronix WaveStar soft-535
ware based on one-period (Fig. 16) samples. For a better visual-536
ization, y axis is limited at 2A. It should be noted that DCSVC537
control gained the low-order harmonics in case of LCL-filter538
usage, as shown in Fig. 17. However, the control in the xy-539
coordinates has a better performance and keeps the spectrum540
in an acceptable level with and without an LCL-filter. Another541
disadvantage of the DCSVC control is the increase of the in-542
verter switching frequency in case of LCL-filter usage. The543
measured inverter temperature with an LCL-filter is about 30%544
higher than the temperature without an LCL-filter. One of the545
solutions for this problem could be a higher inductance for the546
LCL-filter.547
The compensation of currents in a four-wire system548
with and without LCL-filter is shown in Fig. 18. It can549
be seen from Fig. 18(b) that the neutral current is reg-550
ulated to zero, based on the proposed control. It should551
be noted that hysteresis controller in a four-wire system552
decreases the performance of an LCL-filter, as shown in553
Fig. 18(c).554
V. CONCLUSION555
In this paper, two DCSVC methods are proposed as a shunt556
APF based on a three-level voltage-source inverter. Two coordi-557
nate systems are studied with one in the xy-coordinates rotating558
synchronously with the fundamental grid-voltage space vec-559
tor, and the other in the stationary αβ-coordinates. The perfor-560
mance of the inverter system with an LCL-filter is analyzed. The561
DCSVC in the xy-coordinates significantly reduces the number562
of switching with the same current ripple (hysteresis band), com-563
pared with a DCSVC in the αβ-coordinates. The APF is able to564
compensate balanced and unbalanced nonlinear load currents of565
a four-wire system with the neutral wire connected to the capac-566
itor midpoint. The neutral current of the three-phase four-wire567
system is regulated and the dc-link neutral-point voltage is bal-568
anced under the sign cubical hysteresis controller. The proposed569
shunt APF can compensate on demand the harmonic currents570
as well as the reactive currents (full compensation of reactive571
currents). It adapts itself within one fundamental period to com- 572
pensate for unexpected variations in the load current, and correct 573
the power factor to near unity in the case of full compensation. 574
Experiments have been conducted on a 30-kVA test bench 575
with an IGBT-based three-level inverter. The simulation and 576
experimental results validated the performance of the proposed 577
APF control. 578
REFERENCES 579
[1] M. Depenbrock, “A generally applicable tool for analyzing power rela- 580tions,” IEEE Trans. Power Syst., vol. 8, no. 2, pp. 381–387, May 1993. 581
[2] H. Akagi, “Active harmonic filters,” Proc. IEEE, vol. 93, no. 12, pp. 315– 582320, Dec. 2005. 583
[3] J. Allmeling, “A control structure for fast harmonics compensation in 584active filters,” IEEE Trans. Power Electron., vol. 19, no. 12, pp. 508–514, 585Mar. 2004. 586
[4] M. Routimo, M. Salo, and H. Tuusa, “Comparison of voltage-source and 587current-source shunt active power filters,” IEEE Trans. Power Electron., 588vol. 22, no. 2, pp. 636–643, Mar. 2007. 589
[5] C. Lascu, L. Asiminoaei, I. Boldea, and F. Blaabjerg, “High performance 590current controller for selective harmonic compensation in active power 591filters,” IEEE Trans. Power Electron., vol. 22, no. 5, pp. 1826–1835, Sep. 5922007. 593
[6] L. Asiminoaei, P. Rodriguez, and F. Blaabjerg, “Application of discon- 594tinuous PWM modulation in active power filters,” IEEE Trans. Power 595Electron., vol. 23, no. 4, pp. 1692–1706, Jul. 2008. 596
[7] M. Asiminoaei, F. Blaabjerg, and S. Hansen, “Evaluation of harmonic 597detection methods for active power filter applications,” in Proc. APEC 5982005, vol. 1, pp. 635–641. 599
[8] O. Vodyakho, D. Hackstein, A. Steimel, and T. Kim, “Novel direct current- 600space-vector control for shunt active power filters based on three-level 601inverters,” in Proc. IEEE 23rd Appl. Power Electron. Conf. (APEC 2008), 602pp. 1868–1873. 603
[9] O. Vodyakho, T. Kim, and S. Kwak, “Comparison of the space vector 604current controls for active power filters,” in Proc. 2008 IEEE Ind. Electron. 605Soc. (IECON), Orlando, FL, Nov., pp. 612–617. 606
[10] M. I. M Montero, E. R. Cadaval, and F. B. Gonzalez, “Comparison of 607control strategies for shunt active power filters in three-phase four-wire 608systems,” IEEE Trans. Power Electron., vol. 22, no. 1, pp. 229–236, Jan. 6092007. 610
[11] O. Vodyakho, T. Kim, and S. Kwak, “Three-level inverter based active 611power filter for the three-phase, four-wire system,” in Proc. IEEE 39th 612Power Electron. Spec. Conf. (PESC 2008), pp. 1874–1880. 613
