Interference assessment: Comparison of reed track circuit computer model and DFT based analysis

Transcription

1 Interference assessment: Comparison of reed track circuit computer model and DFT based analysis V. Staudt', D. Wurgler^ * Institute for Generation and Application of Electrical Energy, Ruhr-Universitat Bochum, D Bochum, Germany, CH-3661 Uetendorf, Switzerland Abstract Compatibility of electric traction vehicles with existing signalling systems is usually assessed by comparing a frequency domain representation of the line current of the vehicle with frequency domain limits. This frequency domain representation of the current is normally reached by applying a Discrete Fourier Transform (DFT) or a Fast Fourier Transform (FFT) algorithm to a time interval of the current. The length of this time interval (window length) and the way in which the values in this time interval are weighted (window function) influence the frequency domain representation considerably and must therefore be selected in accordance with the signalling system to be protected from interference. This paper first describes a model of a reed track circuit receiver based on a linear filter and its validation based on laboratory tests. It then compares the frequency domain representation of this filter to frequency domain representations of window functions used with DFT. From this comparison window length and window function as well as a post-processing algorithm for the DFT results are selected. The aim of this selection is to obtain an assessment method based on DFT which comes close to the behaviour of the filter and hence to the behaviour of the track circuit receiver. Transients (for example transformer inrushes) are very important when assessing compatibility. They can best be treated using time domain methods. Time domain comparisons of the output of a sliding DFT algorithm to the output of the linear filter clearly demonstrate the suitability of the proposed algorithm to the assessment of transients.

2 oco, C.A. Brebbia J.Allan, R.J. Hill, G. Sciutto & S. Sone (Editors) 1 Introduction Every electric locomotive in operation has to fulfil strict interference requirements set by the respective railway operator. Normally conformity to these requirements is checked before and while a new locomotive is first put into service. Various unavoidable factors, for example pantograph bouncing, transformer inrush or filter charging and limited switching frequency of power electronic devices, cause undesirable current and voltage components during normal operation of every conceivable traction drive. The interference requirements have to allow for such unavoidable current components, but protect the installed signalling equipment from interference causing malfunction. A reed track circuit receiver manufactured by Alstom is chosen as an example to demonstrate a way how known DFT methods can be used as basis for assessing interference not only in steady state, but also during transients. The whole scope of interference and interoperability of electric rail vehicles, including the "transfer function" linking the current caused by the electric rail vehicle with the voltage at the terminals of a track circuit receiver, is currently being treated in a project jointly funded by the European Community and the Swiss government. The project is entitled "Electrical System Compatibility for Advanced Rail Vehicles", ESCARV [1]. The results and findings presented in this paper are part of this project. 2 Transients Transients often exceed the permitted interference limits when analysed with methods such as DFT or band pass filters. But they cannot simply be disregarded as a "disturbance" of the analysis. Whether such transients are critical or not depends on the reaction of the signalling systems. Ideally, the chosen analysis method should mimic the reaction of the signalling system under all conditions, both steady state and transient. This can best be reached using limits and models directly oriented at the physical behaviour of the equipment to be protected. The limits should be applicable to steady state and transient conditions, which is not easy when using frequency domain limits. This paper describes a way how reliable frequency domain limits for a reed track circuit receiver can be set. Under steady state conditions an analysis of the track voltage is relatively easy. Transient conditions pose a challenge: The vehicles cannot comply with pessimistic limits and methods under the usual transient conditions; raising the interference limits generally above the transient levels could be unsafe for the signalling systems. A wrong side failure, where a track section monitored by a track circuit receiver is wrongly reported to be free, is the worst case of interference. It can be caused by the distorted line current of a locomotive [2] if the interference voltage at the terminals of the track circuit receiver is mistaken as the transmitter signal [3].

