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This article studies the parameter estimation to the system response from the discrete measurement data. By constructing the dynamical rolling cost functions and using the nonlinear optimization, the gradient identification method is presented for estimating the parameters of the sine response signal with double frequency. In order to overcome the difficulty for determining the step size and deduce the influence of noises, the stochastic gradient identification method is derived to estimate the signal parameters. For the purpose of improving the accuracy, a multi-innovation stochastic gradient parameter estimation algorithm is presented using the moving window data. Finally, the simulation examples are provided to test the algorithm performance.

Under fault conditions, Photovoltaic-Storage-Charging Integrated Stations (PSCISs) are regarded as a key resource for enhancing distribution network resilience. However, traditional centralized optimization fails to account for conflicts of interest between the distribution network and PSCISs and neglects the actual response behavior of EV users. To address these issues, a coordinated emergency operation strategy for distribution networks and PSCISs based on the master–slave game is proposed. Firstly, a bilevel optimization framework based on the master–slave game is constructed, where the upper level performs system-level coordination and the lower level handles autonomous decision-making. For the upper level, the minimization of distribution network operation cost is set as the optimization objective by the dispatching center to determine power purchase prices and load shedding rates, which serve as guidance signals for lower-level PSCISs. In terms of the lower level, a dual-factor S-shaped response curve is introduced into the lower-level model to precisely characterize EV users’ nonlinear response behavior to price incentives. Furthermore, based on the signals received from the upper level, the maximization of each PSCIS’s profit is set as the optimization objective to determine the PV output, storage dispatch, and V2G incentive prices. Subsequently, Model Predictive Control (MPC) is employed to implement rolling optimization during the fault period, addressing the source-load uncertainties. Finally, an improved IEEE 33-node distribution network is used for case analysis and validation of the proposed operation strategy. The results indicate that the proposed strategy can effectively coordinate the interests of multiple parties, achieving synergistic improvements in both the economy and reliability of the distribution network.

The dynamic performance of the feed-drive system in CNC machine tools directly influences the accuracy of machined parts. To enhance the motion control performance of CNC machine tools, a high-precision model of the feed-drive system is critical. However, current modeling methods for feed-drive systems seldom consider time-varying factors such as loads, wear, and lubrication. As a result, the model accuracy degrades when the system characteristics are affected by these time-varying factors. In this paper, a rolling optimization method with partial weights frozen is developed to realize quick iterative learning of a data-driven model for a feed drive system with time-varying characteristics using a small amount of data. First, the long short-term memory fully connected (LSTM-FC) network is built and divided into feature extraction and output fitting parts based on their functions. Then, a weight freezing-based rolling optimization method is applied. The weights in the feature extraction part are frozen, which preserves the learned common knowledge and patterns by solidifying the way that high-dimensional features are extracted from the input. By adjusting the weights in the output fitting part, the extracted high-dimensional features are remapped to the new data distribution changed by time-varying factors. Finally, the performance of the developed rolling optimization method is confirmed by experiments. The results show that the proposed rolling optimization method reduces the maximum prediction errors by 49.5% and the total training time by 96.3% compared with existing methods, which demonstrates that the proposed method can restore model accuracy when the system characteristics change due to time-varying factors, and significantly accelerate the optimization process by rolling optimization.

The large-scale integration of renewable energy and electric vehicles introduces grid-connected power fluctuations in microgrids. To address this, this paper proposes a novel two-stage optimization scheduling strategy that balances economic efficiency and grid compatibility. In the first stage, a multi-objective optimization model is formulated to minimize both operating costs and power fluctuations, and the Improved Multi-Objective Grey Wolf Optimization algorithm—incorporating the Bernoulli chaotic map—is employed to solve it efficiently. In the intra-day phase, a rolling tracking strategy based on model predictive control is proposed to address ultra-short-term forecasting errors, and a multi-unit hierarchical error compensation mechanism is designed. This mechanism prioritizes the use of supercapacitors to absorb high-frequency fluctuations, followed by the coordinated use of batteries, electric vehicle clusters, and micro gas turbines to mitigate residual deviations, thereby effectively reducing the operational burden on individual energy storage devices. Finally, a comparative analysis of six simulation cases was conducted using a weighted evaluation metric that integrates average power deviation values and interconnection line power fluctuations. The results confirm that this strategy not only significantly smooths grid-connected power fluctuations but also demonstrates exceptional robustness and adaptability under extreme forecast error scenarios.

To cope with the variability of electricity consumption patterns, this study proposes an online rolling optimization-based energy efficiency management strategy for smart homes, which considers user preferences on energy saving and electricity comfort. A weight parameter is used to balance these two objectives and users can set them according to their own electricity preferences. The strategy employs predictive models based on historical data and future inputs to forecast system outputs, and applies feedback correction to compensate prediction errors. In order to better express the power consumption satisfaction of users, two measures of user satisfaction are introduced: utility comfort and temperature comfort. Finally, the simulation result shows that the proposed method achieves an average energy reduction rate of 13.97%, which demonstrates that our strategy can achieve significant reductions in power consumption while enhancing user satisfaction.

