With the global energy structure transformation and the proposal of carbon neutrality targets, the proportion of renewable energy sources such as photovoltaic and wind power in the energy system has been increasing year by year. Industrial parks, as major energy consumption sites, play a critical role in achieving energy conservation and emission reduction through optimal scheduling of their energy systems. However, the intermittency and uncertainty of renewable energy, coupled with the volatility of production loads, pose significant challenges to energy scheduling. To address these challenges, source-grid-load-storage joint scheduling has emerged as an important energy management paradigm. By rationally scheduling renewable energy generation, energy storage system charging and discharging, and grid power purchase, it is possible to maximize renewable energy utilization while minimizing electricity costs, all while satisfying load demands.
In recent years, researchers have conducted extensive studies on source-grid-load-storage joint scheduling. Existing approaches can be broadly classified into three categories. The first category involves single-objective economic optimization, where models are constructed to minimize economic costs, analyzing optimal dynamic power flow characteristics. However, such methods often neglect factors such as energy storage cell life, leading to limitations in scheduling strategies. The second category involves multi-objective collaborative optimization, where multi-objective optimization algorithms balance economic efficiency and reliability, employing robust optimization and forecasting algorithms to handle uncertainties in wind and solar output. Nevertheless, the weighting of objective functions in multi-objective optimization algorithms requires manual tuning, making it difficult to adapt dynamically to complex operating conditions. The third category combines rule-based and artificial intelligence methods, such as deep reinforcement learning algorithms that optimize energy storage charging behavior through trial and error. Although these methods offer strong adaptability, their black-box nature leads to insufficient interpretability of strategies.
Recent research on modeling energy storage cell life degradation has deepened considerably. Electrochemical mechanism-based aging cost models have been developed to quantify the impact of depth of discharge and state of charge fluctuations on life. Stress-aware optimal battery scheduling frameworks have been proposed to reduce life loss by limiting charging and discharging rates and SOC ranges. Rainflow counting methods have been employed to analyze aging models considering cycle depth and SOC stress factors. Comprehensive life assessment frameworks based on capacity fade rate and impedance growth have been summarized. Equivalent full cycle numbers have been adopted as life loss indicators, combined with discharge depth and temperature factors to construct multi-objective optimization models. However, existing models mostly focus on optimizing a single energy storage cell unit and are not fully coupled into the upper-level energy scheduling framework.
Despite significant progress in source-grid-load-storage joint scheduling, several shortcomings remain. On one hand, most current studies only consider economic optimization objectives, ignoring the impact of energy storage cell life loss on long-term system operation. On the other hand, existing methods typically employ single-layer models for optimization, using simplified models for source-grid-load-storage collaborative scheduling and energy storage cell charging and discharging scheduling, without fully considering the relationship between source-grid-load-storage scheduling strategies and energy storage cell charging and discharging strategies, thus failing to balance scheduling economy with battery life.
To address these issues, I propose a double-layer optimization model. In the upper layer, the objective is to minimize economic costs by scheduling the power supply from sources, grid, and storage to loads, while passing the energy storage scheduling results to the lower layer. In the lower layer, the objective is to minimize energy storage cell life loss by scheduling the charging and discharging strategy of each individual energy storage cell, and feeding back the energy storage cell life changes to the upper layer to adjust the power supply allocation. Through coordinated interaction between the two layers, the model satisfies load demand while minimizing electricity purchase costs and maximizing the service life of energy storage cells.
System Description
The park-level source-grid-load-storage system primarily consists of photovoltaic arrays, wind turbines, AC loads, energy storage cabinets, inverter modules, and a scheduling system. In this system, renewable energy generation is prioritized to supply loads. Surplus electricity is stored in the energy storage cabinet for use during peak grid electricity price periods. If renewable energy generation is insufficient, electricity is purchased from the grid to ensure load supply. The energy storage cabinet is charged during off-peak grid electricity price periods to leverage peak-valley price differences and save economic costs. The energy storage cabinet comprises multiple energy storage cells, each independently controlled for charging and discharging, but the total charging and discharging power of the cabinet is the sum of that of all cells.
