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Abstract:The power transformer is one of the most critical and expensive components for the stable operation of the power system. Hence, how to obtain the health condition of transformer is of great importance for power utilities. Multi-attribute decision-making (MADM), due to its ability of solving multi-source information problems, has become a quite effective tool to evaluate the health condition of transformers. Currently, the analytic hierarchy process (AHP) and Dempster-Shafer theory are two popular methods to solve MADM problems; however, these techniques rarely consider one-sidedness of the single weighting method and the exclusiveness hypothesis of the Dempster-Shafer theory. To overcome these limitations, this paper introduces a novel decision-making model, which integrates the merits of fuzzy set theory, game theory and modified evidence combination extended by D numbers, to evaluate the health condition of transformers. A four-level framework, which includes three factors and seventeen sub-factors, is put forward to facilitate the evaluation model. The model points out the following: First, the fuzzy set theory is employed to obtain the original basic probability assignments for all indices. Second, the subjective and objective weights of indices, which are calculated by fuzzy AHP and entropy weight, respectively, are integrated to generate the comprehensive weights based on game theory. Finally, based on the above two steps, the modified evidence combination extended by D numbers, which avoids the limitation of the exclusiveness hypothesis in the application of Dempster-Shafer theory, is proposed to obtain the final assessment results of transformers. Case studies are given to demonstrate the proposed modeling process. The results show the effectiveness and engineering practicability of the model in transformer condition assessment.

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A novel secrecy scenario of uplink non-orthogonal multiple access (NOMA) along with cooperative jammer(s) to improve secrecy performance is studied in this work. We first characterize secrecy performance in terms of positive secrecy rate probability, secrecy outage probability (SOP) and effective secrecy throughput (EST), and derive the closed-expressions of individual secrecy performance. The analytical results not only show an improvement on secrecy performance with the aid of cooperative jamming, but also clearly illustrate how each jammer affects the secrecy performance. We then continue the study of the individual secrecy performance for its asymptotic behaviors, and reveal it is only dependent on its relative distance to the eavesdropper over the desired receiver in a high signal-to-noise ratio (SNR) regime. Finally, the maximization of overall secrecy performance is covered by investigating two optimization problems: 1) optimal selection of jammer(s) under the same transmit power; 2) optimal power allocation to each transmitter, including jammers, under the constraint of limited total transmit power. The solutions to these two problems are presented and demonstrated by an appropriate case. INDEX TERMS Cooperative jamming, non-orthogonal multiple access (NOMA), successive interference cancellation (SIC), secrecy performance, zero-forcing (ZF). I. INTRODUCTION A. BACKGROUND