# An Integrated Approach to Optimal Charging Scheduling of Electric Vehicles Integrated with Improved Medium-Voltage Network Reconfiguration for Power Loss Minimization

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## Abstract

**:**

## 1. Introduction

_{2}emissions [3,4].

## 2. Problem Formulation

_{c}is the loss function, t is a one-hour time interval over the time period (T = 24 h), I

_{i}is the current in the branch i, nb is the total number of branches, and k

_{i}is the variable that represents the topology status of the branches (0 = open, 1 = closed). This topology is determined during the network reconfiguration process. EVs act as the charging load on the network; their random connection with the network increases the I

_{i}flowing in the ith branch, which may result in the overloading of the line, thus causing high line losses. To limit this current, a smart selection of the EVs is required, which minimizes objection function states in Expression (1). The formulated objective is subject to various constraints. In the EV charging environment, the total load demand of a system includes the EV charging load and the residential load. At any instant of time ($t$), this total load demand should not exceed the maximum demand level of a system to avoid overloading the system. Expressions (2) and (3) show that the constraint can limit the dispatch of uneconomical units to meet the extra demand and save the operational cost of the system.

^{Max demand}is the peak residential load demand throughout a day. However, if a random charging is performed during this interval, this will violate the constraint with increased system losses. In addition, P

_{j}

^{load}(t) is the total power consumption at the bus j for the time interval (t), P

_{j}

^{Re sidential}(t) is the residential load demand at the bus j for time step (t), and P

_{j}

^{EV}(t) is the EV load demand at the bus j in a time interval (t). To ensure power, the quality of the system voltage magnitude at each node must be within the permissible ranges determined by the utilities companies. In this paper, the upper voltage limit of 10% (1.10 per unit) and lower voltage limit of 6% (0.94 per unit) are tested [22].

_{min}and V

_{max}are the minimum and maximum allowable voltages, respectively, and V

_{j}is the voltage at the node j. Similarly, at every scheduling step of SOC consideration, it is very important to determine the EV energy demand. This constraint is very helpful for the health and safety of the battery. Here, the SOC constraint with upper and lower limits is defined in Expression (5) as

_{k,min}is the minimum state of charge of Kth EV, which is assumed as 20% of rated capacity. In addition, SOC

_{k,max}is the maximum charging capacity of Kth EV, and SOC

_{k}is the current state of charge of Kth EV when it connects with the system. In the scheduling process, it is assumed that once a particular EV is selected for the charging, it will not disconnect from the system until it attains its required SOC. The distribution network operates with radial configuration due to its simple and economical design. Radial configuration is typically used as a constraint for network reconfiguration. Network reconfiguration provides a new topology of the network by altering the closed/open status of the switches. However, the network should not lose its radial topology when switches change their status. Radial network configuration is used as a constraint while implementing network reconfiguration in the second stage of the research and is handled by all spanning trees algorithms [23].

## 3. Proposed Algorithm for Optimal Charging Scheduling Integrated with Network Reconfiguration

#### 3.1. Optimal EV Charging Scheduling

_{max}, it is no longer a part of the scheduling algorithm. At the end of every time step, optimal hourly scheduled load data are obtained, which reflect the minimum network power loss. Once the Stage 1 task is completed, then hourly load data, which consist of conventional and scheduled charging load of EVs, are then fed to a later stage of network reconfiguration. In this stage, the same BPSO algorithm is used, and an hourly optimal network configuration is determined in the presence of the scheduled EVs charging load, thereby reducing network losses and improving network performance. The radiality, which is the main constraint of this stage, ensures the unidirectional power flow of the system. This stage determines the optimal combinations of network switches that should be opened so that power flowing through the branches follows the shortest possible path, thus generating minimum power loss. The solution process of network reconfiguration is illustrated in the second stage of Figure 1, in which each stage is implemented with the BPSO algorithm and is detailed in the following section.

