# A Nature-Inspired Algorithm to Enable the E-Mobility Participation in the Ancillary Service Market

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Related Works

## 3. System Model

#### 3.1. Electricity Market Participation

#### 3.2. Vehicle Model

Algorithm 1. Fleet Modeling |

1: for d $=$ 1:${N}_{days}^{tot}$ do |

2: for $id$ $=$ 1: ${N}_{fleet}^{tot}$ do |

$3:{n}^{id,d}{}_{rent}$ ← number of rents |

4: for $r=1:{n}_{rent}^{id,d}$ do |

5: ${t}_{in}^{r,id}$ ← starting rent time |

6: $\mathsf{\Delta}{t}_{rent}^{r,id}$ ← rent duration |

7: $\mathsf{\Delta}{d}_{rent}^{r,id}$ ← distance covered |

8: ${v}^{r,id}=\mathsf{\Delta}{d}_{rent}^{r,id}$/$\mathsf{\Delta}{t}_{rent}^{r,id}$ ← mean speed during rent |

9: if ${v}^{r,id}>{v}_{MAX}$ or ${t}_{in}^{r+1,id}>{D}_{time}^{id,r}$ |

10: go to line 5 |

11: end if |

12: $rn{d}_{CS}$ ← Boolean extraction (if TRUE, an EV is connected to a CS) |

13: if $rn{d}_{CS}=$ TRUE |

$14:\mathrm{select}\mathrm{the}\mathrm{arrival}\mathrm{CS}\mathrm{from}\mathrm{the}\mathrm{set}\mathrm{of}{\mathit{C}\mathit{S}}_{adm}^{id}$ |

15: end if |

16: end for |

17: end for |

18: end for |

## 4. Optimization Problem

## 5. The h-ABC Approach

#### 5.1. Initial Population

- Due to Time (DtT) in which the charge priority is computed considering the difference between ${D}_{time}^{ev}$ and $\mathsf{\Delta}{t}_{chg}^{ev}$.
- Arrival Time (AT) in which the EV charge priority is determined considering a first-in first-served approach.

#### 5.2. Employed Bee

Algorithm 2. Heuristic research |

1: for p = 1:${N}_{FS}^{}$ do |

2: ${t}_{crit}$ ← time step with the highest $Cos{t}_{imb}^{p}$ |

3: if ${P}_{abs}^{p}\left({t}_{crit}\right)>{P}_{req}^{}\left({t}_{crit}\right)$ |

4: find $ev$ such that $s{t}^{ev,p}$ = ${t}_{crit}$ and select the one with $Max\left(tar{d}_{ev}\right)$ |

$5:{t}_{crit}$ $\leftarrow {P}_{abs}^{p}\left({t}_{post}\right){P}_{req}\left({t}_{post}\right)$$\mathrm{and}{t}_{post}$${t}_{crit}$ |

6: $s{t}^{ev,p}$$={t}_{post}$ |

7: else |

8: find $ev$such that $s{t}^{ev,p}$ = ${t}_{crit}$ and select the one with $Min(tar{d}_{ev}$), so $s{t}^{ev,p}$ = ${t}_{crit}$ |

9: end if |

10: end for |

#### 5.3. Onlooker Bee

#### 5.4. Scout Bee

#### 5.5. Convergence Criteria

## 6. Case Study

## 7. ABC/h-ABC Comparison

^{−30}. Hence, it is possible to conclude, with high statistical confidence, that the proposed methodology outperforms the standard ABC.

## 8. Numerical Results

## 9. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

Acronyms: | |

ABC | Artificial Bee Colony |

AS | Ancillary Service |

$\mathrm{ASM}$ | Ancillary Services Market |

$\mathrm{AT}$ | Arrival Time |

$\mathrm{BSP}$ | Balancing Service Provider |

$\mathrm{CCA}$ | Centralized Control Architecture |

$\mathrm{CS}$ | Charging Station |

$\mathrm{DAM}$ | Day-Ahead Market |

$\mathrm{DtT}$ | Due to Time |

$\mathrm{EV}$ | Electric Vehicle |

h-ABC | Hybrid-Artificial Bee Colony |

$\mathrm{HP}$ | Hydro Power |

$\mathrm{SoC}$ | State of Charge |

$\mathrm{TSO}$ | Transmission System Operator |

$\mathrm{V}1\mathrm{G}$ | Unidirectional Grid to Vehicle |

$\mathrm{V}2\mathrm{G}$ | Bidirectional Vehicle to Grid |

Parameters and Variables: | |

${C}_{btr}^{}$ | Vehicle’s battery capacity |

${C}_{Bill}$ | Daily electricity bill cost |

${C}_{imb}$ | Daily imbalance cost |

${C}_{rent}$ | Daily cost of non-fulfillment of the charging |

$\mathit{C}\mathit{S}$ | Matrix containing the topology data of Charging Stations |

