Note : Les descriptions sont présentées dans la langue officielle dans laquelle elles ont été soumises.
CA 02602980 2007-09-19
METHOD AND SYSTEM FOR REAL TIME IDENTIFICATION OF
VOLTAGE STABILITY VIA IDENTIFICATION OF WEAKEST LINES AND
BUSES CONTRIBUTING TO POWER SYSTEM COLLAPSE
Field of the Invention
This invention relates to methods of preventing voltage collapse of power
systems in
electric utilities, and more particularly to methods of real time monitoring
of voltage
stability at such utilities.
Background of the Invention
The problem of voltage instability has been a major concern of electric
utilities for a
long time. This problem has drawn great interest as voltage instability-
related outage
events occur around the world and result in blackouts. Although considerable
efforts
have been devoted to voltage stability assessment methods, most are only
usable in
off-line applications.
The most popular method of assessing voltage stability is the use of
continuation
power flow to identify the collapse point where the system power flow
diverges, as
disclosed in "Assessment of Voltage Security Methods and Tools", EPRI report
TR-
105214, 1995; and Taylor C W, "Power system voltage stability [M]," McGraw-
Hill,
Inc., New York, America, 1994. This method is widely employed in the industry,
and
serves as a reference to new methods. Disadvantages of the continuation power
flow
method include:
= Considerable system-wide power flow calculations making the method difficult
to
implement in a real time application;
= Impossible to accurately handle actual time-dependent load characteristics
(voltage-
and frequency-related loads);
= Possible premature divergence in system continuation power flows;
= Inaccurate line parameters (resistance and reactance of lines), which are
assumed to
be constant in any environment or weather condition;
DM VAN/260254-OOI04/6737612.1 1
CA 02602980 2007-09-19
= Inconsistency between off-line model and real life situation; and
= Incapability to identify weak lines and buses that cause system collapse.
Various voltage stability indices have been proposed for voltage instability.
The
indices may be divided into two types: system-wide indices and localized
indices. The
system-wide indices are based on system power flow calculations (as disclosed
in
Young Huei Hong, Ching Tsai Pan, and Wen Wei Lin, "Fast calculation of a
voltage
stability index of power systems [J]," IEEE Trans. on Power Syst., vol. 12,
no. 4, pp.
1555-1560, Nov. 1997; and P Kessel, H Glavitsch, "Estimating the voltage
stability of
a power system [J]," IEEE Trans on Power Delivery, vol. PWRD-1, no.3, pp. 346-
354,
July 1986) and thus have the same disadvantages as the continuation power flow
method. The localized indices focus on individual buses (as disclosed in Ivan
Smon,
Gregor Verbic, and Ferdinand Gubina, "Local voltage-stability index using
Tellegen's
theorem [J]," IEEE Trans. on Power Syst., vol. 21, no. 3, pp. 1267-1275, Aug.
2006;
and K. Vu, M.M. Begovic, D. Novosel and M. M. Saha, "Use of local measurements
to estimate voltage stability margin," IEEE Trans. Power Systems, Vol. 14, No.
3,
pp1029-1035, August 1999) or lines (as disclosed in M. Moghavvemi and M.O.
Faruque, "Power system security and voltage collapse: a line outage based
indicator
for prediction [J]," Electrical Power and Energy Systems, Vol. 21, pp.455-461,
1999;
B. Venkatesh, R. Ranjan, and H.B. Gooi, "Optimal reconfiguration of radial
distribution systems to maximize loadability [J]," IEEE Trans. on Power Syst.,
vol. 19,
no. 1, pp. 260-266, Feb. 2004; and M. Moghavvemi "New method for indicating
voltage stability condition in power system [C]," Proceeding of IEE
International
Power Engineering Conference, IPEC 97, Singapore, pp. 223-227), and generally
do
not require continuation power flow calculations and are relatively easy for
use in the
on-line environment. However, problems of prior art localized indices include
inaccuracy in theoretical derivation and calculations; and incapability to
filter invalid
measurements. The indices Lp and Lq, given in the Moghavvemi references above,
cannot reach the expected value at the system collapse point even in the
results of the
authors' example. In fact, studies found that these two indices are based on
an
implied assumption of the line impedance factor being equal to the power
factor,
which is not true in most cases. The index presented in the Venkatesh
reference
targets a radial distribution line with an assumption of constant voltage at
the sending
DM_VAN/260254-00104/6737612.1 2
CA 02602980 2007-09-19
bus, which is not true in looped transmission systems. Also, its denominator
can be
mathematically zero in which case the index becomes meaningless. Particularly,
all
the existing line indices do not consider impacts of the whole system beyond
the line
so they do not provide accurate and correct information in actual
applications.
The localized index disclosed in the Smon and Vu references, and in the US
Patent
No. 6219591 and US Patent No. 6690175 is based on the Thevenin theorem and
conceptually can be used in real time applications. Unfortunately, such index
and
method have the following concerns and disadvantages:
= The calculation of the index requires measurements of voltages and currents
in at
least two system states and is based on the assumption that the equivalent
Thevenin
voltage and impedance are constant in the two system states. If the two system
states are far apart, this assumption is invalid whereas if they are too
close, it may
result in a large calculation error for the estimate of equivalent Thevenin
impedance.
This assumption therefore, causes inaccuracy and difficulties in the actual
implementation.
= The method has no way to identify any wrong or invalid measurement. If any
measurement of voltages or currents is incorrect or has a relatively large
error,
which can happen in any real measurement system, the index becomes useless.
= The index cannot identify the weak lines that cause system collapse.
= The method cannot be implemented using the existing SCADA (Supervisory
Control And Data Acquisition) measurements and EMS (Energy Management
Systems), which are available at utility control centers.
US Patent No. 6232167 discloses a method to identify weak lines (branches)
only. US
Patent No. 6904372 disclose a method to identify weak buses only. Neither of
these
methods is designed for identification of system instability. US Patent No.
5610834
discloses a method to improve voltage stability using a P-V curve approach,
and US
Patent No. 5745368 discloses a method to reduce computing efforts in
calculating the
voltage collapse point on a P-V or Q-V curve. Such methods are based on off-
line
system power flow calculations and cannot be used in a real time environment.
US
Patent No. 7096175 discloses a technique to predict system stability by using
phasor
DM VAN/260254-00104/6737612.1 3
CA 02602980 2007-09-19
measurements and conducting a fast system power flow calculation after a
contingency. However, the time-varying characteristics of line parameters
(resistance
and reactance) are not considered. Also, the method cannot be used to identify
weakest lines or buses that cause system instability as its criterion is based
on the
divergence of power flow calculations of whole system.
Summary of the Invention
The method and system according to the invention provide a new localized
voltage
stability index, referred to herein as Extended Line Stability Index (ELSI),
the method
of calculating the ESLI, and implementation aspects in a real time
environment. Some
features of the method and system according to the invention include:
= Simultaneous and real time identification of system instability as well as
weakest
lines (branches) and buses causing system collapse;
= No system-wide power flow calculations are required (the system can perform
very
fast calculations that generally take less than 0.1-0.5 seconds);
= Real time estimation of time-varying system parameters (line resistance,
reactance
and grounding admittance);
= Automatic handling of actual load characteristics (voltage-related or
frequency-
related loads);
= Capable of filtering invalid or bad measurements;
= Less calculation errors compared to methods based on the Thevenin theorem;
= Can be used to trigger a RAS (remedial action scheme) for protecting the
power
system from voltage collapse; and
= Can be implemented using either Phasor Measurement Unit (PMU) information
(which provides greater accuracy) or existing SCADA information and EMS
environment.
