Optimal Placement of Facts From Dynamic Performance Viewpoint

Copyright © IFAC Power Plants and Power Systems Control, Seoul, Korea. 2003

PUBLICATIONS www.elsevier.com/locate/ifac

OPTIMAL PLACEMENT OF FACTS FROM DYNAMIC PERFORMANCE VIEWPOINT

Motoki Yanagitani*

Ryousuke Shizawa Toshiya Ohtaka

Shinichi Iwamoto

Dept. ofElectrical Engineering and Bioscience, Waseda University, Tokyo. Japan

Abstract: UPFC, which is one of the FACTS devices, can control transmission line reactances and phase angles. In this paper we propose a method for determining the optimal allocation of UPFC devices. In this method, for a multi-machine power system first through numerical simulations severe fault conditions are found. Then a UPFC device is allocated to different buses and behaviors of the control inputs under the severe fault conditions are studied. The less control effort for the system equipped with UPFC means the most efficient UPFC allocation. The effectiveness of the proposed method is shown using a four-machine eleven bus power system model. Copyright © 2003 IFAC Keywords; power system, FACTS, UPFC , transient stability, optimal placement

I.INTRODUCTION Recently, because of the difficulty of constructing new transmission lines, long-distance and large-capacity transmissions have been unavoidable. This may cause transient/voltage stability problems and loop flow problems that are not desirable in mesh systems. In 1988, Electric Power Research Institute (EPRI) of the United States, proposed a novel concept of a transmission system called FACTS (Flexible AC Transmission Systems) as one of the solutions to such problems. FACTS introduces the modem power electronics technology into the AC transmission system, and regulates bus voltages, line reactances and phase angles of the transmission systems fast and flexibly. It can greatly increase transmission power and load flow control capability, enhance power system stability, and damp power oscillations. ----_._---

*

Motoki Yanagitani is presently with RECRUIT Co, Lld, Japan.

So far, a variety of FACTS devices have been researched. UPFC (Unified Power Flow Controller) is one of the excellent FACTS devices. It can control both the power transmission line reactances and the phase angles in high-speed, and it is field-tested in an electric power system of the United States. Originally, FACTS devices have been developed to control the power flow fast and flexibly. However, using the FACTS devices only for power flow control does not make the best use of the high speed of the FACTS devices to its maximum usage. Therefore, a lot of studies, which used the FACTS devices for transient stability came out. Moreover, the optimal placement problem can come out when FACTS devices are installed in an electric power system. In most of the latest studies about the optimal placement of FACTS devices, aims of the optimal placement are the overload elimination, steady state stability and voltage stability. These are optimal placement examples where the merit of FACTS devices which has the high-speed control performance is not employed fully.

1121

Busi

It is desired to tackle the optimal placement

problem using FACTS devices for power system stabilization control. In this paper, it considers applying FACTS devices to system stabilization first. UPFC is applied to system stabilization as typical FACTS device. As the procedure, first, the equivalent model of the FACTS devices which is needed in the case of the transient stability analysis is created, and a linearized model of a power system is obtained based on it. The optimal control theory (LQR) is used as the control technique. Next, we propose an optimal placement method of FACTS devices for transient stability. This is the optimal placement method considering stability aspect and the financial aspect (efficiency aspect) at the time of using FACTS devices for system stabilization. In the actual situation, no effective index about transient stability exists. Then, in this paper, the amount of changes of the generator phase differences and the amount of changes of the control operation variables of FACTS devices at the time of carrying out system stabilization are used as the index. When there are few amounts of control operations or few amounts of changes of generator phase differences at the time of using FACTS devices for system stabilization, it will be judged that it is an excellent installation location for economical aspect (efficiency aspect). As a procedure, first, FACTS apparatus is installed in all the places in the system, and all the faults considered in each of the installation place are examined. The optimal location place is selected to measure the amount of control operations of the FACTS devices and the amount of changes of generator phase differences to all the faults.

VjLO j Transmission Line

Series Transformer

I

u~~~8~ I

.'L.

---,N--j' GT~.GTO

'.1

[~~~_~on~r~;~:J Fig.1 OutlineofUPFC UPFC is a FACTS device which can apply the voltage VuLo u with an arbitrary magnitude and a phase shift angle for the transmission voltage to control the secondary voltage of the series transformer using the voltage generated by the self-excited inverter. Moreover, UPFC applied voltage VuLou is controlled with the power converter. However, UPFC controller receives the limitation according to the converter characteristics. In this paper, UPFC is assumed to impress the voltage VuLou with arbitrary magnitude and phase shift angle on the bus voltage at bus i. 2.2 Formulation o/power system with UPFC First, the differential equation of the generator is given by (1)-(8). (I) (2)

•.

