Control of electric power systems

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Control of electric power systemsMagdi S. Mahmoud a & ABdulla Ismail aa Department of Electrical Engineering, UAE University, PO Box17555, Al-Ain, United Arab EmiratesPublished online: 13 May 2010.

To cite this article: Magdi S. Mahmoud & ABdulla Ismail (2003) Control of electric power systems ,Systems Analysis Modelling Simulation, 43:12, 1639-1673, DOI: 10.1080/02329290310001593001

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Systems Analysis Modelling SimulationVol. 43, No. 12, December 2003, pp. 1639–1673

CONTROL OF ELECTRIC POWER SYSTEMS

MAGDI S. MAHMOUD* and ABDULLA ISMAIL

Department of Electrical Engineering, UAE University, PO Box 17555, Al-Ain,United Arab Emirates

(Received 6 December 2000)

The increase in size and complexity of interconnected electric power systems, coupled with the industrial com-mitment to maximize security at a minimum cost, has led to the development of many special control devices.These control devices ensure that the electric power system is able to operate, without instability, under a widerange of system conditions. This article presents a tutorial overview of the basic concepts and techniques ofcontrol for stability in electric power systems. Emphasis is placed on the robustness of the overall electricpower system along with modifications to the basic control necessary to achieve this robustness. Different sta-bility concepts are illustrated and the associated stabilizing mechanisms and equipment are described. Tofacilitate the implementation of the stability criteria, models of power system components are described.Special considerations are then given to the tuning of the automatic voltage regulators and the associatedanalytical tools for steady-state regulation as well as small- and large-signal performance. Next, the issueof automatic generation control is critically examined before an efficient system-wide control scheme ispresented. This scheme gurantees power system stability against any disturbance occuring anywhere in thepower network. Some important topics like control during restoration, overvoltage control, new conceptsin interconnected power system control, coordinated voltage control and artificial neural networks inpower systems are discussed.

Keywords: Power system stability; Control; Robustness

1. INTRODUCTION

Over the past four decades, problems associated with power system stability haveemerged and these have formed the basis for many technical studies, field tests, andnew controllers have been installed at power plants. These problems had to do withelectric power oscillations on interties between large power pools and they encompassedstability problems associated with single generators, or banks of generators, connectedto large systems. In recent years, electric power systems world-wide have grownmarkedly in size and complexity [1]. In order to maximize efficiency of generationand distribution of electric power, the interconnections between individual utilitieshave increased and the generators have been required to operate at maximum limitsfor extensive periods of time. Additionally, the most economic sites for generation

*He was with the Arab Academy for Sciences and Technology, Egypt. Email: [email protected]

ISSN 0232-9298 print: ISSN 1029-4902 online � 2003 Taylor & Francis Ltd

DOI: 10.1080/02329290310001593001

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plants are often remote from load centers and the power must be transmitted over longdistances. The majority of power system interconnections are made through ACtransmission lines and the interconnected generators run synchronously. In a largeinterconnected system, such as that in North America, there may be thousands ofsynchronous generators in service to supply the load. Each generator normally hasseparate controls that are used to regulate the real and reactive power supplied bythe generator to the system [2–10].

Transients in power systems are analyzed using many levels of modeling detail. At oneextreme is the study of electromagnetic transients initiated by steep wavefront pulses(such as lightning strikes); at the other extreme is the study of long-term transients,with periods of several minutes or more, involving the interaction between slowautomatic controls and manual control by system operators. And in between is thestudy of electromechanical oscillations among the synchronous generators within thesystem. Control for the stability of the electromechanical oscillations is more interestingand will be under focus here. The time period of concern is from 1 to 40 s following adisturbance, and the frequency range is from 0.1 to 2.0Hz. Because of the separationbetween the frequency of the three types of oscillations, each can be studied usingsimplified dynamic models. In electromechanical oscillation studies, detailed modelsare used for machines, including their excitation and governing systems, but thehigh-frequency network transients are ignored, as are the low-frequency steam turbineboiler dynamics and the slow system controls (such as on-load tap changers). Typically,the resulting system is governed by nonlinear differential equations, which describe theinterchange of electromechanical energy between the generators through the transmis-sion network.

Because of their essential nonlinearity, the stability of electric power systems dependson the severity of the applied disturbances. Criteria for power system design specify thetypes of fault the system must be able to withstand without major loss of synchronismand consequent breakup. It is also critical that the power system remains stable whileoperating with no faults. Power system analysis refers to these separate, but related,stability problems as transient stability and small-signal stability, respectively. By andlarge, the system operating conditions are restricted most by the need to maintaintransient stability. In recent years, however, as power systems have been operatedwith higher power transfer levels to meet economic constraints, small-signal stabilityproblems have become apparent. In order to achieve the required high transfers ofpower, the controls associated with the generators have become critical.

In special cases, asynchronous DC transmission is utilized with controlled rectifica-tion at one end and controlled inversion at the other. In association with DC links,and in order to achieve a uniform voltage distribution through the power system,thyristor-controlled capacitors and reactors (static var compensators) have beenfound necessary. These devices provide additional local controls that have significanteffects on power system stability [11,12].

The power system control designer must ensure that the power system is stable locallyand globally. Global control is achieved through correct design and coordination of thelocal controls of the individual components of the power system and by restricting theallowable operating conditions of the system. In this tutorial presentation, a numberof stability problems and their control solutions are described. In this regard, differentstability concepts are illustrated and the associated stabilizing mechanisms and equip-ment are described. Models of power system components are fully described in order to

1640 M.S. MAHMOUD AND A. ISMAIL

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facilitate the implementation of the stability criteria. Special considerations are thengiven to the tuning of the automatic voltage regulators and the associated analyticaltools for steady-state regulation as well as small- and large-signal performance.Next the issue of automatic generation control is illuminated before an efficientsystem-wide control scheme is presented. Some important topics like control duringrestoration, overvoltage control, new concepts in interconnected power system control,coordinated voltage control and artificial neural networks in power systems arediscussed.

2. OVERVIEW OF POWER SYSTEM STABILITY CONCEPTS

In this section, we present different concepts of stability arising in power systems [1–5].

2.1. Background: Synchronous Machine Stability

Admittedly, power systems rely on synchronous machines for the generation of electri-cal power. Thus, a necessary condition for the transmission and exchange of power isthat all generators rotate in synchronism. The concept of power system stability relatesto the ability of generators on a system to maintain synchronism and the tenancy to returnand remain at a steady-state operation point following a system disturbance.

2.1.1. Generator and Infinite Bias

Initially, we consider a remote generator connected radially to a major substation of avery large system, as shown in Fig. 1. The transmission system feeds into the largesystem or infinite bus, which assumes that its voltage is so strongly influenced bylarge nearby generation that it is independent of events at the remote generator.In terms of the voltages:

Eo := infinite bus voltageEt :=generator terminal voltageE 0

q :=generator internal voltage behind transient reactanceEq :=generator internal voltage behind synchronous reactance

a phasor diagram is displayed on Fig. 2, where the angle difference indicates a realpower flow from the generator into the infinite bus. It should be remarked that in

FIGURE 1 Single-machine power system.

CONTROL OF ELECTRIC POWER SYSTEMS 1641

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the classical steady-state stability, the voltage Eq and the power angle �ss are used in thecharacteristic electrical power flow equation. On the other hand, for simpletransient and dynamic stability analyses, it is more appropriate to use the voltageE0q behind transient reactance and the angle � between this voltage and the infinite

bus voltage. Therefore, the generator electrical power can be expressed as:

PE ¼E0qEo

X 0d þ Xe

sin � ð1Þ

The power-angle characteristic is plotted in Fig. 3, where the steady-state operatingpoint occurs when the electrical power out of the generator change PE is balancedby the mechanical turbine power PM. Obviously, a change in angle away from theoperating point will result in a power imbalance which eventually acts to accelerateor decelerate the rotor toward the new operating point.

2.1.2. Transient Stability

Transient stability is primarily concerned with the immediate effects of transmissionline disturbances on generator synchronism. Typical behavior of a generator in

FIGURE 3 Synchronous machine power-angle curve.

FIGURE 2 Generator-infinite bus phasor diagram.


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response to a fault condition is illustrated in Fig. 4. Starting from the initial operatingpoint (point 1), a close-in transmission line fault causes the generator electrical powerPE to be drastically reduced. The resulting difference between electrical power andmechanical turbine power causes the generator rotor to accelerate with respect to thesystem, increasing the power angle (point 2). When the default is cleared, the electricalpower is restored to a level corresponding to the appropriate point on the power-anglecurve (point 3). Clearly the fault necessarily removes one or more transmission elementsfrom service and at least temporarily weakens the transmission system. After clearingthe fault, the electrical power out of the generator becomes greater than the turbinepower, which causes the unit to decelerate (point 4) and hence reduces the momentumthe rotor gained during the fault. If there is enough retarding torque after fault clearingto make up for the acceleration during the fault, the generator will be transiently stableon the first swing and will move back toward its operating point in a short time (0.5 sor less) from the inception of the fault. If the retarding torque is insufficient, the powerangle will continue to increase until synchronism with the power system is lost.

