Reliability Analysis of MV Electric Distribution Networks Including Distributed Generation and ICT Infrastructure

In recent years, the increased distributed generation (DG) capacity in electric distribution systems has been observed. Therefore, it is necessary to research existing structures of distribution networks as well as to develop new (future) system structures. There are many works on the reliability of distribution systems with installed DG sources. This paper deals with a reliability analysis for both present and future medium voltage (MV) electric distribution system structures. The impact of DG technology used and energy source location on the power supply reliability has been analyzed. The reliability models of electrical power devices, conventional and renewable energy sources as well as information and communications technology (ICT) components have been proposed. Main contribution of this paper are the results of performed calculations, which have been analyzed for specific system structures (two typical present network structures and two future network structures), using detailed information on DG types, their locations and power capacities, as well as distribution system automation applied (automatic stand-by switching on—ASS and automatic power restoration—APR). The reliability of the smart grid consisting of the distribution network and the coupled communications network was simulated and assessed. The observations and conclusions based on calculation results have been made. More detailed modeling and consideration of system automation of distribution grids with DG units coupled with the communication systems allows the design and application of more reliable MV network structures.


Introduction
The increasing penetration of distributed energy generation (DG) from renewable energy sources (RES) contributes to a decrease in greenhouse gases emission and reduces the dependency on fossil energy sources. At the same time, however, this trend means the electric power networks cannot continue to operate as before. The power grids were originally designed for the classical, hierarchical system with a unidirectional power flow from the central generation, through transmission and distribution level up to the loads. DGs nowadays largely feed directly to the distribution networks, which were not designed for this purpose. Therefore, the planning, operation and maintenance of distribution networks need to be changed.
In power system planning and operation, effective reliability analysis and assessment are key aspects. The reliability of the electric power system is usually expressed as a measure of the ability of the system to provide the customers with a sufficient supply. Continuous energy supply is one of the most important success criteria of a power system. However, also provides communication between markets, forecast applications and web services for the customers, which supports the management of the demand and supply process [46].
The issue of reliability of electric distribution systems with DG sources installed in them was broadly discussed in many publications. Quite often there is a lack of any detailed information on distribution network structures (parameters of distribution transformers, data on overhead lines and underground cables) and on DG source types, as well as their power capacities and locations, considered in the existing papers is observed. Moreover, the details on the reliability parameters of distribution system components being considered in these publications are often missing. We intend to present such details in this paper. We are convinced there is still a research space to present different, more detailed studies on reliability of electric distribution systems with integrated DG sources (for various network structures and data describing them) as well as ICT components.
This paper concentrates on the reliability analysis for both present and future electric distribution system structures. Two present electric distribution system structures are considered: a typical urban distribution network (UDN) and typical rural distribution network (RDN). Moreover, two future electric distribution system structures are analyzed: the urban distribution network with connected microgrids (DNMG) and active managed distribution network (AMDN). The impact of DG technology used, energy source locations, and their power capacity on the power supply reliability have been analyzed. The reliability models of electrical power devices, conventional and renewable energy sources, as well as information and communication technology (ICT) components have also been proposed.
The main contribution of this paper is investigating the analyzed subject in a more thorough way, that is: giving detailed data on considered distribution networks structures; on reliability parameters of distribution network components; on DG source types, as well as their power capacities and locations, for which the reliability calculations have been made, taking into account distribution system automation (automatic stand-by switching on (ASS) and automatic power restoration (APR)); presenting the results (seven commonly known reliability indices) achieved from the carried out computations and discussing the results (indices). The impact of DG type on these reliability indices has been investigated. It is worth noting, the reliability assessment of smart grid, i.e., electric power network coupled with the communication network, has also been done. We would like to highlight that this paper relates to MV distribution grids, for which reliability indices are the worst among all electric power distribution networks, as it is reported e.g., in [47][48][49]. Therefore, the importance of this paper on practical applications can be seen.
This paper evaluates reliability of four electric distribution system structures (two present ones and two future ones) and presents the reliability indices obtained for these structures. In our opinion, more detailed modeling and consideration of system automation of the distribution grids with DG units coupled with the communication systems allows for the design and application of such MV network structures for which the best reliability indices can be obtained.

