direct power control switching table concept and analysis for

Corresponding author : [email protected] of Power Electronics and Industrial Control (LEPCI), Setif University1, Algeria

Copyright © JES 2013 on-line : journals/esrgroups.org/jes

A. ChaouiJ-P. GaubertA. Bouafia

J. Electrical Systems 9-1 (2013): 52-65

Regular paper

Direct Power Control SwitchingTable Concept and Analysis for

Three-phase Shunt ActivePower Filter

JESJournal ofElectricalSystems

This paper deals with the concept and analysis of direct power control (DPC) for a shuntactive power filter (SAPF). From the topology of the SAPF and its equivalent scheme a newpredefined switching table is designed by analyzing the voltage source inverter (VSI) switchingvectors effect on the total derivatives of instantaneous active and reactive power. To maintainthe VSI dc-bus voltage at the required level an IP controller is used to obtain the active powercontrol. The active and reactive powers are directly controlled by selecting the optimalswitching state. The main advantages of this method are that it provides a sinusoidal sourcecurrent and unity power factor with no need of linear current controllers and coordinatestransformations or modulators. Extensive simulation and experimental results obtained fromsteady and transient states have proven the excellent performance and verify the validity andeffectiveness of the proposed power control scheme.

Keywords: Direct power control; Harmonics; IP controller; PLL; Shunt active power filter;Switching table.

1. INTRODUCTION

Having as main task to improve source power quality and performed its unity powerfactor, three-phase VSIs continue to take a major place in many grid-connected applicationssuch as active power filter, uninterruptible power systems, and distributed generatingsystems using renewable energy sources (e.g., photovoltaic, wind power, etc .).

However, the proliferations of non linear loads, with the generalization of staticconverters in industrial activities and by consumers, result in a deterioration of the qualityof voltage and current waveforms and affect the reliability of power electronic equipments[1], [2]. Traditionally, passive LC filters have been used to eliminate lower order harmonics(5th, 7th, 11th…) of the line current and then limit the flow of harmonic currents in thedistribution system. Nevertheless, these passive second order filters present manydisadvantages such as series and parallel resonances, tuning problems and complexity in thepower system, particularly in case of an increase in the number of harmonic componentsthat have to be cancelled [3]. Nowadays, active filters are an interesting alternative topassive filters or in association with hybrid structures [4]-[6]. For harmonic depollution andreactive power compensation, the most common solution is the three-phase SAPF. Thisactive filter, based on a three-phase VSI, is connected in parallel with non-linear loads toeliminate current harmonics and compensate reactive power and also to ensure the stabilityof the system. The performance of the SAPF depends on the design of the structure,strategies control and the robustness of the controllers [7]. In order to control the SAPF andachieve a proper power flow regulation in a power system, voltage-oriented control (VOC),which provides a good dynamic response by an internal current control loop, is widely used[8],[9]. As an alternative to this control method, other control strategies have been proposedin recent publications, such as predictive control and direct power control (DPC) [10]-[12].

DPC has become more widely used over the last few years due to the advantages of fast


53

dynamic performance and simple control implementation when compared with othermethods. which are based on the instantaneous active and reactive power control loops, orso-called “p-q Theory” which was introduced by Akagi et al. in 1983 [13], [14].With DPCthere are not internal current control loops and no PWM modulator bloc, because theconverter switching states are selected by a switching table based on the instantaneouserrors between the commanded and estimated values of the active and reactive power, andvoltage position vector. Therefore, the key point of the DPC implementation is a correctand fast estimation of the active and the reactive line power. The DPC method is based onthe direct torque control (DTC) witch was originally proposed for controlling an inductionmotor in 1986 by Takahashi and Nogushi [15]. In 1995, Mannienen has introduced basicprinciples of the DTC control method applied to the line converter [16]. The physicalstructure of the line converter may be exactly similar to the motor converter, the onlyexceptions being the connection to the grid instead of the motor and the introduction of theline filter. Firstly, the DPC was proposed by Noguchi in 1998 for PWM converter withoutpower source voltage sensors [17], and developed by Malinowski in 2001 based on virtualflux estimation for three-phase PWM rectifiers system [18]. Using space-vector modulation(SVM), Malinowski et al. proposed a new DPC strategy with constant switching frequency[19], although these control strategies based on modulation techniques have been classifiedindirect power control (IPC) techniques [20]. Recently, the DPC was applied for activefiltering function of three-phase boost rectifiers and pure shunt active power filters [21]-[23].

