In the context of global energy structure transformation and ecological protection demands, the new energy vehicle sector has embraced substantial development opportunities. As the core technological carrier in this field, the electric vehicle has become a crucial pathway for transportation emission reduction in various countries, owing to its environmental friendliness and superior energy utilization efficiency. The primary challenge facing current onboard energy storage systems is the difficulty in simultaneously satisfying both energy storage capacity and output power requirements. Addressing this issue, this research establishes a dynamic energy distribution model for a hybrid energy storage system by integrating the differentiated energy storage characteristics of lithium-ion batteries and supercapacitors.
1 Introduction
The rapid advancement of the automotive industry has contributed to significant socioeconomic progress, yet it has likewise triggered considerable ecological challenges that cannot be overlooked. In this context, electrified transportation solutions demonstrating high efficiency, zero emissions, and low-noise operation have captured industry-wide attention. Energy management strategy optimization within an electric vehicle directly affects the vehicle’s comprehensive driving range, dynamic response characteristics, charging efficiency, and battery endurance metrics, making it a focal research direction for new energy vehicles.
Compared to conventional internal combustion engine vehicles, electric vehicles demonstrate exceptional advantages in environmental conservation, energy conversion efficiency, noise reduction, and intelligent connectivity. Current mainstream electric vehicle models primarily depend on lithium batteries as their energy carrier, which present notable merits in energy density but encounter technical challenges including limited power density, prolonged charging durations, finite cycle life, and elevated manufacturing expenses. These limitations are particularly evident under high-frequency charge-discharge cycles, where battery performance deterioration substantially impacts user experience.
Given the inherent characteristics of electrochemical energy storage devices, investigating supplementary energy solutions has become a viable approach to overcome these technological constraints. In the field of innovative energy storage devices, supercapacitors demonstrate unique technical advantages. They offer millisecond-level charge-discharge response, over one million cycle life, outstanding broad temperature range adaptability, and environmentally friendly characteristics. However, their relatively low energy density per unit mass restricts their capacity to independently serve as vehicle propulsion sources.
Given this framework, the research proposes an integrated energy storage architecture built on lithium battery-supercapacitor synergy. This solution fully utilizes the high energy storage density advantage of the lithium battery system and the high-power output advantage of supercapacitors, thereby forming a functionally complementary hybrid power supply system. In exploring energy allocation strategies for hybrid energy storage systems under varied operating conditions, this work seeks to enhance dynamic performance and energy efficiency of electric vehicles while providing both theoretical foundations and engineering solutions for sustainable development within the new energy vehicle sector.
2 Modeling and Characterization of Hybrid Energy Storage System Components
A comprehensive analysis of operating characteristics was performed for lithium-ion batteries, supercapacitors, and bidirectional DC/DC converters. This analysis supported the establishment of a lithium battery dynamic internal resistance model, a supercapacitor equivalent model, and a DC/DC converter efficiency model. These models supply the theoretical basis for subsequent powertrain parameter optimization and power device selection.
2.1 Lithium-ion Battery Analysis and Modeling
Lithium-ion batteries, when evaluated as an energy source for electric vehicles, show strong technical fit. By 2025, the projected annual power lithium battery installation in China is expected to reach 752.4 GWh, with supporting vehicle driving range enhanced by 150% relative to nickel-metal hydride systems.
The open-circuit voltage of a lithium battery demonstrates a typical three-stage variation pattern in response to state of charge (SOC). The internal resistance is influenced by the interplay of several factors, including the properties of electrode and electrolyte materials chosen, the manufacturing processes implemented, current parameters during cycling (particularly magnitude and rate of change), environmental temperature conditions, and cumulative service time that leads to progressive structural degradation and capacity fade.
