**1. Introduction**

With energy shortages and environmental pollution problems becoming more pronounced, the global energy structure is gradually undergoing a transformation. Countries around the world are taking steps to achieve sustainable, green and efficient energy systems. New energy vehicles, especially electric vehicles, are gaining widespread attention due to their low pollution and high energy efficiency. By the end of 2021, the number of new energy vehicles worldwide had exceeded 10 million. In the Chinese urban bus system, many diesel buses have been replaced by energy-efficient and environmentally friendly electric buses [1]. Compared to traditional diesel buses, electric buses have more advantages in the public transport system. However, there are still some problems, such as difficulties in charging demand evaluation, vehicle route planning and battery energy storage system design. These issues are closely related to the range of electric buses and the energy consumption of vehicles under specific operating conditions [2]. Therefore, the study of an accurate vehicle energy consumption estimation model can solve the above problems, which is of great significance to the popularization of electric buses. The driving energy consumption of electric buses is affected by drivers' habits and working conditions. For electric buses on the same route, the difference in driving energy consumption under different working conditions can reach 40%. Therefore, information such as the temperature and departure time under current operating conditions need to be considered so as to accurately estimate the energy consumption of the vehicle.

**Citation:** Li, X.; Wang, T.; Li, J.; Tian, Y.; Tian, J. Energy Consumption Estimation for Electric Buses Based on a Physical and Data-Driven Fusion Model. *Energies* **2022**, *15*, 4160. https://doi.org/10.3390/en15114160

Academic Editors: Alon Kuperman, Alessandro Lampasi and Michele Pastorelli

Received: 18 March 2022 Accepted: 2 June 2022 Published: 6 June 2022

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The energy consumption of an electric vehicle is related to the vehicle powertrain dynamic performance, such as the windproof area of the vehicle, vehicle charging efficiency, etc. It is also influenced by the habits of drivers and environmental factors. As a result, it is difficult to achieve an accurate estimation of the energy consumption of a vehicle [3]. However, the national monitoring and management platform for new energy vehicles (NEVS) in China has enabled the aggregation of massive amounts of data on new energy vehicles. The platform can provide a large amount of vehicle driving data for the analysis and modeling of vehicle energy consumption.

Many related studies have been performed in this area. Yuan et al. [4] modeled vehicle powertrain dynamics by simulating driving data on a computer. An energy consumption model for electric vehicles was achieved. In the model, the energy of an electric vehicle is mainly consumed by rolling drag, air resistance and kinetic energy, and the error of the model is about 3%. However, the model only considers energy consumption under laboratory conditions and does not further consider possible congestion and air-conditioning factors in the actual driving process. Bracco et al. [5] used a simulation model to analyze the effects of different variables on energy consumption and the battery charging state. The results show that the number of passengers has the greatest impact on the energy consumption of electric vehicles. Qi et al. [6] used positive kinetic energy and negative kinetic energy to decompose the energy consumption under actual traffic congestion. Based on this decomposition, a data-driven model was established. The model is used to estimate the energy consumption of electric vehicles on the road, and the actual traffic conditions are taken into account. The model needs a lot of data input to obtain the accurate positive and negative kinetic energy of the vehicle. After simplifying the input to the average speed, the model error is 7%. Hao et al. [7] analyzed the energy consumption of electric buses, minibuses and taxis in Beijing. Through statistical analysis, vehicle energy consumption in different seasons and driving conditions was obtained. It was found that the energy consumption of electric vehicles per kilometer is lower than that at 5 ◦C. This shows that the energy transmission efficiency of the battery will change at different temperatures. Miraftabzadeh et al. [8] considered the driving route and weather conditions in the modeling process. Using a data-driven modeling method, the energy consumption prediction model of an electric taxi was established. In addition, by calculating the energy consumption of taxis on weekdays and weekends, the author compiled a taxi energy consumption table. The table shows that the month with the highest energy consumption of taxis in New York City is April, while July is the month with the lowest energy consumption. Al-Wreikat et al. [9] analyzed the effect of ambient temperature on the energy consumption of electric vehicles. They found that vehicles consumed 28% more energy at low temperatures of 0–15 degrees than at medium temperatures of 15–25 degrees. Björnsson et al. [10] designed a physical model of powertrain dynamics. The energy recovery performance in the braking process was analyzed. The research shows that under urban conditions, the energy regeneration potential per kilometer is higher under the condition of low average speed and multiple starts and stops. It lays a foundation for the study of the urban bus recovery coefficient. The energy consumption of electric vehicles has been modeled by many approaches.

According to the literature review, previous studies have considered physical modeling methods or artificial intelligence algorithms to obtain vehicle energy consumption models. However, vehicle energy consumption is the result of multiple factors. The energy consumption estimation results obtained by a single method or a single type of model are less reliable. Moreover, in practical applications, there is a lack of an energy consumption estimation model with limited input features for driving decision making. It is necessary to design a more reliable energy consumption estimation model with few input features. To address these issues, a physical and data-driven fusion model for vehicle energy consumption is proposed in this paper. Part of the energy consumed by the vehicle during driving can be expressed by physical formulas, such as the energy consumed by rolling resistance and air resistance [11]. The direct application of formula modeling will reduce the complexity of the model. Other driving factors also affect the driving energy consumption

of vehicles, such as the vehicle departure time, the ambient temperature, etc. For these factors that cannot be expressed by the formula, the data-driven model is selected. Finally, the two models are fused to estimate vehicle energy consumption.

The content of each section is as follows: In Section 2, the statistical analysis of electric bus data is performed. The original data are preprocessed and reconstructed to obtain continuous data in the vehicle charging and driving cycle process. In Section 3, the energy consumption estimation model is designed. A physical vehicle energy consumption model is developed based on the powertrain dynamic performance of the electric bus. Model parameters are initially calibrated using the least-squares method. In addition, the factors affecting fluctuations in vehicle energy consumption, such as driving habits and environmental factors, are summarized and analyzed. The CatBoost decision tree model is used to characterize the effects. Finally, the two models are fused to obtain the final estimation result of vehicle energy consumption. In Section 4, the energy consumption estimation model is analyzed and validated. Some conclusions are presented in Section 5.

#### **2. Data Statistics and Analysis**

The electric bus data came from the National Monitoring and Management Platform for NEVS. The original data were collected by on-board terminals on electric buses and uploaded to the data platform. The dataset includes 38 items, such as the sampling time, battery management system (BMS) number, battery pack voltage, battery current, state of charge (SOC), minimum cell voltage, maximum cell voltage, minimum temperature, maximum temperature, etc. A detailed description of the items used in this paper is shown in Table 1. The data cover ten electric buses on the same bus route in one year. The travel distance is approximately 34 km. There are 24 stops along the route. After one round trip, the buses will be charged at the starting point of the bus stations. The purpose of this section is to process the original data and obtain the data on vehicle speed, data acquisition time, temperature, accelerator pedal value and deceleration pedal value. The data will be further processed for vehicle energy consumption modeling.


**Table 1.** A detailed description of the items used in this paper.
