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Research ArticleTransient Stability Enhancement of Multimachine Power SystemUsing Robust and Novel Controller Based CSC-STATCOM

Sandeep Gupta1 and Ramesh Kumar Tripathi2

1Department of Electrical Engineering RIET Jaipur 302026 India2Department of Electrical Engineering MNNIT Allahabad 211004 India

Correspondence should be addressed to Sandeep Gupta jecsandeepgmailcom

Received 3 August 2014 Revised 22 December 2014 Accepted 23 December 2014

Academic Editor Francesco Profumo

Copyright copy 2015 S Gupta and R K Tripathi This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

A current source converter (CSC) based static synchronous compensator (STATCOM) is a shunt flexible AC transmission system(FACTS) device which has a vital role as a stability support for small and large transient instability in an interconnected powernetwork This paper investigates the impact of a novel and robust pole-shifting controller for CSC-STATCOM to improve thetransient stability of the multimachine power system The proposed algorithm utilizes CSC based STATCOM to supply reactivepower to the test system to maintain the transient stability in the event of severe contingency Firstly modeling and pole-shiftingcontroller design for CSC based STATCOM are stated After that we show the impact of the proposedmethod in the multimachinepower system with different disturbances Here applicability of the proposed scheme is demonstrated through simulation inMATLAB and the simulation results show an improvement in the transient stability of multimachine power system with CSC-STATCOM Also clearly shown the robustness and effectiveness of CSC-STATCOM are better rather than other shunt FACTSdevices (SVC and VSC-STATCOM) by comparing the results in this paper

1 Introduction

The continuous developments of electrical loads due to themodification of the society structure result in todayrsquos trans-mission structure to be faced close to their stability restric-tions So the renovation of urban and rural power networkis more and more necessary Due to governmental financialand green climate reasons it is not always possible toconstruct new transmission lines to relieve the power systemstability problem at the existing overloaded transmissionlines As a result the utility industry is facing the challengeof efficient utilization of the existing AC transmission linesin power system networks So transient stability voltageregulation damping oscillations and so forth are the mostimportant operating issues that electrical engineers are facingduring power transfer at high levels

In above power quality problems transient stability is oneof the most important key factors during power transfer athigh levels According to the literature transient stability of a

power system is its ability tomaintain synchronous operationof the machines when subjected to a large disturbance [1]While the generator excitation system with PSS (power sys-tem stabilizer) can maintain excitation control and stabilityit is not adequate to sustain the stability of power system forlarge faults or overloading occurs near to generator terminals[2]

So many researchers worked on this problem in findingthe solution for a long timeThese solutions are such as usingwide-area measurement signals [3] phasor measurementunit [4] and flexible AC transmission system In thesesolutions one of the powerful methods for enhancing thetransient stability is to use flexible AC transmission system(FACTS) devices [5ndash8] Even though the prime objective ofshunt FACTS devices (SVC STATCOM) is to maintain busvoltage by absorbing (or injecting) reactive power they arealso competent of improving the system stability by diminish-ing (or increasing) the capability of power transfer when themachine angle decreases (increases) which is accomplished

Hindawi Publishing CorporationAdvances in Power ElectronicsVolume 2015 Article ID 626731 12 pageshttpdxdoiorg1011552015626731

2 Advances in Power Electronics

by operating the shunt FACTS devices in inductive (capaci-tive) mode

In many research papers [2 9ndash11] the different typesof these devices with different control techniques are usedfor improving transient stability In between these FACTSdevices the STATCOM is valuable for enhancement powersystem dynamic stability and frequency stabilization due tothe more rapid output response lower harmonics superiorcontrol stability and small size and so forth [7 12] By theirinverter configuration basic type of STATCOM topologycan be realized by either a current-source converter (CSC)or a voltage-source converter (VSC) [13ndash17] But recentresearch confirms several merits of CSC based STATCOMover VSC based STATCOM [18 19] These advantages arehigh converter reliability quick starting and inherent short-circuit protection and the output current of the converteris directly controlled and in low switching frequency thisreduces the filtering requirements comparedwith the case of aVSCTherefore CSC based STATCOM is very useful in powersystems rather than VSC based STATCOM in many cases

Presently the most used techniques for controller designof FACTS devices are the Proportional Integration (PI) PIDcontroller [20] pole-shifting controller and linear quadraticregulator (LQR) [21] But LQR and pole-shifting algorithmsgive quicker response in comparison to PI and PID algorithm[22] LQR controller gain (119870) can be calculated by solvingthe Riccati equation and 119870 is also dependent on the twocost functions (119876 119877) So Riccati equation solvers have somelimitations which relate to the input arguments But poleshifting method does not face this type of any problem Sopole shifting method gives a better and robust performancein comparison to other methods

The main contribution of this paper is the application ofproposed pole-shifting controller based CSC-STATCOM forimprovement of power system stability in terms of transientstability by injecting (or absorbing) reactive power In thispaper the proposed scheme is used in the multimachinepower transmission system with dynamic loads under agrievous disturbance condition (three-phase fault or heavyloading) to enhancement of power system transient stabilitystudies and to observe the impact of the CSC based STAT-COM on electromechanical oscillations and transmissioncapacity Furthermore the obtained outcomes from theproposed algorithm based CSC-STATCOM are compared tothe obtained outcomes from the other shunt FACTS devices(SVCandVSC-STATCOM)which are used in previousworks[23 24]

The rest of the paper is prepared as follows Section 2discusses the circuit modeling and proposed pole-shiftingcontroller designing for CSC based STATCOM A two-areapower system is described with a CSC-STATCOM devicein Section 3 Simulation results of the test system with andwithout CSC based STATCOM for severe contingency areshown in Section 4 to improve the transient stability of themultimachine power system Comparison among differentshunt FACTS devices (SVC VSC-STATCOM and CSC-STATCOM) is also described in Section 4 Finally Section 5concludes this paper

Idc

iR

iS

iT

R L

C

Ldc Rdc

CR

CS

CT

S1 S3

S2 S4

S5

S6

R

S

T

iSR

iSS

iST

iCR

MV Bus

Figure 1 The representation of CSC based STATCOM 119894119878119877 119894119878119878 119894119878119879

line current V119862119877 V119862119878 V119862119879 voltages across the filter capacitors V

119877 V119878

V119879 line voltages 119868dc dc-side current 119877dc converter switching and

conduction losses 119871dc smoothing inductor 119862 filter capacitance 119871inductance of the line reactor 119877 resistance of the line reactor

2 Mathematical Modeling of Pole-ShiftingController Based CSC-STATCOM

21 CSC Based STATCOM Model In this section to verifythe response of the STATCOM on dynamic performancethe mathematical modeling and control strategy of a CSCbased STATCOM are needed to be presented So in thedesigning of controller for CSC based STATCOM the statespace equations from the CSC-STATCOM circuit must beintroduced To minimize the complexity of mathematicalcalculation the theory of 119889119902 transformation of currentshas been applied in this circuit which makes the 119889 and119902 components independent parameters Figure 1 shows thecircuit diagram of a typical CSC based STATCOM

The basic mathematical equations of the CSC basedSTATCOM have been derived in the literature [19] There-fore only brief details of the primary equations for CSC-STATCOMare given here for the readersrsquo convenience Basedon the equivalent circuit of CSC-STATCOM as shown inFigure 1 the differential equations for the system can beachieved which are derived in the abc frame and thentransformed into the synchronous 119889119902 frame using 119889119902 trans-formation method [25]

119889

119889119905119868dc = minus

119877dc119871dc

119868dc minus3

2119871dc119872119889119881119889minus

3

2119871dc119872119902119881119902 (1)

119889

119889119905119868119889= minus

119877

119871119868119889+ 120596119868119902minus1

119871

119864119889

119899+1

119871119881119889 (2)

119889

119889119905119868119902 = minus120596119868119889 minus

119877

119871119868119902 +

1

119871119881119902 (3)

119889

119889119905119881119889 = minus

1

119862119868119889 + 120596119881119902 +

1

119862119872119889119868dc (4)

119889

119889119905119881119902 = minus

1

119862119868119902 minus 120596119881

119889+1

119862119872119902119868dc (5)

In above differential equations 119872119889and 119872

119902are the two

input variables Two output variables are 119868dc and 119868119902 Here 120596

is the rotation frequency of the system and this is equal to the

Advances in Power Electronics 3

nominal frequency of the system voltage 119868119889and 119868119902are the 119889-

axis and 119902-axis components of the line current 119872119889and 119872

119902

are 119889-axis and 119902-axis components of the system modulatingsignal respectively 119864

119889and 119864

119902are direct and quadrature axis

of system voltage Here 119864119902is taken as a zero 119881

119889and 119881

119902are

the 119889-axis and 119902-axis components of the voltage across filtercapacitor respectively

Equation (1) shows that controller for CSC based STAT-COMhas nonlinearity characteristic So this nonlinear prop-erty can be removed by accurately modeling of CSC basedSTATCOM From (1) to (5) it can be seen that nonlinearproperty in the CSC-STATCOM model is due to the partof 119868dc This nonlinear property is removed with the help ofactive power balance equationHere it has been assumed thatthe power loss in the switches and resistance 119877dc is ignoredand the turns ratio of the shunt transformer is n 1 Here itis considered that generated power from the AC-source side(119875ac) is equal to absorbed power by DC-source side (119875dc) andpower loss at this time is negligible So this can be written inequation form as

119875ac = 119875dc 997904rArr minus3119864119889

2119899119868119889 = 119871dc119868dc

119889

119889119905119868dc + 119877dc119868

2

dc (6)

After using power balance equation and mathematicalcalculation nonlinear characteristic is removed from (1)Finally the equation is obtained below

119889

119889119905(1198682

dc) = minus2119877dc119871dc

(1198682

dc) minus3119864119889

119871dc119899119868119889 (7)

In (7) state variable (119868dc) is replaced by the state variable(1198682dc) to make the dynamic equation linear Finally theresulting better dynamic and robust model of the STATCOMin matrix form can be derived as

119889

119889119905

[[[[[

[

(119894dc)2

119894119889

119894119902

V119888119889

V119888119902

]]]]]

]

=

[[[[[[[[[[[[[

[

minus2119877dc119871dc

3119864119889

119871dc1198990 0 0

0 minus119877

119871120596119900

1

1198710

0 minus120596119900

minus119877

1198710

1

119871

0 minus1

1198620 0 120596119900

0 0 minus1

119862minus120596119900

0

]]]]]]]]]]]]]

]

lowast

[[[[[

[

(119894dc)2

119894119889

119894119902

V119888119889

V119888119902

]]]]]

]

+

[[[[[[[[

[

0 0

0 0

0 0

1

1198620

01

119862

]]]]]]]]

]

lowast [119868119894119889

119868119894119902

] +

[[[[[[

[

0

minus1

1198710

0

0

]]]]]]

]

lowast 119864119889

(8)

Above modeling of CSC based STATCOM is written inthe form of modern control methods that is state-spacerepresentation For state-space modeling of the system nextsection has been considered

22 Pole-Shifting Controller Design The pole-shifting tech-nique is one of the basic controlmethods which are employedin feedback control system theoryTheoretically pole-shiftingtechnique is to set the preferred pole position and tomove thepole position of the system to that preferred pole positionto get the desired system outcomes [26] Here poles ofsystem are shifted because the position of the poles relateddirectly to the eigenvalues of the system which control thedynamic characteristics of the system outcomes But for thismethod the system must be controllable In the dynamicmodeling of systems state-space equations involve threetypes of variables state variables (119909) and input (119906) and output(119910) variables with disturbance (119890) So comparing (8) with thestandard state-space representation that is

= 119860119909 + 119861119906 + 119865119890

119910 = 119862119909

(9)

We get the system matrices as

119909 = [1198682

dc 119894119889119894119902119881119889119881119902]119879

119906 = [119868119894119889 119868119894119902]119879

119890 = 119864119889 119910 = [119868

2

dc 119868119902]119879

119860 =

[[[[[[[[[[[[[

[


minus3119864119889

119871dc0 0 0

0 minus119877

119871120596

1

1198710

0 minus120596 minus119877

1198710

1

119871

0 minus1

1198880 0 120596

0 0 minus1

119888minus120596 0

]]]]]]]]]]]]]