A method of identifying voltage instability in a power system having a
plurality of
monitored transmission lines is provided, including (a) receiving periodic
input
DM VAN/260254-00104/6737612.I 4
CA 02602980 2007-09-19
regarding said plurality of transmission lines; (b) calculating an index for
each of said
plurality of transmission lines in said power system using said input; and (c)
identifying a weakest line amongst said plurality of transmission lines, said
weakest
line having a lowest calculated index amongst said plurality of transmission
lines.
The periodic input may be received from a plurality of phasor measurement
units, the
inputs including, a voltage magnitude Vi at a sending bus i, a voltage
magnitude V at
a receiving bus j of each transmission line i-j, , a voltage angle 9i at the
sending bus
and a voltage angle 6i at the receiving bus; a line power flow PIj+jQij with a
charging
reactive power included at the receiving bus; and a line power flow Pi+jQi
with a
charging reactive power included at the sending bus. The index for each of the
transmission lines between the sending bus i and the receiving bus j, may be
calculated as:
BLSI= V `2 >_ 1
2[R,jPõ +X,j+ (R;; +X;; )(Pj +(Q,;),)l
wherein Rij+jX y, is a line impedance associated with the transmission line i -
j, and
the line impedance is calculated using the input, the input received from a
plurality of
phasor measurement units; Pj;+jQ*;j is a line power flow with a charging
reactive
power excluded at the receiving bus j, wherein Pij is received from the phasor
measurement units, and Q*jJ is calculated using the input; and Vi is a voltage
at the
sending bus and is received from the phasor measurement units.
The index for each of the transmission lines between a sending bus i and a
receiving
bus j, may be calculated as:
ELSI= Ek > 1
2[RkjPij +XkjQij F (Rkj +Xkj)(Pj +(Qii)2)]
wherein Rkj+jXkj is an equivalent extended line impedance associated with the
transmission line i - j, and is calculated using the input, the input received
from a
plurality of phasor measurement units; Pij+jQ*;1' is a line power flow with a
charging
reactive power excluded at the receiving bus j, wherein Pij is received from
the phasor
measurement units and Q*;j is calculated using the received input; and Ek is
an
D MV AN/260254-00104/6737612.1 5
CA 02602980 2007-09-19
equivalent source voltage, and is calculated using the received input from the
plurality
of phasor measurement units.
If the index of at least one transmission line in the power system is equal to
or less
than a predetermined threshold, a remedial action scheme may be undertaken to
protect the system from voltage collapse. The remedial action scheme may
protect
the system from voltage collapse in a normal operation state of the system or
in a
contingency state of the system.
The periodic input may be received from a state estimator using supervisory
control
and data acquisition measurements, the input including a line impedance
associated
with the transmission line; a voltage magnitude at a sending bus and a voltage
magnitude at a receiving bus of the transmission line respectively, a voltage
angle at
the sending bus and a voltage angle at the receiving bus of the line; a line
power flow
with a charging reactive power at the receiving bus;, a line reactive power
flow at the
receiving bus; and a line power flow with a charging reactive power at the
sending
bus.
A method of using synchronized measurements from phasor measurement units to
calculate a plurality of indices is provided, each of the indices associated
with a
transmission line within a power system, for predicting voltage instability of
the
power system including (a) receiving periodic measurements from the phasor
measurement units; (b) filtering invalid data amongst the measurements; (c)
estimating parameters associated with the transmission lines; and (d)
calculating the
indices associated with the transmission lines. The measurements may be
voltage
phasors and current phasors at a sending bus and a receiving bus of each of
the
transmission lines; and the parameters may bee resistance, reactance and
grounding
admittance of each of the transmission lines.
A method of identifying voltage instability in a power system having a
plurality of
monitored lines, via identification of a weakest line in said system capable
of
contributing to the collapse of said system, is provided, including the steps
of: (a)
obtaining measurements associated with each of the transmission lines from a
measurement source; (b) obtaining values of a plurality of parameters
associated with
DM_VAN/260254-00104/6737612.1 6
CA 02602980 2007-09-19
the plurality of power lines; and (c) calculating an index for each of the
plurality of
lines, such that the lowest index associated with a line identifies the
weakest line.
The measurement source may be a state estimator using supervisory control and
data
acquisition measurements.
The measurements for each of the transmission lines i - j may include: a
voltage
magnitude V; at a sending bus i and a voltage magnitude Vj of a receiving bus
j of the
line i-j; and a voltage angle 9; at the sending bus i; and a voltage angle Bi
at the
receiving bus i; a line power flow P;j+jQ;~ with a charging reactive power
included at
the receiving bus; and a line power flow P;+jQ; with a charging reactive power
included at the sending bus.
The method may include filtering invalid measurements from the measurements
obtained from the phasor measurement units; and the parameters may include
resistance, reactance and admittance of each of the transmission lines, and
the values
of at least one of the plurality of parameters may be estimated.
A system for identifying voltage instability in a power grid is provided
including: a
plurality of monitored transmission lines; a computer; and a measurement
source,
wherein the measurement source provides measurements associated with at least
some
of the transmission lines to the computer, and the computer calculates an
index for
each of the plurality of transmission lines, such that the lowest value index
associated
with the lines identifies a weakest transmission line amongst the plurality of
transmission lines. The measurement source may be a state estimator using
supervisory control and data acquisition measurements. The measurement source
may be a plurality of phasor measurement units.
Brief Description of the Figures
Figure 1 is a one-line diagram of a typical transmission line i-j;
Figure 2 is an equivalent representation of a transmission line i-j and the
system
outside the line i-j;
Figure 3 is a representation of the IEEE 30 bus test system;
DM VAN/260254-00104/6737612.1 7
CA 02602980 2007-09-19
Figure 4 is a chart showing the ELSI of the two weakest lines decreasing as
the load
at Bus 30 increases;
Figure 5 is a representation of a portion of the British Columbia Transmission
Corporation system;
Figure 6 is a chart showing the ELSI of line 5L96 of the British Columbia
Transmission Corporation (BCTC) system in normal states (decreasing as its
loading
level is stressed);
Figure 7 is a chart showing the ELSI of line 5L96 while line 5L91 is out-of-
service
(decreasing as its loading level is stressed);
Figure 8 is a chart showing the ELSI of line 5L92 while line 5L91 is out-of-
service
(decreasing as its loading level is stressed);
Figure 9 is a chart showing the ELSI of line 5L98 while line 5L91 is out-of-
service
(decreasing as its loading level is stressed);
Figure 10 is a chart showing the ELSI of line 5L96 (a sudden decline towards
1.0
after line 5L91 trips); and
Figure 11 is a chart showing the ELSI of line 5L96 when line 5L91 trips at two
different loading levels of line 5L96.
Detailed Description of the Invention
Note that in this document, the unit of all quantities is referenced in per
unit system;
all quantities related to real or reactive power refer to the total power in
three phases;
and voltage quantities to refer to the line voltage.
