Development of a Power Flow Management Strategy for a Hybrid Racing Car Aimed at Minimizing Lap Time

Abstract

Hybrid systems have recently become widespread in motorsports due to advantages such as increased power through the use of electric motors and reduced fuel consumption thanks to regenerative braking. Achieving high performance from a hybrid powertrain requires a highly efficient control system for managing power flows between the internal combustion engine (ICE) and the electric motor. The goal of this study is to develop a control algorithm for a hybrid powertrain aimed at minimizing lap times compared to traditional vehicles equipped with an ICE. To achieve this objective, a mathematical vehicle model based on the tractive balance equation was used. Lap time simulations were conducted for both a traditional ICE vehicle and a hybrid system. The results showed that the hybrid vehicle has a significant advantage in lap time; however, the energy from a fully charged battery would only be sufficient for two laps. To address this issue, a hybrid system control algorithm is proposed, which maintains the energy balance of the battery throughout the entire lap while still providing better lap times compared to a vehicle equipped with a traditional ICE.

1. Introduction

The idea of using hybrid technologies in motorsport is not new. As early as the late 20th century, there were attempts to introduce electric motors to improve the performance of racing cars. However, the first significant steps in this direction were made in the early 2000s. The Lexus GS 450 h became one of the first examples of a hybrid racing vehicle [1]. It participated in the 24 h of Tokachi race and was equipped with a parallel hybrid system. This car finished 17th out of 33 vehicles, which was quite a good result for a new technology. The most significant event was the introduction of the Kinetic Energy Recovery System (KERS) in Formula 1 in 2009 [2]. This system allowed energy generated during braking to be stored and temporarily used to increase power output. This became the first major step toward hybridization in modern motorsport. For example, the KERS in top-tier racing categories can harvest up to 0.56 kWh of energy per lap and provide an additional 118 kW boost for approximately 17 s, directly translating to faster lap times [3]. This quantified performance enhancement demonstrates that hybrid technology is no longer an option but a necessity for maintaining competitiveness.

Hybrid systems have several key advantages, including increased power thanks to electric motors, fuel savings through regenerative braking, strategic opportunities for effective power management in critical moments, and reduced emissions that comply with current environmental standards. The aim of this work is to develop a hybrid powertrain control algorithm to achieve the minimum lap time compared to traditional vehicles equipped with an internal combustion engine (ICE). Although numerous studies on hybrid systems have optimized energy management for fuel efficiency and comfort in mass-produced city cars [4,5,6,7], research focusing on the distinct objective of lap time minimization for racing applications is limited. The article [8] investigated the possibility of reducing lap time by changing gear ratios in the hybrid power module transmission. Despite the proven impact of this factor on performance, the proposed approach does not include an algorithm for effective control of the electric motor and ICE operation, which is key to maintaining energy balance over a long distance. The results of work [9] demonstrate the influence of individual parameters of a hybrid vehicle on lap time; however, the proposed method did not lead to achieving its minimum value. While the authors of [10] offer a detailed classification of artificial intelligence architectures and methods applied to hybrid powertrain civil vehicles, their review does not cover the area of racing applications, where the objective functions and operating conditions are fundamentally different. In [11], a framework for automatically retraining the control strategy of a hybrid electric vehicle’s powertrain using supervised machine learning was developed. Their adaptive approach uses real-time driving data to optimize fuel efficiency. However, this methodology is not intended for motorsports, where the goal shifts from efficiency to minimizing lap times under extreme operating conditions. The works of Salazar et al. [12,13,14] propose complex algorithms based on Model Predictive Control (MPC) for optimizing the Formula 1 hybrid system, focusing on global energy allocation and real-time adaptation. However, their methods are computationally intensive and are focused on the specific architecture of F1. Ref. [15] employed dynamic programming to optimize the energy management of a series hybrid electric race car, focusing on lap time minimization through optimal power allocation between the engine-generator and electric motor. While this approach provides a theoretical performance benchmark for racing hybrid vehicles, its computational complexity limits real-time application, highlighting a gap for practical control strategies. Recent studies of transport system energy efficiency [16,17] show that current trends are shifting toward adaptive control strategies that combine multi-objective energy flow optimization, taking into account component degradation and real-world operating conditions. In particular, studies [16,17] demonstrate the effectiveness of predictive control in increasing powertrain efficiency while preserving battery life. The literature review revealed that existing studies of hybrid systems either focus on the fuel efficiency of road cars or propose complex theoretical methods (MPC, dynamic programming) that are not applicable to real racing conditions. In contrast, the present study proposes a practical control algorithm for a parallel hybrid transmission that minimizes lap time while maintaining energy balance over the entire distance. The key advantage of the approach is computational efficiency and adaptability to real racing conditions.

