627

Mechanical quantity Rotor coil mechanical torque T w m ] Angular velocity o [rads] Moment of inertia

J [ k n . mil

FAULT TRANSIENT CALCULATION ON CONDITION OF SYSTEM SWING AND ANALYSIS OF RELAYING PROTECTION

Electrical quantity

current I[Al

Node voltage u[V]

Capacity over the ground CIF]

[I 1 Department of Elcrtrical Engineering, Tiinghua Univertity, China 121 Ikpartmrnt of Electrical Engineering, Tianjin University, China

INTRODUCTION and complicated, so we ignore it in this paper.

The characteristic of relaying protection on condition of system swing is one of important problem in study of relaying protection. Digital simulation is widely used to study relaying protection, such as EMTP (Electromagnetic Transient Program)"I. Data resource provided by transient simulation is not collected form power system, but if the accurate model is used, the transient process of power system can be simulated exactly. But because changes of frequency and angle are ignored in the electromagnetic transient program, the complicated transient on condition of system swing cannot be calculated

For calculating changes of frequency and angle, the new electromagnetic model of synchronous generator need be built. Considering the salient-pole reaction, stator coil transient and rotor coil mechanical characteristics, the united synthetic companion model of synchronous generator is built by integrate the electromagnetic transient, mechanical transient and port equation of synchronous generators. Based on the spectral analysis, the modified Euler model can not only avoid oscillation of numerical calculation hut also improve the simulating accuracy. The fault electromagnetic transient on condition of system swing is simulated by synthetic companion model of generator. Distance protection element of LFP-901A, the transmission line protection, is taken for example to analyze action of the protection and its swing block component on condition of system swing.

BASIC PRINCIPLE

The equation of synchronous generator is described by dqO coordinate system. The relationship between each several part is showed in Fig.1 (a). In this paper, We use the method of analogy to unite electromagnetic parameters and mechanical parameters, and use synthetic companion model to build the model of partition between broken line. Using the method, without pre-comection, the simulating accuracy is greatly improved and the interface between generator and system is simplified. We call it "companion model in step" which can be calculated with net in step (show in Fig. 1 (b)). The time constant of control system is bigger

The constitution of generator

- I

Elecbic conductance I/R[S] [ N d r a d ]

SYNTHETIC COMPANION MODEL OF GENERATOR

We'll calculate axis d parameters of synthetic companion model as example. The equivalent circuit and companion model of axis d is showed in Fig.3. We make

di =(,I., - M , ) . P + ~ , R , + w y l , + l l d differencing, and dt

assume that flux linkage does not jump in o,l.v w-4

0 2004 The Institution of Electrical Engineers. Printed and published by the IEE, Michael Faraday House, Six Hills Way, Stevenage, SGI 2AY

628

1

U

I Fig.2 The companion model of axis d

1 I 2 (1)

] ' i d . " * , +pv,.. +-*"V,."+, 2(L, - M d )

Us,.*, = [Rd +

+%'Vq."+[Rd- W - M d ) ] . .

Id." '5 ," +('d.n + U d , m + , ) h

Assuming AS = S,,, - S, , the equation is

ug, .+ud = ~ ( [ c o s 8 , . c o s ~ - s i n 8 , . s i n ~ ] . u , , ,

+[cos($. --a). cos --sin(@, --a) -sin -1. ug,"

+[cos($, +-a). cos -- sin($, +-a). sin -1. U,,,}

2 A 6 A e 3 2 2

2 A@ 2 A 0 3 2 3 2 2 ' A O . 2 A 0 3 2 3 2

(2)

+-[cos(- e"+, +e") .un."+, +cos(I-?---x).ug,",, e +e 2 3 2 2 3

0 +e 2 +cos(- +Tx)%+,l

We assume: (a) ,8=8 (Becauseof A#-0)

(b) S,,, =S, +w,h.

Equation ( 2 ) can be change as follow:

2 2 2 2

2 e -e, ud,"+ud =-([cad" .(1-8,,,-8,)-sinsn

+LcOs(en --=I . ( I -8,,,-8,

+[COS(Q" 2 +-a).(- Q"4 -e")-sin(Q" +--71).p O"4

3 2 2 2

3 2 )-sin(em --n) 3 .S,,,-S,]. 2 (3) 2

3 2 3 2 2 o h oh 2

a 3 2 2 3 . +-[cos(8, +A). ua."+, +COS(O" + A --a) 'U*,",,

+cos(S, +I +-a). U,,",,]

Where = ub = U,, U < = u4

o h 2 2 3

We combine equation (3) with (1) and assume o = U,, 6 = u 8 . The parameter can be obtained by:

',,"+I = GdUS,n+l + 'd

The equivalent electric conductance is:

COMPENSATORY METHOD OF JUMP QUANTITY BASED ON SPECTRAL ANALYSIS

When we analyze power system, whatever voltage or current waveforms of elements are, they must have their spectral characteristics. According to these, we can analyze errors of jump models and calculate whole error by principle of superposition. We assume voltage and current of elements as follow.

629

i, = In sin( of + p,)

in+l = I , sin(wt + pi + O H )

U, = U , s i n ( w f + p u ) u . , ~ = U , sin(wr + p, + O H )

(6 )

If we combine equation (6) into jump mode, model calculation error of frequency w will be given by its mismatching quantity. When energization has many frequency components, each frequency component can add to calculate compensatory error.

