The landscape of power systems has progressively evolved from the traditional paradigm of “Generation-Transmission-Distribution-Utilization” to one that incorporates “Storage” as a fundamental pillar. In this new architecture, energy storage battery systems, particularly electrochemical storage, have demonstrated significant value. On the grid side, demonstration projects have validated their capabilities in peak shaving, valley filling, and integrating renewable energy. However, research and application on the user side, especially within large industrial parks, remain relatively underexplored. For these substantial consumers, operating under a two-part tariff system that combines capacity charges with time-of-use energy rates, strategic load management is crucial for cost reduction. Deploying electrochemical energy storage battery systems within industrial parks offers a fast-response solution for peak shaving and valley filling, presenting a promising avenue for economic optimization. Nevertheless, the high cost of energy storage battery units remains a primary barrier to widespread adoption. A critical aspect often overlooked in dispatch optimization is the accelerated degradation of the energy storage battery caused by frequent charge-discharge cycles. Accurately modeling this life loss and devising dispatch strategies to mitigate it are therefore essential for unlocking the full economic potential of user-side energy storage battery systems.
A significant challenge lies in balancing the accuracy and computational efficiency of the energy storage battery life loss model. Some methods simplistically estimate cost based on the theoretical lifespan, underestimating degradation under frequent cycling. Others assume a linear relationship between cost and Depth of Discharge (DOD), which lacks precision. While non-linear models based on DOD offer better accuracy, incorporating them directly as high-order decision variables can drastically slow down optimization solvers. Therefore, developing a model that maintains reasonable accuracy while ensuring fast solve times is necessary for practical, day-ahead scheduling.
Furthermore, large-scale industrial parks typically require substantial storage capacity, often met by systems comprising multiple individual energy storage battery units or stacks. These units may have varying efficiencies, states of health, and capacities due to differences in age, manufacturer, or operational history. Traditional dispatch models that aggregate multiple units into a single, monolithic storage entity fail to capture this heterogeneity. This aggregated approach reduces scheduling flexibility, can lead to uneven wear (such as over-charging or over-discharging specific units), and ultimately shortens the overall system’s life. Since user-side parks generally deploy a manageable number of units, independently modeling each energy storage battery unit is computationally feasible and can significantly enhance operational precision, flexibility, and longevity.
This paper establishes an economical dispatch optimization model for grid-connected industrial parks that integrates renewable energy, local load, and electrochemical storage, with a dedicated focus on energy storage battery lifetime. The model employs a DOD-based method to quantify the daily life loss cost of the energy storage battery, which is then piecewise linearized to enhance solving speed. It independently models each energy storage battery unit within a system to improve dispatch accuracy and coordination. Additionally, a State of Charge (SOC) health evaluation function is incorporated into the secondary optimization objectives to further prolong energy storage battery life and ensure balanced operation among units. The validity and economic superiority of the proposed model are demonstrated through a case study based on a typical industrial park load profile.
1. Modeling Battery Lifetime Degradation
1.1 Semi-Empirical Battery Life Model
The lifespan of an electrochemical energy storage battery is heavily influenced by its operational regime. Under infrequent, full-cycle daily use, a battery may last its expected calendar life. However, frequent charge-discharge cycles, especially at high Depth of Discharge (DOD), significantly accelerate capacity fade and reduce usable life. Therefore, short-term dispatch planning must account for the number of cycles per day and their associated DOD. For Lithium Iron Phosphate (LFP) batteries, a common chemistry for stationary storage, the relationship between cycle life and DOD can be expressed by a power-law equation derived from empirical data. Typical cycle life data for an LFP energy storage battery is shown in the table below.
| Depth of Discharge (DOD) | Cycle Life (N_cal) |
|---|---|
| 0.4 | 7,200 |
| 0.6 | 6,000 |
| 0.8 | 5,200 |
| 1.0 | 4,700 |
Fitting this data yields the following relationship:
$$N_{cal} = 4700 \times (DOD)^{-0.5}$$
where \(N_{cal}\) is the cycle life to retirement at a given constant DOD, and the exponent \(-0.5\) is the fitted constant \(a\) for this specific battery type. This non-linear equation clearly shows that increasing the DOD drastically reduces the cycle life of the energy storage battery.