In this regard, the excitation system, forcing during and following the fault attempts toincrease the electrical, pourer output by reining the generator internal voltage E 0

q, thusincreasing PMax. Fast and powerful excitation systems can improve transient stability,although the effect is limited due mainly to the large field inductance of the generatorwhich prevents a sudden change in E0

q for a sudden increase in exciter output voltage.In present-day systems, a machine’s transient stability on the first swing does not

guarantee that it will return to its steady-state operating point in a well-dampedmanner and thus be stable in an oscillatory mode. This deficiency has been rectifiedin recent years through the use of very rapid fault detection methods and modern circuitbreakers.

System effects such as sudden changes in load, short circuits, and transmission lineswitching not only introduce transient disturbances on machines, but also may giverise to less stable operating conditions. For example, if a transmission line must betripped due to a fault, the resulting system may be much weaker than that existingprior to the fault and oscillatory instability may result.

FIGURE 4 Power-angle curve illustrating transient stability.


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2.2. Oscillatory Stability

Following a power system disturbance, whether it is a large disturbance or just a mini-mal load change on the system, a generating unit will characteristically tend to oscillatearound its operating point until it again reaches steady-state. A related discussion onsuch behavior follows.

2.2.1. Mechanical System Analog

The characteristics of post-fault oscillations are known to be analogous to the motionof the standard spring–mass systems shown in Fig. 5, where the dynamic nature can beexpressed by:

Md2x

dt2þDm

dx

dtþ K�x ¼ 0 ð2Þ

Given that the value of the mechanical damping Dm is relatively small, the foregoingcharacteristic equation describes the motion as a damped sinusoidal oscillation withfundamental frequency

!m ffi

ffiffiffiffiffiK

M

rð3Þ

Interestingly enough, the foregoing mechanical systems compare with the two simplepower systems shown in Fig. 6. In Fig. 6(A), a single generator or group of generatorsat a plant sending power across a transmission system having an equivalent externalreactance Xe to a very large system or infinite bus is provided. The relative motionof the generator will oscillate against the infinite bus similar to the oscillatorymotion of the mechanical mass against a fixed reference or ‘‘brick wall’’. The total iner-tia of the generating unit rotor (normally given as an H constant) acts like the mass inthe mechanical system. The change in electrical power of the generator for changes inmachine angle acts as a restoring force similar to the spring in the mechanical system. Inthe same way, oscillations will occur between two power systems which are linked by tie

FIGURE 5 Mechanical spring–mass systems: (A) single mass and fixed reference; (B) two masses.


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lines, as represented in Fig. 6(B). In this case, the mode shape of the characteristic oscil-lation will be one system swinging against the other system, much like the two-massmechanical system in Fig. 5(B).

2.2.2. Characteristic Dynamic Equation

For a synchronous machine under constant field excitation, a first-order approximationof its dynamic motion is obtained by relating the angular acceleration of the generatorrotor to the torques imposed on the rotor. For small changes, the behavior is describedby the ‘‘swing equation’’:

2H

!s

d2�

dt2þ

D

!s

d�

dtþ Ks�� ¼ 0 ð4Þ

where �� (rad) is the rotor angle deviation from the steady-state operating point; H(kW-s/kVA) is the inertia constant of the rotor of the generating unit (or groupof units); D (pu power/pu freq. change) is the damping coefficient representing frictionand windage, prime mover and load damping, . . . etc; !s (rad/sec) is the synchronousfrequency; Ks (pu �P/rad) is the synchronizing coefficient.

In (3), the term Ks�� is called the synchronizing power that tends to accelerate ordecelerate the rotating inertia back toward the synchronous operating point, see Fig. 7.

For small damping, the inherent modal frequency is approximated by:

!n ffi

ffiffiffiffiffiffiffiffiffiffiKs!s

2H

rrad=s ð5Þ

2.2.3. Local vs Interarea Oscillations

Following both small and large disturbances, a power system experiences low-frequency oscillations. Basically, there are two distinct types of dynamic oscillationswhich have been known to present serious problems:

One type occurs when a generating unit (or group of units) at a station isswinging with respect to the rest of the system. Such oscillations are called ‘local

FIGURE 6 Simple power systems: (A) single plant and infinite bus; (B) two systems with tie lineconnection.


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mode’ oscillations and tend to occur when a very weak transmission line exists betweena machine and its load center.

Another type of oscillations, known as ‘interarea modes’, are more complex becausethey usually involve combinations of many machines on one part of a system swingingagainst machines on another part of the system. These oscillations tend to occurbetween large pools of power areas.

By and large, the characteristic frequency of the interarea modes of oscillation isin the range (0.1–0.8)Hz and tends to be smaller than that of the local modes of oscilla-tion, which is the range (0.8–2.0)Hz. Stability analysis of interarea modes of oscillationhas been performed using state space techniques [16]. The lower modal frequency andthe fact that many machines participate in the mode make interarea oscillations moredifficult to control than local oscillations. Nevertheless, it has not been found necessaryto use centralized controls to stabilize these modes.

In practice, power systems contain inherent damping effects which tend to damp outdynamic oscillations. Even with the proper conditions exist for dynamic instability (thatis, high network reactances, line outages, high load levels, . . .), the natural damping ofthe system, represented by the positive D term, will prevent any sustained oscillationsunless a source of negative damping is introduced.

By and large, the degree of power systems is less important than in many othercontrol problems. What is required is for the power system to remain stable over awide range of operating conditions.

3. LOCAL GENERATOR STABILITY

The two most important controllers on modern synchronous generators are the speedgovernor (SP) and the automatic voltage regulator (AVR). In an interconnected system,neither fulfill their nominal function alone: the SG also controls the active powersupplied by the generator to the system; the AVR controls the reactive power suppliedby the generator to the system.

3.1. Speed Governor (SG)

For ease of reference, a simplified schematic diagram of a traditional governor system isshown in Fig. 8, which is applicable to both steam and water turbines. The sensing

FIGURE 7 Power-angle curve showing derivation of synchronizing coefficient.


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device, which is sensitive to change of speed, is the time-honored Watt centrifugalgovernor. There are two weights moving radially outwards as their speed of rotationincreases and thus move a sleeve on the central spindle. This sleeve movement is trans-mitted by a lever mechanism to the pilot-valve piston and hence the servo-motor isoperated. A dead band is present in the mechanism since the speed must change by acertain amount before the valve commences to operate due to friction and mechanicalbacklash. The finite time taken for the main steam valve to move due to delays in thehydraulic pilot-valve and servo-motor systems is about (0.2–0.3) s: In an ideal governorcharacteristic of a large steam turbo-alternator, there is about 4% drop in speedbetween no load and full load. Because of the requirement of high response speed,low dead band, and speed accuracy and load control the mechanical governor hasbeen replaced in large turbo-generators by electro-hydraulic governing. Recently, elec-tronic controls have been used which require an electro-hydraulic conversion stageusing conventional servo valves. An important feature of the governor system is themechanism by means of which the governor sleeve and hence the main-valve positionscan be changed and adjusted quite apart from when actuated by the speed changes. Thisis accomplished by the speed changer or ‘‘speeder motor’’.

3.2. Automatic Voltage Regulator (AVR)

The major function of the voltage regulator (VR) is to continually adjust the generatorexcitation level in response to changes in generator terminal voltage. The VR acts toaccurately maintain a desired generator voltage and change the excitation level inresponse to disturbances on the power system. A block diagram of the major elementsassociated with a generating unit under voltage regulator control is shown in Fig. 9.Observe that any change in the terminal voltage magnitude ET from the reference setpoint provides an error signal (�e) to the VR, which in turn calls for a change inexcitation level. A delay is incurred in this voltage feedback loop due to the response

FIGURE 8 Basic governor control system.


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in machine flux (E0g) for a change in generator field voltage (EFD). This delay is due to

the large inductance of the generator field winding. Typically for a generator on-line,this delay can be represented by a time-constant T 0

d which is usually in the range of2 sec. Note in this case that the swing equation becomes:

2H

!s

d2�

dt2þ

D

!s

d�

dtþ Ks��þ Kq�E 0

g ¼ 0 ð6Þ

where the term Kq �E0g comes mainly from changes in excitation level, as determined

by the control action of the VR with phase lags due to the exciter and generatorfield circuit.

