The limitations of the conventional master-slave-splitting (MSS) method, which is commonly applied to power flow and optimal power flow in integrated transmission and distribution (I-T&D) networks, are first analyzed. Considering that the MSS method suffers from a slow convergence rate or even divergence under some circumstances, a least-squares-based iterative (LSI) method is proposed. Compared with the MSS method, the LSI method modifies the iterative variables in each iteration by solving a least-squares problem with the information in previous iterations. A practical implementation and a parameter tuning strategy for the LSI method are discussed. Furthermore, a LSI-PF method is proposed to solve I-T&D power flow and a LSI-heterogeneous decomposition (LSI-HGD) method is proposed to solve optimal power flow. Numerical experiments demonstrate that the proposed LSI-PF and LSI-HGD methods can achieve the same accuracy as the benchmark methods. Meanwhile, these LSI methods, with appropriate settings, significantly enhance the convergence and efficiency of conventional methods. Also, in some cases, where conventional methods diverge, these LSI methods can still converge.

To enhance the cost-effectiveness of bulk hybrid AC-DC power systems and promote wind consumption, this paper proposes a two-stage risk-based robust reserve scheduling (RRRS) model. Different from traditional robust optimization, the proposed model applies an adjustable uncertainty set rather than a fixed one. Thereby, the operational risk is optimized together with the dispatch schedules, with a reasonable admissible region of wind power obtained correspondingly. In addition, both the operational base point and adjustment capacity of tie-lines are optimized in the RRRS model, which enables reserve sharing among the connected areas to handle the significant wind uncertainties. Based on the alternating direction method of multipliers (ADMM), a fully distributed framework is presented to solve the RRRS model in a distributed way. A dynamic penalty factor adjustment strategy (DPA) is also developed and applied to enhance its convergence properties. Since only limited information needs to be exchanged during the solution process, the communication burden is reduced and regional information is protected. Case studies on the 2-area 12-bus system and 3-area 354-bus system illustrate the effectiveness of the proposed model and approach.

To satisfy the requirements of accurate operational risk assessment of integrated transmission and distribution networks (I-T&D), an integrated operational risk assessment (I-ORA) algorithm is proposed. Specific cases demonstrate that an I-ORA is necessary because it provides accurate handling of the coupling between transmission and distribution networks, accurate analysis of power supply mode (PSM) changes of important users and helps to improve security and stability of power grid operations. Two key technical requirements in the I-ORA algorithm are realized, i.e., integrated topology analysis and integrated power flow calculation. Under a certain contingency, integrated topology analysis is used to assess the risks of substation power cuts, network split and PSM changes of important users, while the integrated power flow calculation, based on the self-adaptive Levenburg-Marquard method and Newton method, can be implemented to assess risks of heavy load/overload and voltage deviation. In addition, the graphics processing unit is used to parallelly process some computation-intensive steps. Numerical experiments show that the proposed I-ORA algorithm can realize accurate assessment for the entire I-T&D. In addition, the efficiency and convergence are satisfying, indicating the proposed I-ORA algorithm can significantly benefit real practice in the coordination operation of I-T&D in the future.