Problem Statement
The main goal of this research was to analyze the impact of a type and location of DG units in present and future distribution network structures on the power supply reliability. The distribution system automation (ASS and APR) has also been considered in the studies. The analysis performed by the authors of this paper has been done for the benchmark structures of the MV distribution networks with the connected DG sources. The benchmark structures (shown in Figures A1, A3 and A4) have also been developed by the authors of this paper. The following reliability indices have been calculated with the use of DIgSILENT PowerFactory software [50,51]: • SAIFI is the System Average Interruption Frequency Index, which provides the average number of interruptions, above 3 min, in the system that a customer experiences during the observation period, mostly in one year. The index is a dimensionless number and can be calculated as follows [52,53]:  (1) where N i is the number of customers interrupted by i-th outage in the observation period and N T is the total number of customers in considered system. • CAIFI (Customer Average Interruption Frequency Index)-total number of all interruptions, above 3 min, divided by the total number of consumers affected by an interruption in the analyzed system. CAIFI can be calculated as follows [53,54]: CAIFI = Total number of customer interruptions Total number of customers affected where CN is the total number of consumers, which experienced one or more outages. • SAIDI is the System Average Interruption Duration Index, and it measures the total duration of an interruption, above 3 min, for the average customer during a given time period. It is normally calculated for the period of one year and presents customer minutes or hours of interruption. Mathematical representation of SAIDI is given in Equation (3) [52,53]: where r i is restoration time and failure duration in the case of consumers interrupted by i-th outage. • CAIDI, the Customer Average Interruption Duration Index represents the average time required to restore service after an outage occurs, which indicates how long an average interruption, above 3 min, lasts. It measures the duration of time that the customer is de-energized per interruption. To calculate the index Equation (4) can be used [52,53]: • ASAI (Average Service Availability Index)-the probability of having all loads supplied. The index is often expressed in a percentage, and it can be calculated from Equation (5) where T is the observation time period, usually one year, and in a non-leap year is equal to 8760 h. • ASUI (Average Service Unavailability Index)-the probability of having one or more loads interrupted, which can be calculated as follows [54]: ASUI = Customer hours service unavailability Customer hours service demand • EENS (Expected Energy Not Supplied)-the total amount of energy which is expected not to be delivered to loads. The index can be calculated from the Equation (7) [53,55]: where P ave,i -the average active power of customers which is interrupted by i-th outage.
A further aim of this research was to analyze the impact of ICT components integrated with the power system on the overall reliability of the smart grid supply. Therefore, a basic distribution power supply system was proposed, for which simulations using the Energies 2022, 15, 5311 6 of 34 sequential Monte Carlo method were carried out. The following reliability indices have been calculated along with the distribution of the results with the use of Matlab software: SAIDI, SAIFI, CAIDI, EENS, ASAI and ASUI.

Reliability Models of Electric Distribution System Components
The operation of an electric power system component can be described as a stochastic process {X t : t ∈ T ∧ X t : Ω → S}, where T is the life cycle time (continuous value), Ω is the space of coexisted events with the operating process of the system element and S = {s 1 , s 2 , . . . , s m } is the finite set of discrete operational states of the system component [56]. According to the element operation types, the states can be functional (full or partial one), stand-by and nonfunctional (failure or planned repair mode, etc.). The transitions between the component states may be caused by random events (failures and repairs), deterministic events (preventive repairs in a scheduled time) and random-deterministic events (conditional realization of preventive repairs).
There are many types of recommended mathematical techniques used in the reliability analysis [50]. Among them one can find as follows: The information about the accuracy and applicability of the aforementioned techniques can be found in many meaningful publications, e.g., [57].

Electrical Power Devices
The elements of an electric distribution system, such as lines, transformers, power switches, busbar of switchgears, protection and control elements are modeled as objects, which can be functional or in failure state. The time between these states is represented as a random variable described by an adequate type of probability distribution. In reliability analyses, the following probability distribution types are most often used [57,58]: • Exponential EXP (λ), λ > 0, λ-the rate parameter; • Weibull WEI (λ, β), λ > 0, β > 0, λ-the scale parameter, β-the shape parameter; • Gamma GAM (b, p), b > 0, p > 0, b-the rate (scale) parameter, p-the shape parameter; • Normal NOR (µ, σ), µ ≥ 0, σ > 0, µ-the expected value, σ-the standard deviation; Log-normal LNOR (µ 0 , σ 0 ), µ 0 ≥ 0, σ 0 > 0, µ 0 -the expected value of natural logarithm, σ 0 -the standard deviation of natural logarithm. Additionally, one can take into consideration the third state that is a preventive repair state with the average annual maintenance duration. A two-state reliability model can be assumed for the MV networks belonging to Polish distribution system operators. Table 1 presents the reliability models of different types of electrical power devices. All the probability distribution parameters have been estimated based on the observations of Polish power distribution systems [59,60].
It is also necessary to determine the adequate reliability model of an equivalent point supplying an analyzed distribution system. The reliability characteristics of that point can be found by an assessment on the power transmission system level or statistical research.
Some reliability analyses take into account the separate characteristics of protection devices (fuses, relays, releases, etc.) and automation equipment (automatic reclosing, standby switching on and others) [61].