1.2 Battery Life Degradation Cost Model
The daily degradation cost of an energy storage battery is a function of its usage pattern. The core idea is to quantify the cycle consumption and translate it into an equivalent daily capital cost. In an ideal daily cycle with a single full charge and discharge at a specific DOD, the equivalent cycle number \(E_z\) relative to a baseline 100% DOD cycle is:
$$E_z = \frac{N_0}{N_{cal}} = \frac{N_0}{N_0 (DOD)^{-a}} = (DOD)^{a}$$
where \(N_0\) is the cycle life at 100% DOD.
In real-world dispatch, the energy storage battery may undergo multiple, irregular partial cycles. The total degradation must account for the incremental aging caused by each discharge segment. The equivalent number of baseline cycles for a day’s operation is calculated by summing the incremental damage from each time interval. This is formalized using the “rainflow” or incremental approach:
$$E_{eq} = \sum_{t=1}^{T} \left| \frac{1}{(DOD_t)^{-a}} – \frac{1}{(DOD_{t-1})^{-a}} \right| = \sum_{t=1}^{T} \left| (DOD_t)^{a} – (DOD_{t-1})^{a} \right|$$
where \(t\) is the time interval (e.g., one hour), \(T\) is the total number of intervals in the dispatch horizon (e.g., 24), and \(DOD_t\) is the depth of discharge at time \(t\). Only the discharge process is considered, as charging typically has a much lesser impact on cycle life for most lithium-ion energy storage battery chemistries.
Using \(E_{eq}\), the projected operational life \(T_{cal}\) (in years) of the energy storage battery under the typical daily usage pattern is:
$$T_{cal} = \frac{N_0}{365 \times E_{eq}}$$
To convert this into a daily cost that properly accounts for the time value of money, the capital recovery factor is applied. The equivalent uniform daily cost \(C_b\) for the energy storage battery, including maintenance, is:
$$C_b = \left( C_{bin} \times \frac{r(1+r)^{T_{cal}}}{(1+r)^{T_{cal}} – 1} + C_{bw} \times T_{cal} \right) / 365$$
where:
\(C_{bin}\) = total initial investment cost of the energy storage battery system,
\(r\) = annual discount rate,
\(C_{bw}\) = annual operation and maintenance cost.
The initial investment and maintenance costs for a system with multiple, independently modeled units are:
$$C_{bin} = \sum_{n=1}^{N} (C_{\bar{P}} \bar{P}_n + C_{\bar{E}} \bar{E}_n)$$
$$C_{bw} = \sum_{n=1}^{N} (C_w \bar{P}_n)$$
where:
\(n\) = index for each energy storage battery unit,
\(N\) = total number of units,
\(C_{\bar{P}}\) = cost per kW of power rating,
\(\bar{P}_n\) = rated charge/discharge power of unit \(n\),
\(C_{\bar{E}}\) = cost per kWh of energy capacity,
\(\bar{E}_n\) = rated energy capacity of unit \(n\),
\(C_w\) = annual maintenance cost per kW of power rating.
In the optimization problem, \(DOD_t\) is a decision variable. The expression for \(C_b\) is a complex, non-linear function of \(DOD_t\), which can hinder fast solution by standard linear or mixed-integer linear programming solvers. To maintain model fidelity while ensuring computational tractability for day-ahead scheduling, the cost function is piecewise linearized. The resulting linearized daily degradation cost \(C^f_b\) is:
$$C^f_b = \sum_{t=1}^{T} (K_d \cdot \Delta DOD_t + B_d)$$
where \(\Delta DOD_t\) is the change in DOD during the discharge phase in time interval \(t\), and \(K_d\), \(B_d\) are the slope and intercept parameters obtained from the piecewise linear approximation of the original non-linear cost function derived from Eq. (5).
2. Optimization Model for Industrial Park Dispatch Considering Battery Lifetime
Industrial consumers are characterized by high, regular power demand and stringent power quality requirements. Industrial parks are well-suited for deploying distributed renewable generation and are subject to two-part tariffs, making them ideal candidates for energy storage battery systems. The primary economic objectives for the energy storage battery in this context are: 1) Energy arbitrage by charging during low-price (valley) periods and discharging during high-price (peak) periods, 2) Reduction of peak demand to lower capacity charges, and 3) Enhancement of local consumption of renewable generation to minimize curtailment penalties.
