In modern active distribution networks, the integration of energy storage systems has become crucial for enhancing grid stability, promoting renewable energy adoption, and optimizing power flow. However, the diverse operational demands pose significant challenges in balancing economic dispatch and real-time flexible control of energy storage cells. This paper addresses these challenges by proposing a novel two-layer distributed energy negotiation management strategy for energy storage cells, leveraging ring communication topology to achieve synchronization and consistency in state-of-charge (SOC) across groups and individual cells. The strategy ensures optimal economic performance while maintaining operational flexibility, making it suitable for dynamic grid environments.
The core of this approach lies in its hierarchical structure: the upper layer employs ring-based communication for group-level SOC synchronization through fixed-point iteration, while the lower layer utilizes a dual-mode balanced circuit to enforce SOC consistency within individual energy storage cells. By analyzing cost factors and applying Lagrangian duality, the strategy derives optimal negotiation characteristics, which are validated through simulations on the IEEE 33 system. The results demonstrate improved cost efficiency, reduced latency, and enhanced control precision compared to conventional methods.
Energy storage cells play a pivotal role in mitigating power fluctuations and supporting grid resilience. However, uncoordinated usage can accelerate degradation and increase operational costs. To address this, we first examine the key cost components associated with energy storage cells, including investment, degradation, and online operation costs. The investment cost for energy storage cells encompasses procurement and construction expenses, modeled as:
$$D = \sum_{n=1}^{N} [k_n E_{n,\text{max}} + a_n (P_{n,\text{max}})^2 + b_n P_{n,\text{max}}] + \sum_{n=1}^{N} (d_n T_{n,\text{pro}} + \text{cost}_{n,\text{fix}})$$
where $E_{n,\text{max}}$ and $P_{n,\text{max}}$ denote the maximum capacity and power of the energy storage cell group $n$, respectively, and $k_n$, $a_n$, $b_n$, $d_n$, $T_{n,\text{pro}}$, and $\text{cost}_{n,\text{fix}}$ are cost coefficients. Degradation cost, reflecting the health state (SOH) reduction over time, is expressed as:
$$R = \sum_{n=1}^{N} Q_n (\text{SOH}_{n,0} – \text{SOH}_{n,T})$$
with $Q_n$ representing the unit degradation cost. Online operation cost, accounting for energy transactions during peak and off-peak periods, is given by:
$$C = \sum_{t=1}^{T} C_t \left( \sum_{k=1}^{K} l_{k,t} + \sum_{m=1}^{M} g_{m,t} + \sum_{n=1}^{N} P_{n,t} \right)$$
where $C_t$ is the electricity pricing function, $l_{k,t}$ and $g_{m,t}$ are load and generation powers, and $P_{n,t}$ is the charge/discharge power of energy storage cell group $n$. The overall objective function minimizes a weighted sum of these costs:
$$F = \mu_1 D + \mu_2 R + \mu_3 C$$
subject to constraints on capacity, power, and SOH limits for each energy storage cell. To derive the optimal negotiation characteristics, we apply Lagrangian duality, formulating the Lagrangian function as:
$$L = \sum_{t=1}^{T} C_t \left( \sum_{k=1}^{K} l_{k,t} + \sum_{m=1}^{M} g_{m,t} + \sum_{n=1}^{N} P_{n,t} \right) + \sum_{n=1}^{N} \sum_{t=1}^{T} \lambda_{n,t} (E_{n,\text{up}} \text{SOC}_{n,t} – E_{n,\text{up}}) + \sum_{n=1}^{N} \sum_{t=1}^{T} \nu_{n,t} (E_{n,\text{low}} – E_{n,\text{up}} \text{SOC}_{n,t}) + \sum_{n=1}^{N} \sum_{t=1}^{T} \xi_{n,t} (P_{n,t} – P_{n,\text{dis}}) + \sum_{n=1}^{N} \sum_{t=1}^{T} \eta_{n,t} (P_{n,\text{char}} – P_{n,t})$$
where $\lambda_{n,t}$, $\nu_{n,t}$, $\xi_{n,t}$, and $\eta_{n,t}$ are Lagrange multipliers. The KKT conditions reveal that for optimality, all energy storage cells must synchronize their SOC increments simultaneously, ensuring efficient negotiation. This insight guides the design of the two-layer management strategy.