Basic line voltage stability index
Described below is the derivation of the basic line stability index (BLSI),
which
demonstrates a concept behind the method according to the invention. After the
derivation of the BSLI is described, the derivation of the extended line
stability index
(ELSI) is provided, which is used in actual applications according to the
invention,
and finally, implementation issues are addressed.
DM-vAN/260254-00104/6737612.1 8
CA 02602980 2007-09-19
In any complex transmission system, if there exists at least one line (branch)
on which
the loading level exceeds the line's maximum transfer capability, the system
will lose
its voltage stability. The maximum transfer capability of a line can be
determined
from the criterion for a system state: if the sending bus voltage exists but
there is no
mathematical solution for the receiving bus voltage due to sufficiently large
loading
level and line impedance, this loading level reaches the maximum transfer
capability
of the line. In other words, if any line loses voltage stability, the whole
system
collapses in this state.
Figure 1 shows the 7t-equivalent circuit of a single line (or branch) in a
looped
transmission system. R;~+jX;~ is the line impedance. Y represents half of the
grounding admittance corresponding to charging reactive power of the line.
viLB;
and VjLe j are the voltage phasors at the sending and receiving buses. P;+jQ;
and
P;+jQ*; are the line power flows respectively before and after the charging
reactive
power at the sending bus i. P,~+jQ*;~ and P;~+jQ,i are the line power flows
before and
after the charging reactive power at the receiving bus j. Q;o and QJo
represent the
charging reactive powers at the sending and receiving ends respectively. In
the real
application, only P;, Q;, P;j and Q;j are measurable through PMUs whereas Q*;
and Q*;j
can be calculated using Q; and Q;j and the charging reactive power. The
charging
reactive power occurs along the line but the total charging reactive power can
be
calculated by the difference between Q; and Q~; minus the reactive losses on
the line.
In the following derivation of BLSI, the line flows of P;+jQ*; and P;i+jQ*;j
between the
nodes A and B are used to develop the concise relationship between voltage
stability
and the parameters and loading of the lines. The use of measurable Q; and Q;j
to
obtain Q*; and Q*;i is described below in respect of the implementation of
real-time
voltage instability identification.
The line (branch) power flow equation of P;;+jQ*;i can be expressed as:
* ~V;LB; -V =LB ~ ~
Pij +jQij =V~LBj l 1 (1)
Ri J + jX ;~
wherein the symbol O denotes the conjugate operation.
Separating Equation (1) into the real and imaginary parts yields:
DM VAN/260254-00104/6737612.1 9
CA 02602980 2007-09-19
Rii Pi~ +Xii Q~ =-V~ +V,Vj cosBji (2)
RijQ -Xi-Pj =ViV. sinB.i (3)
wherein Bji=9i-Bi.
By eliminating the angle difference 9ii from Equations (2) and (3), the
following
double quadratic equation with V? as an unknown variable is obtained:
~ 2
*
V4+2(RijPj+XijQij- )Vj +(Rj+Xi?)(Pi.j +(Qij)2)=0 (4)
When the discriminant of Equation (4) is greater than or equal to 0, that is,
2 2
RijPj+XijQ~-V2 -(R~+X~)(I'ij +(Q~ ij)2)?0 (5)
then Equation (4) has the following two solutions:
~ v
V~ = -Rij Pij + X ij Qij ' 2
2 2
RijPj+XijQ~j ~ -(R;~+X~)(Pj +(Qij)2) (6)
As (R;~+X,~)(Py +(Q~)2)>_0, it follows that:
2 2 ~ * V-2
RijPij+XijQ'j -VZ -(Ri~+Xij)(Pj +(Qij)2 < RijPj+XijQij~
So that Vj can have two positive real number solutions from Equation (6), the
following Equation (7) must hold:
2
RijPij +XijQij* - Vi-<0 (7)
2
Therefore, Equation (5) can be re-written as:
DM VAN/260254-00104/6737612.1 10
CA 02602980 2007-09-19
BLSI= Vi2 (8)
2[R;~P,=~+x;jQy+ (Ry+x,)(P~+(Q~)2)l
The BLSI index in Equation (8) has the following implications:
= The BLSI must be larger than or equal to 1.0 so that the receiving bus
voltage Vj
has a mathematical solution that is operational in real life.
= When the BLSI is equal to 1.0, the two positive number solutions of Equation
(6)
become the same, meaning that the PV curve nose point or the maximum
loadability of the line (branch) is reached.
= The BLSI can be used to identify weak lines (branches) and buses (receiving
bus
of weak lines) in a system. The closer to 1.0 the BLSI of a line, the weaker
the
line. It can also be used to predict voltage instability of a system state,
since as
long as the BLSI of at least one line in the system is sufficiently close to
1.0, the
system reaches its collapse point.
= When the BLSI is larger than 1.0, the maximum loadability of the line can be
approximately estimated by BLSI*S;~ where S_= P.' + Q , therefore (BLSI-
1)*Sq represents the line loading margin in the current system state. The
estimate of the line maximum loadability is accurate only when BLSI=1.0
whereas it is approximate when BLSI >1Ø This is because V; is different for
the system states when BLSI=1.0 and BLSI>1Ø The closer to 1.0 the index
BLSI is, the more accurate the estimate is of line maximum loadability. The
approximate estimate is still useful and meaningful as when the BLSI is much
larger than 1.0, the system is secure and a relatively larger error in the
estimate
is not important. When the BLSI approaches 1.0, the system moves towards the
collapse point and the estimate becomes more accurate.
Extended line voltage stability index
Above has been provided the derivation and use of the line voltage stability
index.
However, the BSLI index is not accurate enough for identification of system
voltage
instability, although it can identify weak lines (branches) and buses in the
system.
This is because the BSLI only considers individual lines, but misses the
impact of the
DM VAfY/26025d-00104/6737612.1 11
CA 02602980 2007-09-19
rest of the power system on the line voltage and line power flow. In other
words, the
line power flow has to traverse external impedance before it reaches the
sending bus
of the line and subsequently transfers over the line. Following is disclosed a
method
to derive the extended line stability index (ELSI) that is based on the BSLI
but
include both impacts of the line itself and the system outside the line.
As shown in Figure 2, the system outside the line i-j can be represented using
an
equivalent source voltage EkLBk and impedance Zki. This means that as long as
the
equivalent Ek Lek and Zki can be determined to produce the fully identical bus
voltages (magnitude and angle) at the two buses i and j, and power flows (real
and
reactive flows) of the line i-j that the system outside the line i-j imposes
on the line,
the equivalent EkLek and Zki have the same effect on the line as does the
external
system outside line, (i.e., the network outside the sending bus i and the
receiving bus
j). . Note that the grounding branch of reactive charging power at the sending
bus is
merged as part of the equivalent impedance Zki. The Zki represents the
impedance that
the power flow on the line i-j encountered, before it arrives at the sending
bus and is
generally smaller than the line impedance as it is an equivalence of the
external
system, which contains many looped and parallel branches.