Several papers, on PWM rectifiers and few of them on active power filters, directlyexploited the switching table of Noguchi for DPC. While, carefully looking at this classical

switching Table Ι, one can note that for all odd sectors ),( oddii if the digitized error signal

state pd changes )10( , the switching vector remains unchanged witch is an inconvenient.

The same observation can be done for qd and even sectors ),( evenii . So, this shows the

limits of this switching table.

This paper is focused on DPC analysis and new switching table conception. From SAPFtopology and its electrical circuit analysis, variations of mains instantaneous active andreactive power are obtained. The predefined switching table concept is based on the effectstudy of the VSI voltage vectors and their position on the instantaneous power variations. Inthe proposed DPC strategy the reference of the instantaneous active power is achieved withthe controller IP by regulating the DC bus voltage of the VSI. the measured voltages andcurrents source allow estimating the instantaneous powers (ps, qs) to be compared to theirreferences. to minimize the number of commutations by excluding null vectors ),( 70 vv , the

control vectors )( 6..1iiv are derived from a decision of the switching table that depends on

the instantaneous active, reactive powers errors states and the position of mains voltagevector (fig. 1).

Table. I: Classical switching table.

dps dqs θ1 θ2 θ3 θ4 θ5 θ6 θ7 θ8 θ9 θ10 θ11 θ12

11 v6 v7 v1 v0 v2 v7 v3 v0 v4 v7 v5 v0

0 v7 v7 v0 v0 v7 v7 v0 v0 v7 v7 v0 v0

01 v6 v1 v1 v2 v2 v3 v3 v4 v4 v5 v5 v6

0 v1 v2 v2 v3 v3 v4 v4 v5 v5 v6 v6 v1

A. Chaoui et al: DPC Switching Table Concept and Analysis for three-phase SAPF

54

),( sv

abc

abcLLP ..

ssss

ssss

s

s

vivi

vivi

q

p

1tan

1

345

6

7

8

910 11

12

v

v

TableSwitching

New

sae

sbesce

Rs Ls Lc Rc

fL fR

LL

LR

sav

scv

sai

sci

si si

sp

sq

),( sv

SelectionSector

dcV

refdcV

refp

refq

dcC

sp

sq sdq

sdp

aS bS cS

ControllerIP

Figure 1: Block diagram of the SAPF under DPC.

Several tests were conducted and simulation results of SAPF under DPC using the newswitching table show the main advantages of the proposed control strategy for theimprovement power quality and its high performance getting a sinusoidal current source,unity power factor operation and robust control of the dc-bus voltage in steady states andtransient.

2. DPC CONCEPT AND ANALYSIS

In the DPC scheme (Fig. 1), to reduce the DC-link capacitor fluctuation voltages andcompensate the system loss, an Integral-Proportional controller (IP) is used in the DC-linkvoltage control loop as it’s mentioned in Fig. 2.

refdcV

dcV)( s

1

pkik

s

1

aT/1

cu ru

s

t

1

2

345

6

7

8

910 11

12

v

vv

Figure 2: IP controller structure. Figure 3: Voltage vector in stationarycoordinates with twelve sectors.

Where )( is represented by

s

dcdc

V

VC ref

3

2 (1)

From Fig. 2, the DC voltage closed loop transfer function can be expressed as


55

//

/2

)(

ipp

ip

dc

dcV

kksks

kk

V

VG

ref

IPdc

(2)

One can see that, the TF contains two poles and does not possess a zero; this proves that theIP controller insures a fast response and a good stability for transient states relatively to thePI controller.Using a pole placement to identify the controller’s parameters for a second order system,we have obtained for the using parameters (Table V) 0.118,k p 54ki . Finally, to limitand smooth mains current at starting and dumping transient time, we have introduced

additionally to the IP controller an anti-windup compensation with its gain -3a 10T , to

deal with the adverse effects caused by control saturation [7].The bloc scheme in Fig. 1 gives the configuration of direct power control where thecommands of reactive power refq (set to zero for unity power factor) and active power

refp (delivered from the outer integral-proportional (IP) DC voltage controller) are

compared with the calculated sp and sq values given by (3), in reactive and active power

hysteresis controllers, respectively.

