Abstract: The prime focus was the concept economicload dispatch (ELD) is one of the main functions ofmodern energy management system, which determinesthe optimal real power setting of generating units withan objective to minimize total fuel cost of thermalplants.It is general fact that reactive power produceddue to reactive components and loads connected to thenetwork, is essential for transmission of active powerthrough transmission and distribution powernetwork.In current dynamic and automatedenvironment, it was essential to analyze and check thedynamic assessment of reactive power of the networksubject to pre and post fault conditions from intervalto interval.
In this paper, we present a novel approach forreactive power optimization (RPO) based on reactivepower planning (RPP) that incorporates nonlinearcombinatorial constrained problem in the field ofpower system analysis. RPP basically serves todetermine the optimal setting and location of thepower system network to satisfy few constraintsfocused on power flow equation and equipmentoperating limits. Reactive Power Planning (RPP)involves allocation and sizing of static reactiveresources for normal operation of the power system.These are devices whose reactive capacity is fixedandinclude series and shunt capacitors, reactors etc.Additionally, dynamic resources are also used in caseof contingency on components such as transformers,transmission lines and power plant units. The powersystem being a practical system has several constraintssuch as capacity limits of the resources, system voltagelimits etc. The IEEE 14-bus network is used as the testnetwork and the code developed using MATLAB forthe RPP problem. Results obtained show a reductionin real and reactive losses and improvement in thevoltage profile.
Keywords: Applied statistics, Power Electronics, PowerSystem, Reactive power planning, soft computingtechniques
1. Introduction
Our technological world has become deeply dependentupon the continuous availability of electrical power.
Commercial power literally enables today’s modern worldto function at its busy pace. Sophisticated technology hasreached deeply into our homes and careers, and with theadvent of e-commerce is continually changing the way weinteract with the rest of world. Now-a-days several solidstate power electronic devices are gaining importance asthe enabling technology not only for integrating varioussystems into Grid but also for operation of conventionalelectrical machines. To identify the requirement andvolume of the reactive power resources for normaloperating conditions in various system constraints is acomplex task.
Reactive power planning (RPP) estimation hasevolved into significant research field within powerelectronics that encompasses the science of estimating theprobable effort essential for developing a power system.Due to the dynamic nature of power electronic devices,the planning techniques focus on development andadvancement involving applied mathematical tools,statistical based algorithms and constraints assumption. Inpractical this issues can be viewed as an optimizationproblem and power network structure is primary factor forrighteous reactive power estimation function at any stageas there is significant lost and cost attached to powersystem network. We employ various factors such asselection, crossover and mutation with the aim ofimproving fitness of subsequent generations for survival.Most of these modern electronic devices are powerelectronic converter inverter based. The non-sinusoidalinput line current drawn by these equipment’s due to inputline rectification generates current harmonics that causessevere problems. These include increased magnitudes ofneutral currents in three-phase systems, overheating oftransformers and induction motors. This creates the needfor some kind of power conditioning. Hence, it becameequally important to limit harmonic content of linecurrents drawn by electronic equipment connected to theelectricity distribution networks. As the use of powerelectronic devices are increasing in our day to day life thepower factor correction (PFC) has become a necessaryfeature of modern AC/DC power electronic appliances.
The focus is to investigate methods to improveEMI, improve efficiency and optimization using FACTSdevices. Thus the overall objective of this work is to
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develop a method that reduce overall Voltage instability inweak system and improve performance of FACTS basedPFC circuits. The complexity of interconnections and thesize of the areas of electric power systems that arecontrolled in a coordinated way are rapidly increasingwhich led to the need of Automatic generation control(AGC). The generic function automatic generation controlwithin a predefined control area depends on the following:
1. Economic dispatch and
2. Load frequency control
Economic Dispatch (ED) is defined as theprocess of allocating optimal power generation levels toeach of the generating units in the station, so that theentire supply demand can be meet in a most economicallymanner. In case the load is fixed (i.e. static economicdispatch), the objective is to calculate, for a single periodof time, the output power of every generating unit.Unfortunately the load of a power system is alwayschanging, so the generators correspondingly respond i.e.with increase in the load the generator produces morepower and vice-versa. This entails for optimal allocationof generators participation in sharing the load at thecurrent interval of time to meet the forecasted loaddemand for the same interval. As per our definition,economic load dispatch is a means that allows thegenerators active and reactive powers to vary within arange to obtain the desired objectives of this researchwhich are as follows
1. to minimize the generation cost,
2. to minimize the total power loss in the powersystem network,
3. to minimize the voltage (and/or current) deviations,and
4. to maximize the quality of the power supplied tothe customers.
