Fast Computation of Steady-State
Stability Limits for Real-time
and Off-line Applications
presented at the 7th International Workshop on Electric
Power Control Centers, May 25-28, 2003, Ortisei, Italy
by
Savu C. Savulescu
ECI
Energy
Concepts
International, Inc.
Summary
ƒHow the electric industry works now
ƒNeed for fast maximum loadability
predictors
ƒTTC vs. stability envelope
ƒTwo-Step Steady-State Stability Limit
Evaluation Paradigm
ƒPaul Dimo's Simplified Steady-State
Stability Approach
ƒPractical implementation
How the Industry Works Now
ƒIn the past, networks were dispatched to follow
pre-planned scenarios
generation scheduled to meet forecasted load
ƒnetwork security assessed off-line and in real-time
ƒ
ystability conditions were predictable
ybroad range of applicability of off-line operating guidelines
ƒToday, networks are dispatched to
accommodate short-term and spot energy
transactions
driven by demand, price and availability
ƒbetween parties across multi-area networks
ƒ
Need for Fast Maximum Loadability
Predictors
ƒOpen Access Transmission mandated by law
but transmission providers can (and do) curtail
transactions that may impact the operating reliability
ƒ
ytransfer limits computed off-line may be very different from the
actual system capability
–need to recalculate limits as often as possible
ƒA mechanism is needed to predict danger
instability phenomena develop rapidly
ƒ
yno time to react
yunits out of synchronism and voltage collapse
how far from instability is the current system state?
ƒ
ƒHigh computational speed is a must
allow time for remedial action if not far from blackout
ƒ
TTC vs. Stability Envelope
ƒSteady-State Stability Limit (SSSL)
concept well understood (see next slide)
ƒthe "limit" is given by the amount of MW (internal
generation + imports) such that, for any loading smaller
than SSSL, the system is "stable" in the sense of small
signal stability
ƒmaximum MW transfer, voltage instability and steadystate instability occur at the same point
ƒ
ysingularity of the "dynamic state" Jacobian
ƒOperating states near this point are not safe
NERC defines the Total Transfer Capability (TTC) as a
safe operating limit
ƒ
no violations of any kind
ƒ
V
E
X
MW
SSSL = Maximum Power Transfer Capability =
TSL
EV
_______
X
TTC - Total Transfer Capability
Safe Operating Limit
(Stability Envelope)
Average Normal Operation
δ
TTC vs. Stability Envelope (cont'd)
ƒTransient Stability Limit (TSL) or TTC (NERC)
a "limit" in the sense defined above is difficult, if not
impossible to determine
ƒ
yit would require examining every possible mix of generation,
load and voltages for a succession of increased MW levels until
the system becomes unstable
TTC (TSL) is an elusive target
ƒhowever, intuitively, it can be asserted that
ƒ
yTSL is always smaller than SSSL
ywhen SSSL increases / decreases, so does TSL
–probably some % level, e.g. TSL < 0.8 SSSL
–steady-state stability reserve
TTC vs. Stability Envelope (cont'd)
ƒInstead of attempting to compute TTC ...
ƒDefine a stability envelope as follows:
first, calculate the maximum power transfer limit then, for a
given x% security margin (stability reserve)
ƒdetermine the safe system MW loading limit that corresponds
to the current operating state
ƒ
ƒHow to...
