Channel characterization of low voltage electric power distribution networks for PLC applications based on measurement campaign

Electrical Power and Energy Systems 116 (2020) 105554

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Channel characterization of low voltage electric power distribution networks for PLC applications based on measurement campaign

T

Antonio A.M. Picoronea, , Thiago R. de Oliveirab, Raimundo Sampaio-Netoc, Mahdi Khosravyd,e, Moisés V. Ribeirod,f ⁎

a

Production Engineering and Mechanics Department, Federal University of Juiz de Fora, Juiz de Fora, Brazil Electronics Department, Federal Institute of Education, Science and Technology of the Southeast of Minas Gerais, Juiz de Fora, Brazil c Pontifícia Universidade Católica do Rio de Janeiro, Rio de Janeiro, Brazil d Electrical Engineering Department, Federal University of Juiz de Fora, Juiz de Fora, Brazil e Electrical Engineering Department, University of the Ryukyus, Okinawa, Japan f Smarti9 LTD., Juiz de Fora, Brazil b

ARTICLE INFO

ABSTRACT

Keywords: Power line communication Channel estimation Channel feature Statistical modeling

This paper focuses on the findings outputted by a comprehensive measurement campaign carried out for characterizing and modeling Brazilian outdoor and low-voltage electric power grids for data communication purposes. In this regard, the statistics of average channel attenuation, root-mean-square delay spread, coherence time, coherence bandwidth and achievable data-rate are analyzed by considering the frequency band from 1.7 MHz up to 100 MHz, and thereof statistical models for some channel features are recommended. The periodic variation of these outdoor and low-voltage electric power grids is quantified and presented as a temporal function of the average channel attenuation. Also, mathematical models based on only two parameters representing the power spectral density of both background and impulsive noises are proposed. The results obtained from numerical analyses offer important information about Brazilian outdoor and low-voltage electric power grids for data communication purposes. Also, they constitute an opportunity for increasing the knowledge about this kind of data communication media and for assisting the design of new generations of effective and reliable power line communication systems.

1. Introduction The needs and demands for connectivity among devices and machines have been putting a considerable research effort for introducing novel generations of telecommunications systems that are suitable for assisting Smart City [1], the Internet of Things (IoT) [2], Smart Grid [3] and Industry 4.0 [4] applications. As a matter of fact, these applications can only succeed if assisted by ubiquitous, pervasive, energy-efficient and sustainable telecommunication infrastructures which can, eventually, integrate the existing telecommunication technologies in homes, vehicles, buildings, industries, among other facilities. Currently, it is well-established that no single telecommunication technology meets all requirements necessary for interconnecting the existing devices and machines due to the remarkable number, the diversity and the complexity of devices and machines as well as the dynamics and resource limitations of data communication media.

Therefore, the implementation of a wide variety of telecommunication systems capable of maximizing the use of the available channel resources is of utmost importance [5,6]. In the realm of the applications mentioned above, power line communication (PLC) systems have emerged as a natural option extensively evaluated in the literature [7–9]. One of the great motivations behind PLC systems lies in their low-cost deployment, ubiquitous, feasibility, and potential for network convergence [10,6,11]. Furthermore, PLC systems can be easily adapted for measuring, monitoring, and controlling the supply and consumption of electricity, water, and gas, among other physical quantities. On the other hand, it is recognized that electric power systems constitute a challenging medium for data communication purposes because they were designed for energy generation, transmission and distribution at mains frequency [12–14]. As electric power grids were not designed and deployed for data communication purposes, they show advantages and limitations that have to be

Corresponding author. E-mail addresses: [email protected] (A.A.M. Picorone), [email protected] (T.R. de Oliveira), [email protected] (R. Sampaio-Neto), [email protected] (M. Khosravy), [email protected] (M.V. Ribeiro). ⁎

https://doi.org/10.1016/j.ijepes.2019.105554 Received 12 March 2019; Received in revised form 28 August 2019; Accepted 17 September 2019 0142-0615/ © 2019 Elsevier Ltd. All rights reserved.

