PHYSCON 2011, Leon, Spain, September, 5September, 8 2011

POWER CONTROL OF VOLTAGE SOURCE CONVERTERFOR DISTRIBUTED GENERATION

Jose Luis Domnguez-GarcaElectrical Engineering Area

IRECSpain

jldominguez@irec.cat

Oriol Gomis-BellmuntCITCEA-UPC

gomis@citcea.upc.eduand

IRECogomis@irec.cat

Fernando BianchiElectrical Engineering Area

IRECSpain

fbianchi@irec.cat

Antoni Sudria`-AndreuCITCEA-UPC

sudria@citcea.upc.eduand

IRECasudria@irec.cat

AbstractThe paper deals with the active and reactive power

control of voltage source converters (VSC) for dis-tributed generation. The control method explained isbased on the instantaneous power theory. The powerconverter regulates the DC-Bus voltage and also con-trols the reactive power injected to the grid. The pre-sented control strategy is evaluated by simulation inMatlab-Simulink.

Key wordsDistributed Generation, Converter control, PLL, Cur-

rent loop, qd0 Transform

1 IntroductionThe rapid increment of renewable power generation

is changing the power system shape, and creating newpower generation concepts as distributed generation.Distributed generation can be defined, according to[Ackermann, Andersson and Soder, 2001], as an elec-tric power source connected directly to the distribu-tion network or on the consumer side of the meter.On the other hand, CIGRE working group 37-23 de-fines it as low rating generation that is neither plannednor dispatched centrally and is usually connected tothe distribution network [CIGRE working group 37-23,1999]. Therefore, from the main ideas of both defini-tions, distributed generation can be understood as lowpower generation that is connected close to the distri-bution network. The power generation technologies in-volved in distributed generation include, for example,wind turbines, small hydro turbines, combined heat andpower (CHP) units, also known as cogeneration, fuelcells and photovoltaics (PV) cells.In order to enhance the quality of the power injected tothe grid by the units of distributed generation, a powerconverter is used between the grid and the generator en-abling the system to be regulated.Different control systems have been studied in order to

provide different grid supports or ride through faultscapability, e.g., frequency support [Hirodontis, Anaya-Lara, Burt and McDonald, 2009][Karlsson, Bjornstedtand Strom, 2005], to guarantee power quality [Hornikand Zhong, 2009], voltage dips [Wang, Duarte andHendrix, 2009], etc. The present paper studies andpresents an active and reactive power control of a con-verter to enable the system to improve the quality of thepower delivered.This paper is organized as follows. In Section II, thesystem under study is described. The Clarke and ParkTransforms are presented in Section III. In section IV,the instantaneous power theory is briefly introduced.The control scheme is developed in section V. In sec-tion VI, the proposed control is validated by means ofsimulation and discussed. Finally, the conclusions aresummarized in Section VII.

2 System descriptionThe system under study is shown in the Figure 1. It is

a power converter transforming the active power deliv-ered by a dc-source, into the active and reactive powersent to the network. The dc-source can be either a pho-tovoltaic cell, a wind turbine connected to a rectifier ora fuel cell.To transform from DC to three-phase AC, it is neces-sary a three-phase inverter. The design of this powerconverter can be done by means of different technolo-gies as diode inverter, thyristor inverter or IGBT in-verter. Because of the ability to regulate active and re-active power, the IGBT inverters are commonly chosento regulate the power delivery.

3 Transformation from abc reference frame toqd0

Current and voltage are usually described as threesinusoidal waves representing the three AC phases (a,b and c). Calculations in abc-frame are complex due

iDCs iDCl

iDCE

+ CE

LlD

C SO

URC

Evla

vlb

vlc

Ll

Ll

ila

ilb

ilc

DC

AC

Figure 1. Scheme of the system

to the sinusoidal components and its variability in thetime-frame.Therefore, in order to facilitate the control designof three-phase inverters the qd0 reference frame isused. In the case of balanced three-phase circuits, theapplication of the Park Transform to three AC variablesreduces to two DC variables, due to the 0-componentin balanced conditions is zero. Thus, simplified cal-culations can be carried out on these transformed DCvariables. Three-phase AC components are recoveredwith the inverse transform.

