19 improvement of power system stability using hvdc … 2/issue1/4 improvement of power...

P. Bapaiah 19

International Journal of Emerging Trends in Electrical and Electronics (IJETEE) Vol. 2, Issue. 1, April-2013.

Improvement of Power System Stability UsingHVDC Controls

P. Bapaiah

Abstract: In an AC/DC power system, emergency poweractions from the HVDC connection are very important,because appropriate fast changes in DC power will reduce thestress on the AC system and the magnitude of the firsttransient swing. An HVDC transmission link is highlycontrollable. Its effective use depends on appropriateutilization of this controllability to ensure desired performanceof the power system.

In this paper, the investigations are carried out on theimprovement of power system stability by utilizing auxiliarycontrols for controlling HVDC power flow. AC/DC load flowusing eliminated variable method is utilized in the transientstability analysis. Transient stability analysis is done on singlemachine system and multimachine system, using differentcontrol signals derived from the AC system. In this work, thecombination of the different signals, which stabilizes thesystem, is found out and its effectiveness is verified.

Key words: HVDC controller, Multi machines, Stability, Powersystem, load modeling.

I. High-Voltage Direct-Current TransmissionRemote generation and system inter connections lead to

a search for efficient power transmission at increasingpower levels. The increase in voltage levels is not alwaysfeasible. The problems of AC transmission particularly inlong distance transmission, has led to the development ofDC transmission. However, as generation and utilization ofpower remains at alternating current, the DC transmissionrequires conversion at two ends, from AC to DC at thesending end and back to AC at the receiving end. Thisconversion is done at converter stations-rectifier at thesending end and inverter at the receiving end. Theconverters are static, using high power thyristors connectedin series to give the required voltage ratings. The physicalprocess of conversion is such that the same station canswitch from rectifier to inverter by simple control action,thus facilitating the power reversal.

P. Bapaiah is currently working as an Assistant Professor in Electrical andElectronics Engineering Department at Amrita Sai Institute of Science andTechnology, Paritala, (INDIA), Email: [email protected].

HVDC Transmission has advantages over ACtransmission in special situations [1]. The following are thetypes of applications for which HVDC transmission hasbeen used:

1. Under water cables longer than about 30 km. ACtransmission is impractical for such distancesbecause of the high capacitance of the cablerequiring intermediate compensation stations.

2. Asynchronous link between two AC systems whereAC ties would not be feasible because of systemstability problems or a difference in nominalfrequencies of the two systems.

3. Transmission of large amounts of power over longdistances by over head lines. HVDC transmissionis a competitive alternative to AC transmission fordistances in excess of about 600 km.

Power System StabilityPower system stability is the ability of an electric power

system, for a given initial operating condition, to regain astate of operating equilibrium after being subjected to aphysical disturbance, with most system variables boundedso that practically the entire system remains intact [2].

The power system is a highly nonlinear system thatoperates in a constantly changing environment; loads,generator outputs and key operating parameters changecontinually. When subjected to a disturbance, the stability ofthe system depends on the initial operating condition as wellas the nature of the disturbance. Stability of an electricpower system is thus a property of the system motionaround an equilibrium set, i.e., the initial operatingcondition. In an equilibrium set, the various opposing forcesthat exist in the system are equal instantaneously or over acycle.

Power systems are subjected to a wide range ofdisturbances, small and large. Small disturbances in theform of load changes occur continually; the system must beable to adjust to the changing conditions and operatesatisfactorily. It must also be able to survive numerousdisturbances of a severe nature, such as a short circuit on atransmission line or loss of a large generator. A largedisturbance may lead to structural changes due to theisolation of the faulted elements. At an equilibrium set, apower system may be stable for a given (large) physicaldisturbance, and unstable for another. It is impractical anduneconomical to design power systems to be stable forevery possible disturbance [2]. The design contingencies areselected on the basis that they have a reasonably highprobability of occurrence. Hence, large-disturbance stabilityalways refers to a specified disturbance scenario.

P. Bapaiah 20


The response of the power system to a disturbance mayinvolve much of the equipment. For instance, a fault on acritical element followed by its isolation by protective relayswill cause variations in power flows, network bus voltages,and machine rotor speeds; the voltage variations will actuateboth generator and transmission network voltage regulators;the generator speed variations will actuate prime movergovernors; and the voltage and frequency variations willaffect the system loads to varying degrees depending ontheir individual characteristics. Further, devices used toprotect individual equipment may respond to variations insystem variables and cause tripping of the equipment,thereby weakening the system and possibly leading tosystem instability. If following a disturbance the powersystem is stable, it will reach a new equilibrium state withthe system integrity preserved i.e., with practically allgenerators and loads connected through a single contiguoustransmission system. Some generators and loads may bedisconnected by the isolation of faulted elements orintentional tripping to preserve the continuity of operation ofbulk of the system. Interconnected systems, for certainsevere disturbances, may also be intentionally split into twoor more “islands” to preserve as much of the generation andload as possible. The actions of automatic controls andpossibly human operators will eventually restore the systemto normal state. On the other hand, if the system is unstable,it will result in a run-away or run-down situation; forexample, a progressive increase in angular separation ofgenerator rotors, or a progressive decrease in bus voltages.An unstable system condition could lead to cascadingoutages and a shutdown of a major portion of the powersystem.

Power systems are continually experiencing fluctuationsof small magnitudes. However, for assessing stability whensubjected to a specified disturbance, it is usually valid toassume that the system is initially in a true steady-stateoperating condition.

Rotor angle stability refers to the ability of synchronousmachines of an interconnected power system to remain insynchronism after being subjected to a disturbance. Itdepends on the ability to maintain/restore equilibriumbetween electromagnetic torque and mechanical torque ofeach synchronous machine in the system. Instability thatmay result occurs in the form of increasing angular swingsof some generators leading to their loss of synchronism withother generators [2].

Loss of synchronism can occur between one machineand the rest of the system, or between groups of machines,with synchronism maintained within each group afterseparating from each other.

HVDC systems have the ability to rapidly control thetransmitted power. Therefore, they have a significant impacton the stability of the associated AC power systems. Anunderstanding of the characteristics of the HVDC systems isessential for the study of the stability of the power system.More importantly, proper design of the HVDC controls is

essential to ensure satisfactory performance of the overallAC/DC system [1].

In this paper, an attempt is made to utilize the aboveadvantage of HVDC systems for the improvement ofstability of the power system.