Letting Zij = Ri~ + jX,~ it follows:
( EkLBk -V,LBi ~ ~ViLBi -VjLBj ~ (9)
Pki - jQki = Pi - jQi = Vi L- Bi) Vi L- Bi Zki ( Zi1
Therefore,
EkLBki -Vi Vi -Vi ZBji
(10)
Zki Zij
wherein 9ki=9k-ei and 9j,=9;-9;,
Therefore:
Zki EkL6ki -Vi (1 1)
Zij Vi -VjLBji
Equation (11) can be re-written as:
DM_VAN/260254-00104/6737612.1 12
CA 02602980 2007-09-19
K- Zki +Zij Zkj - EkLBki -VjLBji Zy Zy Vi -V jLBji (12)
Equivalently:
EkL6ki =VjLBji+K=(Vi-VjLBji) (13)
Assuming that two power flow states are available and are expressed by the
subscripts
I and 2 respectively, it follows:
EkZOki =VjlLejil+K'(Vi1 -VjlLojil) (14)
EkZOki =Vj2LBji2 +K-(Vi2 -V j2L9ji2) (15)
Solving Equations (14) and (15) yields:
K- VjlLejil-Vj2Leji2 (16)
(Vj]L9 jil -V j2LBji2)-(Vil -Vi2)
Once Kis obtained, EkZOki and Zkj can be calculated from Equations (13) and
(12).
In the extended line between the buses k and j, the section between buses i
and j is the
actual line i j, whereas the section between buses k and i represents the
effect of the
external system outside the line i-j in such a way that the power flow on line
i j is
produced from the equivalent source at the bus voltage Ek and must go through
the
equivalent impedance of Zki first, before arriving at the sending bus i of the
actual line,
and then flowing on the line with the impedance of Zij and reaching the
receiving bus j.
The equivalent source voltage and impedance create the same bus voltages and
power
flows of the line as the whole system. Therefore, similar to the derivation of
the BSLI
described above, the line voltage stability index for the maximum transfer
capability
of the extended line, including the external system effect, can be calculated
using
Equation (8) if Vi and Ry+jXij are replaced by Ek and Zkj=Rkj +jXkj.
Therefore, the
ESLI for the extended line is calculated as:
2
ELS1= Ek >_ 1 (17)
2[RkjPj +' ~'kjQij + (Rkj +Xkj)(Pj {'(Qij)2)I
DM_VAN/260254-00104/6737612.1 13
CA 02602980 2007-09-19
Note the following:
= To identify system instability and weakest lines (branches) and buses, the
index
ESLI rather than the BSLI should be used, as the index ESLI includes the
effects of
both the line itself and the external system outside the line, which is
accurate,
whereas the BSLI only reflects the effect of the line itself and is not
sufficiently
accurate.
= The BSLI is also useful for identifying weak lines (branches) and buses in a
relative
sense and providing the information about the maximum transfer capability of
the
line itself.
= The index ELSI can be used for any line including those without load at its
receiving bus (such as tie lines or other branches with a heavy loading level,
which
may often have a voltage instability problem). The weakest line/bus in a
system
causes system instability.
= The equivalent source voltage and impedance in the derivation of the
extended
index are completely different from the equivalent source voltage and
impedance
used in the Thevenin theorem. There is no concept of Thevenin load in the
method
according to the invention. Note that unlike the Thevenin load, the line
impedance
does not return to another end of the equivalent voltage source. Also, the
angle
Bk;=Bk-6; in the equivalent voltage source EkLBk; is the difference between
voltage
angles at two buses but not a voltage angle at a single bus. Particularly, the
equivalence impedance Zk; is never equal to the line impedance Z;j when the
line
reaches voltage instability.
= Somewhat similar to (but different from) the bus index method that is based
on the
Thevenin theorem, the two system states are needed to calculate the equivalent
source voltage Ek and impedance Zki. This assumption may create a small but
acceptable error in calculations. It can be seen from Equations (16), (12) and
(13)
that the calculation error is only associated with K, and the effect of K on
the
estimates of Ek and Zk; is just a small portion. In other words, the Zk; is
just a part of
the total extended line impedance Zkj, and in most cases, Zk; is smaller than
the
impedance of actual line Z;~, whereas Z;~, which plays a dominant role, can be
DM_VAN/260254-00104/6737612.1 14
CA 02602980 2007-09-19
accurately estimated using the PMU information in the real time application
(as
disclosed below). Therefore, the calculation error due to the two system state
assumption in the presented method should be much smaller than that in the
Thevenin theorem based method.
= As disclosed in relation to the BLSI, a loading margin for the extended line
can be
calculated using the ELSI, i.e., (ELSI-1)*S;;.
Implementation of real-time voltage instability identification
The method and index presented above can be implemented in a real time manner
using synchronized PMU information or in an on-line manner using the existing
SCADA and EMS at a control center of a utility.
A. Basic tasks in implementation using synchronized PMU information
One of the advantages of the presented method is the fact that the ELSI only
requires
the information of voltage magnitude at the sending bus, line power flows at
the
receiving bus, and line parameters, all of which can be acquired in a real
time manner
through synchronized PMU measurements. The PMUs transmit measurements to a
control center, which has a computer. The computer receives the measurements
and
carries out the calculations. The computer is conventional, having a memory,
fixed
storage, a processor, input means and output means. The PMU devices are
installed
at two sides of the critical lines monitored, which may include tie lines,
long distance
lines with a heavy loading level, long distance radial lines and other
important lines.
The application of PMUs is currently limited to phasor monitoring and
enhancement
in the state estimator function within EMS. The system according to the
invention
provides an application of PMU for simultaneously identifying system voltage
instability with the weakest lines and buses and protecting the system from
voltage
collapse.
The real time implementation includes the following three basic tasks:
(1) A sampled measurement from a PMU (including any or all of voltage
magnitudes,
angles, real and reactive powers) may include invalid data. False data that is
caused by failure or malfunction of PMU devices or communication channels may
DM VAN/2602-54-00104I6737612.I 15
CA 02602980 2007-09-19
or may not be recognized using features of PMU measurements. Particularly,
some errors that are only associated with accuracy of measurements cannot be
identified by the PMU itself. Identifying and filtering out invalid
measurements is
therefore the first task that must be completed in implementation.
(2) The line (branch) parameters (resistance, reactance of lines and
admittance
representing reactive charging power) cannot be directly measured by PMU.
These parameters vary with the environment and weather (such as temperature)
conditions. Therefore it is necessary to perform a real time estimate of line
parameters. The assumption of constant line parameters in the prior art is not
reasonable in real time applications.
(3) Once invalid measurements are filtered out and line parameters are
estimated, the
most recent measurements from the PMU are used to calculate the real time ELSI
of all lines monitored. The smallest ELSI provides information about how far
away the current system state is from the collapse point and which line
(branch)
and bus are the weakest line and bus causing system instability.
In the following disclosure, the iT equivalence of a line shown in Figure 1 is
used to
illustrate the implementation process. Generally, this equivalence is
sufficient,
although it is not difficult to extend the concept to a multiple 71
equivalence circuit in
the process of invalid data filtering and parameter estimation if it is
necessary in the
actual application.
The V;, 9;, Vj, 6j, P, Q;, P;j and Q;j are the bus voltages (magnitude and
angles) and
line power flows (real and reactive powers) at both sides of a line,
respectively, and
are directly obtained from the measurements of PMU in a real time manner.
