A Fuzzy Energy Management Strategy for the Coordination of Electric Vehicle Charging in Low Voltage Distribution Grids

: Electric vehicles (EVs) have become widespread during the last decade because of the distinct advantages they o ﬀ er compared to the conventional ones. However, the increased penetration of EVs in the global transportation market has led increased electricity demands, which is expected to a ﬀ ect the operation of energy distribution systems. In the present paper, a demonstration about the e ﬀ ects of uncontrolled EVs charging in a case study low voltage (LV) network is demonstrated and a fuzzy energy management strategy for the coordination of EV charging in LV networks is presented, by including the distance of the EVs from the transformers in the fuzzy management systems for the ﬁrst time. The Institute of Electrical and Electronics Engineers (IEEE) European Test Feeder is used as a case study low voltage distribution grid. In particular, the developed system conﬁguration takes into consideration the architecture of the grid, the ampacities of the lines and the voltages at the system’s buses. Moreover, electric vehicles are considered as agent-based models, which are characterized by the model of each EV, the state-of-charge of their batteries and the charging power. In particular, an investigation into the e ﬀ ects of uncontrolled charging is performed, in which two approaches are examined. The ﬁrst approach investigates the maximum number of chargeable EVs in the case study network and how it is inﬂuenced by the grid’s household loads. The second approach examines the number of network undervoltages and lines ampacity violations in a set of simulation scenarios. The results of the ﬁrst approach show that the distance of the EVs from the networks substation a ﬀ ects the maximum number of chargeable EVs in a signiﬁcant manner. Based on the observed results of the two approaches, a fuzzy management system is designed for the coordination of EV changing, which takes into account the distance from the EV charging points to the feeder substation, the state-of-charge of the EVs’ batteries and the EVs’ charging delay time.


Introduction
The world's transportation and electric power generation sectors are the major consumers of fossil fuels, resulting in high carbon dioxide emissions and an energy supply crisis [1]. The wide use of electric vehicles (EVs), as an alternative transportation technology, is expected to mitigate undesirable environmental air pollution and reduce the strong dependence of the transportation sector on oil as management system was developed for the coordination of EV charging, with respect to the grid's constraints. The proposed fuzzy-based controller considers the SoC of each EV, the distance of each EV from the substation and the charging delay time, in order to determine the priority of each EV in the charging process. To the best of the authors' knowledge, this is the first time that the distance of the EVs from the network's substation is used as a variable in a fuzzy controller for the coordination of the charging process in LV networks. The results of the examined simulation scenarios showed that the consideration of the distance may decreases the mean EV charging time. Moreover, an integrated framework for the modelling and simulation of EVs and distribution grids in a common environment is presented, by using the MATLAB ® Environment, (MathWorks, Natick, MA, USA) and the OpenDSS (EPRI, Palo Alto, CA, USA).
The rest of the paper is organized as follows: in Section 2, the case study distribution grid, the modelling of the EVs and the overall simulations framework is presented, along with a short introduction to fuzzy systems. In Section 3, the investigation on the effects of uncontrolled charging process in the case study LV system is presented. Section 4 describes the design and simulations study of the fuzzy energy management system for the coordination of EV charging in energy distribution networks. The paper concludes with Section 5, wherein the key points of the investigation are summarized and the basic structure of the proposed charging strategy is referred and discussed, along with some directions of future research work.

System Topology
The selected system is a modification of the IEEE European Low Voltage Test Feeder, which formulated to consider EV charging points. This network represents a typical European distribution system (three-phase low-voltage feeder) with a base frequency of 50 Hz. The network starts from an 800 kVA delta-wye transformer, which steps down the voltage from 11 kV to 416 V, with a power factor (PFload) equal to 0.95, by using a total three phase network of 907 lines and 903 buses, in which 55 are load buses and 848 buses are used to connect the feeder's lines across the network. The network feeds 55 single phase residential loads ( Figure 1). The connected loads in each system's phase are: (i) 21 loads in phase A, (ii) 19 loads in phase B, (iii) 15 loads in phase C. The entire required feeder's data are available in model's online dataset [40]. The single-phase diagram of the feeder and the location of each residential load in the network are presented in Figure 1. The distances of each load from the grid's substation are presented in Figure 2.   The dataset of the IEEE European Low Voltage Test Feeder includes typical daily power curves for each network's residential load [40]. The transformer's load curve is depicted in Figure 3. The consumed power for each system's phase is shown in Figure 4, while Table 1 presents the total peak load and the average daily energy consumption for the transformer and for each phase, separately.  7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 Distance (km) Load index The dataset of the IEEE European Low Voltage Test Feeder includes typical daily power curves for each network's residential load [40]. The transformer's load curve is depicted in Figure 3. The consumed power for each system's phase is shown in Figure 4, while Table 1 presents the total peak load and the average daily energy consumption for the transformer and for each phase, separately. The dataset of the IEEE European Low Voltage Test Feeder includes typical daily power curves for each network's residential load [40]. The transformer's load curve is depicted in Figure 3. The consumed power for each system's phase is shown in Figure 4, while Table 1 presents the total peak load and the average daily energy consumption for the transformer and for each phase, separately.  7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 Distance (km) Load index   The selected network was reformulated since no electric vehicles were considered originally. Hence, it is now considered that each house has also an electric vehicle, which connects to the distribution grid, by battery chargers. Therefore, a fixed number of 55 charging points are considered to the network. A schematic representation of the overall system configuration is illustrated in Figure  5. The model consists of the following components: (a) the radial low voltage network, (b) the distributed household loads, and (c) the electric vehicles and battery chargers.  The selected network was reformulated since no electric vehicles were considered originally. Hence, it is now considered that each house has also an electric vehicle, which connects to the distribution grid, by battery chargers. Therefore, a fixed number of 55 charging points are considered to the network. A schematic representation of the overall system configuration is illustrated in Figure 5. The model consists of the following components: (a) the radial low voltage network, (b) the distributed household loads, and (c) the electric vehicles and battery chargers.

