Digital Twin Modeling of a Solar Car Based on the Hybrid Model Method with Data-Driven and Mechanistic

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Article Digital Twin Modeling of a Solar Car Based on the Hybrid Model Method with Data-Driven and Mechanistic

Luchang Bai, Youtong Zhang *, Hongqian Wei , Junbo Dong and Wei Tian

Laboratory of Low Emission Vehicle, Beijing Institute of Technology, Beijing 100081, China; [email protected] (L.B.); [email protected] (H.W.); [email protected] (J.D.); [email protected] (W.T.) * Correspondence: [email protected]

Featured Application: This technology is expected to be used in energy management of new energy vehicles.

Abstract: Solar cars are energy-sensitive and affected by many factors. In order to achieve optimal energy management of solar cars, it is necessary to comprehensively characterize the energy ﬂow of vehicular components. To model these components which are hard to formulate, this study stimulates a solar car with the digital twin (DT) technology to accurately characterize energy. Based on the hybrid modeling approach combining mechanistic and data-driven technologies, the DT model of a solar car is established with a designed cloud platform server based on Transmission Control Protocol (TCP) to realize data interaction between physical and virtual entities. The DT model is

further modified by the offline optimization data of drive motors, and the energy consumption is evaluated with the DT system in the real-world experiment. Specifically, the energy consumption

Citation: Bai, L.; Zhang, Y.; Wei, H.; error between the experiment and simulation is less than 5.17%, which suggests that the established Dong, J.; Tian, W. Digital Twin DT model can accurately stimulate energy consumption. Generally, this study lays the foundation Modeling of a Solar Car Based on the for subsequent performance optimization research. Hybrid Model Method with Data-Driven and Mechanistic. Appl. Keywords: solar car; digital twin; hybrid modeling; energy consumption test Sci. 2021, 11, 6399. https://doi.org/ 10.3390/app11146399

Academic Editor: Alexandre 1. Introduction Carvalho Vehicles nowadays have become an indispensable means of transportation for people; however, emissions of traditional fuel vehicles accelerate global warming, which urges Received: 2 June 2021 Accepted: 7 July 2021 nations around the world to develop new energy vehicles. Solar cars, as a kind of new Published: 11 July 2021 energy vehicle, not only have the advantages of pure electric vehicles with zero emissions, but also can use on-board solar cells to truly realize green travel [1]. However, at the

Publisher’s Note: MDPI stays neutral current stage, the energy utilization rate of solar energy is low, and solar cars only exist in with regard to jurisdictional claims in laboratory research. Kohei et al. [2] detailed the process of developing and manufacturing published maps and institutional afﬁl- a solar car as a ﬁnal project. Suita et al. [3] described the drive performance of the solar iations. car and proposed a maximum power tracking algorithm, and then presented a motor comparison method based on energy consumption, travel speed optimization, and total travelling distance. Ustun et al. [4] proposed an energy management method for solar vehicles and validated it on a racing car of the Istanbul University of Technology Solar

Copyright: © 2021 by the authors. Team. Vinnichenko et al. [5] proposed the optimization of the solar vehicle shape to cool Licensee MDPI, Basel, Switzerland. down the photovoltaic modules to increase power generation in addition to reducing air This article is an open access article resistance. Mambou et al. [6] of the University of Johannesburg Solar Team designed and distributed under the terms and validated a dedicated tracking and monitoring system for the solar car based on the team’s conditions of the Creative Commons participation in the 2014 South African Solar Car Challenge and analyzed the interference Attribution (CC BY) license (https:// and immunity of WIFI wireless communication along the race route. A machine learning- creativecommons.org/licenses/by/ based solar radiation forecasting system was proposed by the University of Michigan Solar 4.0/).

Appl. Sci. 2021, 11, 6399. https://doi.org/10.3390/app11146399 https://www.mdpi.com/journal/applsci Appl. Sci. 2021, 11, 6399 2 of 17

Team and IBM Watson Research Center [7] and performed well in the WSC 2015 and 2016 North American Solar Car Challenge. Although some progress has been made in the development of solar cars recently, there are still many problems, such as inaccurate energy estimation especially under complex and variable road environments. With the above problems, it is hard to accurately describe the solar energy acquisition and utilization, since all energy consumption of the components can only be tested offline at the current stage, a process which contains large errors. With the development of new generation information technologies such as cloud computing, Internet of Things, and big data, digital twin (DT) has emerged. This technology creates virtual models of physical entities digitally, simulates the behavior of physical entities in the real environment with the help of data, and adds or extends new capabilities to physical entities by means of virtual–real connection feedback, data fusion analysis, and iterative optimization of decisions. Therefore, the utilization of DT can effectively online fit solar cars and greatly reduce the investment in human, material and financial resources, etc. The first step of DT is to create high-fidelity virtual models, which is also one of the main challenges of DT as it requires realistic reproduction of geometry, properties, behaviors, and rules of physical entities [8]. These models should not only be consistent with the physical entity in terms of geometric structure but should also be able to simulate the spatiotemporal state, behavior, and functionality of the physical entity [9,10]. Mukherjee et al. [11] performed a DT of a 3D printer to reduce the number of trial-and- error tests, which shortens the time between design and production, and Kousi et al. [12] proposed a production system in infrastructure of DT models before providing an industrial case study of an automotive front axle assembly. Matulis et al. [13] presented a case study of creating and training a DT of a robotic arm as a virtual space created using Unity for artificial intelligence training, and Vachalek et al. [14] performed a simulation based on a Siemens application called Plant Simulation (PS), a simulation tool for DT of factory production lines. Mohammadi et al. [15] introduced a DT of a smart city paradigm that improves insight into the technical interactions of urban human-machine infrastructures. However, most of these mentioned simulation approaches suffer from poor flexibility and complex configurations. In fact, the DT often contains multiple subsystems, and it is difficult to build accurate mechanistic models for complex physical systems. In contrast, a data-driven approach uses historical and real-time operational data of the system to update, revise, connect, and supplement the numerical model [16], fusing system mechanics and operational data to better evaluate the system dynamically in real time [17–19]. In the field of automotive manufacturing, research targeting DT is also evolving [20,21]. Peng et al. [22,23] proposed a health metric estimation method based on the DT for condition monitoring of power electronic converters, demonstrating the application of Buck DC-DC converters. A digital copy of the experimental prototype was built, which included the power stage, sampling circuit and closed-loop controller. Li et al. [24] proposed a cloud BMS to build a DT of the battery system that could ensure continuous and accurate monitoring of the battery state, but it did not give a specific DT model. Ramachandran et al. [25], for a similar purpose, used equivalent battery circuit modeling and real-time RLS updates to construct a DT that provides accurate insights into battery charge estimation and conditions for the BMS. Krishnan et al. [26] developed health monitoring and prognostics for PMSM by creating an intelligent digital twin (i-DT) in MATLAB / Simulink. Next, a remote health monitoring and diagnostic center (RHMPC) was developed to remotely monitor motor performance through cloud communication from EV service providers. Ezhilarasu et al. [27] presented how DT can be integrated with integrated vehicle health management (IVHM) for condition-based maintenance (CBM) of vehicles to provide targeted components and systems of vehicles with customized maintenance plans. Magargle et al. [28] created a simulation-based DT model combined with an integrated model of the braking system to support thermal monitoring and predictive maintenance of the vehicle braking system. Zakrajsek et al. [29] performed health inspection of vehicle tire subsystems based on DT. Jain et al. [30] created a DT of a complete photovoltaic energy conversion unit (PVECU), Appl. Sci. 2021, 11, 6399 3 of 17

