7i.analysis of ssr with three-level twelve-pulse vsc-based interline power-flow controller

7/28/2019 7I.analysis of SSR With Three-Level Twelve-Pulse VSC-Based Interline Power-Flow Controller

1/8


2/8

PADIYAR AND PRABHU: ANALYSIS OF SSR WITH VSC-BASED POWER-FLOW CONTROLLER 1689

both active and reactive voltage (and, hence, control of reactive

and active power) is desired. The other VSC is designated as

a support system which can inject series reactive voltageindependently [5], [7]. The capacitor voltage is regulated by dc

voltage controller of the support VSC.The dc voltage controller regulates the capacitor voltage and

maintains power balance between two converters. The power

balance can be expressed mathematically as

(1)

The independent control variables with the IPFC using two

VSCs are reactive voltage injections in two lines and active

voltage injection in prime VSC (hence, three degrees offreedom for the system shown in Fig. 1). When the active

voltage injection ofprime VSC is zero, the IPFC works sim-ilar to independent SSSCs in steady state with losses supplied

by the support VSC.

In the caseof the unified power-flow controller (UPFC), a sig-nificant increase in the damping of torsional modes is achieved

by emulating a positive resistance with the injection of seriesactive voltage [8]. A major objective of this paper is to investi-

gate the effect of active voltage injection by primeVSC of theIPFC controller on SSR damping for different operating modes.

In this paper, the interline power-flow controller (IPFC) isrealized by two three-level, 12-pulse VSCs. As there is no pub-

lished work on the analysis of SSR with IPFC, it becomes es-

sential to establish the validity of the models used. This is per-

formed by using a detailed nonlinear three-phase system model

(including the switching action within the VSC) for transient

simulation which is also used to validate the models em-ployed for the linear analysis.

The study is carried out based on eigenvalue analysis and

transient simulation. The modeling of the system neglecting

VSC is detailed (including network transients) and can be ex-

pressed in variables or (three) phase variables. The model-lingof VSC isbasedon 1) variables (neglecting harmonicsin the output voltages of the converters) and 2) phase variables

and the use of switching functions. The damping torque anal-

ysis, eigenvalue analysis, and the controller design is based on

the model while the transient simulation considers bothmodels of VSC. It is shown that series active voltage injection by

IPFC in the resistance emulation mode can effectively be used

as an SSR countermeasure.

This paper is organized as follows. The modelling of the IPFC

is described in Section II. The methods used for the analysis ofSSR are described in Section III while a case study is presented

in Section IV. Section V presents the conclusions.

II. MODELLING OF IPFC WITH THREE-LEVEL VSC

In the power circuit of an IPFC, the converter is usually

either a multipulse and/or a multilevel configuration. The con-trol of injected voltage magnitude by pulse-width modulation

(PWM) with two-level topology demands higher switching

frequency and leads to increased losses. The three-level con-

verter topology can achieve the goal by varying dead angle

with fundamental switching frequency [9]. The time period in

a cycle during which the converter pole voltage is zero is given

as [10]. The converters that allow the variation of bothmagnitude and the phase angle of converter output voltage are

Fig. 2. Equivalent circuit of a VSC viewed from the ac side.

classified as TYPE-1 converters [11]. Here, a combination of12-pulse and a three-level configuration [10] is considered. Thethree-level converter topology greatly reduces the harmonic

distortion on the ac side [5], [9]. The detailed three-phase model

of IPFC is developed by modeling the converter operation by

switching functions [10].

A. Mathematical Model in D-Q Frame of Reference

When switching functions are approximated by their fun-

damental frequency componentsneglecting harmonics, IPFCcan be modeled by transforming the three-phase voltages and

currents into variables using Krons transformation [4],[12]. The equivalent circuit of a VSC viewed from the ac side is

shown in Fig. 2.

In Fig. 2, and are the resistance and reactance

of the interfacing transformer of VSC- . The magnitude control

of the th converter output voltage is achieved by modu-

lating the conduction period affected by the dead angle of

individual converters.

The output voltage of the th converter can be represented in

the frame of reference as

(2)

(3)

(4)

where

;

for a 12-pulse converter;transformation ratio of the interfacing transformer

;angle of the th line current;

angle by which the fundamental component of

the th converter output voltage leads the th line

current . With the two converter IPFC , 2.

