ATP-EMTP evaluation of relaying algorithms for series-compensated line

Transcription

1 AP-EMP evaluation o relaying algorithms or series-compensated line M. M. Saha, E. osolowski, J. Izykowski, P. Pierz Abstract A group o the algorithms aimed at measuring a ault-loop impedance or digital distance relay has been considered. he algorithms gathered in two basic amilies have been tested: methods based upon Fourier orthogonal components with using both ull-cycle and hal-cycle data windows; methods ounded on dierential equation techniques (our variants with applied various digital dierentiation rules and additional pre-iltration). Extensive simulation studies have been perormed or comparing the measuring techniques. ecommendations with respect to impedance algorithms or protection o series compensated lines are stated. he other studied algorithm is related with ault direction discrimination or the considered series compensated line arrangement. Sample simulation results are presented and discussed. Keywords: transmission line, series capacitor compensation, aults, digital distance protection, impedance algorithms, AP- EMP simulation. I I. INODUCION ncreased transmittable power, improved power system stability, reduced transmission losses, improved voltage control and lexible power low control are the primarily reasons behind installing Series Capacitors (SCs) on long power transmission lines. he installation costs usually do not exceed 5-3% o a new line and are not aected by the environmental concerns []. SCs, when set on a line, create, however, certain problems or its protective devices [], [3] and ault locators [4]. When a series compensated line suers a ault behind its SCs, as seen rom the relaying point (Fig. ault F or the elay A and the ault F or the elay B), a ault loop considered by a distance relay contains, depending on type o ault, one or even two complexes o SCs and their overvoltage protecting arresters (usually Metal-Oxide Varistors (MOVs)). he presence o MOVs makes a ault loop strongly nonlinear and nature o transients o the relaying signals is entirely dierent than or traditional lines []. Improvement o series compensated line protection calls or detailed investigation o both impedance measuring algorithms and auxiliary algorithms dedicated or ault detection, phase M. M. Saha is with ABB AB, S-7 59, Västerås, Sweden ( o corresponding author: murari.saha@se.abb.com). E. osolowski, J. Izykowski and P. Pierz are with Wroclaw University o echnology, Wybrzeze Wyspianskiego 7, 5-37 Wroclaw, Poland ( s: {eugeniusz.rosolowski; jan.izykowski; piotr.pierz}@pwr.edu.pl). Paper submitted to the International Conerence on Power Systems ransients (IPS5) in Cavtat, Croatia June 5-8, 5 selection, direction detection. his paper is ocused on speeding-up the measurement o a ault-loop impedance. In case o the considered protection, a high speed is expected, while or ault location or an inspection-repair purpose a speed is not important and thus complex calculations can be applied, as or example as presented in [5] [7]. he other contribution o this paper relies on investigation o the algorithm or ault direction discrimination [8], also in an environment o the studied arrangement (Fig.). A B SYSEM A F 3 SCs ~ ~ CVs A {v A } Cs A F F MOVs Cs B AI-GAPs {i A } {i B } P elay A elay B Fig.. Schematic diagram o the studied series compensated system SYSEM B CVs B {v B } he sotware package AP-EMP [9] was used or generating ault data under versatile aults on the line. A single-circuit ully transposed transmission line A B (Fig. ) is considered as compensated at 7% rate with a three-phase bank o series capacitors (SCs) installed in the middle. Calculation o the ault loop impedance used or comparing with an impedance characteristic requires selecting proper relaying voltage and current. his is a state o the art o distance protection technique [], []. In case o the considered here ully transposed line, the residual-current compensation is applied or phase-to-earth aults. In turn, or unsymmetrical lines [] the phase-current-compensation technique has to be applied. II. MODEL OF SEIES COMPENSAED LINE he line (3 km, 4 kv, 5 Hz) is modeled using the transposed Clarke model. Line impedances or the positiveand zero-sequence were assumed in modeling as: Z L =.35 Ω/km, 85 o ; Z L =.65 Ω/km, 75 o. he MOVs were modeled as non-linear resistors approximated by the standard v i characteristic (Fig. c): v i= P V () EF where: q, P, V EF MOV parameters. he parameters o () assumed in this study were: q=3, P= ka, V EF =5 kv. Each MOV is protected rom overheating by iring the complementary air-gap by the thermal (overload) protection q