2.2 Modeling Approach Selection
Lithium battery modeling approaches generally fall into electrochemical models and equivalent circuit models. Electrochemical models rely on numerous partial differential equations requiring extensive parameters and significant computational effort. Equivalent circuit models, however, apply fundamental circuit theory to represent the battery using ideal voltage sources combined with capacitors and resistors. Three principal equivalent circuit models were evaluated:
| Model | Advantages | Disadvantages |
|---|---|---|
| Rint Model | Simple structure, straightforward computation | Fails to account for polarization phenomena and complex electrochemical behavior |
| Thevenin Model | Enhanced parameter identification accuracy, reflects polarization effects | Does not capture open-circuit voltage variation from accumulated current |
| PNGV Model | High precision, detailed behavior simulation across operating modes | High model complexity and extensive parameters |
Considering the specific research focus and balancing model fidelity against parameter identification complexity, the Rint equivalent circuit model was selected. Based on Kirchhoff’s voltage and current laws, the following relationships were derived:
$$U_{L} = U_{OC} – IR \tag{1}$$
where \(U_{OC}\) represents the open-circuit voltage (V), I refers to the charge/discharge current (A), R denotes the equivalent internal resistance (\(\Omega\)), and \(U_{L}\) is the terminal voltage. Treating the discharge current as positive, battery output power \(P_{b}\) can be expressed as:
$$P_{b} = U_{L}I = (U_{OC} – IR)I \tag{2}$$
Solving the resulting quadratic equation yields the discharge current:
$$I_{bat} = \frac{U_{OC}(SOC) – \sqrt{U_{OC}^{2}(SOC) – 4R(SOC)P_{b}}}{2R(SOC)} \tag{3}$$
For SOC estimation, the ampere-hour integration method was applied. Assuming coulombic efficiency \(\eta = 1\), the battery SOC satisfies:
$$SOC_{b} = SOC_{0} – \frac{1}{3600Q}\int_{0}^{t} I \, dt \tag{4}$$
where \(SOC_{0}\) denotes the initial state of charge and Q is the battery capacity in ampere-hours. Based on this mathematical framework, a lithium battery simulation model was developed in MATLAB/Simulink. During battery operation, when output power remains consistent, high-voltage low-current operation is preferred over low-voltage high-current scenarios, since high discharge currents accelerate electrode material degradation and shorten battery service life.
2.3 Supercapacitor Characterization and Modeling
Supercapacitors occupy a unique niche between conventional capacitors and batteries among energy storage technologies. Their exceptional power density capabilities enable very rapid charge-discharge cycles, rendering them highly suited for applications demanding high instantaneous power. Within a hybrid energy storage architecture, they effectively perform “peak shaving” on battery current during charge-discharge operations, thereby enhancing system energy efficiency and stability.
The main performance parameters include capacitance C (F), stored energy E (Wh), rated voltage \(U_{cst}\), energy state SOE, and state of charge SOC. The stored energy bears a quadratic relationship to operating voltage:
$$E = \frac{1}{2}CU^{2} \tag{5}$$
The energy state SOE is:
$$SOE = \frac{\frac{1}{2}CU_{SC}^{2}}{\frac{1}{2}CU_{SC\_max}^{2}} = \frac{U_{SC}^{2}}{U_{SC\_max}^{2}} \tag{6}$$
After comparing model alternatives including the simplified first-order RC model, classical model, ladder model, and three-branch model, the classical equivalent model was chosen to represent supercapacitor operational behavior. This model incorporates a series resistance R to capture ohmic losses and a parallel resistance to represent leakage current. The derived relationship follows:
$$U_{cap} = U_C – I_{cap}R_S \tag{7}$$
For SOC estimation, the ampere-hour integration method is again applied. The model structure is presented in Table 2 below.
| Parameter | Value | Unit |
|---|---|---|
| Rated voltage of single cell | 2.5 | V |
| Rated capacitance of single cell | 1500 | F |
| Number of series-connected cells | 159 | – |
| Total pack voltage | 397 | V |
2.4 DC/DC Converter Modeling and Efficiency Characteristics
The bidirectional DC/DC converter functions as a critical power regulation unit enabling bidirectional energy flow between energy storage components. Due to the supercapacitor’s voltage dependence on SOC and the battery’s relatively stable terminal voltage, the bidirectional Buck/Boost converter was chosen. Its circuit includes filter capacitors, an energy storage inductor, and IGBT switching devices.
For the bidirectional DC/DC converter efficiency characteristics, the efficiency \(\eta\) is defined by:
$$\eta = \frac{U_{OUT}I_{OUT}}{U_{IN}I_{IN}} \times 100\% \tag{8}$$
DC/DC converter efficiency is substantially influenced by the voltage ratio between battery pack and supercapacitor pack (\(U_{bat}/U_{SC}\)). When the voltage ratio approaches unity, conversion efficiency reaches its highest point, and energy losses are minimized. To enable accurate system simulation, a two-dimensional look-up table interpolation method was implemented in Simulink to construct the DC/DC efficiency model.
