On-line Discrete Wavelet Transfor in EMTP Environent and Applications in Protection Relaying N. Perera, A.D. Rajapakse and R.P. Jayasinghe Abstract--This paper describes the developent of an on-line discrete wavelet transfor tool for an electroagnetic transient siulation progra. Multi-resolution properties of wavelet transfor ake it ideally suitable for analyzing power syste transient signals which consist of non-periodic high frequency oscillations superiposed on power frequency signal. New power syste devices such as power quality onitors and protective relays based on algoriths involving wavelet transforation are eerging. Thus, it is highly useful for power syste electroagnetic transient siulation progras to have integrated capability for wavelet transforation. This paper also briefly presents several applications of wavelet transforation in power syste protection and power quality onitoring. Keywords: Electroagnetic transient siulation, Wavelet transfors, Applications of wavelet transfor in power syste, Power syste protection, Power quality. W. NTRODUCTON avelets are atheatical functions that decopose a signal into different frequency coponents, and then study each coponent with a resolution atched to its scale []. They have added advantages over traditional Fourier ethods because wavelet transforation localizes inforation in the tie-frequency plane; and capable of trading frequency resolution with tie resolution and vice-versa. These properties have ade Wavelets transforation highly suitable for analyzing physical situations where the signal contains discontinuities and sharp spikes [],[]. Wavefors associated with fast electroagnetic transients are typically non-periodic and contains both high frequency oscillations and localized ipulses superiposed on power frequency and its haronics. These characteristics present a proble for traditional Fourier analysis because its use assues a periodic signal and because a wide-band signal requires denser sapling and longer tie periods to aintain good resolution in the low frequencies [3]. On the other hand, This work was supported by Manitoba HVDC Research Centre, Manitoba, Canada. N. Perera and A.D. Rajapakse are with Departent of Electrical and Coputer Engineering, University of Manitoba, Canada (e-ail: nuwan@ee.uanioba.ca, athula@ee.uanitoba.ca). R.P. Jayasinghe is with Manitoba HVDC Research Centre (e-ail: jayas@hvdc.ca). Presented at the nternational Conference on Power Systes Transients (PST 7) in Lyon, France on June -7, 7 ulti-resolution properties of wavelets transfor ake the well suited to analyze transient signal superiposed on a continuous fundaental. Due to the wide variety of signals and probles encountered in power engineering, there are various applications of wavelet transfor. These include detection, and analysis of power quality disturbances and power quality data copression [], [5], high voltage insulation condition onitoring [6], fault detection [7], [8], and disturbance classification [9]. Several power engineering products based on wavelet transforation such as protective relays [] and power quality onitors [] are now eerging. Electroagnetic transient progras (etp-type progras) are widely used for power syste studies involving power quality issues, protection syste operation, etc. An integrated tool that can be used to perfor wavelet transforation of the siulated wavefors is a highly useful feature for those studies investigating wavelet transforation based techniques. Although several wavelet transfor progras such as MATLAB wavelet toolbox are available, their use generally requires siulated wavefors to be saved in data files and then perfor the analysis external to the etp-type siulation. The novelty of the proposed coponent is that it can be used to perfor the wavelet transfor as the wavefors are generated by the siulation. Thus it is possible to siulate systes such as protective relays based on wavelet transforation in a closed loop anner. This paper is organized as following. Section gives a brief introduction to the wavelet transforation for the benefit of readers not failiar with wavelet transforation. Then the ipleentation of wavelet transforation using filter banks is explained in Section. A brief description of the usage and capabilities of the wavelet tool developed is given in Section V. Section V presents several application exaples, and conclusions are given in Section V.. WAVELET TRANSFORMATON The wavelet transforations can be Continuous Wavelet Transforation (CWT) or Discrete Wavelet Transforation (DWT). f f(t) is a signal with a finite energy, its CWT is defined as CWT Ψ where, f * a, b ) f ( a, b) = ( t) Ψ ( t dt ()
