Method for performing a voltage stability security assessment for a power transmission system

A method for performing a voltage stability security assessment for a region of an electric power transmission system having a plurality of buses and a plurality of sources of reactive reserves coupled thereto. The plurality of buses are grouped into a plurality of voltage control areas such that each of the buses within each voltage control area has a substantially similar reactive margin and voltage at the minimum of the corresponding reactive power versus voltage relationship. A corresponding reactive reserve basin is determined for each of at least one of the voltage control areas. Each reactive reserve basin comprises at least one of the sources of reactive reserves selected in dependence upon a measure of the reactive reserves depleted at a predetermined operating point of the electric power transmission system. A single contingency analysis is performed by computing a corresponding quantity for each reactive reserve basin in response to each of a plurality of single contingencies. The corresponding quantity is representative of a reduction in the reactive reserves within the reactive reserve basin. A multiple contingency analysis is performed for each reactive reserve basin using the single contingencies whose corresponding quantity exceeds a predetermined threshold.

TECHNICAL FIELD 
This invention relates generally to planning of electrical power 
transmission systems, and more particularly, to a method for performing a 
voltage stability assessment for power transmission systems. 
BACKGROUND ART 
There are a number of potential voltage instability problems which can 
arise within an electrical power system. Some of these instability 
problems occur in distribution systems used for distributing electrical 
power to utility customers. Many of the sources of these distribution 
system voltage stability problems have existed for years, and their causes 
and solutions are well known in the art. 
Other problems occur in transmission systems, which are used for 
transporting bulk power from generation stations to load centers. These 
stability problems result from such causes as facility outages, clearing 
of short circuit faults, and increases in load power or inter-area power 
transfer in a transmission network. Many of these transmission system 
voltage instability problems have been encountered only in recent years. 
These instability problems have occurred as a result of recent trends 
toward: locating generation stations distantly from load centers which 
limits the effectiveness of their voltage controls, requiring utilities 
allow power shipment across their transmission system by independent power 
producers or other utilities, and deterring construction of needed 
transmission networks, to name a few. 
A slow-spreading, uncontrollable decline in voltage, known as voltage 
collapse, is a specific type of transmission system voltage instability. 
Voltage collapse results when generators reach their field current limits 
which causes a disabling of their excitation voltage control systems. 
Voltage collapse has recently caused major blackouts in a number of 
different countries around the world. 
In order to reduce the possibility of voltage collapse in a power system, 
and more generally, improve the stability of the power system, system 
planning is performed by many utility companies. First, a mathematical 
model representative of the basic elements of the power system, and their 
interconnection, is constructed. These basic elements include generating 
stations, transformers, transmission lines, and sources of reactive 
reserves such as synchronous voltage condensers and capacitor banks. Next, 
various computational techniques for analyzing system stability are 
performed using a suitably programmed computer. Based on this analysis, 
proposed enhancements are formulated in an ad-hoc manner for improving 
voltage stability security. The mathematical model can be updated based 
upon these proposed enhancements so that the resulting system stability 
security can be analyzed. Enhancements which attain predetermined design 
objectives are then physically implemented in the actual power system. The 
process of system planning is continual in that it must be regularly 
performed in light of changing circumstances. 
In mathematical terms, voltage collapse occurs when equilibrium equations 
associated with the mathematical model of the transmission system do not 
have unique local solutions. This results either when a local solution 
does not exist or when multiple solutions exist. The point at which the 
equilibrium equations no longer have a solution or a unique solution is 
often associated with some physical or control capability limit of the 
power system. 
Current methods for assessing proximity to classic voltage instability are 
based on some measure of how close a load flow Jacobian is to a 
singularity condition, since a singular load flow Jacobian implies that 
there is not a unique solution. These proximity measures include: (i) the 
smallest eigenvalue approaching zero, (ii) the minimum singular value, 
(iii) various sensitivity matrices, (iv) the reactive power flow-voltage 
level (Q-V) curve margin, (v) the real power flow-voltage level (P-V) 
curve margin, and (vi) eigenvalue approximation measures of load flow 
Jacobian singularity. 
The eigenvalue and minimum singular value methods are disadvantageous in 
their lacking an indication of the actual locations and causes of voltage 
instability. Moreover, these methods have been known to produce misleading 
results with respect to causes of voltage instability as well as the 
locations and types of enhancements necessary to improve voltage stability 
security. Furthermore, the computational requirements for the eigenvalue 
and minimum singular value methods are relatively high. The sensitivity 
matrix methods have many of the same difficulties as the eigenvalue and 
singular value methods resulting from being linear incremental measures 
for a highly-nonlinear discontinuous process. 
Regardless of the method employed for assessing proximity to classic 
voltage instability, existing methods employed by many utility companies 
assume that there is only one voltage instability problem. Further, it is 
assumed that one distributed reactive power loading pattern test detects 
the one voltage instability problem. 
It is known that a voltage control area may be defined as an electrically 
isolated bus group in a power system. Reactive reserves in each voltage 
control area may be distributed via secondary voltage control so that no 
generator or station would exhaust reserves before all the other 
generators in the voltage control area. Although this secondary voltage 
control is effective in preventing classic voltage instability, previously 
defined voltage control areas are no longer valid whenever the originally 
existing transmission grid is enhanced so that bus groups are no longer as 
isolated. A further disadvantage of this approach is that the reactive 
reserves for controlling each voltage control area are limited to be 
within the voltage control area. 
