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This paper addresses multiphase matrix converter (MPMCs) modulated with Venturini's classical scalar approach. The solution to obtain time-varying modulation functions was limited to 3 × 3 configuration, which was later extended to 3 × n configuration. The equations had four constants that were common to all modulation functions; out of which two were defined arbitrarily and other two were found analytically by reducing the equation to a two-variable optimisation problem. However, in this work, an attempt is made to provide flexibility in finding other solutions by taking all the constants as variables. Thus, Differential Evolution (DE) algorithm is adopted in the proposed modulation approach to solve the complex equations thus obtained. Another aim is to find the solution for the MPMC, where inputs are more than three. It is found that the optimal solutions exist only for 3 × n configuration and are in close approximation with the results of analytical approach. Other solutions were found for certain input and output frequencies and voltage transfer ratios whose results are discussed. It is also found that the solution does not exist for configurations with input phases are other than three. The discussion is supported by simulation and experimental results on a 3 × 7 matrix converter at various values of voltage transfer ratios and input/output frequencies.

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Determination of accurate operating states of the power system is one of the most challenging tasks due to integration of large number of solar PVs into the power system. Since these sources of energy are inertialess generations, hence may cause instability issues if highly penetrated. Hence, precise monitoring and control of such systems with higher PV penetration is a critical issue to address both in terms of the total number of PV sources in the system and the percentage of penetration. Phasor Measurement Units (PMUs), with their time synchronizing abilities, have made this task a bit easier. However, traditional centralized data handling architecture at control centers are becoming redundant due to various limitations such as data handling, computational constraints etc. To overcome this, a distributed PMU-PDC architecture approach is utilized in this paper. Since local PDC (Phasor Data Concentrator) in an n-area power system can run separate optimization algorithms, by combining the results of these optimization algorithms of n-area PDCs, we can get a much more accurate global consensus about the current operating state of the system. The presented work is divided into two parts. First, the analysis of power system stability is performed in terms of the total number of Photovoltaic Source (PV) in the system and the percentage of PV penetration. Then, the accuracy of the method is tested both in terms of the number of PMUs in each area along with their channel capacities. Low-frequency oscillations have been simulated on IEEE-68 standard bus system using MATLAB, and the modes of oscillation are estimated using the Alternating Direction Method of Multipliers (ADMM) algorithm. INDEX TERMSWide-Area Measurement System (WAMS), Phasor Measurement Unit (PMU), Phasor Data Concentrator (PDC), Alternating Direction Method of Multipliers (ADMM)

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