Coordinated Thermal and Electrical Balancing for Lithium-Ion Cells

Abstract

State-of-charge (SOC) and temperature inconsistencies among lithium-ion battery cells can significantly degrade the performance, safety, and lifespan of battery packs. To address this issue, this paper proposes a dynamic balancing strategy that simultaneously regulates both SOC and cell temperature in real time. Each battery cell is connected to an individual Boost converter, enabling independent control of energy flow. An outer loop is adopted to stabilize the pack-level bus voltage. The balancing factors for SOC and temperature are adaptively fused using a Particle Swarm Optimization (PSO) algorithm, which dynamically adjusts the weightings based on real-time operating conditions. This approach allows the controller to prioritize either thermal or electrical balance when needed, ensuring robust performance under varying load and environmental disturbances. Simulation-based validation on a multi-cell lithium-ion pack demonstrates that the proposed method effectively reduces SOC and temperature deviation, improves pack-level energy utilization, and extends operational stability compared to fixed-weight balancing strategies.

1. Introduction

Lithium-ion batteries (LIBs) have become the predominant energy storage technology in modern applications, such as electric vehicles (EVs), renewable energy systems, aerospace, and consumer electronics, due to their high energy density, long cycle life, and favorable power characteristics [1,2,3,4,5]. However, the performance and reliability of a battery pack are significantly affected by internal inconsistencies among individual cells, especially in terms of state-of-charge (SOC) [6], temperature [7], internal resistance [8], and aging conditions [9,10]. These discrepancies arise from factors such as manufacturing variations, different thermal environments, uneven usage histories, and natural cell-to-cell degradation over time [11,12,13,14].

Among these factors, SOC and temperature heterogeneities are particularly critical. Imbalances in SOC can lead to early overcharge or over-discharge of certain cells, reducing usable capacity and accelerating aging [15]. Meanwhile, thermal imbalance can result in localized hotspots that not only degrade electrochemical performance but also increase the risk of thermal runaway. These two parameters are strongly coupled [16]: temperature influences reaction kinetics, internal resistance, and self-discharge rates, while uneven current distribution caused by SOC mismatch can further exacerbate thermal gradients. Therefore, achieving coordinated SOC and thermal balancing is vital for enhancing energy efficiency, prolonging battery lifespan, and ensuring safety [17].

Traditional battery management systems (BMS) often address these issues independently. SOC balancing is commonly achieved via passive dissipative circuits [18] or active DC-DC converters [19,20,21,22], while thermal regulation relies on external cooling systems such as air, liquid, or phase change materials [23,24,25]. However, such decoupled strategies are often inadequate under dynamic load conditions, where real-time adaptation and multi-variable coordination are required. Moreover, many existing balancing strategies are based on fixed control rules or single-objective optimization, which may lead to trade-offs, such as prioritizing SOC at the expense of thermal safety [15], or vice versa.

To address these challenges, this paper proposes a real-time, unified control framework that dynamically balances both SOC and temperature across a lithium-ion battery pack. Each cell is equipped with a dedicated bidirectional power converter, enabling flexible energy redistribution. A unified control loop is designed to simultaneously regulate multiple objectives: electrochemical balance, thermal consistency, and system-level voltage stability.

The PSO algorithm is adopted in this work due to its balance between computational efficiency and global optimization capability. Unlike model predictive control (MPC) or other optimal control strategies that require complex predictive models or gradient information, PSO operates with simple update rules and exhibits fast convergence even in nonlinear, non-convex cost landscapes. This makes it particularly suitable for real-time battery balancing tasks implemented on resource-constrained embedded platforms. The controller dynamically evaluates the current operating state of each cell and generates coordinated control signals using PSO algorithm. Unlike conventional dual-loop or hierarchical schemes, the proposed unified structure simplifies the control architecture, reduces latency, and improves response under time-varying and nonlinear operating conditions.

Furthermore, the balancing framework is scalable and not restricted to second-life batteries, making it suitable for both newly manufactured and aged battery systems. The proposed methodology can be adapted to include additional control objectives, such as state-of-health (SOH), internal impedance, or energy throughput, enabling broader applicability in intelligent battery management. The effectiveness of the proposed control strategy is validated through simulation tests under discharge scenarios.

