# Two-Stage Fuzzy Logic Inference Algorithm for Maximizing the Quality of Performance under the Operational Constraints of Power Grid in Electric Vehicle Parking Lots

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## Abstract

**:**

## 1. Introduction

^{req}), the current PL occupancy and the updated available power from the grid. These are temporal and spatial based varying parameters with a higher level of uncertainty and thereby resulting in a dynamic and complex system. In practice, the drivers and the PL operators perceptions on several of the above parameters are highly imprecise. For instance, the driver’s description of SoC is likely to be non-specific and qualitative, for instance: enough, low or high. Similarly, the postulation of PL operators about the available power is simply as low, medium or high. In order to efficiently utilize the energy usage, the scheduling of charging and discharging of EVs can play an important role and should consider the aforementioned factors from both the power grid and EV domains. However, the uncertain behavior of EV owners and the requirements of both EVs and of the power grid present challenges for the PL operators to efficiently schedule EVs operation and thus affecting their QoP.

- The energy requirements of the EV owners are identified using realistic traveling distance patterns from the US national household travel survey (NHTS) and their G2V and V2G operations are formulated and solved through a TSFLIA.
- The first stage fuzzy inference system (FIS) is developed based on the real data obtained from the NHTS to compute the aggregated charging and discharging energies of EVs according to their next trip travelling distances. The second stage FIS utilizes the inputs from EVs and the power grid to determine an adequately accurate charging and discharging preferences for each of the connected EVs.
- The TSFLIA is developed with five sub-algorithms: (1) Manage_new_arrival, (2) First_stage_FLM (Fuzzy Logic Module), (3) Second_stage_FLM, (4) Manage_charge_discharge, and (5) Manage_departure. The registration of new arriving EVs, the departure of served EVs and the maintenance of PL occupancies are serviced by Manage_new_arrival and Manage_departure. The First_stage_FLM resolves the departure time from home and arrival time to PL to compute the SoC and required SoC of EVs according to their traveled and next trip distances and categorizes the operation of EVs in G2V, V2G and idle modes. The Second_stage_FLM account an accurate preference for each of the connected EVs by comprehensively solving the complexity of temporal based varying available power, required SoC for the next trip and EVs remaining parking duration. In each sampling period, the scheduled G2V and V2G operations of EVs are controlled according to their preference values through the sub-algorithm Manage_charge_discharge.
- The proposed TSFLIA is applied to three different PLs connected to the IEEE 34-node distribution system and the results are validated against the FLIA.

## 2. Related Work

## 3. Proposed Two-Stage Fuzzy Logic Inference Algorithm

#### 3.1. System Model of the Proposed TSFLIA

^{req}), remaining parking duration (RPD) and the updated available power (UAP) through the second stage of fuzzy logic inference. Furthermore, an advanced metering infrastructure (AMI) is used for updating the baseload to the distribution system operators and to the PL operators using wide-area-network (WAN) [25]. Similarly, the EV owners information is collected using a local area network (LAN) between the PL and the CSs [26]. Owners of EVs provide all the necessary information, plug-in the connectors to their EVs and leave the PL for their planned activities such as movie/restaurant/shopping mall, etc. This information includes the EVs departure time from home, arrival and departure times to and from PL. The charging and discharging process is controlled by the PL controller where at any scheduling period an appropriate preference value for decision is made according to the SoC

^{req}, RPD, and the UAP from the power grid through the use of the fuzzy inference mechanism. The aforementioned input parameters are based on the PDFs obtained from the NHTS and from the power grid.

#### 3.1.1. National Household Survey Data and the Probability based Functions

- (1)
- Arrival and departure PDF: The arrival time (from home to PL) and departure time (from PL to home) of EVs are considered to follow a normal distribution function as given in Equation (1) and shown in Figure 3a, and Figure 3b, respectively [32]:$$F\left(t\right)=\frac{1}{\sqrt[\sigma ]{2\pi}}{e}^{\raisebox{1ex}{$-{\left(t-\mu \right)}^{2}$}\!\left/ \!\raisebox{-1ex}{$2{\sigma}^{2}$}\right.,0t24}$$
- (2)
- Traveled distance PDF: A normal distribution with ${\mu}_{dis}^{tra}=\text{}3.744$ and ${\sigma}_{dis}^{tra}\text{}=\text{}0.396$ is considered for traveled distance in [33]. However, for sizable battery capacity with longer all-electric range (AER) [34], this work considers a normal distribution with ${\mu}_{dis}^{tra}=\text{}7.488$ and ${\sigma}_{dis}^{tra}=\text{}0.792$ to model the traveled distance as shown in Figure 3c.
- (3)
- Parking duration PDF: A normal distribution function with ${\mu}_{EV}^{PD}=8.99$ and ${\sigma}_{EV}^{PD}=1.92$ is considered to model the parking duration of EVs as shown in Figure 3d. The values for mean and standard deviation are given in Ref. [35] provide a reasonable parking duration; therefore, the same values are adopted in this work.