Methods are also known which employ a voltage zone defined as a group of 
one or more tightly-coupled generator P-V buses together with the union of 
the sets of load buses they mutually support. In such methods, amount of 
reactive power supply to maintain an acceptable voltage level is 
controlled. A disadvantage of this approach, however, is that 
characterizing a voltage stability margin in terms of voltage does not 
protect against classic voltage collapse. 
Current engineering methods of locating potential voltage instability 
problems includes simulating all single line outage contingencies, and 
identifying those that do not solve as causing voltage instability. 
However, the lack of a solution is not a guarantee of voltage instability; 
a lack of a solution can occur because: the load flow Newton-Raphson-based 
algorithms are not guaranteed to converge from any particular starting 
solution, but converge only when the starting point is sufficiently close 
to the solution; the load flow convergence is not guaranteed even when the 
system is close to a solution if the solution is close to a bifurcation; 
round-off error affects the load flow convergence; and discontinuous 
changes due to switching of shunt elements, or outages of generators or 
lines can have a dramatic effect on whether the load flow algorithm will 
converge to a solution. The converged solutions for all single outages 
only indicates that there are no bifurcations. In order to attempt to 
prove that the absence of a converged solution is caused by voltage 
instability, substantial manpower and computer processing time are 
required. In one such method, the absence of a converged solution is 
determined to be due to voltage collapse if one can add a fictitious 
generator with infinite reactive supply at some bus to obtain a converged 
load flow solution. This method is not foolproof, and furthermore, does 
not indicate the causes of voltage instability nor indicate where it 
occurs. 
However, current methods are incapable of identifying all of the many 
different voltage stability problems that can occur in a transmission 
system. A very routine operating change or supposedly insignificant 
contingency in a remote region of the system, followed by another 
contingency, can cause voltage instability. Furthermore, voltage 
instability may occur in many different sub-regions of the system. Current 
methods lack diagnostic procedures for identifying causes of specific 
voltage stability problems, as well as systematic and intelligent 
enhancement procedures for preventing voltage instability problems. 
SUMMARY OF THE INVENTION 
For the foregoing reasons, the need exists for a method of identifying 
potential locations of voltage instability problems, and determining 
corrective measures to reduce the likelihood of voltage instability. 
It is thus an object of the present invention to provide an improved method 
for determining potential voltage instability problems in an electrical 
power transmission system. 
Another object of the present invention is to provide a method of 
identifying single contingencies that cause voltage instability in an 
electrical power transmission system. A further object is to provide a 
method of identifying multiple contingencies, transfer patterns and 
levels, and loading patterns and levels that cause voltage instability in 
an electrical power transmission system. 
In carrying out the above objects, the present invention provides a method 
of performing a contingency analysis for a region of an electric power 
transmission system having a plurality of buses and a plurality of sources 
of reactive reserves coupled thereto. The plurality of buses are grouped 
into a plurality of voltage control areas such that each of the buses 
within each voltage control area has a similar corresponding reactive 
power versus voltage relationship. A corresponding reactive reserve basin 
for each of at least one of the voltage control areas is determined. Each 
reactive reserve basin comprises at least one of the sources of reactive 
reserves selected in dependence upon a measure of the reactive reserves 
depleted at a predetermined operating point of the power system. A single 
contingency analysis is performed by computing a corresponding quantity 
for each reactive reserve basin in response to each of a plurality of 
single contingencies. The corresponding quantity is representative of a 
reduction in the reactive reserves within the reactive reserve basin. A 
multiple contingency analysis is performed for each reactive reserve basin 
based upon the single contingencies whose corresponding quantity exceeds a 
predetermined threshold. 
The present invention further provides a method of performing a voltage 
stability assessment for a region of an electric power transmission system 
having a plurality of buses and a plurality of sources of reactive 
reserves coupled thereto. The plurality of buses are grouped into a 
plurality of voltage control areas such that each of the bases within each 
voltage control area has a similar corresponding reactive power versus 
voltage relationship. At least one of the voltage control areas whose 
buses therewithin have a voltage at the minimum of the corresponding 
reactive power versus voltage relationship which exceeds a voltage 
threshold is selected. A corresponding reactive reserve basin is 
determined for each of the at least one of the voltage control areas, 
wherein the reactive reserve basin comprises at least one of the sources 
of reactive reserves selected in dependence upon a measure of the reactive 
reserves depleted at a predetermined operating point of the electric power 
transmission system. A single contingency analysis is performed by 
computing a corresponding quantity for each reactive reserve basin in 
response to each of a plurality of single fault contingencies, wherein the 
corresponding quantity is representative of a reduction in the reactive 
reserves within the reactive reserve basin, and wherein the plurality of 
single contingencies includes at least one single generator outage and at 
least one single line outage. The single contingencies whose corresponding 
quantity exceeds a predetermined threshold are selected. The voltage 
stability for single and multiple contingencies with a plurality of 
transfer and loading patterns are assessed, wherein the single and 
multiple contingencies are based upon the selected single contingencies. 
These and other objects, features and advantages will be readily apparent 
upon consideration of the following description, appended claims, and 
accompanying drawings.

