ELEKTROTEHNI ˇ SKI VESTNIK 78(4): 171–176, 2011
ENGLISH EDITION
Simple digital ﬁlter implementation of the HV PLC
channel model
Asmir Gogi´ c
1;y
, Nermin Suljanovi´ c
1
, Aljo Mujˇ ci´ c
1
, Mitja Kolenc
2
, Jurij F. Tasiˇ c
2
and
Matej Zajc
2
1
Faculty of Electrical Engineering, University of Tuzla, Franjevaˇ cka 2, 75000 Tuzla, Bosnia and Herzegovina
2
Digital Signal, Image and Video Processing Laboratory, Faculty of Electrical Engineering, University of
Ljubljana, Trˇ zaˇ ska 25, 1000 Ljubljana, Slovenia
y
E-mail: asmir.gogic@untz.ba
Abstract. The paper presents a simple implementation model of the high-voltage power line communication
(HV PLC) channel using digital ﬁlters. The model utilizes three identical ﬁnite impulse response (FIR) ﬁlters.
The amplitude characteristic of the FIR ﬁlters matches the HV PLC channel amplitude characteristic for a
given coupling, without taking into consideration reﬂection. The reﬂection phenomenon occurring at the HV
power line terminals is implemented in the model by using a parallel feedback branch and additional ﬁlter
delay corresponding to the traveling time of the reﬂected wave. The approach presented in this paper is applied
to a 400 kV power line with three phase conductors in horizontal disposition. Results are given for two optimal
couplings, middle phase to ground and outer phase to middle phase coupling.
Keywords: Power grid, power-line channel, channel modelling, power-line communications
1 INTRODUCTION
The recent research in the Smart Grid domain has rein-
troduced the interest for HV PLC [1]. The latest trends
in power system operation and control incorporate com-
prehensive measurements over large geographic areas.
This fact increases the amount of data to be transmitted
and requires a communication system with an adequate
bandwidth and reliability. Even though optical links in-
corporated in HV power lines will completely fulﬁll this
task, these links are not always available. Utilization of
power lines for the communication services is generally
motivated by long distances in different countries around
the globe where power lines usually present the only
infrastructure. Furthermore, a redundant communication
path is always required.
Analog PLC (aPLC) systems over HV power lines
are usually used in transmission of voice, protection
signals and low bit rate data for the power utility
purposes. For the current SCADA (Supervisory Control
and Data Acquisition) systems and communications with
RTUs (Remote Terminal Units), aPLC system presents
a satisfactory solution. Also, aPLC is commonly used
in protection systems of HV power lines. Compared
to the aPLC system, digital HV PLC systems (dPLC)
can achieve higher bit rates by utilizing digital com-
munication techniques. Another advantage of dPLC is
compatibility with other digital equipment. Nowadays,
Received August 12, 2011
Accepted October 15, 2011
dPLC covers transmission of voice and data. On the
other hand, aPLC is still used for protection due to its
reliability, robustness and low costs.
HV PLC communications utilize the frequency range
from 30 to 500 kHz, which is divided into bands [2].
The aPLC channel bandwidth is 4 kHz. On the other
hand, the dPLC channel bandwidth should be a multiple
of 4kHz bands to be compatible with the analog PLC
systems. Frequency planning demands an extra care to
avoid interference with other channels and with local
radio and navigation stations.
The digital PLC system design is grounded more on
the communication characteristics of HV power lines
than analog, making new requirements for accurate de-
termination of HV power-line frequency characteristics
[3]. Selection of appropriate communication techniques
such as modulation, channel coding, and equalization
are directly related to these characteristics.
A discrete-frequency communication model of HV
power line appropriate for dPLC analysis is available [3],
[4]. This paper describes digital ﬁlter implementation
of the proposed model in the manner to be used in
numerical simulations of communication systems. Such
model is appropriate for the implementation using FPGA
technology. Time and costs required for HV PLC device
ﬁeld testing can be reduced by usage of FPGA based
channel model for laboratory tests.
