# A Novel Algorithm for Controlling Active and Reactive Power Flows of Electric Vehicles in Buildings and Its Impact on the Distribution Network

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## Abstract

**:**

## 1. Introduction

#### 1.1. Problem Statement

_{2}and other harmful gases (SO

_{2}, NO

_{x}, etc.) [1]. Plug-in hybrid electric vehicles (PHEVs) and fully battery electric vehicles (BEVs) are lumped together in this study by (EVs), in which the vehicles can be connected to the grid. EVs will definitely support the future deployment of smart grids because they are considered as a spinning reserve and able to store and deliver energy whenever it is needed. The integration of EVs has many benefits, such as providing ancillary services to the grid [2,3], and providing stability when fluctuant renewable energy sources are connected to the network [1,4,5]. Despite all the advantages that EVs can provide the smart grid, their integration should be supervised and controlled to maximize the profit from their existence. Hence, extensive studies should be conducted to propose the best optimization algorithms and control strategies that maximize the benefit of integrating EVs into the distribution systems.

#### 1.2. Literature Review

#### 1.3. Impediments and Barriers of Other Studies

#### 1.4. Contributions

- Main and branch circuit breaker rating into the optimization model,
- Upper and lower limits of both active and reactive power on the distribution transformer,
- real charging and discharging power profiles of the EVs,
- It predicts and calculates the available power to be consumed at each instant and inform the end-user how much energy is left to use every day to charge his EV while respecting the power and energy limits at home,
- It informs the end-user how much energy he should reduce at home in order to attain the desired State of Charge level,
- The discharging mode could be selected according to the EV owner’s desire,
- The algorithm gives the EV owner the choice to participate or not in the ancillary services such as voltage and power flow regulations.