2. Modeling of Battery Dynamics

In order to design an effective real-time balancing controller, a comprehensive model that captures the coupled electrochemical and thermal behavior of lithium-ion battery cells, along with the dynamics of the associated power electronics, is essential. This section presents the modeling framework adopted in this work, which includes the electrical, thermal, and converter subsystems.

2.1. Electrical Model of a Single Cell

Each battery cell is modeled using a simplified Thevenin-based equivalent circuit, which provides a good trade-off between accuracy and computational efficiency. The cell is represented by an open-circuit voltage source V_OC(SOC), a series resistance R_S, and a parallel RC network that captures dynamic polarization behavior:

$$\left\{\begin{array}{l}{\displaystyle \frac{d{V}_{RC}}{dt}}=-{\displaystyle \frac{V_{RC}}{R_p{C}_p}}+{\displaystyle \frac{I}{R_p}}\\ V_{cell}=V_{OC}(SOC)-I{R}_S-V_{RC}\end{array}\right.$$

(1)

The SOC dynamics are described as follows:

$${\displaystyle \frac{d(SOC)}{dt}}=-{\displaystyle \frac{I}{Q_{cell}}}$$

(2)

where V_cell is the terminal voltage of the cell, V_RC is the voltage across the RC network, R_p and C_p are the polarization resistance and polarization capacitance, I is the current flowing into the cell (positive for discharge), and Q_cell is the nominal capacity of the cell. The open-circuit voltage V_OC(SOC) is a nonlinear function of SOC and is typically obtained from experimental lookup tables or fitted empirical equations.

2.2. Thermal Model of a Single Cell

The thermal behavior of each cell is modeled using a lumped 1-RC thermal model, assuming uniform temperature distribution within the cell. The model accounts for both ohmic and polarization heat generation, as well as thermal conduction to the environment:

$$C_{th}{\displaystyle \frac{dT}{dt}}=Q_{gen}-{\displaystyle \frac{T-T_{env}}{R_{th}}}$$

(3)

where T is the cell temperature, C_th is the thermal capacitance, R_th is the thermal resistance to ambient, Q_gen is the total heat generated, and T_env is ambient temperature.

This model captures the impact of dynamic current and cell impedance on temperature rise and allows for estimation of transient thermal behavior under varying load conditions.

2.3. Converter and Power Stage Model

To enable cell-level energy balancing, each lithium-ion cell is connected to a dedicated bidirectional DC-DC converter, which facilitates both charge injection and extraction. In this work, as shown in Figure 1, a non-isolated Boost converter topology is adopted, which operates in Boost mode during discharging. In this structure, the battery cells are not physically connected in series, but their converter outputs are, emulating a series-connected battery pack.

Each cell is interfaced with a bidirectional Boost converter, which allows independent control of charge/discharge power. The simplified averaged model of the converter is as follows:

$$V_{bus}={\displaystyle \sum _{i=1}^N\frac{V_{cell,i}}{1-D_i}} (Boost Mode)$$

(4)

where $D_i\in [0,1]$ is the duty cycle of the i-th converter, V_cell,i is the terminal voltage of cell i, and V_bus is the shared system bus voltage. The control signal $D_i(i=1,\cdots ,N)$ is generated by the balancing controller and determines the amount and direction of power transfer.

2.4. Unified State-Space Model

For a specific cell j, it is supposed that during one control period, its temperature and bus voltage change little. The average current over this control period is used as a variable in the ampere-time integration method. The discrete state equations as follows, where k and k + 1 represent the starting and ending points of the period ($t_{k+1}-t_k=\tau$):

$$\left\{\begin{array}{c}SO{C}_j(k+1)=SO{C}_j(k)-{\displaystyle \frac{\tau }{Q_j}}{\displaystyle \frac{I_{bus}(k)}{1-D_j(k)}}\\ T_j(k+1)=(1-{\displaystyle \frac{\tau hA}{C_{th}}})T_j(k)+{\displaystyle \frac{\tau hA}{C_{th}}}{T}_{env}\\ +{\displaystyle \frac{R_j\tau }{C_{th}}}{\displaystyle \frac{I_{bus}^2(k)}{{[1-D_j(k)]}^2}}\end{array}\right.$$

(5)

where τ is the duration of the period, Q_j is j-th capacity, D_j(k) is the j-th duty cycle at k moment, I_bus(k) is the bus current at k moment, h is heat transfer coefficient, A is heat transfer area, and R_j is the j-th lumped resistance. Moreover, in order to simplify the expression, the following abbreviations apply: ${\epsilon }_j={\displaystyle \frac{\tau }{Q_j}}$, ${\mu }_j=1-{\displaystyle \frac{\tau hA}{C_{th}}}$, ${\theta }_j=1-{\mu }_j$, and ${\rho }_j={\displaystyle \frac{R_j\tau }{C_{th}}}$.