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a priori known for allowing the maximization of the use of channel resources under the existing constraints (e.g., regulatory and technological). Several contributions have addressed measurement and characterization of electric power systems for data communication considering both narrowband (0 500 kHz) [15,16] and broadband (1.7 100 MHz) [17,18] frequency bandwidths. Note that the terms broadband and narrowband in the PLC field follow the definition stated in [19]. Regarding broadband frequencies, indoor and low-voltage (LV), in which the voltage level is lower than 1 kV, PLC channel measurement campaigns were conducted in US [20,21] besides other countries, such as France [22–24], Italy [18], Germany, Spain, Belgium, United Kingdom [24], and Brazil [11,25,26], and references therein. Regarding outdoor and medium-voltage (MV) (i.e., voltage levels are between 1 kV an 69 kV), PLC channel measurement campaigns are reported in few contributions [27–30] because the access to medium-voltage electric power network is a complex and costly task to be accomplished. Focusing only on the outdoor and low-voltage electric power grids, some few contributions related to developed countries deserve attention. For instance, an outdoor and low-voltage electric power grids measurement campaign was carried out in Germany to evaluate the average channel attenuation (ACA), channel dispersion in the timedomain and to analyze the additive noise [31]. In [32], the results of a modest measurement campaign reported an effort to characterize the Indian low-voltage and outdoor electric power grids by analyzing ACA, delay spread, and coherence bandwidth (CB). In China, the ACA of outdoor and low-voltage PLC channels were evaluated in the frequency band delimited by 2 and 20 MHz [33], respectively. In general, the behavior of outdoor low-voltage electric power distribution network (LV-EPDN) as a data communication medium is not yet well-known because representative measurement campaigns, which need to be carried around the world, are missing. As a matter of fact, worldwide measurement campaigns constitute a very important initiative for providing the necessary information for correctly characterizing such time-varying channels, which are, with more emphasis, defined as periodically stochastic systems [12]. The lack of such information is associated with the necessity and cost for the mobilization of specialized electrician teams, the use of special vehicles, the use of robust measuring instruments, and the adoption of safety training for all those involved with the field measurements. In Brazil as well as in the rest of the world, electric power utilities require safety training in works with electricity [34] and works at height [35] for all people involved 1. According to the literature, few research efforts have addressed the outdoor LV-EPDN regarding the broadband frequency band (i.e., 1.7 100 MHz). Moreover, discussions about the main features that quantify the suitability of outdoor LV-EPDN for data communication purposes are sparsely found in few contributions and cover different frequency bands. For instance, some contributions addressed only a few features that are relevant to show the appropriateness of outdoor LVEPDN for data communication purposes [32,33]. On the other hand, all of them discuss outdoor LV-EPDN in the frequency band up to 30 MHz. This choice of frequency band makes sense because the PLC regulation in Europe. Based on the fact that Brazilian regulation for broadband PLC system covers the frequency band between 1.7 and 50 MHz and the frequency band allowed by the Federal Communication Commission from the United States covers the frequency band between 1.7 and 86 MHz, it is clear the necessity for providing more investigation related to outdoor LV-EPDN by covering such frequency bands. In this regard, this paper aims to increase the awareness and knowledge of outdoor LV-EPDN as media for providing pervasive data communication infrastructure. Towards this end, the main

contributions of this paper are as follows:

• The discussion of an extensive measurement campaign conducted on • •

Brazilian outdoor LV-EPDN covering the frequency band between 1.7 and 100 MHz. The reported measurement campaign was carried out in an urban area in the city of Juiz de Fora, Minas Gerais state, Brazil. The characterization of Brazilian outdoor and low-voltage PLC channels through the ACA, average channel frequency response (ACFR), root-mean-square delay spread (RMS-DS), CB and coherence time (CT) features, which are statistically modeled, and the calculation of achievable data-rates. The analysis and modeling of the power spectral density of the additive noise found in Brazilian outdoor LV-EPDN by considering the background noise and the mix of impulsive and background noises.

Based on the numerical analyses, the following remarks deserve attention:

• Abrupt variation of ACA can occur due to switching loads using

• • • •

typical rectifiers, which are synchronized or non-synchronized with the mains frequency. Also, a linear approximation can model the mean value of ACA in the frequency domain. In terms of the attenuation related to the frequency increase, a linear approximation is also representative for modeling ACFR. The RMS-DS of Brazilian outdoor and low-voltage PLC channels is lower than its counterpart related to indoor and low-voltage PLC channels. Moreover, the RMS-DS value for the former channels is a random variable, which can be modeled by the inverse Gaussian probability distribution. The CB of Brazilian outdoor and low-voltage PLC channels is, on average, three times the value of the CB associated with the Brazilian indoor and low-voltage PLC channels. Also, it is a random variable that can be modeled by the inverse Gaussian probability distribution. Far over 80% of the Brazilian outdoor and low-voltage PLC channels, the CT values are longer than four times the CT values of the Brazilian indoor and low-voltage PLC channels. In average, the additive noises in Brazilian outdoor and low-voltage electric power grids own less power than their counterparts in indoor and low-voltage Brazilian electric power grids.

