Download Feedback Control of Five-Level PWM Rectifier: Application to the S

124
Feedback Control of Five-Level PWM Rectifier:
Application to the Stabilization of DC Voltages
of Five-Level NPC Active Power Filter
T. Abdelkrim1, E.M. Berkouk2, K. Benamrane1, T. Benslimane3
1
Applied Research Unit on Renewable Energies,
Industrial zone, B.P. 88, Ghardaïa, Algeria.
2
Laboratory of Process Control, Polytechnic National School,
Street Hassen Badi, El Harrach, B.P. 182 Algiers, Algeria.
3
University of M’sila, BP. 166, street Ichbilia, M’sila, Algeria.
[email protected], [email protected]
Abstract—The purpose of this paper is to develop a control
and regulation method of input DC voltages of five-level
Neutral Point Clamping (NPC) Active Power Filter (APF). This
APF is applied for the enhancement of 5,5kV (ph-ph) network
power quality by compensation of harmonic currents produced
by an induction motor speed variator. In the first part, the
authors present a topology of five-level NPC Voltage Source
Inverter (VSI), and then, they propose a model of this
converter and its PWM control strategy. In the second part,
the control strategy of five-level PWM current rectifier is
presented. In the third part, to remedy to instability problem of
the input DC voltages of the APF, the authors propose
feedback control of the five-level PWM rectifier followed by
clamping bridge filter. After that, the sliding mode regulator
used to control the APF is developed. The application of the
proposed feedback control algorithm to the studied cascade
offers the possibility of stabilizing the DC voltages of APF.
Stable DC bus supply associated with sliding regulator of APF
allows getting low-harmonic content network currents with
unity power factor. In all over, the instability problem
associated with use of multilevel APF is solved. The obtained
results are full of promise to use the multilevel APF in high
voltage and great power applications.
Index Terms—Active power filter, NPC multilevel inverter,
feedback control, PWM rectifier, clamping bridge.
I. INTRODUCTION
The increasing use of control systems based on power
electronics in industry involves more and more disturbance
problems in the level of the electrical power supply
networks [1]. Thus, one remarks a regular increase in
currents harmonic distortion and unbalance rates, as well as
an important consumption of the reactive power. These
harmonic currents yield voltage harmonics and unbalances
via impedance of power supply network, which infects the
sinusoidal waveform of the electrical power supply voltage.
These disturbances of course have bad consequences on
electrical equipments, such as strong heating, sudden
stopping of the revolving machines or even the total
destruction of these equipments.
Several solutions for reducing harmonic current in
electrical power supply networks were proposed. Those
which satisfy more the industrial constraints are the active
compensators such as shunt active filter, series active filter
and combined shunt-series active filters.
In fact, the main role of active filtering is to constantly
control the harmonic distortion in an active way by the
compensation of the harmonics [2,3]. European standards
CEI 61000-3-4 and CEI 61000-3-6 define low, medium and
high voltage power supply networks harmonic currents
limits [4].
Research on the shunt active filters implied different
works concerning harmonics identification methods such as
Fourier transform method [5], the method of synchronous
reference frame (d-q) [6], and control strategies such as
sliding mode regulators, artificial neural networks and fuzzy
logic controllers [7-9]. The structures of the filters also
knew an evolution, from two-level converters [10,11] to
multilevel converters [12-14]. In high power applications,
this latter is more adequate, compared to the conventional
two-level structure, simply because of the low harmonic
distortion rate of source voltage and current, low switching
frequency besides no need to use transformer [15-18].
Various topologies are developed such as flying capacitor
multilevel converters, diode clamped multilevel converters,
NPC multilevel converters, and H bridge multilevel
converters.
The unbalance of the different DC voltage sources of the
multi-level (NPC) active power filters constitutes the major
limitation for the use of these power converters.
The objective of this paper is to stabilise the input DC
voltages of five-level NPC APF. For this purpose, a
feedback control of five-level PWM rectifier followed by
clamping bridge filter is used. This APF is applied for the
enhancement of 5,5kV (ph-ph) network power quality by
compensation of harmonic currents produced by an
induction motor speed variator (Fig. 1).
First part is dedicated to the presentation of model of the
three phases five-level NPC VSI with its four carriers
triangulo-sinusoidal PWM control strategy. In the second
part, the modelling and control of five-level PWM current
rectifier is presented. After that the control strategy of the
input DC voltages of multilevel NPC APF is developed. The
five-level shunt APF is controlled using a sliding mode
regulator. At the end, simulation results are presented.
125
m =1 : for the lower half leg;
m =0 : for the upper half leg
Table 1 gives the electrical quantities characterising
each leg.
TABLE 1. EXCITATION TABLE OF A LEG K OF FIVE-LEVEL NPC VSI
Figure 1. Synoptic diagram of application of shunt APF on
power supply fed cascaded thyristor bridge rectifier-two
level VSI-induction motor
II. MODELLING OF FIVE-LEVEL NPC VOLTAGE SOURCE
INVERTER
II.1. Modelling of five-level NPC VSI

