A Brief Review of Power System Dynamic Stability Characteristics

7/28/2019 A Brief Review of Power System Dynamic Stability Characteristics

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Centre for Distributed Generation andSustainable Electrical Energy

A Brief Review of Power System Dynamic

Stability Characteristics

Summary report

M. Hughes, O. Anaya-Lara, N. J enkins and G. Strbac

October 2004


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A brief review of power system dynamic stability characteristics

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Table of Contents

Table of Contents.........................................................................................................2Executive Summary..................................................................................................... 3

List of Figures..............................................................................................................5List of Symbols and Abbreviations............................................................................. 5

1. Introduction........................................................................................................62. Assessment of dynamic stability........................................................................ 6

2.1 Comments on generator dynamic behaviour................................................6

3. Influences on dynamic stability characteristics..................................................73.1 Generator operating conditions....................................................................7

3.2 Network line reactance.................................................................................9

3.3 Influence of turbine governor control ........................................................103.4 Influence of Automatic Voltage Regulator (AVR) excitation control....... 11

3.5 Influence of a Power System Stabiliser (PSS) ...........................................12

3.6 Influence of Fixed Speed Induction Generator (FSIG) based wind farms. 14

3.7 Influence of Doubly Fed Induction Generator (DFIG) based wind farms.15

4. Conclusions......................................................................................................16


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Executive Summary

A power system is continually subjected to changes in its load and operatingconditions and it is essential that the system posses the ability to maintain stable

operation when subjected to disturbances. The ability to maintain stable operation inthe presence of small disturbances is referred to in the power systems field asdynamic stability. The purpose of this report is to very briefly look at the dynamiccharacteristics of generators, their prime movers and controls and highlight the waythat their contributions to system dynamic stability are influenced by the operatingconditions and system interconnections. The impact on dynamic stability of newtypes of energy sources such as wind generation based on fixed speed and doubly fedinductions generator wind turbines is also considered in this report.

For the purpose of this report the dynamic stability characteristics of the simplenetwork of is considered. Although not proposed as an approximate analogue, thesystem in some ways can be considered representative of the English-Scottishnetwork, with a mixed generation Scottish system transporting power to the largersystem of England and Wales. Case studies are carried out to demonstrate thesignificance of relevant parameters and assess dynamic stability of the system viaeigenvalue analysis.

A number of factors that impact the system stability performance were investigatedincluding (i) loading conditions, (ii) network characteristics, (iii) turbine governorcontrol, (iv) automatic voltage regulator (v) power system stabiliser and (v) influenceof fixed speed and doubly fed induction generators.

It was confirmed that increased value of network line reactance gives rise to highervalues of generator load angle and reduced generator damping. Furthermore, the highvalue of load angle associated with leading power factor operation is shown toreduce generator damping and hence making the system less stable. It wasdemonstrated that governor control of steam and gas turbines may reduce systemdamping and the impact of inertia was discussed. Furthermore, negative impact thatautomatic voltage control may have on system damping is examined and thestabilising effects of power system stabilisers demonstrated. It was shown that underoscillatory system conditions PSS induces a component of electrical power that is inphase with rotor speed variations, thereby improving damping.

Much speculation exists concerning the influence of wind farms on system operationand stability. Wind farms based on Fixed Speed Induction Generators (FSIGs) havepoor transient stability characteristics but this report shows that they add significantlyto the damping of the system. The operating characteristic of a synchronousgenerator is such that power output changes are most directly linked to changes inrotor angle. Since, damping is governed by torque (or power) variations in phasewith speed variations, the natural response of a generator connected to a powernetwork is oscillatory. The operating characteristic of an induction machine is suchthat torque changes are related directly to speed changes. With an induction


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generator, therefore, under oscillatory system conditions the torque variationsproduced are predominantly in phase with speed variations. Consequently, underoscillatory conditions the power variation imposed on the synchronous generators ispredominantly damping power so that the introduction of an FSIG on to a systemimproves the system damping. Although damping contribution of a doubly fed

induction generator (DFIG) tends to be less than that of a FSIG, the results indicatethat significant improvement in the system damping and dynamic stability margin isprovided.


