# A novel PLC channel modeling method and channel characteristic analysis of a smart distribution grid

- Jian Le
^{1}Email author, - Cao Wang
^{1}, - Wu Zhou
^{1}, - Yong-yan Liu
^{1}and - Wei Cai
^{2}

**2**:14

https://doi.org/10.1186/s41601-017-0044-2

© The Author(s) 2017

**Received: **3 December 2016

**Accepted: **10 March 2017

**Published: **17 April 2017

## Abstract

Power line carrier (PLC) technology plays an increasingly important role in the realization of cost-effective communication in a smart distribution grid. No current channel modeling method is universally applicable to more complex topologies that may emerge in smart grids, such as ring and mesh topologies. This paper presents a novel PLC channel modeling method based on the information node concept, and the universality and feasibility of the proposed method are demonstrated with applications in modeling networks with ring and mesh topologies. The factors that affect the channel characteristics of the networks and the laws that govern their behaviors for different types of topologies are analyzed. The validity and effectiveness of the proposed method are proven using simulation and laboratory tests. This paper provides the necessary theoretical basis and technical means to design the PLC modulation method for smart distribution grids.

## Keywords

## 1 Introduction

Reliable and cost-effective communication networks are the basis and premise for the realization of Smart Grids. The power line carrier (PLC) technology [1–3], which has been applied in traditional power systems to transfer voice or data at high speed over the power line with a power flow, is considered a suitable candidate [4, 5]. However, the channel of the PLC has high-frequency selectivity with complex signal attenuation because of the poor working condition, serious interference, and large time variation. As a result, numerous studies have considered the power-line channel modeling method to accurately establish an effective PLC transmission model and select the best transmission frequency according to the frequency selectivity transmission characteristic [6–8].

The existing channel modeling methods can be divided into time-domain [9–12] and frequency-domain types [13–18]. Time-domain methods, which can be further divided into top-down [9, 10] and bottom-up [11, 12] types according to the approach used to obtain the necessary parameters, treat the PLC channel as a multi-path environment and use the reflection model to represent the physical characteristics of the channel. The top-down method regards the PLC channel as a multi-path model and uses curve fitting techniques to obtain the required parameters based on the actual measurement results of the transmission characteristics. Various curve fitting techniques are used, and the complexity and time variation of the PLC channels cause large differences between measurement results. Hence, the models obtained by different researchers are notably different, and none can guarantee the best performance under all operation conditions of the network. The main principle of the bottom-up methods is to consider the reflection and attenuation at the impedance mismatch points and subsequently enumerate, simplify, and classify all paths between the signal transmitter and the information receiver based on the actual network topology. This type of method simplifies the forward traveling wave to such an extent that it results in large errors. The method is also computationally expensive and can only be applied to the tree topology.

To calculate the transmission characteristics of the entire network, frequency-domain methods break the entire network into several cascaded sub-networks and calculate the transmission matrix [13–15] or scattering matrix [16–18] for each sub-network. This type of method has the advantage of considering the reflective properties of all signals regardless of the network complexity. However, it cannot be easily applied in the ring and mesh topologies, which may emerge in smart distribution grids, because these topologies cannot be broken into sub-networks. H. Meng [18] derived a channel model method for a ring topology using scattering parameters; however, this method has difficulty considering multiple rings and mesh topologies.

A new modeling method to analyze the transfer characteristics of the PLC channel of a network with arbitrary topology is proposed in this paper, and its application in the network with a ring or mesh topology is demonstrated in detail [19]. The remainder of this paper is structured as follows. In Section II, the principle of the channel modeling method based on the information node concept is presented. Section III shows the application of the proposed method in a network with ring topology; the validity and effectiveness of this method is proven by simulation and laboratory test. The influence laws that govern the channel characteristics of a network with complex mesh topology are analyzed by simulation and laboratory test results in Section V. Finally, in Section VI, the main findings of this paper are summarized.