Over the past decades, extensive research onoptimization models and algorithms for ELD problemshave been explored and exploited. In addition to thetraditional methods such as equal incremental method,dynamic programming (DP), Lagrangian relaxationmethod (LR), artificial intelligence methods such asgenetic algorithm (GA) chaos optimization algorithm(COA), and particle swarm optimization (PSO)[63] havebeen successfully employed to solve the ELD problems.However, with the dramatic increase in the number ofgenerating units, existing stochastic algorithms may resultin the curse of dimensionality, and the difficulty ofoptimizing calculation redoubled as well as theconsuming-time. There is considerable interest in mergingor combining neural networks, fuzzy logic and geneticalgorithm based systems into a functional system toovercome their individual weakness. This innovative ideaof integration brings the low-level learning andcomputational power of neural network into fuzzy logic
systems and merges the high level human-like thinkingand reasoning of fuzzy logic systems into neuralnetworks. Similarly integration with genetic algorithmresults in solution optimization. Such synergism ofintegrating neural networks and these techniques into afunctional system provides a new direction towards therealization of intelligent systems, which are unaffected bymodel complexities.
The present article proposes to work on softcomputation based alternate solutions for optimaloperation of power system as these methods are robustand computationally simple as compared to the classicalmethods. Reactive power Planning (RPP) is known to be alarge-scale nonlinear combinatorial constrained problemin the field of power system analysis. RPP basically servesto determine the optimal setting of the power systemnetwork to satisfy few constraints discussed in the abovesection such as the power flow equation system securityand equipment operating limits. Several researchers andpower engineering experts have tried to solve and analyzeRPP via optimization (i.e. Reactive Power Optimization)by developing various search strategies and frameworksas solving this problem has a drastic impact on theeconomic load dispatch. Due the important role ofreactive power, it is necessary to plan on its availabilityand quantity in a power system. RPP refers to the propersizing and location of reactive power resources for normaloperating conditions and also in case of a contingency ordisturbance within the power system. In the short-term,RPP is known as reactive power optimization (RPO) andits purpose in a power system is to identify the controlvariables that minimize a given objective function whilesatisfying the unit and system constraints. Scheduling ofreactive power in an optimum manner reduces circulatingVAR (volt ampere reactive), thereby promoting a uniformvoltage profile which leads to appreciable power savingon account of reduced system losses.
In the long term RPP seeks to identify locationand sizes of RP resources. This is done subject to varioussystem constraints such as voltage limits and capacity ofresources. Due to the load fluctuations in a power system,it is necessary to have compensators that that can inject ordraw RP both continuously and instantaneously from thepower system so as to balance between the RP at thesending end and that at the receiving end. Theoptimization problem will be formulated with constraintssuch as generator limits, power balance equation, ramplimits and prohibited zone etc. Different soft computingmethods discussed above will be employed to solve theELD problem with RPO assessment with diverse andconflicting constraints. Soft computing approaches areknown to perform well under such uncertain conditionsdue to their simplicity and flexibility.
Suitable performance indices will be developedusing soft computing techniques to effectively measurethe severity of a contingency. Data will be generated usingconventional techniques in wide range of system
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operating conditions by changing loads and generations atall nodes. The focus of the proposed research study willbe to investigate the most appropriate and economicalmethodology to meet the committed load demand.
The conventional methods take long time inachieving the solution to optimization problems,preventing their use in real time. The proposed work willbe helpful in real time application. In real time loaddispatch, operator uses his judgment based on hisexperience to handle continuously changing situations.Proposed work based on soft computing approaches suchas ANN, GA and their hybrid combinations will besuitable for real time applications. A salient feature of theproposed approach is that the solution time growsapproximately linearly with problem size as compared todynamic programming where the time increasesgeometrically with problem dimension.
Integration of soft computing techniques isexpected to produce accurate results under uncertain andunpredictable operating conditions prevailing in practicalpower system. The results are expected to be useful topower utilities in their on-line contingency selection-ranking and reactive power dispatch at energy controlcenters. Dynamic ELD solution will be useful in therestructured environment where market is governed on thebasis of spot prices. The main objective of this paper is toexplain the impact of effective reactive power planning.Genetic algorithm is used as the optimization techniquefor this multi-objective problem. GA operators are to beunderstood in detail and used to write a program inMATLAB simulation software package to solve the RPPproblem. The effectiveness of the GA is verified on anIEEE 14 bus system to give an optimal solution. Theobjectives can be thus stated as;
a) To understand the importance of the powerelectronic devices and analyze their correspondingfunctionalities within the boundaries of the powersystem network constraints.
b) To determine the location and size of RPC whileminimizing cost, losses and maintaining voltagestability subject to the power system constraints.
c) To understand Genetic Algorithm and use it to findthe optimal solution
The rest of the paper is organized with section 2deals with detail background survey on the existing workswith complete analysis on drawbacks and conceptsemployed. While section 3, discusses power electronicdevices with their operations and schematics that areemployed for enhancing and estimation of the proposedalgorithm. Section 4 deals with the basic estimationalgorithm based on GA with detail algorithm steps andcomplete architecture. Section 5 presents the simulationanalysis of the IEEE 14-bus system under variousconditions. Finally section 6, presents the conclusion andfeature work.
