providing transient stability by excitation system...

Scientia Iranica D (2019) 26(3), 1652{1663

Sharif University of TechnologyScientia Iranica

Transactions D: Computer Science & Engineering and Electrical Engineeringhttp://scientiairanica.sharif.edu

Providing transient stability by excitation systemresponse improvement methods through long-termcontracts

A. Khandani and A. Akbari Foroud�

Faculty of Electrical and Computer Engineering, Semnan University, Semnan, Iran.

Received 6 April 2016; received in revised form 31 December 2016; accepted 30 May 2017

KEYWORDSExcitation systems;Transient stability;Single machineequivalent (SIME);Transient StabilityConstrainedOptimal Power Flow(TSC-OPF).

Abstract. Maintaining network stability and encouraging generation companies toget involved in stability-maintaining objective are major concerns of an IndependentSystem Operator (ISO) in a deregulated power system. Excitation system of synchronousgenerators is e�ective and well-known equipment, which has a signi�cant e�ect onnetwork stability. Therefore, improving performance of this system can enhance networkstability. However, utilizing the methods that improve the performance of excitation systemimposes cost on generation companies. This paper proposes a motivation mechanism forenhancing transient stability that encourages generation companies to improve performanceof excitation system. In this mechanism, besides excitation system response improvingmethods, a transient stability constrained optimal power ow is solved in order to ensuremaintaining transient stability under di�erent contingencies. A 4-bus test system, an IEEE14-bus test system, and an IEEE 118-bus test system are used to illustrate the e�ectivenessof the proposed mechanism. Implementation results show that the proposed mechanismnot only provides required transient stability margin with minimum operation cost, butalso does not restrict generators production capability.© 2019 Sharif University of Technology. All rights reserved.

1. Introduction

Transient stability is the ability of power systems tomaintain synchronism in the event of large distur-bances. Such disturbances can increase generators'rotor angle deviation; therefore, if corrective actionsfail, synchronization with the network will be lost [1].Excitation system of synchronous generators is ef-fective for primary control action, which maintainstransient stability of power systems. Excitation systemsupplies required �eld current to keep generator in

*. Corresponding author. Fax: +98-23-33654089E-mail addresses: [email protected] (A.Khandani); [email protected] (A. Akbari Foroud)

doi: 10.24200/sci.2017.4511

synchronization with the network. A quick excitationsystem response can increase synchronization torque ofa generator in order to maintain synchronism with thenetwork. As a result, the response rate of excitationsystem has a signi�cant e�ect on network stability.Various parameters a�ect performance of the excitationsystem. These parameters include ceiling voltage,ceiling current, nominal response of the system, voltageexcitation system response time, etc. Numerous meth-ods have been proposed to modify these parameters forimproving performance of the excitation system thatcan be divided into three general categories:

1. Expansion capability of excitation system;

2. Improvement response of controller;

3. Modi�cation input signal of controller.

A. Khandani and A. Akbari Foroud/Scientia Iranica, Transactions D: Computer Science & ... 26 (2019) 1652{1663 1653

Exceeding of overexcitation limit, Generator Capabil-ity Curve (GCC) expansion, control response improve-ment, and High Side Voltage Control (HSVC) are someof these methods. These methods are called `improvingmethods' in this paper. Simple implementation andoperation, non-restriction of generators production ca-pability, and good performance are some features of theimproving methods. While installation and operationcosts of the improving methods discourage GenerationCompanies (GenCos) from utilizing these methods. IfGenCos do not utilize the improving methods, otherpreventive control actions may be used to enhancenetwork stability.