Turbine speed-governing systems are known to have the potential for influencingdynamic stability, although not to the extent experienced by excitation systems. Sincegovernor systems (essentially electromechanical) are, by and large, slower acting thanexcitation systems (basically electrical), lower frequency interarea oscillations aregenerally more prone to governor effects than are local oscillations.

A block-diagram of a generator and its associated governor as well as voltage-regulator control systems is shown in Fig. 10. Two factors have a large influence onthe dynamic response of the prime mover:

(a) entrained steam between the inlet valves and the first stage of the turbine (in largemachines this can be sufficient to cause loss of synchronism after the valves haveclosed);

(b) the storage action in the reheater which causes the output of the low-pressureturbine to lag behind that of the high-pressure side. By and large, most largegenerators are equipped with the two major control loops: the automatic voltageregulator (AVR) loop controls the magnitude of the terminal voltage whereas theautomatic load-frequency control (ALFC) loop regulates the megawatt outputand frequency (speed) of the generator.

One way to account for both of these effects is to write down the transfer functionrelating the prime mover torque �Tp to the valve opening �d as:

�TpðsÞ

�dðsÞ¼

GsGr

ð1þ �s sÞð1þ �r sÞð7Þ

FIGURE 9 Block diagram of generator under voltage regulator control.


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where Gs is the entrained steam constant; Gr is the reheater gain constant; �s is theentrained steam time constant; �r is the reheater time constant.

Also the transfer function relating steam-valve opening to changes in speed due to thegovernor feedback loop is given by

�dðsÞ

�!ðsÞ¼

Gt

ð1þ �g sÞð1þ �p sÞð1þ �v sÞð8Þ

where Gt is the a constant relating system-valve lift to speed change; �g is the governor-relay time constant; �p is the primary-relay time constant; �v is the secondary-valve-relay time constant.

An alternative way to examine the dynamic effects of the governor is to derive thetransfer function G(s) between the governor speed signal input �! and the resultantchange in turbine power �Pm. This function can be added to the familiar ‘‘swing’’equation as follows:

2H

!s

d2�

dt2þ

D

!s

d�

dtþ Ks��þ GðsÞ�! ¼ 0 ð9Þ

Since �!¼ d�/dt, the governor contribution would be expected to be in the properphase relationship to provide additional damping.

In steam units, large phase lags due to steam delay and additional control lags mayvery well result in a contribution which lowers overall damping. Nevertheless, the smallmagnitude of the contribution usually results in the effect being negligible, especially forthe higher frequency local oscillations. In steam governing systems with faster actingcontrols, various compensation controls can be added to reduce the possible dynamicinteraction effects of the governor.

Modern steam turbines, with very fast electrohydraulic governor valve drives, arenow being used, which have been found to give rise of torsional instabilities similarto those caused by early power system stabilizers. Torsional filters have proved effectivein this type of instability.

FIGURE 10 Block diagram of complete turbo-alternator control systems.


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Hydro turbines generally have inherently lower time constants, and thus the effects ofthe governor on damping may be more pronounced. Also, the effects of water inertia onthe resultant mechanical power are considered detrimental to damping of oscillations.

With hydraulic generators, the governor auxiliary controls, which set the transientdroop and reset time, require careful tuning to assure stability of the generator bothwhen running in isolation from the rest of system and when synchronized to thesystem. With the introduction of electrohydraulic gate controls in modern hydraulicturbine governors, there is scope for the introduction of modern radical controldesign.

3.3. Power System Stabilizer (PSS)

In power systems control, it is generally recognized that normal feedback controlactions of VRs and SGs on generating units have the potential of contributing negativedamping which, in principle, can cause undamped modes of dynamic oscillations.Direct evidence of this has been seen by the fact that sustained oscillations on powersystems have been stopped simply by switching voltage regulators from automatic tomanual control. It should be remarked however that removing VRs from service isnot a realistic solution to the problem in view of the beneficial features of the VRswhich would then be lost. The fortunate aspect of the problem is that the same VR con-trol which causes negative damping can be supplied with supplementary controls tocontribute positive damping for oscillatory stabilization (refer to Fig. 9). One reason-able way to improve damping is to feed a supplementary signal to the VR that canincrease damping by sensing some additional measurable quantity. In doing so, notonly can the undamping effect of VR control be canceled, but damping can be increasedso as to allow operation even beyond the steady-state stability limit. This is the funda-mental idea behind the power system stabilizer (PSS). The supplementary signal of aPSS may be derived from such quantities as changes in shaft speed (�!), generator elec-trical frequency (�f), or electrical power (�PE).

A block diagram showing the major elements of a typical PSS is shown in Fig. 11.A special speed, frequency or power transducer converts the stabilizing signal to acontrol voltage. The transducer output is then phase-shifted by an adjustable lead-lag network which acts to compensate for time-delays in the generator and excitationsystem. The resulting signal is amplified to a desired level and sent through a signalwash-out module which functions to continuously balance the stabilizer output andthus prevent it from biasing the generator voltage for prolonged frequency or powerexcursions. The output limiter serves to prevent the stabilizer output signal from caus-ing excessive voltage changes upon load rejection and to retain the beneficial action ofregulator forcing during severe system disturbances.

FIGURE 11 Major elements of power system stabilizer.


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For proper damping action, PSS control settings must be determined, involving thelead, lag and gain adjustments of the stabilizer. These settings vary from unit to unitsince the dynamic response of a generating unit depends on both the machine andexternal system. Also, particular PSS settings designed to suppress intertia oscillationsmay not be effective in damping local machine–system oscillations. This has called foran effective setting procedure and among those that are widely accepted by utilitiesare the frequency response tests based on measurements of terminal voltagedeviations in response to sinusoidal inputs. Alternatively, one can seek differentdynamic compensation methods of control systems for designing PSS. Although PSSdevices are apparently straightforward, a number of practical difficulties with suchdevices have occured.

One of the most serious difficulties experienced with early versions of PSS fitted tosteam-turbine-driven generators was their interaction with the turbine-shaft dynamicsand consequent instability of the first torsional mode. The reason for the interactionwas twofold. First, speed measurement at the generator rotor contains a strongcomponent of the torsional mode. Second, the stabilizer compensation is essentially aphase-lead circuit, which in turn increases the high-frequency gain of the stabilizer. Achange in the location of the speed measurement transducers to a node of the lowesttorsional together with tuned torsional filters was the first solution to this problem.However, this led to additional ‘‘exciter modes’’ which restricted the stabilizer gainand, hence, the achievable damping of the electromechanical mode. Recently, thereare PSSs which achieve rejection of the torsional modes and speed. In these devices,the additional exciter mode introduced by the stabilizer is far less sensitive to the stabi-lizer gain and, thus, higher values of electromechanical mode damping may beobtained.

Under transient conditions following a severe fault, the action of a speed input powersystem stabilizer is often opposite to that required. It is important that PSS output berestricted both in the positive and negative directions. The negative limit is the mostcritical. It is normally set in the range [�5!�10]% percent of the rated terminal volt-age setting. The positive limit is normally set to 20% of the rated terminal voltagesetting.

PSS on large generating units can be designed to help damp interarea modes in whichthe generators are significant participants. Therefore, it is important that the dynamiccompensator associated with each PSS is designed to ensure a positive contribution todamping of all modes having frequencies between (0.1 and 0.2)Hz. This may entail aslight reduction in the damping of the higher-frequency local modes.

At the lower end of the interarea mode frequency range, both hydraulic and steamturbine dynamics can affect the damping of the mode. The nonminimum-phase charac-teristic of the hydraulic turbine can cause the turbine torque to increase with increasingspeed rather than decrease, as required to damp system oscillations. In steam turbines,the reheater stage time constant is the critical element, which may introduce a phase lagand reduce the low-frequency damping. In both types of turbine, a simple phase-leadcompensator may be used in the governor to ensure that the turbine characteristicsdo not increase the risk of low-frequency, interarea instability.

It is a standard fact that the power system design and its operating limits are usuallybased on extensive simulation of the nonlinear system electromechanical dynamics,where major generating units are frequently equipped by fast-acting AVRs as well asPSSs. Additional overriding nonlinear controls may also be necessary.


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4. POWER SYSTEM MODELS

Reliable analysis of power system stability requires the ability to obtain accurate simu-lation studies. This can only be done if suitable models exist for the various componentsof the power system.

Models are needed for the transmission network, for loads, and for generators. Thetransmission network is represented by its positive-sequence equivalent circuit. Bulkloads at transmission system buses are usually represented by various functions ofbus voltage and frequency.

Generating units are represented in varying detail, depending on their assessed con-tribution and the method of simulation. These representations range from the classicalconstant voltage behind transient reactance to models with detailed rotor circuit repre-sentation. They can also include representation of the excitation systems with supple-mentary controls, and speed-governor systems.

