Electric Vehicle Power Consumption Modelling Method Based on Improved Ant Colony Optimization-Support Vector Regression

Abstract

Accurate forecasting of electric vehicle (EV) power consumption per unit mileage serves as the cornerstone for determining diurnal variations in EV charging loads. To enhance the prediction accuracy of EV power consumption per unit mileage, this paper proposes a modelling method grounded in an improved Ant Colony Optimization-Support Vector Regression (ACO-SVR) framework. This method integrates the effects of both temperature and speed on the power consumption per unit mileage of EVs. Initially, we analyze the influence mechanism of driving speed and ambient temperature on EV power consumption, elucidating the relationship between power consumption per unit mileage and these factors. Subsequently, we construct an ACO-SVR model utilizing an improved ant colony optimization algorithm, fitting the relationship between power consumption, speed, and temperature to derive the EV power consumption per unit mileage model. Finally, leveraging operational data from EVs in Guangdong, Hong Kong, and Macao as a case study, we validate the energy consumption model of EVs by considering factors such as ambient temperature and driving speed. The results demonstrate that the model proposed in this paper is both accurate and effective.

1. Introduction

Against the backdrop of the current increasingly severe global environmental challenges, the low-carbon transformation of the transport sector has garnered significant global attention. EVs have been rapidly developed due to their clean, environmentally friendly, and energy-saving advantages, and with the large-scale promotion of EVs, the EV load has become an important load in the power system. However, the highly stochastic nature of EV charging loads, superimposed on conventional loads, can lead to peak demands that exacerbate existing peak loads [1]. In order to provide support for the planning and operation of the distribution network and the charging management and scheduling, it is necessary to elucidate the variations in the charging load of EVs. Notably, the power consumption of EVs per unit mileage exerts a substantial influence on the spatial and temporal distribution of charging loads, meaning the research on the energy consumption of EVs has become a hot research topic for many scholars.

In modelling the power consumption of EVs, Wang et al. [2] analyzed spatial and temporal distribution factors of EV charging loads and constructed a model of EV electricity consumption per unit kilometre under varying road conditions. Zhang et al. [3] introduced the traffic impedance function to quantify road congestion and subsequently modelled the power consumption of EVs under different congestion conditions. For Xing et al. [4], seasonal characteristics were considered, and the influence of temperature on the additional energy consumption of EVs was analyzed, resulting in the construction of an EV energy consumption model that incorporates the temperature factor. Xing et al. [5] employed fuzzy logic to establish the relationship between EV range and two key factors, traffic and weather conditions, in order to obtain the power consumption per kilometre. In Jiang et al. [6], the factors affecting battery power were investigated, and the energy consumption change curve of EVs was constructed. Tang et al. [7] derived the traffic congestion evaluation method based on the travel chain model, and the charging load prediction model is established based on traffic conditions. For Xu et al. [8], travel data were processed and analyzed to establish a power consumption model per unit mileage. In Yan et al. [9], a real-time energy consumption model for EVs was constructed by incorporating a traffic congestion factor. Zhang et al. [10] built a short-term EV charging load prediction model using weather as a feature vector input to analyze similar days. In conclusion, existing EV energy consumption models primarily focus on modelling single influencing factors such as temperature and road conditions, but the influence of temperature and speed on EV energy consumption is a complex problem involving many aspects, and optimizing the calculation of EV power consumption per unit mileage from one aspect alone is not complete.

Based on the above issues, in this paper, an improved ACO-SVR-based EV power consumption modelling method is proposed based on the key factors affecting EV power consumption per unit mileage. The methodology initially dissects the physical factors affecting the power consumption per unit mileage of electric vehicles and pinpoints those factors that exert a significant impact and are mutually independent. Subsequently, by examining the voltage and current discharged from the batteries during vehicle operation within the electric vehicle health dataset, along with the driving speed and ambient temperature at that instance, it ascertains the power consumption per unit mileage in that specific state, thereby establishing a refined ACO-SVR power consumption per unit mile model. The main contributions of this paper are described as follows:

(1)

This paper delves into the mechanism by which driving speed and ambient temperature influence EV power consumption, elucidating the relationship between power consumption per unit mileage and variations in the temperature and speed of EVs. This paper proposes an EV power consumption model that jointly considers temperature and speed. In comparison to models that solely consider temperature or speed, it exhibits superior accuracy in predicting power consumption per unit mile under various operating conditions. This enhanced predictive capability facilitates the formulation of a more efficacious power management strategy for users, tailored to their environmental conditions, and concurrently provides a valuable reference for enhancing the accuracy of EV load predictions.

(2)

This paper is grounded in the modelling and analysis of actual driving data. Compared to data tested on a test bench, it demonstrates greater responsiveness to variations in vehicle power consumption when speed variations or temperature fluctuations occur frequently. This responsiveness is instrumental in the development of driving behaviour optimization strategies for drivers.