]

119861 =

[[[[[[[[

[

0 0

0 0

0 0

1

1198880

01

119888

]]]]]]]]

]

119862 =

[[[[[

[

1 0

0 0

0 1

0 0

0 0

]]]]]

]

119879

119865 =

[[[[[[

[

0

minus1

1198710

0

0

]]]]]]

]

(10)

In the above equations (9) five system states two controlinputs and two control outputs are presented where 119909 is thestate vector 119906 is the input vector 119860 is the basis matrix 119861 isthe input matrix and 119890 is disturbance input

If the controller is set as

119906 = minus119870 lowast 119909 + 119869 lowast 119910ref + 119873 lowast 119890 (11)

then the state equation of closed loop can be written as

= (119860 minus 119861 lowast 119870) lowast 119909 + 119869 lowast 119910ref + 119861 lowast 119873 lowast 119890 + 119865 lowast 119890 (12)

Here for steady state condition

= 0 (13)

Then

119910 = 119862 lowast (119860 minus 119861 lowast 119870)minus1lowast [119861 lowast 119869 lowast 119910ref + 119861 lowast 119873 lowast 119890 + 119865 lowast 119890]

(14)


B C

A

minusK

xx yu

CSC-STATCOM

Ldc

Rdc

Pole-shiftingcontroller

Output responses formultimachine power

system

I2dc(ref ) yrefandIq(ref)

N lowast Ed F lowast Ed

1SJ+++

+++

Figure 2 Control structure of pole-shifting controller based CSC-STATCOM

where 119869 = (119862lowast(minus(119860minus119861lowast119870)minus1)lowast119861)minus1 and119873 = ((119862lowast(minus119860+119861lowast

119870)minus1lowast119861))minus1lowast(119862lowast(minus119860+119861lowast119870)

minus1lowast119865) these constant values are

found out from a mathematical calculation for tracking thereference output value (119910ref) by the system output value (119910)Here 119870 is the state-feedback gain matrix The gain matrix 119870is designed in such a way that (15) is satisfied with the desiredpoles

|119904119868 minus (119860 minus 119861119870)| = (119904 minus 1198751) (119904 minus 119875

2) sdot sdot sdot (119904 minus 119875

119899) (15)

where 1198751 1198752 119875

119899are the desired pole locations Equation

(15) is the desired characteristic polynomial equation Thevalues of 119875

1 1198752 119875

119899are selected such that the system

becomes stable and all closed-loop eigenvalues are located inthe left half of the complex-plane The final configuration ofthe proposed pole-shifting controller based CSC-STATCOMis shown in Figure 2

All the required parameters for the structure of pole-shifting controller based CSC-STATCOM are given in theappendix

3 Two-Area Power System withCSC-STATCOM Facts Device

In this section consider a two-area power systemwith a CSC-STATCOMat bus 119887 is connected through a long transmissionsystem where CSC-STATCOM is used as a shunt currentsource device Figure 3 shows this type of representationThe dynamic model of the machine with a CSC-STATCOMcan be written in the differential algebraic equation form asfollows

120575 = 120596 (16)

=1

119872[119875119898minus 119875119890119900minus 119875

csc119890] (17)

Here 120596 is the rotor speed 120575 is the rotor angle 119875119898 is themechanical input power of generator the output electricalpower without CSC-STATCOM is represented by 119875

119890119900 and119872

is the moment of inertia of the rotor Equation (17) is alsocalled swing equation The additional factor of the outputelectrical power of generator from a CSC-STATCOM is 119875csc

119890

in the swing equation

Real power flow

L1 L2

Sending end Receiving enda b c

ICSC

jX1 jX2

E1ang120575 E2ang0∘Edang120579b

Area 1 Area 2

CSC basedSTATCOM device

Ldc

Rdc

Figure 3 A single line diagramof two-area power systemwithCSC-STATCOM

Here for calculation of 119875csc119890

we assume the CSC-STATCOM works in capacitive mode Then the injectedcurrent fromCSC-STATCOM to test system can bewritten as

119868csc = 119868cscang (120579119887119900 minus 90∘) (18)

where 120579119887119900 is the voltage angle at bus 119887 in absentia of CSC-STATCOM In Figure 3 the magnitude (119864119889) and angle (120579119887)of voltage at bus 119887 can be computed as

120579119887 = tanminus1 [ 119883

21198641sin 120575

11988321198641cos 120575 + 119883

11198642

] (19)

119864119889 = (

11988321198641 cos (120575 minus 120579119887119900) + 11988311198642cos 120579119887119900

1198831+ 1198832

)

+ (11988311198832

1198831+ 1198832

119868csc)

(20)

From (20) it can be said that the voltage magnitude ofbus 119887 (119864

119889) depends on the STATCOM current (119868csc) In (17)

the electrical output power 119875csc119890

of machine due to a CSC-STATCOM can be expressed as

119875csc119890

=1198641119864119889

1198831

sin (120575 minus 120579119887) (21)


a

bc

d

ef

g

1205750 120575c 120575m0

Prefault curve A

Fault durationcurve B Pf

e

Postfault curve C

Postfault curve C

Ad

Aa

Pm

Power

Angle

Ppe (Icsc gt 0)

Pe(Icsc = 0)

(Icsc lt 0)

Figure 4 Power-angle characteristic of the test system with a CSC-STATCOM

Finally using (20) and (21) the total electrical output (119875119890)

of machine with CSC-STATCOM can be written as

119875119890= 119875119890119900+ 119875

csc119890

997904rArr 119875119890= 119875119890119900+

119883111988321198641

(1198831+ 1198832)1198831

119868csc sin (120575 minus 120579119887)

(22)

All above equations are represented for the capacitivemode of CSC-STATCOM So if the inductive mode ofoperation is needed in the system then 119868csc is replaced by minus119868cscin (18) (20) and (22) With the help of (17) the power-anglecurve of the test system can be drawn for stability analysis asshown in Figure 4

The power-angle (119875-120575) curve of the test system withouta CSC-STATCOM is represented by curve 119860 (also calledprefault condition) in Figure 4 Here the mechanical inputis 119875119898 electrical output is 119875

119890 and initial angle is 120575

0 When a

fault occurs 119875119890suddenly decreases and the operation shifts

from point 119886 to point 119887 at curve 119861 and thus the machinestarts accelerating from point 119887 to point 119888 where acceleratingpower [119875

119886= (119875119898minus 119875119890)] gt 0 At fault clearing 119875

119890suddenly

increases and the area 119886-119887-119888-119889-119886 represents the acceleratingarea 119860

119886as defined in (23) If the CSC-STATCOM operates

in a capacitive mode (at fault clearing) 119875119890increases to point

119890 at curve 119862 (also called postfault condition) At this time119875119886is negative Thus the machine starts decelerating but its

angle continues to increase from point 119890 to the point119891 until itreaches a maximum allowable value 120575119898 at point 119891 for systemstability The area 119890-119891-119892-119889-119890 represents the decelerating area119860119889 as defined in (23) From previous literature [1] equal areacriterion for stability of the system can be written as

int

120575119888

1205750

(119875119898 minus 119875119891

119890) 119889120575 = int

120575119898

120575119888

(119875119901

119890minus 119875119898) 119889120575 997904rArr 119860119886 = 119860119889 (23)

This equation is generated from Figure 4 where 120575119888is

critical clearing angle 119875119901119890is an electrical output for postfault

condition 119875119891119890is an electrical output during fault condition

From Figure 4 we clearly see for capacitive mode operation(119868csc gt 0) of CSC-STATCOMdevice the119875-120575 curve is not onlyuplifted but also displaced toward right and that enduesmore

decelerating area and hence higher stability limit After thatSection 4 is considered to verify the impact of the proposedcontroller based CSC-STATCOMmodeling in the analysis ofthemultimachine power system stability in terms of transientstability studies

4 Simulation Results

41 Multimachine Power System under Study In this sectiontwo-area four-machine power system is considered for thetest system study For this type of test system a 500 kVtransmission system with four hydraulic power plants (G1G2 G3 and G4) connected through 500-km long transmis-sion line is taken as shown in Figure 5 Here combinationof machine G1 and machine G2 represents the area 1 andcombination of machine G3 and machine G4 representsthe area 2 A rating of first (G1) and second (G2) powergeneration plant is 138 kv1000MVA The electrical outputsof the third (G3) and fourth (G4) power plant are 3000MVAOne 6000MW large resistive load is connected at the busB3 and another 1000MW resistive load is connected atthe bus B1 as shown in Figure 5 In this figure 828MWpower is flowing through bus B2 944MW and 877MWpower are flowing through buses B4 and B5 respectively and2487MW and 2643MW power are flowing through busesB6 and B7 respectively These values are based on powerflow calculation To improve the transient stability of thetest-system after disturbances (faults or heavy loading) apole-shifting controller based CSC-STATCOM is connectedat the mid-point of transmission line (at bus B2) In orderto previous work [27] shunt FACTS devices give maximumefficiency when connected at the mid-point of transmissionline Here each hydraulic generating unit is assembled witha turbine-governor set excitation system and synchronousgenerator But the hydraulic generating unit is not explainedin this paperThis is explained in [1] All the data required forthis test system model are given in the appendix

Now a severe contingency will be applied to the test sys-tem and to observe the impact of the pole-shifting controllerbased CSC-STATCOM for maintaining the system stabilitythrough MATLABSIMULINK

42 Case ImdashShort-Circuit Fault In this case it is consideredthat a three-phase fault is occurring at near bus B1 at 119905 =

01 s and is cleared at 0277 s The impact of system with andwithout CSC based STATCOM to this disturbance is shownin Figures 6 7 8 9 and 10 Here simulation is carried outfor 9 s to observe the nature of transients It is clear thatthe system without CSC-STATCOM is unstable upon theclearance of the fault from Figures 6 to 8 But this systemwithpole-shifting controller based CSC-STATCOM is restoredand stable upon the clearance of the fault and settled downafter about 3 to 4 s in Figures 7 to 10 Synchronism in betweenfour machine system is also maintained in these figures InFigure 7 1205751 1205752 1205753 and 120575

4are the rotor angles of machines

G1 G2 G3 and G4 respectively Figure 7 represents thevariation of rotor angles differences of the multimachinesystem In Figure 8 speed of machines G1 G2 G3 and G4


B410km

B1250km B2 250km

B310km 25km

B6

B7B5

25km

944MW

877

MW

2643

MW

2487MW828MW

Z4Z3 Z1 Z2 Z4 Z3

G1

G2

G4

G3

CSC-STATCOM

Three-phase fault(case I)

Heavy loading(case II)

Area 1 Area 2

Load center(1000MW)

Load center(6000MW)

1000MVA

1000

MVA

3000

MVA

3000MVA

LdcRdc

138kV500kV138 kV500kV

138

kV500

kV

138

kV500

kV

Figure 5 The single line diagram of the test-system model for transient stability study of multimachine power system

0 1 2 3 4 5 60

1

2

For bus B1For bus B2For bus B3

Time (s)

Volta

ge at

bus

es B

1B2

and

B3

(pu)

(a) Positive sequence voltages at different buses B1 B2 and B3

0 1 2 3 4 5 6

0

2

Line

pow

er fl

owat

bus

B2

(MW

)

Time (s)

minus2

times103

(b) Power flow at bus B2

Figure 6 System response without CSC-STATCOM for a three-phase fault (case I)

is represented by 1205961 1205962 1205963 and 1205964 respectively Here thecritical clearing time (CCT) of fault is also found out for thetest system stability by simulationThe fault time is increasedin simulation to find the critical stability margin thus CCTis obtained CCT is defined as the maximal fault durationfor which the system remains transiently stable [1] CCT ofthe fault for the system with and without CSC-STATCOMis 325ms and 276ms respectively as shown in Table 1 So itshows that CCT of fault is also increased due to the impactof pole-shifting controller based CSC-STATCOM Clearlywaveforms show that proposed topology ismore effective androbust performance than that of the without pole-shifting