#### 3.1.2. First Stage Fuzzy Logic Inference System

**Fuzzification of Input Parameters:**

**Fuzzy Inference System for Traveled Distance:**

**Defuzzification of Traveled Distance:**

#### 3.1.3. Problem Formulation and Objective Function

^{req}of an EV are the functions of the traveled distance, next trip distance, all-electric range (AER) and the battery capacity and can be computed according to Equations (2) and (3) [40]:

- G2V operation: The EVs are considered to perform the G2V if their required SoCs are greater than their corresponding initial SoCs.
- V2G operation: The EVs with required SoCs less than their initial SoCs are scheduled to participate in V2G operation.
- Idle (no-participation): The EVs are considered to remain idle if their required SoCs are equivalent to their initial SoCs.

^{req}and the full battery capacity in G2V operation can be computed according to Equation (4) while the amount of discharging energy in V2G operation can be computed according to Equation (5). The amount of charging and discharging of an EV is 0 (i.e., idle/no participation in G2V and V2G) if it’s current and required SoCs are equivalent, as given in Equation (6):

#### 3.1.4. Second Stage Fuzzy Logic Inference System

^{req}, and the owner’s choice of RPD. Therefore, these parameters are considered as the input variables to the second stage of FIS. Each of the inputs is normalized and linearized in their corresponding minimum and maximum ranges and fuzzified to be represented through membership functions.

^{req}which is normalized from very low to very high and is represented in 0–1. The SoC

^{req}is modeled with five linguistic terms including Very Low (VL), Low (L), Medium (M), High (H) and Very High (VH) respectively. Similarly, the UAP is normalized from low available power to high available power and is linearly structured in the range 0–200 [20]. The associated linguistic terms are Very Low Available Power (VLAP), Low Available Power (LAP), Medium Available Power (MAP), High Available Power (HAP) and Very High Available Power (VHAP). The output variable of the second stage is fuzzified with three membership functions and is linearly represented in the range of 0–1. The linguistic term for each of the output membership functions is Low Preference (LPF), Medium Preference (MPF) and High Preference (HPF). The membership functions of the inputs and output variables are graphically depicted from Figure 5a–d, respectively.

**Rule # 8:**IF (SD, 0.25) AND (L, 0.3) AND (MAP, 0.8) THEN (MPF, 0.25)

**Rule # 9:**IF (SD, 0.25) AND (L, 0.3) AND (HAP, 0.1) THEN (MPF, 0.1)

**Rule # 13:**IF (SD, 0.25) AND (M, 0.6) AND (MAP, 0.8) THEN (MPF, 0.25)

**Rule # 14:**IF (SD, 0.25) AND (M, 0.6) AND (HAP, 0.1) THEN (MPF, 0.1)

**Rule # 23:**IF (AD, 0.75) AND (L, 0.3) AND (MAP, 0.8) THEN (MPF, 0.3)

**Rule # 24:**IF (AD, 0.75) AND (L, 0.3) AND (HAP, 0.1) THEN (MPF, 0.1)

**Rule # 28:**IF (AD, 0.75) AND (M, 0.6) AND (MAP, 0.8) THEN (HPF, 0.6)

**Rule # 29:**IF (AD, 0.75) AND (M, 0.6) AND (HAP, 0.1) THEN (HPF, 0.1)

^{req}and for the ith EV, it can be computed based on the $So{C}_{E{V}_{i}}^{req}$ and $B{C}_{E{V}_{i}}$ as given by Equation (27). The negative sign in Equation (27) shows the discharging of EV. The EVs with satisfied and unsatisfied QoE are represented by ${\mathcal{N}}_{\mathrm{EV}}{}_{satisfied}$ and ${\mathcal{N}}_{\mathrm{EV}}{}_{Unsatisfied}$ variables, respectively. The PL QoP is the function of EVs with satisfied/unsatisfied QoE and the total number of EVs and can as given by Equation (28):

#### 3.1.5. Pseudocode of the Proposed TSFLIA

Algorithm 1: | Two-Stage Fuzzy Logic Inference Main Algorithm |

Algorithm 2 | Manage_new_arrivals (${\mathcal{N}}_{EV},\text{}{H}_{EV}^{dep},\text{}P{L}_{EV}^{arr},P{L}_{EV}^{dep},\text{}B{C}_{EV},\text{}AE{R}_{EV},\text{}RP{D}_{EV}$,${M}_{EV}^{NTD},$${\mathcal{M}}_{CS}$) |

Algorithm 3 | First_stage_FLM (${M}_{EV}^{tr},\text{}{H}_{t}^{dep},\text{}P{L}_{t}^{arr},\text{}So{C}_{EV},\text{}So{C}_{EV}^{req},\text{}B{C}_{EV},\text{}{F}_{EV},\text{}j$) |

1. | FIS.load(rules file) */ Load the fuzzy rule file from Table 1 */ |

2. | /* Evaluate through FIS and categorize the EVs into G2V, V2G, and idle using Equations (4)–(6) */ ${M}_{EV}^{tr}\left[j\right]\leftarrow \mathrm{FIS}.\mathrm{Evaluate}\left({H}_{t}^{dep}\left[j\right],\text{}P{L}_{t}^{arr}\left[j\right]\right)$ |