The dc-side capacitor is described by the dynamical equation

as

(5)

where

;

;

and components of line-1 current ;

and components of line-2 current .


3/8

1690 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 22, NO. 3, JULY 2007

Fig. 3. IPFC controller.

B. Converter Control

Fig. 3 shows the schematic representation for converter con-

trol. In this controller, the magnitude, which is a function of

(for a constant ) and phase angle of the converter

voltage are used to control reactive and active voltage.

The support VSC regulates the dc capacitor voltage at aconstant value. The active voltage reference ofsupportVSC isobtained from the dc voltage controller while forprimeVSCs,it is obtained from constant resistance emulation. The reactive

voltage reference of support and prime VSCs can be keptconstant or obtained from the active power controller.

In Fig. 3, and are calculated as

(6)

(7)

We can define the injected reactive ( component of theinjected voltage in quadrature with line current) and the active

( component of injected voltage in phase with line current)

voltages in terms of variables in the frame ( and )as follows:

(8)

(9)

Here, positive implies that the VSC injects inductive voltage

and positive implies that it draws real power from the line.

III. ANALYSIS OF SSR

The two aspect of SSR are: 1) steady-state SSR [induction

generator effect (IGE) and torsional interaction (TI)] and 2) tran-

sient torques [4]. The analysis of steady-state SSR can be per-

formed by linearized models at the operating point and include

damping torque analysis and eigenvalue analysis. The analysis

of transient SSR requires a transient simulation of the nonlinear

model of the system. For the analysis of SSR, it is adequate to

model the transmission line by lumped resistance and induc-

tance to consider the line transients. The generator stator tran-

sients are also considered along with a detailed (2.2) model of

the generator [12]. The excitation system, including PSS, is alsoconsidered.

Fig. 4. Interaction between mechanical and electrical system.

A. Damping Torque Analysis

Damping torque analysis is a frequency-domain method

which can be used to screen the system conditions that give

rise to potential SSR problems. The significance of this ap-

proach is that it enables the planners to decide upon a suitable

countermeasure for the mitigation of the detrimental effectsof SSR. The damping torque method gives a quick check to

determine the torsional mode stability. The system is assumed

to be stable if the net damping torque at any of the torsional

mode frequencies is positive [13].

The interaction between the electrical and mechanical system

can be represented by the block diagram shown in Fig. 4.

At any given oscillation frequency of the generator rotor, the

component of electrical torque in phase with the rotor

speed is called damping torque.

The expression for the damping torque coefficient due

to the external transmission network is derived in [4] as

(10)

When the IGE is neglected (as it does not have a significant

effect on the prediction of torsional mode stability), the gener-

ator can be represented by the classical model [8].

When the mechanical damping is zero, the instability of th

torsional mode frequency is determined from the criterion

and the decrement factor can be approximately

expressed as [4], [13]

(11)

where is the modal inertia for the th mode.It is observed, generally, that the damping torque introduced

by the electrical system is at a negative peak at a frequency cor-

responding to the complement of the electrical resonance fre-

quency . The complement is defined as

(12)

where is the fundamental frequency.

B. Eigenvalue Analysis

In this analysis, generator model (2.2) [12] is considered. The

electromechanical system consists of the multimass mechan-ical system, the generator, the excitation system, power system


4/8


5/8


TABLE I

EIGENVALUES OF THE DETAILED SYSTEM WITH AND WITHOUT IPFC

are better damped for Case 2). This results from the fact that the

loop resistance inserted by IPFC is more for Case 2). This pointis explained in some detail later. The damping of other torsional

modes (mode 2 and 3) is not significantly affected by the oper-

ating modes of IPFC.

Table I also gives the eigenvalues of the system for Case

1) when is reduced to 0.1776 (from the previous value of

0.2496) while isincreasedto 0.192 toretain the samevalue

of hybrid compensation (0.3696 p.u.) (see last column). It is ob-

served that the network resonance frequency is reduced

which increases the frequency of the subsynchronous netwok

mode to 177.16 rad/s (which does not coincide with

any of the torsional modes) and the system is found to be stable.

This suggests that it is possible to detune the network resonance

frequency by the proper selection of the combination offixed

capacitor and injected series reactive voltage for a given com-

pensation level, when the line has hybrid compensation. This is

also observed with the case studies considered for SSSC in [6],

[10], and [17].