Changes in generators operation points can be oneof the preventive control actions for providing networkstability. In this method, operation points of genera-tors are modi�ed to make system stable in probablydisturbances. Transient Stability Constrained OptimalPower Flow (TSC-OPF) is a preventive control actionwhich is utilized to optimize operation point of gen-erators in order to provide transient stability of thesystem. This topic was discussed in several articles [2-6]. In [2-4], rotor angle equations were considered as atransient stability constraint in optimal power ow. Asrotor angle equations were di�erential equations, theywere converted into an algebraic set of equations tosolve TSC-OPF as a standard nonlinear optimization.Researchers in this �eld focus on converting di�erentialequations and solving standard TSC-OPF. In [2], au-thors converted the di�erential equations into numeri-cal equivalent algebraic ones and used a standard non-linear programming technique for solving TSC-OPF.In [3], authors proposed an enhanced discretizationmethod to reduce the converted system dimension andimprove computational e�ciency of the optimizationalgorithm. In [4], authors modelled transient stabilityas an objective function besides active power cost and,then, solved this multi-objective optimization by Non-dominated Sorting Genetic Algorithm II (NSGA-II).In [5,6], time domain simulation was performed toanalyse transient stability of the system and simulationresults were utilized in optimal power ow. In [5],simulation results determined critical and non-criticalgenerators of the system. Critical generators werethe generators that lose synchronism in the eventof contingency. In that method, active powers ofthe critical generators were decreased to enhance thetransient stability of the system. In [6], results oftime domain simulation were converted into a singleequation as a transient stability constraint in OPF.Active power of generators, machine angle, magnitudeand angle of buses voltage, and other optimizationvariables were used to determine the initial operationpoint to increase transient stability of the system. Inthat paper, the initial operation point was changed tosatisfy transient stability constraint. In addition, some

new methods based on modern heuristic methods wereused to solve TSC-OPF [7]. In [7], authors proposeda method to estimate Critical Clearing Time (CCT)by the dual-kriging method. Results of this estimationwere included in a single transient stability constraintof the TSC-OPF. Therefore, di�erential algebraic equa-tions were excluded from TSC-OPF and standard opti-mization method was used to solve problem. Authorsin [8] reviewed di�erent TSC-OPF methods and im-plemented some of these methods. In addition, meritsand demerits of the studied methods compared to eachother were investigated in [8]. However, it shouldbe considered that all the above-mentioned TSC-OPFmethods cause an increase in the operation cost ofthe system, because active power outputs of generatorsare rescheduled in order to increase transient stabilityof the system. Moreover, restriction of active andreactive power generation due to the changing of thegenerators operation points is another disadvantage ofthose methods.

As described, utilizing of the improving meth-ods for excitation system response imposes costs onGenCos, thus discouraging them from utilizing thesemethods. On the other side, other preventive meth-ods for providing transient stability, such as TSC-OPF, cause an increase in system operation cost andrestrict generators capacity. Therefore, this paperproposes a motivation mechanism to encourage GenCosto utilize the improving methods. Transient stabilityenhancement by utilizing the improving methods doesnot change optimal operation point of the systemin which system operation cost is minimal. If thedesired transient stability margin is not provided onlyby utilizing the improving methods, then a changein generators' operation points is used to provide themuch needed stability margin. In this paper, TSC-OPFis used alongside the improving methods to minimizethe cost of active power rescheduling and provide thedesired transient stability of the system. Innovationsand contributions of this paper are summarized asfollows:

1. The proposed mechanism maximizes transient sta-bility and minimizes operation cost of the systemby considering e�ects of the improving methods onnetwork stability;

2. This mechanism provides required motivation forGenCos to utilize the improving methods;

3. In this mechanism, GenCos capacity for powergenerating is not restricted;

4. In this mechanism, operation point of the system forproviding transient stability is the same operationpoint that minimizes network operation cost;

5. In this mechanism, both of the improving methods

1654 A. Khandani and A. Akbari Foroud/Scientia Iranica, Transactions D: Computer Science & ... 26 (2019) 1652{1663

and TSC-OPF are considered for providing tran-sient stability.

The rest of the paper is organized as follows. Thesecond section describes the improving methods forexcitation system response. The third section in-troduces the methodology used in transient stabilityanalysis. The `transient stability providing' mechanismis presented in Section 4. Section 5 investigates the casestudy, and Section 6 concludes this paper.

2. The improving methods for excitationsystem response

Performance of excitation system a�ects stability ofthe system. Results of previous researches show thata fast-response AVR and a high ceiling voltage excitersigni�cantly reduce �rst rotor angle swing of generatorsin the event of contingency [9]. Excitation systemresponse depends on the controller and limitation ofthe excitation system. Therefore, in this section, fourmethods that a�ect the excitation system responseare described. Overexcitation limit exceeding andGenerator Capability Curve (GCC) expansion enlargethe capability of the excitation system and cause anincrease in the ceiling voltage of the exciter. Controllerresponse improvement and High Side Voltage Control(HSVC) enhance control performance of excitationsystem and cause a decrease in response time of thecontrol system.

