Power Flow Control and Solutions With Multiple and Multi-type FACTS Devices

Electric Power Systems Research 74 (2005) 341351

Power flow control and solutions with multiple andmulti-type FACTS devices

Narayana Prasad Padhy, M.A. Abdel MoamenDepartment of Electrical Engineering, Indian Institute of Technology, Roorkee 247 667, India

Received 16 April 2004; received in revised form 7 October 2004; accepted 7 October 2004Available online 12 January 2005

Abstract

In this paper, a new generalized current injection model of the modified power system using NewtonRaphson power flow algorithm hasbeen proposed for desired power transfer with Flexible AC Transmission Systems (FACTS) devices. So that the FACTS devices can beincorporated in the proposed algorithm and, therefore, whole system with these devices can be easily converted to power injection modelswithout change of original admittance and the Jacobian matrices. Power flow algorithm has been modeled in such a way that it can easily beextended to multiple and multi-type FACTS devices by adding a new Jacobian corresponding to that new device only. Power flow algorithmw d UnifiedP or multiplea he proposeda

K

1

stalatiscflrhti

, inquire-Thisis-

ceptsns-in

isthe

es inn ofwer

d bynse of. Theossi-for

ltingy be,

0d

ith the presence of Thyristor Controlled Series Compensators (TCSC), Unified Power Flow Controller (UPFC), and Generalizeower Flow Controller (GUPFC) has been formulated and solved. To demonstrate the performance of the proposed algorithm fnd multi-type FACTS devices, different case studies of IEEE 30-bus system has been considered and the results are tabulated. Tlgorithm is independent of the size of the system and initial starting conditions of the FACTS devices.2004 Elsevier B.V. All rights reserved.

eywords:FACTS; TCSC; UPFC; GUPFC; Load flow

. Introduction

An electric power system consists of three principle divi-ions, the generating stations, the transmission systems, andhe distribution systems. Electric power is produced by gener-tors, consumed by loads, and transmitted from generators to

oads by the transmission system. The transmission systemsre the connecting links between the generating stations and

he distribution systems and lead to other power systems overnterconnections[2,16]. In the present day scenario, transmis-ion systems are becoming increasingly stressed, more diffi-ult to operate, and more insecure with unscheduled powerows and higher losses because of growing demand and tightestrictions on the construction of new lines. However, manyigh-voltage transmission systems are operating below their

hermal ratings due to constraints, such as voltage and stabil-ty limits.

Corresponding author. Fax: +91 1332 73560.E-mail address:[email protected] (N.P. Padhy).

In addition, existing traditional transmission facilitiesmost cases, are not designed to handle the control rements of complex, highly interconnected power systems.overall situation requires the review of traditional transmsion methods and practices and the creation of new conwhich would allow the use of existing generation and tramission lines up to their full capabilities without reductionsystem stability and security[12,17]. Another reason thatforcing the review of traditional transmission methods istendency of modern power systems to follow the changtodays global economy that are leading to deregulatioelectrical power markets in order to transfer desired poand stimulate competition between utilities.

In the past, most control of power systems was aidemechanical devices and actions. This came at the expeproviding greater operating margins and redundanciesrapid development of power electronics has made it pble to design power electronic equipment of high ratinghigh voltage systems. The voltage stability problem resufrom transmission system and cheap power transfer ma378-7796/$ see front matter 2004 Elsevier B.V. All rights reserved.oi:10.1016/j.epsr.2004.10.010

342 N.P. Padhy, M.A.A. Moamen / Electric Power Systems Research 74 (2005) 341351

Fig. 1. Injection current modeling for power system elements.

at least partly, improved by use of the equipment well-knownas Flexible AC Transmission Systems (FACTS) controllers.This concept was introduced by the Electric Power ResearchInstitute (EPRI) in the late 1980. The objective of FACTSdevices mainly Thyristor Controlled Series Compensators(TCSC), Unified Power Flow Controller (UPFC), General-ized Unified Power Flow Controller (GUPFC), and InterlinePower Flow Controller (IPFC), etc. technology is to bring asystem under control and to transmit power as ordered bycontrol center economically[10,20]. It also allows increas-ing the usable transmission capacity to its maximum thermallimits.

With the progress of installing FACTS devices[3,7], thelatest generation of FACTS devices, named, the Convert-ible Static Compensators (CSC) was recently installed at theMarcy 345 kV substation. Several innovative operating con-cepts have been introduced to the historic development andapplication of FACTS. There are several possibilities of op-erating configurations by combining two or more converterblocks with flexibility. Among them there are two novel op-erating configurations, namely GUPFC and IPFC, which aresignificantly extended to control power flows of multi-linesrather than control power flow of single line by a TCSC andUPFC[1,4].