£"(0

=

_£-,,1""'(':....)-_£2-'~(c.:.')_-_(:-X":'''''-'(''_-_X----=.:~(c.:."_)/..:.,,,,-,-(,)

(4)

EI"u, =

2. SYSTEM STABILIZATlON CONTROL USING UPFC 2.1 UPFC (Unified Power Flow Controller) UPFC is one of the FACTS devices which can control the power transmission line reactances and phase angles in the transmission electric power component in high speed. Fig. I shows the outline of UPFC. UPFC has a parallel transformer, a series transformer, and a self-excited inverter of the GTO (Gate Turn OffThyristor) control.

TaU}

0(" : phase angle [rad] E~(q :

(j)u, : generator speed Cpu]

internal voltage Cpu] E #1(') : field voltage Cpu]

Idu"I.(,)

: generator current [pu]

Vd(o)' V.("

: terminal voltage Cpu] : magnitude of terminal voltage Cpu] : active power Cpu] : nominal generator speed [rad/s] : mechanical input Cpu] : inertia constant [sec]

V,", P'(o)

(j)" Pm ("

M("

1122

(3)

T Jo(i)

DI .)

:

damping [pu]

X d(i) , X ,('1 : synchronous reactance [pu] X~(il

: transient reactance [pu]

'do(i)

:

time constant of rotator [sec]

:

initial value of V. li ) [pu]

E[dOli)

:

initial value of E«I(i) [pu]

K all }

: AYR gain [pu]

'a(i)

:time constant ofAYR [sec] h(i)' W(i)' E;(i)'

..,

= It;;,tJcli."E;,,) +(X",,- X~,,,)SIi.,/,,,,1

and E fdli) are determined depending on I dli) and I,ll)' Then, the generator current considering UPFC

{hp}

effect is derived. Generally, the terminal voltage of the n-machine electric power system is given by (9). -

. • • -

~i.')

V=eJ'E,-jXdl+(X,-Xd)e'

;:

¥;i,.)ej;'··'J

5,.,.) :; sin ( - t5(i) + 15,,) + ~Ii,') ) C,..•) :; cos( - I5Ii) + 15", + ~Ii,') )

-j(~-4)

•

It;.,kJS(i,k}E;(k) + (X,(k) - X~(k)CIi .• /,,,) I .-,

(bp)

V. OI .)

From (1)-(8), it is understood that

=

1.(9)

SUlil :; sin( -15(1)

if

: terminal voltage (row vector, phasor)

1

: generator current (row vector, phasor)

From (14) and (15),

E; ,I, : row vector, phasor e j6 , X~ , (X, - X~) ,ejlx/2-6) : diagonal matrix

We assume that UPFC is installed near a generator p. The UPFC output Vu L t5 u is impressed on the terminal voltage of the generator p. Therefore, the terminal voltage considering UPFC effect changes from (9) into (10). -

-

-

v+Vu =ejJE;-jX~/+(X,-X~)e

v;, :; [0

.. . 0 VU~dv

'

1,+vu(lO)

0 ... 0] T

The generator current considering UPFC effect is given by (11 ).

(11)

-

•

-

•

Y:; (r."

+ jX~

I(~-J)

V

i

considering UPFC

2.3 UPFC output calculation method

This chapter shows a method of calculating the Vu L t5 u . In this paper, the UPFC output discrete-time linear control theory is applied to the control of the UPFC output VuL t5 u . From (14) and (15), the UPFC output magnitude Vu has strong correlation with Generator p current I dIp) , I,IP) .

Vu

is

is calculated by

deviation of

_

u

I, + YVu (12)

I dIP) , I.IPI ),

M dU ,M,u

(infinitesimal

and 0 u is calculated by /1 t5

(infinite simal deviation of

hIP)'

Thus, the continuous-time linear system equation for the UPFC control system design has been obtained. When (1 )-(8) is approximated linearly (taking an infinitesimal deviation), the continuous-time linear system equation is obtained shown in (16).

f'

From (12), generator

I,(.}

And, UPFC output phase shift angle h u is strong correlation in Generator p phase angle h CP )' Then,

Y. : reduced admittance matrix When (10) is substituted into (11) and eliminated, (12) is obtained. -

Id(i)and

effect are determined. By solving equation (1)"'-(8), (14), and (15) , the dynamics of the generator can be obtained. However, the initial values of phase angles, angular velocities, internal voltages, and field voltages must be obtained by power flow calculations. In addition, we have to give UPFC imputs during the simulation period.

-j{::'-4J-

(; .. p)

1= Ye/DE, + Y(X, - Xd)e'

+~Ii,P) +I5'Ii} ) CUIi} "cos( -t5'i} +~Ii,P) +t5",} )

current is given by (13).

x(t) = Ao x(t) + Bo u(t) { yet) = Co x(t) + Do u(t)

(13)

(14), (15) are obtained when (13) is changed in the d-q coordinates and decomposed into the d and q axis elements.