2 (Fig. ). he MOV protection was modeled as energy-based using AP-EMP MODELS: the energy absorbed by the MOV is integrated and the MOV becomes shunted by iring the air-gap (the signal DOWN causes closing o the type 3 switch) when this energy reaches its pre-deined limit. v A a) b) c) VOLAGE / V_EF v A i A..8.4 * MOV i A C o D L D type 3 P IN E DOWN COMP E lim DOWN CUEN / P Fig.. Modelling o series capacitor equipped with MOV: a) adopted scheme, b) structure o algorithm or thermal protection o MOV, c) voltagecurrent characteristic o MOV. he relay measuring chain was modeled as well. Capacitive Voltage ransormers (CVs) were represented by their 4 th order linear models while Current ransormers (Cs) were simulated taking into account their saturation branches. he analog anti-aliasing ilters were represented by the nd order approximation with the cut-o requency set at / 3 o the sampling rate s ( s = khz was assumed in this study). Variety o conditions with respect to the supplying systems were considered. In all the tests o this paper the impedances o the local (A) and remote (B) sources were taken as identical and equal to: Z s =Z s =5 Ω, 85 o, Z s =6.6 Ω, 85 o. he remote sources were delayed by o with respect to the local sources. III. FOUIE MEHODS Distance protection o a transmission line requires measurement o a ault loop impedance (, ). Comparison o the measured impedance with the characteristics properly shaped on an impedance plan enables to make a decision whether a ault occurred in the protection zone or not. In order to provide adequately ast disconnection o a aulted line such a decision ought to be made very ast within time shorter than a undamental requency period or modern relays. he aim o this study is to develop the measuring algorithm or ast operating relays applied or protection o series compensated lines. First, the Fourier methods have been taken into consideration. According to them impedance components (, ) o a ault loop are estimated with the orthogonal components o voltage and current rom a ault-loop []: ucic + usis = ic + is () usic ucis = i + i c where: u c, i c, u s, i s direct (cosine) and quadratic (sine) orthogonal components o voltage and current, respectively. Both the ull-cycle and the hal-cycle Fourier algorithms or calculation o the orthogonal components are considered. he sample a-b ault at 5 km rom the substation A with ault resistance. Ω (Fig. ault F ) is taken or showing perormance o the considered algorithms. Figs. 3A and 3B presents phase voltages and currents at both the substations. he relay at the substation A sees this ault as behind the SCs&MOVs, while the relay at the substation B as on a conventional line (i.e. not compensated). High requency distortion o the waveorms is more visible in the case o the substation A (caused by the MOVs switching between linear and non-linear operating modes). he phase currents at the substation B contain, analogously as in uncompensated lines, the DC components. SIDE A: hree-phase current (A) Fig. 3A. hree-phase voltage and current signals measured at the substation A under the sample a-b ault. s

3 SIDE B: hree-phase current ( 4 A) SIDE B: hree-phase voltage ( 5 V) Fig. 3B. hree-phase voltage and current signals measured at the substation B under the sample a-b ault. Fig. 4 depicts the estimation o impedance seen rom the substations A and B using the ull-cycle Fourier algorithm. he estimates measured at the substation A settle almost ater 3 ms, what is not acceptable or modern ultra-high speed relays. On the other hand, the estimates at the substation B (the corresponding ault loop does not contain the SCs&MOVs) settle ater ms (the window length). he large overshoots result rom the phase inversion o the side B currents. SIDE B: Fault-loop impedance [ ] Fig.4. Fault loop impedance estimation with the use o Fourier ull-cycle ilters. Fig. 5 displays the impedance estimation with the use o hal-cycle Fourier ilters. he impedance at the substation A settles ater some 3 ms (also unacceptable) and one observes the danger o dynamic overreaching. he impedance at the substation B settles ater ms (the window length). Fig. 5. Fault loop impedance estimation with the use o Fourier hal-cycle ilters.