Load flow calculations of various transit scenarios in mod-ern power systems estimates approximately 35% of overalla on is

about 40%. So, FACTS devices will be applied to regulate thereactive power flows in the system. Hence, it has been con-cluded that analysis of power flow with multiple and multi-type FACTS devices became important in the modern powersystems.

2. Power flow equations

The term power flow refers to the flows of real and reac-tive power that occur during steady state condition in a powersystem. In summary, the system elements can be representedin steady state using the injection current per-phase modelsare shown inFig. 1.

The calculation of power flows is performed with all of theavailable information given in the form of interconnection ofnodes and power injections. All of the system interconnec-tions between nodes are combined into a single matrix knownas theYbus, or the admittance bus matrix.

2.1. Bus admittance matrix (Ybus)

All the models described inFig. 1can be put together toform the following system as shown inFig. 2.

Where, n is the number of buses;ng, the number of gener-ators,nd, the number of loads; andnf is the number of FACTSd

nt flowctive power losses and the reactive power consumpti

Fig. 2. Curreevices.

conventions.

N.P. Padhy, M.A.A. Moamen / Electric Power Systems Research 74 (2005) 341351 343

[Y] is the sparsen symmetrical matrix. However, for asingle phase network with phase shifting devices, it is onlystructurally symmetrical but not numerically. To calculate [Y]with FACTS devices, it is necessary to incorporate each andevery two-port matrix equation of all the branches and shuntelements in the power system. This is carried out with the aidof Eq.(1):

[Y] = [A][B][A]T (1)where the scalar matrix [A] and complex matrix [B] are de-fined as below

[A] = [Af At] and [B] =[Bff BftBtf Btt

](2)

Once the admittance matrix has been calculated for theentire system then the injected powers need to be calculated.Power is considered to be injected into the transmission sys-tem at the generation and load buses as well as FACTS de-vices terminals. For a bus with a generator connected to thetransmission system will simply be the output power of thegenerator, since generators are supported to inject power intothe transmission system. For a load bus it will be the negativeinjection of power. For a bus with FACTS device connected,the injection power at the terminals of the FACTS devicesmay be either positive or negative. For busses with genera-t nets

2

owa ctingb ge

a

s

wY

Therefore, the apparent power lossSLossalong the generaltwo-port network element, shown inFig. 3can be calculatedand shown in Eq.(5):

SLoss= V 2f (Yf0 + Yft ) + V 2t (Yt0 + Yft )(VfYftVt + VtYftVf )

= V 2f Yf0 + V 2t Yt0 + (V 2f + V 2t (VfVt + VtVf ))Yft= V 2f Yf0 + V 2t Yt0 + (V 2f + V 2t 2VfVt cosft )Yft= V 2f Yf0 + V 2t Yt0 + |Vf Vt|2Yft

(5)

whereft = f t and|Vf Vt| is the magnitude of (Vf Vt).

3. Load flow procedure with facts devices

Since the NewtonRaphson load flow procedure employspartial derivatives of the network equations with respect tothe voltage angles and magnitudesV. There are two maineffects for power flow calculation with the incorporation ofFACTS devices.

3.1. Based on the admittance matrices of the networkelements.

n bee ma-t s aren pert

to the

ad. as a

ix.

wsa de-v n outo ond-i temi Thisp flowi

3e

henb , it isa ssionl TSd tionsors, loads and FACTS devices, the injection will be theum of the three values.

.2. Two-port network implementation

To illustrate the power flow equations, the power flcross the general two-port network element conneuses f and t shown inFig. 3is considered and the followinquations are obtained.

The injected active and reactive power at bus-f (Pf andQf )re:

Pf = gffV 2f + (gft cosft + bft sinft )VfVtQf = bffV 2f + (gft sinft bft cosft )VfVt

(3)

imilarly,

Pt = gttV 2t + (gtf costf + btf sintf )VfVtQt = bttV 2t + (gtf sintf btf costf )VfVt

(4)

hereft = f t = ft , Yff = Ytt = gff + jbff = Yf0 +ft andYft = Ytf = gft + jbft = Yft

Fig. 3. General two-port network element.The admittance matrices for the FACTS devices caasily incorporated with the nodal two-port admittance

rices of the transmission lines. These modified matriceow required to be incorporated into the power flow as

he following categories:

Series connected FACTS devices are incorporated inadmittance matrix.Shunt connected FACTS devices are modeled as a loCombined series-shunt FACTS devices are modeledload as well as incorporated into the admittance matr

After a power flow is converged, the active power flolong the transmission lines with this particular FACTSice can be determined. This power is subsequently takef the parallel active load and connected to the corresp

ng bus. In this way, the operating point of the power syss changed and a new power flow solution is obtained.rocess is repeated until the tolerance level of the power

s reached.

