MODELLING OF INDOOR LOW VOLTAGE POWER-LINE CABLES IN THE HIGH FREQUENCY RANGE

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1 MODEING OF INDOOR OW VOTAGE POWER-INE CABES IN THE HIGH FREQUENCY RANGE I.C.Papaleonidopoulos*, C.G.Karagiannopoulos*, N.J. Theodorou*, C.E.Anagnostopoulos**, I.E.Anagnostopoulos** * National Technical University of Athens, Department of Electrical and Computer Engineering, High Voltages and Electric Measurements aboratory, 9 Heroon Polytechniou Str., GR 57-8 Athens, Greece. * *National Technical University of Athens, Department of Electrical and Computer Engineering, Multimedia aboratory, 9 Heroon Polytechniou Str., GR 57-8 Athens, Greece. Author contact address: ABSTRACT Considering Power ine Communications over the ow Voltage network, propagation characteristics of mains cabling in the High Frequency range are being examined. A theoretical model of indoor single-phase sheathed tricels with conductors of circular cross section in the -MHz-frequency area is being introduced. Verification of the model proposed has been performed, involving transfer function measurements of appli sample s, which seem to follow quite well the theoretically anticipated behavior. I. INTRODUCTION Power ine Communications (PC) technology is emerging as a rapidly developing field, likely to offer competitive techniques for numerous communication applications. Current research is mainly focusing on two aspects, of which the first is aimed at converting mains cabling into a ocal Area Network (AN), such as Ethernet, whereas the second and more ambitious one has to do with supplying telecommunication services through the ow Voltage (V) allocation network. Also transferring communication traffic through the Medium Voltage (MV) grid is being considered. In order to deliver reliable up to date indoor networking services for households or companies, and sufficient connection to the backbone telecommunication network, whether it is the V allocation network, Public Switched Telephone Network (PSTN) or other supplier, transmission rates of at least Mbps would be needed. As to developing sufficient systems for such applications, several modern digital high-speed modulating and/or multiplexing schemes are being examined. Achieving the data rates defined above would demand use of the High Frequency (HF) band, as the Hartley- Shannon Theorem, given by (), implies []. P C = BT log + bit/s () N C : channel s capacity B T : channel s frequency bandwidth P : mean power of transmitted signal at reception N : mean power of additive Gaussian noise at reception However, power electric network proves to be particularly inhospitable when operating as transfer medium in the area of MHz. The s used for indoor installations are designed to transfer electric power, not information. Power lines transmission behavior displays considerable frequency dependence. Amplitude degradation and phase shift should propagating HF signals suffer through such s, vary appreciably by frequency []. There hasn t though yet been developed a general analytical transfer model of indoor V s, that would precisely specify the line s transfer parameters in terms of the cabling s dimensions and structure materials. In this paper, a model describing indoor V s HF propagation properties is derived, which applies to single-phase tricels with circular conductors and cross section as Fig. illustrates. The model proposed has been verified by relevant transfer-function measurements over appli types that are widely used in Greece for external electrical installations in buildings. Figure. Cable s cross-section II. THEORETICA ANAYSIS Considering the case of single-phase distribution, the structure depicted above comprises a phase conductor, the neutral and the ground one. Each conductor is vested