3. | ${\mathrm{SoC}}_{EV}\left[j\right]$$\leftarrow \left[\left[1-\left(\raisebox{1ex}{${M}_{EV}^{tra}\left[j\right]$}\!\left/ \!\raisebox{-1ex}{${\mathrm{AER}}_{EV}\left[j\right]$}\right.\right)\right]\ast B{C}_{EV}\left[j\right]\text{}\right]$or$\left(0.2\ast B{C}_{EV}[j\right)$ |

4. | $So{C}_{EV}^{req}\left[j\right]$$\leftarrow $$\left[\left[\left[\text{}\left(\raisebox{1ex}{${M}_{EV}^{NTD}\left[j\right]$}\!\left/ \!\raisebox{-1ex}{${\mathrm{AER}}_{EV}\left[j\right]$}\right.\right)\right]+0.2\right]\ast B{C}_{EV}\left[j\right]\text{}\right]$or$B{C}_{EV}\left[j\right]$ |

5. | If ($So{C}_{EV}^{req}\left[j\right]\ge $ $B{C}_{EV}$[j]) |

6. | |${F}_{EV}\left[j\right]$$\leftarrow $${f}_{c}$. /* Set flag for full charge and compute QoE according to Equation (27) */ |

7. | Else if ($So{C}_{EV}^{req}\left[j\right]>So{C}_{EV}\left[j\right]So{C}_{EV}^{req}\left[j\right]$ $B{C}_{EV}$[j]) |

8. | |${F}_{EV}\left[j\right]$$\leftarrow $${p}_{c}$ /* Set flag for partial charge and compute QoE according to Equation (27) */ |

9. | Else if ($So{C}_{EV}^{req}\left[j\right]$$==So{C}_{EV}\left[j\right]$) |

10. | |${F}_{EV}\left[j\right]\leftarrow $${l}_{d}$ /* Set flag for idle and compute QoE according to Equation (27) */ |

11. | Else if ($So{C}_{EV}\left[j\right]>So{C}_{EV}^{req}\left[j\right]$) |

12. | |${F}_{EV}\left[j\right]$$\leftarrow $${d}_{s}$ /* Flag for discharge and compute QoE according to Equation (27) */ |

13. | End |

14. | Return updated $So{C}_{EV},So{C}_{EV}^{req},$ and ${F}_{EV}$ |

Algorithm 4 | Second_stage_FLM$(UAP,\text{}P{F}_{EV},RP{D}_{EV},\text{}So{C}_{EV}^{req},So{C}_{EV},{N}_{EV}^{cha},\text{}{D}_{EV},i,j$) |

Algorithm 5 | Manage_charge_discharge (${D}_{EV},UAP$${F}_{EV},So{C}_{EV},\text{}BL,\text{}TL,\text{}{P}_{C},\text{}{P}_{D},\text{}\eta ,\text{}i,j$) |

Algorithm 6 | Manage_departure (${\mathcal{N}}_{EV}$,$\text{}So{C}_{EV}$,$\text{}So{C}_{EV}^{req},B{C}_{EV},Qo{E}_{sucf}\text{},\text{}Qo{E}_{unsucf}\text{},\text{}i$) |

1. | Check the departure time constraints defined by Equation (19) |

2. | If ($So{C}_{EV}\left[i\right]\ge B{C}_{EV}\left[i\right]\left|\right|So{C}_{EV}\left[i\right]\ge So{C}_{EV}^{req}\left[i\right]$) |

3. | |$Qo{E}_{sucf}$$\leftarrow $$Qo{E}_{sucf}$ + 1 |

4. | Else if ($So{C}_{EV}\left[i\right]\le So{C}_{EV}^{req}\left[i\right]$) |

5. | |$Qo{E}_{unsucf}$$\leftarrow $$Qo{E}_{unsucf}$ + 1 |

6. | End if |

7. | ${\mathcal{N}}_{EV}\left[i\right]$$\leftarrow $${\mathcal{N}}_{EV}\left[i\right]$ −1 /*Decrement list of EVs*/ |

8. | Return updated ${\mathcal{N}}_{EV},Qo{E}_{sucf}$ and $Qo{E}_{unsucf}$ |

## 4. Simulation Results and Discussion

#### 4.1. Simulation Setting and Assumption

#### 4.2. Simulation Results

^{req}of EVs in the PL connected to buses number 820, 834 and 844, respectively. The SoCs at the time of arrival are computed based on their traveled distance, while the required SoCs are computed according to their next traveling distance. It can be observed that in each of the PLs, a different number of EVs are requesting for charging and discharging operations. The EVs requesting the charging operations are about 58%, 61.5% and 66.5%, while the EVs with discharging requests are about 42%, 38.5% and 33.5% in the PLs at buses number 820, 834 and 844, respectively. The charging and discharging behaviors of these PLs with respect to the two different schemes are shown in Figure 12. The FLIA schedules the EVs according to the logic α-cut and β-cut properties of fuzzy logic theory where these values were set as α = 0.8 and β = 0.3. The EVs with the value of PF variable equal to or less than β values are scheduled for charging while those with the value of PF variable equal to or greater than α are scheduled for discharging operations. The TSFLIA computes the required SoC according to the next trip traveling distance and utilizes the available power more efficiently for maximizing the EV owners QoE.