BEST MODES FOR CARRYING OUT THE INVENTION 
The method of the present invention overcomes the disadvantages of previous 
security assessment methods and systems by intelligently selecting single 
contingencies used in performing a multiple contingency analysis. More 
specifically, the single contingencies used in performing the multiple 
contingency analysis are selected based upon the reduction in reactive 
reserves in a region of the electrical power transmission system known as 
a reactive reserve basin. Moreover, the method of the present invention 
produces a hierarchical control structure wherein a lack of 
controllability provides evidence of a potential voltage instability 
problem. 
In general, the method of the present invention is capable of identifying 
totally independent voltage stability problems that affect fairly isolated 
sections of one or more utilities. A unique voltage stability problem 
occurs when a Q-V curve computed at any bus in a sufficiently coherent 
group has the same shape, minimum, and reactive reserve basin. The 
neighboring voltage control areas with reactive supply devices that 
exhaust nearly all reactive reserves upon reaching the minimum of the Q-V 
curve computed in some critical voltage control area is a reactive reserve 
basin for that critical voltage control area. A global voltage stability 
problem occurs when the reactive reserves in a large number of voltage 
control areas are exhausted. Global reactive reserve basins for different 
voltage stability problems do not contain any of the same voltage control 
areas. Each global voltage stability problem is prevented by a unique and 
non-overlapping set of reactive supply devices belonging to its reactive 
reserve basin. 
For each global stability problem, a large set of local stability problems 
lie nested therewithin. In turn, each local stability problem has a 
different reactive reserve basin associated therewith. However, these 
local reactive reserve basins overlap. As a result, the possibility exists 
that a generator, switchable shunt capacitor or SVC belongs to several 
local reactive reserve basins. 
When the reactive reserves in a voltage control area are exhausted, all 
reactive reserve basins to which that voltage control area belongs 
experience a significant step change toward voltage instability. The local 
reactive reserve basin that exhausts all reactive reserves in all voltage 
control areas due to contingencies or operating changes is the local 
reactive reserve basin that experiences voltage instability, as long as 
the contingencies or operating changes directly impact the critical 
voltage control area where the Q-V curve is computed to determine that 
reactive reserve basin. The exhaustion of all reactive reserves for all 
voltage control areas in a local reactive reserve basin produces voltage 
instability for that critical voltage control area because that critical 
voltage control area cannot obtain all the reactive supply needed to cope 
with the contingencies or operating changes. As used herein, a contingency 
may be any unexpected discrete change in the transmission system due to 
equipment loss (such as a generator, transmission line, or transformer) or 
a short circuit (typically referred to as a fault contingency). 
A locally most vulnerable critical voltage control area and reactive 
reserve basin is one that belongs to almost every local reactive reserve 
basin also belonging to a global reactive reserve basin. This locally most 
vulnerable reactive reserve basin has relatively small reserves that 
exhaust rapidly for Q-V curve stress tests computed for almost every local 
critical voltage control area which has local reactive reserve basins that 
are subsets of a global reactive reserve basin. Such locally most 
vulnerable reactive reserve basins should be the focus of any system 
enhancements. 
It should be noted that local voltage stability problems are those brought 
on by contingencies or operating changes and not the global voltage 
stability problems which would most often only develop out of a spreading 
local voltage stability problem. Generally, all such local voltage 
stability problems need be addressed, not just the locally most 
vulnerable. This is so because each local stability problem, including the 
locally most vulnerable, may be brought on by different contingencies or 
operating changes that cause reduction of, or partially cut off, the 
reactive reserves associated with the critical voltage control area. 
More specifically, the method of the present invention employs Q-V curve 
tests for determining a hierarchical control structure which indicates 
that voltage instability occurs when a lack of controllability is evident. 
Performing a multiple contingency analysis is illustrated by the flow 
chart shown in FIG. 1. The multiple contingency analysis is to be 
performed for a region of a power system having a plurality of buses and a 
plurality of sources of reactive reserves coupled thereto. 
In block 100, the plurality of buses are grouped into voltage control areas 
in dependence upon a corresponding reactive power versus voltage 
relationship for each of the buses. More specifically, each voltage 
control area is defined as a coherent bus group where adding a reactive 
load at any bus in the group produces nearly identical Q-V curves in both 
shape and magnitude. As a result, each voltage control area has a unique 
voltage instability caused by a local incremental reactive supply problem. 
In block 102, determining a corresponding reactive reserve basin for each 
of at least one of the voltage control areas is performed. Each reactive 
reserve basin comprises at least one source of reactive reserves selected 
in dependence upon a quantity representative of the reactive reserves 
exhausted at a predetermined operating point of the power system. The at 
least one source of reactive reserves contained within the reactive 
reserve basin form a set of stabilizing controls for the corresponding 
voltage control area. Preferably, the predetermined operating point of the 
power system is the minimum of the Q-V curve. It is also preferred that 
the total reserves in a voltage control area be depleted by a certain 
percentage and/or below a certain level before the reactive sources in the 
voltage control area added to a reactive reserve basin. 
A single contingency analysis is performed by block 104. More specifically, 
a quantity representative of the reactive reserves depleted in response to 
each of a plurality of single contingencies is computed. These single 
contingencies include single line outages and single generator outages. 
Using the information computed in the single contingency analysis, a 
multiple contingency analysis is performed in block 106. The multiple 
contingencies selected for analysis comprise at least two of the single 
contingencies whose corresponding reactive reserve depletion quantity 
exceeds a predetermined threshold. The multiple contingency analysis is 
performed for at least one reactive reserve basin. 
