Electromagnetic fields modeling of power line communication (PLC)

Transcription

1 Electroagnetic fields odeling of power line counication (PLC) Wei Weiqi UROP 3 School of Electrical and Electronic Engineering Nanyang echnological University E-ail: @ntu.edu.sg Keyword: power line counication, radiation Abstract n this project, the circuit odel of a straight 3-line PLC syste with a pure EM input signal has been deduced. he detail process of odeling, the assuptions we ade and its atheatical expression will be showed. he radiation field (E & H fields) of a given point in the near field space has been calculated with the help of Matlab progra. Due to the liitation of tie, we only did the siplest case of the PLC radiation probles. Further research work ay proceed to the PLC syste with a bend, or a non pure EM ode signal radiation calculation.. ntroduction he technology of Power-line-counications (referred to as PLC in the industry) was firstly introduced in 94 s. t was used by power utilities for siple teleetering and control of electrical equipent in their networks. Not until recent years, is it again a superstar of any telecounication researchers and it has been a rapidly evolving arket that utilizes electricity power lines for the high-speed transission of data and voice services.. Background & Current Situation: he Power-line-counication (PLC) is very popular because of the concept of No new wires, which it was built on. All the wired networks we are using now required an extra network cable, which eans we have to have an extra cable network built besides the power supply network. t is not only tie consuing but also very expensive. On the contrary, by using the technology of PLC, there is no additional network needed hence no extra construction work needed, as every roo, old or new, ust have a power supply to it (in ajority cases). With PLC we could siply connect all PCs fro every roo within the sae unit, and all units within the sae house. However, the L power lines which the PLC based on present an extreely harsh environent for high frequency counication signals []. n other words, the noise and signal distortion becoes very coplicated when the frequency goes high. Moreover, there is always another key point to be worried when frequency is high. hat is the high frequency signal radiation. he radiation of high frequency PLC signal (3-lines) was indeed what we were interested in this project. Because of all the uncertainties above, up to now, there is only USA, Gerany and Britain those three countries have soe PLC application within liited areas, and the bandwidth is controlled below MHz.. Literature Review: here were soe literatures published on the analyzing of the radiation of PLC under wide frequency range. However, so far as know, none of the was related to the PLC through the 3-line indoor power supply transission line. Esailian, Kschischang and Gulak [3], have done a research