2.1. Overexcitation limit exceedingActive and reactive power generation limits of thesynchronous generator are de�ned by its capabilitycurve. Capability of generating reactive power isusually limited by the �eld winding current. Overexci-tation limit is the upper limit of capability curve thatrestricts reactive power generation. This limit protectsgenerator's rotor winding from overcurrent in a steady-state operation. IEEE/ANSI C50.13 is an operationalstandard for exceeding overexcitation limit [10]. Ac-cording to this standard, generators' rotor winding cansupport short-time overloading. Figure 1 shows thisstandard curve that depicts the relationship betweenthe excitation current exceeding and acceptable delayfor reducing this current. Some papers discussedthe importance of OEL modelling and its e�ect onnetwork stability in [11,12]. Moreover, authors in [13]studied the e�ect of the excitation ceiling voltage ratioon transient stability, and experimentally illustratedthat the increase of excitation ceiling voltage improvestransient stability of the system. Therefore, accuratemodelling of OEL was studied in some papers, anddi�erent models were proposed for OEL modelling.

Overheating may occur in rotor winding dueto the delay of the control equipment, time of heatreduction after �eld current decreasing, and repetitive

Figure 1. Coordination of OEL and IEEE/ANSI C50.13standard.

occurrence of overloading [14]. In typical OEL, a se-curity margin is considered to protect the synchronousgenerator from overheating. Figure 1 shows the marginbetween the actual implementation of OEL (the dottedcurve) and IEEE/ANSI C50.13 standard (the solidcurve). Reduction of this security margin can increaseoutput power of the generators and enhance the systemstability. The authors in [14] proposed an advancedOEL that allows the generator to supply power up to itsmaximum limits by reducing this security margin. Inthat method, limiting margin of overexcitation limiterwas estimated based on the �eld current and voltagemeasurement of the generator. The authors in [14]explained that the advanced OEL improved stability ofthe system and, also, protected generators �eld windingfrom overheating.

2.2. Controller responseNumerous papers studied the excitation system re-sponse of synchronous generator and proposed variousmethods for improving this response. These papersdemonstrated that the fast voltage control improvedvoltage stability and transient stability of the system.These methods include using the PID controller inAVR, using the genetic algorithm and fuzzy logicapproach to tuning AVR, adjusting the coe�cients ofthe excitation system for achieving better response,etc. [15-17].

Authors in [16] analysed performance of a com-bined genetic algorithm, radial basis function neuralnetwork, and Sugeno fuzzy logic approach to tuninga PID controller for an AVR system; they showedthat this method could enhance transient response ofthe AVR system. In addition, authors in [17] useda Linear Quadratic Gaussian (LQG) control methodto design a wide area damping controller. Simulationresults of [17] showed that the proposed LQG controllerimproved inter-area oscillation damping and enhancedsmall signal and transient stability of the system.


Figure 2. Construction of the HSVC method [19].

2.3. High side voltage controlThe advanced High Side Voltage Control (HSVC)regulator controls high side voltage of the generatortransformer without using a direct feedback. Structureand implementation of the HSVC have been obtainedby upgrading auxiliary generator excitation controlsystems such as Line Drop Compensation (LDC) andthe Power System Voltage Regulator (PSVR). HSVCimproves voltage stability and enhances rotor angelstability of the system [18].

Authors in [19] studied the e�ect of HSVC onstatic voltage stability and damping of oscillation inpower systems. Moreover, HSVC increases loadabilityof the system [19]. Figure 2 depicts construction of theadvance HSVC.

2.4. Expansion of generator capability curveExcess heat from generators must be reduced to keepdi�erent components of the generator at predeterminedtemperatures. Utilization of hydrogen is a commonmethod for cooling the generator in modern powerplants. In hydrogen cooling generators, the hydrogenpressure is increased to expand the capability curve ofthe generator. Similarly, in the cooling air generator,the cooling air temperature is decreased to expand thecapability curve of the generator. Figure 3 shows theexpansion of the Generator Capability Curve (GCC)by reducing the cooling air temperature from 46�C to34�C [20]. Authors in [20] proposed a method in orderto modify OEL, Under Excitation Limit (UEL), andother excitation system limits in response to changesin a coolant condition such as hydrogen pressure orcooling air temperature. Therefore, expansion ofgenerators capability curve increases their productioncapacity.

