Design of Robust Controller for VSC based HVDCusing Genetic Algorithm

M. JanakiSchool of Electrical Engineering

VIT UniversityVellore, Tamilnadu.

Email: janaki.m@vit.ac.in

R. ThirumalaivasanSchool of Electrical Engineering

VIT UniversityVellore, Tamilnadu.

Email: thirumalai.r@vit.ac.in

Nagesh PrabhuDepartment of EEE

NMAM Institute of TechnologyNitte, Karnataka.

Email: prabhunagesh@rediffmail.com

Abstract—The Voltage Source Converter based HVDC pro-vides asynchronous interconnection between two AC systems.The use of VSC HVDC enables independent control of realand reactive power. The VSC based HVDC transmission systemconsists of two converter stations connected by a dc cable/line.This paper presents modelling and the design of controller forVSC HVDC. The various operating cases of VSC HVDC areconsidered. In each case there are several controllers gains inHVDC link. A systematic approach is used for selecting thecontroller parameters and Genetic Algorithm (GA) is used fortuning the controller parameters. The various operating cases ofVSC HVDC are considered in controller parameters optimiza-tion. The GA enables the usage of the same controller gains forall operating cases while maintaining the system stability.

Index Terms—Eigenvalue, HVDC, Voltage Source Converter(VSC), Genetic Algorithm (GA).

I. INTRODUCTION

The VSC based HVDC transmission is getting more attrac-tion due to the fast development of advanced power electronicdevices with turn-off capability, especially IGBT’s. The VSCbased HVDC is based on turn-off devices which has severaladvantages over conventional HVDC based on thyrister [1]-[3]. The point to point VSC based HVDC transmission systemconsists of two converter stations connected by a dc cable.The active and reactive power can be controlled independentlyin all four quadrants by controlling the magnitude and phaseangle of the converter output voltage. When one converteroperates on dc voltage control, the other converter operates onactive power control for balanced active power flow [4]. Whenpower flow is zero in dc line, the two converters operate asindependent STATCOMs.

In this paper, VSC is realized with twenty four pulsethree level converter, and Type-I controller [5], [6] is con-sidered for controlling both the magnitude and phase angleof converter output voltage. The paper presents modeling anddesign of controller for VSC HVDC. A systematic approachis used for selecting the controller parameters and GeneticAlgorithm (GA) is used for tuning the controller parameters.Each converter has two controllers in outer loop and twocontrollers in inner loop. The outer loop controllers namelyDC voltage/power and AC bus voltage set the reference valueof real and reactive currents respectively. The reactive currentreference is obtained from AC bus voltage control or it can be

kept constant. The real and reactive controllers form the innerloop of the converter controller.

The paper is organized as, introduction in section-I, mod-eling of VSC based HVDC in section-II, a case study isdescribed in section-III, the design of controller for VSCHVDC and transient simulation are presented in section-IV.The conclusions of the paper derived from the results are givenin section-V.

II. MODELING OF VSC HVDCThe system diagram of HVDC trasnmission system with

two VSCs is shown in Fig. 1. The electromechanical systemconsists of generator 2.2 model, six mass mechanical system,Power System Stabilizer (PSS) and the transmission line. TheVSC HVDC and long transmission ac line are originated froma substation which receives power from the turbine-generatorwhose data is adapted from IEEE First Benchmark model[7], [8]. VSC HVDC provides asynchronous link between ACsystem-1 and AC system-2. The details of the study systemare depicted in Fig. 1.

, ,s2R

VSC1

,

VSC2

s1 ,R

,

I

,

AC system−1

e1R

e1I

e1X

dc1X

cbcg cbcg s2X

b1E

1V

s1XcI

cB

, X ttR

gV

dc1V

I

dc2V

dcmV

cmb

dc2idc1i

dL2

R1

X1

AC system−2

1 I2Eb2

Rdc2 Xdc2Rdc1

idL1i

Fig. 1. System diagram of VSC HVDC

Neglecting the harmonics and approximating the switch-ing functions by their fundamental components, VSC basedHVDC is modelled by transforming the 3-phase voltages andcurrents to D-Q using Kron’s transformation [8], [9].

