In modern DC microgrids, the integration of renewable energy sources and constant power loads introduces significant challenges in maintaining bus voltage stability and ensuring the state-of-charge (SOC) consistency among distributed energy storage units. To address these issues, we propose a hierarchical control framework for hybrid battery energy storage systems (HBESS) that combines a primary voltage regulation layer with a secondary dynamic power distribution layer. Our approach is particularly designed for heterogeneous battery types—such as lithium-ion and sodium-ion cells—with different capacities, efficiencies, and dynamic characteristics. The primary controller employs a nonsmooth control law augmented with a nonlinear disturbance observer to robustly stabilize the DC bus voltage under large load variations, including constant power loads. The secondary controller implements a novel dynamic SOC balancing strategy that not only drives all energy storage units to a uniform SOC but also adapts to plug-and-play operations, ensuring that the balancing speed is adjustable. Both simulation and experimental results validate the effectiveness of our method in achieving fast voltage recovery and SOC equalization under various operating scenarios, including load step changes and unit connection/disconnection events.
Battery energy storage systems (BESS) play a pivotal role in smoothing renewable energy fluctuations and improving power quality in DC microgrids. However, the inherent variability in battery aging, temperature, and chemistry leads to SOC mismatches among parallel-connected units. Traditional droop-based methods often fail to achieve simultaneous voltage regulation and SOC balancing, especially in the presence of constant power loads (CPLs) that exhibit negative incremental impedance. Our proposed hybrid battery energy storage systems (HBESS) architecture exploits the complementary strengths of different battery technologies—lithium-ion for high energy density and sodium-ion for safety and cost—while mitigating the limitations of each. The dynamic SOC balancing control strategy we design enables the system to adaptively compute a consensus point, which dynamically shifts based on the current SOC distribution, and then adjusts the droop coefficients of each converter in real time. This ensures that all energy storage units reach the same SOC before the charging or discharging limits are encountered, regardless of their initial SOC or capacity.
System Modeling and Problem Formulation
We consider a single-bus autonomous DC microgrid operating in islanded mode, where all renewable sources are aggregated as constant power sources (CPSs), and the load comprises both resistive and constant power loads (CPLs). The HBESS consists of N battery energy storage units (ESUs), each interfaced to the DC bus via a bidirectional DC-DC converter. The schematic of the system is depicted in the following figure.
The average state-space model of the i-th converter is given by:
$$
L_i \dot{i}_{Li} = E_i – (1-d_i) v_{Ci}, \quad C_i \dot{v}_{Ci} = (1-d_i) i_{Li} – \frac{P_i}{v_{Ci}} – \frac{v_{Ci}}{R_{0i}}
$$
where $E_i$ is the low-side battery voltage, $L_i$ and $C_i$ are the inductor and capacitor values, $d_i$ is the duty cycle, and $P_i$ denotes the net constant power absorbed by the i-th ESU from the bus. The load includes both resistive and constant power components; we model the lumped CPL as $P_{\text{CPL}} – P_{\text{CPS}}$, where $P_{\text{CPL}}$ and $P_{\text{CPS}}$ are the total constant power consumption and generation, respectively.
To facilitate linearization-based control design, we apply a feedback linearization transformation. Define the state variables as $x_{1,i} = 0.5 L_i i_{Li}^2 + 0.5 C_i v_{Ci}^2$ and $x_{2,i} = E_i i_{Li} – v_{Ci}^2 / R_i$. The transformed model becomes:
$$
\dot{x}_{1,i} = x_{2,i} + \zeta_{1,i}, \quad \dot{x}_{2,i} = u_i + \zeta_{2,i}
$$
where $\zeta_{1,i}$ and $\zeta_{2,i}$ represent lumped uncertainties and disturbances, and $u_i$ is a virtual control input. The actual duty cycle $d_i$ can be recovered from $u_i$ via algebraic relations.
For SOC estimation, we adopt the coulomb-counting (ampere-hour integration) method:
$$
\text{SOC}_i(t) = \text{SOC}_i(0) – \frac{\eta_i}{Q_{\text{Wh},i}} \int_0^t E_i I_i \, d\tau
$$
where $\eta_i$ is the Coulombic efficiency, $Q_{\text{Wh},i}$ is the energy capacity in watt-hours, and $I_i$ is the battery current. The lithium-ion and sodium-ion batteries exhibit different efficiencies: $\eta_{\text{Li}} = 0.95$, $\eta_{\text{Na}} = 0.92$ in our experiments.
Dual-Layer Control Design
Our control architecture consists of two layers that interact through droop-based reference voltage generation. The primary layer (Layer-1) aims to track the reference voltage $v_{ref}$ using a nonsmooth controller combined with a nonlinear disturbance observer (NDO) to reject uncertainties. The secondary layer (Layer-2) dynamically adjusts the droop coefficients to enforce SOC balancing among all ESUs, even under plug-and-play conditions.