detailed analysis -- good for off-line studies, but not (or ... not
yet) suitable for fast simulations
ƒfast approximate methods -- useful for quick decision making
ƒ
ybut the speed must be predicated on solid theoretical ground
Two-Step Steady-State Stability Limit
Evaluation Paradigm
ƒStep 1: run a quick stability check
determine "how far from instability"
ƒidentify "stability envelope"
ƒ
ybased on a user-defined "x% security margin"
when evaluating MW transactions across multi-area
systems, run stability checks on
ƒ
yspecific areas within larger networks
yinterchange interfaces between areas
ƒStep 2: if needed, go to full analysis
cases situated outside the stability envelope may
need to be evaluated in detail
ƒ
Paul Dimo's Simplified Steady-State
Stability Approach
ƒField-proven -- published in RGE in November 1961
used in production-grade studies for many years
ƒPrix Montefiore in 1981
ƒ
ƒPredicated on
short-circuit currents
ƒ
yradial network of short-circuit admittances
practical steady-state stability criteria
ƒ
ysimple algebraic computations instead of eigenvalues
simplified representation of generators
ƒ
yall the machines are modeled -- constant e.m.f. behind x'd
fictitious load-center - Zero Power Balance Network
ƒ
yFelix Wu (1978) identified theoretical conditions for correctness
”case worsening procedure”
ƒ
yinstead of successive load-flows
Short-Circuit Currents
ƒBarbier & Barret (1980)
used short-circuit currents to develop critical voltage and
maximum power transfer formulae
ƒ
ƒPaul Dimo (1961)
used short-circuit currents to formulate the dQ/dV criterion
for steady-state stability
ƒ
ƒNext slides illustrate the concept of "short-circuit
currents" - the system "as seen" from a load bus
physically, the currents flow from generators to load
ƒmathematically, generators are connected to each load bus
through short-circuit admittances
ƒ
Ieq = Ish-c - Ysh-c Vload
Iload = Ish-c - Ish-c no-load
(Barbier-Barret)
(Dimo)
Sample Power System
1
2
L1
G
L2
Sample System Replaced with the
Short-Circuit Currents
System "seen" from L1
System "seen" from L2
2
2
G
1
L1
G
1
L2
Another View of the
Short-Circuit Currents Model -- the REI Net
m
m
1
G
1
G
i
i
Ii = Σ Yim Em - Yii Vi
Yii = Σ Yim + Yio
Ii = Σ Yim Em - (Σ Yii + Yio) Vi
Ishc-noload
Iload
Ii = Ii-sc - Ii-o
The Zero Power Balance Network Concept
adding a network without losses to obtain a Single Load Center
j
i
Y o-j
Loads
Synchronous Machines
O'
Fictitious Ground
YFL
Other Injections
V FL
I' FL
Single Load Center
I FL S
Ground
FL
Steady-State Stability Criteria
ƒsteady-state stability criteria
exact -- eigenvalues of the characteristic equation
ƒalgebraic -- singularity of the Jacobian matrix (J) for the
"dynamic state equations"
ƒpractical -- dQ/dV, dP/dδ and dP/dV
ƒ
yVenikov, Dimo: under certain conditions, the dQ/dV and J criteria are
equivalent
ysuitable for the short-circuit currents model
Suggested reading:
V. Venikov, "Transient Processes in Electrical Power Systems", MIR
Publishers, Moscow, 1977
Barbier, C., Barret, J.P., "An Analysis of Phenomena of Voltage Collapse on a
Transmission System", RGE, Paris, Vol. 89, 10, 672-690
Dimo, Paul, "Etude de la Stabilite Statique et du Reglage de Tension",
Revue Generale de l'Electricite RGE, Paris, 1961, Vol. 70, 11, 552-556
Steady-State Stability Criteria (cont'd)
For m generators connected radially to a load bus through shortcircuit admittances, dQ/dV can be computed with the formula
dQ/dV = Σ(YmEm/cosδm) - 2(ΣYm + Yload)V
Yload = Qload/VV
= e.m.f. behind transient or synchronous reactance of
Em
the machine m
= internal angle of machine m
δm
= admittance between machine m and the single-load bus
Ym
V
= voltage magnitude at the single-load bus
Practical Implementation
Near-Blackout Event
August 22, 2002
ETESA, Panama
15:14:37 hours - lighting strike
on 220 kV circuit -- permanent
short-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 hours
three units come back on line
voltage starts to improve
1950s Practical Steady-State Stability Criteria - Venikov, Markovici, Moscow, USSR
1961 Short-Circuit Currents Method Steady-State Stability Analysis - Dimo, RGE, Paris
1980 Short-Circuit Currents Method Voltage Stability Analysis - Barret, Barbier, RGE, Paris
1990-1992 Steady-State Stability Monitor Prototype - EPRI, Palo Alto, CA
Sponsorship from Southern Company Services, Birmingham, AL
1993
Method Presented at IEEE Winter Power Meeting, New York, NY
1994
QuickStab announcement -- first experimental installations at
Southern Company Services, Birmingham, AL
IREQ HydroQuebec, Montreal, Canada
QuickStab® -- production-grade off-line and real-time
1998-2000
CPTEE, Sao Paulo, Brazil (Off-line and Real-time)
OPSIS, Caracas, Venezuela (Real-time on Compaq Unix)
Southern Company Services (Windows NT & SUN Solaris)
TTI, Guatemala (Off-line on Windows 98)
MultiArea QuickStab® (MultiArea Transfer Capability Analyzer)
2001-2002
ETESA, Panama: Off-line on Windows 2000
Real-time on Compaq Unix
MultiArea QuickStab® on the Web
2002-2003 ETESA, Panama -- TRANSELECTRICA, Romania
2003 -- QuickStab® Professional