# EVB-Supportive Energy Management for Residential Systems with Renewable Energy Supply

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## Abstract

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## 1. Introduction

## 2. Default Setting and System Parameters

## 3. Day-Ahead Probabilistic PV Generation Forecast

## 4. Optimization Model

#### 4.1. Notations and Parameters

#### 4.2. System Layouts and Models

#### 4.2.1. SP Model for the Default Setting

**Default system**, as shown in Figure 2, is a modern PV system that combines solar panels and battery storage in one place. The electricity generated from solar panels can be consumed right away or be stored in a home battery for later usage. This can improve self-consumption and ease the load and pressure on the grid. In addition, the home battery can also be used as a route to reduce energy bills by carrying electricity from off-peak hours to peak hours. We assume that the EV battery can only be charged at home from the grid, so essentially the two storage systems are not interacting with each other and the EV system is not influenced by the power supply from solar panels.

#### 4.2.2. SP Model for (a) Hybrid System

**(a) Hybrid System**is an extension of the default system by allowing EV battery to be charged by home battery. This system is proposed considering the possibility of a high generation from the solar panel beyond the daily household consumption. The remaining amount can then be used to charge the EV battery so as to save electricity bills. This scenario should work well when the solar generation is high and the home battery is relatively large. Major differences from the default system lie in five constraints:

#### 4.2.3. SP Model for (b) Hybrid System with EVB Supply

**(b) Hybrid System with EVB Supply**is an extension of the hybrid system by allowing home appliances to be supplied from the electric vehicle battery (EVB). This system is motivated by the fact that normally the house occupiers come back home together with the EV, so that the EVB connection is available during the peak demand hours. By pushing remaining energy from EVB to supply home appliances when parking at home, one can further reduce the electricity purchase from the grid during peak rate hours. This would enable the maximum usage of the EV battery as an energy storage, which is available to be charged during the off-peak night hours and to be discharged to supply home appliances during the peak hours. This scenario should work well when the home battery is relatively small. Major differences from system (a) lie in three constraints:

#### 4.2.4. SP Model for (c) On-Grid System

**(c) On-grid System**is a benchmark system which has no home battery installed. The excess solar electricity after supplying home appliances at time t, denoted by ${s}^{t}$, can be uploaded to the grid to get power credits. This is shown by the link between the solar panel and the grids in Figure 3. Provided that the surplus can be sold back to the grid at a discounted price with discount rate $\gamma $, the objective function for second stage problem has to be updated to include the income.

#### 4.2.5. SP Model for (d) On-Grid System with EVB Supply

**(d) On-grid System with EVB Supply**is an extension of the on-grid system. It assumes no home battery but allows home appliances to be driven by EV battery. Essentially, we assume that the EV battery takes the role of home battery. A major difference lies in the fact that the EV battery is not available throughout the day and it can only be charged/used when the EV is parked at home, so it will miss the peak hours of solar generation and therefore has limited ability to store surplus solar power generations. The EV battery is more likely to serve only as a tool to bring cheaper electricity to peak hours. The SP model can be modified based on the one for an on-grid system.

## 5. Numerical Results

#### 5.1. Experiment Settings and System Parameters

**Electricity supply:**${A}_{i}^{t},i\in \{S,G\}$ In practice, the electricity grid can supply as much energy as what is needed by a household, so this problem has no constraints on the amount of electricity from the grid (${A}_{G}^{t}$). On the other hand, how much electricity we can generate from the PV system installed at home is under significant uncertainty, which has to be predicted to feed into the model.

