Analysis of Subsynchronous Oscillations atCapacitor Commutated Converters

Holger Muller and Gerd Balzer

Abstract—When interconnecting two large asynchronous powersystems using HVDC technology with a high transmission capac-ity, the short-circuit power of the connected networks can be lowcompared to the rated dc power. For this reason stability problemsmight occur during the operation of the HVDC system. Especiallywhen operated at weak inverter side networks ac faults can resultin severe disturbances of the HVDC system. Therefore a new typeof HVDC converter, the Capacitor Commutated Converter (CCC)can be used.

Furthermore if the network on the rectifier side has a highimpedance, there can also occur stability problems. In this pa-per the torsional interaction between the rectifier controller of theHVDC and the mechanical turbine-generator system of a nearbypower station is modeled and analyzed for different SCR of therectifier side network.

The design of a subsynchronous damping controller (SSDC) ispresented for counteracting emerging subsynchronous oscillationsthat are insufficiently damped. The enhanced damping effect ofthe SSDC is shown and the improvement of the stability of thesystem is indicated especially when operated at low SCR of therectifier side network.

Index Terms— HVDC transmission, capacitor commutatedconverter, CCC, subsynchronous oscillation, SSDC, high-powertransmission

I. INTRODUCTION

IN Europe and in other parts of the world there are effortsof using the advantages of interconnected networks and the

emerging positive synergy effects. For instance after the suc-cessful synchronous operation of the CENTREL network andthe UCTE system there is the possibility to benefit from anelectrical interconnection between the UCTE and the Russianpower system UPS/IPS using a high-power East-West intercon-nection over the distance of about 2000km from Germany toRussia [1].

This transmission system connects power systems in differ-ent time zones. Due to superposition of the individual loadcurves the load peaks in both systems can be balanced. In thisway the installed power capacities can be reduced and there isthe possibility of utilizing the power plants more efficiently andeconomically [2].

Due to the differences in power system management and con-trol the High-Voltage Direct-Current (HVDC) technology todayis the only possibility to interconnect the two asynchronous net-works and to economically transmit large quantities of powerover long distances.

Dipl.-Ing. H. Muller and Prof. Dr.-Ing. G. Balzer are working with theDepartment of Electrical Power Systems at the Darmstadt University of Tech-nology, Darmstadt, Germany. (email: Holger.Mueller@eev.tu-darmstadt.de)This work was sponsored and supported by the “Deutsche Forschungsgemein-schaft” (DFG), Bonn, Germany.

In the beginning of the design of the transmission systemthe basis conditions are specified. Thus the maximum capacitylevel for the HVDC transmission is determined and the differentcomponents are designed. When having a high transmitted dcpower, the relation of the short-circuit power at the points of in-terconnection to the transmitted power can become low. Hencethe consumption of reactive power of the HVDC converter canemerge as a problem with inverter side networks having a lowshort circuit ratio (SCR).

With the Capacitor Commutated Converter (CCC) a newconcept of HVDC systems was presented some years ago [3],[4], [5]. The commutation capacitor provides an additionalcommutation voltage resulting in smaller apparent extinctionangles and hence in a reduced reactive power consumption. Theoperation of the CCC at networks with low SCR is thereforeimproved [6], [7].

On the other hand when the rectifier side network has alow SCR the stability of the transmission system can also beeffected. There can occur torsional interaction between theHVDC controls with the subsynchronous torsional modes ofthe turbine-generator system. This results in badly or even neg-atively damped subsynchronous oscillations (SSO) [8].

In this paper the modeling of a high-power HVDC trans-mission system using conventional and CCC technology is de-scribed. A power plant situated nearby the rectifier station is de-signed including a spring-mass model for considering the me-chanical part the the generator and for identifying its naturalfrequencies. The subsynchronous interaction between HVDCcontroller and generator is shown depending on the SCR of theac network. To increase the damping of the SSO a subsyn-chronous damping controller (SSDC) is used and the effect onthe HVDC as well as the CCC system is described.

II. THE HVDC TRANSMISSION SYSTEM

The basic parameters are determined in this section whichare important for the design of the system model using theCCC technology as well as the conventional HVDC con-verter. The model is then realized in the simulation programPSCAD/EMTDC for performing transient simulations.