Primary Voltage Control
The NDO estimates the uncertain terms $\zeta_{1,i}$ and $\zeta_{2,i}$ as:
$$
\dot{p}_1 = -l_1 (x_{1,i} – \hat{x}_{1,i} – p_1), \quad \hat{\zeta}_{1,i} = p_1 + l_1 x_{1,i}
$$
$$
\dot{p}_2 = -l_2 (x_{2,i} – \hat{x}_{2,i} – p_2), \quad \hat{\zeta}_{2,i} = p_2 + l_2 x_{2,i}
$$
with observer gains $l_1 = 500$, $l_2 = 200$. The reference states are defined as:
$$
x_{1,r,i} = 0.5 L_i i_{Li}^2 + 0.5 C_i v_{ref}^2, \quad x_{2,r,i} = \dot{x}_{1,r,i} – \hat{\zeta}_{1,i}, \quad x_{3,r,i} = \dot{x}_{2,r,i} – \hat{\zeta}_{2,i}
$$
Then the nonsmooth control law is:
$$
v_i = -k_1 \lfloor e_{1,i} \rceil^{\alpha_1} – k_2 \lfloor e_{2,i} \rceil^{\alpha_2}, \quad u_i = v_i + x_{3,r,i}
$$
where $e_{1,i} = x_{1,i} – x_{1,r,i}$, $e_{2,i} = (x_{2,i} – x_{2,r,i})/\lambda$, $\alpha_1 = \alpha$, $\alpha_2 = 2\alpha/(1+\alpha)$ with $\alpha \in (-0.5,0)$, and coefficients $k_1=8$, $k_2=16$, $\lambda = 1000$. This controller ensures finite-time convergence and inherent robustness against CPL instability.
Secondary SOC Balancing Control
The secondary layer calculates a droop coefficient $m_i$ for each converter that depends on both the unit’s current SOC and the average remaining capacity estimated via consensus. The overall reference voltage for the i-th ESU is:
$$
v_{ref,i} = V^* – m_i P_i
$$
where $V^*$ is the nominal bus voltage (100 V) and $P_i$ is the output power of the i-th unit. To account for different battery capacities and types, we first compute a base droop gain $\phi_i$ such that $\phi_i / Q_{\text{Wh},i} = \text{constant}$ across all units. The total equivalent droop is then:
$$
\frac{1}{m_{\text{eq}}} = \sum_{i=1}^N \frac{1}{\phi_i} \quad \Rightarrow \quad \phi_i = \frac{\Delta V_{\text{max}}}{\sum \phi_i^{-1}} \cdot \frac{1}{P_{\text{rating}}}
$$
We employ a nonsmooth average consensus algorithm to estimate the global average remaining capacity $\hat{\theta}_i$:
$$
\dot{\theta}_i = -\gamma \sum_{j=1}^N \left[ \beta \right] \left( \theta_i – \theta_j \right) – \boldsymbol{\Theta} \sigma_i, \quad \hat{\theta}_i = \theta_i + \sigma_i
$$
where $\theta_i$ is the distance from the current SOC to the consensus point (CP):
$$
\theta_i =
\begin{cases}
\text{SOC}_i – \text{CP}, & \text{discharge mode} \\
\text{CP} – \text{SOC}_i, & \text{charge mode}
\end{cases}
$$
Finally, the droop coefficient for the i-th unit is:
$$
m_i = \frac{\phi_i}{\eta_i} \left( \frac{\hat{\theta}_i}{\theta_i} \right)^2
$$
This formulation makes the droop inversely proportional to the square of the relative remaining capacity, thereby accelerating the SOC convergence among battery energy storage systems.
Dynamic Consensus Point Generation
The consensus point (CP) is not fixed but dynamically adjusted according to the current SOC distribution and plug-and-play events. The logic is as follows:
- If $\max(\text{SOC}_i) – \min(\text{SOC}_i) > \Delta\overline{\text{SOC}}$ (upper threshold, e.g., $10^{-1}$), then set $\text{CP} = \min(\text{SOC}_i) – \chi$, where $\chi$ is a small step (e.g., 10).
- If $\max(\text{SOC}_i) – \min(\text{SOC}_i) \le \Delta\underline{\text{SOC}}$ (lower threshold, e.g., $10^{-5}$), then set $\text{CP} = \underline{\text{SOC}}$ (discharge limit) or $\overline{\text{SOC}}$ (charge limit) to lock the balance.
- When a new unit is plugged in, the CP immediately shifts to $\min(\text{SOC}_i) – \chi$ if the spread exceeds the upper threshold.
- When a unit is unplugged, the same rule is applied to the remaining units.