3. Transient stability analysis

Several methods for transient stability analysis inves-tigate e�ects of the improving methods on transientstability. These methods can be divided into three

Figure 3. Expansion of the Generator Capability Curve(GCC).

general categories [21]: time domain simulation, directmethod, and hybrid method. Time Domain Simulation(TDS) method simulates the dynamic behaviour of thesystem very close to its real operation and allows usingthe detailed model in the simulation [1]. However,this method is not able to determine the cause ofinstability, margin of stability, and design adequatecontrol measures. In addition, the burden of thecomputation for solving di�erential equations is theweakness of this method [1]. On the other side, adirect method limits the analysis of power systemtransient stability to during-fault period and, thus,reduces computation burden. The main problem of thismethod is system simpli�cation that causes equipmentmodelling restriction. Therefore, in this paper, ahybrid method is used in order to combine advantagesof the TDS method and direct method. The necessityof the accurate modelling of the system equipment,especially generator's excitation system and overexci-tation limit, leads one to use TDS. In addition, criticalgenerators are required to be determined, causingsystem instability; therefore, transient stability marginof the system leads to the use of the direct method.

In this paper, a single-machine equivalent method(SIME) is used to connect TDS method with the directmethod. In the SIME method, a multi-machine systemis reduced to a two-machine model and, then, reducedto a One-Machine In�nite Bus (OMIB) system [1]. Thefact that a multi-machine system can be reduced toan OMIB is well known in power system. However,previous methods restricted modelling of the system.The main achievement of the SIME method is thatany modelling level for a large power system can beconsidered. SIME correlates TDS method with Equal


Area Criterion (EAC) and provides a very importantadvantage, that is, identi�cation of critical machinesresponsible for the system instability.

In the SIME method, a heuristic limit on rotor an-gle deviation, which is derived from TDS, �rst identi�escritical generators; then, two groups of machines can beconsidered: critical and non-critical groups. Afterward,these two groups are converted into a two-machinesystem; then, this two-machine system is reduced to anOMIB through Eqs. (1)-(7). Now, transient stabilityof the system can be analysed by ECA for the OMIB.The following equations are used to convert a detailedmodel of power system into an OMIB. A more detaileddescription of SIME can be found in [1].

�(t) � 1MC

XK2C

MK�K(t)� 1MNC

Xj2NC

Mj�j(t);(1)

Pm(t)=M

0@ 1MC

Xk2C

Pmk(t)� 1MNC

Xj2NC

Pmj(t)

1A ;(2)

Pe(t)=M

0@ 1MC

Xk2C

Pek(t)� 1MNC

Xj2NC

Pej(t)

1A ;(3)

Pa(t) = Pm(t)� Pe(t); (4)

MC =XK2C

MK ; (5)

MNC =Xj2NC

Mj ; (6)

M =MCMNC

MC +MNC: (7)

In the above equations, �j(t) is the rotor angle,Pmj(t) is the mechanical power, Pej(t) is the electricalpower, and Mj is the inertia coe�cient for generatorj. In addition, �(t) is the rotor angle, Pm(t) is themechanical power, Pe(t) is the electrical power, Pa(t)is the accelerating power, and M is the inertia coe�-cient of the corresponding OMIB. In these equations,subscript C represents a critical group, and subscriptNC represents a non-critical group.

4. Motivation mechanism for providingtransient stability

Providing and installing new control equipment haslong-term e�ects on the system, enhancing transientstability of the system. However, imposed cost onGenCos, due to installing new control equipment, dis-courages these companies from utilizing the improvingmethods. Therefore, this paper proposes a long-term

contract between ISO and GenCos for providing tran-sient stability of the system. In this contract, ISO �rstdetermines required stability margin (required CriticalClearing Time-CCT). Afterward, GenCos undertaketo provide this stability margin and, reciprocally, ISOpays transient stability providing the cost to them. Thecost of providing transient stability can be determinedbased on the value of transient stability for ISO, whichcan be considered as the amount of cost that ISOmust pay for providing this stability margin by othermethods (such as changes in generators active power).ISO can pay part of this saved cost to GenCos in orderto encourage them to utilize the improving methods.Utilization of these methods de�nitely has a lowercost in comparison to the other methods for providingtransient stability. Advanced OEL and HSVC areimplemented as software functions in a digital AVRsimilar to other functions of digital AVR such as PowerSystem Stabilizer (PSS), Line Drop Compensator(LDC), etc. [14]. Controller response improvement canbe performed by con�guring AVR for a better response.Expansion of the generator capability curve can becarried out by the coordination between limitationsand protection functions of excitation system for bettercooling operation; therefore, it can be implementedusing excitation system functions [20]. Therefore,part of the saved cost due to the use of improvingmethods can compensate GenCos cost for utilizingthese methods.

