POPWER QUALITY USING GENETIC ALGORITHM IN POWER SYSTEM Prof. Sanjay Shrivastava
Ass. Prof., Guru Ramdas Khalsa Institute of Science & Technology Jabalpur, MP, India Email Id:- harshilshri@gmail.com
Abstract—In the developed model synchronous generator is represented by model. Which includes both the generator main field winding and the damper winding in q-axis so as to evaluate the impact of PSS and FACTS-based controller on power system stability? The model can be can be used for teaching the power system stability phenomena, and also for research works especially to develop generator controllers using advanced technologies.
Further, to avoid adverse interactions, PSS and FACTS-based controller is simultaneously designed employing genetic algorithm (GA). The non-linear simulation results are presented for the example power system under various disturbance conditions to validate the effectiveness of the proposed modeling and simultaneous design approach.
Keywords—Genetic algorithm, modeling and simulation, MATLAB/SIMULINK, power system stabilizer, thermistor controlled series compensator, simultaneous design, power system stability.
I. INTRODUCTION
ITH the advent of flexible ac transmission system(FACTS) devices, such as thermistor controlled series compensator (TCSC), static synchronous compensator(STATCOM) and unified power flow controller (UPFC), the unified model of single-machine infinite-bus (SMIB) power system installed with a TCSC, STATCOM and a UPFC have been developed. These models are the popular tools amongst power engineers for studying the dynamic behavior of synchronous generators, with a view to design control equipment. However, the model only takes into account the generator main field winding and the generator damping windings are not accounted for.
Further, these liner methods cannot properly capture complex dynamics of the system especially during major disturbances. This presents difficulties for designing the FACTS controllers in that, the controllers designed to provide desired performance at small signal condition do not guarantee acceptable performance in the event of major disturbances. In [5], a systematic procedure for modeling, simulation and optimal tuning of TCSC controller in a SMIB power system was presented where the MATLAB/SIMULINK based model was developed and genetic algorithm (GA) was employed to design the TCSC controller.
However, the model only takes into account the generator main field winding and the synchronous machine was represented by model 1.0. For more reasonable evaluation of a SMIB power
system with FACTS controller, a higher- order synchronous machine model (model1.1), which includes one damper winding along the q-axis, is reported in the literature. As power system stabilizers(PSS) are now routinely used in the industry, this paper considers a SMIB power system installed with a PSS and a FACTS controller, where the synchronous machine is represented by a higher order model (model 1.1).
The problem of PSS parameter tuning in the presence of FACTS-based controller is a complex exercise, as uncoordinated local control of these controllers may cause destabilizing interactions. To improve overall system performance, many researches were done on the coordination between PSS and FACTS power oscillation damping (POD) controllers. A number of conventional techniques have been reported in the literature pertaining to design problems of conventional power system stabilizers namely: the Eigen value assignment, mathematical programming, gradient procedure for optimization and also the modern control theory.
Unfortunately, the conventional techniques are time consuming as they are iterative and require heavy computation burden and slow convergence. In addition, the search process is susceptible to be trapped in local minima and the solution obtained may not be optimal.GA is becoming popular for solving the optimization problems in different fields of application, mainly because of their robustness in
finding an optimal solution and ability to provide a near-optimal solution close to a global minimum. Unlike strict mathematical methods, the GA does not require the condition that the variables in the optimization problem be continuous and different; it only requires that the problem to be solved can be computed.
GA employs search procedures based on the mechanics of natural selection and survival of the fittest. The GAs, which use a multiple-point instead of a single-point search and work with the coded structure of variables instead of the actual variables, require only the objective function, thereby making searching for a global optimum simpler [11]. Therefore, in the present work GA is employed to simultaneously tune the parameters of PSS and FACTS controller. This paper is organized as follows.
In Section II, the modeling of power system under study, which is a SMIBpower system with a PSS and a thermistor controlled seriescompensator (TCSC), is presented. The proposed controllerstructures and problem formulation are described in SectionIII. A short overview of GA is presented in Section IV.Simulation results are provided and discussed in Section Vand conclusions are given in Section VI.
II. POWER SYSTEM UNDER STUDY The SMIB power system with TCSC shown in Fig. 1 isconsidered in this study. The synchronous generator isdelivering power to the infinite-bus through a double circuittransmission line and a TCSC. In Fig. 1, Vtand Ebare thegenerator terminal and infinite bus voltage respectively; XT ,X L and XTH represent the reactance of the transformer,transmission line per circuit and the The venin’s impedance ofthe receiving end system respectively.
Fig. 1 Single-machine infinite-bus power system with TCSC
A. MODELING THE SYNCHRONOUS GENERATOR INFINITE-BUS POWER SYSTEM
The synchronous generator is represented by model 1.1, i.e.with field circuit and one equivalent damper on q-axis. Themachine equations are [12]:
The electrical torque Teis expressed in terms of variablesE’d,E' q,id and i. q as:
For a lossless network, the stator algebraic equations andthe network equations are expressed as:
Solving the above equations, the variables id and i. q canbe obtained as:
The above notation for the variables and parametersdescribed are standard and defined in the nomenclature. Formore details, the readers are suggested to refer.
B. MODELING THE THERMISTOR CONTROLLED SERIES COMPENSATOR (TCSC)
TCSC is one of the most important and best known seriesFACTS controllers. It has been in use for many years toincrease line power transfer as well as to enhance systemstability. It consists of three components: capacitor banks,bypass inductor and bidirectional thermistors.
The firing anglesof the thermistors are controlled to adjust the TCSC reactance inaccordance with a system control algorithm, normally inresponse to some system parameter variations.