t b ( ) Ψa, b ( t) = a Ψ () a The function Ψ(t) is the basis function or the other wavelet, the asterisk denote a coplex conjugate, and a (, R) is the scale paraeter and b ( R) is the translation paraeter. The other wavelet function ust satisfy several conditions: it should be short and oscillatory, i.e. it ust have zero average and decay quickly at both ends. Several exaples of wavelets are shown in Fig... FLTER BANK MPLEMENTATON OF DWT A. Decoposition and Reconstruction DWT can be ipleented efficiently as a filter bank as shown in Fig. [],[]. This ipleentation is coonly known as Mallat tree algorith and consists of series of lowpass filters and their dual high pass filters. H(n) denotes a high pass filter and L(n) is its dual low pass filter. The filter coefficients are deterined by the type of other wavelet selected. The circle with downward arrow behind denotes down sapling by a factor of. The outputs d, d, d 3, etc. are called the detail wavelet coefficients while the output fro the last low pass filter is referred to as the approxiation wavelet coefficient. t is possible to obtain the original signal f(t) through wavelet series reconstruction. The reconstruction can also be carried out efficiently using a tree algorith as shown in Fig. 3. The filters and are the inverse filters of H(n) and L(n) respectively. n Fig. 3, the circles with upward arrow behind denotes up sapling by a factor of. Fig.. Different types of wavelets n discrete wavelet transforation, other wavelet is dilated and translated discretely by selecting a = a o ; b= nb (3) oao where a o (>) and b o (>) are fixed real values and and n are positive integers. Then the discretized other wavelet becoes t nboao Ψ n, () t = Ψ( ) () a a o o The corresponding discrete wavelet transforation is given by * DWTΨ f (, n) = f ( k) Ψn, ( k) (5) k DWT provides a decoposition of a signal into sub bands with a bandwidth that increases linearly with frequency. n the case of dyadic transfor corresponding to ao = and bo =, the result is geoetric scaling, i.e., /a, /a and translation by, n, n This scaling gives the DWT logarithic frequency coverage in contrast to the unifor frequency coverage of Fourier transforation. H(n) D(n) f(n) H(n) L(n) Fig.. Mallat tree algorith for wavelet decoposition Level-3 d3 Level- d Level- Fig. 3. Wavelet reconstruction d H( n) B. Multilevel Decoposition and Reconstruction The reconstruction algorith can be used to provide the wavelet coefficients of different scales a finer tie resolution. Fig. illustrates this process: decoposition of sapled signal x(n) for three levels and use of up sapling and filtering to obtain finer reconstruction wavelet coefficients. The original signal x(n) can now be easily reconstructed siply by adding the reconstruction wavelet coefficients: the detail coefficients D(n), D(n), D3(n) and approxiation coefficient A3(n). Note that all these coefficients now have the sae sapling rate as the original signal. L(n) Level- d Level- d H( n) L(n) Level-3 d3 f(n) x(n) H(n) D(n) L(n) H(n) D3(n) L(n) L(n) A3(n) Fig.. Multilevel wavelet reconstruction
V. WAVELET TRANSFORM TOOL N EMTP ENVRONMENT Siulation of devices that use wavelet transfor based techniques is essential for research and developent as well as for validating the suitability of those new devices for practical applications. Since etp-type progras are widely used for studies concerning power quality issues, protection, and transients in power systes, the capability of applying wavelet transforation in etp environent itself will provide any advantages. Although there are several free/coercial software tools available for wavelet analysis, they can be used only for post siulation analyses using the wavefors saved to data files. This is not obviously a convenient way, especially when siulations are needed to carry out repetitively. On the other hand, since the analysis has to be carried out after copleting the