4.1. Procedure of the proposed mechanismFigure 4 shows the owchart of the proposed mech-anism for providing desired transient stability of thesystem. A step-by-step implementation procedure ofthis mechanism is described in the following:

1. In the proposed mechanism, ISO �rst contractswith GenCos for providing desired stability margin(contract between ISO and GenCos). The value oftransient stability for ISO determines the amount ofpaid cost to GenCos by ISO. This value depends onseveral factors such as the importance of transientstability for the system and the cost of transientstability enhancement;

2. After contract, GenCos implement the improve-ment methods that are mentioned in agreementbetween GenCo and ISO;

3. The improved network is the studied network inthe initial operation point in which the improvingmethods are implemented in excitation systems ofgenerators;

4. A conventional OPF is run to determine the optimalpower ow of the studied network based on GenCos'bids. In this step, a transient stability constraint isnot considered;


Figure 4. Flowchart of the proposed mechanism.

5. Then contingency screening is carried out in theimproved network to separate stable from unstablecontingencies. Contingency screening is performedusing SIME described in [22]. In this method,TDS is carried out for the system and, then, itsresults are utilized by SIME in order to evaluatethe stability condition of contingencies. As utilizingthe improving methods enhances transient stabilityof the system, it is expected that the number ofcritical contingencies reduces or the number reacheszero. In the case of unstable contingency, criticaland non-critical generators, stability margin, andoperation point of the system are saved and sent tostep 7;

6. If all of the contingencies are stable, the procedureis �nished; else, Transient Stability ConstrainedOptimal Power Flow (TSC-OPF) is performed forproviding stability in unstable contingencies byrescheduling the critical generators;

7. Transient stability of the system can be increased byreducing the total active power of critical generatorsin the network. Eq. (8) is used to show the amountof active power which is generated by the criticalgenerators. Pcgi is the amount of active power ofeach critical generator in the network. P0 is thetotal active power of critical generators in previousscheduling, and �P is the amount of changes inactive power of critical generators for enhancing

transient stability. The critical and non-criticalgenerators are determined by the SIME method.Moreover, �P is determined based on stabilitymargin by the SIME method [1].Xi2CG

Pcgi � P0 ��P: (8)

The amount of �P is shared between criticalgenerators based on their angular deviation atinstability time. In multi unstable contingencies,this �P is shared between critical generators, whichare common in unstable contingencies. Detaileddescriptions of critical generators rescheduling canbe found in [5].

8. TSC-OPF, which is described in the following sec-tion (Section 4.2), is run for determining operationpoint of non-critical generators. It should be notedthat the operation point of the critical generatorswas determined in step 7. After determining theoperation point of all generators, the procedure goesback to step 5 to check the stability of the systemin the new operating condition.

4.2. The TSC-OPF formulationTSC-OPF is used to optimize operation point of thegenerators in order to provide transient stability ofthe system. Objective functions and constraints aredescribed in the following. The amount of activepower of non-critical generators represents decisionvariables. In addition, cost of active power reschedulingand new scheduling of generators are outputs of thisoptimization.

4.2.1. Objective functionThe purpose of this paper is to maintain systemstability with minimum operation cost by utilizing theimproving methods. Therefore, the objective functionof TSC-OPF is to minimize the total cost of activepower rescheduling.

minXi2G

C(�Pi): (9)

4.2.2. ConstraintsEqual constraints are production and consumptionequality of active and reactive powers at each bus inthe network.

Pgi � Pli �Xj2�

Pij(Vi; Vj ; �i; �j) = 0; (10)

Qgi �Qli �Xj2�

Qij(Vi; Vj ; �i; �j) = 0; (11)

where Pgi and Qgi are active and reactive powersgenerated at bus i; Pli and Qli are active and reactive


powers consumed at bus i; Pij and Qij are active andreactive power ows between bus i and bus j. Vi and�i are voltage magnitude and voltage angle at bus i,respectively.

Non-equal constraints in the optimization are:

Branch current limits:

Iij(Vi; Vj ; �i; �j) � Imaxij : (12)

Bus voltage limits:

V mini � Vi � V max

i : (13)

Restriction of active and reactive powers in genera-tors:

Pmingi � Pgi � Pmax

gi ; (14)

Qmingi � Qgi � Qmax

gi : (15)

In this paper, TSC-OPF is only used to ensure provid-ing desired transient stability of the system, while thedesired transient stability is not provided by the im-proving methods (i.e., the remaining transient stabilitymargin will be supplied through changing generators'operation point). In this paper, the method presentedin [5] is developed in order to comprise the improvingmethods in transient stability of the system. In thisTSC-OPF, active power of critical generators is shiftedto non-critical generators for providing transient sta-bility under unstable contingencies. As described,detailed modelling of system equipment induces us touse the method of [5]. Instead of this method, themethod of [6] can be used for TSC-OPF that causes anincrease in complexity of the problem.

