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Broadband transmission characteristics of overhead high-voltage power line communication channels.

1. INTRODUCTION

Due to ubiquitous nature of the low-voltage (LV), medium-voltage (MV), and high-voltage (HV) power grids, the structure of these grids is the key to developing an advanced IP-based power system, offering a plethora of potential smart grid (SG) applications, such as ubiquitous grid surveillance at small cost, continuous monitoring, real time adjustment of sensitive loads, and optimal response to power demand during critical circumstances [1-3]. Moreover, the need for delivering broadband last mile access in remote and/or underdeveloped areas provides a strong motivation for the deployment of broadband over power lines (BPL) networks through the entire grid [4-11].

The first power line communications (PLC) efforts put in place by power utilities over HV lines in the early 1920s with the goal of providing operational telephone services and data communications across large geographical distances [12-15]. Today, although the more significant transformation to upcoming SG technology is expected to take place on the MV and LV distribution power grids, the HV transmission power grids will have to catch the train of upcoming BPL/SG changes [16-20].

Utilities employ either the overhead or the underground HV transmission power grid for new urban, suburban, and rural installations. The choice is made according to different criteria like cost requirements, existing grid topology, and urban plan constraints [20-27].

When considered as a transmission medium for communications signals, the overhead and underground power grids are subjected to attenuation, multipath due to various reflections, noise, and electromagnetic interference (EMI) [28-36]. Each of the aforementioned adverse factors affects the overall performance and the design of BPL systems [37-40].

Due to the evolution of broadband communications and SG applications, the development of accurate models to describe signal transmission at high frequencies along the HV transmission power lines is essential. As usually done in LV/BPL and MV/BPL transmission, a hybrid model is employed to examine the behavior of BPL transmission channels installed on BPL multiconductor transmission line (MTL) structures [5,28-30,41-46]. This hybrid model follows: (i) a bottom-up approach consisting of an appropriate combination of similarity transformations and MTL theory to determine the propagation constant and the characteristic impedance of the modes supported [4052]; and (ii) a top-down approach based either on multipath-model presented in [22, 37, 53, 54] or on cascaded matrices of two-port network modules to determine the end-to-end attenuation and phase response of BPL channel connections [22, 30, 31, 37, 41, 43, 45, 49, 52, 55, 56]. In this paper, the chain scattering matrix or T -matrix (TM) method, which is outlined in [30, 41, 52, 56], is applied to evaluate the HV/BPL channel characteristics.

The hybrid model approach, based on a priori computations, takes into account accurately determined parameters such as the MTL configuration and grid topology. This approach is flexible and accurate determining, consequently, any changes of the transfer characteristics related to relevant factors of the HV/BPL system configuration [42,45,49,55,57]. The influence of factors, such as the physical properties of the cables used, the MTL configuration, the coupling scheme applied, the end-to-end distance, and the number and the electrical length encountered along the end-to-end HV/BPL signal propagation are investigated based on numerical results concerning simulated overhead HV/BPL topologies.

The rest of this paper is organized as follows: In Section 2, the modal behavior of BPL propagation is discussed along with the necessary assumptions concerning overhead HV/BPL transmission. Section 3 deals with signal transmission via power lines by the TM method which is applied for the evaluation of the end-to-end modal transfer functions. In Section 4, numerical results are provided, aiming at marking out how the various features of the overhead HV transmission power grids influence BPL transmission. Section 5 concludes the paper.

2. THE PHYSICAL BPL LAYER

The overhead HV power grid differs considerably from transmission via twisted-pair, coaxial, or fiber-optic cables due to the significant differences of the network structure and the physical properties of the power cables used [7, 21, 22, 29, 31, 34, 41, 42, 55].