In this work, the structure of the developed hybrid racing vehicle with a parallel configuration is presented. The approach to mathematical modeling based on the tractive balance equation of vehicle motion is described. Using the mathematical model, the lap time results of a car with a traditional ICE and a hybrid car using an electric motor and a battery are compared. The results showed that the car with the hybrid system has a significant advantage in lap time; however, there is a problem of complete battery discharge after the second lap of the race. To solve this problem, a hybrid system control algorithm is proposed, which allows maintaining the energy balance of the battery throughout the entire lap, while providing better lap times compared to a car equipped with a traditional ICE.

2. The Object of Research

The object of the study is the FDR 12 sports racing vehicle. The goal of the FDR Moscow racing team of the Moscow Polytechnic University (MPU) was to create a racing prototype with a hybrid powertrain that could compete with cars built on traditional ICE architecture. The prototype belongs to the CN group—special racing cars based on a space frame or monocoque, to which the suspension and powertrain components are attached. The car is primarily intended for participation in the REC (Russian Endurance Challenge) racing series. The FDR 12 racing prototype was announced in May 2025 (Figure 1).

3. Review and Selection of the Hybrid Layout Type

There are three main types of hybrid layouts: parallel, series, and series-parallel (Figure 2) [18]. In parallel layouts, ICE and the electric motor can deliver power to the wheels either separately or simultaneously through the transmission (Figure 2a). This layout, for example, is used in the Porsche 919 Hybrid (LMP1) and Toyota GR010 Hybrid (LMH) racing cars [19,20]. The key advantages of the parallel layout are its structural simplicity, which requires the integration of an electric motor, inverter, and battery, as well as minimal weight compared to other types of hybrid systems. Racing cars with a series hybrid system are rare. In such a system, the ICE functions exclusively as a generator, producing electricity for the electric motor, which directly drives the wheels (Figure 2b). This type of hybrid system is often used in passenger cars, where its advantages are fuel savings and low emission levels. Series layouts have gained popularity in the premium segment of Chinese automakers, such as the Aito M9, Avatr 07, Li L9, Yangwang U8, and others [21]. The series-parallel hybrid (also known as “mixed” or “combined”) is a type of hybrid powertrain that combines the advantages of both series and parallel systems (Figure 2c). This layout allows the ICE and electric motor to be used together or separately, as well as to switch operating modes depending on driving conditions. This layout is the most complex and, like the series system, has not become widespread in motorsport. The pioneer in the use of the mixed layout is Toyota with its Prius model. The mixed hybrid layout has also become common among Chinese manufacturers, for example, in models such as the Geely Xingyue L Hi-P, BYD Han L, Denza N9, and others.

Analysis of various hybrid system configurations demonstrates that the parallel layout has become the most widespread. This is due to its structural simplicity, which, in turn, ensures the minimum weight of the power unit. In modern Formula 1 racing cars, a parallel hybrid layout is used, known as KERS. Currently, this system is designated as the Motor Generator Unit—Kinetic (MGU-K). This system is a motor-generator connected to the crankshaft of the ICE. Its operating principle is based on the recuperation of kinetic energy during braking, which is then converted into electrical energy and directed to recharge the battery. The resulting electrical energy can be used for a short-term increase in the power of the power unit during acceleration. As a rule, this mode is used for tactical purposes to perform overtaking maneuvers. A detailed diagram of the MGU-K operation is shown in Figure 3 [22].