3.1 Clarke TransformationThe Clarke Transformation allows to change the

three dimension vector into two dimension vector(abc-frame to .frame).

(xx

)=

2

3

(1 12032

32

)xaxbxc

(1)This transformation can be understood as the pro-jection of the three axis onto a stationary two-axisreference frame, as it is shown in the figure 2. It isimportant to remark that it is possible to expand thevariable change matrix 1 to a 3x3 matrix 2, includinga 0 component (called homopolar component), whichis orthogonal to (, ) axis and usually a constantvalue (zero if the system is balanced). In this way thetransformation is bijective.

xxx0

= 23

1 12 120 32 3212

12

12

xaxbxc

(2)3.2 Park TransformationThe Park Transformation describes a rotation of an

orthogonal system ((, ) to (q, d)). The rotation isrepresented in the figure 3.

b

c

a

xabc

x

x

Figure 2. Representation of the Clarke Transformation

(xqxd

)=

(sin() cos()cos() sin()

)(xx

)(3)

q

d

xabc

xd xq

Figure 3. Rotation of the reference (, ) an angle

Again, the rotation can be expressed as a 3x3 matrixincluding the rotation orthogonal axis, which is thesame axis in (, , 0) and (q, d, 0) references, althougha vector rotation on a constant plain is expressed as a2x2 matrix.

xqxdx0

=sin() cos() 0cos() sin() 0

0 0 1

xxx0

(4)

3.3 qd0 TransformationThe qd0 Transformation includes the Clark and Park

Transformations, combining both transformations inone matrix.Hence, the Park Transformation with an angle of avector xabc R3) in the abc frame is given by

xqd0 = T ()xabc (5)

with

T () =2

3

cos() cos( 2pi3 ) cos( + 2pi3 )sin() sin( 2pi3 ) sin( + 2pi3 )12

12

12

(6)Then it can be said that the vector xqd0 is the vectorxabc in the dq0 frame on the angle reference.Since the matrix T () is invertible; the inverse trans-formation can be obtained as

xabc = T1()xqd0 (7)

with

T1() =

cos() sin() 1cos( 2pi3 ) sin( 2pi3 ) 1cos( + 2pi3 ) sin( +

2pi3 ) 1

(8)In conclusion, the qd0 transform can be interpreted asthe projection of the abc-frame variables onto a rotatingtwo-axis reference frame.

4 Instantaneous power theoryThroughout the paper, the instantaneous power the-

ory for balanced three-phase systems under sinusoidalconditions developed by Akagi [Akagi, Watanabe andAredes, 2007] is considered. A balanced three-phasesystem under sinusoidal conditions is defined as athree-phase system with equal amplitudes and 2pi/3 rad(120o) the angle between all the phases.Therefore, the instantaneous voltages and currents inabc frame can be written as:

xa =2Xcos(t+ )

xb =2Xcos(t+ 2pi/3)

xc =2Xcos(t+ + 2pi/3)

(9)

Electrical theory defines 3 different types of electricalpower: Apparent (S), Active (P) and Reactive (Q). TheApparent power in abc frame is expressed as: S = V I = P + jQWhere V and I are the phasor (phase vector) represen-tation of the voltage and the current.

Applying the Clarke and Park transformations de-scribed previously, the active and reactive power canbe expressed as:

P = 32 (vi + vi)Q = 32 (vi vi)

(10)

in the (,) frame and

P = 32 (vqiq + vdid)Q = 32 (vqid vdiq)

(11)

in the (q,d) frame.

5 Converter ControlThe purpose of the control of the power converter

is to regulate the reactive power and DC bus voltagewhich regulates active power. The DC bus voltage andthe reactive power references determine the currentreferences which determine the voltages to be appliedon the grid side.Figure 4 depicts the block diagram of grid sidecontrol. The reference currents are calculated bymeans of independent variables as active and reactivepower set-points, that is explained in the currentloops subsection. Furthermore, by means of the qd0Transformation, explained above, the control changeabc-frame currents to qd-currents, to compare themwith the reference currents. The angle necessary, tocalculate the Park Transformation and to synchronizethe system with the grid, is obtained by means thePLL, that is explained later, from the grid voltage.