(3)

In comparison to the estimation outcomes of the standalone SVR model and the unmodified ACO-SVR model, the refined ACO-SVR algorithm proposed in this paper exhibits superior estimation accuracy. This enhancement underscores the overall efficacy and reliability of the proposed power consumption modelling method.

2. Analysis of Factors Affecting Electricity Consumption per Unit Mile

Power consumption per unit mile for EVs is defined as the ratio of the total power consumed to the mileage travelled, as expressed in Equation (1):

$$E={\displaystyle \frac{{\displaystyle \underset{0}{\overset{t_i}{\int }}{P}_{\mathrm{i}}d{t}_i}}{S_i}}$$

(1)

where E represents power consumption per unit mile, with the unit of measure being kWh/km;$P_i$ represents the amount of electricity consumed during driving, which includes the motor power consumption $P_{ei}$ and auxiliary equipment power consumption $P_{ti}$, with the unit of measure being KW; $S_i$ represents trip distance, with the unit of measure being km; and $t_i$ represents the trip time, with the unit of measure being hours (h).

Compared to conventional fuel vehicles, the power consumption of EVs is specifically influenced by factors such as the battery energy management system of EVs, the road class, level of congestion, driving behaviour of the vehicle owner, and the settings of auxiliary equipment such as air-conditioning and heating for starting and stopping [11]. Factors such as weather conditions, driving behaviour, road class, and traffic congestion initially affect the speed at which an EV travels. This speed subsequently influences the output power of the electric motor, and therefore the power consumption per unit mile of the EV. Temperature primarily affects the operation of auxiliary equipment and the discharging capacity of batteries, and it also has a direct impact on the power consumption per unit mile of EVs. Collectively, two factors, travelling speed and temperature, play a decisive role in determining the power consumption per unit mile for EVs.

2.1. Effect of Speed on Electricity Consumption per Unit Mile

The energy consumed by an EV to sustain a constant forward velocity is generated primarily by the electric motor, as quantified in Equation (2):

$$P_{ei}={\displaystyle \frac{M(S)\cdot S(v)}{9.5488\eta (S)}}$$

(2)

where v represents the travelling speed of the EV, measured in km/h, S(v) represents the rotation speed of the motor, measured in RPM, where its size changes with the speed of EV; M(S) represents the torque of the motor, with the unit of measure being Nm, and where its size will change with the rotation speed of the motor; and η(S) represents the motor output efficiency, and its size will also change with the rotation speed of the motor.

The diagram of the drive motor’s external characteristics is shown in Figure 1 [12]. As can be seen from Figure 1, the motor of an EV is a constant torque starter. When the motor starts, the torque remains constant as the motor speed increases. When the motor reaches its rated power, the torque becomes inversely proportional to the motor speed as the speed continues to increase. Therefore, the expression for torque and motor speed is shown in Equation (3):

$$M(S)=\left\{\begin{array}{cc}{k}_1& S<S_1\\ {\displaystyle \frac{k_2}{S}}& S\ge S_1\end{array}\right.$$

(3)

where $k_1$ represents the torque value before the motor reaches its rated output power; $k_2$ represents the inverse coefficient of torque versus motor speed after the motor reaches its rated output power; and S₁ represents the speed of the motor when the motor reaches rated output power [13].

At the starting stage of the motor, the output efficiency of the motor is a certain value and remains constant. When the motor reaches the rated output power and the motor terminal voltage reaches the voltage limit output by the controller, the motor enters the high-speed weak magnetism zone as the motor speed continues to increase. Due to the fact that the depth of weak magnetism increases with the increase in speed, and the straight-axis weak magnetism current does not perform any work, the copper loss of the motor increases with the depth of weak magnetism. This results in the lower efficiency of the motor in the high-speed zone [14]. Therefore, the motor output efficiency is described by Equation (4):

$$\eta (S)=\left\{\begin{array}{cc}{k}_3& S<S_1\\ {\displaystyle \frac{k_4}{S^2}}& S\ge S_1\end{array}\right.$$

(4)

where $k_3$ represents the constant value of the motor output efficiency during the start-up phase; $k_4$ represents the inverse coefficient of the motor output efficiency relative to the motor speed squared after the motor has reached its rated output power.

Most of the EVs on the market today are equipped with frequency conversion brushless motors combined with single-speed gearboxes, which results in a fixed transmission ratio for the motor [15]. This means that the motor’s speed is directly proportional to the vehicle’s speed, as described by Equation (5):

$$S(v)=k_{5}v$$

(5)

where $k_5$ represents the constant coefficient of proportionality between the EV’s speed and the motor’s speed; v represents the travelling speed of the EV, measured in km/h.

