12 rajunitrate.pdf

7/27/2019 12 rajunitrate.pdf

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Fast Computation of SteadyFast Computation of Steady--StateState

Stability Limits for RealStability Limits for Real--timetime

and Offand Off--line Applicationsline Applications

presented at the 7th International Workshop on Electricpresented at the 7th International Workshop on Electric

Power Control Centers, May 25Power Control Centers, May 25--28, 2003, Ortisei, Italy28, 2003, Ortisei, Italy

byby

Savu C. SavulescuSavu C. SavulescuEnergy

Concepts

International, Inc.

CIE


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SummarySummary

How the electric industry works nowHow the electric industry works now

Need for fast maximum loadabilityNeed for fast maximum loadability

predictorspredictors

TTC vs. stability envelopeTTC vs. stability envelopeTwoTwo--Step SteadyStep Steady--State Stability LimitState Stability Limit

Evaluation ParadigmEvaluation Paradigm

Paul Dimo's Simplified SteadyPaul Dimo's Simplified Steady--StateState

Stability ApproachStability Approach

Practical implementationPractical implementation


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How the Industry Works NowHow the Industry Works NowIn the past, networks were dispatched to followIn the past, networks were dispatched to follow

prepre--planned scenariosplanned scenariosgeneration scheduled to meet forecasted loadgeneration scheduled to meet forecasted load

network security assessed offnetwork security assessed off--line and in realline and in real--timetime

yystability conditions were predictablestability conditions were predictableyybroad range of applicability of offbroad range of applicability of off--line operating guidelinesline operating guidelines

Today, networks are dispatched toToday, networks are dispatched to

accommodate shortaccommodate short--term and spotterm and spot energyenergytransactionstransactions

driven by demand, price and availabilitydriven by demand, price and availability

between parties across multibetween parties across multi--area networksarea networks


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Need for Fast Maximum LoadabilityNeed for Fast Maximum Loadability

PredictorsPredictors

Open Access Transmission mandated by lawOpen Access Transmission mandated by law

but transmission providersbut transmission providers cancan (and(and dodo) curtail) curtailtransactions that may impact the operating reliabilitytransactions that may impact the operating reliability

yytransfer limits computed offtransfer limits computed off--line may be very different from theline may be very different from the

actual system capabilityactual system capability

need to recalculate limits as often as possibleneed to recalculate limits as often as possible

A mechanism is needed toA mechanism is needed to predictpredict dangerdanger

instability phenomena develop rapidlyinstability phenomena develop rapidly

yyno time to reactno time to reactyyunits out of synchronism and voltage collapseunits out of synchronism and voltage collapse

how far from instability is the current system state?how far from instability is the current system state?

High computational speed is aHigh computational speed is a mustmustallow time for remedial action if not far from blackoutallow time for remedial action if not far from blackout


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TTC vs. Stability EnvelopeTTC vs. Stability EnvelopeSteadySteady--State Stability Limit (SSSL)State Stability Limit (SSSL)

concept well understood (see next slide)concept well understood (see next slide)the "limit" is given by the amount of MW (internalthe "limit" is given by the amount of MW (internal

generation + imports) such that, for any loading smallergeneration + imports) such that, for any loading smaller

than SSSL, the system is "stable" in the sense of smallthan SSSL, the system is "stable" in the sense of small

signal stabilitysignal stability

maximum MW transfer, voltage instability and steadymaximum MW transfer, voltage instability and steady--

state instability occur at the same pointstate instability occur at the same point

yysingularity of the "dynamic state" Jacobiansingularity of the "dynamic state" Jacobian

Operating states near this point are not safeOperating states near this point are not safe

NERC defines the Total Transfer Capability (TTC) as aNERC defines the Total Transfer Capability (TTC) as a

safe operating limitsafe operating limitno violations of any kindno violations of any kind


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TSL

MW

SSSL = Maximum Power Transfer Capability =E V

_______

X

Average Normal Operation

TTC - Total Transfer Capability

Safe Operating Limit(Stability Envelope)

X

VE


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TTC vs. Stability Envelope (cont'd)TTC vs. Stability Envelope (cont'd)

Transient Stability Limit (TSL) or TTC (NERC)Transient Stability Limit (TSL) or TTC (NERC)

a "limit" in the sense defined above is difficult, if nota "limit" in the sense defined above is difficult, if notimpossible to determineimpossible to determine

yyit would require examining every possible mix of generation,it would require examining every possible mix of generation,

load and voltages for a succession of increased MW levels untilload and voltages for a succession of increased MW levels until

the system becomes unstablethe system becomes unstable

TTC (TSL) is an elusive targetTTC (TSL) is an elusive target

however, intuitively, it can be asserted thathowever, intuitively, it can be asserted that

yyTSL isTSL is alwaysalways smaller than SSSLsmaller than SSSLyywhen SSSL increases / decreases, so does TSLwhen SSSL increases / decreases, so does TSL

probably some % level, e.g. TSL < 0.8 SSSLprobably some % level, e.g. TSL < 0.8 SSSL

steadysteady--state stability reservestate stability reserve


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TTC vs. Stability Envelope (cont'd)TTC vs. Stability Envelope (cont'd)

Instead of attempting to compute TTC ...Instead of attempting to compute TTC ...