Distributed Generation Sources
From the point of view of a modeling and reliability assessment, DG sources can be divided into two classes: • Sources based on conventional energy carriers, such as diesel oil, gas, biogas, etc., • Sources based on renewable energy carriers, such as wind, solar radiation, water, etc.
In the first case, the availability of the energy source for generation is highly probable. On the other hand, the availability of the renewable energy resources (second group) requires considering more appropriate probabilistic models [62].

Conventional Energy Sources
The conventional electric energy sources are:
Depending on the type of service, the aforementioned energy sources can be modeled as the following Markov chain: • Two-state model-in case of continuous service; determined by the failure rate λ and the repair rate µ, • Four-state model-in case of peak service; shown in Figure 1 Both the standby anticipation rate ρ and operation rate ν should be determined individually depending on the analyzed electric distribution system. The reliability parameters of engine-driven generators (EDG) and turbine-driven generators (TDG) can be found in Table 2. The values of parameters ν and ρ have been arbitrarily selected.
One can observe a much lower failure rate λ for generation units (both EDG and TDG) operating in peak service. This fact obviously results from less wear of individual components of a generation unit. Therefore, the possibility of failure is decreased. The TDG exhibit the lowest failure rates of units in peak service. Simultaneously, the lower repair rate is observed in comparison to other cases. It is attributable to a relatively small number of long-duration events.
In recent years, a new type of gas turbine, microturbine (MT), has become a fully developed technology. As MT's have only relatively recently been used as the commercial generation sources, there is not wide access to reliability data obtained from a long-time operation of this DG type. The same problem concerns the fuel cells (FC) as a relatively new technology in an industrial and commercial usage.  is a probability value of unsuccessful unit starting, ν is an operation rate, ρ is a sta failure rate and μ is a repair rate [63].
Both the standby anticipation rate ρ and operation rate ν should be de vidually depending on the analyzed electric distribution system. The relia ters of engine-driven generators (EDG) and turbine-driven generators (TDG in Table 2. The values of parameters ν and ρ have been arbitrarily selected. One can observe a much lower failure rate λ for generation units (both operating in peak service. This fact obviously results from less wear of indi nents of a generation unit. Therefore, the possibility of failure is decreased hibit the lowest failure rates of units in peak service. Simultaneously, the lo is observed in comparison to other cases. It is attributable to a relatively sm long-duration events. In recent years, a new type of gas turbine, microturbine (MT), has b developed technology. As MT's have only relatively recently been used as t generation sources, there is not wide access to reliability data obtained fro operation of this DG type. The same problem concerns the fuel cells (FC) new technology in an industrial and commercial usage.
As in case of EDG and TDG, MT and FC can be modeled using a two state Markov chain with the failure rate λ and repair rate μ as well as a Four-state reliability model of a conventional generation unit operating in peak service. P S is a probability value of unsuccessful unit starting, ν is an operation rate, ρ is a standby rate, λ is a failure rate and µ is a repair rate [63]. As in case of EDG and TDG, MT and FC can be modeled using a two-state or fourstate Markov chain with the failure rate λ and repair rate µ as well as a probability of unsuccessful DG unit starting P S . For the reliability calculation purpose λ, µ and P S have been obtained from the manufacturers data available only for peak service. The same values of parameters ν and ρ as for EDG and TDG have been assumed. All of these are presented in Table 3. The reliability parameters presented in Table 3 have been obtained based on the data given by different manufacturers (catalogues and brochures). It is necessary to treat these values a little distrustfully. These reliability parameters come from laboratory research, which cannot reflect the real conditions in an operating process.

Renewable Energy Sources
Among the most popular renewable energy sources in electric distribution systems, there are small hydro power plants (SHPP), small wind-turbine power plants (WTPP) and photovoltaic power plants (PVPP).
The parameters of different energy carriers (i.e., a river flow, wind speed and solar radiation) can be modeled as the homogenous Markov chain with the states representing different intervals of available energy and the transition rates between λ ij (transition rate from state i to state j). The general reliability model of a renewable generation system is shown in Figure 2.
given by different manufacturers (catalogues and brochures). It is necessar values a little distrustfully. These reliability parameters come from labora which cannot reflect the real conditions in an operating process.

Renewable Energy Sources
Among the most popular renewable energy sources in electric distrib there are small hydro power plants (SHPP), small wind-turbine power plan photovoltaic power plants (PVPP).
The parameters of different energy carriers (i.e., a river flow, wind sp radiation) can be modeled as the homogenous Markov chain with the state different intervals of available energy and the transition rates between λij ( from state i to state j). The general reliability model of a renewable genera shown in Figure 2. In order to represent the reliability of particular types of renewable e the authors of this paper have found an exemplary number of states, fractio apparent power corresponding to the state and values of the transition rate states [29,62,65]. All of these are presented in Tables 4-6. In order to represent the reliability of particular types of renewable energy sources, the authors of this paper have found an exemplary number of states, fraction of DG rated apparent power corresponding to the state and values of the transition rates between the states [29,62,65]. All of these are presented in Tables 4-6.   It is necessary to mention the values of fraction the DG rated apparent power given in Table 4. The state U.1 concerns a situation when a wind speed is less than the cut-in wind speed of a wind turbine and the power generation equals 0. No power generation is also in the state U.4. In this case, the wind speed is greater than the cut-out wind speed when a wind turbine is switched off.