From Equations (3)–(5), the energy consumed by the EV in maintaining a certain forward speed is shown in Equation (6):

$$P_{ei}(v)=\left\{\begin{array}{cc}{\displaystyle \frac{k_1\cdot k_{5}v}{k_3\cdot 9.5488}}& v<v_1\\ {\displaystyle \frac{k_2\cdot k_5^2{v}^2}{k_4\cdot 9.5488}}& v\ge v_1\end{array}\right.$$

(6)

In the initial stage of vehicle operation until a certain speed is attained, the torque remains constant while the motor output power increases proportionally with speed. Once the speed surpasses a specific threshold, the motor achieves a steady power output. However, as the speed continues to rise, there is a corresponding decrease in torque which necessitates higher electric energy consumption to sustain high-speed operation of the motor. Consequently, this leads to a reduction in motor efficiency and an increase in energy consumption by the EV [16].

Taking the data of EV operation in the Guangdong–Hong Kong–Macao Bay Area as an example, the rule for the change in EV power consumption with speed is obtained and shown in Figure 2. The trend in the variation of this figure is consistent with the intrinsic influence mechanism described by Equation (6).

2.2. Effect of Temperature on Power Consumption per Mile

The effect of temperature on the power consumption per unit mile of an EV is primarily manifested in the starting and stopping of auxiliary equipment, as well as the discharging capacity of the battery [17].

Air conditioning, as important auxiliary equipment for EVs, has a significant impact on their energy consumption. Reference [18] provides an expression relating the starting probability of air conditioning relative to temperature, as shown in Equation (7):

$$f_T(T)={\displaystyle \frac{1}{\sqrt{2\pi }{\sigma }_{T}T}}{e}^{-{\displaystyle \frac{{\left(T-{\mu }_T\right)}^2}{2{\sigma }_T^2}}}$$

(7)

where $f_T\left(T\right)$ represents EV air conditioning starting probability; $T$ represents the current ambient temperature, with the unit of measure being °C; and ${\mu }_T$ and ${\sigma }_T$ are coefficients to be fitted. Air conditioners operate with different coefficients under different operating conditions: in the heating condition, ${\mu }_T=10.82$, ${\sigma }_T$ = 2.14; in the refrigeration condition, ${\mu }_T$ = 29.4, ${\sigma }_T$ = 1.75.

The air-conditioning system of EVs is switched on at different temperatures, and it consumes varying amounts of electricity. Reference [19] obtains the relationship between ambient temperature and air-conditioning power consumption, as shown in Equation (8):

$${\theta }_{air}=f(T)=\left\{\begin{array}{cc}33.47{(T_{set}-T_{amb})}^{1.324}& T_{amb}<T_{set}\\ 33.69{(T_{amb}-T_{set})}^{1.084}& T_{amb}>T_{set}\end{array}\right.$$

(8)

where ${\theta }_{air}$ represents air-conditioning power consumption; $T_{amb}$ represents ambient temperature; and $T_{set}$ represents the cabin set temperature, which is generally 22 °C.

The ambient temperature not only affects the power consumption through the starting and stopping of auxiliary equipment, but also influences the internal discharge capacity of the battery. Therefore, the energy consumed by an EV travelling the same distance varies at different ambient temperatures.

At lower temperatures, the activity of active substances in the battery decreases, the internal chemical reaction rate of the battery slows down, and at the same time, the temperature decreases, and the viscosity of the electrolyte increases, which leads to an increase in the internal resistance of the battery, resulting in a lower discharge efficiency of the battery. At this time, the power consumption of electric vehicles is large; before reaching the optimal temperature, as the temperature increases, the internal chemical reaction of the battery accelerates, the discharge efficiency gradually increases, and the power consumption per unit mileage of the electric vehicle gradually decreases; after that, as the temperature continues to rise, the anode of the battery experiences degradation that leads to the decomposition of the electrolyte, and the activity of lithium ions decreases. At the same time, the high temperature produces side reactions. The inorganic substances produced by the reaction precipitate on the surface of the anode, causing a nonlinear increase in the battery internal resistance and the performance of the battery materials; deterioration, ultimately leading to a decrease in the battery discharge efficiency; and the power consumption of the electric vehicle during the same mileage to increase rapidly [20,21,22]. Therefore, the relationship between the power consumption per unit mileage of EVs and temperature is as shown in Equation (9):

$$P_T(T)=k_6{T}^2+k_{7}T+k_8$$

(9)

where $P_{ti}$ represents additional power consumption due to temperature, measured in kWh/km; $k_6,k_7,k_8$ represent the coefficients to be fitted.