Bk 2
Bk 3
VkM
1
1
1
U c1  U c 2
1
1
0
U c1
1
0
0
0
0
1
0
0
0
0
 U c3
 U c3  U c 4
The output voltages relatively to the middle point M of
the inverter, using the half leg connection functions, are
given as follows:




F11b 
F18  F10b 
F10b 
VAM  F17  F11b 


V   F  F b U  F b Uc  F  F b U   F b U
BM
27
21
c1
21
2
28
20
c3
20
c4









 

F37  F31
F31b 
F38  F30b 
F30b 
VC
b 
M


 


 
(4)
The simple output voltages are defined as follows:
The three phases five-level NPC VSI is constituted by three
legs and four DC voltage sources. Every arm has eight bidirectional switches, six in series and two in parallel, and
two diodes to get the zero voltage for VKM (Fig. 2). Every
switch is composed by a transistor and a diode in antiparallel [19].
Bk1


V A 
 2  1  1 VAM 
  1 
   
V


1
2

1
B
  3
 VBM 
V
 1  2 VCM
1
C

(5)
The input currents of the inverter using the connection
functions and load currents are given as follows:
 id 1  F17 i1  F27i2  F37 i3

b
b
b
 id 2  F11i1  F21i2  F31i3
 id 3  F18i1  F28i2  F38i3
 i  F bi  F b i  F b i
10 1
20 2
30 3
 d4
(6)
id 0  i1  i2  i3  id 1  id 2  id 3  id 4
The input filter model is defined as follows:
 dU c1
 C1 dt  Ired  id1  id 2
 dU
c2
C2
 Ired  id
2

dt
 dU
c3
 C3
 Ired  id1  id 2  id 0
dt

dU c 4

C4
 Ired  id1  id 2  id 3  id 0
dt
Figure 2. Five-level NPC voltage source inverter
The switch connection function FKS indicates the opened
or closed state of the switch TDKS:
1
FKS  
0
if TD KS close
if TD KS open
(1)
II.2. PWM strategy of the five-level NPC VSI
For a leg k of the three phases five-level NPC VSI,
several complementary laws control are possible. The
optimal control law of this inverter is:
 F K 5  1  FK 1

 FK 4  1  FK 2
F  1 F
 K6
K3
(2)
b
Half leg connection function FKm
is defined as:
 F Kb1  F K 1F K 2F K 3
 b
 FK 0  FK 4 FK 5 FK 6
(7)
(3)