${c}_{imb}$ | Imbalance fee |

${c}_{lost}$ | Fee in case of non-fulfillment of the charging |

${c}_{rent}$ | Carsharing tariff for the users |

${D}_{time}^{id}$ | Charging deadline for the id-th vehicle |

${E}_{abs}$ | Total daily energy absorbed |

${\overline{e}}_{cons}$ | Mean energy consumption of the EV |

$fi{t}_{p}$ | Fitness function of the p-th solution |

$Im{b}_{\%}$ | Normalized daily imbalance |

$Li{m}_{p}$ | Exploitation value of the p-th solution |

$Li{m}_{MAX}$ | Maximum exploitation limit |

${N}_{days}^{tot}$ | Number of simulated days |

${N}_{exp}$ | Number of expected EV connections in the following time steps |

${N}_{fleet}^{tot}$ | Number of EVs in the fleet |

${N}_{FS}$ | Number of solutions simultaneously evaluated by the optimization algorithm |

${N}_{main}$ | Maximum number of optimization iterations |

${n}_{rent}^{id,d}$ | Number of rents during the d-th day for the id-th EV |

${\mathit{P}}^{\mathit{t}}$ | Matrix containing the connected EVs’ information |

${P}_{0}$ | Power Baseline Schedule |

${P}_{AS}$ | Power accepted in the ASM |

${P}_{abs}$ | Power absorbed by the carsharing operator |

${P}^{i}{}_{chg}$ | Charging power of the i-th vehicle |

${P}_{req}$ | Power Request Schedule |

${p}_{AS}$ | Remuneration for the AS provision |

${p}_{DAM}$ | DAM price |

${R}_{AS}$ | Daily remuneration from the AS provision |

$rn{g}_{min}$ | Minimum range required by the carsharing operator |

$So{C}_{int}^{r,id}/So{C}_{CS,con}^{r,id}$ | State of Charge before/after the rent |

$s{t}^{id}$ | Initial charging time for the id-th EV (optimization variable) |

${\overrightarrow{\mathit{T}}}_{\mathit{D}}{}^{}$ | Vector containing the time steps in day D |

${\overrightarrow{\mathit{T}}}_{\mathit{f}}$ | Upcoming time steps considered during the optimization process performed in ${t}_{0}$ |

$t$ | Generic time step |

${t}_{AS}$ | Time steps with an AS request |

${t}_{in}^{}$ | Rent starting time |

${t}_{0}$ | Current time step |

${\overrightarrow{\mathit{t}}}_{\mathit{t}\mathit{o}\mathit{t}}$ | Vector containing all the simulated time steps |

$tard$ | Tardiness function |

$\mathsf{\Delta}Cos{t}_{}$ | Cost variation w.r.t. the benchmark scenario |

$\mathsf{\Delta}{t}_{rent}^{r}$ | Duration of the r-th rent |

$\mathsf{\Delta}{d}_{rent}^{r}$ | Distance covered during r-th rent |

$\mathsf{\Delta}{t}_{chg}^{id}$ | Charging time of the id-th EV |

$\tau $ | Time step resolution adopted |

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**Figure 3.**Mean value of the objective function in ABC and h-ABC as a function of computational time.

**Figure 6.**Comparison between the power schedule and the power absorbed, in Sch and No Sch scenarios.

**Figure 10.**Map of cost reduction of the proposed scheduler, normalized w.r.t the No Sch total cost, for different coefficient combinations.

Variable Modeled | Distribution and Parameters Adopted |
---|---|

$\mathrm{Rent}\mathrm{duration}(\mathsf{\Delta}{t}_{rent}$) (min) | Gamma distribution $k=2.98\theta =5.51$ |

$\mathrm{Rent}\mathrm{turnover}({n}_{rent}^{}$) (rents/day) | Integer normal distribution $\mu $$=4\sigma $ = 1 |

$\mathrm{Distance}\mathrm{covered}(\mathsf{\Delta}{d}_{ev}$) (km) | Log-logistic $\mu =1.49\theta =0.43$ |

Algorithm Parameter | Optimal Value Found | |
---|---|---|

ABC | h-ABC | |

$\mathrm{N}\xb0\mathrm{main}\mathrm{algorithm}\mathrm{iteration}({N}_{main}$) | 200 | 260 |