.2. Based on the injection power of the networklements

The load flow equations with FACTS devices, can te obtained and referred directly as for a generic casessumed that FACTS device is embedded in a transmi

ine between node-f and node-t. Therefore, for the FACevice embedded transmission line, the load flow equa


can be expressed as follows:

Pi =n

j=1ViYijVjcos(i j ij) and

Qi =n

j=1ViYijVjsin(i j ij) (6)

where (referred toFig. 2) with presence of FACTS devices

Pi = PGi PLi + PFi andQi = QGi QLi +QFi (7)wherei = 1.2,. . ., n.

And for lines without FACTS devices (if i= f and t):Pi = PGi PLi andQi = QGi QLi (8)wherePFi(=Pinji ) andQFi(=Qinji ) are the FACTS devicesreal and reactive powers, respectively injected at bus-i (i = fand t). After FACTS devices are added in the transmissionline between buses f and t, injection power should be addedto Eq.(6).

Therefore, at bus-f, Eq.(6) becomes

PGf Pdf =n

j=1VfYfjVj cos(f j fj) + Pinjf

n (9)

S

wQ de-fa PFCa

4

a

i

where,

Gft =XcR(2X+Xc)

(R2 +X2)(R2 + (X+Xc)2)and

Bft =Xc(R2 X(X+Xc))

(R2 +X2)(R2 + (X+Xc)2)(13)

and,Z (=R+ jX) is transmission line impedance, Xc is themagnitude ofXTCSC andft = f t = tf .

4.1. Operating constraints of the TCSC

According to the operating principle of the TCSC, it cancontrol the active power flow for the line l (between bus-f andbus-t where the TCSC is installed).

The real power constraint of the TCSC is,

Pft = Pft PSpecft = 0 (14)

wherePSpecft is the specified power flow of the line l andPft isthe calculated power flow of the line l, and may be expressedas follows:

Pft = GffV 2f + (Gft cosft + Bft sinft )VfVt (15)

w

B

ancea

X

w

K

4p

us-t,a

S nt,t Eq.( owerfl steme om-p d asf

F

w ld dQGf Qdf =j=1

VfYfjVj sin(f j fj) +Qinjf

imilarly, for bus-t

PGt Pdt =n

j=1VtYtjVj cos(t j tj) + Pinjt

QGt Qdt =n

j=1VtYtjVj sin(t j tj) +Qinjt

(10)

heren is the total number of buses.Pinjf , Qinjf , Pinjt, andinjt (i) are the injected real and reactive power at nond node-t and their values for TCSC, UPFC, and GUre discussed in the following sections.

. Power flow equations of the TCSC

The real powerPTCSCfinj and reactive powerQTCSCfinj injection

t bus-f and bus-t can be derived[8]:

PTCSCfinj = GffV 2f + (Gft cosft + Bft sinft )VfVtQTCSCfinj = BffV 2f + (Gft sinft Bft cosft )VfVt

(11)

Similarly, the real powerPTCSCtinj and reactive powerQTCSCtinj

njections at bus-t can be expressed as:

PTCSCtinj = GttV 2t + (Gtf costf + Btf sintf )VfVtQTCSCtinj = BttV 2t + (Gtf sintf Btf costf )VfVt

(12)hereGff = RR2+(X+XC)2 , Gft = RR2+(X+XC)2 ,

ft = (X+XC)R2+(X+XC)2 andft = f t.The fundamental frequency of TCSC equivalent react

s a function of the TCSC firing angle is:

TCSC = Xc +K1(2 + sin 2K2 cos2 ( tan() tan) (16)

here = , = 12f

LC

and XLC = XcXLXcXL ,1 = Xc+XLC , K2 = 4(XLC)

2

XL.