There are two dominant constraints for HV power
lines to be used for communication purposes: the corona
noise and reﬂection. The corona on HV power line refers
172 GOGI
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a phenomenon of ionization of air surrounding charged
conductor (power-line phase conductor). In general, the
HV power line as a communication channel is char-
acterized by a relatively high noise level compared to
the other communication media since noise is time-
variant and weather dependent. Moreover, a power line
itself is a noise source. The noise level caused by the
corona strongly varies in the power-frequency period
and is dominant during rainy and snowy weather. The
second important property of the power-line channel is
reﬂection since the HV power line is not terminated with
a characteristic impedance. The presence of reﬂection
introduces echoes in the impulse response and oscil-
lations in the frequency characteristics (amplitude and
phase characteristics, group delay, input impedance) of
the PLC channel, and consequently introduces a smaller
signal-to-noise ratio (SNR) and higher bit error rates
(BER) in a digital communication system.
Digital ﬁlter implementation of the proposed HV PLC
channel model provides a frequency response (amplitude
and phase characteristic) that incorporates the reﬂection
phenomenon. Noise generation is not included in this
implementation. Noise implementation in the HV PLC
channel is described in [5].
2 DISCRETE FREQUENCY MODEL BASED
ON REFLECTION COEFFICIENTS
The wave propagation phenomenon along the power
line is described by the telegrapher’s equations. Time-
harmonic voltage and current propagation on a trans-
mission line is considered and time t is ommited as
argument in telegrapher’s equations. Since the HV power
line is considered as a multiconductor line, voltage V
and current I at an arbitrary point on the power line
are found from the telegrapher’s equations in the matrix
form:
d
2
V(x)
dx
2
  ZYV(x) =   dE(x)
dx
+ ZJ(x) (1)
d
2
I(x)
dx
2
  YZI(x) =   dJ(x)
dx
+ YE(x) (2)
Elements of matrices Z and Y form a set of primary
parameters of the power line parallel to the earth plane.
Those parameters are determined by geometrical de-
sign of the power line and electrical parameters of the
conductors and earth [4]. Inﬂuence of the earth with
ﬁnite conductivity is considered in the manner deﬁned
by Carson [6]. In the above equations, vectors E(x)
and J(x) represent the voltage and current sources
distributed along the line. In general, vectors E(x) and
J(x) model the noise sources on the HV power line.
V oltage source E(x) represents interference with other
PLC devices and radio stations. Current sources J(x)
on the HV power line are usually used to represent
the noise appearing due to corona [5]. In a passive
network, vectors E(x) and J(x) are equal zero. Eqs. (1)
and (2) are written in the original (phase) coordinates.
Therefore, vectors V and I correspond to the phase
values in the three phase system. The solution of these
equations is found through modal transformation [4], [7]
V = SV
s
; I = QI
s
(3)
which introduces modal coordinates where the voltage
and current are described by vectors V
s
and I
s
.
Complex matrix S is chosen to be a matrix of eigen-
vectors of product   2
= ZY while matrix Q equals
to (S
T
)
  1
.   denotes the propagation function matrix
in phase coordinates. Transformation deﬁned by (3) de-
couples equations (1) and (2) into a set of ordinary non-
homogeneous differential equations that can be written
in a matrix form
d
2
V
s
(x)
dx
2
=   2
V
s
(x) + Z
s
J
s
(x)  dE
s
(x)
dx
(4)
d
2
I
s
(x)
dx
2
=   2
I
s
(x) + Y
s
E
s
(x)  dJ
s
(x)
dx
(5)
Solution of the ordinary differential equation set corre-
sponds to the wave (natural) modes that are independent
from each other and posses their own propagation func-
tions and characteristic impedances.