including PV energy, source-level power converters, and controllers, which is capable of effectively troubleshooting complex systems without the need for physical analysis. To a large extent, these studies have contributed to the penetration of DT in the field of smart vehicles, but they have mostly focused on the component level, illustrating the characteristics of a particular subsystem of the vehicle, and research on DT for the whole vehicle is very limited. However, the study of the whole vehicle is much more meaningful because it fully considers the interactions between the subsystems, which is more comprehensive and realistic. Therefore, the knowledge gap of such research exists in the following aspects: (1) simulation modeling methods are mostly inflexible and error-prone with complex configurations; (2) DT model lacks data-driven real-time updates and parallel operation with entities; (3) there is a lack of research on the characteristics of the whole vehicle. In summary, DT breaks through the limitations of previous simulation techniques in the design phase and local applications [31] to achieve multi-physical field coupling and data linkage between virtual and physical entities to improve simulation accuracy. In the face of complex systems and multivariable environments, DT can reflect the entity system information more comprehensively, accurately and in real time [32,33]. The purpose and novelties of this paper are as follows: 1. In this paper, the energy consumption and operation of each component of the solar car are significantly stimulated with the DT technology, and then a mature architecture of the whole vehicle energy consumption is established accordingly. 2. A new DT framework based on a hybrid modeling approach coupled with SVM techniques is proposed to address the solar car energy consumption problem. This framework can effectively combine mechanistic and data-driven modeling to improve the accuracy of DT systems. 3. This study deploys a cloud server based with Transmission Control Protocol (TCP) to achieve real-time data acquisition and interaction between the real solar car and the DT system.

2. Architecture of the DT System of Solar Car The DT system architecture of a solar car contains four layers: physical layer, connection layer, virtual layer and service layer, and the composition architecture is shown in Figure1. The physical layer is composed of physical objects, and mainly includes the solar car, as well as the internal and external environment, and the various operational logics existing between them. Concretely, the external environment in this system includes weather conditions such as temperature, wind and light intensity, and road conditions such as road slope and road surface unevenness. The actual vehicle used in this system is the self-developed “Sun Shuttle III” four-seater solar car. The appearance and speciﬁcations are shown in Figure2 and Table1, respectively.

Table 1. Speciﬁcations of “Sun Shuttle III”.

Parameters Values Curb Mass 395 kg Dimensions 5000 × 1650 × 1200 mm Wheelbase 2850 mm Battery Capacity 20 kWh Solar Panel Area 5 m2 Max Power 12 kW Top Speed 130 km/h Range 700 km Appl. Sci. 2021, 11, 6399 4 of 17

Appl. Sci. 2021, 11, 6399 4 of 17 Appl. Sci. 2021, 11, 6399 4 of 17

Figure 1. Elements of the presented architecture.

The physical layer is composed of physical objects, and mainly includes the solar car, as well as the internal and external environment, and the various operational logics existing between them. Concretely, the external environment in this system includes weather conditions such as temperature, wind and light intensity, and road conditions such as road slope and road surface unevenness. The actual vehicle used in this system is the self-

developed “Sun Shuttle III” four-seater solar car. The appearance and specifications are FigureFigureshown 1. in Elements Figure of 2 andthe pres presented Tableented 1, architecture.respectively. architecture. The physical layer is composed of physical objects, and mainly includes the solar car, as well as the internal and external environment, and the various operational logics existing between them. Concretely, the external environment in this system includes weather conditions such as temperature, wind and light intensity, and road conditions such as road slope and road surface unevenness. The actual vehicle used in this system is the self- developed “Sun Shuttle III” four-seater solar car. The appearance and specifications are shown in Figure 2 and Table 1, respectively.

FigureFigure 2. 2.Appearance Appearance of of “Sun “Sun Shuttle Shuttle III”. III”.

TableThe 1. Specifications connection layerof “Sun is alsoShuttle named III”. the data layer. In this system, in addition to the inherent data in the physical space, the data also includes multi-mode and multi-type Parameters Values operational data collected by various sensors in real time. Based on the 4G communication Curb Mass 395 kg technology and TCP,Dimensions the collected sensor data are ﬁnally transmitted 5000 × 1650 to× 1200 the cloudmm platform to realize the informationWheelbase interaction between physical and virtual 2850 entities. mm FigureThe 2. Appearance virtualBattery layer, of “SunCapacity also Shuttle called theIII”. model layer, refers to the DT 20 kWh model of the solar car, which is a virtualSolar copy Panel of Area the physical entity, including the mechanism 5 m² model and the data-drivenTable 1. Specifications model.Max The of Power “Sun model Shuttle is jointly III”. built by CarSim (an automotive 12 kW system simulation software developedTop by Speed Mechanical Simulation Corporation) and 130 Simulink, km/h which can run Parameters Values in parallel and interactRange with the real vehicle in real time. Among 700 them, km “dynamic” is the Curb Mass 395 kg key characteristic of this model, which means the model needs to have the abilities of Dimensions 5000 × 1650 × 1200 mm self-learning and self-adjustment. Wheelbase 2850 mm The service layer, i.e., the functional application of the DT, includes but is not limited to Battery Capacity 20 kWh dynamic monitoring,Solar Panel report Area output, data analysis, data storage, and 5 m² algorithm optimization. After the DT modelMax runsPower in simulation, it can perform real-time 12 kW monitoring of the real vehicle, driving strategyTop Speed optimization and energy consumption 130 prediction, km/h etc. Range 700 km Appl. Sci. 2021, 11, 6399 5 of 17