#### 1.5. Paper Organization

## 2. Problem Formulation

#### 2.1. Objective Function

#### 2.2. Constraints

#### 2.2.1. Mode of Operation

#### 2.2.2. Active Power Constraints

#### 2.2.3. State of Charge (SOC) Constraints

#### 2.2.4. Reactive Power Constraints

#### 2.2.5. Voltage Constraint

#### 2.3. Management of Home Power

#### 2.4. Proposed Algorithm to Solve the Problem

Proposed Algorithm: |

- 1
**Input Data**- 2
- Electric Vehicle:
- 3
- -Charging and discharging efficiency
- 4
- -State of Charge (SOC): Initial, final, minimum, maximum
- 5
- -Battery Capacity
- 6
- -Minimum and maximum acceptable charging and discharging power rate
- 7
- -Arrival and departure time of the EV
- 8
- -Battery internal characteristics
- 9
- Power Network:
- 10
- -Minimum and maximum voltage limits
- 11
- -Electricity Price
- 12
- -Transformer active power rating ${P}_{t}^{DT\text{}Limit}$
- 13
- Home:
- 14
- -Main and branch circuit breaker limits and ratings
- 15
- -Baseload power demand
- 16
- -Voltage measurement
- 17
- -Minimum and Maximum Active Power Limits
- 18
- -Minimum and Maximum Reactive Power Limits Equations (29)–(31)
- 19
**Calculate the values of:**- 20
- Respected Upper Limit of the Active Power Equation (6)
- 21
- Active Power Limit for the branch circuit breaker Equation (7)
- 22
- Maximum available active power at home at instant “t” Equation (8)
- 23
- Minimum Active Power Limit Equation (9)
- 24
- Available energy at home to charge the EV Equation (20)
- 25
**While**“Available energy at home to charge EV” < “Needed energy to**…**charge the EV to the desired SOC level” as in Equations (34) and (35),- 26
- Ask the user to reduce the power consumption of some appliances at home
- 27
**End While**- 28
- Existing reactive power demand at home Equations (27) and (28)
- 29
**Optimization Process**- 30
- Optimize the total load according to the objective function Equation (1)
- 31
- Subject to the Constraints Equations (36) to (26)
- 32
- Output of the Optimization
- 33
- -Charging and Discharging Profile of the EV Equations (10), (11), (17), (18)
- 34
- -Status of the charging and discharging mode of the EV Equations (2)–(4)
- 35
- -Total Active Power demand at home Equation (5)
- 36
- -Final State of Charge of the EV’s battery Equation (19)
- 37
**Calculation on the transformer level (Active and Reactive power demand)**- 38
- Do the same steps as before for all homes on the same transformer
- 39
- Calculate the total active power of all homes on the transformer ${P}_{t}^{DT\text{}Load}$
- 40
- Calculate the total reactive power of all homes on the transformer ${Q}_{t}^{DT\text{}Load}$
- 41
**If**${P}_{t}^{DT\text{}Load}{P}_{t}^{DT\text{}Limit}$,- 42
- Reduce $RULP\left(t\right)$ and ${\alpha}_{MCB}\left(t\right)$ at homes
- 43
- Go back to
**Step 19**and start recalculating all the values - 44
**End If**%(steps from 19 to 41 are repeated until ${\mathrm{P}}_{\mathrm{t}}^{\mathrm{DT}\text{}\mathrm{Load}}\le {\mathrm{P}}_{\mathrm{t}}^{\mathrm{DT}\text{}\mathrm{Limit}}$)- 45
- Measure the voltage on the transformer ${\mathrm{V}}_{\mathrm{t}}^{\mathrm{DT}}$
- 46
**If**${\mathrm{V}}_{\mathrm{t}}^{\mathrm{DT}}<{\mathrm{V}}_{\mathrm{min}}^{\mathrm{DT}}$,- 47
- EVs inject reactive power respecting its maximum and minimum limits as in Equations (31) and (32)
- 48
- Go back to
**Step 45**and measure ${\mathrm{V}}_{\mathrm{t}}^{\mathrm{DT}}$ - 49
**End If**%(steps are repeated until ${\mathrm{V}}_{\mathrm{t}}^{\mathrm{DT}}\ge {\mathrm{V}}_{\mathrm{min}}^{\mathrm{DT}}$)- 50
**If**${\mathrm{V}}_{\mathrm{t}}^{\mathrm{DT}}>{\mathrm{V}}_{\mathrm{max}}^{\mathrm{DT}}$,- 51
- EVs absorb reactive power respecting its maximum and minimum limits as in Equations (31) and (32)
- 52
- Go back to
**Step 45**and measure ${\mathrm{V}}_{\mathrm{t}}^{\mathrm{DT}}$ - 53
**End If**%(steps are repeated until ${\mathrm{V}}_{\mathrm{t}}^{\mathrm{DT}}<{\mathrm{V}}_{\mathrm{max}}^{\mathrm{DT}}$)- 54
**Repeat the whole procedure for the next time interval**${t}_{\mathrm{next}}={t}_{\mathrm{initial}}+\mathsf{\Delta}t$
End of the Algorithm |

## 3. Results and Discussions for a Single Home

#### 3.1. Different Scenarios Are Studied at Home

#### 3.2. Considerations for a Single Home

#### 3.3. Results for a Single Home

#### 3.3.1. Power and Charging Rates Profiles

#### 3.3.2. Voltage Profiles

#### 3.3.3. Energy Cost Profiles

## 4. Results and Discussions for a Cluster of Homes in the Same Bus

#### 4.1. Considerations for a Cluster of Homes on the Same Bus

#### 4.2. Results for a Cluster of Homes on the Same Bus

## 5. Summary of the Main Outcomes of the Proposed Algorithm

- The power limit of the transformer is respected,
- The techno-economic losses on the transformer and lines of the network are reduced,
- Voltage limits on the network and transformer are respected,
- The electricity cost at home is minimized.

