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With the expansion and enhancement of the power transmission network, short-circuit current (SCC) has become a major concern in grid operations. While transmission switching is one effective solution to reduce the SCC without investing in additional equipment, switching lines could threaten system N-1 security. To find an efficient, and secure, yet economic switching solution, this paper proposes an optimal transmission switching model with SCC limitation and N-1 reliability. As the relationship between SCC and integer variables associated with the line states is coupled, nonlinear and difficult to explicitly express, an effective linearization method is proposed. Theoretical analysis of the linearization error is performed using an illustrative example. Case studies have shown that the linearization error is generally small and decreases rapidly with the increase of electrical distance. Based on the linearized expression for SCC, a transmission switching model with SCC limitation and N-1 reliability constraints is proposed. Furthermore, to assure the calculation accuracy for the SCC, an iterative algorithm is designed to compensate for the linearization error. Case studies on the modified IEEE 30-bus, 118-bus and practically-sized 300-bus systems validate the effectiveness of the proposed model and algorithm. The solving efficiency of the model is investigated and discussed as well.

Palette images are widely used in multimedia and Internet applications. In this paper, a new method for data hiding in palette images with security protection by color ordering and mapping, as well as parameter randomization, is proposed. First, image pixels are classified as data embeddable or nonembeddable, and only the former ones are used to embed secret data. The proposed idea of data hiding is based on the use of a new type of color-ordering relationship, from which a color-mapping function is defined with binary values as output. When a secret data bit is to be embedded, a data-embeddable pixel is selected, and its color is adjusted to make the output of the color-mapping function equal to the secret bit value. The embedded secret data can be extracted correctly and quickly from the resulting stego-image by merely inspecting the outputs of the color-mapping function. Indetectability of the secret information embedded by the proposed method is also analyzed and confirmed. Furthermore, a number of possible security enhancement measures based on parameter randomization in the data-embedding process are proposed to protect the hidden data in the stego-image. The randomization effect is created by the use of a secret key and a number of random number-generating functions. The proposed data hiding method was tested with a variety of palette images. The experimental results show that secret data can be embedded and extracted successfully without producing visual artifacts in the cover image. A good balance between stego-image quality and data-embedding capacity can be achieved, which proves the efficiency and feasibility of the proposed method for practical applications.Index Terms-Color palette, color-mapping function, color-ordering relationship, cover image, data hiding, palette image, parameter randomization, random number-generating function, security protection, stego-image.

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