Information and Communication Devices
To implement future smart grid functions, the information and communication technology (ICT) is needed. The ICT devices integrated in a power system collect, process and transfer data within the infrastructure. This requires robust communication channels to ensure reliable data flow. For that they use different sorts of communication media, such as Power Line Communication (PLC), Digital Subscriber Lines (xDSLs), fiber optics, IEEE 802.11 (WLAN), IEEE 802.16 (WiMAX), GSM/GPRS, IEEE 802.15.4 (Zigbee), depending on application, technical characteristics and feasibility [41,66]. Several types of devices are installed in integrated communication networks in smart grids, such as phasor measurement unit (PMU), remote terminal unit (RTU), programmable logic controller (PLC), gateway, router, modem, Digital Protective Relay (DPR), Digital Fault Recorder (DFR), PQ meter and smart meter. The types of these devices depend on their application and tasks such as measuring the electrical parameters, controlling the automation systems, transferring collected data and resaving control signals from the control center applications. The comparison of ICT devices, protocols and typical functions in power system is given in Table 7. Communication network equipment can fail causing interruptions in data transfer, information exchange and other corresponding services. Both hardware and software can be affected for various reasons, impacting the reliability of the communication network. The reliability parameters like mean time between failure (MTBF) and mean time to repair (MTTR) for chosen devices: phasor measurement unit (PMU), remote terminal unit (RTU), programmable logic controller (PLC), gateway and router are given in Table 8. These values are calculated based on literature research on simulation models, laboratory tests and vendors' data presented in [70][71][72].

Interdependencies Modeling of Coupled Electric Power System and ICT Infrastructures
With the rise of smart grid technologies, the interdependencies of communication technologies and electric power systems become an important aspect in the development of both networks [73]. Modeling such interdependencies will be even more complex in the planning and future operation of multi-energy systems (MES) integrating various energy converters and sources of different physical nature [74].
Infrastructures interdependencies are based on physical and functional relationships among individual components both within and between systems. To characterize the effects of failure propagation from the single component or system to mutually dependent interconnected systems the structure modeling of complex infrastructures can be used [75]. The individual operating conditions of the component in the system can be analyzed and the fault propagation can be reduced by having fast recognition of threats, redundancy design and alternative modes of operation [76]. The concept of complex networks theory [77], which is based on the graph theory, can be used to describe and analyze critical infrastructures on a large scale with multifaceted topologies [78]. The interdependency modeling techniques of coupled infrastructures for integrating ICT within the electric power system (EPS) are offered in [33,34].
A graph can represent a network with its set of components and connections between them. Applying graph representation to the coupled EPS and ICT infrastructures, the vertices indicate system components such as buses, gateways and routers while edges correspond to the power lines, cables and communication links. In order to characterize the interdependencies between the infrastructures they can be classified as follows:

•
Connection of an electric node with another electric node, which characterize typical power flow in the electric power grid; • Connection of a communication node with another communication node that corresponds to a data flow; • Connection of an electric node to a communication node that represents an electricity supply for the ICT infrastructure; • Connection of a communication node to an electric node which is responsible for sending and requesting information to and from the power system component.

Tool for Reliability Analysis
The reliability assessment in electric power distribution systems has been carried out with the use of DIgSILENT PowerFactory software (PF). This software enables an assessment of different reliability indices for power systems in a generation area (hierarchical level HL I) as well as in transmission and distribution system (hierarchical levels HL II and HLIII adequately).
The procedure of a reliability assessment in PF is shown in Figure 3, according to [51].
Energies 2022, 15, x FOR PEER REVIEW Figure 3. Flow diagram of the reliability assessment in PF software.
The first step is modeling an electric power network structure wher quirements are met (no overloading, acceptable voltage deviations, etc.). Fo work components, the failure models are defined by giving a description o ate probability distributions.
The next stage of the reliability assessment is to generate a list of syst vant with the failure models and load models. In other words, it is a comb or more simultaneous faults and a specific load condition. For each syste defined power system reactions are analyzed such as: Finally, the system state generation combined with the failure effect an the calculation of statistic indices. The detailed description of the used algor be found in [79].