3 359 3 The reed track circuit receiver Reed track circuits have very narrow band pass characteristics, but the permitted interference levels at the reed frequencies are extremely low. The effects of transients and of noise and errors introduced by the measurement and analysis system often reach or exceed the permitted interference levels. This was the motivation to find analysis methods matching the behaviour of the reed receiver as closely as possible both for steady state and for transients. Reed track circuits were designed for compatibility with phase angle controlled vehicles. The operating frequencies were selected outside of the harmonic pattern of the 50 Hz supply frequency. Phase angle controlled vehicles produce essentially multiples of the supply frequency. Modern inverter locomotives produce lower levels of interference, but they produce noise in between the supply harmonics and can therefore invade the operating frequencies of Reed track circuits. A reed track circuit receiver lent to Ruhr-Universitat Bochum by Alstom could be tested in detail in the laboratory. The main components of the receiver are shown in Fig. 1. It declares a track section as free, if a sufficiently high voltage component with a frequency determined mainly by the receiver filter is present in the track voltage UTF between the rails. This voltage component is generated by a suitable feed unit and short-circuited by rail vehicles present on the track section. from track tnpv filter (electrical band pass filter) *RF URF rpppivpr filtf&r (electromechanical reed filter) *RA URAJ 'TR receiver amplifier UTR track relay TF RF RA TR Figure 1 Main components of reed track circuit receiver A model of the reed track circuit receiver valid for transient and steady state signals has been built and validated. The validity of the model developed can best be verified using a test signal which has its energy concentrated in a frequency region close to 372 Hz, but is non-stationary. A wavelet type signal fulfils these requirements [4]. Fig. 2 shows the reaction of the reed track circuit receiver and of its model to a wavelet type signal. The simulated relay current is always slightly above the measured relay current, because during model development the parameters were always chosen such, that the model is a little more sensitive and therefore pessimistic. In this case the model declares the track to be free, while the track circuit receiver itself is slightly below the pick limit. Fig. 2 also shows that the reed track circuit receiver is excited mainly by the beginning and the end of the wavelet, but not so much by the centre part, although the energy of the wavelet is concentrated around 372 Hz.

4 360 simulation: relay engaged L- Figure 2: Reaction of a reed track circuit receiver and of its model to a wavelet-type input signal track filter input voltage relay current (simulated) relay pick limit -20 Because of the receiver amplifier and the generation of a d.c. relay current the receiver and the detailed model both contain non-linear parts making an exact frequency domain characterisation difficult. 4 Frequency domain characterisation Limits set in the frequency domain must somehow cope with the problems posed by transients and by non-linear effects. This is often done by applying bursts to the track circuit receiver and characterising its reaction. A burst in this context is a signal which is sinusoidal during a given time interval and zero everywhere else. Limits resulting from bursts can not easily be applied to other transient conditions, like transformer inrushes (or filter charging in case of d.c. traction vehicles). Setting limits based on selected DFT methods leads to improved results. 4.1 Limits based on bursts Limits based on bursts usually follow two steps: Determination of an attenuation characteristic. Determination of amplitude and duration of a burst with centre frequency which just makes the receiver pick.

5 In case of the reed track circuit receiver the attenuation characteristic is identical with the combined filter characteristic of track filter and reed filter. It is depicted in Fig. 3. The amplitude vs. duration characteristic as measured in the laboratory is shown in Fig burst duration / s extrapolation measurements interpolation extrapolation measured: track and reed filter > ^nn relative amplitude / % Figure 3: Filter characteristic of model Figure 4: Duration of burst needed for and of track and reed filter picking of relay Fig. 4 shows that for example a burst of 500 ms with a relative amplitude of 247 % makes the relay pick. The associated limit (without safety margin) would be: A locomotive current with a 372 Hz component equivalent to a relative amplitude of 247 % shall not last longer than 500 ms. At the maximum allowable relative amplitude of 360 % the limit would be 330 ms. These limits leave the question of quickly and correctly detecting a 372 Hz component open. 4.2 DFT, FFT and window functions Any DFT (or FFT) is characterised completely by three basic parameters: The time interval [0, Ty[ given by the base period Ty. The number D of samples taken during one base interval. The window function applied (for example rectangular or Hanning). With these parameters, the base frequency fy = 1/Ty, the sampling time TS = Tb/D and the sampling frequency f% = 1/Ts =D-fy result. Additionally, the time signal is supposed to be periodic with period Ty. This leads to a discrete spectrum. Each discrete frequency with its amplitude and phase resulting from DFT is from here on called "line" [5]. The rectangular window as function of the number n of a sample is given by Wrect(n) = 1; 0<n<D (1) with the associated Fourier Transform The Hanning window is given by D Whann(n) = j - [ 1 - cos(^-^)]; 0 < n < D with the associated Fourier Transform (2) (3)