**Electricity demand:**${U}_{j}^{t},j\in \{V,T,D\}$ The households consumption data (without EV), i.e., ${U}_{T}^{t}$ and ${U}_{D}^{t}$, are extracted from the household electricity survey [9]. In this study, we deploy the average household consumption data over all household types, in order to explore the optimal household electricity system settings under the typical UK consumption pattern. Devices (excluding EV) in households are categorised into two groups, i.e., major appliances (white goods) and small appliances and electronic devices (brown goods). Figure 4 summarises the hourly consumption level of these two categories (green and orange lines), together with other key information of the system like average daily PV generation and electricity price patterns. It can be seen that the peak demand occurs between 6:00 p.m.–9:00 p.m., which is the typical cooking and family entertaining time after working hours. High peak-load price applies to this period’s consumption, which forms the major part of high electricity bills.

**Electricity prices:**${P}_{i}^{t},i\in \{S,G\}$ For electricity prices, we take a typical time-of-use (TOU) electricity tariff that is provided by the eastern region household electricity surveys [9]. A day is divided into four time intervals, and each has its own electricity prices (${P}_{G}^{t}$) as shown by the red line in Figure 4. On the other hand, we assume that the electricity generated by solar panels (${P}_{S}^{t}$) is free of charge by ignoring the installation and maintenance costs. When customers upload energy back to the grid, they receive credits for doing so, and this is called Feed-in-tariff. In this study, we test through different levels of Feed-in-tariff, $\gamma $, between 0–60% of the lowest price of the TOU tariffs.

**Energy storage capacity:**${C}_{k},k\in \{E,B\}$ Being consistent with industrial production, here we assume that a 30 kWh (${C}_{E}$) lithium-ion electric-vehicle battery is installed, which provides up to 160 km range per charge. As for the home battery ${C}_{B}$, we are aiming to find the influence of it so we examine the options ranging from 0–30 kWh. The battery round-trip efficiency is the fraction of energy put into the storage that can be retrieved afterwards. Here, we set it to 80% according to [49].

#### 5.2. Scenarios of Solar PV Generation

#### 5.3. Results of SP Models

#### 5.4. Managerial Insights

- In general, EV batteries cannot fully replace HB because: (a) It cannot be charged by solar PV in our experimental setting; (b) It is not at home when solar PV generation reaches the maximum level.
- Supposing that considerable rewards are paid for “selling” back electricity, e.g., at a rate of $40\%$ of the lowest tariff, HEMS without home battery outperforms those with home batteries, and depends less on the solar generation level.
- When home battery is not installed, allowing EVB supply to home appliances saves 5–15% of the daily bill. Therefore, once EV replaces petrol/diesel cars in the future, households having solar PV but no home battery installed can benefit from using their EVB as alternative home energy storage.
- When home battery is large (over 10 kWh), allowing transmission from HB to EVB saves 21–58% of the daily bill with minimum 2 kWh solar generation. This suggests the future development directions of battery charging/discharging routes.

## 6. Conclusions and Future Work

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**The average household electricity consumption profile for a typical UK home [10].

**Figure 4.**Average 24-h UK household electricity profile and PV generation curves on summer weekdays.

Indicators | Definition |

S | solar PV generation system |

G | regional electricity grid |

E | electric vehicle battery |

B | home battery |

V | electric vehicle |

T | typical household appliances or major appliances used for routine housekeeping tasks such as cooking, washing laundry, or food preservation |

D | small household appliances including portable/semi-portable machines such as microwave ovens, toasters, humidifiers, coffeemakers, and other electronic devices |

Indices | |

i | electricity supply sources, $i\in \{S,G\}$ |

j | power demand categories, $j\in \{V,T,D\}$ |

k | energy storage, $k\in \{E,B\}$ |

t | time intervals, $t\in \{1,2,\dots ,h\}$, where $h=24$ |

Parameters | |

${P}_{i}^{t}$ | [£/kWh], cost of electricity from resource i at time t, $i\in \{S,G\},$ $t\in \{1,2,\dots ,h\}$ |

${A}_{i}^{t}$ | [kW], amount of electricity supply from source i at time t, $i\in \{S,G\},$ $t\in \{1,2,\dots ,h\}$ |

${U}_{j}^{t}$ | [kW], amount of electricity demand from category j at time t, $j\in \{V,T,D\},t\in \{1,2,\dots ,h\}$ |