0 2 4 6 80

50100

No CSC-STATCOM (unstable)

With CSC-STATCOM(stable)

Time (s)

1205751minus1205754

(deg

)

(a)

0 2 4 6 8

050

100No CSC-STATCOM

(unstable) With CSC-STATCOM(stable)

Time (s)

1205752minus1205754

(deg

)

minus50

(b)

0 2 4 6 80

5

No CSC-STATCOM (unstable) With CSC-STATCOM

(stable)

Time (s)

1205753minus1205754

(deg

)

(c)

Figure 7 Variation of rotor angles differences of the test system forcase I

controller based CSC-STATCOM in terms of settling timeCCT and transient stability of the test-system

43 Case IImdashLarge Loading For heavy loading case onelarge series load centre (200MW6000Mvar) is connectedat near bus B1 (ie at near machine G2) in Figure 5 Thislarge loading is occurring only at time period 01 s to 0466 sDue to this disturbance the simulation results of test systemwith and without CSC-STATCOM are shown in Figures 11to 15 Clearly the system is unstable in the absence of thepole-shifting controller based CSC-STATCOM device due to




0 1 2 3 4 5 6 7 8 9

0

002

1205961minus1205964

(pu)

Time (s)

minus002

(a) Speed difference variation of machines G1 and G4



0 1 2 3 4 5 6 7 8 9

0

2

1205963minus1205964

(pu)

Time (s)

minus2

times10minus3

(b) Speed difference variation of machines G3 and G4

Figure 8 Speed differences variation of the test system for case I

7 8 90 1 2 3 4 5 60

1

2


Time (s)

Volta

ge at

bus

es B

1B2

and

B3

(pu)


7 8 9

0

5

0 1 2 3 4 5 6Line

pow

er fl

owat

bus

B2

(MW

)

Time (s)

minus5

times103


Figure 9 Test system response with pole-shifting controller basedCSC-STATCOM for a three-phase fault (case I)

Table 1 CCT of disturbances for the system stability with differenttopologies

Casenumber System with different topologies Critical clearing

time (CCT)

1 Without CSC-STATCOM 276msWith CSC-STATCOM 325ms


this disturbance in Figures 11 to 13 and 15 But system withpole-shifting controller based CSC-STATCOM is continuingstable condition in Figures 12 to 15 In Figure 12 120575

1 1205752 1205753

Mac

hine

term

inal

Time (s)0 1 2 3 4 5 6 7 8 9

05

1

15

volta

gesV

t1V

t2(p

u)

Vt1Vt2

Vt3Vt4

(a)

Reac

tive p

ower

(Mva

r)

Time (s)0 1 2 3 4 5 6 7 8 9

050

100150

(b)

Figure 10 For case 1 (a) terminal voltages 1198811199051 1198811199052 1198811199053 and 119881

1199054

of machine generators G1 G2 G3 and G4 with CSC-STATCOMrespectively (b) reactive power inject (or absorb) by pole-shiftingcontroller based CSC-STATCOM

0 1 2 3 4 5 60

1

2


Volta

ge at

bus

es B

1B2

and

B3

(pu)

Time (s)


0 1 2 3 4 5 6Time (s)

0

2

Line

pow

er fl

owat

bus

B2

(MW

)

minus2

times103


Figure 11 Test-system response without CSC-STATCOM with aheavy loading (case II)

and 1205754 are the rotor angles of machines G1 G2 G3 andG4 respectively Figure 12 represents the variation of rotorangles differences of the multimachine system In Figure 13speeds of machines G1 G2 G3 and G4 are represented by1205961 1205962 1205963 and 120596

4 respectively System voltages at different

buses B1 B2 and B3 with proposed scheme are shown inFigure 14 Here CCT for the system with and without CSC-STATCOM is 764ms and 465ms respectively which are


Table 2 CCT of disturbances for the test system stability with different shunt FACTS devices

S number Type of disturbances FACTS devices Critical clearing time (CCT)

1 Fault conditionWith SVC 285ms

With VSC-STATCOM 288msWith CSC-STATCOM 325ms

2 Heavy loading conditionWith SVC 486ms


0 2 4 6 8 10 12Time (s)



1205751minus1205754

050

100

minus50

(a)

0 2 4 6 8 10 12Time (s)



050

100

1205752minus1205754

minus50

(b)

10

0 2 4 6 8 10 12Time (s)


(stable)0

5

1205753minus1205754

(c)

Figure 12 Variation of rotor angles differences of the test system incase II

provided in Table 1 Clearly shown CCT for test system isbetter due to the impact of pole-shifting controller basedCSC-STATCOM Hence the performance of the proposedscheme is still satisfactory in this case

44 Case IIImdashA Comparative Study In order to show therobustness performance of the proposed scheme for improv-ing the transient stability of the system after this obtainedoutcomes from the proposed pole-shifting controller basedCSC-STATCOM are compared to the obtained outcomesfrom the other shunt FACTS devices (SVC and VSC basedSTATCOM)which have been used in somemost cited papers[23 24] In this case it has been assumed that the test systemis same for all shunt FACTS devices and all shunt FACTSdevices have the same rating (200Mvar) After this we checkthe impact of these shunt FACTS devices on the test systemwith three-phase fault condition The obtained simulationresults with these shunt FACTS devices are compared inFigure 16 In this figure system with SVC is reached inunstable condition Here three-phase fault duration is 01 sto 0285 s CCT for the system with different shunt FACTS

devices is shown in Table 2 If heavy loading condition isapplied during 01 s to 0486 s in this case then effect of thisdisturbance is shown in Figure 17 In all figures of Figures 16and 17 multimachine power system with proposed topologybased CSC-STATCOM is continuing stable condition Inthese figures the oscillations are damped more quickly andsettled down after 3 to 4 sec by proposed topology basedCSC-STATCOM in comparison to other devices In this com-parative study transient stability margin is also increased byincreasing the CCT with the help of CSC-STATCOM devicefrom Table 2 Clearly waveforms show that CSC-STATCOMis more effective and robust performance than that of othershunt FACTS devices (SVC and VSC-STATCOM) in termsof oscillation damping settling time CCT and transient sta-bility of the multimachine power system in Figures 16 and 17

5 Conclusions

In this paper the dynamic modeling of CSC based STAT-COM is studied and proposed pole-shifting controller for thebest input-output response of CSC-STATCOM is presentedin order to enhance the system transient stability of themultimachine power system with the different disturbancesThe novelty in proposed approach lies in the fact thattransient stability of a two-area four-machine power systemis improved and critical clearing time of the disturbance isalso increased In this work the proposed scheme is verifiedfrom MATLAB package It has been also observed thatpole-shifting controller based CSC-STATCOM can be morereliable and very effective rather than other shunt FACTSdevices (SVC and VSC-STATCOM) in terms of oscillationdamping CCT and transient stability of a multimachinepower system So finally it can be said that CSC basedSTATCOM can be regarded as an alternative FACTS deviceto that of other shunt FACTS devices

Appendix

Parameters for various components used in the test systemconfiguration of Figure 5 are considered (all parameters arein pu unless specified otherwise) (see Table 3)

For All Generators of Multimachine Power System Consider119881119866= 138 kV 119877

119904= 0003 119891 = 50Hz 119883

119889= 1305 1198831015840

119889=

0296 11988310158401015840119889

= 0252 1198831015840119902= 050 11988310158401015840

119902= 0243 1198791015840

119889= 101 s

11987910158401015840

119889= 0053 s119867 = 37 s


004

0 2 4 6 8 10 12Time (s)


(stable)0002

1205961minus1205964

(pu)

minus002


0 2 4 6 8 10 12Time (s)


(stable)0

2

1205963minus1205964

(pu)

minus2

times10minus3


Figure 13 Speed differences variation of the multimachine system in case II

0 2 4 6 8 10 120

05

1

15


Time (s)

Volta

ge at

bus

es B

1B2

and

B3

(pu)


0123

0 2 4 6 8 10 12Time (s)

Line

pow

er fl

owat

bus

B2

(MW

)

minus1

times103


Figure 14 Test system response with pole-shifting controller based CSC-STATCOM for a heavy loading (case II)

0 02 04 06 08 1099

0995

1

1005

101

1015No CSC-STATCOM

(unstable)


minus02

Spee

d1205961

(pu)

Rotor angle 1205751 (rad)

(a)

0 02 04 06 08 1

0995

1

1005

101No CSC-STATCOM

(unstable)


minus02

Spee

d1205962

(pu)


(b)

Figure 15 Speed versus rotor angle graph for (a) machine G1 (b) machine G2

Table 3 Rating of multimachine system

Machine Input mechanical power (pu) Output electrical power (MW) Power rating (MVA) Bus typeG1 095 950 1000 PV generation busG2 088 880 1000 Swing busG3 083 2490 3000 PV generation busG4 0883 2649 3000 Swing bus


0 1 2 3 4 5 6 7 8 9

0

001

002

Time (s)

With SVC(unstable)

With CSC-STATCOM

With VSC-STATCOM

(stable)

1205961minus1205964

(pu)

minus002

minus001


0 1 2 3 4 5 6 7 8 9Time (s)

With SVC(unstable)

With CSC-STATCOM

With VSC-STATCOM

(stable)0

1

2

1205963minus1205964

(pu)

minus2

minus1

times10minus3


0 1 2 3 4 5 6 7 8 9Time (s)

With SVC(unstable)

With CSC-STATCOM

With VSC-STATCOM

(stable)0

50

100

150

200

minus50

1205751minus1205754

(deg

)

(c) Variation of rotor angles difference of machines G1 and G4

0 1 2 3 4 5 6 7 8 9Time (s)

With SVC(unstable)

With CSC-STATCOM

With VSC-STATCOM

(stable)

0

2

4

6

8

1205753minus1205754

(deg

)

(d) Variation of rotor angles difference of machines G3 and G4

Figure 16 System response with different shunt FACTS devices (SVC CSC-STATCOM and VSC-STATCOM) for fault condition (case III)

0 2 4 6 8 10 12

(a) Speed difference variation of machines G1 and G4Time (s)

0 2 4 6 8 10 12Time (s)

0 2 4 6 8 10 12Time (s)

0 2 4 6 8 10 12Time (s)



0

2

4

6

8

10

SVCVSC-STATCOMCSC-STATCOM



0

001

002 With SVC(unstable)

With SVC(unstable) With SVC

(unstable)

With CSC-STATCOM

With VSC-STATCOM

(stable)

(stable)

(stable)

With SVC(unstable)

With CSC-STATCOM

With VSC-STATCOM

(stable)1205961minus1205964

(pu)

minus002

minus001 0

50

100

150

minus50

1205751minus1205754

(deg

)

0

1

2

1205963minus1205964

(pu)

minus2

minus1

times10minus3

1205753minus1205754

(deg

)

Figure 17 System response with different shunt FACTS devices (SVC CSC-STATCOM and VSC-STATCOM) in a heavy loading condition(case III)


(119877119904is stator winding resistance of generators 119881

119866is

generator voltage (119871-119871) 119891 is frequency 119883119889is synchronous

reactance of generators 1198831015840119889and 119883

10158401015840

119889are the transient and

subtransient reactance of generators in the direct-axis 1198831015840119902

and 11988310158401015840

119902are the transient and subtransient reactance of gen-

erators in the quadrature-axis 1198791015840119889and 119879

10158401015840

119889are the transient

and subtransient open-circuit time constant 119867 the inertiaconstant of machine)

For Excitation Systems of Machines (G1 G2 G3 and G4)Regulator gain and time constant (119870119886 and119879119886) are 200 0001 sgain and time constant of exciter (119870119890 and 119879119890) are 1 0 sdamping filter gain and time constant (119870119891 and 119879119891) are 000101 s upper and lower limit of the regulator output are 0 7

Parameters of Shunt FACTS Devices

SVC system nominal voltage (119871-119871) 500 kV 119891 50Hz119870119901= 3 119870

119894= 500 119881ref = 1

VSC-STATCOM system nominal voltage (119871-119871)500 kV DC link nominal voltage 40 kV DC linkcapacitance 00375120583F 119891 50Hz119870