II. AC/DC Load FlowIn transient stability studies it is prerequisite to do

AC/DC load flow calculations in order to obtain systemconditions prior to the disturbance. The simplest way ofintegrating a DC link into the AC load flow is representingit by constant active and reactive power injections at the twoterminal buses in the AC systems. Thus the two terminalAC/DC buses are represented as a PQ-bus with a constant,voltage independent active and reactive power. Howeverthis is clearly an inadequate representation where the linkscontribution to AC system reactive power and voltageconditions is significant, since the accurate operating modeof the link and its terminal equipment are ignored [3].

Traditionally, two different approaches have been usedto solve the power flow equations for hybrid AC/DCsystems. The first approach is the sequential method, inwhich the AC and DC equations are solved separately ineach iteration. The sequential method is easy to implement,but convergence problems may occur in certain situations.The other approach is the unified method, in which thesolution vector is extended with the DC-variables, whichcan also be referred to as extended variable method. Thedrawback with the extended variable method is that it iscomplex to program and hard to combine withdevelopments in AC power flow solution techniques.

The eliminated variable method used here [4] overcomesthese difficulties. The basic idea is to treat the real andreactive powers consumed by the converters as voltagedependent loads. The DC equations are solved analyticallyor numerically and the DC variables are eliminated from thepower flow equations. The method is unified, since theeffect of the DC-link is included in the Jacobian. It is,however, not an extended variable method, since no DCvariables are added to the solution vector.

DC System Model:The equations describing the steady state behavior of a

monopolar DC link can be summarized as follows.

3 2 3cosdr r tr r c dV a V X I

(2.1)

3 2 3cosdi i ti i c dV aV X I

(2.2)

dr di d dV V r I (2.3)

dr dr dP V I (2.4)

di di dP V I (2.5)

3 2dr r tr dS k a V I

(2.6)

P. Bapaiah 21


3 2di i ti dS k aV I

(2.7)

2 2dr dr drQ S P (2.8)

2 2di di diQ S P (2.9)

AC/DC Power Flow Equations:When the DC-link is included in the power flow

equations, only the mismatch equations at the converterterminal AC buses have to be modified.

, , ,spec actr tr tr dr tr ti dcP P P v P V V x (2.10)

, , ,spec acti ti ti di tr ti dcP P P v P V V x (2.11)

, , ,spec actr tr tr dr tr ti dcQ Q Q v Q V V x (2.12)

, , ,spec acti ti ti di tr ti dcQ Q Q v Q V V x (2.13)

where xdc is a vector of internal DC-variables. The DC-variables satisfy

, , 0tr ti dcR V V x (2.14)where R is a set of equations given by (2.1)-(2.3) and fourcontrol specifications.

In the extended variable method, (2.15) is solved iteratively.

0

0 /

/0 0 0

t t

t t t

dc

P H NA

PQ J L V V

CQ V V

D ER x

(2.15)

In the sequential method, (2.14) is solved after each iterationof (2.16).

/H NPJ LQ V V

(2.16)

Control Modes:Seven variables and three independent equations, (2.1)-

(2.3), are introduced when a DC-link is included. Hence,four specifications have to be made in order to define aunique solution. The control modes used here aresummarized in Table 2.1, it will suffice to illustrate theanalytical elimination procedure.

Control mode A is the base case, which in the wellknown current margin control corresponds to one terminalcontrolling the voltage and the other the current, orequivalently the power. The control angles and the DC-voltage are specified, and the converter transformer tappositions are varied in order to meet these specifications.The other modes in Table 2.1 are obtained from mode A ifvariables hit their limits during the power flow

computations, or if the time scale is such that the taps can beassumed to be fixed. The modes that are obtained whenlimits are encountered depend on the control strategy of theHVDC-scheme, and this must be accounted for in thecomputations. For modes B - D, ar determines r and aidetermines the direct voltage, which normally is the case forcurrent control in the rectifier. For modes E - G, ardetermines the direct voltage. Subscript ‘I’ refers to constantcurrent control.Table 0.1: Control modes

ControlMode

SpecifiedVariables

Ar i diV diP

Bra i diV diP

Cr i ia diP

Dra i ia diP

Er i ra diP

Fr ia diV diP

Gr ia ra diP

AI r i diV dIBI ra i diV dICI r i ia dIDI ra i ia dIEI r i ra dIFI r ia diV dIGI r ia ra dI

The taps are assumed to be continuous variables.Discrete tap positions can be taken into account by firstassuming continuous taps and subsequently fix the taps atappropriate values.

The Eliminated Variable Method:In the eliminated variable method, the equations in

(2.14) are, in principle, solved for xdc.xdc = f(Vtr, Vti) (2.17)

The real and reactive powers consumed by theconverters can then be written as functions of Vtr and Vti.

Pdr = Pdr(Vtr, Vti, xdc)= Pdr(Vtr, Vti, f(Vtr, Vti))= Pdr(Vtr, Vti) (2.18)

It is not needed to derive explicit functions for the realand reactive powers, only to find a sequence ofcomputations such that the real and reactive powers andtheir partial derivatives w.r.t. the AC terminal voltages canbe computed. If all real and reactive powers are written asfunctions of Vtr and Vti, (2.15) can be replaced by (2.19).

/H NPJ LQ V V

(2.19)

P. Bapaiah 22


,' ,ac

dr tr titrtr tr

tr tr

P V VPN tr tr V VV V

(2.20)

,' ,ac

dr tr titrti ti

ti ti

P V VPN tr ti V VV V

(2.21)

,' ,ac

di tr tititr tr

tr tr

P V VPN ti tr V VV V

(2.22)

,' ,ac

di tr tititi ti

ti ti

P V VPN ti ti V VV V

(2.23)

'L is modified analogously. Thus, in the eliminatedvariable method, four mismatch equations and up to eightelements of the Jacobian have to be modified, but no newvariables are added to the solution vector, when a DC-linkis included in the power flow. The partial derivatives arethose required by (2.19); ∂Pdr(Vtr,Vti)/∂Vtr, for example, isthe derivative of Pdr w.r.t. Vtr, assuming Vti is kept constant.The DC variables, however, are not kept constant asopposed to ∂Pdr(Vtr,Vti,xdc)/∂Vtr, which is used in (2.15).Although (2.19) looks like (2.16), it is mathematically moresimilar to (2.15). The Jacobian in (2.19) is howevernormally more well-conditioned than the one in (2.15).