A typical case of 150 kV single-circuit overhead HV transmission line is depicted in Fig. 1. Three parallel phase conductors spaced by [[DELTA].sub.p] in the range from 6.60 m to 8.95 m are suspended at heights [h.sub.p] ranging from 19 m to 19.95 m above lossy ground--conductors 1, 2, and 3--. Moreover, two parallel neutral conductors spaced by [[DELTA].sub.n] in the range from 9.30 m to 12.10 m hang at heights [h.sub.n] ranging from 23.75 m to 24.7m--conductors 4 and 5--. This three-phase five-conductor overhead HV distribution line configuration is considered in the present work consisting of ACSR GROSBEK 3 x 374.77[mm.sup.2] + 2 x 322.26 [mm.sup.2] conductors [25-27,58-61].

The ground is considered as the reference conductor. The conductivity of the ground is assumed [[sigma].sub.g] = 5mS/m and its relative permittivity [[epsilon].sub.rg] = 13, which is a realistic scenario [7,28,41,42,55]. The impact of imperfect ground on signal propagation over overhead power lines was analyzed in [28, 41, 42, 55, 57, 62-64]. This formulation has the advantage that, contrary to other available models for overhead power lines [65-68], it is suitable for transmission at high frequencies above lossy ground and for broadband applications of overhead LV/BPL, MV/BPL, and HV/BPL systems.

Through a matrix approach, the standard TL analysis can be extended to the MTL case which involves more than two conductors. Compared to a two-conductor line supporting one forward- and one backward-traveling wave, an MTL structure with n + 1 conductors parallel to the z axis as depicted in Fig. 1 may support n pairs of forward- and backward-traveling waves with corresponding propagation constants. These waves may be described by a coupled set of 2n first-order partial differential equations relating the line voltages [V.sub.i](z,t), i = 1, ..., n to the line currents Ii(z,t), i = 1, ..., n. Each pair of forward- and backward-traveling waves is referred to as a mode [29, 41, 47, 48].

In the case of overhead HV distribution lines involving three-phase conductors and two neutral conductors (n = 5) over lossy plane ground, five modes may be supported, namely [2,7,20,21,24,25,41-44, 47-50, 55, 57-59, 62-64, 69-71]:

* Common mode (CM, i = 1) of overhead HV/BPL transmission which propagates via the five conductors and returns via the ground. [[gamma].sub.CM] constitutes the CM propagation constant.

* Differential modes (DMs) of overhead HV/BPL transmission ([DM.sub.i-1], i = 2, 3, 4, 5) which propagate and return via the five

conductors. [gamma]DMi-1, i = 2, ..., 5 constitute the propagation

constants of [DM.sub.i-1], i = 2, ..., 5, respectively.

[FIGURE 1 OMITTED]

The attenuation coefficients [[alpha].sub.CM] = [Re.sub.{[gamma]CM}] and [[alpha].sub.DMi-1] = [Re.sub.{[gamma]DMi-1}], i = 2, ..., 5 of the CM and the four DMs, respectively, are evaluated using the method

presented in [20,24,25, 28,41,42, 55, 5759,62-64, 70, 71] and are plotted versus frequency in Fig. 2(a) for the configuration depicted in Fig. 1. The absolute value of phase delays [[beta].sub.CM] = [Im.sub.{[gamma]DMi-1}] and [[beta].sub.DMi-1] = [Im.sub.{[gamma]DMi-1}], i = 2, ..., 5 of the CM and the four DMs, respectively, [20, 24, 25, 28, 41, 42, 55, 57-59, 62-64, 70, 71] are also plotted versus frequency in Fig. 2(b).