To analyze the effect of combined temperature on the starting and stopping of auxiliary equipment and the discharge capacity of batteries, we take the data on the operation of EVs in the Guangdong–Hong Kong–Macao Greater Bay Area as an example. By doing rendering, we obtain the law of change for EV power consumption with speed, as shown in Figure 3. The trend in the variation of this figure is consistent with the intrinsic influence mechanism described by Equation (9).

3. Modelled Power Consumption per Unit Mile Based on Improved ACO-SVR

In summary, optimizing the calculation of power consumption per unit mile for EVs is not comprehensive enough when viewed from a single aspect. This is because the effect of temperature and speed on the energy consumption of EVs is a complex issue that involves multiple factors. Therefore, this paper establishes and improves a neural network for ACO-SVR by analyzing a large number of relevant samples, in order to obtain the specific relationship between vehicle power consumption per unit mile and temperature and speed.

3.1. Modelling of EV Power Consumption per Mile

Based on the described mechanism of the influence of temperature and speed on power consumption, the regression function for power consumption per unit mileage of an EV is formulated as shown in (10):

$$P(V_i,T_i)=\left\{\begin{array}{cc}{\displaystyle \frac{k_1\cdot k_{5}v}{k_3\cdot 9.5488}}+k_6{T}^2+k_{7}T+k_8& v<v_1\\ {\displaystyle \frac{k_2\cdot k_5^2{v}^2}{k_4\cdot 9.5488}}+k_6{T}^2+k_{7}T+k_8& v\ge v_1\end{array}\right.$$

(10)

where $P(V_i,T_i)$ represents power consumption per unit mileage of EV at a speed of $V_i$ and an ambient temperature of $T_i$, measured in kWh/km; v represents the travelling speed of EVs, with the unit of measure being km/h; T represents the current ambient temperature, with the unit of measure being °C; and $k_1,k_2,k_3,k_4,k_5,k_6,k_7,k_8$ represent the coefficients to be fitted. $v_1$ is the speed when the output power of the electric vehicle motor reaches the rated power, which is generally 60 km/h [23].

Due to the existence of $k_5^2$ in Equation (10), there is a nonlinear part, and Support Vector Regression (SVR) is a machine learning algorithm used to deal with nonlinear regression problems. It is based on the concept of Support Vector Machines (SVM) and models regression by minimizing the error between the training data points and the model predictions within a pipeline with a bandwidth of ε [24].

It can be seen from Equation (10) that the relationship between power consumption, speed, and temperature presents a polynomial relationship, so the kernel function expression of SVR is shown in (11):

$$K(V,T,V\prime ,T\prime )={(\sigma (V^{2}V{\prime }^2+TT{\prime }^2))}^d$$

(11)

where V and V′ is the velocity value of any two different samples; T and T′ is the temperature value of any two different samples; d is the degree of the polynomial kernel function due to the existence of a binomial, so is at least 2; and $\sigma$ is the scale parameter, which controls the computation of the similarity between the feature vectors, i.e., the velocity and the temperature, and when $\sigma$ is small, the distance between the feature vectors has a small impact on the kernel function, which may lead to an increase in the sensitivity of the model to noise. When $\sigma$ is larger, the distance between the feature vectors has a greater effect on the kernel function, which may lead to a decrease in the sensitivity of the model to noise. Therefore, an appropriate value needs to be chosen to balance the generalization ability of the model and the sensitivity to noise.

The objective function for setting the SVR is shown in (12):

$$\min \left[{\displaystyle \frac{1}{2}}{‖\omega ‖}^2\right]+C{\displaystyle \sum _{i=1}^N\left|f(x_i)-y_i\right|}$$

(12)

where ω is the weight vector; C is the penalty factor; N is the size of the training sample; $f\left(x_i\right)$ is the predicted value; and $y_i$ is the true value. The penalty factor C is used to control the degree of punishment of the model for training error and relaxation variables. When C is larger, the model is more inclined to reduce the training error, which reduces the tolerance of outliers and easily leads to overfitting. Conversely, when C is small, the model is more inclined to keep the model simple, that is, the model needs less training error, which can easily lead to unlearning.

Thus, it can be seen that parameter C and $\sigma$ of the support vector regression machine have an important effect on the performance of the model. and the selection of inappropriate parameters can lead to overfitting or underfitting problems in SVR models [25].

The ant colony algorithm (ACO) is an intelligent optimization algorithm that simulates the foraging behaviour of ants. It can quickly find the optimal solution in the parameter space, effectively avoiding the subjectivity and randomness of the human selection of parameters, thereby improving the generalization ability of the model. Therefore, in order to solve the overfitting or underfitting problem caused by improper parameter selection, this paper uses the ACO to dynamically and globally optimize the penalty factor C and the kernel function coefficient σ in the SVR algorithm. The problem of over-fitting or under-fitting of the model caused by the subjectivity of human selection is avoided.