The eigenvalues of matrix ZY deﬁne the square of
modal propagation functions   2
. Propagation function
  is a diagonal matrix N  N whose elements are
modal propagation functions. The power line with three
phase conductors in horizontal disposition has three
modes as presented in Fig. 1. The highest attenuation
characterizes the ground mode where energy propagates
through three phase conductors (Fig. 1) and returns
via the ground. The ground mode has much higher
attenuation than other two modes and ground mode
component disappears approximately after 20  30 km
[4]. Modes 1 and 2 have signiﬁcantly lower attenuation
Figure 1. Three modes of the HV power line with three phase
conductors in horizontal disposition
since their energy propagates and returns through phase
conductors. High-frequency power-line characteristics
(amplitude and phase characteristics) can be computed
using the method of reﬂection coefﬁcients in modal
coordinates [4]. The method is brieﬂy described in this
section, while derivation of the amplitude and phase
characteristic expressions for a given coupling is pre-
sented in [8] with details. A problem that arises in
derivations of such expressions is related to the multi-
conductor system, e.g. the voltages at all output ports
are related to the all the voltages at all input ports.
SIMPLE DIGITAL FILTER IMPLEMENTATION OF THE HV PLC CHANNEL MODEL 173
Denoting V
1
and I
1
as the voltage and current at
the sending terminal, and V
2
and I
2
at the receiving
terminal, the amplitude and phase characteristics can be
computed from the equations
  = 10 log
        V
2
I
2
V
1
I
1
        [dB] (6)
  =Im
  ln
V
2
I
2
V
1
I
1
  (7)
For the homogeneous power line, voltages at transmit-
ting V
1
and receiving end V
2
are related with voltage
transfer matrix T
V
2
= TV
1
(8)
and in modal coordinates
V
2s
= T
s
V
1s
(9)
Matrix T
s
is the voltage transfer matrix in modal
coordinates and is equal to [4]
T
s
= (I + K
2s
)e
   l
(I + K
1s
)
  1
(10)
where K
1s
and K
2s
represent the modal reﬂection coef-
ﬁcients at the sending and receiving ends, respectively,
while e
   l
is a diagonal matrix. In the case of a power
line with three conductors, it is a 3x3 matrix
e
   l
=
0
@
e
    0l
0 0
0 e
    1l
0
0 0 e
    2l
1
A
(11)
The order of matrices K
1s
and K
2s
is determined by the
number of modes, that is the number of conductors. The
modal reﬂection coefﬁcient at the receiving end is found
from reﬂection coefﬁcient K
2
in phase coordinates as
K
2s
=    1
K
2
  (12)
while matrix K
2
is computed via line characteristic
impedance Z
c
and load admittance Y
L
= (Z
L
)
  1
.
K
2
= (I + Y
L
Z
c
)
  1
(I + Y
L
Z
c
)
= (Z
c
+ Z
L
)
  1
(Z
c
  Z
L
) (13)
Matrix   is normalized matrix S in respect to the ﬁrst
row. The modal reﬂection coefﬁcient at the sending line
end is computed from
K
1s
=e
   l
K
2s
e
   l
(14)
Vector of the phase currents at the transmitting end is
I
1
= Y
in
V
1
(15)
where Y
in
is the input admittance matrix
Y
in
= Y
c
(I  K
1
) (I + K
1
)
  1
(16)
Using load admittance matrix Y
L
, the current at the
receiving terminal is computed as
I
2
= Y
L
V
2
(17)
This concept allows computation of the frequency re-
sponse of the HV PLC channel for different couplings
using equations (6) and (7). Furthermore, the middle
phase to ground coupling and the outer phase to middle
phase coupling are denoted as optimal couplings for
the HV power line with phase conductors in horizontal
disposition [4]. The presented method is applied to
the 400 kV power line with three phase conductors in
horizontal disposition. The computed amplitude charac-
teristic and group delay in the 24 kHz band are given
in Figures 2 and 3, respectively. Signal reﬂection at
200 203 206 209 212 215 218 221 224
  5:1
  5
  4:9
  4:8
  4:7
  4:6
f(kHz)
  (dB)
Figure 2. Amplitude charactersitic for the 400 kV power line
and middle phase to ground coupling
200 203 206 209 212 215 218 221 224
0:14
0:15
0:16
0:17
0:18
0:19
0:2
f(kHz)
  (ms)
Figure 3. Group delay for the 400 kV power line and middle
phase to ground coupling
the HV power line terminals is due to the mismatch
between the power-line characteristic impedance and
the termination impedance. As a consequence of the
reﬂection phenomenon, oscillations in the amplitude
characteristic and the group delay appear. The period
between two neighboring maximum and minimum of
these oscillations is found as
  f
max  min
=
v
4l
(18)
Since wave velocity v is approximately 300 000 km/s,
for a line l = 50 km long the period of oscillations
equals to 1.5 kHz.