As far as the spectral behavior of the modes is concerned, the following characteristics should be noted

(i) As it concerns the overhead HV/BPL transmission channels, in the lower part of the frequency spectrum--up to approximately 20 MHz--the attenuation coefficient of the CM is higher compared to that of the other DMs; hence, practically, only the DMs propagate. The opposite is observed at frequencies above 20 MHz, where the CM and the DMs coexist resulting to multimode propagation. The shape of CM is explained by considering that at high frequencies the penetration depth into the lossy ground becomes negligible compared to the wavelength; therefore, propagation takes place entirely above the ground as in the lossless case. The peak exhibited by CM is attributed to the resonance occurring inside the ground which, as frequency increases, is initially inductive and, then, capacitive. As to the DMs of overhead HV/BPL transmission, since the relevant influence of the lossy ground is negligible, the DMs attenuation coefficients are primarily affected by the losses and the skin-effect in the conductors. This almost identical spectral behavior of attenuation coefficients has also been observed in overhead LV/BPL and MV/BPL transmission [28, 29, 32, 33, 41, 42, 55, 57, 63, 64, 72-74].

(ii) The phase delays of the CM and the DMs exhibit a linear behavior with respect to frequency and depend on the surrounding media (air) properties. This almost identical spectral behavior of phase delays has also been observed in overhead and underground LV/BPL and MV/BPL transmission [22, 2629, 32, 33, 42, 43, 46, 49, 50, 55, 57, 72-74].

[FIGURE 2 OMITTED]

As it has already been presented in [25, 28, 29, 41, 70], the modal voltages [V.sup.m](z) = [[[V.sup.m.sub.1](z) ... [V.sup.m.sub.5](z)].sup.T] and the modal currents [I.sup.m](z) = [[[I.sup.m](z) ... [I.sup.m.sub.5](z)].sup.T] may be related to the respective line quantities V(z) = [[[V.sub.1](z) ... [V.sub.5](z)].sup.T] and I(z) = [[[I.sub.1](z) ... [I.sub.5](z)].sup.T] via the similarity transformations [29, 41, 43, 47, 48]

V(z) = [T.sub.V] x [V.sup.m] (z) (1)

I(z) = [T.sub.I] x [I.sup.m](z) (2)

where [[x].sup.T] denotes the transpose of a matrix, [T.sub.V] and [T.sub.I] are 5 x 5 matrices depending on the frequency, the physical properties of the cables, and the geometry of the MTL configuration [20, 24, 25, 29, 41, 43, 47, 48, 58, 59, 70, 71]. Through the aforementioned equations, the line voltages and currents are expressed as appropriate superpositions of the respective modal quantities. From (1)

[V.sup.m](0) = [T.sup.-1.sub.V] * V(0) (3)

The above modes excited--each with its own propagation characteristics--may be examined separately across the overall overhead HV transmission network, under the following three assumptions [28, 41-43, 46, 51]:

A1. Cables with identical eigenmodes are used throughout the network. The branches and termination points are perfectly balanced ensuring that there is no mode mixing anywhere in the network.

A2. The branching cables are identical to the transmission cables and the mode propagation constants of all the cable segments are assumed to be the same.

A3. The termination points behave independently of frequency since they are either ideal matches--achieved using adaptive modal impedance matching [75, 76]--or open circuit terminations.

The three assumptions were already made in the analysis of LV/BPL and MV/BPL transmission [28,30,41-43,46,51]. They are necessary to validate a simple model, so that a more thorough view of the channel attenuation due to cable losses, branches and terminations may be established. Because of the above assumptions, the five modes supported by the overhead HV/BPL configuration are completely separate giving rise to five independent transmission channels which simultaneously carry BPL signals. This complete mode separation along the entire overhead HV/BPL transmission network has also been encountered in overhead LV/BPL and MV/BPL transmission where four and three modes, respectively, exist [28-30, 41, 42, 72].

