Load Flow Calculation for Flexible AC Transmission Systems

Copyright © IFAC Control of Power Systems and Power Plants, Beijing, China, 1997

Load Flow Calculation For Flexible AC Transmission Cheo Liyi

Pu Tiaojiao

Li Linchuao

Doog Lei

Syst~ms

Kang Xi

Dept.oj Electrical Engineering and Automation Tian Jin University Tian Jin 300072

Abstract: In this paper, a comprehensive mathematical model of load flow for Flexible AC Transmission Systems (FACTS) with Unified Power Flow Controller (UPFC) is presented basing on the analysis of basic principle and operation states for UPFC. The model can use fast P-Q decoupled load flow method. Examples of test system show that the proposed model and method have good convergence. An effective tool is provided by the load flow computer program to analyze the load flow and calculate initial value of dynamic state for FACTS with UPFC. Copyright © 1998 IFAC Keywords: FACTS, UPFC , Load Flow Calculation

flow and dynamic state performance of power system, it is quite necessary to study the load flow mathematical model and algorithm of FACTS with UPFC.This paper presents a synthetic load flow calculation model and algorithm of FACTS with UPFC. The load flow model applies a general ex-pression to describe varieties of UPFC functions and any combination of them, in which the fast P-Q decoupled method can be used with the advantages of fast convergence and saving memory.

I. INTRODUCTION In the last of 1980's, Electric Power Research Institute (EPRI)of America first proposed a novel transnusslOn system called Flexible AC Transmission Systems (FACTS) (Hingorani, 1988), which introduces the modem power electronic technology and modem automation control technology into the AC trans- mission, and regulates bus voltage, line impedance, phase angle of the transmission systems fast and flexibly. It can greatly increase translnitted power and load flow control capability, enhance power system stability and damp power oscillition. Later, many kinds of FACTS devices have been presented in the literatures(Gyugyi, 1992: Ledu. et a\. , 1992), such as Thyristor Controlled Static Var Compensator (SVC), Thyristor Controlled Series Compensation ( TCSC), Thyristor Controlled Phase Shifter (TCPS) and Unified Power Flow Controller (UPFC). In particular, UPFC can concurrently or selectively act as SVC,TCSC,TCPS, not only greatly reduce device cost, but also improve devices operating flexibility. So UPFC is the universal and most effective device of FACTS equipment with a perfect application perspective.

2. BASIC PRINCIPLES OF THE UPFC The UPFC consists of a shunt transformer T,h ' Inverter 1, Inverter 2, Controller and a series transformer Tse' as shown in Fig. 1.

In order to analyze the influence of UPFC on load

Fig. I

203

The basic structrue ofUPFC

Inverter 2 provides an injected AC voltageE", in series with transmission line via series transformer T" Under controlled by the controller, the

•

l;

/110

= k sh

•

V 1 eJ/J

The additional injected poewer of node k, I are:

transmission line impedance and two terminal voltage magnitudes and phases can be changed by

.

adjusting E.. . The current flowing through T

. Where 8., 8 1 is phase of

second coil equals transmission line current j jJ. So the power of UPFC injected line is determined by

it., it I

respectively,

8/t1=8. - 8 1

I

From equation (4), the additional injected real and reactive power of node k, I can be obtained as :

E..

and transmission line current j jJ , whose real power is provided by Inverter 1 via its DC output terminal. From this point of view, Inverter 2 can be taken as a comprehensive device which can act as voltageregulating, series compensatng, phase shifting and any com- bination of them. Except for providing real power to Inverter 2, Inverter 1 can generate reactive power to system or absorb reactive power from system. Therefore, Inverter I can be take as a controllable shunt static Var compensator.

Pt,k = kIloV/cosP-k..V:gjJcosa +k..V/b/tlsina Qt,k = -kIloV.l sinp + k..V: gjJsina + k.,V.1bjJcosa P4J = k.,V.~g~os(8jJ +a)-k..V.Vp/tlsin(8jJ +a) Q4J = -k.. V.~gjJsin(8jJ +a)-k..V.VP/tlcos(8jJ +a)

(5)

Equation (5) is the general expression of additional injected power in load flow calculation for FACTS with UPFC. For different functions of UPFC ,the corresponding control variables k", kilo' A., P are different.

