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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.

The modeling and multi-energy flow calculation of an integrated energy system (IES) are the bases of its operation and planning. This paper establishes the models of various energy sub-systems and the coupling equipment for an electricity-gas-thermal IES, and an integrated multi-energy flow calculation model of the IES is constructed. A simplified calculation method for the compressor model in a natural gas network, one which is not included in a loop and works in constant compression ratio mode, is also proposed based on the concept of model reduction. In addition, a numerical conversion method for dealing with the conflict between nominal value and per unit value in the multi-energy flow calculation of IES is described. A case study is given to verify the correctness and speed of the proposed method, and the electricity-gas-thermal coupling interaction characteristics among sub-systems are studied.

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.

Considering the increasing coupling between transmission and distribution networks, an affine arithmetic-based interval power flow algorithm of integrated transmission and distribution (I-T&D) networks is proposed. First, a novel two-step approximation method for sine and cosine functions is proposed to reduce the number of noise variables in the affine form of the injected power, as the basis of the proposed algorithm. Then, this algorithm is divided into four stages, which are implemented alternatively between a transmission system operator (TSO) and multiple distribution system operators (DSOs) by exchanging parameters at TSO-DSO boundaries. Three-phase unbalanced I-T&D networks and boundary tap changer action are also discussed. In addition, an asynchronous power flow method is proposed to mitigate the influences of communication networks on the proposed interval power flow algorithm. Numerical experiments demonstrate the effectiveness of the proposed two-step approximation method, as well as the conservative property, fairly good approximation effect, high efficiency, and low data exchange amount of the proposed algorithm in various circumstances, including single-phase and three-phase networks, varying degrees of unbalance, various smart inverter controls, etc.

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.

A transmission contingency analysis (TCA) method based on data-driven equivalencing of radial DN distribution networks is proposed. First, an offline-online-combined data-driven model training method is proposed. The historical data are exploited during offline model training considering the uncertainties of loads and distributed generations to achieve partially prepared root nodal power injection functions, where root nodal voltage magnitudes are taken as arguments. After that, the real-time data of loads and DGs are used to determine all coefficients in these functions. In the proposed TCA, DNs will be equivalent to simplified models by distribution system operators (DSOs) with the data-driven method and the models will be sent to the transmission system operator (TSO). Then, TSO can complete the TCA independently. Numerical experiments show that the proposed TCA approach has similar accuracy and higher efficiency compared with the traditional global-power-flow-based TCA approach. It not only significantly reduces communication time between TSO and DSOs, but also saves calculation times, which may benefit real practice in the coordination operation of transmission-distribution-coupled systems in the future.

As the coupling between transmission systems and distribution systems is significantly enhanced, transmission-distribution coordinated optimisation becomes more and more necessary. Considering that the objectives of the transmission system operator (TSO) and the distribution system operator (DSO) are usually significantly different in the type and dimension, a synthesised-objective collaborative model is proposed in this study, by normalising different objectives, introducing a weight factor to reflect the importance degree difference of multiple objectives and constructing a common objective. Then, a modified heterogeneous decomposition (M-HGD) algorithm is proposed to solve the model. In the M-HGD, two modifications on the update of iterative variables and the stop criteria are proposed, which effectively relieves the fluctuation of the iterative variables and restrains the tail effect of the convergence curve. The proposed model and algorithm can avoid privacy issues between the TSO and the DSO, achieve Pareto optimality solutions, and have powerful flexibility. Numerical experiments validate the effectiveness of the proposed model and demonstrate that the M-HGD has high accuracy and has better convergence and efficiency than traditional distributed optimisation methods.

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.

This paper proposes two fast calculation algorithms for the determination of the saddle-node bifurcation point of islanded microgrids, which use bisection search and parabolic approximation respectively. The Levenberg-Marquardt algorithm is applied to obtain the least-squares solution in the infeasible region of power flow equations. The bisection search algorithm uses the least-squares solution to determine whether the current trial step reaches the power flow infeasible region, and finally approaches the saddle-node bifurcation point. The parabolic approximation algorithm performs a parabolic approximation to ‘the least-squares value’ – ‘load margin’ curve in the infeasible region, and the zero point of the curve is corresponding to the required saddle-node bifurcation point. The case analysis shows that the two algorithms proposed in this paper have the advantages of high accuracy, high computational efficiency, and strong robustness.