Technical Constraints for Grid Distribution System Operation
All electric households' needs ought to be covered at 100% throughout the day. Therefore, the system must cover specific technical constraints, in order to ensure the grid's stability and safe operation and performance.
The voltage constraints of the distribution system will be considered by setting the upper and lower limits to correspond to voltage regulation limits. The voltage limits are set to ±5% (Vmin = 0.95 pu and Vmax = 1.05 pu) which is typical of many distribution systems. Thus, the following constraint must be considered for the voltage for each phase: m in m ax fo r 1, ..., n .
where k and n are the bus number and total number of buses, respectively. The second constraint is for setting the upper limit of the ampacity. Taking into consideration the necessary data obtained by [41], the types of each line of feeder are presented in Figure 6 and the upper limit of grid's lines ampacities are presented in Table 2. Thus, the following constraint must be considered for the ampacity for each phase: m a x f o r 1, ..., n .
where k and n are the line number and total number of lines, respectively. The transformer's rated power is not taken into consideration in the present work, since the consumed power does not exceed the operational limits in any of the examined simulation scenarios.

Technical Constraints for Grid Distribution System Operation
All electric households' needs ought to be covered at 100% throughout the day. Therefore, the system must cover specific technical constraints, in order to ensure the grid's stability and safe operation and performance.
The voltage constraints of the distribution system will be considered by setting the upper and lower limits to correspond to voltage regulation limits. The voltage limits are set to ±5% (V min = 0.95 pu and V max = 1.05 pu) which is typical of many distribution systems. Thus, the following constraint must be considered for the voltage for each phase: where k and n are the bus number and total number of buses, respectively. The second constraint is for setting the upper limit of the ampacity. Taking into consideration the necessary data obtained by [41], the types of each line of feeder are presented in Figure 6 and the upper limit of grid's lines ampacities are presented in Table 2. Thus, the following constraint must be considered for the ampacity for each phase: where k and n are the line number and total number of lines, respectively. The transformer's rated power is not taken into consideration in the present work, since the consumed power does not exceed the operational limits in any of the examined simulation scenarios.    Table 2.

Electric Vehicle Agent
The electric vehicles are represented by agents. The structure of EV agents is shown in Figure 7. EV agents are defined by their attributes and their behavior.
The attributes of the agents are: • The EV's model, which defines the capacity of its battery and the energy consumption per km • The EV's index, which declares the location of its charging point to the grid • The EV's battery state-of-charge (SoC) • The EV's state, which defines if the vehicle takes a trip, is connected to grid and charging, or is parked • The EV's charging signal, which declares if the vehicle will charge at a given time interval and it is produced by the charging management algorithm The behavior of each EV includes the charging and mobility procedures. When a specific EV, say n, is charged, its SoC of each vehicle's battery increases, based on Equation (3) [42]: where, Q n and I ch are the total capacity and the charging current at each interval time of the each EV, respectively.
Energies 2020, 13, 3709 9 of 34 EV agent's mobility behavior, when EVs are not parked or connected to the charging points, is calculated based on the average energy consumption per km of each EV's model and the distance travelled. When an EV takes a trip, the SoC at each time step is calculated by Equation (4): where, ECPK is the energy consumption per km, E max,n is the rated battery's energy capacity of the EV and l is the distance travelled at each time step.
Energies 2020, 13, x FOR PEER REVIEW 9 of 34 EV agent's mobility behavior, when EVs are not parked or connected to the charging points, is calculated based on the average energy consumption per km of each EV's model and the distance travelled. When an EV takes a trip, the SoC at each time step is calculated by Equation (4): where, ECPK is the energy consumption per km, Emax,n is the rated battery's energy capacity of the EV and l is the distance travelled at each time step. In the present paper, five different commercial EVs are used for the simulation purposes. The models and their basic technical characteristics are presented in Table 3 [43,44]. As mentioned by the EV manufacturers, the SoC of their batteries is limited between 20-80%. The charging of the upper 10-20% SoC window leads to increased batteries degradation [45]. This concept is also considered in the present study.
In addition, it is assumed that a battery charger has been installed in each house. The EV battery charger must have the ability to charge the battery of each EV. According to the battery sizes of Table  3, the EV battery capacities range from just over 30 kWh (33 kWh, BMW i3) to over 70 kWh (75 kWh, Tesla Model S-75). Taking into consideration the power ability of the grid and with emphasis given on the EV battery life optimization (depth of discharge equal to 60%), a typical battery charger is considered with available rated power of 7.4 kW, AC current of 32 A and efficiency (η) of 88 % [45,46].
A typical daily behavior of each EV is depicted in Figure 8, according to the above-mentioned charging (Equation (3)) and discharging (Equation (4)) principles. The same trip has been considered for all the examined EVs. Specifically, the total distance travelled by the EVs is 100 km; 70 km between 7:00 h and 13:00 h, and 30 km between 16:00 h and 19:00 h. According to the Table 3, the Nissan Leaf has the lowest battery capacity and the second greater ECPK. The combination of these variables leads to a faster reduction of the SoC, compared to the other examined EV models, and this is observed in Figure 8. In the present paper, five different commercial EVs are used for the simulation purposes. The models and their basic technical characteristics are presented in Table 3 [43,44]. As mentioned by the EV manufacturers, the SoC of their batteries is limited between 20-80%. The charging of the upper 10-20% SoC window leads to increased batteries degradation [45]. This concept is also considered in the present study.
In addition, it is assumed that a battery charger has been installed in each house. The EV battery charger must have the ability to charge the battery of each EV. According to the battery sizes of Table 3, the EV battery capacities range from just over 30 kWh (33 kWh, BMW i3) to over 70 kWh (75 kWh, Tesla Model S-75). Taking into consideration the power ability of the grid and with emphasis given on the EV battery life optimization (depth of discharge equal to 60%), a typical battery charger is considered with available rated power of 7.4 kW, AC current of 32 A and efficiency (η) of 88 % [45,46].
A typical daily behavior of each EV is depicted in Figure 8, according to the above-mentioned charging (Equation (3)) and discharging (Equation (4)) principles. The same trip has been considered for all the examined EVs. Specifically, the total distance travelled by the EVs is 100 km; 70 km between 7:00 h and 13:00 h, and 30 km between 16:00 h and 19:00 h. According to the Table 3, the Nissan Leaf has the lowest battery capacity and the second greater ECPK. The combination of these variables leads to a faster reduction of the SoC, compared to the other examined EV models, and this is observed in Figure 8.