## 5. Conclusions

**Research limitations:**There are several other aspects such as forecasting the next trip distance and robustness analysis in terms of time analysis & fairness of the proposed algorithm. In the future, the work will be extended with sophisticated scenarios for approximating an adequate next trip distance requirement using neural network models, and conducting fairness and time analysis (i.e., complexity and execution time).

**Research Implications:**In order to realize the role of electric vehicles as prosumers, the future parking lots are regarded as a platform that can efficiently utilize the EVs aggregated load as well as the power supply resources in grid-to-vehicle and vehicle-to-grid modes. Therefore, there is a need to study the implications of EVs parking lots by developing models for sustainable development such as social, environmental and market economics.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Nour, M.; Said, S.M.; Ali, A.; Farkas, C. Smart Charging of Electric Vehicles According to Electricity Price. In Proceedings of the Conference on Innovative Trends in Computer Engineering (ITCE), Aswan, Egypt, 8–9 February 2020; pp. 432–437. [Google Scholar]
- Tan, K.M.; Ramachandaramurthy, V.K.; Yong, J.Y.; Padmanaban, S.; Mihet-Popa, L.; Blaabjerg, F. Minimization of load variance in power grids—Investigation on optimal vehicle-to-grid scheduling. Energies
**2017**, 10, 1880. [Google Scholar] [CrossRef][Green Version] - Neyestani, N.; Catalão, J.P. The value of reserve for plug-in electric vehicle parking lots. In Proceedings of the 2017 IEEE Manchester PowerTech, Manchester, UK, 18–22 June 2017; pp. 1–6. [Google Scholar]
- Neyestani, N.; Damavandi, M.Y.; Shafie-Khah, M.; Bakirtzis, A.G.; Catalão, J.P. Plug-in electric vehicles parking lot equilibria with energy and reserve markets. IEEE Trans. Power Syst.
**2016**, 32, 2001–2016. [Google Scholar] [CrossRef] - Moghaddam, Z.; Ahmad, I.; Habibi, D.; Phung, Q.V. Smart charging strategy for electric vehicle charging stations. IEEE Trans. Transp. Electrif.
**2017**, 4, 76–88. [Google Scholar] [CrossRef] - Hariri, A.O.; El Hariri, M.; Youssef, T.; Mohammed, O.A. A bilateral decision support platform for public charging of connected electric vehicles. IEEE Trans. Veh. Technol.
**2018**, 68, 129–140. [Google Scholar] [CrossRef] - An, J.; Wen, G.; Xu, W. Improved results on Fuzzy H∞ filter design for TS Fuzzy systems. Discret. Dyn. Nat. Soc.
**2010**, 2010, 1–21. [Google Scholar] [CrossRef][Green Version] - An, J.; Li, T.; Wen, G.; Li, R. New stability conditions for uncertain TS fuzzy systems with interval time-varying delay. Int. J. Control Autom. Syst.
**2012**, 10, 490–497. [Google Scholar] [CrossRef] - Park, J.; Sim, Y.; Lee, G.; Cho, D.-H. A Fuzzy Logic Based Electric Vehicle Scheduling in Smart Charging Network. In Proceedings of the 2019 16th IEEE Annual Consumer Communications & Networking Conference (CCNC), Las Vegas, NV, USA, 11–14 January 2019; pp. 1–6. [Google Scholar]
- Hariri, A.O.; Esfahani, M.M.; Mohammed, O. A Cognitive Price-Based Approach for Real-Time Management of En-Route Electric Vehicles. In Proceedings of the 2018 IEEE Transportation Electrification Conference and Expo (ITEC), Long Beach, CA, USA, 15 June 2018; pp. 922–927. [Google Scholar]
- Sah, B.; Kumar, P.; Rayudu, R.; Bose, S.K.; Inala, K.P. Impact of Sampling in the Operation of Vehicle to Grid and its Mitigation. IEEE Trans. Ind. Inform.
**2018**, 15, 3923–3933. [Google Scholar] [CrossRef] - Singh, M.; Kumar, P.; Kar, I. Implementation of vehicle to grid infrastructure using fuzzy logic controller. IEEE Trans. Smart Grid
**2012**, 3, 565–577. [Google Scholar] [CrossRef] - Mehta, R.; Srinivasan, D.; Trivedi, A. Optimal Charging Scheduling of Plug-In Electric Vehicles for Maximizing Penetration within a Workplace Car Park. In Proceedings of the 2016 IEEE Congress on Evolutionary Computation (CEC), Vancouver, BC, Canada, 24–26 July 2016; pp. 3646–3653. [Google Scholar]
- Mirzaei, M.J.; Kazemi, A.; Homaee, O. A probabilistic approach to determine optimal capacity and location of electric vehicles parking lots in distribution networks. IEEE Trans. Ind. Inform.
**2015**, 12, 1963–1972. [Google Scholar] [CrossRef] - Yao, L.; Damiran, Z.; Lim, W.H. A Fuzzy Logic Based Charging Scheme for Electric Vechicle Parking Station. In Proceedings of the 2016 IEEE 16th International Conference on Environment and Electrical Engineering (EEEIC), Florence, Italy, 7–10 June 2016; pp. 1–6. [Google Scholar]
- Akhavan-Rezai, E.; Shaaban, M.F.; El-Saadany, E.F.; Karray, F. Online Intelligent Demand Management of Plug-In Electric Vehicles in Future Smart Parking Lots. IEEE Syst. J.