(Note
that the initial measurements are voltage and current phasors but these can be
easily
converted to line power flows.) The estimation of line parameters of RjJ, X;j
and Y and
calculation of real time ELSI indices for all lines monitored are performed at
a given
time interval (such as every 2-5 minutes for parameter estimation and every 5
seconds
for ELSI calculation). PMU devices can create synchronized phasor data at a
rate of
10-30 samples per second or faster, and therefore there are considerable
sampling data
available in a given interval. Note that the rate of waveform sampling can be
up to
3000 or more samples per second. The parameters of R,;, X,j and Y may vary
with the
DM VAN/260254-00104/6737612.1 16
CA 02602980 2007-09-19
environment and weather conditions around the line in a relatively long period
(such
as more than half an hour). However, unlike the measurements of voltages and
line
(branch) power flows, the parameters are sufficiently stable (constant or
minor
fluctuations) in a short interval (for example, a couple of minutes). The
effect of
parameter estimation is twofold. The parameters should be re-estimated at a
given
interval in a real time manner whereas their stability in a very short time is
utilized to
filter invalid measurements.
B. Filtering invalid measurements
A number of sets of sampling data (measurements) are taken in the given
interval. For
each set of measurements, the following data filtering process is performed:
1. The Ry, X;~ and Y from the last estimation are used as a reference.
2. The charging reactive powers are calculated by:
Qi0 = Vi2Y (18)
Qjo = V~ Y (19)
3. The equivalent reactive power flows on the line within the points A and B
are
calculated by:
Qi = Qi + Qto (20)
Qij =Qij -Qjo (21)
4. The reactive loss on the line is estimated by:
QQ~ = X `~ (P2 + (Q` )2 ) (22)
V~2
~Q~ X ij (P~ + (Q~j )2 (23)
V2
DM_VAN/260254-00104/6737612.1 17
CA 02602980 2007-09-19
OQ = OQ] + AQ2 (24)
2
The reactive loss is estimated from the two buses respectively and Equation
(24) provides the average estimation from the two buses.
5. The parameter Y is updated using the measured reactive power flows at the
two buses and the estimated line loss by:
Y(new) = Q`j -Q` +AQ (25)
Vi 2 + V 2
A threshold for filtering accuracy is specified. The threshold is based on the
precision of PMU measurements, error transfer relationship between the
measurements and Y, and possible small change of Y in the given short
interval,
which can be determined through testing and pre-estimation. For example, if
5% is used as the threshold, when Y(new) is larger than 1.05xY(old) or smaller
than 0.95xY(old) wherein Y(old) refers to the value of Y in the last
estimation,
this whole set of measurements (V;, B;, V;, 8i, P;, Q;, P;j and Qy) may be
viewed
as unreliable data and abandoned.
6. The equivalent charging reactive power at the receiving bus is updated by:
Qj0 (new) = V~ Y(new) (26)
7. The line reactive power on the line at the receiving end is updated by:
Qij = Qij - Q j0 (new) (27)
8. The parameters R,~ and X,~ are estimated using Equations (2) and (3).
Letting
RijPj +XtjQ~ =-V~ +V~VjCos9ji=a (28)
R~jQ~~ -XIjP~~ =ViVjSin9ji =b (29)
It can be derived from Equations (28) and (29) that:
DM VAN/260254-00104/6737612.1 18
CA 02602980 2007-09-19
~
aPij +bQij
Rij (new) - 2 * (30)
Pi + (Qij )2
aQ = - bP, j
X ij (new) _ ~ * (31)
Pij + (Qij )2
Similarly, a threshold for filtering accuracy is specified. The threshold is
based
on the precision of PMU measurements, error transfer relationship between
the measurements and R;j or Xij, and possible small change of R;j or X;j in
the
given short interval, which can be determined through testing and pre-
estimation. For example, if 5% is used as the threshold, when either R,j(new)
is
larger than 1.05xR;j(old) or smaller than 0.95xR;j(old), or X;j(new) is larger
than 1.05xXi~(old) or smaller than 0.95xXij(old), this whole set of
measurements (Vi, 9i, Vj, 9j, Pi, Qi, P,j and Qij) is viewed as unreliable
data and
may be abandoned.
If the number of reliable sets of measurements is smaller than a specified
threshold
(such as 10), more sampling data should be used until the specified threshold
is met.
If all sets of measurements for a line in the given interval are filtered out
as invalid
data, a warning message should be sent to operators. Consecutive warning
messages
indicate that the PMU devices for that particular line may be in an abnormal
situation.
C. Estimating Rl~, Xy and Y
Each of the estimated parameters in the above process is based on individual
sampling data at a time point, and is used for the purpose of filtering
invalid data. The
parameters should be re-estimated using a group of sampling data to minimize
errors.
It is assumed that M reliable sets of measurements are obtained after the
filtering
process.
The parameter Y is re-estimated using the average of the M estimated Y values
obtained using the M reliable sets of measurements in the filtering process:
M
Y Yk (new)
Y(estim) = k-I M (32)
DM VAN/260254-00104/6737612.1 19
CA 02602980 2007-09-19
wherein Yk(new) is the value obtained using Equation (25) corresponding to the
kth
reliable set of measurements after filtering.
The parameter Rij or X;j is also re-estimated using the average of the M
estimated Rij
or X;j values obtained using the M reliable sets of measurements in the
filtering
process:
M
Y- R~jk (new)
Rij (estim) = k-i M (33)
M
E X;jk (new)
X,j (estim) = k-l M (34)
wherein Rljk(new) and Xyk(new) are, respectively, the values obtained using
Equations
(30) and (31) corresponding to the kth reliable set of measurements after
filtering.
The standard deviations of Ry(estim) and Xy(estim) are calculated using the
following
equations:
M
~ [R~jk (new) - Rij (estim)] 2
Rij (sd) = k=1 M -1 (35)
M
~ [X ijk (new) - X,j (estim)]2
X~j (sd) = k_1 M -1 (36)
If either Ry(sd)/R,j(estim) or Xy(sd)/X~f(estim) is larger than a threshold
(expressed as a
%), the estimated Rij and Xy obtained using Equations (33) and (34) are
abandoned
and the parameters R~~ and X~j are re-estimated using the following method.
This
threshold is generally selected as a half of the threshold for filtering
accuracy (see
step 8 above).
Equations (28) and (29) are re-written as:
DM_VAN/260254-00104/6737612.1 20
CA 02602980 2007-09-19
Rij +cX~j = d (37)
Rij +eXij = f (38)
wherein:
c (39)
Pij
-VI +ViV jCosBy
d= (40)
Pij
- Pj
e = * (41)
Qij
ViV j Sin9;j
f = (42)
Qij
Applying the least square method to Equation (37) with the M sets of reliable
measurements results in:
Rij, (estim)=d-cXijt(estim) (43)
Xijt(estim)= Scd (44)
Scc
wherein:
M
_ Edk
d=k-1 (45)
M
M
Ilck
k~ (46)
DMV AN/260254-00104/6737612.1 21
CA 02602980 2007-09-19
M
Scd = E (ck - E)(d k - d ) (47)
k=1
S'C _ Y (ck - c ) 2 (48)
k=1
Similarly, applying the least square method to Equation (38) with the M sets
of
reliable measurements results in:
R~~2 (estim) = f-eX ~~2 (estim) (49)
W
Xi~2(estim) = ef (50)
Wee
wherein:
M
E fk
k M (51)
M
Y, ek
e = k ~ (52)
M _
Wef = Y- (ek - e )(fk - f ) (53)
k=1
Wee = E(ek - e ) 2 (54)
k=1
The subscript k indicates the value corresponding to the kth reliable set of
measurements after filtering.
