In this work, we propose a dynamic power optimization control method designed specifically for large-scale dynamic reconfigurable battery energy storage stations. The method explicitly accounts for the heterogeneous operating states and multi-dimensional dynamic boundary constraints of numerous energy storage units within the station. By establishing a comprehensive system operation and maintenance optimization model that integrates key factors such as degradation cost, temperature regulation cost, operation and maintenance cost, and state-of-charge balance of each energy storage cell, we aim to significantly improve the economic efficiency of the station while maintaining operational safety. The weights of these objectives are determined using a multivariate fixed-weight method based on fuzzy set theory. Simulation results demonstrate that the proposed method can reduce overall operating costs by 15.83% and improve the state-of-charge consistency by 33.3% compared to conventional strategies.
The dynamic reconfigurable battery system enables intrinsic safety through millisecond-scale topological reconfiguration of energy storage cells. However, the independent and real-time reconfiguration of each unit leads to diverse operating conditions and varying constraint boundaries among the massive number of energy storage cells in a large-scale station. This diversity significantly increases the operation and maintenance complexity and cost. Our proposed method addresses this challenge by dynamically adjusting the power output of each energy storage cell based on its real-time state and the updated constraints after each reconfiguration event.
Model Formulation
We consider a storage station composed of \(n\) independent energy storage cells. The total power command from the grid is denoted by \(P\). Each cell, indexed by \(i\), has its own state-of-charge \(S_i\), discharge efficiency \(\eta_i\), and dynamic power limits imposed by its reconfigurable battery network.
Operation and Maintenance Cost
The maintenance cost for all energy storage cells is expressed as:
$$
C_{\text{fix}} = T_c \sum_{i=1}^{n} K_i^f |P_i|
$$
where \(T_c\) is the scheduling period, \(P_i\) is the output power of the \(i\)-th energy storage cell, and \(K_i^f\) is the unit maintenance cost per kilowatt-hour. This cost accounts for the regular maintenance activities required for each energy storage cell.
Temperature Regulation Cost
The thermal management cost is derived from the heat generated by each energy storage cell. The total heat generation power consists of battery loss heat \(Q_b(i)\), converter loss heat \(Q_c(i)\), and heat conduction to the environment \(Q_{ev}(i)\). Using a bilinear approximation, we have:
$$
\begin{aligned}
Q_b(i) &= (1-\eta_1)(P_{\text{dis}} + P_{\text{cha}}) \\
Q_c(i) &= \left(\frac{1}{\eta_2}-1\right)|P_i|
\end{aligned}
$$
where \(\eta_1\) is the battery efficiency and \(\eta_2\) is the converter efficiency. The temperature regulation cost is then:
$$
C_{\text{tem}} = K \sum_{i=1}^{n} \frac{P_{\text{pri}} Q(i)}{|P_i|}
$$
with \(K\) being the conversion factor between thermal power and electric power (taken as 2.6), and \(P_{\text{pri}}\) the electricity price during the period. Proper thermal management ensures that every energy storage cell operates within its safe temperature range.
Battery Degradation Cost
The degradation of each energy storage cell depends on its depth of discharge and discharge rate. The degradation cost is modeled as:
$$
L_{\text{loss}}^i = T K_i^l \left(\frac{1}{\eta_i}-1\right) P_i
$$
where the degradation coefficient \(K_i^l\) is given by:
$$
K_i^l = k_l \left(\frac{C_a}{C_R}\right)^{-\alpha_1} + \left(\frac{M_a}{M_R}\right)^{-\alpha_2} e^{\alpha_1 – \alpha_2}
$$
with \(C_a\) and \(C_R\) being actual and rated capacity, \(M_a\) and \(M_R\) actual and rated depth of discharge, and \(\alpha_1, \alpha_2\) fitting coefficients (0.9 and 1.69 respectively). This term penalizes the aging of each energy storage cell, encouraging operation that prolongs its lifespan.
State-of-Charge Balance
After the power allocation, the state-of-charge of each energy storage cell is updated as:
$$
S_i^{\text{new}} = S_i – \frac{P_i T}{E_{\text{max}}}
$$
where \(E_{\text{max}}\) is the maximum energy capacity. The objective for SOC balance is to minimize the variance among all cells:
$$
f_{\text{SOC}} = \frac{1}{n} \sum_{i=1}^{n} \left(S_i^{\text{new}} – S_{\text{avg}}\right)^2
$$
where \(S_{\text{avg}}\) is the average SOC after the scheduling period. A lower variance indicates better consistency among energy storage cells, which enhances overall system reliability and available capacity.