119901= 50119870

119894= 1000

119881ref = 1Pole-shifting controller based CSC-STATCOM systemnominal voltage (119871-119871) 500 kV 119877dc = 001Ω 119871dc =

40mH 119862 = 400 120583F 119877 = 03Ω 119871 = 2mH 120596 = 314119864119889(ref) = 1 PI parameters (119870119901 = 70 119870119894 = 1800)

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] P Kundur Power System Stability and Control McGraw-HillNew York NY USA 1994

[2] M A Abido ldquoPower system stability enhancement using factscontrollers a reviewrdquo The Arabian Journal for Science andEngineering vol 34 no 2 pp 153ndash172 2009

[3] C-X Dou S-L Guo and X-Z Zhang ldquoImprovement of tran-sient stability for power systems using wide-area measurementsignalsrdquo Electrical Engineering vol 91 no 3 pp 133ndash143 2009

[4] X D Liu Y Li Z J Liu et al ldquoA novel fast transient stabilityprediction method based on pmurdquo in Proceedings of the IEEEPower amp Energy Society General Meeting ( PES rsquo09) pp 1ndash5IEEE Calgary Canada July 2009

[5] R J Nelson J Bian D G Ramey T A Lemak T R Rietmanand J E Hill ldquoTransient stability enhancement with FACTScontrollersrdquo in Proceedings of the 6th International Conferenceon AC and DC Power Transmission pp 269ndash274 May 1996

[6] S H Hosseini and A Ajami ldquoTransient stability enhancementof AC transmission system using STATCOMrdquo in Proceedings ofthe IEEE Region 10 Conference on Computers CommunicationsControl and Power Engineering (TENCON rsquo02) vol 3 pp 1809ndash1812 October 2002

[7] M H Haque ldquoImprovement of first swing stability limit byutilizing full benefit of shunt facts devicesrdquo IEEE Transactionson Power Systems vol 19 no 4 pp 1894ndash1902 2004

[8] Y L Tan and YWang ldquoA robust nonlinear excitation and SMEScontroller for transient stabilizationrdquo International Journal ofElectrical Power and Energy System vol 26 no 5 pp 325ndash3322004

[9] A Chakraborty S K Musunuri A K Srivastava and AK Kondabathini ldquoIntegrating STATCOM and battery energystorage system for power system transient stability a review andapplicationrdquoAdvances in Power Electronics vol 2012 Article ID676010 12 pages 2012

[10] N C Sahoo B K Panigrahi P K Dash and G Panda ldquoMul-tivariable nonlinear control of STATCOM for synchronousgenerator stabilizationrdquo International Journal of Electrical Powerand Energy System vol 26 no 1 pp 37ndash48 2004

[11] H Tsai C Chu and S Lee ldquoPassivity-based nonlinear STAT-COM controller design for improving transient stability ofpower systemsrdquo in Proceedings of the IEEEPES Transmissionand Distribution Conference amp Exhibition Asia and Pacific pp1ndash5 IEEE Dalian China 2005

[12] Y L Tan ldquoAnalysis of line compensation by shunt-connectedFACTS controllers a comparison between SVC and STAT-COMrdquo IEEE Power Engineering Review vol 19 no 8 pp 57ndash581999

[13] N G Hingorani and L Gyugyi Understanding FACTS Con-cepts and Technology of Flexible AC Transmission Systems IEEEPress New York NY USA 1999

[14] L Gyugyi ldquoApplication characteristics of converter-basedFACTS controllersrdquo in Proceedings of the International Confer-ence on Power SystemTechnology (PowerCon rsquo00) vol 1 pp 391ndash396 Piscataway NJ USA December 2000

[15] B Han S Moon J Park and G Karady ldquoStatic synchronouscompensator using thyristor PWM current source inverterrdquoIEEE Transactions on Power Delivery vol 15 no 4 pp 1285ndash1290 2000

[16] H F Bilgin and M Ermis ldquoCurrent source converter basedSTATCOM operating principles design and field perfor-mancerdquo Electric Power Systems Research vol 81 no 2 pp 478ndash487 2011

[17] S Gupta R K Tripathi and R D Shukla ldquoVoltage stabilityimprovement in power systems using facts controllers state-of-the-art reviewrdquo in Proceedings of the IEEE InternationalConference on Power Control and Embedded Systems (ICPCES2010) pp 1ndash8 Allahabad India December 2010

[18] M Kazerani and Y Ye ldquoComparative evaluation of three-phase PWM voltage- and current-source converter topologiesin FACTS applicationsrdquo in Proceedings of the IEEE Power Engi-neering Society Summer Meeting vol 1 pp 473ndash479 July 2002

[19] D Shen and P W Lehn ldquoModeling analysis and control of acurrent source inverter-based STATCOMrdquo IEEE Transactionson Power Delivery vol 17 no 1 pp 248ndash253 2002

[20] Y Ni L Jiao S Chen and B Zhang ldquoApplication of a nonlinearPID controller on STATCOM with a differential trackerrdquo inProceedings of the 2nd International Conference on EnergyManagement and Power Delivery (EMPD rsquo98) pp 29ndash34 NewYork NY USA March 1998

[21] S Gupta and R K Tripathi ldquoAn LQR and pole placementcontroller for CSC based STATCOMrdquo in Proceedings of theInternational Conference on Power Energy and Control (ICPECrsquo13) pp 115ndash119 February 2013

[22] P Rao M L Crow and Z Yang ldquoSTATCOM control forpower system voltage control applicationsrdquo IEEE Transactionson Power Delivery vol 15 no 4 pp 1311ndash1317 2000


[23] S Panda and R N Patel ldquoImproving power system transientstability with an off-centre location of shunt FACTS devicesrdquoJournal of Electrical Engineering vol 57 no 6 pp 365ndash3682006

[24] Z Y Zou Q Y Jiang Y J Cao and H F Wang ldquoNormalform analysis of interactions among multiple SVC controllersin power systemsrdquo IEE ProceedingsmdashGeneration Transmissionand Distribution vol 152 no 4 pp 469ndash474 2005

[25] C Schauder and H Mehta ldquoVector analysis and control ofadvanced static VAR compensatorsrdquo IEE Proceedings C Genera-tion Transmission and Distribution vol 140 no 4 pp 299ndash3061993

[26] S Gupta and R K Tripathi ldquoTransient stability assessmentof two-area power system with robust controller based CSC-STATCOMrdquo Journal of Control Engineering and Applied Infor-matics vol 16 no 3 pp 3ndash12 2014

[27] B T Ooi M Kazerani R Marceau et al ldquoMid-point sitting offacts devices in transmission linesrdquo IEEE Transactions on PowerDelivery vol 12 no 4 pp 1717ndash1722 1997

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Control Scienceand Engineering

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Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

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Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



by operating the shunt FACTS devices in inductive (capaci-tive) mode

In many research papers [2 9ndash11] the different typesof these devices with different control techniques are usedfor improving transient stability In between these FACTSdevices the STATCOM is valuable for enhancement powersystem dynamic stability and frequency stabilization due tothe more rapid output response lower harmonics superiorcontrol stability and small size and so forth [7 12] By theirinverter configuration basic type of STATCOM topologycan be realized by either a current-source converter (CSC)or a voltage-source converter (VSC) [13ndash17] But recentresearch confirms several merits of CSC based STATCOMover VSC based STATCOM [18 19] These advantages arehigh converter reliability quick starting and inherent short-circuit protection and the output current of the converteris directly controlled and in low switching frequency thisreduces the filtering requirements comparedwith the case of aVSCTherefore CSC based STATCOM is very useful in powersystems rather than VSC based STATCOM in many cases

Presently the most used techniques for controller designof FACTS devices are the Proportional Integration (PI) PIDcontroller [20] pole-shifting controller and linear quadraticregulator (LQR) [21] But LQR and pole-shifting algorithmsgive quicker response in comparison to PI and PID algorithm[22] LQR controller gain (119870) can be calculated by solvingthe Riccati equation and 119870 is also dependent on the twocost functions (119876 119877) So Riccati equation solvers have somelimitations which relate to the input arguments But poleshifting method does not face this type of any problem Sopole shifting method gives a better and robust performancein comparison to other methods

The main contribution of this paper is the application ofproposed pole-shifting controller based CSC-STATCOM forimprovement of power system stability in terms of transientstability by injecting (or absorbing) reactive power In thispaper the proposed scheme is used in the multimachinepower transmission system with dynamic loads under agrievous disturbance condition (three-phase fault or heavyloading) to enhancement of power system transient stabilitystudies and to observe the impact of the CSC based STAT-COM on electromechanical oscillations and transmissioncapacity Furthermore the obtained outcomes from theproposed algorithm based CSC-STATCOM are compared tothe obtained outcomes from the other shunt FACTS devices(SVCandVSC-STATCOM)which are used in previousworks[23 24]

The rest of the paper is prepared as follows Section 2discusses the circuit modeling and proposed pole-shiftingcontroller designing for CSC based STATCOM A two-areapower system is described with a CSC-STATCOM devicein Section 3 Simulation results of the test system with andwithout CSC based STATCOM for severe contingency areshown in Section 4 to improve the transient stability of themultimachine power system Comparison among differentshunt FACTS devices (SVC VSC-STATCOM and CSC-STATCOM) is also described in Section 4 Finally Section 5concludes this paper

Idc

iR

iS

iT

R L

C

Ldc Rdc

CR

CS

CT

S1 S3

S2 S4

S5

S6

R

S

T

iSR

iSS

iST

iCR

MV Bus

Figure 1 The representation of CSC based STATCOM 119894119878119877 119894119878119878 119894119878119879

line current V119862119877 V119862119878 V119862119879 voltages across the filter capacitors V

119877 V119878

V119879 line voltages 119868dc dc-side current 119877dc converter switching and

conduction losses 119871dc smoothing inductor 119862 filter capacitance 119871inductance of the line reactor 119877 resistance of the line reactor

2 Mathematical Modeling of Pole-ShiftingController Based CSC-STATCOM

21 CSC Based STATCOM Model In this section to verifythe response of the STATCOM on dynamic performancethe mathematical modeling and control strategy of a CSCbased STATCOM are needed to be presented So in thedesigning of controller for CSC based STATCOM the statespace equations from the CSC-STATCOM circuit must beintroduced To minimize the complexity of mathematicalcalculation the theory of 119889119902 transformation of currentshas been applied in this circuit which makes the 119889 and119902 components independent parameters Figure 1 shows thecircuit diagram of a typical CSC based STATCOM

The basic mathematical equations of the CSC basedSTATCOM have been derived in the literature [19] There-fore only brief details of the primary equations for CSC-STATCOMare given here for the readersrsquo convenience Basedon the equivalent circuit of CSC-STATCOM as shown inFigure 1 the differential equations for the system can beachieved which are derived in the abc frame and thentransformed into the synchronous 119889119902 frame using 119889119902 trans-formation method [25]

119889

119889119905119868dc = minus

119877dc119871dc

119868dc minus3

2119871dc119872119889119881119889minus

3

2119871dc119872119902119881119902 (1)

119889

119889119905119868119889= minus

119877

119871119868119889+ 120596119868119902minus1

119871

119864119889

119899+1

119871119881119889 (2)

119889

119889119905119868119902 = minus120596119868119889 minus

119877

119871119868119902 +

1

119871119881119902 (3)

119889

119889119905119881119889 = minus

1

119862119868119889 + 120596119881119902 +

1

119862119872119889119868dc (4)

119889

119889119905119881119902 = minus

1

119862119868119902 minus 120596119881

119889+1

119862119872119902119868dc (5)

In above differential equations 119872119889and 119872

119902are the two

input variables Two output variables are 119868dc and 119868119902 Here 120596

is the rotation frequency of the system and this is equal to the




119902


119889and 119864



119889and 119881

119902are



119875ac = 119875dc 997904rArr minus3119864119889

2119899119868119889 = 119871dc119868dc

119889

119889119905119868dc + 119877dc119868

2

dc (6)


119889

119889119905(1198682

dc) = minus2119877dc119871dc

(1198682

dc) minus3119864119889

119871dc119899119868119889 (7)


