A Study of the Impact of Reduced Inertia in Power Systems

A Study of the Impact of Reduced Inertia in Power Systems∗

Urmila [email protected]

James O’[email protected]

Abhishek [email protected]

Thomas [email protected]

Jeff [email protected]

Abstract

Inertia in power systems plays an important role inmaintaining the stability and reliability of the systemby counteracting changes in frequency. However,the traditional sources of synchronous generation arebeing displaced by renewable resources, which oftenhave no inherent inertia. This paper investigatesthe impact of reduced system inertia on severalaspects of the dynamic stability of power systems,such as angular stability, primary frequency response,and oscillatory modes. This study is performedon a large–scale 2000 bus synthetic Texas modelby selectively replacing synchronous generators withinverter–based generation resources. This paperalso compares the analysis results obtained bythe above–mentioned inertia-reduction approach ofrenewable integration with another approach in whichthe inertia constant of all synchronous generators isdecreased. This paper demonstrates that only reducingthe inertia of all synchronous generators in a systemdoes not provide an accurate analysis of the challengesassociated with the reduced system inertia caused byrenewable integration.

1. Introduction

Traditionally, the majority of generators in powersystems have been synchronous providing sufficientinertial frequency response during transient events.However, recent technological advancements haveresulted in a significant increase in the amount ofpenetration of renewable energy generation resources

∗This work was supported by the DOE - Office of Water Powerfor contract 72167A under B&R W0102000 at the Pacific NorthwestNational Laboratory. Pacific Northwest National Laboratory isoperated by Battelle for DOE under contract DE-AC05-76RL01830.

U. Agrawal, J. O’Brien, A. Somani and J. Dagle are with PacificNorthwest National Laboratory, Richland, WA, 99352 USA

T. Mosier is with Idaho National Laboratory, Idaho Falls, ID,83402 USA

[1]. This is largely being driven by mandates inrenewable portfolio standards which also results inthe loss of large synchronous generators (mostly coalplants). These renewable energy resources are mostlyconnected to the grid through power–electronic devicesand therefore do not contribute to the system inertia,causing a decrease in the overall system inertial responseduring transient events [2]. The current power systemhas been designed around large synchronous generatorsand load, with the system inertia playing an importantrole in determining the stability of a system. In thiscontext, it is important to understand the impact ofreduced inertia on stability of a system consisting ofboth synchronous generators and inertia-less generatorswith different level of renewable energy integration.

Several studies have been carried out to analyze theimpact of increasing renewable energy penetration onthe power systems. References [3] and [4] discussedthe challenges associated with the high level penetrationof wind generation in power systems. Reference [5]studied the effect of reduced inertia on angular stability,[6] studied the impact of increased penetration ofDFIG–based wind turbine generators on transient andsmall-signal stability of power systems, [2] studied theimpact of wind power integration on power systemsfrequency response. Reference [1] determined theamount of inertia required in the system during highlevel penetration of wind energy and [7] studied thelocational impact of inertia on primary frequencyresponse using a large scale Texas synthetic networkmodel. NREL also performed the Eastern RenewableGeneration Integration Study (ERGIS) to analyze theoperational impacts of increased renewable energypenetration in the Eastern Interconnection, the detail ofwhich can be found in [8]. So far, most of the studiesare either carried out on a small scale or only applies theapproach of changing inertia constant of synchronousgenerators to study the impact of reduced inertia.

This paper presents a thorough analysis of the impactof reduced system inertia on dynamic performance ofpower systems that includes angular stability, primary

Proceedings of the 53rd Hawaii International Conference on System Sciences | 2020

Page 3010URI: https://hdl.handle.net/10125/64109978-0-9981331-3-3(CC BY-NC-ND 4.0)

frequency response, and system oscillatory modes usinga large scale synthetic network model. Two methodsof reducing inertia are implemented and compared forsuitability: (a) reducing the inertia constant of allsynchronous generators uniformly, and (b) selectivelyreplacing synchronous generators with non–inertialgenerators. Based on the results obtained, this paperdemonstrates that studies carried out to analyze theimpact of reduced system inertia by only changinginertia constant of synchronous generators does notaccurately portray the challenges associated with theintegration of renewable energy sources.