In FIG. 2, a flow chart illustrates grouping the buses into voltage control 
areas in accordance with the present invention. Voltage control areas are 
defined as coherent bus groups where the Q-V curve computed at any bus in 
that coherent group has virtually identical voltage and reactive margin at 
the Q-V curve minimum. Furthermore, the shape and slope of the Q-V curve 
computed at any bus in the voltage control area should be nearly 
identical. Based on the above definition, the voltage control areas are 
determined using a coherent group clustering algorithm. An initial value 
of a control parameter, alpha, for the clustering algorithm is selected in 
block 120. The coherent group clustering algorithm employed is based on 
eliminating the weakest connections from each network bus until the sum of 
reactive power-voltage Jacobian elements for eliminated branches is less 
than a parameter alpha times the largest diagonal element of the reactive 
power-voltage Jacobian matrix. The isolated bus groups identified for a 
particular alpha are the coherent bus groups for that alpha value. This 
step of isolating bus groups in dependence upon the alpha parameter is 
illustrated by block 122. 
For smaller values of alpha selected in block 120, the bus groups are 
continuously split until each bus group comprises a single bus. On the 
contrary, if alpha is selected to be relatively large in block 120, all 
buses belong to one bus group. In block 124, a level of coherency within 
bus groups as well as a concomitant incoherency between bus groups is 
examined based upon the Q-V curves. In particular, the Q-V curves are 
examined to determine whether all buses in each bus cluster have 
substantially the same Q-V curve minimum. If the Q-V curve minima are not 
substantially the same, then flow of the routine is directed back up to 
block 120 where a new value of alpha is selected. If the Q-V curve minima 
are substantially the same, then the routine is exited by return block 
126. 
Determining the reactive reserve basin for each of at least one of the 
voltage control areas is illustrated by the flow chart in FIG. 3. In block 
140, a set of test voltage control areas is selected. The selected test 
voltage control areas are those that have large shunt capacitive supply, 
or an increase in reactive loss or reactive supply as Q-V curves are 
computed in neighboring test voltage control areas. Line charging, shunt 
capacitive withdrawal, series I.sup.2 X series reactive loss, increased 
reactive inductive or capacitive shunts due to under load tap changers, or 
switchable shunt capacitors or reactors cause the increase in reactive 
loss or supply in a voltage control area. A Q-V curve is computed in each 
test voltage control area that has satisfied these conditions as Q-V 
curves were computed in other voltage control areas. Reactive reserve 
basins are only determined for those test voltage control areas, called 
critical voltage control areas, with Q-V curves having a large voltage and 
a small reactive margin at the minimum of the Q-V curve. In practice, the 
minimum of the Q-V curve can be obtained using a standard Newton-Raphson 
algorithm. 
For each critical voltage control area, the voltage control areas which 
experience a reduction in reserves greater than a predetermined threshold 
at the Q-V curve minimum is selected in block 142. In practice, the 
predetermined threshold is measured on a relative scale and is selected to 
be less than 100%. In one embodiment, the reactive reserve basin includes 
voltage control areas which experience greater than 75% reduction in 
reserves in computing the Q-V curve down to the Q-V curve minimum. This 
logic is aimed at guaranteeing that every reactive reserve basin is robust 
in the sense that no contingency or operating change that causes voltage 
instability on the test voltage control area can exhaust all of the 
reactive supply and voltage control reserve in a voltage control area 
outside those voltage control areas contained in the reactive reserve 
basin computed. 
In the flow chart of FIG. 3, the reactive reserve basins are computed only 
for the selected subset of voltage control areas that are predicted to be 
vulnerable to voltage instability by having large capacitive supply, 
experiencing large shunt capacitive supply increases, or experiencing 
inductive increases as Q-V curves are computed in other test voltage 
control areas having Q-V curve voltage minima greater than a threshold and 
reactive minima smaller than another threshold. Moreover, the use of 
reactive reserve quantities provides an accumulative proximity measure 
that makes voltage stability assessment practical because it is an 
exhaustible resource that always correlates well with proximity to voltage 
instability and is easily computed for a contingency. 
In such a manner, unique global voltage stability problems can be 
identified that have large numbers of voltage control areas and are nearly 
disjoint. Most, if not all, voltage stability problems that ever occur are 
local. Moreover, a multiplicity of local voltage stability problems are 
associated with each global voltage stability problem. Indeed, local 
voltage stability problems may be determined with a local reactive reserve 
basin that is substantially a subset of some global reactive reserve 
basin. Identifying critical voltage control areas for each local stability 
problem and their reactive reserve basins identifies the location of each 
stability problem, what reactive reserves prevent each local stability 
problem from occurring, and why each local voltage instability occurs. 
Still further, the locally most vulnerable reactive reserve basin may be 
determined that lies within virtually every other local reactive reserve 
basin according to the Q-V curve with nearly the largest voltage maxima 
and nearly the smallest reactive minima. Thereafter, its reserves are 
rapidly exhausted for the Q-V curve computed in the critical voltage 
control areas associated with the global and all nested local reactive 
reserve basins. However, despite the fact that the Q-V curve may have the 
largest voltage minima and the largest reactive margin, it may not be the 
most probable local voltage stability problem because there may not be 
severe contingencies that directly impact its critical voltage control 
area because it lies in a remote and low voltage part of the system. This 
leads to contingency selection for each local reactive reserve basin where 
in some utilities the same contingencies affect the global and all locals, 
and yet in other utilities different contingencies affect different locals 
within a global reactive reserve basin. 