Assumptions and Limitations
The urban and rural structures of present electric distribution network with distributed generation have been investigated. Different structures o bution networks with embedded generation have been also analyzed, such The first step is modeling an electric power network structure where technical requirements are met (no overloading, acceptable voltage deviations, etc.). For all main network components, the failure models are defined by giving a description of the appropriate probability distributions.
The next stage of the reliability assessment is to generate a list of system states relevant with the failure models and load models. In other words, it is a combination of one or more simultaneous faults and a specific load condition. For each system state, some defined power system reactions are analyzed such as: Finally, the system state generation combined with the failure effect analysis updates the calculation of statistic indices. The detailed description of the used algorithm in PF can be found in [79].

Assumptions and Limitations
The urban and rural structures of present electric distribution networks (UDN, RDN) with distributed generation have been investigated. Different structures of future distribution networks with embedded generation have been also analyzed, such as: active managed MV distribution network (AMDN) and MV distribution network with connected LV microgrids (DNMG). The diagrams and parameters of all the basic structures (as a starting point of analysis) are shown in detail in Appendices A-D.
In Poland any part of the electric distribution system (both MV and LV network) controlled by distribution system operators cannot operate in islanded mode. The autonomous operation is admitted only for power networks and installations belonging to a consumer. For that restriction, the islanded operation of UDN and RDN is not admitted.
In the loop structures, i.e., UDN and DNMG, the ASS as well as the APR have been considered in the reliability assessment. All the MV distribution system models do not take into consideration a possibility of power supply reserve (e.g., with the use of ASS) on the level of LV distribution network For all investigated DG sources, the reliability models described in Section 3.2 have been assumed. The reliability models of the energy storages (chemical battery and flywheel) have been not considered in this analysis.

Results of Test Calculations
Before the reliability indices have been calculated, the load flow analysis had been carried out for all investigated distribution network structures. Branch overloading and the excess of permissible voltage deviation in nodes has not been observed. All the calculated system reliability indices for all considered present and future distribution networks are presented in Tables 9-12.  Three variants of DG unit location are considered. Based on UDN_1 variant as a basic UDN structure (see Figure A1), a node including the PVPP and BES connected changes There are also three variants of DG unit location to be considered. Based on RDN_1 variant as a basic RDN structure (see Figure A3), a node the WTPP and BES are connected to changes from no. 72 to no. 43 (RDN_2) and no. 71 (RDN_3). In each variant, three cases of different power generation levels of the considered WTPP and BES are analyzed, i.e., Case_1-2.4 MW, Case_2-1.6 MW and Case_3-0.8 MW. The other DG sources do not change the location in all variants and the power generation values in all cases.
Three variants of MG location are considered. Based on DNMG_1 variant as a basic DNMG structure (see Figure A4), a MG is connected to changes from no. 6 to no. 3 (DNMG_2) and no. 1 (DNMG_3). In the second variant (DNMG_2) a load equivalent is shifted from node no. 3 to node no. 6. In the third variant (DNMG_3) an additional load equivalent is connected to node no. 6 (P = 100 kW, Q = 20 kvar). In each variant the change of only one of two microsources in considered MG is analyzed in three cases: Case_1-WTPP (170 kW); MT (30 kW), Case_2-WTPP (170 kW); FC (30 kW), Case_3-WTPP (170 kW); PVPP (30 kW). In all the cases reactive power generated in microsources is equal to 0 kvar.
Three variants of DG unit location are considered. Based on AMDN_1 variant as a basic AMDN structure (see Figure A5), a node the DG unit is connected to changes from no. 4 to no. 2 (AMDN_2) and no. 1 (AMDN_3). In each variant, five cases of different types of the considered DG unit are analyzed, i.e., Case_1-WTPP, Case_2-PVPP, Case_3-EDG, Case_4-TDG, Case_5-SHPP. The change of power generation level of the DG unit is not considered.
For AMDN_1 variant an impact of automatic on-load tap changer at the 110 kV/MV transformer on the maximum active and reactive power generated by a DG unit has been analyzed as well. The branch power capacity and permissible voltage deviation (±10%) was the criterion used to determine the maximum power generation. The first investigated case assumes the peak load and 110 kV/MV transformer operation without on-load tap changer. Maximum values of active and reactive power generated by the DG source are P = 14.3 MW and Q = 4.3 Mvar adequately at +10% voltage deviation. In the second case (peak-off load and transformer operation without on-load tap changer) the DG unit can generate only P = 1.8 MW and Q = 0.54 Mvar. The last case assumes the automatic on-load tap changer at the transformer as well as the peak-off load, the DG source can generate the power up to the cable load capacity (the line between nodes no. 3 and 4).