The connection layer is also named the data layer. In this system, in addition to the inherent data in the physical space, the data also includes multi-mode and multi-type operational data collected by various sensors in real time. Based on the 4G communication technology and TCP, the collected sensor data are finally transmitted to the cloud platform to realize the information interaction between physical and virtual entities. The virtual layer, also called the model layer, refers to the DT model of the solar car, which is a virtual copy of the physical entity, including the mechanism model and the data-driven model. The model is jointly built by CarSim (an automotive system simulation software developed by Mechanical Simulation Corporation) and Simulink, which can run in parallel and interact with the real vehicle in real time. Among them, “dynamic” is the key characteristic of this model, which means the model needs to have the abilities of self-learning and self-adjustment. The service layer, i.e., the functional application of the DT, includes but is not limited to dynamic monitoring, report output, data analysis, data storage, and algorithm optimization. After the DT model runs in simulation, it can perform real-time monitoring of the real vehicle, driving strategy optimization and energy consumption prediction, etc.

3. Construction of The DT Model 3.1. Solar Car Modeling Ideas

Appl. Sci. 2021, 11, 6399 Solar cars are generally composed of five parts: power battery system, electric5 of 17 drive system, steering system, braking system, and driving system. The main difference from pure electric vehicles is the addition of photovoltaic cell arrays and a solar inverter to the power system, in addition to the conventional power battery pack [34,35]. 3. ConstructionOne-to-one of mapping the DT Model modeling of solar cars is too difficult to achieve and would also 3.1.significantly Solar Car Modelingreduce the Ideas operational efficiency. Accordingly, the DT is performed for the energySolar consumption cars are generally of the composedreal vehicle of to five ma parts:ximize power the mapping battery system, of the electricenergy driveflow and system,consumption steering on system, the basis braking of ensuring system, andeffici drivingency and system. feasibility. The main The difference overall modeling from pureframework electric is vehicles shown is in the Figure addition 3. The of photovoltaic solar panels cell receive arrays solar and radiation a solar inverter and are to theexcited power system, in addition to the conventional power battery pack [34,35]. to generate electrical energy. The generated electrical energy will give priority to driving One-to-one mapping modeling of solar cars is too difficult to achieve and would also the solar car, and the remaining part will charge the power battery system. The electric significantly reduce the operational efficiency. Accordingly, the DT is performed for the drive system drives the solar car by motor and receives the torque demand from the load energy consumption of the real vehicle to maximize the mapping of the energy flow and consumptionmodel. The load on themodel basis includes of ensuring windward efficiency resistance, and feasibility. rolling resistance, The overall hill modeling climbing re- frameworksistance, acceleration is shown in resistance Figure3. The and solar stray panels losses receive [36,37]. solar radiation and are excited to generateIn addition electrical to energy. the internal The generated mechanism electrical and response energy will to givethe external priority toenvironment, driving the the solarDT model car, and should the remaining include the part geometric will charge model the power describing battery the system. physical The object electric appearance drive systemdimensions drives and the composition solar car by motor style and[38,39]. receives The thegeometric torque demandmodel of from this the solar load car model. was first Theconstructed load model by includesSolidWorks, windward then imported resistance, into rolling CarSim resistance, in parts, hill and climbing finally resistance, integrated to accelerationcomplete the resistance geometric and model. stray losses [36,37].

Figure 3.3. OverallOverall modeling modeling framework framework diagram. diagram.

In addition to the internal mechanism and response to the external environment, the DT model should include the geometric model describing the physical object appearance dimensions and composition style [38,39]. The geometric model of this solar car was ﬁrst constructed by SolidWorks, then imported into CarSim in parts, and ﬁnally integrated to complete the geometric model.

3.2. Mechanism Modeling: PV Cell and Electric Drive System 3.2.1. Photovoltaic Cell Model The output characteristics of photovoltaic (PV) cells are similar to those of semiconductor diodes, where the current varies exponentially with voltage when light is available. The photogenerated current is regarded as a constant current source. The material body resistance and the P-N junction cross boundary area carrier load and contact resistance are equivalent to the series resistance Rs. The leakage current at the edge is equivalent to the shunt resistance Rsh, and the equivalent circuit of a single photovoltaic cell is shown in Figure4. Appl. Sci. 2021, 11, 6399 6 of 17

3.2. Mechanism Modeling: PV Cell and Electric Drive System 3.2.1. Photovoltaic Cell Model The output characteristics of photovoltaic (PV) cells are similar to those of semiconductor diodes, where the current varies exponentially with voltage when light is available. The photogenerated current is regarded as a constant current source. The material body resistance and the P-N junction cross boundary area carrier load and contact resistance Appl. Sci. 2021, 11, 6399 are equivalent to the series resistance Rs. The leakage current at the edge is equivalent6 of 17to the shunt resistance Rsh, and the equivalent circuit of a single photovoltaic cell is shown in Figure 4.

FigureFigure 4.4. EquivalentEquivalent circuitcircuit ofof photovoltaicphotovoltaic cell.cell.

TheThe PVPV cellcell outputoutput currentcurrent expressionexpression isis givengivenby bythe thefollowing followingequation: equation: q(U + IRs) U + IRs I = Iph − I exp − 1 − (1)(1) 0 AkT Rsh

where Iph is the photogenerated current; I0 denotes the saturation dark current (reverse where Iph is the photogenerated current; I0 denotes the saturation dark current (reverse saturationsaturation current) current) of the of PV the cell PV in ce thell absencein the absence of light; ofq islight; the electronicq is the electronic charge, 1.6 charge,× 10− 191.6C ×; −19 U10is theC; U voltage is the voltage on the load on the resistance, load resistance, V; Rsh is V; the Rsh shunt is the resistance, shunt resistance,Ω; Rs is Ω the; Rs series is the −23 resistance,series resistance,Ω; k is Ω the; k Boltzmannis the Boltzmann constant, constant, 1.38 × 1.3810− ×23 10J/K; J/K;T is T the is the cell cell temperature, temperature, K; AK;is A the is the ideality ideality factor factor of of the the diode, diode, and and takes takes the the value value of of 1.2. 1.2. The The photogenerated photogenerated and and reversereverse saturationsaturation currentscurrents areare solvedsolved byby thethe followingfollowing equations:equations:

 α•(T−Tr )+Isc  Iph = Iro •Ir 3 (2) T qEg 1 1 (2)  I0 = Irs Tr exp[ Ak ( Tr − T )]

where α is the short-circuit current temperature coefficient and takes the value of α 1.06where× 10 is− 5theA/K; short-circuitTr is the idealcurrent reference temperature operating coefficient temperature, and takes 298.15 the value K; Isc of is1.06 the × −5 solar10 A/K; panel Tr short-circuit is the ideal reference current, and operatingIr is the temperature, actual light intensity;298.15 K; IscIro isis the the solar ideal panel light intensity,short-circuit 1000 current, W/m 2and; Irs Iris is the the saturation actual light current; intensity;Eg Irois is the the forbidden ideal light band intensity, width 1000 of 2 theW/m semiconductor; Irs is the saturation material, current; taken Eg as is 1.1. the forbidden band width of the semiconductor material,In the taken actual as PV1.1. cell, the Rsh resistance value tends to inﬁnity, so the third term on the rightIn the side actual of Equation PV cell, (1)the canRsh beresistance equated value to 0, whiletends theto infinity, PV module so the is athird multi-piece term on series-parallelthe right side package.of Equation The (1) mathematical can be equated model to 0, of while the PV the cell PV array module is as follows:is a multi-piece series-parallel package. The mathematical model of the PV cell array is as follows: q(U + IRs) I = mIph − mI exp − 1 (3) 0 nAkT (3)

wherewhere mm isis thethe numbernumber ofof cellscells inin parallelparallel inin thethe modulemodule andand nn isis thethe numbernumber ofof cellscells inin seriesseries inin thethe module.module. 3.2.2. Drive Motor Model 3.2.2. Drive Motor Model The drive motor—named the permanent magnet synchronous hub motor—of the The drive motor—named the permanent magnet synchronous hub motor—of the so- solar car is modeled by using mathematical equations and table look-up methods. The lar car is modeled by using mathematical equations and table look-up methods. The rela- relationship between accelerator pedal opening and output torque refers to the follow- tionship between accelerator pedal opening and output torque refers to the following ing equation: equation: β · 80, 0.02 ≤ β ≤ 1 T = (4) out 0, 0 ≤ β ≤ 0.02 where 80 represents the maximum torque in Nm that this drive motor can provide, and β is the throttle pedal opening, whose value range is [0, 1]. The motor output power and output current are calculated by the following equation: Pout = Tout · W Pin (5) Iout = U Appl. Sci. 2021, 11, 6399 7 of 17

(4)

where 80 represents the maximum torque in Nm that this drive motor can provide, and β is the throttle pedal opening, whose value range is [0,1]. The motor output power and output current are calculated by the following equation:

Appl. Sci. 2021, 11, 6399 7 of(5) 17

where W is the motor rotating speed, Pout is the motor output power, Pin is the input power, where W is the motor rotating speed, P is the motor output power, P is the input power, and U is the input voltage. The motor outefficiency is calculated by the followingin equation: and U is the input voltage. The motor efﬁciency is calculated by the following equation:

P (6) η = out = f (T, W) (6) P where η is the motor efficiency as a functionin of motor rotating speed W and motor torque whereT. The ηmotoris the is motor modeled efﬁciency using asthe a look-up function table of motor module rotating in Simulink, speed W whereand motor the value torque of Tη. is The measured motor is experimentally. modeled using The the look-upexperimental table modulemotor efficiency in Simulink, MAP where is shown the value in Figure of η is5. measured experimentally. The experimental motor efﬁciency MAP is shown in Figure5.

Figure 5. Motor efﬁciencyefficiency MAP. 3.3. Modeling of Power Battery Based on Data-Driven 3.3. Modeling of Power Battery Based on Data-driven 3.3.1. Power Battery Mathematical Model 3.3.1. Power Battery Mathematical Model The solar car power battery is a lithium-ion battery, and the basis of the battery modelingThe solar is to car determine power battery the characteristic is a lithium-ion functions battery, of the and electric the basis potential of the battery and internal mod- resistanceeling is to ofdetermine the lithium-ion the characteristic battery, which functions are obtained of the electric based onpotential the relationship and internal of there- batterysistance state of the of lithium-ion charge value battery, SOC (state which of charge)are obtained variation based [40 on,41 ].the This relationship model includes of the threebattery parts: state calculation of charge value of available SOC (state battery of capacity,charge) variation calculation [40,41]. of battery This SOCmodel value, includes and calculationthree parts: ofcalculation battery terminal of available voltage. battery capacity, calculation of battery SOC value, and calculationThe available of battery battery terminal capacity voltage. is calculated by the following equation: The available battery capacity is calculated by the following equation: Z t Qu(t) = Q0 − λIdt (7) 0 (7)

where Qu(t) is the remaining available capacity at time t, Q0 is the initial capacity, λ is the charge/discharge efﬁciency, and I is the battery current. The SOC value is calculated by the following equation: R t λIdt SOC(t) = SOC(0) − 0 (8) CN

where SOC(t) is the SOC value at time t, SOC(0) is the initial SOC value, and CN is the rated capacity of the battery. The battery terminal voltage is calculated by the following equation:

u(τ, SOC) = E(τ, SOC) − IR(τ, SOC) (9)

where E(τ, SOC) denotes the open-circuit voltage as a function of temperature τ and SOC; R(τ, SOC) denotes the internal resistance of the battery as a function of temperature τ and SOC. The correspondence between R and E is obtained through experiments, as shown in Figure6a,b below, respectively. It can be seen that it is difﬁcult to establish Appl. Sci. 2021, 11, 6399 8 of 17

where Qu(t) is the remaining available capacity at time t, Q0 is the initial capacity, is the charge/discharge efficiency, and I is the battery current. The SOC value is calculated by the following equation:

(8)

where SOC(t) is the SOC value at time t, SOC(0) is the initial SOC value, and CN is the rated capacity of the battery. The battery terminal voltage is calculated by the following equation: (9)

Appl. Sci. 2021, 11, 6399 where E(τ, SOC) denotes the open-circuit voltage as a function of temperature τ and8 SOC of 17 ; R(τ, SOC) denotes the internal resistance of the battery as a function of temperature τ and SOC. The correspondence between R and E is obtained through experiments, as shown in Figure 6a,b below, respectively. It can be seen that it is difficult to establish the relationship the relationship between the terminal voltage of a lithium battery and its measurable between the terminal voltage of a lithium battery and its measurable parameters by pure parameters by pure mechanistic modeling, which includes temperature, voltage, current, mechanistic modeling, which includes temperature, voltage, current, internal resistance internal resistance and SOC at the current moment. Therefore, the support vector machine and SOC at the current moment. Therefore, the support vector machine (SVM) is intro- (SVM) is introduced to solve this problem. duced to solve this problem.

