*6.1. Data Description*

In this case study, the alliance consists of 10 wind turbines and 1 shared energy storage, and the operational parameters of the SES are shown in Table 1. To model the wind power output uncertainty, this paper adjusted the real electricity generated by a wind power

plant in a certain northwest region proportionally as the wind power forecast value, and used Monte Carlo sampling to generate multiple wind power output scenarios for each sub-wind-power plant based on the statistical error of the forecast value. Then, this paper used the scenario reduction method to limit the number of scenarios to 10. The market prices were obtained from publicly available data of the PJM electricity market, and the price penalty factors *ϕdown* and *ϕup* in REM were taken as 0.8 and 1.2, respectively.


**Table 1.** Model parameters.

#### *6.2. Results and Discussion*

Based on the existing REB, the reasonable allocation of EES battery capacity and power is critical to SES system planning. If the ES capacity allocated to wind turbines in the REB is too small, it will be difficult to effectively absorb wind power. If the ES capacity is too large, the investment and operation costs will be too high, which could significantly affect the financial advantages of SES. This paper studies the effect of SES capacity allocation on alliance revenue. Figure 3 demonstrates that alliance members experience an increase in market revenue as the energy storage capacity rises, reaching a peak at a certain point when the capacity is relatively low. However, surpassing the optimal energy storage capacity linked to maximum profit leads to a subsequent decline in the members' profitability. This decline can be attributed to excessive energy storage capacity, which introduces redundancy in energy storage resources. The resulting high investment and operational costs associated with this surplus capacity contribute to diminished profits for alliance members. In this case study, for most wind turbines, the ES capacity ratio corresponding to the maximum revenue is mostly between 14% and 21%.

Additionally, Figure 4 shows a significant increase in revenue for wind turbines 7–10, indicating that these four wind turbines need to bear a high SES investment cost. To balance the economic profits of the alliance and ES investment costs, the most suitable SES capacity ratio is within the 17–20% interval, which means that the SES capacity allocation for the REB is most suitable within the range of 90–110 MW. This paper chooses 100 MW as the optimal SES capacity configuration for the REB, and studies the optimized operation and cost allocation of the 100 MW.

The scheduling and operation status of SES with or without considering the cost of dynamic degradation of ES are presented in Figure 5.

**Figure 3.** Revenue of alliance members.

**Figure 4.** The revenue increase rate of alliance members.

**Figure 5.** The SOC of energy storage.

In Figure 5, M1 represents the SoC of SES when dynamic attenuation characteristics are not taken into consideration, and M2 represents the SoC of SES when dynamic attenuation characteristics are taken into consideration. And dark blue represents the initial SoC of the ES, green represents an increase in the value of the SoC, and red represents a decrease in SoC. By comparing the SOC of SES with and without considering the dynamic attenuation, it can be observed that when there is a significant difference between the real-time output of the wind turbine and the previously declared power, the SOC of SES changes extensively. This indicates that the REM power of the ES is also substantial, and the storage device can adjust the overall clear power through its charging-and-discharging behavior to maintain the power balance. Consequently, the storage device can minimize the effects of unpredictability in wind power output on system operation, improving the overall alliance revenue. Moreover, compared to the scenario without considering dynamic attenuation, when dynamic attenuation is considered, the SOC change frequency and amplitude of SES are more conservative. This results in a reduced number of chargingand-discharging cycles and a reduced frequency of deep charging or discharging, leading to a smoother change in energy capacity. This prolongs the service life of SES. When dynamic attenuation is not considered, the ES device tends to increase the revenue of various entities in the energy market through frequent charging-and-discharging behavior to maximize overall revenue. However, when dynamic attenuation is considered, the utilization rate of the storage device is significantly reduced to achieve higher total alliance revenue, leading to a lower clear power in the real-time balance market and a lowered frequency of charging-and-discharging behavior.

By analyzing the cross-sections of different stages of SES, it is shown in Figure 6 that when the ES capacity drops below 20%, the optimal scheduling requirement under the initial state has deviated. This will reduce its ability to improve the anti-peak properties of wind power and reduce the imbalance settlement cost of wind power. This further indicates the necessity of considering the dynamic degradation of ES to avoid excessive use of SES.