The rest of the paper is organized as follows:Section II provides some theoretical background tohelp understand the problem addressed in this paperalong with different aspects of power systems studiedin this paper to analyze the impact of reduced systeminertia. Section III describes the system model andthe approaches used in the paper to perform the study,Section III provides results and discussion, and sectionIV summarizes the conclusion.

2. Background theory

This section briefly describes system inertialresponse and it’s significance in maintaining systemreliable operations, and different metrics used to analyzethe impact of reduced inertia on the system.

2.1. Inertial response

Machine inertia is the fastest possible frequencystabilization method as shown in Figure 1 and Figure 2.Inertia is innate to machines that rotate synchronouslyin proportion to the grid’s frequency. Once a gridevent occurs, the physical mass of the rotating bodyexperiences a torque due to the change in frequencyof the electrical grid. This torque induces a transferof kinetic energy due to the machine’s rotation tothe electrical grid. The transfer of energy from themachine to the electrical grid works to slow the rateof change of frequency (ROCOF) of the electrical gridinstantaneously. Per unit inertia constant H is definedas kinetic energy in watt-seconds at rated speed, ω0,divided by the apparent power in per unit base Pmva,

H =Jω0

2

2Pmva, (1)

where J is the rotor moment of inertia in kg−m2. Thisinertia constant depends on the rotor moment of inertia,J , and this moment of inertia is equal to the weight ofthe rotating parts multiplied by the square of radians ofgyration [9].

Figure 1. Archetypal frequency pattern after

frequency deviation event. Reproduced from [10]

Figure 2. Sequence of frequency response and

recovery actions. Reproduced from [11].

System inertia plays a great role in ensuringreliability of grid operations by arresting the initialchange in frequency after an event. With increasingrenewable integration, this inertial response, providedby rotating machines, has been continuously decreasingand thereby affecting the system primary frequencyresponse and therefore system reliable operations. Inaddition to the primary frequency response, reductionin system inertia also affects transient angle stability,as discussed later in greater detail, affecting system’sstability margin.

2.2. Rate of Change of Frequency (ROCOF)

ROCOF gives the measure of the change infrequency with time (df/dt) following a system event,and is determined by the system inertia and themagnitude of the system event [12]. Traditionally,ROCOF was less significant for system stability studiesas power systems mainly consisted of synchronousgenerators limiting the ROCOF. However, withincreasing renewable integration, ROCOF has becomerelevant for system dynamic stability studies. Reducedsystem inertia can result in large ROCOF values, whichin turn can affect system reliable operations because

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of mechanical limitations of individual synchronousmachines as described in [12].

2.3. Transient angle stability

“It is the ability of the system to remain insynchronism when subjected to large disturbances [13].”For the system to maintain stability following a largetransient events, the rotor angular separation needs tobe within a certain limit as determined by equal areacriterion method.

2.4. Frequency nadir

The frequency nadir is given by the minimumfrequency at which the system frequency is arrestedfollowing a transient event, such as loss of a generator.This nadir point is determined by the spinning reserveavailable for primary frequency response and systeminertia. The frequency nadir determines if theunder-frequency load-shedding is initiated or not suchthat if the frequency decreases below certain specifiedvalue then load-tripping relays will be activated.

2.5. Small-signal stability

“It is the ability of the system to maintainsynchronism when subjected to small disturbances[13]”. The small–signal stability margin of a system isdetermined by system modes, which are given by theeigenvalues of system state matrix,

λi = σi + jωi, (2)

where j =√−1 and λi is the ith mode of the system.

These modes are characterized by their frequenciesgiven by

fi =ωi

2πHz (3)

and damping coefficients given by σi. The dampingratio, ζi, of a system mode is given by

ζ =−σi√

σ12 + ω12. (4)

The damping ratio of system modes give a measure ofthe small signal stability margin of the system. A systemconsisting of a mode with damping ratio close to zeroindicates that the system is vulnerable to system events.Therefore, it is very important that system modes haveenough damping ratio (>5%) such that the system stillexhibits positive damping ratio after occurrence of atransient event. Usually, power system stabilizers (PSS)

are used to improve the damping ratio of system modes.These PSS parameter settings are system specific andare tuned to improve the damping ratio of these systemmodes.