4 he results o the tests rom Figs. 4 and 5 clearly show that the Fourier methods are not suitable or series compensated line protection. IV. DIFFEENIAL EQUAION MEHODS FO IMPEDANCE MEASUEMEN It is assumed that the ault loop circuit is described analogously as or a traditional (uncompensated) line by the ollowing dierential equation: di( t) i ( t) + L = u( t) (3) dt It is worth to notice that in (3) u and i are measured, while and L are to be estimated. o obtain a measuring algorithm the eq. (3) must be irst written in a digital orm: a + Ld = b (4) a + Ld = b rom which the sought values and L are derived constituting the impedance algorithm: db db = ad ad (5) ab ab = ω a d a d where: ω the radian undamental requency, a, a, b, b, d, d coeicients dependent on the way o digital approximation o (3). A. Dierential equation method with application o rectangular dierentiation he operator o dierentiation in the continuous time in (3) is replaced by the rectangular numerical rule [] in the discrete time domain. o obtain proper phase shit introduced by this operation (+9 o or the undamental requency), averages or two successive samples o u and i are taken instead o samples o these signals directly. In order to originate two independent equations, (3) is written or two successive samples and the coeicients in (4) are: a + i( k ) ] a k ) + i( k ) ] b = [ u( + u( k ) ] b = [ u( k ) + u( k ) ] (6) d i( k ) ] d k ) i( k ) ] where: sampling period. Fig. 6 presents the estimation process with the use o this method (the equation (5) combined with the ormulas (6)) or the same ault case as beore in Figs. 4 and 5. he measurement at the substation B (no SCs&MOVs in a ault loop) is very ast (below 5 ms) and accurate (no dynamic overreaching, no oscillations). However, when executed at the side A, or which a ault loop contains SCs&MOVs, poor time response o the algorithm is observed. Large oscillations caused by the MOVs switching between linear and non-linear operating modes are observed. Such oscillations are deinitely unacceptable. SIDE B: Fault-loop impedance [ ] Fig. 6. Fault loop impedance estimation with the use o dierential equation based method with rectangular dierentiation B. Dierential equation method with application o rectangular dierentiation and digital pre-iltration he algorithm rom the subsection A displays signiicant dynamic errors due to mismatch o the used model o the process (dierential equation or the L circuit) and the actual process (irst o all operation o SCs&MOVs; line shunt capacitances; transients o Cs, CVs and analogue ilters). his generates noise in the estimates, located mainly in the high requency region. hereore, measurement may be improved by applying additional pre-iltration o the voltage and current signals prior executing (6) and (5). Consequently, (6) is replaced by (7): a = [ i ( + i ( k ) ] a = [ i ( k ) + i ( k ) ] b = [ u ( + u ( k ) ] b = [ u ( k ) + u ( k ) ] (7) d= [ i ( i ( k ) ] d = [ i ( k ) i ( k ) ] where: subscript denotes digital pre-iltration. he pre-iltration has been done using Fourier hal-cycle cosine ilter or both current and voltage signals. Such the preiltration o low-pass type is reasonable or this particular application as the DC components are eliminated by the equation (5) itsel.

5 Fig. 7 presents the measurement process using the method (5) combined with (7) or the same ault case as beore in Figs. 4, 5, 6. he impedance seen rom the substation B settles in some ms (length o the data window or the pre-iltration). In turn, as seen rom the substation A (SCs&MOVs in a ault loop), the settling time or the resistance and the reactance is around a hal undamental requency cycle. As a result o preiltration the high requency oscillations are removed rom the resulting impedance components (compare with Fig. 6). where: d = a = i b = u (, a (, b = i = u ( k ), ( k ), [ 3i ( 4i ( k ) + i ( k ) ], ω d = (8) d ω d = [ 3i ( k ) 4i ( k ) + i ( k 3) ], d π π 4π ( cos( )) + sin( ) N N sin( ) N N number o samples in one undamental req. cycle. As in subsection B, hal-cycle cosine Fourier ilters have been used or the digital pre-iltration o both voltage and current signals (the subscript ). Fig. 8 presents the example o the measuring process with the use o this method or the same ault case as beore in Figs. 4, 5, 6, 7. At the substation A the settling time is around three quarters o a cycle, while about hal a cycle or the substation B. he algorithm perorms similarly as the algorithm rom the subsection B. SIDE A: Fault-loop impedance [Ω] 4 3, Eq. (5) & (8) Fig. 7. Fault loop impedance estimation with the use o dierential equation based method with rectangular dierentiation and hal-cycle pre-iltration. C. Dierential equation method with application o