Scholarly article on topic 'Firefly algorithm optimized fuzzy PID controller for AGC of multi-area multi-source power systems with UPFC and SMES'

Firefly algorithm optimized fuzzy PID controller for AGC of multi-area multi-source power systems with UPFC and SMES Academic research paper on "Electrical engineering, electronic engineering, information engineering"

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{"Automatic generation control (AGC)" / "Generation rate constraint (GRC)" / "Firefly algorithm (FA)" / "Fuzzy logic controller" / "Unified power flow controller (UPFC)" / "Superconducting magnetic energy storage (SMES)"}

Abstract of research paper on Electrical engineering, electronic engineering, information engineering, author of scientific article — Pratap Chandra Pradhan, Rabindra Kumar Sahu, Sidhartha Panda

Abstract In this paper, a Firefly Algorithm (FA) optimized fuzzy PID controller is proposed for Automatic Generation Control (AGC) of multi-area multi-source power system. Initially, a two area six units power system is used and the gains of the fuzzy PID controller are optimized employing FA optimization technique using an ITAE criterion. The superiority of the proposed FA optimized fuzzy PID controller has been demonstrated by comparing the results with some recently published approaches such as optimal control and Differential Evolution (DE) optimized PID controller for the identical interconnected power system. Then, physical constraints such as Time Delay (TD), reheat turbine and Generation Rate Constraint (GRC) are included in the system model and the superiority of FA is demonstrated by comparing the results over DE, Gravitational Search Algorithm (GSA) and Genetic Algorithm (GA) optimization techniques for the same interconnected power system. Additionally, a Unified Power Flow Controller (UPFC) is placed in the tie-line and Superconducting Magnetic Energy Storage (SMES) units are considered in both areas. Simulation results show that the system performances are improved significantly with the proposed UPFC and SMES units. Sensitivity analysis of the system is performed by varying the system parameters and operating load conditions from their nominal values. It is observed that the optimum gains of the proposed controller need not be reset even if the system is subjected to wide variation in loading condition and system parameters. Finally, the effectiveness of the proposed controller design is verified by considering different types of load patterns.

Academic research paper on topic "Firefly algorithm optimized fuzzy PID controller for AGC of multi-area multi-source power systems with UPFC and SMES"

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Engineering Science and Technology, an International Journal ■■ (2015) I

Contents lists available at ScienceDirect

Engineering Science and Technology, an International Journal

journal homepage: http://www.elsevier.com/locate/jestch

Full Length Article

Firefly algorithm optimized fuzzy PID controller for AGC of multi-area multi-source power systems with UPFC and SMES

Pratap Chandra Pradhana, Rabindra Kumar Sahub *, Sidhartha Pandab

a Department of Electrical Engineering, DRIEMS, Cuttack 754 022, Odisha, India b Department of Electrical Engineering, VSSUT, Burla 768018, Odisha, India

ARTICLE INFO

ABSTRACT

Article history: Received 4 March 2015 Received in revised form 1 August 2015 Accepted 17 August 2015 Available online

Keywords:

Automatic generation control (AGC)

Generation rate constraint (GRC)

Firefly algorithm (FA)

Fuzzy logic controller

Unified power flow controller (UPFC)

Superconducting magnetic energy storage

(SMES)

In this paper, a Firefly Algorithm (FA) optimized fuzzy PID controller is proposed for Automatic Generation Control (AGC) of multi-area multi-source power system. Initially, a two area six units power system is used and the gains of the fuzzy PID controller are optimized employing FA optimization technique using an ITAE criterion. The superiority of the proposed FA optimized fuzzy PID controller has been demonstrated by comparing the results with some recently published approaches such as optimal control and Differential Evolution (DE) optimized PID controller for the identical interconnected power system. Then, physical constraints such as Time Delay (TD), reheat turbine and Generation Rate Constraint (GRC) are included in the system model and the superiority of FA is demonstrated by comparing the results over DE, Gravitational Search Algorithm (GSA) and Genetic Algorithm (GA) optimization techniques for the same interconnected power system. Additionally, a Unified Power Flow Controller (UPFC) is placed in the tie-line and Superconducting Magnetic Energy Storage (SMES) units are considered in both areas. Simulation results show that the system performances are improved significantly with the proposed UPFC and SMES units. Sensitivity analysis of the system is performed by varying the system parameters and operating load conditions from their nominal values. It is observed that the optimum gains of the proposed controller need not be reset even if the system is subjected to wide variation in loading condition and system parameters. Finally, the effectiveness of the proposed controller design is verified by considering different types of load patterns.

Copyright © 2015 The Authors. Production and hosting by Elsevier B.V. on behalf of Karabuk University.

This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

1. Introduction

The main objective of power system utility is to maintain continuous supply of electrical power with an acceptable quality, to all the consumers in the system. The power system will be in equilibrium, when there is a balance between electrical power demand and the power generated. There are two basic control mechanisms used to achieve reactive power balance (acceptable voltage profile) and real power balance (acceptable frequency values). The former is called Automatic Voltage Regulator (AVR) and latter is called Automatic Generation Control (AGC) [1]. The goal of AGC in an interconnected power system is to minimize the transient deviations in area frequency, tie-line power interchange and to ensure their steady state errors to be zeros [2]. A considerable drop in frequency could result in high magnetizing currents in induction motors and transformers. The wide-spread use of electric clocks and the

* Corresponding author. Tel.: +91 9439702316, fax: +91 66324302 04. E-mail address: rksahu123@gmail.com (R.K. Sahu). Peer review under responsibility of Karabuk University.

use of frequency for other timing purposes require accurate maintenance of synchronous time which is proportional to frequency as well as its integral. According to Indian Electricity Grid Code (IEGC), if the rated system frequency is 50 Hz and the target range for frequency control should be 49.0 Hz-50.0 Hz, the statutory acceptable limits are 48.5-51.5 Hz. However, the users of the electric power change the loads randomly and momentarily. This results in sudden appearance of generation-load mismatches. The mismatch power enters into/drawn for the rotor thus causing a change generator speed and hence the system frequency (as frequency is closely related to the generator speed). It is impossible to maintain the balances between generation and load without control. So, a control system is essential to cancel the effects of the random load changes and to keep the frequency at the standard value. The AGC loop continuously regulates the active power output of the generator to match with the randomly varying load [3].