Fuzzy Logic Based Controllers
Fuzzy logic is a mathematical framework which is widely used in many control applications, by extending binary logic sets to a more general fuzzy ones, in which, the elements of the sets partially exist [47].
In complex control systems, the definition of the controllers' precise objectives, based on traditional control methods, is a difficult process. The coordination of EV charging in distribution networks is one of them. The logic of fuzzy-based controllers overcomes the existing drawbacks. The architecture of a typical fuzzy based controller is presented in Figure 9.

Fuzzy Logic Based Controllers
Fuzzy logic is a mathematical framework which is widely used in many control applications, by extending binary logic sets to a more general fuzzy ones, in which, the elements of the sets partially exist [47].
In complex control systems, the definition of the controllers' precise objectives, based on traditional control methods, is a difficult process. The coordination of EV charging in distribution networks is one of them. The logic of fuzzy-based controllers overcomes the existing drawbacks. The architecture of a typical fuzzy based controller is presented in Figure 9.
The fuzzification of the fuzzy controller includes the conversation of the controller's crisp input values into a set of fuzzy linguistic values, by using membership functions. The most widely used membership functions for the fuzzification of the controller's input set are the Gaussian, triangular, and trapezoidal ones. The produced linguistic values are read by the fuzzy interface system (FIS), which is the core of the Fuzzy Logic Controller (FLC). The FIS, based on the stored knowledge of the controlled procedure, maps the linguistic inputs to the output linguistic outputs, by performing approximate reasoning. The output of the FIS is driven to the defuzzifier, which converts the gathered from the FIS fizzy values into crisp output values. The conversation of the fuzzy linguistic output values into crisp values is also based on the output membership functions, such as the inputs [48]. The fuzzification of the fuzzy controller includes the conversation of the controller's crisp input values into a set of fuzzy linguistic values, by using membership functions. The most widely used membership functions for the fuzzification of the controller's input set are the Gaussian, triangular, and trapezoidal ones. The produced linguistic values are read by the fuzzy interface system (FIS), which is the core of the Fuzzy Logic Controller (FLC). The FIS, based on the stored knowledge of the controlled procedure, maps the linguistic inputs to the output linguistic outputs, by performing approximate reasoning. The output of the FIS is driven to the defuzzifier, which converts the gathered from the FIS fizzy values into crisp output values. The conversation of the fuzzy linguistic output values into crisp values is also based on the output membership functions, such as the inputs [48].

Modelling and Simulation Framework
The environment of the low voltage grid was modelled and implemented by using the OpenDSS, an electric power distribution system simulator (DSS), which is designed for supporting distributed resource integration and grid modernization efforts, and used for the power flow calculations of the low voltage network [49,50]. MATLAB ® software environment was used for the design, modelling and simulation of EV agents. Thus, the OpenDSS COM Interface (EPRI, Palo Alto, CA, USA)was used for the connection of the OpenDSS and the MATLAB ® routines. In addition, Matlab was used for the development of the FIS for the centralized control of EVs charging behavior. The structure of the total framework is presented in Figure 10.

Modelling and Simulation Framework
The environment of the low voltage grid was modelled and implemented by using the OpenDSS, an electric power distribution system simulator (DSS), which is designed for supporting distributed resource integration and grid modernization efforts, and used for the power flow calculations of the low voltage network [49,50]. MATLAB ® software environment was used for the design, modelling and simulation of EV agents. Thus, the OpenDSS COM Interface (EPRI, Palo Alto, CA, USA) was used for the connection of the OpenDSS and the MATLAB ® routines. In addition, Matlab was used for the development of the FIS for the centralized control of EVs charging behavior. The structure of the total framework is presented in Figure 10. The fuzzification of the fuzzy controller includes the conversation of the controller's crisp input values into a set of fuzzy linguistic values, by using membership functions. The most widely used membership functions for the fuzzification of the controller's input set are the Gaussian, triangular, and trapezoidal ones. The produced linguistic values are read by the fuzzy interface system (FIS), which is the core of the Fuzzy Logic Controller (FLC). The FIS, based on the stored knowledge of the controlled procedure, maps the linguistic inputs to the output linguistic outputs, by performing approximate reasoning. The output of the FIS is driven to the defuzzifier, which converts the gathered from the FIS fizzy values into crisp output values. The conversation of the fuzzy linguistic output values into crisp values is also based on the output membership functions, such as the inputs [48].

Modelling and Simulation Framework
The environment of the low voltage grid was modelled and implemented by using the OpenDSS, an electric power distribution system simulator (DSS), which is designed for supporting distributed resource integration and grid modernization efforts, and used for the power flow calculations of the low voltage network [49,50]. MATLAB ® software environment was used for the design, modelling and simulation of EV agents. Thus, the OpenDSS COM Interface (EPRI, Palo Alto, CA, USA)was used for the connection of the OpenDSS and the MATLAB ® routines. In addition, Matlab was used for the development of the FIS for the centralized control of EVs charging behavior. The structure of the total framework is presented in Figure 10.