As we all know, the backward Euler method can avoid oscillation of numerical calculation, so it is usually used in calculation ofjump quantity But its truncation error is too great and needs to be compen~ated[~I.

The equation of branch RL is L! !=~-R , . Its

model of the backward Euler method is shown as follow. df

. . (7) L+1 -5 - L-- %+I -%+I H

Combining equation (6) into (7), we gain (8): LI Left = A [ s i n ( W i + p, + O H ) - sin( of + p,)] H

_ . 2 sin -cos( wf + pi + -) H 2 2

- L I , OH OH -

di ~

= OH ., . OH "+- (?) sin-L-

2 di

We can conclude from equation (8) that each side of the model built by the backward Euler method is not balanceable with another. It is caused by calculation method instead of excitation source. If we match both sides of equation, the calculation method can be modified. It is known by analyzing system that the frequency of voltage and current only holds definite frequency band and there is only one main frequency. If we calculate the main frequency, the whole error can be reduced. Assuming that the main frequency is w,(SOHr or 60Hz), we modified the equation.

(9)

~ c o s ~ . ( c o s ~ ) ' . ( I + j i ~ - - j t ~ - ) ( u o H O H ~ oH o,H , -Ri , ) 2 1+- "+- 2 2 2

The modified eauation is:

/ 2 O H - O L o H

2 2 2 = ( c o s L ) '.[U,+, -Rin+, + u f g o ( i , , , +;")]

Where (-)-'H, B = 2. w H w,H w L o,H fg 7 2 2 2

By the same way, we can gain modified model of branch RC too.The equivalent circuit of generator is composed with branches RL or RC. So we can also build its compensatoty method ofjump quantity based on spectral analysis.

FAULT SIMULATION AND PROTECTION ANALYSIS

Because the new electromagnetic model of synchronous generator is used, the long-term transient and system swing can be simulated accurately. The Central China Power System (CCPS) is taken for example (Shown in Fig.3)I3I.

E2 E3

Fig.3 The Central China Power System (CCPS)

The single-phase short circuit sault of phase A is occurs on Ge-feng Line. The distance between the fault point and Ge-Zhouba is 6Vh of full length. Protections on both sides cut fault a t 2 0 h s after fault occurs.

The current and voltage waves of Ge-Shuang Line are showed in Fig.4. (a) is calculating results of the new electromagnetic model of synchronous generator. (b) is calculating results of EMTP which ignores changes of frequency and angle. By analyzing (a) and (b), it can be concluded that the generator model of the simple electromagnetic transient simulation is not suitable to analysis the long-term transient on condition of system swing and the model of this paper can calculate changes of frequency and angel in long-term transient and simulate the fault transient accurately.

The simulation results are suitable to different protection. Distance protection elements LFP-901A'41, the transmission line protection, is taken for example to explain that the model of this paper is more suitable to simulate the long-term transient with system swing and very important to analyze the protection on condition of system swing.

630

With the swing block component

Without the swing block component

3.43u I.

-3. 13u

b

I I

paper EMTP The swing block No system component works swing, and protection do protection do

not operates not operates Protection acts No system falsely in 0.32s swing,

protection do not operates

0 . 8 1 , 4 5 I 1 I I I

(a) Calculating results of the self-adaptive simulation

0 1 1 z 3 4 5 * i 8 D I

(b) Calculating results of EMTP Fig.2 Line

The current and voltage waves of Ge-Shuang

The criterion of positive sequence and negative sequence synthetical current super imposed component are used to distinguish faults and system swing in LFP-901A protection.

l ~ z l > 1.25Afi, +0.21, (12)

MIc = qiA, t K I A 2 ) is positive sequence and negative sequence synthetical current super imposed component, AIn is fixed value, I , rated current.

Input the simulating results of the model of this paper and EMTP and analyze the protection. Analyzing results are showed in Table 2.

TABLE2 Analyzing results of protection I Input results of this 1 Input results of I

The simulating results show that the model of this paper can calculate system swing and protection will operate falsely without the swing block component. But on same condition, protection will not operate falsely when Calculating results of EMTP are input. That is, it is very important to protection analysis whether system swing is calculated.

CONCLUSION

For calculating the fault transient on condition of system swing, changes of frequency and angle are taken into account in this paper. Considering the salient-pole reaction, stator coil transient and rotor coil mechanical characteristics, the united synthetic companion model of synchronous generators is built by integrate the electromagnetic transient, mechanical transient and port equation of synchronous generators. Based on the spectral analysis, the modified Euler model can not only avoid oscillation of numerical calculation but also improve the simulating accuracy. The fault electromagnetic transient on condition of system swing is simulated by synthetic companion model of generator. Distance protection element of LFP-901 A, the transmission line protection, is taken for example to analyze action of the protection and its swing block component on condition of system swing.

ACKNOWLEDGEMENT

The authors are grateful for the support of National

Natural Science Foundation of China (NSFC No. 500771 I, 50377019) and National Natural Science

International Cooperation Foundation of China P o .

50140430686)

REFERNCES

H.W.Dommel. EMTP Theory Book. Beijing: Hydraulic and Electric Power Press, 1990.

J.P.Barret. Power System Simulation. London: Chapman & Hall, 1997.

P Q Wang, C Y Chen, L Y Chen, X Z Dong. Automation of Electric Power Svstems. 2002, 26, supplement:X3-87..

Z Y Xu. New Type Distance protection of transmission line. Beijing: Hydraulic and Eletric Power Press, 2002.