2. Background
In past few decades, relatively very little headway was made within the field of power electronicsengineering with prime focus on power optimizationtechniques, while the level and frequency associated withthe power system network over runs were becoming vitaland increasing exponentially to numerous largeorganizations. In later years, several organizations focusedon the effective and efficient framework of ReactivePower Planning (RPP) and evolved into a lucrative andlandmark project with reference to power system networkdevelopment. Detailed literature survey on reactive powerusing conventional as well as different soft computingapproaches is done and a brief review is presented here.
Economic load dispatch
Economic load dispatch (ELD) is one of the mainfunctions of modern energy management system, whichdetermines the optimal real power setting of generatingunits with an objective to minimize total fuel cost ofthermal plants. Optimization is done by minimizingselected objective functions while maintaining anacceptable system performance in term of generatorcapability limits and output of the compensating devices.The objective functions, also known as cost functions maypresent economic costs, system security, or otherobjectives [1]. Many techniques such as the lambdaiteration method, base point and participation method anddynamic programming method [2,3] have replacedobsolete techniques such as the best point loading andbase load methods . All these methods consider ELDproblem as a convex optimization problem and assumethat the whole of unit operating range between minimumand maximum generation limit is available for operation.
Economic load dispatch problem has been solvedby researchers using conventional as well as modernmethods employing different objective functions. Inpractical systems, the operating range of all units isrestricted by their ramp limits [4], and prohibitedoperating zone due to physical operational limitations.With advances in digital computing, a number oftechniques have been developed for generation costoptimization. Although the most commonly used methodin literature is the lambda iteration [5] due to itssimplicity, its application to large scale model is notfeasible due to oscillatory problems. Also, the constrainthandling capability of the technique is questionable.Efficient dispatch schemes are still being developed togive minimum cost with least solution time. Various ANNbased methods have been proposed for the ELD problem[6-12]. Application of Hopfield method [13], two phaseneural network [14] and Radial basis function [15] can befound in literature. Methods based on GA [16], fuzzylogic [27], fuzzy GA combination [17, 18] andcombination of GA with other methods [19] is alsoreported in literature. Paper [20] handles the multi
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objective ELD problem with particle swarm optimizationtechnique.
Soft computing methods
Researchers worldwide are increasingly proposing softcomputing methods as alternate approaches for solvingpower system optimization and other problems, as thesemethods are based on natural phenomena and hence aremore robust and suitable for real world problems. Theyhave parallel computation, fault tolerance and simplemodeling techniques, which make them attractive forpractical problems. Load shedding decisions based onfuzzy reasoning and neural classifications have beenproposed to avoid voltage collapse [21]. Geneticalgorithm based reactive power optimization has beenemployed to assess the impact of outages and to enhancevoltage security margin by optimal dispatch of reactivesources [22,23]. The concept of fuzzy logic and artificialneural network, when integrated with genetic algorithm[22,23,24] results in models which can handle non-linearity and imprecision and produce flexible practicalsolutions.
Noteworthy contribution in the field of proposed work
Over the past few years, several approachesusing soft computing techniques have been proposed forsolving the on line ELD problems with environmental andsecurity constraints. Multi layer Perceptron [14] and RBFbased approaches are very fast because they map totaldemand with individual generations, for minimumoperating cost. The main advantage with ANN basedapproaches lies in achieving accurate solutions withoutincreasing computational complexity. A variety of Hopfields models [25] have been employed for solving ELDproblems. Recently a two phase neural network (TPNN)[14] has been proposed which deals with all theconstraints in real time and can be realized in hardware forfaster operation. Walter and Sheble [16] proposed Geneticalgorithm, as a tool for optimal generation schedulingincorporating the valve point loadings and demonstratedthat this approach was many times faster that the dynamicprogramming approach. Later GA was proposed for ELDof generators having prohibited operating zones [26]. Thenetwork constraints have been included and effect ofcoding of variables on solution accuracy has beendemonstrated. Paper [27] presents the solution of ELDproblem with conflicting constraints of minimum fuel costand minimum emission, employing fuzzy satisfactionmaximizing approach. Recently a combination of GA withfuzzy logic [28], GA with tabu search [29] and particleswarm optimization has been proposed for the ELDproblem. Reference [30] proposed a new fuzzy dynamicELD model assuming uncertain cost coefficients, suitablefor the day-ahead market. The problem is solved by acombination of GA and quasi-simplex technique.