sss jqpS

scsbsasbsascsascsb

scscsbsbsasa

ivvivvivvj

iviviv

3

1)(

(3)

The digitized variables psd , qsd and the line voltage vector position )/( ssn VVarctgform a digital word, which by accessing the address of lookup table selects the appropriatevoltage vector according to the switching table. For this purpose, the stationary coordinatesare divided into 12 sectors, as shown in Fig. 3, and the sectors can be numerically expressedas:

12,...,2,16

)1(6

)2( nnn n

(4)

Now, for the conception of the new switching table one must develop the instantaneousactive, reactive powers variations equations and analyse them as a function of vectorsvoltage and their positions.

2.1 SAPF instantaneous powers variations development

The electrical model per phase representation of SAPF, associated to the non linear load,connected to AC mains is shown by Fig. 4.

)(te

)(tis

sLsR fLfR

)(ti f

)(tvs)(tv f

)(tiL

mainsAC LoadL-N SAPF

Figure 4: Equivalent circuit diagram of the SAPF connected to a non-linear load fed by analternative source.


56

From Fig. 4,one can write the electrical equations in stationary coordinates as

(5)

(6)

(7)

By subtracting (6) from (5) and neglecting the influence of the resistances fR , sR

dt

diLve

Ldt

di fff

s

s

1

(8)

From (8) and for a discrete sampling time sT , the variation source current vector is obtainedas follows:

s

fff

s

ss

T

iLve

L

Ti

(9)

On the other hand and from (7) one can write

(10)

Where )1(Li and

)(hLi are the fundamental and harmonics non linear load currents

components respectively in stationary frame.From (10) one can observe that by controlling the source or the filter currents we have thesame dynamic but with inversion of the sign to move from one control variable to another.The substitution of (10) in (09) allows obtaining

][ f

fs

ss ve

LL

Ti

(11)

Witch can be rewrite in vector form

f

f

fs

s

s

s

v

v

e

e

LL

T

i

i(12)

Also; in same frame and for a balanced three-phase system, instantaneous active andreactive powers are defined as follows [24]-[26]

fsL

fff

fsf

sss

ss

iii

iRdt

diLvv

iRdt

diLve

fs

fhLsLhLLfsL

ii

iiiiiiiii

)( )()1()()1(


57

s

s

s

s

i

i

ee

ee

q

p(13)

If the sampling time sT is assumed very small compared to that of the source, the changeof the source voltage can be negligible. Then, active and reactive power changes dependonly on currents ones and can be estimated for the next control cycle as follows:

s

s

s

s

i

i

ee

ee

q

p(14)

By replacing (12) in (14) one can obtain

ff

ff

fs

s

f

f

fs

s

s

s

veve

veveee

LL

T

ve

ve

LL

T

ee

ee

q

p 22 )()( (15)

From (15) one can deduce that the change in active and reactive power depends on VSIoutput voltage )( fv witch can take seven possible states. As result, there are different

ways of selecting the corresponding switching state that controls the evolution in active andreactive power. So, the change in active and reactive power, for )6,...,2,1,0(i , are given

by the following set:

)6,...,2,1,0(

)()()(

)()(22

)( )()(

i

ififfs

sis

ififfs

sis

veveLL

Tq

veveeeLL

Tp

(16)

2.2 New switching table elaboration

a-Normalized powers equations

Firstly, the voltage vector of the balanced source can be written in the stationary frameas:

)sin(

)cos(

2/32/30

2/12/11

3

2

e

e

e

e

e

e

c

b

a

(17)

By replacing (17) in (16), the powers expressions will become:

)6,...,2,1,0(

)()()(

)()(

2)(

)sin()cos(

)sin()cos(

i

ififfs

sis

ififfs

s

fs

sis

vveLL

Tq

vveLL

Te

LL

Tp

(18)

Secondly, to obtain a normalized form of equations, one can define these VSI voltagecomponents forms:


58

0

3)1(sin

2

3

3)1(cos

2

3

)0()0(

)()(

)()(

)6,...,2,1,0(

ff

dc

ifif

dc

ifif

vv

iV

vv

iV

vv

withi(19)

Using (18) and (19), the normalized powers equations can be obtained as:

)6,...,2,1,0(

)()()(

)(

)()()(

)(

)sin()cos(

32

)sin()cos(2

3

32

i

ifif

dcfs

s

isis

ififdc

dcfs

s

isis

vv

VeLL

T

qq

vvV

e

VeLL

T

pp

(20)

For a better controllability of the SAPF, the first term of the active power variation of (20)must verify the follow condition:

3sin0

2

3

p

dcp

K

V

eK

(21)

b- The selection of the best ΔpK value

From (21), many values can be given to pK . Hence, before selecting the best value, firstly

it’s important to give an idea on a bad choice of pK and its impact on the switching table

conception.