Past studies, which are based on reducing systeminertia by reducing the inertia of synchronousgenerators, have concluded that reducing the systeminertia results in an increase in the frequency of systemmodes resulting in faster frequency dynamics in thesystem [7, 14].

3. System modeling and simulationscenarios

This paper uses a 2000-bus Texas synthetic networkmodel to carry out the simulations, the details of whichcan be found in [15]. All the simulations were carriedout using the PowerWorld Simulator. In the Texasbase–case model, the total load was close to 67,000MW with renewable energy penetration, mostly wind,composing 13.37% of the load served. The frequencyresponse reserve capacity was equal to 13,500 MW.The total system inertia was equal to 381.34 GW·s,which was obtained by taking sum of the inertia ofall synchronous generators in the system model. Themodel consists of eight areas: Coast, East, North, NorthCentral, South, South Central, West, and Far West.The wind and solar generators were modeled usingtype-4 machine model equipped with an exciter andconnected to the grid through power-electronics devices.The type–4 machine model was used primarily becausemodern wind generators are mostly power–electronicsbased with no inherent inertia. The parametersused for modeling wind and solar generators weretaken from the existing WECC (Western ElectricityCoordinating Council) system model for 2025 heavysummer operating case.

The two approaches used to study the impact ofreduced system inertia are:

3.1. Reducing inertia of synchronousgenerators (Approach–1)

In this approach, the inertia of synchronousgenerators were reduced to study the impact of thereduced inertia without making any changes to therenewable integration level. For this, the inertiaconstant, as defined in (1), in the generator machinemodel was reduced by a given percentage for allthe synchronous generators in the system. All otherparameters in the machine model and exciter modelwere unchanged.

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3.2. Replacing synchronous generators withinertia-less generators (Approach–2)

Unlike approach-1, this is a realistic approach tostudy the challenges associated with the increasedpenetration of inertia–less generators connected to thegrid through power–electronics. In this approach,the conventional synchronous generators were replacedwith type–4 inertia–less wind generators equipped withan exciter. The synchronous generators to be replacedwere selected across all areas, such that the proportionof inertia among different areas were similar to thatin the base-case, to obtain a wind penetration level of20%, 30%, 40%, 55%, 60%, 65% and 70%. Figure 3shows the percentage change in the inertia of the systemcorresponding to the different level of wind penetration.This percent change in the system inertia was then usedin the first approach to modify the inertia of synchronousgenerators such that the same set of values of the totalsystem inertia were used in the two approaches. Also,the dispatch, system load and stress were same for allthe cases in both the approaches.

10 20 30 40 50 60 70

% wind penetration level

0

20

40

60

80

% d

ecre

ase in s

yste

m inert

ia

Figure 3. % decrease in system inertia because of

increased wind penetration level

4. Results and Discussions

During transient events, inertia provided bysynchronous generators counteracts the changes infrequency, and therefore helps with maintaining angularand frequency stability. This paper studies the impactof reduced system inertia on these aspects of powersystems transient stability, which includes rotor angledeviations and primary frequency response. Thispaper also analyzes the impact of reduced systeminertia on the system small-signal stability margin.For this, system modes were estimated for the twoinertia–reduction approaches.

Transient–stability analysis was performed to obtainmaximum rotor angle, minimum rate of change offrequency (ROCOF) and frequency nadir following a

(a) Rotor angle

(b) Rate of change of frequency

(c) Bus frequency

Figure 4. Transient stability analysis results obtained

for the base–case.

transient event. Modal analysis was performed toobtain the estimates of system modes using ringdownoscillations caused by the transient event. The transientevent comprised of tripping of two 1350 MW nucleargenerators located in the coast area. Following the trips,maximum rotor angle, frequency nadir and minimumROCOF values were obtained. The maximum rotorangle is given by the maximum of the rotor angledeviation observed in any generator in the systemfollowing the transient event; frequency nadir is givenby the minimum frequency observed in any of the busesin the system; and minimum ROCOF is given by theminimum of the ROCOF observed in any of the systembuses. Figure 4 show the generator rotor angle, ROCOF,

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(a) Rotor angle

(b) Bus frequency


for the approach–1 with inertia reduced by 70% as

compared to the base–case.

and bus–frequency observed in the system following thetransient event for the base case with a wind penetrationlevel of 13.37% and total system inertia of 381.34 GW·s;Figure 5 and Figure 6 are associated with the casehaving system inertia reduced by close to 70% usingapproach–1 and approach–2, respectively. The rindownoscillation caused by this transient event, as shown inFigure 4(c) for the base–case, was then used to obtainsystem mode estimates using Prony analysis, describedin [16], to estimate frequency of system modes. Figure7 shows generators in different areas oscillating againsteach other, following the transient event, with thegenerators located in the same colored area oscillatingtogether.