Soft computing methods are extensively beingproposed for ensuring secure operation of power system.Artificial neural networks [31-35], fuzzy logic [36] and
fuzzy neural networks [37-40] have been proposed forstatic and dynamic security assessment and contingencyranking issues. Genetic algorithm based methods areproposed for reactive power optimization [42] anddispatch [41].
The biogeography based optimization (BBO) bymodifying its migration models can make it more realistic.This BBO technique is then applied on simple economicload dispatch (ELD) problem and ELD with valve pointeffect to analyze the effect of different migrationmodels.[43]The combination of particle swarmoptimization (PSO) and biogeography-based optimization(BBO) algorithm to solve constrained economic loaddispatch (ELD)[61] problems in power system,considering valve point nonlinearities of generators,prohibited operating zones, ramp rate and spinningreserve. PSO is a well popular and robust evolutionaryalgorithm for solving global optimization problems,whereas BBO is a relatively new biogeography inspiredalgorithm. The hybridization of PSO and BBO(HPSOBBO) is proposed to improve the convergencespeed and solution quality. This method also producesstable convergence characteristic and avoids prematureconvergence. [44]
The economic load dispatch (ELD) plays an importantrole in power system operation and control. Differenttechniques have been used to solve these problems.Recently, the soft computing techniques have widely usedin practical applications. Reference [45] gives thesuccessful implementation of four evolutionaryalgorithms, namely particle swarm optimization (PSO),particle swarm optimization with constriction factorapproach (PSOCF A), particle swarm optimization withinertia weight factor approach (PSOIWA) and particleswarm optimization with constriction factor and inertiaweight factor approach (PSOCFIWA) algorithms are usedto economic load dispatch problem. Here prohibited zoneand ramp-rate limit constraints are considered to solve thisproblem. Power output of each generating unit andoptimum fuel cost obtained using all four algorithms havebeen compared.
The optimization problem will be formulatedwith constraints such as generator limits, power balanceequation, ramp limits and prohibited zone etc. Differentsoft computing methods discussed above will beemployed to solve the ELD problem with RPO assessmentwith diverse and conflicting constraints. Soft computingapproaches are known to perform well under suchuncertain conditions due to their simplicity and flexibility.
Suitable performance indices will be developed using softcomputing techniques to effectively measure the severityof a contingency. Data will be generated usingconventional techniques in wide range of systemoperating conditions by changing loads and generations atall nodes. The focus of the proposed research study willbe to investigate the most appropriate and economical
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methodology to meet the committed load demand. In thisthesis, we focus of the planning of possible reactive powerunits locations so as to improve the overall power systemnetwork stability scenario.
2.1 Reactive Power
Reactive power (RP) is the imaginary component ofcomplex power stored in form of magnetic and electricfields by inductors and capacitors respectively. RP isneeded for transfer of real or useful power in an ACsystem to maintain voltage stability of the power system.Most loads in an AC power system are either inductive orcapacitive in nature. This implies that the power in thesystem is complex power,= + ∗Where, P is the real/active power component while Q isthe imaginary or reactive power component. The activepower is the useful power necessary to do work and ismeasured in Watts. The reactive power on the other handalternates and is returned to the source. It is measured inVAR. It is stored in the form of electrical fields incapacitors or magnetic fields in inductors. It is useful inmaintaining voltage levels stable and its absence may leadto voltage collapse partially or totally (blackout).It isgeneral fact that reactive power (even though imaginary)produced due to reactive components and loads connectedto the network, is essential for transmission of activepower through transmission and distribution powernetwork. However, the permissible level of reactive powerin a system is commonly calculated based on power factorjudged by the power network operator.
In current dynamic and automated environment,we found it was intriguing to analyze and check thefeasibility of dynamic assessment of reactive power frominterval to interval. The prime motivation for addressingthis problem was that it is an important aspect incontrolling the power system’s operation and planning.Thus in this thesis, we present a Reactive Power Planningproblem that will be formulated with constraints such asgenerator limits, power balance equation, ramp limits andprohibited zone etc.
Inequality Constraints:
1. Voltage Constraints: ≤ ≤≤ ≤Where, “ ” & “ ” are the lower and
upper limits of the magnitude, “ ” is the voltagemagnitude of the system. “ ” & “ are thelower and upper limits of the phase, “ ” is the voltagephase of the system.
2. Generator Constraints: ≤ ≤
≤ ≤Where, “ ” & “ ” are the lower and
upper limits of the active power generation at thegenerator side, “ ” is the active power generated of thesystem. “ ” & “ are the lower and upper limits ofthe reactive power at the bus of the system, “ ” is thereactive power at the bus of the system
The loading (in KVA) of the generator should notexceed the prescribed value.