The ACO, proposed by Italian scholar M. Dorigo in 1991 [26], is a heuristic search algorithm based on population optimization that exhibits adaptability and robustness. However, due to the inherent characteristics of the ACO [27], the pheromone tends to cluster on individual road sections during operation, potentially leading to a local optimum. Therefore, this paper proposes an improvement to the pheromone concentration to avoid falling into the local optimum.

3.2. Improved Ant Colony Optimization Algorithm

The ant colony optimization algorithm is a computing method that simulates the foraging behaviour of ants in nature. It uses pheromone exchange and cooperation between individual ants to find optimal solutions to problems. In the algorithm, each ant selects the city to visit next based on the pheromone concentration and heuristic information on the path, and updates the pheromones on the path after completing a cycle. Over time, the evaporation of pheromones and the path selection of ants work together to gradually converge to the optimal or near-optimal solution. The probability of an ant moving from position i→j at time t as shown (13):

$$p_{ij}^k(t)=\left\{\begin{array}{cc}{\displaystyle \frac{{\tau }_{ij}^{\alpha }(t){\eta }_{ij}^{\beta }(t)}{{\displaystyle \sum _{a\in S}{\tau }_{ia}^{\alpha }(t){\eta }_{ia}^{\beta }(t)}}}& j\in S\\ 0& j\notin S\end{array}\right.$$

(13)

where $p_{ij}^k\left(t\right)$ is the transition probability of worker ant $k$ from position$i$→$j$ at time $t$; ${\tau }_{ij}\left(t\right)$ is the pheromone concentration on path i→j at time t; ${\mathsf{\eta }}_{ij}\left(t\right)$ is the heuristic information of position i→j, and its magnitude is usually ${\displaystyle \frac{1}{d_{ij}}}$, and $d_{ij}\left(t\right)$ is the path length between point i and point j; a = {1, 2…S}, where S is the set of feasible points; α is the pheromone importance factor; and β is the heuristic factor.

The ants primarily rely on the pheromone concentration on the path to select the next path, with a higher pheromone concentration indicating a higher probability of being chosen by the ants. Therefore, the pheromone concentration at each iteration plays a crucial role in path selection. In order to enhance the speed of the ACO, accelerate convergence, and increase the likelihood that the path chosen by the ant in the previous cycle is shorter than the one chosen in the next cycle, the pheromone concentration formula is improved, as shown in (14):

$$\begin{array}{l}{\tau }_{ij}(t)=(1-\rho )\cdot {\tau }_{ij}(t)+\lambda {\displaystyle \sum _{k=1}^m\frac{1}{d_{ij}^k(t)}}+\Delta t_{ij}^k(t)\\ \Delta t_{ij}^k(t)=\left\{\begin{array}{cc}{\displaystyle \frac{Q}{d_{ij}(t)}}\hfill & d_{ij}(t)<d_{ij}(t-1)\\ 0\hfill & \mathrm{other}\end{array}\right.\end{array}$$

(14)

where ρ is the evaporation rate (or attenuation coefficient) of the pheromone, which is usually in the range of (0, 1); λ is the extra strengthening factor of the pheromone; ${∆\tau }_{ij}$ is the increase in the pheromone; and Q is the intensity of the pheromone, which is a positive constant used to adjust the intensity of the pheromone update.

The pheromone importance factor α reflects the relative importance of the amount of information accumulated by the ants during their movement in guiding their search. An α value that is too large will increase the probability of the ants choosing a previously travelled path again, resulting in a decrease in search randomness. Conversely, an α value that is too small will fall into a local optimum. Therefore, it is proposed to change the importance of the pheromone so that it is a dynamic parameter. As the number of iterations increases, the level of importance grows, as shown in (15):

$$\alpha =\left\{\begin{array}{cc}1.5\hfill & k<0.25K\hfill \\ 2.5\hfill & 0.25K\le k\le 0.8K\hfill \\ 3.5\hfill & k>0.8K\hfill \end{array}\right.$$

(15)

where K represents the maximum number of iterations.

At the beginning of the iteration, the pheromone importance factor α is set to a small value to encourage deep search and enhance the global search capability of the ACO. In the middle of the iteration, α is adjusted to 2.5 to ensure that the ACO maintains its search capability without falling into a local optimum. At the end of the iteration, the pheromone importance factor α is increased to a larger value to accelerate convergence and ultimately lead to the stable convergence of results.

3.3. ACO-SVR Algorithm Flow

The improved ACO-SVR-based modelling process is shown in Figure 4, and the specific steps are as follows.