Investigation of Maximum Chargeable EVs in the Case Study Grid
The considered feeder has been designed without the penetration of EVs, like most distribution networks. Consequently, EVs will have an increased grid impact. From the grid point of view, the aim is to investigate the maximum number of EVs that can be charged, by avoiding grid's abnormal operation (bus voltages and lines ampacity must within the limits, according to Equation (1) and Equation (2)). To this end, two different case studies were examined. The first case study (CS1) examines the maximum number of EVs that can be charged, from the nearest to the furthest charging points, by increasing the number of connected EVs to grid in an ascending relation to the distance of

Investigation of Maximum Chargeable EVs in the Case Study Grid
The considered feeder has been designed without the penetration of EVs, like most distribution networks. Consequently, EVs will have an increased grid impact. From the grid point of view, the aim is to investigate the maximum number of EVs that can be charged, by avoiding grid's abnormal operation (bus voltages and lines ampacity must within the limits, according to Equations (1) and (2)). To this end, two different case studies were examined. The first case study (CS1) examines the maximum number of EVs that can be charged, from the nearest to the furthest charging points, by increasing the number of connected EVs to grid in an ascending relation to the distance of each load from the substation. In the second case study (CS2), the maximum number of connected EVs is calculated by starting the penetration of EVs to the grid, from the furthest charging point. In both scenarios, the households' power consumption of each load is covered. The objective is to examine the maximum chargeable EVs at each time step for the overall model and for each phase separately. The simulations are referring to a 24 h time period, with 1 min time step. Figure 11 depicts the maximum allowed EVs in each of the two scenarios. Figure 12 presents the maximum chargeable EVs for each grid's phase, separately. Furthermore, in order to quantify and discuss the results of Figures 11 and 12, two basic statistics are used: (i) the mean of the chargeable EVs, which is calculated by Equation (5), and (ii) the variance of the chargeable EVs, which is calculated by Equation (6). The results are presented in Table 4.
where n i is the number of chargeable EVs at timestep i, N is the total number of the simulation timesteps, N mean the mean of the chargeable EVs and var the variance of chargeable EVs.
Energies 2020, 13, x FOR PEER REVIEW 12 of 34 each load from the substation. In the second case study (CS2), the maximum number of connected EVs is calculated by starting the penetration of EVs to the grid, from the furthest charging point. In both scenarios, the households' power consumption of each load is covered. The objective is to examine the maximum chargeable EVs at each time step for the overall model and for each phase separately. The simulations are referring to a 24 h time period, with 1 min time step. Figure 11 depicts the maximum allowed EVs in each of the two scenarios. Figure 12 presents the maximum chargeable EVs for each grid's phase, separately. Furthermore, in order to quantify and discuss the results of Figures 11 and 12, two basic statistics are used: (i) the mean of the chargeable EVs , which is calculated by Equation (5), and (ii) the variance of the chargeable EVs, which is calculated by Equation (6). The results are presented in Table 4.
where ni is the number of chargeable EVs at timestep i, N is the total number of the simulation timesteps, Nmean the mean of the chargeable EVs and var the variance of chargeable EVs.   According to Figures 11 and 12, it is clear that the location and the distance of the charging EVs influence the total number of EVs chargeable on the grid. The results show that the adopted EVs, which are closer to the substation, such as in CS1, cause less power losses in the network's lines and the voltages at the buses are more stable.
The results of Table 4 show that the total mean utilization of chargeable EVs in CS1 is 21.5 % more than in CS2. Thus, the variance of the maximum chargeable EVs in CS2 is smaller than in CS1. This fact indicates that the influence of a grid's household loads on the maximum EV utilization is greater when EVs are located near the substation totally and for each phase separately. The increased number of chargeable EVs in CS1, compared to CS2, was expected. The aforementioned facts show that the distance and the location of EVs in the grid's topology is a major factor which affects the maximum EV utilization. Therefore, in the present paper, the distance of the EVs' charging points from the main system's substation is considered in the proposed energy management system.

Investigation of Unctrolled Charging Effects on the Case Study Grid's Buses and Lines.
Four different uncontrolled charging scenarios are assessed in term of their grid impact, by changing the time space in which EVs are connected to the grid in order to be charged. The aim of the simulation scenarios is to demonstrate the effects of EVs uncontrolled charging in the number of  According to Figures 11 and 12, it is clear that the location and the distance of the charging EVs influence the total number of EVs chargeable on the grid. The results show that the adopted EVs, which are closer to the substation, such as in CS1, cause less power losses in the network's lines and the voltages at the buses are more stable.
The results of Table 4 show that the total mean utilization of chargeable EVs in CS1 is 21.5 % more than in CS2. Thus, the variance of the maximum chargeable EVs in CS2 is smaller than in CS1. This fact indicates that the influence of a grid's household loads on the maximum EV utilization is greater when EVs are located near the substation totally and for each phase separately. The increased number of chargeable EVs in CS1, compared to CS2, was expected. The aforementioned facts show that the distance and the location of EVs in the grid's topology is a major factor which affects the maximum EV utilization. Therefore, in the present paper, the distance of the EVs' charging points from the main system's substation is considered in the proposed energy management system.

