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With large‐scale wind farms connected to AC/DC network, the transient stability assessment (TSA) of the power system becomes more and more difficult. Among them, estimating the region of attraction (ROA) of the equilibrium point is a traditional but still challenging problem. Based on the Lyapunov stability theory, this paper proposes a new approach to obtain the enlarged estimation of the ROA. The optimization and updating strategy of shape function in the sum of squares (SOS) optimization problem are studied to reduce the conservatism of estimation result. In the proposed method, the gravitational search algorithm (GSA) is employed to optimize the coefficients of initial shape function to improve estimation performance. Based on the time‐domain simulation (TDS) of expected faults, the fitness value for shape function optimization is calculated using the values of state variables at the fault clearing time and the system stability information. Furthermore, the optimal Lyapunov function is computed by introducing the update condition of shape function and adjusting the iteration strategy of the ROA estimation algorithm. Finally, the proposed method is applied to a two‐machine‐infinite‐bus system and a more complex nine‐bus AC/DC system with wind power. And the effectiveness of the proposed method is verified by comparing with the existing ROA estimation methods. [ABSTRACT FROM AUTHOR]

With the interconnection of large power networks, transient voltage stability of AC/DC power systems has been paid more attention in recent years. To investigate main influence of generating facility, high-voltage direct current (HVDC) and motor load for transient voltage stability, from the perspective of the generalised branch potential energy, the new indexes, and analysis method is proposed here. First, an energy function for AC/DC system is constructed with major dynamic components, namely classical HVDC control systems and motors in third-order model. Accordingly, the influence effects of the above major dynamic elements are investigated based on indexes from the corresponding generalised branch potential energy. With the rule of change in transient potential energy distribution in the network and information in stability margins, an evaluating procedure is established. Here, the judgment of transient voltage stability employs a heuristic energy function method. Finally, simulation tests on three-machine system with a HVDC transmission line are conducted in PSAT package, and the obtained results demonstrate the feasibility and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

• The AC/DC system can be modeled as a switched nonlinear system. • The equations representing the transient characteristics of a DC system are reflected in the process of transient stability domain estimation. • The continuous piecewise Lyapunov function and stability domain estimation algorithm for the AC/DC system are proposed. • The effects of different SOS approximation methods on the results are shown under the influence of numerical problems. Transient stability analysis is a traditional yet significant topic in power systems. The switching control schemes of the HVDC converter station after fault bring new challenges to the direct method of transient stability analysis in AC/DC power systems. To apply the direct method to investigate the transient stability of power systems accommodating the switching characteristics of the line commutated converter (LCC) HVDC, continuous piecewise Lyapunov functions are constructed for a whole AC/DC system model including several classical LCC-HVDC control modes, and the continuity of Lyapunov functions is studied and guaranteed in transitions between control modes. Then, the Sum-of-Squares optimization is employed to find the optimal continuous piecewise Lyapunov functions. Finally, the transient stability domain is estimated for a sample system including the main control loops of LCC-HVDC, a three-order generator model, and a one-order exciter model. Tests in MATLAB environment are conducted to demonstrate the feasibility of this method. [ABSTRACT FROM AUTHOR]