(1)

Pre-processing of the EV operation dataset is performed to calculate the power consumption per unit mile for EVs at each moment in time, as shown in (16):

$$\theta ={\displaystyle \frac{{\displaystyle \underset{t_1}{\overset{t_2}{\int }}U(t)I(t)dt}}{1000{\displaystyle \underset{t_1}{\overset{t_2}{\int }}v(t)dt}}}$$

(16)

where $\theta$ represents the EV power consumption per unit mile, with the unit of measure being kWh/km; U(t) represents the output voltage of the EV battery at time (t),with the unit of measure being volts (V); I(t) represents the output electric current of the EV battery at time (t), with the unit of measure being amperes (A); and v(t) represents the EV at time (t), with the unit of measure being km/h.

(2)

Normalized preprocessing is performed on the temperature, speed, and the resulting sample data on electricity consumption per unit mile, as shown in (17):

$$y^{\prime }={\displaystyle \frac{y-y_{\min }}{y_{\max }-y_{\min }}}$$

(17)

where $y$ represents the sample data before normalization; $y^{\prime }$ represents the sample data after normalization; $y_{min}$ represents the minimum value in the sample data; and $y_{max}$ represents the maximum value in the sample data.

(3)

Initially, multiple parameters in the ACO-SVR algorithm are set. Then, the normalized training samples are substituted into the algorithm for training, and the algorithm error is calculated.

(4)

The parameters C and σ of the SVR are optimized using the ACO. The optimal parameters are then substituted into the SVR model for further processing. If the SVR is not optimized, continue with step (4).

(5)

By training, the correlation coefficients are solved for. Finally, the ACO-SVR estimation expression is obtained, which is used as a prediction model for EV power consumption per unit mile.

4. Results

The verification of this method uses 80,000 sets of data from the operating dataset of 10 BYD Qin New Energy 2019 high-endurance versions manufactured in 2019 in the Guangdong–Hong Kong–Macao Greater Bay Area from 1 November 2020 to 31 October 2022 and electric vehicles equipped with a 53.1 kWh ternary lithium battery. The operating data include the speed of the electric vehicle while driving, the ambient temperature, the output voltage of the battery pack, and the output current. The data sample is divided into three independent parts, namely the training set, the verification set, and the test set. Among them, the training set accounts for 70%, and the test set and the prediction set each account for 15%.

4.1. Analysis of Electric Vehicle Power Consumption per Mile Model Results

Figure 5 illustrates a plot of EV power consumption per unit mile versus speed and temperature. As can be seen from the graph, when the speed is constant, the power consumption of EVs per unit mile tends to decrease and then increase as the temperature rises. This trend is primarily attributed to the discharge capacity of the battery and the start–stop behaviour of auxiliary equipment. Additionally, when the temperature is constant, the EV power consumption per unit mile gradually increases with rising speed. This is due to the fact that as speed increases, air resistance also increases, requiring the EV to consume more energy to overcome this resistance.

Figure 6 presents the variation in EV power consumption per unit mile versus speed at temperatures of 10 °C, 15 °C, 20 °C, 25 °C, and 30 °C, respectively. As seen in the graph, the power consumption per unit mileage gradually increases with rising speed, regardless of the temperature. However, the magnitude of this increase varies at different temperatures. Specifically, at 10 °C, the increase in power consumption is the largest, reaching 78.76%, while at 30 °C, the increase in power consumption is the smallest, at only 12.53%. The main reasons for these differences are as follows.

At low temperatures, the performance of EV batteries is primarily affected. The low temperature reduces the reaction rate and conductivity of the battery, resulting in low battery energy utilization. At the same time, a low temperature also increases the air resistance of the EV, so that the motor requires more energy to overcome this resistance. As speed increases, air resistance becomes greater, and the motor needs to supply more power, further increasing the power consumption per unit mileage.

In contrast, high-temperature environments have a lesser impact on battery performance in EVs. Although high temperatures can lead to an increase in battery self-discharge, the conductivity of the battery in a high-temperature environment is better, and the reaction rate is faster. This results in higher available battery energy. Additionally, the high-temperature environment reduces air density, lowering the air resistance of the EV. As a result, the motor requires less energy, and the increase in power consumption per unit mileage is smaller. It can be seen that, at low temperatures, speed has a greater effect on power consumption per unit mileage, while at high temperatures, speed has a relatively smaller effect on power consumption per unit mileage.

Figure 7 illustrates the variation in power consumption per unit mile versus temperature for EVs at speeds of 20 km/h, 40 km/h, 60 km/h, 80 km/h, and 100 km/h, respectively. It can be observed from the figure that, regardless of speed, the power consumption per unit mile exhibits a tendency to decrease and then increase as the temperature rises.

Energy consumption is lowest at temperatures ranging from 20 °C to 25 °C. This is because this temperature band represents the optimum temperature for battery operation. At these temperatures, the reaction rate and conductivity of EV batteries are usually the highest, resulting in the lowest power consumption.

