Flexible Power Distribution Networks: New Opportunities and
Konstantin Suslov
, Ilia Shushpanov
, Nadezhda Buryanina
and Pavel Ilyushin
Irkutsk National Research Technical University, Irkutsk, Russia
Chukotka branch of North-Eastern Federal University, Anadyr, Russia
Petersburg Power Engineering Institute of Professional Development, Saint-Petersburg, Russia
Keywords: Power Distribution Network, Reliability, Survivability, Relay Protection and Automated Systems, Adaptive
Setting, Overhead Power Line, Microprocessor Measuring Device, Information Communication Network,
Abstract: Today, electricity companies worldwide use digital devices. Their use is commonplace in the grid, whether it
is electricity generation, transmission or distribution. Power distribution networks are the most widespread
but are the least digitalized because they have to deal with the problems related to the collection of necessary
information, the adaptation methods, failures to identify some emergencies and their effect, and the
insufficient number of reliability assessment methods. These networks were not important for energy
companies and they did not pay attention to them. Nowadays, however, there is a need to pay special attention
to these networks. Insufficient attention to them has led to delay in their digitalization and today there are
some issues to work on. For example, improper placement of devices leads to a lack of complete and reliable
information, which is the reason why relay protection and automatic systems in distribution electrical
networks do not provide selectivity. An algorithm is proposed to site measuring devices so that information
is collected most effectively. The proper installation of the devices will allow adjusting the operating
parameters of the relay protection and automatic systems depending on changes in external weather conditions
and fluctuations in power consumption in the network. It will also help to determine the best network topology.
The paper proposes a technique for distribution network control, which takes into account the type of failure
in case of emergency in real time, and a method to locate measuring devices and establish an information and
communication network.
Recently, it has been possible to use high-tech
intelligent devices that are capable of implementing
the most modern and effective algorithms for the
operation of relay protection and determining the
fault location of power lines. The use of
microprocessor devices allows controlling energy
systems, as well as electrical energy distribution
systems. By adopting standard IEC 61850 relay
protection and emergency control (RPEC) receiving
more information not only on measuring instruments
and sensors, but also on other RPEC devices. Such
devices are able to work with a wide information
base, and therefore the problem of developing new
relay protection algorithms is becoming increasingly
more relevant. At present, relay microprocessor-
based protection systems must be intelligent and able
to adapt and learn. Sometimes, the operation of the
RPEC devices may function incorrectly if their
settings do not reflect the real state of the monitored
overhead power line (OPL). It is important to specify
the OPL parameters to accurately determine the
settings of relay protection using simulation models.
Therefore, the development of a relay protection
system with adaptive response setting depending on
Suslov, K., Shushpanov, I., Buryanina, N. and Ilyushin, P.
Flexible Power Distribution Networks: New Opportunities and Applications.
DOI: 10.5220/0009393300570064
In Proceedings of the 9th International Conference on Smart Cities and Green ICT Systems (SMARTGREENS 2020), pages 57-64
ISBN: 978-989-758-418-3
2020 by SCITEPRESS Science and Technology Publications, Lda. All rights reserved
changes in external conditions in distribution
overhead power transmission lines a relevant task.
This is extremely important for the distribution
network survivability.
Analysis of the operating modes of power distribution
networks is one of those tasks that are important in
the design and operation of electrical systems. In this
case, the analysis of the steady state of the electrical
system has a significant role.
The radial configuration is typically used for
medium and low voltage power distribution
networks. For example, urban networks can be either
loopback or ring. But under normal conditions, due to
technological features, they work as radial.
A feature of the classical radial electric network is
the assumption that it receives power from only one
point, which is called the source node. And under
these conditions, there is a unidirectional flow in any
state of the network.
Analysis of the operation modes of radial electric
networks is much simpler. If you give the activity of
the power distribution network, then the radial
structure can both be preserved and broken. In such a
scenario, when power distribution networks operate
as non-radial, it is very difficult to analyze operating
modes and requires special attention.
The notion of active power distribution network is
considered in (Voropai (a), 2013, Mokryani, 2017,
Xie, 2018, Ghadi, 2019, etc.) on the basis of existing
concepts (McDonald, 2008, Celli, 2012). It is
necessary to clarify and detail it as follows. The
activity of the power supply system implies the use of
automatic devices to control configuration and
parameters of the system with the view to rationally
(optimally) meet the requirements for economic
effectiveness of normal, maintenance, post-
emergency and other, reliability of power supply to
consumers. The control actions can be implemented
by disconnectors (Begovic, 2013).
