# Review and Progress towards the Capacity Boost of Overhead and Underground Medium-Voltage and Low-Voltage Broadband over Power Lines Networks: Cooperative Communications through  Two- and Three-Hop Repeater Systems

Authors: Athanasios G. Lazaropoulos
Journal: ISRN Electronics
 (2013)

---

## Abstract

This paper reviews and analyzes the broadband capacity and the coexistence potential of overhead and underground medium-voltage/broadband over power lines (MV/BPL) and low-voltage/broadband over power lines (LV/BPL) topologies when one and two repeaters are additively deployed between their existing transmitting and receiving ends (overhead and underground MV/BPL and LV/BPL topologies with two- and three-hop repeater system, respectively). The contribution of this paper is four fold. First, the factors that influence the broadband capacity performance of overhead and underground MV/BPL and LV/BPL topologies with multihop repeater systems are identified, namely the number of repeaters, the distribution power grid type—either overhead or underground, either MV or LV, the initial distribution BPL topology, the multiconductor transmission line configuration, and coupling scheme applied. Second, the well-validated applicability of two-hop repeater systems is now extended in overhead and underground LV/BPL and MV/BPL networks. The significant mitigating role of two-hop repeater systems against capacity losses due to aggravated topologies or different coupling schemes is verified. Third, the deployment upgrade of two- to three-hop repeater systems in distribution BPL topologies is first examined in terms of broadband capacity performance. To study the occurred capacity improvement, suitable capacity contour plots are first proposed. Fourth, multi-hop repeater systems are identified as valuable technology solution so that the required intraoperability between overhead and underground MV/BPL and LV/BPL networks, which is a prerequisite condition before BPL systems symbiosis with other broadband technologies (interoperability), is promoted.


---

## Body

## 1. Introduction

The limited investments made in the energy sector during the last decades, as well as the integration of new smart grid (SG) requirements such as the renewable and distributed energy source integration, microgrids, demand side management, and demand response programs trigger significant efforts towards modernization of power distribution grid—either overhead or underground, either medium voltage (MV) or lowc voltage (LV) power grids—[1, 2]. The deployment of broadband over power lines (BPL) networks across the entire distribution grid can help towards the development of an advanced IP-based power system equipped with a plethora of SG applications [3–5].Exploiting the strong aspects of multihop and relay-based communications, which have been studied either in wireless [6–8] or in BPL environments [9–15], the distribution BPL networks that consist of the cascade of respective distribution BPL topologies are upgraded through the ad hoc insertion of repeaters between their existing transmitting and receiving ends. These upgraded topologies are referred to as distribution BPL topologies with two- or three-hop repeater systems when one or two repeaters are deployed, respectively. Due to this insertion of one or two repeaters across their end-to-end transmission paths, the upgraded distribution BPL topologies consist of two or three new distribution BPL connections, respectively.The well-established hybrid method, which is usually employed to examine the spectral behavior of various BPL channels installed on multiconductor transmission line (MTL) structures, is also adopted in this paper [1, 3, 16–23]. Based on its accurate numerical results, several factors affecting broadband capacity performance of either conventional distribution BPL topologies (i.e., distribution BPL topologies where no repeaters are installed) or upgraded distribution BPL topologies with multihop repeater system (either two- or three-hop repeater systems) are identified, namely, the number of repeaters, the allocation of the repeaters across the end-to-end transmission paths, the distribution power grid type—either overhead or underground, either MV or LV—the power grid topology, the MTL configuration, and the coupling scheme applied that is, how the BPL signal is injected onto power lines.Already verified in the case of overhead transmission BPL networks in [13], the applicability of two-hop repeater systems is now extended in order to further harmonize distribution BPL networks. More specifically, in the case of distribution BPL topologies, two-hop repeater systems are proven to be effective remedy for the capacity losses that occur due to either aggravated BPL topologies or less spectral-efficient coupling schemes.Expanding the concept of two-hop repeater systems, the capacity performance of distribution BPL topologies with three-hop repeater systems is first investigated. It is verified that three-hop repeater systems assure even higher capacity performance and greater capacity flexibility in comparison with two-hop ones for a great number of different power grid types and distribution BPL topologies. Actually, the significant capacity boost through the implementation of three-hop repeater systems is studied through the capacity metric of capacity contour plots.Therefore, exploiting common and/or scalable capacity capabilities offered by the deployment of multihop repeater systems among different distribution BPL networks, new significant and interesting capacity tradeoffs may occur. In addition, the combination of scalable capacities with standardized topologies offers a decisive step towards the intraoperability of distribution BPL networks that is, coexistence and integration of distribution BPL topologies in a SG environment.The rest of this paper is organized as follows. In Section2, an overview of the factors, which influence capacity behavior, that concern BPL transmission via overhead and underground MV and LV power grid is given. In Section 3, the modal behavior of BPL propagation is discussed along with the necessary assumptions concerning BPL signal transmission. Section 4 deals with noise characteristics, electromagnetic interference (EMI) regulations and their respective power constraints, and the evaluation of the capacity delivered by distribution BPL networks when multihop repeater systems are deployed. Section 5 deals with simulations of various overhead and underground MV/BPL and LV/BPL topologies aiming at marking out how two-hop repeater systems may improve broadband capacity performance when different distribution BPL topologies and coupling schemes occur. In addition, the importance of installing three-hop repeater systems across conventional distribution BPL networks is highlighted through the capacity contour plots. Section 6 concludes this paper.


## 2. Overview of Overhead and Underground MV/BPL and LV/BPL MTL Configurations

### 2.1. The Overhead MV Power Distribution Grid

A typical case of overhead MV distribution line is depicted in Figure1(a). Overhead MV distribution lines hang at typical heights hMV ranging from 8 m to 10 m above ground. Typically, three parallel noninsulated phase conductors spaced by ΔMV in the range from 0.3 m to 1 m are used above lossy ground. This three-phase overhead MV distribution line configuration is considered in the present work consisting of ACSR 3 × 95 mm2 conductors [1, 3, 17, 18, 24, 25].Figure 1
Typical multiconductor structures [3]. (a) Overhead MV. (b) Overhead LV. (c) Underground MV. (d) Underground LV.The ground is considered as the reference conductor. The conductivity of the ground is assumedσg=5 mS/m and its relative permittivity εrg=13, which is a realistic scenario [3, 13, 17–19, 21, 23, 25, 26]. The impact of imperfect ground on signal propagation over power lines was analyzed in [17, 18, 21, 23, 25–27].


### 2.2. The Overhead LV Power Distribution Grid

A typical case of overhead LV distribution line is depicted in Figure1(b). Four parallel noninsulated conductors are suspended one above the other spaced by ΔLV in the range from 0.3 m to 0.5 m and located at heights hLV ranging from 6 m to 10 m above ground for the lowest conductor. The upper conductor is the neutral, while the lower three conductors are the three phases. This three-phase four-conductor overhead LV distribution line configuration is considered in the present work consisting of ASTER 3 × 54.6 mm2 + 1 × 34.4 mm2 conductors [3, 28–31]. The ground is considered as the reference conductor as well as it is characterized by the aforementioned properties.


### 2.3. The Underground MV Power Distribution Grid

The underground MV distribution line that will be examined is the three-phase sector-type PILC distribution-class cable (8/10 kV, 3 × 95 mm2 Cu, PILC) buried 1 m inside the ground with the aforementioned ground properties. The cable arrangement consists of the three-phase three-sector-type conductors, one shield conductor, and one armor conductor, see Figure 1(c). The shield and the armor are grounded at both ends [3, 19, 28, 32, 33]. The shield acts as a ground return path and as a reference conductor [3, 21, 24, 34–36]. Signal transmission via three-phase underground power lines has been analyzed in [19, 21, 34, 35, 37] where the analytical formulation has been demonstrated.


### 2.4. The Underground LV Power Distribution Grid

The underground LV distribution line that will be examined in this paper is the three-phase four-conductor core-type YJV underground LV distribution cable (4 × 25 mm2 Cu, XLPE) buried 1 m inside the ground with the aforementioned ground properties. The layout of this cable is depicted in Figure 1(d). The cable arrangement consists of the three-phase three-core-type conductors, one core-type neutral conductor, and one shield conductor. The shield is grounded at both ends and acts as a ground return path and as a reference conductor [21]. Signal transmission via three-phase underground power lines has been analyzed in [16, 19, 21] where the analytical formulation has been demonstrated.