**2015**, 10, 483–494. [Google Scholar] [CrossRef] - Jiyao, A.; Tang, J.; Yu, Y. Fuzzy Multi-Objective Optimized with Efficient Energy and Time-Varying Price for EV Charging System. In Proceedings of the Proceedings on the International Conference on Artificial Intelligence (ICAI), Las Vegas, NV, USA, 12–15 July 2010; pp. 47–53. [Google Scholar]
- Mohamed, A.; Salehi, V.; Ma, T.; Mohammed, O. Real-time energy management algorithm for plug-in hybrid electric vehicle charging parks involving sustainable energy. IEEE Trans. Sustain. Energy
**2013**, 5, 577–586. [Google Scholar] [CrossRef] - Hussain, S.; Ahmed, M.A.; Lee, K.-B.; Kim, Y.-C. Fuzzy Logic Weight Based Charging Scheme for Optimal Distribution of Charging Power among Electric Vehicles in a Parking Lot. Energies
**2020**, 13, 3119. [Google Scholar] [CrossRef] - Hussain, S.; Ahmed, M.A.; Kim, Y.-C. Efficient Power Management Algorithm Based on Fuzzy Logic Inference for Electric Vehicles Parking Lot. IEEE Access
**2019**, 7, 65467–65485. [Google Scholar] [CrossRef] - Vaidya, B.; Mouftah, H.T. Smart electric vehicle charging management for smart cities. IET Smart Cities
**2020**, 2, 4–13. [Google Scholar] [CrossRef] - Wang, G.; Zhang, Y.; Fang, Z.; Wang, S.; Zhang, F.; Zhang, D. FairCharge: A data-driven fairness-aware charging recommendation system for large-scale electric taxi fleets. Proc. ACM Interact. Mob. Wearable Ubiquitous Technol.
**2020**, 4, 1–25. [Google Scholar] [CrossRef][Green Version] - Dubey, A.; Santoso, S. Electric vehicle charging on residential distribution systems: Impacts and mitigations. IEEE Access
**2015**, 3, 1871–1893. [Google Scholar] [CrossRef] - Kuran, M.Ş.; Viana, A.C.; Iannone, L.; Kofman, D.; Mermoud, G.; Vasseur, J.P. A smart parking lot management system for scheduling the recharging of electric vehicles. IEEE Trans. Smart Grid
**2015**, 6, 2942–2953. [Google Scholar] [CrossRef] - Hussain, S.; Muhammad, F.; Kim, Y.-C. Communication Network Architecture Based on Logical Nodes for Electric Vehicles. In Proceedings of the 2017 International Symposium on Information Technology Convergence, Shijiazhuang, China, 19–21 October 2017; pp. 321–326. [Google Scholar]
- Nijhuis, M.; Gibescu, M.; Cobben, J. Valuation of measurement data for low voltage network expansion planning. Electr. Power Syst. Res.
**2017**, 151, 59–67. [Google Scholar] [CrossRef] - National Household Travel Survey. Available online: http://nhts.ornl.gov (accessed on 1 January 2019).
- Tan, J.; Wang, L. Integration of plug-in hybrid electric vehicles into residential distribution grid based on two-layer intelligent optimization. IEEE Trans. Smart Grid
**2014**, 5, 1774–1784. [Google Scholar] [CrossRef] - Mu, Y.; Wu, J.; Jenkins, N.; Jia, H.; Wang, C. A spatial–temporal model for grid impact analysis of plug-in electric vehicles. Appl. Energy
**2014**, 114, 456–465. [Google Scholar] [CrossRef][Green Version] - Rezaee, S.; Farjah, E.; Khorramdel, B. Probabilistic analysis of plug-in electric vehicles impact on electrical grid through homes and parking lots. IEEE Trans. Sustain. Energy
**2013**, 4, 1024–1033. [Google Scholar] [CrossRef] - Stephens, T. An Agent-Based Model of Energy Demand and Emissions from Plug-In Hybrid Electric Vehicle Use. Master’s Thesis, University of Michigan, Ann Arbor, MI, USA, 31 August 2010. [Google Scholar]
- Preethi, A.A.; Nesamalar, J.J.D.; Suganya, S.; Raja, S.C. Economic Scheduling of Plug-In Hybrid Electric Vehicle Considering Various Travel Patterns. In Proceedings of the 2018 National Power Engineering Conference (NPEC), Madurai, India, 9–10 March 2018; pp. 1–7. [Google Scholar]
- Mendoza, C.C.; Quintero, A.M.; Santamaria, F. Estimation of electric energy required by electric vehicles based on travelled distances in a residential zone. Tecciencia
**2016**, 11, 17–24. [Google Scholar] [CrossRef] - Du, J.; Li, F.; Li, J.; Wu, X.; Song, Z.; Zou, Y.; Ouyang, M. Evaluating the technological evolution of battery electric buses: China as a case. Energy
**2019**, 176, 309–319. [Google Scholar] [CrossRef] - Ma, T.; Mohammed, O.A. Optimal charging of plug-in electric vehicles for a car-park infrastructure. IEEE Trans. Ind. Appl.
**2014**, 50, 2323–2330. [Google Scholar] [CrossRef] - Andrenacci, N.; Genovese, A.; Ragona, R. Determination of the level of service and customer crowding for electric charging stations through fuzzy models and simulation techniques. Appl. Energy
**2017**, 208, 97–107. [Google Scholar] [CrossRef] - Bai, Y.; Wang, D. Fundamentals of Fuzzy Logic Control—Fuzzy Sets, Fuzzy Rules and Defuzzifications. In Advanced Fuzzy Logic Technologies in Industrial Applications; Springer: Berlin/Heidelberg, Germany, 2006; pp. 17–36. [Google Scholar]
- Abdelsamad, S.F.; Morsi, W.G.; Sidhu, T.S. Probabilistic impact of transportation electrification on the loss-of-life of distribution transformers in the presence of rooftop solar photovoltaic. IEEE Trans. Sustain. Energy