The two converters are of three level twenty four pulseconfiguration. The magnitude and phase angle of converteroutput voltage can be controlled simultaneously for controllingactive and reactive power flows respectively.

j

jjj

jj

j

R s

X s

+

I

i +V

θ

θ α

V

j

Fig. 2. Equivalent circuit of VSC viewed from ac bus

The VSC equivalent circuit viewed from ac bus is shown inFig. 2. In Fig. 2, Rsj and Xsj are the resistance and reactanceof the interfacing transformer of V SCj . The converter outputvoltage in D-Q frame is given by

V ij =

√

V ijD

2+ V i

jQ

2 (1)

where V ijD and V i

jQ are the D and Q components of VSCoutput voltage.

The jth converter current in D-Q is given by the followingequations as

dIjD

dt= −

RsjωB

Xsj

IjD − ω0IjQ +ωB

Xsj

[VjD − V ijD] (2)

dIjQ

dt= ω0IjD −

RsjωB

Xsj

IjQ +ωB

Xsj

[VjQ − V ijQ] (3)

In this system j = 1, 2. The dc-side capacitors of the VSCsare described by the dynamical equations as,

dVdc1

dt= −

ωB

bcRp

Vdc1 −ωB

bc

Idc1 −ωB

bc

IdL1 (4)

dVdc2

dt= −

ωB

bcRp

Vdc2 −ωB

bc

Idc2 +ωB

bc

IdL2 (5)

whereIdcj = −[kmjsin(θj + αj)IjD + kmjcos(θj + αj)IjQ]

where αj is the phase angle by which the fundamentalcomponent of jth converter output voltage leads the jth acbus voltage Vj . IdL1 and IdL2 are the dc link currents in theleft and righthand side sections and are described as

dIdL1

dt=

ωB

Xdc1[Vdc1 − Vdcm − Rdc1IdL1] (6)

dIdL2

dt=

ωB

Xdc2[Vdcm − Vdc2 − Rdc2IdL2] (7)

dVdcm

dt= −

ωB

bcm

IdL1 −ωB

bcm

IdL2 (8)

Where kmj = k′cosβj is the modulation index. k′ =kρjVdcb/Vacb. For a 24-pulse converter k = 4

√

6/π. ρj isthe transformation ratio of the interfacing transformer for jth

converter. Vdcb and Vacb are the base voltages of the dc andac side respectively.

A. Converter Controller

In a VSC HVDC system, one converter has to control theDC voltage and other converter can operate on constant DCpower control. Accordingly, in a VSC HVDC terminal the var-ious modes of control, like DC link voltage(Vdcj)/power(Pj)and constant ac bus voltage(Vj)/reactive current(IRj) are con-sidered. The DC voltage/power controller sets the referencevalue for real current(IPjref ) and the reference value ofreactive current (IRjref ) of VSCs is set by ac bus voltagecontroller, or it can be a constant. These two controllersform the outer loop. The real and reactive current controllersform the inner loop. Hence for each converter there are fourcontrollers as shown in Fig. 3. The magnitude control of thejth converter output voltage V i

j is achieved by modulatingthe conduction period affected by the dead angle βj of theindividual converters. αj and βj are calculated as,

αj = tan−1

[

VRj(ord)

VPj(ord)

]

(9)

βj = cos−1

√

V 2Pj(ord) + V 2

Rj(ord)

k′Vdcj

(10)

α βand

Calculator

KS

1 + s Tm

1

VP (ord)j

VR (ord)j

α

βΣ

Σ PI

PI

+

IR

V

IR

IR XS

ref

ref

−

−−−+

Σ PIΣ PI

−

+

P

XSIPVdc 1

+

+

−

−

Σ PI

+

−

Σ

Σ−

+

+

V

Σ+

refPj

refVdc j

j

refVj

j

j

j

j

j

j

IP ref

j

j

jj

j

j

j

Fig. 3. Controller for VSC HVDC.

The various operating combinations of the VSC HVDCare given in Table I. The reference value of reactive current

TABLE IOPERATING COMBINATIONS OF VSC HVDC CONTROLLERS

Case VSC1(Rectifier) VSC2(Inverter)Controller-1 Controller-2 Controller-1 Controller-2

1 Power Reactive Current DC Voltage Reactive Current2 Power AC Voltage DC Voltage Reactive Current3 DC Voltage Reactive Current Power Reactive Current4 DC Voltage AC Voltage Power Reactive Current

VSC1(Inverter) VSC2(Rectifier)5 Power Reactive Current DC Voltage Reactive Current6 Power AC Voltage DC Voltage Reactive Current7 DC Voltage Reactive Current Power Reactive Current8 DC Voltage AC Voltage Power Reactive Current

(IRjref ) of VSCs is set by ac bus voltage controller, or it canbe a constant. Since converter-2 is connected to infinite bus,the reactive current reference is kept constant.

