## 4 Discussion  
### Case Parameters  
This study selects a wind/storage system from an industrial park in Jiangsu Province, China, as the research object. The scheduling horizon is set to 24 h with a time interval of 10 min, resulting in 144 sampling points per day. The data are obtained from the actual operation records of the wind farm in the park, covering a typical month (30 days) of wind power forecasts and corresponding actual output data. The forecasting error data from the first 29 days are used to construct the probabilistic model and scenario set of wind power output, while the forecasted data for the 30 th day serve as the input for optimization and scheduling.  
During the generation of wind power output scenarios for Day 30, a combination of the Copula method and KDE is employed to generate 100 candidate output scenarios via random sampling. Subsequently, the \(k\)-means clustering method is applied to extract 10 representative scenarios along with their corresponding probability weights, in order to reduce computational complexity while preserving the representativeness of the scenario set. Figure 4 illustrates the curve distribution of the 10 representative wind power output scenarios selected via \(k\)-means clustering.  
The confidence level for the CVaR constraint is set to 0.90. The parameters of the LiFePO\({}_{4}\) battery energy storage system are listed in Table 1. In particular, the initial \(SOC\) of the storage system is treated as a decision variable for optimization, while the terminal \(SOC\) is fixed at 0.5 to ensure that the system retains a certain level of dispatchability at the end of the scheduling horizon. The cost coefficient for the initial \(SOC\) is set to 0.45 CNY/kWh.  
Figure 4: Wind power output scenario curves after K-means clustering.  
Moreover, to account for the impact of electricity price fluctuations on the charge/discharge strategy of the storage system, a time-of-use (TOU) pricing mechanism is introduced, as shown in Table 2. The electricity purchase price refers to the cost of buying electricity from the grid, while the selling price corresponds to the feed-in tariff for wind power. On this basis, to further incentivize arbitrage scheduling by leveraging the peak-valley electricity price spread, a peak-valley arbitrage incentive coefficient \(\gamma\) is introduced, with a value of 0.5.  
To ensure the practicality and reproducibility of the proposed method, the wind power system is modeled using a representative commercial wind turbine. Specifically, a 4 MW horizontal-axis wind turbine is considered, with a cut-in wind speed of 3 m/s, a rated wind speed of 12 m/s, and a cut-out wind speed of 25 m/s.  
To further reduce the economic losses caused by wind power scheduling deviations across scenarios, the objective function incorporates a deviation penalty cost, which is jointly determined by the electricity purchase price and a dynamic penalty coefficient. The penalty cost for each time period is listed in Table 3. Specifically, a higher penalty coefficient (2.0) is assigned to peak periods to reflect their elevated economic impact. For flat and valley periods, a unified coefficient of 1.5 is adopted to balance their differing electricity prices with the system's overall sensitivity to deviations during non-peak hours.