Two degree of freedom internal model control-PID design for LFC of power systems via logarithmic approximations

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Load frequency controller has been designed for reduced order model of single area and two-area reheat hydro-thermal power system through internal model control – proportional integral derivative (IMC-PID) control techniques. The controller design method is based on two degree of freedom (2DOF) internal model control which combines with model order reduction technique. Here, in spite of taking full order system model a reduced order model has been considered for 2DOF-IMC-PID design and the designed controller is directly applied to full order system model. The Logarithmic based model order reduction technique is proposed to reduce the single and two-area high order power systems for the application of controller design.The proposed IMC-PID design of reduced order model achieves good dynamic response and robustness against load disturbance with the original high order system.

1. Introduction

The performance of the large scale power systems may deteriorate due to the existence of rapid load disturbances, uncertainties of parameters, operational variations, etc. Therefore, the robustness and stability are extremely important to design load frequency controller (LFC) for large scale power systems. But it is very difficult to design a robust controller in a large power system because of complexity; nonlinearity as well as higher order of the system. In the current scenario of power system, the basic burden of the systems is to maintain the stability between power generation and power demand, where power system offers to users a high-quality electric power with reliability. Fluctuations occurred in the power demand may affect the frequency of the electrical utilities as well as the power flow of tie-line between control areas. Consequently the load frequency controllers (LFCs) are being designed to maintain the system frequency in an organized manner, adjust the generator units founded primarily on area control error (ACE), building the area control error inclines to zero under the endless tuning of active power thus generation of whole system and load power well match accordingly. It is due to the fact that a controller of better design would provide better control.

Thus the load frequency controller can be considered as an objective optimization and robust control problem [1–8] which counteracts sudden load disturbances, parameter uncertainty and also able to perform well under prescribed overshoot, settling time, frequency and tie line power deviation [1]. In year 2009, Ganapathy [8] has proposed a decentralized LFC for interconnected power systems with Governor Dead Band and superconducting magnetic energy storage (SMES) units using multi-objective evolutionary algorithm (MOEA). Sahaj et al. [9] have proposed a decentralized proportional integral derivativeload frequency control (PID-LFC) for perturbed multi-area power systems, where power system performance of LFC is based on stability boundary locus. The design technique [9] creates parametric uncertainties, such type of perturbations are considered posteriori in the literature of LFC till now. Swati et al. [10] have evaluated the parameter uncertainty considering the concept of fractional order control, further designed a robust controller, which has been compared with internal model control – proportional integral derivative (IMC-PID) whereas Sathya [11] has suggested a LFC for interconnected power system using bat inspired algorithm constructed.

Also under the restructured power system scenario, a method has been proposed [12] in implementing the concept of load following in an automatic generation control. The proposed system [12] is validated on two area hydrothermal power system considering with and without contract violation. Further three-area unified power system is examined [13] as a test system under the condition of various different loadings. To stabilize the two area multi-unit hydro-hydropower system, a different kind of frequency stabilizers i.e. static synchronous series compensator (SSSC), superconducting magnetic energy storage (SMES), thyristor control phase shifter etc. has been proposed in the automatic generation system [14]. The several objective optimization problems have been explained by means of an optimization algorithm through clustering based selection [15]. In a few decades to optimize the controller gains of multi area power systems, various optimization techniques [16–20] have been proposed for the designing of three degree of freedom-proportional integral derivative (3DOF-PID) and cascade controllers [19,20]. With the application of biogeography based optimized technique [16–18] a successful 3DOF-PID controller [16,18] and 3DOF-ID controller [17] has been designed for unequal four/two area thermal systems and two area hydro-thermal deregulated systems respectively.

Further to improve the tracking performance, a data based method [21] has been developed for iterative tuning of the parameters in 3-DOF control structure. The data base tuning method comprises of three aspects. Firstly, use of input and output data, where it eliminates the cost while obtaining an accurate model. Secondly, it can be used as a tuning tool of controller. Thirdly, it gives the improved tracking performance without any change in control structure. Also for flexible motion systems, a jerk feedforward (JFF) controller is proposed [22] which are based on flexible mode and rigid body mode. An analysis has been done for correction of power factor in three phase system via reduced order modelling [23], where the control strategy uses three inner reduced order current controllers and an outer voltage loop for voltage regulation. It offers fast transient response, simple control strategy and better-quality power factor.

As per above discussion, to design a load frequency control, a mathematical model of high order power system may pose difficulties in its analysis, synthesis and identification. Most of the time higher order system may produce an unrealizable controller, which results in sluggish response with more computational effort. Therefore, it is desirable to approximate it by a low order model which retains the main qualitative properties of the original high order system such as time constant, damping ratio, stability, etc. So, several model order reduction methods in time domain [24–28] and frequency domain [29–34] have been proposed by numerous researchers to reduce the order of large-scale power system model into a suitable order. The quality of a reduction method is judged by the way it is utilized. One of the main objectives of the order reduction is to design a LFC for power systems, which can effectively control the original high order system so that overall system is of low order and is easy to understand. Thus, the model order reduction helps in better understanding of the systems. Also, some advantages of reduced order models are 1) Less computational effort in system simulation problems. 2) Design of the controller numerically more efficient. 3) Able to obtain simpler control laws.

