A New ICT-based Modeling for the Power Grid
N. Benjamin Sendama and Aawatif Hayar
Smart city, RITM, ENSEM, Hassan II University, Casablanca, Morocco
Keywords: Energy Flow, Microgrid, Power Line Communication, Single Virtual Power Source.
Abstract: The purpose of this work is to propose a new theoretical and mathematical model that describes the energy
flow over a microgrid, à small portion of a power grid. Indeed, there is similarity between a transmission
channel made up of several transmitters/receivers and the microgrid involving various energy
sources/consumers. This has been the premise which prompt us to conduct this study and develop a new
model of the microgrid. The propounded model is not to contest or to interrogate electromechanical results
about the flow of electricity. It rather brings another way of seeing the energy flow. Moreover, this
framework bears in mind intermittent energy sources. The inclusion of renewable energy sources in the
conventional power grid has to be taken into account in order to come up with a model that is faithful to the
current state of the grid. On the basis of a MIMO (multiple-input and multiple-output) channel, the proposed
architecture consists of a Single Virtual Power Source (SVPS) serving its energy at several energy
consumption points. Its energy flow’s shape is a Gaussian as it will be demonstrated throughout this paper.
1 INTRODUCTION
An expertise of the microgrid is one of the most
current crucial matter. Understanding, modelling the
architecture of such a system, from an electrical
point of view, which connects electricity end-
consumers is of absolute necessity. This turns out to
be even more significant due to:
the integration of information and
communication technology “ICT” into the grid
(it is undergoing many transformations which
make it complex);
The integration of less predictable energies
sources such as solar, wind ... which can degrade
the reliability and quality of service of the grid;
Taking into account new electrical uses like the
electric vehicles, a multitude of electrical and
electronic devices that increase the demand for
electricity ...
Therefore, it is capital to understand the functioning
of the power grid for further improvements. The aim
of this paper was to look into the power grid
demeanour and establish a new mathematical model
that brings to light the flow of energy throughout a
microgrid, because the existence of such a model
could lead to sustainable research.
To back our results up, a brief but consistent
overview in the literature about power grid models
in terms of electricity flow was done. The most
common power grid model is presented by (Grainger
and Stevenson,1994), (Andersson, 2008), and
(Zimmerman and Murillo-Sanchez 2015). This
model relies on elements suitable for power flow
analysis such as lines and cables, transformers, shunt
elements, loads, generators... It gives the expressions
for the active and reactive power flows along the
power grid.
One of the solutions proposed is called "load-
flow study", which is a numerical analysis of the
flow of electric power in an interconnected system.
It is based on non-linear relationships between
voltage and current at every bus system. Generally,
for each grid of n independent buses, we can write n
equations relating voltage to current as follows:
⋯
⋯
…
⋯
(1)
where I is the vector of n currents injected into the
bus, V is the vector of the n bus voltage, and Y is
called the admittance matrix buses. This approach
follows Kirchhoff’s circuits laws. Its aim is to get
the magnitude and phase angle of the voltage at
each bus. It requires knowledge of a variety of
information at each bus.
The mathematical model that we propose in this
Sendama, N. and Hayar, A.
A New ICT-based Modeling for the Power Grid.
DOI: 10.5220/0006358003050310
In Proceedings of the 6th International Conference on Smart Cities and Green ICT Systems (SMARTGREENS 2017), pages 305-310
ISBN: 978-989-758-241-7
Copyright © 2017 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved
305
paper has been developed under the assumption that
our microgrid connects households at the same level
of voltage. The problem was then to study an energy
flow through an electric cable that covers a well-
defined area.
We started with a lumped equivalent model of an
electric cable, and, through its communication
channel model, we tried to extricate a model that
describes the electrical energy flow over a power
grid.
The structure of this paper is as follows: In
section II we talk about the microgrid and then
briefly present the electromagnetic wave
propagation on a wire. In section III, with the help of
a probabilistic approach, we present a Single Input
Single Output (SISO) Power Line Communication
(PLC) modeling. On the hinge of these two
descriptions, we propose a new model that describes
the flow of energy throughout the microgrid in
Section IV. Finally, in section VI we end our work
with a brief conclusion, but that sums up well our
contribution in this research area.
2 SYSTEM MODEL
2.1 Microgrid
According to (Association Smart Grid Suisse, 2016),
a smart grid is an electrical grid linking electricity
production, consumption and storage, and
coordinating them autonomously. Within a smart
grid, Information and Communication Technologies
play an essential role: By providing a two-way and
real-time communication between all components of
the power grid, they make it possible to control
every point on the grid to ensure its efficiency,
reliability and durability in an intelligent and
automated manner. The intention is a constant
regulation of electrical energy, where there is a
counterbalance between the energy produced and the
energy consumed.