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List of Figures

Fig. 1. Generic network model. ................................................................................... 7

Fig. 2. Influence of Generator 2 active power output P2............................................. 8Fig. 3. Influence of Generator 2 reactive power Q2.................................................... 9Fig. 4. Influence of network line reactance X2............................................................ 9Fig. 5. Influence of Generator 2 steam turbine governor gain Kds2......................... 10Fig. 6. Influence of Generator 2 gas turbine governor gain Kdg2............................. 11Fig. 7. Influence of Generator 2 AVR voltage feedback gain Kv2. .......................... 12Fig. 8. Influence of Generator 2 AVR current feedback gain Ki2............................. 13Fig. 9. Influence of Generator 2 Power System Stabiliser Kpps2............................. 13Fig. 10. Influence of Generator 1 Power System Stabiliser Kpps1........................... 14Fig. 11. Influence of Fixed Speed Induction Generator (FSIG) wind farm size. ...... 15Fig. 12. Influence of Doubly Fed Induction Generator (DFIG) wind farm size........ 16

List of Symbols and Abbreviations

G1 Generator 1

G2 Generator 2

P2 Generator 2 active power output

Q2 Generator 2 reactive power output

PF2 Generator 2 power factor

X1, X2, X3 Transmission system reactances

Kds2 Generator 2 steam turbine governor gain

Kdg2 Generator 2 gas turbine governor gain

AVR Automatic Voltage Regulator

Kv2 Feedback gain of AVR voltage control loop

Ki2 Feedback gain of AVR current control loop

PSS Power System Stabiliser

Kpps1 Gain of Power System Stabiliser in generator 1

Kpps2 Gain of Power System Stabiliser in generator 2

FSIG Fixed Speed Induction GeneratorDFIG Doubly Fed Induction Generator

PU Per Unit


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1. IntroductionA power system is continually subjected to changes in its load and operating conditions and

it is essential that the system has the ability to maintain stable operation when subjected todisturbances. The ability to maintain stable operation in the presence of small disturbances isreferred to in the power systems field as dynamic stability. A power system is very complexand its dynamic stability characteristics are influenced by the complex interaction of itsgenerating stations, transmission and distribution networks, its operating levels and loads.Before any understanding of the complexities of power system dynamic stability is possible,an appreciation of the fundamental dynamic characteristics of basic system components andthe factors that influence them and their contributions to overall stability characteristics isessential. The purpose of this report is to very briefly look at the dynamic characteristics ofgenerators, their prime movers and controls and highlight the way that their contributions tosystem dynamic stability are influenced by the operating conditions and systeminterconnections.

2.Assessment of dynamic stabilityThe most direct way to assess dynamic stability is via eigenvalue analysis of a model of thepower system. Once the non-linear model of the system has been linearised, manytechniques are available for the calculation of the system eigenvalues. For stability, all of theeigenvalues must lie in the left half complex plane. Any eigenvalue in the right half planedenotes an unstable dynamic mode and system instability. The way in which systemoperating conditions, system parameters and controllers influence dynamic stability can bedemonstrated by observing their influence on the loci of critical eigenvalues, i.e. theeigenvalues furthest to the right in the complex plane.

For the purpose of this report the dynamic stability characteristics of the simple network ofFig. 1 will be considered. The network consists of three generating stations. Generators 1 and2 supply power to the local load on bus 4 and to the major power system represented bygenerator 3 and its load. Generators 1 and 2 can be represented as synchronous generatorsdriven by either steam or gas turbines and generator 2 can also represent a windfarmemploying either fixed-speed or doubly-fed induction generators. Generator 3 is a steamturbine driven synchronous generator. Generator 3 is of the order 5 times the combined sizeof generators 1 and 2. Although not proposed as an approximate analogue, the system insome ways can be considered representative of the English-Scottish network, with a mixedgeneration Scottish system transporting power to the larger system of England and Wales.