## 2 Channel modeling approach based on information node (Methods)

### 2.1 Network topology and information nodes

*C*

_{ m }and

*C*

_{ n }in Fig. 1, and the termination nodes connect to at least one of the loads or the signal source, such as

*T*

_{1},

*T*

_{2},

*T*

_{ i }, and

*T*

_{ j }in Fig. 1.

*V*

_{ S }and

*Z*

_{ S }are the amplitude and impedance of the signal source, respectively.

In this paper, a new concept called the “information node”, which can cover important information regarding the node voltage and current, is introduced to help describe the state of the network. Several information nodes are placed at the points as closely as possible around a network node. For example, *D*
_{
t11} and *D*
_{
t12} are the information nodes related to the signal source impedance *Z*
_{
s
} and power line *Line_*1, respectively, which connect to termination node *T*
_{1}, and *D*
_{
cn1} is the information node of power line *Line_k*, which connects to internal node *C*
_{
n
}. Thus, at least two relevant information nodes should be assigned to a network node except for the signal source, where the voltages of the signal source and at information node *D*
_{
t11} are different because of the internal impedance *Z*
_{
S
}. Therefore, an additional information node *D*
_{
s
} should be introduced between the signal source and *D*
_{
t11}, as shown in Fig. 1.

By placing all necessary information nodes into the network, the problem of determining the transmission characteristic between signal sourc*e V*
_{S} and each receiver is converted into a problem of determining the transmission characteristic between information node *D*
_{
S
} and the information node related to each receiver (e.g., *D*
_{
t22} if the receiver is located at node *T*
_{2}).

### 2.2 Network equations based on information nodes

*m*power lines and

*n*loads in the power network in Fig. 1. According to the principle of setting the information nodes, 2

*m*and

*n*information nodes are respectively linked with

*m*power lines and

*n*information nodes because a power line must be connected between two information nodes, whereas a load is always related to only one information node. Because the special information nodes

*D*

_{ S }and

*D*

_{ t11}are related to the signal source, the total number

*S*of information nodes in the network is:

Obviously, the voltage of and the current flowing out of an information node are two unknown quantities. Thus, there are 4 *m* + 2*n* + 4 unknown quantities for the entire network. In this paper, the reference direction of the node current is out of the node.

*V*-

*I*relationships between information nodes

*D*

_{ cm1}and

*D*

_{ cn1}are:

where *x* is the length of the power line *Line_k*, and *γ* and *Z*
_{
C
} are the propagation constant and characteristic impedance of this power line, respectively. We can list two equations similar to Eq. (2) for each power line; therefore, 2 *m* equations can be obtained for *m* power lines.

*Load_*1 in Fig. 1, its voltage

*U*

_{ t22}and current

*I*

_{ t22}must satisfy Ohm’s Law, i.e.,

where *Z*
_{
L1} is the load impedance of *Load_*1. Thus, *n* equations can be obtained for *n* loads.

*k*information nodes that are related to a network node

*C*

_{ n }, as shown in Fig. 3.

*k*independent equations for this network node as:

For a network with *m* power lines, *n* loads, and one signal source, there must be 2 *m* + *n* + 1 information nodes, and each node is related to one and only one of the network nodes (*Ds* is excluded). Thus, 2 *m* + *n* + 1 independent equations can be listed for all network nodes.

*D*

_{ t11}and

*D*

_{ S }, which are related to signal source

*V*

_{ S }, the following two equations are deduced:

where *Z*
_{
S
} is the internal impedance of signal source V_{S}.