In a practically interconnected power system, the generation normally comprises of a mix of thermal, hydro, nuclear and gas power generation. However, owing to their high efficiency, nuclear plants are generally kept at base load close to their maximum output with no participation in AGC. Gas power generation is ideal for meeting

http://dx.doi.org/10.1016/jjestch.2015.08.007

2215-0986/Copyright © 2015 The Authors. Production and hosting by Elsevier B.V. on behalf of Karabuk University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

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the varying load demand. So, Gas plants are used to meet peak demands only [4,5]. Parmar et al. have reported in [4] a multi-sources generation including thermal-hydro-gas systems, considering HVDC link connected in parallel with existing AC link for stabilizing frequency oscillation and used an optimal output feedback controller for frequency stabilization. Recently, Mohanty et al. [5] have studied the controller parameters tuning of Differential Evolution (DE) algorithm and its application to optimize the parameters of I, PI and PID controllers of multi-sources power system. The authors have demonstrated the superiority of DE approach over optimal output feedback controller for the same power systems. Keeping in view the present power scenario, combination of multi-source power generation is considered with their corresponding participation factors.

When the governor system is not able to absorb the frequency fluctuations due to its slow response, active power source with fast response such as Superconducting Magnetic Energy Storage (SMES) is highly effective in improving the dynamic performance of the system [6,7]. In Banerjee et al. [8], the effectiveness of small-sized superconducting and normal loss types Magnetic Energy Storage (MES) units for load frequency control is investigated and means of best utilizing the small energy storage capacity of such units to improve the dynamics performance of large power areas are suggested. As the SMES unit is capable of concurrently controlling both active and reactive powers [9], it is one of the most effective and vital stabilizer of frequency oscillations. The feasibility of SMES for improving load frequency performance has been reported in literature [10,11]. The recent advances in power electronics have led to the development of the Flexible Alternating Current Transmission Systems (FACTS) controllers in power systems. FACTS controllers are capable of controlling the network condition in a very fast manner and can be employed for improving the performance of a power system. The Unified Power Flow Controller (UPFC) is member of the FACTS family with very versatile features. UPFC which consists of a series and shunt converter connected by a common dc link capacitor can simultaneously perform the function of transmission line real and active power flow control in addition to UPFC bus voltage /shunt reactive power control [12]. The impact of different FACTS controllers such as Static Synchronous Series Compensator (SSSC) and Thyristor Controlled Phase Shifter (TCPS) in coordination with SMES for AGC has been reported in literature [13,14]. In view of the above, AGC in presence of SMES and UPFC has been carried out in the present paper.

Literature study reveals that several control strategies have been proposed by many researchers over the past decades for AGC of power system [15]. Many control and optimization techniques such as conventional [16], optimal control [4], Genetic Algorithm [17], Particle Swarm Optimization [18], Bacteria Foraging Optimization Algorithm [19], Artificial Neural Network [20], linear-quadratic optimal output feedback controller [21], sub-optimal controller [22], AGC with wind generators and flywheel energy storage system [23] etc. have been proposed for AGC.

To get an accurate insight of the AGC problem, it is necessary to include the important physical constraints in the system model. The major physical constraints which affect the power system performance are Time Delay (TD) and Generation Rate Constraint (GRC) [3]. In view of the above, TD and GRC associated with both communication channels and signal processing are considered in the present paper to have more realistic power system.

In the load frequency control, integral controller is sufficient to reduce the frequency and tie-line power deviations and bring them back to nominal values. However, the disadvantage of integral controller is that it might produce a closed loop system with significantly slower response times. To improve the system performance, Proportional Integral (PI), Integral Derivative (ID), Proportional Integral Derivative (PID) and Integral Double Derivative (IDD) controllers have

been proposed in literature [4,5,16]. However, the above conventional controllers perform satisfactorily at the operating point at which the controllers are designed and their performance degrades when there is any change in operating point or in system parameter. It has been reported by many researchers that Fuzzy Logic Controller (FLC) improves the closed loop performance of I/PI/PID controller and can handle any changes in operating point or in system parameter by online updating of the controller parameters [24-26]. Fuzzy logic based PID controller can be successfully used for all nonlinear system but there is no specific mathematical formulation to decide the proper choice of fuzzy parameters (such as inputs, scaling factors, membership functions, rule base etc.). Normally these parameters are selected by using certain empirical rules and therefore may not be the optimal parameters. Improper selection of input-output scaling factor may affect the performance of FLC to a greater extent.

It is obvious from literature survey that the performance of the power system depends on the controller structure and the techniques employed to optimize the controller parameters. Hence, proposing and implementing new controller approaches using high performance heuristic optimization algorithms to real world problems are always welcome. Recently, a new biologically-inspired meta-heuristic algorithm, known as the Firefly Algorithm (FA), has been developed by Yang [27,28]. FA is a population based search algorithm inspired by the flashing behavior of fireflies. It has been successfully employed to solve the nonlinear and non-convex optimization problems [29]. Recent research shows that FA is very efficient and could outperform other meta-heuristic algorithms [30].

In view of the above, a maiden attempt has been made in this paper to apply an FA optimization technique to tune the input and output scaling factors of fuzzy PID controller for the AGC of multi area power systems with the consideration of time delay, reheat turbine and Generation Rate Constraint (GRC). The structure of the fuzzy PID used here is inherited from a combination of fuzzy PI and fuzzy PD controllers from Mudi and Pal and Sahu et al. [24,26], with Kj and K2 as input scaling factors of Fuzzy Logic Controller (FLC). The FLC output is multiplied KP, its integral and derivative are multiplied K and KD respectively, and then summed to give the total controller output. Fixed membership functions and rule base are assumed for the FLC structure. The input scaling factors (Kj and K2) and output scaling factors (KP, K and KD) are optimized in presence of FLC employing FA technique to minimize the objective function. The results are compared with some recently published approaches such as DE optimized PID controller and optimal control. The superiority of FA over GA, GSA and DE techniques is also demonstrated. Further, UPFC is employed in series with the tie-line in coordination with SMES to improve the dynamic performance of the power system. Finally, sensitivity analysis is carried out by varying the loading condition and system parameters.