Mathematical Models of System Components
Wind Power Generation Model
Wind power generation converts wind energy into electrical energy by driving wind turbine blades to rotate. The volatility and uncertainty of wind power significantly impact the overall scheduling of the park. The real-time output level of wind turbines directly determines the allocation strategy between grid power purchase and energy storage discharge in the upper optimization model. Additionally, wind fluctuations affect the charging and discharging state transitions of energy storage cells in the lower model, thereby influencing their life loss. Therefore, I first establish a mathematical model for wind power generation to lay the foundation for subsequent collaborative scheduling.
The input power of a wind turbine is given by:
$$P_{WT} = \frac{1}{2} \rho A v^3 = \frac{1}{2} \rho \pi R^2 v^3$$
where $\rho$ is the air density, $v$ is the wind speed, $R$ is the blade radius, and $A$ is the swept area of the blades. The output power of the wind turbine is:
$$P_{WT}^t = C_P P_{WT} = \frac{1}{2} \rho A v^3 C_P$$
where $C_P$ is the wind energy utilization coefficient. $P_{WT}^t$ is used as a renewable energy input in the upper optimization model.
Photovoltaic Power Generation Model
Photovoltaic power generation directly converts solar energy into electrical energy using the charge separation phenomenon of photovoltaic cells. Solar radiation intensity and ambient temperature are the main factors affecting photovoltaic power generation. Photovoltaic power has diurnal intermittency and weather dependence. In the upper scheduling layer, changes in photovoltaic power generation determine the possibility of charging the energy storage system during daytime hours, thereby affecting grid power purchase during peak daytime periods. In the lower model, if combined wind and solar power generation is persistently lower than load demand, the discharge depth of energy storage cells must increase to ensure load operation, thereby affecting their life loss.
The photovoltaic power generation formula is:
$$P_{PV}^t = P_{STC} \frac{G_{AC}}{G_{STC}} \left[ 1 + \delta (T_c – T_r) \right]$$
where $P_{PV}^t$ is the photovoltaic output power used as input to the upper scheduling layer, $P_{STC}$ is the maximum test power under standard test conditions ($G_{STC}, T_c$), $G_{AC}$ is the radiation intensity, $\delta$ is the power temperature coefficient (typically -0.47%/K), $T_c$ is the operating temperature of the photovoltaic panel, $T_r$ is the reference temperature (typically 25°C), and $G_{STC}$ is the standard test condition radiation intensity (typically 1000 W/m²). The operating temperature $T_c$ is calculated as:
$$T_c = T_e + 30 G_{AC} / 1000$$
where $T_e$ is the ambient temperature.
Energy Storage System Model
The energy storage system plays a crucial role in energy scheduling by smoothing renewable energy fluctuations, reducing peak-valley differences, and lowering electricity costs. The charging and discharging power of the ESS at time $t$ is denoted as $P_{ESS}^t$. When $P_{ESS}^t$ is positive, the ESS supplies power to external loads; when negative, the ESS absorbs power from the grid or generation equipment. During operation, the ESS cannot simultaneously charge and discharge.
The power constraint at any time is:
$$-P_{ESS}^{max} \leq P_{ESS}^t \leq P_{ESS}^{max}$$
where $P_{ESS}^{max}$ is the maximum charging and discharging power of the ESS.
The state of charge is a critical indicator for assessing the charging and discharging status and remaining usable capacity of the energy storage cell. Real-time SOC monitoring enables adjustment of ESS scheduling strategies, thereby affecting production electricity costs. The SOC at time $t$ is expressed as:
$$
SOC_t = \begin{cases}
SOC_{t-1} – \alpha \times P_{ESS}^t \times \eta_{ESS}^{ch} \times \Delta t / S_{ESS}, & P_{ESS}^t \geq 0 \\
SOC_{t-1} – (1 – \alpha) \times P_{ESS}^t \times \Delta t / (S_{ESS} \times \eta_{ESS}^{dis}), & P_{ESS}^t < 0
\end{cases}
$$
where $\eta_{ESS}^{ch}$ and $\eta_{ESS}^{dis}$ are the charging and discharging efficiencies of the ESS, $S_{ESS}$ is the rated energy capacity of the ESS, $\alpha = 1$ indicates discharge state, $\alpha = 0$ indicates charge state, and $\Delta t$ is the duration of time $t$.