## 6. Conclusions and Future Work

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

Abbreviations | |

DSO | Distribution system operator |

DT | Distribution transformer |

EV | Electric vehicle |

IEEE | Institute of Electrical and Electronic Engineering |

RES | Renewable energy sources |

SOC | State of charge of the battery in the electric vehicle |

U-EV | Uncoordinated Charging Strategy for Electric Vehicles |

CC-EV | Coordinated Charging Strategy for Electric Vehicles |

CCD-EV | Our proposed Coordinated Charging and Discharging Strategy for Electric Vehicles |

Symbols | |

${\alpha}_{MCB}\left(t\right)$, ${\alpha}_{BCB}\left(t\right)$ | Avoiding tripping factors of the main and branch circuit breakers [-] |

$\mathsf{\Delta}t$ | Time step interval, e.g., 0.5 h in this study [h] |

$\phi \left(t\right)$ | Phase angle |

$C{B}_{NR}$, $C{B}_{NR}^{PEV}$ | Main and branch circuit breaker nominal rates, respectively [kW] |

${C}_{Elec}\left(t\right)$ | Electricity cost at instant “$t$” [$/kWh] |

${P}_{A}^{Max}\left(t\right)$ | Maximum available active power at home at instant “$t$” [kW] |

${P}_{B,C}^{Max}\left(t\right)$ | Maximum charging power limit for a certain SOC of the battery [kW] |

${P}_{B,DC}^{Max}\left(t\right)$ | Maximum discharging power limits for a certain SOC of the battery [kW] |

${P}_{C}\left(t\right)$ | Absorbed active power by the EV using charging mode [kW] |

${P}_{DC}\left(t\right)$ | Injected active power by the EV using discharging mode [kW] |

${P}_{Load}\left(t\right)$ | Baseload power demand of the home without EV [kW] |

${P}_{BCB}^{RL}\left(t\right)$ | Power limit not to be overpassed on the EV branch circuit breaker (BCB) [kW] |

${P}_{t}^{HL}$ | Active power limit at home [kW] |

${P}_{t}^{HL\_CB}$ | Active power limit of the main circuit breaker at home [kW] |

${P}_{t}^{TL}$ | Active power limit on the distribution transformer [kW] |

$P{F}_{Min}$, $P{F}_{Max}$ | Minimum and maximum power factor limits |

${Q}_{A}\left(t\right)$ | Absorbed reactive power by the EV [kVAR] |

${Q}_{I}\left(t\right)$ | Injective reactive power by the EV [kVAR] |

${Q}_{Load}\left(t\right)$ | Reactive power demand of the home without EV [kVAR] |

$RLLP\left(t\right)$ | Respected Lower Limit of the Active Power for the total load including the EV at instant “$t$” [kW] |

$RLLQ\left(t\right)$ | Respected Lower Limit of the Reactive Power for the total load including the EV at instant “$t$” [kVAR] |

$RULP\left(t\right)$ | Respected upper limit of active power at instant “$t$” for the total load [kW] |

$RULQ\left(t\right)$ | Respected upper limit of reactive power at instant “$t$” for the total load [kVAR] |

${S}_{A}\left(t\right)$ | Algorithm decision result, it is equal to 1 if the decision is about performing charging or discharging, and 0 if no action should be performed [-] |

${S}_{C}\left(t\right)$, ${S}_{DC}\left(t\right)$,$\text{}{S}_{I}\left(t\right)$ | Binary flags of the charging, discharging, and idle modes, respectively. (“1” means the mode is turned on; otherwise, it is “0”, and just one mode at a time could be applied) [-] |

${S}_{g}\left(t\right)$ | Status of the load, $RULP\left(t\right)-{P}_{Load}\left(t\right)>0$, and “0” otherwise [-] |

${S}_{l}\left(t\right)$ | Status of the load,$\text{}{S}_{l}\left(t\right)=1$ if $RULP\left(t\right)-{P}_{Load}\left(t\right)<0$, and “0” otherwise [-] |

${S}_{Plug}\left(t\right)$ | Plug status of the EV, it is equal to “1” if the vehicle is connected to the grid, and “0” otherwise [-] |

${S}_{Total}\left(t\right)$ | Total apparent power at home |

$SO{C}_{DF}$ | Desired final state of charge of the battery in the EV |

$T$ | Period of time for the study [h] |

${t}_{A}$ | Arrival time of the EV to the home when it is plugged-in [h] |

$U\left(x\right)$ | Binary function that is equal to one when $x>0$, otherwise it is zero [-] |

$V$ | Nominal voltage, (i.e., 220 V) [V] |

${V}_{t}^{DT}$ | Voltage measured on the transformer [V] |

${V}_{min}^{DT}$, ${V}_{max}^{DT}$ | Minimum and maximum voltage limits on the transformer [V] |

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**Figure 2.**Impact of reactive power on the voltage profile. Case 2, without injecting reactive power, Case 3 with injecting reactive power.

