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Confronted with uncertainties, especially from large amounts of renewable energy sources, power flow studies need further analysis to cover the range of voltage magnitude and transferred power. To address this issue, this work proposes a novel interval power flow for the radial network by the use of an extended, simplified DistFlow formulation, which can be transformed into a set of interval linear equations. Furthermore, the Krawczyk iteration method, including an approximate inverse preconditioner using Frobenius norm minimisation, is employed to solve this problem. The approximate inverse preconditioner guarantees the convergence of the iterative method and has the potential for parallel implementation. In addition, to avoid generating a dense approximate inverse matrix in the preconditioning step, a dropping strategy is introduced to perform a sparse representation, which can significantly reduce the memory requirement and ease the matrix operation burden. The proposed methods are demonstrated on 33-bus, 69-bus, 123-bus, and several large systems. A comparison with interval LU decomposition, interval Gauss elimination method, and Monte Carlo simulation verifies its effectiveness. [ABSTRACT FROM AUTHOR]

When large wind farms are centrally integrated in a power grid, cascading tripping faults induced by voltage issues are becoming a great challenge. This paper therefore proposes a concept of static voltage security region to guarantee that the voltage will remain within operation limits under both base conditions and N-1 contingencies. For large wind farms, significant computational effort is required to calculate the exact boundary of the proposed security region. To reduce this computational burden and facilitate the overall analysis, the characteristics of the security region are first analyzed, and its boundary components are shown to be strictly convex. Approximate security regions are then proposed, which are formed by a set of linear cutting planes based on special operating points known as near points and inner points. The security region encompassed by cutting planes is a good approximation to the actual security region. The proposed procedures are demonstrated on a modified nine-bus system with two wind farms. The simulation confirmed that the cutting plane technique can provide a very good approximation to the actual security region. [ABSTRACT FROM AUTHOR]

In Part I of this work, a static voltage security region was introduced to guarantee the safety of wind farm reactive power outputs under both base conditions and N-1 contingency. In this paper, a mathematical representation of the approximate N-1 security region has further studied to provide better coordination among wind farms and help prevent cascading tripping following a single wind farm trip. Besides, the influence of active power on the security region is studied. The proposed methods are demonstrated for N-1 contingency cases in a nine-bus system. The simulations verify that the N-1 security region is a small subset of the security region under base conditions. They also illustrate the fact that if the system is simply operated below the reactive power limits, without coordination among the wind farms, the static voltage is likely to exceed its limit. A two-step optimal adjustment strategy is introduced to shift insecure operating points into the security region under N-1 contingency. Through extensive numerical studies, the effectiveness of the proposed technique is confirmed. [ABSTRACT FROM AUTHOR]