For , it was observed that the results were not af-

fected by the absence of resistance emulation (and is held

constant). However, for being not equal to zero, there are

differences in the results as will be shown later.

It is to be noted that the injection of positive real voltage in

line-2 (positive and, hence, positive ) causes the neg-

ative real voltage injection in line-1 ( and, hence,

negative ). This is because the positive real voltage injec-tion in line-2 causes active power to be fed to line-1 from line-2

to maintain power balance in the dc link (Positive in line-2

draws real power from line-2 and supplies it to line-1 via the

dc link). Neglecting losses in the IPFC, we can express this be-

havior of IPFC from (1) as

(13)

(14)

(15)

The steady-statevariationof with obtainedby loadflow for the study system is shown in Fig. 6 for case-1. The

Fig. 6. Variation ofR

withR

.

operating points with , 0.015, 0.06, and 0.015 in per

unit are shown in Fig. 6 as A, B, C, and D, respectively.

It is to be noted from Fig. 6 that for a given change in ,

a change in is small as the current in line-1 is higher com-

pared to line-2. Hence,an increase in positive gives a small

increase in negative and the net loop resistance comprising

line-1 and 2 is increased. On the other hand, the negative re-

sistance injection in line-2 causes the net loop resistance to benegative.

Table II, column 2, gives the eigenvalues of the combined

system when series real voltage is set to 0.060 p.u. for

case-1 and the controller emulates (positive) resistance in series

with line 2 of the prime system. All of the torsional modes are

stable in this case. Comparing the results given in Tables I and II,

it is observed that the damping of mode-1 is improved with real

voltage injection, while the damping of mode-2 is marginally

reduced.

It was observed that when and the resistance

emulation is disabled, the torsional mode 1 becomes unstable

(with the eigenvalues of ). This shows that the

resistance emulation is essential, in general, to damp the criticaltorsional mode when required.


6/8


TABLE II

EIGENVALUES OF THE DETAILED SYSTEM WITH IPFC (CASE 1)AND

X = ( 0 : 2 4 9 6 + 0 : 1 2 ) = 0 : 3 6 9 6 p : u :

Fig. 7. Simulation with detailed three-phase model of IPFC for a pulse changein T ( V = 0 : 0 0 ) for Case 1).

Table II, column-3, gives the eigenvalues of the combined

system when series real voltage is set to 0.015 p.u. for

case 1 and the controller emulates negative resistance in series

with the line-2 of the prime system. It is observed that the

damping of torsional mode 2 is increased (compared to the case

with ). The damping of the subynchronous network

mode is significantly reduced in comparison with the eigenvalue

results with or 0.060. It is observed that when

, the subsynchronous network mode becomes unstable

as the net loop resistance comprising lines 1 and 2 becomeslarge negative. However, these results are not given here. In all

cases, the damping of mode-3 is practically constant as its modal

inertia is very large.

B. Transient Simulation

The transient simulation of the combined nonlinear system

with and the detailed three-phase model of the system is

carried out using MATLAB-SIMULINK [14].

The simulation results for a 10% decrease in input mechanical

torque applied at 0.5 s and removed at 1 s with case-1 (for

) using the three-phase model of IPFC is shown in

Fig. 7.

The simulation results for case-1 with the model andwith the three-phase model of IPFC are shown in Figs. 8 and

Fig. 8. Simulation with a detailedD Q model of the IPFC for a pulse change

in T ( V = 0 : 0 6 ) for Case 1).

Fig. 9. Simulation with a detailed three-phase model of the IPFC for a pulsechange in

T ( V = 0 : 0 6 )

for Case 1).

9, respectively, for 0.06. It is observed that the system

is stable (as predicted from the eigenvalue analysis). It is to be

noted that there is a good match between the simulation results

(variation of rotor angle and LPGEN section torques) ob-

tained with and three-phase models of IPFC.

C. Discussion

It was shown in [8] that the emulation of positive resistance

by the series connected VSC in a UPFC improves the damping

of the critical torsional mode. Similar results are expected in the

case of IPFC also. However, the problem is complicated by the

fact that, with IPFC connected in two parallel lines, the injec-

tion of positive series resistance in the prime line is accompa-

nied by the injection of negative resistance in the parallel line

in which support VSC is connected. Since the net resistance de-

termines the damping, it is necessary to select the prime line

with the smaller operating current such that, the loop resistance

is increased. The results of the case study prove this assertion asin example considered, the line 2 which carries about half the


7/8


Fig. 10. Sensitivity of damping torque for variation in V .

current in line 1, is suited for the prime VSC with positive real

voltage injection. If prime VSC is connected in line 1, it must

operate with negative real voltage injection.