Two-level carrier-based PWM techniques have been
extended to multilevel inverters using several triangular
carrier signals and one reference signal per phase. For Nlevel inverter, (N - 1) carriers with the same frequency fc
and same peak-to-peak amplitude Ac are disposed such that
the bands they occupy are contiguous. The reference, or
modulation, wave form has peak-to-peak amplitude Am and
frequency fm, and its centred in the middle of the carrier set.
The reference is continuously compared with each of the
carrier signals (Fig. 3)[20-22]
126
400
Vref Up1 Up2 Up3 Up4
300
200
100
0
-100
-200
-300
-400
0.02
0.022 0.024
0.026 0.028
0.03 0.032 0.034
Time(s)
0.036 0.038
0.04
Figure 3. Triangulo-sinusoidal strategy with four bipolar
carriers
The different input DC voltages of the inverter are fed by
a battery E (Fig. 2). Fig. 4 shows the simple output voltage
VA of the five-level NPC VSI. Fig. 5 displays the voltages
across input capacitors. It can be noted that these capacitors
voltages are unbalanced.
Figure 6. Five-level PWM current rectifier topology
500
400
 k  2 ⋅ di ⇒ Bi1  0, Bi 2  0, Bi 3  0.
di    2 ⋅ di ⇒ B  0, B  0, B  1.
k
i1
i2
i3

−
di



di
⇒
B

1,
B

0,
B

k
i1
i2
i 3  0.
 − 2 ⋅ di   −di ⇒ B  1, B  1, B  0.
i1
i2
i3
300
200
VA(V)
100
0
-100
-200

k


   −2 ⋅ di ⇒ Bi1  1, Bi 2  1, Bi 3  1.
-300
-400
-500
0.02
0.022
0.024
0.026
0.028
0.03
0.032
0.034
0.036
0.038
0.04
240
190
230
Uc2(V)
Uc1(V)
Figure 4. Simple output voltage VA
200
180
170
200
240
190
230
180
170
160
0.05
Time(s)
0.1
reci0ref
is the difference between reference current ireci0ref and
source current ireci0.
di: hysteresis band width
0
0.05
Time(s)
0.1
220
210
0
−i
220
200
0.1
Uc4(V)
Uc3(V)
0.05
Time(s)
reci0
k
210
0
k
with:  k  i
Time(s)
160
(8)
200
0
0.05
Time(s)
0.1
Figure 5. Inverter input capacitors voltages
III. MODELLING AND CONTROL OF FIVE-LEVEL PWM
CURRENT RECTIFIER
The advantages of five-level PWM current rectifier
topology (Figure 6) are well known and have been applied
in medium voltage and high power applications in the last
years. The reversibility of the five-level VSI allows it to
work as current rectifier [22].
The basic principle of the five-level hysteresis current
control is based on the classical hysteresis control applied to
conventional two-level inverters. The five-level hysteresis
control algorithm is given by equation (8).
IV. CONTROL STRATEGY OF THE INPUT DC VOLTAGES OF
MULTILEVEL NPC APF
In this part, one proposes to remedy to the instability
problem of the input DC voltages of five-level APF, by
using a clamping bridge filter and feedback control of the
output DC voltages of PWM multilevel rectifier [21-24].
IV.1. Modelling and Control of Clamping Bridge
The clamping bridge cell is a simple circuit constituted by
a transistor and a resistor in series connected in parallel with
a capacitor as shown in Figure 7. The transistors are
controlled in order to maintain equality of the different
voltages [25-26].
The model of the intermediate filter with clamping bridge
is defined by the following equation:
dU ci 
 I rec i  ir (i 1)  ic (i 1) − id i − ir i
dt
U
with:
iri  Ti ci
Ri
Ci
(9)
127
Different quantities Irectm, iload and ic are defined as
follows:
irec1 2 ⋅ irec2 - irec3 - 2 ⋅ irec4

Irectm 
2

id1  2 ⋅ id2 - id3 - 2 ⋅ id4
i

 load 
2

i c  Irectm − i load



(14)
By using of the power conservation principle and
neglecting of joules loss in the resistor Rr, and by
considering a sinusoidal supply network current in phase
with corresponding voltage Vsi, it can be written:
3Vsi ireci 0  4 ⋅U rectm ⋅ (ic  iload )
Figure 7. Clamping bridge cell
The transistor is controlled using the following algorithm:
  i  U ci − U cref