Investigation of Unctrolled Charging Effects on the Case Study Grid's Buses and Lines
Four different uncontrolled charging scenarios are assessed in term of their grid impact, by changing the time space in which EVs are connected to the grid in order to be charged. The aim of the simulation scenarios is to demonstrate the effects of EVs uncontrolled charging in the number of the grid's buses and lines and to evaluate the proposed energy management system in Section 4. In all scenarios, the same loads demand profiles are considered ( Figure 3) and also the same types of EVs (Table 3). Initially, in all scenarios, the EVs are parked and are fully charged. The four scenarios are: (i) Scenario 1: EVs depart at 9:00 h and connect to the grid at 14:00 h.
This scenario represents a worst-case scenario, in which EVs are connected to the grid at the same time. In this scenario, the EVs depart from each house is scheduled at 9:00 h. After taking a trip between 9:00 h and 14:00 h, they return at 14:00 h to the charging points in order to be charged. The present scenario is considered in order to examine the system's behavior in a stressed grid's situation.
In this scenario EVs depart from their house between 7:00 h and 9:00 h. After taking a trip, they arrive at the charging points between 14:00 h and 16:00 h. The departure and arrival times of each EV are calculated randomly based on uniform distribution. In this scenario, the EVs arrive at their charging points in a time window of two hours.
In this scenario EVs depart from their house between 7:00 h and 9:00 h. After taking a trip, they return to the charging points between 14:00 h and 18:00 h. The departure and arrival times of each EV are calculated randomly based on uniform distribution. The present scenario is considered in order to examine the system's behavior in a stressed situation. Both Scenarios 2 and 3 are also examined in order to investigate the effect of the arriving time windows on the grid's stability. Thus, they represent more realistic scenarios compared with Scenario 1. The difference between Scenarios 2 and 3 is the arrival time window, in which EVs are returning to the charging points in order to be charged. In Scenario 3, the arrival time window has been extended by two hours, compared to the arrival time window of Scenario 2.
(iv) Scenario 4: EVs are randomly connected to the grid or disconnected at certain times.
In this scenario, the EVs' state changes randomly during the simulation period. The aim of this scenario is to investigate the existence of bus undervoltages and lines overloads when the EVs takes more than one trip and their state changes randomly. The parameters of the simulation scenarios are summarized in Table 5.  Figure 13 illustrates the state of each EV, which is determined based on the times that the EVs: (i) travel, means that the EVs consume energy from the battery banks (legend titled "On Trip" in Figure 13), (ii) are parked without being charged (legend titled "Parked" in Figure 13), and (iii) are connected to the network in order to be charged (legend titled "Charge" in Figure 13), for the four scenarios.  Table 6 shows the number and the model of EVs that used in the simulation scenarios. In Figure  14 the EVs' battery capacities and the stored energy are presented, when EVs are connected to grid in order to be charged, for Scenarios 1-3. The EVs' stored energy of Scenario 4 is not depicted, because the EVs are connected to grid, in order to be charged, more than once (multiple trips). Figures 15-18 depict the number grid's buses that have undervoltages and the number of the overloaded lines for each simulation scenario, respectively.   Table 6 shows the number and the model of EVs that used in the simulation scenarios. In Figure 14 the EVs' battery capacities and the stored energy are presented, when EVs are connected to grid in order to be charged, for Scenarios 1-3. The EVs' stored energy of Scenario 4 is not depicted, because the EVs are connected to grid, in order to be charged, more than once (multiple trips). Figures 15-18 depict the number grid's buses that have undervoltages and the number of the overloaded lines for each simulation scenario, respectively.   Table 6 shows the number and the model of EVs that used in the simulation scenarios. In Figure  14 the EVs' battery capacities and the stored energy are presented, when EVs are connected to grid in order to be charged, for Scenarios 1-3. The EVs' stored energy of Scenario 4 is not depicted, because the EVs are connected to grid, in order to be charged, more than once (multiple trips). Figures 15-18 depict the number grid's buses that have undervoltages and the number of the overloaded lines for each simulation scenario, respectively.   The results of Figure 15 refer to the worst-case scenario (Scenario 1), in which all EVs arrive to the charging points at the same simulation time. Figure 15a refers to the number of the system's buses, which present undervoltages and Figure 15b Figure 17. In comparison with the results of Scenario 2 (Figure 16), the number of the affected lines and buses that appeared in Scenario 3 is reduced, because of the double increased time window. However, even, in this scenario, the constraints of the system are violated. Phase B is affected at 16:00 h, while in phase A, minor number of lines is overloaded at 18:00 h. The time differences of the violations in phases A and B are related to the residential energy consumption of phase A, which is increased compared to phase B, as shown in Figure 4a,b, respectively. Scenario 3 examines the behavior of the grid, when EVs arrive at the charging points, in a time window of 4 h. The results are shown in Figure 17. In comparison with the results of Scenario 2 (Figure 16), the number of the affected lines and buses that appeared in Scenario 3 is reduced, because of the double increased time window. However, even, in this scenario, the constraints of the system are violated. Phase B is affected at 16:00 h, while in phase A, minor number of lines is overloaded at 18:00 h. The time differences of the violations in phases A and B are related to the residential energy consumption of phase A, which is increased compared to phase B, as shown in Figures 4a and 4b, respectively. (a)

Overview
In the previous section, it was clearly demonstrated that the location and the distance of the charging EVs from the network's Medium Voltage to Low Voltage (MV/LV) transformer has a significant impact on the grid's stability. This fact imposes the necessity to take into consideration the connection location of each charging vehicle to the grid and its distance from the substation. In this section, a charging priority system for the coordination of EVs, when the distribution system cannot support all the vehicles, is proposed. The aim of the designed fuzzy CEMS is to define the charging priority of each EV in order to select the number of EVs, which can be charged and to select the EVs, which will be charged based on their charging priority and with respect to the network's constraints. The flowchart of the proposed fuzzy charging management system is presented in Figure 19. Algorithm 1 presents the pseudocode for the selection of the chargeable EVs based on their charging priorities.

Overview
In the previous section, it was clearly demonstrated that the location and the distance of the charging EVs from the network's Medium Voltage to Low Voltage (MV/LV) transformer has a significant impact on the grid's stability. This fact imposes the necessity to take into consideration the connection location of each charging vehicle to the grid and its distance from the substation. In this section, a charging priority system for the coordination of EVs, when the distribution system cannot support all the vehicles, is proposed. The aim of the designed fuzzy CEMS is to define the charging priority of each EV in order to select the number of EVs, which can be charged and to select the EVs, which will be charged based on their charging priority and with respect to the network's constraints. The flowchart of the proposed fuzzy charging management system is presented in Figure 19. Algorithm 1 presents the pseudocode for the selection of the chargeable EVs based on their charging priorities.

Overview
In the previous section, it was clearly demonstrated that the location and the distance of the charging EVs from the network's Medium Voltage to Low Voltage (MV/LV) transformer has a significant impact on the grid's stability. This fact imposes the necessity to take into consideration the connection location of each charging vehicle to the grid and its distance from the substation. In this section, a charging priority system for the coordination of EVs, when the distribution system cannot support all the vehicles, is proposed. The aim of the designed fuzzy CEMS is to define the charging priority of each EV in order to select the number of EVs, which can be charged and to select the EVs, which will be charged based on their charging priority and with respect to the network's constraints. The flowchart of the proposed fuzzy charging management system is presented in Figure 19. Algorithm 1 presents the pseudocode for the selection of the chargeable EVs based on their charging priorities.  Get the charging priorities of the EVs from the Fuzzy Logic Controller 3: Create a list for each phase that include the EVs to be charged and sorted in an ascending order of charging priority.