3.1 The UPFC functions as series compensator

3. MATIffiMATICAL MODEL OF THE UPFC

In this case , corresponding phasor diagram is shown in Fig3. .

The equivalent circuit of UPFC shows in Fig.2 .

ikJ i v., z ~ ~ k-. 1 V ~-I Vi

CP /~ (a)

k~1 \f)Jm

~

Fig.3

Series compensation phasor diagram

1".

=

If the degree of compensation is s, then (b)

(c)

Fig. 2. The equivalent circuits ofUPFC

kilo =0

(6)

p=o

(7) (8)

k .. =sxjJ fjJ/V.

a. =rt!2-( 8. - ~jJ)

Based on voltage source and current source quivalent transfer theory, Fig. 2(a) is equivalent to circuits in Fig. 2(b) (c). Fig. 2.(b) shows the circuit represented by equivalent current source. Fig. 2.(c) shows the circuit represented by equivalent injected power.

Since

. =ljJ L tPjJ =(V.. -VI)/ .

]jJ

+ j (l-s) X

jJ'

(9) Zlds'

where ZMI = RjJ

k.re and a. can be obtained.

3.2 The UPFC functions as shunt var compensator The equivalent injected current of two tenninal node k , I of transmission line are respectively:

. Given shunt Var compensation capacity is Q., then the control variables are k., =0

(1)

Where

. . Is<

.

= E" / Z jJ = E", ( gjJ + bjJ )

(2)

0.=0 kilo =Q. /

(3)

P=~2

Defining:

204

v.

1

(10) (1) (12) (13)

(21)

3.3 The UPFC functions as phase shifter 3.5 The UPFC functions as multi-funcations

In this case, the corresponding phasor diagram is shown in Fig. 4.

In this case, the corresponding phasor diagram is shown in Fig6.

Fig.4 Phase shifter phasor diagram If given phase shift angle is a .then a. = 1[/2

(14) (15)

k,. = tg8 E s< contains the component in phase with

Phasor diagram of mUlti-functions

Fig.6

Given that series compensation degree is s, terminal voltage regulating coefficient is k" phase shifting

j" , so

Inverter 2 exchanges real power with transmission systems. The exchanged real power is provided by inverter I , that is ,

angle is

. E

se

e , shunt Var compensation capacity is

Qc'

is composed of series compensation voltage

Re(-Vi ISh)=Re(E,. I,,) , also since Im(V. Ish)=O,

component Vs, tenninal voltage regulating voltage

from this,

component V. , phase shifting voltage component Ve , that is

.

km = -k~g" - k,.g"V. I ~sino"

.

Vi

Es<=k" ~=O

eJa =Vs+V.+Ve

(22)

Where by define

(17)

V. =ks Vi eja'l

V =k Ve Jaja.

3.4 The UPFCfunctions as voltage regulating

. . Vg = kg V e . •

•

(23)

i

t

In this case , corresponding phasor diagram is shown in Fig.5 .

From above derivation, k. =k,

a. =0

.

kg =tgO

V.

(24)

ag =n/2

ks =sx"I" IV. as =n/2-(8c rPiJ)

.

Where IiJ

Fig.5 Phasor diagram of voltage regulation

. . .

= IiJLrPit=[(l+k,)Vt+Vg-VJj I Zkjs ,

From

this equation ltiJ and rPit can be obtained. Byequations (22) and (23) k se and a. can be determined. In

Given that terminal voltage regulating coefficient is k,. then

•

A

•

A

additon, since Re( - V t Ish) = Re(E I iJ) and s<

0.=0 k" = k,

(18) (19)

ImcV

Jsh) = Qc, so k sh and ~ can be calculated.

Up to here, control variables k", km' a., ~ all can be determined under any function of UPFC. Substituting these control variables into equation(5), the additional equivalent injected power of UPFC as varieties of functions can be obtained.