It was shown in [6] and [8] that the injection of constant reac-

tive voltage by series-connected VSC has no appreciable effect

on the electrical resonance frequency in the network with hybrid

compensation with fixed series capacitors. This observation canbe utilized to reduce the risk of SSR by appropriately selecting

the value of the series capacitor and making up for the required

(total) compensation by injecting constant reactive voltage. By

ensuring that the torsional mode frequency (which is unaffectedby the electrical network) does not lie close to the complement

of the electrical resonance frequency, the risk of SSR is avoided.

Although less accurate, the damping torque method can be

used to predict the potential SSR problems under various system

operating conditions. The variation of damping torque with tor-

sional frequency for case-1 is shown in Fig. 10 for various values

of . Referring to Fig. 10, peak negative damping is reduced

substantially with positive real voltage injection ,

in the line-2. However, negative real voltage injection

increases the peak negative damping. Although the peak

negative damping is decreased with positive resistance emula-

tion, the damping at higher frequencies is reduced whereas it is

increased at lower frequencies. These results are in agreementwith eigenvalue results.

Referring to (15), it should be noted that when the current of

two parallel transmission lines is nearly same, the injection of

positive active voltage in a line causes nearly equal negative real

voltage injection in the other line and there is not much increase

in the net loop resistance comprising the two lines. However, it

is possible to obtain a difference in the line currents by control

over the injected series reactive voltages. Thus, an increase of

net loop resistance of the transmission lines can be achieved and

is found to be effective in the damping of SSR. The choice of

the prime converter is based on the operating currents in the two

lines. The converter connected to the line carrying lesser current

should be operated as a prime converter with positive resistanceemulation [see (15)].

V. CONCLUSION

In this paper, we have presented the analysis and simulation

of SSR with an IPFC-compensated system which is reported for

the first time. The application of the model is validated by

the transient simulation of the three-phase model of IPFC. It

is observed that the model is quite accurate in predicting

the system performance. The effectiveness of various operatingmodes of the two VSCs comprising IPFC in damping SSR has

been investigated.

There is no appreciable difference in the resonance frequency

of the electrical network as the total series compensation (in a

hybrid compensation scheme) is increased by increasing the se-

ries reactive voltage injected instead of the series capacitor. This

reduces the risk of SSR since the fixed capacitor can be chosen

such that the electrical resonance frequency does not coincide

with the complement of the torsional modal frequency (which

is practically independent of the electrical network). This in-

dicates the possibility of detuning SSR by adjusting the series

reactive voltage wherever feasible. In addition, the injection ofseries real voltage by IPFC (to emulate positive resistance in

the transmission loop) as a SSR countermeasure is a novel tech-

nique and improves the damping of the critical torsional mode.

APPENDIX

SYSTEM DATA

The data for the electromechanical system pertaining to IEEE

SBM model [15] is based on a 600-MVA and 500-kV base. All

of the data given below are in per unit (p.u.) based on previously

mentioned base values.

IPFC controller (rating of each VSC is 100 MVA)

, .

Constant resistance emulation controller ,

.

DC voltage controller , .

The impedance of interfacing transformers is merged with the

line impedances.

REFERENCES

[1] M. C. Hall and D. A. Hodges, Experience with 500 kV subsyn-chronous resonance and resulting turbine generator shaft damage atMohave generating station, Analysis and Control of SubsynchronousResonance 1976, IEEE Publ. 76 CH 1066-O-PWR.

[2] C. E. J. Bowler, D. N. Ewart, and C. Concordia, Self excited torsionalfrequency oscillations with series capacitors,IEEE Trans. Power App.

Syst., vol. PAS-92, no. 5, pp. 16881695, Sep. 1973.[3] L. A. Kilgore, D. G. Ramey, and M. C. Hall, Simplified transmission

and generation system analysis procedures for subsynchronous reso-

nance problems, IEEE Trans. Power App. Syst., vol. PAS-96, no. 6,pp. 18401846, Nov./Dec. 1977.