The rest of this paper is organized as follows: Section 2 discusses the measurement setup and campaign while Section 3 briefly describes the well-established features, which are used to characterize PLC channels. Sections 4 and 5, respectively, cover the numerical results and the analyses of the measured additive noises and PLC channels. Finally, Section 6 states concluding remarks. 2. Measurement setup and campaign This section briefly discusses the measurement setup designed to carry out the measurement campaign covering the channel frequency responses and additive noises. Also, it details the adopted tools and features for estimating and characterizing channel frequency response (CFR) of PLC channels, which were collected from the measured data set obtained during the measurement campaign carried out in the city of Juiz de Fora, Minas Gerais state, Brazil. 2.1. The measurement setup Fig. 1 shows the block diagram of the designed measurement setup for estimating CFR of PLC channels associated with outdoor LV-EPDN and measuring the corresponding additive noises. Essentially, it is constituted by the following three main components (equipment/device):

1 The measurement of outdoor and low-voltage electric power grids are less complex than the measurement of medium-voltage electric power grids.

2

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Table 1 Parameters adopted for performing CFR estimation based on the HS-OFDM scheme, see in [38]. Description

Value

Frequency bandwidth Sampling frequency

B = 100 MHz fs = 2B MHz N = 2, 048 2N = 4, 096 BPSK Lcp = 512

Number of sub-carriers Length of the HS-OFDM symbol Digital modulation Length of the cyclic prefix Subband frequency bandwidth

Time duration of the HS-OFDM symbol Length of the sequence {yj [n]}

Fig. 1. Block diagram of the measurement setup.

• TX

•

•

Number of samples used to compute mt Number of shifts in the vector mt calculus

Equipment: it is the equipment responsible for injecting a sounding-based signal, which occupies a predefined frequency band, into the electric power grids. It is composed of an arbitrary signal generator board mounted into a rugged personal computer, signal amplifier and PLC coupling device. A pre-designed sounding sequence, which is composed of a sequence of Hermitian symmetric orthogonal frequency division multiplexing (HS-OFDM) symbols [36], is loaded into the signal generator board and its continuoustime (analog) version is injected into the electric power grids through a PLC coupling device. RX Equipment: It is responsible for extracting the signal, which occupies a predefined frequency band, from the electric power grids. It records the received signal at the monitoring point in the electric power grids by using a capacitive PLC coupling device equipped with the data digitizer. If the TX Equipment is ON, the sounding signal is continuously transmitted, and the recorded signal by RX allows to estimate the CFR of the PLC channel; otherwise, the additive noise is obtained from the acquires signal. PLC Coupling Device: It is necessary a coupling circuit for safe connection of both signal generator and data digitizer to an electric power grid. The used capacitive PLC coupling device is composed of an analog high-pass filter for filtering the mains signal, electric protection circuit, galvanic isolation and an analog low-pass filter, which is required for agreeing with the sampling theorem [37]. Insertion loss lower than 2 dB in the frequency band between 1.7 MHz and 100 MHz was observed in the designed capacitive PLC coupling device. This device applies to both TX and RX equipment.

f

= 48.83 kHz 23.04 µ s Lj = 9, 216 Kd = 8 R = 128

Fig. 2. RX equipment installed on the pole.

It is important to emphasize that CFR estimations of PLC channels, obtained from the measured outdoor LV-EPDN, are yielded by applying the channel estimation methodology described in [38], which makes use of the sounding approach [39] and the use of the HS-OFDM scheme to perform one CFR estimation during each time interval, which corresponds to the time duration of only one HS-OFDM symbol. Note that the transmitted signal is composed of consecutive HS-OFDM symbols [40]. The set of parameters and their corresponding values, which are used by this methodology in the current measurement setup, are in Table 1. Note that the use of fs = 200 MHz results in a frequency resolution (frequency bandwidth of each subband) f = fs /(2N ) 48.83 kHz. Note that for performing baseband transmission, the length of the discrete-time version of an HS-OFDM symbol is 2N + Lcp [36], where Lcp is the length of the cyclic prefix. We adopt N = 2, 048 subcarriers, which agree with [38], because the time duration of one HS-OFDM symbol equal to Tsym = (2N + Lcp) T , T = 1/fs informs that one estimate of the CFR of the PLC channel is obtained every 23.04 µ s, approximately - for more details see [41].