2.1 Objective Function
The dispatch optimization aims to minimize a composite objective function \(F\) that balances primary economic costs with secondary battery health objectives:
$$\min(F) = \min(C_1 + \lambda F_2)$$
Here, \(C_1\) is the total economic cost function, and \(F_2\) is the SOC health evaluation function. The weighting coefficient \(\lambda\) is set such that the scale of \(\lambda F_2\) is subordinate to \(C_1\), ensuring economic performance remains the primary driver while still influencing battery-friendly behavior.
2.1.1 Economic Cost Function (C₁)
The economic cost encompasses all daily monetary expenditures:
$$C_1 = C_e + C_d + C_r + C^f_b$$
a) Energy Charge (\(C_e\)): This is the cost of electricity purchased from the grid at time-of-use rates.
$$C_e = \sum_{t=1}^{T} \rho(t) \cdot P_N(t)$$
where \(\rho(t)\) is the electricity price at time \(t\), and \(P_N(t)\) is the power drawn from the grid.
b) Demand Charge (\(C_d\)): A monthly fee based on the highest peak power demand (measured in kW or kVA) during the billing period. For daily optimization, it is modeled as a penalty on the daily peak power \(P_{peak}\).
$$C_d = \begin{cases}
\alpha M, & \text{if } P_{peak} \leq 1.02M \\
\alpha M + 2\alpha (P_{peak} – 1.02M), & \text{if } P_{peak} > 1.02M
\end{cases}$$
where \(\alpha\) is the demand charge rate per kW, \(M\) is a contracted baseline demand, and \(P_{peak} = \max(P_N(t))\).
c) Renewable Generation Cost (\(C_r\)): Includes the cost of purchasing renewable power (if any) and a penalty for curtailment to incentivize full utilization.
$$C_r = \sum_{t=1}^{T} \left[ C_{NE} P_{NE,use}(t) + C_{pun} (P_{NE}(t) – P_{NE,use}(t)) \right]$$
where \(C_{NE}\) is the cost per kWh of renewable power, \(C_{pun}\) is the penalty cost per kWh of curtailed renewable power, \(P_{NE}(t)\) is the total available renewable power, and \(P_{NE,use}(t)\) is the renewable power actually used by the park.
d) Battery Degradation Cost (\(C^f_b\)): The piecewise linearized daily cost of energy storage battery life loss, as defined in Eq. (9).
2.1.2 SOC Health Evaluation Function (F₂)
This secondary function promotes operating practices that extend energy storage battery life and improve coordination among multiple units. It consists of two components:
a) SOC Coordination Index (\(F_{ave}\)): Penalizes deviations of individual unit SOC from the average SOC of all units. This discourages situations where one unit is consistently over-cycled while others remain idle, promoting even wear.
$$F_{ave} = \sum_{t=1}^{T} \sum_{n=1}^{N} | SOC_{ave}(t) – SOC_n(t) |$$
where \(SOC_{ave}(t) = \frac{1}{N}\sum_{n=1}^{N} SOC_n(t)\) is the average SOC of all units at time \(t\), and \(SOC_n(t)\) is the SOC of unit \(n\).
b) SOC Fluctuation Index (\(F_{wav}\)): Penalizes large fluctuations in the SOC of each individual unit over the dispatch horizon. Smoothing the SOC trajectory reduces stress on the energy storage battery.
$$F_{wav} = \sum_{t=1}^{T} \sum_{n=1}^{N} | SOC_{n,avg} – SOC_n(t) |$$
where \(SOC_{n,avg} = \frac{1}{T}\sum_{t=1}^{T} SOC_n(t)\) is the time-averaged SOC for unit \(n\).
Thus, the complete health function is:
$$F_2 = F_{ave} + F_{wav}$$
2.2 Constraints
The optimization is subject to the following operational constraints:
1) Power Balance Constraint: The total power must be balanced at every time step.
$$P_N(t) + P_{NE,use}(t) + P_{dis}^{bat}(t) = P_{cha}^{bat}(t) + P_L(t), \quad \forall t$$
where \(P_{dis}^{bat}(t) = \sum_{n=1}^{N}P_{dis,n}^{bat}(t)\) is the total discharge power from all energy storage battery units, \(P_{cha}^{bat}(t) = \sum_{n=1}^{N}P_{cha,n}^{bat}(t)\) is the total charge power, and \(P_L(t)\) is the park’s load. For each unit, \(P_{dis,n}^{bat}(t)\) and \(P_{cha,n}^{bat}(t)\) cannot be non-zero simultaneously.
