For the nonintrusive load monitoring problem, we propose a new efficient mixed-integer linear programming model. Compared to other optimization-based models that are only capable of distinguishing between the on/off states of appliances, our model takes it a step further by incorporating continuous power variables and constructing power feature constraints, allowing for a more accurate fitting of the power consumption of each appliance. To improve the computation efficiency of our model, we present new state constraints, new linear penalty terms, new state transition constraints, and new minimum active time constraints. To extract features from load data containing noise efficiently, we propose automatic feature extraction algorithms based on distributionally robust optimization theory and linear regression. These algorithms can extract power boundary features, power fluctuation features, and minimum active time features. Our proposed method and six state-of-the-art optimization-based methods are tested on the almanac of minutely power dataset (AMPds) and REFIT to verify the performance of the proposed method. The results show that our method outperforms other methods in terms of disaggregation accuracy and computational efficiency. Moreover, our load feature extraction algorithms can effectively reduce the noise interference in the data. Our modeling approach can improve the computational efficiency of other optimization-based methods.

Accurately and efficiently evaluating the influence of pile–soil interaction on the overall natural frequency of wind turbines is one of the difficulties in current offshore wind power design. To improve the structural safety and reliability of the offshore wind turbine (OWT) systems, a new closed-form solution method of the overall natural frequency of OWTs considering pile–soil interactions with highly effective calculations is established. In this method, Hamilton’s principle and the equivalent coupled spring model (ECS model) were firstly combined. In Hamilton’s theory, the Timoshenko beam assumption and continuum element theory considering the three-dimensional displacement field of soil were used to simulate the large-diameter monopile–soil interaction under lateral load in multilayer soil. Case studies were used to validate the proposed method’s correctness and efficiency. The results show that when compared with the data of 13 offshore wind projects reported in existing research papers, the difference between the overall natural frequency calculated by the proposed method and that reported in this study is within ±10%. This calculation method achieves the goal of convenient, fast and accurate prediction of the overall natural frequency of offshore wind systems.

In this article, we propose a new multistage semianticipativity model based on the distributionally robust optimization framework for dc power flow unit commitment problems with uncertain wind power. The proposed model constructs a flexible ambiguity set considering predicted wind power, which can flexibly adjust the robustness of the model according to the reliability of the predicted information. Moreover, a new approximation method based on the principal component analysis (PCA) is presented. After selecting the appropriate projection dimension, this method can improve the computation efficiency of the proposed model. At the same time, we propose a new linear decision rule based on PCA and provide the methods to address the problem that the time information disappears after using PCA. The characteristics of the proposed semianticipativity model are shown in a one-unit three-hour instance. Meanwhile, the performance of the proposed model and PCA-based approximate method is verified in six instances.

Non-intrusive load monitoring (NILM), a sophisticated load monitoring technology, has garnered considerable interest for its potential to assist consumers in lowering their energy expenditures. In this paper, we present a continuous non-convex optimization model for NILM that employs the norm-box constraint to convert the discrete integer variables in the model into continuous ones. Subsequently, we apply the alternating direction method of multipliers (ADMM) algorithm to tackle the non-convex problem. To enhance the sluggish convergence of the ADMM algorithm, we introduce a linear penalty term based on relaxation distance (RD) to supplant the conventional quadratic penalty term. Furthermore, we devise a heuristic refinement method based on neighborhood search (NS) to augment the solution quality of our algorithm. Simultaneously, by utilizing a dynamic window partitioning technique, the NILM task can be split into multiple small subtasks. These subtasks can be allocated to multiple consumer electronics with computing capabilities to achieve distributed computing. Ultimately, we validate our proposed algorithm on the AMPds dataset, and the experimental results demonstrate that it has faster convergence and yields better solutions compared to a state-of-the-art solver and traditional ADMM algorithms. Using our algorithm, the NILM system can offer consumers efficient, convenient, and economical services.

Simplified methods of static free head stiffness of the semi-rigid foundation under lateral loads were limited to flexible or rigid behavior by the critical length of piles. This would lead to errors when predicting the static or dynamic performance of their upper structures in OWT Systems. This paper presents a comprehensive analysis of the head static stiffness of the semi-rigid pile without considering the critical length. Firstly, case studies using the energy-based variational method encompassing nearly twenty thousand cases were conducted. These cases involved different types of foundations, including steel pipe piles and concrete caissons, in three types of soil: homogeneous soil, linearly inhomogeneous soil, and heterogeneous soil. Through the analysis of these cases, a series of polynomial equations of three kinds of head static stiffness, containing the relative stiffness of the pile and soil, the slenderness ratio, and Poisson’s ratio, were developed to capture the semi-rigid behavior of the foundations. Furthermore, the lateral deflection, the rotation for concrete caissons in the bridge projects, and several natural frequencies of three cases about the OWT system considering the SSI effect were carried out. the error of high-order frequency of the OWT system reached 13% after considering the semi-rigid effect of the foundation.