According to the variation of the thermistor firing angle (α)or conduction angle (σ), this process can be modeled as afast switch between corresponding reactance offered to thepower system.
Assuming that the total current passingthrough the TCSC is sinusoidal;
the equivalent reactance at thefundamental frequency can be represented as a variablereactance XTCSC. There exists a steady-state relationshipbetween α and the reactance XTCSC. This relationship can bedescribed by the following equation.
Since the relationship between α and the equivalentfundamental frequency reactance offered by TCSC,XTCSC (α ) is a unique-valued function, the TCSC
ismodeled here as a variable capacitive reactance within theoperating region defined by the limits imposed by α.
ThusXTCSCmin ≤ XTCSC ≤ XTCSCmax, with XTCSCmax = XTCSC (αmin) andXTCSCmin = XTCSC(1800) = XC. In this paper, the controller isassumed to operate only in the capacitive region, i.e., αmin > αrwhere αr corresponds to the resonant point, as the inductiveregion associated with 900 < α < αr induces high harmonicsthat cannot be properly modeled in stability studies.
III. PROBLEM FORMULATION
The structure of TCSC-based damping controller, tomodulate the reactance offered by the TCSC, XTCSC (α) isshown in Fig. 2. The input signal of the proposed controllers isthe speed deviation (Δω), and the output signal is the reactanceoffered by the TCSC, XTCSC (α) . The structure consists of again block with gain KT, a signal washout block and two-stagephase compensation blocks. The signal washout block servesas a high-pass filter, with the time constant TWT, high enoughto allow signals associated with oscillations in input signal topass unchanged.
Fig. 2 Structure of TCSC-based controller C. PROBLEM FORMULATION
In the present study, a washout time constant of TWT = TWP=1.0s is used. The controller gains KT &KP and the timeconstants T1T,T2T,T3T, T4T
&T1P,T2P,T3P and T4P are to bedetermined. In case of PSS, the stabilizing signal output VS iszero during steady state conditions. Following a
disturbance,the signal VS is modified according to the change in the Δωduring dynamic conditions. In case of TCSC- based controller,Δσand σ 0 are constant during steady state conditions.During dynamic conditions, conduction angle (σ) and henceXTCSC (α) is modulated to improve power system stability.The desired value of compensation is obtained through thechange in the conduction angle (Δσ), according to thevariation in Δω.
The effective conduction angle σ duringdynamic conditions is given by:
D. OBJECTIVE FUNCTION
It has been shown that that for the TCSC- based controllerdesign problem, the best system response is obtained when thecontroller parameters are optimized using integral of timemultiplied absolute value of the error (ITAE) as objectivefunction [15]. In view of the above, in this paper, the objectivefunction is defined as follows:
IV. OVERVIEW OF GENETIC ALGORITHM (GA)
GA has been used for optimizing the parameters of thecontrol system that are complex and difficult to solve byconventional optimization methods. GA maintains a set ofcandidate solutions called population and repeatedly modifiesthem. At each step, the GA selects individuals from thecurrent population to be parents and uses them to produce thechildren for the next generation. Candidate solutions areusually represented as strings of fixed length, calledchromosomes. A fitness or objective function is used to reflectthe goodness of each member of the population.
Given arandom initial population, GA operates in cycles calledgenerations, as follows:
Each member of the population is evaluated using afitness function.
The population undergoes reproduction in a number ofiterations. One or more parents
are chosen stochastically,but strings with higher fitness values have higherprobability ofcontributing an offspring.
Genetic operators, such as crossover and mutation, areapplied to parents to produce offspring.
The offspring are inserted into the population and theprocess is repeated.
Fig. 3 Flowchart of the genetic algorithm The computational flow chart of the GA optimizationapproach followed in the present paper is shown in Fig. 4.
V. RESULTS AND DISCUSSIONS
The objective function is evaluated for each individual bysimulating the system dynamic model considering a threephasefault at the generator terminal busbar at t = 1.0 sec. Forthe purpose of optimization of equation (16), routines fromGA toolbox were used. The fitness function comes from time domainsimulation of power system model shown in.Using each set of controllers’
parameters, the time-domainsimulation is performed and the fitness value is determined.
Good solutions are selected, and by means of the GAoperators, new and
better solutions are achieved.
Thisprocedure continues until a desired termination criterion isachieved. Although the chances of GA giving a local optimalsolution are very few, sometimes getting a suboptimal solutionis also possible. While applying GA, a number of parametersare required to be specified. An appropriate choice of theseparameters affects the speed of convergence of the algorithm.For different problems, it is possible that the same parametersfor GA do not give the best solution, and so these can bechanged according to the situation.
The parameters for GAoptimization routines used in the present paper are given in.The description of these operators and their propertiescan be found in reference. One more important point thataffects the optimal solution more or less is the range forunknowns. For the very first execution of the programmer, awider solution space can be given and after getting thesolution one can shorten the solution space nearer to thevalues obtained in the previous iteration.
Optimization isterminated by the prespecified number of generations.
Thebest individual of the final generation is the solution. Theoptimized parameters are shown in shows theconvergence rate objective function J with the number ofgenerations.
VI. CONCLUSION
A systematic procedure for modeling and simulation of apower system installed with a PSS and a FACTS-basedcontroller is presented in this paper. The model is developed inthe MATLAB/SIMULINK environment which provides ameans for carrying out power system stability analysis and forexplaining the generator dynamic behavior as affected by aPSS and FACTS. In this model, the synchronous generatorwith field circuit and one equivalent damper on q-axis isconsidered which is far more realistic compared to the modelavailable in open literature.
Further, to avoid adverseinteractions, the
proposed controllers are
simultaneouslydesigned.
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