(a) (b)

FigureFigure 6. 6.Internal Internal resistance resistance and and open open circuit circuit voltage voltage characteristics characteristics of of the the battery: battery: ( a(a)) Description Description of of what what is is contained contained in in thethe ﬁrst first panel; panel; ( b(b)) Description Description of of what what is is contained contained in in the the second second panel. panel.

3.3.2.3.3.2. SVM-BasedSVM-Based Data-DrivenData-driven ModelingModeling FromFrom the the previous previous section, section, it it can can be be seen seen that that the the internal internal chemistry chemistry of theof the power power cell cell is complex,is complex, with with many many inﬂuencing influencing factors factors such su asch temperature as temperature uncertainty, uncertainty, aging aging conditions, condi- andtions, dynamic and dynamic operating operating conditions, conditions, which iswhich a highly is a nonlinearhighly nonlinear system [system42]. In the[42]. face In the of thisface situation, of this situation, a data-driven a data-driven modeling modelin approachg approach based on based SVM on techniques SVM techniques is proposed is pro- to solveposed the to currentsolve the nonlinear current nonlinear problems problems and improve and improve the prediction the prediction accuracy accuracy of the model. of the Themodel. temperature The temperatureτ, voltage τ,V voltage, SOC value V, SOC of value the battery of the at battery the previous at the previous moment momentS, current S, I,current and internal I, and resistanceinternal resistanceR were selected R were asselected input variables,as input variables, and the voltageand theat voltage the battery at the terminalbattery terminalyi was the yi was output. the output. The sample The sample points pointsXi at anyXi at moment any momenti can i becan expressed be expressed as i−1 i i i i Xasi = S , τ , V , I , R .. ByBy mapping mapping each each one one with with a a nonlinear nonlinear function functionΦ Ф(x)(x)to to the the high-dimensional high-dimensional feature feature space,space, and and performing performing linear linear regression regression operations operations in in the the high-dimensionalhigh-dimensional feature feature space, space, thethe effect effect of of nonlinear nonlinear regression regression in in the the original original space space can can be be obtained, obtained, and and the the regression regression estimationestimation function functionf fcan can bebe expressedexpressedas: as:

f (x) = ω · φ(x) + b (10)

where w is the normal vector of the optimal hyperplane, its dimension is the dimension of the feature space, and b is the threshold value. For a given nonlinear sample set T = {(x1, y1), (x2, y2), ··· , (xi, yi)}, xi ∈ R, yi ∈ R, the optimization problem is:

l 1 2 ∗ min 2 kwk + C ∑ ξi + ξi ω,b i=1  − · ( ) − ≤ +  yi ω φ xi b ξi ε (11)  ω · φ(x ) − b − y ≤ ξ∗ + ε s.t. i i i ξ , ξ∗ ≥ 0, i = 1, 2, ··· , l  i i  C > 0

* where ξi, ξi is the relaxation factor, which represents the degree to which the group of samples does not satisfy the constraint. C represents the penalty factor, which indicates the Appl. Sci. 2021, 11, 6399 9 of 17

strength of the constraint that some of the samples can be allowed not to be completely divided by the hyperplane intact, and ε is the insensitivity loss factor, which represents the error in the true value that can be allowed within some upper and lower range. The exact expression of the regression estimation function is obtained by solving it using the Lagrange multiplier method:

1 ∗ ∗ f (x, αi, αi ) = ∑(αi − αi )φ(xi)φ xj + b (12) i=1

* where αi, αi ≥ 0 is the Lagrangian multiplier. Using Wolfe’s pairwise theory and introduc- ing the kernel function k xi, xj = φ(xi) · φ xj , the ﬁnal regression estimation function is shown in Equation (13):

l ∗ ∗ f (x, αi, αi ) = ∑(αi − αi )k xi, xj + b (13) i=1

The radial basis function is chosen as the kernel function because the radial basis kernel function performs better on highly nonlinear problems. The expression of the radial basis kernel function is: 2 K xi, xj = exp −γ xi − xj (14)

where γ = 1/2σ2 is the kernel function parameter.

3.4. Complete Solar Car Model The above power battery system, PV module and electric drive system were modeled in Simulink, while the rest of the vehicle was modeled in the CarSim software. The important parameter settings in CarSim are shown in Table2. The built-in powertrain settings in CarSim were changed to external input access, i.e., the torque output from the drive motor in Simulink was used as the input to the powertrain here.

Table 2. Important parameter settings in CarSim.

Parameters Values Sprung Mass 420 kg Axial Load Distribution Ratio 40:60 Mass Center of Sprung Mass 520 cm Drag Coefﬁcient 0.16 Frontal Area 1.45 m2 No-load Tire Radius 280 mm Drive Form Rear hub motor direct drive Maximum Brake Pedal 400 N Input Force Ratio of Front and Rear Braking Force 55:45

The joint simulation model of the whole vehicle is shown in the following Figure7. Appl. Sci. 2021, 11, 6399 10 of 17

Appl. Sci. 2021, 11, 6399 10 of 17

Maximum Brake Pedal 400 N MaximumInput BrakeForce Pedal 400 N Ratio of FrontInput and Rear Force Braking Force 55:45 Appl. Sci. 2021, 11, 6399 Ratio of Front and Rear Braking Force 55:45 10 of 17 The joint simulation model of the whole vehicle is shown in the following Figure 7. The joint simulation model of the whole vehicle is shown in the following Figure 7.

Figure 7. Simulink simulation model of the whole vehicle. FigureFigure 7.7. SimulinkSimulink simulationsimulation modelmodel ofof thethe wholewhole vehicle.vehicle. 4. Validation and Discussion 4.4.1.4. ValidationValidation Construction andand of Discussion Discussionthe Test Platform 4.1. Construction of the Test Platform 4.1.1.4.1. Construction Server Software of the DesignTest Platform 4.1.1. Server Software Design 4.1.1.The Server most Software important Design feature of DT is the two-way communication between physical The most important feature of DT is the two-way communication between physical and virtual,The most and important it is realized feature by establishing of DT is th ea two-waycloud server communication based on TCP. between In this process,physical and virtual, and it is realized by establishing a cloud server based on TCP. In this process, the data acquisition card collects sensor signals and sends them to the host computer theand data virtual, acquisition and it is realized card collects by establishing sensor signals a cloud and server sends based them on to TCP. the hostIn this computer process, through a USB interface. The host computer then sends the data to the cloud server throughthe data aacquisition USB interface. card collects The host sensor computer signals then and sends sends the them data to to the the host cloud computer server through TCP and the cloud server saves the data as data files. Finally, the data of the throughthrough TCP a USB and interface. the cloud serverThe host saves computer the data then as data sends ﬁles. the Finally, data the to datathe ofcloud the wholeserver whole vehicle are read, updated, analyzed and calculated in real time by MATLAB to vehiclethrough are TCP read, and updated, the cloud analyzed server andsaves calculated the data in as real data time files. by MATLABFinally, the to data realize of thethe informationrealizewhole thevehicle information interaction are read, betweeninteraction updated, the betweenanalyzed virtual entitythe and virtual andcalculated the entity physical inand real the entity, time physical real-timeby MATLAB entity, energy real- to consumptiontimerealize energy the information consumption calculation, interaction data calculation, monitoring between data andthe monitoring virtual other functions.entity and and other the The functions.physical data transmission entity, The datareal- principletransmissiontime energy of the principleconsumption cloud platform of the calculation, cloud is shown platform data in Figure ismonitoring shown8. in Figure and other 8. functions. The data transmission principle of the cloud platform is shown in Figure 8.