The TM method--considered in Section 3--models the spectral relationship between [V.sup.m.sub.i](z), i = 1, ..., 5 and [V.sup.m.sub.i](0), i = 1, ..., 5 proposing operators [H.sup.m.sub.i](z), i = 1, ..., 5 so that

[V.sup.m](z) = [H.sup.m]{[V.sup.m](0)} (4)

where

[H.sup.m] {x} = diag{[H.sup.m.sub.i]{x} ... [H.sup.m.sub.i] {x}} (5)

is a diagonal matrix operator whose elements [H.sup.m.sub.i], i = 1, ..., 5 are the modal transfer functions [28,29,41]. Combining (1) and (5), the 5 x 5 matrix channel transfer function H{x} relating V(z) with V(0) through

V(z) = H {V(0)} (6)

is determined from

H {x} = [T.sub.V] * [H.sup.m]{x} x [T.sup.-1.sub.V] (7)

Based on (5), the 5 x 5 matrix transfer function H{x} of the overhead HV/BPL transmission network is determined. Similar expressions have been derived in the overhead LV/BPL and MV/BPL cases [28-30, 41, 44, 69].

According to how signals are injected onto overhead HV/BPL transmission lines, two different coupling schemes exist [29, 73, 77]:

* Wire-to-Wire (WtW) when the signal is injected between two conductors; say between conductors p and q [not equal to] p, p,q = 1,..., 5. For the WtW coupling configurations, the relative excitation voltage relationship which is applied to the five conductors at z = 0 is given by

V(0) = [V.sup.WtW] (0) x [C.sup.WtW] (8)

where [V.sup.WtW] (0) is the source equivalent Thevenin dipole voltage and [C.sup.WtW] is the 5 x 1 WtW coupling column vector with zero elements except in rows p and q where the values are equal to 0.5 and -0.5, respectively. Following the same procedure, the load equivalent Thevenin dipole voltage [V.sup.WtW] (z) is given from

[V.sup.WtW](z)= [[[C.sup.WtW]].sup.T] x V(z) (9)

Combining (6), (7), (8), and (9), the coupling WtW channel transfer function [H.sup.WtW]{x} is determined by

[H.sup.WtW]{x} = [[[C.sup.WtW]].sup.T] x [T.sub.V] x [H.sup.m] x [T.sup.-1.sub.V] x [C.sup.WtW] (10)

W tW coupling between conductors p and q will be detoned as [WtW.sup.p-q], hereafter.

* Wire-to-Ground (WtG) when the signal is injected onto one conductor and returns via the ground; say between conductor s, s = 1, ..., 5 and the ground. Similar expressions with (10) may be derived in WtG coupling configurations. The coupling WtG channel transfer function [H.sup.WtG]{x} is given from

[H.sup.WtG]{x} = [[C.sup.WtG]] x [T.sub.V] x [H.sup.m]{x} x [T.sup.-1.sub.V] x [C.sup.WtG] (11)

where [C.sup.WtG] is the 5 x 1 WtG coupling column vector with zero elements except in row s where the value is equal to 1. WtG coupling between conductor s and ground will be detoned as [WtG.sup.s], hereafter.

When WtW injection is done, the DMs are mainly excited, whereas the primary excitation of the CM is generated due to the lack of symmetry of the cable configuration; hence, BPL transmission is accomplished mostly via the DMs. This has also observed in WtW injection in overhead MV/BPL transmission and in Phase-to-Phase (PtP) injection in underground MV/BPL transmission [7, 2830, 41, 42, 55, 62, 72, 77].

When WtG injection is applied, both the CM and DMs are excited. This has also been observed in WtG injection in overhead MV/BPL transmission and in Shield-to-Phase (StP) injection in underground MV/BPL transmission [7, 28-30, 41, 42, 55, 62, 72, 77].

3. EVALUATION OF THE END-TO-END MODAL TRANSFER FUNCTION

In this paper, the TM method will be used to determine the modal transfer function of the independent modal BPL transmission channel in the light of scattering matrix theory [30,41,52,56]. TM method is presented analytically in [30].

To apply the TM method, an end-to-end overhead BPL connection is separated into elementary segments--network modules--, each of them comprising the successive branches encountered--see Fig. 3(a) --. Signal transmission through the various network modules is taken into account based on the respective chain scattering matrices. A typical overhead BPL end-to-end connection comprises branch-type network modules, as depicted in Fig. 3(b), while A and B are assumed matched to the characteristic impedance of the mode considered [22,37,42].