However, the implementation of such systems
encounters many difficulties. Except for a few
research projects, nowhere in the world exists a
smart grid that has fully automated control of
consumer devices and production facilities
(Association Smart Grid Suisse, 2016). As a result,
the deployment of small smart grids, commonly
called microgrids, is seen as "a simpler alternative to
implement and could therefore play a leading role in
the deployment of smart grids" (Smart Grids-CRE,
2017).
A microgrid is a grouping of interconnected
loads and decentralized energy sources in an area
whose electric boundary is clearly defined, and
which acts as a single controllable entity with
respect to the main grid (Office of Electricity
Delivery & Energy Reliability, 2015). It can operate
either in stand-alone (island) mode, connected to the
main network or switch between these two modes.
The microgrid studied in this paper delimits a
residential neighbourhood whose households are
represented by the index i, varying from 1 to n. As it
has been mentioned, the whole network is at the
same voltage level, i.e., The last electrical substation
closer to the electricity-consuming elements is
located to the interconnection point of the microgrid
to the conventional power grid (a delivery substation
generally of 20 kV / 400 V). Figure 1 shows the
model of our microgrid.
Figure 1: Microgrid representation.
Each house ∈
1,
has its specific electricity
needs Ni and, depending on available energy sources
(solar/wind/fuel cell), it can produce an amount Pi of
electricity.
2.2 Electromagnetic Wave Propagation
on an Electric Wire
Electromagnetic wave propagation results from the
evolution and progression of a wave within a
medium. Propagating in an electric wire, the
transmitted signal undergoes various phenomena
such as reflection, signal attenuation, multipath
phenomenon… This means that there will be many
received signals which are distorted, mitigated and
delayed.
Let’s consider a small portion of an electric wire.
Because of the wire imperfect constitution, the wave
propagation is characterized by a distortion in terms
of distance and frequency. By applying the
transmission line theory on a d length line without
derivation, such as that illustrated on Figure 2, the
frequency response of the section is then written:
0
(2)
Where U is the voltage on the line at the distance x
SMARTGREENS 2017 - 6th International Conference on Smart Cities and Green ICT Systems
306
and γ represent the propagation constant of an
electromagnetic wave.
Figure 2: Equivalent lumped elements of a transmission
line model.
The propagation constant for any conductor is
calculated from the primary line coefficients by
means of the equation bellow:
(3)
Where ω is the angular frequency. The real part α,
and the imaginary part β of the propagation constant
represent respectively the attenuation constant and
the phase constant. (Errede, 2015) gives a very
detailed demonstration of this.
In a typical scenario, an infinite number of
propagation paths is theoretically possible (several
observable reflections on the wire). This is due to
the electrical grid impedance which practically
always mismatches. The frequency response of the
section is then transformed as:
(4)
Where
and τ
i
are respectively the ponderation
factor and arrival time of a multipath component i.
N
p
is the dominant number of paths (Zimmermann
and Dostert, 2002). The gain term
reflect the
product of the reflection and transmission factors
experienced by the i path as shown on Figure 3. The
ratio between the distance d
i
and the wave
propagation velocity ν
i
is equal to the delay τ
i
. ν
i
depends on the type of material that made up the
line. Note that γ depends on the resistance R,
inductance L, the conductance G and the capacitance
C, which are characteristic properties of the
transmission line.
Moreover, the reflection and transmission
coefficients differ from one grid to another. Thus,
the electric characterization of the grid needs prior
knowledge (the intrinsic characteristics of power
lines): This is called a bottom-up characterization.
Figure 3: Signal propagation over a transmission power
line.
3 POWER LINE
COMMUNICATION
A PLC channel model was firstly formalized by
Zimmerman (Zimmerman and Dostert, 2002). It is a
system that transmit information on an electric wire
operating at any voltage stage. Equation (4) of the
preceding section actually introduces the PLC
channel characterization using the determinist
approach. It has been pointed out that knowing the
characteristics of the electric wire is necessary. This
means a lot of resources and much time, without
guaranteeing an extrapolation of the model to
another grid (other than the one studied).
A statistical model turns out to be of great
necessity to take into account of a larger amount of
cases. The passage of the frequency response into
the time domain by the inverse Fourier transform
gives us the impulse response of the PLC channel. It
is expressed as:
,
(5)
Where each i path is characterized by its propagation
delay τ
i
, the attenuation factor
and phase θ
i
. In
fact, every transmitted signal undergoes interactions
like electromagnetic reflections, diffractions,
refractions, and each of these interactions induces a
phase for each path.