**2015**, 6, 1565–1573. [Google Scholar] [CrossRef] - Geiles, T.J.; Islam, S. Impact of PEV Charging and Rooftop PV Penetration on Distribution Transformer Life. In Proceedings of the 2013 IEEE Power & Energy Society General Meeting, Vancouver, BC, Canada, 21—25 July 2013; pp. 1–5. [Google Scholar]
- Mehta, R.; Srinivasan, D.; Khambadkone, A.M.; Yang, J.; Trivedi, A. Smart charging strategies for optimal integration of plug-in electric vehicles within existing distribution system infrastructure. IEEE Trans. Smart Grid
**2016**, 9, 299–312. [Google Scholar] [CrossRef] - Kong, P.-Y.; Karagiannidis, G.K. Charging schemes for plug-in hybrid electric vehicles in smart grid: A survey. IEEE Access
**2016**, 4, 6846–6875. [Google Scholar] [CrossRef] - El-Bayeh, C.Z.; Mougharbel, I.; Saad, M.; Chandra, A.; Lefebvre, S.; Asber, D.; Lenoir, L. A Novel Approach for Sizing Electric Vehicles Parking Lot Located at Any Bus on a Network. In Proceedings of the 2016 IEEE Power and Energy Society General Meeting (PESGM), Boston, MA, USA, 17–21 July 2016; pp. 1–5. [Google Scholar]
- Li, Y.; Yang, Z.; Li, G.; Mu, Y.; Zhao, D.; Chen, C.; Shen, B. Optimal scheduling of isolated microgrid with an electric vehicle battery swapping station in multi-stakeholder scenarios: A bi-level programming approach via real-time pricing. Appl. Energy
**2018**, 232, 54–68. [Google Scholar] [CrossRef][Green Version] - Shahidinejad, S.; Filizadeh, S.; Bibeau, E. Profile of charging load on the grid due to plug-in vehicles. IEEE Trans. Smart Grid
**2011**, 3, 135–141. [Google Scholar] [CrossRef] - Shah, B.; Iqbal, F.; Abbas, A.; Kim, K.-I. Fuzzy logic-based guaranteed lifetime protocol for real-time wireless sensor networks. Sensors
**2015**, 15, 20373–20391. [Google Scholar] [CrossRef] [PubMed] - Clement-Nyns, K.; Haesen, E.; Driesen, J. The impact of charging plug-in hybrid electric vehicles on a residential distribution grid. IEEE Trans. Power Syst.
**2009**, 25, 371–380. [Google Scholar] - Lu, S.; Samaan, N.; Diao, R.; Elizondo, M.; Jin, C.; Mayhorn, E.; Zhang, Y.; Kirkham, H. Centralized and decentralized control for demand response. In Proceedings of the ISGT 2011, Anaheim, CA, USA, 17–19 January 2011; pp. 1–8. [Google Scholar]
- Brodt-Giles, D. WREF 2012: OPENEI-An Open Energy Data and Information Exchange for International Audiences. Available online: https://www.osti.gov/biblio/1063035 (accessed on 1 January 2019).
- Mazidi, M.; Abbaspour, A.; Fotuhi-Firuzabad, M.; Rastegar, M. Optimal Allocation of PHEV Parking Lots to Minimize Distribution System Losses. In Proceedings of the 2015 IEEE Eindhoven PowerTech, Eindhoven, The Netherlands, 29 June–2 July 2015; pp. 1–6. [Google Scholar]
- Cingolani, P.; Alcalá-Fdez, J. jFuzzyLogic: A java library to design fuzzy logic controllers according to the standard for fuzzy control programming. Int. J. Comput. Intell. Syst.
**2013**, 6, 61–75. [Google Scholar] [CrossRef][Green Version] - Tamura, S.; Kikuchi, T. V2G Strategy for Frequency Regulation Based on Economic Evaluation Considering EV Battery Longevity. In Proceedings of the 2018 IEEE International Telecommunications Energy Conference (INTELEC), Turino, Italy, 7–11 October 2018; pp. 1–6. [Google Scholar]
- Wang, Q.; Jiang, B.; Li, B.; Yan, Y. A critical review of thermal management models and solutions of lithium-ion batteries for the development of pure electric vehicles. Renew. Sustain. Energy Rev.
**2016**, 64, 106–128. [Google Scholar] [CrossRef] - Wang, Y.; Gao, Q.; Wang, G.; Lu, P.; Zhao, M.; Bao, W. A review on research status and key technologies of battery thermal management and its enhanced safety. Int. J. Energy Res.
**2018**, 42, 4008–4033. [Google Scholar] [CrossRef] - Kongjeen, Y.; Bhumkittipich, K. Impact of plug-in electric vehicles integrated into power distribution system based on voltage-dependent power flow analysis. Energies
**2018**, 11, 1571. [Google Scholar] [CrossRef][Green Version] - Holtsmark, B.; Skonhoft, A. The Norwegian support and subsidy policy of electric cars. Should it be adopted by other countries? Environ. Sci. Policy
**2014**, 42, 160–168. [Google Scholar] [CrossRef] - Miedema, G.; Infrastructure, E.C. Revolutionizing Fast Charging for Electric Vehicles. EV Charg. Infrastruct.
**2012**, 1–6. [Google Scholar] - Shafiee, S.; Fotuhi-Firuzabad, M.; Rastegar, M. Investigating the impacts of plug-in hybrid electric vehicles on power distribution systems. IEEE Trans. Smart Grid
**2013**, 4, 1351–1360. [Google Scholar] [CrossRef]

