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The article presents an algorithm for determining the modes with maximum power for long distance equivalent power systems in various configurations with a simplified representation of the excitation system of synchronous generators. Given the large volume of calculations and analytical transformations, a feature has been identified that allows one to determine the disturbance of static stability (out-of-step mode). The indicated sign is the extremum of the function of free term of the characteristic equation. A quantitative and qualitative analysis of the eigenvalues of the coefficient matrix of the system of linearized differential equations of electromechanical transients has been performed to confirm the proposed approach to determining stability. The dependence of the coefficients of the characteristic equation was studied in the course of the analysis with a change in the length of power lines and the power of the considered power units. The indicated coefficients were obtained after mathematical transformations of the system of linearized differential equations of electromechanical transients. According to the results of studies, it was found that among the roots of the characteristic equation that determine the electromechanical movement in the power system, there is a redistribution of material parts, while there is an increase in the attenuation of low-frequency oscillations. In the presence of excitation controllers using channels with respect to the derivative of the operating parameters, the redistribution of the material parts responsible for the attenuation of electromechanical vibrations is even more pronounced. Based on the results and conclusions, the authors proposed a generalized method for studying the stability of power system based on the appearance of low-frequency oscillations. This technique with simplified models allows you to evaluate the maximum transmitted power without the occurrence of electromechanical vibrations, i.e. while maintaining the static vibrational stability, which allows to reduce the volume of the considered design modes for power systems of very different structures.

The existing localization algorithms for coherently distributed (CD) sources fail to achieve the best localization performance because of position information loss and error accumulation. To solve this problem, this study proposed a novel direct position determination (DPD) algorithm that profits from the characteristics of noncircular signals. Based on the parameterization assumption of CD sources, the DPD localization model is initially constructed and an extended subspace data fusion-based DPD algorithm is subsequently proposed by decomposing the extended covariance matrices, which are constructed by combining the characteristics of noncircular sources. The algorithm achieves a low complexity and a high efficiency by avoiding the calculation of the intermediate variables. Specifically, the closed-form expression of the Cramer-Rao lower bound for CD noncircular sources is also derived. Simulation results show that, compared with existing DPD algorithms, the proposed algorithm improves the multitarget localization capability and achieves high-accuracy results.

This paper discusses the localization problem for strictly noncircular sources based on Doppler shifts and angle of arrival (AOA). The conventional location methods, called two-step methods, first extract measurement parameters from the signals, and then estimate the position from these parameters. Unlike the conventional two-step methods, direct position determination (DPD) methods can locate emitter in a single step without estimating intermediate parameters, thereby receiving higher location accuracy. However, existing DPD algorithms focusing on moving receivers remain few, and ignore exploiting the noncircular property of sources to enhance the localization accuracy. To solve these problems, this paper develops a decoupled maximum likelihood (ML) DPD algorithm for strictly noncircular sources based on Doppler shifts and AOA. First, we reconstruct the DPD optimization model by exploiting the noncircular property of sources and using Doppler shifts to meet the moving receivers application. Then, since the prescribed ML DPD algorithm for multiple sources will suffer huge computation load, a decoupled iterative idea is applied to it. Compared with the straightforward implementation of ML estimators, our method substantially reduces the computation complexity via decoupling the position of each emitter from the other emitters in each iteration. In addition, we derive the Cramér-Rao Bound for strictly noncircular sources, and prove it is lower than that of circular sources. Simulation results demonstrate that the proposed algorithm achieves convergence through only a few iterations, and receives superior performance than other location methods in the test scenarios.

Compared with conventional two-step localization algorithms which are implemented by initially estimating localization parameters and then calculating the target position, the performance of direct position determination (DPD) algorithm is superior in terms of high estimation accuracy and strong resolution capability. DPD algorithms can make full use of the characteristics of signals to improve positioning performance. Using this localization mechanism as basis, this study develops a novel DPD algorithm that profits from the characteristics of orthogonal frequency division multiplexing (OFDM) signals based on the time and angle of arrival. First, the DPD optimization model is constructed based on maximum likelihood criterion and the characteristic of multiple carrier modulation technique of OFDM signals. Then, an extended subspace data fusion-based DPD algorithm is developed by constructing and decomposing the extended covariance matrices. The algorithm fuses the extended subspace data to estimate the target position without calculating the intermediate variables, which is less complex and more efficient. These properties can avoid the limitations of two-step algorithms. The last but important result is a derivation of the closed-form expression of Cramer-Rao lower bound (CRLB) on the position estimation variance for OFDM sources. Simulation results show that, the algorithm proposed in this paper outperforms existing DPD algorithms and conventional two-step localization algorithms. Especially under the condition of low signal-to-noise ratio, its localization accuracy is close to the CRLB.