In each case there are several controllers gains to be selectedfor HVDC link. The selection of controller parameters isbased on a systematic approach using Genetic Algorithm. Theparameter optimization based on GA [10] considers the variousoperating cases of VSC HVDC as given in Table I.

III. A CASE STUDY

The system diagram of HVDC trasnmission system withtwo VSCs is shown in Fig. 1. The controller design andanalysis is performed with the following assumptions andinitial operating conditions.

1) The generator supplies 0.125 p.u power to transmissionsystem.

2) The generator terminal voltage is 1.0 p.u.3) The converter bus voltage magnitudes are set at 1.0 p.u.4) In rectifier operation, HVDC cable power P1 is set at 0.9

p.u. The reactive powers drawn by the two converters areset to zero Q1 = Q2 = 0. The base values of ac systemare 300 MVA, 500 kV and the dc voltage base is 300kV.

5) The ESCR of the system at bus1 is 3.5.6) In all the transient simulation a step change of 10%

decrease in reference value is applied at 1 sec andremoved at 3 sec.

IV. DESIGN OF CONTROLLER

The optimization problem for controller parameters selec-tion using Genetic Algorithm [11] is presented in this section.The selection of controller parameters is based on a systematicapproach [12] considering the eight operating cases of VSCHVDC.

A. Description of Optimization Problem and Application ofGA

Consider a system described by the equation

X = [A(r)]XY = [C]X

(11)

In Equation-11, matrix [A(r)] contains one or more ad-justable parameters. [r] is the set of controller gains need

be optimized. The optimization of controller parameters isbased on minimizing the standard infinite time quadraticperformance index and can be stated as,

J =

∫

∞

t

Y tY dt (12)

Considering the system is stable, J can be expressed as

J = XT PX (13)

where P is a positive definite matrix and solved from theliapunov equation

PA + AT P = −Q (14)

where Q = CtCFrom this the objective function is obtained as

J =∑

i

tr[Pi] (15)

which is to be minimized. where ’i’ is 1 to 8 casesof VSC HVDC. Genetic Algorithm is used for tuning thecontroller parameters based on the objective function definedin Equation-15. The parameter optimization based on GAconsiders the various operating cases of VSC HVDC as givenin Table I. The GA enables the usage of the same controllergains for all operating cases while maintaining the systemstability.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5−0.15

−0.1

0

0.1

Time in sec

Rea

ctiv

e C

urre

nt I R

1

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50.8

0.85

0.9

0.95

1

Time in sec

DC

Vol

tage

, Vdc

2

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50.8

0.85

0.9

0.95

Time in sec

Pow

er, P

1

Fig. 4. Step response of reactive current, power and DC voltage for case-1with optimal controller parameters.

B. Transient simulation

The transient simulation of the combined system withoptimal controller parameters obtained using GA is carried outin MATLAB-SIMULINK [13]. The results for step change inreactive current, power and DC voltage references in case-1 to case-8 are shown in Fig. 4 to Fig. 11, and it is clearthat, the transient responses are good with optimal controllerparameters.

TABLE IIEIGENVALUES OF THE COMBINED SYSTEM

Torsional EigenvalueMode Case − 1 Case − 2 Case − 3 Case − 4

0 −1.0033 ± j 6.8833 −1.2937 ± j 6.9322 −0.9897 ± j 6.8563 −1.2862 ± j 6.9333

1 −0.2167 ± j 98.928 −0.2146 ± j 98.927 −0.2328 ± j 98.921 −0.2323 ± j 98.918

2 −0.0738 ± j 127.01 −0.0737 ± j 127.01 −0.0745 ± j 127.01 −0.0745 ± j 127.01

3 −0.6449 ± j 160.58 −0.6449 ± j 160.58 −0.6464 ± j 160.58 −0.6465 ± j 160.58

4 −0.3607 ± j 202.94 −0.3607 ± j 202.94 −0.3620 ± j 202.95 −0.3622 ± j 202.95

5 −1.8504 ± j 298.17 −1.8504 ± j 298.17 −1.8504 ± j 298.17 −1.8504 ± j 298.17

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50.75

0.8

0.85

0.9

0.95

Time in sec

Pow

er, P

1

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50.8

0.85

0.9

0.95

1

Time in sec

DC

Vol

tage

, Vdc

2

Fig. 5. Step response of power and DC voltage for case-2 with optimalcontroller parameters.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5−0.05