2. Materials and methods

2.1. Power system model

A two area six unit thermal, hydro and gas power system [4,5] as shown in Fig. 1 is considered for design and analysis purpose. Each area comprises reheat thermal, hydro and gas generating units. A fuzzy PID controller is considered for each unit. In Fig. 1, RT, RH, and RG are the regulation parameters of thermal, hydro and gas units respectively; B, and B2 represent the frequency bias parameters; ACE-i and ACE2 stands for Area Control Errors; UT, UH and UG are the control outputs for thermal, hydro and gas units respectively; KT, KH and KG are the participation factors of thermal, hydro and gas generating units, respectively; TG is speed governor time constant of thermal unit in sec; Tt is steam turbine time constant in sec; Kr is the steam turbine reheat constant; Tr is the steam turbine

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i t 1 SMES

^ AREA 1

1 1 1

Rg1 Rh 1 Rt 1

1 + sTsMES

Thermal power plant with reheat turbine, GRC & time delay

1 + sTG1

1 + sKriTri

1 + sTr1

Hydro power plant with governor, GRC & time delay

1 + sTRs\

1 1 - sTw 1

1 + stgh 1 1 + 0.5sTW 1 У

1 + strh 1

Gas turbine power plant with time delay

1 1+ SXC 1 - sTcR1 1 Kg

bg + scg 1+ sYc 1+ sTF1 1 + sTcD1

AREA 2

Thermal power plant with reheat turbine, GRC & time delay

T| n^i Ji

1 + sTps

1 + sTuPFC

2*3.14*T12

1 + stg 2

1 + sKr 2T 2

1 + sTr 2

Hydro power plant with governor, GRC & time delay

1 + stgh 2

1- sTw 2

* 1 + 0.5sTw 2 у

1 + STrs 2

1 + sTrh 2

• + • + ■ +

Gas turbine power plant with time delay

1 1 + sXc 1 - sTcr 2 1 Kg

bg + scg 1+ sYc 1+ STf 2 1 + STcd 2

1 Rh 2

1 + sTps

1 + sTsMES

Fig. 1. Transfer function model of multi-area multi-source interconnected power system.

reheat time constant in sec; TW is nominal starting time of water in penstock in sec; Trs is the hydro turbine speed governor reset time in sec; Trh is hydro turbine speed governor transient droop time constant in sec; Tgh is hydro turbine speed governor main servo time constant in sec; XC is the lead time constant of gas turbine speed governor in sec; YC is the lag time constant of gas turbine speed governor in sec; cg is the gas turbine valve positioner; bg is the gas turbine constant of valve positioner; TF is the gas turbine fuel time constant in sec; TCR is the gas turbine combustion reaction time delay in sec; TCD is the gas turbine compressor discharge volume-time constant in sec; KP power system gain in Hz/puMW; TP is the power system time constant in sec; T12 is the synchronizing coefficient and AFj and AF2 are the system frequency deviations in Hz. The relevant parameters are given in Appendix.

For more realistic analysis, the major physical constraints which affect the power system performance are Reheat turbine, Generation Rate Constraint (GRC) and time delay. In a power system having steam and hydro plants, power generation can change only at a specified maximum rate. The reheat units have a generation rate of about 3-10% pu MW/min [31]. The typical value of permissible rate of generation for hydro plant is relatively much higher. Typical value of GRC for hydro plants is 270%/min for raising generation and

360%/min for lowering generation [20]. Owing to the growing complexity of power systems in deregulated environment, communication delays become a significant challenge in the AGC analysis. Time delays can degrade a system's performance and even cause system instability. Typical value of time delays is considered 2 sec for the present study [31]. In view of the above, Reheat turbine, GRC and time delay are included in the system model.

2.2. Controller structure and objective function

To control the frequency, fuzzy PID controllers are provided in each area. The structure of fuzzy PID controller is shown in Fig. 2 [24].

The error inputs to the controllers are the respective Area Control Errors (ACE) given by:

e, (t) = ACE, = B, AF, + APTie (1)

e2 (t) = ACE2 = B2AF2 - APTie (2)

Fuzzy controller uses error (e) and derivative of error (e) as input signals. The outputs of the fuzzy controllers UT, UH and UG are the

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Derivative gain Derivative Fig. 2. Structure of proposed fuzzy PID controller.

control inputs of the power system. The input scaling factors are the tuneable parameters K, and K2. The proportional, integral and derivative gains of fuzzy PID controller are represented by KP, KI and KD respectively. Triangular membership functions are used with five fuzzy linguistic variables such as NB (negative big), NS (negative small), Z (zero), PS (positive small) and PB (positive big) for both the inputs and the output. Membership functions for error, error derivative and FLC output are shown in Fig. 3. Mamdani fuzzy interface engine is selected for this work. The FLC output is determined by using centre of gravity method of defuzzification. The two-dimensional rule base for error, error derivative and FLC output is shown in Table 1.

In the design of modern heuristic optimization technique based controller, the objective function is first defined based on the desired specifications and constraints. Typical output specifications in the time domain are peak overshooting, rise time, settling time, and steady-state error. The commonly used integral based error criteria are as follows: Integral of Squared Error (ISE), Integral of Absolute Error (IAE), Integral of Time multiplied Squared Error (ITSE) and Integral of Time multiply by Absolute Error (ITAE). ITAE integrates the absolute error multiplied by the time over time. ITAE technique weights errors which exist after a long time much more heavily than those at the start of the response. The time multiplication term penalizes the error more at the later stages than at the beginning and hence effectively reduces the settling time. ITAE tuning produces systems which settle much more quickly than ISE and IAE tuning methods. Since the absolute error is included in the ITAE criterion, the maximum percentage of overshoot is also minimized. ITSE based controller provides large controller output for a sudden change in set point which is not advantageous from controller design point of view. It has been reported in literature that ITAE gives a better performance compared to other integral based performance criteria [32]. Therefore, ITAE is used as objective function in this paper to optimize the scaling factors and proportional, integral and

derivative gains of fuzzy PID controller. Expression for the ITAE objective function is depicted in equation (3).

J = ITAE = J (( + IAF2I + |AP№|)■ t■ dt (3)

In the above equation, AF and AF2 are the system frequency deviations; APTie is the incremental change in tie line power; tsim is the time range of simulation.