Define aDefine a stability envelopestability envelope as follows:as follows:first, calculate the maximum power transfer limit then, for afirst, calculate the maximum power transfer limit then, for a

given x% security margin (stability reserve)given x% security margin (stability reserve)

determine the safe system MW loading limit that correspondsdetermine the safe system MW loading limit that corresponds

to the current operating stateto the current operating state

How to...How to...

detailed analysisdetailed analysis ---- good for offgood for off--line studies, but not (or ... notline studies, but not (or ... notyetyet) suitable for fast simulations) suitable for fast simulations

fast approximate methodsfast approximate methods ---- useful for quick decision makinguseful for quick decision making

yybut the speed must be predicated on solid theoretical groundbut the speed must be predicated on solid theoretical ground


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TwoTwo--Step SteadyStep Steady--State Stability LimitState Stability Limit

Evaluation ParadigmEvaluation Paradigm

Step 1: run a quick stability checkStep 1: run a quick stability check

determine "how far from instability"determine "how far from instability"

identify "stability envelope"identify "stability envelope"

yybased on a userbased on a user--defined "x% security margin"defined "x% security margin"

when evaluating MW transactions across multiwhen evaluating MW transactions across multi--areaareasystems, run stability checks onsystems, run stability checks on

yyspecific areas within larger networksspecific areas within larger networks

yyinterchange interfaces between areasinterchange interfaces between areas

Step 2: if needed, go to full analysisStep 2: if needed, go to full analysis

cases situated outside the stability envelope maycases situated outside the stability envelope may

need to be evaluated in detailneed to be evaluated in detail


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Paul Dimo's Simplified SteadyPaul Dimo's Simplified Steady--StateState

Stability ApproachStability ApproachFieldField--provenproven ---- published in RGE in November 1961published in RGE in November 1961

used in productionused in production--grade studies for many yearsgrade studies for many years

Prix Montefiore in 1981Prix Montefiore in 1981

Predicated onPredicated on

shortshort--circuit currentscircuit currents

yyradial network of shortradial network of short--circuit admittancescircuit admittances

practical steadypractical steady--state stability criteriastate stability criteria

yysimple algebraic computations instead of eigenvaluessimple algebraic computations instead of eigenvalues

simplified representation of generatorssimplified representation of generatorsyyall the machines are modeledall the machines are modeled ---- constant e.m.f. behind x'dconstant e.m.f. behind x'd

fictitious loadfictitious load--centercenter-- Zero Power Balance NetworkZero Power Balance Network

yyFelix Wu (1978) identified theoretical conditions for correctnesFelix Wu (1978) identified theoretical conditions for correctnesss

case worsening procedurecase worsening procedureyyinstead of successive loadinstead of successive load--flowsflows


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ShortShort--Circuit CurrentsCircuit Currents

Barbier & Barret (1980)Barbier & Barret (1980)

used shortused short--circuit currents to develop critical voltage andcircuit currents to develop critical voltage andmaximum power transfer formulaemaximum power transfer formulae

Paul Dimo (1961)Paul Dimo (1961)

used shortused short--circuit currents to formulate the dQ/dV criterioncircuit currents to formulate the dQ/dV criterionfor steadyfor steady--state stabilitystate stability

Next slides illustrate the concept of "shortNext slides illustrate the concept of "short--circuitcircuit

currents"currents" -- the system "as seen" from a load busthe system "as seen" from a load bus

physically, the currents flow from generators to loadphysically, the currents flow from generators to load

mathematically, generators are connected to each load busmathematically, generators are connected to each load bus

through shortthrough short--circuit admittancescircuit admittances

IIeqeq == IIshsh--cc --YYshsh--cc VVloadload (Barbier(Barbier--Barret)Barret)

IIloadload == IIshsh--cc -- IIshsh--c noc no--loadload (Dimo)(Dimo)


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Sample Power System

L11

2 L2

G


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Sample System Replaced with the

Short-Circuit Currents

System "seen" from L1 System "seen" from L2

2

L1

2

L2

G G1 1


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Another View of the

Short-Circuit Currents Model -- the REI Net

1

i

m

i

m

1 G

G

Yii = Yim + YioIshc-noload Iload

Ii = Yim Em - Yii Vi

Ii = Yim Em - ( Yii + Yio) Vi Ii = Ii-sc - Ii-o


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The Zero Power Balance Network Concept

adding a network without losses to obtain a Single Load Center

i j

YFL I'FL

Yo-j

Synchronous MachinesFictitious Ground

Loads

O'

