مدل‌سازی نامعین خطی پارامتر متغیر سیستم‌های قدرت با بهکارگیری نگاشت مجموعه پارامتر بر پایه الگوریتم تحلیل مولفه‌های اصلی جهت طراحی پایدارساز مقاوم

نویسندگان

تهران - دانشگاه شاهد - دانشکده فنی و مهندسی

چکیده

در این مقاله روشی نوین برای مدل‌سازی خطی پارامتر-متغیر (LPV) پلی‌تاپیک نامعین سیستم‌های قدرت بر اساس رویکرد نگاشت مجموعه پارامتر (PSM) بر پایه الگوریتم تحلیل مولفه‌های اصلی (PCA) ارائه شده است. ابتدا با خطی‌سازی معادلات سیستم حول مجموعه نقاطی از پاسخ گذرای دینامیکی، یک مدل LPV اولیه تولید می‌شود، سپس با به‌کارگیری تکنیک PSM برپایه الگوریتم PCA، تعداد مدل‌های خطی کاهش‌یافته و یک مدل پلی‌تاپیک کاهش‌یافته شکل می‌گیرد. برای پوشش اثرات غیرخطی سیستم و همچنین خطاهای ناشی از کاهش مدل‌ها، برای هر یک از مدل‌ها مقداری نامعینی در نظر گرفته می‌شود. یک کنترل‌کننده جایابی قطب مقاوم طراحی می‌شود تا قطب‌های مدل پلی‌تاپیک کاهش‌یافته را در یک ناحیه نامعادله ماتریسی خطی (LMI) قرار دهد، به‌طوری‌که سیستم از ضریب میرایی مناسبی برخوردار شود. یک شرط کافی به‌منظور تضمین پایداری مجانبی برای سیستم حلقه بسته، در برابر نامعینی‌ها نیز ارائه می‌شود. در انتها، کنترل‌کننده پیشنهادی، جهت طراحی یک PSS برای  یک سیستم قدرت تک-ماشینه و نیز در شرایط چند-ماشینه استفاده و شبیه‌سازی می‌شود. و نتایج آن با پاسخ PSS رایج استاندارد مقایسه می‌شود. نتایج شبیه‌سازی رفتار مقاوم کنترل‌کننده پیشنهادی را در شرایط مختلف بهره‌برداری و در برابر خطاهای متفاوت نشان می‌دهد.

کلیدواژه‌ها

عنوان مقاله [English]

Uncertain LPV Modeling of Power Systems using PCA-Based Parameter Set Mapping for Robust PSS Designing

نویسندگان [English]

  • M. B. Abolhasani Jabali
  • M. H. Kazemi
Department of Electrical Engineering, Shahed University, Tehran, Iran
چکیده [English]

This paper presents a new methodology for uncertain polytopic linear parameter-varying (LPV) modeling of power systems based on parameter set mapping (PSM) with principle component analysis (PCA). At first, an LPV representation of the system dynamics is generated by linearization of its usual differential-algebraic equations about the transient operating points. Then, the PCA-based PSM algorithm is used to reduce the number of models and generate a reduced polytopic LPV model. Because of the system nonlinearity and approximations of model reduction, some uncertainties are considered for each model. A robust pole placement controller is designed to assign the poles of polytopic model in a linear matrix inequality (LMI) region such that the response of the system has a proper damping ratio. A sufficient condition is also proposed to guarantee the asymptotic stability of the closed loop model against the uncertainties. Finally, the proposed controller is synthesized as a power system stabilizer (PSS). It is considered for a single-machine power system and then it is simulated in multi-machine case and compared its performance with a tuned standard conventional PSS and other cases of the controller. The results show the robust performance of the proposed controller especially in different operation conditions and faults.

کلیدواژه‌ها [English]

  • PSS
  • LPV modeling
  • PCA algorithm
  • LMI regions

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