Performing a single contingency analysis is illustrated by the flow chart 
in FIG. 4. This single contingency analysis is performed for each critical 
voltage control area and its associated reactive reserve basin. In block 
160, a single contingency is simulated. Specific types of single 
contingencies include single generator outages and single line outages. 
The reactive reserves in each reactive reserve basin are computed for the 
single contingency in block 162. Conditional block 164 examines whether 
there are more single contingencies to be simulated. If so, flow of the 
routine is directed back up to block 160 where another single contingency 
is simulated. If no further contingencies are to be simulated, then the 
contingencies in each reactive reserve basin are ranked from smallest to 
largest based upon the reactive reserves exhausted by block 166. In block 
168, the single line outages which exhaust more than a predetermined 
percentage of the reserves in each voltage control area are listed. 
In block 170, the two largest reactive capacity generators in each reactive 
reserve basin which exhaust more than a predetermined percentage of its 
reserve for some contingency are selected. These generators are placed on 
a generators list. The two lists formed in blocks 168 and 170 are used in 
forming multiple contingencies in a subsequent multiple contingency 
analysis. 
Performing multiple contingency analysis is illustrated by the flow chart 
in FIG. 5. Using the list of single contingencies formed in block 168, a 
list of double line outages is formed in block 180. Similarly, using the 
list of generators formed in block 170, a list of double generator outages 
is formed in block 182. In block 184, a combination of line and generator 
outages from the lists formed in blocks 168 and 170 are used to form a 
combination list. The step of performing an analysis of contingencies 
based upon the lists produced in blocks 180, 182, and 184, is illustrated 
by block 186. 
Software for determining the voltage control areas is illustrated by the 
flow chart in FIG. 6. In block 200, an initialization step is performed 
wherein a seed bus, a number of branches, and a minimum voltage level are 
selected in order to define a region of interest. Next, the Q-V curves are 
run and reactive reserve basins are determined at all buses in the region 
of interest in block 202. In block 204, a voting procedure is employed to 
select alpha where the Q-V curves computed at all buses in each bus 
cluster has substantially the same Q-V curve minimum and reactive reserve 
basin. The parameter alpha decides the size of the coherent bus clusters 
which form voltage control areas. As alpha decreases, the size of the 
coherent bus clusters increases through aggregation of coherent bus 
clusters identified for larger alpha values. This search procedure 
eliminates the need for a user to make a judgment on where the differences 
in voltage changes at buses within coherent bus groups increases from very 
small values, and the voltage change differences between buses in 
different bus groups for a disturbance suddenly increase to large values 
as alpha decreases. 
In the search procedure for alpha, a bounded interval of potential values 
of alpha is first selected. The procedure places a disturbance, namely a 
voltage change at some seed bus, and calculates the changes in voltage and 
angle at each bus due to the disturbance. The procedure finds bus clusters 
for ten equally-spaced alpha values in this bounded interval, and then 
finds the smallest alpha value where the voltage and angle changes within 
the bus group satisfy the following equations: 
EQU .DELTA.V.sub.j -.DELTA.V.sub.i .ltoreq.k.sub.1 .DELTA.V.sub.i 
EQU .DELTA..theta..sub.j -.DELTA..theta..sub.i .ltoreq.k.sub.2 
.DELTA..theta..sub.i 
where .DELTA.V is a voltage change, .DELTA..theta.is an angle change, i and 
j are indices representing two buses within a bus group, and k.sub.1 and 
k.sub.2 are fixed parameters. 
The results are confirmed as voltage control areas by running Q-V curves at 
all buses in the voltage control areas to establish if alpha was selected 
properly such that the minima of the Q-V curves and the reactive reserve 
basin obtained from the minima of the Q-V curves are identical. If the 
alpha value was chosen correctly so that the Q-V curve minima and reactive 
reserve basins computed at every bus in the bus clusters selected are 
identical, the user has obtained the voltage control areas and proper 
alpha value for obtaining these voltage control areas. If the alpha value 
was not correctly selected because the Q-V curve minima and reactive 
reserve basins are not identical for buses in a voltage control area, 
several larger values of alpha that produce smaller bus cluster groups can 
be examined until bus clusters which have nearly identical Q-V curve 
minima and reactive reserve basins are found. Hence, computing voltage 
control areas in this manner is based on both the level of coherency 
within bus clusters and the level of incoherency across bus clusters. 
Alternative embodiments can be formed which explicitly use the definition 
of voltage control area in order to find alpha. More specifically, an 
alternative embodiment would search for the value of alpha that is as 
small as possible, i.e. which produces the largest bus cluster, and yet 
assures that the Q-V curves computed at every bus in each bus cluster has 
nearly identical Q-V curve minima and reactive reserve basins. The search 
for alpha would only concentrate on bus clusters in some region of 
interest, which are buses above a certain voltage rating and at most three 
circuit branches from some seed bus. 
Turning now to FIG. 7, a flow chart of a contingency selection program is 
illustrated. As seen therein, a contingency selection and ranking for 
contingencies and operating changes that bring a particular test voltage 
control area and its reactive reserve basin closest to voltage instability 
is performed. The contingency selection and rankings are performed for 
each critical voltage control area and associated reactive reserve basin. 
In block 210, a single line outage contingency is simulated. The reserves 
in each reactive reserve basin are computed for that contingency in block 
212. In conditional block 214, it is determined whether or not there are 
any other contingencies to be simulated. If there are further 
contingencies to be simulated, then flow of the method is returned back to 
block 210. If there are no additional contingencies to be simulated, then 
flow of the routine advances to block 216. 