2.1Comments on generator dynamic behaviourWhen a generator feeding power into a large network is subjected to a small disturbance, thedynamic response of the generator rotor with respect to the system is oscillatory with, ingeneral, relatively light damping. This produces oscillatory variations in the magnitudes ofthe generator voltage, currents, power and torque.

Under such circumstances it is often useful to consider the influence of controllers andsystem elements on performance in terms of their influence on synchronising power and


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damping power. Oscillations in power (or torque) resulting from the disturbance areconsidered to be expressible in terms of two components. One is the component of poweroscillations that is in phase with rotor angle oscillations; this is termed the synchronisingpower component. The other is the component in phase with rotor speed oscillations; this istermed the damping power component.

Generator1 Generator 2

MainSystem

Load

Bus1 Bus2

Bus3

Bus4X1 X2

X3

Fig. 1. Generic network model.

A controller that increases the magnitude of the power component in phase with rotor speed,i.e. the damping power, will improve the damping of the system oscillations. Any increaseproduced in the synchronising power component indicates that changes in rotor angle

produce greater changes in the restoring torque on the generator shaft, which helps ensurethat the generator remains in synchronism with the system being supplied.

The term synchronising power (or torque) is, in addition, often applied to large disturbancesituations, such as behaviour following three-phase system faults. Here the term simplyapplies to the load power (or load torque) developed, which is predominantly related to theswing in rotor angle. This load torque acts on the rotor and in such a direction as to return itto the final equilibrium value of rotor angle where the system is again in a steady conditionand in synchronism with the system being supplied.

3.Influences on dynamic stability characteristics3.1Generator operating conditions

The generator operating condition has a large impact on the generator and the systemdynamic characteristics. As the generator power output operating level is adjusted inresponse to the load demand, the operating load angle of the generator changes and this has aconsiderable influence on generator damping. The major source of generator damping is viathe rotor q axis damper circuits. At low values of power output, where the load angle issmall, the q axis damping is high and the contribution from the d axis circuits is small. With


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increased power output, as the load angle increases, the damping contribution of the q axisreduces. Increased contribution from the d axis circuits is insufficient to compensate for thisand the generator damping reduces. This is demonstrated in Fig. 2, which shows that as thegenerator power increases the critical eigenvalue is shifted to the right half and for thehighest value considered the critical eigenvalue enters the right half plane indicatingdynamic instability.

Fig. 2. Influence of Generator 2 active power output P2.P2 =0.28, 0.56, 0.84 PU. G1: Steam turbine. G2: Steam turbine.

A more dramatic change in generator damping is observed when the operating Power Factor(PF) moves from lagging to leading. Under conditions of heavy system load the currents inthe transmission and distribution lines of the network are high giving rise to heavyabsorption of reactive power. This creates the need for the generators to generate reactivepower and operate under lagging power factor conditions. Under light loading conditions thecurrents in the transmission and distribution lines of the network are low, the reactive powerabsorbed by the line reactances is low and capacitive effects dominate. This leads to reactivepower being generated by the network and under such conditions it is desirable for thegenerators to absorb reactive power and operate under leading power factor conditions.

Lagging power factor conditions are achieved by applying a high value of field voltage(thereby producing a high value of the internally generated voltage in the generator stator).

The change to leading power factor conditions is achieved by reducing the field voltage (andconsequently the internally generated voltage in the stator). To achieve the same outputpower at a lower value of excitation voltage requires an increased value of the operating loadangle. The high value of load angle associated with leading power factor operation leads to aseverely reduced contribution from the q axis circuits and generator damping is greatlyreduced. This is demonstrated by the plot of Fig. 3, which shows that as reactive powerchanges from lagging to leading the critical eigenvalue is shifted markedly towards the rightand instability results for a modest value of leading reactive power.