3. Spare Capacity Constraints:
These constraints are essential to meet a forced outage ofone or more alternators within the system and anunexpected load which may be applied on the system. Thetotal power generation should be such that it should meetload demand, various losses and minimum spare capacity,i.e. G ≥ Pp + Pso
4. Transmission Line Constraints:
The flow of active power and reactive power in thetransmission line is limited by the thermal capability ofthe circuit generally expressed as
Cp ≤ Cpmax ;
Cpmax is the maximum loading capacity of the Pth line.
5. Transformer Tapping Constraints:
For an auto-transformer, the minimum tap settings is zeroand maximum can be 1, i.e.
0 ≤ t ≤ 1.0 .
Similarly, in case of a two winding transformer, if thereare tappings on the secondary side, we have
0 ≤ t ≤ n ; n is known as the transformation ratio.
Equality Constraints:
These constraints focus on active and reactivepower equations only.
3. Power Electronic Devices
Generally there are two sources of reactive power (RP)i.e. capacitors and inductors/reactors. Capacitors storeelectrical energy in the form of electric fields hencegenerates RP. Reactors store electrical energy in the formof magnetic fields and therefore absorb reactive power[22].There are two types of RP resources; static resourcesand dynamic resources
3.1Static /Passive Resources
These are resources that have fixed reactive power outputthat cannot be changed instantaneously. The reactivepower generated/absorbed by a capacitor/reactor,=
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Where, V is the bus voltage and X the reactance; X=ωLfor inductor of inductance, L (in henries) and X=1/ (ωC)for a capacitor (in farads).Its generation is fixed andproportional to X, but the voltage of its connecting buscannot be directly controlled. In other words, a bus with aconnected capacitor/reactor is, in fact, a PQ bus. [1]
Shunt compensation is more or less like loadcompensation with all the advantages associated with it.There’s need to point out here that shuntcapacitors/inductors cannot be distributed uniformly alongthe line. These are normally connected at the end of theline and/or at midpoint of the line. Shunt capacitors raisethe load power factor (pf) which greatly increases thepower transmitted over the line as it is not required tocarry the reactive power. The power transmission can beincreased by using shunt compensation but for fulfillingthe requirements it would required large capacitorbank,which imposed the limitation and would becomeimpractical. So transmission capacity can be improved byadopting series compensation or by higher transmissionvoltages.
When switched capacitors are employed forcompensation, these should be disconnected immediatelyunder light load conditions to avoid excessive voltage riseand ferro-resonance in presence of transformer [46],this isbecause charging current should be kept below the ratedfull-load current of the line. The charging current is by Bc
|V|, where Bc is the total capacitive susceptance of the lineand |V| is the rated voltage to neutral. If the total inductivesusceptance is Br due to several inductors connected(shunt compensation) from line to neutral at appropriateplaces along the line, then the charging current would be:-= − ∗ | | = | | 1 −Where 1 − is the reduction factor for charging
current while is the shuntcompensation factor. This
implies that the receiving end voltage is reduced thereforereducing Ferranti effect as the load decreases.
3.2 Dynamic / Active resources
These are resources whose reactive power capability canbe changed instantly, and its value is dictated by thesystem conditions. These have the advantage of voltagecontrol and load stabilization thereby ensuring generatorsoperate at near unity power factor and minimizingblackouts.
Static Var Compensator (SVC): This is an automatedimpedance matching device that comprises capacitor bankfixed or switched (controlled) or fixed capacitor bank andswitched reactor bank in parallel. These compensatorsdraw reactive power (leading or lagging) from the linethere by regulating voltage, improving both steady-stateand transient stability and reducing voltage and currentunbalances. They also have the ability to damp out sub-
harmonic oscillations in HVDC application. The termstatic in their name implies that it has no significantmoving parts. The dynamic nature of the SVC lies in theuse of thyristors connected in series and inverse parallel(forming thyristor valves). Voltage regulation is providedby means of a closed loop controller.