Similarly with phase shifter function, existing Re( - ViI sh )= Re( E,. I,,), also since •

i

A

Im(Vi Ish)= 0, so km = (l + k,)k,g" - k,g,,~ I V.coso""

(20)

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4. LOAD FLOW CALCULATION OF FACTS 5. EXAMPLES ANALYSIS Load flow calculation of FACTS can use fast P-Q decoupled method. considered the additional injected power of equation (5) as additional injected power of node k, I with UPFC, then the equations to be solved in power flow calculation of FACTS are [M] = [Ps + Pb - P(V,b"}] } (25) [~Q]=[Qs +Qb -Q(V,b"}]

r

where

i=k i=I

Pbi = P;

Qbi=

i:t: k, i :t: I

t"Q;

i

The examples of this paper are the EPRI of china test system I, 11. When UPFC is placed in a transmission line, the convergence of the power flow calculation is very well using the method presented by this paper, the convergence and calculation accuracy are in the same levels compared with the traditional P-Q decoupled method.

=k

Several cases for placing UPFCs in different transmission lines are tested, and good convergence and corrected results are obtained.

i=l i :t: k, i :t: I

6, CONCLUSIONS

Using Newton-method to solve the power flow equation (25), then the iterated equations are

M] [H'J' N'L' ] [~V/V M ] [~Q =

Where H'=H+Hb

H = iP(V ,b") / ab"

Hb = iPb / ab"

N'=N+N b

N =iP(V,b") / bY

J' =J +Jb

J = i5Q(J/ , b") / ab"

Nb =iPb / bY J d =i5Qd / ab"

L'=L+Lb

L = CQ(V ,b") / bY

Lb =CQb / bY

Since V; "" Vj

,

COSO jj

""

1,

(1) The method proposed in the paper can unified represents FACTS power flow equations of varieties ofUPFC functions.

(26)

(2) The power flow equations can conveniently use fast P-Q decoupled to calculate the FACTS power flow with many UPFCs under varieties of functions, also suited for calculated power flow of traditional AC transmission system. (3) The calculated results of example systems show the method proposed in the paper all have good convergence for FACTS power flow calculation of FACTS under varieties of UPFC functions with wide range of control parameters.

X ij then

'ij«

To seris compensation function 5

H w = H tJi = Lw = LtJi = bkJ Vt ' 1-5

ACKNOWLEDGMENT This research was supported by NSFC (59477017).

To phase shifting and tenninal voltage regulating function , considered phase shifting angle e and terminal voltage coefficient k, are relatively small,Therefore, H b , N d

,

Jd

,

REFERENCES

Lb can be neglected

Hingorani N.G. (1988). High Power Electronics And Flexible AC Transmission Systems, IEEE Power Eng.Rev, pp.2-3. L. Gyugyi(l 992). Unified Power Flow Control Concept For Flexible AC Transmission systems, IEE proceedings, Vol. 139, No. 4, pp.323-331. A.Ledu, G.Tontini,M.Winfield(1992). Which FACTS EqUipment For Which Neeil? CIGRE paper, 14/37/38-08, pp. 1-7. Wu Shouyuan, Zhou Xiaoxin,et al, (1995). Steady State Analysis And Load Flow Calculation Of Unified Power Flow Controller In Power System, Power System Technology, Vol. 19, No. 4, pp. 1-7.

in power flow calculation . To multi-functions of UPFC, in terms of the above analysis, only need to consider Hb andLd of series compensation function. Taking fast P-Q decoupled method, the iterated equations in power flow calculation are as following: [M /V]<'o = [B' +B~]~c:5'K)V(K)1 [~Q / vt·} = [B" + B~1~V(K) O(K+I) = c:5'K) _ ~c:5'K)

(27)

V(K+I ) = V(AI _ ~V ( X)

Where B'

""*

B"

""*

=

=

B'

tJi

B"

tJi

= _5_ b

E'

= _5_ b

B"

J-s kJ,

1-5 kJ'

=

diJ

B' .ut

diJ

=

B" .ut

= __5_ b

J-s kJ

= __5_ b

1-5 kJ

In the above, the determining correctly of

B~

and B~'

make iterated calculation have good convergence, and total computed time be small.

206