# Optimized Scheduling of EV Charging in Solar Parking Lots for Local Peak Reduction under EV Demand Uncertainty

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## Abstract

**:**

## 1. Introduction

## 2. System Description

#### 2.1. Solar Parking Lots

#### 2.2. Batteries

#### 2.3. Electric Vehicle Supply Equipment

#### 2.4. Electric Vehicle Load Profile

#### 2.4.1. EV Arrival and Departure

#### 2.4.2. EV State of Charge on Arrival

## 3. Methods for Charge Scheduling

- No EV demand forecast: EV charging is scheduled without a forecast of energy demand for EVs arriving in the future
- Average EV demand forecast: EV charging is scheduled with a single forecast of energy demand for EVs arriving in the future which is based on average values.
- Robust EV demand forecast: EV charging is scheduled to be robust across a range of possible energy demands for EVs arriving in the future

#### 3.1. Problem Formulation with Perfect Forecasting

#### 3.2. Inclusion of Uncertainty in Forecasting

#### 3.2.1. Uncertainty in PV Forecasting

#### 3.2.2. Uncertainty in EV Forecasting

#### 3.3. No EV Demand Forecast

#### 3.4. Average EV Demand Forecast

#### 3.5. Robust EV Demand Forecast

## 4. Results and Discussion

#### 4.1. Example Simulations

#### 4.2. Maximum Annual Peak Exchange with the Grid

#### 4.3. Duration of Peak Loads

## 5. Conclusions

- No EV demand forecast: EV charging is scheduled without a forecast of energy demand for EVs arriving in the future
- Average EV demand forecast: EV charging is scheduled with a single forecast of energy demand for EVs arriving in the future which is based on average values.
- Robust EV demand forecast: EV charging is scheduled to be robust across a range of possible energy demands for EVs arriving in the future

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## List of Symbols

Symbol | Definition | Unit | Note |

${E}_{fcst}\left(t\right)$ | Forecasted PV generation: ${E}_{PV}\left(t\right)+{\omega}_{PV}\left(t\right)$ | kWh | |

${E}_{grid}^{max}$ | $max\left({E}_{grid}\left(k\right),\dots ,{E}_{grid}(k+{N}_{p}-1)\right)$ | kWh | |

${E}_{grid}^{min}$ | Max energy that can be sent to the grid | kWh | 32 kWh = 120 kW $\xb71.05\xb7\Delta t$ |

${E}_{grid}\left(t\right)$ | Grid exchange: ${E}_{load}\left(t\right)-{E}_{PV}\left(t\right)+{\sum}_{i=1}^{{N}_{b}}{E}_{i}\left(t\right)$ | kWh | |

${E}_{i}\left(t\right)$ | Energy to (+) or from (-) battery i at time t | kWh | |

${E}_{load}\left(t\right)$ | Load from lighting at time t | kWh | |

${E}_{PV}\left(t\right)$ | Generation from solar power at time t | kWh | |

i | Index for each battery, 1–40 = EVs, 41 = fixed storage | - | $i\in \{1,\dots ,{N}_{b}\}$ |

k | Current time step | - | $k\in \{1,\dots ,{N}_{T}\}$ |

${M}_{i}$ | Max possible value of ${E}_{i}$ $={P}_{i}^{max}\xb7\Delta t$ | kWh | |

${m}_{i}$ | Min possible value of ${E}_{i}$: $=-{P}_{i}^{max}\xb7\Delta t$ | kWh | |

${N}_{b}$ | Total number of batteries | - | 41 = 40 EVs + 1 battery |

${N}_{e}$ | Number of errors in the bounded set | - | 10,000 |

${N}_{p}$ | Number of time steps in MPC time horizon | - | $96=24\xb74$ |

${N}_{T}$ | Number of time steps in one full simulation | - | 34,944 = 24 · 4 · 364 |

${P}_{i}^{max}$ | Maximum power to or from battery i | kW | EVs 7.4 kW, battery 50 kW |

${S}_{i}\left(t\right)$ | Energy stored in battery i at time t | kWh | |

${S}_{i}^{max}\left(t\right)$ | Maximum energy allowed in battery i at time t | kWh | |

${S}_{i}^{min}\left(t\right)$ | Minimum energy allowed in battery i at time t | kWh | |

$\overline{{S}_{i}^{max}}\left(t\right)$ | Average value for the max energy in battery i at time t | kWh | |