Analytical Elimination:To illustrate the procedure, the analytical elimination is

carried out in detail for some representative modes. It issufficient to find Pd and Sd at each converter, since Qd thencan be computed with (2.8) or (2.9). The partial derivativesfor all modes in Table2.1 are shown in Table 2.2 and Table2.3.

Control Mode A:[αr γi Vdi Pdi]

Since both the voltage and power at the inverter arespecified, the direct current can be computed with (2.5), andPdr can then be found by combining (2.3), (2.4) and (2.5)

Pdr = Pdi + Rd Id2 (2.24)

If we combine (2.l), (2.6) and (2.24), we obtain

23

cos

di d c d

drr

P R X IS k

di l lk P P Q (2.25)Analogously, for Sdi:

cosdi di l di l

i

kS P Q k P Q (2.26)

Thus, all real and reactive powers consumed by theconverters can be precomputed, and including the dc-link inthe power flow is trivial for this control mode. The same istrue for any specification of the form [αr γi x1 x2], where x1and x2 are any two variables of [Pdr Pdi Vdr Vdi Id]. The factthat the real and reactive powers can be precomputed forthis case is well known.

Control Mode B:[αr γi Vdi Pdi]

This mode occurs e.g. if the tap changer at the rectifierhits a limit in control mode A under current control in therectifier. Since Pdi and Vdi are specified, Id, Vdr, Pdr and Sdicomputed as for mode A. Since αr is specified, Sdr iscomputed with (2.6) instead of (2.25).

3 2drtr tr r d dr

tr

SV V k a I SV

(2.27)

2dr dr

trtr dr

Q SVV Q

(2.28)

The formulas for mode BI are essentially identical; theonly difference is that Pdi, rather than Id, is computed with(2.5). In general, when two of the variables of [Pdr Pdi VdrVdi Id] are specified, the other three can be computed from(2.3)-(2.5).

Control Mode C:[αr γi ai Pdi]

These specifications are valid e.g. if the tap changer atthe inverter hits a limit in mode A under current control inthe rectifier. Combining (2.2) and (2.5) gives

23 2 3cosdi i ti i d c dP a V I X I

(2.29)

If we solve for Id, we obtain

21 1 2d ti ti diI c V c V c P (2.30)

21

1 21 2

d ti

ti ti di

I c VcV c V c P

(2.31)

where

1cos2

i i

c

acX

(2.32)

2 3 c

cX

(2.33)

Define ∂Ii as

ti di

d ti

V III V

(2.34)

Since Pdi is specified, both its partials are zero. Pdr is givenby (2.24), and its partial derivatives by:

0drtr

tr

PVV

(2.35)

22 2dr ti dti d d l i

ti d ti

P V IV R I P IV I V

(2.36)

Since ia is specified, Sdi is computed with (2.7), and thepartial derivatives of Qdi are given by

0ditr

tr

QVV

(2.37)

2

1di diti i

ti di

Q SV IV Q

(2.38)

Qdr and its partial derivatives are computed from (25)

P. Bapaiah 23


2drti i l l

ti

SV I k P QV

(2.39)

0drtr

tr

QVV

(2.40)

2dr iti dr l l l dr

ti dr

Q IV k S Q P PPV Q

(2.41)

Other ModesThe partial derivatives for the other control modes can

be derived analogously; if the tap changer controlling thecontrol angle is specified (modes B, D, F, G), only thereactive power at that converter will depend oncorresponding AC voltage.

If the tap changer controlling the direct voltage isspecified (modes C, D, E, G), all the real and reactivepowers will depend on the AC voltage at that terminal.Equations (2.30) or (2.43) are used to find the direct currentfor constant power control.

If the tap changer position is specified at a converter, Sdis computed with (2.6) or (2.7), otherwise (2.25) or (2.26)are used. The partial derivatives for all modes in Table 2.1are summarized in Table 2.2 and Table 2.3Table 0.2: Partial derivatives for modes with the directvoltage determined by ai

Mode

Pdr

Vtr

QdrVtrVtr

PdrVtiVti

QdrVtiVti

Pdi

Vtr

Qdi

Vtr

PdiVtiVti

QdiVtiVti

A 0 0 0 0 0 0 0 0AI 0 0 0 0 0 0 0 0

B 02

Sdr

Qdr0 0 0 0 0 0

BI 02

Sdr

Qdr0 0 0 0 0 0

C 0 0 2P Iil 2 Ii k S P Q P Pdr l l dr l

Qdr

0 0 0 2

1Sdi IiQdi

CI 0 0 P Qdi l P Qdi l k S Pdr dr

Qdr

0 0 P Qdi l

PdiQ Qdi lQdi

D 02

Sdr

Qdr2P Iil

22

Ii S P Pdr l drQdr

0 0 0

2

1Sdi IiQdi

DI 02

Sdr

QdrP Qdi l

P Qdi l PdrQdr

0 0 P Qdi l

PdiQ Qdi lQdi

Table 0.3: Partial derivatives for modes with the directvoltage determined by ar

Mode

PdrVtrVtr

QdrVtrVtr

Pdr

Vti

Qdr

Vti

PdiVtrVtr

ditr

tr

QVV

Pdi

Vti

QdiVtiVti

E 2P Irl 21 2S I P I Pr rdr l dr

Qdr

0 0 0

2 Ir Q k Sl diQdi

0 0

EI P Qdr lPdrQ Qdr lQdr 0 0 P Qdr l

P Qdr l k S Pdi diQdi

0 0

F 0 0 0 0 0 0 02

Sdi

Qdi

FI 0 0 0 0 0 0 02

Sdi

Qdi

G 2 rP Il 21 2S I P I Pr rdr l dr

Qdr

0 0 0

2Sdi IrQdi 0

2Sdi

Qdi

GI P Qdr lPdrQ Qdr lQdr 0 0 P Qdr l

P Qdr l PdiQdi

0

2Sdi

Qdi

∂Ir in Table 2.3 is defined as

tr dr

d tr

V III V

(2.42)

where

23 3 4d tr tr diI c V c V c P (2.43)

33 cos

2 3r r

d c

acR X

(2.44)

4 3d c

cR X

(2.45)

A drawback with the analytical elimination is that theformulas have to be re-derived for other DC systemconfigurations or if other specifications are used.