The reﬂected waves on the power line manifest them-
selves as echoes in the time domain. The echo delay
is determined by the line length and velocity of signal
propagation. Obviously, the echo delay is correlated with
the period of oscillations in the frequency domain. Inten-
sity of echoes is determined by the reﬂection coefﬁcient
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and line attenuation, and is proportional to the amplitude
of oscillations in the frequency domain.
The second phase mode strongly impacts the reﬂec-
tion intensity since this modal channel is characterized
by the lowest attenuation. Additionally, the mismatch
between impedances at the line terminals causes energy
transfer between different modal channels. The value of
the exchanged energy between modes can be seen in the
modal reﬂection coefﬁcient matrix given by (12).
3 FIR FILTER IMPLEMENTATION
This section describes a procedure for a simple FIR ﬁlter
implementation of the HV PLC channel. The frequency
response of the model corresponds to the frequency
characteristics of the PLC channel with incorporated
reﬂection. Oscillations in the amplitude characteristic
and group delay are present in the proposed model.
However, they will deviate from those found in the
detailed model. A simple implementation model is given
in Figure 4. Three FIR ﬁlters are identical and de-
FIR
k
2
FIR k
1
FIR
z
  d
+ k
2 +
V
1
V
2
Figure 4. Simple FIR ﬁlter implementation model
signed using a simulated discrete frequency response of
the HV PLC channel with no reﬂection. The reﬂected
wave propagation (echo) is inserted through the parallel
branch, coefﬁcients k
1
and k
2
and the delay for d
samples. Even though these coefﬁcients are introduced
into the model as reﬂection coefﬁcients, their values are
determined in the manner that the frequency response of
the simple model matches the simulated characteristics
as close as possible. As a consequence of such approach,
values ofk
1
andk
2
are not limited to the range [  1; 1].
Therefore, we made a signiﬁcant simpliﬁcation by taking
scalar constants to act as reﬂection coefﬁcients instead of
the frequency-dependent matrices (explained in Section
2). The number of samples d is computed from the
sampling frequency and the signal propagation delay.
The simulated discrete frequency response of the HV
PLC channel using the method of reﬂection coefﬁcients
is the input data for the implementation based on FIR
ﬁlters. Alternatively, parameters of the simple FIR model
can be determined using the measured HV PLC channel
characteristics [9]. The amplitude characteristic of the
FIR ﬁlter corresponds to the HV PLC channel character-
istic without incorporated reﬂection. Since the FIR ﬁlter
is characterized by a linear phase, it doesn’t describe
the PLC channel phase. This is the ﬁrst assumption that
introduces deviation of the implemented model from
the detailed model computed in accordance with the
methodology given in Section 2.
