# Renewable Energy Tracking and Optimization in a Hybrid Electric Vehicle Charging Station

^{*}

## Abstract

**:**

## Featured Application

**The multicriteria methodology for the scheduling of a hybrid EV charging station could be applied to any commercial EV charging station. The driver’s preferences about the amount of renewable energy share can be easily implemented in a charging software application.**

## Abstract

## 1. Introduction

- (a)
- Voltage dips during periods of EV charging (particularly for fast chargers);
- (b)
- Reduction in power quality (both slow and fast charging stations are sources of harmonic distortion);
- (c)
- EV battery deterioration and capacity decrease (due to the battery’s voltage level or temperature increase);
- (d)
- Overloading of distribution network transformers;
- (e)
- Increased energy losses (especially with larger direct current (DC) fast charging station penetration)

- the simultaneous optimization of charging/discharging BES and EV charging power;
- the implementation of energy tracking methodology that monitors the origin of energy from and to the battery;
- the multiobjective optimization of different conflicting criteria.

## 2. Energy Tracking Methodology

#### 2.1. Energy Tracking during Battery Charge/Discharge

_{S}, and the accumulated energy from the grid with SOC

_{G}. The battery power P

_{B}, the share of battery power from solar energy P

_{BS}and the share of battery power from the grid P

_{BG}will be positive if the battery is charging and negative if it is discharging. The charge and discharge behavior of the battery during the time step Δt can be generically modeled as follows:

_{c}

_{/d}equals η

_{c}when charging and 1/η

_{d}when discharging the battery. If the total power that discharges the battery is P

_{B}, then the power from renewable sources (P

_{BS}) and the grid (P

_{BG}) are given by Equations (5) and (6), respectively:

#### 2.2. Energy Tracking during EV Charging

_{S}), power from the public grid (P

_{G}), battery power originating from the PV panel (P

_{BS}), and battery power originating from the grid (P

_{BG}).

#### 2.3. Battery Degradation Model

_{loss}is the percentage of capacity loss induced by cycling. Both factors B

_{1}and B

_{2,}are functions of temperature. I

_{rate}is the charge/discharge rate expressed as a C-rate. Ah is the total Ah-throughput for a given period. Coefficient values and units are given in [34].

## 3. Optimization Problem

_{t}, the criterion can be mathematically represented in (14). c

_{B}represents the levelized daily costs of battery installation and operation (€/kWh·day).

- u
_{i}(x_{i}) = the single-attribute utility value for attribute i with value x_{i}(ranges from 0 to 1); - k
_{i}= a parameter from the tradeoffs for component i; - K = a normalization constant.

_{res}), minimal battery and energy costs (U

_{tc}), and minimal battery degradation (U

_{bd}). In the second step, the multiobjective optimization is performed applying MAUT for the utility aggregation (20). Individual utilities for renewable energy, costs and battery degradation are represented in Equations (25)–(27), respectively.

_{B}

_{,t}and 24 EV charging powers P

_{EV}

_{,t}). The fitness function is given with the Equation (22), obtained after the calculation of (13)–(15) and (20)–(25). Equality constraints are given in Equations (1)–(4) and (7)–(11). Inequality constraints relating to the maximal and minimal charging/discharging powers and battery state of charge are given in Equations (16)–(19). The Matlab GA solver was used with the size of the initial population of 200.

## 4. Results

_{S}) and load demand (P

_{L})—the power from the grid (P

_{g}), battery power (P

_{bat}), and the optimized EV charging power (P

_{ev}). Figure 5b represents the state of charge (SOC) of two virtual “battery compartments”—for renewable solar energy (SOC

_{S}) and energy from the grid (SOC

_{g}). Figure 5c gives the EV solar (P

_{evs}) power component and grid component (P

_{evg}), while Figure 5d represents the share of battery power from renewables (P

_{bs}) and battery power coming from the stored grid energy (P

_{bg}) in the optimized charge and discharge battery schedule.

_{1}= k

_{2}= k

_{3}= 0.33. Results are presented in Figure 6.

_{i}for single criteria are obtained using the scalarization expressions (24)–(26). Optimization results for the complementary multi-attribute case are presented in Figure 7.

_{1}= 0.6, k

_{2}= 0.3 and k

_{3}= 0.1. The graph represents the values of the individual utility function and the total utility function for different system configurations, starting from the case when the battery is not installed at all (C = 0) to the maximum capacity of 70 kWh. The calculation for all configurations was done with the same relative parameters: the initial state of charge of the battery is equal to one half of the battery capacity (SOC

_{0}= 0.5 C), where the initial shares of energy from the network and solar panels are equally distributed (SOC

_{BS}

_{,0}= SOC

_{BG}

_{,0}= 0.5 SOC

_{0}).

_{1}= 0.2, k

_{2}= k

_{3}= 0.3; K = 0.3. The results are shown in Figure 9.

## 5. Discussion

_{bd}= 1), the total costs are also close to the minimum values (U

_{sc}= 0.9), but the share of energy from renewable sources is the lowest (U

_{res}= 0.62). As the capacity increases, the value of this function increases to a maximum of (U

_{res}= 0.85). This value also determines the total maximum of the system. As battery capacity continues to grow, the share of renewables is not increased due to constrained battery charging and discharging power.