4:
Perform grid's power flow analysis 5: If voltage or ampacity violation occur in a phase then 6: Remove EV with the lowest priority from each corresponding list 7: Return to action 3 8: else 9: Charge the selected EVs 10: end if 11: end for

Proposed Fuzzy Interface System
The charging priority of each EV, at each time step is calculated by a real time Mamdani type fuzzy interface controller, where its inputs are the vehicle's battery SoC, which ranges from 20% to 90%, the delay time, in which the EV is connected to grid and waiting to charge and ranges from 0 to 60 min, and the distance of the EV's charger from the LV grid's substation, which ranges from 0 to 0.3 km. The sets of the aforementioned crisp input values are converted into fuzzy linguistic values, by using the input membership functions, as defined in Figure 20a-c, respectively. The output's membership function is shown in Figure 20d. The membership functions declare the degree of membership of the considered variables in each of the fuzzy sets accordingly. The selection of the shapes and the numbers of the membership functions for the three input variables have been selected based on the experience of the research team [34,51,52]. In the proposed FIS, all the linguistic variables include five fuzzy sets, in which the left-right shoulders are triangular membership functions and the other three are trapezoidal membership functions. The same number and shape of the membership functions is applied in both input and output variables. The definition of the different considered linguistic variables of the inputs and the output membership functions are presented in Table 7.

Proposed Fuzzy Interface System
The charging priority of each EV, at each time step is calculated by a real time Mamdani type fuzzy interface controller, where its inputs are the vehicle's battery SoC, which ranges from 20% to 90%, the delay time, in which the EV is connected to grid and waiting to charge and ranges from 0 to 60 min, and the distance of the EV's charger from the LV grid's substation, which ranges from 0 to 0.3 km. The sets of the aforementioned crisp input values are converted into fuzzy linguistic values, by using the input membership functions, as defined in Figures 20a,b,c, respectively. The output's membership function is shown in Figure 20d. The membership functions declare the degree of membership of the considered variables in each of the fuzzy sets accordingly. The selection of the shapes and the numbers of the membership functions for the three input variables have been selected based on the experience of the research team [34,51,52]. In the proposed FIS, all the linguistic variables include five fuzzy sets, in which the left-right shoulders are triangular membership functions and the other three are trapezoidal membership functions. The same number and shape of the membership functions is applied in both input and output variables. The definition of the different considered linguistic variables of the inputs and the output membership functions are presented in Table 7.  The fuzzy interface system includes the membership functions of the input variables, the membership function of the output variable and the set of the fuzzy rules. The fuzzy rules map the linguistic input variables (SoC, distance, delay time) to the output variable by using a list of IF-THEN statements. In the present FIS, there are three linguistic inputs, each one with five levels. Hence, 125 fuzzy rules have been defined. Tables 8-12 present the fuzzy rules in matrix form, for each EVs' distance fuzzy state, respectively. The rules for each of the routines were developed based on the knowledge and experience of the members of the research team [34,51,52,53]. It is clear that a given set of the input linguistic values may enable several fuzzy rules at the same time. The linguistic inputs of the SoC, the distance and the charging delay time are combining together in order to establish a rule strength for each fuzzy rule. In order to calculate the charging priority linguistic value, from the several consequents of the fuzzy rules, the min-max aggregation method has been used. The decision surfaces of the proposed FIS are presented in Figure 21. The surfaces are three-dimensional curves that represent the mapping from inputs to output, taking into consideration the membership functions and the fuzzy rules of the system.   The fuzzy interface system includes the membership functions of the input variables, the membership function of the output variable and the set of the fuzzy rules. The fuzzy rules map the linguistic input variables (SoC, distance, delay time) to the output variable by using a list of IF-THEN statements. In the present FIS, there are three linguistic inputs, each one with five levels. Hence, 125 fuzzy rules have been defined. Tables 8-12 present the fuzzy rules in matrix form, for each EVs' distance fuzzy state, respectively. The rules for each of the routines were developed based on the knowledge and experience of the members of the research team [34,[51][52][53]. It is clear that a given set of the input linguistic values may enable several fuzzy rules at the same time. The linguistic inputs of the SoC, the distance and the charging delay time are combining together in order to establish a rule strength for each fuzzy rule. In order to calculate the charging priority linguistic value, from the several consequents of the fuzzy rules, the min-max aggregation method has been used. The decision surfaces of the proposed FIS are presented in Figure 21. The surfaces are three-dimensional curves that represent the mapping from inputs to output, taking into consideration the membership functions and the fuzzy rules of the system.    The charging priority of each EV is calculated based on the defuzzification process of the FIS, which converts the linguistic charging priority variable, as extracted from the fuzzy interface system, into a numerical value, which ranges from 0 to 1. The defuzzification of the FIS is based on the center of the gravity (centroid), since it is the most suitable technique that can be applied in the application [34,[51][52][53]. The EV with the highest output value gets the highest priority in order to be charged at its nominal power. The charging priority of each EV is calculated based on the defuzzification process of the FIS, which converts the linguistic charging priority variable, as extracted from the fuzzy interface system, into a numerical value, which ranges from 0 to 1. The defuzzification of the FIS is based on the center of the gravity (centroid), since it is the most suitable technique that can be applied in the application [34,51,52,53]. The EV with the highest output value gets the highest priority in order to be charged at its nominal power.

Simulation Scenarios and Results
The total developed framework is used for the examination of CEMS impact in low distribution grids and the evaluation of charging management algorithm by examining a variety of scenarios, based on the behavior and the state of EVs. In order to examine the operation of the proposed fuzzy charging algorithm the aforementioned Scenarios 1-4, as presented in Section 3.2, are considered. Figure 22 illustrates the state of each EV for each simulation scenario. The numerical results, corresponding to the times of the charging states, as presented in Figure 22, are reported in Appendix A.