2 on the calculation of radiation of power line by using the antenna theory but it was based on a - line power line syste, and the linkage to ground was ignored. H.Meng and others [6] have developed a novel approach of the radiation calculation of the 3-line indoor power supply syste. However, the approach is only applicable to courtiers with shielding outside the power line syste..3 Objective & Liitation: he objective of this project was to set up the atheatical odel of a straight 3-line power line syste, analyze the radiation caused by the high frequency injected PLC signal. n following parts, the detailed odeling process will be given as well as the atheatical expression. At last, the radiation of the 3-line PLC syste pure EM signal input has been prograed and calculated.. Methodology n this part of the report, the assuptions ade for this odeling and soe special techniques used in this project will be introduced. We have tried out any different ways to do the odeling. Only the final ethod we chose was shown and explained.. Lup Circuit S Distributed Circuit: When we tried to analyze the power lines under PLC signal condition, the first thing cae into our ind was we ay not be able to apply the traditional power supply transission line analysis ethod under 5Hz to our case, in which the signal is under MHz or s of MHz. Both Lup Circuit ethod and the Distributed Circuit obey the Maxwell s wave propagation theory. hey were developed to siplify the calculation of circuit analysis under different conditions (i.e. different frequency ranges). One of the ajor differences between these two ethods is in Lup Circuit heory; the propagation tie through the circuit is zero. his eans that at the oent you inject the current at the input, there will be current at output (or the return path) of the circuit. However, this will only be true if it works under low frequency. Or uch clearer to say, it is only true when the circuit size is far saller copared to the signal wavelength. (e.g. in 5Hz, the wavelength is? = c/f, where is c is the speed of light in free space, thus? = 3^8 / 5 = 6^6 (), far larger than the noral circuit size.) On the other hand, when frequency increases, especially under MHz or higher, this ay not be true as the circuit size becoes coparable to the signal wavelength. n such cases, the distributed circuit ethod ust be applied. he distributed circuit theory siply divides the whole transission line into any sall pieces, and considers each piece has a return path itself. hus the current on the distributed circuit will not be the sae at different location even it is on the sae transission line.. PCB S PLC: Having decided which circuit theory to be used, the next thing is to set up the graphical odel of the 3-line power line syste. n order to do that, we have borrowed soe techniques used to analyze the PCB probles which are relatively well exained copared to the PLC probles. With soe iproveents and assuptions, finally we found the solution. Although we can find the siilarities between the power lines and strip lines, they do have soe differences, especially on grounding. For PCB board circuit, ground is just a piece of etal on the other side of the dielectric aterial. t is a perfect ground plate and very near to the strip lines. Because of that, all the PCB related probles norally could not ignore the effect brought in by the ground plate. However, when we coe to the 3-line PLC syste, it changes a lot. here are two Grounds in the 3- line PLC syste. One is the so called Ground Line, the line included in the 3-line itself. he other ground is the wall or the floor where the 3-line PLC syste is placed. hese two Grounds are different fro each other and neither of the can be analog to the ground plate in the PCB proble. Firstly, the Ground Line is not so grounded. his refers to the truth that the Ground Line in the 3- line PLC syste is only grounded under DC (direct current) condition. Fro Figure we noticed that, actually there is only one point of the Ground Line that is grounded of the whole house. hus in our case, we considered the Ground Line as another conductor with the sae self characteristics as Live Line and Neutral Line. Secondly, the wall or floor is not a perfect ground in usual cases, and was ignored in our odeling. We had two reasons for doing this. Firstly, we assued that the signal linkage to the ground (the wall or floor) would be so sall that can be negligible. We ade this assuption based on:. under MHz ~ 3MHz copper is a good conductor, while wall is not a perfect ground, thus signal flows on wall would be very sall;

3 Es. Unlike the strip lines syste the 3-line PLC syste does provide the return path for the signal. he second reason we ignored the ground (the wall or floor) in our project is due the coplexity of the ground condition itself. he property of the wall or floor will be largely changed based on the weather condition, the aterial used to build it, and even the decoration we put on it. For general purpose research, and to ake the odeling process sipler we ignored the effect brought in by the ground (wall or floor)..3 Why EM Wave: EM wave eans there is no field on the wave propagation direction. t can only exist when the conductor is lossless. And the lossless transission line is one of our assuptions to this project. With the pure EM ode signal is, under this ode, we could deterine the paraeters of a transission line by eans of the ethod we used under static conditions. his is because under EM ode, the transission line paraeters will be alost constant with the changing of frequency. his would bring us an easy way to get the values of all capacitances and inductances we concerned. With all above, we were ready to do the real thing now. he following part is the process of the deduction of the atheatical expression of the odeling. 3. Matheatical Deduction With all the theories ready, the next step we did in our project was to coe out the atheatical expression of the odel. What we concerned here was the siplest counication network using PLC technology. t was a network between two PCs with straight power lines connected in between. Following is the physical expression of the two PCs network: i - - L L L3 L L3 Live Neutral Ground L3 C C3 C3 LL L All the eleents shown on the graph are unity length based. he AC source is treated as the signal injection point, and the L represents the signal receiving end. he input ipedance LL j o tan( β l) i = o ; o j LL tan( β l) As LL 8, i = j ocot( β l) ; f we take the neutral line as reference, we will be able to coe out the & Y atrix for the 3-line syste [7]. =j?l=jw LL-L LL3-L-L3 C C3 Y = j? C= j? - C3 LL3-L-L3 LL3-L3 - C3 C3 C3 f we write the & also in atrix for: (z) = ( z) ( z) (z) = ( z) ( z) Notice that, we write the transission line equations in frequency doain as [8]: d = - (z) n order to get the uncoupled transission line equations fro (5) & (6), we ay do the nd differentiation to each of the equations with respect to z. After differentiation, we substituted the (5) & (6) to the nd order equations, then we get: f we define a transforation atrix such that the general solution of the atrix becoes: () () (3) (4) d = - Y (z) (5) d ( z) = ( z ) Y d ( z) = ( z ) Y (7) (8) ( z) = ( z) (9) (6)