The Rij and X;j are estimated by:
Ri~ 1(estim) + R~~ 2 (estim)
Ri~ (estim) = (55)
2
DM VAN/260254-00104/6737612.1 22
CA 02602980 2007-09-19
X;j i (estim) + X ;j 2 (estim)
X;j (estim) = (56)
2
In a high voltage transmission system, R;~ is much smaller than X;j, and P;J
is generally
much larger than Q*;j. It is possible that in numerical calculations, Equation
(37) is
more accurate than Equation (38) for estimation of R;j whereas that Equation
(38) is
more accurate than Equation (37) for estimation of X;j. An alternative
approach in an
actual application is to use both Equations (37) and (38) first as described
above.
Then, if the difference between R,~i(estim) and Rij2(estim), or between
X;jl(estim) and
X;j2(estim), exceeds a threshold (in a relative percentage), only R;j/(estim)
and
Xy2(estim) are used as the final estimates.
The derivation above is based on the fact that three phases in a transmission
system
are symmetrical and therefore a single phase model is used in power flow
calculation
modeling. Similar to SCADA measurements, PMU devices provide separate
measurements of phases A, B and C, which may have slight differences among
them.
The total real and reactive line power flows of the three phases can be
obtained by
summing up the line power flows that are calculated from measured voltage and
current phasors of three individual phases. For voltage phasors, which are
required in
the calculations, the following two approaches can be used:
(1) The average of the measured voltage magnitudes or angles of phases A, B
and C
is used or the measured voltage magnitude and angle of one selected phase with
the best measurement precision (for example, phase A) is used. This is the
traditional method used in the exiting EMS.
(2) The voltage phasors of phases A, B and C and the total three phase power
flows
are used to estimate three sets of line parameters. The final parameter
estimate is
the average of the three estimates using the voltage phasors of phases A, B
and C.
D. Calculating the index ELSI
PMU measurements include time stamps. For each monitored line, reliable sets
of
measurements after invalid data filtering are used to calculate the index
ELSI. The Rij
and X;~ may be estimated in a relatively long interval such as every 2-5
minutes
whereas the ELSI may be calculated in a relatively short interval such as
every 5
DM_VAN/260254-00104/6737612.1 23
CA 02602980 2007-09-19
seconds in the normal state. If a contingency occurs during the 5 second
interval, the
ELSI is calculated right after the contingency. In the calculation of ELSI,
the last
estimated R;j and X# are utilized. The calculation of ELSI can be completed
within
0.1-0.5 seconds. As mentioned above, calculating the equivalent source voltage
and
impedance uses measurements of two system states. If the two states are so
close that
there is no effective difference in the measured voltage and power flow of the
line
between the two system states, the second state is skipped and the next system
state is
used until an effective difference is found. If there is no effective
difference between
the two system stats in the whole current interval, the last ELSI calculated
in the last
interval is used as the ELSI in the current interval. This is because if there
is no
effective change between the two states, system instability will not happen.
Therefore,
there may be only one or multiple ELSI index values in the given interval
depending
on differences between system states, and whether or not there is any outage
event in
the given interval.
E. Use of the index ELSI
In normal states, there only exit relatively small disturbances (such gradual
load
and/or generation changes), however, it is still possible that cumulative
changes may
cause the system to gradually move towards a collapse point. The index ELSI is
used
to monitor the weak lines/buses and predict the distance of the system state
from
voltage instability in a real time manner.
For a contingency (outage of a major system component), there are two
situations:
(1) The system does not lose voltage stability following a contingency. Most
cases
belong to this situation. In this situation, the index ELSI is calculated
before and
after the contingency. The index ELSI should show a decline but should still
be
larger than 1.0 after a contingency. The difference between the index value
after
the contingency and 1.0 provides the information about how close the system is
to the collapse point allowing the operator can decide what measures need to
be
taken to avoid possible voltage instability.
(2) The system will lose voltage stability following a contingency. This is a
rare
situation. For this situation, there are two approaches to using the index
ELSI.
DM_VAN/260254-00104/6737612.1 24
CA 02602980 2007-09-19
(a) Post-outage action. The index ELSI may be used to trigger a
load/generation
shedding remedial action scheme (RAS) for voltage instability. Generally, the
process of a system losing voltage stability takes at least a few seconds or
longer. This is partly because bus loads around the weakest lines/buses
causing voltage instability decrease as the voltage drops, which slows down
the speed of the system losing voltage stability. In such a case, the
contingency triggers an immediate calculation of ELSI (between two regular
calculation points in the given interval). The calculation time of the index
ELSI after a contingency (0.1-0.5 seconds) is sufficiently fast to trigger a
load/generation shedding RAS before the system collapses.
(b) Pre-outage action. The application of the index ELSI may be combined with
the study-mode (off-line) analysis. A threshold of the index ELSI for a
contingency can be found in advance through the continuation power flow
analysis in a study mode. When the real time value of the index ELSI
approaches the threshold, the operator should make a decision: either take a
risk by doing nothing but arming the RAS, or take a measure to reduce the
power flow on the critical line with the ELSI near the threshold, or on the
line
whose outage will cause the critical line to exceed its maximum transfer
capability.
F. Implementation using existing SCADA and EMS
If insufficient PMU devices are installed in the system, on-line
identification of
voltage collapse and weak lines/buses using the method according to the
invention
and ELSI index can be still implemented on the existing Energy Management
System
(EMS) at control centers. As the measurements from SCADA do not include angle
data, and other data are not synchronized measurements, measurements from
SCADA
are not directly used. However, the information of on-line system states
including bus
voltages (magnitude and angle) and line power flows (real and reactive powers)
is
available through the state estimator which uses the SCADA measurements, and
power flow calculations following the state estimation. The on-line power
flows are
calculated continuously every four minutes in most existing EMS systems.
Neither
the filtering process nor line parameter estimation is needed. Actually, the
state
estimation can play a role of SCADA data filtering but it cannot perform line
DM_V AN/260254-00104/6737612.1 25
CA 02602980 2007-09-19
parameter estimation, which requires synchronized measurements. Although the
ELSI index obtained using the existing SCADA and EMS information is less
accurate
than that obtained using the PMU information, it can still provide on-line
prediction
of voltage instability and weak lines/buses.
Test cases
The presented method and ELSI index were tested by using the system
continuation
power flow that is accepted by the industry as a reference method for voltage
stability
study. Voltages and line flows obtained from considerable power flow
calculations
were used as "measurements". The tests were conducted on the four IEEE test
systems, a utility system in China and the utility system operated and planned
by the
British Columbia Transmission Corporation in Canada. More than 30 cases in
total
were considered with different conditions (such as stressing loads at some
buses or all
buses, stressing generations, considering or not considering generator limits,
etc.).
All test cases indicate that the ELSI index of at least one line or a couple
of lines is
near 1.0 (less 1.01) at the system collapse point (just before the power flow
divergence) whereas the ELSI indices of all lines monitored are much larger
than 1.0
in the normal system states when the system power flow is far away from
divergence.