0

0.05

0.1

0.15

Time in sec

Rea

ctiv

e C

urre

nt I R

2

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50.8

0.85

0.9

0.95

1

Time in sec

DC

Vol

tage

, Vdc

1

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5−0.9

−0.85

−0.8

−0.75

−0.7

Time in sec

Pow

er, P

2

Fig. 6. Step response of reactive current, power and DC voltage for case-3with optimal controller parameters.

C. Eigenvalue analysis

The eigenvalues of the combined system linearized at anoperating point are computed from system matrix and aregiven in Table II and Table III for eight operating cases. It isto be noted from Table II and Table III that, all the eigenvalues

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5−0.9

−0.85

−0.8

−0.75

−0.7

Time in sec

Pow

er, P

2

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50.8

0.85

0.9

0.95

1

Time in sec

DC

Vol

tage

, Vdc

1

Fig. 7. Step response of power and DC voltage for case-4 with optimalcontroller parameters.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5−0.95

−0.9

−0.85

−0.8

−0.75

Time in sec

Pow

er, P

1

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50.86

0.88

0.9

0.92

0.94

0.96

0.98

Time in sec

DC

Vol

tage

, Vdc

2

Fig. 8. Step response of reactive current, power and DC voltage for case-5with optimal controller parameters.

have negative real part in case-1 to case-8 . Hence, it is evidentthat the system is stable in all eight operating cases withoptimal controller parameters. The Genetic Algorithm enablesthe usage of the same controller gains for all operating caseswhile maintaining the system stability.

TABLE IIIEIGENVALUES OF THE COMBINED SYSTEM

Torsional EigenvalueMode Case − 5 Case − 6 Case − 7 Case − 8

0 −1.3567 ± j 6.2744 −1.1941 ± j 6.7270 −1.3861 ± j 6.2864 −1.2013 ± j 6.7227

1 −0.2579 ± j 98.918 −0.2604 ± j 98.915 −0.2364 ± j 98.925 −0.2365 ± j 98.923

2 −0.0755 ± j 127.01 −0.0756 ± j 127.01 −0.0745 ± j 127.01 −0.0745 ± j 127.01

3 −0.6484 ± j 160.58 −0.6485 ± j 160.58 −0.6464 ± j 160.58 −0.6465 ± j 160.58

4 −0.3638 ± j 202.95 −0.3640 ± j 202.95 −0.3621 ± j 202.94 −0.3622 ± j 202.94

5 −1.8504 ± j 298.17 −1.8504 ± j 298.17 −1.8504 ± j 298.17 −1.8504 ± j 298.17

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5−0.95

−0.9

−0.85

−0.8

−0.75

Time in sec

Pow

er, P

1

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50.86

0.88

0.9

0.92

0.94

0.96

0.98

Time in sec

DC

Vol

tage

, Vdc

2

Fig. 9. Step response of power and DC voltage for case-6 with optimalcontroller parameters.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50.8

0.85

0.9

0.95

1

Time in sec

Pow

er, P

2

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50.84

0.86

0.88

0.9

0.92

0.94

0.96

Time in sec

DC

Vol

tage

, Vdc

1

Fig. 10. Step response of power and DC voltage for case-7 with optimalcontroller parameters.

V. CONCLUSION

A systematic method for VSC HVDC controller parameterstuning is proposed. The converter controller parameters areselected based on a systematic approach using Genetic Al-gorithm. The GA enables the usage of the same controller

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50.8

0.85

0.9

0.95

1

Time in sec

Pow

er, P

2

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50.84

0.86

0.88

0.9

0.92

0.94

0.96

Time in sec

DC

Vol

tage

, Vdc

1

Fig. 11. Step response of power and DC voltage for case-8 with optimalcontroller parameters.

gains for all operating cases while maintaining the systemstability. The analysis is based on eigenvalue and transientsimulation is carried out to validate the performance of thesystem with same controller parameters in various operatingcases. The transient response is excellent in all the operatingcases with optimal controller parameters. The results show therobustness and suitability of designed controller for variousoperating cases.

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[13] Using MATLAB-SIMULINK, The MathWorks, Inc., Natick, MA, 1999.