Other Injections

VFL

Ground

I FLS

Single Load Center

FL


17/21

SteadySteady--State Stability CriteriaState Stability Criteria

steadysteady--state stability criteriastate stability criteria

exactexact ---- eigenvalues of the characteristic equationeigenvalues of the characteristic equationalgebraicalgebraic ---- singularity of the Jacobian matrix (J) for thesingularity of the Jacobian matrix (J) for the

"dynamic state equations""dynamic state equations"

practicalpractical ---- dQ/dV, dP/ddQ/dV, dP/d and dP/dVand dP/dVyyVenikov, Dimo: under certain conditions, the dQ/dV and J criteriVenikov, Dimo: under certain conditions, the dQ/dV and J criteria area are

equivalentequivalent

yysuitable for the shortsuitable for the short--circuit currents modelcircuit currents model

Suggested readingSuggested reading::

V. Venikov, "Transient Processes in Electrical Power Systems", MV. Venikov, "Transient Processes in Electrical Power Systems", MIRIR

Publishers, Moscow, 1977Publishers, Moscow, 1977

Barbier, C., Barret, J.P., "An Analysis of Phenomena of VoltageBarbier, C., Barret, J.P., "An Analysis of Phenomena of Voltage Collapse on aCollapse on a

Transmission System", RGE, Paris, Vol. 89, 10, 672Transmission System", RGE, Paris, Vol. 89, 10, 672--690690

Dimo, Paul, "Etude de la Stabilite Statique et du Reglage de TenDimo, Paul, "Etude de la Stabilite Statique et du Reglage de Tension",sion",

Revue Generale de l'Electricite RGE, Paris, 1961, Vol. 70, 11, 5Revue Generale de l'Electricite RGE, Paris, 1961, Vol. 70, 11, 55252--556556


18/21

SteadySteady--State Stability Criteria (cont'd)State Stability Criteria (cont'd)

For m generators connected radially to a load bus through shortFor m generators connected radially to a load bus through short--

circuit admittances, dQ/dV can be computed with the formulacircuit admittances, dQ/dV can be computed with the formula

dQ/dV =dQ/dV = (Y(YmmEEmm/cos/cosmm)) --2(2(YYmm + Y+ Yloadload)V)V

YYloadload = Q= Qloadload/VV/VV

EEmm = e.m.f. behind transient or synchronous reactance of= e.m.f. behind transient or synchronous reactance of

the machine mthe machine m

mm = internal angle of machine m= internal angle of machine mYYmm = admittance between machine m and the single= admittance between machine m and the single--load busload bus

VV = voltage magnitude at the single= voltage magnitude at the single--load busload bus


19/21

Practical ImplementationPractical Implementation

N Bl k t E t


20/21

Near-Blackout Event

August 22, 2002

ETESA, Panama

15:14:37 hours - lighting strike

on 220 kV circuit -- permanentshort-circuit

15:15:00 hours -- loss of

generation

15:18:43 hours -- three more

units are lost

load shedding request not

honored by DisCos

severe reduction of MVAr

15:26:00 to 15:27:00 hoursthree units come back on line

voltage starts to improve

1950s Practical Steady-State Stability Criteria - Venikov, Markovici, Moscow, USSR


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1980 Short-Circuit Currents Method Voltage Stability Analysis - Barret, Barbier, RGE, Paris

1961 Short-Circuit Currents Method Steady-State Stability Analysis - Dimo, RGE, Paris

Sponsorship from Southern Company Services, Birmingham, AL1990-1992 Steady-State Stability Monitor Prototype - EPRI, Palo Alto, CA

1993 Method Presented at IEEE Winter Power Meeting, New York, NY

1994 QuickStab announcement -- first experimental installations at

Southern Company Services, Birmingham, ALIREQ HydroQuebec, Montreal, Canada

QuickStab-- production-grade off-line and real-time

OPSIS, Caracas, Venezuela (Real-time on Compaq Unix)Southern Company Services (Windows NT & SUN Solaris)

1998-2000 CPTEE, Sao Paulo, Brazil (Off-line and Real-time)

TTI, Guatemala (Off-line on Windows 98)

MultiArea QuickStabon the Web

2001-2002 ETESA, Panama: Off-line on Windows 2000Real-time on Compaq Unix

MultiArea QuickStab(MultiArea Transfer Capability Analyzer)

2002-2003 ETESA, Panama -- TRANSELECTRICA, Romania

2003 -- QuickStabProfessional

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12 rajunitrate.pdf