The growing penetration of renewable energy has brought significant challenges for modern power system operation. Academic research and industrial practice show that adjusting unit commitment (UC) scheduling periodically according to new forecasts of renewable power provides a promising way to improve system stability and economy; however, this greatly increases the computational burden for solution methods. In this paper, a deep reinforcement learning (DRL) method is proposed to obtain timely and reliable solutions for rolling-horizon UC (RHUC). First, based on historical data and day-ahead point forecasting, a data-driven method is designed to construct typical wind power scenarios that are regarded as components of the state space of DRL. Second, a rolling mechanism is proposed to dynamically update the state space based on real-time wind power data. Third, unlike existing reinforcement learning-based UC solution methods that segment the continuous outputs of generators as discrete variables, all the variables in RHUC are regarded as continuous. Additionally, a series of updating regulations are defined to ensure that the model is realistic. Thus, a DRL algorithm, the twin delayed deep deterministic policy gradient (TD3), can be utilized to effectively solve the problem. Finally, several case studies are conducted based on different test systems to demonstrate the efficiency of the proposed method. According to the experimental results, the proposed algorithm can obtain high-quality solutions in a considerably shorter time than traditional methods, which leads to a reduction of at least 1.1% in the power system operation cost.

Thermal storage electric heating (TSEH), as a prevalent variable load resource, offers significant potential for enhancing system flexibility when aggregated into a cluster. To address the uncertainties of renewable energy and load forecasting in active distribution networks (ADN), this paper proposes a multi-timescale coordinated optimal dispatch strategy that incorporates TSEH clusters. It utilizes the thermal storage characteristics and short-term regulation capabilities of TSEH, along with the rapid and gradual response characteristics of resources in active distribution grids, to develop a coordinated optimization dispatch mechanism for day-ahead, intraday, and real-time stages. It provides a coordinated optimized dispatch technique across several timescales for active distribution grids, taking into account the integration of TSEH clusters. The proposed method is validated on a modified IEEE 33-node system. Simulation results demonstrate that the participation of TSEH in collaborative optimization significantly reduces the total system operating cost by 8.71% compared to the scenario without TSEH. This cost reduction is attributed to a 10.84% decrease in interaction costs with the main grid and a 47.41% reduction in network loss costs, validating effective peak shaving and valley filling. The multi-timescale framework further enhances economic efficiency, with overall operating costs progressively decreasing by 3.91% (intraday) and 4.59% (real-time), and interaction costs further reduced by 5.34% and 9.25%, respectively. Moreover, the approach enhances system stability by effectively suppressing node voltage fluctuations and ensuring all voltages remain within safe operating limits during real-time operation. Therefore, the proposed approach achieves rational coordination of diverse resources, significantly improving the economic efficiency and stability of ADNs.

As one of the most widely used rolling optimization methods, model predictive control (MPC) can effectively deal with constrained problems with multivariate. However, MPC relies on the accurate system dynamics model, which means that the nonlinear terms in the system model such as some irregular disturbances or noises will weaken the control effect. On the other hand, machine learning has been shown to work well on black-box systems, so the idea of using deep learning to handle nonlinear terms is feasible. This paper studies a method for applying deep learning to MPC, which is to use convolutional neural networks to fit nonlinear terms of the system model and thus remove their effects by using methods such as precise compensation. The paper also compares traditional and convolutional neural networks and the simulation results show that this method can achieve good control effect.

With the integration of renewable energy into traction power supply systems at a high proportion and penetration level, the intermittency and randomness of renewable energy output significantly intensify the fluctuation characteristics of traction loads, posing severe challenges to the stable operation and precise dispatch of the system. To effectively address the dynamic tracking and anti-disturbance issues arising from the dual uncertainties of source and load, this paper proposes a dual-timescale two-layer optimization dispatch strategy based on Model Predictive Control (MPC). In the upper-layer optimization, with the objective of optimal system economic operation, a multi-step rolling optimization method is adopted to formulate a long-timescale baseline dispatch plan, fully considering the temporal correlation of photovoltaic and wind power outputs and the periodic characteristics of traction loads. In the lower-layer optimization, aimed at smoothing power fluctuations and correcting prediction deviations, the technical advantages of supercapacitors—high power density and fast response—are utilized to perform real-time tracking and dynamic compensation of the upper-layer baseline plan. This effectively reduces the impact of prediction errors on control accuracy, achieves smooth control of tie-line power, and enhances overall system stability. Case study results based on an actual railway traction power supply system demonstrate that the proposed method can fully leverage the coordinated and complementary characteristics of the hybrid energy storage system, effectively suppress power fluctuations from renewable energy output and traction loads, and achieve economic operation objectives while ensuring system disturbance rejection performance, thereby validating the effectiveness and practicality of the strategy.

The development of new energy vehicles, particularly electric vehicles (EVs) and hydrogen fuel cell vehicles (HFCVs), represents a strategic initiative to address climate change and foster sustainable development. Integrating PV with hydrogen production into hybrid electricity-hydrogen energy stations enhances land and energy efficiency but introduces scheduling challenges due to uncertainties. A multi-time scale scheduling framework, which includes day-ahead and intraday optimization, is established using fuzzy chance-constrained programming to minimize costs while considering the uncertainties of PV generation and charging/refueling demand. Correspondingly, trapezoidal membership function and triangular membership function are used for the fuzzy quantification of day-ahead and intraday predictions of photovoltaic power generation and load demands. The system achieves 29.37% lower carbon emissions and 17.73% reduced annualized costs compared to day-ahead-only scheduling. This is enabled by real-time tracking of PV/load fluctuations and optimized electrolyzer/fuel cell operations, maximizing renewable energy utilization. The proposed multi-time scale framework dynamically addresses short-term fluctuations in PV generation and load demand induced by weather variability and temporal dynamics. By characterizing PV/load uncertainties through fuzzy methods, it enables formulation of chance-constrained programming models for operational risk quantification. The confidence level – reflecting decision-makers’ reliability expectations – progressively increases with refined temporal resolution, balancing economic efficiency and operational reliability.