[FIGURE 3 OMITTED]

To determine the end-to-end modal transfer function one has to evaluate:

1. the scattering matrices [S.sub.k], k = 1,2, ..., N + 1 of the network modules;

2. the respective chain scattering matrices [T.sub.k], k = 1,2, ..., N + 1;

3. the chain scattering matrix [T.sub.overall] of the end-to-end connection considered as a cascade of N + 1 network modules, that is,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and

4. the respective end-to-end Soverall matrix from

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (12)

where [T.sub.pq], p,q = 1,2, are the elements of [T.sub.overall] .

The end-to-end modal transfer function is given by the element S2of the matrix [S.sub.overall] of (12), that is

[H.sup.m.sub.i]{x} = [H.sup.m.sub.i](f)= [S.sub.21] = 1/[T.sub.11], i = 1, ..., 5 (13)

4. NUMERICAL RESULTS AND DISCUSSION

The simulations of various types of overhead HV/BPL transmission channels aim at investigating: (a) their broadband transmission characteristics; and (b) how their spectral behavior is affected by the overhead grid topology. As mentioned in Section 2, since the modes supported by the overhead HV/BPL configurations may be examined separately, it is assumed for simplicity that the BPL signal is injected directly into the modes [28-30, 41-45, 47-51, 55]; thus, the complicated modal analysis of [47,48], briefly described in Section 2, is avoided.

For the numerical computations, the three-phase five-conductor overhead HV transmission line configuration depicted in Fig. 1, has been considered. As previously mentioned, the modes supported by the overhead HV/BPL cable configuration may be examined separately. The following discussion will focus on the transmission characteristics related to: (i) the CM and the DMs of the overhead HV/BPL systems; and (ii) the WtW and the WtG coupling schemes related to overhead HV/BPL systems, as well.

The simple overhead HV/BPL topology of Fig. 3(a), having N branches has been considered. With reference to Fig. 3(c), the transmitting and the receiving ends are assumed matched to the characteristic impedance of the mode considered, whereas the branch terminations [Z.sub.bk], k = 1,2, ..., N are assumed open circuit [2,25,28-30,41,42,58-60,70].

Today, thousands of HV lines are installed in more than 120 countries for a total length of some millions of km. These lines stretch from approximately 25 km to 190 km from the generator before reaching any population centers. Consequently, average path lengths up to 100 km are encountered in the overhead HV case. Shorter branches in the range of 10 km to 50 km are used in order to connect HV transmission lines either between them or with HV/MV substations [2, 5, 21, 25-27, 58-60, 70, 78, 79].

To compare the equivalent modal with the coupling scheme channels, the following representative overhead HV/BPL topology has been examined--see Fig. 3(c)--:

* The "LOS" transmission along the average end-to-end distance L = [L.sub.1] + ... + [L.sub.n+1] = 100 km when no branches are encountered. This topology corresponds to Line-of-Sight transmission in wireless channels.

In Figs. 4(a) and 4(c), the end-to-end channel attenuation and the phase response, respectively, are plotted versus frequency for the "LOS" transmission case for the propagation of [DM.sub.1], [DM.sub.2], [DM.sub.3], [DM.sub.4], and CM. Among the twenty possible WtW and five possible WtG configurations, in Figs. 4(b) and 4(d), the end-to-end coupling channel attenuation and the phase response, respectively, for the "LOS" transmission case for the coupling schemes [WtW.sup.1-2], [WtW.sup.2-1], [WtW.sup.1-3], [WtW.sup.5-2], [WtG.sup.1], and [WtG.sup.4] are plotted versus frequency.