siulations, siulation of devices that use wavelet transfor cannot be perfored. The online wavelet transforation tool developed here enable siulating systes such as protective relays based on wavelet transforation in a closed loop anner. A. DWT Tool n the present study, an online wavelet transforation tool was developed in PSCAD/EMTDC software. However, this can be ipleented in any other etp-type progra. The block diagra in Fig. 5 shows the processing steps involved. Filter coefficients database Anti-aliasing filter Sapling Data buffer Wavelet decoposition Wavelet reconstruction (Approxiation) nput signal (Details) Reconstruction wavelet coefficients Fig. 5. Processing steps involved in the DWT tool As applications ay need signal sapling intervals that are different fro the siulation tie step, a provision is allowed for re-sapling the input signal at a frequency selected by the user. An anti-aliasing filter is also provided for filtering out high frequency noise. The cutoff frequency of the anti-aliasing filter is autoatically deterined based on the sapling frequency selected. A provision is provided to disable the antialiasing filtering if required. Sapled data is placed in a buffer before the decoposition and reconstruction is perfored. User can specify the type of other wavelet. Currently nine types of other wavelets have been ipleented: Harr, Daubechies (DB) (order,,, and 8), Sylets (Sy) (order,,, and 8), Coeiflets (order and ) (Harr, Daubechies order, and Sylet order are essentially the sae). n addition, a user can specify the level of details coputed. This selection requires a change in the diension of the output. The total nuber of coefficients calculated is equal to the nuber of detail levels plus one (for the approxiation coponent). B. Validation The accuracy of coputation is validated by coparing with MATLAB wavelet toolbox, which is one of the ost widely used tools for wavelet analysis. Fig. 6 shows a saple of results which copares the wavelet coefficients of a signal with transient (top ost graph) obtained through MATLAB and the DWT tool developed in PSCAD/EMTDC. 8 Signal - 5 Approxiation A6 - Detail D Detail D - 5 Detail D3 Detail D - Detail D5-5 Detail D6.6.8....6.8 Tie (s) Fig. 6. Coparison of the wavelet coefficients calculated using MATLAB wavelet tool box (thin lines), and the PSCAD DWT tool (thick lines) for a saple wavefor. The other wavelet used is Sy8. Note that the online calculation in PSCAD results in a tie lag (Δt). TABLE DATA WNDOW SZES (NUMBER OF SGNAL SAMPLES) REQURED FOR ONLNE DSCRETE WAVELET TRANSFORM. Level Haar Db/sy Db/sy Db8/sy8 Coif Coif 6 3 3 7 5 3 8 3 7 6 5 8 6 6 5 338 8 6 5 3 6 3 69 5 6 6 5 63 39 For the case shown in Fig. 6, Sy8 other wavelet was used. Shown in thicker lines are the results fro the Δt
] ] PSCAD/EMTDC online DWT tool (transforation was perfored as the signal being generated fro the siulation). MATLAB results were obtained at the end of siulation by using a recorded wavefor. Except for the tie delay, both curves were found to be identical. Tie delay, which cannot be avoided in online calculation, is dependent on the data window size (nuber of signal saples) required to perfor the calculation. Table- gives the data window sizes required for different types of other wavelets at different detail levels to perfor online DWT. V. APPLCATONS OF WAVELET TRANSFORM TOOL For an external fault such as F, wavelet coefficients of the transients currents easured on the non faulted branches are opposite in sign copared to those easured on the faulted branch. This sign difference can be clearly observed in s shown in Fig. 9, and can be used to deterine the direction of fault. f such relays can be installed at strategic locations on a power network and counication is provided between the neighboring relays, faulted segents can be deterined very fast: all the inforation required is obtained within half a cycle. Application of such a schee for a 3 kv, bus transission network is shown in Fig.. A. Rapid solation of Faults Wavelet transfor can be used to quickly identify the direction of fault currents using initial transients in the currents (or voltages) due to the fault []. n order to explain the principle, consider a relay installed at a busbar interconnecting three lines segents as shown in