Transient Stability Studies:Transient stability studies provide information related to

the capability of a power system to remain in synchronismduring major disturbances resulting from either the loss ofgenerating or transmission facilities, sudden or sustainedload changes, or momentary faults. Specifically, thesestudies provide the changes in the voltages, currents,powers, speeds, and torques of the machines of the power

P. Bapaiah 24


system, as well as the changes in system voltages and powerflows, during and immediately following a disturbance. Thedegree of stability of a power system is an important factorin the planning of new facilities. In order to provide thereliability required by the dependence on continuous electricservice, it is necessary that power systems be designed to bestable under any conceivable disturbance.

The performance of the power system during thetransient period can be obtained from the networkperformance equations. The performance equation using thebus frame of reference in either the impedance or admittanceform has been used in transient stability calculations.

The operating characteristics of synchronous andinduction machines are described by sets of differentialequations. The number of differential equations required fora machine depends on the details needed to representaccurately the machine performance.

A transient stability analysis is performed by combininga solution of the algebraic equations describing the networkwith a numerical solution of the differential equations. Thesolution of the network equations retains the identity of thesystem and thereby provides access to system voltages andcurrents during the transient period [5].

As compared with rotor long-time constants, the AC andDC-transmission systems respond rapidly to network andload changes. The time constants associated with thenetwork variables are extremely small and can be neglectedwithout significant loss of accuracy. The synchronousmachine stator time constants may also be taken as zero.

The DC link is assumed here to maintain normaloperation throughout the disturbance. This approach is notvalid for larger disturbances such as converter faults, DC-line faults and AC faults close to the converter stations,these disturbances can cause commutation failures and alterthe normal conduction sequence [6].

III. SYSTEM REPRESENTATION

Generator RepresentationThe synchronous machine is represented by a voltage

source, in back of a transient reactance, that is constant inmagnitude but changes in angular position. Thisrepresentation neglects the effect of saliency and assumesconstant flux linkages and a small change in speed. If themachine rotor speed is assumed constant at synchronousspeed, a normal and accepted assumption for stabilitystudies, then M is constant. If the rotational power losses ofthe machine due to such effects as windage and friction areignored, then the accelerating power equals the differencebetween the mechanical power and the electrical power [6].The classical model can be described by the following set ofdifferential and algebraic equations:Differential:

2

2

2

m e

d fdtd d f P Pdt dt H

Algebraic:' '

t a t d tE E r I jx I where E’=voltage back of transient reactance

Et=machine terminal voltageIt=machine terminal currentra=armature resistance

'dx =transient reactance

Figure 0.1: Generator Classical model

Representation of LoadsPower system loads, other than motors represented by

equivalent circuits, can be treated in several ways during thetransient period. The commonly used representations areeither static impedance or admittance to ground, constantreal and reactive power, or a combination of theserepresentations. The parameters associated with staticimpedance and constant current representations are obtainedfrom the scheduled bus loads and the bus voltagescalculated from a load flow solution for the power systemprior to a disturbance [5]. The initial value of the current fora constant current representation is obtained from

*lp lp

pop

P jQI

E

The static admittance Ypo used to represent the load at bus P,can be obtained from

popo

p

IY

E

where Ep is the calculated bus voltage, Plp and Qlp are thescheduled bus loads. Diagonal elements of Admittancematrix (Y – Bus) corresponding to the load bus are modifiedusing the Ypo.

Representation of HVDC SystemsEach DC system tends to have unique characteristics

tailored to meet the specific needs of its application.Therefore, standard models of fixed structures have not beendeveloped for representation of DC systems in stabilitystudies [1].a) Converter model

P. Bapaiah 25


i) Simplified modelHere valve switching is neglected and the converter is

represented by the average DC voltage equation. This modelis similar to that used in power flow analysis. Thetransformer tap is assumed to be constant as the tap changerdynamics are very slow [7]. This model is inaccurate duringsevere disturbances. It cannot handle commutation failuresand cannot predict the converter behavior duringunsymmetrical faults.

ii) Detailed modelHere, the valve switching is incorporated and the model

is free from the drawbacks associated with the simplifiedmodel. However the transient simulation of converter nowrequires integration step size as small as 50 – 100 μs. Thisimplies heavy computation burden, so it is used only forshort duration (say 0.2 sec) immediately after thedisturbance.

b) Converter controller modelsi) Response type model

The dynamics of the CEA and CC are neglected andonly the steady – state controller characteristics arerepresented. The main feature of this type of controllermodel is that the configuration and the parameters of thecontroller are assumed to designed at a later stage basing onthe requirement.

ii) Detailed representationIt requires the analysis of actual control circuitry and the

establishment of a dynamic equivalent with a frequencyresponse which matches the actual controller response. Thisis used along with the detailed converter model.

c) DC network modeli) Resistive network

Here DC network is represented as resistive networkignoring energy storage elements. This approach is validwhen DC lines are short and or for back to back HVDClinks and smoothing reactors are of moderate size.

ii) Transfer function representationFor a two terminal DC link with the response type

controller, an alternative representation of the DC networkis to use a transfer function (Fig. 2.2) instead of a resistance.In this case, the time constant Tdc represents the delay inestablishing the DC current after a step change in the orderis given.

Figure 0.2: Transfer Function Model

iii) Dynamic representationAs the frequency bandwidth of the response model

considered in the transient stability studies is modest, it isadequate to represent the dc network by a simple equivalentcircuit of the type shown in figure no 2.3. Even here, theshunt branches may be neglected.

Figure 0.3: Equivalent Circuit

Runge-Kutta methodIn the application of the Runge-Kutta fourth-order

approximation, the changes in the internal voltage anglesand machine speeds, again for the simplified machinerepresentation, are determined from

1 2 3 4

1 2 3 4

1 2 261 2 26

i i i ii t t

i i i ii t t

k k k k

l l l l

i=1,2,…,no. of generators.

The k’s and l’s are the changes in i and i respectively,obtained using derivatives evaluated at predeterminedpoints. For this procedure the network equations are to besolved four times.

Steps of the AC-DC Transient Stability StudyGenerally, the DC scheme interconnects two or more,

otherwise independent, AC systems and the stabilityassessment is carried out for each of them separately, takinginto account the power constraints at the converter terminal.If the DC link is part of a single (synchronous) AC system,the converter constraints will apply to each of the nodescontaining a converter terminal. The basic structure oftransient stability program is given below [5]:

1) The initial bus voltages are obtained from theAC/DC load flow solution prior to the disturbance.

2) After the AC/DC load flow solution is obtained, themachine currents and voltages behind transientreactance are calculated.