The frequency response of the system given in Figure
4 is
H(j!) = (1 +k
2
)F (j!) +k
1
k
2
(1 +k
2
)F
3
(j!)e
j!d
(19)
where F (j!) is the frequency response of the three
identical FIR ﬁlters. The amplitude characteristic in dB
can be computed using the previous equation as
  dB
(j!) = 20 logj(1 +k
2
)F (j!) + (20)
+k
1
k
2
(1 +k
2
)F
3
(j!)e
j!d
j
= 20 logjF (j!)j + 20 logj1 +k
2
j +
20 log
    1 +k
1
k
2
F
2
(j!)e
j!d
    In order to discuss the meaning of the three terms in
the above expression, we will consider the simulated
amplitude characteristic given in Figure 5. This char-
acteristic corresponds to 400 kV power line, 50 km
long, and the middle phase to ground coupling. The
red dashed line in Figure 5 represents the PLC channel
amplitude characteristic without reﬂection. The ﬁrst term
in (20) determines this characteristic. The FIR ﬁlter
in the implementation model (Figure 4) is designed to
match this amplitude characteristic. Since the frequency
range utilized for the HV PLC communications is 500
kHz, the sampling frequency of the designed FIR ﬁlter
is chosen to be 1 MHz. The observed shift in Figure 5
50 100 150 200 250 300 350 400 450 500
  8
  7:5
  7
  6:5
  6
  5:5
  5
  4:5
  4
  3:5
f(kHz)
  (dB)
with reﬂections
without reﬂections
Figure 5. Simulated HV PLC channel amplitude characteristic
for the middle phase to ground coupling
between the characteristics with and without reﬂection
corresponds to the second term in (20). Coefﬁcient k
2
is computed to align these two characteristics
20 logj1 +k
2
j = 1:5)k
2
= 10
1:5=20
  1 = 0:1885
(21)
The last term in (20), that contains coefﬁcients k
1
and
k
2
, represents oscillations in the amplitude characteristic
due to reﬂection. Coefﬁcient k
1
is calculated so that
oscillations in the phase characteristic are adequate. The
SIMPLE DIGITAL FILTER IMPLEMENTATION OF THE HV PLC CHANNEL MODEL 175
phase of the model given in Figure 4 is
argfH(j!)g =  (!)+
+ arctan
  k1k2jF(j!)j
2
sin(  (!)+!d)
1+k1k2jF(j!)j
2
cos(  (!)+!d)
  (22)
where   (!) = argfF (j!)g. To simplify determination
of coefﬁcientk
2
,a =k
1
k
2
jF (j!)j
2
andx =  (!)+!d
in the previous expression will be substituted:
argfH(j!)g =  (!) + arctan
  a sin(x)
1 +a cos(x)
  =
=  (!) +     (!) (23)
Term     (!) is periodic function of!. Since intensity
of oscillations in the simulated phase characteristic is
known, we can determine the value of parameter a
that corresponds to the amplitude of these oscillations
(Figure 6).
0 2 4 6 8 10 12 14 16
  0:6
  0:4
  0:2
0
0:2
0:4
0:6
  x(rad)
    (rad)
a=0.2
a=0.5
Figure 6. Oscillations     (!)
The amplitude of oscillations   = max f    (!)g  minf    (!)g varies with parameter a. The relation
between   anda, according to (23), is provided in Table
I for some characteristic values of a.
Table 1. Correlation between parameter a and the oscillation
amplitude in the phase characteristic
a 0:1 0:2 0.3 0.4 0.5 0.6
  0.200 0.403 0.609 0.823 1.047 1.287
The amplitude oscillation in the phase characteristic
that corresponds to the amplitude characteristic given
in Figure 5 approximately equals 0.2 rad. According to
Table I, we choose a = 0:1. Since coefﬁcients k
1
and
k
2
are constants in order to keep the model simple and
jF (j!)j changes in the 1.5 dB range (Figure 5), we
choosejF (j!)j = 5dB, that isjF (j!)j
2
= (0:5623)
2
=
0:3162. Therefore, coefﬁcient k
1
can be calculated as
k
1
k
2
jF (j!)j
2
= 0:1 ) k
1
k
2
= 0:3162 ) k
1
= 1:81
(24)
The amplitude characteristic of the simple system for
computed coefﬁcients k
1
and k
2
and the FIR ﬁlter
with amplitude characteristic given by the red line in
Figure 5 is presented in Figure 7. Since oscillations are
more emphasized in the group delay than in the phase
characteristic, the group delay of this system is given
in Figure 8. Comparing the amplitude characteristics
presented in Figures 5 and 7, we observe very intensive
oscillations in the amplitude characteristic of the simple
model. This is due to that coefﬁcients k
1
and k
2
are
computed to match the amplitude of oscillations in
the simulated phase characteristic. Determination of the
coefﬁcients in the manner to achieve oscillations in the
simulated amplitude characteristic would lead to a much
lower oscillation amplitude in the phase characteristic of
the simple model.