Fig.7. Aerial ode- currents[ka] Measureents at - -.5.55.5 - -.5.55.5 Aerial ode- currents[ka] Measureents at Y - -.5.55.5 - -.5.55.5 Aerial ode- currents[ka] Measureents at Z - -.5.55.5 - -.5.55.5 Fig. 7. Wavelet based relay at a busbar interconnecting three lines Three sets of CTs easure the currents on each branch at, Y, and Z. A fault in the region between the CTs, such as fault F, is an internal fault whereas a fault outside the CTs, such as fault F, is an external fault. The easured three-phase currents are transfored to odal doain using the constant Clark s transforation atrix in (6) before applying wavelet transfor. a = (6) b 3 3 3 3 c n (6), a, b, and c are the phase currents and,, and 3 are the odal coponents. Only the coponents, and 3, which are known as aerial ode coponents, are used for the fault locations. By using these two coponents all types of ground and ungrounded faults can be handled. Thus the use of odal transfored quantities gives soe coputational advantage, in addition to providing decoupled signals. n the following analysis, Level- wavelet transfor coefficients (s) obtained with DB other wavelet were used. For an internal fault such as F, s of the currents easured at, Y and Z will all have the sae sign as shown in Fig. 8. Aerial ode- [ka]. -. -..5.55.5 Aerial ode- [ka]. -. -..5.55.5 Aerial ode- [ka]. -. -..5.55.5 Fig.8. Phase currents, corresponding odal signals and their s for an internal fault between phases A and B. Aerial ode- [ka] Phase currents[ka Aerial ode currents[ka Measureents at -.5.55.5 -.5.55.5.5 -.5.5.55.5 Aerial ode- [ka] Aerial ode currents[ka] Measureents at Y -.5.55.5 -.5.55.5.5 -.5.5.55.5 -.5.55.5 Fig. 9. Phase currents, corresponding odal signals and their s for an external fault between phases A and B. Aerial ode- [ka] Aerial ode currents[ka] Measureents at Z -.5.55.5.5 -.5.5.55.5
G nfinite bus 9 [Eternal ] B A C D R 7 Counication link G E F H R G K G3 8 L J R6 [External] M 3 Fig.. Wavelet based protection schee. Arrows indicate fault current directions identified by each relay Aerial ode- s Aerial ode- s 5 Fig.. Wavelet coefficients observed by R3 and R R3 F A G Fig. shows the wavelet coefficients observed at bus-3 and bus-. of branch M has a sign opposite to those of the other branches connected to bus-3. Siilarly, of branch Q has a sign opposite to those of the other branches connected to bus-. Fro the above inforation, R3 deterines that the fault is in the direction of bus-, while R deterines that the fault is in the direction of bus-3. f counication is provided, R3 and R can jointly deterine that the fault is in the line M-Q connecting the. n Fig., fault type (internal/external) and fault direction as identified by each relay are also indicated. B. Fault Location using Traveling Waves Distance to a fault can be estiated using traveling waves originating fro the fault [3]. Consider a fault locater installed at a busbar connecting three line segents A, B and C in Fig.. Y B Counication link s at R3 Z C R.5 K J -.5 L M.6.68.65.656.66 Tie (s) s at R - N Q O S -.6.68.65.656.66 Tie (s) P R T 6 R5 N V O Q P R U 5 S Fig.. Two faults F and F occur on a segent connected to a relay agent and their lattice diagras n order to explain the concept, consider two ungrounded faults; fault F close to the near end of Segent-A and fault F close to the reote end of the sae segent. Fig. also shows the lattice diagra for the resulting traveling waves; dotted lines correspond to F and the dark lines correspond to F. n order to estiate the fault distance, it is necessary to find the tie between the arrival of successive traveling wave fronts originating or reflected fro the fault. For exaple, for fault F, t and t are the arrival ties of the transient originating fro the fault and its first reflection fro the fault, respectively. Knowing the traveling tie (t - t ), and assuing the propagation speed to be that of light, the distance to the fault can be estiated. The tie interval (t - t ) can be estiated by using the s of the currents as shown in Fig. 3a.. Fault F Measureents at -.... Measureents at Y. -.... Measureents at Z. Fault F 5 x -3 Measureents at..3..5 5 x -3 Measureents at Y..3..5 5 x -3 Measureents at Z -......3..5 t t t t t3 (a) (b) Fig. 3. Transients observed at three easureent points for fault F and F.