Fig. 3. TX equipment installed near to the consumer’s electric power meter.

box was designed and built to accommodate the equipment used in the RX and TX sides. In the measurement campaign, the metallic box related to the RX side was installed in a pole while the box for the TX side was installed near the consumer’s energy meter. It is important to state that the measurement of PLC channels demand the use of TX and RX equipment while the measurement of the additive noise only requires the use of the RX equipment. The choice of the segments of the outdoor LV-EPDN was based on the facilities for accessing them. Also, we took into account the types of consumers’ connections, being single-phase, and the type of power

2.2. Measurement campaign Figs. 2 and 3 shows the installation of RX and TX equipment, respectively, of the measurement setup in the field. Note that the metallic 3

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lines, which are multiplexed with different colors for each phase. Regarding the type of consumers, the choice was in favor of the economic class because it offers the best opportunity for broadband and outdoor PLC system in Brazil. In other words, the chosen environment for performing the measurement campaign is representative of typical Brazilian residential consumers that may benefit from PLC systems. During the measurement campaign with the used of both TX and RX metallic boxes, a data set of consecutive channel estimates that correspond to 33 cycles of the mains signal of several and representative outdoor LV-EPDN was constituted. Due to the characteristics of Brazilian outdoor LV-EPDN, the distances between the metallic box range from 3 m up to 100 m, with mean values of 15 m, 50 m and 85 m depending on the measured outdoor and low-voltage electric power grids. In each cycle of mains signal, which corresponds to 16.67 ms (60 Hz is the mains frequency in Brazil), approximately 723 estimates of CFR of PLC channels were collected. As a result, the total number of CFR estimates is 23, 919. By using only the RX metallic box, the acquisition of the additive noises in outdoor LV-EPDN could be carried out [42]. Each measurement corresponds to 3, 500, 000 consecutive samples of the additive noise covering the frequency band between 1.7 and 100 MHz, which approximately corresponds to 17.5 ms. The choice of this number is due to the maximum storage capacity of the data acquisition board used in the RX equipment. The total amount of the collected waveforms of the additive noise is equal to 175.

square root of the second central moment of a power delay profile. For a discrete-time channel impulse response, the RMS-DS value is expressed as [11]

= Ts

Lh 1

µ0 =

n2|h [n]|2 , |h [n]|2

n=0

R (e j ) =

(4)

H (e j ) H † (e j (

+

) )d

,

(5)

) is the Fourier transform of the discrete-time rein which presentation of a linear and time-invariant PLC channel, † denotes 2 denotes the angular frequency conjugate operator and 0 resolution in the transform domain. The value of the coherence bandwidth ( Bc ) in the discrete-time domain is such that H (e j

|R (e j

Bc )|

(6)

= |R (1)|,

|0 < 1 is the correlation level informing that the where channel frequency response does not vary considerably when [0, Bc ]. Assuming a sampling frequency equal to fs = 2B Hz, in which B is the frequency bandwidth, the coherence bandwidth (Bc ) in the continuous time-domain is expressed as Bc =

Bc

2

fs ,

(7)

in which Bc refers to the frequency bandwidth associated with a given value of . 3.4. Coherence time The coherence time is the time duration in which the channel impulse response of a PLC channel is considered time-invariant. Following [44], the evaluation of the coherence time may be carried out by assuming that the PLC channel is an WSSUS process. Then, the coherence time of the channel is related to the coherence time of the complex gains of the channel, l [n], which incorporate both attenuation and phase deviations due to l = 1, 2, …, L multiple reflections of the signal in the communication medium. In its turn, the coherence index between samples of l [n], taken m samples apart, is given by [44]

(1)

where |. | denotes the modulus operator, H [k ] is the kth sample of a discrete-time channel frequency response. Note that ACA can be considered as a random variable. On the other hand, the average subchannel attenuation of a discrete-time CFR (ACFR) in dB is given by in which k = 0, …, N

and µ0 = |h [n]|2

n=0 Lh 1

The coherence bandwidth reflects how selective the channel frequency response is. It is obtained from [23]

N 1

Ac [k ] = 20log10 (E {|H [k ]|}),

n= 0 Lh 1

3.3. Coherence bandwidth

The ACA in dB is expressed as [11]

|H [k ]|2 ,

Lh 1

n|h [n]|2

and Ts = 1/fs is the sampling period. Note that 0 is the RMS-DS normalized to a unitary sampling time, µ 0 is the average delay and h [n] is the nth sample of the discrete-time channel impulse response. Note that RMS-DS is evaluated over the support of the channel impulse response in the discrete-time domain.

3.1. Average channel attenuation

k=0

(3)

n=0

Let us assume that PLC channels are modeled as band-limited in the baseband and frequency selective wide-sense stationary uncorrelated scattering (WSSUS). Also, assume that during a time interval shorter than the coherence time, the channel impulse response (CIR) is timeinvariant. Therefore, the CIR of the PLC channel during this time in|t [0, Th ) , and its corresponding continuous-time terval is h (t ) ||f | < B , in which B is the frequency Fourier transform is H (f ) bandwidth occupied by the PLC channel. Note that h [n] = h (t )|t = nTs , where n = 0, 1, 2, …, Lh 1 and Ts is the sampling period, owns the discrete-time Fourier transform given by H (e j ) . Moreover, H [k ], k = 0, 1, …, 2N 1 is the discrete Fourier transform of the zeropadded version of the discrete-time impulse response of the time-in2N , in which N denotes variant PLC channel {h [n]}nLh= 0 1 because Lh the number of subbands of an HS-OFDM symbol. Based on the aforementioned formulation and following Refs. [13,43,18,38,11], the features extracted from the outdoor PLC channels are as follows: ACA, ACFR, RMS-DS, CT, CB and achievable data-rates.These features are briefly outlined in Sections 3.1–3.5.