4 Where (7); = (Where is a by coplex atrix and is a by atrix). hen substitute the equation (9) back to (8) yields: d ( z) = Y ( z) () he transforation atrix is defined to be a atrix that would ake the Y atrix diagonalized, in other words, Y Or in ore detail forat: Once is calculated, we could siply get the atrix fro equation (9), thus we can get & respectively. Where c is defined as he transforation atrix can be calculated once the & Y atrixes are set up, however, in order to solve atrix we still need to know the atrix. here are four unknown constant in the atrix, thus we need four boundary conditions to solve the. he additional four conditions can be found at the sending & receiving end of the 3-line syste, they are: () = Es; () = -i () ; ( l ) = L ( l) ; ( ) = ; l = = γ γ γ () We now substitute the equation () back to (), we can get the uncoupled the equation as: d ( z) = γ (z) () (z) e γ z = γ z e e γ z - γ e z (3) γ z γ z ( z) = ( z) = ( e e ) (4) ( z γ z γ z ) = ( e e ) (5) c = c Y γ (6) he only thing that ay need soe ore discussion here is the 4 th condition, ( l ) =. Refer to figure 7, notice that we assue the receiving end ipedance between Neutral and Ground Line to be infinite. hat is why the current to be zero there. n real world, unless there is soe fault occurs, the ground line should be always in open circuit condition, thus our assuption should be valid. With the boundary conditions substitute into equation (4) & (5), we found another set of ± Matrix equation for solving : ( ( c C s ) L = s i ; = C ; C L Es = L ; = ; s = ; L With all the inforation above, we could easily find the solution for ) e γ ± l ( c ) s γ l ( e C ) L fro equation (7), thus we could get the atrix of (z) fro equation (3), and then we could get the (z) atrix fro equation (9), thus get the value of & for a given z location. A detailed calculation progra is provided in Appendix A with full coents aside. he next step is to calculate the E & H field caused by the 3-line syste to a certain point in space with the location of the point known to us. n the calculation of the E & H field caused by a transission line, Robert and Paul [5] introduced a ethod that divide the transission line into any pieces, consider each piece as a sall electrical(agnetic) dipole; calculate the H field induced by every dipole to the point which is concerned. hen add the H field caused by each dipole together, will give us the total H field caused by one transission line. (Here notice that, the H field caused by every dipole along the sae straight line to the given point will be in the sae s L (7)