2.3. Modeling of UPFC in AGC

During the last decade, continuous and fast improvement of power electronics technology has made Flexible AC Transmission Systems (FACTS) a promising concept for power system applications. With the application of FACTS technology, power flow along transmission lines can be more flexibly controlled. The Unified Power Flow Controller (UPFC) is regarded as one of the most versatile devices in the FACTS family which has the capability to control the power flow in the transmission line, improve the transient stability, alleviate system oscillation and offer voltage support [12,33]. The two area power system with a UPFC as shown in Fig. 4 is considered in this study [34]. The UPFC is installed in series with a tieline and provides damping of oscillations in the tie-line power. In Fig. 4, Vse is the series voltage magnitude and t/>se is the phase angle of series voltage. The shunt converter injects controllable shunt voltage such that the real component of the current in the shunt branch balance the real power demanded by the series converter. It is clear from Fig. 4 that the complex power at the receiving end of the line is

, _ —Uvs + ve - V)

Pred - JQreactive = Vr hine = Vr j-j(X)-|

Fig. 3. Membership functions for error, error derivative and FLC output.

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Table 1

Rule base for error, derivative of error and FLC output.

NB NS Z PS PB

NB NB NB NS NS Z

NS NB NS NS Z PS

Z NS NS Z PS PS

PS NS Z PS PS PB

PB Z PS PS PB PB

The above equation, ifVse = 0, represents that the real power is an uncompensated system. Whereas the UPFC series voltage magnitude can be controlled between 0 and Vse max, and its phase angle (fse) can be controlled between 0 and 360° at any power angle. The UPFC based controller can be represented in AGC as [35]

APupfc (s) = j—1-IaF (s) (7)

I 1 + Si UPFC J where Tupfc is the time constant of UPFC.

where Vse = Z(Ss -fe) (5)

Solving the equation (4), the real part is as given below

Preal = Sin(S) + Sin (S - fe ) = P0 (S) + Pse (S, ) (6)

Fig. 4. Two-area interconnected power system with UPFC.

2.4. Modeling ofSMES in AGC

Superconducting Magnetic Energy Storage (SMES) is a device which can store the electrical power from the grid in the magnetic field of a coil. The magnetic field of coil is made of superconducting wire with near-zero loss of energy. SMESs can store and refurbish huge values of energy almost instantaneously. Therefore the power system can discharge high levels of power within a fraction of a cycle to avoid a rapid loss in the line power. The SMES is consisting of inductor-converter unit, dc super-conducting inductor, AC/ DC converter and a step down transformer [13]. The stability of the SMES unit is superior to other power storage devices, because all parts of an SMES unit are static. Fig. 5 shows the schematic diagram of SMES unit in the power system. During normal operation of the grid, the superconducting coil will be charged to a set value (normally less than the maximum charge) from the utility grid. The DC magnetic coil is connected to the AC grid through a Power Conversion System (PCS) which includes an inverter/ rectifier. After being charged, the superconducting coil conducts current, which supports an electromagnetic field, with virtually no losses. The coil is kept at very low temperature by immersion in a bath of liquid helium.

The stored energy is almost rapidly released through the PCS to the grid as AC power when there is a sudden rise in the demand of load. The coil charges back to its initial value of current as control mechanisms start working to set the power system to the new

AC system Transformer 2

Fig. 5. SMES circuit diagram.

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Fig. 6. Dynamic responses of the system without controller and physical constraints for 1% step increase load in area-1.

equilibrium condition. During sudden release of loads, the coil rapidly gets charged toward its full value, thus absorbing some portion of the excess energy in the system. The excess energy absorbed is released and the coil current attains its normal value as the system returns to its steady state. In view of the above two SMES, units are

established in area-1 and area-2 in order to stabilize frequency oscillations as shown in Fig. 1. The input signal of the SMES controller is p.u. frequency deviation ( AF ) and the output is the change in control vector [APSM£S].The controller gains Ksmes and the time constant Tsmes are to be optimized.

Fig. 7. Flow chart of Firefly Algorithm.

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Table 2

FA optimized Fuzzy PID Controller parameters for system without physical constraints.

Generation types/controller gains/ FA optimized parameters

Thermal Ki 0.5517

K2 0.5322

Kpi 1.6912

Kn 0.7014

Kdi 1.1754

Hydro Кз 0.4531

K4 0.0026

Kp2 1.0763

Ki2 1.8706

Kd2 0.2035

Gas К5 1.7860

Кб 0.9070

Крз 1.8203

Кз 1.8554

Kd3 0.7338

3. Overview of firefly algorithm

The Firefly Algorithm (FA) is a population-based algorithm developed by Yang [27]. Fireflies are characterized by their flashing light produced by biochemical process bioluminescence. The flashing light may serve as the main courtship signals for mating. It is based on the following three idealized behavior of the flashing characteristics of fireflies [28]:

• All fireflies are unisex and are attracted to other fireflies regardless of their sex.

• The degree of the attractiveness of a firefly is proportional to its brightness. Their attractiveness is proportional to their light

______i ! ! !

V" /j ..........- .j..................

................. f-jf / i

г ................ v___if...........i.................

i J..Î:...........i.................

..........1................

............:................ (a) -----DE: PID [5] -FA:Fuzzy PID " 1

" i i

-0.005

E. -0.015 U-F-

^ -0.02 -0.025 -0.03

0 5 10 15 20 25 30

Time(S)

-0.005

I -0.01

-0.015 -0.02

-0.025

.........Optimal control [4]

-----DE: PID [5]

-FA:Fuzzy PID

15 Time(S)

--Ï-1-•Л I

Optimal control [4] DE: PID [5] FA:Fuzzy PID

0 5 10 15 20 25 30

Time(S)

Fig. 8. Dynamic responses of the system without considering the physical constraints for 1% step increase load in area-1. (a) Frequency deviation of area-1; (b) Frequency deviation of area-2; (c) Tie-line power deviation.

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Table 3

Comparison of simulation results over 50 independent runs for different techniques with physical constraints.

Algorithm Minimum Average Maximum Standard dev.