2) Renewable Generation Constraint:
$$0 \leq P_{NE}(t) \leq P_{NE}^{max}, \quad \forall t$$
3) Energy Storage Battery Unit Constraints: For each independent unit \(n\):
$$
\begin{aligned}
&0 \leq P_{cha,n}^{bat}(t) \leq \bar{P}_n \cdot u_{cha,n}(t) \\
&0 \leq P_{dis,n}^{bat}(t) \leq \bar{P}_n \cdot u_{dis,n}(t) \\
&u_{cha,n}(t) + u_{dis,n}(t) \leq 1 \\
&SOC^{min} \leq SOC_n(t) \leq SOC^{max} \\
&SOC_n(t) = SOC_n(t-1) + \left( \frac{\eta_{cha} P_{cha,n}^{bat}(t)}{\bar{E}_n} – \frac{P_{dis,n}^{bat}(t)}{\eta_{dis} \bar{E}_n} \right) \Delta t
\end{aligned}
$$
where \(u_{cha,n}(t)\) and \(u_{dis,n}(t)\) are binary variables indicating charge/discharge status, \(\eta_{cha}\) and \(\eta_{dis}\) are charge and discharge efficiencies, and \(\Delta t\) is the duration of a time interval.
3. Case Study and Analysis
3.1 Case Setup
The proposed model is applied to a typical summer day for an industrial park with a peak load of 9 MW. The park hosts a 0.5 MW wind farm. An electrochemical energy storage battery system is installed, initially comprising one 250 kW / 500 kWh unit. Later, a second unit of 250 kW / 450 kWh is added to the system, reflecting a common expansion scenario. The key financial and technical parameters are summarized below.
| Parameter | Value |
|---|---|
| Battery Power Cost (\(C_{\bar{P}}\)) | 600 CNY/kW |
| Battery Energy Cost (\(C_{\bar{E}}\)) | 1800 CNY/kWh |
| Battery Annual Maintenance Cost (\(C_w\)) | 97 CNY/kW-year |
| Wind Power Purchase Cost (\(C_{NE}\)) | 0.4 CNY/kWh |
| Wind Curtailment Penalty (\(C_{pun}\)) | 1.0 CNY/kWh |
| Battery SOC Limits (\(SOC^{min}\), \(SOC^{max}\)) | 0.1, 0.9 |
| Battery Charge/Discharge Efficiency (\(\eta_{cha}, \eta_{dis}\)) | 0.95, 0.95 |
| Annual Discount Rate (\(r\)) | 0.05 |
The time-of-use electricity price structure is as follows: Peak (08:00-12:00, 17:00-21:00): 1.07 CNY/kWh; Off-Peak (12:00-17:00, 21:00-24:00): 0.64 CNY/kWh; Valley (00:00-08:00): 0.31 CNY/kWh. The park’s load and wind generation profile for the day are illustrated in the figure below (Note: The provided image link has been placed in the introduction. For analysis, we describe the profile: the load is high between 07:00-19:00, and wind generation is intermittent).
The objective function weighting is set so that the ratio of \(C_1\) to \(\lambda F_2\) is approximately 50:1, ensuring economics dominate. The optimization problem is formulated as a Mixed-Integer Linear Programming (MILP) model and solved using the Gurobi solver via MATLAB.
To validate the effectiveness of the proposed model, four dispatch strategies are compared:
Strategy A (Proposed): Full model with independent unit modeling, battery life cost (\(C^f_b\)), and SOC health function (\(F_2\)).
Strategy B: Model without considering battery life cost (i.e., \(C^f_b = 0\)).
Strategy C: Model without the SOC health function \(F_2\).
Strategy D: Traditional model where the two energy storage battery units are aggregated into a single 500 kW / 950 kWh entity.
For Strategies A and C, the initial SOCs for the two units are set to 0.6 and 0.4, respectively, and the dispatch is required to bring both back to 0.5 by the end of the day to ensure a consistent starting point for the next day.