The SOC and temperature states of the N cells are incorporated into a set of vector equations:

$$\left\{\begin{array}{c}\mathit{SOC}(k+1)=\mathit{A}\cdot \mathit{SOC}(k)+\mathit{B}\cdot {\mathit{D}}_1(k)\\ \mathit{T}(k+1)=\mathit{C}\cdot \mathit{T}(k)+\mathit{E}\cdot {\mathit{D}}_1(k)+\mathit{F}\cdot T_{env}.\end{array}\right.$$

(6)

The boldface letters in (6) represent a set of an N-dimensional vector or an $N\times N$ matrix. As state variable, SOC with temperature is of the following form:

$$\left\{\begin{array}{c}\mathit{S}\mathit{O}\mathit{C}(k)=[SO{C}_1(k) SO{C}_2(k) \cdots SO{C}_N(k){]}^{\mathrm{T}}\\ \mathit{T}(k)=[T_1(k) T_2(k) \cdots T_N(k){]}^{\mathrm{T}}.\end{array}\right.$$

(7)

As an input variable, the symbol $\odot$ denotes the Hadamard product, and the expression containing the duty cycle is as follows:

$$\left\{\begin{array}{l}{\mathit{D}}_1(k)=[{\displaystyle \frac{1}{1-D_1(k)}} {\displaystyle \frac{1}{1-D_2(k)}} \cdots {\displaystyle \frac{1}{1-D_N(k)}} {]}^{\mathrm{T}}\\ {\mathit{D}}_2(k)={\mathit{D}}_1(k)\odot {\mathit{D}}_1(k).\end{array}\right.$$

(8)

To represent this discrete system in more detail, the state matrix is of the following form:

$$\mathit{A}=\left[\begin{array}{cccc}1& 0& \cdots & 0\\ 0& 1& \cdots & 0\\ ⋮& ⋮& ⋮& ⋮\\ 0& 0& \cdots & 1\end{array}\right]$$

(9)

$$\mathit{C}=\left[\begin{array}{cccc}{\mu }_1& 0& \cdots & 0\\ 0& {\mu }_2& \cdots & 0\\ ⋮& ⋮& ⋮& ⋮\\ 0& 0& \cdots & {\mu }_N\end{array}\right]$$

(10)

And the input matrix is of the following form:

$$\mathit{B}=\left[\begin{array}{cccc}-{\epsilon }_1{I}_{bus}(k)& 0& \cdots & 0\\ 0& -{\epsilon }_2{I}_{bus}(k)& \cdots & 0\\ ⋮& ⋮& ⋮& ⋮\\ 0& 0& \cdots & -{\epsilon }_N{I}_{bus}(k)\end{array}\right]$$

(11)

$$\mathit{E}=\left[\begin{array}{cccc}{\rho }_1{I}_{bus}^2(k)& 0& \cdots & 0\\ 0& {\rho }_2{I}_{bus}^2(k)& \cdots & 0\\ ⋮& ⋮& ⋮& ⋮\\ 0& 0& \cdots & {\rho }_N{I}_{bus}^2(k)\end{array}\right]$$

(12)

$$\mathit{F}={\left[\begin{array}{cccc}{\theta }_1& {\theta }_2& \cdots & {\theta }_N\end{array}\right]}^{\mathrm{T}}$$

(13)

3. Control Strategy for Multi-Objective Balancing

This section presents the real-time control strategy used to achieve dynamic balancing of both SOC and temperature across lithium-ion battery cells. Building on the unified system model introduced in Section 2, a centralized multi-objective control framework is designed to generate coordinated converter control signals, ensuring energy redistribution and thermal consistency while maintaining bus voltage stability.

The control system adopts a centralized, unified control loop that evaluates the electrothermal state of all cells in the pack and dynamically computes optimal duty cycles $d_i$ for each Boost converter.