.2. Implementation of TCSC in NewtonRaphsonower flow

Let the TCSC is now connected between bus-f and bnd the real power flow in line ft are controlled toPSpecft .

incePSpecft is a constant for the given control requiremehe real power flow in line ft can be calculated from15). In the presence of TCSC devices, the linearized pow equations must be combined with the linearized syquations corresponding to the rest of the network. A cact NewtonRaphson power flow algorithm is presente

ollows:

(X)i = JiXi (17)

hereX is the solution vector andJ is the matrix of partiaerivatives ofF(X) with respect toX, Jacobian matrix, an


Fig. 4. Equivalent circuit of UPFC in a transmission line.

they can be calculated as:

F (X) =

Pf

Pt

Qf

Qt

Pft

,X =

f

t

Vf

Vt

(18)

and

J =

Pf

f

Pf

t

Pf

Vf

Pf

Vt

Pf

Pt

f

Pt

t

Pt

Vf

Pt

Vt

Pt

Qf

f

Qf

t

Qf

Vf

Qf

Vt

Qf

Qt

f

Qt

t

Qt

Vf

Qt

Vt

Qt

Pft

f

Pft

t

Pft

Vf

Pft

Vt

Pft

(19)

wherePf,Qf,Pt andQt are the active and reactivepower mismatches at buses f, and t, respectively.Pf,Qf, PtandQt are the sum of active and reactive power flows leavingtm theT

Csfi

5

inF in-jr d asf

sfs

fs +

And the real powerPUPFCtinj and reactive powerQUPFCtinj in-

jections at bus-t can be expressed by

PTCSCtinj = V 2t Gtt + VfVt(Gtf costf + Btf sintf )+VtVs(Gtf costs Btf sints)

QTCSCtinj = V 2t Btt + VfVt(Gtf sintf + Btf costf )+VtVs(Gtf sints Btf costs)

(21)

where

Yff = Gff + jBff = Y2ffZs

1+ YffZs +1

Zp,

Ytt = Gtt + jBtt = YftYtfZs1+ YffZs and

Yft = Ytf = Gft + jBtf = YffYftZs1+ YffZs (22)

and,

Yff = Ytt = Gff + jBff = Y + jBc2 andYft = Ytf = Gft + jBft = Y (23)whereY =1/Z andZ (=R+ jX) transmission line impedanceandft = f t = tf .

5

anc owerfl FCi

T

w s-f.t is

r

V

ws of

t

w erfl ndr

he buses f and t, respectively.Pft is the real power flowismatch for the line l (between bus-f and bus-t in whichCSC is installed). = i+1 i is the incremental change in the TCS

ring angle. Also superscript i indicate iteration.

. Power flow equations of the UPFC

According to the equivalent circuit of the UPFC shownig. 4, the power flow equations can be derived and the

ected real and reactive power at bus-f (PUPFCfinj ) and (QUPFCfinj ),

espectively of a line having a UPFC may be obtaineollows [5,6,9,11,1315,18]:

PUPFCfinj = V 2f Gff + VfVt(Gftcosft + Bftsinft ) + VfVs(Gff co

QUPFCfinj = V 2f Bff + VfVt(Gftsinft + Bftcosft ) + VfVs(Gff sinBff sinfs) + VfVp(Gpcosfp Bpsinfp)

Bff cosfs) + VfVp(Gpcosfp + Bpcosfp)(20)

.1. Operating constraints of the UPFC

According to the operating principle of the UPFC, it control the voltage at bus-f and the active and reactive pow for the line l (between bus-f and bus-t in which the UPs installed).

he voltage constraint of the UPFC is, Vf VSpecf = 0(24)

hereVSpecf is the specified voltage control reference at buIn the implementation, the above equality constrain

eplaced by the following inequality constraints

Specf Vf VSpecf + (25)here is a specified very small value.The active and reactive power flow control constraint

he UPFC are

Pft = Pft PSpecft = 0

Qft = Qft QSpecft = 0(26)

herePSpecft , QSpecft are specified active and reactive pow

ows, respectively.Pft andQft are the calculated active aeactive power flows in the linel. It may be expressed by:


Pft = V 2f Gff + VfVt(Gft cosft Bft sinft ) + VfVs(Gff cosfs Bff sinfs) + VfVp(Gp cosfp Bp sinfp)Qft = V 2f Bff + VfVt(Gft sinft + Bft cosft ) + VfVs(Gff sinfs + Bff cosfs) + VfVp(Gp cosfp + Bp cosfp)

(27)

where,

Yff = Gff + jBff =Yff

1+ YffZsYft = Ytf = Gft + jBtf =

Yft1+ YffZs

Ytt = Gtt + jBtt = Ytt YftYtfZs1+ YffZs

Yp = 1

Zp

(28)