Let’s apply the PLC we have introduced above
on the microgrid presented on Figure 1, where
houses communicate one another (Single Input
Single Output). If we assume that the signal remains
A New ICT-based Modeling for the Power Grid
307
the same for periods of time superior to the duration
of the information symbols, as done in (Canete,
2003), the PLC channel can be considered time-
invariant. Thereby the model proposed by Bello
(1963) known as Wide-Sense Stationary
Uncorrelated Scattering (WSSUS) can adopted to
model our propagation channel. This model
considers that the impulse response is wide-sense
stationary and the different paths are uncorrelated.
Note that, within our microgrid, the distance
between the transmission and reception would not
vary over time, the Doppler Effect will not be
considered in the following channel characterization.
The complex impulse response of the PLC channel
becomes then:
(6)
4 ELECTRICAL POWER FLOW
MODEL
Let’s come back to the real issue of this paper,
namely the power flow modeling. Considering both
energy sources and needs within the microgrid on
Figure 1, the flow of electricity from one house to
another could be schematized as displayed on this
figure:
Figure 4: The microgrid’s energy flow elements.
Where:
expresses energy injected by house i onto the
microgrid
represent house i energy needs handled by
energy produced on place (the same house i)
represent residual energy needs of house i
which are to be handled by other energy sources
The sum of
and
speaks for the total energy
needs of the house i
Based on this architecture described, energy flow at
a given house j is run by the two equations:
⋯
⋯
∗
⋮
⋮
∗
(7)
(8)
Where:
reflects line losses of injected energy
,
from any house i toward house j
stands for energy provided by the main grid
is line losses occurred from point 0 to
house j
represents the energy produced by house i
It is obvious that when the house that injects
energy corresponds to the house for which the needs
are calculated. In this case, there is no line losses
(
1). This means that row vector , named
weighting factor by the following, is inversely
proportional to the line losses it represents.
0
1
(9)
Considering the whole system, it is clear that energy
at the point of usage i equals to the energy produced
at same point i, plus the energy produced elsewhere,
obviously after suffering losses during transport.
This is to say that, in terms of energy flow, our
system includes multiple energy inputs
, multiple
energy outputs
and multiple paths that energy
borrows to get from one point to another. The
energy mix is then expressed as follow:
⋮
⋯
⋮⋱⋮
⋯
∗
⋮
⋮
∗10)
Which can be also written ∗, where
column vectors N, P, M represent respectively the
houses energy needs, the houses injected energy and
the main grid energy (basically energy outside the
considerer microgrid).
is an n-by-n matrix that represent the
weighting factor of each path I of energy flow all
along the microgrid. It is clear that
. is a
symmetric matrix whose all main diagonal elements
equal to 1(they stand for both the production and the
consumption of energy at the same house: this
means that there is no line losses).
Note that the second part of the equation is
composed of a sum of the energy sources. This was
done on purpose in order to propose to consider
electricity as if it comes from a single source: A
SMARTGREENS 2017 - 6th International Conference on Smart Cities and Green ICT Systems
308
Single Virtual Power Source (SVPS). Figure 5
illustrates this.
Figure 5: Single Virtual Power Source architecture.
The SVPS energy comes from different sources
strewed throughout the microgrid. Virtually, this
energy makes it to the SPPS with an asynchronous.
It is due to the fact that energy is neither produced
nor injected onto the microgrid at the same time.
This randomness of the energy includes a delay
during each
accounting in the virtual source. The
energy of our SVPS
is therefore given by:
t
t
(11)
Where
stands for energy provided by the main
grid (sources other than microgrid’s), and
,⋯,
represent energy injected by different
houses of the microgrid.
Moreover, the electricity delivered by this virtual
source passes through various paths
, while it goes
to the different houses to meet their needs. As
displayed below, these two things combined reveal a
multi-path phenomenon in our architecture.
Figure 6: Multipath phenomenon of the SVPS
architecture.
Relying on the architecture that we have described,
we can observe a strong resemblance between the
energy flow represented in Figure 5 and the
transmission of an electromagnetic wave over a PLC
channel described in its section III.
Table 1: Analogy between the PLC channel and the
proposed model based on a single virtual power source.
PLC
Proposed power grid
model based on SVPS
Transmitter Single Virtual Power
Source
Receiver House i
Multipath phenomenon
from transmitter to
receiver due to the high
frequency
Multipath phenomenon
due to the relation
between the SVPS and
house i
Scattered signal as a
function of time
Line losses as a
function of distance
In the case of a PLC, the propagation delays from
various paths vary randomly and as we said. So a
large number of propagation paths is unavoidable.