5. Case study

In this section, the proposed mechanism for providingtransient stability is analysed. This section has twoseparate parts. In uence of the improving methods ontransient stability is illustrated in the �rst part, whileresults of the proposed mechanism implementation forproviding transient stability are presented in the secondpart.

5.1. E�ects of the improving methods ontransient stability

A 4-bus network, which is shown in Figure 5, issimulated in MATLAB. The dynamic model of asynchronous generator and supplementary equipment(including hydraulic turbine, governor, and a ST1excitation system) are simulated in MATLAB [23]. TheOEL model of [11] is used in simulation. HSVC isimplemented based on the model of [19].

To study the e�ect of the improving methods, thedynamic behaviour of the system will be discussed in

Figure 5. A simple 4-bus test network.

Figure 6. Controller response to a disturbance. 1: Fastresponse (300/0.001s+1); 2: slow response (50/0.001s+1).

the presence of a three-phase short circuit in the linebetween buses 1 and 2. Table 1 shows the e�ect of theimproving methods on transient stability of the system.

Exceeding the rated current in the excitationsystem (by using standard ANSI C50.13) improves thetransient stability of the system more than 5 cycles. Inthis situation, network will be stable in the presenceof a 12-cycle 3-phase short circuit. To show theimpact of AVR controller on transient stability, thecoe�cients of the controller are con�gured as shownin Figure 6. In this �gure, the �rst controller has afast response, and the second one has a slow response.Concomitant use of standard ANSI C50.13 and fastresponse controller make system stable over the 12-cycle short-circuit current.

As mentioned, expansion of generator capabilitycurve is another method that a�ects system transientstability. In this paper, it is assumed that bettercooling system of generators increases the output powerof generators to 120% of nominal power. The networkwill be stable over the 15-cycle short-circuit currentby considering this assumption and allowing OELexceeding.


Table 1. Simulation results for enhancing transient stability of 4-bus network.

Used control method Critical clearing time(cycle)

Base control condition 7OEL exceeding without AVR adjustment 9OEL Exceeding (OELE) and AVR Adjustment (AVRA) 12OELE, AVRA and GCC expansion 15OELE, AVRA and HSVC 13OELE, AVRA, GCC expansion and HSVC 17

Figure 7. IEEE 14-bus network.

Based on Table 1, the use of HSVC improvestransient stability of the system. Using HSVC alongwith two other methods makes the system stable overthe 17-cycle short-circuit current. This represents a 10-cycle improvement in transient stability of the system.

5.2. Implementation of the proposedmechanism on IEEE 14-bus network

IEEE 14-bus network, shown in Figure 7, is simulatedin MATLAB in order to demonstrate the e�ectivenessof the proposed mechanism in providing transientstability. The dynamic model of the synchronousgenerators and supplementary equipment (includinghydraulic turbine, governor, and a ST1 excitationsystem) are simulated in MATLAB. The OEL modelof [11] is used in simulation. In addition, HSVC isimplemented based on the model of [19]. The systemtransient stability is studied in two cases:

1. Three-phase fault occurs in transmission lines inorder to determine the fault critical clearing time.The worst position of the short circuit is the nearestpoint to generators;

2. The second survey is the occurrence of single con-tingency in the network. This event occurs as a

tripped line outage after a short circuit (5 cyclesafter fault occurrence).

Studying three-phase short circuits near the gen-erators of the network determines that the most likelyinstability corresponds to the occurrence of short cir-cuits in line 1 between bus 1 and bus 2. In thissituation, the system in base control condition can onlysustain short circuits with 4 cycle's duration.

5.2.1. Fault critical clearing timeIn order to compare the proposed mechanism, provid-ing transient stability, with the conventional method,two conditions are considered. In the �rst condition,it is assumed that GenCos abstain from using theimproving methods. Therefore, ISO uses conventionalmethods for providing transient stability. In thiscondition, active power of generators is rescheduledto increase stability margin of the system. Thiscondition is called base control condition. The secondone, in which the improving methods are used inall generators of this network, is called an improvednetwork. Utilizing the improving methods provideswhole or a part of desired transient stability margin.If the improving methods cannot satisfy the desiredstability level entirely, a change in active power ofgenerators is used, too.

