پخش توان در سیستم‌های قدرت با شرایط نزدیک به غیرقابل‌حل با تلفیق ماتریس‌های ژاکوبین و قطری غیرتکین

نوع مقاله : علمی-پژوهشی

نویسندگان

دانشکده فنی و مهندسی - دانشگاه شهرکرد

چکیده

سیستم‌های قدرت برمبنای دترمینان ماتریس ژاکوبین آن‌ها در مسئله پخش توان، به سیستم‌های با شرایط مطلوب، شرایط بد و غیرقابل‌حل تقسیم‌بندی می‌شوند. در این مقاله، روشی ساده و ابتکاری براساس روش نیوتن برای حل مسائل پخش توان در حالت‌هایی که سیستم قدرت در شرایط غیرقابل‌حل یا نزدیک به غیرقابل‌حل قرار گرفته ‌است، ارائه شده‌است. این روش برمبنای تلفیق ماتریس معکوس ژاکوبین با ماتریس قطری غیرتکین بنا شده‌است. اعمال این روش، باعث تغییر مقادیر ویژه صفر و تغییر این مقادیر به یک مقدار در همسایگی مقدار ویژه صفر می‌شود. روش پیشنهادی برروی سیستم‌های 2 شین، 11شین، 14 شین و 118 شین مورد ارزیابی قرار گرفته ‌است و نشان داده‌شده که اعمال الگوریتم پیشنهادی در سیستم‌های قدرت با ابعاد مختلف، می‌تواند زمان محاسبات و تعداد تکرار را در مقایسه با روش‌های دیگر کاهش دهد.

کلیدواژه‌ها


عنوان مقاله [English]

Power Flow of Unsolvable Power Systems using Combination of Jacobian and Nonsingular Diagonal Matrices

نویسندگان [English]

  • S. Y. Derakhshandeh
  • R. Pourbagher
Faculty of Engineering, Shahrekord University, Shahrekord, Iran
چکیده [English]

Based on the determinant of the Jacobian matrix in the power flow (PF) problem, power systems are categorized to well-conditioned, ill-conditioned and unsolvable systems. In this paper, a novel and simple approach based on Newton technique is presented to solve the PF problems in the unsolvable power flow cases in the power systems. The presented method is based on combination of the inverse of Jacobian matrix to a nonsingular diagonal matrix. Application of the proposed method causes to change the zero eigenvalues to new values in their neighborhoods. The application of the presented algorithm in various scale power systems (2-bus, 11-bus, 14-bus and 118-bus) indicates that the proposed formulation decreases the computation time and number of iterations in comparison with benchmark methods.

کلیدواژه‌ها [English]

  • Jacobian matrix
  • power flow
  • unsolvable system
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