The resulting signal is a sum of a random module
and phase components. Thus equation (6) is
approached by a complex variable whose quadrature
components I and Q are independent and trail a
Gaussian distribution. The envelope of this signal
follows a Rayleigh law defined by the following
equation:
(12)
Figure 7: Shape of the impulse response of a typical
Gaussian filter.
With
. σ is the standard deviation of
the real part I or imaginary part Q. From a
probabilistic point of view, the randomness of
equation (6) means that its realization converges to a
known form: The Gaussian shape representation in
time domain is illustrated by this:
As it has been evoked previously, energy that
will be delivered by our virtual source
is the
sum of all the energy sources at the level of the
microgrid plus energy from the main grid.
Furthermore, through the study conducted in this
paper, similarity has been pointed out between the
A New ICT-based Modeling for the Power Grid
309
PLC and our system. The resemblance between the
proposed model and the radio channel is not
physical, but rather mathematical: For the PLC
model, the transmitter is a time invariant source
unlike the channel which might be variant if we take
into account the impact of loads on the wave
propagation.
Regarding our model, energy flows over a time
invariant channel (households therefore charges are
at known positions) but the SVPS is time variant due
to asynchronous of the energy production mentioned
above. Thenceforth the same applies to our
microgrid. The electrical energy flow within
the microgrid can be expressed as:
(13)
The energy flow is a function of the distance d,
where reflects the temporal asynchronous of
the energy injection onto the grid and energy line
losses heading to different point of usage (house i).
It is a summation of several random phenomena,
both temporal and spatial.
This resemblance between equation (6) and (13)
leads us to conclude that the energy flow is
Gaussian-shaped. However, this first study
represents the foundation of further work that is to
follow. It will consist in the model validation,
preferably by real data, or by simulations on
appropriate platforms.
5 CONCLUSIONS
While there are still many questions about models of
a power grid, and many possible ways to address
this issue, our aim in this paper was to propose a
new model of the electric flow: Disregarding the
need of knowing different parameters of the grid at
each bus (active power, reactive power, power
factor), we demonstrated that a microgrid can be
assimilated to a transmission channel which conveys
energy from a Single Virtual Power Source to
multiple energy consuming points.
In regards to the energy flow, equation (6) whose
shape is characterized by a Gaussian was utterly
approximated by equation (13). This is due to the
fact that the whole energy flowing through the grid
is actually a sum of a certain random amount of
energy injected by different sources. This is also
braced by the fact that energy undergoes various
phenomena such as line losses and multiple
scattering due to different paths.
The proposed mathematical model will be of
precious assistance in the smart grids: For example,
during the grid characterization, the development of
energy allocation strategies…
REFERENCES
Andersson, G., 2008. Power Flow Analysis Fault Analysis
Power Systems Dynamics and Stability, Lecture on
Modelling and Analysis of Electric Power Systems at
EEH - Power Systems Laboratory ETH Zurich.
Association Smart Grid Suisse (VSAS), 2016. Document
connaissances de base Smart grid.
Bello. P. A., 1963. Characterization of Randomly Time-
invariant Linear Channels. IEEE Transactions on
Communications and Systems, Vol. 11(4), pp. 360–
393.
Canete, F., Cortés, J., Dıez, L., Entrambasaguas, J., 2003.
Modeling and evaluation of the indoor power line
channel, IEEE Communication Magazine, vol. 41, pp.
41–47.
Errede, S., 2015. Lecture note 7 on Electromagnetic wave
propagation in conductors at UIUC, Physics 436 EM
Fields & Sources.
Grainger, J., Stevenson, W., 2015. Power System
Analysis, McGraw–Hill, New York.
Office of Electricity Delivery & Energy Reliability, 2015.
DOE Microgrids Program Overview, Power Systems
Engineering Research and Development.
Smart Grids – CRE, 2017. website [website], available at:
<http://www.smartgrids-
cre.fr/index.php?p=microgrids> [Accessed 14 January
2017].
Zimmermann, M., Dostert, K., 2002. A Multi-Path Signal
Propagation Model for the Power Line Channel in the
High Frequency Range, IEEE Trans. Commun., vol.
50, no4, pp 553–559.
Zimmerman, R. D., Murillo-Sanchez, C. E., 2015.
Matpower 5.1 User’s Manual, Power Systems
Engineering Research Center.
SMARTGREENS 2017 - 6th International Conference on Smart Cities and Green ICT Systems
310