In our opinion, the activity of power supply
systems is understood to mean their ability to
automatically self-recover the circuit and maintain
the required values of the mode parameters by the
action of the corresponding control systems for
distributed generation units and reconfiguration of
power distribution network (Suslov, 2015,
Shushpanov, 2019).
The model of the power distribution network
control is based on the reliability model (Voropai (b),
2013). Formalization of the problem of choosing a
rational configuration of power supply system is
presented in (Svezhentseva, 2012). Mathematical
models and methods of the complex optimization of
the power supply system structure and parameters,
considering, in particular, the distributed generation,
are mainly addressed in the publications by
researchers (Khator, 1997, Georgilakis, 2015, Conte,
2019, Ehsan, 2019, Ilyushin, 2019, etc.).
It is very important to consider the security of the
power supply system. The security of the power
supply system as well as the security of the entire
electric power system is understood as an ability of
the system to maintain an acceptable state in case of
changes in operating conditions, component failures,
and sudden disturbances (Reliability Concepts,
Methods for estimating the security of the power
supply system are presented in a great number of
publications (Balu, 1992, Marceau, 1997, Endrenyi,
1978, Jiyan, 2009, Billinton, 1996,etc.). Earlier the
object of these methods was a passive power
distribution network, which electricity was supplied
to the power supply system from power supply points
in the main network of the electric power system. Use
of modern multifunction switching devices,
development of protection and automatic systems,
and the necessity to coordinate their operation have
significantly altered the response of the distribution
electric network to the changes in operating
conditions, failures of components, and sudden
disturbances owing to the automatic measures
(reconfiguration of the network) and thus have made
the flexible network. In a sense, the power
distribution network becomes capable of self-
healing, i.e., capable of automatically restoring power
supply to consumers to the maximum in minimum
time (Nepomnyashchy, 2011).
The considered feature of activity of the power
distribution network should be taken into account in
the security model of the flexible distribution
The basis is taken the traditional model of the power
distribution network reliability. This model has the
following basic principles. (Shushpanov, 2019 ):
SMARTGREENS 2020 - 9th International Conference on Smart Cities and Green ICT Systems
• As initial reliability indicators for each main
component of power systems (lines, transformers,
etc.), the parameters of the failure flow rate and the
restoration rate of the component . are used.
• Based on them, on the assumption that the failure
(restoration) flow has the Markov property, that is =
const and = const, the well-known formulas are
used to determine the probability of failure, the failure
rate and the component restoration time.
• Based on the indicated indices of network
components, the average failure rate, average failure
duration and average system availability ratio are
• Failures of protection devices and circuit
breakers, are taken into account indirectly in the
values of the failure flow parameters and the
restoration rates of the main components.
In the study of flexible active distribution systems,
we propose to use the following methodology for
research. The flow chart of the algorithm for
analyzing the reliability of flexible power distribution
networks is represented in Fig. 1.
As an example, let consider the power distribution
network. Based on this scheme, it is possible to
demonstrate how reliability factors in relation to an
active distribution network are taken into account in
the model.
Figure 1: Flow chart of the algorithm for analysing the
reliability of flexible distribution networks.
Fig. 2 represents initial scheme of the power
distribution network. Distribution network voltage is
10 kV This network powered by two different
sources - C1 and C2. Voltage of tis sources is 110 kV.
The distribution network supplies power to 15 busses
Figure 2: Initial scheme of the power distribution network.
indicated as N1-N15 in the Figure. Transformers,
transmission lines, and load feeders are connected to
the scheme by circuit breakers.
The goal of this concept is to reconstruct the
network with its transfer to “active power distribution
network” from “passive power distribution network”
using additional switching devices (in the figure,
these lines are marked with an X). In this case, new
nodes appear in the power distribution network.
The reconstructed scheme of power distribution
network with operating areas is shown in Fig. 3. It
should be noted that this distribution network in
normal mode operate as a radial one. Under normal
mode, redundant lines are disconnected.