(10)
U ci
 if  i  dr then Ti  1⇒ ir i  Ti
R
i

then Ti  0 ⇒ ir i  0
if  i 
−dr
dr hysteresis band width.
IV.2. Multi DC Bus Link Voltage Controller
In this part, one proposes to enslave the output DC
voltage of five-level PWM current rectifier using a PI-based
feedback control. The synoptic diagram of five-level PWM
current rectifier control is shown in Figure 8 [21-22]. The
transfer functions GI(S) and GV(S) are expressed as follows:
ireci 0
(1 / Rr )

Vsi 1  (Lr / Rr ) ⋅ S
1
GV (S ) 
C⋅S
GI (S ) 
(11)
(12)
Figure 8. Synoptic diagram of five-level PWM current
rectifier control
The modelling of this loop is based on the instantaneous
power conservation principle with no loss hypothesis. This
loop imposes the root mean square (rms) value of network
current [27].
Input and output powers are:
3

L r di 2reci0
2
P

(V
i
−
R
i
−
)
r reci0
 in ∑ si reci0
2 dt
i 1

4
Pout  ∑ (U rcii reci )  4U cm (i c  i load )

i 1
(13)
(15)
V. ACTIVE POWER FILTER CONTROL
A medium voltage source of 5.5kV, 50Hz feeds an
induction motor speed variator as illustrated in Fig. 1. This
load produces a distorted current of 97 % THD which is
above the tolerated THD limit standard. This current with its
spectral analysis are presented in Fig. 9.
Torque and speed features of this motor are presented in
Fig. 10. At t=10s, rated torque (Tn=7.6kN.m) is applied. It is
noticed that the speed turns back to its reference (1500 rpm)
after a slight decrease.
Active power filter is controlled using sliding mode
regulator [7-9] [28],[29]. From the model of active filter
associated to supply network (16) and by considering the
error between harmonic current reference and the active
filter current as sliding surface (17), and the smooth
continuous function as attractive control function (18), one
gets the control law (19).
V frefK −VK  R f i fK  Lf (difK / dt)
with:
VK  VsK − RsiSK − Ls (disK / dt) ;
(16)
K = 1,2 and 3
S s  i frefK − i fK
(17)
U n  k.(S s /( S s   ))
(18)
V frefK  R f i fK  L f (di frefK / dt)  VK  k (S s /( S s   ))
(19)
The input DC bus of NPC five-level shunt APF is fed by
a five-level PWM current rectifier followed by clamping
bridge filter. The application of the feedback control on the
rectifier allows getting a stable total output DC voltage.
Balancing capacitors voltages is guaranteed by the clamping
bridge filter.
Figure 11 shows DC bus capacitors voltages before and
after application of clamping bridges. Before t=22s, these
voltages diverge, but the average voltages remains constant
(Ucm). Application of clamping bridges allows getting stable
capacitors voltages around there reference of 3kV.
Figure 12 presents first phase of PWM five-level rectifier
current irec10 and its reference current irec10ref before and after
application of clamping bridge. Part of the power is
dissipated in resistances of clamping bridges, which justifies
the increase in the amplitude of the current. This current has
a 0.006 total harmonic distortion and in phase with the
voltage as shown in figure 13.
128
80
60
i r e c 1 0 1 ( A ) , i r e c 1 0 r e f( A )
Reference identified harmonic current ifref1 and output
filter current if1 are almost superimposed as presented in
Figure 14.
Figure 15.a presents main source voltage Vs1 and current
is1 after harmonic current compensation. Spectral analysis is
presented in Figure 15.b. It is shown that source current is
almost sinusoidal with THD less than 5% and unity power
factor. This THD would not have been obtained if the input
DC capacitors voltages of APF were unbalanced.
40
20
0
-20
-40
-60
-80
21.5