For modal analysis, rotor angle measurementsof synchronous generators were used to calculatefrequency measurements, given by the time derivativeof rotor angle measurements. The estimated frequencymeasurements measured at different generator buseswere then used for performing modal analysis. Thesimulated data were generated at the rate of 120 samplesper second and later decimated to a frequency of 8samples per second. Usually, for modal analysis, thedata are decimated to a frequency of 4-5 samples persecond as the system modes of interest are in the range

(a) Rotor angle

(b) Bus frequency


for the approach–2 with inertia reduced by 70% as

compared to the base–case.

of up to 2 Hz [17]. However, with reduced systeminertia, to account for the possibility of existence offaster frequency dynamics, as described in [7] and [14],a higher sampling frequency was used. The Pronyanalysis based on multiple–signals, described in [16],was used to obtain system mode estimates.

Figure 8 through Figure 10 summarizes the resultsobtained using the two inertia–reduction approaches.In the plots, the results obtained for a 0% decreasein the system inertia corresponds to the base–case.Figure 8 illustrates the impact of system inertia on theprimary frequency response. Figure 8(a) compares theamount of frequency response reserve (FRR) availablefor different cases in each simulation scenario. Forthe first approach in which only the inertia constantof the generator machine model was changed thus theFRR is retained. However, in the second approach,synchronous online generation is displaced by wind.Wind generation is not assumed to have any FRRavailable, and hence, did not contribute to the primaryfrequency response. Due to this, the amount of totalFRR decreases with this approach. This availability ofthe primary frequency response affects the frequencynadir and, as expected, the frequency nadir has lower

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Figure 7. Illustration of generators of different areas

oscillating against each other.

value for the second approach as compared to the firstapproach as shown in Figure 8(c). The decrease in theFRR was dependent on the generators that were replacedand so the decrease in the FRR was not consistent fordifferent wind penetration level as seen in Figure 8(a).The ROCOF for the two approaches closely matched,illustrating that this metric is highly dependent on thetotal system inertia for transient events with similarimpact.

Figure 9 compares the effect of the reduced systeminertia on the angular stability of the system. Duringtransient events, if the rotor angle increases beyondsome maximum value, then the generator can go outof synchronism. As can be seen in Figure 9, themaximum rotor angle observed following the transientevent for the two approaches follow different patterneven though the system inertia for both the approacheswere equivalent in the different cases. In the firstapproach, the observed maximum rotor angle decreased,while in the second approach, it increased. This resultis quite expected. As the synchronous generators arereplaced with the wind generators, each of the remainingfewer synchronous generators has to contribute morepower for the same amount of lost generation andthus results in an increased rotor angle. For the firstapproach, a small decrease in the maximum rotor angledeviation with decrease in the system inertia mighthave been caused by the redistribution of the powercontribution of different generators, during the transientevent, caused by the decrease in the kinetic energy(inertia) of all synchronous generators. Therefore, basedon the result for the second approach, it can be said

0 10 20 30 40 50 60 70

% decrease in system inertia

0.6

0.8

1

1.2

1.4

1.6

Fre

quency r

esponse r

eserv

e (

MW

)

104

Approach-1

Approach-2

(a) Frequency response reserve (MW)

0 10 20 30 40 50 60 70


0.4

0.6

0.8

1

1.2

RO

CO

F (

Hz/S

ec)

Approach-1

Approach-2

(b) Rate of change of frequency

0 10 20 30 40 50 60 70


59.2

59.3

59.4

59.5

59.6

59.7

59.8

Fre

quency n

adir (

Hz)

Approach-1

Approach-2

(c) Frequency nadir

Figure 8. Comparison of the available primary

frequency response for the two inertia–reduction

approaches.

that increasing penetration of inertia–less generatorsreduces the angular–stability margin of the system andcan potentially lead to a first–swing instability issueat some point. This was not observed in the resultsobtained using the first approach.