The active and reactive power flow control constraints ofthe UPFC are,

Pi = Pi PSpeci = 0Qi = Qi QSpeci = 0

(29)

where i = f and t,PSpeci ,QSpeci are specified active and reactive

p

5p

bus-fa

al , thel thel of then thmi

F

w ld dt

F

and

J =

Pf

f

Pf

t

Pf

Vf

Pf

Vt

Pf

s

Pf

p

Pf

Vs

Pt

f

Pt

t

Pt

Vf

Pt

Vt

Pt

s

Pt

p

Pt

Vs

Qf

f

Qf

t

Qf

Vf

Qf

Vt

Qf

s

Qf

p

Qf

Vs

Qt

f

Qt

t

Qt

Vf

Qt

Vt

Qt

s

Qt

p

Qt

Vs

Pft

f

Pft

t

Pft

Vf

Pft

Vt

Pft

s

Pft

p

Pft

Vs

Qft

f

Qft

t

Qft

Vf

Qft

Vt

Qft

s

Qft

p

Qft

Vs

PE

f

PE

t

PE

Vf

PE

Vt

PE

s

PE

p

PE

Vs

(32)

wherePf,Qf,Pt andQt, are the active and reactivepower mismatches at the terminal buses f and t, respectively.Pf,Qf, Pt andQt are the sum of active and reactive powerflows leaving the terminal buses f and t, respectively.Pft andQft are the active and reactive power flow mismatches forthe line l, respectively. AndPE is the active power exchangebetween the converters via the common DC link.

6

wni

P

ower flows at bus-i, respectively.

.2. Implementation of UPFC in NewtonRaphsonower flow solution

Let us consider that a UPFC is connected betweennd bus-t, subject to control of voltage at bus-f (VSpecf ) and

ctive power (PSpecft ) and reactive power (QSpecft ) flow in the

ine ft, respectively. In the presence of UPFC devicesinearized power flow equations must be combined withinearized system of equations corresponding to the restetwork. A compact NewtonRaphson power flow algori

s presented as follows:

(X)i = JiXi (30)


hey can be calculated as:

(X) =

Pf

Pt

Qf

Qt

Pft

Qft

PE

,X =

f

t

Vf

Vt

s

p

Vs

(31). Power flow equations of the GUPFC

According to the equivalent circuit of the GUPFC shon Fig. 5the power flow equations can be derived[19]:

f = V 2f Gff VfVpf(Gpf cos(f pf) + Bpf sin(f pf))

n

i=1VfVmi (Gfmi cos(f mi ) + Bfmi sin(f fmi ))

n

i=1VfVsi (Gfmi cos(f si ) + Bfmi sin(f si ))

(33)

Fig. 5. The equivalent circuit of the GUPFC.


Qf = V 2f Bff VfVpf(Gpf sin(f pf) Bpf cos(f pf))

n

i=1VfVmi (Gfmi sin(f mi ) Bfmi cos(f fmi ))

n

i=1VfVsi (Gfmi sin(f si ) Bfmi cos(f si ))

(34)

Similarly, the active and reactive power flows,Pli ,Qli for theGUPFC are

Pli = Real(Vmi Ili )Qli = Imag(Vmi Ili )

(35)

and can be expressed by

Pli = V 2miGii + VfVmi (Gfmi cos(f mi )Bfmi sin(f fmi ))+VmiVsi (Gfmi cos(mi si ) + Bfmi sin(mi si ))

(36)

Qli = V 2miBii + VfVmi (Gfmi sin(f mi )+Bfmi cos(f fmi )) + VmiVsi (Gfmi sin(mi si )

6

theo (b

P

o

P

undc

6.2. Control constraints of the GUPFC

The GUPFC shown inFig. 4, control the voltage at bus-f and active and reactive power flows of lines l1 (betweenbuses f and m1) and l2 (between buses f and m2). Supposethe sending ends of two lines are connected with bus-m1 andbus-m2, respectively. Therefore, the active and reactive powerflows of the two lines at the sending ends are

S l1 = Pl1 + jQl1S l2 = Pl2 + jQl2

. (42)

The voltage constraint of the GUPFC is

Vf VSpecf = 0 (43)

whereVSpecf is the specified voltage control reference at bus-f.In the implementation, the above equality constraint is

replaced by the following inequality constraints

VSpecf Vf VSpecf + (44)

ws of

t

w dr

6p

-vi on-v ctivep viat

ithG

F

w ld dt

Bfmi cos(mi si )). (37)