The "LOS" transmission channels present low-loss characteristics at frequencies ranging from 1 MHz to 100 MHz over a 100 km repeater span. The fact that overhead HV/BPL lines resemble a low loss transmission system shows as an attractive alternative broadband technology [25, 28-30, 41-43, 49, 55, 60]. Comparing Figs. 4(a), 4(b), 4(c), and 4(d), as it has already been mentioned, WtW coupling schemes are primarily affected by the propagation of DMs, whereas WtG coupling schemes are influenced by CM. Moreover, [WtW.sup.1-2] and [WtW.sup.2-1] present identical spectral behavior validating channel isotropy characterizing BPL point-to-point links [5, 46, 58, 59, 70, 78].

Theoretically, EMI problems are caused by both the CM and the four DMs. Practically, EMI caused by the DM modes is not considered significant because the far field radiation caused by each DM mode is zero. However, the CM current flow may cause significant EMI levels [10, 80-83]. As BPL transmission is primarily accomplished by the DM currents [80], any unintentional transmission on the CM current flow--generated by unbalances of the power line cables which convert part of the injected/transmitted DM signals into CM signals --should be avoided, since the CM current flow is the main cause of EMI from BPL networks [81]. Nevertheless, as it is observed in Fig. 4(b), the WtG coupling schemes are favorable in comparison with WtW ones due to their lower channel attenuation. Hence, a tradeoff between EMI protection and BPL channel attenuation/capacity is outlined.

[FIGURE 4 OMITTED]

However, as usually done to simplify the analysis and due to relatively comparable results among modal and coupling scheme channels--as it concerns the end-to-end attenuation and the phase response of the "LOS" transmission case--[13, 17, 28-31,42,55,59,72,84], only one mode--say [DM.sub.4]--for overhead HV/BPL system will be examined, hereafter. This assumption does not affect the generality of the analysis concerning the transmission characteristics of the examined HV/BPL systems in the range from 1 MHz to 100 MHz, provides a representative picture of the real world overhead HV/BPL network situation, and is adopted for the sake of terseness and simplicity.

With reference to Fig. 3(c), five indicative overhead HV topologies, concerning end-to-end connections of average lengths equal to 100 km, have been examined. These topologies are the "LOS" transmission topology referred to above and [2, 21, 25, 58-60, 70, 78, 79]:

1. A typical urban topology (urban case A) with N = 3 branches ([L.sub.1] = 4.6 km, [L.sub.2] = 48.5 km, [L.sub.3] = 33.7km, [L.sub.4] = 13.2 km, [L.sub.b1] = 27.6km, [L.sub.b2] = 17.2km, [L.sub.b3] = 33.1km). This topology supplies energy one large residential area and one major city.

2. An aggravated urban topology (urban case B) with N = 4 branches ([L.sub.1] = 0.5 km, [L.sub.2] = 15.8 km, [L.sub.3] = 13.1 km, [L.sub.4] = 55.5 km, [L.sub.5] = 15.1km, [L.sub.b1] = 19 km, [L.sub.b2] = 22.7 km, [L.sub.b3] = 17.1km, [L.sub.b4] = 18km). This topology supplies energy two major cities.

3. A typical suburban topology (suburban case) with N = 2 branches ([L.sub.1] = 36.1km, [L.sub.2] = 51km, [L.sub.3] = 12.9 km, [L.sub.b1] = 46.8 km, [L.sub.b2] = 13.4 km). This topology describes three nodes of a ring HV line connection.

4. A typical rural topology (rural case) with only N = 1 branch ([L.sub.1] = 15 km, [L.sub.2] = 85 km, [L.sub.b1] = 21.1 km). This topology carries power to a city located 15 km from the generator.

In Figs. 5(a) and 5(b), the end-to-end channel attenuation and the phase response, respectively, are plotted with respect to frequency for the aforementioned five indicative topologies for the propagation of [DM.sub.4]. As it has already been investigated in [22, 28, 30, 37, 41, 73, 74, 85, 86], the spectral behavior of the end to-end channel attenuation depends drastically on the frequency, the physical properties of the cables used, the end-to-end--"LOS"--distance, and the number and the electrical length of the branches encountered along the end-to-end transmission path. However, phase responses present a rather identical linear behavior versus frequency regardless of the overhead HV/BPL topology.