[4] K. R. Padiyar, Analysis of Subsynchronous Resonance in Power Sys-tems. Norwell, MA: Kluwer, 1999.

[5] N. G. Hingorani and L. Gyugyi, Understanding FACTS. Piscataway,NJ: IEEE Press, 2000.

[6] K.R. Padiyarand N.Prabhu,A comparative study of SSRcharacteris-tics of TCSC andSSSC, presentedat thePSCC Conf., Liege,Belgium,Aug. 2005.

[7] L. Gyugyi, K. K. Sen, and C. D. Schauder, The interline power flowcontroller concept: A new approach to power flow management intransmission systems, IEEE Trans. Power Del., vol. 14, no. 3, pp.11151122, Jul. 1999.

[8] K. R. Padiyar and N. Prabhu, Investigation of SSR characteristics ofunified power flow controller, Elect. Power Syst. Res., vol. 74, pp.211221, May 2005.


8/8


[9] K. K. Sen and E. J. Stacy, UPFCUnified power flow controller:Theory, modelling and applications, IEEE Trans. Power Del., vol. 13,no. 4, pp. 14531460, Oct. 1998.

[10] K. R. Padiyar and N. Prabhu, Analysis of subsynchronous resonancewith three level twelve-pulse VSC based SSSC, in Proc. IEEETENCON, Oct. 1417, 2003, pp. 7680.

[11] C. Schauder and H. Mehta, Vector analysis and control of advancedstatic VAR compensators, Proc. Inst. Elect. Eng. C, vol. 140, no. 4,

pp. 299306, Jul. 1993.[12] K. R. Padiyar, Power System DynamicsStability and Con-trolSecond Edition. Hyderabad, India: B. S. Publications, 2002.

[13] I. M. Canay, A novel approach to the torsional interactions and elec-tricaldamping of thesynchronous machine, Part-I: Theory, Part-II: Ap-

plication to an arbitrary network, IEEE Trans. Power App. Syst., vol.PAS-101, no. 10, pp. 36303647, Oct. 1982.

[14] Using MATLAB-SIMULINK. Natick, MA: Math Works, Inc., 1999.[15] IEEE SSR working group, Second benchmark model for computer

simulation of subsynchronous resonance, IEEE Trans. Power App.Syst., vol. PAS-104, no. 5, pp. 10571066, May 1985.

[16] K. R. Padiyar and N. Prabhu, Modelling, control design and analysisof VSC based HVDC transmission systems, presented at the IEEEPOWERCON, Singapore, Nov. 2124, 2004.

[17] N. Prabhu,Analysis of subsynchronous resonance with voltage sourceconverter based FACTS and HVDC controllers, Ph.D. dissertation,Dept. Elect. Eng., Indian Inst. Sci., Bangalore, India, Sep. 2004.

K. R. Padiyar (SM91) received the B.E. degree in electrical engineering fromPoona University, Poona, India, in 1962, the M.E. degree from the Indian In-stitute of Science (I.I.Sc.), Bangalore, in 1964, and the Ph.D. degree from theUniversity of Waterloo, Waterloo, ON, Canada, in 1972.

Currently, he is an Honorary Professor of Electrical Engineering at the I.I.Sc.He was with the Indian Institute of Technology, Kanpur, India, from 1976 to1987, prior to joining I.I.Sc. His research interests are in the area of HVDC andFACTS, system dynamics, and control. He has authored three books and many

papers.Dr. Padiyar is a Fellow of the Indian National Academy of Engineering.

Nagesh Prabhu received the Dipl. Elect. Engg. degree from Karnataka Poly-technic, Mangalore, India, in 1986, the M.Tech. degree in power and energysystems from N.I.T. Karnataka, Surathkal, India (formerly Karnataka Regional

Engineering College) in 1995, and the Ph.D. degree from the Indian Institute ofScience, Bangalore, in 2005.

Currently, he is Professor of Electronics and Communication Engineering atthe VEL S.R.S. College of Multimedia (Engineering), Chennai. He was withthe N.M.A.M Institute of Technology, Nitte, from 1986 to 1998 and with J.N.N.College of Engineering, Shimoga, from 1998to 2006, prior to joining Vel S.R.S.College of Multimedia. His research interests are power system dynamics andcontrol, HVDC and FACTS, and custom power controllers.

7i.analysis of ssr with three-level twelve-pulse vsc-based interline power-flow controller

Documents