T. Abdelkrim1, E.M. Berkouk2, K. Benamrane1, T. Benslimane3

1Applied Research Unit on Renewable Energies, Industrial zone, B.P. 88, Ghardaïa, Algeria.

2Laboratory of Process Control, Polytechnic National School, Street Hassen Badi, El Harrach, B.P. 182 Algiers, Algeria.

3University of M’sila, BP. 166, street Ichbilia, M’sila, Algeria. tameur2@yahoo.fr, bens082002@yahoo.fr

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.

Feedback Control of Five-Level PWM Rectifier: Application to the Stabilization of DC Voltages of Five-Level NPC Active Power Filter

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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 The three phases five-level NPC VSI is constituted by three legs and four DC voltage sources. Every arm has eight bi-directional 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 anti-parallel [19].

Figure 2. Five-level NPC voltage source inverter

The switch connection function FKS indicates the opened

or closed state of the switch TDKS:

=openTDif0closeTDif1

FKS

KSKS

(1)

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:

−=−=−=

36

24

15

111

KK

KK

KK

FFFFFF

(2)

Half leg connection function bKmF is defined as:

==

6540

3211

KKKb

K

KKKb

K

FFFFFFFF (3)

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

1kB 2kB 3kB kMV 1 1 1

21 cc UU + 1 1 0

1cU 1 0 0 0 0 0 1

3cU− 0 0 0

43 cc UU −− The output voltages relatively to the middle point M of

the inverter, using the half leg connection functions, are given as follows:

4

30

20

10

3

3038

2028

1018

2

31

21

11

1

3137

2127

1117

cb

b

b

cb

b

b

b

b

b

cb

b

b

CM

BM

AM

UFFF

UFFFFFF

UcFFF

UFFFFFF

VVV

−

+++

−

+

+++

=

(4)

The simple output voltages are defined as follows:

−−−−−−

=

CM

BM

AM

C

B

A

VVV

VVV

211121112

31 (5)

The input currents of the inverter using the connection functions and load currents are given as follows:

−−−−++=++=++=++=++=

43213210

3302201104

3382281183

3312211112

3372271171

ddddd

bbbd

d

bbbd

d

iiiiiiiiiFiFiFiiFiFiFiiFiFiFiiFiFiFi

(6)

The input filter model is defined as follows:

−−−−=

−−−=

−=

−−=

0321

021

2

21

44

33

22

11

ididididIreddt

dUC

idididIreddt

dUC

idIreddt

dUC

ididIreddt

dUC

c

c

c

c

(7)

II.2. PWM strategy of the five-level NPC VSI

Two-level carrier-based PWM techniques have been extended to multilevel inverters using several triangular carrier signals and one reference signal per phase. For N-level 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]

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0.02 0.022 0.024 0.026 0.028 0.03 0.032 0.034 0.036 0.038 0.04-400

-300

-200

-100

0

100

200

300

400

Time(s)

Vre

f Up1

Up2

Up3

Up4

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.

0.02 0.022 0.024 0.026 0.028 0.03 0.032 0.034 0.036 0.038 0.04-500

-400

-300

-200

-100

0

100

200

300

400

500

VA(V

)

Time(s)

Figure 4. Simple output voltage VA

0 0.05 0.1160

170

180

190

200

Uc1

(V)

Time(s)0 0.05 0.1

200

210

220

230

240

Uc2

(V)

Time(s)

0 0.05 0.1160

170

180

190

200

Uc3

(V)

Time(s)0 0.05 0.1

200

210

220

230

240

Uc4

(V)

Time(s) 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).