In modern circuit racing conditions, this hybrid configuration demonstrates a high level of efficiency, which determined its selection as the basic platform for the development of the FDR 12 prototype. The presented layout is shown in Figure 4. The key component of the system is the ICE, which serves as the main source of torque transmitted to the rear axle via the transmission. An electric motor is integrated into the crankshaft of the ICE, and its operation is controlled by an inverter. The inverter, in turn, converts the direct current voltage of the battery into alternating current to control the electric motor in traction mode.

4. Mathematical Description of the Model

4.1. Mathematical Description of Vehicle Movement

To simplify the calculations, a straight-line motion model was chosen. The use of a straight-line motion model is justified for the primary goal of this study: the initial development and benchmarking of a power flow management algorithm. This approach allows us to isolate and analyze the core challenge of balancing energy recovery and deployment to minimize lap time, without the added complexity of lateral dynamics. The model effectively captures the high-energy events (heavy acceleration and braking) that dominate energy consumption on a lap, making it a valid tool for this specific development phase.

The graphical interpretation of the force diagram acting on the vehicle during motion is shown in Figure 5. The following assumptions are made in the diagram: road conditions are identical for all wheels, so the rolling resistance forces for all wheels are the same; losses associated with the suspension are not taken into account; forces directed perpendicular to the movement of the vehicle are not considered. The following forces are shown in the calculation diagram: $F_T$—circumferential force on the driving wheels (tractive force); $F_{\psi }$—road resistance force (the sum of rolling resistance and resistance forces when moving uphill); $F_A$—air resistance force; $F_d$—resistance force to the acceleration of rotating and translational masses.

The motion of a vehicle is characterized by the tractive balance equation [23]:

$$F_T=F_{\psi }+F_A+F_d.$$

(1)

The tractive force $F_T$ on the wheel is determined by the formula:

$$F_T={\displaystyle \frac{M_m\times u_{tr}}{r_d\times {\eta }_{tr}}},$$

(2)

where $u_{tr}$—overall transmission gear ratio; ${\eta }_{tr}$—transmission efficiency; $r_d$—dynamic rolling radius of the wheel, m; $M_m$—traction motor torque, N × m.

The road resistance force $F_{\psi }$ is calculated as follows:

$$F_{\psi }=G_a\left(fcos\alpha \left(1+A_f{v}^2\right)+sin\alpha \right),$$

(3)

where $G_a$—vehicle weight, N; $f$—rolling resistance coefficient; $\alpha$—road gradient; $A_f$—speed influence coefficient on rolling resistance, s²/m² [24]; $v$—vehicle speed, m/s.

The air resistance force $F_A$ is equal to:

$$F_A=C_x\rho {\displaystyle \frac{v^2}{2}}A,$$

(4)

where $C_x$—drag coefficient (aerodynamic coefficient); $\rho$—air density, kg/m³; $A$—frontal area, m².

The resistance force to the acceleration of translational and rotational masses $F_d$ is determined by the formula:

$$F_d=\delta M_{a}a,$$

(5)

where $\delta$—coefficient accounting for rotating masses; $M_a$—vehicle mass, kg; $a$—vehicle acceleration in the direction of motion, m/s².

To determine the coefficient accounting for rotating masses $\delta$ it is necessary to determine the moments of inertia of all rotating components:

$$\delta =1+ {\displaystyle \frac{I_{rot}{i}_{ratio}\eta +I_{tr}+I_{wh}{n}_{wh}}{M_a{r}_k^2}},$$

(6)

where $I_{rot}$—moment of inertia of the electric motor rotor, kg∙m²; $i_{ratio}$—transmission gear ratio from the motor rotor to the wheel; $\eta$—transmission efficiency; $I_{tr}$—moment of inertia of the transmission, kg∙m²; $I_{wh}$—moment of inertia of the wheel, kg∙m²; $n_{wh}$—number of wheels; $M_a$—vehicle mass, kg; $r_k$—rolling radius without slip, m.