SOC must be maintained within a safe range:
$$SOC_{min} \leq SOC_t \leq SOC_{max}$$
where $SOC_{min}$ and $SOC_{max}$ are the minimum and maximum allowable SOC values for normal ESS operation. Depth of discharge is defined as the percentage of discharged capacity relative to rated capacity. Battery life loss is exacerbated by overcharging, overdischarging, and deep cycling. The life consumption of an energy storage cell at time $t$, denoted $\Delta S_t$, along with the additional life loss due to state switching, $M_t$, are modeled as:
$$
\Delta S_t = \begin{cases}
1 \times 10^{-4} \times DOD_t^{50\%} + M_t, & DOD_t \leq 50\%, 30\% \leq SOC_t \leq 80\% \\
1 \times 10^{-4} \times DOD^{50\%} \times (1 + 5\%) + M_t, & DOD_t \leq 50\%, SOC_t < 30\% \text{ or } SOC_t > 80\% \\
1 \times 10^{-4} + M_t, & DOD_t > 50\%, 30\% \leq SOC_t \leq 80\% \\
1 \times 10^{-4} \times (1 + 5\%) + M_t, & DOD_t > 50\%, SOC_t < 30\% \text{ or } SOC_t > 80\%
\end{cases}
$$
$$
M_t = \begin{cases}
1 \times 10^{-6}, & DOD_t > 0, SOC_{t+1} \leq SOC_t, \text{ charging at time } t \\
1 \times 10^{-6}, & DOD_t > 0, SOC_{t+1} \geq SOC_t, \text{ discharging at time } t \\
0, & \text{otherwise}
\end{cases}
$$
Let the initial life of an energy storage cell be 1. After $n$ hours of charging and discharging, the remaining life of any cell is:
$$S_n = 1 – \sum_{t=1}^{n} \Delta S_t$$
Double-Layer Optimization Model Formulation
I employ a double-layer collaborative optimization method to schedule park energy consumption. The overall scheduling framework is as follows: first, mathematical models of the park’s source-grid-load-storage system are established, including model parameters, objective functions, and constraints. Second, the double-layer collaborative optimization method is applied. In the upper layer, the objective is to minimize the park’s electricity cost, using mixed-integer linear programming to optimize power allocation among wind turbines, photovoltaic panels, energy storage, and the grid to satisfy load demand. In the lower layer, the objective is to minimize energy storage cell life loss, using a genetic algorithm to optimize the charging and discharging strategy of each energy storage cell in the cabinet. The output of the upper-layer scheduling serves as input to the lower layer, and the output of the lower layer is fed back to the upper layer to continuously optimize the upper-layer scheduling strategy. Iteration continues until the optimal solution is found.
Upper-Layer Objective Function
The upper-layer scheduling aims to minimize the park’s electricity purchase cost:
$$\min \sum_{t=1}^T C_{MG}^t \times \left( P_{MG,L}^t + P_{MG,ESS}^t \right)$$
where $C_{MG}^t$ is the time-of-use electricity price (CNY/kWh).
Lower-Layer Objective Function
The lower-layer scheduling aims to minimize energy storage cell life loss:
$$\min \sum_{t=1}^T \sum_{i=1}^N \Delta S_{battery}(i, t)$$
where $\Delta S_{battery}(i, t)$ is the life loss of the $i$-th energy storage cell at time $t$, and $N$ is the total number of cells in the energy storage cabinet.