#### 3.2. BPSO Algorithm

_{i}and velocity V

_{i}in a d-dimensional search space. The position of a particle X

_{i}is represented as a vector in a binary space (i.e., X

_{i}$\in \left\{0,1\right\})$, whereas the particle’s velocity is a vector in the continuous solution space.

_{i}

^{(K+1)}is the particle’s velocity in the range V

_{max}= 4; V

_{min}= −4. In addition, P

_{best,i}

^{k}is the personal/local best position of particle i up to iteration number k, P

_{best,i}

^{k}is the global best position among all P

_{best,i}

^{k}up to iteration number k, ω is the inertia weight linearly varied from 0.9 to 0.4, C

_{1}and C

_{2}are the acceleration factors in the range of 2.0–2.05, and $ran{d}_{1}\text{}\mathrm{and}\text{}ran{d}_{2}$ are the random numbers in the range of (0, 1). Unlike the conventional PSO, in the BPSO algorithm the position of a particle represents a bit and its mutation from zero to one or one to zero is carried out with transformation function (i.e., sigmoid function), which is expressed as

## 4. Results and Discussion

#### 4.1. Modified IEEE 33-Node Medium-Voltage Network

#### 4.2. Uncoordinated EV Charging

#### 4.3. Coordinated EV Charging

#### 4.4. Coordinated EV Charging with Network Reconfiguration

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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S.NO. | From Node | To Node | Switch | R (Ω) | X (Ω) | P (kW) | P.F |
---|---|---|---|---|---|---|---|

1 | 1 | 2 | S1 | 0.0922 | 0.0470 | 40 | 0.9 |

2 | 2 | 3 | S2 | 0.4930 | 0.2512 | 45 | |

3 | 3 | 4 | S3 | 0.3660 | 0.1864 | 60 | |

4 | 4 | 5 | S4 | 0.3811 | 0.1941 | 30 | |

5 | 5 | 6 | S5 | 0.8190 | 0.7070 | 60 | |

6 | 6 | 7 | S6 | 0.1872 | 0.6188 | 100 | |

7 | 7 | 8 | S7 | 1.7114 | 0.2351 | 100 | |

8 | 8 | 9 | S8 | 1.0300 | 0.7400 | 60 | |

9 | 9 | 10 | S9 | 1.0440 | 0.7400 | 60 | |

10 | 10 | 11 | S10 | 0.1966 | 0.0651 | 40 | |

11 | 11 | 12 | S11 | 0.3744 | 0.1298 | 60 | |

12 | 12 | 13 | S12 | 1.4680 | 1.1549 | 30 | |

13 | 13 | 14 | S13 | 0.5416 | 0.7129 | 60 | |

14 | 14 | 15 | S14 | 0.5910 | 0.5260 | 60 | |

15 | 15 | 16 | S15 | 0.7460 | 0.7462 | 60 | |

16 | 16 | 17 | S16 | 1.2890 | 1.2889 | 60 | |

17 | 17 | 18 | S17 | 0.7320 | 0.7320 | 45 | |

18 | 2 | 19 | S18 | 0.1640 | 0.1640 | 45 | |

19 | 19 | 20 | S19 | 1.5042 | 1.5042 | 45 | |

20 | 20 | 21 | S20 | 0.4095 | 0.4095 | 45 | |

21 | 21 | 22 | S21 | 0.7089 | 0.7089 | 45 | |

22 | 3 | 23 | S22 | 0.4512 | 0.4512 | 45 | |

23 | 23 | 24 | S23 | 0.8980 | 0.8980 | 100 | |

24 | 24 | 25 | S24 | 0.8960 | 0.8959 | 100 | |

25 | 6 | 26 | S25 | 0.2031 | 0.2031 | 30 | |

26 | 26 | 27 | S27 | 0.2842 | 0.2842 | 30. | |

27 | 27 | 28 | S28 | 1.0589 | 1.0589 | 30 | |

28 | 28 | 29 | S29 | 0.8043 | 0.8043 | 60 | |

29 | 29 | 30 | S30 | 0.5074 | 0.5074 | 100 | |

30 | 30 | 31 | S31 | 0.9745 | 0.9745 | 82.5 | |

31 | 31 | 32 | S32 | 0.3105 | 0.3105 | 100 | |

32 | 32 | 33 | S33 | 0.3411 | 0.3411 | 30 | |

Tie Switches (Normally open to maintain the radial topology of the network) | |||||||