**Figure 2.**Two different types of EV owner’s daily trips: (

**a**) Routine trip between home and workplace; (

**b**) Non-routine trip among the home, workplace and intermediate places.

**Figure 3.**Probability distribution functions of arrival and departure time, distance and stay duration: (

**a**) PDF of normal distribution for departure and arrival time from/to home; (

**b**) PDF of normal distribution for departure and arrival time from/to PL; (

**c**) PDF of normal distribution for distance traveled; (

**d**) PDF of normal distribution for parking duration.

**Figure 4.**Membership functions of the fuzzified input and output variables for first stage FIS: (

**a**) Membership functions of departure time from home; (

**b**) Membership functions of arrival time to PL; (

**c**) Membership functions of mileage traveled.

**Figure 5.**Membership functions of the fuzzified input and output variables for the second stage FIS: (

**a**) Membership functions of remaining parking duration; (

**b**) Membership functions of required SoC; (

**c**) Membership functions of updated available power; (

**d**) Membership functions of preference.

**Figure 6.**Illustration of min-max operation for calculating the value of the PF variable for an EV with PD = 7-time slots, $So{C}^{req}$ = 28 kWh, and UAP = 105 kW.

**Figure 9.**Random distribution of arrival and departure times of EVs for the PLs connected to the three buses: (

**a**) Represent the PL at bus #820; (

**b**) Represent the PL at bus #834; (

**c**) Represent the PL at bus #844.

**Figure 11.**Battery capacities, arrival time SoC and required amount of energies according to the EVs next trip distances for the PLs connected to the three buses: (

**a**) Represents the PL connected to the bus #820; (

**b**) Represents the PL connected to the bus #834; (

**c**) Represents the PL connected to the bus #844.

**Figure 12.**Charging and discharging operation of EVs in the PLs connected to the three buses: (

**a**) Represents the PL connected to the bus #820; (

**b**) Represents the PL connected to the bus #834; (

**c**) Represents the PL connected to the bus #844.

**Figure 13.**Total load profile of the PLs connected to the three buses: (

**a**) Represents the PL connected to the bus #820; (

**b**) Represents the PL connected to the bus #834; (

**c**) Represents the PL connected to the bus #844.

**Figure 14.**The QoP with respect to FLIA and TSFLIA for the PLs connected to the three buses: (

**a**) Represents the PL connected to the bus #820; (

**b**) Represents the PL connected to the bus #834; (

**c**) Represents the PL connected to the bus #844.

${\mathit{M}}^{\mathit{t}\mathit{r}\mathit{a}}\text{}$ | $\mathit{P}{\mathit{L}}_{\mathit{t}}^{\mathit{a}\mathit{r}\mathit{r}}\text{}$ | |||||
---|---|---|---|---|---|---|