.1. Operating constraints of the GUPFC

According to the operating principle of the GUPFC,perating constraint representing active power exchangePE)etween converters via the common DC link is:

E= Re(VpfIpf

ni

Vsi Isi

)= 0 (38)

r

E= V 2pfGpf VfVpf(Gpf cos(f pf) + Bpf sin(f pf))

n

i=1VmiVsi (Gfmi cos(si mi ) + Bfmi sin(si fmi ))

+n

i=1V 2siGfmi VfVsi (Gfmi cos(f si )

+Bfmi sin(f si )) = 0. (39)

The equivalent controllable injected voltage source boonstraints are

Vminp Vp Vmaxpminp p maxp

(40)

Vminsi Vsi Vmaxsiminsi si maxsi

. (41)here is a specified very small value.The active and reactive power flow control constraint

he GUPFC are

Pif PSpecif = 0Qif QSpecif = 0

(45)

herei = 1, 2,. . .,n, . . . PSpecif ,QSpecif are specified active an

eactive power flows, respectively.

.3. Implementation of GUPFC in NewtonRaphsonower flow solution

For a GUPFC with one shunt converter andn series conerters, the control degrees of freedom of any of thenwhere= 1, 2,. . ., n series converters are two while the shunt certer has only one control degree of freedom since the aower exchange among then+ 1, series-shunt converters

he common DC link should be balanced.A compact NewtonRaphson power flow algorithm w

UPFC is presented as follows:

(X)i = JiXi (46)


hey can be calculated as


F (X) =

Pf

Pm1

Pm2

Qf

Qm1

Qm2

PE

Pl1

Pl2

Ql1

Ql2

,X =

f

m1

m2

Vf

Vm1

Vm2

s1

s2

p

Vs1

Vs2

(47)

J

Pf

f

Pf

m1

Pf

m2

Pf

Vf

Pf

Vm1

Pf

Vm2

Pf

s1

Pf

s2

Pf

Vs1

Pf

Vs2

Pf

p

Pm1

f

Pm1

m10

Pm1

Vf

Pm1

Vm10

Pm1

s10

Pm1

Vs10 0

Pm2

f0

Pm2

m2

Pm2

Vf0

Pm2

Vm20

Pm2

s20

Pm2

Vs20

Qf

f

Qf

m1

Qf

m2

Qf

Vf

Qf

Vm1

Qf

Vm2

Qf

s1

Qf

s2

Qf

Vs1

Qf

Vs2

Qf

p

Qm1

f

Qm1

m10

Qm1

Vf

Qm1

Vm10

Qm1

s10

Qm1

Vs10 0

0

PE

s1Pl1

s1

0

Ql1

s1

0

wabs usesf ngeb

7

theN 30b beet EE3 ec-t ration4 low-

ing six case studies have been carried out to determine themodels effectiveness:

Case 1. Single TCSC DeviceTo obtain power flow solutions with single TCSCs, param-

eters, such as capacitanceC= 0.00020 pu and a variable in-ductanceL= 0.0150 pu are considered for all cases. TCSC de-vices are installed in branch numbers 2 (TCSC1), 3 (TCSC2),and 6 (TCSC3) as shown inFig. 5 one by one respectively.The range of reactances of the installed TCSCs is appro-priately chosen between70% and +20% of existing linereactances (i.e.0.7X: 0.2X). WhereX is the reactance of

t n ofT

d 6w .18,3 beenm nedl lla-t t-at beenp

thc flowi in-s ine,=

Qm2

f0

Qm2

m2

Qm2

Vf0

Qm2

Vm2PE

f

PE

m1

PE

m2

PE

Vf

PE

Vm1

PE

Vm2Pl1

f

Pl1

m10

Pl1

Vf

Pl1

Vm10

Pl2

f0

Pl2

m2

Pl2

Vf0

Pl2

Vm2Ql1

f

Ql1

m10

Ql1

Vf

Ql1

Vm10

Ql2

f0

Ql2

m2

Ql2

Vf0

Ql2

Vm2

here Pf,Qf,Pm1,Qm1,Pm2,Qm2, are thective and reactive power mismatches at bus-f, bus-m1 andus-m2, respectively.Pf,Qf, Pm1,Qm1, Pm2,Qm2 are theum of active and reactive power flows leaving the b, m1 and m2, respectively. PE is the active power exchaetween the converters via the common DC link.