1 N

µ02 ,

= Ts µ0

where

3. Sets of extracted features

Ac = 10log10

0

l

(2)

[m] =

in which m given by

1 and E {·} denotes the expectation operator.

† l [n + 2 l [n]|}

E { l [n] E {|

m]}

,

(8)

. Thus, the correlation index of the PLC channel is

L

Pl

3.2. Root mean squared delay spread

h [m] =

The RMS-DS represents the distribution of the transmitted power over various paths in a multipath environment. It can be defined as the

l=1

l

[m] ; 0

L

Pl l =1

4

|

h [m]|

1, (9)

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where Pl = E {| l2 [n]|} is the average power of the lth path. Hence, the CT of the channel can be obtained through

| h [m]|

(10)

,

|0 < 1 refers to the minimum correlation index adwhere mitted to characterize the PLC channel as time-invariant during the time interval m t = Tc , in which t = Ts . By adopting the HS-OFDM scheme, which is the version of the orthogonal frequency division multiplexing (OFDM) scheme for baseband data communication [40], the CT value for given correlation index , denoted by Tc , can be estimated by using [44] (11)

Tc = Mc (2N + Lcp) Ts,

where Mc is the number of consecutive channel estimations needed to reach a correlation equal to , Ts = 1/ fs denotes the sampling period, N is the number of subcarriers and Lcp is the length of the cyclic prefix used by HS-OFDM symbols. 3.5. Achievable data-rate Let us assume that the frequency response of PLC channels associated with outdoor LV-EPDN is frequency selective, the additive noise is a colored Gaussian random process, and the choice of N ensures that the normalized signal to noise ratio [45] is flat within each subchannel. The achievable data-rate is given by [46]

R = max SX [k]

B N

N 1

log 2 1 + k=0

SX [k ]|H [k ]|2 SN [k ]

[bps],

Fig. 4. Two types of additive noise: (a) background noise (|v [n]| < Vlim ) and (b) impulsive noise (|v [n]| Vlim ).

(12)

(2B /N ) SX [k ] PX . Note that SX [k ] and SN [k ] denote subject to the power spectral densities (PSD) of the transmitted signal in the kth subcarrier and the additive noise in the kth subchannel, respectively, while PX is the total transmission power. N 1 k=0

Fig. 5. dashed line (- - -): PSD of measured noises. Continuous line (—): Models for PSD of the additive noises.

4. Additive noise: Numerical results This section offers details of additive noise signals, which were recorded from the outdoor LV-EPDN during the measurement campaign. For the sake of clearness, the spectral results are presented in the continuous-time domain. According to the measurement campaign, additive noise data sequences ({v [n]} ) composed of Nv = 3, 500, 000 samples were constituted. Part of each data set is classified as background noise if its absolute value is less than a given threshold, Vlim + , (i.e., |v [n]| < Vlim, n = 0, 1, …, Nv 1). Otherwise, the additive noise is classified as impulsive noise. Fig. 4a and Fig. 4b respectively show the two classes of noise adopted for modeling the additive noise when Vlim = 50 mV. It is important to emphasize that in Fig. 4b are the addition of background and impulsive noises when the amplitude of the measured noise is higher than Vlim . Indeed, the impulsive noise in Fig. 4b is the sum of impulsive and background noises. Fig. 5 shows PSD of measured background and impulsive noises. As can be seen, the background noise owns an almost flat PSD while the impulsive noise presents an exponential decaying behavior, which is intrinsically related to the impulsiveness of this noise. Note that this plot shows the presence of some narrowband signals, which are transmitted by primary users in accord with the telecommunication regulations. Furthermore, the PSD of background and impulsive noises can be modeled considering only two parameters, obtained by applying the least-squares approximation to PSD of the measured noises. Similar to [47], the model for the PSD is given by