600
0.9
22.5
-200
150
23.975
Vs1
100
0.8
0.4
ire c10
0.3
0.1
23.97
0.9
(b)
0.5
-400
23.965
1
0.6
0.2
-600
23.96
23.5
0.7
Vs1/40(V), irec10(A)
(a)
0
harmonic amplitude( pu )
200
23
time(s)
Figure 12. PWM rectifier current irec10 and its reference
irec10ref
0.8
0
23.98
0
10
time(s)
20
30
40
50
harmonic row
50
(a)
0
-50
harmonic amplitude( pu )
400
is1(A)
22
1
0.7
0.6
0.5
(b)
0.4
0.3
0.2
Figure 9. Current drawn by the induction motor speed
variator (THD = 0.97)
-100
0.1
-150
23.96
2000
7
x 10
T o rq u e (N m )
500
5
10
15
30
40
50
400
-1
20
20
harmonic row
2
1
0
10
(b)
3
200
0
0
0
0
23.98
600
4
if1(A ), ifref1(A )
S p e e d (rp m )
(a)
23.975
Figure 13. Input voltage and current of PWM rectifier and
spectral analysis of current (THD=0.006)
5
1000
23.97
time(s)
6
1500
23.965
4
0
5
10
Time(s)
15
20
Time(s)
0
-200
Figure 10. Induction motor mechanical speed and torque
-400
-600
23.96
23.965
23.97
23.975
23.98
Uc3
400
3100
23.99
23.995
24
Figure 14. Reference harmonic current ifref1 and filter
output current if1
3300
3200
23.985
time(s)
Uc1
1
Ucref
0.9
300
3000
Ucm
2800
Uc2
2700
U c4
2600
15
16
17
18
19
20
21
22
23
time(s)
Figure 11. DC bus condensers voltages before and after
application of clamping bridges
100
(a)
0
-100
24
-200
harm o ni c am p li tud e ( p u )
0.8
200
2900
V s 1/1 5 (V ), is 1 (A )
U c 1 (V ),U c 2 (V ),U c 3 (V ),U c 4 (V ),U c m (V ),U c re f(V )
3400
0.7
0.6
0.5
(b)
0.4
0.3
0.2
-300
-400
23.96
0.1
23.965
23.97
time(s)
23.975
23.98
0
0
10
20
30
40
50
harmonic row
Figure 15. Main source voltage Vs1 and current is1 with
its spectral analysis (THD=0.047)
129
Simulation Parameters:
Main source:
Vph-ph=5,5kV, Rs = 0.0001Ω, Ls = 0.001H.
Induction motor:
Pn=1.2MW, Ωn=1500rpm, Tn=7.6kN.m, VIM(ph-ph) = 2300V,
J=46kg.m2, Rsm=0.0406Ω, Rrm=0.0308Ω, Lrm=0.0591H,
Lsm=0.0591H, M=0.0581H.
Active power filter:
Rf = 0.001Ω, Lf = 0.003H, fc=6kHz.
Clamping bridge:
Ucref=3000V, C=0.05F, R= 5Ω.
Five-level PWM rectifier:
Ucrefr=3000V, Lr=0.05H, Rr=0.01Ω
[6]
[7]
[8]
[9]
[10]
[11]
[12]
VI. CONCLUSION
In this paper, one studies the problem of unbalanced input
capacitors DC voltages of five-level NPC shunt active
power filter supplied by five-level PWM rectifier.
The modelling of the five-level NPC inverter shows that it
is equivalent to four two-level inverters in series. The study
of the instability problem of the input DC voltages of this
converter shows that its different input voltages are not
stables, which implies a bad harmonic current
compensation.
To solve this instability problem, one proposes to use a
clamping bridge filter to improve input DC voltages
balance.
In spite of this solution, the output voltage of five-level
rectifier is not constant. To remedy to this problem, one
proposes the feedback control of its output voltage. The
application of the proposed feedback control algorithm to
the rectifier shows a good voltage tracking.
Feedback control algorithm of the rectifier associated with
clamping bridge filter makes stable the input DC voltages of
five-level APF.
The proposed control algorithm opens the door to
different applications of NPC multilevel converters in high
power utilities such as, motor drives, doubly fed induction
generators, power supply networks interconnection. This
work can also be extended to series active power filters.
In active power filter applications, the proposed control
makes possible:
- Active power filtering in medium voltage without
using transformer.
- Low total harmonic distortion of main source
currents.
[13]
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