The mathematical form in which these models are utilized depends upon the particu-lar method of simulation. Large-scale computer studies performed in the time-domaininvolve the repetitive calculation of the varying electrical power at each generator. Themodels in such studies involve differential equations which are converted into differenceequations with small discrete time steps. For dynamic stability analyses in thefrequency-domain models are generally linearized in the form of transfer functionsusing the Laplace operator s. This form of model allows the use of the state-space tech-niques, frequency response analysis, and roo locus calculations.

4.1. Generator Models

A convenient method of analyzing simple oscillatory stability problems is to obtain alinearized generator model using the assumption that the generator motion about theoperating point is very small, see Fig. 12. Such a model relates the pertinent variablesof electrical torque (�Te), speed (�!), angle (��), terminal voltage (�ET) and fieldvoltage (�EFD).

It describes a generator as it behaves when connected through an external reactanceto an infinite bus, and therefore it is applicable for illustrating generator dynamic beha-vior as well as being useful in the analysis of actual local mode dynamic stability prob-lems. The model applies to a D–Q axis generator representation with a field circuit inthe direct axis, but without subtransient armortisseur or solid iron eddy current effectsin either axis.

FIGURE 12 Small-signal model of generator transmission line and infinite bus.


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The effect of the VR can be simply included in the model by adding a feedbackbranch to the block diagram between the model output (�ET), representing VR sen-sing, and the model input (�EFD), representing generator field voltage or excitationsystem output voltage.

In a similar way, a PSS branch can be included between the model output speed (�!)and the voltage regulator. A speed-governor can also be represented as a path between(�!) and the mechanical turbine torque (�Tm).

Small signal response of the system can be obtained by simulating the linearizedmodel using suitable computer-aided packages like MATLAB, CYME, ETAP,EMTP, DOC, to name a few. By writing down the state-space model, in terms of thestate variables {�E 0

q, �Te, �!, ��}, modern control design techniques can be directlyapplicable. The state-space model also lends itself to representation of multi-machinepower systems in which the feedback path through block K1 in Fig. 12 would also bedependent on the angles of many other generators.

An alternative type of small-signal model representing a generator and infinite bususes a transfer function approach rather than the simulation diagram approach. Thismodel, shown in Fig. 13, directly feedback its two outputs (�ET for VR feedbackand �! for PSS feedback) with its single input (�EFD) by the transfer functions:

�ET

�EFD¼

NG1ðsÞ

DGðsÞð10Þ

�!

�EFD¼

NG2ðsÞ

DGðsÞð11Þ

Indeed, the order of these transfer functions depends upon the complexity of thegenerator modeling. If one uses the same assumptions used in obtaining the model ofFig. 12, the transfer function are third-order. Multivariable control theory [post]can be fairly applied to the transfer function of Fig. 13 to yield the behavior of thegain and phase angle versus frequency, hence obtaining gain and phase margins, and/or examine the variation of the closed-loop eigenvalues of the entire system with PSSgain.

FIGURE 13 Polynomial transfer function model of generator and excitation system.


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4.2. Excitation System Models

Excitation system models have been developed which are quite suitable for large, severedisturbances as well as for small perturbations. Just as with generator representation,excitation system models can be relatively simple or more complex in order to representactual equipment characteristics quite closely. Again, the complexity of the modelingshould depend upon the particular application and the assessment of whether or notthe increased complexity will have any significant impact on the results.

Most modern excitation systems employ either a separate AC machine whose outputis rectified to obtain DC excitation power to the generator field or a static system usingpower transformers and thyristors. Figure 14 is a simple block diagram of an excitationsystem employing a rotating exciter with its associated VR control scheme. Thisconforms with IEEE standards. The exciter time constant TE and gain constant KE

are inherent characteristics of the exciter itself. The saturation SE of the exciter isusually expressed as a function of the exciter output voltage EFD. In a linearizedsmall-signal model, SE can be represented as the incremental saturation at the operatingpoint.

The generator terminal voltage is the major voltage regulator input, filtered by atransducer time constant TR which is very small and may often be neglected. Thefirst summing point compares VT with the regulator reference VREF to determine thevoltage error signal to the regulator. The main regulator amplifier is represented by again KA, which is adjustable, and a time constant TA representing the inherent amplifierfiltering, usually less than 0.03 s. Following this, the maximum and minimum limits ofthe regulator are imposed such that large error signals do not cause the regulator toexceed its practical limits. Usually the forward gain KA is set at a large value,and thus by closing the terminal voltage feedback loop, instability will result at approxi-mately 3–5Hz unless an additional function is provided to stabilize the control loop.The excitation system stabilizer provides control loop damping using a feedbackfrom the exciter through a rate-sensing transfer function with adjustable parametersKF and TF.

An alternative excitation scheme is shown in Fig. 15 based on a transformer-fedstatic excitation system. In this system, the excitation power is obtained from thegenerator terminals and thus the output limits are dependent on the terminal voltage

FIGURE 14 Block diagram of excitation system with rotating exciter.


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magnitude VT. For excitation system stabilization, the model provides for a feedbackpath through KF, similar to that in Fig. 14. However, since the output voltage can bevery noisy in the static system, this stabilization is often implemented by transientgain reduction (TGR) in the forward loop which can be performed by a lag-lead net-work with TB>TC.

4.3. Power System Stabilizer Model

A generalized representation of a power system stabilizer used for supplying a supple-mentary signal to the voltage regulator for oscillatory improvement is shown in Fig. 16.Some common PSS input signals VSI are: Frequency, rotor speed, and acceleratingpower. The high frequency filters allow the representation of torsional filters, whetherthey are used to suppress potentially unstable torsional oscillations through the PSSor simply to filter torsional noise as sensed by as speed pickup. Phase compensationis generally accomplished by adjustable lead-lag functions (T1–T4) providing phaselead over the dynamic frequency range of interest. Most PSS applications use twoor three stages of phase compensation. An adjustable stabilizer amplifier gain KS is gen-erally maximized within the constraints imposed by the stability of the PSS controlloop. The signal wash-out function is a high-pass filter with a long time constant T5

(2–20 s) which allows normal signals to pass unchanged and removes prolonged DC sig-nals. The output limiter clips the control signal at specified limits to prevent the PSSoutput from overriding the normal voltage regulator forcing during transientconditions.

FIGURE 16 Power system stabilizer model.

FIGURE 15 Block diagram of potential-source static excitation system.


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4.4. Speed Governor System Models

As with excitation systems, there are various types of speed-governing systems in usetoday – from mechanical-hydraulic, to analog electrohydraulic, to digital electrohy-draulic. Each of these types has various possible designs, each requiring its own particu-lar model parameters. In addition, the characteristics of the turbine, whether steam orhydro, vary from unit to unit. Generalized models for speed governor control systemsand turbine systems have been developed and available in numerous references.

4.5. Load Models

Since bus voltage and frequency are not constant during system disturbances and oscil-lations, the method in which bus loads are modeled can affect study results. Mostmodern stability programs have a provision for the individual representation of busloads as function of bus voltage, bus frequency, or both.

The general representation for real P and reactive Q bus load can be expressed as:

P ¼ ðAþ BV þ CV2Þ ð1þ G�f Þ ð12Þ

Q ¼ ðDþ EV þ FV2Þ ð1þH�f Þ ð13Þ

where V is the per unit bus voltage magnitude and �f is the bus frequency deviation.In stability studies, the change in load due to frequency is generally negligible comparedto the effects due to voltage. Neglecting frequency, load can be classified as:

ð1Þ Constant Impedance . . .P ¼CV2, Q ¼ FV2

ð2Þ ConstantCurrent . . .P ¼BV , Q ¼ EV

ð1Þ Constant MVA . . .P ¼A, Q ¼ D

The relationships between MVA and voltage for these discrete types of loads are shownin Fig. 17. Actual loads are generally a composite of many different load characteristics.The constant current load model is often used as a simplified compromise for compositeloads.

FIGURE 17 Relationship between load MVA and bus voltage for simple load types.


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5. VOLTAGE REGULATOR TUNING CONSIDERATIONS

There are three major categories in which the tuning of the VR control settings affectsunit and system performance; these are

Steady-state terminal voltage regulationLarge-signal transient performance andSmall-signal performance

Final voltage regulator adjustments are often a compromise in satisfying criteria inthese areas.

5.1. Steady-state Regulation

One of the functions of a VR is to maintain terminal voltage at a pre-set value, regard-less of changing requirements of excitation due to changes in load and systemconditions. With reference to Fig. 14, this is done by a feedback of terminal voltageand an amplification of the voltage error signal with a gain KA. If KA is expressed inper unit, neglecting machine saturation, the steady-state voltage error in per unit willbe approximately 1/KA. Thus, a high value of KA is desirable for good steady-state volt-age regulation. Values of KA used in actual systems are typically 200–400 per unit.