Observations
Based on the test calculation results the following observations have been made:

•
Looking at the reliability indices calculated for UDN and RDN one can certainly state that location and type of DG source does not directly affect the power supply reliability. The APR application in UDN definitely improves all the investigated reliability indices, i.e., SAIFI, CAIFI, SAIDI, CAIDI, EENS, ASAI, ASUI). • Three considered variants of DG source location in AMDN have been compared. Looking at ASAI index, the highest value is for "AMDN_1" and the lowest one is for "AMDN_2". There is also an impact of DG types on both the interruption frequency and interruption duration. • An impact of DG type on reliability indices is also noticeable for DNMG. For all considered DNMG variants, the lowest ASAI value is observed in "Case_3" with WTPP and PVPP connected to a microgrid. Analyzing three variants of microgrid locations, the highest ASAI value is observed for "DNMG_1". In addition, "DNMG_3" characterizes the lowest value of ASAI index. • Both the interruption frequency (SAIFI, CAIFI) and interruption duration (SAIDI, CAIDI) for UDN are lower than for RDN.

• The interruption frequency (SAIFI, CAIFI) calculated for RDN is about tenfold higher than for AMDN with DG unit connected (except the variant AMDN_3 in which the ratio is about four). An interesting observation about interruption durations is made.
The values of CAIDI index are almost comparable to one another, but the SAIDI for AMDN is over twelvefold lower than for RDN structure. This observation shows the strongly irregular distribution of the repair duration in the analyzed AMDN structure. • DNMG with connected LV microgrids does not significantly improve the power supply reliability in comparison to UDN with APR.

Model Structure
A simple distribution system structure was created to analyze the reliability assessment of an electric power network coupled with a communications network [80,81], see Figure A6 in Appendix E. Integrated communication allows for monitoring all nodes in the network, and thus faster detection of the location of failures in the power network and taking corrective actions. The component aging is disregarded and only the constant failure rate related to their useful life is analyzed. Since failures in the power system usually occur randomly, the sequential Monte Carlo method was employed to simulate and assess a smart grid's reliability over time. The method produces a distribution of possible outcomes rather than a single expected value.
The artificial operating/failure histories of the relevant smart grid elements are generated. The period during which the element is operating is called time to failure (TTF). The period during which the element fails is called time to repair (TTR).
The parameters TTF, TTR constitute random variables and may have different probability distributions. Exponential distribution is used here to assess the reliability of both the electric power distribution system and the communications network. The exponential distribution's probability distribution function is described as follows [80,82]: The method for generating an artificial failure history of a component is presented in Figure 4. Each time interval is computed with different random numbers. This simulates contingencies occurring in a real system realistically. • Both the interruption frequency (SAIFI, CAIFI) and interruption duration (SAIDI, CAIDI) for UDN are lower than for RDN.

•
The interruption frequency (SAIFI, CAIFI) calculated for RDN is about tenfold higher than for AMDN with DG unit connected (except the variant AMDN_3 in which the ratio is about four). An interesting observation about interruption durations is made. The values of CAIDI index are almost comparable to one another, but the SAIDI for AMDN is over twelvefold lower than for RDN structure. This observation shows the strongly irregular distribution of the repair duration in the analyzed AMDN structure. • DNMG with connected LV microgrids does not significantly improve the power supply reliability in comparison to UDN with APR.

Model Structure
A simple distribution system structure was created to analyze the reliability assessment of an electric power network coupled with a communications network [80,81], see Figure A6 in Appendix E. Integrated communication allows for monitoring all nodes in the network, and thus faster detection of the location of failures in the power network and taking corrective actions. The component aging is disregarded and only the constant failure rate related to their useful life is analyzed. Since failures in the power system usually occur randomly, the sequential Monte Carlo method was employed to simulate and assess a smart grid's reliability over time. The method produces a distribution of possible outcomes rather than a single expected value.
The artificial operating/failure histories of the relevant smart grid elements are generated. The period during which the element is operating is called time to failure (TTF). The period during which the element fails is called time to repair (TTR).
The parameters TTF, TTR constitute random variables and may have different probability distributions. Exponential distribution is used here to assess the reliability of both the electric power distribution system and the communications network. The exponential distribution's probability distribution function is described as follows [80,82]: The method for generating an artificial failure history of a component is presented in Figure 4. Each time interval is computed with different random numbers. This simulates contingencies occurring in a real system realistically. TTF and TTR are calculated for a given failure rate and repair rate from Table 13   TTF and TTR are calculated for a given failure rate and repair rate from Table 13 with the formulas [83]: where u i , u j are random numbers uniformly distributed in the range of 0-1 and λ and µ are the failure rate and the repair rate, respectively. The communications infrastructure in smart grid supplies additional information on power system states, thus improving overall network performance. It enables faster detection of and response to failures or even prevents their occurrence. Accessing information faster facilitates earlier dispatching of service teams or faster responses by different system operators to potential imbalances in power systems, for instance.
By extension, communications shorten interruption times. This method, thus, entails shortening interruption times by shortening the time to repair for combined system. The shorter time to repair is denoted as TTR SG (see Figure 5) and simulated. Since communications are assumed to improve distribution system reliability, their absence or failure do not diminish an electric power system's (EPS) performance, as shown on the right in Figure 5. where ui, uj are random numbers uniformly distributed in the range of 0-1 and λ and μ are the failure rate and the repair rate, respectively. The communications infrastructure in smart grid supplies additional information on power system states, thus improving overall network performance. It enables faster detection of and response to failures or even prevents their occurrence. Accessing information faster facilitates earlier dispatching of service teams or faster responses by different system operators to potential imbalances in power systems, for instance.
By extension, communications shorten interruption times. This method, thus, entails shortening interruption times by shortening the time to repair for combined system. The shorter time to repair is denoted as TTRSG (see Figure 5) and simulated. Since communications are assumed to improve distribution system reliability, their absence or failure do not diminish an electric power system's (EPS) performance, as shown on the right in

