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ALGORITHMIC MODELS AND VIRTUAL RELAYS I N DISTANCE PROTECTION IMPLEMENTATION

Y Liamets, S Ivanov, A Chevelev, D Eremeev, G Nudelman, J. Zakonjsek

Research Centre BRESLER, Russia; ABB Automation, Russia; ABB Automation Technology Products, Sweden

Abstract. The present report proceeds with' consideration of equivalent transformations of models, conditions, and measurements associated with simulation of specific elements of power transmission and its fault zone identification. Key words: models, multiple-wire system, transformer, distance protection, virtual relays.

1. INTRODUCTION

The subject touched upon in this report is rather wide. Some general ideas were stated in the previous report [I]. The method of cascade equivalenting applied to short-circuit calculation with detection of free process components and to creation of algorithmic models involved in relay protection synthesis has been further developed 121. Besides, the method of virtual relays is being considered; in [3] its capabilities were illustrated by the remote backup protection as an example, and here the problem of identification of power line fault zone, the 'main one in the distance protection, is discussed.

2. CASCADE EQUIVALENTING

2.1. Multiple-wire systems

2.1.1 Vectors of multiple-wire system. Assume that W[2n] is the Laplace representation of total vector of all currents and phase voltages at arbitrary point of n- wire power transmission, V[m] is m-dimensional vector composed of m currents and (or) voltages related to the group out of m wires, V*[m] is a vector of non-included currents and (or) voltages, i.e.

W[2n]=[V[n],V*[n]] . If the system currents and

voltages are strongly differentiated V = U, V' = I , let's call the total vector an ordered one

W.[2n] = [U[n],I[n]]' . The total vector can be composed of ordered and unordered parts

T

where m + p = n

2.1.2. Description of homogeneous section of power line. Vector W.(x), where x is a coordinate along the power line, is described by the following equation

with a (2nx2n)-dimensional matrix of primary oarameters

where Zn and Bo are submatrices of Laplace representations of proper and mutual resistances and capacitance coefficients. Solution of the equation (1)

W,(x) = exp(-Hx)W,(O) gives for the line section with length I

W,, = A.Wz., Wz, = B,W,.

A. = expHI, B, = exp(-HI) = A;'.

2.1.3. Special wires. A wire violating the cascade connection conditions is assumed to be a special one, i.e. broken, short-circuited to ground or to some other wire. The method of cascade equivalenting makes possible to restore cascade connection in such common cases. If in any section of the line there are m special and, accordingly, p = n -m normal wires, the system condition in this place will he characterized by

unordered vector W[2n] = [W[2p],V[m],O[m]]T with

V' = 0 . The section of power transmission line with special wires is therefore a particular case of the multipole described in [I]. The solution stated in [l] for a canonical case ml = m2 = m is also valid here. Non- canonical cases, when numbers of special wires on the input and output of the power line section are different, need to be normalized.

2.1.3.1. Special wires prevalence on input (ml >m2). Normalization lies in extraction of m1 -m, zero and redundant quantities of the input vector, and at the same time in isolation of as many elements in the outmt one.

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

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Equivalent description of a line section concerns normal wires only

Wl[2nl -2ml]=AeqW2[2n2-ml -pi2],

A, = A,, - AI~A;:AJI, and the isolated output quantities are expressed via the basic output vector

VJm, -m2]=-A;~A3,W2[2n2 -m, - m 2 ] .

2.1.3.2. Special wires prevalence on output (m, < m,). Normalization is carried out in the reverse order

The peculiarity of this case is that equivalenting applies to the input vector also

Wl,[2n, -m, -m21=A,,W2[Zn2 -2m21,

A,, = A , , -AlZAi:A*l,

Wleq = W,[2nl -m, -m,]-A12A;:Vl[m2 -m,].

2.2. Cascade model of three-phase transformer

Peculiarities of cascade modeling of transformer are determined by a number of restrictions subdivided into internal (magnetic core construction) and external (number of windings related to input or output; winding tappings). Equivalenting is meant to provide cascade connection of the following three blocks: primary winding, magnetic core and secondary winding (figure 1). ,-, U,, U,,

Fig. 1. Multiple core transformer model R, - core reluctances

2.2.1. A triple core transformer. The limitation a), + a)B + a)c = 0 excludes a common wire from the magnetic circuit model and its matrix after the transition to phase-to-phase magnetomotive force (m.m.0 is reduced down to the dimension 4x4

W m l = A m 2 W m 2 , Wm=[a)AQBFACFBC]T'

Matrices of primary and secondary windings are changed accordingly. Rearrangement brings the primary winding equation to the following representation

where W,, =[UAl U,, I,, I B I l T . It results in

w q , e , =we, - A I , I ~ A & U C ~ =*eq1Wm, 2

A,, =A, , , , - A 1 , 1 2 A i , ~ 2 A 1 , 2 1 '

The excluded current IC, and m.m.f Fcl can he determined in case of need by means of primary quantities:

FCl = 'i;2('Cl ~ A 3 . 2 1 w m 1 ) ~

'Cl = A3,3,Wm1 + A3,32FCI '

Secondary winding equation is brought to the view

*3JI *,,I2

[ a2L Tz = ] = [ ~ 3 , 2 1 A3.31 A3,22][::], A3,32

where W, =[UA2 UB2 UC2 I,, I,,T. As a result a reduced description is obtained

Wm2 = Aeq3We2 ,

*eq3 - A 3 , 1 2 A ~ ~ 2 A 3 , 3 1 ) w e 2 '

The following can be determined separately

IC2 =-A<i2A3,31we2 3

= A3,21We2 + A3,221C2'

After all the transformations have been made the matrix of direct transmission of the transformer connecting a four-dimensional vector We,,e1 with an output five-

dimensional vector W, can be represented as a product

=AeqlAmZAeq3

3. EQUIVALENTING OF ALGOFUTHMIC MODEL

An algorithmic model allows evaluating a vector W,[2p2] of quantities at fault point using an observed values vector Ws1[2pll. Regarding the fault point the power transmission can be subdivided into the following two parts - transmitting and receiving ones connected to each other by means of p 2 damaged and q undamaged wires (fig. 2). It is supposed that their equivalent descriptions has been subjected to normalization, therefore special wires on the output of a transmitting and on the input of a receiving multipole are excluded. It's obvious that on the input of the transmitting system in addition to the observed wires some possible special wires must be considered and only special wires must be allowed on the output of the receiving system.