GA 1.0507 1.1234 1.5932 0.7943

GSA 0.9291 1.0032 1.2851 0.5029

DE 0.7459 0.8419 0.9814 0.4173

FA 0.6542 0.7215 0.8015 0.3121

intensity. Thus, for any two flashing fireflies, less bright firefly moves toward the brighter one. As brightness is proportional to distance, more brightness means less distance between two fireflies. If any two flashing fireflies have the same brightness, then they move randomly.

• The brightness of a firefly is determined by the objective function to be optimized.

Table 6

Optimized Fuzzy PID controller and SMES parameters with UPFC & SMES.

Optimum controller gains With UPFC only With UPFC & SMES

Thermal Ki 1.4425 1.7447

K2 1.2469 1.7222

Kpi 1.3682 0.7600

K,i 0.7230 0.8464

Kdi 0.2116 0.0776

Hydro K3 0.9102 0.6792

K4 1.5666 1.9432

KP2 0.8504 0.7823

K,2 0.3973 0.4311

KD2 1.1487 1.1281

Gas K5 0.6754 1.9086

Кб 0.3044 1.9726

Kp3 1.5351 0.8592

K13 1.8084 0.9927

Kd3 0.4847 0.0817

SMES KsMES - 0.9834

TsMES - 0.0181

For proper design of FA, two important issues need to be defined: the variation of light intensity ( I) and the formulation of attractiveness ( p). The attractiveness of a firefly is determined by its light intensity or brightness and the brightness is associated with the objective function. The light intensity I(r) varies with the distance r monotonically and exponentially as:

I (r ) = ¡0e

ß = ß0e~n

where ß0 is the attractiveness at r = 0.

The distance between any two fireflies st and sj is expressed as Euclidean distance by the base firefly algorithm as:

where I0 is the original light intensity and 7 is the light absorption coefficient.

As a firefly's attractiveness is proportional to the light intensity seen by adjacent fireflies, the attractiveness p of a firefly is defined as:

Table 4

Optimized Fuzzy PID controller parameters without UPFC and SMES with physical constraints.

Optimum controller gains/techniques Without UPFC & SMES

GA GSA DE FA

Thermal Ki 0.2558 0.3622 0.4894 0.3136

K2 1.0991 0.7753 0.4051 0.6521

Kpi 0.8925 1.7243 1.3323 1.7598

K,i 0.1232 1.4693 1.3211 1.4675

Kdi 1.2157 1.8188 1.1649 1.9593

Hydro K3 0.9705 0.6482 0.4127 0.6281

K4 1.7810 1.6131 1.3451 1.7890

KP2 0.1567 0.0597 0.0718 0.0882

Kl2 1.5604 0.6866 0.6005 0.8743

KD2 1.4825 0.6904 0.8435 0.7980

Gas K5 1.5979 0.3026 0.4051 0.4940

K6 1.4687 0.5757 0.4575 0.6214

KP3 0.7930 1.2271 1.1918 1.3734

Ki3 0.6752 0.6076 0.7242 0.7597

Kd3 0.2096 0.6473 0.7206 0.8804

Table 5

Comparison of performance index without UPFC and SMES with physical constraints.

Parameters Without UPFC & SMES

GA GSA DE FA

ITAE 1.0507 0.9291 0.7459 0.6542

Settling time (Ts) (sec) AFi 27.59 28.55 28.16 17.23

AF2 28.29 28.52 29.65 22.37

APTie 19.43 16.43 12.32 16.66

Peak overshoot x 10-3 AFi 5.20 5.80 5.30 5.10

AF2 3.00 3.00 3.10 2.50

APTie 0.50 0.70 0.50 0.50

Table 7

Comparison of performance index with UPFC and SMES.

Parameters With UPFC only With UPFC & SMES

ITAE 0.3397 0.2957

Settling time (Ts) (sec) AFi 7.20 3.57

AF2 10.21 9.28

APTie 6.51 6.47

Peak overshoot x 10-3 AFi 0.20 0.19

AF2 1.20 0.41

APTie 0.40 0.17

Table 8

System eigenvalues and minimum damping ratio without and with controller.

Without Controller

With Controller without UPFC and SMES

With Controller in presence of UPFC

With Controller in presence of both UPFC and SMES

9.1753 -20.3895 -93.5824 -94.1426

8.2743 -20.3896 -20.3895 -48.5124

7.1479 -16.7730 -20.3784 -45.8625

7.4473 -16.7718 -16.7730 -20.3728

2.3850 -5.5222 -16.8492 -20.2873

2.3704 -5.4897 -6.5934 -16.8811

1.7236 -3.8000 -5.5222 -17.6835

1.6988 -3.7752 -4.0686±1.7077i -14.0559

1.2460 -2.7689 -3.7752 -7.0701

1.0869 -2.4152 -3.6007 -4.2511 ± 1.4782i

0.2312 ± 0.9965i -0.3036 ± 1.9440i -2.4152 -4.5730 ± 0.6929i

0.1329 ± 1.4253i -0.8736 ± 0.6794i -0.8736±0.6794i -3.5732

0.1793 ± 1.2724i -0.8484 -0.9961 -3.4787

0.3818 -0.2331 -0.4914 -0.9487

0.1049 -0.0950 -0.2331 -0.9367

0.0428 -0.0426 -0.0944 -0.2693

0.0426 -0.0345 -0.0426 -0.1137

0.0345 -5.0000 -0.0345 -0.0935

5.5000 -5.0000 -5.0000 -0.0373

5.0000 -5.0000 -0.0345

-5.0000

-5.0000

MDR = 0.0629

MDR = 0.0930

MDR = 0.1001

MDR = 0.1345

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*j =|Si -Sj|| = H (Sik - sjk )2 (10)

where n denotes the dimensionality of the problem.