**Figure 6.** Operation of energy storage before and after degradation.

If fixed decay cost for payment of SES is applied without considering its dynamic characteristic changes, and if ES state parameters are not updated during its usage, and if the charging and discharging costs remain constant and do not change with the changes in charging and discharging capacities, then the health status of the ES cannot be adequately represented, and the overuse of ES cannot be avoided in the sharing mode. This paper proposes that updating the characteristic parameters of ES in a timely manner according to its operating conditions and accounting for the decay cost of ES during different usage stages based on charging and discharging quantities can more reasonably improve the system benefits on the basis of reducing the loss of ES life.

Based on the revenue obtained by wind turbines and SES forming alliances and wind turbines participating in the market individually, the revenue increase brought by forming alliances can be derived. The results are shown in Table 2. Comparing the final revenue situation, it can be seen that after multiple wind turbines share ES, their revenue has increased, but the increase proportion is different, mainly due to the different prediction accuracies of each wind turbine. Wind turbine 9 achieved a 28.61% increase in revenue compared to participating in the market individually, while wind turbine 3, which has the least revenue increase, has also achieved 1.01 times the revenue when participating in the market individually after constructing SES. It is evident that the model proposed in this paper, which involves multiple wind turbines jointly sharing ES to participate in market operation, can take into account the interests of all parties and improve the overall revenue.

**Table 2.** Revenue increase rate of each wind turbine.


Comparing the different profits of wind power with the same installed capacity in Figure 7, it can be observed that the distinct profitability of wind power producers with the same capacity are due to different prediction errors. The larger the deviation between the real and reported power data of a wind turbine, the higher the corresponding imbalance costs it incurs, which results in lower actual profits of the RE station than expected. Meanwhile, the profit of a single wind turbine, when forming alliances with other wind turbines and ES, may not increase significantly even if its profitability is high, mainly because the wind turbine itself is already highly matched with the load, and the complementary effects between multiple wind turbines and the regulating function of ES do not significantly reduce their output deviation.

**Figure 7.** Revenue increase rate of each wind farm.

According to the proportion of revenue improvement from each wind turbine to the total revenue increase, the investment and degradation costs of SES are allocated, and the higher the revenue increase rate of a wind turbine, the more SES cost it needs to bear. This can ensure enthusiasm for cooperation of all alliance members and the stability of the alliance.

As shown in Figure 8, by comparing the day-ahead and real-time revenues of ten wind farms, it can be seen that the capacity and prediction error of wind turbines both affect their share of investment in SES. In an RE field, wind turbines with larger errors between actual capacity and output and reported values need to bear higher initial investment costs of SES.

**Figure 8.** Revenue increase rate of different market members.

The day-ahead revenues of wind farm 3 and wind farm 4 are basically the same, but the investment expense of ES required varies greatly. This is mainly because wind farm 3 has better matching with the load, which can better meet the load demand in each period with its own output characteristics, and therefore has less demand for peak-shaving and filling of ES and flexibility value, resulting in a smaller proportion of corresponding shared investment. The real-time revenue of wind farm 4 and wind farm 7 is basically the same, but the cost of SES is different, indicating that wind turbines with different capacities still need to bear a larger proportion of initial investment costs of ES even if their prediction accuracy is similar.

The impact of wind turbine output prediction accuracy on the cost allocation of an SES alliance is analyzed below, and the results are presented in Figure 9.

As seen in Figures 8 and 9, it can be observed that wind turbines 7, 8, 9, and 10 have higher improvement rates in revenue and higher SES costs. As prediction accuracy improves, the SES cost of each wind turbine unit, especially those with higher revenue increase rates, decreases to varying degrees. This is because the improvement in prediction accuracy reduces the deviation between the pre-bid power and real-time output of each unit, leading to decreased demand for ES capacity and subsequently lowering the SES investment cost. Moreover, the improvement in prediction accuracy reduces the frequency and power of charging and discharging, resulting in a lower degradation cost due to the ES cycle. Therefore, each member of the alliance will also see a reduction in their corresponding SES costs. Additionally, due to the different prediction accuracy of each unit, their demand for ES when participating in the spot market is also different, leading to varying changes in the cost sharing. For turbine 9, which has the highest improvement rate in revenue, when its prediction accuracy improves by 5%, the shared cost can be reduced by about 6%, which is conducive to incentivizing alliance members to actively participate in the spot market and enhancing their market competitiveness.