Simulation Scenarios and Results
The total developed framework is used for the examination of CEMS impact in low distribution grids and the evaluation of charging management algorithm by examining a variety of scenarios, based on the behavior and the state of EVs. In order to examine the operation of the proposed fuzzy charging algorithm the aforementioned Scenarios 1-4, as presented in Section 3.2, are considered. Figure 22 illustrates the state of each EV for each simulation scenario. The numerical results, corresponding to the times of the charging states, as presented in Figure 22, are reported in Appendix A. The results of Figure 22 show how the fuzzy energy management strategy affects the charging state of each EV. According to the results of Figures 22a and 22b most of the EVs are suffering from charging delay times because of the increased number of charging EVs, which arrive at the charging points at the same time in Scenario 1 and within a relatively small charging window of two hours in Scenario 2. On the other hand, the EVs' charging state is also affected in Scenarios 3 and 4, although to a less extent compared to the results of Scenarios 1 and 2. Figure 23 depicts the totally simulation's minimum values of SoC, that each EV experiences in Scenario 4. A first approach for the evaluation of the fuzzy management strategy is based on Scenario 4, which is used in order to evaluate the operation of the proposed energy management strategy based on the capability of the EVs to travel within the scenario ranges, by keeping the batteries SoC within the manufacturers' proposed limits. According to the Figure 23, which presents the minimum SoC of Green color declares that EVs are parked; Red color declares that EVs are travelled; Blue color declares that EVs are charging; Yellow color declares that EVs are connected but not charged due to low priority.
The results of Figure 22 show how the fuzzy energy management strategy affects the charging state of each EV. According to the results of Figure 22a,b most of the EVs are suffering from charging delay times because of the increased number of charging EVs, which arrive at the charging points at the same time in Scenario 1 and within a relatively small charging window of two hours in Scenario 2. On the other hand, the EVs' charging state is also affected in Scenarios 3 and 4, although to a less extent compared to the results of Scenarios 1 and 2. Figure 23 depicts the totally simulation's minimum values of SoC, that each EV experiences in Scenario 4. The results of Figure 22 show how the fuzzy energy management strategy affects the charging state of each EV. According to the results of Figures 22a and 22b most of the EVs are suffering from charging delay times because of the increased number of charging EVs, which arrive at the charging points at the same time in Scenario 1 and within a relatively small charging window of two hours in Scenario 2. On the other hand, the EVs' charging state is also affected in Scenarios 3 and 4, although to a less extent compared to the results of Scenarios 1 and 2. Figure 23 depicts the totally simulation's minimum values of SoC, that each EV experiences in Scenario 4. A first approach for the evaluation of the fuzzy management strategy is based on Scenario 4, which is used in order to evaluate the operation of the proposed energy management strategy based on the capability of the EVs to travel within the scenario ranges, by keeping the batteries SoC within the manufacturers' proposed limits. According to the Figure 23, which presents the minimum SoC of A first approach for the evaluation of the fuzzy management strategy is based on Scenario 4, which is used in order to evaluate the operation of the proposed energy management strategy based on the capability of the EVs to travel within the scenario ranges, by keeping the batteries SoC within the manufacturers' proposed limits. According to the Figure 23, which presents the minimum SoC Energies 2020, 13, 3709 28 of 34 of each EV's battery in the total simulation of Scenario 4, all EVs are capable of travelling their trip distances, without battery energy issues.
The second system's evaluation approach focuses on the charging behavior of the EVs in simulation Scenarios 1-3 Figure 24 depicts the EVs' charging times, based on the priorities, given by the energy management system, thus, the minimum charging times, in which EVs' would be charged, in case that the network could support the EVs' charging without exceeding the limits of the technical constraints. In this approach, Scenario 4 is not examined due to the randomness of EV's state and charging times.
Energies 2020, 13, x FOR PEER REVIEW 28 of 34 each EV's battery in the total simulation of Scenario 4, all EVs are capable of travelling their trip distances, without battery energy issues.
The second system's evaluation approach focuses on the charging behavior of the EVs in simulation Scenarios 1-3 Figure 24 depicts the EVs' charging times, based on the priorities, given by the energy management system, thus, the minimum charging times, in which EVs' would be charged, in case that the network could support the EVs' charging without exceeding the limits of the technical constraints. In this approach, Scenario 4 is not examined due to the randomness of EV's state and charging times. Let us consider, as an example, EV 50. According to the Figure 2, the charging point of this EV is one of the furthest from the grid's substation. By examining the charging behavior in Scenario 1 (Figure 22a and Figure 24a), it is shown that the EV, when arriving at the charging point, delays longer than the other EVs, due to the fact that the distance of the charging points from the main substation is one of the key factors considered in the proposed energy management system. The EV stands for charging due to its low priority according to the fuzzy energy management system. The low SoC and the fact that the charge of this EV is delayed, urges the controller to increase the priority of the EV. Furthermore, the priority of the EVs, which are charged during the EV's delay period, decreases. After that, the EV begins to charge. In Scenarios 2 and 3, there is a time window of two and four hours respectively, in which EVs are connected to the charging points. The EV 50 arrives at 14:40 h in Scenario 2 and at 15:35 h in Scenario 3. In this period, the EVs, which are charged, do not affect the normal operation of the distribution grid and this fact allows all the connected EVs to be charged, along with EV 50. By assessing the whole operation of the system, as depicted in Figure 24, it is evident that the distance of the charging points influences the charging time of the EVs and the factors of charging delay time as well as the SoC ensure the charging of the furthest from the substation EVs, by increasing their priorities. Moreover, by examining the results of the Scenarios 2 and 3 in Figures 22b and 22c it is shown that a reduced amount of EVs suffers from charging delay Let us consider, as an example, EV 50. According to the Figure 2, the charging point of this EV is one of the furthest from the grid's substation. By examining the charging behavior in Scenario 1 (Figures 22a and 24a), it is shown that the EV, when arriving at the charging point, delays longer than the other EVs, due to the fact that the distance of the charging points from the main substation is one of the key factors considered in the proposed energy management system. The EV stands for charging due to its low priority according to the fuzzy energy management system. The low SoC and the fact that the charge of this EV is delayed, urges the controller to increase the priority of the EV. Furthermore, the priority of the EVs, which are charged during the EV's delay period, decreases. After that, the EV begins to charge. In Scenarios 2 and 3, there is a time window of two and four hours respectively, in which EVs are connected to the charging points. The EV 50 arrives at 14:40 h in Scenario 2 and at 15:35 h in Scenario 3. In this period, the EVs, which are charged, do not affect the normal operation of the distribution grid and this fact allows all the connected EVs to be charged, along with EV 50. By assessing the whole operation of the system, as depicted in Figure 24, it is evident that the distance of the charging points influences the charging time of the EVs and the factors of charging delay time as well as the SoC ensure the charging of the furthest from the substation EVs, by increasing their priorities. Moreover, by examining the results of the Scenarios 2 and 3 in Figure 22b,c it is shown that a reduced amount of EVs suffers from charging delay times, compared to the results of Scenario 1, which is depicted in Figure 24a. However, most of the EVs suffer from charging delay times.
Furthermore, the EVs' charging times of the proposed FLC, denoted here as FLC + , are compared with a second modified FLC denoted here as FLC − , in which the distance of EVs from the main substation does not taken into consideration. The FLC − determines the priority of each EV, based on the EVs' SoC and the charging delay times respectively. The SoC, charging delay time and the charging priority membership functions are the same, as considered in FLC + (Figure 20a,c,d). The surface of the FLC − is depicted in Figure 21a. The simulation results of the FLC − and FLC + , for the simulation Scenarios 1, 2 and 3, are presented in Figure 25, while Table 13 reports the mean charging times in both FLC − and FLC + and the achieved mean charging time reduction in FLC + .
Energies 2020, 13, x FOR PEER REVIEW 29 of 34 times, compared to the results of Scenario 1, which is depicted in Figure 24a. However, most of the EVs suffer from charging delay times. Furthermore, the EVs' charging times of the proposed FLC, denoted here as FLC + , are compared with a second modified FLC denoted here as FLC − , in which the distance of EVs from the main substation does not taken into consideration. The FLC − determines the priority of each EV, based on the EVs' SoC and the charging delay times respectively. The SoC, charging delay time and the charging priority membership functions are the same, as considered in FLC + (Figures 20a,c and Figure  20d). The surface of the FLC − is depicted in Figure 21a. The simulation results of the FLC − and FLC + , for the simulation Scenarios 1, 2 and 3, are presented in Figure 25, while Table 13 reports the mean charging times in both FLC − and FLC + and the achieved mean charging time reduction in FLC + .
The results clearly show that the enable of the distance as a parameter in the FLC affects the charging behavior of the EVs in a positive way. The charging times of the EVs near the network's substation significantly decreasing, according to Figure 25a  Moreover, in Figures 25a-c it is shown that FLC + allocates the charging times of EVs, better than FLC − . Furthermore, the introduction of the distance in the proposed energy management system  The results clearly show that the enable of the distance as a parameter in the FLC affects the charging behavior of the EVs in a positive way. The charging times of the EVs near the network's substation significantly decreasing, according to Figure 25a. Despite of the significant reduction of the charging time of the EVs near the substation, the charging times of the furthest EVs, do not affected significantly, i.e. The charging time of EV 49 increases up to 30 min. In the FLC + .
Moreover, in Figure 25a-c it is shown that FLC + allocates the charging times of EVs, better than FLC − . Furthermore, the introduction of the distance in the proposed energy management system reduces the mean charging time, up to 14.7%. The consideration of the distance, as a variable in energy management systems for the coordination of EVs' charging, seems to improve the overall EVs' charging behavior and to reduce the EVs' charging times.