The upper layer employs a ring communication topology, where each energy storage cell group exchanges SOC increment information unidirectionally. The SOC increment for group $n$ at time $t$ is defined as $\gamma_{n,t} = \text{SOC}_{n,t+1} – \text{SOC}_{n,t}$. The negotiation update rule is:
$$\gamma_{1,t}^{\tau+1} = \gamma_{1,t}^* + a_{N,1} (\gamma_{N,t}^{\tau} – \gamma_{1,t}^{\tau})$$
$$\gamma_{n,t}^{\tau+1} = \gamma_{n,t}^{\tau} + a_{n-1,n} (\gamma_{n-1,t}^{\tau} – \gamma_{n,t}^{\tau}) \quad \forall n \neq 1$$
where $\tau$ is the iteration index, $\gamma_{n,t}^*$ is the steady-state command for group 1, and $a_{n-1,n}$ is a control parameter. The power command for each energy storage cell group is derived as:
$$P_{n,t}^{\tau+1} = \left( E_{n,\text{up}} \gamma_{n,t}^{\tau+1} \right)^{1/\alpha_n}$$
This process converges to a state where all groups achieve identical SOC increments, with convergence speed dependent on the maximum capacity ratio. The ring communication ensures low latency and robustness, with average delays around 4 seconds in simulations.
The lower layer focuses on maintaining SOC consistency within each energy storage cell group using a dual-mode balanced circuit. This circuit facilitates active energy transfer between cells via inductive storage and switching matrices. During charging, the circuit operates in Boost-Buck mode to discharge high-SOC cells and charge low-SOC ones; during discharging, it switches to Buck mode. The control logic alternates between charging and discharging modes to accelerate convergence and reduce capacity demands on the balancing source. The SOC dynamics for individual energy storage cells are modeled as:
$$\text{SOC}_{n,i,t+1} = \text{SOC}_{n,i,t} + \frac{1}{E_{n,\text{up}}} P_{n,i,t}^{\alpha_{n,i}}$$
$$\text{SOH}_{n,i,t+1} = \text{SOH}_{n,i,t} – \beta_{n,i} \exp(\psi_{n,i} |P_{n,i,t}| – \theta_{n,i}) – \phi_{n,i,1} \frac{P_{n,i,t}^{\alpha_{n,i}}}{E_{n,\text{up}}} – \phi_{n,i,2} – \sigma_{n,i,1} \exp[-\sigma_{n,i,2} (\sigma_{n,i,3} |P_{n,i,t}|)^{-1}]$$
where $i$ denotes the individual cell within group $n$, and $\alpha_{n,i}$, $\beta_{n,i}$, $\psi_{n,i}$, $\theta_{n,i}$, $\phi_{n,i,1}$, $\phi_{n,i,2}$, $\sigma_{n,i,1}$, $\sigma_{n,i,2}$, and $\sigma_{n,i,3}$ are cell-specific parameters. The balanced circuit enables rapid SOC equalization, reducing maximum SOC differences from 18% to 0.2% within 600–760 seconds in tests.
To validate the strategy, simulations were conducted on an IEEE 33-node system with 10 energy storage cell groups, each comprising 4 cells. The parameters for these energy storage cells are summarized in Table 1, highlighting variations in capacity and degradation coefficients.