According, mainly, to the picture obtained from their spectral behavior of channel attenuation--see Fig. 5(a)--, the overhead BPL topologies may be classified into three major channel classes (see also [28-30, 40, 84] for other LV/BPL and MV/BPL channels):

* "LOS" channels, when no branches are encountered and, consequently, no spectral notches are observed. This case corresponds to the best possible overhead HV/BPL transmission conditions, encountered primarily in rural areas where long-distance transmission occurs.

* Good channels, when the number of branches is small and their electrical length is large. Shallow spectral notches are observed. Overhead HV/BPL transmission primarily near rural and suburban areas belongs to this channel class.

* Bad channels, when the number of branches is large and their electrical length is small. Deep spectral notches are observed. Overhead HV/BPL transmission near major cities and large residential areas belongs to this channel class.

[FIGURE 5 OMITTED]

The spectral behavior of the above overhead HV/BPL channel classes affects critically the transmission characteristics of overhead BPL channels.

Apart from causing spectral notches, the various branches also cause additional stepwise discontinuities to the channel attenuation at each branch encountered along the end-to-end transmission path. The attenuation discontinuity at each branch is examined in Figs. 6(a) and 6(b), where the channel attenuation of [DM.sub.4] is plotted versus the distance from the transmitting end--see Fig. 3(a), point A--for the above five indicative topologies at f = 25 MHz and f = 75 MHz, respectively. In Figs. 6(c) and 6(d), the respective phase response curves are also plotted in relation with the distance from the transmitting end at f = 25 MHz and f = 75 MHz, respectively.

Observing Figs. 6(a), 6(b), 6(c), and 6(d), several useful remarks may be drawn.

* Due to reflections and multipath propagation caused by branches, spectral notches are observed in the channel attenuation, which are superimposed on the exponential "LOS" attenuation. Unlike channel attenuation, phase response curves present a frequency-selective linear overlapping behavior versus the distance from the transmitting end regardless of the overhead HV/BPL topology considered.

* In most overhead HV/BPL channels, "LOS" distance rather than multipath is identified as the dominant attenuation factor affecting signal transmission. Therefore, in urban and suburban environments denser overhead HV/BPL networks are preferable. The respective shorter end-to-end connections are primarily affected by multipath [5, 25-27, 58-60, 70, 78, 87].

* The attenuation discontinuity at each branch depends on the frequency and on its electrical length. As the branches become longer, the spectral behavior of the BPL networks tends to converge to the spectral behavior of the respective BPL networks with branch terminations matched to the characteristic impedance of the mode examined; namely, approximately a two-way power divider per each branch [22, 31, 37, 74, 79, 85].

[FIGURE 6 OMITTED]

To demonstrate the spectral effect of branch length on the attenuation discontinuity at each branch, in Fig. 7(a), the attenuation discontinuity of DM4 at the first branch--point [A.sub.1], see Fig. 3(a)--is plotted versus frequency for the urban case B, Topology 1--same as urban case B but with five times shorter branches ([L.sub.1] = 0.5 km, [L.sub.2] = 15.8 km, [L.sub.3] = 13.1km, [L.sub.4] = 55.5 km, [L.sub.5] = 15.1km, [L.sub.b1] = 3.8 km, [L.sub.b2] = 4.5 km, [L.sub.b3] = 3.4 km, [L.sub.b4] = 3.6 km) --, and Topology 2--same as urban case B but with five times longer branches ([L.sub.1] = 0.5 km, [L.sub.2] = 15.8 km, [L.sub.3] = 13.1 km, [L.sub.4] = 55.5 km, [L.sub.5] = 15.1 km, [L.sub.b1] = 95 km, [L.sub.b2] = 113.5 km, [L.sub.b3] = 85.5 km, [L.sub.b4] = 90 km)--. In Figs. 7(b), 7(c), and 7(d), similar plots are given for the second, the third, and the fourth branch--points [A.sub.2], [A.sub.3], and [A.sub.4], respectively, see Fig. 3(a)--, respectively.