S. No. | From Node | To Node | Tie Switches | ||||

1 | 8 | 21 | S33 | ||||

2 | 9 | 15 | S34 | ||||

3 | 12 | 22 | S35 | ||||

4 | 18 | 33 | S36 | ||||

5 | 25 | 29 | S37 |

Parameters | Uncoordinated Charging | Coordinated Charging without Network Reconfiguration | Coordinated Charging with Network Reconfiguration | ||||||
---|---|---|---|---|---|---|---|---|---|

${V}_{ref}$ $\left(p.u\right)$ | ${V}_{i}$ $\left(p.u\right)$ | $\Delta V$ $(\%)$ | ${V}_{ref}$ $\left(p.u\right)$ | ${V}_{i}$ $\left(p.u\right)$ | $\Delta V$ $(\%)$ | ${V}_{ref}$ $\left(p.u\right)$ | $\Delta V$ $(\%)$ | $\Delta V$ $(\%)$ | |

Minimum Voltage Deviation (%) $\Delta {V}_{min}=\frac{{V}_{ref}-{V}_{i,max}}{{V}_{ref}}\times $100$\%$ | 1 | 0.96 | 4 | 1 | 0.96 | 4 | 1 | 0.97 | 3 |

Maximum Voltage deviation (%) $\Delta {V}_{max}=\frac{{V}_{ref}-{V}_{i,min}}{{V}_{ref}}\times $100$\%$ | 1 | 0.93 | 7 | 1 | 0.94 | 6 | 1 | 0.95 | 5 |

Current loading (p.u) ${I}_{s,\text{}min}$ | 0.86 | 0.86 | 0.85 | ||||||

Current loading (p.u) ${I}_{s,max}$ | 1.03 | 1.00 | 0.99 | ||||||

Power loss (kW) ${P}_{\text{}loss,min}$ | 75 | 75 | 51 | ||||||

Power loss (kW) ${P}_{loss,max}$ | 104 | 99 | 68 | ||||||

Energy loss (MWh) | 2.22 | 2.20 | 1.51 | ||||||

Open Switches | S33, S34, S35, S36, S37 | S33, S34, S35, S36, S37 | S7, S9, S14, S28, S31 |

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**MDPI and ACS Style**

Amin, A.; Tareen, W.U.K.; Usman, M.; Memon, K.A.; Horan, B.; Mahmood, A.; Mekhilef, S.
An Integrated Approach to Optimal Charging Scheduling of Electric Vehicles Integrated with Improved Medium-Voltage Network Reconfiguration for Power Loss Minimization. *Sustainability* **2020**, *12*, 9211.
https://doi.org/10.3390/su12219211

**AMA Style**

Amin A, Tareen WUK, Usman M, Memon KA, Horan B, Mahmood A, Mekhilef S.
An Integrated Approach to Optimal Charging Scheduling of Electric Vehicles Integrated with Improved Medium-Voltage Network Reconfiguration for Power Loss Minimization. *Sustainability*. 2020; 12(21):9211.
https://doi.org/10.3390/su12219211

**Chicago/Turabian Style**

Amin, Adil, Wajahat Ullah Khan Tareen, Muhammad Usman, Kamran Ali Memon, Ben Horan, Anzar Mahmood, and Saad Mekhilef.
2020. "An Integrated Approach to Optimal Charging Scheduling of Electric Vehicles Integrated with Improved Medium-Voltage Network Reconfiguration for Power Loss Minimization" *Sustainability* 12, no. 21: 9211.
https://doi.org/10.3390/su12219211