. Case studies

In order to demonstrate the performance ofewtonRaphson power flow with FACTS devices, IEEEus system is considered. The proposed model has alsoested for multiple and multi-type FACTS devices. The IE0-bus system shown inFig. 6has been used to test the eff

iveness of the proposed model. The system has 6 geneLTC transformers, and 41 transmission lines. The folQm2

s20

Qm2

Vs20

PE

s2

PE

Vs1

PE

Vs2

PE

p

0Pl1

Vs10 0

Pl2

s20

Pl2

Vs20

0Ql1

m10 0

Ql2

s20

Ql2

Vs20

(48)

n

,

he corresponding transmission line in which installatioCSCs are desired.

The real power flows in the line number 2, 3 anithout FACTS devices of the IEEE 30-bus system are 401.47 and 39.36 MW, respectively. An attempt has nowade to control the real power flows in the above-mentio

ines to 50, 28.5, and 40 MW, respectively with the instaion of TCSCs. The value ofXTCSC in both pu and percenge and its corresponding firing angle (final) of the TCSCs

o meet the above mentioned desired power flow hasresented inTable 1.

Table 1shows that if TCSC is installed in line-2 wiapacitive reactance 40% of this line, the real powerncreased from 40.18 to 50 MW. In addition, if TCSC istalled in line-3 with inductive reactance 16.7% of this l


Fig. 6. The IEEE 30-bus system.

the real power flow decreased from 31.47 to 28.5 MW. Sim-ilarly, if TCSC is installed in line-6 with inductive reactance2.8% of this line, the real power flow increased from 39.36to 40 MW.

Case 2. Multiple TCSC devices:Now two TCSC devices are installed in branch numbers 2

and 3 (TCSC1 & TCSC2), 2 and 6 (TCSC1 & TCSC3) and3 and 6 (TCSC2 & TCSC3), respectively. In addition, threeTCSCs are installed in branches 2, 3 and 6 simultaneouslyfor analysis.

An attempt has been made to control the real power flowsin the line numbes 2, 3 and 650, 28.5, and 40 MW, respec-tively with the installation of multiple TCSCs. The valuesof XTCSCand their corresponding firing angles (final) of themultiple TCSCs to meet the above mentioned desired powerflow has been presented inTable 2.

Table 1Power flow results of IEEE 30-bus system with single TCSC

Line no.

2 3 6

13a 24a 26a

final (degree) 48.1 12.68 8.73XTCSC (pu) 0.074 0.029 0.005Compensation (%) 40.0% 16.70% 2.80%Power flow without TCSC (MW) 40.18 31.47 39.36S

Table 2Power flow results of IEEE 30-bus system with multiple TCSC installation

No. of TCSCs

Two Three

2, 3a 2 and 6a 3 and 6a 2, 3, and 6a

2final (degree) 47.57 47.30 44.473final (degree) 6.70 13.07 47.106final (degree) 4.90 10.06 48.00X2TCSC(pu) 0.08 0.083 0.0123X3TCSC(pu) 0.02 0.032 0.0850X6TCSC(pu) 0.033 0.006 0.0750

a Line no.

Case 3. Single UPFC device:UPFC device has been installed on branch number 7 (bus

4bus 6) (UPFC1) and 9 (bus 6bus 7)(UPFC2) one by oneas shown inFig. 5. These devices are installed nearer to buses4 and 6, respectively. The parameters of UPFC device usedin this paper is shown inTable 3.

Table 3UPFC device parameters in pu

Xs 0.02Xp 0.02Vmaxs 0.5Vp 1.0Smaxs 1.0Smaxp 1.0pecified power flow with TCSC (MW) 50.00 28.50 40.00a Bus no.


Table 4Power flow results of IEEE 30-bus system with one UPFC installation

Branch

7 9

46a 67a

s (degree) 36.38 43.25p (degree) 4.71 5.67Vs (pu) 0.053 0.113Power flow without UPFC MVA 34.85 j4.56 22.63 +j2.79Power flow with UPFC MVA 40 j5 30 +j4

a Bus no.

WhereXs, Vmaxs andSmaxs are impedance, maximum volt-

age and maximum apparent power of series injected source,respectively.Xs,Vp andSmaxp are impedance, maximum volt-age and maximum apparent power of shunt injected source,respectively.

The real and reactive power flows in line number 7 and 9are (34.85 j4.56) MVA and (22.63 +j2.79) MVA, respec-tively without FACTS devices. An attempt has been made tocontrol both the real and reactive power flows in the above-mentioned lines to (40 j5) MVA and (30 +j4) MVA, respec-tively with the installation of UPFCs. The control parametervalues ofVs, s andp to meet the above mentioned desiredpower flow has been presented inTable 4.