The Algorithm Used
The reliability simulations are based on the time sequential Monte Carlo technique. This method has been adapted into the proposed approach of Smart Grid reliability assessment. The algorithm used to compute reliability indices of electric power distribution systems (EPS), communications networks (ICT) and integrated Smart Grid (SG) system is presented in a block diagram in Figure 6.

The Algorithm Used
The reliability simulations are based on the time sequential Monte Carlo technique. This method has been adapted into the proposed approach of Smart Grid reliability assessment. The algorithm used to compute reliability indices of electric power distribution systems (EPS), communications networks (ICT) and integrated Smart Grid (SG) system is presented in a block diagram in Figure 6.
The program starts with definition of system input data such as network topology with location of the components, failure and repair rates and connected loads. The number of sample years (N) and simulation period (T) are also entered in this step. The simulation begins with generating random numbers [0,1] for each element in the system and converting them into time to failure (TTF) using equation 4. In the next step, the element with the shortest TTF is determined, i.e., the component that will fail first. In the conditional block, it is then checked to see if the found minimal TTF value matches within one year. If this is not a case, it means that the TTF is longer than 8760 h and within this year no failure occurs. Further steps will be skipped and random numbers of TTF are computed again for all elements. If the TTF is shorter than 8760 h, the time to repair (TTR) will be computed for that element which indicates its out of operation state duration. Moreover, its location in the interconnection matrix as well as the location of any load nodes which can be influenced by the given component is also determined. After that, a new random number is generated for that component and converted into new TTF. Simulation time has to be updated for each element according to Equation (11). The updated TTF value indicates subsequent time of failure occurrence and is compared with previously generated TTFs of other components. After that, the TTR for other elements can be computed. These procedures are repeated in a loop for each element until the simulation period (e.g., one year) is completed and all of the simulation sequences comprising the defined number of years are finished. Then, the reliability parameters of each component, such as failure and repair rate as well as unavailability, are computed. Finally, based on these parameters, the reliability indices for the whole system are calculated for the total sample number of years (N).
The program starts with definition of system input data such as network with location of the components, failure and repair rates and connected loads. T ber of sample years (N) and simulation period (T) are also entered in this step. T Figure 6. Sequential Monte Carlo algorithm [81,82].

Simulation Results
The simulations of an integrated smart grid system were run with the structure illustrated in Figure A6. In the simulations, component failures and the existence of communication were considered, and generation parameters were omitted. In order to calculate the relevant reliability indicators, the number of customers has been taken into account.
Simulations of N = 100 years with the step-in sequence of one year (8760 h) with the resolution of one hour were run using the input data presented in Table 13. Faster responses to failures, shorten the time to repair for the smart grid. The results of reliability parameters obtained with time sequential simulation are strongly influenced from the failure, repair rates and system structure. The distribution of reliability indices significantly depends on the number of simulated years.
Simulation results are presented in Table 14 and Figure 7. The average system indices show that the electric power system with a communications infrastructure is more reliable. The presence of ICT shortens interruption times, represented by the SAIDI index.  The CAIDI index representing the average interruption duration is significantly smaller in electric power systems with ICT than in systems without communications. This is due to the shorter break times.