3 Hybrid Energy Storage System Configuration and Power Distribution Strategy
3.1 Topology Architecture Selection
Depending on the placement of power conversion devices, hybrid energy storage topologies can be classified into four types: passive parallel, supercapacitor-side semi-active, battery-side semi-active, and fully active structures. The system maintains dynamic power balance as expressed by:
$$P_{req} = P_{bat} + P_{sc} \tag{9}$$
where \(P_{bat}\) is the battery pack output power, \(P_{sc}\) is the supercapacitor module power, and \(P_{req}\) represents the DC bus power demand.
After quantitative analysis of these configurations, the supercapacitor-side DC/DC semi-active control configuration was selected for this research due to its combined superiority in dynamic response, cycle life, and cost-effectiveness. This selected topology architecture is presented in Table 3.
| Topology Type | Description | Key Characteristics |
|---|---|---|
| Passive Parallel | Battery and supercapacitor directly connected to DC bus | No power electronics interface; limited energy utilization; essentially obsolete |
| Supercapacitor-side Semi-active | Supercapacitor connects via bidirectional DC/DC to share bus with battery | Optimized energy utilization; simpler algorithm; selected for this study |
| Battery-side Semi-active | Battery connects through DC/DC; supercapacitor is directly on bus | Shields battery from transients; but system efficiency is reduced |
| Fully Active | Both storage units interface through dedicated DC/DC converters | Maximum flexibility; higher cost and control complexity |
3.2 Operational Modes and Power Demand Analysis
The operational modes of the hybrid energy storage electric vehicle comprise four scenarios. In single energy storage unit mode, which arises during vehicle launch or transient acceleration with high power requirements, the supercapacitor independently supplies energy. During steady-state cruising at low acceleration demands, the power battery operates individually. In conditions such as hill climbing or rapid acceleration, the supercapacitor and power battery supply power simultaneously, where the lithium battery provides base power and the supercapacitor compensates the power differential. During regenerative braking on deceleration or downhill, the drive motor changes to generating mode, prioritizing energy recovery through the supercapacitor before charging the battery pack.
At any moment, the total system output capability is characterized by:
$$P_{total}(t) = P_{bat}(t) + P_{sc}(t) \tag{10}$$
In an ideal system without internal losses, \(P_{req}(t) = P_{total}(t)\). Through a dynamic power distribution strategy, power allocation coefficients \(K_b\) and \(K_c\) are introduced where:
$$P_{bat}(t) = K_b P_{req}(t), \quad P_{sc}(t) = K_c P_{req}(t) \tag{11}$$
subject to the energy conservation constraint:
$$K_b + K_c = 1 \tag{12}$$
3.3 Rule-Based Energy Management Strategy
The rule-based strategy determines power distribution based on preset threshold conditions and modal switching logic. For the low-power region where the motor power demand is limited, the battery energy storage unit independently supplies power. During high-load operation, the hybrid energy storage system engages in coordinated power delivery. A first-order inertia element is implemented for power decoupling, using a filter function to mitigate battery supply fluctuations:
$$F(s) = \frac{1}{1 + \tau s} \tag{13}$$
with time constant \(\tau = 10\) seconds. When regenerative braking is activated and the supercapacitor SOC is below 0.8, the supercapacitor prioritizes absorbing pulse energy. A minimum supercapacitor SOC of 0.2 was established to maintain reliable transient power support capability.
3.4 Fuzzy Logic Control Strategy Design
Traditional rule-based control methods allocate energy according to set rules and exhibit limited adaptability to varying operating conditions. To overcome such rigidity, a fuzzy control strategy was designed introducing real-time SOC levels of the hybrid storage components and overall vehicle power demand as input variables. The structure integrates four principal components: fuzzification, knowledge base, inference mechanism, and defuzzification.
Three input domains partition the power requirement into regions: high positive, low positive, and regenerative braking. For load power demand \(P_{req}\), seven fuzzy levels are established: {NB, NM, NS, ZE, PS, PM, PB}, with the discourse universe normalized to an interval of [-0.2, 1]. The battery SOC and supercapacitor SOC define three fuzzy sets: {LE, ME, GE}, on a normalized [0,1] scale. The output power distribution factor \(K_{bat}\) utilizes five fuzzy classifications: {LE, ML, ME, MB, GE}.