50 100 150 200 250 300 350 400 450 500
  8
  7:5
  7
  6:5
  6
  5:5
  5
  4:5
  4
  3:5
  3
f(kHz)
  (dB)
Figure 7. Amplitude characteristic of the implemented model
for the middle phase to ground coupling
50 100 150 200 250 300 350 400 450 500
0:13
0:14
0:15
0:16
0:17
0:18
0:19
0:2
f(kHz)
  (ms)
Figure 8. Group delay of the implemented model for the
middle phase to ground coupling
The approach presented in the paper led to an im-
plementation model whose characteristics don’t signif-
icantly deviate from the computed model based on the
reﬂection coefﬁcients. On the other hand, such simple
model ensures adequate phase nonlinearities with more
intensive nonlinearities in the amplitude characteristic.
This is acceptable when the model is used for the HV
PLC modem testing. The presented methodology is also
applied to the outer phase to middle phase coupling and
400 kV power line.
The simulated amplitude characteristic is given in
Figure 9. Figures 10 and 11 show the amplitude char-
acteristic and group delay of the model. The advantage
of the proposed model is simplicity and straight for-
ward implementation with the FPGA technology. The
frequency characteristics of the simple model differ from
the simulated characteristics in the more emphasized
oscillations in the amplitude characteristics. However,
176 GOGI
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the simple model incorporates the reﬂection phenomena
on the HV power lines which is a crucial factor, to-
gether with the corona noise, for the HV PLC modem
performance.
50 100 150 200 250 300 350 400 450 500
  5:5
  5
  4:5
  4
  3:5
  3
  2:5
  2
  1:5
  1
f(kHz)
  (dB)
with reﬂections
without reﬂections
Figure 9. Simulated HV PLC channel characteristic for the
outer phase to middle phase coupling
50 100 150 200 250 300 350 400 450 500
  5:5
  5
  4:5
  4
  3:5
  3
  2:5
  2
  1:5
  1
f(kHz)
  (dB)
Figure 10. Amplitude characteristic of the implemented model
for the outer phase to middle phase coupling
50 100 150 200 250 300 350 400 450 500
0:12
0:13
0:14
0:15
0:16
0:17
0:18
0:19
f(kHz)
  (ms)
Figure 11. Group delay of the implemented model for the outer
phase to middle phase coupling
4 CONCLUSION
The paper proposes a simple implementation model of
the HV PLC channel based on FIR ﬁlters. Parameters of
the proposed model are determined using the simulated
discrete frequency characteristics of the HV PLC chan-
nel. These parameters can also be computed using the
measured frequency characteristics. The simple model
incorporates reﬂection for being, the crucial factor for
the HV PLC modem performance. Corona noise gener-
ation is not treated in the paper.
An advantage of the given model is simplicity and
straight forward implementation using the FPGA tech-
nology. Relative drawbacks are more emphasized os-
cillations in the amplitude characteristic of the simple
model than in the simulated amplitude characteristic.
5 ACKNOWLEDGEMENT
The work is supported by the Ministry of Higher Ed-
ucation, Science and Technology, Slovenia, under the
Scientiﬁc Program P2-0246.
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in Low Radio-Frequency Range”, IEEE Transactions on Power
Delivery, V olume:22, Issue:4, pp.2142 - 2149, 2007.
Asmir Gogi´ c is a Teaching Assistant with the University of Tuzla,
Bosnia and Herzegovina. His research interests are in modeling and
simulation of communication networks, channels and protocols.
Nermin Suljanovi´ c is an Associate Professor with the University of
Tuzla, Bosnia and Herzegovina. His research interest is the digital
communications, communication channel modeling and computer net-
works.
Aljo Mujˇ ci´ c is an Associate Professor with the University of Tuzla,
Bosnia and Herzegovina. His research interests are in the areas
of power-line communications, optical communications, information
theory and coding techniques.
Mitja Kolenc is a Researcher at the Faculty of Electrical Engineering,
University of Ljubljana. His research ﬁelds are RT digital signal
processing and intelligent power networks.
Jurij F. Tasiˇ c is a Full Professor at the Faculty of Electrical Engi-
neering, University of Ljubljana, and head of the Laboratory for digital
signal, image and video processing. His research ﬁelds are in domains
of digital signal processing and adaptive systems.
Matej Zajc is an Assistant Professor at the Faculty of Electrical
Engineering, University of Ljubljana. He is active in the domain of
digital communication systems and digital signal processing.