$\mathrm{N}\xb0\mathrm{candidate}\mathrm{solution}({N}_{FS}$) | 30 | 22 |

$\mathrm{Scout}\mathrm{bee}\mathrm{limit}(Li{m}_{max}$) | 150 | 100 |

Scenario | $\mathbf{P}(\mathit{S}\mathit{o}{\mathit{C}}_{\mathit{o}\mathit{u}\mathit{t}}=1)$ | $\mathbf{P}(\mathit{S}\mathit{o}{\mathit{C}}_{\mathit{o}\mathit{u}\mathit{t}}0.9)$ | $\mathbf{P}(\mathit{S}\mathit{o}{\mathit{C}}_{\mathit{o}\mathit{u}\mathit{t}}0.8)$ | $\mathbf{P}(\mathit{S}\mathit{o}{\mathit{C}}_{\mathit{o}\mathit{u}\mathit{t}}0.7)$ | $\mathbf{P}(\mathit{S}\mathit{o}{\mathit{C}}_{\mathit{o}\mathit{u}\mathit{t}}0.6)$ | $\mathbf{P}(\mathit{S}\mathit{o}{\mathit{C}}_{\mathit{o}\mathit{u}\mathit{t}}0.5)$ | $\mathbf{P}(\mathit{S}\mathit{o}{\mathit{C}}_{\mathit{o}\mathit{u}\mathit{t}}0.4)$ |
---|---|---|---|---|---|---|---|

No Sch | 90.1% | 5.4% | 2.4% | 1.1% | 0.5% | 0% | 0% |

Sch | 85.0% | 6.5% | 2.9% | 1.3% | 0.6% | 0.04% | 0.02% |

**Table 4.**Economic results of the No Sch and Sch scenarios (in % w.r.t. the total cost of the No Sch scenario; negative values are actually incomes).

${\mathit{C}}_{\mathit{B}\mathit{i}\mathit{l}\mathit{l},\mathit{\%}}$ | ${\mathit{C}}_{\mathit{i}\mathit{m}\mathit{b},\mathit{\%}}$ | ${\mathit{R}}_{\mathit{A}\mathit{S},\mathit{\%}}$ | ${\mathit{C}}_{\mathit{r}\mathit{e}\mathit{n}\mathit{t},\mathit{\%}}$ | ${\Delta}\mathit{C}\mathit{o}\mathit{s}{\mathit{t}}_{\mathit{\%}}$ | ||
---|---|---|---|---|---|---|

No Sch | mean (%) (Max; std) | 87.7% (98.5; 14.0) | 12.3% (55.7; 7.3) | - | 0% (0; 0) | 100% |

Sch | Mean (%) (Max; std) | 87.7% (97.5; 10.1) | 0.9% (7.6; 1.3) | $-$3.3% (11.5; 2.8) | 0.4% (4.0; 0.6) | 85.7% |

800 EVs | 3200 EVs | |||||
---|---|---|---|---|---|---|

No Sch | Sch | ${\Delta}$ | No Sch | Sch | ${\Delta}$ | |

${C}_{Bill,\%}$ (%) | 84.0 | 83.9 | −0.1 | 90.3 | 90.1 | −0.2 |

${C}_{imb,\%}$ (%) | 16.0 | 0.9 | −15.1 | 9.7 | 1.1 | −8.6 |

${R}_{AS,\%}$ (%) | - | −3.1 | −3.1 | - | −3.6 | −3.6 |

${C}_{rent,\%}$ (%) | 0 | 0.6 | +0.6 | 0 | 0.3 | +0.3 |

$\mathsf{\Delta}Cos{t}_{\%}$ (%) | 100 | 82.3 | −17.7 | 100 | 87.9 | −12.1 |

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## Share and Cite

**MDPI and ACS Style**

Falabretti, D.; Gulotta, F.
A Nature-Inspired Algorithm to Enable the E-Mobility Participation in the Ancillary Service Market. *Energies* **2022**, *15*, 3023.
https://doi.org/10.3390/en15093023

**AMA Style**

Falabretti D, Gulotta F.
A Nature-Inspired Algorithm to Enable the E-Mobility Participation in the Ancillary Service Market. *Energies*. 2022; 15(9):3023.
https://doi.org/10.3390/en15093023

**Chicago/Turabian Style**

Falabretti, Davide, and Francesco Gulotta.
2022. "A Nature-Inspired Algorithm to Enable the E-Mobility Participation in the Ancillary Service Market" *Energies* 15, no. 9: 3023.
https://doi.org/10.3390/en15093023