5.2. Large-signal Performance

Large-signal performance involves changes in control system variables where themagnitude is sufficiently great that nonlinearities must be included for realistic results.For excitation systems, this usually involves transient disturbances which cause high orlow generator voltage, calling for excitation forcing conditions at ceiling.

Voltage regulator tuning to obtain satisfactory large-signal performance involves theability of the control system to derive the voltage output to ceiling during large transi-ent disturbances. The ability of the VR output to reach ceiling depends on the transientregulator gain K 0

REG. For the excitation system in Fig. 14, K 0REG is governed by rate

feedback gain KF and is approximately equal 1/KF, as long as KA is a relatively largevalue (>200 p.u.).

One practical criterion in tuning regulators is that forcing at positive ceiling beobtained for a disturbance involving a 10% reduction in terminal voltage. The transientregulator gain required to achieve this condition is approximately:

K 0REG ¼

p:u: ceiling� p:u: operating pt:

p:u:�VTð14Þ

where the ceiling and operating values correspond to the per unit exciter output volt-ages, based on no-load air-gap excitation conditions.

5.3. Small-signal Performance

Small-signal performance of an excitation control system is the response to signalswhich are small enough that the operation of the system can be considered to belinear. Response can be defined in terms of real-time parameters (transient response),


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or in terms of gain, phase angle, and frequency (frequency response), or by eigenvalueanalysis. The primary objective in tuning a VR for small-signal performance is to obtaina responsive, yet stable, control system behavior. In addition, where a potential oscil-latory stability problem exists and a decision has been made not to employ a PSS, ade-tuning of the VR for improvement in power system damping should be considered.

A typical transient response of a feedback control system to a small step change ininput is shown in Fig. 18. The principal characteristics which are affected by controlsettings are the rise time, overshoot, and settling time. The objective in tuning theVR is to minimize these three indices.

Although a higher KA and a lower KF will eventually decrease the rise time of thetransient response, they will also tend to increase the overshoot and the settling time.Therefore, the control setting generally becomes a compromise between fast responseand stable response. It is generally accepted that an excitation system transient responsewith an overshoot of 5–15% is a good compromise.

Frequency response characteristics are also helpful in assessing excitation systemcontrol loop stability. A typical open-loop frequency response characteristic of an exci-tation control system with the synchronous machine open-circuited is shown in Fig. 19.The principal characteristics of interest are:

1. G ‘‘low frequency gain’’ Larger values provide better steady-state voltage regulation2. !c ‘‘crossover frequency’’ Larger values indicate faster response3. �m ‘‘phase margin’’ Larger values provide more stable operation4. Gm ‘‘gain margin’’ Larger values provide more stable operation

In tuning the VR, an improvement made in one index will most likely be to the detri-ment of one or more other indices. For instance, an increase in regulator gain KA willshift the gain curve in Fig. 19 upward. This will increase the low-frequency gain andcrossover frequency, which is good; but it will decrease the phase margin and gain

FIGURE 18 Typical time response of feedback control system to a step change in input.


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margin, which is not good. In general, a phase margin of 40� or more and a gain marginof 6db or more is considered good design practice for obtaining stable, non-oscillatory excitation control system.

Figure 20 shows the corresponding closed-loop frequency response of an excitationcontrol system. Here, the parameters of interest are:

1. !B ‘‘bandwidth’’ Larger values indicate faster response2. Mp ‘‘peak value’’ Larger values indicate oscillatory response

In general, a value of Mp in the range [1.1–1.5] is considered good design practice.

5.4. Analytical Tools

Because of the size of power models being used in stability analysis, specially developedcomputer packages are being used. These allow the inclusion of efficient and numeri-cally stable routines for almost all mathematical techniques and numerical linearalgebra needed for transient stability. For small-signal performance, modal analysesare being performed based on eigen-structure properties. Truly large models havebeen constructed and employed in computer simulation studies and with the detailedmodeling of AVRs and SGs, the size has potentially reached 15 000. Clearly, theconsistency of data for such system models is as much a concern as the mathematicaltechniques of modeling and analysis.

In regular power system design, the stability problems encountered are often morelocal in nature, and therefore reduced-order models can be determined that adequatelyrepresent the power system for their study. In particular, the design of AVRs,governors, and PSSs for small-signal stability can often be performed using a modelof a single generator connected via a transmission line into a constant voltage source

FIGURE 19 Typical open-loop frequency response of an excitation control system with the synchronousmachine open-circuited.


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(infinite bus). Large models of the system are, however, still necessary to check theselocally designed controllers for their effect on the global stability of the powersystem. For transmission system design and the determination of operating limits toensure transient stability in the first few seconds following a fault, a reduced-ordersystem may be simulated that retains detail in an area close to the fault, with distantgenerators represented by aggregate models [10–12]. Low-frequency interarea oscilla-tions excited by severe disturbances may lead to groups of generators losing synchron-ism after several periods. Accurate simulation of this phenomenon requires extensivesystem modeling beyond the immediate vicinity of the fault. Although it may be poss-ible to produce reduced-order models, the concepts of close and distant areas maynot be valid. Additional work is required on system reduction techniques to allowthe retention of the low-frequency modes, accurate in both frequency and damping,and which maintain the basic structure of the original power system models.

Validation of the simulation models is continuing progress. Field tests, which canbe carried out with no risk to system performance, are used in major utilities to improvethe detailed modeling of this particularly important plant. This indeed leaves in ques-tion the accuracy of simulations following major system disturbances. Transientsfollowing naturally occuring faults are usually monitored and compared with simula-tions of the same events in order to provide pointers to the need for dynamic modelrefinements.

6. AUTOMATIC GENERATION CONTROL (AGC)

Power system loads and losses are sensitive to frequency. Data captured right afterfrequency disturbances indicate that their aggregate initial change is in the same direc-tion as the frequency.

FIGURE 20 Typical closed-loop frequency response of an excitation control system with the synchronousmachine open-circuited.


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Once a generating unit is tripped or a block of load is added to the system, the powermismatch is initially compensated by an extraction of kinetic energy from system iner-tial storage which causes a declining system frequency. As the frequency decreases, thepower taken by loads decreases. Equilibrium for large systems is often obtained whenthe frequency sensitive reduction of loads balances the output power of the tripped unitor that delivered to the added block of load at the resulting (new) frequency. If thiseffect halts the frequency decline, it usually does so in less than 2 s.

If the mismatch is large enough to cause the frequency to deviate beyond the gover-nor deadband of generating units, their output will be increased by governor action.For such mismatches, an equilibrium is obtained when the reduction in the powertaken by loads plus the increased generation due to governor action compensates forthe mismatch. Such equilibrium is normally obtained within a few seconds after thetripping of a unit or connection of the additional load.

Many governor deadbands are beyond 35mHz. This amount of frequency deviationrequires the upset of more than 1000MW in the eastern interconnection of USA. Thus,in this interconnection many governors may be called upon as speed stabilizers only afew times per month.

Given present-day level of frequency sensitivities, many isolated systems not neces-sarily small in capacity perform satisfactorily without automatic generation control.This means that at the expense of some frequency deviation, generation adjustmentby governors provides ample opportunity for a follow-up manual control of units.Under normal changes of load, the objectives of follow-up manual control are toreturn the frequency to the schedule, to minimize production cost, and to operate thepower system at an adequate level of security.

The purpose of automatic generation control (AGC) is to effectively replace themanual control. As it automatically responds to normal load changes, AGC reducesthe response time to a minute or two, more or less. Mainly due to delays associatedwith physically limited response rates of energy conversion, further reduction in theresponse time of ACC is neither possible nor desirable.

ACC realizes generation changes in the power system by sending signals to unitsunder its control. The design and performance of an AGC system is very dependenton how units respond to such signals. Unit response characteristics vary widely andare dependent on many factors such as:

. Type of generating unit; for example fossil-fired, combustion turbine, combinedcycle, nuclear or hydro.

. Type of fuel being used; for example coal, oil, gas, or uranium.

. Generic plant type; for example drum-type or one-through boiler, boiling- or pres-surized-water nuclear steam supply, high- or low-head hydro plant.

. Type of plant control; for example boiler-follower, turbine-follow, or coordinated.

. Operating point; frequently the ability of unit to respond is different at one loadpoint than another. For example, operation near a valve point will be differentthan operation between valve points.

. Operator actions; unit operators may take a unit off AGC control for variousreasons. Problems with auxiliaries such as boiler feed pumps, and coal mills aretwo examples.