So, for example by taking 2/2pK (which verify (21)), the behaviours of

)(isp and )(isq as function of VSI voltage vectors in the first sector ( 300 ), is

shown in Fig.5.

)3(sp

)0(sp)6(sp

)2(sp

)1(sp

)5(sp

)(

)4(sp )3(sq

)(

)2(sq

)4(sq

)1(sq

)5(sq

)6(sq

)0(sq

(a) (b)Figure 5: Active (a) and reactive (b) power variations behaviour under different voltage vectors for

sector 1 ( 2/2pK ).


59

From Fig.5, it can be summarized in Table II the different vectors that affect the sign ofvariations in active and reactive powers for sector 1.

TABLE. II: The vectors involved on powers variations signs for sector 1 ( 2/2pK ).

SECTOR 1 0 sq 0 sq

0 sp v4 OR v3 OR v2(partially) v6 OR v5

0 sp v2 (partially) v1

So from the Table II, we see that there is one case which’s directly acceptable since there isa single vector (v1) ensures the condition ( 00 ss qp ). While for the cases

( 00 ss qp ) and ( 00 ss qp ) we notice that there is a problem of choice

among the three vectors (v4, v3, v2) and the two vectors (v6, v5), respectively. In addition to

that, there is a single vector (v2) which provides partially that ( 00 ss qp ). Finally,

we note that the same problem is repeated for the other sectors.Therefore, to overcome these inconvenient and obtain a single vector for each condition,the best value choice’s is for 2/1pK . From which, one can deduce the DC bus voltage

reference equation:

sp

dcdc

p Ue

K

eV

V

eK ref

6

2/12

3

2

3

2

3

(22)

With eUs is the line to line RMS mains voltage value.

Using the value of 2/1pK , the new powers variations behaviour in sector 1 are shown

in Fig.6.

)4(sp

)5(sp

)3(sp

)0(sp

)6(sp

)2(sp

)1(sp

)(

)4(sq

)1(sq

)0(sq

)3(sq

)2(sq

)5(sq

)6(sq

)((a) (b)

Figure 6: Active (a) and reactive (b) power variations behaviour under different voltage vectors forsector 1( 2/1pK ).

From Fig.6 and taking into account vectors providing a maximum variation in )(isp , we

can deduce Table III without any partial impact vectors.


60

TABLE. III: The vectors involved on powers variations signs for sector 1 ( 2/1pK ).

SECTOR 1 0 sq 0 sq

0 sp v4 v5

0 sp v2 v1

c- A new switching table

By introducing (22) in (20), we obtain:

)6,...,2,1,0(

)()()(

)()()(

)sin()cos(

)sin()cos(2

1

i

ififis

ififis

vvq

vvp

(23)

Finally, taking in count (19), the normalized powers variations for the SAPF can be writtenas:

6/116/

3)1(sin

3)1(cos

2

1

)6,...,2,1,0(

)(

)(

ifor

iq

ip

is

is

(24)

Then, the inverter voltage vectors effect on the normalized powers variations behaviour forthe twelve sectors is shown by Fig. 7. Based on the above study, the correspondingswitching table is summarized in Table IV.

)4(sp )5(sp )6(sp )1(sp )2(sp )3(sp

)(

)4(sq )5(sq )6(sq )1(sq)3(sq)2(sq

)(

(a) (b)Figure 7: Active (a) and reactive (b) power variations behaviour under different voltage vectors in all

sectors.