Gear dierentiation rule his method is a variant o the method deined in the subsection B. he rectangular rule is replaced by the threepoint Gear dierentiation [] which introduces or the undamental requency exactly 9 o phase shit between the signal and its numerically computed derivative. Consequently, no additional (compensating) computations are needed or the signals (as it was necessary in the method described in the subsection B). It is, however, necessary to apply an extra preiltration too. hus, the equations replacing (7) are as ollows: SIDE B: Fault-loop impedance [Ω] 3 Eq. (5) & (8) Fig. 8. Fault loop impedance estimation with the use o dierential equation based method with Gear three point dierentiation and hal-cycle preiltration

6 D. Dierential equation method with application o rectangular dierentiation and orthogonal components In this method, the current and voltage signals are irst split into their orthogonal components as the dierential equation (3) is valid or both direct and quadratic components o the signals. Solving such as system with respect to sought and one gets the measuring algorithm in the orm o (5), but combined with the ollowing coeicients: a = [ is ( + is( k ) ] a = [ ic ( k ) + ic ( k ) ] b = [ us ( + us ( k ) ] b = [ uc ( k ) + uc ( k ) ] (9) d= [ is( is ( k ) ] d = [ ic ( k ) ic ( k ) ] where: subscripts s, c denote quadratic (sine) and direct (cosine) orthogonal components. In this paper Fourier hal-cycle sine/cosine ilters have been used to extract the orthogonal components o both current and voltage. Fig. 9 displays the sample results o applying the algorithm (5) in combination with (9) or the previously used test ault. hey illustrate good perormance o this algorithm, as at both ends o the line the settling time is shorter than a cycle. SIDE A: Fault-loop impedance [Ω] SIDE B: Fault-loop impedance [Ω] 4 3 Eq. (5) & (9) Eq. (5) & (9) Fig. 9. Fault loop impedance estimation with the use o dierential equation based method with rectangular dierentiation combined with orthogonal components. V. FAUL DIECION DISCIMINAION he phenomena speciic to a series compensated line aect also the auxiliary unctions o its distance relay including ault detection, phase selection and direction detection. All these blocks are essentially important or the overall perormance o the complete distance relay. A directional element becomes essential or a complete distance relay when a ault to be cleared occurs very close to a relaying point. he traditional approach to mitigate the problem o the voltage all is to apply an additional polarization voltage. It may be done by []: (a) cross polarization o a voltage signal, (b) memory polarization o a voltage signal. Also, a combination o the above two approaches is possible. Further improvement is achieved when processing the change in current signals. his idea applies ull cross polarization or the directional measurement. he polarizing voltage is taken entirely rom the healthy phases. he change in the phase current is used or the directionality to eliminate the inluence o load current. An impedance is calculated or each phase. As or example, or the phase a, the impedance is calculated by utilizing: U Z bc a = () I a_lt I a_pre For the detection o ault in orward direction the argument or the calculated impedance shall be within: 5 to 5 degrees []. McLaren et al. [8] rearranged the well-known direction detection principle or ast acting numerical relays. he concept is based on computing the incremental positive sequence impedance deined by the increments (pre-ault quantities subtracted rom the ault ones) in positive sequence o voltage and current: ( U lt U pre) positive seq. Z= () ( I I ) lt pre positive seq. he incremental positive sequence impedance enables very reliable direction detection. For a orward ault such the impedance is a local source impedance (as to the value and with the negative sign to account or the act that the current is lowing rom a source to a orward ault location). While or a reverse ault, this impedance equals the line impedance plus the remote source impedance. Certainly, or a seriescompensated line, the line impedance must be understood as the line inductive impedance itsel plus the capacitive impedance o the series C equivalent o the parallel arrangement o a series capacitor and its MOV []. Fig. presents perormance o the positive-sequence direction element rom the substation A under the considered sample a-b ault (Fig. ault F ). he computed incremental positive sequence impedances lays in this case basically in the 3 rd quadrant (resistance and reactance are negative) and settles at the value equal to the positive sequence impedance o the local source multiplied by ( ). he SCs&MOVs cause large