$\overline{{S}_{i}^{min}}\left(t\right)$ | Average value for the min energy in battery i at time t | kWh | |

t | time step within MPC horizon | - | $t\in \{k,\dots ,k+{N}_{p}-1\}$ |

${z}_{i}\left(t\right)$ | ${z}_{i}\left(t\right)={\delta}_{i}\left(t\right)\xb7{E}_{i}\left(t\right)$ | kWh | |

$\Delta t$ | Length of a single time step | h | 15 min = 0.25 h |

${\delta}_{i}\left(t\right)$ | For battery i at time t: 0 if discharging, 1 if charging | $\{0,1\}$ | |

${\eta}_{chg,i}$ | Charging efficiency of battery i | - | |

${\eta}_{dis,i}$ | Discharging efficiency of battery i | - | |

${\Omega}_{PV}^{\ast}\left(t\right)$ | Bounded set of PV forecasting errors $\{{\omega}_{PV}^{\left(1\right)},\dots ,{\omega}_{PV}^{\left({N}_{e}\right)}\}$ | - | |

${\omega}_{PV}\left(t\right)$ | PV forecasting error at time t | kWh | |

${\omega}_{PV}^{max}\left(t\right)$ | Max PV forecasting error in set ${\Omega}_{PV}^{\ast}\left(t\right)$ | kWh | |

${\omega}_{PV}^{min}\left(t\right)$ | Min PV forecasting error in the set ${\Omega}_{PV}^{\ast}\left(t\right)$ | kWh | |

${\omega}_{{S}_{i}^{max}}\left(t\right)$ | Uncertainty in the value of ${S}_{i}^{max}\left(t\right)-{S}_{i}^{min}\left(t\right)$ | kWh | |

${\omega}_{{S}_{i}^{min}}\left(t\right)$ | Uncertainty in the value of ${S}_{i}^{min}\left(t\right)-{S}_{i}^{min}(t-1)$ | kWh |

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**Figure 3.**Comparison of energy flows in the solar parking lot with unscheduled charging as opposed to charging with perfect forecasts.

**Figure 4.**Comparison of energy flows in the solar parking lot with no EV demand forecast, a single average EV demand forecast and a robust consideration of EV demand forecasting.

Characteristic | Value |
---|---|

Module technology | Monocrystalline silicon |

Module rated power | 300 kWp (60 cell) |

Module rated efficiency | 18.33% at STC |

Array installed capacity | 120 kWp |

Site latitude | 5158′ N |

Site longitude | 455′ E |

Array azimuth | 0 (South) |

Array tilt | 13 |

Parking spaces | 40 spaces |

Carport roof topology | Monopitch (single tilt angle for entire roof) |

Annual production (DC) | 133,625 kWh |

Capacity factor (DC) | 12.7% |

EV Type | Mean | Standard Deviation | Lower Bound | Upper Bound |
---|---|---|---|---|

BEV | 50% | 18% | 0% | 90% |

PHEV | 45% | 30% | 0% | 90% |

Nr. | Scenario | Annual Peak Power (kW) | Relative Peak Reduction (%) |
---|---|---|---|

Ref | Unscheduled charging | 147 | 0% |

1 | No EV forecast | 123 | 16% (↓) |

2 | Average EV forecast | 94 | 36% (↓) |

3 | Robust EV forecast | 90 | 39% (↓) |

Ref | Perfect forecasting | 67 | 54% (↓) |

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**MDPI and ACS Style**

Ghotge, R.; Snow, Y.; Farahani, S.; Lukszo, Z.; van Wijk, A.
Optimized Scheduling of EV Charging in Solar Parking Lots for Local Peak Reduction under EV Demand Uncertainty. *Energies* **2020**, *13*, 1275.
https://doi.org/10.3390/en13051275

**AMA Style**

Ghotge R, Snow Y, Farahani S, Lukszo Z, van Wijk A.
Optimized Scheduling of EV Charging in Solar Parking Lots for Local Peak Reduction under EV Demand Uncertainty. *Energies*. 2020; 13(5):1275.
https://doi.org/10.3390/en13051275

**Chicago/Turabian Style**

Ghotge, Rishabh, Yitzhak Snow, Samira Farahani, Zofia Lukszo, and Ad van Wijk.
2020. "Optimized Scheduling of EV Charging in Solar Parking Lots for Local Peak Reduction under EV Demand Uncertainty" *Energies* 13, no. 5: 1275.
https://doi.org/10.3390/en13051275