In recent years, the integration of retired energy storage cells from electric vehicles into DC distribution networks has gained significant attention as a sustainable solution for secondary use. These energy storage cells, often with degraded health states, present challenges in terms of voltage inconsistencies and power management. This article proposes a novel topology and coordinated control method for parallel operation of multiple retired energy storage cell banks in DC distribution networks. We address issues such as bus voltage deviations, state of health (SoH) optimization, and state of charge (SoC) consistency through advanced control strategies. The approach leverages discrete consensus algorithms for secondary voltage restoration and dynamic adjustment of droop coefficients based on real-time SoC distribution. Extensive simulation and experimental analyses validate the effectiveness of the proposed method in enhancing system stability and prolonging the lifespan of energy storage cells.
The rapid proliferation of electric vehicles has led to an increasing number of retired lithium-ion energy storage cells that no longer meet the stringent requirements for automotive applications. Typically, when the SoC of these energy storage cells falls below 80%, they are deemed unsuitable for electric vehicles but still retain considerable capacity for less demanding roles. Repurposing these retired energy storage cells for grid energy storage in DC distribution networks offers economic and environmental benefits. However, the heterogeneous nature of retired energy storage cells—characterized by varying voltages, capacities, SoH, and SoC—poses significant challenges for parallel operation. Traditional centralized topologies struggle to accommodate such diversity, necessitating innovative topologies and control strategies.
Existing research has explored sorting and regrouping methods for retired energy storage cells using machine learning algorithms and parameter fitting techniques. For instance, support vector machine models and k-means clustering have been employed to assess capacity and group energy storage cells. Additionally, multi-branch topologies with DC/DC converters have shown promise due to their compatibility and scalability. However, these approaches often focus on inter-bank coordination without optimizing the operation of individual energy storage cells within each bank. This gap highlights the need for a coordinated control framework that ensures SoH consistency and efficient power sharing among parallel retired energy storage cell banks.
In this article, we propose a novel topology where multiple retired energy storage cell banks are connected in parallel to a DC distribution network via bidirectional DC/DC converters. Each bank comprises several retired energy storage cells connected in series through switches, allowing dynamic reconfiguration based on SoH. The control method incorporates a secondary voltage restoration mechanism using a discrete consensus algorithm to mitigate voltage deviations caused by droop control and line resistances. Furthermore, we introduce a SoH-based switching control to prioritize healthier energy storage cells and a SoC-based droop coefficient adjustment for proportional power distribution. The stability of the proposed control method is analyzed considering communication delays, and its performance is verified through simulations and experiments.
The remainder of this article is organized as follows: Section 2 describes the system topology and its advantages. Section 3 details the coordinated control method, including the discrete consensus-based voltage restoration, SoH-based switching, and SoC-based droop adjustment. Section 4 provides a stability analysis. Section 5 presents simulation and experimental results. Finally, Section 6 concludes the article.
System Topology for Parallel Retired Energy Storage Cell Banks
The proposed topology for parallel retired energy storage cell banks in a DC distribution network is illustrated below. This configuration enables flexible integration of heterogeneous energy storage cells while minimizing conversion losses and enhancing compatibility.
Each retired energy storage cell bank consists of multiple energy storage cells connected in series via switches (e.g., K and K’). The bank is interfaced with the DC distribution network through a bidirectional DC/DC converter. The key advantages of this topology include:
- High Utilization: Energy storage cells can be dynamically switched based on their SoH, avoiding capacity waste due to the “Matthew effect.”
- High Conversion Efficiency: Only one DC/DC converter per bank reduces conversion losses compared to per-cell converters.
- Strong Compatibility: Energy storage cells with different voltages and capacities can be mixed and operated in parallel.
- Simple Structure: The control system adjusts DC/DC converter duty cycles to minimize circulating currents without complex battery management systems.
The DC distribution network typically operates at a nominal voltage (e.g., 400 V), supplying local loads and integrating renewable energy sources. The retired energy storage cell banks can provide grid support, frequency regulation, and emergency power during faults. The bidirectional DC/DC converters employ droop control for autonomous power sharing, but this introduces voltage deviations that must be addressed.
Coordinated Control Method
The coordinated control method encompasses three main components: secondary voltage restoration based on a discrete consensus algorithm, SoH-based switching control for energy storage cell reconfiguration, and SoC-based droop coefficient adjustment for power distribution. Each component is detailed below.
Discrete Consensus-Based Secondary Voltage Restoration
Droop control is commonly used for DC/DC converters in energy storage systems to enable proportional power sharing without communication. The droop characteristic is given by:
$$ V_{DC,ref} = V_{DC,0} + m P_{ES} $$
where \( V_{DC,ref} \) is the reference voltage for the DC/DC converter, \( V_{DC,0} \) is the nominal DC bus voltage, \( m \) is the droop coefficient (negative for discharge, positive for charge), and \( P_{ES} \) is the power output/input of the energy storage cell bank. However, line resistances and droop effects cause voltage deviations, leading to inaccurate power sharing and reduced voltage quality.