3.2 Results and Discussion
The SOC trajectories for the two energy storage battery units under different strategies reveal significant insights. Under Strategy B (ignoring life cost), the units exhibit more frequent and deeper charge-discharge cycles compared to Strategy A, indicating a more aggressive usage pattern that would lead to faster degradation. Strategy C (without health function) shows larger and more frequent deviations between the SOCs of the two units, and each unit spends more time at the SOC limits (0.1 and 0.9). This increases the risk of over-charge or over-discharge for individual units and demonstrates poor coordination. Strategy D (aggregated model) produces a single SOC curve that, while similar in overall shape to the average SOC in Strategy A, misses the nuances of coordinating two distinct units with different initial states.
The calculated daily costs for the industrial park under the four strategies are presented in the table below. The energy costs (\(C_e\)) and renewable costs (\(C_r\)) are similar across all strategies, as the primary load must be met and wind is fully utilized due to the curtailment penalty.
| Cost Component / Strategy | Strategy A (Proposed) | Strategy B (No Life Cost) | Strategy C (No Health Fn.) | Strategy D (Aggregated) |
|---|---|---|---|---|
| Demand Charge (\(C_d\)) | 8,470 | 8,470 | 8,470 | 8,470 |
| Energy Charge (\(C_e\)) | 55,575 | 55,495 | 55,568 | 55,700 |
| Renewable Cost (\(C_r\)) | 2,881 | 2,881 | 2,881 | 2,881 |
| Battery Degradation Cost (\(C^f_b\)) | 961 | 1,409 | 968 | 866 |
| Total Daily Cost (\(C_1\)) | 67,887 | 68,255 | 67,887 | 67,917 |
Analysis of Results:
1. Impact of Modeling Battery Life: Comparing Strategy A and Strategy B, the total cost is 368 CNY lower when battery life degradation is modeled (Strategy A). This saving comes directly from the reduced energy storage battery degradation cost (961 vs. 1,409 CNY), as the optimizer actively avoids cycles that are excessively costly in terms of life loss. This confirms that incorporating a accurate energy storage battery life model is economically beneficial.
2. Impact of the SOC Health Function: The total costs for Strategy A and Strategy C are nearly identical. However, the energy storage battery degradation cost in Strategy C is slightly higher (968 vs. 961 CNY). More importantly, the SOC analysis showed that Strategy C leads to less coordinated and potentially more stressful operation for the individual units. The health function \(F_2\) thus achieves its goal of promoting battery-friendly operation without compromising the primary economic objective.
3. Impact of Independent Unit Modeling: Strategy D (aggregated model) results in a total cost 30 CNY higher than the proposed Strategy A. While its calculated degradation cost is lower (866 CNY), this is an artifact of the simplified model which cannot capture the inefficiencies and constraints of coordinating two separate units with different capacities and initial states. This leads to a sub-optimal schedule, reflected in a higher energy charge (55,700 CNY). This demonstrates that independent modeling of energy storage battery units provides more accurate and economically superior dispatch decisions.
4. Conclusion
This paper presents an economical dispatch optimization model for industrial parks that explicitly addresses the lifetime degradation cost of electrochemical energy storage battery systems. The core contributions are threefold. First, a Depth-of-Discharge (DOD) based model is employed to estimate energy storage battery life loss, and the associated non-linear cost is piecewise linearized to maintain computational efficiency for practical day-ahead scheduling. Second, recognizing the practical configuration of large-scale storage, the model independently characterizes each energy storage battery unit within a system, enabling more precise and flexible dispatch that accounts for unit heterogeneity. Third, a State of Charge (SOC) health evaluation function is integrated as a secondary objective to encourage operational practices that reduce stress on individual units and improve inter-unit coordination.
The case study on a typical industrial park validates the model’s effectiveness. The results demonstrate that: 1) Considering energy storage battery life degradation in the optimization directly reduces the daily operational cost by avoiding dispatch actions that cause excessive wear; 2) Independently modeling multiple energy storage battery units leads to more accurate and economically favorable schedules compared to the traditional aggregated approach; and 3) The SOC health function successfully promotes battery-friendly operation, such as balanced cycling among units, without incurring an economic penalty. The proposed model provides a practical and effective framework for industrial parks to maximize the economic benefits of their energy storage battery investments while proactively managing and extending the asset’s operational lifetime.