3) The initial speed is equated to 2 f and the initialmechanical power is equated to the real poweroutput of each machine prior to the disturbance.

4) The network data is modified for the newrepresentation. Extra nodes are added to representthe generator internal voltages. Admittance matrixis modified to incorporate the load representation.

5) Set time, t=0;6) If there is any switching operation or change in

fault condition, modify network data accordinglyand run the AC/DC load flow.

7) Using Runge-Kutta method, solve the machinedifferential equations to find the changes in theinternal voltage angle and machine speeds.

8) Internal voltage angles and machine speeds areupdated and are stored for plotting.

9) AC/DC load flow is run to get the new outputpowers of the machine.

10) Advance time, t=t+Δt.

P. Bapaiah 26


11) Check for time limit, if t ≤ tmax repeat the processfrom step 6, else plot the graphs of internal voltageangle variations and stop the process.

Basing on the plots, that we get from the aboveprocedure it can be decided whether the system is stable orunstable. In case of multi machine system stability analysisthe plot of relative angles is done to evaluate the stability.

a. Basic Control PrinciplesThe HVDC system is basically constant-current

controlled for the following two important reasons: To limit overcurrent and minimize damage due to

faults. To prevent the system from running down due to

fluctuations of the ac voltages.It is because of the high-speed constant current control

characteristic that the HVDC system operation is very stable[1]. The following are the significant aspects of the basiccontrol system:

a) The rectifier is provided with a current control andan α-limit control. The minimum α reference is setat about 50 so that sufficient positive voltage acrossthe valve exists at the time of firing, to ensuresuccessful commutation. In the current controlmode, a closed loop regulator controls the firingangle and hence the dc voltage to maintain thedirect current equal to the current order. Tapchanger control of the converter transformer bringsα with in the range of 100 to 200. A time delay isused to prevent unnecessary tap movements duringexcursions of α.

b) The inverter is provided with a constant extinctionangle (CEA) control and current control. In theCEA control mode, γ is regulated to a value ofabout 150. This value represents a trade-offbetween acceptable var consumption and a low riskof commutation failure. Tap changer control isused to bring the value of γ close to the desiredrange of 150 to 200.

c) Under normal conditions, the rectifier is on currentcontrol mode and the inverter is on CEA controlmode. If there is a reduction in the ac voltage atrectifier end, the rectifier firing angle decreasesuntil it hits the αmin limit. At this point, the rectifierswitches to αmin control and the inverter willassume current control.

d) To ensure satisfactory operation and equipmentsafety, several limits are recognized in establishingthe current order: maximum current limit,minimum current limit, and voltage-dependentcurrent limit.

e) Higher-level controls may be used, in addition tothe above basic controls, to improve AC/DCsystem interaction and enhance AC systemperformance.

All schemes used to date have used the above modes ofoperation for the rectifier and the inverter. However, thereare some situations that may warrant serious investigation ofa control scheme in which the inverter is operated

continuously in current control mode and the rectifier in α-minimum control mode. Enhanced performance into weaksystems may be one case.

b. Controls for Enhancement of AC SystemPerformance

In a DC transmission system, the basic controlledquantity is the direct current, controlled by the action of therectifier with the direct voltage maintained by the inverter.A DC link controlled in this manner buffers one AC systemfrom disturbances on the other. However, it does not allowthe flow of synchronizing power which assists inmaintaining stability of AC systems. The converters ineffect appear to the AC systems as frequency-insensitiveloads and this may contribute to negative damping of systemswings [1]. Further, the DC links may contribute to voltagecollapse during swings by drawing excessive reactivepower.

Supplementary controls are therefore often required toexploit the controllability of DC links for enhancing the ACsystem dynamic performance. There are a variety of suchhigher level controls used in practice. Their performanceobjectives vary depending on the characteristics of theassociated AC systems. The following are the major reasonsfor using supplementary control of DC links:

Improvement of damping of AC systemelectromechanical oscillations.

Improvement of transient stability. Isolation of system disturbance. Frequency control of small isolated systems. Reactive power regulation and dynamic voltage

support.

The controls used tend to be unique to each system. Todate, no attempt has been made to develop generalizedcontrol schemes applicable to all systems. Thesupplementary controls use signals derived from the ACsystems to modulate the DC quantities. The modulatingsignals can be frequency, voltage magnitude and angle, andline flows. The particular choice depends on the systemcharacteristics and the desired results.

In order to augment transient stability limit large signalmodulation is used, thereby improving system security.Large changes in the power flow in the DC link are requiredto compensate for tripping of loads, generators or AC ties.While overload capability in DC links is useful, the limitsimposed by ratings of the link usually do not curtail thebenefits of power modulation. Hence, significantimprovements can be expected out of the use of DC links inemergency control. The rapid response of DC linkcontrollers makes it possible to arrest large fluctuations inthe frequency by matching generation to the load in the areato which the DC link is connected [7]. It is desirable toobtain control signals locally. Some of the controls that canbe used are as follows: Rotor frequency of adjacent generator Frequency at the converter bus Power or current in adjacent, parallel AC tie.

P. Bapaiah 27


Phase angle changes in the AC system [8].

The above signals work satisfactorily for the singlemachine system case. However, in the case of multimachinesystem it may be necessary to employ control signalsderived from relative angle deviation, speed deviation andacceleration and different combinations of these signals.Apart from linear controllers, (like P, PI and PIDcontrollers) Fuzzy logic controllers can also be employedwhich are known to give better performance. The output ofFuzzy Logic Controller is utilized to modulate the powerorder of the DC control, which in turn modulates the DCpower.

The stabilizing control is implemented through largesignal modulation of power in response to a control signalderived from the AC system variables. The effectiveness ofthe control can be enhanced by increased overload rating ofthe converters which permit short – term overloads. Thus,the rapid controllability of power in a DC link can be usedto advantage in improving the transient stability of the ACsystem in which the DC link is embedded. The power flowcan even be reversed in a short time (less than 0.25sec).Thus, DC link control can be viewed as an alternative to fastvalving or braking resistor.