Table 2 shows the results of transient stabilityprovided for IEEE 14-bus network by the conventionalmethod and the proposed mechanism. This tablepresents the amount of active power rescheduling foreach of the generators, total rescheduling cost, andcritical clearing time. In the base control condition,transient stability is improved by a change in gen-erators operation point. However, in the improvednetwork, transient stability is provided by the proposedmechanism of this paper. Changes in generatorsoperation point can improve transient stability of thesystem in only 5 cycles. Therefore, this method leadscritical clearing time to 9 cycles for the base controlcondition. However, the proposed mechanism canimprove the network transient stability over 9 cycles.Thus, utilizing the improving methods makes systemstable for the 13-cycle short circuit. Comparing theresults indicates that the improving methods not only


Table 2. Providing transient stability for IEEE 14-bus network.

Base control condition Improved networkActive power rescheduling for G1 (MW) -60.7 0Active power rescheduling for G2 (MW) 58.7 0Total rescheduling cost ($/h) 456.52 0Critical clearing time (Cycle) 9 13

Table 3. Providing transient stability for critical contingencies by utilization of the improving methods.

Contingency OELexceeding

AVRadjustment

HSVC GCCexpansion

Total powerrescheduling

C1 X X X X 0C2 X X | | 0C3 X X | | 0

save 456 dollar per hour, but also improve networktransient stability more than the conventional method.

Di�erent methods can be used to enhance tran-sient stability of the system. These methods includeexcitation system response improving methods [10-20],active power rescheduling [2-8], and FACTS devicesinstallation [24-26]. Performances of the improvingmethods and active power rescheduling are comparedin this paper. Another conventional method fortransient stability enhancement is the installation of aThyristor Control Series Capacitor (TCSC). Transientstability improvement by this method is dependent onthe installing location of TCSC. For a better compari-son between the improving methods and conventionalmethods, a TCSC is installed in line 2 between bus 1and bus 5. Installing this TCSC leads to the enhance-ment of transient stability of the system about 4 cycles.Therefore, the studied network is stable in the presenceof 8-cycle short circuit in line 1 between bus 1 and bus2. As expected, the use of this device has installationcost. This method imposes about 0.3 million dollarcost on ISO per year. This cost is calculated based onEqs. (16)-(18) [27]:

CTCSC =0:0015S2TCSC � 0:713STCSC

+ 153:75 ($/KVAR); (16)

ICTCSC = CTCSC � STCSC � 1000 ($); (17)

AICTCSC = ICTCSCir(1 + ir)LT

(1 + ir)LT � 1($/year): (18)

In Eq. (17), CTCSC is cost of TCSC, and STCSC isoperating range of TCSC. Investment cost is convertedinto annual cost by Eq. (18). In Eq. (18), lifetime (LT)of this equipment and interest rate (ir) are consideredto be 15 years and 0.05, respectively.

Installation of the TCSC has lower cost in com-parison to rescheduling of active power. If rescheduling

of active power imposes 456 $/h on ISO just for 8hours in a day (peak time), then this method mayimpose about 1.3 million dollar cost on ISO per year,while TCSC installation has 0.3 million dollar costper year. However, each one of these two methodshas considerable cost, as comparison to the improvingmethods of excitation system. Therefore, a part ofsaved cost due to the use of the improving methods(instead of active power rescheduling or TCSC instal-lation) can compensate for the cost imposed on GenCosfor installing and using the improving methods.

5.2.2. Single contingency analysisIn order to investigate the transient stability of thenetwork in case of single contingency, the methoddescribed in [22] is used to screen the contingencies.Therefore, only the events, which lead networks toinstability, are examined. In this network, three singlecontingencies will lead to network instability. Thesecontingencies include tripped line outage after a 3-phase short circuit with 5-cycle length in lines betweenbus 1 and bus 2 (C1), between bus 1 and bus 5 (C2),and between buses 2 and bus 5 (C3).

Transient stability for these events can be pro-vided by utilizing the improving methods. In occur-rence of C1, all of the improving methods (describedin Section 2) are required to provide transient stabilityof the network. While transient stability for two otherevents can be provided by using AVR adjustment andOEL exceeding. Table 3 shows the related simulationresults. As this table illustrates, utilizing the improvingmethods can provide system transient stability, andthere is no need for the rescheduling of the generators.