Two examples are provided herein to demonstrate the feasibility and
effectiveness of
the method and system according to the invention.
A. IEEE 30 bus test system
Figure 3 shows the single-line diagram of the IEEE 30 bus system. The data and
original single-line diagram of this system is available at the web site
http://www.ee.washington.edu/research/pstca/, which is hereby incorporated by
reference. The system was stressed by increasing both real and reactive loads
at Bus
30. Multiple system power flows are solved using the commercial power flow
program.
The following observations were made from the results of the test:
= At the beginning, the index ELSI of all lines was much larger than 1.0 (from
2.4 to
30.0)
DM_VAN/260254-00104/6737612.1 26
CA 02602980 2007-09-19
= At stressing, the ELSI indices of line 27-30 and line 29-30 gradually
decreased and
approached 1.0 at the collapse point (from 4.5134 to 1.0014 for line 27-30 and
from
6.021 to 1.0024 for line 29-30).
= The ELSI index of line 27-29 was secondly close to 1.0 at the collapse point
(1.0555). The index ELSI of all other lines were still much larger than 1.0 at
the
collapse point (from 1.25 to 3.0). The ELSI of line 28-27 was the lowest of
all other
lines.
= The weakest lines 27-30 and 29-30 and secondly weakest line 27-29 were
accurately identified using their ELSI indices. The system lost voltage
stability due
to the two weakest lines when their ELSI indices were near 1Ø
= The weakest bus 30, which is the receiving bus of the two weakest lines, was
identified. At the collapse point, the voltages at bus 27, 29 and 30 were
0.846,
0.732 and 0.635 (in p.u.), respectively.
= Table I below presents the results showing that the ELSI indices of four
lines (bus
27 - bus 29, bus 27 - bus 30, bus 29 - bus 30 and bus 28 - bus 27) decreased
as the
load (in MW) at Bus 30 increased. The numbers in the column "Lambda" are
multiples of increased loads with regard to the base load of 10.6 MW at the
beginning.
DM_VAN/260254-00104/6737612.1 27
CA 02602980 2007-09-19
Table I ELSI of four lines (decreasing as the load at Bus 30 increasing)
Lam bda Vp 27-29 27-30 29-30 28-27
..., ....... .. . ......... . ......... . ..... ., ,. .
1.188679 5. 6677, 4. 51 34 , 6. 02 I'll 5. 1 542
1_377358 4.8271 ' :3. 86 1 2' .-~i. 047f3 4. 7::3OEi
_.._
1.566038 4. 1 426 3. 2724 4. O 1 Fi4 4. 0474
1 754717 :3. .-riH:14 2. 8 6:16 :3. 4696:3_ 6541 1.943396 ;3. 1:388 2.5657 :3.
0262 3. 3692 2_132075 2. 8903 2. 3126 2. 7005 3_ 141
2_320755 2.654 2.0876 ' 2. 335, 2_ 8443 2.528302 2. :3425 1. 8t(Fi'~.' `L.
09i^34 `L. (i4y5
2.698113 2. 1705 1. 7477~ 1. 9256 2. 46 1 1
2.886792 2.0051 1.6205, 1_ 7679' 2_ :309 3.075472 1_ 8389 1. 50 13 1_ 6 18F3;
2. 1 722
3.264151 1.6996 1.3971 1_ 4F3L 2. 0328 3.45283 1. 587:3 1.3132. 1 -3803 1. y 1
2 t;
3.641 509 1.465.5 1. 230 l 1.2798 1_ 7943
3.8301 89 1.342 1 1. 1502 1 I l-i42 1.6345 4.01 8868 1.`e.':345 1- 08:3:3 1.
10:37 1.5096
4_066038 1. 1775 i 1.0485 1. 0626 1. 4:334
4. 1 13208 1. 1102 1 . 020 1 1. 0272 1. 33561
4. 1 22642 1.09,94 1.0121 1.0159 1.3022
4. 1 32075 10809 1. 0083 1.0117 1.2951
, ...... ..... ... ... . . . .... .. ... .............. ..
4.141509 1.0762, 1. 0064 1.0089 1. 286 L
4.150943 1. O6H2 1. OO:3F3 1 . 0054: 1. 274Fi
....___ _. ........ ____ . . ...... . . ..............:
4_ 1 60377 1. 0555 1. 00 1 4 1. 0024 1. 2.9311 =
= Figure 4 graphically shows how the ELSI indices of the two weakest lines
(bus 27 -
bus 30 and bus 29 - bus 30) varied with the increased load at Bus 30 (in
multiples).
B. BCTC system
The system power flow case used in testing had 15,161 buses and 19,403
branches,
including the partial system model of the west USA network. Figure 5 shows a
partial
representation of the system. General information and some particulars of the
BCTC
system are available at http://www.bctc.com/the_transmission_system, which is
hereby incorporated by reference. Previous operation studies had shown that
when
line 5L91 is out-of-service or trips, lines 5L92, 5L96 and 5L98 have much
higher
loading levels. It was also known from such operation studies that when three
local
generator plants at KCL, ALH and SEV have high outputs, and if line 5L91
trips, then
line 5L96 may exceed its transfer capability causing system collapse. This was
an
appropriate example for testing, as the results obtained from the method
according to
the invention and the ELSI index should have been consistent with what was
known
from operational experience. Commercial software was used to conduct system
continuation power flow calculations in the following four test cases.
DM VAIY/260254-00104/6737612.1 28
CA 02602980 2007-09-19
(1) In the normal system state with the line 5L91 in service, the generation
at
KCL, ALH and SEV generators was increased to stress the power flow on the
line 5L96. In this case, line 5L96 should have sufficient transfer capability
and the system should have no voltage instability problem.
(2) With the line 5L91 out-of-service, the generation at KCL, ALH and SEV
generators was increased to stress the power flow on the lines 5L92, 5L96 and
5L98 until the system lost voltage stability.
(3) In the normal system state with line 5L91 in service, the generation at
KCL,
ALH and SEV generators was increased to stress power flows on the line
5L96. The line 5L91 trips at one point at which the system would be
extremely close to voltage instability following such trip.
(4) Line 5L91 trips when line 5L96 has different loading levels in the normal
state.
The ELSI indices of 5L96 were examined before and after line 5L91 tripped.
It is noted that the operation conditions in the four cases have some
differences. In
Cases (1) and (2), the power flow to USA at the Nelway phase shifter is fixed
at zero
whereas in Cases (3) and (4), this exporting power flow is not fixed, so that
part of
increased generation will flow into the USA network, decreasing the loading
pressure
on lines 5L96, 5L98 and 5L92. This means that more generation outputs at the
local
generators are required to achieve the same loading level on the three lines.
Also,
there are more reactive power supports at reactive sources around 5L96 and
5L98 in
Cases (3) and (4) than in Cases (1) and (2).
Case (1): Normal states, stress power flow on 5L96
The results are shown in Table 2 and Figure 6. It can be seen that as the
power flow
on line 5L96 is stressed, the ELSI index decreased. However, when the
generation of
all three local generator plants basically reached their maximum capacities,
the ELSI
was still much larger than 1.0, indicating that both 5L96 and the system have
no
voltage instability problem in the normal states.