IV. Proposed WorkIn this work, the advantage of fast HVDC power

modulation is utilized to improve the stability of the systemwith different types of controllers and control signals.

i. Case 1A single machine system is considered with parallel AC andDC transmission, having a Type – 0 Auxiliary controller anda Proportional Integral type current controller for the HVDCsystem. Here, the control signals are derived from generatorspeed deviation, generator phase angle deviation andvariations of power in the parallel AC line are used andcombinations of these signals are also utilized.

ii. Case 2A multi machine system is considered with a HVDC link

having a Proportional Integral current controller. Theauxiliary controller is a constant gain controller which isgiven with different control signals from the AC system.The control signals are derived from relative generatorangles, relative speed variations and accelerations ofdifferent generators.

iii. Auxiliary Stabilizing ControllerA Type- 0 controller is used here and is shown in figure

4.1. By this, we can get fast response by increasing the gainconstant (Kw) or decreasing the time constant (Tw) [7]. Thegain constant (Kw) varies from 0.0 to 1.0 and time constantvaries from 0.01 to 0.1. These two constants depend onsystem size and magnitude of the disturbance. Similarly thistype of auxiliary controller is tested for a single machineAC/DC system at different gain constants (Kw) andsatisfactory results are obtained.

Figure 0.4: Type - 0 Controller

iv. Constant Current ControllerHere Proportional Integral (PI) type controller is used

[7]. This type of controller has feedback signal (IDC) toregulate the firing angle (Alfa) at the rectifier end tomaintain the DC link current constant and the same is shownin figure 4.2.

Figure 0.5: Constant Current Controller

v. Test SystemA single machine system connected to infinite bus

through parallel AC and DC links is considered and isshown in figure 4.3.

Figure 0.6: Parallel AC and DC system

The single machine system, using the Type – 0 auxiliarycontroller and a Proportional Integral type current controllerfor HVDC link is used to demonstrate the enhancement ofstability by utilizing the controllability of the HVDC line.The DC link is represented by a simplified transfer functionmodel. The following numerical data on 100 MVA base isused.

vi. System Data Generator :

Pg=3.0 pu H=6.0 puXd=0.1 pu D=0.01F=50Hz

AC transmission lines:

P. Bapaiah 28


Xeq = 0.15 pu Transformer:

Xt=0.05 pu DC link:

K1=0.4 K2=0.3 Tw=0.05Ld=0.03 Rd=0.05 Xc=0.126

Initial conditionsδ=0.6435Δw =0Id=0.8957Alfa=0.279Vdi=0.99

The analysis is performed using the disturbances likevariations in mechanical power (0.3 pu) and outage of oneof the parallel AC lines. The stability of the system isenhanced utilizing different stabilizing signals for powermodulation in the HVDC link.

vii. Case A: Mechanical Power VariationsThe mechanical power of the generator is increased by

0.3 pu and different control signals from the AC system areutilized for the stability improvement. Without any externalcontrol signal applied to the HVDC system the stabilityanalysis is performed and the generator angle plot is asshown in figure no. 4.4. Considering variations in speed andparallel AC tie power variations different control signals areapplied to HVDC controller. The plots of phase angles ofgenerator for different stabilizing signals are shown infigures 4.5 – 4.9.

0 2 4 6 8 10 12

0.65

0.7

0.75

0.8

0.85

0.9

0.95

time(sec)

del(rad)

del

Figure 0.7: Plot of Generator angle without any externalcontrol signal applied

0 2 4 6 8 10 12

0.65

0.7

0.75

0.8

0.85

0.9

0.95

time(sec)

del(rad)

del

Figure 0.8: Plot of Generator angle with Δw as the auxiliarystabilizing signal (Kw= 1.4)

0 2 4 6 8 10 12 14 16 18 20

0.65

0.7

0.75

0.8

0.85

0.9

0.95

time(sec)

del(rad)

del

Figure 0.9: Plot of generator angle with ΔPac (change inpower of adjacent AC line) as the auxiliary stabilizing signal

(Kw= 0.1).

0 2 4 6 8 10 12 14 16 18 20

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

time(sec)

del(rad)

del

Figure 0.10: plot of generator angle with ddt

as the

auxiliary stabilizing signal (Kd=0.45).

P. Bapaiah 29


0 2 4 6 8 10 12

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

time(sec)

del(rad)

del

Kd=0.12,Kp=1.4

Figure 0.11: Plot of generator angle with Kp* Δw

+Kd* ddt

as the auxiliary stabilizing signal (Kp=1.4,

Kd =0.12).

0 2 4 6 8 10 12 14 16 18 20

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

time(sec)

del(rad)

del

Kd=0.12,Kp=1.4,Ki=0.04

Figure 0.12: plot of generator angle with Kp* Δw

+Kd* ddt

+KiΔδ as the auxiliary stabilizing signal

(Kp=1.4, Kd =0.12, Ki=0.04).

viii. Case B: Line OutageOne of the parallel AC lines is given outage, here the

two ac lines are assumed to be similar. Therefore thisdisturbance can be reflected by varying the value of Xeq,which represents the equivalent reactance of both the lines.Here, once again the different signals are utilized forstability improvement. The plots of generator angles fordifferent stabilizing signals are shown in figures 4.10 – 4.15.

0 2 4 6 8 10 120.639

0.64

0.641

0.642

0.643

0.644

0.645

0.646

0.647

0.648

0.649

time(sec)

del(rad)

del

Figure 0.13: Plot of generator angle without any externalcontrol signal.

0 2 4 6 8 10 120.6425

0.643

0.6435

0.644

0.6445

0.645

0.6455

0.646

0.6465

0.647

time(sec)

del(rad)

del

Figure 0.14: plot of generator angle with Δw as the auxiliarystabilizing signal (Kw=4.5).

0 2 4 6 8 10 12 14 16 18 200.6425

0.643

0.6435

0.644

0.6445

0.645

0.6455

0.646

0.6465

0.647

time(sec)

del(rad)

del

Figure 0.15: plot of generator angle with ΔPac (change inpower of adjacent AC line) as the auxiliary stabilizing signal(Kw=2).

P. Bapaiah 30


0 2 4 6 8 10 120.641

0.642

0.643

0.644

0.645

0.646

0.647

0.648

0.649

time(sec)

del(rad)

del

Figure 0.16: plot of generator angle with ddt

as the

auxiliary stabilizing signal (Kd=1).

0 2 4 6 8 10 120.6425

0.643

0.6435

0.644

0.6445

0.645

0.6455

0.646

0.6465

0.647

time(sec)

del(rad)

del

Figure 0.17: plot of generator angle with Kp* Δw

+Kd* ddt

as the auxiliary stabilizing signal (Kp=4.5,

Kd =0.5).