### 2.5. Indicative Overhead and Underground Distribution BPL Topologies

In accordance with [3, 13, 16, 24–26, 28, 34, 38–43], average path lengths of the order of 1000 m and 200 m are encountered in overhead and underground distribution BPL topologies, respectively.With reference to Figure2, five indicative overhead distribution BPL topologies concerning end-to-end connections of average lengths equal to 1000 m, which are detailed in Table 1, are examined, namely, (i) overhead urban case A, (ii) overhead urban case B, (iii) overhead suburban case (iv) overhead rural case and (v) overhead “LOS” transmission along the same end-to-end distance L=L1+⋯+LN+1=1000 m. This topology corresponds to Line of Sight transmission in wireless channels. Note that these five indicative overhead distribution BPL topologies are common to both overhead MV/BPL and overhead LV/BPL networks [3].Table 1
Five indicative overhead distribution BPL topologies [3, 17, 18, 20].
Denotation
Description
Number of branches(N)
Lengths of distribution TLs[L1⋯LN+1]
Lengths of branch TLs[Lb1⋯LbN]
Overhead urban case A
A typical urban topology
3
[500 m 200 m 100 m 200 m]
[8 m 13 m 10 m]
Overhead urban case B
An aggravated urban topology
5
[200 m 50 m 100 m 200 m 300 m 150 m]
[12 m 5 m 28 m 41 m 17 m]
Overhead suburban case
A typical suburban topology
2
[500 m 400 m 100 m]
[50 m 10 m]
Overhead rural case
A typical rural topology
1
[600 m 400 m]
[300 m]
Overhead “LOS” case
“LOS” transmission
0
[1000 m]
—Figure 2
End-to-end upgraded distribution BPL connection withN branches.Similarly to overhead distribution BPL case, five indicative underground distribution BPL topologies concerning average 200 m long end-to-end connections, which are detailed in Table2, are also examined in this paper, namely, (i) urban case A, (ii) urban case B, (iii) underground suburban case, (iv) underground rural case, and (v) underground “LOS” transmission along the same end-to-end distance L=L1+⋯+LN+1=200 m. Again, note that these five indicative underground distribution BPL topologies are common to both underground MV/BPL and underground LV/BPL networks [3].Table 2
Five indicative underground distribution BPL topologies [3, 16, 20].
Denotation
Description
Number of branches(N)
Lengths of distribution TLs[L1⋯LN+1]
Lengths of branch TLs[Lb1⋯LbN]
Underground urban case A
A typical urban topology
3
[70 m 55 m 45 m 30 m]
[12 m 7 m 21 m]
Underground urban case B
An aggravated urban topology
5
[40 m 10 m 20 m 40 m 60 m 30 m]
[22 m 12 m 8 m 2 m 17 m]
Underground suburban case
A typical suburban topology
2
[50 m 100 m 50 m]
[60 m 30 m]
Underground rural case
A typical rural topology
1
[50 m 150 m]
[100 m]
Underground “LOS” case
“LOS” transmission
0
[200 m]
—During the following analysis, the distribution BPL topology of Figure2, having N branches and multiple repeaters, is considered. In order to simplify the following analysis without affecting its generality, the branching TLs are assumed identical to the distribution TLs, and the interconnections between the distribution and branch conductors are fully activated. In addition, the transmitting and the receiving ends are assumed matched to the characteristic impedance of distribution TLs, whereas the branch terminations are assumed open circuits. These topological and circuital parameters of the indicative distribution BPL topologies  are  detailed  in [1, 3, 16–28, 34, 38–43].


## 2.1. The Overhead MV Power Distribution Grid

A typical case of overhead MV distribution line is depicted in Figure1(a). Overhead MV distribution lines hang at typical heights hMV ranging from 8 m to 10 m above ground. Typically, three parallel noninsulated phase conductors spaced by ΔMV in the range from 0.3 m to 1 m are used above lossy ground. This three-phase overhead MV distribution line configuration is considered in the present work consisting of ACSR 3 × 95 mm2 conductors [1, 3, 17, 18, 24, 25].Figure 1
Typical multiconductor structures [3]. (a) Overhead MV. (b) Overhead LV. (c) Underground MV. (d) Underground LV.The ground is considered as the reference conductor. The conductivity of the ground is assumedσg=5 mS/m and its relative permittivity εrg=13, which is a realistic scenario [3, 13, 17–19, 21, 23, 25, 26]. The impact of imperfect ground on signal propagation over power lines was analyzed in [17, 18, 21, 23, 25–27].


## 2.2. The Overhead LV Power Distribution Grid

A typical case of overhead LV distribution line is depicted in Figure1(b). Four parallel noninsulated conductors are suspended one above the other spaced by ΔLV in the range from 0.3 m to 0.5 m and located at heights hLV ranging from 6 m to 10 m above ground for the lowest conductor. The upper conductor is the neutral, while the lower three conductors are the three phases. This three-phase four-conductor overhead LV distribution line configuration is considered in the present work consisting of ASTER 3 × 54.6 mm2 + 1 × 34.4 mm2 conductors [3, 28–31]. The ground is considered as the reference conductor as well as it is characterized by the aforementioned properties.


## 2.3. The Underground MV Power Distribution Grid

The underground MV distribution line that will be examined is the three-phase sector-type PILC distribution-class cable (8/10 kV, 3 × 95 mm2 Cu, PILC) buried 1 m inside the ground with the aforementioned ground properties. The cable arrangement consists of the three-phase three-sector-type conductors, one shield conductor, and one armor conductor, see Figure 1(c). The shield and the armor are grounded at both ends [3, 19, 28, 32, 33]. The shield acts as a ground return path and as a reference conductor [3, 21, 24, 34–36]. Signal transmission via three-phase underground power lines has been analyzed in [19, 21, 34, 35, 37] where the analytical formulation has been demonstrated.


## 2.4. The Underground LV Power Distribution Grid

The underground LV distribution line that will be examined in this paper is the three-phase four-conductor core-type YJV underground LV distribution cable (4 × 25 mm2 Cu, XLPE) buried 1 m inside the ground with the aforementioned ground properties. The layout of this cable is depicted in Figure 1(d). The cable arrangement consists of the three-phase three-core-type conductors, one core-type neutral conductor, and one shield conductor. The shield is grounded at both ends and acts as a ground return path and as a reference conductor [21]. Signal transmission via three-phase underground power lines has been analyzed in [16, 19, 21] where the analytical formulation has been demonstrated.