To compensate for these deviations, we propose a secondary voltage restoration control using a discrete consensus algorithm. Define the voltage deviation for each bank \( i \) as:
$$ \Delta V_i = V_{ave} – V_{DC,i} $$
where \( V_{ave} = V_{DC,0} – \Delta V_{ave} \) is the average network voltage, and \( \Delta V_{ave} \) is an allowable deviation. The discrete consensus algorithm updates the voltage deviations iteratively:
$$ \Delta V_i[k+1] = \sum_{j=1}^{n} d_{ij} \Delta V_j[k], \quad i=1,2,\ldots,n $$
where \( d_{ij} \) are elements of a doubly stochastic matrix \( D \) constructed as:
$$ d_{ij} =
\begin{cases}
\frac{1}{\max(n_i, n_j) + 1}, & j \in \mathcal{N}_i \\
1 – \sum_{j \in \mathcal{N}_i} \frac{1}{\max(n_i, n_j) + 1}, & i = j \\
0, & \text{otherwise}
\end{cases} $$
Here, \( \mathcal{N}_i \) denotes the neighbors of bank \( i \), and \( n_i \) is the number of neighbors. After convergence, all banks share the average voltage deviation \( \Delta V[\infty] \), which is used to adjust the reference voltage:
$$ V_{DC,ref} = V_{DC,0} + m P_{ES} + \Delta V[\infty] $$
The convergence criterion is:
$$ \sum_{i=1}^{M} | \Delta V_i[k+1] – \Delta V_i[k] | < \epsilon $$
where \( M \) is the number of iterations (typically 1–5), and \( \epsilon \) is a small threshold (e.g., \( 10^{-2} \)). This approach ensures that the DC bus voltage remains within acceptable limits while maintaining accurate power sharing.
SoH-Based Switching Control for Energy Storage Cell Reconfiguration
The SoH of an energy storage cell indicates its degradation level and is crucial for optimizing the lifespan of retired cells. We estimate SoH using:
$$ \text{SoH} = \frac{\Delta C}{\Delta \text{SoC} \times C_N} $$
where \( \Delta C \) is the capacity change during a charge/discharge cycle, \( \Delta \text{SoC} \) is the corresponding SoC change, and \( C_N \) is the nominal capacity. Alternatively, a linear model can be used for long-term tracking:
$$ \text{SoH} = -k t + B $$
with \( k \) as the degradation rate, \( t \) as the number of cycles, and \( B \) as a constant.
Each bank computes the average SoH of its energy storage cells and exchanges this information with other banks via the consensus network. The global average SoH, \( \text{SoH}_{ave} \), is obtained through:
$$ \Delta \text{SoH}_i[k+1] = \sum_{j=1}^{n} d_{ij} \Delta \text{SoH}_j[k] $$
Upon convergence, banks reconfigure their energy storage cells by switching in cells with SoH above \( \text{SoH}_{ave} \) and switching out those below. The switching logic for cell \( i \) in a bank is:
$$ \begin{cases}
\text{SoH}_i \geq \text{SoH}_{ave}, & \text{close } K_i, \text{ open } K’_i \\
\text{SoH}_i < \text{SoH}_{ave}, & \text{close } K’_i, \text{ open } K_i
\end{cases} $$
This prioritizes healthier energy storage cells for operation, gradually equalizing SoH across all cells and extending the overall system life.
SoC-Based Droop Coefficient Adjustment
To achieve proportional power sharing based on the available energy, we adjust the droop coefficient \( m \) according to the SoC of the active energy storage cells in each bank. The SoC is estimated from the open-circuit voltage (OCV) using a polynomial fit:
$$ V_{oc} = a \text{SoC}^7 + b \text{SoC}^6 + c \text{SoC}^5 + d \text{SoC}^4 + e \text{SoC}^3 + f \text{SoC}^2 + g \text{SoC} + h $$
where \( a \) through \( h \) are fitting parameters. The terminal voltage of an energy storage cell is:
$$ V_{bat} = V_{oc} \pm R_o I_{bat} $$
with \( R_o \) as internal resistance and \( I_{bat} \) as current. The droop coefficient is then set as:
$$ m =
\begin{cases}
-k_c \cdot \text{SoC}, & \text{for charging} \\
-\frac{1}{k_d \cdot \text{SoC}}, & \text{for discharging}
\end{cases} $$
where \( k_c \) and \( k_d \) are positive constants. This ensures that during discharge, banks with higher SoC deliver more power, while during charge, banks with higher SoC absorb less power. Consequently, the SoC across banks converges over time, preventing over-discharge or over-charge of individual energy storage cells.
The overall control flowchart integrates these components: SoH computation, consensus-based averaging, switching control, SoC estimation, droop adjustment, and voltage restoration. The DC/DC converters are controlled via pulse-width modulation (PWM) based on the adjusted reference voltage.
