04-06!11!08!57!22_dc-link voltage control and performance analysis of statcom

8/10/2019 04-06!11!08!57!22_DC-Link Voltage Control and Performance Analysis of StatCom

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magnitude Ug of StatCom can be derived from vectorrelationship in Fig.2 (a) as following:

Es

U

I L

Ig

Ug

L

Ug

Es

U

I L

Ig

UgUg

(a) inductive load

(b) capacitive load

L

Fig. 2 Electrical vector relations under inductive and capacitive load

22 )cos()coscos(

cos)(cos

LLsLLss

LLsss

ILIrE

ILjrEU

+=

+= (1)

UILU LLgg + sin (2)

If the resistance rgof StatCom branch is not equal to

zero the equation (2) can be transformed as:

22 )sin()sin(

sin)(

LLgLLg

LLggg

IrILU

ILjrUU

++=

+= (3)

Under the state of equation (3) the vectorgU

and U are

not at same direction, there is small angle between them.

With equation (1) and (2) or (1) and (3) the relationship

between Ug and can be easy derived. In fact, equations(1) (3) imply that StatCom plays a role of reactive

power-source. However, the needed excitation energy of

this reactive power comes not from another outside source,but from power network itself. This is the basic conceptionof the StatCom. For the capacitor load the minus symbol

must be taken before Lin the equations above.

III. OPERATION PRINCIPLE OF DOUBLE

THREE-POINT STATCOM

StatCom is commonly constructed with voltage-superposedrealizing manner in order to reduce harmonics to the powernetwork, especially at the higher voltage levels [3,4]. Dual

three-point StatCom consist of two inverters which aredirectly connected to the two second windings of main

transformer respectively, one second winding is ofdelta-formed connection, another is of star-formedconnection as shown in Fig.3. The two second-windings ofdelta- and star-formed connections would produce 300

electrical angles between the two inputs of inverters inorder to obtain better output effect. The magnitude of

DC-link voltage should keep in certain range if StatCom isdemanded to work properly. As StatCom inputs reactivepower or outputs reactive power, the DC-link voltagewould be lower or higher referenced with the voltage level

of same configuration rectifier.The three-point means there are three electrical

potentials in the DC-link circuit, i.e. +, and 0

terminals. The terminal M in the Fig.3 is potential 0,which is the neutral point potential of second winding of

star-form if the potential difference of these two points iszero, i.e. common-mode voltage (the voltage betweenneutral point of AC side and the neutral point of DC side)is zero under this assumption. The total bridges of identical

configuration are 6 for this type of StatCom, any bridge has4 GTOs; there are three bridges pertained to one second

windings linked to phase a, b, and c respectively, whilst theremaining bridges are pertained to another windings.Furthermore, any GTO is inversely connected a power

diode for protection and proper work of StatCom.

Y

M

T11

T12

T13

T14

T21

T22

T23

T24

E1

E2

ua1 ub1 uc1 ua2 ub2 uc2

D11

D12

D13

D14

D21

D22

D23

D24

D10

D20

D40

C

C

T

Ls iL

igUs

is

U

Fig. 3 Simple StatCom topology of dual three-point

For a given bridge the output-state can be easy controlled.The top two power elements should be turned on if + is

needed to be outputted by the bridge; The lower two power

elements should be turned on if is needed to be

outputted; The bridge outputs 0 if the middle two powerelements turned on.

Supporting that the voltages E1 and E2 crossing the twocondensers C respectively in Fig.3 are equal, i.e. E=E1=E2,and the E is kept constant in operation. In order to get idealsine wave output, the control words of corresponding three

phase bridges should be produced as Fig.4 (a), (b) and (c).Assuming that the neutral point of star-windings or the

virtual neutral point of delta-windings is represented as n,the three-phase symmetry voltage should satisfy thecondition of Van+Vbn+Vcn=0. As Van, Vbnand Vcnare equalrespectively. The common-mode voltage uM-n can beexpressed as:

3/)( 111 McMbManM uuuu ++= (4)The corresponding waves of uM-n and phase voltage ofstar-connected winding are shown in Fig. 4(d) and (e). Fig.(f) is the output voltage of phase b of inverter 1#. Curve (e)subtracting curve (f) is curve (g), which is outputline-voltage ua1b1of inverter 1#.With the similar operation manner of inverter 1#, the

output line-voltage ua2b2 of inverter 2# which is linked todelta-connected second windings of main transform is inFig.4 (h). It is clear that the later lags behind the formerwith 300. This is the reason of using delta- and star-

connected windings. The total induced voltage (i.e. theprimary side voltage induced by secondary windings of

main transformer) of phase a to the power system byStatCom is shown in Fig.4 (i) which is the sum of (e) + (h).Considering the realizing principle of Fig.4 the 24 outputstates of dual three-point StatCom in Fig.4 (i) can be

depicted with 24 vectors of , coordinates axis in Fig.5

of a period. Clearly a circle track is nearly formed by thevector top point of 24 states, this indicates that the total


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output wave in the time domain is similar as sine wave,and the harmonic pollution produced by StatCom to powersystem would be small when the DC-link voltage weremaintained in constant under operation.

1 3 5 7 9 11 13 15 17 19 21 23 1 3

2 4 6 8 10 12 14 16 18 20 22 24 2

ua1_M

ub1_ M

uc1_M

uM_n

ua2_b2

ua1n

ua

t

t

t

t

t

t

t

E

-EE

-EE

-EE/3

-E/3

E

2E

2E/34E/3

E

ub1 nt

ua1b1

10E/33E

8E/35E/3

2E/3

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i )

Fig. 4 Realizing principles of dual three-point StatCom

1 23

4

5

6

7

8

9

10

11

121314

15

16

17

18

19

20

21

22

23

24

Fig. 5 Corresponding vectors of 24 states

IV. INNER-NESTEDVOLTAGECONTROL

STRAGEGY

Inner-nested voltage control strategy implies that theDC-link voltage acts as feedback quantity in the inner

control loop. If the control object is system reactive powerand node-voltage at the user input-terminal, the typicalcontrol system of StatCom could be designed as Fig.6. The

basic principle of this control system could ensure minimalreactive power flowing through the transmission line, andobtain a proper and stable node voltage. As DC-linkvoltage is placed in the inner control loop, so it can beadjusted quickly to get a corresponding DC-link voltage Ed

for a given reactive power qgd. in Fig.6 is a control angleof StatCom; it could be said to be the angle between thevector of infinite power system voltage and equivalent

voltage-source vector of StatCom. The relation of withother electrical quantities is shown in Fig.2.

According to Fig.6 the control equations based on , synchronous rotated coordinates are written as

( ) SS iEq 5.1= (5)

( ) ( ) += dtqqkqqku gdqigdqpgd (6)

( ) += dtuukuuk gdduigddup )( (7)Where qgd is the desired value of reactive power flowingthrough transmission line, it could be set to zero as an idealstate; kqp, kup, kqi and kui are proportional and integralcoefficients of PI controller for q and Ud control loop

respectively. In the interesting of simulation, the equationsfor the first state could be written also by using of the

equivalent topology neglecting the role of snubber:

+

+

- +

+

-

Fig. 6 Control block-diagram of StatCom

CONTROL SIMULATION AND ANALYSIS

Assuming that the voltage of infinite system is 400V,capacitance C of DC-link is 1mF, the inductance sum Lgofdistribution inductance and filter inductance in StatCombranch is 0.85mH, equivalent resistance rg of StatCom

branch is 2.17m, equivalent resistance and inductance oftransmission line are 2.5m and 0.1758mH respectively,equivalent load current is 200A power-factor of load is

cosL = cos600, system frequency f =50Hz.

Through the modeling and calculating matrix of equation(8) based on C, the stable simulation output of dual

three-point StatCom can be depicted in Fig. 7. Fig.7 (a)shows node-voltage and system current flowing through

transmission line with and coordinates; while Fig.7 (b)shows the DC-link voltage Ed, reactive power q flowing

through transmission line and control angle in the sameperiod as Fig.7 (a).Under above assumption of system parameters and withproper control parameters of PI controller the reactivepower flowing through transmission line is very small for

such system, this means that the designed control system inFig.6 would at least reduce reactive power from power

system. The node-voltage is of a little distortion, but thebasic content of 50Hz takes over 99% of total effectivevalue, and the main 23rdand 25thharmonics are under theallowable level (2.7% and 1.93% respectively). The

distorted max value of node-voltage is 329.3V. DC-linkvoltage Edfluctuates with DC component plus 6

thand 24

th

harmonics, the average DC-link voltage is 567V under theoperation conditions.