Thyristors are used as the switching devices for SVCs.They are connected in anti-parallel to switch a capacitor/reactor unit in stepwise control. [46] When the circuitrycan adjust the firing angle then the unit acts ascontinuously variable. Various schemes exist as discussedbelow.
a) Thyristor controlled reactor (TCR): Athyristor-controlled-reactor compensator consistsof a combination of six pulse or twelve pulsethyristor-controlled reactors with a fixed shuntcapacitor bank. The reactive power is changed byadjusting the thyristor firing angle. TCRs arecharacterized by continuous control, no transientsand generation of harmonics. The control systemconsists of voltage (and current) measuringdevices, a controller for error-signalconditioning, a linearizing circuit and one ormore synchronizing circuits [1]
b) Thyristor switched capacitor (TSC): Consistsof only thyristor switched capacitor bank splitinto equal number of units of equal ratings toachieve a step-wise control. They are applied as adiscretely variable reactive power source, wherethis type of voltage support is deemed adequate.All switching takes place when the voltageacross the thyristor valve is zero, thus providingalmost transient free switching. Disconnection iseffected by suppressing the firing to the thyristor.
c) Combined TCR and TSC: This is the optimumsolution in majority of the cases. With this,continuous variable reactive power is obtainedthroughout the complete control range. Fullcontrol of both inductive and capacitive parts ofthe compensator is obtained. This is a veryadvantageous feature allowing optimumperformance in case of a contingency e.g. linefault, load rejection etc. The circuit in Figure1below shows a one line diagram of a typical SVCemploying a TCR,TSC, harmonic filter,mechanically switched capacitor and amechanically switched are connected to the gridthrough a transformer on the secondary side coolthe thyristors. The harmonic filter is used tosmooth the waveform by eliminating odd orderharmonics [46]
Static Synchronous Compensator (STATCOM)
This is a regulating device based on voltage sourceconverter and can act as source/sink of R Pin a powersystem to improve voltage stability and/or power factor. It
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comprises of a voltage source behind a reactor. Thevoltage source is created from a DC capacitor andtherefore has very little active power capability. Itsreactive power however depends on the magnitude of thevoltage at source converter(VSC). This means if thevoltage of the VSC is lower than that at the point ofconnection, the STATCOM absorbs RP and vice-versa. Itsresponse time is faster than that of the SVC mainly due tothe use IGBJTs of the VSC. It also provides betterreactive support for low AC voltages than SVC as its RPdecreases linearly with AC voltage(by maintaining therated current). Its disadvantage however is the fact that itexhibits more losses than the SVC and is more expensivethus limiting its use. [46, 47]
Figure 1: The line diagram of a typical SVC employingTCR, TSC and others
Synchronous Condenser
This is a synchronous motor operating at no-load andhaving variable excitation over a widerange. Its field canbe controlled by a voltage regulator to generate RP whenoverexcited orabsorb RP when under-excited as needed toadjust grid voltage. The kinetic energy stored inthe rotorcan help to stabilize short circuits or rapidly fluctuatingloads. These have theadvantage of no generation ofharmonics but have high energy losses compared to staticcapacitors. They are usually hydrogen cooled [46, 48].
4. Proposed Framework
Genetic algorithm is part of evolutionary algorithm (EA)and is a search algorithm based onthe process of naturalselection. In genetic algorithms, the mechanics of naturalselection and genetics are emulated artificially. The basicoptimization procedure involves nothing more thanprocessinghighly fit individuals in order to produce betterindividuals as the search progresses. Atypical geneticalgorithm cycle involves four major processes, i.e.:-fitness evaluation, selection, recombination andreproduction [49].
4.1 Generation of Initial population
These are randomly generated with the population sizedependent on nature of the problem but allowing entirerange of possible solutions. There are two methods ofchoosing the initial population. One uses randomly
generated solutions created by a random number generatorand is preferred for problems where no prior knowledgeexists. The second method is used where prior knowledgeof the problem exists and therefore requirements are setthat solutions have to meet to be part of the initialsolution. This has the advantage of faster convergence. Inthis paper, we employ the initial method of randomlygenerating wherein no prior knowledge of the problemexists.
4.2 Solution Coding
The parameters to be optimized are usually represented ina string form since genetic operators are suitable for thistype of representation. Different representation schemesmight cause different performances in terms of accuracyand computation time. There are two common methodsused for representation of optimization problems i.e.binary representation and real number/ integerrepresentation. When a binary representation scheme isemployed, an important issue is to decide the number ofbits used to encode the parameters to be optimized. Eachparameter should be encoded with the optimal number ofbits covering all possible solutions in the solution space.When too few or too many bits are used the performancecan be adversely affected. GA works on the encoding of aproblem, not on the problem itself. This access will lowmore freedom and resolution for modifying the parameterfeatures to arrive at the optimal solution [50].
4.3 Fitness Evaluation Function
This acts as an interface between the GA and theoptimization problem. The GA assesses solutions for theirquality according to the information produced by this unitand not by using direct information about their structure.The quality of a proposed solution is usually calculateddepending on how well the solution performs the desiredfunctions and satisfies the given constraints since the GAis a search technique and must be limited to exploring areasonable region of variable space. Generally fitness isapplied to maximization, however since most optimizationproblem involve cost then they become minimizationproblems. In this case therefore, the fittest individuals willhave the lowest value of the associated objective function.The fitness function is normally used to transform theobjective function value into a measure of relative fitness[50].