A major input to AGC for a single power control area is the system frequency. Themore acceptable the generation trend, the more acceptable becomes the frequency


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trend, and vice versa. Attributes of ACC strategies from different aspects over a selectedtime window (duration of their comparison) are grouped into the following:

. The strategy which accumulates lower fuel cost over the time window is preferred.

. The strategy should maintain a sufficient level of reserved control range and a suffi-cient level of control rate.

. The strategy should operate the system with a better security margin as specifiedby the system management.

. The strategy which accumulates lower cost associated with the wear and tear ofregulation for all units combined is preferred.

. The strategy which requires less effort from system operators is recommended.

. The strategy which provides timely recommendation for changing the output of unitsthat are manually controlled and/or changing the automatic regulation band ispreferred.

. The strategy should provide meaningful alarms and requires less computing power.

In general, neither the follow-up manual control nor AGC is able or expected to play anyrole in limiting the magnitude of the first frequency swing which occurs within secondsafter the loss of a block of generation or load in the system. In fact, in the USA, theprocedure in most control areas requires AGC to be suspended when the frequencydeviates 200mHz or more. For where change of generation due to governor actionand change of load due to its sensitivity to frequency are not enough to intercept therun-away frequency, over- and under-frequency relays are among the last resorts forshedding loads to prevent system collapse, or tripping generating units to preventtheir damage.

7. GLOBALLY ROBUST CONTROL SCHEME

Over the last decade, it has been observed that the interconnected power system in theUSA has become less stable. This is a trend that seemingly will continue as deregulationof the energy industries continues. Consequently, the large interconnected subsystemsthat coordinate their activities have begun to detect sustained oscillations in theirsimulation analysis. Real oscillations have also been observed following a majordisturbance like removal of a fault or loss of a major transmission line. One of themore prominent examples of this phenomenon is the 0.7Hz oscillation that arises inthe Western System Coordinating Council (WSCC) following the loss of one of theAC or DC interties between the Pacific Northwest and California. Indeed, preventingthis sustained oscillation is of great interest since the potential for an oscillation causeslow operational limits to be set on transfer level on the interties. As frequency deregula-tion increases, there is a possibility for oscillations to appear during normal steady-stateoperation. This has attracted the attention of investigators to formulate acontrol strategy that will work effectively both during transient periods followingmajor interruptions and at steady-state.

A power system control (PSC) strategy called globally robust decentralized controlscheme (GRDCS) has been recently proposed by recognizing the following facts:

1. No power control strategy can claim to be globally stable.There is always a disturbance waiting in the wings that will defeat any reasonable con-trol strategy.


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2. Control strategies can be distinguished by the class of disturbances against whichthey are effective.

Some control strategies are designed to work against specific disturbances. This wasindeed the normal procedure before deregulation since in the regulated environment,the topology of the interconnected grid was reasonably well fixed, and certain contin-gencies (disturbances) could be identified as the most destabilizing.

What is required under deregulation is a control strategy that will counteract a widevariety of disturbances that may occur anywhere in the system. The approach of addingPSSs, which are designed using linearized models, to specific machines to damp low-frequency oscillations arising from specific disturbances (or set of disturbances) isnot a strategy that will be effective in the future [12].

The GRDCS is a power system control that uses a nonlinear model of the generatorand a second-order model of the turbine-governor and implicitly including the excita-tion system. It is designed not only to damp out sustained oscillations, but also tostabilize a power system against almost all reasonable disturbances that might takeplace anywhere in the power system. It is based on local linear feedback at each genera-tor therefore yielding a completely decentralized scheme and it is designed independentof the internal voltage. The basic tool of design is the direct method of Lyapunovcoupled with a judicious choice of the Lyapunov function to guarantee the robustnessof the control to parameter and load variations as well as changes in the power systemtopology.

8. CONTROL OF ELECTRIC POWER SYSTEM RESTORATION

It is known that in mathematical modeling of power systems, the operating conditioncan be described by two sets of equations: The equality (or load flow) constraintsand the inequality (or limit) constrains. The load flow constraints impose the require-ment that the customer load demand be met at all times, while the limit constraintsreflect the fact that the system variables (voltage magnitudes) must always be keptwithin limits representing the physical limitations of the power system equipment.Engineering practices have indicated that power system operation can be describedas being in one of three operating states [10]:

normal,emergency, orrestorative

A power system is said to be in restorative state whenever the set of limit constraintsis satisfied, but the set of load flow equations is not completely satisfied. This meansthat the restorative state is characterized by feasible operation of the power systemequipment but with portions of the load not being served and/or with loss of systemintegrity. Clearly, the control objective in this state would be to effect a transitionfrom a partial to a maximum ‘‘feasible’’ load condition in the minimum possibleamount, of time.

Even though today’s bulk power systems provide a very reliable supply of electricpower, transitions into a restorative state (generally manifested as blackouts or brown-outs) are not rare events. The restoration of service following a severe disturbance is avery complex process which typically involves all of the components of the power


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system, including generation, transmission, and distribution. By developing generalsystem restoration plans electric utilities have traditionally handled the relatively fewinstants of transitions into the restorative state. These plans provide general guidelineson what to do in case the power system experiences a severe disturbance resulting in lossof integrity and/or load. By and large, these restorative guidelines do not take intoaccount many of the possible system structure and/or operating conditions that canbe encountered during the restoration process. Additionally, the guidelines tend to begeneral and complex, and in many cases are of little help to the power system operators,who in general have little familiarity with operations in a restorative state.

From a power utilities standpoint, there have been growing concerns of

1. an increased likelihood of modern power systems sojourning into a restorative state,2. very high costs involved in operating the power system in such a state, and3. lack of effective restoration control strategies.

8.1. A Hierarchical Interactive Approach

The restoration control problem can be formulated in general terms as follows

minx, uc

Fðx, ucÞ

subject to

_xx ¼ f ðx, uc, udÞ

gðx, uc, udÞ ¼ 0

hðx, uc, udÞ � 0

ð15Þ

where, F represents the objective criterion; f, g, and h are nonlinear constraint functions,x is the vector of dependent system variables (such as voltage magnitudes at load busesand system frequency); ud is the vector of uncontrollable inputs (which includes the loaddemands, the interconnection flows, and the system contingencies such as system faultsand equipment malfunction); and uc is the vector of control inputs (generated eitherlocally or by the control center).

The elements of x, uc, and ud are functions which evolve in time. It is typical toassume that the portion of ud corresponding to the system contingencies is fixed andknown.

The objective criterion of the restoration control problem is in general a multi-objective function, composed of at least the following three separate objectives:

(i) to minimize the restoration time,(ii) to maximize the load served at all times, and(iii) to minimize the number and the magnitude of the control actions to be taken.

The foregoing three objectives are typically in conflict. Connecting too much load atany given point in time (to maximize the amount of load served) can cause a severefrequency decline which may trigger the load shedding relays, thus delaying the overallrestoration process.

The vector of control variables (uc) can be partitioned into a set of discrete controlvariables, y, and a set of continuous control variables, u; that is utc ¼ ½ yt, ut�:


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The discrete variables include such controls as changes to the system configuration (forexample, reconnecting system branches), and settings of certain system components (forexample, in-phase controllable transformers). The vector of continuous variables iscomposed of controls which can be varied continuously (within limits), such as activeand reactive power generations.

The ‘constraints’ associated with the problem are of two types, namely algebraic anddifferential. The algebraic equations are the nonlinear load flow relationships, and theconstraints related to a safe operation of the equipment. The differential equationsrepresent the dynamic behavior of some of the important system components, suchas the generation units.

Any realistic real-time solution to the restoration control problem should take intoconsideration its particular structure and characteristics. A hierarchical interactiveapproach suggests partitioning the time horizon for control into several scales, accord-ing to the time available for determining and executing a control decision. The interactivefeature of the approach is based on the concept that it is the power system operatorswho will supervise, and in many instants direct, the computations leading to the deter-mination of a given control strategy. Looked at in this light, the approach serves as aninteractive tool for aiding the power system operators in making the correct decisionsrelated to the restoration process.

The hierarchical approach assumes the time horizon for restoration control will bepartitioned into ‘‘small’’ time periods (or stages), that the uncontrollable inputs (ortheir models) will be known at the beginning of each stage, and that they will notchange during the entire duration of a given stage, see Fig. 21 This reduces the controlproblem to determining a control vector uc(K) for all stages K; this input is determinedand executed at the beginning of each stage, and is assumed to remain constantthroughout that stage. The set of restorative control actions available at any stage ofthe restoration procedure can be classified into the following four categories:

1. changes to the generation patterns,2. changes to the system structure and/or connectivity,3. changes to the load patterns, and4. changes to the settings of the continuous control variables.

FIGURE 21 Dynamics of the restoration procedure.