5 H (z) = direction, thus we can just add the together to get the total H field.) B( z) ( z) k = { J( kρ)sin( ωt) Y ( kρ)cos( ωt)} µ 4 o Where: k is the wave nuber; ( x ) Y ( are respectively Bessel functions of order, first and second kind; J ( x) = x / ; (8) Y ( x) = /( π x) ( x ln( x / )) / π; Both (z) and H(z) are the function of z, with the z changes fro z= (the sending end) to z = l (the receiving end) we are able to get the total H field for each line. Notice that, in the H field calculation above, we actually assued that it was a part of an infinite transission line. n other words, although we consider the transission line is l in length, we have ignored the two ends irregular radiation of it. here is another assuption we ade in this calculation. When applying equation (8), we actually have assued that k ρ <<, or say that the radiation field of the point we concern is very near the power line. Further research work ay be done on the condition where k ρ >=. he total H field induced by the 3-line syste will be the vector suation of the H field caused by each line. We should realize that as we have assued the signal input is pure EM wave, there would be no H field coponent in the z (the propagation) direction in all three lines. hus we can siply decopose the H field induced by every line into x & y coponent and then add the up respectively. Once the total H field is know to us, we can siply get the E field by forula: E = H p (9); Notice that, generally speaking, the equation (9) can only be approxiately true when the point we concern is far fro the signal source (e.g. the plane wave case). However, in the case of pure EM wave travels over a lossless transission line, equation (9) will still hold [9]. his case exactly falls into our assuption, thus we could still use equation (9) in spite of what we concern is actually the near field fro the signal source. n further research works, if the signal input is not a pure EM wave, equation (9) will no longer hold. hen soe other eans need to be used to calculate the H field under the near field condition. With all the calculation above, we have finally got the E and H field to a certain point in space. t is a tie dependent value, thus it is also possible for us to find out when the radiation will reach axiu fro the resultant forula. With the radiation calculated, we have successfully achieved the ain purpose of this project. 4. Conclusion he ain objective of this project is to odel the 3-line PLC syste, and calculate its radiation due to pure EM signal input. Having worked very hard for the past 7 weeks, we have successfully achieved the ain purpose set to this project. he odel of a straight 3-line syste has been set up, its atheatical expression has been deduced, and the radiation by the pure EM signal input has been prograed and calculated. Because of the short tie span, we only dealt with the siplest proble in the PLC probles. We have assued that the input signal is a pure EM wave that travels along the lossless transission lines. We also assued that the ground plane where the power line is placed can be ignored in the field calculation due to its own characteristics. We finally assued that the near field is the doinant force in the calculation of the signal radiation. n future research work, experiental easureent should be carried out to verify the odel we set up. And further analysis on the non pure EM signal travels on the transission line with bends on it ay be carried out to ake the odel ore realistic. 5. Acknowledgeents he author would like to take this chance to express his sincere gratefulness to Dr an Soon Yi, his supervisor, for Dr an s patience and guidance during the project, and special thanks to Miss Luo Wuqiong for her great help in the project 6. References [] P.A. Brown, High Frequency Conditioned Power Networks, UC Annual Conference Proceedings, 3th July 4th Aug 995. [] L.. ang, P.L. So, E. Gunawan, S. Chen,.. Lie, Y.L. Guan,

6 Characterization of n-house Power Distribution Lines For High- Speed Data ransission, Proceedings of the 5th nternational Power Engineering Conference (PEC ), May, pp. 7-. [3].Esailian, F.R.Kschischang, and P.G.Gulak, Capacity Distribution of Radiation- Liited n-building power Lines [4] Rober G.Olsen, Jeffrey L.Yong, and David C.Chang, Electroagnetic Wave Propagation on a hin Wire above Earth, EEE ransactions on antennas and propagation, ol.48.no.9, Septeber. [5] Robert G.Olsen and Paul S.Wong, Characteristics of Low Frequency Electric and Magnetic Fields n he icinity of Electric Power Lines, EEE ransactions on Power Delivery, ol.7, No.4, October 99, [6] H.Meng, S.Chen, Y.L.Guan, C.L.Law, P.L.So, E.Gunawan, and..lie, A ransission Line Model for High- Frequency Power Line Counication Channel, [7] Paul R.Karel, Gabriel D.Colef and Rayond L. Caisa, ntroduction to Electroagnetic and Microwave Engineering, A Wiley-nterscience Publication 998, [8] Li Huadong, A study of Radiated Eission fro digital PCBs with Narrow Ground Plane, Subitted to Nanyang echnological University EEE school, 999; [9] Collin, R.E., Field heory of Guided Waves, McGraw-Hill, New York, 96 [] David K.Cheng Fundaentals of Engineering Electroagnetics, Prentice-Hall, 993 o: the characteristic ipedance between two transission lines, for lossless transission lines in our case, o = L ; C L: the self inductance of Live Line; L: the self inductance of Neutral Line; L3: the self inductance of Ground Line; L: the utual inductance between Live and Neutral Line; L3: the utual inductance between Neutral and Ground Line; L3: the utual inductance between Live and Ground Line; C: the utual capacitance between Live and Neutral Line; C3: the utual capacitance between Neutral and Ground Line; C3: the utual capacitance between Live and Ground Line; (z): the Live to Neutral voltage; (z): the Ground to Neutral voltage; : the current through Live Line; : the current through Ground Line; l: the total length of the transission line; z: the distance fro the AC source to the point of L we concern;? : the angular frequency,? = pf; k: the wavenuber = p/(wqvelength); 7. Appendix i: the input ipedance look into Neutral and Ground Line; LL: the output ipedance between Neutral and Ground Line, considered being infinity in our case;