**Figure 4.**Electricity cost (electricity rate) profile for, fixed price, time-of-use price, and dynamic price.

Parameters | Without EVs | U-EV | CC-EV | CCD-EV |
---|---|---|---|---|

Circuit Breaker (kW) | 7.36 kW | 7.36 kW | 7.36 kW | 7.36 kW |

Load in (kW) | 4.9282 Min 8.1590 Max | 4.9385 Min 10.079 Max | 4.9385 Min 8.1590 Max | 4.9385 Min 7.3600 Max |

Circuit Breaker (A) | 40A | 40A | 40A | 40A |

Line current in (A) | 26.783 Min 44.342 Max | 26.839 Min 54.777 Max | 26.839 Min 44.342 Max | 26.839 Min 40.000 Max |

Voltage (V) | 225 Min 228.17 Max | 223.12 Min 228.17 Max | 225 Min 228.16 Max | 225.78 Min 228.16 Max |

Voltage Drop in (%) Advised limit is 2% | 0.797 Min 2.1747 Max | 0.797 Min 2.993 Max | 0.801 Min 2.174 Max | 0.801 Min 1.834 Max |

Power Losses (kW) | 0.0809 Min 0.2218 Max 6.128 Total 0.0000% | 0.0812 Min 0.3384 Max 7.896 Total +28.8594% | 0.0812 Min 0.2218 Max 7.653 Total +24.8875% | 0.0812 Min 0.1805 Max 7.650 Total +24.8466% |

Parameters | Without EV | U-EV | CC-EV | CCD-EV |
---|---|---|---|---|

Fixed Cost ($) | 0.1692 Min 0.2802 Max 10.023 Total | 0.1692 Min 0.3462 Max 11.264 Total | 0.1692 Min 0.2802 Max 11.264 Total | 0.1692 Min 0.2802 Max 11.264 Total |

Time-Of-Use ($) | 0.1478 Min 0.4079 Max 10.330 Total | 0.1478 Min 0.5039 Max 11.702 Total | 0.1478 Min 0.4079 Max 11.414 Total | 0.1478 Min 0.4079 Max 11.382 Total |

Dynamic Price ($) | 0.1467 Min 0.4022 Max 10.960 Total | 0.1467 Min 0.4969 Max 12.356 Total | 0.1467 Min 0.4022 Max 12.151 Total | 0.1467 Min 0.4022 Max 12.135 Total |

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## Share and Cite

**MDPI and ACS Style**

El-Bayeh, C.Z.; Alzaareer, K.; Brahmi, B.; Zellagui, M.
A Novel Algorithm for Controlling Active and Reactive Power Flows of Electric Vehicles in Buildings and Its Impact on the Distribution Network. *World Electr. Veh. J.* **2020**, *11*, 43.
https://doi.org/10.3390/wevj11020043

**AMA Style**

El-Bayeh CZ, Alzaareer K, Brahmi B, Zellagui M.
A Novel Algorithm for Controlling Active and Reactive Power Flows of Electric Vehicles in Buildings and Its Impact on the Distribution Network. *World Electric Vehicle Journal*. 2020; 11(2):43.
https://doi.org/10.3390/wevj11020043

**Chicago/Turabian Style**

El-Bayeh, Claude Ziad, Khaled Alzaareer, Brahim Brahmi, and Mohamed Zellagui.
2020. "A Novel Algorithm for Controlling Active and Reactive Power Flows of Electric Vehicles in Buildings and Its Impact on the Distribution Network" *World Electric Vehicle Journal* 11, no. 2: 43.
https://doi.org/10.3390/wevj11020043