Triangular membership functions were chosen for fuzzifying the demand power \(P_{req}\), while Gaussian-shaped functions were applied to the SOC inputs and the \(K_{bat}\) output. The fuzzification of the demand power applies the normalization:
$$P’ = P – \frac{P_{req\_min} + P_{req\_max}}{2} \tag{14}$$
where \(P_{req\_min}\) and \(P_{req\_max}\) represent the minimum and maximum demand power. The fuzzy rule set was established through consideration of system operation modes and engineering expertise. A representative selection of rules is provided in the following table.
| \(P_{req}\) | \(SOC_{bat}\) | \(SOC_{sc}\) | \(K_{bat}\) |
|---|---|---|---|
| PS | LE | GE | GE |
| PS | ME | GE | GE |
| PB | GE | GE | MB |
| NB | LE | ME | ME |
| ZE | LE | LE | LE |
| NM | ME | LE | ML |
For defuzzification, the weighted average method was adopted as expressed by:
$$x_{0} = \frac{\sum_{i=0}^{n} x_{i}\mu_{U}(x_{i})}{\sum_{i=0}^{n}\mu_{U}(x_{i})} \tag{15}$$
3.5 SSA-Optimized Fuzzy Control Strategy
Since conventional fuzzy control strategies traditionally rely on manual experience and domain expertise, the Sparrow Search Algorithm (SSA) was implemented to establish a global optimization mechanism enabling optimal configuration of fuzzy controller membership functions and rule bases. SSA categorizes individuals into explorers responsible for global searching, followers conducting local development, and scouts performing risk monitoring. Explorer position updates follow:
$$x_{i,j}^{t+1} = \begin{cases} x_{i,j}^{t} \cdot \exp\left(-\frac{i}{\alpha \cdot iter_{max}}\right), & R < ST \\ x_{i,j}^{t} + Q \cdot L, & R \geq ST \end{cases} \tag{16}$$
Here, \(iter_{max}\) is the maximum iteration count, \(\alpha\) is a uniformly distributed random number, \(Q\) is a random number following standard normal distribution, and \(ST\) is the safety threshold. When the perceived risk level \(R < ST\), the explorer judges the current region safe and conducts local refinement near the optimum. When \(R \geq ST\), all explorers must terminate current exploration paths and initiate global migration. Follower positions are updated according to:
$$x_{i,j}^{t+1} = \begin{cases} Q \cdot \exp\left(\frac{x_{w,j}^{t} – x_{i,j}^{t}}{i^{2}}\right), & i > n/2 \\ x_{P,j}^{t+1} + |x_{i,j}^{t} – x_{P,j}^{t+1}| \cdot A^{+} \cdot L, & i \leq n/2 \end{cases} \tag{17}$$
where \(x_{w,j}^{t}\) denotes the global worst position and \(x_{P,j}^{t}\) is the current best position. Scout updates are described by:
$$x_{i,j}^{t+1} = \begin{cases} x_{i,j}^{t} + \beta \cdot |x_{i,j}^{t} – x_{P,j}^{t}|, & f_i \neq f_g \\ x_{i,j}^{t} + K \cdot \frac{x_{i,j}^{t} – x_{w,j}^{t}}{|f_i – f_w| + \varepsilon}, & f_i = f_g \end{cases} \tag{18}$$
To optimize the membership function parameters while suppressing battery capacity fade and enhancing system efficiency, an optimization model was constructed with 36 membership parameters forming a 36-dimensional solution space. The objective function was formulated as:
$$f(x) = \chi_{1} \cdot \max I_{bat} + \chi_{2} \cdot \frac{\sum P_{bat}}{S} \tag{19}$$
subject to the constraints:
$$\begin{cases} x_{1} \leq x_{2} \leq \cdots \leq x_{14} \\ 0.2 \leq x_{15} \leq x_{16} \leq \cdots \leq x_{20} \leq 1 \\ 0 \leq x_{21} \leq x_{22} \leq \cdots \leq x_{26} \leq 1 \\ 0 \leq x_{27} \leq x_{28} \leq \cdots \leq x_{36} \leq 1 \end{cases} \tag{20}$$
where \(I_{max}\) is the maximum allowable battery discharge current, \(\sum P_{bat}\) denotes total battery output power, \(S\) is the cycle distance, and the weighting factors \(\chi_{1} = \chi_{2} = 0.5\). The SSA settings included population size N = 50, dimensionality D = 36, maximum iterations \(iter_{max}\) = 100, and safety threshold ST = 0.8.