DC

AC

Decoupling

Vlabc

ilabc

Q l*E*

Grid

Vzabc

+

-EPI

PE*

ild* ilq*

Vzq

PLL

Vzq

Vzd=0

grid

Vzq

x

/

x

/2/3 2/3

T()

ilqd

Ilqd*

+- PI

++

T()-1

Vlqd

Figure 4. Grid Control Scheme

5.1 PLLThe system control is designed in the qd frame. There-

fore, it is necessary to know which angle will be used

to obtain the desired reference. In this case, it is inter-esting to set the reference where voltage d-componentis zero.To find this angle it is usually used a phase locked loop(PLL). A basic scheme of a three-phase PLL, as it isshown in 5, consists in a comparison of the voltage d-component with a constant zero, the obtained error isregulated by a PI controller. The output of the con-troller is the grid frequency. The grid angle is obtainedby integration of the frequency. The grid angle is intro-duced in the Park Transform to calculate the qd voltagecomponents.The design of the controller parameters is detailed byS.K. Chung [Chung, 2000]

ParkTransformation

PI1s

+

Vd

Vabc

0

-

Vq

Figure 5. Scheme of Phase Locked Loop

5.2 Reference calculationThe q-axis may be aligned to the grid voltage, allow-

ing active and reactive decoupled control. To controlthe reactive power, a ild reference is computed as:

ild =2 Ql3 vzq (12)

The active power, which is responsible for the evolu-tion of the dc bus voltage, is controlled by the ilq. Alinear controller is usually designed to control the dcbus voltage and to keep it constant.

ilq =2 P E3 vzq (13)

The DC link voltage behavior is defined (in Laplacedomain) by the following equation

EDC = EDC0 +1

s C (iDCl iDCp) (14)

where the current values iDCp and iDCl can be

calculated as

iDCp =iabcp vabcp

E=PDCpE

(15a)

iDCl =iabcl vabcl

E(15b)

The control loop scheme is shown in Figure 6; The de-sign of both proportional and integral parameters of thePI controller is explained in [Junyent-Ferre`, 2007].

EPI

* IDCl*

E

+

-

IDCs

+

+

Figure 6. DC Bus Control Scheme

5.3 Current LoopsThe current control is implemented by the following

state linearization feedback:

(vlqvld

)=

(vlq + vzq Ll g ildvld + Ll g ilq

)(16)

where vlq and vld are the voltage control values. Thedecoupling can be described as:

d

dt

(ilqild

)=

( rlLl 00 rlLl

)(ilqild

)+

( 1Ll

0

0 1Ll

)(vlqvld

)(17)

5.4 Current Controller TuningThe controller is designed by means of the so-called

internal model control (IMC) theory [Harneforns andNee, 1998]. The parameters of a PI controller, with thegoal of obtain a desired bandwidth , which appear dueto a low-pass filter included by the IMC, are:

Kp = Ll Ki = rl (18)

6 Simulation ResultsThe system, previously described, is simulated with

Matlab-Simulink.The control of the converter is evaluated in twodifferent scenarios: a change in the active power

reference and a change in the reactive power reference.Also both PLL and qd0 Transformation response areevaluated to show how properly they work.

6.1 PLL & qd0 TransformIn the Figure 7, it can be observed that the Phase

Locked Loop (PLL) presented above has a good be-havior, reaching quickly the desired value. It is alsointeresting to note that the PLL controller behaves asa first order system. So, it satisfies the plant definitionthat appears in [Chung, 2000], where is related the PIcontroller parameters with the period of the system.

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1310

311

312

313

314

315

316

317

318

319

320Phase Locked Loop

time (s)

frequ

ency

(Hz)

Frequency CalculatedGrid Frequency

Figure 7. Dynamical response of the Phase Locked Loop system

In the Figure 8, can be observed an example of three-phase voltages in abc and what shape they take afterthe Park Transform. It is important to be noted thatthe chosen angle, which is given by the PLL controller,is the right one because the voltages in qd frame areconstant values.