Multi‑Objective Optimization and Constraints
The overall objective function is a weighted sum of the four components:
$$
F = \omega_1 C_{\text{fix}} + \omega_2 C_{\text{tem}} + \omega_3 \sum_{i=1}^{n} L_{\text{loss}}^i + \omega_4 f_{\text{SOC}}
$$
The weights are determined using a multivariate fixed-weight method based on fuzzy set theory. The qualitative ranking matrix for the four objectives (maintenance, temperature, degradation, SOC balance) is constructed, and after normalization, the weights are:
| Objective | Weight \(\omega\) |
|---|---|
| Operation & Maintenance Cost | 0.2727 |
| Temperature Regulation Cost | 0.2727 |
| Battery Degradation Cost | 0.2727 |
| SOC Balance | 0.1819 |
The following constraints are imposed:
- Power limits of each energy storage cell: \(P_{\min} \le P_i \le P_{\max}\) (updated after each reconfiguration).
- SOC safety thresholds: \(S_{\min} \le S_i(t) \le S_{\max}\).
- Total power balance: \(\sum_{i=1}^{n} P_i = P\).
- Dynamic reconfiguration constraint: the maximum output power of each cell is dynamically determined by the topology, i.e., \(P_{\max} = V_{\text{dc}} I_{\text{dc max}} \eta_{\text{PCS}}\), where \(V_{\text{dc}} = M V_B\) and \(I_{\text{dc max}} = n_i I_B\).
These constraints ensure that every energy storage cell operates within its safe and feasible region, while the reconfigurable battery network continuously reshapes the achievable power boundaries.
Solution Algorithm
We employ an improved particle swarm optimization algorithm to solve the multi-objective optimization problem. The fitness function is directly the weighted objective \(F\). The algorithm incorporates adaptive inertia weight and learning factors:
$$
\begin{aligned}
\omega &= \omega_{\max} – (\omega_{\max} – \omega_{\min}) \frac{t}{t_{\max}} \\
c_1 = c_2 &= c_{\max} – (c_{\max} – c_{\min}) \frac{t}{t_{\max}}
\end{aligned}
$$
with \(\omega_{\max}=0.9\), \(\omega_{\min}=0.7\), \(c_{\max}=1.5\), \(c_{\min}=1.0\). The iterative process updates particle positions and velocities, and constraints are enforced by adjusting infeasible solutions. The algorithm converges within 20 iterations, and the average computation time per scheduling period is about 0.2-0.3 seconds, well within the typical reconfiguration cycle of the dynamic battery network.
Simulation Results
We simulate a storage station with six independent energy storage cells. The initial parameters are listed below:
| Parameter | Cell 1 | Cell 2 | Cell 3 | Cell 4 | Cell 5 | Cell 6 |
|---|---|---|---|---|---|---|
| Initial SOC (%) | 85 | 80 | 88 | 75 | 78 | 82 |
| Depth of Discharge (%) | 80 | 80 | 80 | 75 | 75 | 75 |
| Discharge Efficiency (%) | 85 | 85 | 85 | 85 | 85 | 85 |
| DC Voltage (V) | 800 | 800 | 800 | 750 | 750 | 750 |
The total power command is set to 100 kW for a duration of 2 hours. We compare three strategies: the proposed dynamic optimization, conventional equal power sharing, and an SOC-imbalance-based method from literature. The power distribution results are:
| Strategy | Cell1 (kW) | Cell2 (kW) | Cell3 (kW) | Cell4 (kW) | Cell5 (kW) | Cell6 (kW) |
|---|---|---|---|---|---|---|
| Equal Sharing | 16.67 | 16.67 | 16.67 | 16.67 | 16.67 | 16.67 |
| Imbalance‑based Method | 23.54 | 13.11 | 27.75 | 8.00 | 10.14 | 17.47 |
| Proposed Method | 13.91 | 16.87 | 15.04 | 12.20 | 16.53 | 15.45 |
After the scheduling period, the SOC variance is calculated. The equal sharing method yields a variance of 0.186%, the imbalance-based method reduces it to 0.119%, while the proposed method achieves only 0.057% — a 33.3% improvement over the imbalance-based method. Furthermore, the total operating cost over 1000 scheduling cycles is compared:
| Strategy | Total Cost (10⁴ CNY) |
|---|---|
| Equal Sharing | 92.24 |
| Imbalance‑based Method | 87.79 |
| Proposed Method | 77.17 |
The proposed method reduces total cost by 15.83% compared to equal sharing. The dynamic reconfiguration feature was further tested with a scenario involving 10 energy storage cells, some with limited capacity. The proposed method avoids overloading and reduces cost by 17.9% compared to the fixed-boundary equal sharing with overload protection.
The illustration above depicts a typical energy storage cell configuration used in our experiments. The integration of dynamic reconfiguration with the proposed optimization ensures that each energy storage cell operates within its dynamically updated limits, contributing to overall station efficiency and safety.
Conclusion
We have developed a dynamic power regulation method tailored for large-scale dynamic reconfigurable battery energy storage stations. By explicitly modeling the heterogeneous states and dynamic constraints of each energy storage cell, and optimizing a weighted sum of maintenance cost, temperature regulation cost, degradation cost, and SOC balance, the method achieves significant improvements in both economic efficiency and state consistency. Simulation results confirm a 15.83% reduction in total operational cost and a 33.3% enhancement in SOC balance. The approach is computationally efficient and adaptable to both steady-state and transient conditions, making it suitable for practical deployment in modern storage stations.