In block 216, the contingencies are ranked in each reactive reserve basin 
based upon reactive reserves. In block 218, the line outages that exhaust 
more than P% of the reserves in each voltage control area are selected and 
placed in a list. Further, the largest two reactive capacity generators in 
each reactive reserve basin that exhausts P% of its reserve for some line 
outage are also selected. These generators are placed in another list. The 
list of generators is used to produce a set of severe single and double 
generator outage contingencies. The list of line outages are used to 
produce a set of severe single and double line outage contingencies. The 
list of generators and line outages is used to produce a set of 
combination line outage and loss of generation contingencies. 
In block 220, the severe single and multiple contingencies are simulated 
and ranked based upon the reactive reserve in a reactive reserve basin. 
The contingency selection routine can be run several times in sequence to 
obtain all of the information on why particular reactive reserve basins 
are vulnerable to voltage instability. The initial run would entail taking 
all single line outages in one or more areas, or in one or more zones or 
areas where voltage instability is to be studied, or in the entire system 
model. 
In a preferred embodiment, the contingency selection routine would output a 
report summarizing the effects of the worst five contingencies for each 
critical reactive reserve basin. The output for each reactive reserve 
basin has an initial summary of the status in the pre-contingency case, 
including the bus names and numbers for all buses in each of the reactive 
reserve basin voltage control areas, the reactive supply capacity and 
reserves for generators, synchronous condensers, and switchable shunt 
capacitors at the bus where the component is located. 
After the initial status of a reactive reserve basin is provided, the five 
worst contingencies for that reactive reserve basin are given. Each 
contingency is described and the reactive supply reserves at all 
generators and switchable shunt capacitors in each reactive reserve basin 
voltage control area are given. The order of voltage control areas in the 
report of voltage control area reactive supply reserves for a particular 
reactive reserve basin is based on the sequence of reserve exhaustion 
during computation of the Q-V curve. The order of voltage control areas 
aid in indicating the order of exhaustion as voltage collapse is 
approached for any contingency for that reactive reserve basin. The order 
of the contingencies presented in the output report for a reactive reserve 
basin is based on the percentage of pre-contingency reactive reserves 
exhausted with the contingency causing the largest percentage reduction 
reported first. The order of the reactive reserve basins presented in the 
output report is sorted so that the reactive reserve basins that 
experience the largest percentage exhaustion of reactive supply on 
generators and switchable shunt capacitors for that reactive reserve 
basin's worst contingency are reported first. 
The contingency selection routine assists the user in determining the 
reactive reserve basins that experience voltage instability because they 
would be the first to be reported. If no reactive reserve basin experience 
voltage instability, the reporting of the reactive reserve basins in the 
order of the largest percentage reduction in total reserves gives only a 
partial indication of the reactive reserve basin with the most severe 
contingencies. Percentage reduction in total reactive reserves of a 
reactive reserve basin is an excellent indicator of the worst contingency 
in a reactive reserve basin and the most vulnerable reactive reserve basin 
when the system is experiencing or is nearly experiencing voltage 
instability. The number of voltage control areas in a reactive reserve 
basin that exhausts reserves and the status of whether or not reactive 
reserves are exhausted on voltage control areas listed at the end of the 
list given for that reactive reserve basin are effective indicators in 
judging proximity to voltage instability when the contingency does not 
bring a reactive reserve basin close to voltage instability. The reason 
for utilizing both indicators for voltage collapse proximity rather than 
percentage reactive reserve reduction is that the system experiences a 
quantum step toward voltage instability after each successive voltage 
control area experiences reserve exhaustion, and experience indicates 
voltage control areas that exhaust reserves near the Q-V curve minimum for 
the pre-contingency case are near the Q-V curve minimum for most 
contingencies. 
An alternative embodiment of the contingency selection routine would 
further include modifying the set of reactive reserve basin voltage 
control areas reserve level for contingencies that lie in the path between 
a reactive reserve basin voltage control area and the test voltage control 
area. Such contingencies can have a reactive reserve basin that does not 
contain the pre-contingency reserve basin voltage control area that is 
totally or partially disconnected from the test voltage control area by 
the line outage contingency. Contingencies that have a modified reactive 
reserve basin and the voltage control area that should be deleted from the 
pre-contingency reactive reserve basin both can be detected by looking for 
contingencies where a reactive reserve basin voltage control area 
experiences little reduction in reserve compared to other severe 
contingencies. The deletion of these voltage control areas from reactive 
reserve basins for those contingencies will make the contingency ranking 
based on reactive reserve basin reactive reserves more accurate without 
requiring the user to make judgments. 
In FIG. 8, performing a reactive reserve basin security assessment is 
illustrated by a flow chart. An initialization step is performed in block 
230 wherein selected data is retrieved. This data includes base case 
simulation data, values of alpha, values of a lower voltage limit where 
attempts to compute a Q-V curve minimum are aborted, and the criterion 
used for selecting the reactive reserve basin voltage control areas. 
In block 232, each critical voltage control area is specified along with 
its test bus. The lists of single line outage, double line outage, single 
loss of generation, double loss of generation, and combination 
contingencies are read in block 234. 