A. Determination of Maximum Transmission Capacity

The maximum capacity level for the HVDC transmission de-pends on the interconnected power systems. The energy ineach system, which is available for exporting, as well as theusable capacities on the tie lines between the local networksis a limiting parameter. The maximum rated dc power Pdr is

HVDC

InverterRectifier

Power System A Power System B

Filter Filter

Compensation Compensation

UR UI

Fig. 1. Equivalent circuit diagram of the HVDC system including compensation and interconnected power systems

mainly limited by the power, which can be provided by the pri-mary and secondary control in the UPS/IPS respectively in theUCTE power system in the worst-case event of a total loss ofthe HVDC system. Hence the capacity of the transmission sys-tem is rated to Pdr = 4000 MW [1].

B. Basic System CharacteristicsTo realize the HVDC transmission with a rated dc power

of 4000 MW, the HVDC model is designed as a bipolar sys-tem with two 6-pulse bridge converters per pole. The rated dcvoltage Udr is ±600 kV, hence the rated dc current is Idr =3.33 kA. The converter bus voltages are 400 kV at the nominaloperation point.

The system will be operated at a certain power schedule.Hence the rectifier is operated in constant dc power controlmode. The inverter is controlled to a minimum extinction an-gle to minimize the required reactive power of the converterbridges.

C. The conventional HVDCThe extinction angle is controlled to the minimum value of

γmin = 18◦. The reactive power consumption of the HVDCconverters is about 60% of the rated dc power at full workload,i. e. about 2400 Mvar. This need has to be met by the ac fil-ters and compensation capacitors connected to both converterbusbars. Therefore two ac filters for the 11th and for the 13th

harmonic and a high-pass filter are installed, each designed tosupply 500 Mvar of reactive power. A schematic diagram of theHVDC model is shown in Fig. 1.

Both networks are modeled by using a three phase voltagesource and an internal impedance representing the short-circuitpower. To indicate the strength of the ac systems according tothe connected HVDC link, the short circuit ratio (SCR) is veryimportant [9]. In the simulations introduced in the followingsections the inverter side network is chosen to be a strong sys-tem with a SCR of 5. Thus it will not affect the stability of thesystem.

In this paper the strength of the rectifier side network is veryimportant and is the main target of investigations. The problemsof operation at networks with low SCR are precisely analysed.So the SCR is changed during the analysis of the systems.

D. The CCC Model

Compared to the conventional HVDC system the CCC hasmany advantages in its steady-state as well as in its transient be-haviour. Due to the additional commutation voltage supportedby the commutation capacitors, which are connected in seriesbetween the converter transformers and the valves as shown inFig. 2, the apparent extinction angle γmin of the inverter is re-duced and kept constant at 2◦ by the inverter controller.

Hence the reactive power consumption is well reduced overthe entire range of operation. Consequentially the capacitorsof the ac filters can be reduced and the filters do not have tobe switched at low loads in order to keep the busbar voltageswithin their operational range. Furthermore the real extinctionangle at the valves becomes larger and the stability of the con-verter at network faults is improved [7].

Fig. 2 shows the circuit diagram of the rectifier side of theCCC and the generator close to the HVDC terminal.

ac network

ac filter

rect

CCC

power station

Fig. 2. Circuit diagram of the CCC rectifier station including the nearby powerplant

To dimension the components and their parameters properly,the dc voltage Ud and the currents through the valves must becalculated precisely. When the dc current is assumed to be con-stant, the commutation angle µ can be determined by iteration

[4], and the dc voltage can be calculated as follows:

Ud =3

π·

µ∫

0

ud δωt +

π

3∫

µ

ud δωt

(1)

=⇒ Udr =6

π·√

2UrT2 ·(cosα + cos(α + µ))

2

+6

π·(π

3−

µ

4

)

· (∆uauf − ∆uab) (2)

The resulting reactive requirement is about 20% of Pdr, i. e.the need of the converter is reduced by 2/3. This power is pro-vided by the harmonic filters. In contrast to the conventionalHVDC only one filter for the 11th and one for the 13th har-monic is installed each supplying 250 Mvar of reactive power.Additionally there is a high-pass filter and a capacitor bank con-nected to the busbars. So the compensation provides 850 Mvaraltogether.