In order to compare the e�ectiveness of theproposed mechanism with that of the conventionalmethod, a change in generators output is used toenhance transient stability of the network for thesecritical contingencies. Table 4 shows results of TSC-OPF implementation on the base control conditionnetwork, where active power rescheduling is used to


Table 4. Providing transient stability for critical contingencies by active power rescheduling.

Contingency �P1 (MW) �P2 (MW)Total rescheduling

cost ($/h)Stabilitycondition

C1 -60.7 58.7 456.52 UnstableC2 -30.7 29.23 259.56 StableC3 -10.7 10.14 31.26 Stable

Table 5. Results of transient stability analyses on IEEE 118-bus network for CCT determination.

ContingencyInitial

operatingcondition

Transient stability providing methodActive powerrescheduling

Utilizing theimproving methods

Line 68-81 7-cycle 10-cycle 11-cycleLine 69-77 15-cycle 24-cycle 30-cycleLine 64-65 17-cycle 23-cycle 155-cycleLine 77-78 19-cycle 28-cycle 95-cycle

enhance transient stability of the system instead of theimproving methods. This table represents active powerrescheduling for each of two generators, total reschedul-ing cost, and network stability status after TSC-OPFimplementation. As the results illustrate, utilizingthe conventional method (active power rescheduling)increases operation cost. In addition to this, activepower rescheduling cannot maintain transient stabilityof the network in the event of C1.

5.3. Implementation of the proposedmechanism in the IEEE 118-bus network

In order to investigate the proposed mechanism indetail, IEEE 118-bus network is simulated in DigSi-lent. Simulation results show that this network inthe initial operating condition can withstand a 7-cycle3-phase short circuit on transmission line 68-81. Inthe initial operating condition, transient stability pro-viding method described in this paper is not utilized,and generators' operating conditions are derived fromthe conventional OPF. In order to enhance transientstability of this system, active power rescheduling isused by TSC-OPF implementation. As seen in Table 5,this method enhances transient stability of this systemto 10 cycles for the 3-phase short circuit fault ontransmission line 68-81. Moreover, the mentionedimproving methods for the excitation system responsesare used in this paper to increase transient stability ofthe system. Utilizing the improving method to achievetransient stability of the system enhances 11 cycles for3-phase short circuit fault on transmission line 68-81.

In this network, in order to enhance transientstability by active power rescheduling, operation costof the system will increase by $301.53 per hour. Ifthis method is needed just for peak time transientstability providing, active power rescheduling increasesby 880 thousand dollars per year. By comparing

implementation results of transient stability of provid-ing methods, it is clear that utilizing the improvingmethods increases transient stability of the systemmuch more than the active power rescheduling.

6. Conclusion

Di�erent control methods were proposed to improvethe excitation system response. As a result of this pa-per, utilizing the improving methods not only improvestransient stability of the system, but also decreasesnetwork operation cost, whereas conventional methods,such as rescheduling of active power of generators, maybe unable to provide transient stability of the systemunder some contingencies. However, utilizing theimproving methods imposes costs on GenCos, discour-aging them from utilizing these methods. Thus, thispaper proposed a motivation mechanism to encourageGenCos to utilize the improving methods through along-term contract between ISO and GenCos. Theproposed mechanism provides the required transientstability margin with minimum cost in comparisonto the other methods. In this contract, GenCos arepaid for utilizing the improving methods in order toprovide required transient stability margin for thesystem. Utilizing the improving methods causes adecrease in the need for active power rescheduling fortransient stability providing, thus reducing generators'restrictions for active power generation. Therefore, theproposed mechanism will bene�t GenCos and reducenetwork operating costs for providing the requiredtransient stability margin.

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Biographies

Ali Khandani received the BS degree in 2009 fromIran University of Science and Technology and theMSc degree in 2012 from Bu-Ali Sina University. Heis currently a PhD student in Semnan University,

Semnan, Iran. His research interests are in the powermarket, power system optimization, power quality, andpower system operation and control.

Asghar Akbari Foroud received the BS degree fromTehran University and the MSc and PhD degreesfrom Tarbiat Modares University, Tehran, Iran. Hebecame an Assistant Professor in 2006 and an AssociateProfessor in 2012 at Semnan University. His �eldsof interest are power system dynamics, operation andcontrol, power market, power system planning, powerquality, and power system distribution.

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