4.4 Genetic Operators
There are three main genetic operators i.e. .selection,crossover and mutation. Others such as inversion andelitism are sometimes applied. The purpose of theoperators is to maintain genetic diversity and combineexisting solutions into new ones.
4.4.1 Selection
This aims to reproduce more copies of individuals whosefitness values are higher than those whose fitness values
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are low. The selection procedure has a significantinfluence on driving the search towards a promising areaand finding good solutions in a short time. There aremainly two selection procedures, i.e. proportional/ roulettewheel selection and ranking based selection.
The ranking-based selection is based on limitingnumber of trials of an individual to prevent them fromgenerating too many offspring. This implies that eachindividual generates an expected number of offspringaccording to the rank of their fitness value. Selectionpressure is the ratio of the probability that the fittestchromosome is selected as a parent to the probability thatthe average chromosome is selected [51]. Retaining thebest individuals in a generation unchanged in the nextgeneration, is called elitism or elitist selection. The idea isto avoid that the observed best fitted individual dies outjust by selecting it for the next generation without anyrandom experiment.
Elitism is widely used for speeding up theconvergence of a GA. It should, however, be used withcaution, because it can lead to premature convergence[52].
4.4.2Crossover
It is used to create new individuals (children) from twoexisting individuals (parents) picked from the currentpopulation by the selection operation. This involveschoosing a random position in the two strings andswapping the bits that occur after this position. In onegeneration the crossover operation is performed on aspecified percentage of the population specified by thecrossover probability, Pc. The crossover rate determinesthe frequency of the crossover operation. It is useful at thestart of optimization to discover a promising region. Alow crossover frequency decreases the speed ofconvergence to such an area. If the frequency is too high,it leads to saturation around one solution. Crossover canalso be performed in two different means: tail-tail andhead-tail crossovers.
The two crossover methods can be changed duringiterations: the head-tail crossover can be used in theearlier generations and then switched to tail-tail crossoverin the later generations for fine tuning [53].
One-point crossover: A crossover operatorthat randomly selects a crossover pointwithin a chromosome then interchanges thetwo parent chromosomes at this point toproduce two new offspring.
Two-point crossover: A crossover operatorthat randomly selects two crossover pointswithin a chromosome then interchanges thetwo parent chromosomes between thesepoints to produce two new offspring.
Uniform Crossover: This uses a fixed mixingratio between two parents. Unlike one- and
two-point crossover, the uniform crossoverenables the parent chromosomes tocontribute the gene level rather than thesegment level. If the mixing ratio is 0.5,approximately half of the genes in theoffspring will come from parent 1 and theother half will come from parent 2.
Three parent crossover: In this technique, thechild is derived from three parents that arerandomly chosen. Each bit of first parent ischecked with bit of second parent whetherthey are same. If same then the bit is takenfor the offspring otherwise the bit from thethird parent is taken for the offspring
Arithmetic crossover: A crossover operatorthat linearly combines two parentchromosome vectors to produce two newoffspring variables according to thefollowing equations:
Offspring1 = β Pmn + (1- β) Pdn
Offspring2 = (1 – β) Pmn+ β Pdn
Where ‘β’ is a random weighting in theinterval [0,1] and Pmn and Pdn are the nthvariables in the mother and fatherchromosomes respectively [51]
Heuristic crossover: It produces a linearextrapolation of the two individuals as given bythe equation below where the variables aredefined as those for arithmetic crossover [52].
Offspring = β (Pmn - Pdn) –Pmn
4.4.3 Mutation
Mutation is applied to each child individually aftercrossover to maintain genetic diversity from onegeneration of a population of algorithm chromosomes tothe next. It alters one or more gene values in achromosome from its initial state with a small probability.It involves selecting a string at random as well as a bitposition at random and changing it from a 1 to a 0or vice-versa. In mutation, the solution may change entirely fromthe previous solution. Hence GA can come to bettersolution by using mutation. Mutation occurs duringevolution according to a user-definable mutationprobability. It is used to escape from a local minimum.
A high mutation rate introduces high diversity in thepopulation and might cause instability. On the other hand,it is usually very difficult for a GA to find a globaloptimal solution with too low a mutation rate. Aftermutation, the new generation is complete and theprocedure begins again with the fitness evaluation of thepopulation.
4.5 Control Parameters
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Important control parameters of a GA include thepopulation size (number of individuals in the population),number of iterations, crossover rate and mutation rate. Thealgorithm runs iteratively until the convergence criterionis achieved.