In Table I and II the main system parameters are specified.The ratings of the converter transformers can be seen as well asthe minimum extinction angle γmin and the installed reactivepower Qc at each converter bus.

TABLE IMAIN SYSTEM PARAMETERS

Pdr Udr γmin `total QC

MW kV ◦ km MVA

HVDC 4000 ±600 18 2000 2500

CCC 4000 ±600 2 2000 850

TABLE IICONVERTER TRANSFORMER RATINGS

SrT UrT1 UrT2 ukr

MVA kV kV %

HVDC 1216 400 258 18

CCC 1069 400 227 18

III. THE GENERATOR MODEL

Near the rectifier station of the HVDC system a power plantis connected to the busbar which can also be seen in Fig. 2. Thegenerator supplies the main part of the transmitted power to thehigh-power transmission system. Therefore it is situated closeto the rectifier to minimize transmission losses.

In this configuration there can occur interaction between theHVDC rectifier controller and the natural frequencies of thepower plant depending on the different variables of the system.Hence the parameters of the generator are specified. The degreeof complexity for modelling the synchronous machine is veryimportant to simulate the subsynchronous effects. Furthermorethe mechanical part of the generator including turbine massesand shaft have to be considered.

A. Basic Generator Parameters

The power plant basically consists of two generators witha rated power SrG = 2 · 1640 MVA providing a rated activepower of PrG = 0.8 ·SrG. So it is able to supply a mager partof the transmitted power by the HVDC.

The generators are connected to the unit transformers at avoltage level of 27 kV, which are directly feeding into the rec-tifier busbar. The generator is controlled to provide a constantactive power. Also the generator terminal voltage is kept at aconstant value of 1.05 p.u.

B. Generator Model

The complexity of the generator model has to be sufficientto show the effects of mechanical oscillations in the time pe-riod of up to 10 s. For analysing effects below the synchronousfrequency, experience has shown that reasonable results maybe obtained by representing both d- and q-axis using a second-order model. Fig. 3 shows the equivalent circuit diagram of thegenerator [10].

d-axis

q-axis

Lhd

Lhq

LF

LD

RD

RFLsd

Lsq

LQ

RQ

LG

RG

Ud

Uq

Efd

w yqr

w ydr

Ra

Ra

Fig. 3. Equivalent circuit diagram of the second-order model of the syn-chronous machine

C. Mass Spring Model

To analyze subsynchronous effects it is not sufficient tomodel only the electrical part of the generator but also to in-clude the rotor masses and the generator shaft between the dif-ferent turbines [8]. This turbine-generator system is a complexmechanical system with natural frequencies above and belowthe synchronous frequency.

Here the subsynchronous range is important. So the mechan-ical system can be modelled using lumped masses with a certaininertia constant Hi which are connected through ideal torsionsprings with the torsional stiffness Ki. Therefore the rotor sys-tem is simulated as a spring-mass model with a high-pressure(HP) and three low-pressure (LP) turbine masses and the gen-erator as indicated in Fig. 4.

HP LPC GenLP

BLP

A

THP

TLPC

TLPB

TLPA

Tel

Fig. 4. Rotor mass spring model

The mechanical torques Ti generated by the turbine sectionscan assumed to be constant. The further modeling of the steamprocess of the power plant is not necessary.

To determine the mode shapes of the system modal analysistechnique is used. With the parameters of the inertia of eachrotor mass and the spring constants of each shaft the differentialequations are calculated. The damping of the shafts and therotor masses is usually low and can be assumed to be zero. Thenatural frequencies of the system with and without damping arenearly identical.

The linearized equations of the system are obtained and thestate matrix Amech is computed. The state vector ~x consists ofthe speed deviations of the rotor masses ωi and the rotor anglesδi as indicated in (4).

~x = Amech · ~x (3)

with

~x =(

ωG ωLPA ωLPB ωLPC ωHP δGen δLPA δLPB δLPC δHP

)T

(4)

Using the state matrix five pairs of eigenvalues can be de-termined and the natural frequencies of the turbine-generatorsystem fMode0...4 are calculated. Hence the modes 0 to 4 listedin Table III are the torsional modes.