The movement of the i-th firefly is attracted to another more attractive firefly j. The movements of fireflies consist of three terms: the current position of i-th firefly, attraction to another more attractive firefly, and a random walk that consists of a randomization parameter a and the random generated number ei from interval [0; 1]. The movement is expressed as:

Si = Si + p0en'2 (Si - Sj ) + a£i (11)

4. Results and discussions

Initially, a two area power system with diverse sources of generations without UPFC, SMES and any physical constraints is considered. The model of the system under study shown in Fig. 1 (without any controller) is developed in MATLAB/SIMULINK environment and a 1% step increase in load is applied in area-1. The

5 0 -5 -10 -15 -20

4 2 0 -2 -4 -6 -8 -10 -12

1 1 . ! 1

v VrV : ; (a)

; GA :without UPFC & SMES GSA:without UPFC & SMES DE :without UPFC & SMES " -FA :without UPFC & SMES 1 1

M il ■ i

10 15 20 25

Time(s)

------GA :without UPFC & SMES

-----GSA:without UPFC & SMES

........ DE :without UPFC & SMES

-FA :without UPFC & SMES

20 Time(s)

Time(s)

Fig. 9. Dynamic responses of the system without UPFC and SMES for 1% step increase load in area-1. (a) Frequency deviation of area-1; (b) Frequency deviation of area-2; (c) Tie-line power deviation.

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system response for the above disturbance is shown in Fig. 6 from which it is clear that even though the primary controller is sufficient to bring back to steady state condition but the steady errors are not zero. To eliminate the steady state errors, controllers are considered and the controller parameters are optimized by Firefly Algorithm (FA).

4.1. Implementation of firefly algorithm

FA is controlled by three parameters: the randomization parameter a, the attractiveness f, and the absorption coefficient Y. These

parameters are generally chosen in the range 0 to 1. Additionally, the number of fireflies and maximum generation should be properly chosen so as to get the satisfactory performance of the algorithm with minimum computational efforts. A series of experiments were conducted to properly choose these control parameters of FA. The tuned control parameters are: number of fireflies = 5; maximum generation = 100; f = 0.2; a = 0.5 and Y = 0.5 [36]. In order to ensure the satisfaction of inequality constraints, the updated solutions/ locations of fireflies are checked. If the solutions fall outside the limiting range, they are fixed to their limiting values. Simulations were conducted on an Intel, core i-3core cpu, of 2.4 GHz and 4 GB

-5 -10 -15

2 0 -2 -4

/1: (a)

! / ; ..........

ï i .......... Without UPFC & SMES -----With UPFC -Proposed with UPFC & SMES i i i i

0 x 10

10 15 20 25 30 Time(s)

-0.5 -1 -1.5 -2 -2.5 -3

----y . i f - v * **Vt~ (b)

c / ' ; ; if i ; f 1 : 1

It J : | if / __________

.....With out UPFC & SMES

v.-' i i -Proposed with UPFC & SMES

10 15 20 25 30 Time(s)

! ! ! !

l ' : ' 1 ' :

i i : ! 1 ! : 1J : !

..........Without UPFC & SMES -----With UPFC

1 I -Proposed with UPFC & SMES i i i i

10 15 20 25 30 Time(s)

Fig. 10. Dynamic responses of the system for 1% step increase load in area-1. (a) Frequency deviation of area-1; (b) Frequency deviation of area-2; (c) Tie-line power deviation.

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Fig. 11. Comparison of settling time. (a) GA: without UPFC& SMES; (b) GSA: without UPFC& SMES; (c) DE: without UPFC& SMES; (d) FA: without UPFC& SMES; (e) FA: with UPFC only; (f) FA: with UPFC& SMES.

RAM computer in the MATLAB 7.10.0.499 (R2010a) environment. The flow chart of proposed FA approach is shown in Fig. 7.

And the gains of the fuzzy PID controller are optimized employing FA technique. The objective function (ITAE) value given by Eq. (3) is determined by simulating the developed model by applying a 1% step load increase in area-1. The optimization was repeated 50 times and best solution obtained corresponding to the minimum objective function is given in Table 2. The dynamic responses of the system without considering the physical constraints for 1% step load increase in area-1 is shown in Fig. 8. To show the superiority of the proposed approach, the results are compared with some recently published approach such as optimal control [4] and DE optimized PID controller [5] for the same interconnected power system. It can be observed from Fig. 8 that significant improvements in terms of settling times, maximum overshoot/undershoot are obtained in the system response with proposed FA optimized fuzzy PID controller compared to optimal control [4] and DE optimized PID controller [5].

In the next step, physical constraints such as Time Delay (TD), reheat turbine and Generation Rate Constraint (GRC) are included in the system model; the minimum, average, maximum and standard deviations of objective function values are summarized in Table 3. The best final solutions obtained in the 50 runs are shown in Table 4. For comparison, the corresponding values of Genetic Algorithm (GA), Gravitational Search Algorithm (GSA) and Differential Evolution (DE) optimized fuzzy PID controllers are also shown in

Tables 3 and 4. The different input parameters of the comparative algorithms are presented below.

i) Genetic Algorithm (GA) [37]: Generation G = 100, Population = 30, crossover rate = 80%., mutation probability = 0.001, Selection = Normal geometric selection, Crossover: Arithmetic crossover, Mutation: Non uniform mutation.

ii) Gravitational Search Algorithm (GSA) [32]: Generation = 100, Population = 30, Gravitational constant (G0) = 100, constant a = 20.

iii) Differential Evolution (DE) [5]:Generation = 100, Population size = 30, Step size = 0.2, Crossover probability = 0.6, Strategy: DE/best/2/bin

From statistical analysis of Table 3, it is clear that minimum objective function value is obtained with proposed FA algorithm (ITAE = 0.6542) compared to GA (ITAE = 1.0507), GSA (ITAE = 0.9291) and DE (ITAE = 0.7459) algorithms. It is also clear from Table 3 that, from evolutionary point of view proposed, FA algorithm out performs other considered techniques in terms of average, maximum and standard deviation values obtained.

4.2. Analysis of results with physical constraints

A 1% step increase in load is applied in area-1 and the corresponding performance index in terms of ITAE value, and settling

Robustness analysis.