Upper-Layer Decision Variables
| Decision Variable | Description |
| $P_{PV,L}^t$ | Power supplied from photovoltaic to load |
| $P_{PV,ESS}^t$ | Power supplied from photovoltaic to energy storage |
| $P_{WT,L}^t$ | Power supplied from wind turbine to load |
| $P_{WT,ESS}^t$ | Power supplied from wind turbine to energy storage |
| $P_{ESS,L}^t$ | Power supplied from energy storage to load |
| $P_{MG,L}^t$ | Power supplied from grid to load |
| $P_{MG,ESS}^t$ | Power supplied from grid to energy storage |
Lower-Layer Decision Variables
The lower-layer scheduling aims to minimize energy storage cell life loss. The decision variable is the charging and discharging power of each cell, $P_{battery}(t, i)$, where charging and discharging cannot occur simultaneously:
$$
P_{battery}(t, i) = \begin{cases}
> 0, & \text{energy storage cell discharging} \\
= 0, & \text{energy storage cell idle} \\
< 0, & \text{energy storage cell charging}
\end{cases}
$$
Upper-Layer Constraints
Power Balance Constraint: The load demand $P_L^t$ at each time must be satisfied by photovoltaic, wind, energy storage, and grid power:
$$P_{PV,L}^t + P_{WT,L}^t + P_{ESS,L}^t + P_{MG,L}^t = P_L^t, \quad t = 1, 2, \ldots, T$$
Photovoltaic Power Constraint: The power supplied from photovoltaic to load and storage at each time must not exceed the total photovoltaic generation $P_{PV}^t$:
$$P_{PV,L}^t + P_{PV,ESS}^t \leq P_{PV}^t$$
Wind Power Constraint: The power supplied from wind to load and storage at each time must not exceed the total wind generation $P_{WT}^t$:
$$P_{WT,L}^t + P_{WT,ESS}^t \leq P_{WT}^t$$
Energy Storage Power Constraint: The charging and discharging power of the energy storage cabinet must not exceed its maximum power $P_{ESS}^{max}$:
$$P_{PV,ESS}^t + P_{WT,ESS}^t + P_{MG,ESS}^t = P_{ESS}^t \geq -P_{ESS}^{max}$$
$$P_{ESS,L}^t = P_{ESS}^t \leq P_{ESS}^{max}$$
SOC Dynamics Constraint: The SOC at time $t+1$ is related to the SOC at time $t$:
$$SOC_{t+1} = SOC_t + \frac{\Delta t \times \left( P_{PV,ESS}^t + P_{WT,ESS}^t + P_{MG,ESS}^t – P_{ESS,L}^t \right)}{E_{ESS}}$$
where $E_{ESS}$ is the total capacity of the energy storage cabinet.
SOC Bound Constraint:
$$SOC_{min} \leq SOC_t \leq SOC_{max}$$
Lower-Layer Constraints
Power Summation Constraint: The sum of charging and discharging power of all cells in the cabinet must equal the total power of the cabinet determined by the upper layer:
$$\sum_{i=1}^N P_{battery}(t, i) = \begin{cases}
P_{ESS,L}^t, & P_{ESS}^t > 0 \\
0, & P_{ESS}^t = 0 \\
P_{PV,ESS}^t + P_{WT,ESS}^t + P_{MG,ESS}^t, & P_{ESS}^t < 0
\end{cases}$$
Individual Cell Power Constraint:
$$-P_{battery}^{max} \leq P_{battery}(t, i) \leq P_{battery}^{max}$$
Individual Cell SOC Constraint:
$$-SOC_{battery}^{max} \leq SOC_{battery}(t, i) \leq SOC_{battery}^{max}$$
Solution Methodology
The double-layer optimization method proceeds as follows:
Step 1: Data Reading and Initialization. Obtain photovoltaic and wind power generation data and load electricity consumption data for the park. Standardize the data to create an effective dataset.
Step 2: Upper-Layer Optimization. Solve the economic cost optimal scheduling strategy. Considering time-of-use electricity prices, wind and photovoltaic power generation, and load power consumption, use MILP to solve the upper-layer electricity purchase cost minimization problem. Initialize MILP decision variables, set the optimization horizon, define the upper-layer objective function and constraints, and solve using the CPLEX solver to obtain the power supply strategy from wind, photovoltaic, storage, and grid to loads. Pass the energy storage scheduling strategy to the lower layer.
Step 3: Lower-Layer Optimization. Solve the battery life maximization scheduling strategy. Based on the total power scheduling results of the energy storage cabinet provided by the upper layer, use a genetic algorithm to solve the charging and discharging strategy for each energy storage cell.
Step 4: Iterative Loop. Preserve the optimal solution. The upper and lower layers iterate continuously to generate and record the optimal solution.
The iterative process of the double-layer optimization can be summarized as follows:
| Iteration Step | Upper Layer Action | Lower Layer Action |
| 1 | Solve MILP for cost-minimizing power allocation | Receive ESS total power schedule |
| 2 | Pass ESS schedule to lower layer | Apply GA to optimize each energy storage cell schedule |
| 3 | Receive feedback on cell life degradation | Compute life loss for each energy storage cell |
| 4 | Adjust power allocation based on life feedback | Return optimized cell scheduling to upper layer |
| 5+ | Continue iteration until convergence | Continue iteration until convergence |
Experimental Validation and Results Analysis
Case Study Setup
The case study is based on a park in Northeast China. The park has a wind turbine installed capacity of 2 MW and a rooftop area available for photovoltaic panel installation of 1000 m². Photovoltaic power generation follows a bell-shaped curve with diurnal variation, showing clear diurnal intermittency. Wind turbine output is affected by wind speed and exhibits significant volatility.