SN (f ) = a + blog10|f |

in dBV 2/Hz,

Table 2 The estimated parameters for the noise models. Type of Noise

a

b

background impulsive

−137.5 −105.3

−2.1 −18.6

5. PLC channel: Numerical results This section focuses on the numerical analyses related to the estimates of outdoor and low-voltage PLC channels (impulsive and frequency responses), which were obtained during the measurement campaign. For carrying out these analyses, the following statistical distributions were taken into account: symmetric (Logistic, Normal and t-Student) and asymmetric (Exponential, Gamma, Inverse Gaussian, Log–logistic, Log-normal, Nakagami, Rayleigh, Rician and Weibull). Adherence tests were conducted by evaluating the associated log-likelihood values, which is the adopted metric to support the choice of the best statistical distribution for modeling a random variable [25]. The CB estimates from the measured outdoor and low-voltage PLC channels are analyzed concerning the correlation coefficient = 0.9. 5.1. Average channel attenuation

(13)

The attenuation of the transmitted signal in the communications medium is one of the most important parameters for the design of communication systems. The attenuation on the outdoor and low-voltage PLC channels is a function of the distance between transmitter and

where a and b are parameters given in dB. The values of a and b modeling the additive noise in Brazilian outdoor LV-EPDN in the frequency band between 1.7 and 100 MHz are in Table 2. 5

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Fig. 8. ACFR: Maximum, mean, minimum and linear approximation of the mean values.

Fig. 6. ACA versus distance: ( ) measured values and (- - -) linear approximation.

receiver equipment (ACA) and the used frequency band (ACFR). + in meters) is reThe values of ACA in terms of distance (d presented by and a robust and linear regression, which is based on the mean square error criterion, is represented by the dashed line in Fig. 6. The linear approximation is expressed as

Adist (d) =

0.4d + 16.71 [dB],

(14)

where Adist (d ) is the linear model of ACA as a function of the distance between transmitter and receiver. As expected, the channel attenuation increases as the distance increases. Also, the ratio of increase is 0.4 dB/ m for all PLC channels collected from Brazilian outdoor LV-EPDN. Fig. 7 shows the variation of the ACA value during three cycles of mains signal. The plot of the mains signal (60 Hz in Brazil) together with ACA highlights the periodically time-varying behavior of outdoor and low-voltage PLC channels. Based on the measured data set, the average time duration of the abrupt variations of ACA ranges from 0.73 ms up to 1.40 ms and its average vale is around 0.98 ms. This type of abrupt and periodically time-varying changes in the ACA value has been reported in previous contributions related to in-home and lowvoltage PLC channels [12,11]. Considering the ACFR feature, Fig. 8 shows the maximum, mean, and minimum values of it in the continuous frequency domain. As can be seen, the mean values of the magnitude response of outdoor and lowvoltage PLC channels exhibit a decay rate of, approximately, 0.4 dB/ MHz. Moreover, Fig. 8 shows a linear approximation of the mean value of ACFR when a robust linear regression fit, which is based on the mean squared error, applies. The resulting linear approximation of the mean value of the magnitude response as a function of the frequency is given by

Afreq (f ) = 0.391f + 36.3 [dB],

Fig. 9. Empirical CDF of RMS-DS and its modeling with the inverse Gaussian distribution.

the estimated RMS-DS values. According to this plot, the RMS-DS values range from 0.13 µ s to 0.30 µ s. Among the chosen statistical distributions, the inverse Gaussian probability distribution [48] with µ = 0.186993 and = 8.71957 yields the best statistical model for this random variable. Statistics of the RMS-DS feature are listed in Table 3. As can be observed, RMS-DS values are shorter than 0.22 µ s in 90% of the measured outdoor and low-voltage PLC channels. Also, the values of RMSDS are close to that ones found in indoor and low-voltage PLC channels (0.20 µ s) [11] if the frequency band (1.7 100 MHz) applies. The estimated mean RMS-DS value is also close to the values obtained in indoor and low-voltage PLC channels, which were previously reported in [49–51]. Also, the RMS-DS values does not exceed 0.30 µ s, which somehow confirms the statement in [52, p.20], that the RMS-DS values of outdoor LV-EPDN are longer than their counterpart in indoor LVEPDNs. As a matter of fact, the RMS-DS values for indoor and lowvoltage electric power networks are between 0.1 µ s and 1.7 µ s in the United States, as reported in [49].

(15)

in which f is in MHz. The knowledge of ACA and ACFR values supports PLC systems designers to come up with resource allocation techniques that are capable of yielding appropriate users’ allocation and resource sharing based on distance and normalized signal-to-noise ratio (SNR).