*m*power lines and

*n*loads, 2

*m*+

*n*+ 2

*m*+

*n*+ 1 + 2 = 4

*m*+ 2

*n*+ 3 independent equations can be obtained based on the above derivations. These equations can be expressed in matrix form as follows:

*A*, we can know that all elements in

*A*are only related to the network topology and component parameters. Because the 4

*m*+ 2

*n*+ 3 equations are independent, the rank of coefficient matrix

*A*is

*m*+ 2

*n*+ 4 unknown variables for the entire network, whereas there are 4

*m*+ 2

*n*+ 3 independent equations in the homogeneous linear equations. Therefore, the ratio of any two unknown variables can be calculated easily by solving Eq. (6). Thus, the voltage transmission characteristics between the signal transmitter and the receiver are:

where *U*
_{
Zi
} is the voltage of the information node related to *Load*_*i*.

By solving Eq. (6), the theoretical expression for the voltage transmission characteristic between the signal transmitter and the receiver can be easily calculated using a conventional software such as MATLAB. Then, the key factors that affect the channel transmission characteristic and the influence law can be conveniently analyzed. This method is applicable to a network with arbitrary topology.

There are few ring topologies and no mesh topology in smart grids till now. However, in IEEE1547, part 4.1.4 “Distributed resources on distribution secondary grid and spot networks” proposes ring topologies and mesh topologies in distribution networks in the future with distributed generation accessed. In this situation, the proposed method will be able to solve the problems that there is no effective channel modeling method for the application of PLC in a network with ring and mesh topologies.

## 3 Channel modeling and laboratory test of a simple ring topology (Results and discussion 1)

*D*

_{1}to

*D*

_{6}and

*D*

_{ S }.

*a*

_{ i }=

*d*

_{ i }

*= ch*(

*r*

_{ i }

*l*

_{ i }),

*b*

_{ i }=

*Z*

_{ C }

*sh*(

*r*

_{ i }

*l*

_{ i }), and

*c*

_{ i }=

*sh*(

*r*

_{ i }

*l*

_{ i })

*/Z*

_{ C }, (

*i*= 1,2);

*Z*

_{ S }is the source impedance, and

*Z*

_{ L }is the load impedance.

*D*

_{ S }and

*D*

_{6}in Fig. 5 is:

*C*

_{0}= 96 pF/m,

*L*

_{0}= 276 nH/m,

*R*

_{0}= 1 mΩ/m,

*G*

_{0}is neglected, and the lengths of

*l*

_{1}and

*l*

_{2}are set to 10 m. The cables and interfaces and part of the physical configuration of the circuit are shown in Figs. 6 and 7, respectively. Figure 8 illustrates an actual waveform from the network analyzer.

The HP8753D network analyzer can easily determine the voltage transfer characteristic of networks with different topologies. The resulting curve is shown on its screen, as shown in Fig. 8, and the data can be easily stored and read using a floppy disk.

## 4 Simulation and laboratory test results for a network with a ring topology (Results and discussion 2)

*C*

_{0}= 96 pF/m,

*L*

_{0}= 276 nH/m,

*R*

_{0}= 1 mΩ/m; and

*G*

_{0}is neglected. Both source internal impedance

*Z*

_{ S }and load impedance

*Z*

_{ L }are 50 Ω; both branch loads

*Z*

_{ L1}and

*Z*

_{ L2}are 0 Ω, i.e., both are short-circuited. In the following, the simulation results of the amplitude-frequency characteristic are obtained using the proposed method, whereas the laboratory test results are measured using the HP8753D network analyzer on a real network.

### 4.1 Changes in trunk length

First, the effect of the trunk length on the amplitude-frequency transmission characteristics is considered*.* The trunk lengths (i.e., *l*
_{1}, *l*
_{2}, *l*
_{3}, and *l*
_{4} in Fig. 11) are identical, and simulations and tests are performed with lengths of 10, 20, 30, and 40 m, whereas the lengths of the branch lines (i.e., *l*
_{5} and *l*
_{6} in Fig. 11) are held constant at 10 m.

*Z*

_{ L }and signal source V

_{S}.

Figure 12 illustrates that the peaks in the amplitude-frequency characteristics fluctuate when the trunk length increases, whereas the locations and amplitudes of the notches do not change. The notches occur at the frequencies of 10, 20, and 30 MHz.