P2 =0.28PF2 =0.887(lagging)

P2 =0.56PF2 =0.95(lagging)

P2 =0.84PF2 =0.96(lagging)


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Fig. 3. Influence of Generator 2 reactive power Q2.Q2 =0.2108 lagging; Q2 =0.05 lagging; Q2 =-0.0936 leading.G1: Steam turbine. G2: Steam turbine.

3.2Network line reactanceIncreased value of network line reactance gives rise to higher values of generator load angleand reduced generator damping. Higher values of line reactance also result in a decrease inthe frequency of local mode oscillations. Fig. 4 shows how the critical eigenvalue is movedtowards the right in the complex plane as the reactance between busbar 2 and busbar 4 is

increased.

Fig. 4. Influence of network line reactance X2.X2 =0.15, 0.3, 0.45 PU. G1: Steam turbine. G2: Steam turbine.

X2 =0.15 X2 =0.3 X2 =0.45

Q2 =0.211PF2 =0.957(lagging)

Q2 =0.05PF2 =0.997(lagging)

Q2 =-0.0936PF2 =0.991(leading)


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3.3Influence of turbine governor controlGovernor control of steam and gas turbines can reduce system damping. The major controlaction of a turbine governor is to adjust the turbine output power as the network load varies.Increased network load leads to increased generator torque, a deceleration of the turbine

shaft and a reduction in speed. The change in speed is detected by the governor and used toincrease the turbine power output to match the demand.

In terms of dynamic contribution, if the turbine power could respond instantaneously to achange in speed, then the governor would contribute a power response directly in phase withspeed variations and thereby contribute directly to damping. The response in power output ofthe turbine is not instantaneous and considerable lag exists in its response to speedvariations. At typical local mode oscillation frequencies, the phase lag introduced by theturbine and governor is greater than 90o and the turbine contributes negative damping. This

characteristic is demonstrated in the plot of the critical eigenvalue loci ofFig. 5. The case isthat of a reheat steam turbine and it can be seen that as the governor gain is increased (i.e.the droop setting is reduced) the critical eigenvalue is driven towards the right half complex

plane. At local mode frequencies the dynamic response of a reheat turbine is effectivelyreduced to that of the high-pressure cylinder only. The long time lag of the reheatereffectively prevents the intermediate and low-pressure cylinders of the turbine fromcontributing to the dynamic response and without the attenuating influence of the reheater,the reduction in damping would be considerably worse.

Fig. 5. Influence of Generator 2 steam turbine governor gain Kds2.Kds2 =0, 25, 100. G1: Steam turbine. G2: Steam turbine.

A similar situation exists for a gas turbine. The phase lag introduced by the governor andturbine at local mode frequencies is of a similar order to that with the steam turbine. Controlis exercised over a larger portion of the total power capability, when compared with thesteam turbine. However the resulting influence over damping is also dependent on the inertiaof the turbine and generator set. In the case of a single-shaft gas turbine the inertia constant

Kds2 =0Kds2 =25

Kds2 =100


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is generally much greater than that of a steam turbine due to the high operating speed of theturbine and compressor. The high inertia attenuates speed variations following systemdisturbances and hence results in reduced turbine power response thereby reducing thenegative damping influence. Fig 6 is for the case of a single-shaft gas turbine. It can be seenthat compared to the steam turbine case, at low values of gain the gas turbine is more stablewith the critical eigenvalue lying deeper in the left half plane due mainly to the higher valueof inertia constant. However, due to the larger phase shift associated with power control loopelements the critical eigenvalue is more sensitive to droop gain variations and is pushed wellinto the right half plane for a droop gain of 100 (equivalent to a 1% droop).

Fig. 6. Influence of Generator 2 gas turbine governor gain Kdg2.Kdg2 =0, 25, 100. G1: Steam turbine. G2: Gas turbine (single shaft).