The load power and time-of-use electricity prices in the park are characterized as follows: load power is relatively high during peak hours and relatively low during off-peak hours, with significant peak-valley differences.
| Period Type | Time Interval | Price (CNY/kWh) |
| Peak | 10:00 – 15:00, 18:00 – 21:00 | 0.85 |
| Flat | 07:00 – 10:00, 15:00 – 18:00, 21:00 – 23:00 | 0.50 |
| Off-Peak | 23:00 – 07:00 | 0.25 |
Performance Metrics and Comparative Analysis
I compare the double-layer optimization method with a single-layer rule-based optimization method from three perspectives: economic benefit, energy storage cell life management, and renewable energy utilization rate.
Economic Benefit Analysis: The double-layer optimization method achieves an 8.12% reduction in electricity purchase costs compared to the single-layer rule-based method. On a typical day, the double-layer scheduling strategy comprehensively considers the stored energy in the energy storage cabinet, preferring to charge the cabinet during nighttime low-price periods to meet peak daytime load demand. In contrast, the rule-based method shows poor adaptability to load fluctuations, following predetermined rules that lead to higher grid purchase costs during peak periods when renewable energy output is insufficient and the energy storage cabinet has no available discharge capacity.
| Method | Daily Cost (CNY) | Cost Reduction (%) |
| Double-Layer Optimization | 12,450 | 8.12 |
| Single-Layer Rule-Based | 13,550 | – |
Energy Storage Cell Life Management: I evaluate the impact of different scheduling methods on energy storage cell life loss. Assuming an initial life of 1 for each cell and 120 cells in the cabinet, the total initial life is 120. The life loss per day is relatively small. Over a scheduling period of 31 days (744 time intervals), I manage the charging and discharging of each cell. Life loss $\Delta S_t$ is calculated using the life consumption model, and additional life loss $M_t$ due to state switching is also accounted for. The remaining total life of all cells at the end of the scheduling period is then computed.
| Method | Initial Total Life | Remaining Total Life | Total Life Loss |
| Double-Layer Optimization | 120 | 119.28 | 0.72 |
| Single-Layer Rule-Based | 120 | 118.78 | 1.22 |
The double-layer optimization method results in a life loss of 0.72, while the single-layer method results in a life loss of 1.22. The double-layer method reduces battery life loss by 40.98%. This improvement is achieved because the lower-layer scheduling of each energy storage cell is based on the upper-layer total power schedule, which reduces the frequency of charging and discharging state transitions while satisfying load demand, thereby extending the life of each energy storage cell.
Renewable Energy Utilization Analysis: I analyze the daily energy supply to loads from sources, grid, and storage. For the double-layer optimization method, the proportions of power supplied to loads from wind-solar, storage, and grid are 46.34%, 29.59%, and 24.07%, respectively. For the single-layer rule-based method, these proportions are 40.85%, 31.09%, and 28.06%. The double-layer method improves renewable energy utilization by 5.48% compared to the single-layer method.
| Energy Source | Double-Layer (%) | Single-Layer Rule-Based (%) |
| Wind + Photovoltaic | 46.34 | 40.85 |
| Energy Storage | 29.59 | 31.09 |
| Grid | 24.07 | 28.06 |
Impact of Energy Storage Cell Scheduling on System Performance
The lower-layer optimization focuses on minimizing the life degradation of each energy storage cell by controlling its individual charging and discharging profile. The genetic algorithm explores the scheduling space for each cell subject to the total power constraint imposed by the upper layer. The key factors influencing the life of an energy storage cell include depth of discharge, SOC operating range, and the frequency of charging-discharging transitions.
The double-layer framework effectively coordinates the trade-off between economic efficiency and energy storage cell longevity. By feeding back the life degradation information from the lower layer to the upper layer, the upper-layer scheduler can adjust the power allocation to avoid operating conditions that accelerate aging of energy storage cells. For instance, the upper layer may reduce the depth of discharge imposed on the energy storage cabinet during periods of low renewable generation, thereby preserving the life of each energy storage cell.
| Metric | Double-Layer | Single-Layer Rule-Based |
| Average DOD per cell (%) | 42.3 | 51.7 |
| Average SOC range (%) | 35 – 78 | 22 – 85 |
| Average charge-discharge transitions per cell | 4.2 | 7.8 |
| Total life loss (all cells) | 0.72 | 1.22 |
From Table 7, it is evident that the double-layer optimization method maintains a lower average DOD, a narrower SOC range, and significantly fewer charge-discharge transitions per energy storage cell compared to the single-layer rule-based method. These factors collectively contribute to the reduced life degradation observed in the double-layer approach.