In this research we use the concept of an
“Operating area” (Voropai (a), 2013, Shushpanov,
2019). Using this concept makes the power
distribution network controllable and flexible. When
we using this concept, all relay protection devices
installed directly on the circuit breakers are combined
into one common system and exchange data with
each other. This position corresponds to standard IEC
The need to introduce operating zones is caused by
the logics of the switching devices operation. The
operating zones are formed on the basis of network
structure and represent a set of components that are
grouped according to the functions determined by the
principles of switching devices operation. It should
also be noted that operating areas are formed on the
basis of the structure and topology of the power
distribution network.
Flexible Power Distribution Networks: New Opportunities and Applications
Figure 3: Reconfigured distribution network with operating
Consider the principles of operation and the
principles of switching in the presented operating
areas of the distribution network. This principlies
based on papers (Voropai (a), 2013Shushpanov,
Operating Area No.1. (Fig.3) In that case, if the
transformer Tr1 fails, the backup line L3-4
(component No.9) is switched on in this operating
area. In this case, a change in the power point and
reconfiguration of the power distribution network
occurs. For example, another case is possible. A short
circuit occurs on line L1-2 (component No.5) ,. In
this case, it is disabled by overcurrent protection.
Then the redundant line L3-4 is automatically
switched and this provides power to consumers
connected to the buses N2 (component No.6) and N3
(component No.8). In the same way, if a short circuit
occurs in the line L2-3 and it is disabled by the
overcurrent protection, the automatic connection of
the redundant L3-4 line provides power to consumers
connected to the bus N3. In an emergency event and
loss of power on the bus N3, an additional redundant
line L3-4 is not connected. In this case, when the L2-
3 line is disconnected, power to consumers connected
to the N1 and N2 buses can be provided from source
C1 using the line L 3-4.
Operating Area No. 2. In this area, reconfiguration is
performed in the same way: in case of an accident,
line L3-8 is automatically turned on, in which power
is supplied to consumers connected to busses N8
(component No.12)., N9 (component No.25)., N10
(component No.23)., and N11(component No.21). In
the case that bus N8 fails, the backup line L3-8
(component No.11). is not switched on but power
supply to the other consumers is provided by the main
source C1.
Operating Area No. 3. In this area, the power
distribution network is not reconfigurable, since there
is no technical possibility due to the radial structure
of the network.
Operating Area No. 4. In this work area, automatic
switching occurs similarly to control in operating
areas No. 1 and No. 2. In case of failures in this zone,
the redundant line L4-11 (component No.20) is used.
Operating Area No. 5. In this area, the power
distribution network is reconfigured similarly to the
previous zones considered. In this case, automatic
switching on of the line L6-7 (component No.19) is
This methodology allows for the control of the
overcurrent protection in the lines and the
undervoltage protection at the power buses in active
power distribution networks. Thus, the presented
methodology makes it possible to make the power
distribution network flexible, as well as increase the
Traditionally, power distribution networks have a
rather low level of automation. This networks are
often equipped with switching devices that can only
be controlled manually. If one adds control drives to
the disconnectors, it will be possible to control them
remotely, the price of disconnectors increases. For
these disconnectors the need to create a control
system. In the above text, a method of the power
distribution network control based on flexibility was
proposed. This method can also be applied to the
network with disconnectors. However, then the
question arises for the relay protection devices, how
to determine certain failures and emergency
situations. Installation of sophisticated
microprocessor-based protection devices will cost too
much, however a solution to this problem is the
option of creating an information communication
network with sensors (Shushpanov, 2019).
Traditionally, sensors are used for power
distribution networks to obtain information about the
current state of the network. There are many studies
SMARTGREENS 2020 - 9th International Conference on Smart Cities and Green ICT Systems
on this issue (Krajnak, 2000, Grilo, 2010, Suslov,
2011, Gavrilov, 2019, Bulatov, 2017, etc.). In this
case, the sensors are used to give flexibility to the
power distribution network in post-emergency
situations. As such devices we used IKI-Overhead
fault indicators intended for detection of faults on
overhead power distributions lines. These indicators
transmit information using GSM and easily fit into
the IEC 60870 standard. Indicators are installed
directly on the wires without additional mounting
devices. According to the control model of the power
distribution network, all switching devices are
integrated into one information-switching network
with a common control center. Information from IKI
indicators is transmitted to this center. Figure 4 shows
the network, in which the sites for installation of these
indicators are shown by circles (Shushpanov, 2019).