| Group | $E_{n,\text{up}}$ (kWh) | $\alpha_n$ | $\beta_n$ | $\psi_n$ | $\theta_n$ | $\sigma_{n,1}$ (×10⁻⁴) | $\sigma_{n,2}$ | $\sigma_{n,3}$ | $\phi_{n,1}$ (×10⁻³) | $\phi_{n,2}$ (×10⁻⁸) |
|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 350 | 1.15 | 31.6 | 0.02 | 19.3 | 1.97 | -80.7 | 0.1 | -5 | 2.05 |
| 2 | 385 | 1.15 | 31.8 | 0.02 | 20.9 | 2.01 | -79.2 | 0.1 | -5 | 2.12 |
| 3 | 425 | 1.15 | 30.3 | 0.02 | 20.9 | 2.01 | -80.0 | 0.1 | -5 | 2.08 |
| 4 | 465 | 1.15 | 31.8 | 0.02 | 19.9 | 1.96 | -80.5 | 0.1 | -5 | 2.08 |
| 5 | 515 | 1.15 | 31.2 | 0.02 | 20.6 | 1.96 | -81.1 | 0.1 | -5 | 2.13 |
| 6 | 565 | 1.15 | 30.2 | 0.02 | 19.2 | 1.99 | -81.3 | 0.1 | -5 | 2.04 |
| 7 | 620 | 1.15 | 30.6 | 0.02 | 19.8 | 2.04 | -80.1 | 0.1 | -5 | 2.11 |
| 8 | 685 | 1.15 | 31.1 | 0.02 | 20.8 | 1.98 | -78.9 | 0.1 | -5 | 2.11 |
| 9 | 750 | 1.15 | 31.9 | 0.02 | 20.5 | 2.00 | -78.9 | 0.1 | -5 | 2.05 |
| 10 | 825 | 1.15 | 31.9 | 0.02 | 20.9 | 1.97 | -79.2 | 0.1 | -5 | 2.08 |
In charging scenarios, with total commands of 200 kW and 800 kW, the ring negotiation achieved power distributions satisfying $P_m / P_n = (E_{m,\text{up}} / E_{n,\text{up}})^{1/\alpha}$, as shown in Table 2 for charging and Table 3 for discharging operations. The average communication delay was approximately 4 seconds, enabling swift adjustments.
| Time (s) | Group 1 (kW) | Group 2 (kW) | Group 3 (kW) | Group 4 (kW) | Group 5 (kW) | Group 6 (kW) | Group 7 (kW) | Group 8 (kW) | Group 9 (kW) | Group 10 (kW) |
|---|---|---|---|---|---|---|---|---|---|---|
| 0–110 | -13.4 | -14.6 | -15.8 | -17.2 | -18.7 | -20.3 | -22.1 | -23.9 | -26.1 | -28.3 |
| 110–600 | -52.9 | -57.5 | -63.2 | -67.9 | -74.6 | -80.1 | -87.0 | -94.5 | -102.7 | -111.6 |
| Time (s) | Group 1 (kW) | Group 2 (kW) | Group 3 (kW) | Group 4 (kW) | Group 5 (kW) | Group 6 (kW) | Group 7 (kW) | Group 8 (kW) | Group 9 (kW) | Group 10 (kW) |
|---|---|---|---|---|---|---|---|---|---|---|
| 0–110 | 13.1 | 14.2 | 15.5 | 16.9 | 18.3 | 20.0 | 21.7 | 23.1 | 25.7 | 27.9 |
| 110–600 | 53.6 | 58.2 | 63.2 | 67.9 | 74.6 | 81.1 | 88.1 | 94.5 | 102.7 | 111.6 |
For intra-group consistency, alternating charge-discharge commands were applied, reducing SOC disparities efficiently. The dual-mode circuit demonstrated robustness, with convergence times under 800 seconds for both scenarios. Economic benefits were evaluated using real load data from a distribution network, comparing the proposed strategy (Scheme 2) against an empirical method (Scheme 1) and an optimization-based approach (Scheme 3). The results, summarized in Table 4, show that Scheme 2 reduced daily costs by $2,609 in spring and $4,173 in autumn, while minimizing power gradient squares $\delta = \sum_{t=1}^{T-1} (p_{t+1} – p_t)^2$, indicating smoother load profiles.
| Scenario | Scheme | 24-hour Cost ($) | Gradient Square $\delta$ (×10⁶) |
|---|---|---|---|
| Spring | Original Load | 108,513 | 2.86 |
| Scheme 1 | 107,680 | 2.61 | |
| Scheme 2 | 105,904 | 2.49 | |
| Scheme 3 | 105,829 | 2.69 | |
| Autumn | Original Load | 171,835 | 5.93 |
| Scheme 1 | 170,743 | 6.27 | |
| Scheme 2 | 167,662 | 6.00 | |
| Scheme 3 | 168,519 | 6.23 |
The proposed two-layer strategy effectively balances economic dispatch and real-time control for energy storage cells, achieving synchronization and consistency with low latency. Future work could explore market dynamics and enhanced communication topologies to further improve robustness. This approach underscores the potential of distributed negotiation in optimizing energy storage cell utilization within active distribution networks.