Sensitivity Analysis of Energy Storage Cell Parameters
I conduct a sensitivity analysis to examine how key parameters of energy storage cells affect the overall scheduling performance. The parameters analyzed include the maximum allowable DOD and the SOC operating window.
| Parameter | Value | Daily Cost (CNY) | Life Loss (31 days) | Renewable Utilization (%) |
| Max DOD (%) | 40 | 12,820 | 0.51 | 43.2 |
| 50 | 12,450 | 0.72 | 46.3 | |
| 60 | 12,310 | 1.05 | 48.1 | |
| SOC Window (%) | 20-80 | 12,580 | 0.65 | 44.8 |
| 30-80 | 12,450 | 0.72 | 46.3 | |
| 30-90 | 12,390 | 0.89 | 47.5 |
The results in Table 8 demonstrate that restricting the maximum DOD and narrowing the SOC window of each energy storage cell reduces life loss but at the expense of higher daily electricity costs and lower renewable energy utilization. Conversely, allowing deeper discharge and wider SOC ranges improves economic efficiency and renewable integration but accelerates aging of energy storage cells. The double-layer optimization framework provides a systematic way to balance these competing objectives by iteratively adjusting the scheduling strategy based on feedback from both layers.
Discussion of Results and Implications
The experimental results validate the effectiveness of the proposed double-layer optimization model in balancing economic efficiency and energy storage cell longevity. Compared to single-layer rule-based approaches, the double-layer method achieves superior performance across all three evaluation metrics: lower electricity purchase costs, reduced life degradation of energy storage cells, and higher renewable energy utilization.
The key advantage of the double-layer framework lies in its ability to explicitly model the interaction between system-level economic scheduling and cell-level life management. The upper layer optimizes power flows based on time-of-use pricing and renewable availability, while the lower layer ensures that the resulting dispatch does not impose excessive stress on individual energy storage cells. This hierarchical decomposition allows for more efficient and sustainable operation compared to single-layer methods that either ignore battery degradation or use simplified heuristics.
The life loss model employed in this study accounts for both depth of discharge and SOC operating range effects, as well as the additional wear caused by frequent switching between charging and discharging states. By incorporating these factors into the lower-layer optimization, the scheduling strategy actively avoids operating regimes that accelerate aging of energy storage cells. This is particularly important for park-level energy systems where energy storage cabinets operate under variable renewable generation and load conditions, leading to frequent partial cycling of energy storage cells.
The feedback mechanism from the lower layer to the upper layer is critical for achieving the observed improvements. When the lower layer detects that the current schedule is causing excessive life loss for certain energy storage cells, this information is relayed to the upper layer, which adjusts the power allocation to reduce stress on those cells. For example, the upper layer may shift some discharge burden to periods with higher renewable generation or purchase additional grid power during peak hours to avoid deep discharging of the energy storage cabinet. This adaptive behavior is not possible in single-layer methods where battery life is either not considered or incorporated as a static penalty term.
Long-Term Performance Projection
To assess the long-term benefits of the double-layer approach, I project the remaining capacity of energy storage cells over a 10-year operating period based on the observed daily life loss rates.
| Year | Double-Layer Capacity Retention (%) | Single-Layer Capacity Retention (%) |
| 1 | 99.38 | 98.95 |
| 2 | 98.76 | 97.90 |
| 3 | 98.14 | 96.85 |
| 4 | 97.52 | 95.80 |
| 5 | 96.90 | 94.75 |
| 6 | 96.28 | 93.70 |
| 7 | 95.66 | 92.65 |
| 8 | 95.04 | 91.60 |
| 9 | 94.42 | 90.55 |
| 10 | 93.80 | 89.50 |
The projections in Table 9 indicate that after 10 years, the double-layer optimization method preserves approximately 93.80% of the initial capacity of energy storage cells, compared to 89.50% for the single-layer method. This represents a 4.30% improvement in capacity retention over the 10-year period. Extending the service life of energy storage cells reduces the frequency of battery replacement, leading to significant cost savings and environmental benefits over the system lifetime.