The architecture is shown in Figure 2, which consists of three main components:

• State Estimator: Acquires real-time cell-level data, including SOC, temperature, and voltage, either through measurement or model-based estimation.
• Multi-Objective Cost Evaluator: Quantifies the global imbalance using a weighted cost function.
• Optimization Engine: Determines the optimal control input $\mathit{u}=\left[\begin{array}{cccc}{D}_1& D_2& \cdots & D_N\end{array}\right]$ to minimize the total imbalance while satisfying operational constraints.

In order to obtain the state error vector of SOC and temperature for each cell, the following matrix is combined with the state vector of all cells:

$${\mathit{M}}_{avg}={\mathit{I}}_N-{\displaystyle \frac{1}{N}}{\mathbf{1}}_{N\times N}=\left[\begin{array}{cccc}1-{\displaystyle \frac{1}{N}}& -{\displaystyle \frac{1}{N}}& \cdots & -{\displaystyle \frac{1}{N}}\\ -{\displaystyle \frac{1}{N}}& 1-{\displaystyle \frac{1}{N}}& \cdots & -{\displaystyle \frac{1}{N}}\\ ⋮& ⋮& ⋮& ⋮\\ -{\displaystyle \frac{1}{N}}& -{\displaystyle \frac{1}{N}}& \cdots & 1-{\displaystyle \frac{1}{N}}\end{array}\right]$$

(14)

The control objective is to minimize the SOC and temperature differences among all battery cells, while also regulating the pack-level bus voltage and limiting converter stress. This is formulated through the following multi-objective cost function:

$$\left\{\begin{array}{c}{\mathit{M}}_{SOC}(k)={\mathit{M}}_{avg}\cdot \mathit{S}\mathit{O}\mathit{C}(k)\\ {\mathit{M}}_T(k)={\mathit{M}}_{avg}\cdot \mathit{T}(k).\end{array}\right.$$

(15)

The cost functions corresponding to SOC and temperature are combined using two weighting factors ${\gamma }_{SOC}$ and ${\gamma }_T$ into the following:

$$\begin{array}{ll}J& ={\gamma }_{SOC}{J}_{SOC}+{\gamma }_T{J}_T\\ & ={\gamma }_{SOC}\cdot \mathit{S}\mathit{O}{\mathit{C}}^{\mathrm{T}}(k)\cdot {\mathit{M}}_{avg}^{\mathrm{T}}\cdot {\mathit{\omega }}_{SOC}\cdot {\mathit{M}}_{avg}\cdot \mathit{S}\mathit{O}\mathit{C}(k)\\ & +{\gamma }_T\cdot {\mathit{T}}^{\mathrm{T}}(k)\cdot {\mathit{M}}_{avg}^{\mathrm{T}}\cdot {\mathit{\omega }}_T\cdot {\mathit{M}}_{avg}\cdot \mathit{T}(k)\end{array}$$

(16)

This structure allows for flexible prioritization depending on system demands. For example, higher ${\gamma }_T$ can be applied during thermal stress events.

According to Equations (6), (8) and (16), the cost function is a function with the environment temperature and duty cycle as variables. To simplify the analysis, it is assumed that the environment temperature remains approximately constant over a period.

Combining the electrical and thermal dynamics with converter behavior, the unified state vector for a pack with N cells is as follows:

$$\mathit{x}={[SO{C}_1 \cdots SO{C}_N T_1 \cdots T_N V_{bus} ]}^{\mathrm{T}}$$

(17)

The control input vector is as follows:

$$\mathit{u}={\left[\begin{array}{cccc}{D}_1& D_2& \cdots & D_N\end{array}\right]}^{\mathrm{T}}$$

(18)