6 362 Computers in Railways Vll Due to the time discrete window functions the spectrum is periodic. For a very low value of D = 11 its magnitude is shown in Fig. 5. All information is contained in the region from d.c. to half of the sampling frequency f*. In time domain, the window function is multiplied with the signal. In frequency domain, this corresponds to a convolution of the frequency domain representation of the time signal and the frequency domain representation of the window function. D =11 Wfift* W, f/fs 0 i''' 'A'''' iij''' ' A '» '» M I i j rect hann Figure 5: Magnitude of the spectrum associated with the time discrete window functions of the rectangular and Banning window 4.3 Limits based on selected DFT methods The frequency domain representation of the window function shown in Fig. 5 can be interpreted as the frequency domain characteristic of a filter associated with each line resulting from the DFT. Because of the convolution the d.c. position on the frequency scale in Fig. 5 is centred on the frequency of each line under consideration. The frequency of each line is an integral multiple of the base frequency fb. The frequency domain characteristic can be compared with that of the filter already seen in Fig. 3. For ease of comparison and simulations the characteristic of the validated model is taken as a reference. Fig. 6 shows the frequency domain comparison for selected window functions and parameters. The functions are scaled such, that the minimal attenuation is identical to that of the model of the reed track circuit filters (0.024 = db) From the safety point of view it is important that the assessment method is more sensitive than the track circuit receiver. The frequency domain characteristic of the DFT should always be slightly above that of the model - at least in a frequency range where interference is possible. Looking at the main lobes of the DFT variants shown in Fig. 6 the rectangular window meets these requirements best. In case of the Manning type windows either the main lobes are too wide, or their side lobes are too low. All characteristics show gaps at the positions of neighbouring lines of the DFT. It has to be checked, whether these gaps can be tolerated or how they can be closed.

7 363 db A H Rect, Is f/hz 380 upper envelope ^ side lobes -100 Figure 6: DFT with selected parameters compared to the model 4.4 Closing the gaps Especially in case of the rectangular window with Ty = ls the gaps closest to the centre frequency of 372 Hz can already be found at 371 Hz and 373 Hz. The attenuation of the reed filter model at this frequency is about 7.38 in comparison to that at the centre frequency. On the one hand such an attenuation only one Hertz away from the centre frequency shows that the reed filter is really a high-q filter, but on the other hand this attenuation does not guarantee total protection from interference. This gap should be closed. A possible approach is to simply add the squared magnitudes of the lines, weighed with the associated attenuation factor resulting from the filter characteristic, and then take the root of this expression: Ares = ^ A3711* A372^ A373!^. (5) This method will be called "extended rectangular" from here on. The computational effort is low, because the DFT computes all lines by default. In a distance of 2 Hz from the centre the attenuation of the filter is already 26.09, making interference unlikely. If necessary these gaps can also be closed by simply including the respective lines - properly attenuated - in eq. (5), too. Often track circuit receivers with similar frequency domain characteristic, but different centre frequencies are used, for example on neighbouring track sections or parallel tracks. In this case only one DFT is calculated for the assessment. Based on the DFT result, (5) is then evaluated once for each centre frequency, selecting the amplitudes associated with this centre frequency.

8 364, C.A. Brebbia J.Allan, R.J. Hill, G. Sciutto & S. Sone (Editors) 5 Simulation results The performance of the proposed assessment methods can best be checked by comparing the reaction of the model and of the DFT based assessment method in time domain. For this, the base interval of the DFT slides along the time signal to be analysed in small steps of 10 ms. Depending on the application, the width of these steps could be increased to reduce calculation effort. With the knowledge gained from Fig. 6 it is possible to select test signals such that the advantages and drawbacks of the methods are pointed out. The first test signal is a burst with 360 % of relative amplitude at 372 Hz and a duration of 1.3 s, see Fig. 7. With the time scale used the waveform of the input voltage cannot be shown, only the region in which it is non-zero. / Manning 0.5 s Manning 1 s extended rect. 1 s rectangular 1 s Manning 2 s 0 1 region of input voltage 2 3 t/s Figure 7: Burst with 360% of relative amplitude at 372 Hz, duration 1.3 s The 2 s Hanning windows is not acceptable because it rises much too slowly. Its output is no longer shown in the next figures. The rectangular and extended rectangular output signals are practically identical in Fig. 7, but their difference can be seen in the Fig. 8, which shows the reaction to a burst with the same amplitude, but a frequency of 370 Hz. Manning 0.5 s contents of circle is enlarged by factor 3 extended rect. 1 s rectangular 1 s \ Hanning 1 s filter n "" ' \ region ^ of input voltage, 2 3 t/s Figure 8: Burst with 360% of relative amplitude at 370 Hz, duration 1.3 s The enlargement shows that the extended rectangular method is closer to the filter than the rectangular method at 500 ms (half the base period) of the burst.