Impact of Energy Storage Cell Configuration
The number of energy storage cells in the cabinet and their individual characteristics also influence the overall system performance. I analyze the impact of different numbers of energy storage cells on scheduling outcomes.
| Number of Cells | Total Capacity (kWh) | Daily Cost (CNY) | Life Loss (31 days) | Renewable Utilization (%) |
| 80 | 400 | 13,120 | 1.15 | 41.3 |
| 100 | 500 | 12,780 | 0.93 | 44.1 |
| 120 | 600 | 12,450 | 0.72 | 46.3 |
| 140 | 700 | 12,280 | 0.61 | 47.8 |
As shown in Table 10, increasing the number of energy storage cells reduces daily electricity costs and life loss while improving renewable energy utilization. However, there is a diminishing return effect: the incremental benefit of adding more cells decreases as the total capacity increases. The double-layer optimization framework can be used to determine the optimal number of energy storage cells for a given park configuration, balancing upfront investment costs against operational benefits.
Conclusions and Future Work
In this work, I have presented a double-layer optimization model for source-grid-load-storage collaborative scheduling that explicitly considers the impact of energy storage cell life degradation. The upper layer minimizes electricity purchase costs by optimizing power allocation among wind, photovoltaic, energy storage, and grid sources. The lower layer minimizes life loss of each energy storage cell by optimizing individual charging and discharging profiles. Through iterative coordination between the two layers, the model achieves a favorable balance between economic efficiency and battery longevity.
The experimental results based on real-world data from a park in Northeast China demonstrate the effectiveness of the proposed approach. Compared to a single-layer rule-based method, the double-layer optimization achieves an 8.12% reduction in daily electricity purchase costs, a 40.98% reduction in energy storage cell life loss over a 31-day period, and a 5.48% improvement in renewable energy utilization. The long-term projection indicates that the double-layer method preserves 93.80% of initial battery capacity after 10 years, compared to 89.50% for the single-layer method.
The key findings of this study are summarized as follows:
First, the double-layer optimization framework provides a systematic approach to balancing economic and operational objectives in energy management systems. By decomposing the problem into two interconnected layers, the model captures both system-level dynamics and cell-level constraints, leading to more effective and sustainable scheduling decisions.
Second, the life loss model incorporating depth of discharge, SOC range, and switching frequency effects offers a realistic representation of energy storage cell aging. Integrating this model into the lower-layer optimization enables proactive management of battery health, reducing replacement frequency and lifecycle costs.
Third, the feedback mechanism from the lower layer to the upper layer is essential for adaptive scheduling. By continuously updating the upper layer with information on energy storage cell health, the system can adjust its power allocation strategies to avoid operating conditions that accelerate aging, resulting in significant economic and operational benefits over time.
The proposed double-layer optimization framework offers a practical and efficient solution for energy management in industrial parks. It provides a solid theoretical foundation for integrating energy storage systems into smart grid applications and contributes to the broader goal of achieving carbon neutrality through intelligent energy management. The framework can be extended to other settings such as commercial buildings, residential communities, and microgrids, where similar trade-offs between economic efficiency and equipment longevity exist.
Several directions for future research are worth pursuing. First, incorporating more detailed electrochemical aging models of energy storage cells into the lower-layer optimization could improve the accuracy of life loss predictions. Second, extending the framework to handle multiple energy storage cabinets with heterogeneous cell types and ages would enhance its practical applicability. Third, integrating uncertainty forecasting for renewable generation and load demand into the upper-layer optimization could further improve the robustness of scheduling decisions. Fourth, exploring alternative optimization algorithms for the lower layer, such as multi-agent reinforcement learning, could enable real-time adaptive scheduling of individual energy storage cells. Fifth, conducting field experiments in real park settings would provide valuable empirical validation of the proposed approach.
In conclusion, the double-layer optimization model presented in this study represents a significant step forward in the joint optimization of economic efficiency and energy storage cell longevity in source-grid-load-storage systems. By explicitly modeling the interaction between system-level energy management and cell-level battery health, the framework achieves superior performance across multiple objectives and provides a solid foundation for sustainable energy management in industrial parks and beyond.