To determine the energy consumption for the movement of the electric vehicle, it is necessary to determine the electric power of the electric motor. The electric power of the electric vehicle’s motor is determined as follows:

$$N_{эл}={\displaystyle \frac{M_{em}\times {\omega }_{em}}{{\eta }_{inv}\times {\eta }_{em}}},$$

(7)

where $M_{em}$—electric motor torque, N·m; ${\omega }_{em}$—electric motor rotor speed, rad/s; ${\eta }_{inv}$—inverter efficiency; ${\eta }_{em}$—electric motor efficiency.

As initial data for the calculation, the characteristics of the vehicle are used, as well as the speed profile according to which the vehicle must move.

4.2. Battery Simulation: The R-Model

The simplest option for modeling a battery cell is an equivalent circuit that includes a constant voltage source $U_{OCV}$ and the internal resistance of the cell $R_{DCIR}$ connected in series, closed on a load (Figure 6). Under load, the dynamic voltage decreases, and during charging, it increases. This circuit is used in cases where high accuracy is not required and the initial data on the batteries are minimal. The open-circuit voltage characteristics $U_{OCV}$ and the cell resistance $R_{DCIR}$ are usually provided by the battery manufacturer. Another advantage of this model is the minimal requirements for the computing resources of a PC [25]. This model is usually complicated to improve accuracy depending on influencing factors such as temperature and SOC. This equivalent circuit is characterized by the voltage drop equation under load $U_{Dyn}$:

$$U_{Dyn}=U_{OCV}-{IR}_{DCIR},$$

(8)

where $U_{OCV}$—open-circuit voltage depending on SOC and temperature, V; $I$—discharge or charge current, A; $R_{DCIR}$—internal resistance of the cell depending on SOC and temperature, Ohm.

4.3. Thermal Model of an Energy Storage Device

The thermal model of energy storage is based on the energy balance of the system. In Figure 7, a schematic representation of the thermal impact model on the battery pack located inside a pack is shown. The battery pack is affected by: internal heating as a result of charging or discharging, heat conduction through the multilayer wall of the pack, external convective and radiative heat exchange with the environment, and the power of thermal management through a heat-dissipating plate [26].

To determine the thermal state of the battery, the thermal balance equation is used [27]:

$$N_{Bat}=N_{Amb}+N_{Heat}+N_{TMS},$$

(9)

where $N_{Bat}$—power affecting the heat capacity of the battery pack, W; $N_{Amb}$—impact of the environment, W; $N_{Heat}$—thermal power generated by charging or discharging the energy storage, W; $N_{TMS}$—thermal power of the thermal management system through the heat-dissipating plate, W.

The thermal performance of a single battery during charging and discharging is determined by the following formula:

$$N_{Heat}=I^2{R}_{DCIR}.$$

(10)

5. Initial Data for the Calculation

The main technical specifications of the FDR12 racing car are presented in

Table 1. Technical characteristics of the FDR12 racing car.

No	Parameter	Value
1	Curb weight, kg	730
2	Gross weight, kg	810
4	Aerodynamic drag coefficient	0.512
6	Height, m	1.047
7	Width, m	1.955
8	Final drive ratio	3.333
9	Transmission	Automatic
10	Number of gears	6
11	Front tires	20/54–13
12	Rear tires	24/57–13

.

The main traction drive is the internal combustion engine, consisting of a VAZ 21126 cylinder block from the manufacturer of serial cars LADA. This engine is equipped with a turbocharger, which allows you to achieve a power of 280 hp (205.94 kW). The graph (Figure 8) shows the torque characteristic obtained on the test bench in the laboratory.