TABLE IIIEIGENVALUES AND TORSIONAL NATURAL FREQUENCIES OF THE ROTOR

MASS MODEL

Torsional mode Eigenvalues Natural frequency f

Mode 0 ±7.07 · i 1.13 Hz

Mode 1 ±52.59 · i 8.37 Hz

Mode 2 ±95.81 · i 15.25 Hz

Mode 3 ±127.49 · i 20.29 Hz

Mode 4 ±148.43 · i 23.62 Hz

IV. SUBSYNCHRONOUS OSCILLATIONS

Using the models of the HVDC system and the power planttorsional interaction can be described and analysed. Especiallywhen the rated dc power is high compared to the short-circuitpower of the rectifier side network, there can occur problemswith insufficiently damped subsynchronous oscillations (SSO).

A. Description of the phenomenon

A transient event stimulates the oscillation of the mechanicalsystem of turbine and generator masses on the shaft and hencegenerates variations in the amplitude and phase angle of theac voltage. For equidistant firing angle control a shift of thevoltage phase causes an equal shift in the firing angle αR. Thiscauses a deviation in both dc voltage and current effecting thelevel of the transmitted power of the HVDC.

The change in the dc power results in the change of the gen-erator electrical torque. Depending on the system parametersthe torsional oscillations can be insufficiently damped and maybecome unstable [9].

B. Unit Interaction Factor

Torsional instability caused by interaction between the con-stant dc power controller at the rectifier and the generator de-pends on various system parameters. These conditions influ-encing the degree of torsional interaction are combined in theUnit Interaction Factor (UIF), which is a measure of the influ-ence of the controller on the torsional mode stability [8]. TheUIF is defined in (5).

UIF =Prd

SrG

·(

1 −SCR ·Prd

SCR ·Prd + SCG

)

(5)

where SCR ·Prd indicates the short-circuit power of the rec-tifier side network and SCG the short-circuit power of the gen-erator. At UIF < 0.1 there is only low interaction. If the UIFis greater then 0.1, there is the possibility of little or undampedsubsynchronous oscillations which can cause damages to therotor shaft.

Two ratios have a significant influence on the UIF. If thetransmitted dc power is large compared to the rated power ofthe generator, there can occur SSO. Also if the electrical dis-tance between generator and HVDC is short in relation to SCRof the power system, i. e. if the SCR of the network is low, thedamping effect of the network on the oscillations will be low. Agraphical representation of the UIF for the conventional HVDCconverter depending on these two ratios is shown in Fig. 5.

1 2 3 40

1

2

3

4

0

Pdr

SrG

SCR PGR dr stable

instable

SCG

Fig. 5. Graphical representation of the stability limit of UIF = 0.1 for theconventional HVDC converter

Due to the high rated dc power, the ratio Prd

SrGis 0.82. In this

case at the conventional HVDC the SCR of the rectifier side

network has to exceed the critical value of SCRcrit = 7.4 toensure a sufficient damping coefficient.

Furthermore the firing angle αR influences the degree of theinteraction. At a high value for αR, i.e. if the HVDC is operatedwith low dc voltage, the damping of the SSO is small. Thisleads to an advantage of the CCC in contrast to the conventionalconverter. Due to the commutation converters the firing angleis well reduced. At the rated operation point the CCC can beoperated with a firing angle αR of 3◦ compared to 21◦ at theconventional converter. The impact of the rectifier controller onthe damping of the torsional modes is minimized and the criticalvalue for the short-circuit power of the network is reduced toSCRcrit = 4.9.

C. Torsional Interactions with HVDC Controls

Thus in contrast to the conventional HVDC the CCC is ableto maintain in stable operation at weaker rectifier side networks.But the point of interconnection can have SCR well below thecritical value. Fig. 6 shows the badly damped torsional oscilla-tion of the system after a short circuit at the rectifier busbar ofthe CCC at a distance of 20km for the period of 50 ms. Thevalue of the SCR is 3, i. e. UIF = 0.3 and thus larger than thestability limit of 0.1.

0 51 2 3t

s

TLPC-LPB

0

1

p.u.