From Figs. 7(a), 7(b), 7(c), and 7(d), it should be mentioned that [29,41,74,79,85]:

* The attenuation discontinuity at each branch depends predominantly on its electrical length. It is verified that as the branches become longer, the spectral notches are reduced with regard both to their depth and to their spectral extent. Thus, the spectral behavior of the HV/BPL networks tends to converge to the spectral behavior of the N cascaded two-way power dividers.

* There may be amplification of the signal power (negative values of the attenuation discontinuity), depending on the HV network configuration. This has also been observed in MV/BPL transmission [41].

From the previous figures, several interesting conclusions concerning HV/BPL transmission characteristics may be deduced as follows.

1. As a broadband communications channel, the overhead HV power grid suffers primarily from "LOS" attenuation and secondarily from multipath which adversely affect the BPL system design and the oncoming SG application performance.

2. Though determined for 100 km long HV connections--compared to the shorter connections of LV and MV cases [2, 7, 21, 22, 2832, 41-44, 86]--, BPL transmission via the overhead HV grid exhibits low loss characteristics favoring the exploitation of HV/BPL bandwidth.

3. Besides the "LOS" attenuation, the overall end-to-end channel attenuation and the signal power discontinuities along the end-to-end transmission path of overhead HV/BPL systems depend on the frequency, the coupling scheme, and the number, the electrical length, and the termination of the various branches encountered along the end-to-end BPL signal propagation. Unlike channel attenuation, phase responses depend primarily on the frequency, the coupling scheme, and the "LOS" distance regardless of the overhead HV/BPL topology considered.

4. If the exact grid configuration is known, the overall spectral behavior may be accurately evaluated providing information about the necessity and the exact location where signal repeaters should be installed and parameters of orthogonal frequency-division multiplexing (OFDM) systems used.

5. As usually done in BPL systems [28-30, 40, 84], overhead HV/BPL channels are classified into three classes depending on their spectral behavior: "LOS" channels; good channels; and bad channels. HV/BPL transmission in the majority of areas is classified into the good channels class.

6. In the SG landscape, overhead and underground LV/BPL, MV/BPL, and HV/BPL systems need to work in a compatible way (intraoperate) before BPL technology interoperates with other broadband technologies, such as wired (e.g., fiber and DSL) and wireless (e.g., WiFi and WiMax) [38,88-90]. The comparable results concerning broadband signal transmission in LV/MV/HV BPL systems is the guarantee towards SG technology integration.

[FIGURE 7 OMITTED]

5. DISCUSSION AND CONCLUSIONS

The transmission characteristics of multiwire overhead HV/BPL networks have been studied applying the TM method. The broadband transmission capability of such networks depends on the frequency, the coupling scheme applied, the physical properties of the cables used, the MTL configuration, the end-to-end--"LOS"--distance, and the number and the electrical length of the branches encountered along the source-to-destination path. These factors determine the usable bandwidth, the position of repeaters, and the OFDM and various resource allocation schemes performance. The low loss nature of overhead HV/BPL systems permits the exploitation of HV/BPL bandwidth and provides with further LV/MV/HV BPL intraoperability options that may actually be of benefit towards a unified transmission/distribution SG power grid.

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A. G. Lazaropoulos *

Zografou Campus, School of Electrical and Computer Engineering, National Technical University of Athens, 9, Iroon Polytechneiou Street, Athens, GR 15780, Greece

Received 14 September 2011, Accepted 8 November 2011, Scheduled 26 November 2011

* Corresponding author: Athanasios G. Lazaropoulos (AGLazaropoulos@gmail.com).
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