The system (6) can then be described in a compact discrete-time form:

$$\mathit{x}(k+1)=f(\mathit{x}(k),\mathit{u}(k))+\mathit{w}(k)$$

(19)

where $w(k)$ denotes external disturbances (e.g., load fluctuations, ambient temperature changes). The nonlinear function $f(\cdot )$ encapsulates the coupled SOC–thermal–converter dynamics of all cells. Using H to denote the number of optimized prediction steps, then the complete optimization problem is expressed as follows:

$$\begin{array}{ll}\underset{{\{\mathit{u}(k+j)\}}_{j=0}^{H-1}}{{\displaystyle \min }}& J(\mathit{x}(k),\mathit{u}(k),\cdots ,\mathit{u}(k+H-1))\\ s.t.& \mathit{x}(k+j+1)=f(\mathit{x}(k+j),\mathit{u}(k+j)), j=0,\cdots ,H-1\\ & SO{C}_{\min }\le SO{C}_i(k+j)\le SO{C}_{\max },T_{\min }\le T_i(k+j)\le T_{\max }\\ & D_{\min }\le D_i(k+j)\le D_{\max },V_{cell,\min }\le V_{cell,i}(k+j)\le V_{cell,\max }\end{array}$$

(20)

The 3D plot of the cost function J versus the duty cycle D₁ and D₂ for a balancing cell containing only two cells is shown in Figure 3. The region framed by the dashed line is the optimal duty cycle for this condition because it corresponds to the smallest cost function.

To realize coordinated electrothermal balancing while maintaining the overall bus voltage at a reference value, the generation of duty cycle commands for each cell-connected DC-DC converter follows the process in Figure 4.

3.1. Generation of Weighting Factors via PSO

First the state of the battery is collected, including the number of cells N, SOC, and temperature T. If the algorithm uses M particles for optimization, the position of each particle is a $1\times N$ vector (each element of this vector represents the weighting factor of the battery of the corresponding order), and $\mathit{p},\mathit{v},\mathit{\eta },{\mathit{\xi }}_1,{\mathit{\xi }}_2$ are all $M\times N$ matrices representing the particle position, velocity, inertia, individual acceleration factor, and global acceleration factor, respectively.

Then the initialization will be performed, which includes setting all the weighting factors to ${\displaystyle \frac{1}{N}}$, random particle positions, velocities, inertia, etc.

At each control interval, a Particle Swarm Optimization (PSO) algorithm is executed to determine the optimal set of balancing weights $l_i\in [0,1], i=1,\cdots ,N$ for each cell. These weights represent the relative participation of each converter in bus voltage support and balancing effort.

The PSO algorithm minimizes a multi-objective cost function that considers both SOC deviation and temperature deviation (as defined at (15)), and returns a set of optimal weights:

$$\mathit{l}=\left[\begin{array}{cccc}{l}_1& l_2& \cdots & l_N\end{array}\right] \mathrm{with} {\displaystyle \sum _{i=1}^N{l}_i=1}$$

(21)

Cells with greater imbalance (either in SOC or temperature) are assigned larger weights, thereby receiving higher participation in energy redistribution.

3.2. Reference Voltage Assignment for Each Converter

Once the balancing weights are determined, a reference voltage $V_{ref,i}$ is assigned to each converter such that the weighted sum of converter outputs equals the system-wide bus voltage reference $V_{bus,ref}$. This ensures bus voltage regulation is preserved during balancing:

$$V_{ref,i}=l_i{\displaystyle \frac{V_{bus,ref}}{{\displaystyle \sum _{j=1}^N{l}_i}}}$$

(22)

This allocation method guarantees that the total series output voltage of the converters satisfies ${\displaystyle \sum _{j=1}^N{V}_{ref,i}=V_{bus,ref}}.$

Moreover, this approach automatically prioritizes cells with greater balancing demand (larger l_i) by assigning them smaller reference voltages (in Boost mode), requiring them to transfer more power.

3.3. Duty Cycle Computation from Reference Voltages

Assuming each converter operates in Boost mode (cell to bus), the duty cycle for the i-th converter is calculated based on the relationship between the local cell voltage $V_{cell,i}$ and the assigned reference output voltage $V_{ref,i}$:

$$D_i=1-{\displaystyle \frac{V_{cell,i}}{V_{ref,i}}} (V_{ref,i}>V_{cell,i})$$

(23)

This work primarily focuses on the discharge (balancing) scenario where the Boost configuration dominates. To ensure feasibility $V_{ref,i}$, must always satisfy the following:

$$V_{ref,i}>V_{cell,i} \& D_i\in [D_{\min },D_{\max }]$$

(24)

where D_min and D_max represent hardware constraints.

When a digitally controlled Boost converter is used to maintain the bus voltage, it is implemented using a discrete Type 3 compensator on the Z-domain, such as $G_{VB}(z)$ in Figure 4, and its control block diagram with the small-signal model is shown in Figure 5.