Figure 6. Five-level PWM current rectifier topology

===⇒⋅−<===⇒−<<⋅−

===⇒<<−===⇒⋅<<

===⇒⋅>

.1,1,12.0,1,12

.0,0,1.1,0,02

.0,0,02

321

321

321

321

321

iiik

iiik

iiik

iiik

iiik

BBBdiBBBdidi

BBBdidiBBBdidi

BBBdi

εε

εε

ε

(8)

with: reci0refireci0ik −=ε

kε is the difference between reference current ireci0ref and source current ireci0. di: hysteresis band width 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:

iridicirirecci

i iiiiIdt

dUC −−++= ++ )1()1(

(9)

with: i

ciiri RU

Ti =

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Figure 7. Clamping bridge cell

The transistor is controlled using the following algorithm:

=⇒=−<

=⇒=>

−=

00

1

irii

i

ciiirii

crefcii

iTthendrifR

UTiTthendrif

UU

ε

ε

ε (10)

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:

SRLR

ViSG

rr

r

si

reciI ⋅+

==)/(1

)/1()( 0 (11)

SCSGV ⋅

=1)( (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:

+==

−−=

∑

∑

=

=4

1iloadccmrecirciout

3

1i

2reci0r2

reci0rreci0siin

)i(i4U)i(UP

)dt

di2LiRi(VP

(13)

Different quantities Irectm, iload and ic are defined as follows:

−=

⋅⋅+=

⋅⋅+=

loadc

load

iIrectmi2

id42-id3-id22id1i2

irec42-irec3-irec22irec1Irectm (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:

)(43 0 loadcrectmrecisi iiUiV +⋅⋅= (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).

)/( dtdiLiRVV fKffKfKfrefK +=− (16)

with: )/( dtdiLiRVV sKsSKssKK −−= ; K = 1,2 and 3

fKfrefKs iiS −= (17)

))/(.( λ+= ssn SSkU (18)

))/(()/( λ++++= ssKfrefKffKffrefK SSkVdtdiLiRV (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.

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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.

23.96 23.965 23.97 23.975 23.98-600

-400

-200

0

200

400

600

time(s)

is1(

A)

0 10 20 30 40 500

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

harmonic row

harm

onic

am

plitu

de( p

u )

( a ) ( b )

Figure 9. Current drawn by the induction motor speed variator (THD = 0.97)

0 5 10 15 200

500

1000

1500

2000

Time(s)

Spe

ed (r

pm)

0 5 10 15 20-1

0

1

2

3

4

5

6

7x 104

Time(s)

Torq

ue (N

m)

( a ) ( b )

Figure 10. Induction motor mechanical speed and torque

15 16 17 18 19 20 21 22 23 242600

2700

2800

2900

3000

3100

3200

3300

3400

Uc1

(V),U

c2(V

),Uc3

(V),U

c4(V

),Ucm

(V),U

cref

(V)

time(s)

Uc1

Uc3

Ucm

Uc2

Uc4

Ucref

Figure 11. DC bus condensers voltages before and after

application of clamping bridges

21.5 22 22.5 23 23.5-80

-60

-40

-20

0

20

40

60

80

time(s)

irec1

01(A

), ire

c10r

ef(A

)

Figure 12. PWM rectifier current irec10 and its reference

irec10ref

23.96 23.965 23.97 23.975 23.98-150

-100

-50

0

50

100

150

time(s)

Vs1

/40(

V),

irec1

0(A

)

0 10 20 30 40 500

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

harmonic row

harm

onic

am

plitu

de( p

u )

( a ) ( b )

Vs1

irec10

Figure 13. Input voltage and current of PWM rectifier and

spectral analysis of current (THD=0.006)

23.96 23.965 23.97 23.975 23.98 23.985 23.99 23.995 24-600

-400

-200

0

200

400

600

time(s)

if1(A

), ifr

ef1(

A)

Figure 14. Reference harmonic current ifref1 and filter

output current if1

23.96 23.965 23.97 23.975 23.98-400

-300

-200

-100

0

100

200

300

400

time(s)

Vs1

/15(

V),

is1(

A)

0 10 20 30 40 500

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

harmonic row

harm

onic

am

plitu

de( p

u )

( a ) ( b )

Figure 15. Main source voltage Vs1 and current is1 with

its spectral analysis (THD=0.047)

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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

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.

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Signal and Communications

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