### 4.2 Changes in branch length

Next, the effect of the branch length on the amplitude-frequency transmission characteristic is simulated and tested. In Fig. 11, we maintained a constant trunk length of *l*
_{1} = *l*
_{2} = *l*
_{3} = *l*
_{4}
*=* 10 m, whereas the branch lengths *l*
_{5} and *l*
_{6} were changed to 10 m, 20 m, 30 m, and 40 m, respectively.

*Z*

_{ L }and signal source V

_{S}. We can learn that the numbers of peaks and notches in the amplitude-frequency characteristic curve increase when the branch length increases (the numbers of notches in Figs. 13a, b, c, and d are 3, 6, 9, and 12, respectively).

### 4.3 Changes in the number of branches

*l*of all lines between adjacent nodes is 10 m; thus, when the number of branches is 2, 4, 6, or 8, the length of ADEB and AFHB is 20, 30, 40, or 50 m, respectively. All branch loads (i.e.,

*Z*

_{ L11},

*Z*

_{ L12}, …,

*Z*

_{ Ln1},

*Z*

_{ Ln2}) are open circuit, and the other parameters are identical to those in Fig. 11.

*Z*

_{ L }and signal source V

_{S}. The peaks of the amplitude-frequency characteristic slightly fluctuate when the branch number increases. There are only 3 notches for various numbers of branches, but the amplitude of the notches increases with an increasing number of branches.

## 5 Simulation and laboratory test results for a network with a mesh topology (Results and discussion 3)

*C*

_{0}= 96 pF/m,

*L*

_{0}= 276 nH/m,

*R*

_{0}= 1 mΩ/m, and

*G*

_{0}is neglected. Source internal impedance

*Z*

_{ S }and load impedance

*Z*

_{ L }are 50 Ω, and branch loads

*Z*

_{ L1}and

*Z*

_{ L2}are 0 Ω. In the following, simulation results of the amplitude frequency characteristics are obtained using the proposed method, and the laboratory test results are measured using a network analyzer on a real network with the topology in Fig. 16.

### 5.1 Changes in front and rear trunk length

First, we maintain a constant trunk length of *l*
_{5} = *l*
_{6} = *l*
_{7} = *l*
_{8} = 10 m, a constant branch length of *l*
_{2} = *l*
_{4} = 10 m, and a constant link branch length of *l*
_{9} = 20 m. We change the front and rear trunk lengths (*l*
_{1} and *l*
_{3}, respectively) to 10, 20, 30, and 40 m.

*Z*

_{ L }and signal source V

_{S}. The amplitude-frequency characteristics vary only slightly for different front and rear trunk lengths; thus, this factor is not considered in the following analysis.

### 5.2 Changes in branch length

In Fig. 16, we maintain a constant front and rear trunk length of *l*
_{1} = *l*
_{3}
*=* 10 m, a trunk length of *l*
_{5} = *l*
_{6} = *l*
_{7} = *l*
_{8} = 5 m, and a link branch length of *l*
_{9} = 10 m; we change the branch lengths *l*
_{2} and *l*
_{4} to 5, 10, 15, and 20 m.

*Z*

_{ L }and signal source V

_{S}.

The branch length significantly affects the amplitude-frequency characteristics; specifically, additional notches appear when the branch length is increased.

### 5.3 Changes in trunk length

In Fig. 16, we maintain constant front and rear trunk lengths of *l*
_{1} = *l*
_{3} = 10 m, a branch length of *l*
_{2} = *l*
_{4} = 5 m, and a link branch length of *l*
_{9} = 10 m. We vary the trunk lengths *l*
_{5}, *l*
_{6}, *l*
_{7}, and *l*
_{8} to 5, 10, 15, and 20 m.

*Z*

_{ L }and signal source V

_{S}.