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

SOC_{t} | Battery state of charge at time t |

SOC_{S}_{,}_{t} | Solar energy share state of charge at time t |

SOC_{G}_{,}_{t} | Public grid energy share state of charge at time t |

C | Battery capacity (kWh) |

k_{c}_{/}_{d} | Charging/discharging efficiency |

P_{B}_{,}_{t} | Battery power at time t (kW) |

P_{BS}_{,} | Battery power originating from solar energy at time t (kW) |

P_{BG}_{,}_{t} | Battery power originating from the public grid at time t (kW) |

P_{EV}_{,}_{t} | Electric vehicle charging power at time t (kW) |

P_{EVS}_{,}_{t} | Electric vehicle charging power originating from solar energy at time t (kW) |

P_{EVG}_{,}_{t} | Electric vehicle charging power originating from the public grid at time t (kW) |

P_{EVBS}_{,}_{t} | Electric vehicle charging power originating from the solar battery share at time t (kW) |

P_{EVBG}_{,}_{t} | Electric vehicle charging power originating from the grid battery share at time t (kW) |

P_{S}_{,}_{i}_{,}_{t}; Q_{S}_{,}_{i}_{,}_{t} | Solar PV plant power at node i, at time t (kW) |

P_{B}_{,}_{i}_{,}_{t}; Q_{B}_{,}_{i}_{,}_{t} | Battery power at node i, at time t (kW) |

P_{L}_{,}_{i}_{,}_{t}; Q_{L}_{,}_{i}_{,}_{t} | Load demand at node i, at time t (kW) |

P_{G}_{,}_{i}_{,}_{t}; Q_{G}_{,}_{i}_{,}_{t} | Public grid power at node i, at time t (kW) |

P_{EV}_{,}_{i}_{,}_{t}; Q_{EV}_{,}_{i}_{,}_{t} | EV charging power at node i, at time t (kW) |

P^{b}_{i,j}; Q^{b}_{i,j} | Power flow in branch b from node i to j |

V_{i}, θ_{i} | Voltage magnitude and angle at the node i |

G_{ij}, B_{ij} | Branch conductance and susceptance from node i to j |

φ_{b} | Total set of branches |

Ah | Energy flow in ampere-hours |

Q_{loss} | Battery degradation (%) |

I_{rate} | Battery charge/discharge rate expressed in capacity ratio C |

c_{t} | Spot energy price at time t (€/kWh) |

c_{B} | Levelized daily battery installation and operation costs (€/kWh∙day) |

U_{res} | Renewable energy share utility function |

U_{tc} | Total costs utility function |

U_{bd} | Battery degradation utility function |

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**Figure 1.**Connection scheme of Photo-voltaic (PV)/battery energy system (BES)/electric vehicles (EV) charging system.

**Figure 2.**Battery charging/discharging from different sources (

**a**) battery charging; (

**b**) battery discharging.

**Figure 5.**Single-criterion optimization results for the maximal solar energy criteria (

**a**) power flows, (

**b**) state of charge (SOC) of battery, (

**c**) EV charging power, (

**d**) battery charge/discharge schedule.

**Figure 6.**Multicriteria optimization results (

**a**) power flows, (

**b**) SOC of battery, (

**c**) EV charging power, (

**d**) battery charge/discharge schedule.

**Figure 7.**Multicriteria optimization results for the complementary case (

**a**) power flows, (

**b**) SOC of battery, (

**c**) EV charging power, (

**d**) battery charge/discharge schedule.

SOC(0) | 20 kWh | P_{B}^{max} | 20 kW |

SOC_{S}(0) | 10 kWh | P_{EV}^{max} | 20 kW |

SOC_{G}(0) | 10 kWh | P_{G}^{max} | 70 kW |

SOC min | 0.1 C | η_{C} | 0.9 |

SOC max | 0.9 C | η_{D} | 0.9 |

c_{B} | 0.4 €/(kWh·day) | C | 30 kWh |

F1 (kWh) | F2 (€) | F3 (%) | |
---|---|---|---|

max F1 | 103.91 | 12,518 | 0.69 |

min F2 | 46.71 | 11,869 | 0.48 |

min F3 | 63.17 | 12,631 | 0 |

F_{1} | U_{1} | F_{2} | U_{2} | F_{3} | U_{3} | U | |
---|---|---|---|---|---|---|---|

k_{1} = 0.2k _{2} = k_{3} = 0.3; K = 0.3 | 87.7 (kWh) | 0.59 | 12,209 (€) | 0.52 | 0.69 (%) | 0.80 | 0.57 |

k_{1} = k_{2} = k_{3} = 0.33; K = 0 | 67.2 (kWh) | 0.34 | 11,963 (€) | 0.53 | 0.41 (%) | 0.88 | 0.62 |

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**MDPI and ACS Style**

Petrusic, A.; Janjic, A.
Renewable Energy Tracking and Optimization in a Hybrid Electric Vehicle Charging Station. *Appl. Sci.* **2021**, *11*, 245.
https://doi.org/10.3390/app11010245

**AMA Style**

Petrusic A, Janjic A.
Renewable Energy Tracking and Optimization in a Hybrid Electric Vehicle Charging Station. *Applied Sciences*. 2021; 11(1):245.
https://doi.org/10.3390/app11010245

**Chicago/Turabian Style**

Petrusic, Andrija, and Aleksandar Janjic.
2021. "Renewable Energy Tracking and Optimization in a Hybrid Electric Vehicle Charging Station" *Applied Sciences* 11, no. 1: 245.
https://doi.org/10.3390/app11010245