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The framework for exploiting this ‘‘time-hierarchy’’ of control decisions in thecontext of power systems is based on multilevel systems theory by decomposing therestorative problem into three control layers; namely, direct, optimizing and adaptive.The direct control level generates high speed and generally localized decisions, whilethe centralized decisions of the optimizing and adaptive levels take longer tunes to begenerated (with the adaptive decisions taking the longest). Typically, automatic genera-tion control (AGC) is a form of direct control, economic dispatch is a form of optimiz-ing control, and unit commitment is a form of adaptive control. This framework makesthe restoration problem more tractable. The proposed hierarchical control structure isshown in Fig. 22, from which we observe the following:

1. the approach assumes the existence of two level of information processingLevel one processing takes place at a local level (for example, at each substation)while level two information processing takes place at the control center,

2. the control strategies generated by the optimizing and adaptive levels are to be actu-ally implemented with the help of both, the relevant application programs and thedirect control level, with the supervision of a restoration coordinator, and

FIGURE 22 Hierarchical control structure.


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3. the operator is able to monitor and even direct the decision making process, whichtakes place at both the optimizing and adaptive layers of control; this is to beachieved via the interface with the restoration coordinator.

In fact, the adaptive level in this approach is not limited to be an entity separatedfrom the system operator, but rather ‘‘adaptive control’’ is generated by a combinedeffort between the system operator and a computer program.

8.2. Overvoltage Control

During the early stages of restoring high voltage overhead and underground transmis-sion lines, the following three related overvoltages areas are of major concern:

. sustained power frequency overvoltages,

. switching transients, and

. harmonic resonances

Sustained power frequency overvoltages are caused by charging currents of lightlyloaded transmission lines. If excessive, these currents may cause underexcitation, oreven self excitation and instability. Sustained overvoltages also overexcite transformers,generate harmonic distortions and cause transformer overheating.

Sustained overvoltages can be controlled by absorbing the large charging reactivepower of the lightly loaded transmission lines. This can be accomplished by:

. having sufficient under-excitation capability on the generators,

. connecting reactive loads (lagging power factors) to the underlying system includingshunt reactors,

. removing all sources of reactive power and switching off shunt capacitors,

. running generators at maximum possible reactive power output to allow margin toadjust for large charging reactive power when lines are switched on,

. operating parallel transformers on different taps to increase circulating currents andreactive power losses,

. energizing only those transmission lines which carry significant load and avoidingthe energization of extra lines which will generate unwanted reactive power, and

. maintaining a low voltage, profile on the transmission lines, since the charging cur-rents are proportional to the square of the voltage.

Transient voltages or switching surges are caused by energizing large segments ofa transmission system or by switching capacitive elements. Switching transients,which are usually highly damped and of short duration, in conjunction with sustainedovervoltages may result in arrester failures. Transient voltages are not usually a signif-icant factor at transmission voltages below 100Kv. At higher transmission voltages,overvoltages caused by switching may become significant, because arrestor operatorvoltages are relatively close to normal system voltage and lines are usually long sothat energy stored on the lines may be large.

Energizing transmission lines or switching capacitive elements causes switchingsurges of fast front, low energy or slow front, high energy transients. Switchingtransients are not usually the limiting factor in re-energizing a system. Generally, ifthe steady-state voltages are less than 1.2 per unit of their normal values, the switchingtransients can be managed by typical arrestors with ease. A notable exemption is


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energizing transformer terminated lines, which may result in harmonic resonance anddamaging overvoltages.

Harmonic resonance voltages are oscillatory undamped or only weakly dampedtemporary overvoltages (TOVs) of long duration. They originate from switchingoperations and equipment nonlinearities. They result from several factors that arecharacteristic of networks during restoration: first the natural frequency of the seriesresonance circuit formed by the source inductance and line charging capacitancemay, under normal operating conditions, be a low multiple of 60Hz; second, ‘‘magne-tizing inrush’’ caused by energizing a transformer produces many harmonics; andfinally during early stages of restoration the lines are highly loaded, resonance thereforeis highly damped, which in turn means the resulting resonance voltages may be veryhigh. If transformers become overexcited due to power frequency overvoltage,harmonic resonance voltage will be sustained or even grow.

Sustained harmonic overvoltages caused by over-excitation of transformers can becontrolled by selecting a transformer tap which equals or exceeds the power frequencyvoltage applied (or lowering system voltage to at or below the tap) before energizing.

Harmonic resonance can be damped by connecting sufficient underlying loads at thesending end of a line, or by connecting dead load on the transformer to be energized.

High source impedance can be reduced by starting more generators and connectingunderlying loads.

The reactive power of a lightly loaded system can be reduced by minimizing thenumber of unloaded lines to be energized and setting the sending-end transformers atthe lowest tap position.

9. NEW CONCEPTS IN INTERCONNECTED POWER SYSTEM CONTROL

Despite the fact that today’s interconnected electric power grids are explosively grow-ing, the automatic generation controls in use today are based on methods developedsome three decades ago. Present control technologies may no longer be adequate tomeet the increased complexity of interconnected system operation. Most utilities areoperating in a business environment that requires minimization of fuel and operatingcosts in the face of an increasing number of operating constraints and uncertainty.

Typically, in North America, there are over 150 control areas which are responsiblefor power system control within their boundaries. Control areas are synchronously tiedto each other into interconnections, within which power can be exchanged and theburden of control can be shared or allocated. The performance of a control area ismeasured by the Area Control Error (ACE). One criterion requires that the valueof ACE, within a control area, must return to zero within ten minutes of previouslyreaching zero. Another criterion requires that the average value of a control area’sACE be within an upper bound during each of the 6 ten-minute period of the hour.

In Western Europe, primary control is effected through governor action from awide variety of generation types. Secondary control is effected through the AGCusing conventional tie-line bias control with computation of ACE. System interchangesare controlled by long-term and short-term contracts.

Within the UK, the electric power system of England and Wales has been privatizedinto twelve regional distribution companies, various generation companies and anindependent transmission system. Generators submit bids to supply generation and


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control services. There are penalties if the services are not delivered per contract, butthere is also compensation if transmission system limitations keep a generator fromproviding service. There is centralized AGC and only a loose form of frequency controlto protect the system equipment, yet reliable, satisfactory electric power service isprovided.

In Japan, some utilities operate at 50Hz while others operate at 60Hz. The ten majorutilities in Japan are responsible for frequency control with the two largest employingflat-frequency control.

9.1. Equity of Control

Interconnected electric utility systems are generally more reliable than isolated systems.Interconnected systems also benefit from economic advantages, such as sharingreserves. Yet in such arrangements, there must be an equity in the sharing or allocationof the control burden. The key question remains of how will the responsibility of inter-connected operation be allocated between those responsible for control.

Open access to the transmission system with participation of nonutility owned gen-eration may require new approaches to establish a cost of control. Considering theneed for reliable operation and control, those responsible for control have a need toestablish ways to evaluate and recover the cost of control.

Besides the current practices, there are a number of modified or alternate approachesthat could also be used to address future control needs. Some of those approaches couldinclude redefining the control area concept, incorporating the unbundling of utility ser-vices, and/or adopting new or revised control concepts and objectives.

9.2. Reliability, Security and Quality of Service

It should be clear that and all future control concepts must not sacrifice the establishedlevel of reliability nor lead toward systems with unacceptable power outages and powershortages. The main objective and challenge will be enhancing the economy withoutsacrificing the security.

There is a cost associated with controlling the frequency as tightly as it is required(for example as in North America). The technically necessary tightness of frequencycontrol is required by power system equipment. For under-frequency, the margin will�0.15!�0.4 to allow for random fluctuations of system load and would depend onthe size of the interconnection.

To maintain a reliable power system with acceptable quality of service, the major ele-ments of control are identified as follows:

frequency control,load following,interchange control,energy accounting,disturbance response,integrated plant/control center control,hardware interfaces, anduser interfaces.


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9.3. Unbundled Control Services

Taking North America as an example: in the early days of the electric utility systems,each utility provided that full range of electric services to supply their customers. Backthen, a single price for the combination of services that went into providing electricityto customers was adequate. Recently, a separation (unbundling) of the electric utilitybusiness into two related but separate industries: The electricity supply industry (gen-eration and transmission) and the electricity service industry (distribution) appearslikely to become a promising trend.

To ensure that there is adequate generation to meet the demand and that the trans-mission and distribution system can reliably distribute that electricity, with thisunbundling, there is still a need for a control system with various services.