5.3. Root mean squared delay spread versus average channel attenuation The relation between ACA and RMS-DS for outdoor and low-voltage PLC channels is shown in Fig. 10. This relation is modeled by using a robust linear regression fit based on the mean squared error, which results in the following expression:

5.2. Temporal dispersion

(16)

= 0.00001A c + 0.19 [µs],

Fig. 9 shows the empirical cumulative distribution function (CDF) of

where is the RMS-DS in microseconds and Ac in decibel. This model shows that RMS-DS is directly proportional to the average channel attenuation of outdoor and low-voltage PLC channels or inversely proportional to the average channel gain, which corroborates with the results presented in [53,18,11] for indoor and low-voltage PLC channels. Table 3 Statistics of RMS-DS in µ s.

RMS-DS

Fig. 7. Periodically time-varying behavior of ACA. 6

Min

Max

Mean

Std

90% above

90% below

0.13

0.30

0.19

0.30

0.16

0.22

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Fig. 10. RMS-DS versus ACA: (o) estimated values and (- - -) linear approximation. Fig. 14. Empirical CDF of CT for the chosen values of . Table 5 The coherence time statistics of outdoor and low-voltage PLC channel in microseconds (ms).

0.99 0.98 0.95 0.90

Fig. 11. Empirical CDF of CB and its modeling with the inverse Gaussian distribution. Table 4 Coherence bandwidth statistics em kHz for

CB

Min

Max

Mean

Std

90% above

90% below

1.38 2.07 3.69 5.76

10.14 >16.36 >16.36 >16.36

4.50 6.55 9.84 12.28

2.70 3.83 4.56 4.21

1.59 2.49 4.10 6.18

9.49 11.70 15.27 16.36

= 0.9 .

Min

Max

Mean

Std

90% above

90% below

247.20

629.21

430.57

75.00

351.24

542.74

Fig. 15. Achievable data-rate of the outdoor and low-voltage PLC channels in the presence of impulsive (I) and background (B) noises. Fig. 12. RMS-DS versus CB for

this random variable. Some statistics of CB are in Table 4. According to this table, for 90% of the data set, the CB values are higher than 351.24 kHz. Moreover, the CB values are about 1.5 lower than their counterparts in Brazilian indoor and low-voltage electric power networks [11] for the frequency band delimited by 1.7 and 100 MHz. Also, the maximum value of CB in Brazilian outdoor LV-EPDN is, approximately, five times lower than those observed in Brazilian indoor and low-voltage electric power networks [11] for the frequency band delimited by 1.7 and 100 MHz.

= 0.9 : (o) measured data and (- - -) model.

5.5. RMS-DS versus coherence bandwidth The relation between RMS-DS and CB features is shown in Fig. 12. Also adopted in [23,18] for indoor and low-voltage PLC channels, the derived model for representing this relation was obtained through a robust approximation, which can be expressed as

Fig. 13. Evolution and average evolution of the correlation index.

5.4. Coherence bandwidth The empirical CDF of the coherence bandwidth is shown in Fig. 11 when = 0.9 is adopted2. In this case, CB varies from 247.2 kHz up to 629.2 kHz and follows, with good approximation, an inverse Gaussian probability distribution ( µ = 430.57, = 14, 323.9 ) is suitable to model

2

The choice of

Bc0.9 =

0.0785

,

(17)

where Bc0.9 refers to the CB value in Hz when = 0.9 is adopted and is the RMS-DS in µ s. The relation Bc0.9 = 0.0785 for Brazilian outdoor LVEPDN is approximately 1.5 greater than the same ratio found in indoor electric power networks in other countries [23,18]. Regarding outdoor and indoor Brazilian low-voltage electric power networks, the values

= 0.9 agrees with [11]. 7

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Table 6 The statistics of Brazilian outdoor and low-voltage PLC channels. Note that CB and CT are obtained when Parameters

Min

Max

T W120 [ms]

0.73

0.98

0.13 247.2 2.07

0.30 629.2 >16.3

ACA [dB/m] ACFR [dB/MHz] RMS-DS [µ s] CB [kHz] CT[ms]

= 0.9 and

= 0.98 , respectively.

Mean

Std

90% above

90% below

1.40

0.12

0.73

1.15

0.03 75.01 3.83

0.16 351.24 2.49

0.22 542.74 11.70

0.40 0.40 0.19 430.6 6.55

Bc0.9 = 0.078 for indoor [11] and Bc0.9 = 0.0785 for outdoor mean that this relation is almost the same for both of them.