4.6 Termination criteria
The number of generations that evolve depends onwhether an acceptable solution is reached or a set numberof iterations are exceeded. Various stopping criteriainclude:-
a) Max iterations- specify the maximum number ofiterations the algorithm performs.
b) Max function evaluations -specifies the maximumnumber of evaluations of the objective and constraintfunctions the algorithm performs.
c) X tolerance specifies the termination tolerance;tolerance is a threshold which, if crossed, stops theiterations of a solver.
d) Function tolerance specifies the termination tolerancefor the objective function value.
e) Nonlinear constraint tolerance specifies the tolerancefor the maximum nonlinear constraint violation.
4.7 Proposed Algorithm
The problem can be solved in a sequence of steps asdiscussed below.
Step 1. Conduct a load-flow study on the IEEE14-bus network.
Step 2. Read data i.e. cost coefficients, numberof iterations, size of population, probabilities ofcrossover and mutation, minimum and maximumreactive power constraints.
Step 3. Generate the initial population of Qrandomly in real code.
Step 4. Calculate the cost for the various valuesof Q.
Step 5. Calculate the fitness of eachchromosome according to the fitness functionand sort. Those that have lowest cost function areselected for the next generation. The averagefitness of the population is also calculated.
Step 6. Selection based on reproductionfollowed by crossover with embedded mutationto create the new population for the nextgeneration.
Step 7. The fitness of the new offspring iscalculated and they are sorted in the ascendingorder. The lowest value of the objective functionmeans better fitness. Therefore the fittest areselected for the next generation.
Step 8. Stop criteria. If the number of iterationsreaches maximum, go to step 10. Otherwise goback to step 4.
Step 9. Run load flow to compute system losseswith values of Q generated and calculates thevoltage profile.
4.8 Proposed Algorithm Block Diagram
In this section, we present a block of the proposedframework based on the GA model for collective choicemaking incorporates non-positioned voting routines,especially the approbation voting technique, with the sethypothesis. It goes for improving gathering agreement onthe cooperative choice result for analysis of the reactivepower compensation devices (power electronic devices)focusing on mitigation of voltage drops.
Figure 2: The block diagram of the proposed frameworkbased on GA
5. Simulation Analysis
MATLAB packed program with functionalitiesMATPOWER are used to analyze the proposed systemagainst commonly used power electronic devices foreffective planning of Reactive power compensation.Simulation results have been taken for various operatingconditions feeding grid under following operationconditions. AC load flow analysis was done usingMatpower 6.0 to determine the system losses and busvoltages. The parameters assumed for GA analysis arepresented below in Table 1
Table 1 GA Parameters
Population Size 60No. of Units 5
Maximum Iterations 500Crossover Probability 0.7 (70%)Mutation Probability 0.01 (1%)
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It is observed that the system losses both real and reactivereduce by about 30% and 20%respectively. This issignificant enough to justify the large investment in RPCsin practical systems. Variations in voltage from theirspecified values also reduced thereby improving systemvoltage stability. The algorithm was found to converge toa global optimum after about 360 generations and with anaverage computational time of about 798 clock-sec. Thesystem voltage is found to be within the limits or slightlyabove by 0.005 but not beyond-10% which was set as thecollapse point.
Figure 3: Snap-shot of system summary
Figure 4: Snap-shot of IEEE 14 bus data withimprovement
Figure 5: Snap shot of individual bus information
Figure 6: Bus voltage magnitudes
Figure 7: Convergence Characteristics
6. Conclusion
The prime focus of this paper was to understand andanalyze the impact of Reactive Power Planning in the
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1.1BUS VOLATGE MAGNITUDES
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field of power systems. We proposed an approach thatcould identify the requirement and volume of the reactivepower resources at various locations subject to pre andpost fault conditions to stabilize the operating conditionsto normal. From the detail analysis and study it has beenevident that the dynamic nature of power electronicdevices improves the faulty conditions significantly andconvergence of the entire system response is relativelyquick. In practical power network structure is primaryfactor for righteous reactive power estimation function atany stage as there is significant lost and cost attached topower system network. We employ various factors suchas selection, crossover and mutation with the aim ofimproving fitness of subsequent generations for survival.
The power system being a practical system has severalconstraints such as capacity limits of the resources, systemvoltage limits etc. The IEEE 14-bus network was used asthe test network and the code developed using MATLABfor analyzing the impact of power electronic devices onthe RPP problem. Results obtained show a reduction inreal and reactive losses and improvement in the voltageprofile i.e. reduced by about 30% and 20%respectively.This is significant enough to justify the large investmentin RPCs in practical systems. Variations in voltage fromtheir specified values also reduced thereby improvingsystem voltage stability. The algorithm was found toconverge to a global optimum after about 360 generationsand with an average computational time of about 798clock-sec. The system voltage is found to be within thelimits or slightly above by 0.005 but not beyond-10%which was set as the collapse point.
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