## 2.5. Indicative Overhead and Underground Distribution BPL Topologies

In accordance with [3, 13, 16, 24–26, 28, 34, 38–43], average path lengths of the order of 1000 m and 200 m are encountered in overhead and underground distribution BPL topologies, respectively.With reference to Figure2, five indicative overhead distribution BPL topologies concerning end-to-end connections of average lengths equal to 1000 m, which are detailed in Table 1, are examined, namely, (i) overhead urban case A, (ii) overhead urban case B, (iii) overhead suburban case (iv) overhead rural case and (v) overhead “LOS” transmission along the same end-to-end distance L=L1+⋯+LN+1=1000 m. This topology corresponds to Line of Sight transmission in wireless channels. Note that these five indicative overhead distribution BPL topologies are common to both overhead MV/BPL and overhead LV/BPL networks [3].Table 1
Five indicative overhead distribution BPL topologies [3, 17, 18, 20].
Denotation
Description
Number of branches(N)
Lengths of distribution TLs[L1⋯LN+1]
Lengths of branch TLs[Lb1⋯LbN]
Overhead urban case A
A typical urban topology
3
[500 m 200 m 100 m 200 m]
[8 m 13 m 10 m]
Overhead urban case B
An aggravated urban topology
5
[200 m 50 m 100 m 200 m 300 m 150 m]
[12 m 5 m 28 m 41 m 17 m]
Overhead suburban case
A typical suburban topology
2
[500 m 400 m 100 m]
[50 m 10 m]
Overhead rural case
A typical rural topology
1
[600 m 400 m]
[300 m]
Overhead “LOS” case
“LOS” transmission
0
[1000 m]
—Figure 2
End-to-end upgraded distribution BPL connection withN branches.Similarly to overhead distribution BPL case, five indicative underground distribution BPL topologies concerning average 200 m long end-to-end connections, which are detailed in Table2, are also examined in this paper, namely, (i) urban case A, (ii) urban case B, (iii) underground suburban case, (iv) underground rural case, and (v) underground “LOS” transmission along the same end-to-end distance L=L1+⋯+LN+1=200 m. Again, note that these five indicative underground distribution BPL topologies are common to both underground MV/BPL and underground LV/BPL networks [3].Table 2
Five indicative underground distribution BPL topologies [3, 16, 20].
Denotation
Description
Number of branches(N)
Lengths of distribution TLs[L1⋯LN+1]
Lengths of branch TLs[Lb1⋯LbN]
Underground urban case A
A typical urban topology
3
[70 m 55 m 45 m 30 m]
[12 m 7 m 21 m]
Underground urban case B
An aggravated urban topology
5
[40 m 10 m 20 m 40 m 60 m 30 m]
[22 m 12 m 8 m 2 m 17 m]
Underground suburban case
A typical suburban topology
2
[50 m 100 m 50 m]
[60 m 30 m]
Underground rural case
A typical rural topology
1
[50 m 150 m]
[100 m]
Underground “LOS” case
“LOS” transmission
0
[200 m]
—During the following analysis, the distribution BPL topology of Figure2, having N branches and multiple repeaters, is considered. In order to simplify the following analysis without affecting its generality, the branching TLs are assumed identical to the distribution TLs, and the interconnections between the distribution and branch conductors are fully activated. In addition, the transmitting and the receiving ends are assumed matched to the characteristic impedance of distribution TLs, whereas the branch terminations are assumed open circuits. These topological and circuital parameters of the indicative distribution BPL topologies  are  detailed  in [1, 3, 16–28, 34, 38–43].


## 3. Modal Analysis of Distribution BPL Networks

### 3.1. The Modal Propagation Analysis

As it has already been analyzed in [1, 3, 13, 16–23, 29, 34, 35, 44, 45], 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 Figures 1(a)–1(d), may support n pairs of forward- and backward-traveling waves with corresponding propagation constants. Each pair of forward- and backward-traveling waves is referred to as a mode. In the case of distribution MTL configurations presented in Figures 1(a)–1(d) and examined in this paper, distribution MV/BPL and LV/BPL MTL structures may support three (n=3) and four (n=4) modes, respectively.As it has already been presented in [1, 3, 13, 16–23, 29, 34, 35, 44, 45], the hybrid method models the spectral relationship between Vim(z), i=1,…,n and Vjm(0), j=1,…,n proposing operators Hi,jm{·}, i, j=1,…,n so that
(1)Vm(z)=Hm{Vm(0)},
where Vm(z)=[V1m(z)⋯Vnm(z)]T are the modal voltages of the n modes supported by the distribution BPL configuration considered, [·]T denotes the transpose of a matrix, Hm{·} is the n×n modal transfer function matrix whose elements Hi,jm{·}, i,j=1,…,n are the modal transfer functions, and Hi,jm denotes the element of matrix Hm{·} in row i of column j.


### 3.2. Coupling Schemes

According to how signals are injected onto overhead and underground distribution BPL transmission lines, two different coupling schemes exist [18, 22, 23, 25, 26]: (i) WtG or StP coupling schemes when the signal is injected onto one conductor and returns via the ground or the shield for overhead or underground distribution BPL connections, respectively, WtG or StP coupling between conductor s and ground or shield will be denoted as WtGs or StPs, respectively; (ii) WtW or PtP coupling schemes when the signal is injected between two conductors for overhead or underground distribution BPL connections, respectively. WtW or PtP coupling between conductors p and q will be denoted as WtWp-q or PtPp-q, respectively.Based on (1), the coupling transfer function HX{·} is given from
(2)HX{·}=[CX]T·TV·Hm{·}·TV-1·CX,
where [·]X denotes the applied coupling scheme, CX is the n×1 coupling column vector detailed in [3], and TV is a n×n matrix depending on the distribution power grid type—either overhead or underground, either MV or LV—the frequency, the physical properties of the cables used, and the geometry of the MTL configuration [3, 5, 10, 12, 13, 18, 23, 24, 37, 46–50].


## 3.1. The Modal Propagation Analysis

As it has already been analyzed in [1, 3, 13, 16–23, 29, 34, 35, 44, 45], 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 Figures 1(a)–1(d), may support n pairs of forward- and backward-traveling waves with corresponding propagation constants. Each pair of forward- and backward-traveling waves is referred to as a mode. In the case of distribution MTL configurations presented in Figures 1(a)–1(d) and examined in this paper, distribution MV/BPL and LV/BPL MTL structures may support three (n=3) and four (n=4) modes, respectively.As it has already been presented in [1, 3, 13, 16–23, 29, 34, 35, 44, 45], the hybrid method models the spectral relationship between Vim(z), i=1,…,n and Vjm(0), j=1,…,n proposing operators Hi,jm{·}, i, j=1,…,n so that
(1)Vm(z)=Hm{Vm(0)},
where Vm(z)=[V1m(z)⋯Vnm(z)]T are the modal voltages of the n modes supported by the distribution BPL configuration considered, [·]T denotes the transpose of a matrix, Hm{·} is the n×n modal transfer function matrix whose elements Hi,jm{·}, i,j=1,…,n are the modal transfer functions, and Hi,jm denotes the element of matrix Hm{·} in row i of column j.


## 3.2. Coupling Schemes

According to how signals are injected onto overhead and underground distribution BPL transmission lines, two different coupling schemes exist [18, 22, 23, 25, 26]: (i) WtG or StP coupling schemes when the signal is injected onto one conductor and returns via the ground or the shield for overhead or underground distribution BPL connections, respectively, WtG or StP coupling between conductor s and ground or shield will be denoted as WtGs or StPs, respectively; (ii) WtW or PtP coupling schemes when the signal is injected between two conductors for overhead or underground distribution BPL connections, respectively. WtW or PtP coupling between conductors p and q will be denoted as WtWp-q or PtPp-q, respectively.Based on (1), the coupling transfer function HX{·} is given from
(2)HX{·}=[CX]T·TV·Hm{·}·TV-1·CX,
where [·]X denotes the applied coupling scheme, CX is the n×1 coupling column vector detailed in [3], and TV is a n×n matrix depending on the distribution power grid type—either overhead or underground, either MV or LV—the frequency, the physical properties of the cables used, and the geometry of the MTL configuration [3, 5, 10, 12, 13, 18, 23, 24, 37, 46–50].


## 4. Noise, EMI Regulations, and Capacity of Distribution BPL Networks

### 4.1. Noise Characteristics

As it has already been mentioned in [10, 13, 18, 20, 25, 26, 28, 51–55], colored background noise and impulsive noise are the dominant types in overhead and underground MV/BPL and LV/BPL networks.As it regards the noise properties of distribution BPL networks in the 3–88 MHz frequency range, a uniform additive white Gaussian noise (AWGN) is assumed. Its power spectral density (PSD) levelsN(f) are equal to −105 dBm/Hz and −135 dBm/Hz for overhead and underground distribution BPL networks, respectively [9, 10, 18, 20, 25, 26, 28, 52, 53, 56].


### 4.2. Electromagnetic Compatibility (EMC) of Distribution BPL Networks with Other Radio Services

To regulate EMI of distribution BPL networks to other already existing communications systems in the same frequency band of operation, appropriate power constraints are imposed.The injected PSD limits (IPSD limits) proposed by Ofcom for compliance with FCC Part 15—analytically presented in [57–59]—are adopted in this paper, namely:(i)
in the 3–30 MHz frequency range, maximum levels of −60 dBm/Hz and −40 dBm/Hz constitute appropriate IPSD limitspcon for overhead and underground distribution BPL networks, respectively(ii)
in the 30–88 MHz frequency range, maximum IPSD limitspcon are equal to −77dBm/Hz and −57dBm/Hz for overhead and underground distribution BPL networks, respectively.These power constraints provide a presumption of compliance with the current FCC Part 15 limits [18, 20, 58].