Figure 8. Cloud platform data transmission principle. Figure 8. Cloud platform data transmission principle. FigureThe 8. Cloud cloud platform server uses data the transmission Windows principle. system; hence, this system uses socket program- mingThe under cloud Windows server uses to establish the Windows a server system; in the hence, cloud this to system receive uses data. socket Socket program- is the handlemingThe under of cloud a communication Windows server touses establish the chain Windows toa server describe system; in th thee cloud IPhence, address to thisreceive andsystem port,data. uses andSocket socket applications is the program- handle of differentofming a communication under computers Windows canchain to send establish to describe requests a server the to theIP in a network ddressthe cloud and or to answerport, receive and network data. applications Socket requests is of the different through handle socket.computersof a communication Socket can is send a network chainrequests to communication describe to the network the IP unit a ddressor supportinganswer and network port, TCP/IP and requests applications and contains through of ﬁve different socket. basic informationSocketcomputers is a networkcan for send conducting communication requests network to the unitnetwork communication: supporting or answer TCP/IP thenetwork protocol and containsrequests used fivethrough for connectionbasic socket. infor- (TCP,mationSocket UDP), isfor a networkconducting the local communication host networ IP addressk communication: unit (server supporting intranet the TCP/IP protocol IP), the and localused contains remotefor connection five protocol basic (TCP,infor- port (0~65535),UDP),mation thefor the localconducting IP addresshost IP networ ofaddress thek remotecommunication: (server host intr (clientanet the extranetIP), protocol the IP),local used and remote for the connection protocol protocol port (TCP, port of the(0~65535),UDP), remote the the process.local IP addresshost The IP communication ofaddress the remote (server host model intr (client isanet shown extranetIP), inthe Figure IP),local and9 .remote the protocol protocol port port of the(0~65535), remote theprocess. IP address The communicati of the remoteon hostmodel (client is shown extranet in Figure IP), and 9. the protocol port of the remote process. The communication model is shown in Figure 9. Appl. Sci. 2021, 11, 6399 11 of 17 Appl.Appl. Sci. Sci. 20212021, 11, 11, 6399, 6399 1111 of of 17 17

FigureFigure 9. 9.9. Socket Socket communication communication model. model.model. 4.1.2. Data Transmission Test 4.1.2.4.1.2. Data Data Transmission Transmission Test Test For the data transmission test, the cloud server was connected through the remote ForFor the the data data transmission transmission test, test, the the cloud cloud server server was was connected connected through through the the remote remote desktop of the local computer, and the communication was carried out between the upper desktopdesktop of of the the local local computer, computer, and and the the commu communicationnication was was carried carried out out between between the the upper upper computer program and the cloud server. After the connection was successfully established, computercomputer program program and and the the cloud cloud server. server. Af Afterter the the connection connection wa was ssuccessfully successfully estab- estab- the upper computer would receive a prompt from the cloud server and then send the lished, the upper computer would receive a prompt from the cloud server and then send lished,vehicle the speed upper data, computer and at the would same receive time, the a pr dataompt received from the by cloud the server server was and observed, then send as the vehicle speed data, and at the same time, the data received by the server was observed, theshown vehicle in Figurespeed data,10. The and test at the results same show time, that the the data communication received by the status server is was good. observed, asas shown shown in in Figure Figure 10. 10. The The test test results results sh showow that that the the communication communication status status is is good. good.

(a(a) ) (b(b) )

FigureFigure 10. 10. Data DataData transfer transfer transfer test: test: test: ( a(a) ()Client:a Client:) Client: interface interface interface for for sending for sending sending data data data from from from the the upper theupper upper computer. computer. computer. ( b(b) ) Server:(Server:b) Server: receiving receiving receiving real-time real-time real-time data. data. data.

4.1.3.4.1.3. Experimental Experimental Design Design InInIn order orderorder to toto verify verify verify the the accuracyaccuracy accuracy ofof of thethe the DT DT DT model model model and and and the the the real-time, real-time, real-time, stability stability stability and and and parallel par- par- alleloperationallel operation operation capability capability capability of theof of the the DT, DT, DT, the the the solar solar solar car car car energy energy energy consumption consumption consumption asas as wellwell well as as the the solar solarsolar panelpanelpanel power powerpower supply supplysupply were werewere tested. tested. tested. The The real real solar solarsolar car carcar and andand the thethe DT DTDT have havehave the thethe same samesame operating operatingoperating conditions,conditions,conditions, and andand the thethe model model model parameters parameters areare are updatedupdated updated byby by sensors sensors sensors to to to finally finally finally obtain obtain obtain the the the results results results of oftheof the the real real real solar solar solar car car car operation operation operation and and and the the the simulation simulati simulation resultson results results of theof of the DT.the DT. TheDT. The The specific specific specific test test equipmenttest equip- equip- mentisment shown is is shown shown in Table in in 3Table Tablebelow, 3 3 below, andbelow, the and and physical the the physical physical test platform test test platform platform built is shownbuilt built is is inshown shown Figure in in11 Figure Figure. 11.11. Table 3. Specifications of test equipment.

Category Type Range Accuracy Voltage Sensor KSD-4U 0–150 V ±0.1% Current Sensor KXK-36 0–50 A ±0.1% Light Intensity Sensor RS-GZ-V05-2 0-65535 Lux ±7%(25 ◦C) Temperature Sensor Pt100 −50–200 °C ±0.35 ◦C Tire Pressure Sensor YB-68 0–5.0 Bar ±0.1Bar Anemometer PM6252B 0.40–30.0 m/s ±0.01 m/s Data Acquisition USB-2000 ±5 V ±0.9 mV Board GPS Sensor WTGAHRS1 - <2 m Accelerometer WTGAHRS1 ±8 g ±0.01 g Appl. Sci. 2021, 11, 6399 1212 of of 17

Figure 11. PhysicalPhysical test test platform.

