In the process of parameter identification, sensitivity analysis is mainly used to determine key parameters with high sensitivity in the model. Sensitivity analysis methods include local sensitivity analysis (LSA) and global sensitivity analysis (GSA). The LSA method has been widely used for power system parameter identification for a long time, while the GSA has started to be used in recent years. However, there is no clear conclusion on the impact of different sensitivity analysis methods on parameter identification results. Therefore, this paper compares and studies the roles that LSA and GSA can play in different parameter identification methods, providing clear guidance for the selection of sensitivity analysis methods and parameter identification methods. The conclusion is as follows. If the identification strategy that only identifies key parameters with high sensitivity is adopted, we recommend still using the existing LSA method. If using a groupwise alternating identification strategy (GAIS) for high- and low-sensitivity parameters, either LSA or GSA can be used. To improve the identification accuracy, it is more important to improve the identification strategy than to change the sensitivity analysis method. When the accuracy of the non-key parameters with low sensitivity cannot be confirmed, using the GAIS is an effective method for ensuring identification accuracy. In addition, it should be noted that the high sensitivity of a parameter does not necessarily mean that the parameter is identifiable, which is revealed by the examples used in this paper.

A single correlation coefficient computed directly from an undecomposed power time series may obscure coupling patterns associated with short-term fluctuations, stage-wise variations, and long-term trends among heterogeneous source and load nodes. To address this issue, this study proposes a multi-timescale source–load coupling correlation analysis method based on the maximal overlap discrete wavelet transform (MODWT). MODWT is first used to decompose multi-node power time series into high-, medium-, and low-frequency components. Within each frequency band, pairwise correlations are calculated over separate time windows and aggregated in Fisher z-space using effective-sample-size-based reliability weights. The resulting scale-specific correlation matrices are then fused according to the fluctuation-energy contributions of the reconstructed components. A case study using one year of 5 min measurements from 12 source–load nodes shows clear scale-dependent coupling patterns: the two photovoltaic (PV) nodes remain strongly correlated across scales, whereas PV–load correlations are generally weak and load–load correlations decrease from the high-frequency scale toward longer time scales. As an illustrative downstream application, the proposed matrices are further used as fixed graph priors in a common joint forecasting model. The proposed graph achieves the lowest training-stage mean squared error (MSE) in 7 of 8 reported configurations and reduces training-stage MSE by approximately 1.1–9.3% relative to the conventional Pearson-correlation graph. Additional test-set results show a similar comparative trend, indicating that the benefit of the proposed multi-timescale correlation information is not confined to the training data and remains evident on unseen samples.

With the increasing penetration of behind-the-meter photovoltaic generation and distributed energy storage, distribution system operators usually observe only the net load at the point of common coupling, while the actual user load and energy storage charging/discharging power are difficult to measure directly. To address this problem, this paper proposes a mode-aware constrained inverse optimization method for behind-the-meter distributed energy storage power estimation under fixed time-of-use tariffs. The proposed method uses net load, photovoltaic power, and tariff information as inputs and estimates the hidden user load, storage power, SOC trajectory, and dominant storage arbitrage mode. A mode-aware joint representation model is developed by introducing single-cycle and dual-cycle charge–discharge templates, daily action intensity factors, mode weights, and local correction terms. In addition, power limits, SOC dynamics, SOC bounds, daily energy balance constraints, tariff-response consistency, and mode selection penalty are incorporated into the inverse optimization framework to improve the physical feasibility and interpretability of the estimation results. Case studies are conducted using a 40-day hybrid dataset with a 1 h sampling interval and a 70%/30% training/testing split. The dataset is constructed from park-level user load and photovoltaic data, while the storage power profile is reconstructed according to typical time-of-use arbitrage operation. For the main dual-cycle testing case, the NRMSEs of storage power, user load, and net load are 14.75%, 3.90%, and 3.76%, respectively. The results show that the proposed method can recover the main variation trend of hidden storage power under the studied fixed time-of-use tariff scenario and provides a preliminary basis for park-level storage monitoring and flexible resource perception.