1.5 1.55 1.6 1.65 1.7 1.751000

800

600

400

200

0

200

400

600

800

1000Park Transformation

time (s)

Volta

ge (V

)

Voltage abc frameVoltage qd frame

Figure 8. Application of Qd0 Transform to a sinusoidal balancedthree-phase voltage

6.2 Variation of Active PowerThe first scenario presented is a change of the active

power reference. Ensuring the capability of delivervariable active power, it is required due to the variabil-ity of the power demand from the consumers. In thisscenario the reactive power reference is set in zero.

In the Figure 9 can be seen the active power referencevarying with steps, and how the active power deliveredto the grid reaches quickly this new setting.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 512

10

8

6

4

2

0

2x 105 Active Power

time (s)

Activ

e Po

wer

(W)

Active Power to the gridReference Active Power

Figure 9. Plot of the change of the active power

Again, as it is shown in the Figure 10, the dc bus volt-age is following the defined value. The peaks appearon the graphic because of the control dynamics, whichacts during the reference value variations.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 51490

1492

1494

1496

1498

1500

1502

1504

1506

1508

1510DC Bus

time (s)

Volta

ge (V

)

Reference VoltageReal Voltage

Figure 10. Variation of the DC Bus Voltage driven by the activepower change

In Figures 11 and 12, it is plotted both q and dcomponents, either of real and reference currents. Thedifference between them is the input of the IMC tocalculate the voltage values. It can be seen that theq-component of the current presents the same behaviorof the active power profile, its calculation is driven bythe expression (13). In the same way, the d-componentwhich is guide by the expression (12) has a constantzero value due to the reactive power is set zero.

6.3 Change of Reactive PowerThe second scenario presented is the change of the

reactive power reference. Regulation of the reactivepower delivery allows the system to keep constant thevoltage in the connection point. In this scenario, theactive power reference is set in 1MW.In the Figure 13, it can be seen the reactive power ref-erence change, which as in the former case has a stepbehavior. As it is expected the reactive power delivered

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5900

800

700

600

500

400

300

200

100

0

100Current qcomponent

time (s)

Curre

nt (A

)

Real qcomponentReference qcomponent

Figure 11. Representation of the q-component of the current withactive power variations

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 525

20

15

10

5

0

5Current dcomponent

time (s)

Curre

nt (A

)

Real dcomponentReference dcomponent

Figure 12. Plotting of the d-component of the current

to the grid matches the new setting with a fast response.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 512

10

8

6

4

2

0

2x 105 Reactive Power

time (s)

Rea

ctiv

e Po

wer

(var)

Reactive Power to the gridReference Reactive Power

Figure 13. Variation of the reference value of the reactive power

In the Figure 14, the dc bus voltage is maintained atconstant value. Again, as in the first scenario, the volt-age presents peaks due to the reactive power changes,that affects the active power sent to the network.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 51485

1490

1495

1500

1505

1510

1515DC Bus

time (s)

Volta

ge (V

)

Reference VoltageReal Voltage

Figure 14. Behavior of the DC Bus Voltage under reactive powervariations

In the Figures 15 and 16, it is plotted the q and dcomponents of the currents. It can be seen that thed-component of the current presents a behavior similarto the reactive power profile. However,in this case,the q-component has not a constant value as it wouldbe expected, since the active power demanded is stillthe same. Then, as the voltage of the network remainsconstants, it is needed a change in the injected current.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5900

800

700

600

500

400

300

200

100

0Current qcomponent

time (s)

Curre

nt (A

)

Real qcomponentReference qcomponent

Figure 15. q-component of the current obtained by the active powerreference

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5900

800

700

600

500

400

300

200

100

0

100Current dcomponent

time (s)

Curre

nt (A

)

Real dcomponentReference dcomponent

Figure 16. d-component of the current obtained by the reactivepower reference

7 ConclusionsThis paper has presented an active and reactive power

control for converters in distributed generation sys-tems. The control of these converters demands the ma-nipulation of three-phase sinusoidal variables, whichmakes difficult to compute the control variables. Tosimplify the design Clark and Park transformationshave been used. In this transformed frame of reference,the control design can be cast as the regulation of DCvariables in two decoupled control loops based on sim-ple proportional-integral-derivative (PID) controllers.Simulation of the control methodology is presented inorder to illustrate the transformation of the variablesand also the ability of the system to regulate the activeand reactive power.

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