### 4.3. Capacity of Distribution BPL Topologies with Multihop Repeater Systems under Fixed EMI Limits

Capacity is the maximum achievable transmission rate over a BPL channel and depends on the power grid type, power grid topology, applied coupling scheme, MTL configuration, noise characteristics, and imposed EMI limits. Extending the definition of capacity, cumulative capacity is defined as the cumulative upper bound of information that can be reliably transmitted over a BPL channel.In the light of information theory [9–15, 18, 20] and with reference to Figure 2, in the case of conventional distribution BPL topologies, their overall capacity C, which is the end-to-end capacity from A to B, is determined from
(3)C=CA→B=fs∑q=0Q-1log2{1+[〈pcon(qfs)〉L〈N(qfs)〉L·|HX(qfs)|2]},
where [·]A→B defines the transmitting (A) and receiving (B) end points, 〈·〉L is an operator that converts dBm/Hz into a linear power ratio (W/Hz), Q is the number of subchannels in the BPL signal frequency range of interest, and fs is the flat-fading subchannel frequency spacing.To investigate the capacity impact of multihop repeater systems installation, first, with reference to Figure2, let us assume that a two-hop repeater system is deployed across an end-to-end distribution BPL topology; its sole repeater is installed at distance R1 from the transmitting end. Hence, the initial distribution BPL topology is divided into two new distribution BPL connections. Due to the bus-bar concatenation of these two connections and taking into account (3), the new overall capacity C′ of the distribution BPL topology with two-hop repeater system is determined as the minimum value of the capacities of these two connections:
(4)C′=min{CA→R1,CR1→B},
where min{x,y} returns the smallest value between either x or y.Similar to two-hop repeater systems case, with reference to Figure2, when a three-hop repeater system is deployed across a distribution BPL topology, two repeaters are installed across its end-to-end transmission path at distances R1 and R2, respectively. Thus, the conventional distribution BPL topology is divided into three new distribution BPL connections. The new overall capacity C′′ of the upgraded distribution BPL topology is determined as the minimum value of the capacities of these three connections:
(5)C′′=min{CA→R1,CR1→R2,CR2→B}.


## 4.1. Noise Characteristics

As it has already been mentioned in [10, 13, 18, 20, 25, 26, 28, 51–55], colored background noise and impulsive noise are the dominant types in overhead and underground MV/BPL and LV/BPL networks.As it regards the noise properties of distribution BPL networks in the 3–88 MHz frequency range, a uniform additive white Gaussian noise (AWGN) is assumed. Its power spectral density (PSD) levelsN(f) are equal to −105 dBm/Hz and −135 dBm/Hz for overhead and underground distribution BPL networks, respectively [9, 10, 18, 20, 25, 26, 28, 52, 53, 56].


## 4.2. Electromagnetic Compatibility (EMC) of Distribution BPL Networks with Other Radio Services

To regulate EMI of distribution BPL networks to other already existing communications systems in the same frequency band of operation, appropriate power constraints are imposed.The injected PSD limits (IPSD limits) proposed by Ofcom for compliance with FCC Part 15—analytically presented in [57–59]—are adopted in this paper, namely:(i)
in the 3–30 MHz frequency range, maximum levels of −60 dBm/Hz and −40 dBm/Hz constitute appropriate IPSD limitspcon for overhead and underground distribution BPL networks, respectively(ii)
in the 30–88 MHz frequency range, maximum IPSD limitspcon are equal to −77dBm/Hz and −57dBm/Hz for overhead and underground distribution BPL networks, respectively.These power constraints provide a presumption of compliance with the current FCC Part 15 limits [18, 20, 58].


## 4.3. Capacity of Distribution BPL Topologies with Multihop Repeater Systems under Fixed EMI Limits

Capacity is the maximum achievable transmission rate over a BPL channel and depends on the power grid type, power grid topology, applied coupling scheme, MTL configuration, noise characteristics, and imposed EMI limits. Extending the definition of capacity, cumulative capacity is defined as the cumulative upper bound of information that can be reliably transmitted over a BPL channel.In the light of information theory [9–15, 18, 20] and with reference to Figure 2, in the case of conventional distribution BPL topologies, their overall capacity C, which is the end-to-end capacity from A to B, is determined from
(3)C=CA→B=fs∑q=0Q-1log2{1+[〈pcon(qfs)〉L〈N(qfs)〉L·|HX(qfs)|2]},
where [·]A→B defines the transmitting (A) and receiving (B) end points, 〈·〉L is an operator that converts dBm/Hz into a linear power ratio (W/Hz), Q is the number of subchannels in the BPL signal frequency range of interest, and fs is the flat-fading subchannel frequency spacing.To investigate the capacity impact of multihop repeater systems installation, first, with reference to Figure2, let us assume that a two-hop repeater system is deployed across an end-to-end distribution BPL topology; its sole repeater is installed at distance R1 from the transmitting end. Hence, the initial distribution BPL topology is divided into two new distribution BPL connections. Due to the bus-bar concatenation of these two connections and taking into account (3), the new overall capacity C′ of the distribution BPL topology with two-hop repeater system is determined as the minimum value of the capacities of these two connections:
(4)C′=min{CA→R1,CR1→B},
where min{x,y} returns the smallest value between either x or y.Similar to two-hop repeater systems case, with reference to Figure2, when a three-hop repeater system is deployed across a distribution BPL topology, two repeaters are installed across its end-to-end transmission path at distances R1 and R2, respectively. Thus, the conventional distribution BPL topology is divided into three new distribution BPL connections. The new overall capacity C′′ of the upgraded distribution BPL topology is determined as the minimum value of the capacities of these three connections:
(5)C′′=min{CA→R1,CR1→R2,CR2→B}.


## 5. Numerical Results and Discussion

The simulations of various types of overhead and underground MV/BPL and LV/BPL topologies with multihop repeater systems aim at investigating their broadband capacity potential and how their capacity performance in the 3–88 MHz frequency band is affected by certain factors, such as distribution power grid type, distribution BPL topology, coupling scheme, and number of repeaters.As it is usually done to simplify the analysis without, however, harming its generality [3, 13, 16, 21, 22], in the case of overhead and underground MV/BPL networks, among the possible 3 WtG/StP and 6 WtW/PtP scheme configurations per each MV distribution power grid type, only WtG1/StP1 and WtW1-2/PtP1-2 coupling schemes will be applied, hereafter. Similarly, in the case of overhead and underground LV/BPL networks, among the possible 4 WtG/StP and 12 WtW/PtP scheme configurations per each LV distribution power grid type, only WtG1/StP1 and WtW1-2/PtP1-2 coupling schemes will be applied, hereafter. This selection of representative coupling schemes is made according to their favorable capacity characteristics [3, 13, 22, 23].


### 5.1. Broadband Capacity Performance of Conventional Distribution BPL Topologies

In order to understand the significant capacity impact of installing multihop repeater systems, first, there is need of recognizing the inherent capacity capabilities of conventional distribution BPL topologies.In Figures3(a) and 3(b), the cumulative capacity is plotted versus frequency for the five indicative overhead MV/BPL topologies when WtG1 and WtW1-2 coupling schemes are applied, respectively. In Figures 3(c) and 3(d), similar curves are given in the case of indicative underground MV/BPL topologies when StP1 and PtP1-2 coupling schemes are deployed, respectively. In Figures 4(a)–4(d), similar plots are drawn in the case of indicative distribution LV/BPL topologies. In Table 3, a synopsis of these simulation results concerning overall capacity C of conventional distribution BPL topologies for different distribution power grid types, indicative BPL topologies, and coupling schemes is reported.Table 3
Overall capacity of conventional distribution BPL networks (OV: overhead; UN: underground).
Urban case A
Urban case B
Suburban case
Rural case
“LOS” case
Capacity(Mbps)
Capacity(Mbps)
Capacity(Mbps)
Capacity(Mbps)
Capacity(Mbps)
OVMV
WtG1
621
493
743
895
905
WtW1-2
485
378
594
743
750
UNMV
StP1
831
700
906
982
1066
PtP1-2
714
595
782
851
928
OVLV
WtG1
633
502
752
906
912
WtW1-2
485
378
593
741
749
UNLV
StP1
1870
1656
1974
2078
2179
PtP1-2
1652
1440
1758
1863
1961Cumulative capacity of the five indicative topologies of conventional MV/BPL networks in the 3–88 MHz frequency band when different coupling schemes are applied.
(a)
Overhead/WtG1
(b)
Overhead/WtW1-2
(c)
Underground/StP1
(d)
Underground/PtP1-2Same as in Figure3 but for conventional overhead and underground LV/BPL networks.
(a)
(b)
(c)
(d)Observing Figures3(a)–3(d), 4(a)–4(d), and Table 3, it is evident that the broadband capacity behavior of distribution BPL topologies highlights their established role either as broadband last mile alternative or as SG partner solution [3, 7, 18, 20]. Despite these favourable capacity results—ranging from 378 Mbps to approximately 2.2 Gbps—the overall capacity drastically depends on the distribution power grid type, the number/length of the branches encountered along the end-to-end transmission path, noise properties, and imposed EMI regulations [18, 20]. In accordance with the picture obtained from their capacity behavior, the general BPL class taxonomy—“LOS,” good, and bad class, see Figures 3(a)–3(d) and 4(a)–4(d)—remains the same in distribution BPL topologies even in terms of capacity [17–22]. Actually, the capacity differences between adjacent BPL classes are significant, being of the order of approximately 100–200 Mbps.Due to the bus-bar nature of distribution BPL networks, the aggravated topologies of BPL networks critically deteriorate the overall network capacity. This network capacity degradation hinders further BPL systems symbiosis with other telecommunications systems [17–22].