The transfer function and gain in the loop can be given by the analysis in Section 2 above, and its detailed expression is shown in (26) to (29), where $G_{vd}(s)$ is transfer function from duty cycle D_i to output voltage V_i, H_vd is the gain coefficient of the voltage feedback loop, $G_{\mathit{zcell},i}\left(s\right)=\frac{1}{Z_{\mathit{cell},i}}$ is the load conductance of the i-th converter, ${\overline{D}}_i$ is the average duty cycle of the converter in the large signal model, $G_{iT}(s)$ is a transfer function from cell current to temperature that is approximated as a first-order inertial element, $k_{l,T}$ and $k_{l,SOC}$ are the linearized gains near the equilibrium point of PSO, which can be obtained by the Jacobian approximation, and $K_{\lambda V}$ is a first-order approximation of the reference voltage under a small perturbation.

$$G_{VB}(z)={\displaystyle \frac{b_0+b_1{z}^{-1}+b_2{z}^{-2}+b_3{z}^{-3}}{1+a_1{z}^{-1}+a_2{z}^{-2}+a_3{z}^{-3}}}$$

(25)

$$G_{vd}(s)={\displaystyle \frac{-V_{cell,i}[-Z_{cell,i}{(1-D_i)}^2+s{L}_i]}{{(1-D_i)}^2[Z_{cell,i}{(1-D_i)}^2+s{L}_i+C_i{L}_i{Z}_{cell,i}{s}^2]}}$$

(26)

$$G_{iT}(s)={\displaystyle \frac{2{\overline{I}}_i{R}_i+{\overline{V}}_{RC}}{C_{th}s+\frac{1}{R_{th}}}}$$

(27)

$$\left\{\begin{array}{c}{k}_{l,T}={\displaystyle \frac{\partial l_i}{\partial T_i}}\\ k_{l,SOC}={\displaystyle \frac{\partial l_i}{\partial SO{C}_i}}\end{array}\right.$$

(28)

$$\left\{\begin{array}{c}{K}_{\lambda V}=V_{bus,ref}\cdot ({\displaystyle \frac{1}{\Lambda }}-{\displaystyle \frac{l_i}{{\Lambda }^2}})\\ \Lambda ={\displaystyle \sum _{i=1}^N{l}_i{K}_{\lambda V}}=V_{bus,ref}\cdot ({\displaystyle \frac{1}{\Lambda }})\end{array}\right.$$

(29)

4. Simulation and Analysis of SOC–Thermal Balancing

To validate the effectiveness of the proposed control strategy for dynamic balancing of the SOC and temperature in lithium-ion batteries, a series of simulations were conducted using a bidirectional power converter based on Boost converters. These simulations were designed to emulate real-world charging and discharging conditions while actively regulating both SOC and thermal behavior.

4.1. Simulation Configuration and Parameters

This subsection describes the simulation setup used to validate the proposed electrothermal balancing control strategy. A custom simulation model was developed, incorporating the electrochemical and thermal dynamics of each cell, the bidirectional converter models, and the centralized controller with PSO-based weight optimization. The relevant battery parameters are summarized in

Table 1. Key parameters used in the simulations.

Parameter	Value	Parameter	Value
Qj	3400 mAh	Cj	47 μF
OCV	3.7 V	Dj	0.2–0.8
Vbus,ref	25 V–30 V	Cth	89.5 J/K
fs	100 kHz	h	5 W/(m2·K)
Lj	15 μH	A	0.004184 m2

, and internal resistance of the battery used for the simulation with the initial SOC value is shown in Figure 6. The initial SOC and internal resistance values were intentionally diversified to emulate real-world inconsistencies among cells, as also considered in previous works [19,20].

The simulation model considers a system composed of four series-connected lithium-ion cells, each with a nominal capacity of 3400 mAh and a typical open-circuit voltage (OCV) of 3.7 V. The pack is operated near a 1C discharge rate, representative of realistic electric vehicle or energy storage use cases. The main bus voltage is regulated to track a reference value of 30 V. To test the dynamic response of the controller, a disturbance is introduced at 1800 s in the form of a step reduction in the bus voltage reference to 20 V, which lasts for 10 min. This models sudden changes in load-side conditions and evaluates the robustness of the balancing and tracking strategy under voltage fluctuations.