TableIn 3. orderSpecifications to ensure of test the equipment. smooth conducting of the test, the test site is required to be in good road condition, capable of being driven on for a long time, and to not affect the normal vehicleCategory driving; hence, the 400 m standardType athletic track onRange campus wasAccuracy chosen as the test site.Voltage The Sensor test was conducted at 40 KSD-4U km/h cruising speed, 0–150 with V a cruising ±0.1% time of 30 min. TheCurrent conditions Sensor on the test day are shown KXK-36 in Table4, and the 0–50 formula A for calculating ±0.1% energyLight consumption Intensity Sensor is shown in Equation RS-GZ-V05-2 (15): 0-65535 Lux ±7%(25 °C) Temperature Sensor Pt100 −50–200 ℃ ±0.35 °C Tire Pressure Sensor Z t YB-68Z t 0-5.0 Bar ±0.1Bar Anemometer W = P · dtPM6252B= (U · I) · dt 0.40–30.0 m/s ±0.01m/s(15) 0 0 Data Acquisition Board USB-2000 ±5 V ±0.9mV where W denotesGPS Sensor the energy consumed inWTGAHRS1 t time in kWh; P denotes - the solar car <2m output power in W;AccelerometerU denotes the bus voltage inWTGAHRS1 V; I denotes the bus current±8g in A; t denotes±0.01g the time in hours. In order to ensure the smooth conducting of the test, the test site is required to be in goodTable road 4. Experimental condition, conditions. capable of being driven on for a long time, and to not affect the normal vehicle driving; hence, the 400 m standard athletic track on campus was chosen as the test site. The test wasCategory conducted at 40 km/h cruising speed, with a Data cruising time of 30 min. The conditions onTemperature the test day are shown in Table 4, and the formula 22 ◦ forC calculating energy consumption is shownWind Speed in Equation (15): <0.5 m/s Light Intensity 9500–100,000 Lux Road Plastic Runway (15) Road Slope <1 Total Load 600 kg where W denotesCruising the energy Speed consumed in t time in kWh; P denotes 40 km/h the solar car output power in W; U denotes the bus voltage in V; I denotes the bus current in A; t denotes the time in hours. 4.2. Experimental Results and Analysis TableAccording 4. Experimental to the conditions. test, the energy consumption of the solar car was 1.063 kWh, and the solar panel charged 0.325 kWh. The test result is shown in Figure 12a. Simulation under the same workingCategory conditions was conducted. The solar car energyData consumption was 1.008 kWh, and theTemperature solar panel charged 0.323 kWh, as shown in Figure22 °C 12b. Wind Speed <0.5 m/s Light Intensity 9500–100,000 Lux Road Plastic Runway Road Slope <1 Total Load 600 kg Cruising Speed 40 km/h Appl. Sci. 2021, 11, 6399 13 of 17

Appl. Sci. 2021, 11, 6399 13 of 17

4.2. Experimental Results and Analysis 4.2. ExperimentalAccording to Results the test, and the Analysis energy consumption of the solar car was 1.063 kwh, and the solarAccording panel charged to the test, 0.325 the kwh. energy The consumptiontest result is shown of the insolar Figure car was12a. 1.063Simulation kwh, andun- der the same working conditions was conducted. The solar car energy consumption was Appl. Sci. 2021, 11, 6399 the solar panel charged 0.325 kwh. The test result is shown in Figure 12a. Simulation13 of un- 17 1.008der the kwh, same and working the solar conditions panel charged was conducted. 0.323 kwh, Theas shown solar carin Figure energy 12b. consumption was 1.008 kwh, and the solar panel charged 0.323 kwh, as shown in Figure 12b.

(a) (b) Figure 12. Comparison (a of) test-simulation results: (a ) Graph (b of) test results; (b) Graph of simulation results. FigureFigure 12. 12.Comparison Comparison of of test-simulation test-simulation results: results: (a) Graph (a) Graph of test of results; test results; (b) Graph (b) ofGraph simulation of simulation results. results. FromFrom thethe testtest resultsresults andand simulationsimulation results,results, thethe energyenergy consumptionconsumption ofof thethe actualactual solarsolar carFromcar waswas the 1.0631.063 testkWh resultskwh andand and thethe simulation simulatedsimulated resu solarsolalts,r carcar the waswas energy 1.0081.008 consumption kWh,kwh, withwith aa difference differenceof the actual ofof 0.0550.055solar kWhkwhcar was and 1.063 an errorerror kwh ofof and 5.17%;5.17%; the thesimulatedthe actualactual solarsolasolarr panelcarpanel was chargingcharging 1.008 kwh, waswas 0.325with0.325 a kWh kwhdifference andand thethe of simulatedsimulated0.055 kwh solarand an panel error charging of 5.17%; was was the 0.323 0.323 actual kwh, kWh, solar with with panel a adifference differencecharging of was of 0.002 0.002 0.325 and and kwh an an errorand error the of of6.15%.simulated 6.15%. solar panel charging was 0.323 kwh, with a difference of 0.002 and an error of 6.15%.However,However, at at thethe samesame time,time, wewe observedobserved thatthat thethe actualactual solarsolar carcar energyenergy consumptionconsumption curvecurveHowever, ﬂuctuatesfluctuates muchat much the same more more time, than than thewe the simulationobserved simulati onthat curve, curve, the andactual and ideally, ideally,solar thecar the energyenergy energy consumption consumption consump- curvetioncurve curve obtained fluctuates obtained by much cruising by more cruising at than 40km/h at the 40 simulati shouldkm/h shouldon be curve, a straight be anda straight line, ideally, so line, we the conducted soenergy we conducted consump- further investigation.furthertion curve investigation. obtained The results byThe cruising ofresults simulated ofat simulate40 vehiclekm/hd should speedvehicle andbe speed a actual straight and vehicle actual line, speedvehicleso we are conductedspeed shown are inshownfurther Figure ininvestigation. 13 Figure, the test 13, resultsthe The test results of results solar of simulate panelof solar outputd panel vehicle current output speed and current and bus actual current and vehicle bus are current shown speed areare in Figureshownshown 14 inin, Figure andFigure the 14, 13, simulation and the the test simulation results of result solarsolars panelpanelof solar outputoutput panel current currentoutput andcurrentand busbus and currentcurrent bus cur- are are shownrentshown are in in shown Figure Figure in 15 14, Figure. and the15. simulation results of solar panel output current and bus current are shown in Figure 15.

