Traditionally, the optimal power flow (OPF) problem is solved in a centralized manner. However, with continuous expansion of the scale of multi-area interconnected power systems, realistic applications of the centralized method face additional challenges. In this paper, we propose a fully decentralized OPF algorithm for multi-area interconnected power systems based on the distributed interior point method, where solving the regional correction equation was converted into solving a parametric quadratic programming problem during each Newton-Raphson iteration. This is a novel approach to tackle the decentralized OPF problems. We analyzed the convergence property of this algorithm. The proposed approach is fully decentralized without central coordinator and parameter tuning, and is robust to network partitioning. Furthermore, this decentralized algorithm enjoys the same convergence performance and accuracy as the centralized interior point method. Results on a 3-bus test system, 4 IEEE test systems, and a real 4-area 6056-bus interconnected system show the benefits of the proposed method.

In this paper, we present an incremental-oriented alternating direction method of multipliers (ADMM) for distributed optimal power flow with discrete variables in distribution networks. This algorithm consists of outer-loop iterations based on the extended interior-point method (EIPM), and inner-loop iterations based on ADMM. The outer-loop EIPM iteration was used to form a regional linear correction equation with coupling relationships between neighboring areas. This enables us to use ADMM to compute the primal–dual directions in a distributed manner. This novel application of ADMM inside EIPM can be considered as an independent linear equation solver; thus, its convergence can be guaranteed. In particular, the updating of the variable increments can be expressed in a closed form, speeding up ADMM. The resulting algorithm has more attractive convergence properties compared to ADMM directly applied to mixed-integer nonlinear programming problems. The convergence analysis is also given. The test results demonstrated that the proposed algorithm converged reliably and obtained a sufficiently feasible solution.

The optimal scheduling of active distribution networks (ADNs) significantly enhances voltage security and reduces costs, particularly as the numbers of distributed generation sources and energy storage devices increase. Therefore, this paper presents a mixed-integer dynamic optimization (MIDO) model for the optimal scheduling of ADNs. This model incorporates loads and distributed generation outputs with continuous trajectories and aims to provide optimal continuous-trajectory schemes for ADNs. The optimization is conducted with the objective of minimizing the daily costs of electricity purchased from distribution substations. However, in practice, discrete control devices are required to adopt a limited number of switching operations, which increase the computational complexity of the MIDO model. Hence, a reduced convex relaxation method is utilized to achieve reduced convex transformation and tight relaxation of the MIDO model with respect to integer variables. This converts the MIDO model into a continuous dynamic optimization model, which is then further approximated as a nonlinear programming model using the Radau collocation method. Meanwhile, the absolute-value constraints limiting the number of switching operations are eliminated by an equivalent conversion to a series of linear inequalities. Numerical simulations on IEEE 33-bus, PG&E 69-bus, and real-world 110-bus ADNs demonstrate the effectiveness and efficiency of the proposed methodology.

With the increasing share of renewable energy in the grid and the enhanced flexibility of the future power system, it is imperative for thermal power companies to explore alternative strategies. The flexible transformation of thermal power units is an effective strategy to address the previously mentioned challenges; however, the factors influencing the diffusion of this technology merit further investigation, yet they have been seldom examined by scholars. To address this gap, this issue is examined using an evolutionary game model of multi-agent complex networks, and a more realistic group structure is established through heterogeneous group differentiation. With factors such as group relationships, diffusion paths, compensation electricity prices, and subsidy intensities as variables, several diffusion scenarios are developed for research purposes. The results indicate that when upper-level enterprises influence the decision-making of lower-level enterprises, technology diffusion is significantly accelerated, and enhanced communication among thermal power enterprises further promotes diffusion. Among thermal power enterprises, leveraging large and medium-sized enterprises to promote the flexibility transformation of units proves to be an effective strategy. With regard to factors like the compensation price for depth peak shaving, the initial application ratio of groups, and the intensity of government subsidies, the compensation price emerges as the key factor. Only with a high compensation price can the other two factors effectively contribute to promoting technology diffusion.

This study examines the decision-making optimization of Power-Generation Enterprises (PGEs) in the green certificate market, with a focus on balancing bidding strategies and carbon-reduction targets. Given the increasing complexity of the green certificate market, the research employs Bayesian games, evolutionary games, and Stackelberg games to systematically analyze the strategic behavior of PGEs and their interactions within the market framework. The findings demonstrate that game theory facilitates cost structure optimization and enhances adaptability to market dynamics under policy-driven incentives and penalties. Additionally, the study explores the integration of stochastic modeling and machine learning techniques to address market uncertainties. These results provide theoretical support for policymakers in designing efficient green electricity market regulations and offer strategic insights for PGEs aligning with carbon neutrality objectives. This work bridges theoretical modeling and practical application, contributing to the advancement of sustainable energy policies and the development of green electricity markets.