Conclusions
The number of EVs in use is expected to increase significantly in future years because of the many advantages they present compared to conventional ones. In the present paper, the effects of uncontrolled charging process in a case study low voltage distribution grid were investigated and a charging coordination management strategy is proposed. The simulation results of the examined penetration scenarios indicate that the voltages in the buses of the system and the thermal limits of the lines are major limiting factors for the penetration of EVs in energy distribution networks. Thus, the distance of the charging EVs from the substation is a major factor for the definition of the maximum chargeable vehicles. The results showed that the mean utilization of chargeable EVs is up to 21.5 % greater, when the location of the charging EVs is near the substation.
Therefore, by evaluating the abovementioned results, an energy management system was developed for the coordination of EVs charging process, in low voltage distributed grids, with respect to network's restrictions, by introducing EVs distance from the substation for the first time as a critical factor for the priority of chargeable EVs. The proposed EV charging management system lies on the fuzzy logic and takes into consideration the SoC of the charging EVs, their distance from the grid's substation and the charging delay time. The results of the examined scenarios show that the use of the distance in the proposed fuzzy management system may reduce the EVs' charging time up to 14.7%. Thus, in all simulation scenarios, the consideration of the EVs' distance from the substation, influence the charging times of the EVs in a positive way, i.e. reduces the charging time of the vehicles and it leads to a better utilization of the grid's energy sources.
Future work will concentrate on the optimization of the weights of the presented fuzzy management system, by minimizing the EVs' charging times, and by introducing more sophisticated charging management algorithms, based on computational intelligence theories.

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

Appendix A
Appendix A presents numerical values of EVs' charging times in FLC + controlled charging. Table A1 reports the charging and stand-by times for each EV and for each simulation scenario respectively, when the fuzzy priority management system is applied. T stand-by refers to the total stand-by time, in which EVs are connected to the charging points, in order to be charged, but they are waiting due to the low priority they have. T charging refers to the charging times, in which EVs are connected to the charging points and are charged. T total refers to the total charging time of EVs, including the overall stand-by and charging times.