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pI = p2 = p , the algorithmic model is made equivalent as a canonical part of the line:

Wr[2Pl=BbqWs1[2Pl,

BI, = B,,,, -Bq,LZB:,32Bq,31

Sending Receiving system system

Fig. 2. Algorithmic model initial representation

In order to make the circuit equivalent let’s represent a receiving system component as a tapping from power transmission (fig. 3).

:y I L ._...._.. ,

Fig. 3. Algorithmic model transformed representation

From the equation of direct transmission of receiving system represented in the form of

we obtain the description via the input conductivity matrix

by means of which we can get the matrices of direct and reverse transmission of the multipole making cascade connection with transmitting system:

I , , L ~ I = Y,u, , [~I , Y, = A ~ ~ , A ; A ,

As a result, let’s represent an algorithmic model in the form of an equivalent multipole (fig. 4) with matrices of direct and reverse transmission

A,, = A,A,,,, , Be, = B e q , A ’

Fig. 4. Algorithmic model in the form of a common multipole

Subsequent transformations are necessary for exclusion of special quantities on the input and output of the equivalent multipole of algorithmic model in order to express Wr[2p,] via W,,[2pl]. lfnumber m of special wires on the input is equal to the number q of special wires on the multipole output and, correspondingly,

4. APPLICATION OF VIRTUAL RELAYS METHOD TO THE DISTANCE PROTECTION

Virtual relays are program modules responding to the output signals of algorithmic models. An output of the model can be considered any of the branches of electric system circuit, both real and supposed fault branches. This is illustrated in fig. 5 , where branches are shown with dotted lines.

Fig. 5 . Power transmission circuit with possible points of virtual relays connection

The letters used in abbreviations designate the following: VR is a virtual relay, B and E is zone beginning and zone end, L and C is connection to the longitudinal branch and, correspondingly, to the crosscut branch with presumed fault. The phase virtual impedance relays are applied to identify single- and three-phase faults, and phase-to-phase relays are used for detection of phase-to-phase faults including double- phase-to-ground faults. Besides, for identification of earth-faults the totalizing relays are used, for example, for phases -s and v

G” =tL +U” )/(I, + L , 1. Informational value of such measurements is determined by the following considerations. Double- phase-to-ground fault, from the point of view of electrical engineering, is interpreted as two commutations: the first one produces phase-to-phase fault K g ) , the second one - the fault K:!? (fig. 6) . An arbitrary value is double changed in the described process: after the first commutation

y(2) = y + y ( 2 ) , - --pl --p”

where rp, is pre-fault quantity,

component; and, finally, after the second commutation:

is the first fault

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Fig.6. A complex fault as a sequence of simple commutations

where V(2)+(1,1’ is the second fault component

transforming the conditions K ( 2 ) to K(’,’) , --pY V(’.’) is the

total fault component of the complex fault. In symmetrical circuit I’giu = -v,?lu, and as a result

--P”

y(LU + y(LU = y + yc2l’~l.l) + y(2l+ll.’) -U -” --“.p, -0,pu --V,PY ’

It turns out, hence, that the measurement z:v contains information about the process of the transformation of Kc2) into K “ , ” , which is not presented in the phase measurements z,, z, and phase-to-phase z,, . The virtual relays form groups, combined by the logical operation AND. For the distance protection supplied with the phase selector it is sufficient to include into every group a pair of virtual relays controlling the faulted channel at the beginning and at the end of the protected zone, e.g. VRBC-VREC or VRBL-VREC. A number of pairs is determined by the condition of approach of achievable protection sensitivity to the identifiability of each type of fault. Pairs differ in setting characteristics of their relays. Figure 7 shows the results of synthesis of protection of 15 h long power transmission line. Fault types differ in identifiability and, consequently, in distance protection sensitivity to them. Three phase faults are identified worst of all. Phase-to-phase fault identifiability is almost twice as high, what is determined by a doubled system impedance as an equivalent generator relative to the fault point. Single- phase faults in this case are inferior to phase-to-phase faults in identifiability: uncertainty of zero-sequence parameters affects adversely, i.e. their turndown range is considerably larger than that of other sequences. The identifiability “champion” is double-phase-to-ground faults what is explained by higher informational richness of their fault components.

Fig.7 Non-identifiability object characteristics I -three-phase, 2 -single-phase, 3 ~ phase-to-phase,

4 - double-phase-to-ground

References

Liamets Y., Podchivaline A., Chevelev A., Nudelman G., Zakonjsek J., 2004, “Equivalent transforms of models, conditions and measurements in relay protection”, DPSP 2004, Amsterdam, Netherlands Liamets Y . , Eremeev D., Nudelman G., 2003, Electrichestvo, ll. 17-27 Liamets Y., Pavlov A., lvanov S., Nudelman G., 2003, “Virtual relays: theory and application to distance protection”, CIGR!? SC-BS Colloquium, Sydney, Australia, Paper 2 13