Case 4. Multiple UPFCNow two UPFC devices are installed in branch numbers

7 and 9 (UPFC1 & UPFC2) nearer to buses 4 and 7, respec-tively. An attempt has been made to control both the realand reactive power flows in the above-mentioned lines to(40 j5) MVA and (30 j5) MVA, respectively with theinstallation of UPFCs. The control parameter values ofVs, sandp to meet the above mentioned desired power flow hasbeen presented inTable 5.

Case 5. Single GUPFC device:A GUPFC device has been installed at bus 15 with com-

m ), re-s erfla e-v e toc ove-m

TP

VPP

Table 6GUPFC Parameters in pu

Xs1 0.02Xs2 0.02Xp 0.02Vmaxs1 0.5Vmaxs2 0.5Vp 1.0Smaxs1 1.0Smaxs2 1.0Smaxp 1.0

Table 7Main results of IEEE 30-bus system with GUPFC installation

Branch

18 22

1512a 1518a

s (degree) 16.58 33.8p (degree) 8.73Vs (pu) 0.032 0.128Power flow without UPFC MVA 18.309 j5.993 6.156 +j1.536Power flow with UPFC MVA 20 j7 7 +j3

a Bus no.

with the installation of GUPFC. The control parameter valuesof Vs ands for line numbers 18 and 22 andp to meet theabove mentioned desired power flow has been presented inTable 7. The parameters of GUPFC device used in this paperare shown inTable 6.

Case 6. Multi-Type FACTS (TCSC & UPFC) devices:Both TCSC and UPFC devices have been installed in

branch number 2 (TCSC1) and 7 (UPFC2) simultaneously.An attempt has been made to control the real power flow of50 MW in line number 2 and both real and reactive powerflow of (40 j5) MVA in line number 7, respectively withthe installation of both TCSC and UPFC. The control param-eters, such as firing angle () of the TCSC andVs, s andp of the UPFC to meet the above mentioned desired powerflow has been presented inTable 8.

Table 8Main results of IEEE 30-bus system with multi-type FACTS installation

FACTS device Branch no.

2 7

13a 46a

TCSCfinal (degree) 48.72 XTCSC (pu) 0.068

U

only connected branches 18 (1512) and 22 (1518pectively and shown inFig. 5. The real and reactive powows in line number 18 and 22 are (18.309 j5.993) MVAnd (6.156 +j1.536) MVA, respectively without FACTS dices shown in Appendix C. An attempt has been madontrol both the real and reactive power flows in the abentioned lines to (20 j7) and (7 +j3) MVA, respectively

able 5ower flow results of IEEE 30-bus system with two UPFC installation

Branch

7 9

46a 76a

s (degree) 25.74 14.83p (degree) 4.79 5.00s (pu) 0.056 0.073ower flow without UPFC MVA 34.85 j4.56 22.63 j2.79ower flow with UPFC MVA 40 j5 30 j5a Bus no.Power flow without TCSC MW 40.18Power flow with TCSC MW 50

PFCs (degree) 23.51p (degree) 3.87Vs (pu) 0.053Power flow without UPFC MVA 34.85 j4.56Power flow with UPFC MVA 40 j5

a Bus no.


8. Conclusion

In this paper, a new generalized current injection modelof the modified power system using NewtonRaphson powerflow algorithm has been developed and demonstrated for de-sired power transfer with the presence of TCSC, UPFC, andGUPFC. To demonstrate the performance of the proposed al-gorithm for multiple and multi-type FACTS devices, differentcase studies of IEEE 30-bus system has been analyzed. Theproposed algorithm is found to be efficient and robust due toits independencies towards the system size and initial startingconditions of the FACTS devices.

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Power flow control and solutions with multiple and multi-type FACTS devicesIntroductionPower flow equationsBus admittance matrix (Ybus)Two-port network implementation

Load flow procedure with facts devicesBased on the admittance matrices of the network elements.Based on the injection power of the network elements

Power flow equations of the TCSCOperating constraints of the TCSCImplementation of TCSC in Newton-Raphson power flow

Power flow equations of the UPFCOperating constraints of the UPFCImplementation of UPFC in Newton-Raphson power flow solution

Power flow equations of the GUPFCOperating constraints of the GUPFCControl constraints of the GUPFCImplementation of GUPFC in Newton-Raphson power flow solution

Case studiesConclusionReferences

Documents

Power Flow Control and Solutions With Multiple and Multi-type FACTS Devices