### 5.2. Broadband Capacity Performance of Distribution BPL Topologies with Two-Hop Repeater Systems

The additive deployment of two-hop repeater systems across conventional distribution BPL networks offers additional degrees of capacity flexibility so that different distribution BPL networks may easily intraoperate as well as interoperate that is, BPL systems cooperation with other well-validated broadband technologies.More specifically, the capacity contribution of two-hop repeater systems is mainly concentrated on the mitigation of capacity differences due to (i) different distribution power grid types, (ii) different topologies, and (iii) different coupling schemes. Therefore, with reference to Figure2 and taking into account the need of scalable capacities among various distribution BPL networks, the appropriate installation position of the sole repeater of a two-hop repeater system across end-to-end transmission paths of more aggravated distribution BPL topologies defines a low-cost and quick solution against the aforementioned causes of capacity discrepancies and performance degradation.In Figures5(a) and 5(b), the overall capacity C′ of overhead MV/BPL topologies with two-hop repeater systems is plotted versus the repeater distance from the transmitting end for the aforementioned indicative topologies when WtG1 and WtW1-2 coupling schemes are applied, respectively. In Figures 5(c) and 5(d), similar curves are plotted in the case of indicative underground MV/BPL topologies when StP1 and PtP1-2 coupling schemes are employed, respectively. In Figures 6(a)–6(d), similar plots are drawn in the case of distribution LV/BPL topologies.Overall capacity of distribution MV/BPL topologies with two-hop repeater systems for the five indicative topologies versus repeater distance from point A—see Figure2—when different coupling schemes are applied.
(a)
Overhead/WtG1
(b)
Overhead/WtW1-2
(c)
Underground/StP1
(d)
Underground/PtP1-2Same as in Figure5 but for overhead and underground LV/BPL topologies with two-hop repeater systems.
(a)
(b)
(c)
(d)From Figures5(a)–5(d) and 6(a)–6(d), it is obvious that the additive insertion of two-hop repeater systems across conventional distribution BPL topologies improves their initial overall capacities regardless of the BPL topology and coupling scheme applied. Actually, in Table 4, the maximum overall capacity of each indicative distribution BPL topology with two-hop repeater system is reported as well as its corresponding repeater distance from the transmitting end when different coupling schemes are applied.Table 4
Overall capacity of distribution BPL topologies with two-hop repeater systems (OV: overhead; UN: underground).
Urban case A
Urban case B
Suburban case
Rural case
“LOS” case
Capacity (Mbps)
Repeater distance (m)
Capacity (Mbps)
Repeater distance (m)
Capacity (Mbps)
Repeater distance (m)
Capacity (Mbps)
Repeater distance (m)
Capacity (Mbps)
Repeater distance (m)
OVMV
WtG1
672
780
601
530
760
500
918
600
922
500
WtW1-2
537
780
475
530
607
900
757
590
761
500
UNMV
StP1
1333
120
872
170
1362
130
1626
90
1693
100
PtP1-2
1164
120
746
170
1193
130
1456
90
1523
100
OVLV
WtG1
679
800
610
550
766
500
924
600
928
500
WtW1-2
538
800
474
550
608
900
756
600
761
500
UNLV
StP1
1959
170
1739
170
2058
150
2201
60
2258
100
PtP1-2
1773
170
1541
170
1866
150
2017
60
2067
100Observing Table4, it is demonstrated that the capacity increase due to the integration of two-hop repeater systems is critical. Since the design of high-bitrate distribution BPL networks imposes strict common capacity thresholds across the overall distribution BPL networks and their corresponding bus-bar-concatenated distribution BPL topologies, two-hop repeater systems offer the necessary capacity boost especially for the bad class topologies.As it has already been presented for channel attenuation characteristics in [3, 13, 20] and also verified from Table 4, WtG/StP coupling schemes attain more favourable results in terms of transmission and capacity metrics in comparison with the respective WtW/PtP ones. However, the significant EMI of WtG/StP coupling schemes to other already licensed wireless communications is their main drawback. Anyway, today’s EMI regulations provide the required protection of BPL operation against other radioservices. Through the deployment of two-hop repeater systems, apart from the mitigation of capacity differences among different topologies, significant capacity divergences may be mitigated when different coupling schemes and EMC requirements occur. More specifically, in order to satisfy strict EMI regulations that are locally and/or periodically imposed, WtG/StP topologies may be equivalently alternated by their respective WtW/PtP topologies when two-hop repeater systems are studiously installed in the latter cases. Hence, interesting capacity tradeoffs among coupling schemes, different EMI regulations, and distribution BPL topologies with two-hop repeater systems can further be defined.