The trunk length has a complex effect on the transmission characteristics. As the trunk length increases, the number of notches change to different numbers in an alternating manner, e.g., 2 notches are present in Fig. 19a and c, whereas 4 notches are present in Fig. 19b and d.

### 5.4 Proportional changes in the mesh length

In Fig. 16, we maintain constant front and rear trunk lengths of *l*
_{1} = *l*
_{3}
*=* 10 m, whereas the trunk length *l*
_{5} = *l*
_{6} = *l*
_{7} = *l*
_{8} is varied to 5, 10, 15, and 20 m, the branch length *l*
_{2} = *l*
_{4} is proportionally changed to 5, 10, 15, and 20 m, and the link branch length *l*
_{9} is proportionally changed to 10, 20, 30, and 40 m.

*Z*

_{ L }and signal source V

_{S}.

The numbers of peaks and notches of the amplitude- frequency characteristics increase with the increase in line length of the mesh topology: the number of notches in Figs. 20a, b, c and d is 2, 4, 6, and 8, respectively.

If the frequency characteristics of the elements in the net can be accurately obtained, the proposed method can be used in a notably wide frequency range. Considering the current accuracy of the frequency characteristics, the requirements of high-speed communication in the PLC in future, and the restrictions of the frequency in simulation and lab test, the proposed method can be used in the range of 1–40 MHz.

## 6 Conclusions

A novel channel modeling method based on the information node that is universally applicable to various topologies that may emerge in smart distribution grids in the future is present in this paper. The applications of this method in a simple ring network and a complex mesh network show that the proposed method has significant advantages over the traditional modeling method, such as clear physical concepts, simple calculations, and ease of implementation with conventional computational software. Based on the proposed method, several meaningful conclusions regarding the influence laws for the channel characteristics of network with ring or mesh topology can be easily drawn, such as that the trunk length has little effect on the transfer characteristic, while the proposed modeling method and the analysis results provide the necessary theoretical basis and technical measure for the design of PLC modulation method for a smart distribution grids.

## Declarations

### Authors’ contributions

JL carried out the studies about the PLC channel modeling theory, participated in the sequence alignment and drafted the manuscript. CW carried out the simulations of the proposed modeling method. WZ and Y-YL carried out the experimental tests and performed the statistical analysis of the results. WC built the theory model of the PLC channel modeling method. All authors read and approved the final manuscript.

### Authors’ information

Jian Le was born in Huanggang, Hubei, China in 1975. Correspondence author. He is currently Associate Professor with the college of electrical engineering, WHU, where he has been working on flexible ac transmission technology and power quality control technology.

Cao Wang was born in Bengbu, Anhui, China in 1995. He received his B.S. degree from the College of Energy and Electrical Engineering at Wuhan University (WHU), Wuhan, China, in 2016. He is now working towards a Master degree in electrical engineering at Wuhan University. He has been researching power quality and its control technology.

Wu Zhou was born in Xiantao, Hubei, China in 1992. He received his B.S. degree from the college of electrical engineering at Hohai University (HHU), Nanjing, China, in 2014. He is currently working towards a Master degree in electrical engineering at Wuhan University. He has been working on research of optimal operation and control in power system.

Yong-yan Liu was born in Changsha, Hunan, China in 1992. She received her B. S. degree from the college of electrical and information engineering at Hunan University (HNU), Changsha, China, in 2014. She is currently working towards a Mater degree in electrical engineering at Wuhan University. She has been working on research of distributed power operation and its control technology.

Wei Cai was born in Qian jiang, Hubei, China in 1987. He received his B.S. and Ph.D degree from the college of electrical engineering at Wuhan University (WHU), Wuhan, China, in 2008 and 2013 respectively. He has been working as engineer within State Grid Electric Power Research Institute, Wuhan, China and has worked on power system operation.

### Competing interests

There is no conflict of interest in the submission of this manuscript, and the manuscript is approved by all authors for publication.

**Open Access**This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

## Authors’ Affiliations

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