0 2 4 6 8 10 120.6425

0.643

0.6435

0.644

0.6445

0.645

0.6455

0.646

0.6465

0.647

time(sec)

del(rad)

del

Figure 0.18: Plot of generator angle with Kp* Δw

+Kd* ddt

+KiΔδ as the auxiliary stabilizing signal

(Kp=1.4, Kd =0.12, Ki=0.0005).

b. Multimachine System AnalysisThe power flow through a HVDC link can be highly

controllable. This fact is utilized to strengthen the powersystem stability. The WSCC – 9 Bus system is consideredfor the stability analysis and is given in the figure 4.16.

Figure 0.19: WSCC 9 Bus System

The scenario adapted for our study is given below:A fault is assumed to occur on Line 4-6, at initial time

zero. It is assumed that a grounded fault occurred near toBus 6 and the line from Bus 4 to Bus 6 is removed after 4cycles. The HVDC line is located between buses 4 –5.Under these conditions, the impact of HVDC on systemstability is presented. Initially, a case in which the HVDCline maintains the same control as in the normal state, inwhich the post-fault HVDC power flow setting remains thesame as before, is investigated. It was found that, the systembecomes unstable. Then a PI controller is designed tostabilize the system. The controls are used to alter powerflow setting in the HVDC line. The system data is given inappendix I.

i. Case I: Uncontrolled CaseFig. 4.17 is a plot of the generator angles for a grounded

fault at Bus 6. The HVDC line is in between buses 4 – 5.The post fault power flow setting through the HVDC line isthe same as the pre-fault power flow setting. No extracontrol mechanism has been employed here. The plot ofrelative angles of the generator is shown in figure 4.18.

0 5 10 15 20 25 30-2

-1

0

1

2

3

4

5

6x 10

4

time(sec)

del(deg)

del1

del2 del3

Figure 0.20: Plot of generator angles without any extracontrol

P. Bapaiah 31


0 5 10 15 20 25 30-1

0

1

2

3

4

5

6

7

8x 104

time(sec)

del(deg)

del13

del12

del23

Figure 0.21: Plot of relative angles with no extra control

From Fig 4.17, it can be seen that angle of generator 1goes unsynchronized from those of generators 2 & 3. Inorder to make the angle of generator 1, to be in step withthose of the other two generator angles, the power mismatchat Bus 1 has to be altered. This can be achieved by changingthe power flow in the HVDC line through an augmentedfeedback control.

When employing a feedback loop, the error signal is definedto average out the acceleration force for all the threemachines as follows [9]:

_ 3 _ 23 2 _ 1

2 1

P mis P misH H p mis

eH

(4.1)

where,P_mis(i) = Real Power Mismatch at Bus ‘i’H(i) = Moment of Inertia of generator ‘i’.

HVDC system’s current controller and line dynamics are notconsidered in this analysis. Accordingly, a realistic simplemodel for HVDC is adopted in the stability calculations.The extra energy introduced by the fault will be eventuallysmoothed out by an AGC as long as the machines are keptsynchronized.

ii. Case II: With PI ControllerSystem stability was augmented using a PI Controller. Thecontrol mechanism employed is given below [9]. Based onthe error signal defined above, the flow in the DC line ischanged as follows:

1k k kdi di p iP P K e K e t dt (4.2)

where,Pdi = Active Power flow at the Inverter terminal.K=Time step.e= Error signal.Kp=Proportional constant (=0.0013).Ki= Integral constant (=0.00061).

Integral of error, I (t), is found out by trapezoidal method.The time interval [0, t] is divided into n time steps with aninterval of Δt. Here k is the Kth time step, ek=error at timestep k and Δt= time step interval (=1/50). Accordingly,for k = 1:n

1 112k k k kI I e e t (4.3)

With initial conditions, e0 =0, I0 = 0, and

0

t

kI e t dt (4.4)

The plot of relative angles of the generators is as shown infigure 4.19 and the plot of generator phase angles is shownin figure 4.20.

0 5 10 15 20 25 30-100

0

100

200

300

400

500

time(sec)

del(deg)

kp=0.0013,ki=0.00061

del13

del13

del23

Figure 0.22: Plot of relative angles with PI control

0 5 10 15 20 25 300

0.5

1

1.5

2

2.5

3

3.5

4x 10

4

time(sec)

del(deg)

kp=0.0013,ki=0.00061

Figure 0.23: Plot of Generator angles with PI control

c.Multimachine System Considering CurrentController and Line Dynamics

Now considering the dynamics associated with the currentcontroller and the DC line the stability study is performedagain. The DC line is represented by the transfer functionmodel.

P. Bapaiah 32


i. Current ControllerHere, proportional integral current controller is used and

is shown in figure 4.21

Figure 0.24: Current controller

ii. Auxiliary controllerHere, a simple constant gain Auxiliary controller isemployed and is shown in figure 4.22. The stability of thesystem is improved by varying the gain constant (Kw) of theabove controller.

Figure 0.25: Constant Gain Controller

iii. Case 1 Uncontrolled caseConsidering the same disturbance as in previous case,

stability study is performed again. Here two extradifferential equations representing the current controller andthe HVDC Line dynamics are to be solved using the Runge– Kutta method. Here the taps are assumed to be constantand the mode shifts are not considered [1]. Without anyextra control mechanism the plots of generator angles andtheir relative difference will be as shown in figure 4.23 andfigure 4.24.

0 5 10 15 20 25 30-4

-3

-2

-1

0

1

2

3

4

5

6x 104

time(sec)

del(deg)

del1

del2

del3

Figure 0.26: Plot of generator angles with no externalcontrol signal applied

0 5 10 15 20 25 30-2

0

2

4

6

8

10x 104

time(sec)

del(deg)

K1=0.0006, K2=0.003

del13

del12

del23

Figure 0.27: Plot of relative angles without any externalcontrol signal

It is clearly seen that the system is becoming unstable,generator 2 and generator 3 are moving together whereasgenerator 1 falling out of synchronism, with this group.Considering the following signals:

1

2 1 3 12 3

2error

(4.5)

2

2 1 3 12 3

2del del del del

error del del

(4.6)

3

_ 3 _ 23 2 _ 1

2 1

P mis P misH H P mis

errorH

(4.7)

The signal error1, represents average error in the speeddifferences between the three generators. The signal error2,represents average error in relative angles between the threegenerators. The signal error3 is defined to average out theacceleration force for all the three machines. Differentcombinations of the above three signals are considered, inorder to improve the stability.

iv. Case 2Considering the signal error3 as the control input, the

plot of relative angles is as shown in the figure no 4.25.