In view of the above discussion, the main objectives of this paper are as follows:

(i)       To develop realizable controller with less computational effort.

(ii)      Design reduced order models by using Logarithmic approximation, which force to track the non-diminishing component associated with the output response of the original model.

(iii)    Design two degree of freedom-internal model control (2DOF-IMC) controller for best reduced order models as well as original model.

(iv)     Apply designed controllers into reduced order model as wellas original high order system.

(v)      Check the performance of designed controllers.

This paper is divided into the following sections: Section 1 contains the introduction part of the paper while the Section 2 explains controller design technique. Section 3 describes the model order reduction technique while Section 4 consists of a Load Frequency Control via IMC-PID Design through reduced order modelling and finally Section 5 concludes the paper.

دو درجه آزادی طراحی مدل کنترل داخلی PID برای LFC سیستم­های قدرت از طریق تقریب لگاریتمی

چکیده

کنترل کننده فرکانس بار برای مدل کاهش مرتبه سیستم قدرت گرمابی یک ناحیه­ای و دو ناحیه­ای مدل کنترل داخلی با استفاده از تکنیک­های کنترل انتگرال مشتقی (IMC-PID) طراحی شده است. روش طراحی کنترل­کننده براساس مدل کنترل داخلی دو درجه آزادی (2DOF) است که با روش کاهش میزان مرتبه مدل ترکیب شده است. در اینجا، به رغم استفاده از مدل سیستم مرتبه کامل، مدل مرتبه­ي کاهش یافته برای طراحی 2DOF-IMC-PID مورد توجه قرار گرفته و کنترل­کننده طراحی شده به طور مستقیم به مدل سیستم مرتبه کامل داده می­شود. روش کاهش الگوریتم مدل بر مبنای لگاریتم پیشنهاد شده است تا سیستم­های قدرت یک ناحیه­ای و دو ناحیه­ای را برای استفاده از طراحی کنترل­کننده کاهش دهد. طراحی IMC-PID پیشنهاد شده از مدل کاهش یافته، پاسخ دینامیکی خوب و خوشفکرانه­ای در برابر اختلال بار با اصل سیستم مرتبه بالا بدست می­دهد.

مقدمه

عملکرد سیستم­های مقیاس بزرگ ممکن است ناشی از وجود اختلالات سریع بار، عدم قطعیت پارامترها، تغییرات عملیاتی و غیره باشد. بنابراین، استحکام و ثبات برای طراحی کنترل فرکانس بار (LFC) برای سیستم­های قدرت مقیاس بزرگ بسیار مهم است. اما به دلیل پیچیدگی، طراحی یک کنترل­کننده قوی در یک سیستم قدرتمند بسیار دشوار است. غیر خطی بودن همینطور مرتبه بالاتر از سیستم. در سناریوی فعلی سیستم قدرت، بار پایه سیستم ها حفظ ثبات بین تولید توان و تقاضای توان است، در حالی که سیستم قدرت به کاربران امکان می­دهد قدرت الکتریکی با کیفیت را با قابلیت اطمینان فراهم کنند. نوسانات ناشی از تقاضای توان ممکن است بر فرکانس تأمین برق و همچنین جریان برق خط بین مناطق کنترل تأثیر بگذارد. در نتیجه، کنترل­کننده­های فرکانس بار (LFC) برای حفظ فرکانس سیستم به صورت سازماندهی طراحی می­شوند ، تنظیمات واحد ژنراتور را که عمدتا بر خطای کنترل منطقه (ACE) متصل شده است، تنظیم می­کنند، خطای کنترل منطقه را به صفر بر اساس تنظیم بی پایان توان اکتیو می رسانند بنابراین تولید کل سیستم و قدرت بار به خوبی مطابقت دارند. این به خاطر این واقعیت است که یک کنترل­کننده طراحی بهتر کنترل بیشتری را فراهم می­کند.

بنابراین کنترل­کننده فرکانس بار را می­توان به عنوان یک مسئله بهینه­سازی هدف و مشکل کنترل در نظر گرفت، که مانع اختلالات بار ناگهانی، عدم قطعیت پارامتر و همچنین توانایی انجام کار تحت شرایط بیش از حد مجاز، زمان استقرار، فرکانس و انحراف قدرت خط است. در سال 2009، Ganapathy یک LFC غیر متمرکز برای سیستم­های متصل شده با گاورنر گروه مرده و ذخیره انرژی مغناطیسی ابررسانایی (SMES) با استفاده از الگوریتم تکامل چند هدفه (MOEA) پیشنهاد کرده است. Sahaj

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