3.6 Dynamic Filtering with Variable Load Constraint Module
To further enhance system effectiveness, a dynamic filtering with variable load coordination module was designed. The moving average filter reduces high-frequency ripple components in battery power, while variable load constraints ensure smooth power transition. The filtering approach applies a moving observation window of N samples to discrete time-series signals. The weighted sliding average filter is characterized by:
$$P_{fc}(t) = \frac{1}{N}\sum_{t=0}^{n-1} \chi_t \cdot P_T(T – t) \tag{21}$$
where N represents the number of data points in the sliding window, \(P_T\) is the battery output power at time T, and \(\chi_t\) denotes the weight coefficients. Through frequency-domain resolution and dynamic fidelity analysis, the optimal window length was set to four sampling periods to maintain transient accuracy while suppressing high-frequency content.
A dynamic gradient limiter was integrated downstream of the smoothing module by establishing the maximum instantaneous power change rate as K = 6.8 kW/s. When the real-time power slope satisfies \(|dP/dt| \geq K\), the gradient limiting module activates, causing the operating point to migrate gradually along an iso-gradient trajectory. This coordinated strategy achieves rational energy distribution within the hybrid storage system of the electric vehicle, ensuring responsiveness while protecting the electrochemical energy storage elements from excessive transient stress.
4 ADVISOR-based Simulation and Results Analysis
4.1 ADVISOR Platform and Secondary Development
The ADVISOR (Advanced Vehicle Simulator) platform developed by the U.S. National Renewable Energy Laboratory was adopted in this research. It employs a hybrid modeling approach combining backward computation with forward validation to achieve accurate results under reduced computational load. However, the standard ADVISOR configuration only supports a single power battery storage architecture, which cannot directly accommodate hybrid energy storage systems. A staged platform adaptation was accordingly performed.
The first stage involved parameter restructuring in the energy storage data directory, converting the Maxwell supercapacitor model to second energy source convention by replacing the “ess” system variables with “ess2” identifiers. A separate configuration file EV_H_defaults_in.m was created to integrate supercapacitor system characteristic parameters. In the vehicle configuration database, the supercapacitor system version identifier and type parameters were injected, enabling visualization and independent editing of the secondary energy source in the GUI. After performing a comprehensive parameter compliance review and validating the configuration mapping in block_diagram_name.m, the system was verified to correctly load the EV_H architecture with independently configurable parameters for both storage units.
4.2 Simulation Setup and Vehicle Parameterization
The UDDS (Urban Dynamometer Driving Schedule) cycle was employed due to its typical transient acceleration characteristics and high-frequency speed fluctuations which capture frequent start-stop and acceleration-deceleration patterns in urban traffic. Key UDDS parameters are summarized in Table 4.
| Driving time (s) | Distance (km) | Max speed (km/h) | Avg speed (km/h) | Max accel (m/s²) | Avg accel (m/s²) | Max decel (m/s²) | Idle time (s) |
|---|---|---|---|---|---|---|---|
| 1369 | 11.99 | 91.25 | 31.51 | 1.48 | 0.5 | -1.48 | 259 |
The vehicle longitudinal dynamics follow the traction force equilibrium equation derived from vehicle dynamics theory:
$$F_t = F_f + F_w + F_i + F_j \tag{22}$$
$$F_t = mgf\cos\alpha + \frac{C_DAv_a^2}{21.5} + mg\sin\alpha + \delta m\frac{dv}{dt} \tag{23}$$
where m is vehicle mass (kg), g is gravitational acceleration, f is rolling resistance coefficient, \(\alpha\) is road grade, \(C_D\) is aerodynamic drag coefficient, and A is frontal area. The main electric vehicle parameters selected are listed in Table 5.