Conclusions
Electrical component failures in distribution systems have been proven the cause of the majority of power interruptions in electric power system.
The number, location, and type of DG sources in existing (conventional) companyowned distribution networks that may not operate in islanded mode have no direct impact on reliability indices. However, a DG unit connection to a distribution network may cause a load alleviation in lines, transformers, etc. and this phenomenon varies the form of the risk function of power system components. The DG sources connected to a distribution network indirectly improves electric service reliability for consumers. DG units may increase voltage in busbars and terminals and short-circuit currents in a distribution system.
Power supply is chiefly improved by providing power redundancy and using remote control switches with distribution system automation, such as ASS, APR and AR (automatic reclosing). The reliability calculations corroborate this. Power interruption frequency and power interruption duration are lower in urban looped distribution networks than in rural distribution networks with feeders supplied from one point. The continued growth of DG capacity in distribution systems requires research and development of new (future) distribution network structures, e.g., actively managed networks (smart grids), microgrids, clustered networks, etc. All of these networks are assumed to be capable of operating autonomously (i.e., islanded and unconnected to the main grid) and to be equipped with distribution system automation (e.g., ASS, APR and AR).
The calculations confirm that the future distribution network structures have higher electrical service reliability than existing distribution networks. Future distribution systems have lower interruption frequencies and durations.
Actively managed distribution networks appear to be a promising idea [84]. Assuming the voltage limitation on network busbars and terminals, the impact of the active on-load tap changer in the 110 kV/MV transformer on the maximum active and reactive power generated by a DG source has been analyzed. This study has demonstrated that the automatic voltage regulator (AVR) at the transformer allows the increase of installed capacity of DG unit connected to the distribution network.
Considering the impact of DG type and locations in future electric distribution networks on the power supply reliability, the results of reliability assessment allow the formulation of the following remarks: • Power supply continuity is higher when DG sources are based on conventional fuels (gas, diesel oil, etc.). The installation of renewable DG units (energy carriers that are hard to forecast) delivers worse results. • Types of microsources in distribution networks with connected LV microgrids affect the reliability indices. This is noticeable in installed microsources based on energy carriers dependent on weather conditions. • The location of DG sources in distribution systems also affects electrical service reliability. The most favorable reliability indices are obtained when the potential maximum number of energy consumers are double-feed (loop: transformer substation-DG unit).
In case of aggregation of supplying sources at the one network busbar or terminal, worse reliability indices are observed.

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The appropriate level of DG power generation is a significant issue. The DG power available ensures peak loads are covered. The level of power generation is often limited by branch power capacity and maximum allowable voltage deviation. Active voltage regulation in power transformers can resolve voltage level problems.
The authors intend to focus on optimizing future distribution system structures and devising an optimal development strategy for existing distribution networks in future studies. This will require the determining of accurate reliability models of electric power equipment, protection and automation systems, DG sources and energy storage systems in different types of network structures.
The use of information and communications technology to monitor, control and protect power systems is an important way to meet the challenges of continuously developing electric power grids. The installation of measurement sensors, automated control systems and communication devices will increase the complexity of such integrated systems, thus requiring new methods for designing and optimal integrating of advanced communications systems in electric power grids.
A reliability assessment of smart grids consisting of an electric power distribution system and an integrated communications network based on Monte Carlo simulation was developed and tested in this study. The simulation algorithm delivers the distributions and average values of reliability indices for smart grids, electric power systems and communications networks. This enabled analyzing the influence of the coexistent ICT infrastructure on the power distribution system's reliability and, thus, the entire smart grid. Although some assumptions were made in the methodology to model the systems, the algorithm developed delivers valuable results for the assessment of reliability when designing and optimizing systems. Widespread use of a reliable information and communications infrastructure will improve smart grids' functionality and reliability.
Since this study concentrates on the monitoring of smart grids with advanced ICT, future studies ought to analyze their control and protection. Applying reliable control and protection schemes to the system will help minimize outages and their impact on overall system operation. Future studies ought to examine more complex models of ICT network operation, including several levels of communication performance, e.g., full communication of all components, full communication of all components with limited quality of service (QoS) and limited communication.

Data Availability Statement: Not applicable.
Acknowledgments: Three of four test MV distribution power network structures used in this paper has been developed under the research project "National Electrical Power Security" supported by the Polish Ministry of Education and Science. Similarly, reliability calculations in the test networks have been carried out under the research project. The smart grid reliability research was carried out within the SECVER project supported by the Federal Ministry of Economic Affairs and Energy (BMWi) in Germany.

Conflicts of Interest:
The authors declare no conflict of interest.

Abbreviation
The following abbreviations are used in this manuscript:     -GTPP Types of energy consumers: R&PU-residential and public utility, IP-industrial (park), ET-electric traction substation. The nodes the DG sources are connected to are marked as gray background. Figure A2. Typical daily load profile (15-min intervals) for residential consumers (a line with the triangles) as well as industrial parks and electric traction substation (a line with the quadrants); based on [85].   XUHAKXS-single-Al core cable, radial field, polythene-coated, polythene sheath, YHAKXS-single-Al core cable, radial field, polythene-coated, polyvinyl chloride sheath, HAKnFty-triple-Al core cable, radial field, paper-coated, steel armor, polyvinyl chloride sheath.