At low temperatures, the energy consumption is the largest, but at different speeds, the reasons for the largest energy consumption are different. When the vehicle is travelling at a lower speed, the load of auxiliary equipment has a more significant impact on the overall EV. As shown by Equation (8) of this paper, the air conditioner consumes different amounts of electrical energy under different operating conditions, with the heating condition consuming more electrical energy than the cooling condition. Therefore, the maximum energy consumption per unit mileage occurs in low-temperature moments when the vehicle is travelling at a low speed. When driving at high speeds, the energy consumption of EVs mainly comes from air resistance. Lower temperatures lead to an increase in air density, thus increasing air resistance. At this time, EVs need to consume more energy to maintain forward momentum, resulting in the maximum energy consumption per unit mileage.

At different speeds, power consumption per unit mile is affected by temperature to varying degrees. At lower speeds, the variation in power consumption with temperature is larger. For example, at 20 km/h, the minimum value of power consumption occurs at 23 °C, which is 0.1259 kWh/km, and the maximum value occurs at 10 °C, which is 0.1799 kWh/km, resulting in a variation of 42.92%. At higher speeds, the variation in power consumption with temperature is smaller. For example, at 100 km/h, the minimum value of power consumption occurs at 22 °C, which is 0.1930 kWh/km, and the maximum value occurs at 10 °C, which is 0.2562 kWh/km, resulting in a variation of 32.91%. It can be seen that the power consumption per unit mile is more affected by temperature when the EV is driven at a lower speed.

4.2. Model Comparison and Error Analysis

Table 1. Parameter result selection comparison.

Model		Optimal (C, σ)	MAE
ACO-SVR	After improvement	(0.0025, 0.0077)	0.0053737
	Before improvement	(0.2453, 0.001)	0.0061498

shows the comparison table of parameter selection of the ACO-SVR model before and after the improvement. It can be seen from Table 1 that the improved ACO-SVR has the smallest mean absolute error (MAE) value in the parameter selection process, and the selected parameters are the best.

In order to further compare the fitting of the coefficients before and after the improvement of the model, let A₁ = $k_1{k}_5/k_3$; A₂ = $k_2{k}_5^2/k_4$; A₃ = $k_6$; A₄ = $k_6$; and A₅ = $k_7$.

Table 2. Comparison of errors before and after ACO-SVR correction.

Evaluation Index		A1	A2	A3	A4	A5	MAPE
ACO-SVR	After improvement	2.69 × 10−4	3.77 × 10−6	3.48 × 10−4	−1.31 × 10−2	0.25	3.5095%
	Before improvement	3.52 × 10−4	4.38 × 10−6	3.55 × 10−4	−1.09 × 10−2	0.33	4.3361%
SVR fitting		3.71 × 10−4	3.92 × 10−6	3.11 × 10−4	−1.56 × 10−2	0.41	6.4797%

shows the fitting of each coefficient in Equation (10). The average absolute percentage error was selected for evaluation. It can be seen from Table 2 that after introducing the ant colony algorithm into SVR, the prediction accuracy has been significantly improved. MAPE using SVR fitting alone decreased from 6.4797% to 4.3361%. This is mainly because traditional support vector regression models usually require manual selection of their kernel function coefficients σ and the hyperparameter C, and the selection of these parameters is crucial to the performance of support vector regression.

Too large a value for σ may result in the model becoming overly sensitive to noise, leading to overfitting. Conversely, too small a value for σ can lead to a kernel function that is too complex and a model that is too flexible. Similarly, too large a value for the hyperparameter C can lead to overfitting, and thus poor generalization performance, while too small a value for C can lead to a poor fit that is prone to underfitting.

The generalization ability of the SVR model is enhanced by the ACO, which initially identifies the optimal values for these two crucial parameters. Furthermore, the ACO possesses a degree of global search capability and adaptivity, which assists in mitigating the issues of model overfitting or underfitting to some extent.

The improved ACO further bolsters the fitness and generalization capabilities of the ACO-SVR model, as demonstrated by the decrease in MAPE from 4.3361% prior to improvement to 3.5095% following the enhancement. This substantial improvement is largely attributable to the fact that the refined ACO elevates the probability of selecting the optimal outcome in subsequent iterations. This positive pheromone feedback mechanism fosters the global search proficiency of ACO and safeguards against the pitfall of converging to local optimal solutions.

To validate the accuracy of the prediction model proposed in this paper in comparison with other EV power consumption models, the prediction performance of the model proposed herein was compared against a temperature-only model and a speed-only model. The goodness-of-fit (R²), root mean square error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE) were chosen as evaluation metrics, and the results are presented in

Table 3. Comparison of errors under different models.