As shown in Figure 10, the capacity demand of SES in each wind turbine unit in the REB also changes when the electricity price penalty coefficient in the REM of the alliance changes. Specifically, when the overgeneration price penalty coefficient *φdown* decreases or the undergeneration price penalty coefficient *φup* increases, the optimal SES allocation capacity in the REB will gradually increase. This is because the change in the electricity price penalty coefficient will increase the capacity demand of SES of each wind turbine unit, which will increase the investment expense of SES, and the charging and discharging powers will also increase, resulting in more frequent charging-and-discharging behaviors, and the decay cost will also increase, leading to a continuous increase in the SES cost borne by each unit. However, since the capacity demand for ES of each turbine is different when the electricity price penalty coefficient changes, the increment of their ES allocation cost is also different.

**Figure 10.** The allocation of ES costs for alliance members under different penalty coefficients.

The output prediction accuracy of each unit is set as shown in Table 3. Combined with Table 3 and Figure 10, for unit 7, 8, and 9, when the electricity price penalty coefficient changes, their increment of ES allocation cost is relatively large. This is mainly because their output prediction accuracy is low, and the day-ahead forecast error is large, which will face higher imbalance penalty fees in the REM. To improve their economic benefits, they will increase the demand for SES to compensate for the fluctuation between their awarded electricity volume and real-time power output, thus reducing the imbalance settlement cost.

**Table 3.** Prediction accuracy of wind turbine.


For units with higher prediction accuracy, when the electricity price penalty coefficient changes, their increment of ES allocation cost increases more conservatively. When *φdown* decreases from 0.9 to 0.8, the ES allocation cost for unit 9 increases by USD 1095, which is about 10 times the increment of the ES allocation cost for unit 4. In addition, for wind turbine units with similar installed capacity, such as units 3, 5, and 10, their increments of ES allocation cost are different due to different prediction accuracies. Obviously, for unit 10 with higher prediction accuracy, the increment in ES demand is smaller, and the ES allocation cost increases more conservatively. For unit 3 with lower prediction accuracy, its increment of ES allocation cost is 1.11 times higher than that of unit 10. In fact, according to the cost allocation mechanism proposed in this article, wind power producers must make a trade-off between implementing higher-cost yet more effective prediction technologies and bearing increased shared energy storage investment costs to maximize their own utility.

#### **7. Conclusions**

This paper provides a detailed modeling of the degradation of shared energy storage lifespan, and analyzes the impact of dynamic degradation characteristics on the operational strategies and capacity allocation schemes of shared energy storage in renewable energy bases. It establishes an optimization model for the optimal operation of shared energy storage in renewable energy bases, taking into account the dynamic degradation characteristics. Furthermore, a cost allocation mechanism is designed to address the diversity in shared energy storage demands. The following results have been confirmed:


In conclusion, the SES optimization model for RE stations, taking into account dynamic decay of EES, is more objective and reasonable. The calculation of profits for different units in the REB has guidance significance for designing SES cost allocation mechanisms. The proposed model is also applicable to photovoltaic power stations. However, there are still some limitations in this paper that can be improved in the future. On the one hand, this paper does not consider network constraints and power flow constraints. In-depth research can be conducted on the capacity configuration of energy storage in renewable energy bases, taking into account power supply security, reliability, and power quality. On the other hand, this study primarily focuses on multiple renewable energy bases and a single shared energy storage system. Future research can investigate the capacity allocation problem for multiple shared energy storage stations.

**Author Contributions:** Conceptualization and investigation, C.S.; conceptualization and formal analysis, B.Z.; resources and methodology, B.W.; data curation and software, W.L.; writing—original draft preparation, Y.Y.; supervision, formal analysis and writing—review & editing, Z.W. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the State Grid Gansu Electric Power Company Science and Technology Project "Research on Energy Storage Participation in Marketization Trading Mechanism Based on New Power Systems" (Grant number: 52272222000H).

**Data Availability Statement:** Datasets are available upon reasonable request.

**Acknowledgments:** The authors are grateful to the editor and anonymous reviewers for their work.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


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