Parameter variation % Change Performance index with UPFC and SMES

Settling time Ts (Sec) Peak over shoot x 10-3 ITAE

AFi AF2 APTie AFi AF2 APTie

Nominal 0 3.57 9.28 6.47 0.19 0.41 0.17 0.2957

Loading condition +25 3.56 9.28 6.47 0.19 0.41 0.17 0.2961

-25 3.57 9.28 6.47 0.19 0.41 0.16 0.2953

Tg +25 3.57 9.19 6.51 0.13 0.40 0.16 0.2456

-25 4.30 10.70 6.62 0.12 0.53 0.11 0.3001

Tt +25 3.54 9.95 6.42 0.15 0.37 0.16 0.3014

-25 5.37 8.26 6.79 0.05 0.16 0.12 0.3102

Trh +25 5.72 8.74 7.31 0.02 0.11 0.13 0.3109

-25 3.70 9.91 6.55 0.14 0.51 0.13 0.3108

Tcd +25 3.62 9.22 6.51 0.17 0.35 0.18 0.2916

-25 5.74 8.27 6.66 0.02 0.12 0.14 0.3102

R +25 3.57 9.28 6.48 0.19 0.41 0.17 0.2958

-25 3.56 9.28 6.49 0.19 0.41 0.17 0.2956

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times (2%) in frequency and tie-line power deviations is shown in Table 5. It is evident from Table 5 that FA outperforms GA, GSA and DE as minimum ITAE value, less settling times and peak overshoots are obtained withFA.

Further, a UPFC is incorporated separately in the tie-line to analyze its effect on the power system performance. Then SMES units are installed in both areas and coordinated with UPFC to study their effect on system performance. The fuzzy PID controller gains, KSMES and TSMES are optimized and the results over 50 independent runs are shown in Table 6. The performance indexes are provided in

Table 7. It is clear from Table 7 that the objective function (ITAE) value is minimized to 0.3397 by employing the UPFC along with fuzzy PID controller. It is also seen that with coordinated application of UPFC and SMES, the ITAE value is further reduced to 0.2957. Table 7 also shows the settling times, peak over shoot and errors with UPFC and SMES. It can be seen from Table 7 that with UPFC and SMES, the settling times of AF], AF2 and APTie are improved compared to others.

The dynamic performance of the system is shown in Fig. 9(a)-(c) for 1% step increase in load in area-1. It is clear from Fig. 9(a)-(c)

!/-. ! ! ! ! !

: \ _______ (a)

ln\ \ ;

V\ \ \ \

.....With — With -Prop out UPFC & SMES UPFC -osed with UPFC & SMES

V; i i i

-5 -10 -15

3 2.5 2 1.5 1

-0.5 -1

10 15 20 25 30 35 40 45 Time(s)

:,• ! ! / \ (b)

# : ! ! ; 11 : ; ; ;

H : ■ ■ ■ ci ; pi: 0: : * : si i i ..........Without UPFC & SMES -----With UPFC -Proposed with UPFC & SMES i i i i

25 Time(s)

:'• ! ! ! ..........With ! ! out UPFC & SMES UPFC ~ osed with UPFC & SMES

-----With

IV —;..........:......... < i : > it-:

< i : : : ' 1 ■ i i

i i : : : '1A] [

\ r^X'-r"' Vi^." "i / (c)

25 Time(s)

Fig. 12. Dynamic responses of the system for 1%step increase load in area-2. (a) Frequency deviation of area-1; (b) Frequency deviation of area-2; (c) Tie-line power deviation.

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that better dynamic performance is obtained by FA optimized fuzzy PID controller compared to GA, GSA and DE optimized fuzzy PID controller. Hence it can be concluded that FA outperform GA, GSA and DE techniques. To evaluate the capability of UPFC and SMES in improving the dynamic performance of the power system, the system dynamic responses with UPFC only and with coordinated application of UPFC and SMES are shown in Fig. 10(a)-(c). Critical analysis of the dynamic responses clearly reveals that significant system performance improvement in terms of minimum undershoot and overshoot in frequency oscillations as well as tie-line power exchange is observed with coordinated application of UPFC and SMES. For better visualization of the improvements with the proposed approach, comparisons of settling times are presented graphically in Fig. 11. It is evident from Fig. 11 that, for the system without UPFC and SMES, less settling times are obtained with proposed FA optimized fuzzy PID controller compared to GA, GSA and DE optimized fuzzy PID controller. The settling times are further reduced with the application of UPFC and minimum settling times are obtained with the FA optimized fuzzy PID controller with coordinated application of UPFC and SMES.

The system eigenvalues with physical constraints for all the above cases are shown in Table 8. It is clear from Table 8 that the system is unstable without controller as all the real parts of

eigenvalues are not negative and hence some poles lie in the right half of s-plane, thus making the system unstable. It is also evident from Table 8 that the system becomes stable with proposed FA optimized Fuzzy PID controller as all the real parts of eigenvalues are negative and hence all the poles lie in the left half of s-plane, thus making the system stable. Further, it can be seen from Table 8 that, in presence of UPFC with controller, the system becomes more stable when the negative real parts are shifted further toward left half of s-plane. Additionally, it can be observed from Table 8 that the system is more stable with proposed FA optimized Fuzzy PID controller in presence of both UPFC and SMES compared to other cases as the real parts of eigenvalues are more negative. The minimum damping ratios (MDR) for all the cases are also provided in Table 8. It is worthwhile to mention here that the MDR should be high to reduce the system oscillations. From Table 8, it is clear that higher MDR value is obtained with proposed controller compared to without controller case. The MDR value is further increased in presence of UPFC and highest MDR value is obtained with controller in presence of both UPFC and SMES. Hence it can be concluded that the proposed approach reduces oscillating state. Fig. 10(a)-(c) validates the above results. It is worthwhile to mention here that when physical constraints such as Time Delay (TD), reheat turbine and Generation Rate Constraint (GRC) are considered, the system

(a) -Nominal loading

+25% of nominal loading

i -------25% of nominal loading i i

10 15 20

Time(s)

(b) -Nominal -----+25% of nominal TG nominal TG "

------+25% of i

10 15 20

Time(s)

Fig. 13. Frequency deviation of area-1 with variation of (a) loading and (b) Tg.

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becomes unstable without controller. In this example, the values of TD is so chosen that the system becomes unstable without controller for a better illustration of capabilities of proposed controllers. However, in the realistic system, primary controller alone may be enough to stabilize the system with some steady state error.

To evaluate the effectiveness of proposed approach with change in location of disturbance, a 1% step increase in load in area-2 is considered at t = 0 s and the system dynamic response is shown in Fig. 12(a)-(c). It is obvious from Fig. 12(a)-(c) that the proposed FA optimized fuzzy PID controller is robust and perform satisfactorily when the location of the disturbance changes. In this case also better results are obtained with proposed FA optimized fuzzy PID controller with coordinated application of UPFC and SMES compared to others.