DM VAN/260254-00104/6737612.1 29
CA 02602980 2007-09-19
Table 2
ELSI of line 5L96 in normal states (decreasing as local generations are
increased)
KCL gen AHL gen SEV gen Pi(MW) ELSI-5L96
143 90 200 657 2.87853
286 180 200 738 2.80791
429 180 200 865 2.57512
572 180 400 956 2.3481
572 180 600 1047 1.93662 572 180 670 1072 1.56245
572 180 695 1081 1.55095
Case (2): 5L91 out-of-service, stress power flows on 5L96, 5L92 and 5L98
The power flows of eight system states were calculated. The ELSI indices of
the lines
5L96, 5L92 and 5L98, whose loading levels had been stressed by the increased
generation of the three local generator plants, were examined. Three of the
eight
power flows cases were filtered out for line 5L92 using the data filtering
method (this
was due to relatively large bus mismatches at the two buses of this line in
power flow
solutions), whereas all eight cases passed the filtering process for lines
5L96 and
5L98.
The results for the three lines 5L96, 5L92 and 5L98 are shown in Tables 3, 4
and 5,
and Figures 7, 8 and 9, respectively. The ELSI indices of 5L96, 5L92 and 5L98
are
1.0018, 1.05719 and 1.74195 at the power flow divergence point. The ELSI
indices
indicate that 5L96 lost voltage stability, 5L92 was close to its voltage
stability limit
and 5L98 did not have any voltage instability problem. The system collapse was
due
to the fact that the power flow on line 5L96 exceeded its maximum transfer
capability.
This was identified by its ESLI index. The ELSI of 5L98 did not monotonically
decrease as the loading level increased. This is because several reactive
power sources
around the receiving bus of 5L98 tried to support its voltage when the line
flow was
stressed. Also less local generation brought a higher loading level on line
5L96 when
5L91 was out-of-service compared to the normal system state in Case (1).
DM VAN/260254-00104/6737612.1 30
CA 02602980 2007-09-19
Table 3
ELSI of 5L96 while 5L91 out-of-service (decreasing as local generations were
increased)
KCL gen ALH gen SEV gen Pi(MW) ELSI-5L96
143 90 125 1161 1.79002
143 180 125 1240 1.69607
286 180 125 1368 1.48183
429 180 125 1493 1.40465
572 180 125 1617 1.2569
572 180 250 1730 1.00437
572 180 300 1763 1.00041
572 180 332 1781 1.0018
572 180 336 diverge
Table 4
ELSI of 5L92 while 5L91 out-of-service (decreasing as local generations were
increased)
KCL gen ALH gen SEV gen Pi(MW) ELSI-5L92
143 180 125 495.4 1.24553
429 180 125 504.1 1.13499
572 180 250 511.8 1.11286
572 180 300 512.4 1.08871
572 180 332 513.2 1.05719
572 180 336
Table 5
ELSI of 5L98 while 5L91 out-of-service (decreasing as local generations were
increased)
KCL gen ALH gen SEV gen Pi(MW) ELSI-5L98
143 90 125 1054 2.43069
143 180 125 1132 2. 35008
286 180 125 1256 1.97799 429 180 125 1378 2.18041
572 180 125 1503 1.62796
572 180 250 1607 1.92112
572 180 300 1637 1.7964
572 180 332 1653 1.74195
572 180 336
DM VAN/260254-00104/6737612.1 31
CA 02602980 2007-09-19
Case (3): 5L91 outage at the critical loading level of 5L96 in stressed normal
states
By increasing the generation of the three local generator plants to stress
5L96, the
loading level on 5L96 reached 1070 MW in a normal state. At this point, 51,91
tripped, resulting in the loading level on 5L96 to suddenly jump to 1879 MW.
The
ELSI dropped from 1.89693 (before the outage) to 1.00217 (after the outage).
Although the system still critically survived right after the outage, a
further stress by
increasing only 8 MW on 5L96 (1887MW-1879MW) led to system collapse (power
flow divergence). This indicated that system instability after line 5L91
outage is
identified by the ELSI. More local generation outputs are required to make the
loading level on line 5L96 reach its maximum capacity in this case than in
Case (2)
because part of increased generation outputs flows into the USA network
through the
tie line due to unfixed flow setting at the Nelway phase shifter. Also, the
maximum
transfer capability of line 5L96 at the collapse point in this case is
slightly larger than
that that in Case (2) because of more reactive power supports around line 5L96
in the
initial operation condition. This is the similar situation in Case (4)
following.
The results are shown in Table 6 and Figure 10.
Table 6
ELSI of 5L96 (a big drop towards 1.0 after 5L91 trips)
KCL gen AHL gen SEV gen Pi ELSI-5L96
143 90 200 657 2.87853:
286 180 200 738 2.80791
429 180 200 865 2.57512
572 180 400 956 2.3481
572 180 600 1047 1.93662
572 180 665 1070 1.89693 (5L91 trips at this point)
572 180 665 1879 1.00217
572 180 675 1883 1.01447
572 180 685 1886 1.00657:
572 180 695 1887 1.b1292 572 180 700 di\,erge
Case (4): 5L91 outage at different loading levels of 5L96 in the normal states
DM_VAN/260254-00104/6737612.1 32
CA 02602980 2007-09-19
(a) Line 5L91 tripped when line 5L96 had a loading level around 950 MW in the
normal state. After the outage, the loading level of line 5L96 jumped to 1689
MW. Correspondingly, the ELSI of line 5L96 dropped from 2.33912 to 1.15887.
The system survived after the outage. The loading of line 5L96 can be still
increased to 1746 MW after the outage while the ELSI decreases to 1.12773. In
this case, no action should be taken before line 5L91 trips.
(b) Line 5L91 tripped when line 5L96 had a loading level of 1079 MW in the
normal
state. After the outage, the loading level of line 5L96 jumped to 1888 MW.
Correspondingly, the ELSI of line 5L96 dropped from 21.70675 to 1.01167. The
system reached a critical state after the outage. A small disturbance after
the
outage (increasing the generation at SEV by 5 MW from 690 MW to 695 MW)
led to system collapse even if the loading on 5L96 no longer increased as the
ELSI reached 1.00669. In this case, a pre-outage action of arming the
generation
shedding RAS should be taken before 5L91 trips.
The results are shown below in Table 7 and Figure 11.
Table 7
ELSI of 5L96 when 5L91 tripping at two different loading levels of 5L96
-,. - -_..,---:
Pi (MW) ELSI-5L96 Pi (MW)\ ELSI -5L96
10725 . 1.56245 956, 2.33912
1079 1.70675 947, 2.27698 (5L91 trips at this point)
1888 1.01167 1689 1.15887
1887 1. 00669 1746 : 1.12773
dKoerges sur\i\oes
The calculations performed in the above described system and method can be
implemented as a series of instructions stored on computer readable memory
within a
computer, such as within RAM, or on computer readable storage medium. The
method and system may be expressed as a series of instructions present in a
carrier
wave embodying a computer data signal to communicate the instructions to a
networked device or server, which when executed by a processor within the
computer,
carry out the method.
DM VAN1260254-00104/6737612.I 33
CA 02602980 2007-09-19
Although the particular preferred embodiments of the invention have been
disclosed
in detail for illustrative purposes, it will be recognized that variations or
modifications
of the disclosed apparatus lie within the scope of the present invention.
DM VAN/260254-00104/6737612.1 34