TABLE. IV: New switching table.

dps dqs θ1 θ2 θ3 θ4 θ5 θ6 θ7 θ8 θ9 θ10 θ11 θ12

11 v3 v4 v4 v5 v5 v6 v6 v1 v1 v2 v2 v3

0 v4 v5 v5 v6 v6 v1 v1 v2 v2 v3 v3 v4

01 v1 v2 v2 v3 v3 v4 v4 v5 v5 v6 v6 v1

0 v6 v1 v1 v2 v2 v3 v3 v4 v4 v5 v5 v6


61

3. SIMULATION RESULTS

To validate the new switching table, a mathematical model corresponding to the diagram inFig.1 was simulated under MATLAB/SIMULINK® using SimPowerSystems with theparameters summarized in Table V.

TABLE. V: Electrical parameters system.Line to Line source voltage Us 87 VSource frequency f 50 HzSource Reactor resistance Rs 0.1 ΩSource Reactor inductance Ls 0.1 mHResistance of reactor Rc 0.01 ΩInductance of reactor Lc 0.566 mHDc-bus voltage Vdc 212 VDc-bus capacitor Cdc 1100 μFSAPF Inductance Lf 5.0 mHSAPF Resistance Rf 0.01 ΩSampling frequency fs 20 kHzLoad resistors RL1 21 ΩLoad resistors RL2 9.54 ΩLoad inductance LL 1 mH

Several simulation tests were conducted to verify feasibility and performance of theproposed DPC. Fig.8 and 9 show that before connecting the SAPF at PCC, and due to thenonlinear load, the source current wasn’t sinusoidal (THDi=26.32%) (Fig.10) and a non-zero reactive power flows in the source.

0.15

vsa,

b,c(

V)

isa,

b,c(

A)

Vdc

(V)

i fa(A

)

Time (s)

refVdc

Figure 8: Source voltages and currents, dc capacitor voltage and filter current behaviours beforeand after SAPF connection.

After starting the SAPF at t=0.15s, the source current becomes quasi-sinusoidal(THDi=2.05%) and in phase with the source voltages. The active power is constant andfollows closely its reference value. The reactive power is zero on average ensuring thereby


62

a unity power factor operation. The dc capacitor voltage reaches its reference in four cyclesof periods and maintains its stability during the steady state.

p s,p

ref(W

)Q

s,q r

ef(V

ar)

Time (s)

θ1θ2 θ3 θ4 θ5

θ6 θ7θ8 θ9

θ10θ11 θ12

0.15

Figure 9: Active and reactive behaviours Powers with their references before and after connecting theSAPF.

(a) (b)Figure 10: Source current and its spectrum (a) before filtering, (b) after filtering.

The dynamic behavior of the proposed DPC under a step change of load ((RL1, LL) → (RL2,

LL)) is presented in Fig. 11. After a short transient, the dc-bus voltage is maintained close toits new reference with good approximation and stability. The line currents maintain theirquasi-sinusoidal waveforms. From this figure, it can be seen that the powers properlyfollow their references in spite of the load change which confirms the robustness of thecontrol. In addition, one can clearly see that the active and the reactive powers controls aredecoupled of each other which is one of the advantages of the proposed DPC.


63

p,p r

ef(W

)q,

q ref

(Var

)vs

abc(

V)

isab

c(A

)V

dc(V

)i f(

A)

Time(s)

refVdc

Figure11: Source voltages and currents, dc capacitor voltage,filter current and powers behaviours during load change.

4. CONCLUSION

To overcome the drawbacks and limits of the classical switching table used in the directpower control strategies, a detail development and analysis of a new switching table arepresented in this paper. This purpose leads us to achieve many goals, which are summariesas follow:

Development of SAPF instantaneous powers variations equations from theelectrical model in the stationary frame.

Optimization of the normalized powers variations for the SAPF by the selectionof the best value pK .

Elaboration of a new switching table based on the study of the normalized activeand reactive powers variations behaviours for different voltage vectors in thetwelve sectors.

Finally, the validation of the proposed DPC using the new switching table for the SAPFwas done with the simulation of the mathematical model under MATLAB/Simulink.Several simulation tests are conducted to confirm the feasibility and high performance ofthe control strategy, showing that the source current which was not sinusoidal(THDi=26.32%) will become quasi-sinusoidal (THDi=2.05%), in phase with sourcevoltage after the introduction of the SAPF. The active power follows closely its referencevalue and the reactive power will be zero in average ensuring thereby a unity power factoroperation.

The transient state tests, whether during the switching on of the SAPF or changing theload, prove the robustness of the control by presenting excellent performance either of timeor overshoot and stability.


64

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direct power control switching table concept and analysis for

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