[12] M. E. Ortuzar, R. E. Carmi, J. W. Dixon, and L. Moran, “Voltage-source 614active power filter based on multilevel converter and ultracapacitor DC 615link,” IEEE Trans. Ind. Electron., vol. 53, no. 2, pp. 477–485, Apr. 6162006. 617
[13] M. P. Kazmierkowski, M. A. Dzienkowski, and W. Sulkowski, “Novel 618space vector based current controllers for PWM inverters,” IEEE Trans. 619Power Electron., vol. 6, no. 1, pp. 158–166, Jan. 1991. 620
[14] J. Hurng-Liahng, W. Kuen-Der, W. Jinn-Chang, and C. Wen-Jung, “A 621three-phase four-wire power filter comprising a three-phase three-wire 622active power filter and a zig–zag transformer,” IEEE Trans. Power Elec- 623tron., vol. 23, no. 1, pp. 252–259, Jan. 2008. 624
[15] J. Pou, D. Boroyevich, and R. Pindado, “Effects of imbalances and non- 625linear loads on the voltage balance of a neutral-point-clamped inverter,” 626IEEE Trans. Power. Electron., vol. 20, no. 1, pp. 123–131, Jan. 2005. 627
[16] Xilinx LogiCore: Fast Fourier Transform v3.2, 2005, Xilinx, Inc. 628[17] J. Ranneberg, “A control of three-level inverter as active power filter with 629
the current control strategy,” Ph.D. dissertation, Technische Univ. Berlin, 630Berlin, 1994. 631
[18] E. Twining and D. G. Holmes, “Grid current regulation of a three-phase 632voltage source inverter with an LCL input filter,” IEEE Trans. Power 633Electron., vol. 18, no. 3, pp. 888–895, May 2003. 634
[19] S. Guoqiao, X. Dehong, C. Luping, and Z. Xuancai, “An improved control 635strategy for grid-connected voltage source inverters with an LCL filter,” 636IEEE Trans. Power Electron., vol. 23, no. 4, pp. 1899–1906, Jul. 2008. 637
[20] L. A. Serpa, S. Ponnaluri, P.M. Barbosa, and J. W. Kolar, “A modified 638direct power control strategy allowing the connection of three-phase in- 639verters to the grid through LCL filters,” IEEE Trans. Ind. Appl., vol. 43, 640no. 45, pp. 1388–1400, Sep./Oct. 2007. 641
IEEE
Proo
f
14 IEEE TRANSACTIONS ON POWER ELECTRONICS
Oleg Vodyakho (S’02–M’07) received the Dr.-Ing.642degree in electrical engineering from the Univer-643sity (FernUniversitat) of Hagen, Hagen, Germany,644in 2007.645
From 2002 to 2003, he was a Fellowship Re-646searcher in the Power Electronics Laboratory, Uni-647versity of Applied Science, Konstanz, Germany. He648was with Nokian Capacitors, Ltd. as a Research En-649gineer from 2003 to 2007. He joined the University650of Michigan—Dearborn in 2007 as a Postdoctoral651Research Associate. His current research interests in-652
clude power electronics system control, power quality issues, and application653and control of inverters and electric drives.654
655
Chris C. Mi (S’00–A’01–M’01–SM’03) received 656the B.S.E.E. and M.S.E.E. degrees from Northwest- 657ern Polytechnical University, Xi’an, China, and the 658Ph.D degree from the University of Toronto, Toronto, 659ON, Canada, all in electrical engineering. 660
He is an Associate Professor of electrical and 661computer engineering, and Director of DTE Power 662Electronics Laboratory at the University of Michi- 663gan, Dearborn. He is also the Chief Technical Officer 664of 1Power Solutions, Inc. He was with General Elec- 665tric Company from 2000 to 2001. He regularly offers 666
a graduate course in electric and hybrid vehicles, and has taught tutorials and led 667seminars on the subject of HEV/PHEV for the Society of Automotive Engineers 668(SAE), the IEEE, the National Science Foundation (NSF), and the National Soci- 669ety of Professional Engineers. He delivered the HEV course to major automotive 670original equipment manufacturers (OEMs) and suppliers, including GM, Ford, 671Chrysler, and Delphi. He has offered the tutorial in five countries, including the 672United States, China, Korea, Malaysia, and Mexico. He has conducted exten- 673sive research in EV/HEV space and is the author or coauthor of more than 100 Q3674articles. He has delivered keynote speeches at many international conferences. 675
Dr. Mi became a member of the Eta Kappa Nu, the Electrical and Computer 676Engineering Honor Society, for being “a leader in education and an example 677of good moral character.” He was the General Chair of the Fifth IEEE Inter- 678national Vehicle Power and Propulsion Conference, Dearborn, MI, September 6797–11, 2009. He was the recipient of the 2007 SAE Environmental Excellence in Q4680Transportation (E2T) Award for “Innovative Education and Training Program in 681Electric, Hybrid, and Fuel Cell Vehicles.” He is the recipient of the 2005 “Dis- 682tinguished Teaching Award” of University of Michigan—Dearborn, the IEEE 683Region 4 “Outstanding Engineer Award,” the IEEE Southeastern Michigan Sec- 684tion “Outstanding Professional Award,” “the National Innovation Award,” and 685the “Government Special Allowance Award.” In December 2007. Q5686