1123

(16)

1,(1) : magnitude of generator current [pu]

Ao , Bo , Co , Do : matrix

That is, if the simulation is performed for t seconds, let the integrated values of the UPFC outputs for t seconds be an index. However, there are two control operation variables (Vu and L 0 u) as described in Chapter n. In order to take into consideration both these two operation variables, in this paper , we define this index as

determined by

x(O),u(O),y(O)

Eq. (16) can be converted into a discrete-time linear system equation (17), and the digital control theory shown in chapter 4 can be applied. Then, the UPFC output Vu L 0 U is determined. Concretely, the UPFC output Vu L 0 U is obtained from (18), (19).

(21 ) x[i+I]= Ax[i]+Bu[i]

(17)

{ y[i] = C x[i] + D u[i]

where R

is a suitable coefficient (22)

(18) (19) VdO(P) '

V.O(P) '

3.3 Optimal placement procedure

The features of each index Table 1.

V,o: initial value

3. OPTIMAL PLACEMENT OF UPFC FOR TRANSIENT STABILITY In this paper, we use two indices for optimal placement of UPFC in consideration of transient stability. They are the amount of changes of the phase differences of the generators and the amount of changes of the UPFC outputs at the time of stabilizing the system using UPFC. These two different indices can select the optimal location based on different purposes, namely, the stability aspect and the efficiency aspect (financial aspect). How to find each index is shown below. 3./ Amount ofchanges ofphase differences

The amount of changes of the generator phase differences is calculated at the time of stabilizing the system using UPFC in the n-machine power system. That is, if the simulation during t second is performed, the integrated value of the generator phase differences for t seconds is calculated for all generators. Let maximum among

!5

_ 1 n

dt be an

index for this fault. In this paper, we define this index as (20)

3.2 Amount ofchanges of UPFC outputs

The same as Chapter ill. i , the amount of changes of the UPFC outputs is calculated at the time of stabilizing the system using UPFC.

Table I

IS

summarized in

The features of each index

index

Features Select

place

Ihe

where ~ amount

Sge

amount

ofchanges

of the place which is

of cltcellent for stability aspect

generator phase

Select the place where amount of control operations SUPFC

of UPFe is

smallest

the place which is

--.

excellent for efficiency aspect (financial aspect)

*It is a severe fault when each index is large, and it is

mild fault when each index is small. An optimal location selection procedure is shown based on this index. where generator end -+ fault point -+

Selection procedure Step I. UPFC is installed at the generator end i. Step 2. A 3- phase to ground fault is caused at each bus near the end j. I in 2 circuits is opened, and re-closed after I sec. The value of each index during that time is calculated. Step 3. step I. ~step 2. is repeated J times. maximum among each J index is defined as Step 4 M4X(Sge(i,j» M4X(SuPFc(i,j» Step 5. Step I. ~Step 4.is repeated I times. Step 6. minimum among each I index is defined as M/N(M4X(Sge(ij))) MIN(MAX(SuPF({i,j») step7. let the installation place i MIN(M4X(Sge(ij») MIN(M4X(SuPFc(ij))) be the optimal allocation.

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4. SIMULATION

From Table 2. we can select the severest fault point in each generator end. The result is shown in

4.1 System stabilization simulation

In this chapter, a 4-machine I I-bus power system model with UPFC is used which is shown in Fig. 2. It is assumed that the UPFC output is impressed on bus 4 (terminal voltage of Generator I). As shown in the figure, fault points are ten places of A - J points. In each case a three-phase to ground fault of one line in double circuits transmission lines occurs. The faulted transmission line is opened after lOO [ms], and reclosed after I [sec).

Table 3. Table 3 III

the severest fault point and index Sge . ta11ed III . eac h generator en d . case UPFC·IS illS installed at generator I end

installed at generator 2 end

installed at generator 3 end

installed at generator 4 end

Severest fault

C

J

D

I

Sge

24.6314

26.7798

24.3555

25.1390

The installed point which have the smallest index Sge in Table 3 is the best point for stability aspect. Therefore we can conclude that the optimal location of UPFC from the viewpoint of stability aspect is generator 3 end.

UPFC

4.2.2 When index SUPFC is used Index values for each fault are indicated in Table 4.

Fig.2

Table 4

4-machine I I-bus power system model with UPFC

4.2 The optimal placement of UPFC in consideration oftransient stability 4.2.1 When index Sge is used Index values for each fault are indicated in Table 2.