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t/ s

u /V

,i/ As u u 329.3V

120.5A ii

q

Ed

q/k

Var

E

/Vd

/degree

t/s

(a) stable U-i of StatCom

(b) E , q, and curves in the same time range as aboved

Fig. 7 Stable output curves of StatCom

It is noted that the effective value of system current i s of

fundament content 50Hz, which takes over 98% of totaleffective value (5

th 13.98%, 4

th 4.73%, 11

th 6.48%, 13

th

3.48%, 23rd 7.0%, 25th 3.7%), is only 73.126A for the200A load current with power-factor cos600=0.5, thisimplies that the StatCom could not only completelycompensate the reactive power needed by load, but also itcould compensate the reactive power needed by the

transmission line, so it does reduce the loss in thetransmission line and boost the node-voltage (effectivefundament value of phase voltage is 229.8V).

iSVG iload

is

t/s

current/A

Fig. 8 Instantaneous current waves under stable operation

With the currents of phase A as example, Fig.8 has given 3

waves together, i.e. the branch current iSVG of StatCom,load current iload, and system current iswhich flows throughtransmission line. It is clear that the phase differencebetween iloadand iSVGis a little smaller than 180

0. From thefigure above, the angle could be concluded that iload lagsbehind iSVG nearly off 157

0. Through the Fourier series

analysis the effective fundament value of iSVG is derivednearly as 176A. As explained before, the effectivefundament value of isis almost 73A, and the load current isexact 200A as designed, these data almost completely meetthe results calculated with ideal circuit theory, this hasexplained that the calculating model and the correspondingequations above are feasible.

Fig. 9 shows the dynamic process for reducing inductiveload current from 200A down to 70A and the lagpower-factor is increased from cos60

0up to cos30

0at the

time 0.25s suddenly. It is clear that system reactive power

is a little smaller; the shift range of control angle is alsoshrunken; the two variables and q change abruptly at the

moment of off-load, but the adjustable time lasts not long(no exceeding 0.5ms). By all appearances, the inner-nestedcontrol loop acts very rapidly, this is useful to stabilizesystem voltage, avoid or decrease electric impulsion.

Furthermore, the average DC-link voltage Ed_avgis reducedfrom 567V down to 529V within 5ms setting time. This

change indicates that the stable DC-link voltage ofStatCom would be different as the reactive power of powersystem varies. The vectors in Fig.2 could explain this,

because the direction and magnitude of voltage drop Ugwill change as that of load current. With the decrease ofload current magnitude the equivalent StatCom voltage

magnitude Ugwill decrease also, this means that DC-linkvoltage Edwill decrease as follow. Keeping the load factorconstant, the different fundamental contents of effective

terminal-voltage of Uand U, and system output currents

of i and i are shown in the table 1 when changing themagnitude of inductive load current.

q/kvar

Ed t=5ms

/degree

E

/Vd

q

t/s

E =567Vd_avg E =529Vd_avg

Fig. 9 Dynamic process when put off inductive load

Table. 1 Fundamental components of terminal voltages and system

currents when inductive load changes (p.u.).

iL

030

U U i i0.5. 1.41483 1.41559 0.531916 0.5376331.0 1.41517 1.41589 1.07929 1.08059

1.5 1.41536 1.41642 1.62821 1.62502

2.0 1.41524 1.41758 2.18740 2.16604

2.5 1.41482 1.41900 2.80019 2.66406

If the impedance Zsover transmission line in Fig.1 is verysmall compared with the load impedance, then thevoltage-drop of StatCom connected point at user-terminalcould be neglected. Through lots of simulations and theanalysis of fast-Fourier algorithm some results would besummarized as follows:

1) Line current will be smaller when load current

includes only pure reactive content as the result ofStatCom compensation.

2) System output current will increase as leading angle ofload current decrease while keeping load currentmagnitude constant.

3) DC-link voltage Ed will be enhanced as loadcharacteristic is transferred from capacitive load toinductive load.

4) DC-link voltage Ed fluctuates mildly when loadpresents inductive characteristic change; otherwise,acute fluctuation of Ed will appear when load

characteristic presents capacitive load.

5) There are compellable turnoffs of power elements

when StatCom acts like adjustable capacitor, whereasthere are only commutations of diodes when StatCom


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acts like adjustable inductor.