### 5.3. Broadband Capacity Performance of Distribution BPL Topologies with Three-Hop Repeater Systems

The urgent need of cooperative communications among distribution BPL networks and other overhead and underground HV/BPL, MV/BPL, and LV/BPL networks under the umbrella of a unified SG environment demands the guarantee of scalable capacities. Although two-hop repeater systems offer significant capacity leverage, their capacity contribution still remains marginal and asthenic.The adoption of three-hop repeater systems delivers the amount of extra capacity that contributes to more relaxed symbiosis among different distribution BPL networks, thus, better satisfying scalable capacity goals. At the same time, the additional cost of deploying one additional repeater in comparison with the overall installation cost of two-hop repeater systems does not become prohibitive.With reference to Figure2, the appropriate installation positions of the two repeaters of a three-hop repeater system across the end-to-end transmission paths of distribution BPL topologies may define a convenient and more capacity-resultful solution to capacity losses due to different power grid types, topologies, and coupling schemes. The capacity performance analysis of upgraded distribution BPL topologies with three-hop repeater systems is studied through the first proposed capacity contour plots; capacity contour plot is defined as a curve connecting repeater installation points where the capacity has the same particular value. When the plots are close together, the capacity variation is steep.In Figures7(a)–7(e), the overall capacity contour plot of overhead MV/BPL topologies with three-hop repeater systems is given versus the repeater A and B distances from the transmitting end for the aforementioned five indicative topologies, respectively, when WtG1 coupling scheme is applied. In Figures 7(f)–7(j), similar curves are plotted when WtW1-2 coupling scheme is employed. In Figures 9(a)–9(j), similar plots are drawn in the case of overhead LV/BPL topologies.Overall capacity contour plots in Mbps of the five indicative overhead MV/BPL topologies versus repeaters distance from point A—see Figure2—when three-hop repeater system is deployed for different coupling schemes (distance span is equal to 10 m). Blue stars indicate maximum overall capacities.
(a)
Urban case A/WtG1
(b)
Urban case B/WtG1
(c)
Suburban case/WtG1
(d)
Rural case/WtG1
(e)
“LOS” transmission case/WtG1
(f)
Urban case A/WtW1-2
(g)
Urban case B/WtW1-2
(h)
Suburban case/WtW1-2
(i)
Rural case/WtW1-2
(j)
“LOS” transmission case/WtW1-2In Figures8(a)–8(e), the overall capacity contour plot of underground MV/BPL topologies with three-hop repeater systems is plotted versus the repeater A and B distances from the transmitting end for the aforementioned five indicative topologies, respectively, when StP1 coupling scheme is applied. In Figures 8(f)–8(j), similar curves are given when PtP1-2 coupling scheme is applied. In Figures 10(a)–10(j), similar curves are plotted in the case of underground LV/BPL topologies.Overall capacity contour plots in Mbps of the five indicative underground MV/BPL topologies versus repeaters distance from point A—see Figure2—when three-hop repeater system is deployed for different coupling schemes (distance span is equal to 10 m). Blue stars indicate maximum overall capacities.
(a)
Urban case A/StP1
(b)
Urban case B/StP1
(c)
Suburban case/StP1
(d)
Rural case/StP1
(e)
“LOS” transmission case/StP1
(f)
Urban case A/PtP1-2
(g)
Urban case B/PtP1-2
(h)
Suburban case/PtP1-2
(i)
Rural case/PtP1-2
(j)
“LOS” transmission case/PtP1-2Same as in Figure7 but for overhead LV/BPL topologies.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
(j)Same as in Figure8 but for underground LV/BPL topologies.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
(j)Note that in Figures7(a)–7(j), 8(a)–8(j), 9(a)–9(j), and 10(a)–10(j), except for the overall capacity contour plots, the maximum overall capacity of each indicative distribution BPL topology with three-hop repeater system is marked onto capacity contour plots as well as its corresponding repeaters locations from the transmitting end.From Figures7(a)–7(j), 8(a)–8(j), 9(a)–9(j), and 10(a)–10(j), it is obvious that the insertion of three-hop repeater systems critically improves the capacities of overhead and underground MV/BPL and LV/BPL topologies. Upgraded distribution BPL networks can comfortably be transformed to multi-Mbps broadband links. Indeed, in Table 5, the maximum overall capacity of each indicative overhead and underground MV/BPL and LV/BPL topology with three-hop repeater system is reported when different coupling schemes occur. In the same table, the corresponding repeaters distances of these maximum overall capacities are also given.Table 5
Maximum Overall Capacity of Distribution BPL Topologies with Three-Hop Repeater Systems (OV: Overhead; UN: Underground).
Urban case A
Urban case B
Suburban case
Rural case
“LOS” case
Capacity (Mbps)
Repeaters distance[A, B] (m)
Capacity (Mbps)
Repeaters distance[A, B] (m)
Capacity (Mbps)
Repeaters distance[A, B] (m)
Capacity (Mbps)
Repeaters distance[A, B] (m)
Capacity (Mbps)
Repeaters distance[A, B] (m)
OVMV
WtG1
817
[790, 510]
736
[250, 360]
853
[900, 930]
926
[450, 640]
929
[310, 660]
WtW1-2
659
[790, 510]
580
[290, 630]
686
[900, 930]
764
[450, 640]
766
[330, 670]
UNMV
StP1
1756
[70, 130]
1728
[60, 120]
1826
[60, 140]
1859
[60, 130]
1893
[60, 130]
PtP1-2
1586
[70, 130]
1558
[60, 120]
1656
[60, 140]
1689
[60, 130]
1723
[60, 130]
OVLV
WtG1
824
[510, 740]
738
[250, 360]
855
[900, 910]
932
[400, 610]
935
[330, 660]
WtW1-2
660
[510, 740]
580
[260, 360]
687
[900, 910]
764
[420, 610]
767
[330, 670]
UNLV
StP1
2175
[80, 130]
2088
[70, 120]
2200
[60, 150]
2232
[50, 80]
2289
[60, 130]
PtP1-2
1987
[80, 130]
1901
[70, 120]
2016
[60, 150]
2043
[50, 90]
2104
[60, 130]From Figures7(a)–7(j), 8(a)–8(j), 9(a)–9(j), 10(a)–10(j), and Table 5, it is clearly shown that distribution BPL topologies with three-hop repeater systems define a more spectral-efficient implementation proposal in comparison with respective conventional BPL topologies and upgraded BPL topologies with two-hop repeater systems regardless of the distribution power grid type, distribution BPL topology, and coupling scheme applied.As it has already been mentioned, distribution BPL topologies with three-hop repeater systems are successfully assessed by the proposed 2-D sets of overall capacity contour plots whereas the respective topologies with two-hop repeater systems define a subset of these 2-D sets: thex- and y-axes of the corresponding contour plots. Therefore, in all the cases examined, three-hop repeater systems suggest a more capacity-thriving repeater system version.Actually, the gradual maximum overall capacity improvement that occurs from conventional distribution BPL topologies to ones with two-hop repeater systems and, finally, to those with three-hop repeater systems is highlighted in Figures11(a)–11(d) where different indicative distribution BPL topologies and coupling schemes are examined.Maximum overall capacity of distribution BPL topologies with three-hop repeater systems (in green), distribution BPL topologies with two-hop repeater systems (in red), and conventional distribution BPL topologies (in blue) when different indicative BPL topologies and coupling scheme occur (OV: overhead, UN: underground, WtG1: WtG1 coupling scheme, WtW1_2: PtP1-2 coupling scheme, StP1: StP1 coupling scheme, and PtP1_2: PtP1-2 coupling scheme).
(a)
Overhead MV/BPL topologies
(b)
Underground MV/BPL topologies
(c)
Underground MV/BPL topologies
(d)
Underground LV/BPL topologiesFrom Figures11(a)–11(d), it is evident that, through the deployment of three-hop repeater systems, apart from the mitigation of capacity discrepancies among different topologies of the same BPL network type, significant capacity differences may be assuaged among overhead and underground MV/BPL and LV/BPL networks.Nevertheless, due to the bus-bar nature of distribution BPL networks, the aggravated topologies of these networks define the overall network capacity. Actually, the most aggravated topologies of BPL networks impose an upper overall network capacity limit (capacity ceiling) that is determined as the minimum of the maximum overall capacities of Figures11(a)–11(d). Multihop repeater systems drastically improve this upper overall network capacity limit; in the case of conventional distribution BPL networks, distribution BPL network with two-hop repeater systems, and distribution BPL networks with three-hop repeater systems, this upper overall network capacity limit is equal to 378 Mbps, 474 Mbps, and 580 Mbps, respectively, corresponding to approximate 100 Mbps increase of overall network capacity limit per each installed repeater.Except for the inherent upper overall network capacity limit, the design of high-bitrate distribution BPL topologies can impose strict common capacity thresholds across the overall network that consists of overhead and underground MV/BPL and LV/BPL topologies in order to satisfy EMC specifications that are locally and/or periodically imposed. Stricter EMC specifications impose lower IPSD limits that create additional capacity degradation in distribution BPL networks. Via the installation of three-hop repeater systems, there is a greater flexibility regarding the capabilities of cooperative overhead and underground MV/BPL and LV/BPL networks when different EMC requirements are adopted.Consequently, the above simulations and numerical results reveal the need of further broadband exploitation of overhead and underground MV/BPL and LV/BPL networks with multihop repeater system under the aegis of a unified transmission/distribution SG power grid. On the basis of multihop repeater systems, the BPL intraoperability/interoperability venture may be further promoted via the concepts of scalable capacities, standardized topologies, and free coupling scheme swap.