Evaluation Index	R2	RMSE	MAE	MAPE
The model proposed in this paper	0.89231	0.0066778	0.0053737	3.5095%
Consider only the temperature model	0.72564	0.035209	0.025965	16.85%
Consider only the speed model	0.79357	0.026328	0.020832	13.2502%

.

As evident from Table 3, in terms of both goodness-of-fit and model error, the model proposed in this paper surpasses both the speed-only model and the temperature-only model. This underscores the notable enhancement in the prediction performance of the EV power consumption per mile model based on the improved ACO-SVR proposed in this paper.

Upon comparing the models, it was discovered that the model that solely considers temperature exhibited the poorest prediction performance. This is primarily due to the fact that the influence of temperature on the power consumption per mile of an EV is primarily manifested in the battery’s discharge performance. However, the discharge performance of the battery is not only influenced by temperature but also by factors such as the number of battery cycles and charging and discharging power, among others. Consequently, considering temperature as the sole factor leads to a decrease in prediction accuracy. In contrast to speed, temperature variations occur relatively slowly, and a power consumption model that only considers temperature cannot effectively capture rapid changes in speed when it is fluctuating rapidly. Therefore, the prediction error when solely considering temperature is larger. However, the model proposed in this paper comprehensively takes into account the effects of temperature variations on battery performance, the start–stop variations of auxiliary equipment on power consumption, and the impact of speed variations on motor output power. As a result, the proposed model demonstrates a higher prediction accuracy.

The power consumption model per unit mileage and the actual power consumption distribution established by considering different factors are shown in Figure 8.

It can be seen from Figure 8 that the power consumption per unit mileage of the model proposed in this paper is highly consistent with the actual electric vehicle. As the sample number increases, the power consumption gradually decreases. This is because the sample numbers in this figure are arranged according to temperature. The larger the sample number, the closer it is to the optimal temperature of the battery. The active substances inside the battery exhibit higher activity and faster chemical reactions, so overall the power consumption is reduced. And it can be seen from the 500th to 600th sets of data that the model proposed in this paper comes relatively close to the values predicted by the model that only considers temperature, and the error with the actual power consumption is small. This is because most models that only consider speed ignore the battery factor and believe that the battery has always been at a level where the level of active substances is relatively high and they react faster. It just so happens that these sets of data are around the optimal temperature, and the additional impact of temperature on power consumption can be ignored. So, at this time, the model that only considers speed is closer to the predicted values of the model proposed in this paper.

In order to further analyze the error distribution of the three models, this paper divides the error as the predicted value minus the actual value; the error box plots of the proposed model and the model considering temperature and speed are plotted, as shown in Figure 9.

It can be seen from the figure that the model proposed in this paper has the smallest prediction error range, indicating that its results are more accurate and its central value is closer to 0 than the other two models, so the prediction results are relatively robust; the model that only considers temperature has a large error range, and the central value is less than 0 and deviates far from 0, which means that the model that only considers temperature is relatively conservative in prediction; for the model that only considers speed, the central value is greater than 0, indicating that its prediction results are more aggressive.

Based on the above, the curve of the power consumption model per unit mileage considering temperature and speed established in this paper is more consistent with the actual power consumption per unit mileage than the models that only consider speed and temperature.

5. Conclusions

As the accurate prediction of EV power consumption is fundamental for determining the daily load variation of EVs, this paper proposes an EV power consumption per mile model based on the improved Ant Colony Optimization-Support Vector Regression (ACO-SVR) framework to enhance the accuracy of power consumption per mile prediction.

Initially, this model analyzes the influence mechanism of EV power consumption per mile and identifies the pertinent factors. Subsequently, it determines the EV power consumption per mile at a specific point in time by studying the EV health dataset, which comprises the voltage and current output of the battery pack and the driving speed of the vehicle. The model takes the driving speed of the vehicle and the ambient temperature at the vehicle’s location as inputs. By utilizing the improved ant colony optimization (ACO) algorithm to optimize the kernel function coefficients σ and hyperparameters C of the Support Vector Regression (SVR), the improved ACO-SVR model for EV power consumption per mile is constructed.

The proposed method is validated using the new energy vehicle dataset from the Guangdong–Hong Kong–Macao Greater Bay Area. The predictors of the model proposed in this paper are compared and validated with those of the SVR-only fit and the unimproved ACO-SVR model. Additionally, the feasibility of the proposed method is verified by comparing and analyzing the temperature-only and velocity-only models with the model proposed in this paper, which takes into account the effect of velocity–temperature.

The power consumption per unit mile model developed in this paper lacks the consideration of traffic state and road class. In the future, the effects of traffic state and road class on power consumption can be further explored to construct an EV power consumption per unit mile model based on multi-traffic state factors.