119889

119889119905

[[[[[

[

(119894dc)2

119894119889

119894119902

V119888119889

V119888119902

]]]]]

]

=

[[[[[[[[[[[[[

[


3119864119889

119871dc1198990 0 0

0 minus119877

119871120596119900

1

1198710

0 minus120596119900

minus119877

1198710

1

119871

0 minus1

1198620 0 120596119900

0 0 minus1

119862minus120596119900

0

]]]]]]]]]]]]]

]

lowast

[[[[[

[

(119894dc)2

119894119889

119894119902

V119888119889

V119888119902

]]]]]

]

+

[[[[[[[[

[

0 0

0 0

0 0

1

1198620

01

119862

]]]]]]]]

]

lowast [119868119894119889

119868119894119902

] +

[[[[[[

[

0

minus1

1198710

0

0

]]]]]]

]

lowast 119864119889

(8)



= 119860119909 + 119861119906 + 119865119890

119910 = 119862119909

(9)


119909 = [1198682

dc 119894119889119894119902119881119889119881119902]119879

119906 = [119868119894119889 119868119894119902]119879

119890 = 119864119889 119910 = [119868

2

dc 119868119902]119879

119860 =

[[[[[[[[[[[[[

[


minus3119864119889

119871dc0 0 0

0 minus119877

119871120596

1

1198710


1198710

1

119871

0 minus1

1198880 0 120596

0 0 minus1

119888minus120596 0

]]]]]]]]]]]]]

]

119861 =

[[[[[[[[

[

0 0

0 0

0 0

1

1198880

01

119888

]]]]]]]]

]

119862 =

[[[[[

[

1 0

0 0

0 1

0 0

0 0

]]]]]

]

119879

119865 =

[[[[[[

[

0

minus1

1198710

0

0

]]]]]]

]

(10)







= 0 (13)

Then


(14)


B C

A

minusK

xx yu

CSC-STATCOM

Ldc

Rdc



system



1SJ+++

+++








119899) (15)

where 1198751 1198752 119875



1 1198752 119875






120575 = 120596 (16)

=1

119872[119875119898minus 119875119890119900minus 119875

csc119890] (17)


119890119900 and119872


119890


Real power flow

L1 L2


ICSC

jX1 jX2


Area 1 Area 2


Ldc

Rdc




119868csc = 119868cscang (120579119887119900 minus 90∘) (18)


120579119887 = tanminus1 [ 119883

21198641sin 120575

11988321198641cos 120575 + 119883

11198642

] (19)

119864119889 = (

11988321198641 cos (120575 minus 120579119887119900) + 11988311198642cos 120579119887119900

1198831+ 1198832

)

+ (11988311198832

1198831+ 1198832

119868csc)

(20)





119875csc119890

=1198641119864119889

1198831

sin (120575 minus 120579119887) (21)


a

bc

d

ef

g

1205750 120575c 120575m0

Prefault curve A


e

Postfault curve C

Postfault curve C

Ad

Aa

Pm

Power

Angle

Ppe (Icsc gt 0)

Pe(Icsc = 0)

(Icsc lt 0)




119875119890= 119875119890119900+ 119875

csc119890

997904rArr 119875119890= 119875119890119900+

119883111988321198641

(1198831+ 1198832)1198831

119868csc sin (120575 minus 120579119887)

(22)




0 When a




119890suddenly






int

120575119888

1205750

(119875119898 minus 119875119891

119890) 119889120575 = int

120575119898

120575119888

(119875119901

119890minus 119875119898) 119889120575 997904rArr 119860119886 = 119860119889 (23)














B410km

B1250km B2 250km

B310km 25km

B6

B7B5

25km

944MW

877

MW

2643

MW

2487MW828MW

Z4Z3 Z1 Z2 Z4 Z3

G1

G2

G4

G3

CSC-STATCOM



Area 1 Area 2

Load center(1000MW)

Load center(6000MW)

1000MVA

1000

MVA

3000

MVA

3000MVA

LdcRdc

138kV500kV138 kV500kV

138

kV500

kV

138

kV500

kV


0 1 2 3 4 5 60

1

2


Time (s)

Volta

ge at

bus

es B

1B2

and

B3

(pu)


0 1 2 3 4 5 6

0

2

Line

pow

er fl

owat

bus

B2

(MW

)

Time (s)

minus2

times103




0 2 4 6 80

50100



Time (s)

1205751minus1205754

(deg

)

(a)

0 2 4 6 8

050

100No CSC-STATCOM


Time (s)

1205752minus1205754

(deg

)

minus50

(b)

0 2 4 6 80

5


(stable)

Time (s)

1205753minus1205754

(deg

)

(c)







0 1 2 3 4 5 6 7 8 9

0

002

1205961minus1205964

(pu)

Time (s)

minus002




0 1 2 3 4 5 6 7 8 9

0

2

1205963minus1205964

(pu)

Time (s)

minus2

times10minus3



7 8 90 1 2 3 4 5 60

1

2


Time (s)

Volta

ge at

bus

es B

1B2

and

B3

(pu)


7 8 9

0

5

0 1 2 3 4 5 6Line

pow

er fl

owat

bus

B2

(MW

)

Time (s)

minus5

times103





time (CCT)




1 1205752 1205753

Mac

hine

term

inal

Time (s)0 1 2 3 4 5 6 7 8 9

05

1

15

volta

gesV

t1V

t2(p

u)

Vt1Vt2

Vt3Vt4

(a)

Reac

tive p

ower

(Mva

r)

Time (s)0 1 2 3 4 5 6 7 8 9

050

100150

(b)


1199054


0 1 2 3 4 5 60

1

2


Volta

ge at

bus

es B

1B2

and

B3

(pu)

Time (s)


0 1 2 3 4 5 6Time (s)

0

2

Line

pow

er fl

owat

bus

B2

(MW

)

minus2

times103













0 2 4 6 8 10 12Time (s)



1205751minus1205754

050

100

minus50

(a)

0 2 4 6 8 10 12Time (s)



050

100

1205752minus1205754

minus50

(b)

10

0 2 4 6 8 10 12Time (s)


(stable)0

5

1205753minus1205754

(c)





5 Conclusions


Appendix



119904= 0003 119891 = 50Hz 119883

119889= 1305 1198831015840

119889=

0296 11988310158401015840119889

= 0252 1198831015840119902= 050 11988310158401015840

119902= 0243 1198791015840

119889= 101 s

11987910158401015840

119889= 0053 s119867 = 37 s


004

0 2 4 6 8 10 12Time (s)


(stable)0002

1205961minus1205964

(pu)

minus002


0 2 4 6 8 10 12Time (s)


(stable)0

2

1205963minus1205964

(pu)

minus2

times10minus3



0 2 4 6 8 10 120

05

1

15


Time (s)

Volta

ge at

bus

es B

1B2

and

B3

(pu)


0123

0 2 4 6 8 10 12Time (s)

Line

pow

er fl

owat

bus

B2

(MW

)

minus1

times103



0 02 04 06 08 1099

0995

1

1005

101

1015No CSC-STATCOM

(unstable)


minus02

Spee

d1205961

(pu)


(a)

0 02 04 06 08 1

0995

1

1005

101No CSC-STATCOM

(unstable)


minus02

Spee

d1205962

(pu)


(b)





0 1 2 3 4 5 6 7 8 9

0

001

002

Time (s)

With SVC(unstable)

With CSC-STATCOM

With VSC-STATCOM

(stable)

1205961minus1205964

(pu)

minus002

minus001


0 1 2 3 4 5 6 7 8 9Time (s)

With SVC(unstable)

With CSC-STATCOM

With VSC-STATCOM

(stable)0

1

2

1205963minus1205964

(pu)

minus2

minus1

times10minus3


0 1 2 3 4 5 6 7 8 9Time (s)

With SVC(unstable)

With CSC-STATCOM

With VSC-STATCOM

(stable)0

50

100

150

200

minus50

1205751minus1205754

(deg

)


0 1 2 3 4 5 6 7 8 9Time (s)

With SVC(unstable)

With CSC-STATCOM

With VSC-STATCOM

(stable)

0

2

4

6

8

1205753minus1205754

(deg

)



0 2 4 6 8 10 12


0 2 4 6 8 10 12Time (s)

0 2 4 6 8 10 12Time (s)

0 2 4 6 8 10 12Time (s)



0

2

4

6

8

10




0

001



(unstable)

With CSC-STATCOM

With VSC-STATCOM

(stable)

(stable)

(stable)

With SVC(unstable)

With CSC-STATCOM

With VSC-STATCOM


(pu)

minus002

minus001 0

50

100

150

minus50

1205751minus1205754

(deg

)

0

1

2

1205963minus1205964

(pu)

minus2

minus1

times10minus3

1205753minus1205754

(deg

)




119866is



10158401015840



and 11988310158401015840



10158401015840






119894= 500 119881ref = 1


119901= 50119870

119894= 1000





References































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












119902


119889and 119864



119889and 119881

119902are



119875ac = 119875dc 997904rArr minus3119864119889

2119899119868119889 = 119871dc119868dc

119889

119889119905119868dc + 119877dc119868

2

dc (6)


119889

119889119905(1198682

dc) = minus2119877dc119871dc

(1198682

dc) minus3119864119889

119871dc119899119868119889 (7)


119889

119889119905

[[[[[

[

(119894dc)2

119894119889

119894119902

V119888119889

V119888119902

]]]]]

]

=

[[[[[[[[[[[[[

[


3119864119889

119871dc1198990 0 0

0 minus119877

119871120596119900

1

1198710

0 minus120596119900

minus119877

1198710

1

119871

0 minus1

1198620 0 120596119900

0 0 minus1

119862minus120596119900

0

]]]]]]]]]]]]]

]

lowast

[[[[[

[

(119894dc)2

119894119889

119894119902

V119888119889

V119888119902

]]]]]

]

+

[[[[[[[[

[

0 0

0 0

0 0

1

1198620

01

119862

]]]]]]]]

]

lowast [119868119894119889

119868119894119902

] +

[[[[[[

[

0

minus1

1198710

0

0

]]]]]]

]

lowast 119864119889

(8)



= 119860119909 + 119861119906 + 119865119890

119910 = 119862119909

(9)


119909 = [1198682

dc 119894119889119894119902119881119889119881119902]119879

119906 = [119868119894119889 119868119894119902]119879

119890 = 119864119889 119910 = [119868

2

dc 119868119902]119879

119860 =

[[[[[[[[[[[[[

[


minus3119864119889

119871dc0 0 0

0 minus119877

119871120596

1

1198710


1198710

1

119871

0 minus1

1198880 0 120596

0 0 minus1

119888minus120596 0

]]]]]]]]]]]]]

]

119861 =

[[[[[[[[

[

0 0

0 0

0 0

1

1198880

01

119888

]]]]]]]]

]

119862 =

[[[[[

[

1 0

0 0

0 1

0 0

0 0

]]]]]

]

119879

119865 =

[[[[[[

[

0

minus1

1198710

0

0

]]]]]]

]

(10)







= 0 (13)

Then


(14)


B C

A

minusK

xx yu

CSC-STATCOM

Ldc

Rdc



system



1SJ+++

+++








119899) (15)

where 1198751 1198752 119875



1 1198752 119875






120575 = 120596 (16)

=1

119872[119875119898minus 119875119890119900minus 119875

csc119890] (17)


119890119900 and119872


119890


Real power flow

L1 L2


ICSC

jX1 jX2


Area 1 Area 2


Ldc

Rdc




119868csc = 119868cscang (120579119887119900 minus 90∘) (18)


120579119887 = tanminus1 [ 119883

21198641sin 120575

11988321198641cos 120575 + 119883

11198642

] (19)

119864119889 = (

11988321198641 cos (120575 minus 120579119887119900) + 11988311198642cos 120579119887119900

1198831+ 1198832

)

+ (11988311198832

1198831+ 1198832

119868csc)

(20)





119875csc119890

=1198641119864119889

1198831

sin (120575 minus 120579119887) (21)


a

bc

d

ef

g

1205750 120575c 120575m0

Prefault curve A


e

Postfault curve C

Postfault curve C

Ad

Aa

Pm

Power

Angle

Ppe (Icsc gt 0)