4.3. Sensitivity analysis

Sensitivity is the ability of a system to perform effectively while its variables are changed within a certain tolerable range [5,31,36]. In this section, robustness of the power system is checked by varying the loading conditions and system parameters from their nominal values (given in appendix) in the range of +25% to -25% without changing the optimum values of fuzzy PID controller gains. The change in operating load condition affects the power system parameters KP and TP. The power system parameters are

calculated for different loading conditions as given in the appendix. The system with UPFC and SMES is considered in all the cases due to their superior performance. Table 9 gives performance of the system for a 1% step load change in area-1 under nominal and varied conditions. Critical examination of Table 9 clearly reveals that ITAE, settling time and peak overshoot values vary within acceptable ranges and are nearby equal to the respective values obtained with nominal system parameter. So it can be concluded that the proposed control approach provides a robust and stable control satisfactorily and the optimum values of controller parameters obtained at the nominal loading with nominal parameters need not be reset for wide changes in the system loading or system parameters. As an example, the frequency deviation response of area-1 with the varied loading condition and TG is shown in Fig. 13(a)-(b). It can be observed from Fig. 13(a)-(b) that the effect of the variation of loading and system time constant TG on the system performance is negligible. So it can be concluded that the proposed control strategy provides a robust control under wide changes in the system loading or system parameters.

Further, to investigate the effectiveness of the proposed controller, different types of random load disturbances are applied to area-1. Fig. 14(a) shows the random step load pattern of power system [38]. The step load is random both in magnitude and duration. The variation in frequency of area-1 is shown in Fig. 14(b). From Fig. 14(b) it is evident that proposed approach shows better

2 1.5 1

-0.5 -1

<1 -0.5

Time (Sec)

! ! ! i i

i i i

e t 4 i (b)

/Ï JTJ fit' : Jg / ( .. . i L 1 / i.s -

......If.......« !............. c : i 1 s

\ .........Without UPFC & SMES -Proposed with UPFC & SMES "

Time(Sec)

Fig. 14. (a) Random step load pattern; (b) Frequency deviation of area-1.

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< -0.05

12 15 18 Time(Sec)

Without UPFC & SMES Proposed with UPFC & SMES

12 15 18 Time(Sec)

Fig. 15. Dynamic responses with variable sinusoidal load. (a) Random sinusoidal pattern; (b) Frequency deviation of area-1.

transient response when the system is incorporated with UPFC & SMES compared to other.

The following sinusoidal load perturbation is applied to area-1 [39].

APS = 0.03sin (4.36t ) + 0.05sin(5.3t )-0.1sin(6t )

The applied sinusoidal pattern is shown in Fig. 15(a) and the frequency response of area-1 is shown in Fig. 15(b). As sinusoidal load disturbance is present in total simulation time, system never damped out. So the performance of the system should be analyzed by the amplitude of oscillations. From Fig. 15(b), it is clear that the oscillations are minimum by employing fuzzy PID controller with UPFC & SMES compared to other. Finally, a random pulse load disturbance [39] is applied to area-1 and its pattern is shown in Fig. 16(a). The frequency response for random load disturbance is shown in Fig. 16(b) and it is clear that the system performs effectively with proposed approach.

5. Conclusion

In this paper, a Firefly Algorithm (FA) optimized fuzzy PID controller has been proposed for Automatic Generation Control of multi-area multi-source power systems. Initially, a two area six units power system without any physical constraints is considered and the optimal gains of the fuzzy PID controller are obtained by FA optimization technique. It is observed that the proposed controller gives superior dynamic performance compared to some recently published approaches such as optimal control [4] and DE optimized PID controller [5] for the same power system. Then physical constraints such as GRC and time delay are considered

and the superiority of FA over GA, GSA and DE is demonstrated. Further, UPFC and SMES are added in the system model in order to improve the system performance. It is observed that when the UPFC unit is placed with the tie-line, dynamic performance of system is improved. Then the impact of SMES in the AGC along with UPFC is also studied. From the simulation results, it is observed that significant improvements of dynamic responses are obtained with coordinated application of UPFC and SMES. Finally, sensitivity analysis is carried out to show the robustness of the controller by varying the loading conditions and system parameters in the range of +25% to -25% from their nominal values. It is observed that the proposed control approach provides a robust and stable control satisfactorily as the parameters of the proposed FA optimized fuzzy PID controllers need not be reset even if the system is subjected to wide variation in loading conditions and system parameters. Different types of random load patterns are applied in area-1 to test the robustness of proposed approach. It is observed from simulation result that proposed controller performed well against random load patterns when system is incorporated with UPFC & SMES compared to other.

Appendix

Nominal parameters of the system investigated are:

Multi-area multi-source system [5]:

B] = B2 = 0.4312 p.u. MW/Hz; RT] = RT2 = RH] = RH2 = RG] = RG2 = 2.4 Hz/ p.u.; TG = 0.06 sec, Ta = Tt2 0.3s, Kri = Kr2 = 0.3; Tri = Tr2 = 10.2 s; Kp] = Kp2 = 68.9655 Hz/p.u. MW; Tpi = Tp2 = 11.49 s; Tu = 0.0433, au = -1, Tw1 = Tw2 = 1.1s, Trs1 = Trs2 = 4.9s, Trh1 = Trh2 = 28.749s, Tgh = Tgh2 = 0.2s, Xc = 0.6s, Yc = 1.1s, cg = 1, bg = 0.049s, Tf = 0.239s, Tcr1 = Tcr2 = 0.01s.

0.2 0.15 0.1 0.05 0

-0.05 -0.1 -0.15 -0.2

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0.08 •o 0.06

P 0.04

0.02 0

0 10 20 30 40 50 60 70 80 90 100

Time(Sec)

0.3 0.2 0.1

□F 0

-0.1 -0.2

0 10 20 30 40 50 60 70 80 90 100

Time(Sec)

Fig. 16. Dynamic response with pulse load pattern. (a) Pulse pattern; (b) Frequency deviation of area-1.

1 1 1 1

! ! (a)

i i ! ! ! ! !

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