## 5.1. Broadband Capacity Performance of Conventional Distribution BPL Topologies

In order to understand the significant capacity impact of installing multihop repeater systems, first, there is need of recognizing the inherent capacity capabilities of conventional distribution BPL topologies.In Figures3(a) and 3(b), the cumulative capacity is plotted versus frequency for the five indicative overhead MV/BPL topologies when WtG1 and WtW1-2 coupling schemes are applied, respectively. In Figures 3(c) and 3(d), similar curves are given in the case of indicative underground MV/BPL topologies when StP1 and PtP1-2 coupling schemes are deployed, respectively. In Figures 4(a)–4(d), similar plots are drawn in the case of indicative distribution LV/BPL topologies. In Table 3, a synopsis of these simulation results concerning overall capacity C of conventional distribution BPL topologies for different distribution power grid types, indicative BPL topologies, and coupling schemes is reported.Table 3
Overall capacity of conventional distribution BPL networks (OV: overhead; UN: underground).
Urban case A
Urban case B
Suburban case
Rural case
“LOS” case
Capacity(Mbps)
Capacity(Mbps)
Capacity(Mbps)
Capacity(Mbps)
Capacity(Mbps)
OVMV
WtG1
621
493
743
895
905
WtW1-2
485
378
594
743
750
UNMV
StP1
831
700
906
982
1066
PtP1-2
714
595
782
851
928
OVLV
WtG1
633
502
752
906
912
WtW1-2
485
378
593
741
749
UNLV
StP1
1870
1656
1974
2078
2179
PtP1-2
1652
1440
1758
1863
1961Cumulative capacity of the five indicative topologies of conventional MV/BPL networks in the 3–88 MHz frequency band when different coupling schemes are applied.
(a)
Overhead/WtG1
(b)
Overhead/WtW1-2
(c)
Underground/StP1
(d)
Underground/PtP1-2Same as in Figure3 but for conventional overhead and underground LV/BPL networks.
(a)
(b)
(c)
(d)Observing Figures3(a)–3(d), 4(a)–4(d), and Table 3, it is evident that the broadband capacity behavior of distribution BPL topologies highlights their established role either as broadband last mile alternative or as SG partner solution [3, 7, 18, 20]. Despite these favourable capacity results—ranging from 378 Mbps to approximately 2.2 Gbps—the overall capacity drastically depends on the distribution power grid type, the number/length of the branches encountered along the end-to-end transmission path, noise properties, and imposed EMI regulations [18, 20]. In accordance with the picture obtained from their capacity behavior, the general BPL class taxonomy—“LOS,” good, and bad class, see Figures 3(a)–3(d) and 4(a)–4(d)—remains the same in distribution BPL topologies even in terms of capacity [17–22]. Actually, the capacity differences between adjacent BPL classes are significant, being of the order of approximately 100–200 Mbps.Due to the bus-bar nature of distribution BPL networks, the aggravated topologies of BPL networks critically deteriorate the overall network capacity. This network capacity degradation hinders further BPL systems symbiosis with other telecommunications systems [17–22].


## 5.2. Broadband Capacity Performance of Distribution BPL Topologies with Two-Hop Repeater Systems

The additive deployment of two-hop repeater systems across conventional distribution BPL networks offers additional degrees of capacity flexibility so that different distribution BPL networks may easily intraoperate as well as interoperate that is, BPL systems cooperation with other well-validated broadband technologies.More specifically, the capacity contribution of two-hop repeater systems is mainly concentrated on the mitigation of capacity differences due to (i) different distribution power grid types, (ii) different topologies, and (iii) different coupling schemes. Therefore, with reference to Figure2 and taking into account the need of scalable capacities among various distribution BPL networks, the appropriate installation position of the sole repeater of a two-hop repeater system across end-to-end transmission paths of more aggravated distribution BPL topologies defines a low-cost and quick solution against the aforementioned causes of capacity discrepancies and performance degradation.In Figures5(a) and 5(b), the overall capacity C′ of overhead MV/BPL topologies with two-hop repeater systems is plotted versus the repeater distance from the transmitting end for the aforementioned indicative topologies when WtG1 and WtW1-2 coupling schemes are applied, respectively. In Figures 5(c) and 5(d), similar curves are plotted in the case of indicative underground MV/BPL topologies when StP1 and PtP1-2 coupling schemes are employed, respectively. In Figures 6(a)–6(d), similar plots are drawn in the case of distribution LV/BPL topologies.Overall capacity of distribution MV/BPL topologies with two-hop repeater systems for the five indicative topologies versus repeater distance from point A—see Figure2—when different coupling schemes are applied.
(a)
Overhead/WtG1
(b)
Overhead/WtW1-2
(c)
Underground/StP1
(d)
Underground/PtP1-2Same as in Figure5 but for overhead and underground LV/BPL topologies with two-hop repeater systems.
(a)
(b)
(c)
(d)From Figures5(a)–5(d) and 6(a)–6(d), it is obvious that the additive insertion of two-hop repeater systems across conventional distribution BPL topologies improves their initial overall capacities regardless of the BPL topology and coupling scheme applied. Actually, in Table 4, the maximum overall capacity of each indicative distribution BPL topology with two-hop repeater system is reported as well as its corresponding repeater distance from the transmitting end when different coupling schemes are applied.Table 4
Overall capacity of distribution BPL topologies with two-hop repeater systems (OV: overhead; UN: underground).
Urban case A
Urban case B
Suburban case
Rural case
“LOS” case
Capacity (Mbps)
Repeater distance (m)
Capacity (Mbps)
Repeater distance (m)
Capacity (Mbps)
Repeater distance (m)
Capacity (Mbps)
Repeater distance (m)
Capacity (Mbps)
Repeater distance (m)
OVMV
WtG1
672
780
601
530
760
500
918
600
922
500
WtW1-2
537
780
475
530
607
900
757
590
761
500
UNMV
StP1
1333
120
872
170
1362
130
1626
90
1693
100
PtP1-2
1164
120
746
170
1193
130
1456
90
1523
100
OVLV
WtG1
679
800
610
550
766
500
924
600
928
500
WtW1-2
538
800
474
550
608
900
756
600
761
500
UNLV
StP1
1959
170
1739
170
2058
150
2201
60
2258
100
PtP1-2
1773
170
1541
170
1866
150
2017
60
2067
100Observing Table4, it is demonstrated that the capacity increase due to the integration of two-hop repeater systems is critical. Since the design of high-bitrate distribution BPL networks imposes strict common capacity thresholds across the overall distribution BPL networks and their corresponding bus-bar-concatenated distribution BPL topologies, two-hop repeater systems offer the necessary capacity boost especially for the bad class topologies.As it has already been presented for channel attenuation characteristics in [3, 13, 20] and also verified from Table 4, WtG/StP coupling schemes attain more favourable results in terms of transmission and capacity metrics in comparison with the respective WtW/PtP ones. However, the significant EMI of WtG/StP coupling schemes to other already licensed wireless communications is their main drawback. Anyway, today’s EMI regulations provide the required protection of BPL operation against other radioservices. Through the deployment of two-hop repeater systems, apart from the mitigation of capacity differences among different topologies, significant capacity divergences may be mitigated when different coupling schemes and EMC requirements occur. More specifically, in order to satisfy strict EMI regulations that are locally and/or periodically imposed, WtG/StP topologies may be equivalently alternated by their respective WtW/PtP topologies when two-hop repeater systems are studiously installed in the latter cases. Hence, interesting capacity tradeoffs among coupling schemes, different EMI regulations, and distribution BPL topologies with two-hop repeater systems can further be defined.