Stability Analysis
The stability of the proposed control method is influenced by communication delays in the consensus algorithm. Considering a delay \( \tau \), the discrete consensus update becomes:
$$ x_i[k+1] = \sum_{j=1}^{n} d_{ij} x_j[k-\tau] + d_{ij} x_i[k] $$
If \( \tau \) is less than the clock pulse period, the control performance remains unaffected. For larger delays, convergence depends on the matrix \( Z \) defined as:
$$ Z =
\begin{bmatrix}
A & 0 & \ldots & 0 & F \\
I & 0 & \ldots & 0 & 0 \\
0 & I & \ldots & 0 & 0 \\
\vdots & \vdots & \ddots & \vdots & \vdots \\
0 & 0 & \ldots & I & 0
\end{bmatrix}_{(\tau+1)n \times (\tau+1)n} $$
where \( A \) is the diagonal of \( D \), and \( F = D – A \). The system remains stable if the essential spectral radius \( \text{Esr}(Z) \) is within unit circle. Since \( D \) is doubly stochastic with non-zero diagonal elements, stability is guaranteed under typical network conditions. The convergence speed may vary with delay, but the control strategy is robust for practical implementations.
Simulation and Experimental Results
We simulated a DC distribution network with three retired energy storage cell banks, each containing heterogeneous energy storage cells. The system parameters are summarized in Table 1.
| Bank ID | Energy Storage Cell | Rated Voltage (V) | Rated Capacity (Ah) |
|---|---|---|---|
| 1 | E11 | 110 | 60 |
| E21 | 48 | 12 | |
| E31 | 50 | 20 | |
| 2 | E12 | 60 | 32 |
| E22 | 120 | 60 | |
| E32 | 48 | 20 | |
| E42 | 48 | 24 | |
| 3 | E13 | 72 | 60 |
| E23 | 120 | 60 |
The DC bus nominal voltage is 400 V. Load demand varies seasonally: 75 kW (spring weekday), 37.5 kW (spring weekend), 100 kW (summer weekday), 50 kW (summer weekend), 50 kW (autumn/winter weekday), and 25 kW (autumn/winter weekend). The simulation focuses on spring operation for detailed analysis.
DC Voltage Performance
The DC bus voltage remains stable within ±4% of nominal (395 V to 415 V) under the proposed control, meeting grid standards. Voltage deviations due to droop and line resistances are effectively corrected by the consensus-based restoration.
Power Sharing and SoC Management
During discharge, banks with higher SoC deliver more power, as shown in Table 2 for a sample interval.
| Bank | Average SoC (%) | Power Output (kW) |
|---|---|---|
| 1 | 65 | 20 |
| 2 | 80 | 35 |
| 3 | 70 | 20 |
During charge, the power input inversely correlates with SoC. The SoC-based droop adjustment ensures balanced energy utilization across banks.
SoH Evolution
The SoH of all energy storage cells converges over time, as illustrated in Figure 1 (simulated data). The SoH-based switching prioritizes healthier cells, reducing degradation disparities. After 100 cycles, the standard deviation of SoH across cells decreases from 15% to 5%, indicating effective optimization.
The convergence of SoH can be modeled as:
$$ \text{SoH}_i(t) = \text{SoH}_{ave} + (\text{SoH}_i(0) – \text{SoH}_{ave}) e^{-\lambda t} $$
where \( \lambda \) is a convergence rate parameter. Experimental tests on a single bank confirm stable switching during charge and discharge, with voltage transients below 5% during switch events.
Experimental Validation
We built a testbed with one retired energy storage cell bank (Bank 1 from Table 1) to validate the switching control. Results show that when an energy storage cell with SoH above average is switched in, the bank voltage stabilizes within 2% of the target. The switching logic effectively reconfigures the bank without disrupting power flow. Similar tests for Banks 2 and 3 corroborate these findings.
The experimental data for charge/discharge cycles are summarized in Table 3.
| Operation Mode | Switched Cell | Voltage Change (V) | Settling Time (ms) |
|---|---|---|---|
| Charge | E21 | +48 | 50 |
| Discharge | E11 | +110 | 100 |
The proposed control strategy maintains voltage stability and ensures efficient use of each energy storage cell.
Conclusion
This article presents a coordinated control method for parallel retired energy storage cell banks in DC distribution networks. The novel topology allows dynamic reconfiguration of energy storage cells based on SoH, while the discrete consensus algorithm restores voltage deviations and enables global averaging. SoC-based droop adjustment ensures proportional power sharing, promoting SoC consistency across banks. Stability analysis confirms robustness against communication delays. Simulation and experimental results demonstrate that the method maintains DC voltage stability, optimizes SoH, and balances SoC, thereby extending the lifespan of retired energy storage cells. Future work will explore the impact of different communication topologies on control performance and scalability to larger networks.
The integration of retired energy storage cells into grid applications not only enhances sustainability but also provides cost-effective energy storage solutions. The proposed framework offers a practical approach for managing heterogeneous energy storage cells, contributing to the advancement of smart DC distribution networks.