FigureFigure 13.13. SimulatedSimulated vehiclevehicle speedspeed andand actualactual vehiclevehicle speedspeed resultresult graph.graph. Figure 13. Simulated vehicle speed and actual vehicle speed result graph. Appl. Sci. 2021, 11, 6399 14 of 17 Appl. Sci. 20212021,, 1111,, 63996399 1414 ofof 1717

FigureFigure 14.14. SolarSolar panelpanel outputoutput currentcurrent andand busbus currentcurrent testtest results.results.

FigureFigure 15.15. SolarSolar panelpanel outputoutput currentcurrent andand busbuss currentcurrentcurrent simulation simulationsimulation results. results.results.

FromFrom FigureFigure 1313,, itit cancan bebe seenseen thatthat bothboth thethethe simulatedsimulatedsimulated speedspeedspeed andandand thethethe actualactualactual speedspeedspeed fluctuatedfluctuatedfluctuated aboveabove and and belowbelow 4040 km/hkm/h km/h afterafter after stabilization,stabilization, stabilization, andand and thethe the degreedegree degree ofof of fluctuationfluctuation fluctuation ofof ofthethe the simulationsimulation simulation resultsresults results waswas was significantlysignificantly significantly smallersmaller smaller thanthan than thatthat that ofof thethe of the actualactual actual speed.speed. speed. DuringDuring During thethe theacceleration acceleration process, process, both both of them of them reached reached thethe expectedexpected the expected speedspeed speed withinwithin within aa shortshort a time;time; short mean-mean- time; meanwhile,while, the actual the actual and simulated and simulated bus currents bus currents were were accompanied accompanied by a large by a large pulse, pulse, and after and afterthethe speedspeed the speed stabilization,stabilization, stabilization, thethe busbus the currentcurrent bus current vavaluelue value droppeddropped dropped backbackback toto thethe to normalnormal the normal level.level. level. AsAs seenseen inin FiguresFigures 1414 andand 1515,, therethere waswas aa periodicperiodic downwarddownward pulsepulse inin thethe solarsolar panelpanel outputoutput currentcurrent value,value, andand thethe currentcurrent valuevalue waswass stablestablestable forforfor thethethe restrestrest of ofof the thethemoments. moments.moments. ByByBy observingobserving thethe test test site site we we found found that that at at one one of of the the curves curves of of the the athletic athletic track, track, there there would would be shadebe shade trees, trees, so when so when the solarthe solar car passedcar passed quickly, quickly, there there would would be a substantialbe aa substantialsubstantial weakening weak-weak- ofening the lightof the intensity, light intensity, and the and light the sensor light sensedsensor thesensed change the change and transmitted and transmitted it to the it DT to modelthethe DTDTat modelmodel the same atat thethe time, samesame thus time,time, causing thusthus causingcausing a short sharp a short drop sharp in thedrop solar in the panel solar output panel current, output andcurrent, after and passing after thepassing shade the trees, shade it would trees, it quickly wouldwould return quicklyquickly to returnreturn normal toto level. normalnormal level.level. TheThe actual bus bus current current value value oscillated oscillated violently violently in in the the process, process, on onthe the one one hand, hand, be- because the solar panel output current dropped at the shade. As known from Section 3.1, cause the solar panel output current dropped at the shade. As known from Section 3.1, the solar car’s direct drive current came from the solar panel and battery, so in order to thethe solarsolar car’scar’s directdirect drivedrive currentcurrent camecame fromfrom thethe solarsolar panelpanel andand battery,battery, soso inin orderorder toto maintain the current speed, the bus current increased to compensate. On the other hand, maintain the current speed, the bus current increasedincreased toto compensate.compensate. OnOn thethe otherother hand,hand, because there are more curves on the athletic track, the motor power demand became because there are more curves on the athletic track, the motor power demand became larger at the curves, so the bus current value also increased. The bus current value of largerlarger atat thethe curves,curves, soso thethe busbus currentcurrent valuevalue also increased. The bus current value of the the simulation was more stable, because in the simulation process, the curve was not simulationsimulation waswas moremore stable,stable, becausebecause inin thethe sisimulation process, the curve was not consid- considered as a factor, and the DT model was simulated according to the linear motion, ered as a factor, and the DT model was simulated according to the linear motion, so its so its change was mainly influenced by the output current of the external solar panel. It change was mainly influenced by the output current of the external solar panel. It can also can also be seen from Figure 15 that the bus current value would change with the output be seen from Figure 15 that the bus currentt valuevalue wouldwould changechange withwith thethe outputoutput currentcurrent current of the solar panel in order to maintain the current speed. of the solar panel in order to maintain the current speed. Appl. Sci. 2021, 11, 6399 15 of 17

5. Conclusions In this study, a DT system of solar car is designed and established based on a hybrid modeling approach. Considering that the complex process objects with partial mechanism knowledge are hard to acquire, a data-driven modeling approach based on SVM is used, while the different features of CarSim and Simulink are fully utilized for joint simulation, which ensures the accuracy of the model on the premise of enhancing the modelling efficiency. Meanwhile, two-way communication between physical and virtual entities based on TCP is realized, which allows the real-time data transfer and parallel operation between the DT model and the real vehicle. In addition, the energy consumption of this model is verified through the real-world vehicle experiment. The error of the energy consumption data is 5.17%, which shows that the DT model has good accuracy and can reflect the current actual vehicle energy consumption, and achieves the expected effect. The present DT system of solar car basically satisfies important characteristics that DT technology has, such as representativeness, reflection, entanglement, servitization, composability, and memoriza- tion [20], and can be considered as a primary stage DT system. In addition, limited by the current experimental site, some of the energy consumption characteristics of the solar car cannot be shown, and further work will consist of finding a more professional experimental site in which to analyze its energy consumption characteristics more comprehensively, and to optimize the support vector machine algorithm in detail.

Author Contributions: Conceptualization, L.B. and Y.Z.; methodology, L.B. and H.W.; software, J.D.; validation, L.B.; formal analysis, W.T.; investigation, Y.Z.; resources, L.B.; data curation, W.T.; writing— original draft preparation, L.B.; writing—review and editing, L.B., Y.Z. and H.W.; visualization, L.B.; supervision, Y.Z. and H.W.; project administration, L.B.; funding acquisition, Y.Z. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Not applicable. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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