نمونه ترجمه تخصصی برق و الکترونیک
Two degree of freedom
internal model control-PID design for LFC of
power systems
via logarithmic approximations
a b s t
r a c t
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.
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
دیدگاه کاربران