This dynamic CP strategy ensures that battery energy storage systems achieve SOC equalization before reaching the safety limits, and it seamlessly supports plug-and-play without manual reconfiguration.
Simulation Results
We simulated a four-unit HBESS in MATLAB/Simulink with parameters listed in the table below. The lithium-ion battery packs have capacities of 5 Ah, 10 Ah, 15 Ah, while the sodium-ion pack is 20 Ah. All nominal voltages are 48 V.
| Parameter | Value |
|---|---|
| Nominal bus voltage $V^*$ | 100 V |
| Converter capacitors $C_i$ | 1100 $\mu$F |
| Inductors $L_i$ | 1 mH |
| Switching frequency | 20 kHz |
| Li-ion capacities (units 1–3) | 5, 10, 15 Ah |
| Na-ion capacity (unit 4) | 20 Ah |
| Coulombic efficiencies | Li: 0.95, Na: 0.92 |
| NDO gains $l_1,l_2$ | 500, 200 |
| Controller coefficients $\alpha,\beta,\Theta,\gamma,\lambda$ | −0.3, −0.6, 10, 1, 1000 |
| Hurwitz coefficients $k_1,k_2$ | 8, 16 |
| SOC thresholds $\Delta\overline{\text{SOC}}, \Delta\underline{\text{SOC}}$ | $10^{-1}, 10^{-5}$ |
| CP step $\chi$ | 10 |
Voltage Regulation Under CPL Variations
We compared our proposed controller with a conventional PI-based dual-loop controller. Three step increases in CPL power were applied: 600 W → 900 W → 1400 W → 2000 W. Our controller maintained the bus voltage within 0.5% of 100 V, whereas the PI controller exhibited voltage drops of up to 3% and longer settling times (over 0.5 s). The NDO effectively compensated for the disturbances, enabling rapid recovery.
SOC Balancing Speed Enhancement
Three ESUs (units 1–3) started with SOCs of 71%, 70%, and 69% in discharge mode (CPL=1000 W). Without the dynamic CP strategy, the SOCs converged after 522 seconds. With the dynamic strategy (CP = Min(SOC)-10 initially), the three units reached uniformity in only 80 seconds—a speed improvement of more than six times. The balancing acceleration is due to the aggressive droop adjustment near the consensus point.
Plug-and-Play Performance in Discharge Mode
We tested the scenario where units are connected/disconnected while the remaining units are still balancing. Initially, units 1–3 operate with SOCs 71%, 70%, 69%, and CP set to 68%. At t=100 s, unit 4 (SOC=67%) is connected. The CP immediately moves to 66% and the four units equalize at t=240 s. Then at t=250 s, unit 4 is disconnected; the CP recalculates and the three remaining units reach uniformity again by t=305 s. Throughout the process, the bus voltage remained stable, and the SOC spread never exceeded 2%. Similar results were obtained when connecting/disconnecting after the units had already balanced.
Experimental Verification
We built a laboratory-scale HBESS consisting of four 48 V battery packs (three lithium-ion of 5/10/15 Ah and one sodium-ion of 20 Ah) interfaced through boost converters to a 100 V DC bus. The controllers were implemented on a dSPACE 1202 platform with a 1/60 s communication delay emulated for the consensus algorithm. A Chroma DC electronic load acted as CPL. Real-time data were acquired and displayed via Control Desk.
Figures below show the experimental results for discharge mode (CPL=600 W). In the first test (Fig. A), unit 4 was connected at t=107 s when the three existing units had SOCs 71%, 70%, 69%. The CP jumped from 68% to 66%, and all four units converged by t=240 s. At t=308 s, unit 4 was disconnected, and the remaining three units regained balance by t=380 s. In the second test (Fig. B), the three units had already balanced (SOC ~68%) before unit 4 was inserted at t=211 s. After connection, the CP moved to 66%, and the four units eventually balanced at t=395 s. Subsequent disconnection at t=422 s caused the three units to re-balance at t=493 s. In all cases, the SOC difference remained within 0.5% after each transient, confirming the effectiveness of our dynamic SOC balancing control strategy for hybrid battery energy storage systems.
Conclusion
In this work, we developed a hierarchical control scheme for DC microgrids equipped with hybrid battery energy storage systems. The primary layer, using a nonsmooth controller with a disturbance observer, ensures fast and robust voltage tracking despite constant power loads. The secondary layer implements a dynamic SOC equalization strategy that adapts the droop coefficients based on a moving consensus point, which is continuously updated to reflect the current SOC distribution and plug-and-play events. Both simulation and experimental results demonstrate that our approach significantly accelerates SOC convergence among heterogeneous battery energy storage units, reduces voltage deviations, and seamlessly accommodates unit connection and disconnection. Future work will focus on incorporating power constraints of different battery chemistries into the CP selection algorithm to further enhance safety and performance.