| Parameter | Value |
|---|---|
| Vehicle curb mass (kg) | 1300 |
| Dimensions L×W×H (mm) | 4320×1710×1515 |
| Frontal area (m²) | 2.4 |
| Wheelbase (mm) | 2500 |
| Wheel radius (m) | 0.3015 |
| Drivetrain efficiency | 0.96 |
| Aerodynamic drag coefficient | 0.3 |
| Rolling resistance coefficient | 0.02 |
Based on the target performance including maximum speed of 130 km/h, acceleration from 0-100 km/h in 10 seconds, maximum gradeability of at least 20%, and driving range of 210 km, the peak power demands were calculated using:
$$P_{\alpha} = \frac{1}{\eta}\left(\frac{Mgf\cos\alpha v_a}{3600} + \frac{C_DAv_a^3}{76140}\right) \tag{24}$$
$$P_{v_{max}} = \frac{1}{\eta}\left(\frac{Mgf v_{max}}{3600} + \frac{C_DAv_{max}^3}{76140}\right) \tag{25}$$
$$P_r = \frac{\delta Mv_b}{3600 \times 1.5t}\left(v_b^2 + \frac{C_DAv_b^2}{52.875}\right) \tag{26}$$
The peak power requirement was determined as 83.88 kW, which determined selection of a 90 kW drive motor. Vehicle performance target validation through the peak-power calculation process yielded a battery pack series configuration of 125 cells and 87 parallel branches. Key battery and supercapacitor parameters are presented in Table 6.
| Component | Parameter | Value |
|---|---|---|
| Lithium Battery Pack | Single cell rated voltage | 3.2 V |
| Single cell capacity | 1500 mAh | |
| Series cells | 125 | |
| Parallel branches | 87 |
4.3 Comparison of Hybrid and Single Storage Architectures
The rule-based control strategy was used as the baseline energy management algorithm to compare hybrid versus single-source configurations on the ADVISOR platform under UDDS conditions. The key battery performance indicators are summarized in Table 7.
| Configuration | Final Battery SOC | Peak Current (A) | Battery Temperature (°C) |
|---|---|---|---|
| Single energy storage | 0.8212 | 185.1 | 32.0 |
| Hybrid energy storage | 0.8297 | 156.3 | 26.12 |
From the SOC comparison, the hybrid configuration achieved a final SOC increase of 0.85%. Peak discharge current was reduced from 185.1 A to 156.3 A, corresponding to a reduction of 28.8 A in current fluctuation amplitude. The observed thermal accumulation reduction of approximately 5.88°C is directly attributable to the supercapacitor effectively absorbing transient power demands, reducing battery internal polarization and consequent ohmic heating. These results validate that the hybrid energy storage architecture provides substantial benefits across the three coupled performance dimensions of battery longevity, system efficiency, and dynamic capability.
4.4 Comparison of Different Energy Management Strategies
To comparatively assess the proposed control methods, four strategies were implemented and evaluated under UDDS conditions: rule-based control, conventional fuzzy control, SSA-optimized fuzzy control, and the SSA-based compound fuzzy control strategy. The comparative results are summarized in Table 8.
| Control Strategy | Battery Remaining SOC | Battery Peak Current (A) | Battery Temperature (°C) |
|---|---|---|---|
| Rule-based control | 0.8297 | 156.3 | 26.12 |
| Fuzzy control | 0.8708 | 75.6 | 24.98 |
| SSA-optimized fuzzy control | 0.8818 | 74.3 | 24.81 |
| SSA compound fuzzy control | 0.8938 | 74.1 | 23.91 |
The simulation results reveal clear distinctions. Relative to the rule-based strategy, the conventional fuzzy control strategy reduced peak current from 156.3 A to 75.6 A, an improvement of more than 80 A. Under the SSA compound fuzzy control strategy, the final battery SOC reached 0.8938, an improvement of 6.41% over the rule-based approach, with the peak current further reduced to 74.1 A. The thermal accumulation decreased by an additional 2.21°C compared to the baseline fuzzy approach. The SSA-optimized fuzzy controller achieves effective avoidance of local optima pitfalls characteristic of conventional fuzzy systems. The integration of sliding average filtering and power-rate limiting effectively smooths the power trajectory, preventing the battery from experiencing high-frequency power oscillations that accelerate capacity degradation.
Additional efficiency analysis demonstrated that the rule-based strategy exhibits deficiencies in battery charge-discharge efficiency utilization, with substantial inefficient operating regions. In contrast, the SSA compound fuzzy control strategy maintained discharge efficiency consistently within the high-efficiency band of 0.9 to 1.0 throughout the UDDS cycle, confirming superior overall energy conversion effectiveness.