2

-1

Fig. 6. Badly damped oscillation of the generator torque between turbine LPBand LPC after a short circuit of 50 ms at 1 s at the CCC rectifier station

To identify the torsional modes causing interaction problems,it is necessary to analyse each mode separately. Therefore eachmode is stimulated in turns with a artificial sine wave havingthe frequency of the natural frequencies of the mechanical rotorsystem fMode0...4. This signal is added to the output of the dcpower control. The oscillation is excited for the period of 1 s.After the stimulation is stopped, the amplitude of the oscillationin the rotor frequency of the generator and in the torque of theturbines is analysed. The decay of the envelope curve can bemeasured and generally described as follows:

x(t) = xD · e−λDt · sin(ωt + ϕ) (6)

Here λD indicates the damping coefficient and is a measure-ment of the decay of the oscillation amplitude. Table IV liststhe damping coefficients of each mode for the conventional andthe capacitor commutated converter at a SCR of 3.

From this table can be seen, that for both HVDC systemsthe damping of mode 1 and especially mode 2 is insufficient.For the conventional HVDC the mode with λD 2 has even apositive damping coefficient. Hence these two torsional modes

TABLE IVCOEFFICIENT OF MODE DAMPING FOR HVDC AND CCC AT A SCR OF 3

Dampingcoefficient

Mode 1 Mode 2 Mode 3 Mode 4

λD,HVDC -0,051 +0,009 -0,011 -0,023

λD,CCC -0,113 -0,061 -0,055 -0,052

are critical for operation at high-impedance networks. Mode 3and 4 are also badly damped, but due to the low amplitude ofthe oscillation the force onto the rotor shaft is not as worse.

D. Subsynchronous Damping Control

To increase the damping of the first and second torsionalmode, a solution is to modify the rectifier control. Here aSubsynchronous Damping Control (SSDC) is inserted into thecontroller as an additional damping path.

The controller has to meet the following basic design objec-tives [11]:

• The SSDC must adequately damp the troublesome tor-sional oscillations

• It must add sufficient damping to the system for all opera-tion conditions

• The transient response of the transmission system must notbe affected by the SSDC

• An input signal should be used which can be obtain lo-cally, i. e. near the rectifier station.

The SSDC which is introduced in this paper has a narrowbandwidth to minimize the amount of disturbance to the HVDCcontrol. The additional path consists of two identical branches.Each branch utilizes a sharp bandpass to isolate the frequencyof the mode and uses the generator frequency as input variable.The signal is filtered and the outputs are subtracted from thefiring angle supplied to the converter bridges of the rectifier sta-tion.

The modified rectifier controller including the artificial stim-ulation and the SSDC is shown in Fig. 7.

-

Idset

FilterIdR +

aR-

p

+bR

+

+

+

Force

Ampl.

fForce sin

BandpassfMode 1

fGen

Filter

Limiter

-

FilterBandpass

fMode 2

aSSDC

Limiter

pTI

1+pt

PI-Controller

Fig. 7. Rectifier control including SSDC and artificial torsional stimulation

The SSDC introduces additional damping to the system. Theamplitude of the artificially stimulated oscillations shows afaster decay. Table V shows the damping coefficients for alltorsional modes of the generator with an active SSDC.

TABLE VCOEFFICIENT OF MODE DAMPING FOR HVDC AND CCC AT A SCR OF 3

WITH ACTIVE SSDC

Dampingcoefficient

Mode 1 Mode 2 Mode 3 Mode 4

λD,HVDC -0,503 -0,782 -0,724 -0,322

λD,CCC -1,657 -0,842 -0,440 -0,106

The values for the decay show clearly the effect of the SSDC.For all natural frequencies the damping coefficients are negativeund well below the results without SSDC although the SCR ofthe network is far beyond its critical value. Hence the stabilityof both the conventional HVDC and the CCC is well improved.

fG 50

Hz

50,4

49,6

TLPA-Gen

1

p.u.

1,5

00 2 4 8

ts

0 2 4 8t

s

0

6

-6

Force

0 2 4 8t

s

°

Pd

p.u.

1

0,80 2 4 8

ts

1,2

Fig. 8. Artificial torsional stimulation of the system over 1 sec

V. TRANSIENT SIMULATIONS

A. Excitation with an Artificial Force

To demonstrate the subsynchronous oscillations and the ef-fect of the SSDC, in this section a part of the transient simu-lations are shown. Using the system models described in thesections before and including the mechanical rotor shaft und

detailed controller representation, the model is realized in thetransient simulation program PSCAD/EMTDC. Using theseresults the different damping coefficients can also be derived.Here the main emphasize in the analysis is the behaviour of theCCC.