Water inrush hazard seriously threatens construction safety of subsea tunnels in unfavorable geological areas. In recent years, a large number of subsea tunnels have been built worldwide, some of which have experienced many water inrush disasters, especially in Japan and Norway. In this paper, a systematic methodology is proposed to rigorously review the current literature about water inrush in subsea tunnels. Emphasis is placed on recorded causes and evolution processes of water inrush, as well as relevant mitigation measures. In particular, the geological conditions that generate such water inrush hazards are initially discussed by counting cases of tunnel water inrush in the past decades (43 cases of water inrush hazards in tunnels (including mountain tunnels)). The process of formation of failure modes of water inrush, and the corresponding research methods (including theoretical, numerical and experimental) are reviewed, and can be used to pave the ways for hazard prevention and future research. This is followed by a summary of the prevention methods and mitigation measures used in practice, and a short discussion of the achievements and limitations of each method. Then combined with the evolution characteristics of the failure area, the water inrush process of different modes is divided into three stages, with a proposed a grouting scheme for each stage. Finally, concluding remarks, current research gaps and future research directions on subsea tunnel water inrush are provided and discussed.

A continuous power flow (CPF) calculation method for the islanded microgrids with droop control is proposed in this paper. The starting point of CPF is solved by the modified factored load flow algorithm. The algorithm ensures the robustness of the starting point calculation with a two-step solution. The tangent prediction method and the Newton-Raphson method are used to determine the prediction and correction steps. Further, this paper proposes an adaptive step size control method based on frequency variation, which avoids the comparison among different nodal voltage magnitudes. In addition, node type switching is considered for handling the limit violations of PV nodes and droop nodes. The case analysis shows that the proposed CPF method has high efficiency and strong robustness.

In this paper, neural network, semi-supervised training, integrated learning, and other techniques are applied to the prediction and analysis of static voltage stability margin of island microgrid power systems and an online prediction method based on the Tri-Training-Lasso-BP network is proposed. The network consists of Tri-Training, the least absolute shrinkage and select operator (Lasso) algorithm and the backpropagation (BP) neural network. The analysis results on an 115-node example show that the proposed method can reduce the requirement of the data volume of the training set, take advantage of the massive data collected during the daily operation of the power system, improve the prediction accuracy of the network and reduce manual intervention. Finally, this paper uses statistical methods to make a comprehensive and objective description of the performance of the method.

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 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 operation. Two key technical requirements in the I-ORA algorithm are realized, integrated topology analysis and integrated power flow calculation. Under a certain contingency, integrated topology analysis is used to assess risks of substation power cut, network split and PSM changes of important users, while the integrated power flow calculation, based on the self-adaptive Leven-burg-Marquard method and Newton method, can be implemented to assess risks of heavy load/overload and voltage deviation. Besides, 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, which indicates that the proposed I-ORA algorithm can significantly benefit real practice in the coordination operation of I-T&D in the future.

A TSO-DSO interactive mechanism is proposed to realize coordinated voltage support of transmission network by reactive power provision, activating flexibility of active distribution networks, such as distributed generations, flexible loads, reactive power compensators, etc. The mechanism consists of four stages: i) TSO sends reactive power request to DSOs; ii) Each DSO forms its reactive power quantity-price curve and sends to TSO; iii) TSO does a global optimization to achieve a voltage support scheme, incorporating its own reactive power provision devices and reactive power quantity-price curves; iv) Each DSO re-optimizes in its local area to reach the voltage support requirement. Based on this mechanism, the specific implementation approaches of the four stages are discussed, and a four-stage distributed algorithm is proposed. The case analysis demonstrates that the proposed mechanism and algorithm can effectively and accurately realize voltage support. Also, the TSO is able to achieve a more cost-effective scheme compared with independent voltage support while the active elements managed by DSOs achieve profits from participating in the coordinated voltage support. Specifically, in the test case presented in this paper, the coordinated scheme can save more than 50% costs and 25% reactive power requirements compared with the traditional one.

This paper presents an asynchronous distributed global power flow method for transmission-distribution coordinated analysis. Considering the communication delays between the transmission system operator (TSO) and distribution system operators (DSOs), this paper introduces ‘partial synchronization’ instead of full synchronization in the traditional synchronous method. Under this mechanism, the TSO needs not to wait for the slowest DSO to complete its power flow calculation and power injection update before the next iteration can proceed. Numerical experiments demonstrate that the proposed asynchronous method takes less time compared with the synchronous method under the same accuracy requirement. Further, this paper proposes a bi-directional network equivalence method to work against non-instantaneous interruptions. Polynomial fitting is used to describe the characteristics of networks, which enables transmission and distribution networks can independently finish power flow calculation when a non-instantaneous interruption happens. Numerical experiments demonstrate that the proposed method can achieve high accuracy.

With the expansion of scale of power system, in order to satisfy the real-time and accuracy requirements of N-1 security, a GPU based real-time N-1 AC power flow algorithm with preconditioned iterative method was proposed. This algorithm concatenated independent power flow problems into one. The concatenated Jacobi matrix was formed by parallel processing, and the linear equations were solved by the direct method or the iterative method according to the scale of equations. The iterative method was designed and parallelly processed based on preconditioning method ILU(0) and Krylov theory. The case analysis shows that, the proposed algorithm has high efficiency, high accuracy and needs small memory footprint, which could be applied to engineering practice.