5 Design of Bottom-Layer Controllers for Hybrid Energy Storage System
The successful implementation of upper-layer energy management strategies depends upon precise power distribution and tracking at the actuator level. A fully active topology architecture was adopted to establish the bottom-level control plant, where both the battery and supercapacitor interface with the DC bus through dedicated bidirectional DC/DC converters.
5.1 State-Space Modeling of Fully Active System
By applying Kirchhoff’s laws and the principle of inductor volt-second balance over a switching period, a fifth-order state-space averaged model of the fully active composite storage system was established. This model uses average inductor currents and capacitor voltages as state variables. The derived state equation follows:
$$\dot{x} = (A_0 + A_1D_1 + A_3D_3)x + Bv \tag{27}$$
where the state vector is defined as:
$$x = \begin{bmatrix} V_1 & V_2 & i_1 & i_2 & V_0 \end{bmatrix}^{T} \tag{28}$$
The matrices \(A_0\), \(A_1\), \(A_3\), and B contain system parameters including inductor values, capacitor values, battery internal resistance, supercapacitor resistance, and IGBT conduction resistances. The duty cycles \(D_1\) and \(D_3\) serve as the control inputs for the two DC/DC converters.
5.2 Sliding Mode Current Controller Design
To achieve accurate current tracking of the two power sources, current errors were defined as:
$$e_1 = y_{ref} – y \tag{29}$$
under the practical assumption of slowly varying current references. A reaching law of the form was designed:
$$\dot{e}_1 = C\dot{x} = -k\,e_1 – \rho\,\mathrm{sgn}(e_1) \tag{30}$$
where k and \(\rho\) are positive definite gain matrices. Combining with the system dynamics of eq. (27), the sliding mode control law was derived as:
$$\begin{bmatrix} D_1 \\ D_3 \end{bmatrix} = \begin{bmatrix} k_1L_1/V_0 & 0 \\ 0 & k_2L_2/V_0 \end{bmatrix} \begin{bmatrix} i_1 – i_{1,ref} \\ i_2 – i_{2,ref} \end{bmatrix} + \begin{bmatrix} \text{feedforward terms} \end{bmatrix} \tag{31}$$
For stability verification, the Lyapunov function:
$$V_1 = \frac{1}{2}e_1^2 \tag{32}$$
yields derivative:
$$\dot{V}_1 = e_1\dot{e}_1 = -k e_1^2 – \rho e_1\,\mathrm{sgn}(e_1) \leq 0 \tag{33}$$
since both k and \(\rho\) are strictly positive, asymptotic stability follows.
5.3 PI-Based Voltage Controller Design
The supercapacitor is tasked with maintaining the DC bus voltage. A reference value \(V_{DC,ref}\) was defined, and the voltage error expressed as:
$$e_2 = V_{DC,ref} – V_{DC} \tag{34}$$
The PI control law generates the supercapacitor current reference:
$$I_{SC,ref} = K_P e_2 + K_I \int_0^t e_2 \, dt – i_{load} \tag{35}$$
Stability analysis using the composite Lyapunov function:
$$V_2 = \frac{1}{2}C_0e_2^2 + \frac{1}{2}K_I\left(\int_0^t e_2 \, dt\right)^2 \tag{36}$$
with its derivative:
$$\dot{V}_2 = C_0e_2\dot{e}_2 + K_I e_2\int_0^t e_2 \, dt \tag{37}$$
after substituting the control law, the derivative reduces to:
$$\dot{V}_2 = -K_P e_2^2 \leq 0 \tag{38}$$
which confirms asymptotic voltage stability. A supervisory control structure was established where the upper energy management strategy generates battery current reference commands and supercapacitor current references from the PI voltage controller output, with both signals subsequently tracked via the sliding mode controllers.