The auxiliary unit of the hybrid system of the car is an electric motor from the manufacturer EMRAX model 188MV LC. The motor has a peak power of 60 kW and a continuous power of 37 kW. The torque and power characteristic is provided by the manufacturer and is shown in Figure 9 [28].

The electric motor in traction mode is powered by a battery. The battery uses high-power cells with a chemical structure LTO from the manufacturer Toshiba model 2.9Ah SCiB™ (Kanagawa, Japan). The OCV and DCIR characteristics were obtained during laboratory tests (Figure 10 and Figure 11).

For the simulation, the Moscow Raceway circuit was chosen, as a series of REC racing sessions are held on this track. The configuration used is GP9, with a length of 3931 m in Figure 12. The duration of a regular REC championship racing session is 4 h, during which the cars complete more than 150 laps.

Since a simplified straight-line mathematical model was used, the driving cycle obtained using the simulator (Figure 13) was taken as the basis. The best lap time in the simulator was 88.4 s.

To account for the maximum speed when cornering, the segments of the cycle involving braking to the boundary speed in the turn were preserved, while the remaining acceleration segments of the cycle were increased by 20% to enable the highest possible acceleration dynamics during the simulation.

6. Simulation Results

Based on the equations given in Section 4, a mathematical model of vehicle motion was developed in the Matlab/Simulink R2023a software package. Fixed-step with a step size of 0.01 s was used for the simulation. The solver type was set to “auto” (Automatic solver selection), which allows the Simulink environment to independently select the most suitable fixed-step solver for a given model configuration. The initial data for calculations were used from Section 5. Based on this mathematical model, the following results were obtained.

6.1. Simulation of the Movement of a Car with a Traditional ICE

It is crucial to note that the objective function of the proposed energy management strategy is the minimization of lap time. This is in direct contrast to energy management strategy for road vehicles, which often aim to minimize fuel consumption. Therefore, all control decisions are optimized for maximum vehicle performance and speed output.

At the first stage, calculations of the lap time were carried out for a car with a traditional ICE, which will later allow for a comparison of the obtained results with the performance indicators of the hybrid version of the racing car. The engine power of the ICE racing car is 280 hp; however, due to the absence of a motor-generator, inverter, battery, and cooling system, the total mass of this car is lighter, amounting to 746 kg including the driver. The best lap time according to the simulation results was 88.14 s.

6.2. Simulation of the Movement of a Hybrid Car with Braking Recovery

In this calculation case, the simulation of the hybrid racing car’s movement was carried out in the mode of additional power provided by the electric motor during acceleration. The electric motor was engaged when the speed exceeded 120 km/h to prevent wheel slip at low speeds due to excessive torque. An energy recuperation system was also implemented during braking before corners. The simulation results are presented in Figure 14. Based on the simulation results, the best lap time was 86.16 s, which is 2.02 s faster than the racing car with an ICE. This difference is significant for a single lap. The top graph in Figure 14 shows the speed of the car, with the first lap being a warm-up lap for heating the tires and reaching maximum speed before starting the second “flying lap”. The second graph displays the power outputs of the ICE and the electric motor, shown in red and green, respectively. The electric motor’s power at the beginning of the first lap was a maximum of 60 kW, but during the movement the power drops and by the beginning of the third lap it dropped to 25 kW (indicated by the green line), which is due to the voltage drop and the current limitation of the battery by the third lap. This is explained by the fact that the electric motor’s consumption during acceleration exceeds the energy recovered during braking, resulting in the battery gradually discharging. The third graph in Figure 14 shows that the battery’s state of charge (SOC) drops throughout the run from 100% to 5%, indicating that in subsequent laps, the car will run solely on ICE power. Using only ICE power, given the increased mass of the hybrid system, leads to worse performance in the following laps. Since the car is intended for endurance races, where the number of laps can exceed 150, using this algorithm may negatively affect the final results. Therefore, it is necessary to modify the algorithm so that the SOC level remains stable throughout the entire race. The final graph shows the battery temperature dynamics. Data analysis shows that at the start of the run, the temperature was +25 °C, and by the start of the third lap, three minutes later, it had reached +37 °C. This temperature increase was due to the excessively high average current during the calculation cycle. Despite this, the achieved temperature of +37 °C remains within the acceptable operating range for this type of battery cell, the upper limit of which is +50 °C.