Pe(Icsc = 0)

(Icsc lt 0)




119875119890= 119875119890119900+ 119875

csc119890

997904rArr 119875119890= 119875119890119900+

119883111988321198641

(1198831+ 1198832)1198831

119868csc sin (120575 minus 120579119887)

(22)




0 When a




119890suddenly






int

120575119888

1205750

(119875119898 minus 119875119891

119890) 119889120575 = int

120575119898

120575119888

(119875119901

119890minus 119875119898) 119889120575 997904rArr 119860119886 = 119860119889 (23)














B410km

B1250km B2 250km

B310km 25km

B6

B7B5

25km

944MW

877

MW

2643

MW

2487MW828MW

Z4Z3 Z1 Z2 Z4 Z3

G1

G2

G4

G3

CSC-STATCOM



Area 1 Area 2

Load center(1000MW)

Load center(6000MW)

1000MVA

1000

MVA

3000

MVA

3000MVA

LdcRdc

138kV500kV138 kV500kV

138

kV500

kV

138

kV500

kV


0 1 2 3 4 5 60

1

2


Time (s)

Volta

ge at

bus

es B

1B2

and

B3

(pu)


0 1 2 3 4 5 6

0

2

Line

pow

er fl

owat

bus

B2

(MW

)

Time (s)

minus2

times103




0 2 4 6 80

50100



Time (s)

1205751minus1205754

(deg

)

(a)

0 2 4 6 8

050

100No CSC-STATCOM


Time (s)

1205752minus1205754

(deg

)

minus50

(b)

0 2 4 6 80

5


(stable)

Time (s)

1205753minus1205754

(deg

)

(c)







0 1 2 3 4 5 6 7 8 9

0

002

1205961minus1205964

(pu)

Time (s)

minus002




0 1 2 3 4 5 6 7 8 9

0

2

1205963minus1205964

(pu)

Time (s)

minus2

times10minus3



7 8 90 1 2 3 4 5 60

1

2


Time (s)

Volta

ge at

bus

es B

1B2

and

B3

(pu)


7 8 9

0

5

0 1 2 3 4 5 6Line

pow

er fl

owat

bus

B2

(MW

)

Time (s)

minus5

times103





time (CCT)




1 1205752 1205753

Mac

hine

term

inal

Time (s)0 1 2 3 4 5 6 7 8 9

05

1

15

volta

gesV

t1V

t2(p

u)

Vt1Vt2

Vt3Vt4

(a)

Reac

tive p

ower

(Mva

r)

Time (s)0 1 2 3 4 5 6 7 8 9

050

100150

(b)


1199054


0 1 2 3 4 5 60

1

2


Volta

ge at

bus

es B

1B2

and

B3

(pu)

Time (s)


0 1 2 3 4 5 6Time (s)

0

2

Line

pow

er fl

owat

bus

B2

(MW

)

minus2

times103













0 2 4 6 8 10 12Time (s)



1205751minus1205754

050

100

minus50

(a)

0 2 4 6 8 10 12Time (s)



050

100

1205752minus1205754

minus50

(b)

10

0 2 4 6 8 10 12Time (s)


(stable)0

5

1205753minus1205754

(c)





5 Conclusions


Appendix



119904= 0003 119891 = 50Hz 119883

119889= 1305 1198831015840

119889=

0296 11988310158401015840119889

= 0252 1198831015840119902= 050 11988310158401015840

119902= 0243 1198791015840

119889= 101 s

11987910158401015840

119889= 0053 s119867 = 37 s


004

0 2 4 6 8 10 12Time (s)


(stable)0002

1205961minus1205964

(pu)

minus002


0 2 4 6 8 10 12Time (s)


(stable)0

2

1205963minus1205964

(pu)

minus2

times10minus3



0 2 4 6 8 10 120

05

1

15


Time (s)

Volta

ge at

bus

es B

1B2

and

B3

(pu)


0123

0 2 4 6 8 10 12Time (s)

Line

pow

er fl

owat

bus

B2

(MW

)

minus1

times103



0 02 04 06 08 1099

0995

1

1005

101

1015No CSC-STATCOM

(unstable)


minus02

Spee

d1205961

(pu)


(a)

0 02 04 06 08 1

0995

1

1005

101No CSC-STATCOM

(unstable)


minus02

Spee

d1205962

(pu)


(b)





0 1 2 3 4 5 6 7 8 9

0

001

002

Time (s)

With SVC(unstable)

With CSC-STATCOM

With VSC-STATCOM

(stable)

1205961minus1205964

(pu)

minus002

minus001


0 1 2 3 4 5 6 7 8 9Time (s)

With SVC(unstable)

With CSC-STATCOM

With VSC-STATCOM

(stable)0

1

2

1205963minus1205964

(pu)

minus2

minus1

times10minus3


0 1 2 3 4 5 6 7 8 9Time (s)

With SVC(unstable)

With CSC-STATCOM

With VSC-STATCOM

(stable)0

50

100

150

200

minus50

1205751minus1205754

(deg

)


0 1 2 3 4 5 6 7 8 9Time (s)

With SVC(unstable)

With CSC-STATCOM

With VSC-STATCOM

(stable)

0

2

4

6

8

1205753minus1205754

(deg

)



0 2 4 6 8 10 12


0 2 4 6 8 10 12Time (s)

0 2 4 6 8 10 12Time (s)

0 2 4 6 8 10 12Time (s)



0

2

4

6

8

10




0

001



(unstable)

With CSC-STATCOM

With VSC-STATCOM

(stable)

(stable)

(stable)

With SVC(unstable)

With CSC-STATCOM

With VSC-STATCOM


(pu)

minus002

minus001 0

50

100

150

minus50

1205751minus1205754

(deg

)

0

1

2

1205963minus1205964

(pu)

minus2

minus1

times10minus3

1205753minus1205754

(deg

)




119866is



10158401015840



and 11988310158401015840



10158401015840






119894= 500 119881ref = 1


119901= 50119870

119894= 1000





References































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










B C

A

minusK

xx yu

CSC-STATCOM

Ldc

Rdc



system



1SJ+++

+++








119899) (15)

where 1198751 1198752 119875



1 1198752 119875






120575 = 120596 (16)

=1

119872[119875119898minus 119875119890119900minus 119875

csc119890] (17)


119890119900 and119872


119890


Real power flow

L1 L2


ICSC

jX1 jX2


Area 1 Area 2


Ldc

Rdc




119868csc = 119868cscang (120579119887119900 minus 90∘) (18)


120579119887 = tanminus1 [ 119883

21198641sin 120575

11988321198641cos 120575 + 119883

11198642

] (19)

119864119889 = (

11988321198641 cos (120575 minus 120579119887119900) + 11988311198642cos 120579119887119900

1198831+ 1198832

)

+ (11988311198832

1198831+ 1198832

119868csc)

(20)





119875csc119890

=1198641119864119889

1198831

sin (120575 minus 120579119887) (21)


a

bc

d

ef

g

1205750 120575c 120575m0

Prefault curve A


e

Postfault curve C

Postfault curve C

Ad

Aa

Pm

Power

Angle

Ppe (Icsc gt 0)

Pe(Icsc = 0)

(Icsc lt 0)




119875119890= 119875119890119900+ 119875

csc119890

997904rArr 119875119890= 119875119890119900+

119883111988321198641

(1198831+ 1198832)1198831

119868csc sin (120575 minus 120579119887)

(22)




0 When a




119890suddenly






int

120575119888

1205750

(119875119898 minus 119875119891

119890) 119889120575 = int

120575119898

120575119888

(119875119901

119890minus 119875119898) 119889120575 997904rArr 119860119886 = 119860119889 (23)














B410km

B1250km B2 250km

B310km 25km

B6

B7B5

25km

944MW

877

MW

2643

MW

2487MW828MW

Z4Z3 Z1 Z2 Z4 Z3

G1

G2

G4

G3

CSC-STATCOM



Area 1 Area 2

Load center(1000MW)

Load center(6000MW)

1000MVA

1000

MVA

3000

MVA

3000MVA

LdcRdc

138kV500kV138 kV500kV

138

kV500

kV

138

kV500

kV


0 1 2 3 4 5 60

1

2


Time (s)

Volta

ge at

bus

es B

1B2

and

B3

(pu)


0 1 2 3 4 5 6

0

2

Line

pow

er fl

owat

bus

B2

(MW

)

Time (s)

minus2

times103




0 2 4 6 80

50100



Time (s)

1205751minus1205754

(deg

)

(a)

0 2 4 6 8

050

100No CSC-STATCOM


Time (s)

1205752minus1205754

(deg

)

minus50

(b)

0 2 4 6 80

5


(stable)

Time (s)

1205753minus1205754

(deg

)

(c)







0 1 2 3 4 5 6 7 8 9

0

002

1205961minus1205964

(pu)

Time (s)

minus002




0 1 2 3 4 5 6 7 8 9

0

2

1205963minus1205964

(pu)

Time (s)

minus2

times10minus3



7 8 90 1 2 3 4 5 60

1

2


Time (s)

Volta

ge at

bus

es B

1B2

and

B3

(pu)


7 8 9

0

5

0 1 2 3 4 5 6Line

pow

er fl

owat

bus

B2

(MW

)

Time (s)

minus5

times103





time (CCT)




1 1205752 1205753

Mac

hine

term

inal

Time (s)0 1 2 3 4 5 6 7 8 9

05

1

15

volta

gesV

t1V

t2(p

u)

Vt1Vt2

Vt3Vt4

(a)

Reac

tive p

ower

(Mva

r)

Time (s)0 1 2 3 4 5 6 7 8 9

050

100150

(b)


1199054


0 1 2 3 4 5 60

1

2


Volta

ge at

bus

es B

1B2

and

B3

(pu)

Time (s)


0 1 2 3 4 5 6Time (s)

0

2

Line

pow

er fl

owat

bus

B2

(MW

)

minus2

times103













0 2 4 6 8 10 12Time (s)



1205751minus1205754

050

100

minus50

(a)

0 2 4 6 8 10 12Time (s)



050

100

1205752minus1205754

minus50

(b)

10

0 2 4 6 8 10 12Time (s)


(stable)0

5

1205753minus1205754

(c)





5 Conclusions


Appendix



119904= 0003 119891 = 50Hz 119883

119889= 1305 1198831015840

119889=

0296 11988310158401015840119889

= 0252 1198831015840119902= 050 11988310158401015840

119902= 0243 1198791015840

119889= 101 s

11987910158401015840

119889= 0053 s119867 = 37 s


004

0 2 4 6 8 10 12Time (s)


(stable)0002

1205961minus1205964

(pu)

minus002


0 2 4 6 8 10 12Time (s)


(stable)0

2

1205963minus1205964

(pu)

minus2

times10minus3



0 2 4 6 8 10 120

05

1

15


Time (s)

Volta

ge at

bus

es B

1B2

and

B3

(pu)


0123

0 2 4 6 8 10 12Time (s)

Line

pow

er fl

owat

bus

B2

(MW

)

minus1

times103



0 02 04 06 08 1099

0995

1

1005

101

1015No CSC-STATCOM

(unstable)


minus02

Spee

d1205961

(pu)


(a)

0 02 04 06 08 1

0995

1

1005

101No CSC-STATCOM

(unstable)


minus02

Spee

d1205962

(pu)


(b)





0 1 2 3 4 5 6 7 8 9

0

001

002

Time (s)

With SVC(unstable)

With CSC-STATCOM

With VSC-STATCOM

(stable)

1205961minus1205964

(pu)

minus002

minus001


0 1 2 3 4 5 6 7 8 9Time (s)

With SVC(unstable)

With CSC-STATCOM

With VSC-STATCOM

(stable)0

1

2

1205963minus1205964

(pu)

minus2

minus1

times10minus3


0 1 2 3 4 5 6 7 8 9Time (s)

With SVC(unstable)

With CSC-STATCOM

With VSC-STATCOM

(stable)0

50

100

150

200

minus50

1205751minus1205754

(deg

)


0 1 2 3 4 5 6 7 8 9Time (s)

With SVC(unstable)