Fig. 10 Dynamic curves of increasing inductive and capacitive load

Fig. 10 shows that, the DC-link voltage Ed will beincreased appreciably from average value lag 2.28p.u up tolag 2.32p.u.within 2ms, while the average value is down to

2.11p.u with load magnitude transferred from lag 1.5p.u tolead 1.5p.u. At this point the DC-link voltage Ed dropsdown to 0.715p.u within 1ms. In the meantime, the reactivepower flowing through transmission line is a litter slowregulated in stable state through a few up and down surgeswithin about 4 milliseconds, it is about 3ms slower

compared with the process of abruptly loaded on inductiveload.Besides, the compensation currents iSVG can quicklyrespond to the sharp transition of load characteristic andmagnitude, and can rapidly enter in a proper compensationstate in both dynamic processes.

It is necessary to note, how the power elements operateduring these transient periods under the control strategy(Fig.6). For instance, the pulse series are originallytriggered as real line in Fig. 11(a). Supposing, at a givetime, load characteristic and its magnitude are quicklychanged from lead factor to lag factor. The corresponding

currents imnare plotted with different type line under idealcondition according to the control principle of Fig. 6.Where subscript m represents phase a, b, or c; n=1 or 2, 1indicates original current before transition, 2 the currentafter transition. The operation states before and aftercapacitive load abruptly put on are shown in Fig. 11(b) and11(c) respectively.

Ua Ub Uc

t

Phase a pulseUa Ub Uc

t

t

t

t1t2 t3 t 4

0t5 t 6

t7 t8

t 9 t 10t11 t12

(a) SVG operating currents shift from capacitive to inductive

ia1ib1 ic1

ia2 ib2ic2

T1 T3 T5

T4 T6 T2

C

Ua

Ub Uc

Ud

(b) t t2 3

T1

T3 T5

T4 T6 T2

C

Ua

Ub

U c

Ud

(c) t t2 3

commutation of diods

Phase b pulse

Phase c pulse

Fig. 11 StatCom state transitions when load changes from capacitive toinductive

CONCLUSION

Dual three-point StatCom could be applied in powersystem used at least for reactive power compensation ofpower system and node-voltage stabilization; the controlstrategy of inner-nested DC-link voltage in Fig.6 could

quickly increase system stability and decrease electricimpulsion. The results through simulation nearly meet the

basic circuit theory; this verifies that the calculation

models and equations are feasible for a judgment to realequipment under operation.

ACKNOWLEDGMENTS

The authors would like to acknowledge Prof. S. Bernet inBerlin University of technology; he was continuouslysupporting the research works during the researchingperiod of one of authors as visiting scholar in Germany. Weappreciate all his scientific cooperators of power electronic,

and the other members for their understanding and helpingin all the past activities.

REFERENCES:

[1] Yu, Q.G./Ding, R.J./Wang, W.H./Han, Y.D. Novel asymmetricalcontrol strategy for STATCOM in FACTS, Proceedings of Fifth

International Power Engineering Conference (IPEC 2001), 17-19

May 2001, Singapore, pp.156-159[2] Cathey, J.J./Moore, W.E. Improvement of generator output and

stability margin by use of a dedicated static VAR compensator.

Electric Power Systems Research, vol.63, no.2, 28 Sept. 2002,

Switzerland, pp.119-125[3] Kincic, S. /Chandra, A. /Babic, S. Five level diode clamped voltage

source inverter and its application in reactive power compensation,

LESCOPE'02. 2002 Large Engineering Systems Conference on

Power Engineering, Halifax, NS, Canada pp.89-92

[4] Hanson, D.J./Horwill, C. /Gemmell, B.D./Monkhouse, D.R. A

STATCOM-based relocatable SVC project in the UK for National

Grid, Proceedings of Winter Meeting of the Power EngineeringSociety, 27-31 Jan. 2002New York, NY, USA, pp.532-537

[5] Constantine H. Houpis, Gray B. Lamont, Digital control systems

Theory, Hardware, Software . 1985 McGraw-Hill, inc. USA.

pp89-92.

[6] Narain G. Hingorani, Laszlo Gyugyi. Understanding FACTS: concepts

and technology of flexible AC transmission systems. IEEE PressMarketing, New York, USA 2000.

AUTHORS ADDRESS

The first author can be contacted at

College of Electrical Power & Electronics Engineering

Huazhong University of Science & Technology1037, Luoyu Road

Wuhan, P.R.China

Postcode: 430074

Email: [email protected]

04-06!11!08!57!22_dc-link voltage control and performance analysis of statcom

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