3.4Influence of Automatic Voltage Regulator (AVR) excitation controlWith constant generator excitation voltage, variations in the generator stator current causedby network load changes would result in unacceptable variations in the generator terminalvoltage. The AVR excitation control scheme detects variations in the generator terminalvoltage and uses these to adjust the field voltage of the generator to maintain the terminalvoltage close to its desired value. The types and designs of excitation control schemes arewide and varied and they possess widely differing performance characteristics. However,whatever the scheme, an unfortunate feature is that the voltage feedback loop of the AVRgives rise to a component of generator power that is in anti-phase with speed variations andconsequently negative damping is introduced which reduces dynamic stability margins.

The influence of the AVR gain of a static excitation control system on dynamic stability isdemonstrated in Fig. 7. As the AVR gain is increased the locus of the critical eigenvalue isshifted towards the right half complex plane.

Kdg2 =0

Kdg2 =25 Kdg2 =100


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Fig. 7. Influence of Generator 2 AVR voltage feedback gain Kv2.Kv2 =25, 100, 200. G1: Steam turbine. G2: Steam turbine.

The adverse influence of the voltage feedback signal on dynamic stability is combated bystabilisation terms in the excitation control loop. In the particular static excitation controlsystem considered, the main stabilisation is provided by a generator field current feedbacksignal. This serves to reduce the effective time constant of the generator field and in doing soreduces the negative damping influence of the voltage feedback signal of the AVR andconsequently improves damping. The beneficial influence of the generator field current

feedback signal is demonstrated in Fig 8. As the gain of the current feedback loop isincreased it can be seen that the critical eigenvalue is driven further to the left of the complexplane thereby providing improved damping.

3.5Influence of a Power System Stabiliser (PSS)Generator and system damping can be improved by introducing a PSS into the excitationcontrol scheme of the generator. Under oscillatory system conditions its purpose is to inducea component of electrical power that is in phase with rotor speed variations, therebyimproving damping. A PSS may be based on a signal derived from generator speed,electrical power or network frequency. The signal is processed via appropriate filters toprovide the required phase relationship between the induced electrical power variations andgenerator rotor speed.

The capability of a PSS, based on an electrical power input signal, introduced on generator 2is demonstrated in Fig. 9. The case considered is that with generator 1 driven by a steamturbine and generator 2 by a gas turbine for a system operating condition that without thepower system stabiliser is unstable. It shows how increasing the gain of the PSS shifts thecritical eigenvalue to the left and out of the right half plane thereby providing stableoperation.

Kv2 =25 Kv2 =100 Kv2 =200


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Fig. 8. Influence of Generator 2 AVR current feedback gain Ki2.Ki2 =0.283, 0.535, 0.87. G1: Steam turbine. G2: Steam turbine.

Fig. 9. Influence of Generator 2 Power System Stabiliser Kpps2.Kpss2 =0, 1.25, 2.0. G1: Steam turbine. G2: Gas turbine.

Fig.10 shows the influence of placing the PSS on generator 1 instead of generator 2. Again,as the PSS gain is increased the critical eigenvalue is shifted to the left and out of the righthalf complex plane. It can be seen that when the PSS is sited on generator 1 it has muchmore influence on stability than when it is sited on generator 2. Since the major causes of thedamping difficulties are the gas turbine governor controller and the leading power factoroperating condition of generator 2, this may appear surprising. The performance of a PSS,however, is influenced by many factors and in the case considered, the gas turbine governor

Ki2 =0.87 Ki2 =0.535 Ki2 =0.283

Kpss2 =0Kpss2 =1.25Kpss2 =2


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controller of generator 2 interacts adversely with the PSS employed reducing itseffectiveness. On generator 1, which employs a steam turbine, interaction with the governorcontroller is much less and a much more effective contribution to system damping isprovided.

Fig. 10. Influence of Generator 1 Power System Stabiliser Kpps1.Kpss1 =0, 0.25, 0.75. G1: Steam turbine. G2: Gas turbine.

3.6Influence of Fixed Speed Induction Generator (FSIG) based wind farmsMuch speculation exists concerning the influence of wind farms on system operation andstability. Wind farms based on Fixed Speed Induction Generators (FSIGs) have poortransient stability characteristics but it can be shown that they add significantly to thedamping of the system.