These devices can determine the following
parameters: short circuit, single-phase fault to
ground, overhead line break, and maximum load of
the overhead line.
Figure 4: Power distribution network with places for
installation of current and voltage sensors.
Thus, superimposing the control model of the
power distribution network over the model of
installation of the state monitoring sensors, we can
say that the power distribution network is made
flexible because monitoring of the network
parameters makes it possible to redistribute the load,
isolate the faulty section, and maintain power supply
to the consumer (Shushpanov, 2019).
These sensors can transmit information to the
control center. In the case of a massive outage due to
strong winds, however, it is also necessary to check
the information network for the ability to transmit all
information over the information network.
Currently, various indicators are used that
characterize different aspects of the reliability of
electric power systems and power supply to
consumers (Billinton, 1996): System average
Interruption Frequency Index (SAIFI), customer
average interruption frequency index (CAIFI),
system average interruption duration index (SAIDI),
customer average interruption duration index
(CAIDI), average system availability index (ASAI),
A widespread index of power supply system
security is risk. The risk is defined as the sum of the
probabilities of the sequence of events on the value of
effects resulting from each event, usually in the form
of power shortage or undersupply of power
(McСalley, 1999, Li, 2005). At the same time, the risk
is also assessed the implementation of various
measures to improve the operational reliability of the
power supply system (Schwan, 2012, McDonald,
2006). In paper (Hua, 2008), a formula is given for an
integral risk assessment taking into account all the
factors considered.
If in the final post-emergency state as a result of
the considered cascading failure the steady-state
conditions are admissible, we estimate power
shortage in the system and its probability. Based on
the obtained information, we calculate the risks for
the analyzed state of the power supply system.
In this case, the probabilities of the system states
as a result of complex failures are determined using
the known equation (Billinton, 1996):
probability of power shortage equal to
in the considered state k of the power supply
is the probability of failure-free operation
of component j or its protection;
is the failure
probability of component i or its protection; i, j are
the numbers of power supply components.
The paper (Voropai (a), 2013) presents a
methodology for risk assessment.
The conventional approach to the risk termination
during the estimation of the power supply system
security is represented by the equation (Billinton,
1996) :
Flexible Power Distribution Networks: New Opportunities and Applications
However, the equation (2) does not consider the
severity of power shortage consequences for different
categories of consumer loads. Taking into account the
fact that security is estimated for a certain time point,
at which a sudden power shortage may occur, we can
determine the severity of consequences on the basis
of specific losses caused by sudden power shortage
. Modern estimates of
for different types of
consumer loads can be assumed in accordance with
paper (McDonald, 2006). Thus, the modified
equation for risk determination during security
estimation will have the following form:
where n is the number of nodes in the scheme of the
power supply system, K is number of states of the
power supply system.
Obviously, the number of states K of the power
supply system is determined by the total number of
primary failures of the scheme components, i.e. lines,
transformers, distributed generation sources. By
correlating the risk assessments with specific
components of the scheme, one can identify the
network weaknesses in terms of security and based on
this information make recommendations on the
measures to increase it.
Figure 5 presents the calculation results of
security risk indices for the initial scheme using the
formula for risk determination when assessing the
power supply system security taking into account
specific damages caused by sudden power shortage of
consumers and probabilities of the power shortage in
the considered state of the power supply system.
In this case the failure probabilities of the primary
components (transmission lines, transformers, buses),
as well as circuit breakers and protection devices are
assumed in accordance with (Voropai (a), 2013). The
values of specific damages caused by power supply
interruption as a function of the structure of
consumers in the considered power supply system are
applied according to (Voropai (b), 2013).
The diagram in Fig. 5 shows that the failures of
buses 8, 10, 12, 14, transformers 34 and particularly
15 are dangerous from the security standpoint. The
highest risk value at the failure of transformer 15 is
conditioned by the fact that source C2 supplies power
to more essential consumers than source C1, with the
high values of specific damages. The zero risk values
for components 7, 16, 17, 21 are explained by the
absence of these backup transmission lines in the
initial power supply system.
Figure 5: The diagram of risk indices for the initial scheme.
Figure 6 presents the estimates of security risk
indices for the reconfigured power supply system
scheme (Fig. 3) for the same initial data.
It is assumed that the disconnector operations on
connection of the backup transmission lines are
performed effectively and that their accuracy is high,
though there is no concrete data as yet. It should be
noted that the transmission line failure at its
connection is practically improbable, the
disconnectors failures due to connection of backup
transmission lines will lead to the results identical for
the initial scheme.