With CSC-STATCOM

With VSC-STATCOM

(stable)

0

2

4

6

8

1205753minus1205754

(deg

)



0 2 4 6 8 10 12


0 2 4 6 8 10 12Time (s)

0 2 4 6 8 10 12Time (s)

0 2 4 6 8 10 12Time (s)



0

2

4

6

8

10




0

001



(unstable)

With CSC-STATCOM

With VSC-STATCOM

(stable)

(stable)

(stable)

With SVC(unstable)

With CSC-STATCOM

With VSC-STATCOM


(pu)

minus002

minus001 0

50

100

150

minus50

1205751minus1205754

(deg

)

0

1

2

1205963minus1205964

(pu)

minus2

minus1

times10minus3

1205753minus1205754

(deg

)




119866is



10158401015840



and 11988310158401015840



10158401015840






119894= 500 119881ref = 1


119901= 50119870

119894= 1000





References































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










a

bc

d

ef

g

1205750 120575c 120575m0

Prefault curve A


e

Postfault curve C

Postfault curve C

Ad

Aa

Pm

Power

Angle

Ppe (Icsc gt 0)

Pe(Icsc = 0)

(Icsc lt 0)




119875119890= 119875119890119900+ 119875

csc119890

997904rArr 119875119890= 119875119890119900+

119883111988321198641

(1198831+ 1198832)1198831

119868csc sin (120575 minus 120579119887)

(22)




0 When a




119890suddenly






int

120575119888

1205750

(119875119898 minus 119875119891

119890) 119889120575 = int

120575119898

120575119888

(119875119901

119890minus 119875119898) 119889120575 997904rArr 119860119886 = 119860119889 (23)














B410km

B1250km B2 250km

B310km 25km

B6

B7B5

25km

944MW

877

MW

2643

MW

2487MW828MW

Z4Z3 Z1 Z2 Z4 Z3

G1

G2

G4

G3

CSC-STATCOM



Area 1 Area 2

Load center(1000MW)

Load center(6000MW)

1000MVA

1000

MVA

3000

MVA

3000MVA

LdcRdc

138kV500kV138 kV500kV

138

kV500

kV

138

kV500

kV


0 1 2 3 4 5 60

1

2


Time (s)

Volta

ge at

bus

es B

1B2

and

B3

(pu)


0 1 2 3 4 5 6

0

2

Line

pow

er fl

owat

bus

B2

(MW

)

Time (s)

minus2

times103




0 2 4 6 80

50100



Time (s)

1205751minus1205754

(deg

)

(a)

0 2 4 6 8

050

100No CSC-STATCOM


Time (s)

1205752minus1205754

(deg

)

minus50

(b)

0 2 4 6 80

5


(stable)

Time (s)

1205753minus1205754

(deg

)

(c)







0 1 2 3 4 5 6 7 8 9

0

002

1205961minus1205964

(pu)

Time (s)

minus002




0 1 2 3 4 5 6 7 8 9

0

2

1205963minus1205964

(pu)

Time (s)

minus2

times10minus3



7 8 90 1 2 3 4 5 60

1

2


Time (s)

Volta

ge at

bus

es B

1B2

and

B3

(pu)


7 8 9

0

5

0 1 2 3 4 5 6Line

pow

er fl

owat

bus

B2

(MW

)

Time (s)

minus5

times103





time (CCT)




1 1205752 1205753

Mac

hine

term

inal

Time (s)0 1 2 3 4 5 6 7 8 9

05

1

15

volta

gesV

t1V

t2(p

u)

Vt1Vt2

Vt3Vt4

(a)

Reac

tive p

ower

(Mva

r)

Time (s)0 1 2 3 4 5 6 7 8 9

050

100150

(b)


1199054


0 1 2 3 4 5 60

1

2


Volta

ge at

bus

es B

1B2

and

B3

(pu)

Time (s)


0 1 2 3 4 5 6Time (s)

0

2

Line

pow

er fl

owat

bus

B2

(MW

)

minus2

times103













0 2 4 6 8 10 12Time (s)



1205751minus1205754

050

100

minus50

(a)

0 2 4 6 8 10 12Time (s)



050

100

1205752minus1205754

minus50

(b)

10

0 2 4 6 8 10 12Time (s)


(stable)0

5

1205753minus1205754

(c)





5 Conclusions


Appendix



119904= 0003 119891 = 50Hz 119883

119889= 1305 1198831015840

119889=

0296 11988310158401015840119889

= 0252 1198831015840119902= 050 11988310158401015840

119902= 0243 1198791015840

119889= 101 s

11987910158401015840

119889= 0053 s119867 = 37 s


004

0 2 4 6 8 10 12Time (s)


(stable)0002

1205961minus1205964

(pu)

minus002


0 2 4 6 8 10 12Time (s)


(stable)0

2

1205963minus1205964

(pu)

minus2

times10minus3



0 2 4 6 8 10 120

05

1

15


Time (s)

Volta

ge at

bus

es B

1B2

and

B3

(pu)


0123

0 2 4 6 8 10 12Time (s)

Line

pow

er fl

owat

bus

B2

(MW

)

minus1

times103



0 02 04 06 08 1099

0995

1

1005

101

1015No CSC-STATCOM

(unstable)


minus02

Spee

d1205961

(pu)


(a)

0 02 04 06 08 1

0995

1

1005

101No CSC-STATCOM

(unstable)


minus02

Spee

d1205962

(pu)


(b)





0 1 2 3 4 5 6 7 8 9

0

001

002

Time (s)

With SVC(unstable)

With CSC-STATCOM

With VSC-STATCOM

(stable)

1205961minus1205964

(pu)

minus002

minus001


0 1 2 3 4 5 6 7 8 9Time (s)

With SVC(unstable)

With CSC-STATCOM

With VSC-STATCOM

(stable)0

1

2

1205963minus1205964

(pu)

minus2

minus1

times10minus3


0 1 2 3 4 5 6 7 8 9Time (s)

With SVC(unstable)

With CSC-STATCOM

With VSC-STATCOM

(stable)0

50

100

150

200

minus50

1205751minus1205754

(deg

)


0 1 2 3 4 5 6 7 8 9Time (s)

With SVC(unstable)

With CSC-STATCOM

With VSC-STATCOM

(stable)

0

2

4

6

8

1205753minus1205754

(deg

)



0 2 4 6 8 10 12


0 2 4 6 8 10 12Time (s)

0 2 4 6 8 10 12Time (s)

0 2 4 6 8 10 12Time (s)



0

2

4

6

8

10




0

001



(unstable)

With CSC-STATCOM

With VSC-STATCOM

(stable)

(stable)

(stable)

With SVC(unstable)

With CSC-STATCOM

With VSC-STATCOM


(pu)

minus002

minus001 0

50

100

150

minus50

1205751minus1205754

(deg

)

0

1

2

1205963minus1205964

(pu)

minus2

minus1

times10minus3

1205753minus1205754

(deg

)




119866is



10158401015840



and 11988310158401015840



10158401015840






119894= 500 119881ref = 1


119901= 50119870

119894= 1000





References































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










B410km

B1250km B2 250km

B310km 25km

B6

B7B5

25km

944MW

877

MW

2643

MW

2487MW828MW

Z4Z3 Z1 Z2 Z4 Z3

G1

G2

G4

G3

CSC-STATCOM



Area 1 Area 2

Load center(1000MW)

Load center(6000MW)

1000MVA

1000

MVA

3000

MVA

3000MVA

LdcRdc

138kV500kV138 kV500kV

138

kV500

kV

138

kV500

kV


0 1 2 3 4 5 60

1

2


Time (s)

Volta

ge at

bus

es B

1B2

and

B3

(pu)


0 1 2 3 4 5 6

0

2

Line

pow

er fl

owat

bus

B2

(MW

)

Time (s)

minus2

times103




0 2 4 6 80

50100



Time (s)

1205751minus1205754

(deg

)

(a)

0 2 4 6 8

050

100No CSC-STATCOM


Time (s)

1205752minus1205754

(deg

)

minus50

(b)

0 2 4 6 80

5


(stable)

Time (s)

1205753minus1205754

(deg

)

(c)







0 1 2 3 4 5 6 7 8 9

0

002

1205961minus1205964

(pu)

Time (s)

minus002




0 1 2 3 4 5 6 7 8 9

0

2

1205963minus1205964

(pu)

Time (s)

minus2

times10minus3



7 8 90 1 2 3 4 5 60

1

2


Time (s)

Volta

ge at

bus

es B

1B2

and

B3

(pu)


7 8 9

0

5

0 1 2 3 4 5 6Line

pow

er fl

owat

bus

B2

(MW

)

Time (s)

minus5

times103





time (CCT)




1 1205752 1205753

Mac

hine

term

inal

Time (s)0 1 2 3 4 5 6 7 8 9

05

1

15

volta

gesV

t1V

t2(p

u)

Vt1Vt2

Vt3Vt4

(a)

Reac

tive p

ower

(Mva

r)

Time (s)0 1 2 3 4 5 6 7 8 9

050

100150

(b)


1199054


0 1 2 3 4 5 60

1

2


Volta

ge at

bus

es B

1B2

and

B3

(pu)

Time (s)


0 1 2 3 4 5 6Time (s)

0

2

Line

pow

er fl

owat

bus

B2

(MW

)

minus2

times103













0 2 4 6 8 10 12Time (s)



1205751minus1205754

050

100

minus50

(a)

0 2 4 6 8 10 12Time (s)



050

100

1205752minus1205754

minus50

(b)

10

0 2 4 6 8 10 12Time (s)


(stable)0

5

1205753minus1205754

(c)





5 Conclusions


Appendix



119904= 0003 119891 = 50Hz 119883

119889= 1305 1198831015840

119889=

0296 11988310158401015840119889

= 0252 1198831015840119902= 050 11988310158401015840

119902= 0243 1198791015840

119889= 101 s

11987910158401015840

119889= 0053 s119867 = 37 s


004

0 2 4 6 8 10 12Time (s)


(stable)0002

1205961minus1205964

(pu)

minus002


0 2 4 6 8 10 12Time (s)


(stable)0

2

1205963minus1205964

(pu)

minus2

times10minus3



0 2 4 6 8 10 120

05

1

15


Time (s)

Volta

ge at

bus

es B

1B2

and

B3

(pu)


0123

0 2 4 6 8 10 12Time (s)

Line

pow

er fl

owat

bus

B2

(MW

)

minus1

times103



0 02 04 06 08 1099

0995

1

1005

101

1015No CSC-STATCOM

(unstable)


minus02

Spee

d1205961

(pu)


(a)

0 02 04 06 08 1

0995

1

1005

101No CSC-STATCOM

(unstable)


minus02

Spee

d1205962

(pu)


(b)





0 1 2 3 4 5 6 7 8 9

0

001

002

Time (s)

With SVC(unstable)

With CSC-STATCOM

With VSC-STATCOM

(stable)

1205961minus1205964

(pu)

minus002

minus001


0 1 2 3 4 5 6 7 8 9Time (s)

With SVC(unstable)

With CSC-STATCOM

With VSC-STATCOM

(stable)0

1

2

1205963minus1205964

(pu)

minus2

minus1

times10minus3


0 1 2 3 4 5 6 7 8 9Time (s)

With SVC(unstable)

With CSC-STATCOM

With VSC-STATCOM

(stable)0

50

100

150

200

minus50

1205751minus1205754

(deg

)


0 1 2 3 4 5 6 7 8 9Time (s)

With SVC(unstable)

With CSC-STATCOM

With VSC-STATCOM

(stable)

0

2

4

6

8

1205753minus1205754

(deg

)



0 2 4 6 8 10 12


0 2 4 6 8 10 12Time (s)

0 2 4 6 8 10 12Time (s)

0 2 4 6 8 10 12Time (s)



0

2

4

6

8

10




0

001



(unstable)

With CSC-STATCOM

With VSC-STATCOM

(stable)

(stable)

(stable)

With SVC(unstable)

With CSC-STATCOM

With VSC-STATCOM


(pu)

minus002

minus001 0

50

100

150

minus50

1205751minus1205754

(deg

)