2 by its insulation coating the core insulation layer and an additional external insulating sheath encloses all three wires, which usually form a twisted triplet, as shown in Fig. []. For permanent installations, one-ply conductors are used, but flexible s are only assembled of litz wires, where metallic conducting fibers get also self-twisted as a whole. Figure. Twisted wires in a single-phase tricel. For modeling purposes, any of the types described above is regarded as a two-conductor plus reference wire transmission line, with surrounding dielectric material of relative dielectric constant ε r. Assuming the three conductors being parallel to each other, effects of twisted-wires mounting are not taken into account. Further approximation adopted has to do with neglecting the air layer section amid the three wires, which indeed is negligibly narrow, and gets even narrower due to the pressure that is enforced by the insulating sheath. In addition, dielectric s discontinuity across demarcation surface between core insulation and the sheath is being ignored. Solid circular conducting cores with equal radii are being adopted, so in the case of flexible tricels formed of multi-core wires, additional approximation is inserted to the model. Wave propagation principles by use of distributedelement analyzing techniques are followed, as wavelength is comparable to distances found in V mains networks, when treating HF signal propagation. Corresponding wavelengths at frequencies -MHz fluctuate from 3m to 5m respectively in free space, whereas typical PC channel distances over an indoor grid are in the range of m to m. Thus the is being described by distributed parameters R,, C and G, denoting respectively per unit length series resistance, series inductance, shunt capacitance and shunt conductance of the line, defined as in Fig. 3. dz Rdz Cdz Gdz Figure 3. Cable s equivalent distributed model In the HF band skin effect becomes dominant. Currents concentrate near the conductor s surface and the ratio of surface electric field to current flow gives internal impedance. By internal, contribution to impedance from fields penetrating the conductor is denoted. This gives, in general, a resistance term (R) and an internal inductance ( in ), the latter to be added to any external inductance contribution arising from the fields outside the conductor ( ex ). Quantities in and ex form the two components of distributed parameter. Distributed shunt capacitance and conductance are characteristic of leakage occurring between conductors, through the s dielectric. Transmission line s configuration specified above parallel two-conductor plus reference wire, having solid conducting cores and being surrounded by the same dielectric material gives the following distributed parameters: R = ex µ r µ πσa f ( d ) a ( d / a) () µ r µ = d Cosh π a (3) R in πf (4) = in + ex (5) πε r ε C = Cosh ( d ) a (6) G = πfc tan δ (7) where α the conductors radius (taken equal for all three), d the distance between the centres of phase and neutral conductors, ε r the relative dielectric constant of the surrounding dielectric material, tanδ its dissipation factor and µ r its relative magnetic permeability [5]. Figure 4. Transmission line Considering a transmission line of length l and characteristic impedance Z, terminated at the load end (position z=l) with impedance Z and excited by a signal generator with impedance Z g at the other end (z=), as displayed in Fig. 4, voltage signals at the line s ends are related as follows: a l V ( l) e e H ( f ) = = V () + ρ e jβl a l ( + ρ ) e jβl (8) where a the attenuation constant, β the phase-angle constant, H(f) the line s transfer function from z= to z=l and ρ the reflection coefficient at z=l [3]. Assuming the case of low-loss lines, it stands Z = C R GZ a = + Z β = πf C (9) () ()

3 Accepting for the dielectric s relevant magnetic permeability µ r, it gets πf ε r β= () c where c =3 8 m/s. The line s amplitude response comes out from (8) to be: H(f) = e ( + ρ ) al al ( + ρ e cos βl) + ( ρ e sin βl) al (3) whereas the phase shift that gets inserted to signals propagating is given by al ρe sin βl φ = βl + Arc tan (4) al + ρ e cos βl Relations (3) and (4) give respectively the theoretically anticipated amplitude response and phase shift of transmission lines being excited and terminated as Fig. 4 illustrates, observing input at z= and output at z=l. III. MEASURING PROCESS AND RESUTS Configuration of experimental set-up has been as in Fig. 4, with reference conductor being grounded. There have been used a Sweep/Function Generator to excite the circuit and a digital real-time oscilloscope interconnected with a laptop, to capture input and output waveforms and perform the measuring functions. Pure resistance elements have been used as terminating loads, with their value being each time close to the s characteristic impedance, but not exactly equal to it. Such slight impedance