9 However, as the 370 Hz line is not included into the extension according to (5), both methods - and also the Hanning with 1 s of base period - go down to amplitude zero after 1 s (the base period). At this moment stationary conditions are reached for a DFT with a base period of Is. Including 370 Hz and 374 Hz into (5) would solve this problem for the extended rectangular method. Because of the wide main lobe the Hanning 0.5 s window still detects the 370 Hz, but with very high amplitude. Selecting a special test signal given by UTF,c(n) = u. [cos(371 - ^p) + cos(372 - ^p-) + cos( ^p) ] (6) reveals severe drawbacks of the Hanning based method, which are due to the wide main lobe (see Fig. 9). 365 A Uo,,,/mV, rectangular 1 s extended rect. 1 s region and shape 2 3 t/s of input voltage Figure 9: Combination of three cosine functions according to (6) While the rectangular methods and the 1 s Hanning window reach stationary conditions after one base period of input signal with values slightly above the filter output, the output of the 0.5 s Hanning window continues to oscillate, partly dropping well below the filter output. Together with the fact that its output is unnecessarily high or unnecessarily quick in the previous examples, it disqualifies this type of window function as basis of the assessment method. A similar example can be constructed for the 1 s Hanning window. The simulation results are clearly in favour of the extended rectangular assessment method. As a final example Fig. 10 shows the reaction of the various methods to a frequency sweep from 360 Hz to 392 Hz during 3.3 s. Manning 1 s region of input voltage Figure 10: Frequency sweep from 360 Hz to 392 Hz, duration 3.3 s t/s

10 366 Again the extended rectangular method leads to an output very close to the filter output. 6 Conclusion A DFT based method is proposed which allows an assessment of steady state and transient signals with respect to their interference with reed track circuit receivers. The results of the laboratory characterisation of the reed track circuit receiver are shortly presented. A validated frequency domain filter model is derived as basis for the selection of suitable DFT methods. Proper reaction to steady state and transient signals is verified by time domain simulations. Only one DFT and small additional calculation effort is needed to correctly assess all reed frequencies, as long as they have similar frequency characteristics at different centre frequencies. The principle of the method can be adapted to other track circuit receivers, if these can be characterised in the frequency domain. 7 Acknowledgements The authors gratefully acknowledge the financial support of the European Commission and the Swiss Department for Education and Science to the research activities presented in this paper. These activities are part of the project Electrical System Compatibility for Advanced Railway Vehicles (ESCARV). The authors wish to thank Alstom Signalling for making a reed track circuit receiver available for characterisation in the laboratory. 8 References [1] Schmidt, S., Terwiesch, P., Wuergler, D., Henning, U. Electrical System Compatibility for Advanced Rail Vehicles: A Survey. 8th Int. Conf. on Harmonics and Quality of Power, Athens, pp , 1998 [2] Steimel A. Line current of AC traction vehicles with electronic power control. EtzArchiv, 12(3), pp.69-79, 1990 [3] Taufiq, J. A., Mellitt, B., Goodman, C. J. Signalling Compatibility of Inverter Drives for Railway Traction. Proceedings, International Conference on the Evolution and Modern Aspects of Industry, pp , 1986 [4] Terwiesch, P. Time-frequency analysis and wavelets: an introduction. Automatisierungstechnik, 46(1), pp.3-14, 1998 [5] Staudt, V. Effects of window functions explained by signals typical to power electronics. 8th Int. Conf. on Harmonics and Quality of Power, Athens, pp , 1998