To ensure stable operation in CCM, the inductor current ripple is selected as 40% of the average current, and the output voltage ripple is limited to 0.5%. Based on these constraints, the converter parameters are designed as shown in Table 1. All converters operate in CCM at a switching frequency of 100 kHz. The passive components for each converter include a 15 μH inductor and a 47 μF output capacitor. To prevent saturation and ensure safe operation, the duty cycle of each converter is constrained within the range of 0.2 to 0.8. The converters are controlled using duty cycle commands generated from the PSO-optimized electrothermal balancing algorithm, which assigns a reference voltage to each converter based on real-time SOC and temperature inputs. Moreover, to prioritize charge balancing while maintaining thermal safety, the weighting factors were empirically set as ${\gamma }_{SOC}=0.75,{\gamma }_T=0.25$. And the resulting Type 3 compensator was implemented in the form of a difference equation with the following coefficients: $b_0=0.1019$, $b_1=-0.0776$, $b_2=-0.1003$, $b_3=0.0776$, $a_1=0.0338$, $a_2=-0.7666$, and $a_3=-0.2672$.

Thermal dynamics of each cell are modeled using a lumped-parameter thermal network that accounts for both self-heating and heat exchange with the ambient environment. The effective thermal surface area of each cell is assumed to be 0.004184 m², and the thermal capacitance is set to 89.5 J/K. A convective heat transfer coefficient of 5 W/(m²·K) is used to model natural air cooling. The ambient temperature is fixed at 20 °C throughout the simulation.

4.2. Simulation Results

To evaluate the effectiveness of the proposed control approach, the SOC and temperature evolution of each cell over time were recorded. The key simulation waveforms are shown below.

As illustrated in Figure 7a, the evolution of the SOC for all four cells is presented over the entire simulation period. During the initial 500 s, the SOC values of the cells remain approximately at their initial levels, preserving the inherent imbalance introduced at the start of the experiment. No significant redistribution occurs in this phase, as the controller primarily operates in observation and initialization mode.

After 500 s, the balancing control is activated, and the SOC disparities begin to decrease gradually under the influence of the PSO-based optimization mechanism. By approximately 1600 s, the maximum SOC deviation among the cells is reduced and stabilized within a margin of ±0.0025, indicating effective dynamic equalization. However, following the imposed bus voltage disturbance at 1800 s, a temporary increase in SOC mismatch is observed. The deviation briefly rises to approximately ±0.005, reflecting the system’s transient adaptation to the altered voltage regulation conditions.

Subsequently, the controller re-establishes balance through adaptive voltage reassignment and converter-level current redistribution. By 2400 s, the SOC deviation is once again confined within ±0.0025, demonstrating full recovery of uniform charge distribution. These results validate the controller’s capacity to maintain high-precision SOC balancing even under variable bus conditions and system perturbations.

As shown in Figure 7b, the temperature responses of all four cells begin from a uniform initial condition of 20 °C. Although Battery 1 exhibits the highest internal resistance among the group, its temperature trajectory remains consistently in the mid-range throughout the discharge process. This behavior reflects the effectiveness of the proposed controller in dynamically reallocating power flow to suppress excessive thermal rise in higher-loss cells.

During the initial 1600 s of the experiment, the temperature difference among cells is tightly regulated, remaining within ±0.5 °C. This indicates strong thermal balancing performance under nominal bus voltage conditions. Between 1800 s and 2400 s, V_bus,ref is deliberately reduced to 20 V. As a result, the overall discharge power across all converters is lowered, leading to reduced heat generation. In this phase, the temperature divergence remains relatively minor, with a maximum deviation within ±0.7 °C.

However, once V_bus,ref is restored to 30 V after 2400 s, a rapid increase in both cell temperatures and inter-cell thermal spread is observed. By the end of the simulation, the maximum temperature difference rises to approximately ±1.5 °C, indicating a notable challenge for real-time thermal management in aged or low-SOC scenarios.

As illustrated in Figure 7c, the reference voltages assigned to each converter exhibit dynamic variations throughout the simulation, reflecting the combined influence of SOC imbalance, thermal deviation, and real-time bus voltage regulation. During the early and middle stages of the experiment (i.e., prior to 1800 s), heat generation within the cells remains limited. Under these conditions, the reference voltages are primarily governed by the initial SOC distribution. A clear positive correlation is observed between the assigned reference voltage and the corresponding cell’s SOC, with higher-SOC cells receiving larger voltage commands to facilitate faster discharge and promote charge equalization.