mismatch at termination end has been taken into account to assess the theoretically expected curves of amplitude response and phase shift. During measuring process, there have been tested sample s of the types NYM.5mm and NYM.5mm, per VDE-5, but the model deployed above applies to any type assembled as in Fig. (e.g. NYAF etc.). Measurements have been conducted for two s of each type, with lengths of 5m and 5m four sample s have totally been examined. Respective transfer function, as defined by (7), at the -MHz range has been observed for each one, by recording Amplitude Response and Phase Delay. Results are set out in figures 5 to, where unbroken lines depict experimental results and dotted curves are derived from the model proposed. Amplitude Response s theoretical diagrams are plotted by virtue of (3), whereas Phase Shift s ones represent (4). Constant β has not been extracted from (), but from (). Information from [4] has been used while extracting the theoretical diagrams. Flexible structure of the samples measured should at this point be mentioned, which means that conducting cores are not solid, but formed of litz wires. Experimental thus conditions fall under the worst approximating case of the model, as far as s configuration is concerned.,9,8,7,6,5,4,3,, Figure 5. Amplitude response of 5m sample 3.5mm Figure 6. Phase shift of 5m sample 3.5mm NYM,9,8,7,6,5,4,3,, Figure 7. Amplitude response of 5m sample 3.5mm Figure 8. Phase shift of 5m sample 3.5mm NYM

4 ,8,6,4, Figure 9. Amplitude response of 5m sample 3.5mm Figure. Phase shift of 5m sample 3.5mm NYM,9,8,7,6,5,4,3,, Figure. Amplitude response of 5m sample 3.5mm Figures. Phase shift of 5m sample 3.5mm NYM IV. DISCUSSION Phase shift resulting from the measurements is identical to theoretically derived respective behaviour, so that the two curves cannot be identified from each other, as it is well apparent from figures 6, 8, and. Taking into account that termination loads used for different series of measurements have each time been close to the s characteristic impedance, reflection coefficient given by (5) takes very low values (ρ <<). Consequently, phase shift is from (4) being determined almost exclusively by phase-angle constant β. As long as β is extracted from (), the s propagation velocity appears in complete accordance with the model introduced herein. Z Z ρ = (5) Z + Z Observing amplitude response, slight deviation comes up between measured graphs and the theoretical ones. In the case of 5m sample s, differences are entirely negligible, ranging like random experimental errors. However, figures 7 and reveal some discrepancy, minor though, at frequencies below MHz. Above MHz both diagrams confirm complete accordance to the model. atency that comes up below MHz is probably set down to approximations that formula () of R comprises. The exact value of R is given as [5]: R = fµ ( ) ( ) r µ Ber q Bei q Bei q Ber q πa Ber q + Bei q Ber q = Re{ J ( ) } q Bei = Im{ J q q (6) (7) ( )} (8) where J (q) denotes the zero-order Bessel function of the first kind, and q r = πfµ µ σα (9) In order for per unit length series resistance to be extracted by () with practically absolute precision, it must stand [5]: πfµ r µ σα >> () Strictly, inequality of () requires that difference between the two quantities would comprise at least two orders of magnitude. In fact though for the s studied herein only above MHz it gets πfµ r µ σα > As R is proportional to square root of frequency, whereas G is proportional to frequency, attenuation constant depends on R on lower frequencies rather, than on higher ones. Such dependence holds irrespective of the s length, but as the Amplitude Response is mainly subject to exponential dependence from distance due to low ρ, as inferred by (3) minor deviation is better observed at longer distances. In any case, the model corresponds

