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Under the background of the new power system, it is important to make full use of the distributed generation in the distribution network to achieve carbon peaking and carbon neutrality goals. With the wide access of distributed power sources, there is bi-directional power flow between the transmission and distribution networks. If the transmission and distribution networks still follow the traditional equivalence method for optimal power calculation, accurate results will not be obtained. Therefore, a transmission-distribution-network-coordinated optimal power flow model is established. The node tearing method is used to decouple the coupling variables of the transmission network and distribution networks. On this basis, the iterative form of the model with immobile points is obtained by mathematical derivation. The traditional heterogeneous decomposition algorithm only uses the latest calculation results for iterative computation. Hence, combining with the Anderson acceleration idea in mathematics, the heterogeneous decomposition algorithm based on Anderson acceleration is proposed by using the historical iteration values to optimize the iterations of immobile points. It is demonstrated by numerical experiments that, the established model can fully utilize the initiative of the distribution networks and reduce carbon emissions. The proposed algorithm has high accuracy. In addition, compared with the heterogeneous decomposition algorithm, its convergence performance is significantly improved.

An iteration-variable-correction (IVC) based method is proposed for solving optimal power flow (OPF) of transmission-distribution-coupled (TDC) systems. First, a TDC system can be divided into a single coordinator and multiple agents. Then, the basic formulation, subproblem construction, and selection of iteration variables are given based on the conventional heterogeneous decomposition algorithm (HGD). Considering the limitations of the conventional HGD, the IVC is proposed. According to the general theory of the IVC, when it is applied to solve TDC OPF, the voltage magnitude of boundary buses and the multipliers corresponding to boundary power injections will be corrected every four iterations with first-order and second-order differential operations on historical results in the previous four iterations. The quadratic convergence of the IVC is proved under several weak assumptions. The numerical experiments demonstrate that the proposed IVC has the same accuracy as the method based on the centralized OPF model. Also, better convergence and efficiency can be achieved under the IVC compared with some conventional decomposition methods, including alternating direction method of multipliers, auxiliary problem principle method, analytical target cascading method, and the HGD. [ABSTRACT FROM AUTHOR]

Considering that the conventional synchronous splitting (MSS) method for power flow calculation of coupled transmission and active distribution (TDC) systems has limitations in efficiency and convergence due to the penetration of distributed generations (DGs) and loop operation, this paper proposes an asynchronous forward-backward-splitting power flow algorithm of TDC systems. In this algorithm, the transmission system operator (TSO) acts as a coordinator and processes forward steps while the distribution system operators (DSOs) act as agents and process backward steps. Two first-in-first-out queues are introduced to realize an asynchronous mechanism, and thus, the TSO does not have to wait for the slowest DSO to complete its power flow calculation and power injection update before the next iteration can proceed. This asynchronous mechanism has a higher efficiency compared with a synchronous one when communication delays exist. In addition, the conventional fixed-point iteration in the MSS method is replaced with the Krasnosel’skii-Mann iteration. The proposed algorithm with appropriate settings will achieve better convergence, especially when active distribution networks are considered, where volt-walt-control-typed and volt-var-control-typed DGs are penetrated. The linear convergence of the proposed algorithm is proved under several assumptions and the parameter tuning issue is discussed with numerical experiments. [ABSTRACT FROM AUTHOR]

This paper introduces a novel successive-intersection-approximation-based power flow method for integrated transmission and distribution networks (I-T&D). In this method, the entire I-T&D is split into the transmission network part, distribution network part, and boundary part. Then, alternate iterations are processed between a transmission network (TN) and several distribution networks (DNs) by exchanging the voltage and power injection of boundary buses. Particularly, the voltage magnitude of the boundary buses will be modified every two iterations by obtaining an intersection with the results in the previous two iterations. The local quadratic convergence of the method is proved strictly. The numerical experiment demonstrates that the proposed method has the same accuracy as the method based on the global model. Also, better convergence and efficiency can be achieved under the proposed method compared with the master-slave-splitting method in several different circumstances, DNs with loops, DNs with distributed generations, DNs with on-load tap changers, large-scale systems, etc. Besides, the proposed method is applied in the contingency analysis, achieving satisfying convergence and efficiency. [ABSTRACT FROM AUTHOR]

An asynchronous heterogeneous decomposition (async‐HGD) algorithm for integrated transmission and distribution networks coordinated optimisation considering communication conditions is proposed. Compared with traditional synchronous HGD (sync‐HGD), a partial synchronisation mechanism is introduced instead of the full synchronisation to alleviate the influence of communication delays. Under this mechanism, the transmission system operator does not need to wait for the slowest distribution system operator to complete its subproblem and update boundary parameters before the next iteration can proceed. Also, a bounded delay is introduced under this mechanism to ensure sufficient freshness of all the updates. Further, the previous value strategy (PVS) and linear regression strategy (LVS) are applied to handle non‐instantaneous interruptions in the communication networks as an improvement of the async‐HGD. Numerical experiments show that considering communication delays in the actual operation; the async‐HGD takes less time to converge compared with the sync‐HGD under appropriate settings. In addition, PVS and LVS can both enhance the robustness of the overall algorithm by achieving approximate solutions, and the LVS can achieve more accurate results compared with the PVS. [ABSTRACT FROM AUTHOR]

To satisfy the robust and real-time requirements of power flow calculation for large-scale power systems, a globally convergent method is proposed with trust-region techniques, which shows satisfying robustness and convergence. Then, this method is combined with Newton's method to achieve a two-stage algorithm, benefiting from their different advantages. In the first stage, the proposed globally convergent method is used for searching power flow solution. When the values of state variables in a certain iteration are close enough to the real operational point, the algorithm enters the second stage to use Newton's method to achieve the solution. This two-stage algorithm can achieve an accurate solution for solvable cases, and can also achieve a least-square solution, which is an approximate solution for unsolvable cases. Numerical experiments show that the proposed globally convergent method and two-stage algorithm have better robustness and efficiency than the existing methods in previous research. They have universality for well- and ill-conditioned systems as well as the cases under ill-conditioned operational modes, heavy loads and inappropriate initial values. They can also handle different limit violations, such as reactive power limit in PV buses and voltage limit with tap changers action, which could significantly benefit real practice. [ABSTRACT FROM AUTHOR]