7 luctuations in both resistance and reactance o the incremental positive-sequence impedance. However, basing on the negative sign o the calculated incremental positive-sequence reactance (or all samples except the st sample) the orward direction (Fig. the ault F or the elay A) is detected reliably and ast. Fig. presents perormance o the positive-sequence direction element rom the substation B under the considered sample orward ault. Again, the computed incremental positive-sequence impedances lays in this case basically in the 3 rd quadrant and settles at the value equal to the positive sequence impedance o the local source multiplied by ( ). he SCs&MOVs as not contained in the ault-loop basically do not inluence the measurement and the calculated quantities are more smooth than in the case o Fig.. SIDE A: Incremental positive-seq. impedance [Ω] Fig.. Fault direction detection by the elay A rom the substation A under the orward ault occurring behind the SCs&MOVs (Fig. - ault F ). SIDE B: Incremental positive-seq. impedance [Ω] Fig.. Fault direction detection by the elay B rom the substation B under the orward ault occurring in ront o the SCs&MOVs (Fig. - ault F ). Full cycle Fourier iltration was used under determining the sequence components or both the tests (Figs. and ). he results o the perormed tests show that the algorithm based on computing an incremental positive sequence impedance enables reliable and ast ault direction detection in an environment o the studied series compensated network. VI. CONCLUSIONS Detailed AP-EMP model o a single-circuit series compensated line including Metal Oxide Varistors (MOVs), Capacitive Voltage ransormers (CVs), Current ransormers (Cs) and anti-aliasing analog ilters has been developed. Extensive simulation studies have been carried out or a variety o ault conditions with the aim o evaluation o relaying algorithms applied or protection o a series compensated line. Algorithms or impedance measurement and or ault direction discrimination have been studied in details. For aults behind SCs&MOVs the undamental requency based methods introduce considerable delay in addition to the delay caused by their data windows. In turn, the dierential equation based methods must be equipped with hal-cycle digital pre-iltration otherwise they give poor time responses or aults behind SCs&MOVs. Basing on the presented examples and the perormed extensive studies or various aults, inally the method combining the dierential equation technique with orthogonal components (subsection C) is inally recommended or ault-loop impedance measurement. he investigations o this paper have been carried out or ully transposed line. It is expected that the introduced impedance algorithms can be applied or untransposed lines as well, however, this calls or additional investigations. he phenomena speciic to a series compensated line aect the perormance o distance relay auxiliary algorithms. Selected results showing perormance o the algorithm or ault direction discrimination are presented and discussed. VII. EFEENCES [] M. M. Saha, J. Izykowski, and E. osolowski, Fault Location on Power Networks, London, Springer,. [] B. Kasztenny, Distance protection o series compensated lines problems and solutions, in Proc. 8th Annual Western Protective elay Conerence, pp. 34,. [3] M. M. Saha, B. Kasztenny, E. osolowski, and J. Izykowski, First zone algorithm or protection o series compensated lines, IEEE rans. Power Delivery, vol. 6, pp. 7, Oct.. [4] M. M. Saha, J. Izykowski, E. osolowski, and B. Kasztenny, A new accurate ault locating algorithm or series compensated lines, IEEE rans. Power Delivery, vol. 4, pp , July 999. [5]. ubeena, M.. Dadash Zadeh, and. P. S. Bains, An accurate oline phasor estimation or ault location in series-compensated lines, IEEE rans. Power Delivery, vol. 9, pp , Apr. 4. [6] C. S. Yu, A reiterative DF to damp decaying dc and subsynchronous requency components in ault current, IEEE rans. Power Delivery, vol., pp , Oct. 6. [7] J. C. Gu, K. Y. Shen, S. L. Yu and C. S. Yu, emoval o DC oset and subsynchronous resonance in current signals or series compensated transmission lines using a novel Fourier ilter algorithm, Elect. Power Syst. es., vol. 76, pp , 6. [8] P. G. McLaren, G. W. Swit, Z. Zhang, E. Dirks,. P. Jayasinghle, and I. Fernando, A new positive sequence directional element or numerical distance relays, in Proc. o the Stockholm Power ech Conerence, Stockholm, Sweden, pp , 995. [9] H. Dommel, Electromagnetic ransient Program, BPA, Portland, Oregon, 986. [] H. Hupauer, P. Schegner and. Simon, Distance protection o unsymmetrical lines, EEP, vol. 6, No., pp. 9-96, 996. [] L. B. Jackson, Digital ilters and signal processing, Kluwer Academic Publishers, 986.