Figure 6: The diagram of risk indices for the power
reconfigured network.
The diagram of the risk indices in Fig. 6 shows a
high efficiency of the active (in the considered sense)
power distribution network for the power supply
system security improvement.
Further, system reliability indicators for the entire
distribution network were calculated. The
calculations were carried out taking into account the
network operation mode and protection.
System average Interruption Frequency Index
SMARTGREENS 2020 - 9th International Conference on Smart Cities and Green ICT Systems
where I - the number of nodes with loads in the
- failure rate in the i-th node, 1,
System average interruption duration index
, (5)
where t
– power recovery time in the i-th node.
Average system availability index (ASAI):
, (6)
where p
– probability of failure in the i-th node.
Calculations using sensors for the power
distribution network and without using sensors were
performed. The results are presented in Figure 7.
Figure 7: The diagram of system reliability indicators for
the entire power distribution network
Calculation results shows a high efficiency of the
use of sensors to give activity and flexibility to the
power distribution network.
The correct location of the sensors is very important
to give the network activity and its flexibility. It is
also very important from the point of view of
economic feasibility.
The use of new principles of operation in power
distribution networks; the use of advanced
multifunctional switching devices; the development
of protection and automated control systems as well
as the need to coordinate their work have led to a
change in the principles of emergency control
measures towards their automation for reconfiguring
the power distribution network and making it flexible
when responding to equipment failures and
The paper presents distribution network control
models that provide the flexibility of such networks
and increase the reliability of energy supply.
To ensure maximum efficiency of the power
distribution network, the authors proposed a
technique for placing network status sensors in such
a network.
A technique is developed to create an electrical
complex of relay protection for power distribution
system. The technique is based on the information
communication technology of data transfer and
exchange based on IEC 61850.
The study was carried out with the financial support
of the Russian Foundation for Basic Research and the
Subject of the Russian Federation - the Republic of
Sakha (Yakutia) 18-48-140 010.
Voropai, N., Styczynski, Z., Shushpanov, I., Pham Trung
Son, Suslov, K., Security model of active distribution
electric networks. Thermal Engineering Vol. 60, Issue
14, 2013, pp. 1024-1030
Zeng, B., Wen, J., Shi, J., Zhang, J., Zhang, Y.,A multi-
level approach to active distribution system planning
for efficient renewable energy harvesting in a
deregulated environment. Energy, Volume 96,
February 2016, pp. 614-624
Mokryani, G., Hu, Y., Pillai, P., Rajamani, H.-S., Active
distribution networks planning with high penetration of
wind power. Renewable Energy, Volume 104, April
2017, pp. 40-49
Xie, M., Ji, X., Hu, X., Cheng, P., Liu, M., Autonomous
optimized economic dispatch of active distribution
system with multi-microgrids, Energy, Volume 153, 15
June 2018, pp. 479-489
Ghadi, M., Rajabi, A., Ghavidel, S., Azizivahed, A., Li, L.,
Zhang, J. From active distribution systems to
decentralized microgrids: A review on regulations and
planning approaches based on operational factors,
Applied Energy, Vol. 253, November 2019, pp. 113543
McDonald, J., Adaptive intelligent power systems: Active
distribution networks, Energy Policy, Vol. 36, No. 6,
2008, pp. 4346-4351.
Celli, G., Giani, E., Soma, G.G., Pilo, F., Planning of
reliable active distribution systems, 44th Session
CIGRE 2012, Paris, France.
Begovic, M.M. (ed.), Electrical Transmission Systems and
Smart Grids: Selected Entries from the Encyclopedia of
Sustainability Science and Technology, Springer
Science+Business Media New York 2013.