0

1

2

1205963minus1205964

(pu)

minus2

minus1

times10minus3

1205753minus1205754

(deg

)




119866is



10158401015840



and 11988310158401015840



10158401015840






119894= 500 119881ref = 1


119901= 50119870

119894= 1000





References































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












0 1 2 3 4 5 6 7 8 9

0

002

1205961minus1205964

(pu)

Time (s)

minus002




0 1 2 3 4 5 6 7 8 9

0

2

1205963minus1205964

(pu)

Time (s)

minus2

times10minus3



7 8 90 1 2 3 4 5 60

1

2


Time (s)

Volta

ge at

bus

es B

1B2

and

B3

(pu)


7 8 9

0

5

0 1 2 3 4 5 6Line

pow

er fl

owat

bus

B2

(MW

)

Time (s)

minus5

times103





time (CCT)




1 1205752 1205753

Mac

hine

term

inal

Time (s)0 1 2 3 4 5 6 7 8 9

05

1

15

volta

gesV

t1V

t2(p

u)

Vt1Vt2

Vt3Vt4

(a)

Reac

tive p

ower

(Mva

r)

Time (s)0 1 2 3 4 5 6 7 8 9

050

100150

(b)


1199054


0 1 2 3 4 5 60

1

2


Volta

ge at

bus

es B

1B2

and

B3

(pu)

Time (s)


0 1 2 3 4 5 6Time (s)

0

2

Line

pow

er fl

owat

bus

B2

(MW

)

minus2

times103













0 2 4 6 8 10 12Time (s)



1205751minus1205754

050

100

minus50

(a)

0 2 4 6 8 10 12Time (s)



050

100

1205752minus1205754

minus50

(b)

10

0 2 4 6 8 10 12Time (s)


(stable)0

5

1205753minus1205754

(c)





5 Conclusions


Appendix



119904= 0003 119891 = 50Hz 119883

119889= 1305 1198831015840

119889=

0296 11988310158401015840119889

= 0252 1198831015840119902= 050 11988310158401015840

119902= 0243 1198791015840

119889= 101 s

11987910158401015840

119889= 0053 s119867 = 37 s


004

0 2 4 6 8 10 12Time (s)


(stable)0002

1205961minus1205964

(pu)

minus002


0 2 4 6 8 10 12Time (s)


(stable)0

2

1205963minus1205964

(pu)

minus2

times10minus3



0 2 4 6 8 10 120

05

1

15


Time (s)

Volta

ge at

bus

es B

1B2

and

B3

(pu)


0123

0 2 4 6 8 10 12Time (s)

Line

pow

er fl

owat

bus

B2

(MW

)

minus1

times103



0 02 04 06 08 1099

0995

1

1005

101

1015No CSC-STATCOM

(unstable)


minus02

Spee

d1205961

(pu)


(a)

0 02 04 06 08 1

0995

1

1005

101No CSC-STATCOM

(unstable)


minus02

Spee

d1205962

(pu)


(b)





0 1 2 3 4 5 6 7 8 9

0

001

002

Time (s)

With SVC(unstable)

With CSC-STATCOM

With VSC-STATCOM

(stable)

1205961minus1205964

(pu)

minus002

minus001


0 1 2 3 4 5 6 7 8 9Time (s)

With SVC(unstable)

With CSC-STATCOM

With VSC-STATCOM

(stable)0

1

2

1205963minus1205964

(pu)

minus2

minus1

times10minus3


0 1 2 3 4 5 6 7 8 9Time (s)

With SVC(unstable)

With CSC-STATCOM

With VSC-STATCOM

(stable)0

50

100

150

200

minus50

1205751minus1205754

(deg

)


0 1 2 3 4 5 6 7 8 9Time (s)

With SVC(unstable)

With CSC-STATCOM

With VSC-STATCOM

(stable)

0

2

4

6

8

1205753minus1205754

(deg

)



0 2 4 6 8 10 12


0 2 4 6 8 10 12Time (s)

0 2 4 6 8 10 12Time (s)

0 2 4 6 8 10 12Time (s)



0

2

4

6

8

10




0

001



(unstable)

With CSC-STATCOM

With VSC-STATCOM

(stable)

(stable)

(stable)

With SVC(unstable)

With CSC-STATCOM

With VSC-STATCOM


(pu)

minus002

minus001 0

50

100

150

minus50

1205751minus1205754

(deg

)

0

1

2

1205963minus1205964

(pu)

minus2

minus1

times10minus3

1205753minus1205754

(deg

)




119866is



10158401015840



and 11988310158401015840



10158401015840






119894= 500 119881ref = 1


119901= 50119870

119894= 1000





References































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation
















0 2 4 6 8 10 12Time (s)



1205751minus1205754

050

100

minus50

(a)

0 2 4 6 8 10 12Time (s)



050

100

1205752minus1205754

minus50

(b)

10

0 2 4 6 8 10 12Time (s)


(stable)0

5

1205753minus1205754

(c)





5 Conclusions


Appendix



119904= 0003 119891 = 50Hz 119883

119889= 1305 1198831015840

119889=

0296 11988310158401015840119889

= 0252 1198831015840119902= 050 11988310158401015840

119902= 0243 1198791015840

119889= 101 s

11987910158401015840

119889= 0053 s119867 = 37 s


004

0 2 4 6 8 10 12Time (s)


(stable)0002

1205961minus1205964

(pu)

minus002


0 2 4 6 8 10 12Time (s)


(stable)0

2

1205963minus1205964

(pu)

minus2

times10minus3



0 2 4 6 8 10 120

05

1

15


Time (s)

Volta

ge at

bus

es B

1B2

and

B3

(pu)


0123

0 2 4 6 8 10 12Time (s)

Line

pow

er fl

owat

bus

B2

(MW

)

minus1

times103



0 02 04 06 08 1099

0995

1

1005

101

1015No CSC-STATCOM

(unstable)


minus02

Spee

d1205961

(pu)


(a)

0 02 04 06 08 1

0995

1

1005

101No CSC-STATCOM

(unstable)


minus02

Spee

d1205962

(pu)


(b)





0 1 2 3 4 5 6 7 8 9

0

001

002

Time (s)

With SVC(unstable)

With CSC-STATCOM

With VSC-STATCOM

(stable)

1205961minus1205964

(pu)

minus002

minus001


0 1 2 3 4 5 6 7 8 9Time (s)

With SVC(unstable)

With CSC-STATCOM

With VSC-STATCOM

(stable)0

1

2

1205963minus1205964

(pu)

minus2

minus1

times10minus3


0 1 2 3 4 5 6 7 8 9Time (s)

With SVC(unstable)

With CSC-STATCOM

With VSC-STATCOM

(stable)0

50

100

150

200

minus50

1205751minus1205754

(deg

)


0 1 2 3 4 5 6 7 8 9Time (s)

With SVC(unstable)

With CSC-STATCOM

With VSC-STATCOM

(stable)

0

2

4

6

8

1205753minus1205754

(deg

)



0 2 4 6 8 10 12


0 2 4 6 8 10 12Time (s)

0 2 4 6 8 10 12Time (s)

0 2 4 6 8 10 12Time (s)



0

2

4

6

8

10




0

001



(unstable)

With CSC-STATCOM

With VSC-STATCOM

(stable)

(stable)

(stable)

With SVC(unstable)

With CSC-STATCOM

With VSC-STATCOM


(pu)

minus002

minus001 0

50

100

150

minus50

1205751minus1205754

(deg

)

0

1

2

1205963minus1205964

(pu)

minus2

minus1

times10minus3

1205753minus1205754

(deg

)




119866is



10158401015840



and 11988310158401015840



10158401015840






119894= 500 119881ref = 1


119901= 50119870

119894= 1000





References































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










004

0 2 4 6 8 10 12Time (s)


(stable)0002

1205961minus1205964

(pu)

minus002


0 2 4 6 8 10 12Time (s)


(stable)0

2

1205963minus1205964

(pu)

minus2

times10minus3



0 2 4 6 8 10 120

05

1

15


Time (s)

Volta

ge at

bus

es B

1B2

and

B3

(pu)


0123

0 2 4 6 8 10 12Time (s)

Line

pow

er fl

owat

bus

B2

(MW

)

minus1

times103



0 02 04 06 08 1099

0995

1

1005

101

1015No CSC-STATCOM

(unstable)


minus02

Spee

d1205961

(pu)


(a)

0 02 04 06 08 1

0995

1

1005

101No CSC-STATCOM

(unstable)


minus02

Spee

d1205962

(pu)


(b)





0 1 2 3 4 5 6 7 8 9

0

001

002

Time (s)

With SVC(unstable)

With CSC-STATCOM

With VSC-STATCOM

(stable)

1205961minus1205964

(pu)

minus002

minus001


0 1 2 3 4 5 6 7 8 9Time (s)

With SVC(unstable)

With CSC-STATCOM

With VSC-STATCOM

(stable)0

1

2

1205963minus1205964

(pu)

minus2

minus1

times10minus3


0 1 2 3 4 5 6 7 8 9Time (s)

With SVC(unstable)

With CSC-STATCOM

With VSC-STATCOM

(stable)0

50

100

150

200

minus50

1205751minus1205754

(deg

)


0 1 2 3 4 5 6 7 8 9Time (s)

With SVC(unstable)

With CSC-STATCOM

With VSC-STATCOM

(stable)

0

2

4

6

8

1205753minus1205754

(deg

)



0 2 4 6 8 10 12


0 2 4 6 8 10 12Time (s)

0 2 4 6 8 10 12Time (s)

0 2 4 6 8 10 12Time (s)



0

2

4

6

8

10




0

001



(unstable)

With CSC-STATCOM

With VSC-STATCOM

(stable)

(stable)

(stable)

With SVC(unstable)

With CSC-STATCOM

With VSC-STATCOM


(pu)

minus002

minus001 0

50

100

150

minus50

1205751minus1205754

(deg

)

0

1

2

1205963minus1205964

(pu)

minus2

minus1

times10minus3

1205753minus1205754

(deg

)




119866is



10158401015840



and 11988310158401015840



10158401015840






119894= 500 119881ref = 1


119901= 50119870

119894= 1000





References































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 1 2 3 4 5 6 7 8 9

0

001

002

Time (s)

With SVC(unstable)

With CSC-STATCOM

With VSC-STATCOM

(stable)

1205961minus1205964

(pu)

minus002

minus001


0 1 2 3 4 5 6 7 8 9Time (s)

With SVC(unstable)

With CSC-STATCOM

With VSC-STATCOM

(stable)0

1

2

1205963minus1205964

(pu)

minus2

minus1

times10minus3


0 1 2 3 4 5 6 7 8 9Time (s)

With SVC(unstable)

With CSC-STATCOM

With VSC-STATCOM

(stable)0

50

100

150

200

minus50

1205751minus1205754

(deg

)


0 1 2 3 4 5 6 7 8 9Time (s)

With SVC(unstable)

With CSC-STATCOM

With VSC-STATCOM

(stable)

0

2

4

6

8

1205753minus1205754

(deg

)



0 2 4 6 8 10 12


0 2 4 6 8 10 12Time (s)

0 2 4 6 8 10 12Time (s)

0 2 4 6 8 10 12Time (s)



0

2

4

6

8

10




0

001



(unstable)

With CSC-STATCOM

With VSC-STATCOM

(stable)

(stable)

(stable)

With SVC(unstable)

With CSC-STATCOM

With VSC-STATCOM


(pu)

minus002

minus001 0

50

100

150

minus50

1205751minus1205754

(deg

)

0

1

2

1205963minus1205964

(pu)

minus2

minus1

times10minus3

1205753minus1205754

(deg

)




119866is



10158401015840



and 11988310158401015840



10158401015840






119894= 500 119881ref = 1


119901= 50119870

119894= 1000





References































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











119866is



10158401015840



and 11988310158401015840



10158401015840






119894= 500 119881ref = 1


119901= 50119870

119894= 1000





References































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation

















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









Download - Research Article Transient Stability Enhancement of ...downloads.hindawi.com/archive/2015/626731.pdfResearch Article Transient Stability Enhancement of Multimachine Power System Using

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