To show the effect of a stimulation of mode 2 of the turbine-generator system, the system is initiated for 1 s using an arti-ficial force with the frequency fMode2 = 15.25 Hz which isadded to the output of the rectifier controller as demonstrated inFig. 7.

In Fig. 8 the response of the system is shown. The force isplotted and the generator frequency fG as well as the torquebetween generator and adjacent turbine MLPA−Gen and the dcpower Pd are presented over the period of 8 s. The rectifier sidenetwork has a SCR of 3, i. e. the UIF has a value of about 0.3,which means the system is above the stability limit.

The figure demonstrates a nearly undamped oscillation af-ter excited with the force. The frequency of the oscillation isfMode2. As described in Table IV the decay of the oscillationamplitude is nearly zero.

50

Hz

50,4

49,6

0

6

-6

1

p.u.

1,5

00 2 4 8

ts

0 2 4 8t

s

0 2 4 8t

s

°

aSSDC

p.u.

1

0,80 2 4 8

ts

1,2

fG

TLPA-Gen

Pd

Fig. 9. Artificial torsional stimulation of the system with active SSDC over1 sec

In Fig. 9 the SSDC is active. Again the system is stimu-lated with the same force. Additionally the output of the SSDCαSSDC is shown. The curves demonstrates a very good im-provement of the transient behaviour of the system. The maxi-mum of the oscillation in fG and MLPA−Gen is reduced and thedecay of the amplitude shows very good damping.

B. Excitation with a Short Circuit

After the increase of the damping coefficient is shown usingthe artificial stimulation of the natural frequency, the transientresponse of the system to a short circuit with and without SSDCis compared.

50

Hz

50,5

49,5

1

p.u.

1,5

00 2 4 8

ts

p.u.

1

0

0 2 4 8t

s

0 2 4 8t

s

fG

TLPA-Gen

Pd

Fig. 10. Excitation of subsynchronous oscillations through a short circuit of50 ms in a distance of 20 km form the rectifier terminal without SSDC at theCCC

Fig. 10 and 11 show the behaviour of the system after a shortcircuit of 50 ms at a distance of 20 km from the rectifier sidebusbar. The SCR of the network is 3. In Fig. 10 can be seenthat all torsional modes of the rotor system are excited and os-cillating with their natural frequency. The amplitude of the SSOis badly damped in both generator frequency and in the torquesof the turbines.

With an active SSDC all natural frequencies are welldamped. After 2-3 s only the compact oscillation of the wholegenerator shaft after the disturbance can be seen. The oscilla-tions between the turbines have decayed.

Hence the modified rectifier controller presents a good solu-tion for improving the damping behaviour of dc power controlof both conventional HVDC and CCC at rectifier side networkswith a low SCR. The transmission system can operate at itsrated dc power even if the UIF is above the stability limit with-out the danger of damaging the generator shaft due to SSO.

Further simulations indicate that the response time of theHVDC rectifier control is not effected by the SSDC. Becauseof the narrow bandwidth approach of the design the impact onthe transient control behaviour is minimized.

VI. CONCLUSION

For high-power HVDC transmission systems like the pro-posed East-West interconnection with a high rated dc powerof 4000 MW the SCR at the point of interconnection of the

50

Hz

50,5

49,5

1

p.u.

1,5

00 2 4 8

ts

p.u.

1

0

0 2 4 8t

s

0 2 4 8t

s

0

6

-60 2 4 8

ts

°

aSSDC

fG

TLPA-Gen

Pd

Fig. 11. Excitation of subsynchronous oscillations through a short circuit of50 ms in a distance of 20 km form the rectifier terminal with SSDC at the CCC

converter to the ac network can cause stability problems. Es-pecially when operated at a inverter side network with a highimpedance, disturbances may occur under full working load.

To counteract these difficulties the capacitor commutatedconverter (CCC) is introduced as a new concept of HVDC con-verters. The CCC shows advantages in its steady-state as wellas transient behaviour particular when operated at weak net-works.

Although a weak connecting point to the rectifier side net-work can result in insufficiently damped subsynchronous oscil-lations. These oscillations are caused by the negative effect ofthe rectifier control of the HVDC on the torsional modes of theturbine-generator system. The CCC shows an improved damp-ing characteristic. But even so a short-circuit ratio of up to 5can result in low damped oscillations and thus damages on therotor shaft of the power plant.