Distribution

Inv. Gaussian Inv. Gaussian

discussed. Also, the tools and features for characterizing the outdoor and low-voltage PLC channels have been described. Based on a measured data set, parameters-based mathematical models of the PSD of background and impulsive noises for Brazilian outdoor LV-EPDN have been introduced. Also, statistical analyses for ACA, ACFR, RMS-DS, CB, and CT have been presented. Achievable data-rates of outdoor and lowvoltage PLC channels in the presence of both impulsive and background noises have been provided and discussed. The numerical results associated with the Brazilian outdoor and low-voltage PLC channels yielded the following findings: i) the RMS-DS value is lower than its counterpart related to indoor and low-voltage PLC channels; ii) the CB value is, on average, three times the value of the CB value associated with the Brazilian indoor and low-voltage PLC channels; iii) far over 80%, the CT values are longer than four times the CT values of the Brazilian indoor and low-voltage PLC channels; iv) in average, the additive noises owns less power than their counterparts indoor and low-voltage PLC channels; and v) achievable data-rates is over hundreds of Mbps when practical values of total transmission power are considered, even in the presence of impulsive noise. Overall, this paper provided a characterization of typical features of outdoor and low-voltage PLC channels, which are necessary for designing PLC systems suitable for Brazilian electric power grids. Finally, but not least, the discussed findings constitute a relevant set of information for providing a better understanding of the diversity of worldwide outdoor and low-voltage electric power grids for data communication purposes.

5.6. Coherence time Fig. 13 show the evolution of the correlation index related to consecutive estimates of measured outdoor and low-voltage PLC channels and its average in the continuous-time domain. Note that h (t ) is the continuous time version of h [m]. The occurrence of some valleys in the correlation index is due to abrupt changes of the CIR of outdoor and low-voltage PLC channels during the zero crossing of the mains voltage. It means that AC-DC converters based on thyristors are the main type of converters observed in the outdoor LV-EPDN. In addition, Fig. 14 shows the CDF of the coherence time. According to this plot, it is observed that CT is not less than 12 ms in 50% of data set for = 0.90 . On the other hand, the CT values shorter than 10 ms [11] are observed in indoor and low-voltage Brazilian PLC channels. In other words, the coherence time of outdoor and low-voltage Brazilian PLC channels is longer than the ones associated with the Brazilian counterpart in indoor facilities. Some of CT statistics are in Table 5 {0.90, 0.95, 0.98, 0.99} . As can be noted, CT values related to when outdoor LV-EPDN are not lower than 1.38 ms and 5.76 ms for = 0.99 and = 0.90 , respectively. 5.7. Achievable data-rate This section analyzes achievable data-rates of the Brazilian outdoor and low-voltage PLC channels. In this regard, the estimates of CFR and the measured additive noise obtained from the measurement campaign were taken into account. Fig. 15 shows the maximum, mean and minimum data-rate of the measured Brazilian outdoor and low-voltage PLC channels in the presence of background and impulsive noises when considering the frequency band of 1.7 100 MHz. These curves were obtained by Eq. (12) considering the PSD of the transmitted signal constant with values ranging from 100 up to 50 dBV2/Hz and estimates of additive noise PSD are based on the model described by Eq. (13) and Table 2. . Although the data sets were obtained during 14 days of measurement in two distinct neighborhoods of the city of Juiz de Fora, by collecting them from 8:00 a.m. to 5:00 p.m., any relevant variations of the analyzed parameters were identified, depending on the time of data collection. It makes sense because low-income consumers are connected to the measured outdoor LV-EPDN. For this reason, the seasonality variable is not appropriate for these analyses. Finally, the relevant information obtained from the analyzed features which support the characterization of Brazilian outdoor and lowvoltage PLC channels are summarized in Table 6.

Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgment This work was in part supported by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) Finance Code 001, FINEP, FAPEMIG, CNPq, P&D ANEEL, CEMIG, INERGE and Smarti9. References [1] Andrisano O, Bartolini I, Bellavista P, Boeri A, Bononi L, Borghetti A, et al. The need of multidisciplinary approaches and engineering tools for the development and implementation of the smart city paradigm. Proc IEEE 2018;106(4):738–60. https://doi.org/10.1109/JPROC.2018.2812836. [2] Minoli D, Sohraby K, Occhiogrosso B. IoT considerations, requirements, and architectures for smart buildings-energy optimization and next-generation building management systems. IEEE Internet Things J 2017;4(1):269–83. https://doi.org/10. 1109/JIOT.2017.2647881. [3] Masera M, Bompard EF, Profumo F, Hadjsaid N. Smart (electricity) grids for smart cities: assessing roles and societal impacts. Proc IEEE 2018;106(4):613–25. https:// doi.org/10.1109/JPROC.2018.2812212. [4] Wollschlaeger M, Sauter T, Jasperneite J. The future of industrial communication: automation networks in the era of the internet of things and industry 4.0. IEEE Ind Electron Mag 2017;11(1):17–27. https://doi.org/10.1109/10.1109/MIE.2017. 2649104. [5] Mehmood Y, Ahmad F, Yaqoob I, Adnane A, Imran M, Guizani S. Internet-of-things-

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