The situation is ore coplicated for a fault such as F, due to the arrival of reflections fro other points before the arrival of wave front reflected fro the fault. For exaple, t and t 3 are the relevant transient arrival ties required to estiate the distance to the fault. However, the transient arriving at tie t (where t < t 3 ) should be ignored in order to correctly estiate the fault distance. This can be achieved with the help of fault direction finding ethod described in the previous section. As seen in Fig. 3b, for transients arriving fro line Segent A, the of the current easured at point has a sign opposite to the s of that easured at the other two points (Y and Z). This perits distinguishing the transient coing fro the fault fro the other transients. C. Power Quality Disturbance Detection Wavelets can also be used to detect the power quality events such as voltage sags and swells, transients, haronics, etc. Detection of such disturbances is necessary for applications such as disturbance recorders: for exaple, change in wavelet coefficients can be used to trigger wavefor recording. Fig. shows an exaple voltage wavefor with a swell and sag, and the corresponding wavelet coefficients. shown in Fig. is the level- detail coefficient obtained with DB8 other wavelet. Voltage (kv) Detail- - -... -. swell -. Tie.....5.3.35. Fig.. Detection of power quality events using wavelets: a voltage swell and a voltage sag V. CONCLUSONS A tool for perforing online discrete wavelet transforation in an etp-type progra (PSCAD/EMTDC) was developed. The online DWT tool handles nine different other wavelet types, and incorporates an integrated antialiasing filter and a sapler. Accuracy of calculations was extensively validated against MATLAB wavelet toolbox. Several applications of DWT in power syste protection and power quality onitoring were presented. The new online DWT tool will stiulate the developent of new wavelet applications in the field of power systes. sag V. REFERENCES [] A. Graps, (3), ntroduction to Wavelets, stituto di Fisica dello Sapazio nterplanetario, Roe, taly, [online]. Available: http://www.aara.co. [] C. H. Lee, Y. J. Wang, and W.L. Huang, A Literature Survey of Wavelets in Power Engineering Applications, in Proc. of Science Council, ROC (A), Vol., No., pp 98,. [3] D.C. Robertson, O.. Caps, J.S. Mayer, and W.B. Gish, Wavelets and Electroagnetic Power Syste Transients, EEE Trans. on Power Delivery, Vol., No., April 996. [] S. Santoso, E.J. Powers, W.M. Grady, Power Quality Disturbance Data Copression using Wavelet Transfor Methods, EEE Trans. on Power Delivery, Vol., No. 3, Jul. 997 [5] H.T. Yang and C.C. 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Turanli, Aquantitative coparison of different other wavelets for characterizing transients in power systes, in Proc. of EEE Canadian Conf. on Electrical and Coputer Engineering, pp. 3 36, May 6 [] J. Stoupis, M. Maharsi, R. Nuqui, S. Kunsan, and R. Das, Ground Alert: Reliable Detection of High pedance Faults Caused by Downed Conductors, ABB Review, No.,. [] R.P.Bingha, D. Kreiss and S. Santoso, Advances in Data Reduction Techniques for Power Quality nstruentation, Dranetz Technologies nc. [online]. Available: http://www.dranetz-bi.co/pdf/ [] N. Perera, A.D. Rajapakse, Agent-Based Protection Schee for Distribution Networks with Distributed Generators, Power Engineering Society General Meeting, 6, pp -6 EEE 8-, June 6. [3] C.Y. Evrenosoglu and A. Abur, "Travelling Wave Based Fault Location for Teed Circuits," EEE Trans. Power Del., vol.., no., pp. 5-, Apr.5. V. BOGRAPHES Nuwan Perera received the B.Sc. (Eng.) degree fro University of Moratuwa, Moratuwa, Sri Lanka, in 3. Currently he is pursuing the MSc. degree in the Departent of Electrical and Coputer Engineering at University of Manitoba, Winnipeg, MB, Canada. His research interests are in power syste protection. Athula D. Rajapakse received the B.Sc. (Eng.) degree fro the University of Moratuwa, Moratuwa, Sri Lanka, in 99, the M.Eng. degree fro the Asian nstitute of Technology, Bangkok, Thailand, in 993, and the Ph.D. degree fro the University of Tokyo, Tokyo, Japan, in 998. Currently, he is an Assistant Professor at the University of Manitoba, Winnipeg, MB, Canada. His research interests include power syste protection, transient siulation of power and power-electronic systes, distributed and renewable energy systes. R.P. Jayasinghe obtained his B.Sc. (Eng) degree fro the University of Moratuwa, Sri Lanka in 987 and Ph.D. degree fro the University of Manitoba in 997. He is currently with the Manitoba HVDC Research Centre. As a Developent Engineer he plays a ajor role in the current developents in PSCAD/EMTDC siulation progra. He is a Registered Professional Engineer in the Province of Manitoba. Dr. Jayasinghe also serves as an adjunct professor at the University of Manitoba.