5.4 Simulation Validation of the Control System
A MATLAB/Simulink simulation platform was constructed to validate the control system performance. The experimental configuration used a DC bus reference voltage of 220 V, an initial battery SOC of 0.9 corresponding to 180 V, and an initial supercapacitor terminal voltage of 150 V. The power switching frequency was set to 10 kHz, with PI gains of \(K_P\) = 20 and \(K_I\) = 3. The sliding mode gains were configured with battery-side parameters of 5 and 0.3, and supercapacitor-side parameters of 500 and 30. Table 9 summarizes the simulation system parameters.
| Parameter | Value |
|---|---|
| Battery-side inductance (\(\mu\)H) | 255 |
| Battery internal resistance (\(\Omega\)) | 0.255 |
| Battery-side filter capacitance (\(\mu\)F) | 69 |
| Supercapacitor-side inductance (\(\mu\)H) | 188 |
| Supercapacitor internal resistance (\(\Omega\)) | 0.161 |
| Supercapacitor-side filter capacitance (\(\mu\)F) | 69 |
| Load-side capacitance (\(\mu\)F) | 14.85 |
| IGBT conduction resistance (m\(\Omega\)) | 21 |
The load power profile combined a step load with a superimposed sinusoidal perturbation component. Simulation results demonstrated accurate tracking of both battery current and supercapacitor current reference commands by the sliding mode controllers, with fast dynamic response and no overshoot in the regulation trajectory. Under abrupt load transitions, the DC bus voltage deviation was limited to a maximum of 0.25 V without any overshoot. The closed-loop system exhibited rapid settling behavior and maintained high steady-state accuracy, confirming that the designed control framework meets the requirements for dynamic response time, steady-state regulation precision, and disturbance rejection capability in the context of electric vehicle hybrid energy storage applications.
6 Conclusions and Future Directions
This research addressed the critical issues of cycle life degradation and transient power response limitations of the power battery in electric vehicles by proposing a lithium battery-supercapacitor hybrid energy storage optimization solution. The principal findings are summarized below.
First, based on vehicle dynamics theory, a driving torque demand model was constructed and integrated with a lithium-ion battery model and a supercapacitor classical equivalent model. The combined architecture established a coupled electromechanical simulation platform. Selecting the supercapacitor-side semi-active topology configuration, simulation modules were developed in Simulink for the lithium battery, supercapacitor, and bidirectional DC/DC converter with an efficiency model using 2-D look-up interpolation. This foundation enabled subsequent dynamic power distribution simulation and operational mode analysis for hybrid energy storage systems.
Second, the rule-based energy management strategy was established, and its comparative evaluation against a single-source system demonstrated that the hybrid configuration significantly reduced high-current discharge events, increased remaining SOC, and validated the overall effectiveness of the hybrid architecture for meeting electric vehicle load demands.
Third, the fuzzy membership function definitions and rule base were constructed according to operating condition characteristics. The Sparrow Search Algorithm was then applied to perform global optimization of the membership function parameters with the dual objectives of suppressing battery capacity degradation and enhancing system efficiency. This was augmented by incorporating a moving average filter module and dynamic gradient constraint feedforward channel. Under UDDS testing, the SSA compound fuzzy control strategy compared to the rule-based approach achieved a 6.41% final SOC improvement, current fluctuation amplitude reduction of approximately 82.2 A, and a temperature rise reduction from 26.12°C to 23.91°C, thereby extending the battery cycle life and increasing vehicle driving range while promoting energy recovery efficiency.
Fourth, for the bottom-level control architecture, a fifth-order state-space averaged model of the fully active topology hybrid storage system was established. A sliding mode current controller was designed for the rapid tracking of both battery and supercapacitor currents, and a PI-based voltage stabilizing controller was derived to maintain DC bus voltage stability. Simulation experiments confirmed that the designed control framework meets all specifications for dynamic response speed, steady-state tracking accuracy, and disturbance rejection capability.
While the current research provides a systematic approach to hybrid storage optimization, several areas warrant further investigation. The validation methodology relies on standardized driving cycles whose dynamic characteristics may deviate from real-world road load spectra. Future studies could integrate telematics multisource data to construct a comprehensive driving condition database incorporating multiple environmental parameters, thereby improving prediction accuracy. The fuzzy inference system presents opportunities for enhancing rule base formulation and online adaptation. The application of multi-objective evolutionary algorithms in combination with deep reinforcement learning frameworks may enable online policy updates for developing self-adaptive energy management systems. Future work should also include comprehensive life-cycle techno-economic evaluation comparing hybrid versus single-source storage configurations, considering initial capital costs, maintenance intervals, and component replacement schedules. Hardware-in-the-loop testing and vehicle-level experimental validation are essential to bridge the gap between simulation outcomes and deployable engineering solutions.