To investigate this problem a model for a transmission sys-tem using both conventional and CCC technology is developed.The design of the model and the basic parameters are described.Also the generator model is introduced considering both theelectrical and the mechanical part of the power plant. Theeigenvalues und natural frequencies of this system are calcu-lated.

The simulation results show that the CCC is similarly af-fected by torsional interactions. To increase the damping of thesubsynchronous oscillations a subsynchronous damping con-troller is presented considering the basic design objectives. Itspositive effect on the transient behaviour of the system is shown

in transient simulations. Thus the SSDC presented indicates agood solution for enhanced damping of both the conventionalHVDC and the CCC converter at networks with low SCR.

REFERENCES[1] H. Brumshagen, U. Radke and F. Berger, “East-West European High

Power Transmission System”, Proceedings of the 36th Cigre Session, CI-GRE, 1996

[2] H.-C. Muller, H.-J. Haubrich and J. Schwarz, “Technical Limits of In-terconnected Systems”, Proceedings of the 34th Cigre Session, CIGRE,1992

[3] T. Jonsson and P.-E. Bjorklund, “Capacitor Commutated Converters forHVDC”, IEEE PES PowerTech Conference, Stockholm, pp. 44-51, June1995

[4] J. Reeve, J.A. Baron and G.A. Hanley, “A Technical Assessment of Arti-ficial Commutation of HVDC Converters with Series Capacitors”, IEEETransactions on Power Apparatus and Systems, Vol. PAS-87, No. 10, pp.1830-1840, October 1968

[5] K. Sadek, M. Pereira, D.P. Brandt, A.M. Gole and A. Daneshpooy, “Ca-pacitor Commutated Converter Circuit Configurations for DC Transmis-sion”, IEEE Transactions on Power Delivery, Vol. 13, No. 4, pp. 1257-1264, October 1998

[6] H. Muller and G. Balzer. Capacitor commutated converters for highpower hvdc transmission. In IEE International Conference on AC andDC Power Transmission, volume 485, pages 60–65, November 2001.

[7] H. Muller and G. Balzer. Modeling and simulation of capacitor commu-tated converters for high-power transmission systems. In InternationalSymposium on Modern Electric Power Systems MEPS’02, September2002.

[8] Prabha Kundur, Power System Satbility and Control, McGraw-Hill, Inc.,1993, pp. 500-513

[9] IEEE Power Engineering Society. IEEE Guide for Planning DC LinksTerminating at AC Locations Having Low Short-Circuit Capacities, ieeestd 1204-1997 edition, Juni 1997.

[10] IEEE Working Group on Modelling and Analysis of System TransientsUsing Digital Programs. Modelling and analysis guidelines for slowtransients - part ii: Controller interactions, harmonic interactions. IEEETransactions on Power Delivery, 11(3):1672–1677, Juli 1996.

[11] R. Piwko and E. Larsen. Hvdc system control for damping of subsyn-chronous oscillations. IEEE Transactions on Power Apparatus and Sys-tems, PAS-101(7):2203–2210, Juli 1982.

APPENDIXPARAMETERS OF THE TURBINE-GENERATOR-SYSTEM

TABLE VIINERTIA CONSTANTS OF THE ROTOR MASSES

Inertia constants Generator

Generator ΘGen kg m2 46959

Turbine LPA ΘLPA kg m2 77166

Turbine LPB ΘLPB kg m2 77166

Turbine LPC ΘLPC kg m2 77112

Turbine HP ΘHP kg m2 9511

TABLE VIISPRING CONSTANTS OF THE SHAFT

Spring constants Generator

Generator - LPA KGen−LPA10

6Nm/rad 379,425

Turbine LPA - LPB KLPA−B10

6Nm/rad 181,106

Turbine LPB - LPC KLPB−C10

6Nm/rad 281,742

Turbine LPC - HP KLPC−HP10

6Nm/rad 318,921

TABLE VIIIINPUT TORQUE OF THE TURBINES

Input torque Generator

Turbine LPA TLPA p.u. 0,24

Turbine LPB TLPB p.u. 0,24

Turbine LPC TLPC p.u. 0,24

Turbine HP THP p.u. 0,28