6.3. ICE Energy Analysis

Based on the conducted energy analysis, it was established that the amount of energy during battery discharge is 1.2 kWh (for the entire driving section), while the energy accumulated during regenerative braking is 0.527 kWh. It should be noted that the charged energy is 56% of the discharged energy. To ensure stable operation of the battery system throughout the entire race, it is necessary to equalize the amounts of charged and discharged energy. At the same time, the energy obtained from recuperation during braking is not sufficient, and therefore it is necessary to identify areas of movement in which additional energy can be obtained from the ICE. One of the key advantages of using electric motors in hybrid systems is the ability to dynamically manage the process of electricity generation with the possibility of additional load on the ICE. For the effective use of the unrealized potential of the ICE to recharge the battery, it is necessary to identify operating modes in which the engine does not operate at full power. The unused power of the ICE, $P_{Unus}$ can be calculated by the formula:

$$P_{Unus}=P_{MaxICE}-P_{UsedICE}$$

(11)

where $P_{MaxICE}$—maximum power of the ICE, W; $P_{UsedICE}$—actual power used by the ICE, W.

Figure 15 shows the results of the simulation modeling of the second lap obtained from previous calculations. The top graph displays the vehicle speed dynamics, while the second graph presents the ICE power characteristics. The maximum ICE power is indicated in red, and the actual power used is shown in blue. Analysis of the graphs reveals specific load patterns of the ICE throughout the racing lap. It was found that the ICE does not operate at full power in two characteristic modes:

-

Immediately after braking. This is due to the fact that when exiting a corner, the driver intentionally limits power delivery to prevent possible skidding of the car;

-

When driving at maximum speed and the ICE also does not operate at full power.

In these conditions, the excess power of the ICE can be effectively used to recharge the battery.

The third graph shows the difference between the maximum available and the actually used power of the ICE, which is limited by the capabilities of the electric generator. The total energy obtained during the generator’s operation is 0.184 kWh.

The energy analysis showed that the combined power generated through energy recuperation and the use of the available power of the ICE is insufficient to ensure equivalence of energy expenditure during battery discharge. In this regard, it becomes necessary to change the control algorithm of the electric motor by reducing the discharge power of the battery system. To reduce the discharge power, it is necessary to increase the threshold for engaging electric motor assistance during acceleration. This approach will purposefully reduce the intensity of battery discharge while maintaining the overall efficiency of the power unit.

6.4. Simulation of the Movement of a Hybrid Car with the Proposed Algorithm for Using ICE Power

To reduce the battery discharge, it is necessary to turn on the electric motor less often. In the previous calculations, the electric motor connection speed was 120 km/h, while the battery energy was enough only to complete the first two laps, in subsequent laps the car moved with a discharged battery and the worst lap time. To avoid battery discharge, it is necessary to increase the setting for the speed of turning on the electric motor to assist the ICE, but at the same time the lap time should not be worse than a car with a traditional ICE. Figure 16 shows a graph of a series of iterative calculations to determine the speed at which the electric motor must be turned on. Since the initial SOC at the start is 50%, at the end of the 3rd lap, the SOC should not fall below 50% in order to maintain the energy balance throughout the race. From the graph it is clear that at a speed of 172 km/h, the SOC is maintained at 51.11%, this means that the energy balance will be maintained throughout the race.

The proposed generator control scheme is shown in Figure 17. If the speed of the car is in the range from 172 to 240 km/h and the throttle pedal is pressed to 100%, the electric motor operates at maximum power in traction mode, assisting the ICE in accelerating the vehicle. During braking, the electric motor switches to generator mode with energy recuperation, which ensures the charging of the battery system. In cases where the accelerator pedal is not at the maximum fuel supply position or when the maximum speed is reached, the electric motor can utilize the unused power of the ICE, converting it into electrical energy and subsequently storing it in the battery.