P. Bapaiah 33


0 5 10 15 20 25 30-1200

-1000

-800

-600

-400

-200

0

200

time(sec)

del(deg)

del12del13

del23

Figure 0.28:Plot of relative angles with error3 as the controlsignal

v. Case 3Considering the combination of error1 and error2 signals asthe control input, the plot of relative angles is as shown infigure no 4.26.

0 2 4 6 8 10 12 14 16 18-80

-60

-40

-20

0

20

40

60

time(sec)

del(deg)

K1=0.0002, K2=0.0008,Kp=0.001, Ki=15

del13del12

del23

Figure 0.29: Plot of relative angles with error1 and error2 ascontrol signals

vi. Case 4Considering the combination of error1 and error3 signals

to generate the required control signal, the plot of relativeangles will be as shown in the figure no 4.27.

0 5 10 15 20 25 30-100

-50

0

50

100

150

time(sec)

del(deg)

Fig 4.27 Plot of relative angles with error1 and error3 as control signals

K1=0.005, K2=0.002,Kp=0.2, Kd=0.08

del23

del12

del13


vii. Case 5Considering the combination of error2 and error3 signals to

generate the control signals, the plot of relative angles willbe as shown in figure no 4.28.

0 2 4 6 8 10 12 14 16 18 20-100

-80

-60

-40

-20

0

20

40

60

80

time(sec)

del(deg)

Fig 4.28 Plot of relative angles with error2 and error3 as control signals

K1=0.0065, K2=0.013,Kp=1.5, Ki=2

del13

del23

del12


viii. Case 6Considering the combination of all the three signals to

generate the control signal, the plots of the relative angleswith different gains are as shown in figure (4.29) and figure(4.30).

0 5 10 15 20 25 30-40

-20

0

20

40

60

80

100

time(sec)

del(deg)

K1=0.0006, K2=0.003,Kp=2.5, Ki=0.01, Kd=0.3

del13

del12del23

Figure no 0.32: Plot of relative angles with PID controller.

P. Bapaiah 34


0 5 10 15 20 25 30-40

-20

0

20

40

60

80

100

time(sec)

del(deg)

K1=0.0006, K2=0.003,Kp=2.5, Ki=0.02, Kd=0.2

del13

del13del23

Figure 0.33: Plot of relative angles with PID controller

The study reveals that the system can be stabilized by usinga controller which produces the control signal given inequation 4.8.

Control signal, error = Kp*error1+ Ki*error2 +Kd*error3 (4.8)Here the signal error2 is the equivalent to the integral of thesignal error1, and the signal error3 is equivalent to thedifferential of the signal error1. Hence, the controllerproposed above is equivalent to a PID controller. Then thecontrol signal can be equivalently represented as in equation4.9.

error= Kp e(t)+Ki Ie(t)+Kd De(t) (4.9)Considering this, the methodology used in variable gain

PID controller scheme can be applied to the abovecontroller, to improve its performance. In the next chapter, aFuzzy PID controller scheme is proposed to improve thestability of the system.

V. CONCLUSIONSFor the variations in the mechanical power of the

generator, in the single machine system, the speed changesignal as a control signal is more effective as shown infigures 4.5 to 4.9. For a parallel line outage, the variation inpower, in the other parallel line, when used as the controlsignal, gives better performance as shown in figures 4.10 to4.15.

When the HVDC current controller and line dynamicsare not considered, the transient stability of themultimachine system after the occurrence of the specifiedfault, is improved by using a PI controller with averageacceleration as the control signal, as shown in figure 4.19

Considering the HVDC current controller and linedynamics, it is observed that the transient stability of themultimachine system is improved only if the combination ofall the three signals derived from relative speed, phase angleand average acceleration are used, as shown in figures 4.23to 4.30. This paper demonstrates that, control mechanismscan be designed and incorporated for HVDC powermodulation, to augment the stability of the power system.

References

[1] P. Kundur, “Power System Stability and Control”, McGraw-Hill, Inc., 1994.

[2] Prabha Kundur, John Paserba, “Definition and Classificationof Power System Stability”, IEEE Trans. on Power Systems.,Vol. 19, No. 2, pp 1387- 1401, May 2004.

[3] A. Panosyan, B. R. Oswald, “Modified Newton- RaphsonLoad Flow Analysis for Integrated AC/DC Power Systems”,

[4] T. Smed, G. Anderson, “A New Approach to AC/DC PowerFlow”, IEEE Trans. on Power Systems., Vol. 6, No. 3, pp1238- 1244, Aug. 1991.

[5] Stagg and El- Abiad, “Computer Methods in Power SystemAnalysis”, International Student Edition, McGraw- Hill,Book Company, 1968.

[6] Jos Arrillaga and Bruce Smith, “AC- DC Power SystemAnalysis”, The Institution of Electrical Engineers, 1998.

[7] K. R. Padiyar, “HVDC Power Transmission Systems”, NewAge International (P) Ltd., 2004.

[8] “IEEE Guide for Planning DC Links Terminating at ACLocations Having Low Short-Circuit Capacities”, TheInstitute of Electrical and Electronics Engineers, Inc., 1997.

[9] Garng M. Huang, Vikram Krishnaswamy, “HVDC Controlsfor Power System Stability”, IEEE Power EngineeringSociety, pp 597- 602, 2002.

[10] Choo Min Lim, Takashi Hiyama, “Application of A Rule-Based Control Scheme for Stability Enhancement of PowerSystems”, pp 1347- 1357, IEEE 1995.

P. Bapaiah received Diploma in Electricaland Electronics Engineering fromA.A.N.M&V.V.R.S.R Polytechnic,Gudlavalleru (INDIA) in 2002. Received hisBachelor degree in Electrical and ElectronicsEngineering from Gudlavalleru EngineeringCollege, Gudlavalleru (INDIA) in

2006.Worked as Site Engineer in MICRON Electricals atHyderabad in 2006-2008. And M.Tech in Power SystemsEngineering from V.R.Siddhartha Engineering College,Vijayawada, Acharya Nagarjuna University Guntur, (INDIA) in2010. He is currently working as an Assistant Professor inElectrical and Electronics Engineering Department at Amrita SaiInstitute of Science and Technology, Paritala, (INDIA). Hisresearch interests include Power Systems, HVDC TransmissionSystems, and Power Quality.

19 improvement of power system stability using hvdc … 2/issue1/4 improvement of power...

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