Table 2

\

index S'Ile for each fault (rad)

installed at

installed at

installed at

installed at

generator I

generator

generator

generator

end

2 end

3 end

A

21.2083

22.1371

21.6837

21.7314

B

20.9981

22.0701

21.6249

21.6544

C

24.6314

23.5549

24.3132

24.1200

D

24.5678

23.4141

24.3555

24.3465

E

20.3493

23.4928

21.5691

21.4972

F

20.3648

24.1168

21.5729

21.5088

G

20.8041

24.8649

22.4332

22.6239

H

20.8376

25.2153

22.7620

22.8856

1

23.7183

26.1179

23.7509

25.1390

J

24.1707

26.7798

23.8763

24.1253

4

end

1\

index SUPFC for each fault(R= 1.3266)

installed at generator

installed

installed

at

at

installed at

generator

generator

generator

2 end

3 end

4 end

I end

A

1.2311

1.4286

1.9663

1.8959

B

1.1284

1.3883

1.7929

1.7583

C

2.0477

1.5338

1.4478

1.7627

D

2.1958

1.5843

1.7708

2.6710

E

0.8101

2.6543

1.3563

1.4401

F

0.8028

2.8989

1.3284

1.4125

G

2.0905

2.9959

2.0322

2.0635

H

2.1031

3.0361

2.3842

2.3020

I

1.6562

2.9999

1.6458

2.2825

J

1.8821

3.0794

1.7596

2.2461

From Table 4 we can select the severest fault point in each generator end. The result is shown in Table 5. The installed point which has the smallest index SUPFC in Table 5 is the best point for efficiency aspect (financial aspect). Therefore we can conclude that the optimal locatin of UPFC from

1125

the viewpoint of efficiency aspect (financial aspect) is generator 1 end.

installed at generator I end

installed at generator 2 end

installed at generator 3 end

installed at generator 4 end

Sge

24.6314

26.7798

24.3555

25.1390

5. CONCLUSION In this paper, an optimal placement method of UPFC in consideration of transient stability has been verified. When choosing the optimal location based on different indices, naturally different results are obtained. Therefore If a diffrent index in consideration of the index other one than the one used in this paper, for example, steady state stability, voltage stability, etc. is used, a different result will come out. However, it is shown, even if it takes two or more indices into consideration, the installation place which was excellent to two or more indices can be selected by changing the priority. If the purpose is narrowed down to one, the optimal location can be selected easily. However, various elements are entangled intricately in an actual power system. Therefore, in case the optimal location is selected, it is thought that elements, such as the stability aspect and the financial aspect, become entangled. It is thought that the proposed method is having a useful approach to solve the electric power system planing problem containing FACTS devices.

SUPFC

2.1958

3.0361

2.3842

2.6710

REFERENCES

Table 5 Severest fault point and index SUPFC . eac h ~ enerator end case UPFC"IS Insta 11ed In

in

installed at generator I end

installed at generator 2 end

installed at generator 3 end

installed at generator 4 end

Severest fault

D

H

H

D

SUPFC

2.1958

3.0361

2.3842

2.6710

4.2.3 When both Sge and SUPFC are used.

Table 3 and 5 are collectively shown in Table 6. Table 6 Severest fault point and index Sge SUPFC Incase UPFC"IS Insta11 ed'In eac h generator en d.

O.Kunitomo, H.Satomura, S.Iwamoto (1998). From Table 6 , index Sge in the case UPFC is installed at generator 1 end is small to the second, and index SUPFC in the case UPFC is installed at generator 3 end is small to the second. Installing at generator I end is good to second for index Sge , that is, it is good to second in consideration of stability. At the same time,it is best for index SUPFC , that is, it is best in consideration of efficiency side (finansial side). Installing at generator 3 end is best for index Sge , that is, it is best in consideration of efficiency side (finansial side). At the same time,it is good to second for index SUPFC , that is, it is good to second in consideration of stability. From the above If it is installed at the generator end I or 3, it is good

A Study on Robust control using FACTS devices

(in Japanese), Trans. ofIEEJ, pp.288-289, 1998 M.Yanagitani, A. Sanai Sabzevary, TOhtaka, S.Iwamoto (2001). A Study on Optimal Placement of UPFC in Power System (in Japanese), IEEJ, PE-01-28, PSE-01-22,

2001 A.Kurita (1993).

for both index Sge and SUPFC . That is, the differences is whether the priority is given to efficiency aspect (financial aspect) or stability aspect.

1126

FACTS vision proposed by EPRI -Fundamental Surve and Numerical Study- (in Japanese).

CRIEPI survey report, T92020, pp.I-36, 1993 Y.Sekine (1984). Power System Transient Stability Analysis (in

Japanese),Ohmusha TKouno, TNkajima, A.Yokoyama (1999). Power System Damping Enhancement using Unified Power

Flow

(in vo1119-B No.3,

Controller(UPFC)

Japanese), Trans. of IEEJ, pp.344-353, 1999