If control services are separately defined and priced, they can be more easilymarketed (bought and sold or equitably exchanged), so there would no longer beany concerns over ‘‘sharing’’ such services. As the value of such services are established,there will probably be more interest in providing them, possibly at a premium rate.Unbundling of electric utility services will help facilitate compensation and competitionin this industry as it opens up more players

9.4. Generation/Load Control and Information Needs

With increasing competition from the opening of the transmission system and increas-ing constraints such as the new environmental regulations, more information and con-trol capabilities are and will be needed to control generation and to some extent load.

A more accurate and efficient method of control will be needed to reduce the control/regulating burden on the generators. Overshooting and hunting as a result of controlaction should be constrained. Furthermore, control objectives leading toward pro-active control with less control action are welcome.

The present evolution of advanced communication and computer technologies canmeet these challenges. To be able to control the more complex power system environ-ments of the near future, more information will be needed to be processed from bothinside and outside of power system. With the added complexity of such future systems,most operations will need to be simulated before actually being implemented. This willrequire more computing power and more detailed and accurate models of the generat-ing plants, transmission system, and neighboring systems.

10. COORDINATED VOLTAGE CONTROL

While the voltage control of an interconnected large-scale power system is widely recog-nized as an important problem, its basic formulation and solution are often utility-specific. Most often voltage control is viewed as a static problem, whose solution isidentical to a centralized open-loop optimization-based VAR/voltage management.The most common tool for solving this problem is an Optimal Load Flow (OLF)type algorithm. In the power literature, this approach is often referred to as the tertiarycontrol. The OLF computes changes in generator voltages to regulate load voltages onthe entire interconnected system.


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A second, different, approach to voltage control coordination relies on spatialdecomposition of interconnected system into regions and an on-line decentralizedclosed-loop controllers for regulating only a few load voltages in each region, referredto as the ‘‘pilot’’ voltages.

For example, in the French system a full automation of system-wide voltage regula-tion is achieved by employing such an intuitive reduced information structure at theregional level (pilot busses) and regional controllers (called secondary voltage control-lers) which control the pilot voltages by adjusting the terminal voltages of the regionalgenerators. Particularly relevant is the fact that this scheme assumes negligible inter-actions with the neighboring regions. In this case, the responsibility for coordinatedvoltage regulation of the entire French network is shared among regional closed-loopcontrollers and the operators at the national control center.

In order to improve the security and economics of the entire system, further automa-tion of the tertiary level is called for. To achieve this, the focus will be on the mid-termbehavior of the power system by considering that the transient response of generatorsand their primary control are assumed stable and very fast. Under this assumption,only steady-state load flow equations are considered and loads are modeled as constantpower devices. This yields a nonconventional problem and can be adequately treated byconsidering a sequence of steady-state voltages. The load voltages are changing inresponse to changes of steady-state set points of generators and the available controlsreact only in response to load voltage deviations at selected nodes (pilot nodes) fromtheir set values. In the terminology of system theory, the control variables are therate of change of generator voltages and the state variables are the actual load voltages,all at each regional level. The coupling between a given region and the rest of the systemis proportional to the reactive flow changes into the area.

An improved secondary voltage regulator is then designed based on both the regionalpilot point voltages and an additional feedback signal (based on the reactive power tie-line flow measurements) to cancel out the effect of interactions. This schemepreserves the regional performance independent of the voltage changes in neighboringregions and remains effective as long as the voltage constraints are not approached. Incases where system-wide reserves are to be re-scheduled or voltage constraints are to beeffectively managed, coordinated voltage control is sought, such that at the regionallevel the voltage control settings on active generators and the corresponding pilotpoint set values deviate least from their optimal values, and at the coordinating levelthe strength of electrical interconnections among the regions and the rate at whichthe coordinating control is enforced.

11. ARTIFICIAL NEURAL NETWORKS IN POWER SYSTEMS

Artificial neural networks (ANNs) are biologically inspired and represent a majorextension of computation. They embody computational paradigms, based on abiological metaphor, to mimic the computations of the brain. The number of ANNapplications to electric power system problems has increased dramatically in the lastdecade, fired by both theoretical and application successes in a variety of disciplines.The theory and application developments associated with ANNs are largely interdisci-plinary. Perhaps the first reported application of ANNs to the power systems area wasin 1988. Since then, ANNs have found many applications and research in this area is


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rapidly gaining momentum. A summary of the ANNs-based application in powersystems is given below along with the ANN model(s):

– On-line security assessment: Multilayer perceptron, Hopfield network;– Load forecasting: Multilayer perceptron, self-organizing feature map;– Fault location: Multilayer perceptron;– Detection of high impedance faults: Multilayer perceptron;– Alarm processing: Multilayer perceptron;– Optimal capacitor switching: Multilayer perceptron;– Tuning of power system stabilizers: Multilayer perceptron;– Boiler monitoring and control: Multilayer perceptron;– Eddy current analysis: Cellular neural networks;– Identification of harmonic sources: Multilayer perceptron;– State estimation: Multilayer perceptron, adaptive linear combiner, structured neuralnetwork;

– Contingency screening: Multilayer perceptron, Hopfield network;– Power converter control: Multilayer perceptron;– DC motor control: Multilayer perceptron;– Transient stability analysis: Multilayer perceptron;– Turbogenerator regulatory control: Multilayer perceptron;– Unit commitment: Multilayer perceptron;– Expansion planning: Multilayer perceptron;

It is quite clear that hack-propagation based perceptron model is the most popularANN scheme employed in electric power systems so far. Modified Hopfield networks;self-organizing feature maps and cellular networks are some of the other schemes usedin the implementations. Commercially available software for designing multilayerperceptron networks has been improved in performance by adding hidden neuronsdynamically during training.

12. GENERAL REMARKS

In this tutorial presentation, we have provided concepts and methodologies of controlfor stability in electrical power systems. It is recognized that the degree of stability ofpower systems is generally less important than in many other control problems.What is really required is the electric power system to remain stable over a widerange of operating conditions. Commonly encountered are oscillations of about 1Hzin frequency with a damping ratio of 0.05, and these are associated with synchronousmachines having slow excitation systems and no power system stabilizers, which giverise to no stability problems. There is little need, therefore, for optimal design ofcontrollers in order to maximize damping.

The modes of oscillation involving the system as a whole, the interarea electromecha-nical oscillations, can normally be stabilized by decentralized controllers placed at thosegenerating units that participate significantly in the mode. However, the advent of multiterminal DC links embedded within the AC system may well require centralized DCpole controls to ensure global system stability.

Robustness of power system control design is important but has been approached ina very practical sense so far. Lack of robustness quickly shows when commissioning


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and operating new plants and immediate steps are necessary to rectify the problemsencountered.

References

[1] B.M. Weedy (1987). Electric Power Systems. Wiley, New York.[2] P. Kundur, D.C. Lee and H.M. Zein El-Din (1981). Power system stabilizers for thermal units: analytical

techniques and on-site validation. IEEE Trans. PAS, 100, 81–95.[3] D.C. Lee, R.E. Beaulieu and J.A.R. Service (1981). A power system stabilizer using speed and electrical

power inputs-designs and field experience. IEEE Trans. PAS, 100, 4151–4157.[4] D.C. Lee, R.E. Beaulieu and G.J. Rogers (1985). Effect of Governor characteristics on turbogenerator

shaft torsionals. IEEE Trans. PAS, 104, 1255–1261.[5] P. Kundur, M. Klein, G.J. Rogers and M.S. Zymno (1988). Application of power system stabilizers for

enhancement of overall system stability. IEEE Trans. PAS, 107, 214–222.[6] D.Y. Wong, G.J. Rogers, B. Porretta and P. Kundur (1989). Eigenvalue analysis of very large power

sytems. IEEE Trans. PAS, 108, 1437–1444.[7] G.J. Rogers (1989). Control for stability in interconnected power systems. IEEE Control Systems

Magazine, 2, 19–22.[8] N. Jaleeli, L.S. VanSlyck, D.N. Ewart, L.H. Fink and A.G. Hoffmann (1992). Understanding automatic

generation control. IEEE Trans. Power Systems, 7, 1106–1122.[9] C. Concordia (1990). Power system objectives’ side effects: good and bad. IEEE Trans. Power Engineering

Review, 3, 12–13.[10] M.R. Stambach and D.N. Ewart (1989). Dynamics of interconnected power systems: A tutorial for

system dispatchers and plant operators. Electric Power Research Institute, Report EL-6360-L. Section 9.[11] V. Sagar, S. Vankayala and N. Rao (1993). Artificial neural networks and their applications to power

systems- A bibliographical Survey. Electric Power Systems Research, 28, 67–79.[12] Jiang, H.J.F. Dorsey, Z. Qu and J. Bond (1993). Toward a global decentralized control for large-scale

power systems. Proc. 32nd IEEE Decision and Control Conference, 3716–3721, San Antonio, TX.


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Control of electric power systems

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