VEAPL | EAPL | NAPL | LAPL | VLAPL | ||

${\mathit{H}}_{\mathit{t}}^{\mathit{d}\mathit{e}\mathit{p}}$ | VEDH | VSMT | SMT | NMT | LMT | VLMT |

EDH | VSMT | SMT | SMT | NMT | LMT | |

NDH | VSMT | VSMT | SMT | NMT | NMT | |

LDH | VLMT | VSMT | VSMT | SMT | SMT | |

VLDH | VLMT | VLMT | VSMT | VSMT | VSMT |

$\mathit{P}\mathit{F}\text{}$ | UAP | |||||
---|---|---|---|---|---|---|

VLAP | LAP | MAP | HAP | VHAP | ||

$So{C}^{req}$ | VL | LPF | LPF | LPF | LPF | MPF |

L | LPF | LPF | MPF | MPF | MPF | |

M | LPF | MPF | MPF | MPF | HPF | |

H | MPF | APF | HPF | HPF | HPF | |

VH | HPF | HPF | HPF | HPF | HPF |

$\mathit{P}\mathit{F}\text{}$ | UAP | |||||
---|---|---|---|---|---|---|

VLAP | LAP | MAP | HAP | VHAP | ||

$So{C}^{req}$ | VL | LPF | LPF | LPF | MPF | MPF |

L | LPF | LPF | MPF | MPF | MPF | |

M | LPF | LPF | HPF | HPF | HPF | |

H | MPF | HPF | HPF | HPF | HPF | |

VH | MPF | HPF | HPF | HPF | HPF |

$\mathit{P}\mathit{F}\text{}$ | UAP | |||||
---|---|---|---|---|---|---|

VLAP | LAP | MAP | HAP | VHAP | ||

$So{C}^{req}$ | VL | LPF | LPF | LPF | LPF | MPF |

L | LPF | LPF | LPF | MPF | MPF | |

M | LPF | LPF | MPF | MPF | MPF | |

H | LPF | LPF | HPF | HPF | HPF | |

VH | MPF | HPF | HPF | HPF | HPF |

Node # | Lumped Load (kW) | Residential Load (kW) | Number of Houses |
---|---|---|---|

860 | 60 | 42 | 15 |

840 | 27 | 19 | 7 |

844 | 405 | 284 | 102 |

848 | 60 | 42 | 15 |

890 | 450 | 315 | 113 |

830 | 45 | 32 | 11 |

Total | 1047 | 733 | 264 |

From Bus # | To Bus # | Lumped Load (kW) | Assumed Residential Load (kW) | Number of Houses |
---|---|---|---|---|

802 | 806 | 55 | 39 | 14 |

808 | 810 | 16 | 11 | 4 |

818 | 820 | 34 | 24 | 9 |

820 | 822 | 135 | 95 | 34 |

816 | 824 | 5 | 4 | 1 |

824 | 826 | 40 | 28 | 10 |

824 | 828 | 4 | 3 | 1 |

828 | 830 | 7 | 5 | 2 |

854 | 856 | 4 | 3 | 1 |

832 | 858 | 15 | 11 | 4 |

858 | 864 | 2 | 1 | 1 |

858 | 834 | 32 | 22 | 8 |

834 | 860 | 146 | 102 | 37 |

860 | 836 | 82 | 57 | 21 |

836 | 840 | 40 | 28 | 10 |

862 | 838 | 28 | 20 | 7 |

842 | 844 | 9 | 6 | 2 |

844 | 846 | 45 | 32 | 11 |

846 | 848 | 23 | 16 | 6 |

Total | 722 | 505 | 182 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Hussain, S.; Lee, K.-B.; A. Ahmed, M.; Hayes, B.; Kim, Y.-C. Two-Stage Fuzzy Logic Inference Algorithm for Maximizing the Quality of Performance under the Operational Constraints of Power Grid in Electric Vehicle Parking Lots. *Energies* **2020**, *13*, 4634.
https://doi.org/10.3390/en13184634

**AMA Style**

Hussain S, Lee K-B, A. Ahmed M, Hayes B, Kim Y-C. Two-Stage Fuzzy Logic Inference Algorithm for Maximizing the Quality of Performance under the Operational Constraints of Power Grid in Electric Vehicle Parking Lots. *Energies*. 2020; 13(18):4634.
https://doi.org/10.3390/en13184634

**Chicago/Turabian Style**

Hussain, Shahid, Ki-Beom Lee, Mohamed A. Ahmed, Barry Hayes, and Young-Chon Kim. 2020. "Two-Stage Fuzzy Logic Inference Algorithm for Maximizing the Quality of Performance under the Operational Constraints of Power Grid in Electric Vehicle Parking Lots" *Energies* 13, no. 18: 4634.
https://doi.org/10.3390/en13184634