In block 236, the Q-V curves are computed for each contingency specified 
for the base case for each voltage control area. In conditional block 238, 
a check for a positive Q-V curve minimum is performed. If a Q-V curve has 
a positive minimum, then execution of the routine is stopped. If there are 
no positive Q-V curve minima, then execution of the routine proceeds to 
block 240. 
In block 240, a transfer pattern and level are read and a Q-V curve is 
computed for each contingency and voltage control area. Conditional block 
242 checks whether or not there is a Q-V curve with a positive minimum. If 
a Q-V curve with a positive minimum exists, then execution of the routine 
is stopped. Otherwise, the transfer level is increased until a positive 
Q-V curve minimum is obtained in block 244. If, at block 246, there are 
additional transfer patterns which need evaluation, then flow of the 
routine is directed back up to block 240. If no additional transfer 
patterns need evaluation, then a load pattern and level is read in block 
248, and a Q-V curve is computed for each contingency and voltage control 
area. If there is a Q-V curve with a positive minimum as detected by 
conditional block 250, then execution of the routine is stopped. 
Otherwise, the load level is increased until a positive Q-V curve minimum 
is obtained in block 252. If, at block 254, additional transfer patterns 
need evaluation, then flow of the routine is directed back up to block 
248. If no additional transfer patterns need evaluation, then execution of 
the routine is completed. 
Ideally, the computed reactive reserve basins are robust. Robustness 
implies that the voltage control areas that experience near exhaustion of 
reserves for all reactive supply and voltage control devices at the Q-V 
curve collapse point in the pre-contingency case can experience exhaustion 
of reserves at the Q-V curve collapse point after: any single contingency, 
transfer, or loading pattern change; or after any combination line outage 
and loss of reactive resource contingency; or after any combination line 
outage/loss of reactive resource contingency and any transfer or loading 
change in any pattern. Demonstrating that the reactive reserve basins are 
robust based on the above definition is illustrated by the flow chart in 
FIG. 9. 
In block 260, a set of line outage contingencies, loss of resource 
contingencies, transfers, real power loading pattern changes, operating 
changes, and combination line outage/loss of resource contingencies that 
are known to exhaust reactive reserves in one or more specified reactive 
reserve basins as well as test buses in critical voltage control areas for 
computing the Q-V curves that produce each of these reactive reserve 
basins are provided as input to the routine. These inputs can be provided 
from the output of the contingency selection routine. 
In block 262, the voltage control areas belonging to a specified reactive 
reserve basin are determined by computing the Q-V curve and its minimum 
for each single or double contingency or operating change specified. The 
reactive reserve basins of the Q-V curve computed at a test bus in a 
critical voltage control area for each single or double contingency or 
operating change are outputted into a table for that critical voltage 
control area by block 264. This table is used to confirm that 
contingencies or operating changes do not exhaust reserves on voltage 
control areas where all reactive supply and voltage control reserves are 
not nearly or completely exhausted when a Q-V curve is computed for the 
pre-contingency case at a test bus in a critical voltage control area. 
Performing an intelligent voltage stability security assessment is 
illustrated by the flow chart in FIG. 10. The procedure involves 
determining, at block 270, the voltage control areas, i.e. the bus 
clusters where the Q-V curves computed at any bus have the same shape and 
the same curve minimum, and the same reactive reserve basin. These bus 
clusters are found based on coherency, in other words, the same voltage 
and angle changes are exhibited at all buses in the voltage control area 
due to any disturbance. Alternatively, the bus clusters are found based on 
controllability, observability, or modal properties. 
Next, the subset of all of the reactive supply resources within voltage 
control areas that exhaust all of their reactive supply at the minimum of 
the Q-V curve computed at any bus in the test voltage control area is 
determined at block 272. The minimum of the Q-V curve can generally be 
obtained using a normal Newton-Raphson algorithm using a standard 
procedure that will obtain the minimum when the direct application of the 
Newton-Raphson algorithm would stop obtaining solutions short of the 
minimum. 
A second condition for buses to belong to a voltage control area is that 
the Q-V curve computed at each bus in a test voltage control area exhausts 
the same reactive supply resources in the same set of voltage control 
areas at the Q-V curve minimum. The subset of reactive supply resources in 
a system exhausted at the Q-V curve minimum is called the reactive reserve 
basin for that voltage control area. The slope of the Q-V curve decreases 
discontinuously each time all of the reactive supply reserves in one of 
the voltage control areas in the reactive reserve basin is exhausted. The 
reactive supply from a reactive reserve basin voltage control area to the 
test voltage control area is maintained as long as one of the voltage 
controls associated with reactive supply devices in a voltage control area 
is active and holds the voltage in that voltage control area. 
The discontinuity in the slope of the Q-V curve occurs not only due to loss 
of reactive supply from the reactive reserve basin voltage control area, 
but occurs due to the increased rate of increase in reactive losses with 
voltage decline that accompanies loss of all voltage control in a voltage 
control area. The reactive reserve basins are computed for only selected 
subsets of voltage control areas that are predicted to be vulnerable to 
voltage instability. The voltage control areas that can experience voltage 
collapse are predicted by determining those that have large shunt 
capacitive supply or experience large reactive network loss change for Q-V 
curves computed to determine the reactive reserve basin for a neighboring 
voltage control area. 
A further step entails determining, at block 274, those reactive reserve 
basins and their associated test voltage control areas that are most 
vulnerable to single or multiple contingencies. The five worst 
contingencies, which either cause voltage collapse by exhausting all 
reactive reserves in the reactive reserve basin or bring the reactive 
reserve basin closest to voltage instability by exhausting the largest 
percentages of the reactive reserves in that reactive reserve basin, are 
also found at block 276. 