5 sufficiently to the s behavior in the whole band tested, and accuracy in practice required is definitely provided. In general, electric power network s topology, formed by replicated star or tree configurations [], causes severe multipath propagation effects [9]. That is to say not only the desired signal, but also one or more delayed and attenuated copies of it from now on being referred to as paths arrive at reception. This is the result of several reflections caused at joints of the network s s, connection boxes, serial connections of s with different characteristic impedance, and in general points of discontinuity, due to impedance mismatches that occur [9]. Resulting intersymbol interference imposes further constraints upon the maximum data rate. The parameter of root mean square (rms) delay spread τ rms is a good measure of channel s time dispersion on account of multipath propagation. It is defined as the square root of the second central moment of the channel s power delay profile, and, assuming the existence of different paths, it can be written in the form of (), where β i and τ i are the amplitude and arrival time respectively of the path i [8]: β i β j ( τ i τ j ) i= j= j> i τ = () rms i= β i Parameter τ rms gives an indication of the maximum data rate that can be achieved without giving rise to intersymbol interference. It is generally admitted that maximum data rate, without diversity of equalization, has to be smaller than a few percent of inverse rms delay spread, i.e. DR max =c (τ rms ) - () where c<.5 [6,7,8]. In order to calculate τ rms it is obviously necessary to know the paths amplitudes and arrival times. In practice though, if desired to estimate the capacity of an indoor PC networking installation, only approximate simulations of the paths amplitude and arrival-time distributions or estimations of the relevant possibility density functions are feasible in terms of the network s extent and topology or based on indicative measurements, comprising though finite accuracy. To maximize the latter it is crucial to precisely know transfer medium s propagation properties, where major usefulness of the model proposed emerges. V. CONCUSION This paper introduces a transfer model for single-phase indoor low voltage s in the HF range. The model is based on wave-propagation consumption, by use of distributed-element transmission-line analyzing techniques, and it has been confirmed by relevant transfer function measurements over selected sample s of different dimensions and lengths. The model proves to describe transfer properties of corresponding types with sufficient precision, forming a reliable and accurate tool of analyzing indoor V cabling in the -MHz frequency range. It proves well out, ensuring the capability of performing precise HF signal propagation analysis over mains electrical grids topologies, facilitating both analytical and statistical grouping and characterization of V PC networks, in order to perform network capacity estimations. REFERENCES [] S. Haykin: Communication Systems, New York: John Wiley & Sons, Inc., nd Edition, 983. [] E.W.G. Bungay and D. McAllister, Electric Cables Handbook, Oxford: Blackwell Science, Second Edition, 99, ap. A6, pp [3] Ν. Κ. Ουζούνογλου, Εισαγωγή στα Μικροκύµατα, Athens: Παπασωτηρίου, Β Έκδοση, 994, ch. 3, pp [4] W. Tillar. Shugg, Handbook of Electrical and Electronic Insulating Materials, New York: IEEE Press, Second Edition, 995, ch., pp [5] S. Ramo, J.R. Whinnery and T. van Duzer, Fields and Waves in Communication Electronics, New York: John Wiley & Sons, Inc., 994, ch. 4, pp. 7-, ch. 5, pp [6] K. Pahlavan and A.H. evesque, Wireless Information Networks, New York: John Wiley & Sons, Inc., 995. [7] H. Hashemi and D. Tholl, Statistical Simulation of the RMS Delay Spread of Indoor Radio Propagation Channels, IEEE Transactions on Vehicular Technology, vol. 43, No., Febuary 994, pp.-. [8] G.A Dimitrakopoulos and C.N. Capsalis, Statistical Modeling of RMS-Delay Spread Under Multipath Fading Conditions in ocal Areas, IEEE Transactions on Vehicular Techology, vol.49, No.5, Septsmber, pp [9] M. Zimmermann and K. Dostert, A Multi-Path Propagation Model for the Power-ine Channel in the High Frequency Range, 3d International Symposium on Power-ine Communications and Its Applications, 999, pp [] C. Assimakopoulos and F.-N. Pavlidou, Measurements and Modelling of In-House Power ines Installation for Broadband Communications, in Proceedings of the 5th International Symposium on Power-ine Communications and Its Applications,, pp [] I.C.Papaleonidopoulos, C.G.Karagiannopoulos, D.P. Agoris, P.D. Bourkas, and N.J. Theodorou, HF Signal Transmission over Power ines and Transfer Function Measurements, in Proceedings of the Sixth IASTED International Conference on Power and Energy Systems,, pp.5-55.

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