## 5.3. Broadband Capacity Performance of Distribution BPL Topologies with Three-Hop Repeater Systems

The urgent need of cooperative communications among distribution BPL networks and other overhead and underground HV/BPL, MV/BPL, and LV/BPL networks under the umbrella of a unified SG environment demands the guarantee of scalable capacities. Although two-hop repeater systems offer significant capacity leverage, their capacity contribution still remains marginal and asthenic.The adoption of three-hop repeater systems delivers the amount of extra capacity that contributes to more relaxed symbiosis among different distribution BPL networks, thus, better satisfying scalable capacity goals. At the same time, the additional cost of deploying one additional repeater in comparison with the overall installation cost of two-hop repeater systems does not become prohibitive.With reference to Figure2, the appropriate installation positions of the two repeaters of a three-hop repeater system across the end-to-end transmission paths of distribution BPL topologies may define a convenient and more capacity-resultful solution to capacity losses due to different power grid types, topologies, and coupling schemes. The capacity performance analysis of upgraded distribution BPL topologies with three-hop repeater systems is studied through the first proposed capacity contour plots; capacity contour plot is defined as a curve connecting repeater installation points where the capacity has the same particular value. When the plots are close together, the capacity variation is steep.In Figures7(a)–7(e), the overall capacity contour plot of overhead MV/BPL topologies with three-hop repeater systems is given versus the repeater A and B distances from the transmitting end for the aforementioned five indicative topologies, respectively, when WtG1 coupling scheme is applied. In Figures 7(f)–7(j), similar curves are plotted when WtW1-2 coupling scheme is employed. In Figures 9(a)–9(j), similar plots are drawn in the case of overhead LV/BPL topologies.Overall capacity contour plots in Mbps of the five indicative overhead MV/BPL topologies versus repeaters distance from point A—see Figure2—when three-hop repeater system is deployed for different coupling schemes (distance span is equal to 10 m). Blue stars indicate maximum overall capacities.
(a)
Urban case A/WtG1
(b)
Urban case B/WtG1
(c)
Suburban case/WtG1
(d)
Rural case/WtG1
(e)
“LOS” transmission case/WtG1
(f)
Urban case A/WtW1-2
(g)
Urban case B/WtW1-2
(h)
Suburban case/WtW1-2
(i)
Rural case/WtW1-2
(j)
“LOS” transmission case/WtW1-2In Figures8(a)–8(e), the overall capacity contour plot of underground MV/BPL topologies with three-hop repeater systems is plotted versus the repeater A and B distances from the transmitting end for the aforementioned five indicative topologies, respectively, when StP1 coupling scheme is applied. In Figures 8(f)–8(j), similar curves are given when PtP1-2 coupling scheme is applied. In Figures 10(a)–10(j), similar curves are plotted in the case of underground LV/BPL topologies.Overall capacity contour plots in Mbps of the five indicative underground MV/BPL topologies versus repeaters distance from point A—see Figure2—when three-hop repeater system is deployed for different coupling schemes (distance span is equal to 10 m). Blue stars indicate maximum overall capacities.
(a)
Urban case A/StP1
(b)
Urban case B/StP1
(c)
Suburban case/StP1
(d)
Rural case/StP1
(e)
“LOS” transmission case/StP1
(f)
Urban case A/PtP1-2
(g)
Urban case B/PtP1-2
(h)
Suburban case/PtP1-2
(i)
Rural case/PtP1-2
(j)
“LOS” transmission case/PtP1-2Same as in Figure7 but for overhead LV/BPL topologies.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
(j)Same as in Figure8 but for underground LV/BPL topologies.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
(j)Note that in Figures7(a)–7(j), 8(a)–8(j), 9(a)–9(j), and 10(a)–10(j), except for the overall capacity contour plots, the maximum overall capacity of each indicative distribution BPL topology with three-hop repeater system is marked onto capacity contour plots as well as its corresponding repeaters locations from the transmitting end.From Figures7(a)–7(j), 8(a)–8(j), 9(a)–9(j), and 10(a)–10(j), it is obvious that the insertion of three-hop repeater systems critically improves the capacities of overhead and underground MV/BPL and LV/BPL topologies. Upgraded distribution BPL networks can comfortably be transformed to multi-Mbps broadband links. Indeed, in Table 5, the maximum overall capacity of each indicative overhead and underground MV/BPL and LV/BPL topology with three-hop repeater system is reported when different coupling schemes occur. In the same table, the corresponding repeaters distances of these maximum overall capacities are also given.Table 5
Maximum Overall Capacity of Distribution BPL Topologies with Three-Hop Repeater Systems (OV: Overhead; UN: Underground).
Urban case A
Urban case B
Suburban case
Rural case
“LOS” case
Capacity (Mbps)
Repeaters distance[A, B] (m)
Capacity (Mbps)
Repeaters distance[A, B] (m)
Capacity (Mbps)
Repeaters distance[A, B] (m)
Capacity (Mbps)
Repeaters distance[A, B] (m)
Capacity (Mbps)
Repeaters distance[A, B] (m)
OVMV
WtG1
817
[790, 510]
736
[250, 360]
853
[900, 930]
926
[450, 640]
929
[310, 660]
WtW1-2
659
[790, 510]
580
[290, 630]
686
[900, 930]
764
[450, 640]
766
[330, 670]
UNMV
StP1
1756
[70, 130]
1728
[60, 120]
1826
[60, 140]
1859
[60, 130]
1893
[60, 130]
PtP1-2
1586
[70, 130]
1558
[60, 120]
1656
[60, 140]
1689
[60, 130]
1723
[60, 130]
OVLV
WtG1
824
[510, 740]
738
[250, 360]
855
[900, 910]
932
[400, 610]
935
[330, 660]
WtW1-2
660
[510, 740]
580
[260, 360]
687
[900, 910]
764
[420, 610]
767
[330, 670]
UNLV
StP1
2175
[80, 130]
2088
[70, 120]
2200
[60, 150]
2232
[50, 80]
2289
[60, 130]
PtP1-2
1987
[80, 130]
1901
[70, 120]
2016
[60, 150]
2043
[50, 90]
2104
[60, 130]From Figures7(a)–7(j), 8(a)–8(j), 9(a)–9(j), 10(a)–10(j), and Table 5, it is clearly shown that distribution BPL topologies with three-hop repeater systems define a more spectral-efficient implementation proposal in comparison with respective conventional BPL topologies and upgraded BPL topologies with two-hop repeater systems regardless of the distribution power grid type, distribution BPL topology, and coupling scheme applied.As it has already been mentioned, distribution BPL topologies with three-hop repeater systems are successfully assessed by the proposed 2-D sets of overall capacity contour plots whereas the respective topologies with two-hop repeater systems define a subset of these 2-D sets: thex- and y-axes of the corresponding contour plots. Therefore, in all the cases examined, three-hop repeater systems suggest a more capacity-thriving repeater system version.Actually, the gradual maximum overall capacity improvement that occurs from conventional distribution BPL topologies to ones with two-hop repeater systems and, finally, to those with three-hop repeater systems is highlighted in Figures11(a)–11(d) where different indicative distribution BPL topologies and coupling schemes are examined.Maximum overall capacity of distribution BPL topologies with three-hop repeater systems (in green), distribution BPL topologies with two-hop repeater systems (in red), and conventional distribution BPL topologies (in blue) when different indicative BPL topologies and coupling scheme occur (OV: overhead, UN: underground, WtG1: WtG1 coupling scheme, WtW1_2: PtP1-2 coupling scheme, StP1: StP1 coupling scheme, and PtP1_2: PtP1-2 coupling scheme).
(a)
Overhead MV/BPL topologies
(b)
Underground MV/BPL topologies
(c)
Underground MV/BPL topologies
(d)
Underground LV/BPL topologiesFrom Figures11(a)–11(d), it is evident that, through the deployment of three-hop repeater systems, apart from the mitigation of capacity discrepancies among different topologies of the same BPL network type, significant capacity differences may be assuaged among overhead and underground MV/BPL and LV/BPL networks.Nevertheless, due to the bus-bar nature of distribution BPL networks, the aggravated topologies of these networks define the overall network capacity. Actually, the most aggravated topologies of BPL networks impose an upper overall network capacity limit (capacity ceiling) that is determined as the minimum of the maximum overall capacities of Figures11(a)–11(d). Multihop repeater systems drastically improve this upper overall network capacity limit; in the case of conventional distribution BPL networks, distribution BPL network with two-hop repeater systems, and distribution BPL networks with three-hop repeater systems, this upper overall network capacity limit is equal to 378 Mbps, 474 Mbps, and 580 Mbps, respectively, corresponding to approximate 100 Mbps increase of overall network capacity limit per each installed repeater.Except for the inherent upper overall network capacity limit, the design of high-bitrate distribution BPL topologies can impose strict common capacity thresholds across the overall network that consists of overhead and underground MV/BPL and LV/BPL topologies in order to satisfy EMC specifications that are locally and/or periodically imposed. Stricter EMC specifications impose lower IPSD limits that create additional capacity degradation in distribution BPL networks. Via the installation of three-hop repeater systems, there is a greater flexibility regarding the capabilities of cooperative overhead and underground MV/BPL and LV/BPL networks when different EMC requirements are adopted.Consequently, the above simulations and numerical results reveal the need of further broadband exploitation of overhead and underground MV/BPL and LV/BPL networks with multihop repeater system under the aegis of a unified transmission/distribution SG power grid. On the basis of multihop repeater systems, the BPL intraoperability/interoperability venture may be further promoted via the concepts of scalable capacities, standardized topologies, and free coupling scheme swap.


## 6. Conclusions

The broadband role of overhead and underground MV/BPL and LV/BPL networks with two- and three-hop repeater systems has been reviewed and analyzed in this paper. Their main contribution is the convenient and quick technology upgrade of the conventional distribution BPL networks offering crucial help towards the design/operation of cooperative distribution BPL networks in the oncoming SG network.



---

*Source: 472190-2013-03-28.xml*