The operating characteristic of a synchronous generator is such that power output changesare most directly linked to changes in rotor angle. Power response to rotor speed oscillationsis due mainly to the damper circuits and is relatively small. Since, damping is governed bytorque (or power) variations in phase with speed variations the natural response of agenerator connected to a power network is oscillatory.

The operating characteristic of an induction machine is such that torque changes are relateddirectly to speed changes. With an induction generator, therefore, under oscillatory systemconditions the torque variations produced are predominantly in phase with speed variations.Consider the situation where an induction generator feeds power into a system,predominantly supplied by synchronous generators and where oscillatory conditions exist.Since an induction generator operates super-synchronously, any increase in systemfrequency reduces the difference between the rotor speed and its stator frequency andtherefore results in a reduction of the generator power output. If the power demanded by thesystem load is considered essentially fixed, then this reduction imposes an increasedelectrical power from the synchronous generators. Since the frequency of the system is

Kpss1 =0Kpss1 =0.25Kpss1 =0.75


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dictated by the rotor speed of the synchronous generators, the power variations produced areessentially in phase with the rotor speed variations. Consequently, under oscillatoryconditions the power variation imposed on the synchronous generators is predominantlydamping power so that the introduction of an FSIG on to a system improves the systemdamping.

Fig. 11. Influence of Fixed Speed Induction Generator (FSIG) wind farm size.G1: Steam turbine. G2: FSIG.

The plot of Fig. 11 is for the situation where generator 1 is a steam turbine drivensynchronous generator and generator 2 is the fixed speed induction generator of a wind farm.The total power generation of the subsystem consisting of generators 1 and 2 is maintainedconstant as the proportion of the power produced by the wind farm is increased. It can beseen that as the proportion of the FSIG based wind farm power is increased, the criticaleigenvalue is shifted to the left in the complex plane indicating improved damping and anincreased dynamic stability margin.

3.7Influence of Doubly Fed Induction Generator (DFIG) based wind farmsWind farms based on Doubly Fed Induction Generators (DFIGs) have superior transientstability characteristics to either FSIGs or Synchronous generators. The control of thefrequency of the three-phase rotor supply decouples the speed of the rotor from the speed ofthe stator flux vector. Consequently, variations in the speed difference between the physicalrotor and the stator flux vector do not result directly in changes in load torque, so that thedamping contribution of a DFIG tends to be less than that of a FSIG. The plot of Fig. 12 isfor the case where generator 1 is a steam turbine driven synchronous generator and generator2 is the doubly fed induction generator of a wind farm. The total generation of the sub-system comprising generators 1 and 2 is maintained constant as the proportion of powergenerated by the wind farm is increased. As the wind power component is increased thecritical eigenvalue is shifted to the left. As expected the shift involved is less than that of the

G1 =2.0FSIG =0.01

G1 =1.5FSIG =0.5

G1 =1.0FSIG =1.0


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FSIG case but the results still indicate that significant improvement in the system dampingand dynamic stability margin is provided.

Fig. 12. Influence of Doubly Fed Induction Generator (DFIG) wind farm size.G1: Steam turbine. G2: DFIG.

4. ConclusionsWhilst power system dynamics is a complex subject and dynamic stability depends on theinteraction of many components with widely varying characteristics, it is hoped that this verybrief report provides an appreciation of some of the fundamental factors that mould thedynamic stability characteristics of a power system. The large scale changes in generatingprofile due to the big expansion proposed in distributed generation and renewable energysources warrants a new look at dynamic stability and the overall control strategies adoptedfor power stations, be they conventional or wind farms, to ensure dynamic compatibility,stability and system integrity.

G1 =2.0DFIG =0.01

G1 =1.6DFIG =0.4

G1 =1.2DFIG =0.8

A Brief Review of Power System Dynamic Stability Characteristics

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