Following the deliberate reduction of the bus voltage reference at 1800 s, the reference voltages for all converters are adjusted downward to maintain compliance with the global voltage constraint. During this interval, V_ref,i of all converters converge to approximately 5 V, indicating uniformly reduced power transfer across the system. This behavior also contributes to the temporary suppression of temperature growth observed during this phase.

After V_bus,ref returns to 30 V, a more complex voltage distribution emerges. Notably, the reference voltage assigned to Converter 1 is significantly reduced to approximately 5.5 V, despite the corresponding cell not having the lowest SOC. This response is attributed to the elevated temperature of Battery 1 observed at that point in the experiment. The controller, in response to both electrochemical and thermal state inputs, intentionally suppresses power throughput through Converter 1 to mitigate further ohmic heating. This targeted adjustment demonstrates the controller’s capacity to incorporate thermal constraints into its balancing decisions, thereby achieving both charge uniformity and thermal safety.

4.3. Result Analysis and Discussion

The simulation results demonstrate the capability of the proposed control strategy to achieve dynamic SOC equalization while maintaining thermal safety within acceptable limits. The standard deviation of both SOC and temperature error vectors (${\mathit{M}}_{SOC}$ and ${\mathit{M}}_T$ according to (15)) could be observed throughout Figure 8: the SOC deviation $\sigma ({\mathit{M}}_{SOC})$ among cells gradually decreases over time under the influence of the PSO-based balancing controller. Starting from a deliberately imposed initial imbalance, the $\sigma ({\mathit{M}}_{SOC})$ is effectively reduced through coordinated redistribution of discharge power. By the end of the simulation, the maximum SOC deviation is confined to approximately 0.0007, indicating near-complete charge uniformity.

In contrast, the temperature deviation $\sigma ({\mathit{M}}_T)$ exhibits a progressive increase over the course of the experiment. This behavior is attributed to the cumulative thermal effects associated with continued current flow, as well as the nonlinear increase in internal resistance at lower SOC levels, particularly in the latter stages of discharge. Despite the controller’s thermal-aware regulation, which partially mitigates temperature divergence through adaptive reference voltage assignment, the system still experiences a gradual rise in thermal nonuniformity. At the conclusion of the simulation, the inter-cell temperature difference reaches 1.6 °C.

These trends confirm the effectiveness and limitations of the proposed strategy. On one hand, the controller successfully achieves high-precision SOC balancing, even in the presence of external disturbances and cell heterogeneity. On the other hand, thermal deviations, though bounded within safe operating limits, tend to accumulate over extended discharge durations, especially when electrochemical degradation (e.g., increased internal resistance) is present. This highlights the importance of integrating long-term thermal modeling and cell aging dynamics into future extensions of the balancing framework.

5. Conclusions

This paper proposed a unified electrothermal balancing control strategy for lithium-ion battery packs, aiming to simultaneously reduce SOC and temperature disparities among cells under dynamic operating conditions. A modular architecture with bi-directional DC-DC converters was employed to enable flexible energy redistribution, while a PSO-based adaptive optimization algorithm was integrated to dynamically adjust control weights based on real-time cell states. Simulation results demonstrated that the proposed method effectively minimizes SOC deviation to within 0.0007, while maintaining temperature differences within 1.6 °C, even in the presence of bus voltage disturbances and varying internal resistance.

The coordinated control of charge and thermal dynamics allows the system to enhance pack-level energy utilization and safety without requiring external thermal management systems. Moreover, the proposed strategy exhibits strong adaptability and robustness, making it suitable for real-time battery management in electric vehicles and energy storage applications.

In practical deployment scenarios, the proposed method has the potential to reduce system cost by eliminating dedicated thermal control hardware and minimizing overdesign margins. At the same time, the improved uniformity in SOC and temperature can enhance energy efficiency and significantly reduce the risk of localized overheating or degradation, thereby improving long-term operational safety. These characteristics highlight the method’s application value in cost-sensitive and safety-critical systems such as electric buses, large-scale grid storage, and second-life battery applications.