As synchronous generators are replaced withnon-inertial generators, fewer generators are availableto participate in oscillations. Thus, change in frequencyand damping ratio of system modes is expected based onthe dynamics of the online synchronous generators andparticipation of these generators in different oscillatorymodes. Figure 10 and Figure 11 compare the effect of

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0 10 20 30 40 50 60 70


65

70

75

80

85

90

Max. ro

tor

angle

(degre

e) Approach-1

Approach-2

Figure 9. Comparison of the effect of reduced

system inertia on the maximum rotor angle observed,

following a transient event, for the two approaches.

reduced system inertia on the frequency and dampingratio of three system modes. For approach-2, wheresynchronous generators are replaced with non-inertialgenerators, some changes in system modes wereobserved. However, the change in the frequency ofsystem modes did not follow any trend with the changein system inertia. Similar results were observed fordamping ratio of system modes, as can be seen in Figure11. Therefore, based on the results obtained, it canbe said that with increased renewable integration, anychanges in system modes will depend on the dynamicsof remaining online synchronous generators and not somuch on system inertia. Therefore, damping ratio ofsystem modes should not be a concern when consideringrenewable integration. However, when the reductionin system inertia was achieved by decreasing inertiaof generators, the impact of system inertia was clearlyobserved in system modes. As can be seen in Figure 10,the system mode frequency increased consistently withthe decrease in the inertia of the generators. This resultwas quite expected as the machines with lower mass(inertia) can oscillate at higher frequency as compared tothe ones with higher mass. Therefore, simply reducinginertia of machines across the system would resultin higher frequency system dynamics, which is notthe case when synchronous generators are replaced byinverter–based generators.

5. Conclusion

This paper analyzes the impact of reduced inertiain power systems using a large scale synthetic Texasmodel. The analysis is carried out by selectivelyreplacing synchronous generators with inertia-less windplants. As illustrated in the paper, the increasingpenetration level of inertia–less generators affects theangular stability margin and primary frequency responseof the system. As the proportion of inertia–less

0 10 20 30 40 50 60 70


0.6

0.7

0.8

0.9

1

1.1

1.2

frequency (

Hz)

Approach-1

Approach-2

(a) Mode–1

0 10 20 30 40 50 60 70


1

1.2

1.4

1.6

1.8

frequency (

Hz)

Approach-1

Approach-2

(b) Mode–2

0 10 20 30 40 50 60 70


1.2

1.4

1.6

1.8

2

2.2

2.4

frequency (

Hz)

Approach-1

Approach-2

(c) Mode–3

Figure 10. Comparison of the impact of reduced

system inertia on frequency of system modes for the

two inertia-reduction approaches.

generators increased, the rotor angle deviation observed,following a transient event, also increased indicatinga lower angular stability margin. Similarly, theavailable spinning reserve decreased as fewer generatorswere available to contribute to the primary frequencyresponse. This calls for a need of the fast frequencyresponse (FFR) generators, which can also includesynthetic inertia and battery storage, that can quicklycontribute to the system frequency recovery followinga generation-loss. The impact of reduced inertia on thesystem modes was not observed and changes in thesemodes were more likely caused by the change in systemtopology with fewer generators available to participatein system oscillations. This paper also demonstrated that

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0 10 20 30 40 50 60 70


5

10

15

20

25

DR

(%

)

Approach-1

Approach-2

(a) Mode–1

0 10 20 30 40 50 60 70


5

10

15

20

25

30

35

DR

(%

)

Approach-1

Approach-2

(b) Mode–2

0 10 20 30 40 50 60 70


10

12

14

16

18

20

22

24

DR

(%

)

Approach-1

Approach-2

(c) Mode–3

Figure 11. Comparison of the impact of reduced

system inertia on the damping ratio of system modes

for the two inertia-reduction approaches.

only reducing inertia of synchronous generators does notprovide an accurate analysis of the challenges associatedwith the increasing level of renewable integration. Asa part of future work, the capability of wind andsolar plants to provide fast frequency response will beexplored as measures to mitigate the impacts of higherlevel of renewable energy integration in the grid.

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A Study of the Impact of Reduced Inertia in Power Systems