A file of single worst line outage contingencies that exhaust P% or more of 
the reactive reserves in any reactive reserve basin is produced at block 
280. Further, a list of worst generator outage contingencies which is also 
produced, at block 280, by identifying the two largest capacity generators 
from each reactive reserve basin where one or more line outage 
contingencies exhaust P% or more of the reactive reserve basin reserves. 
These two contingency lists are used to produce, at block 282, a list of 
all single line outages, all single generator outages, all double line 
outages, all double generator outages, and combination line and generator 
outages. Also, a list of test voltage control areas where P% or more of 
the reactive reserves were exhausted by single line outages is produced. 
These files are used to compute Q-V curve minima and reactive reserve basin 
voltage control areas with reactive reserves for every contingency in the 
lists for each reactive reserve basin test voltage control area specified. 
Although the number of contingencies in the lists is preferably limited to 
the projected ten worst contingencies, a user may be allowed to run all of 
the other contingencies. 
In block 284, a security assessment for single and multiple contingencies 
with different transfer and loading patterns is performed. Transfer limits 
are determined for each anticipated transfer pattern (specified by a group 
of generators with increasing generation in some percentage of the total 
transfer level and a group of generators with decreasing generation in 
some percentage of the total transfer level). The transfer level is 
increased in increments and Q-V curves are computed for all reactive 
reserve basin critical voltage control areas and all single and multiple 
contingencies. If all Q-V curves for all single and multiple contingencies 
in every critical voltage control area have negative Q-V reactive minima 
(implying voltage stability) the total transfer level is incremented again 
and all Q-V curves are recomputed. This process is repeated until one Q-V 
curve has Q-V curve positive minima (implying voltage instability). The 
total transfer level limit for the transfer pattern is thus determined. A 
transfer pattern level limit is computed for each anticipated transfer 
pattern and the reactive reserve basin where the Q-V curve is positive for 
one or more single or multiple contingencies is noted. 
The same process is repeated for loading patterns to find those reactive 
reserve basins that have positive Q-V curve minima for one or more 
contingencies. The reactive reserve basins that constrain each transfer 
(or loading pattern) and the contingencies that cause the voltage 
instability for that transfer (or loading pattern) are used as the basis 
of designing enhancements that prevent voltage instability in that 
reactive reserve basin for those contingencies and a desired level of 
transfer (possibly larger than the current transfer limit). It should be 
noted that the general planning design criterion for voltage instability 
only requires that a power system survive a worst combination generator 
and line outage and does not require that a system survive a double line 
outage contingency. 
If the load flow will not solve for some contingency, transfer pattern and 
level, or loading pattern and level, reactive reserves are increased in 
all generators in each global reactive reserve basin, one at a time. If 
the addition of reactive reserves in some global reactive reserve basin 
allows a Q-V curve load flow solution to be computed, then the 
contingency, transfer pattern and level, and loading pattern and level 
would cause a voltage instability in that global reactive reserve basin. 
This feature allows on to determine whether a contingency, or transfer or 
loading pattern causes a voltage instability in some other global reactive 
reserve basin than the one being studied. 
If one has performed the above assessment of transfer limits for each 
anticipated transfer pattern and loading limits for each anticipated 
loading pattern, one can determine the transfer pattern limits that need 
to be increased and the desired level, as well as the loading pattern 
limits that need to be increased and their desired levels. For each 
transfer (or loading) pattern where the design criterion is not satisfied 
out to the desired limit, one knows the local reactive reserve basin or 
basins and the contingencies that cause voltage instability in that 
reactive reserve basin or basins. 
The previously described embodiments of the present invention have many 
advantages. By determining single contingencies which exhaust more that 
pre-specified percentage of reactive reserves, a computationally efficient 
method of performing multiple contingency analysis results. The resulting 
method is capable of selecting multiple loss of reactive resources, line 
outages, and combinations thereof, for performing an analysis of the 
effect of multiple contingencies on each reactive reserve basin. 
Furthermore, embodiments of the present invention are capable of 
identifying the specific critical voltage control area and reactive 
reserve basin that is brought to voltage instability after some 
contingency by a particular transfer or loading pattern change that can 
cause voltage instability in a voltage control area. 
Another advantage is that the present invention identifies a global 
stability problem and each local voltage stability problem. The loss of 
stability for each such problem is caused by a lack of sufficient reactive 
supply to its critical voltage control area. The reactive reserve basin in 
the critical voltage control areas that maintain voltage and thereby 
prevent the reactive losses that consume and choke off reactive supply 
from outside, as well as inside, the respective reactive reserve basin 
from reaching the critical voltage control area. A global voltage 
stability problem generally has many individual local voltage stability 
problems and each can occur due to different contingencies or in some 
cases due to the same severe contingencies that cause loss of local 
voltage stability for several critical voltage control areas by exhausting 
their reactive reserve basin reserves. The advantages still further 
include detecting each critical voltage control area, its reactive reserve 
basin, the severe single and multiple contingencies that cause voltage 
instability in several local reactive reserve basins and may even cause a 
global voltage instability. 
While the best modes for carrying out the invention have been described in 
detail, those familiar with the art to which this invention relates will 
recognize various alternative designs and embodiments for practicing the 
invention as defined by the following claims.