Figure 18 presents the simulation results of the racing car’s performance with the proposed electric motor control algorithm. The top graph demonstrates the dynamics of the vehicle’s speed over several laps. The middle graph illustrates the distribution of power between the ICE and the electric motor. Analysis shows that the power of the electric motor, both in traction and generator modes, remains stable throughout the entire modeling period, with no signs of power reduction. The third graph reflects the state of charge (SOC) of the battery, which is maintained within a stable range from 45% to 60%. The best lap time according to the simulation results was 87.66 s, which is 0.48 s faster than the car with a traditional ICE. The obtained results indicate that, despite a slight increase in vehicle mass due to the use of the hybrid powertrain, a significant improvement in lap time performance is achieved. The final graph shows the battery temperature dynamics. Data analysis shows that the initial temperature was +25 °C, reaching a plateau in the +35 °C to +36 °C range by the end of the third lap. This indicates that the thermal regime has reached a steady state, with no further significant temperature increases expected during the race. The obtained values (+36 °C) are within the acceptable operating range for the battery cells used.

The constraint SOC is fundamental to the control strategy. It ensures the battery remains within its operational limits, preventing shutdown and, most importantly, ensuring it can consistently provide the high power required for performance acceleration phases, thereby directly supporting the core objective of lap time minimization.

7. Conclusions

As part of the conducted research, a comparative simulation of two racing car concepts was carried out: one equipped with a traditional ICE and the other with a hybrid powertrain, including an electric motor, inverter, and battery. The analysis showed that the increased mass of the hybrid car negatively affects the efficiency of completing a racing lap. To minimize this effect, an electric motor control strategy was developed. The use of the electric motor on all straight sections of the track provides a significant acceleration advantage, which positively affects the lap time. Furthermore, the ability to use electric power for acceleration contributes to a reduction in harmful emissions directly on the track, aligning with the growing environmental focus in modern motorsport.

However, there is a limitation on the duration of effective operation of the hybrid system: the energy reserve of the battery allows for maximum performance only for two laps. When the battery is discharged, the efficiency of the hybrid car becomes lower than that of the traditional ICE counterpart. To solve this problem, a control algorithm was proposed that provides for recharging the battery using the excess power of the ICE when cornering and at maximum speed modes, where maximum engine output is not required. To maintain a stable battery charge level throughout the race, the threshold speed for activating the electric motor at full power in acceleration assist mode was increased. The obtained results demonstrate an improvement in lap time for the hybrid version of the car by 0.48 s. In endurance race conditions lasting four hours, the potential time gap from the car with a traditional ICE can reach 70 s. The conducted study confirms the significant advantage of hybrid technologies in motorsport. The algorithm’s practical significance lies in its implementation simplicity, enabling real-world deployment without sophisticated computational infrastructure, while delivering measurable performance gains and energy sustainability essential for competitive endurance racing.

It should be noted that this study is based on mathematical modeling results, which may differ from actual results due to simplified model assumptions. Errors may be due to incomplete consideration of dynamic loads, temperature conditions of powertrain components, and external track conditions. To address this critical aspect and improve the algorithm’s practical applicability, future research will prioritize a comprehensive analysis of reliability and sensitivity to variable parameters. This will include testing the strategy’s sensitivity to perturbations of key input parameters, such as driver driving style, profile and lap time variations, and changes in road surface profile. Further studies are planned to examine the selection of optimal key parameters, such as engine and electric motor power, battery parameters, and gearshift logic. Full-scale testing of a prototype vehicle is necessary to verify the results. Further research is planned to focus on implementing this algorithm in the vehicle’s onboard controller and conducting racing experiments to compare the simulation results with empirical data, which will further improve the model’s accuracy and strategy’s reliability.