${C}_{k}$ | [kWh], capacity of energy storage $k,k\in \{E,B\}$ |

${\delta}^{t}$ | indicator showing if EV is available at home during interval $t,$ $t\in \{1,2,\dots ,h\}$ |

$\rho $ | conversion rate of power transmission |

$\gamma $ | energy selling price as a proportion to the lowest ToU tariff (when selling of energy is allowed) |

Variables | |

${x}_{i,j}^{t}$ | [kW], amount of electricity transmission from i to j at time t, $i\in \{S,G\},$ $j\in \{V,T,D\},t\in \{1,2,\dots ,h\}$ |

${y}_{i,k}^{t}$ | [kW], amount of electricity transmission from i to k at time t, $i\in \{S,G\},k\in \{E,B\},t\in \{1,2,\dots ,h\}$ |

${w}_{k,{k}^{\prime}}^{t}$ | [kW], amount of electricity transmission between energy storage at time t, $k,{k}^{\prime}\in \{E,B\},t\in \{1,2,\dots ,h\}$ |

${z}_{k,j}^{t}$ | [kW], amount of electricity transmission from k to j at time t, $k\in \{E,B\},j\in \{V,T,D\},t\in \{1,2,\dots ,h\}$ |

${l}_{k}^{t}$ | [kWh], storage level of type k battery at time t, $k\in \{E,B\},t\in \{1,2,\dots ,h\}$ |

${s}^{t}$ | [kW], amount of surplus electricity generated from solar PV during interval $t,t\in \{1,2,\dots ,h\}$ |

Systems | Residential Power Systems with Solar PV and EV | |||
---|---|---|---|---|

Including Home Battery | Allowing Charge of EVB From Home Battery | Allowing Home Apps. Supplied from EVB | Allowing Selling Energy to the Grid | |

Default System | Yes | No | No | No |

(a) Hybrid System | Yes | Yes | No | No |

(b) Hybrid System with EVB Supply | Yes | Yes | Yes | No |

(c) On-grid System | No | No | No | Yes |

(d) On-grid System with EVB Supply | No | No | Yes | Yes |

Stage | Parameter | Estimate | Remark | ||
---|---|---|---|---|---|

1-kWh | 2-kWh | 3kWh | (Cloud Level) | ||

1st stage | ${\beta}_{0}$ | 0.805 | 1.610 | 2.414 | Fine |

${\beta}_{1}$ | −0.025 | −0.051 | −0.076 | Partly cloudy | |

${\beta}_{2}$ | −0.041 | −0.081 | −0.122 | Mostly cloudy | |

${\beta}_{3}$ | −0.391 | −0.782 | −1.173 | Cloudy | |

${\beta}_{4}$ | −0.660 | −1.321 | −1.981 | Showers | |

2nd stage | ${\sigma}_{a}^{2}$ | 0.009 | 0.037 | 0.083 | |

${\sigma}^{2}$ | 0.014 | 0.055 | 0.137 |

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**MDPI and ACS Style**

Yang, X.; Chitsuphaphan, T.; Dai, H.; Meng, F.
EVB-Supportive Energy Management for Residential Systems with Renewable Energy Supply. *World Electr. Veh. J.* **2022**, *13*, 122.
https://doi.org/10.3390/wevj13070122

**AMA Style**

Yang X, Chitsuphaphan T, Dai H, Meng F.
EVB-Supportive Energy Management for Residential Systems with Renewable Energy Supply. *World Electric Vehicle Journal*. 2022; 13(7):122.
https://doi.org/10.3390/wevj13070122

**Chicago/Turabian Style**

Yang, Xinan, Thanet Chitsuphaphan, Hongsheng Dai, and Fanlin Meng.
2022. "EVB-Supportive Energy Management for Residential Systems with Renewable Energy Supply" *World Electric Vehicle Journal* 13, no. 7: 122.
https://doi.org/10.3390/wevj13070122