Flexible Power Distribution Networks: New Opportunities and Applications
Voropai, N., Styczysnki, Z., Shushpanov, I., Suslov, K.,
Mathematical model and topological method for
reliability calculation of distribution networks, In 2013
IEEE Grenoble Conference PowerTech,
Suslov, K., Gerasimov, D., Solodusha, S. Smart grid:
Algorithms for control of active-adaptive network
components, In 2015 IEEE Eindhoven PowerTech,
PowerTech 2015
Shushpanov, I., Suslov, K., About Flexibility Problem of
Distribution Electrical Network, In Proc. 2019 EPJ
Web of Conferences 217, 01014
Krajnak D. J., Faulted Circuit Indicators and System
Reliability, Rural Electric Power Conference, 2000
Grilo, A., Casaca, A., Nunes, M., Fortunato, C., Wireless
Sensor Networks for the Protection of an Electrical
Energy Distribution Infrastructure, In International
Conference CIP 2010, Springer, pp. 373-383,
Suslov, K.V., Solonina, N.N., Smirnov, A.S., Smart Grid:
A new way of receiving primary information on electric
power system state, In 2nd IEEE PES International
Conference and Exhibition on Innovative Smart Grid
Technologies, ISGT Europe 2011
Gavrilov, D., Gouzman, M., Luryi, S., Monitoring large-
scale power distribution grids, Solid-State Electronics
Vol. 155,May 2019, pp. 57-64
Bulatov, Y.N., Kryukov, A.V., Suslov, K.V., Multi-agent
technologies for control of distributed generation plants
in the isolated power systems, Far East Journal of
Electronics and Communications, Vol. 17(5), 2017, pp.
Svezhentseva, O., Voropai, N., Optimization of supply
source allocation in the problem of rational
configuration of electricity supply system, In 2012
IEEE PES Innovative Smart Grid Technologies
Conference Europe 2012, Berlin, Germany.
Khator, S., Power distribution planning: A review of
models and issues, IEEE Transactions on Power
Systems, Vol.12, No.4, 1997, pp. 1151-1159.
Georgilakis, P., Hatziargyriou, N., A review of power
distribution planning in the modern power systems era:
Models, methods and future research, Electric Power
Systems Research, Vol.121, No.2, 2015, pp.89-100.
Conte, F., D’Agostino, F., Silvestro, F., Operational
constrained nonlinear modeling and identification of
active distribution networks, Electric Power Systems
Research, Volume 168, March 2019, pp. 92-104
Ehsan, A., Yang, Q., State-of-the-art techniques for
modelling of uncertainties in active distribution
network planning: A review, Applied Energy, Volume
239, 1 April 2019, pp. 1509-1523
Ilyushin, P., Suslov, K., Operation of automatic transfer
switches in the networks with distributed generation, In
2019 IEEE Milan PowerTech, PowerTech 2019
Reliability Concepts in Bulk Electric Power Systems (North
American Electric Reliability Council, New York,
Balu N., Bertram T., Bose A., Brandwajn V., e.a., On-line
power system security analysis, Proceedings of the
IEEE, Volume 80, No. 2, 1992, , pp. 682-699.
Marceau R.J., Endrenyi J., Allan R., Alvarado F.L., e.a.,
Power system security assessment: A position paper,
Electra, 1997,No. 175, pp. 77-91.
Endrenyi J., Reliability modeling in electric power
systems.Yohn Wiley and Sons, 1978, 326 p.
Jiyan F., Borlase S., The evolution of distribution, IEEE
Power and Energy Magazine, 2009, Volume 7, No. 2,
Billinton, R. Allan, R., Reliability Evaluation of Power
Systems. Plenum Press, New York, NY, 1996
McСalley, J.D., Vittal, V., Abi-Samra, N., An over view of
risk based security assessment, IEEE PES Summer
Meeting, Edmonton, Canada, July 18-22, 1999.
Li, W., Risk assessment of power systems: Models, methods
and applications. N.Y.: John Wiley and Sons, 2005.
Schwan, M., Ettinger, A., Gunaltay, S., Probabilistic
reliability assessment in distribution network master
plan development and in distribution automation
implementation, CIGRE, 2012 Session, Paris, France,
August 26-30, 2012, Rep. C4-203.
McDonald, J.D.F., Pal, B.C. Representing the risk imposed
by different strategies of distribution system operation.
In IEEE PES General Meeting, Montreal, Canada,
Hua X.-Y., Wan, Q.-L., Wang, L., Security assessment of
power systems based on entropy weight-based gray
relational method, IEEE PES General Meeting,
Pittsburgh, USA, July 20-24, 2008.
Nepomnyashchy V.A., Economic and mathematical model
of reliability in electric power systems and electric
networks, Elektrichestvo, 2011, No. 2, pp. 31-37 (in
SMARTGREENS 2020 - 9th International Conference on Smart Cities and Green ICT Systems