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130 From smart grid to internet of energy

any prior information about impedance variations of loads, employed power
cables and network topology [3, 7, 43–47]. Deriving a general and universal
channel model for power lines is not possible since there are many parameters
affecting characteristic behavior of the PLC channel when compared to other
traditional wired channel types. Furthermore, signal attenuation and interfer-
ence of PLC channels may be affected by structural characteristics of buildings
such as single-family houses, high-rise buildings, multi-flat buildings with riser
or common meter room and so forth [48, 49]. Moreover, infrastructures of elec-
trical transmission and distribution systems may be different in countries [50–
52]. As a result of these differences, the PLC channels have very dynamic char-
acteristics and present dissimilar behaviors in different locations.
Hensen and Schulz proposed a basic model to define channel transfer func-
tion of power lines in [43]. In this model, channel attenuation was only modeled
as an increasing parameter with higher frequencies. The drawback of this chan-
nel model was that it was not taken into account multipath propagation effect.
After Hensen and Schulz’s channel model, Philipps [44] and Zimmermann [45]
identified different PLC channel model that takes into account multipath
effects. Philipps model defined the channel impulse responses through Dirac
pulses that symbolize the sum of the signals coming from N various branches.
The mathematical definition of Philipps model can be expressed as follows:

N
X
HfðÞ ¼ ρ e j2πfτ i (4.1)
i
i¼1
where ρ i stands for reflection parameter while τ i shows delay time. Another
channel model, which was introduced by Zimmermann and Dostert [45],
included an additional parameter to Philipps model for describing channel
attenuation. The analytical expression of this model can be given as follows:
N
X k
ð
ð
HfðÞ ¼ g i e a 0 + a 1 f Þ d i e j2πfd i =v pÞ (4.2)
i¼1
where g i , d i and v p denote weighting parameter, line length and propagation
speed, respectively. In addition a 0 , a 1 , and k parameters show frequency depen-
dent attenuation [53]. While first exponential function in Eq. (4.2) represents
attenuation, second one defines delaying time. After these channel model pro-
posals, novel PLC channel models with various approaches that were suggested
by considering structural differences of power systems of countries also intro-
duced by researchers. These new models were based on two-port transmission
line presentation of electrical network [37–42], statistical modeling approaches
unlike the deterministic models [46, 47] and computation of multipath propa-
gations via matrix approach [54–56].
When the PLC channel models suggested both for special countries and envi-
ronments are taken into account, they can be also grouped according to the def-
inition domains. While first approach of channel modeling is realized in time
domain [17, 54–56], the second method defines the channel in frequency domain