CA2188678A1

CA2188678A1 - Method for performing a voltage stability security assessment for a power transmission system

Info

Publication number: CA2188678A1
Application number: CA002188678A
Authority: CA
Inventors: Robert Anthony Schlueter
Original assignee: Individual
Current assignee: Michigan State University MSU
Priority date: 1994-04-29
Filing date: 1995-04-17
Publication date: 1995-11-09
Also published as: US5594659A; WO1995030266A1; JPH09512698A; EP0757855A1

Abstract

A method for performing a voltage stability security assessment for a region of an electric 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.

Description

~:V0 95/30266 2 1 8 8 6 7 8 METHOD FOR PE:RFORMING A
VOLTAGE STABILITY SE~:UKIl Y A.~.~l;A~.~.l~T
FOR A POWE~ TRANSMISSION SYSTli~M
Technical Field This invention relates generally to plAnnin~
O'A' electrical power trAncm; qqi An systems, and more p~Articularly, to a Dethod for per~orming a voltage ~tabi1itY A--- t for power trAncm; Csi~n systems.
R~ ,ulld ~rt There are a number of potential voltage in~tability problems which can arise within an electri-cal power system. Some of these instability problems occur in distribution systems used for distributing Qlectrical power to utility ,u:~L 6. Nany of the sources of these distribution system voltage stability problems have existed for years, and their causes and 3A~l.,t;,Anq ~Are well known in the art.
Other problems occur in tr~nAmiq~itAn systems, which are used for LLrAn~uLLing bulk power from genera-tion ~tations to load centers. These stability problem~
result rrO~ such causes as facility outages, clearing of short circuit faults, and increases in load power or inter-area power transfer in a trAn-m;~qinn network.
25any of these trAn~mi qqit~n system voltage instability problems have been Pn~ uu"~- d only in recent years.
These instability problems have O~;~ ULL-a A as a result of recent trends toward: locating generation stations dist~ntly from load centers which limits the effec-tiveness of their voltage controls, requiring utilities W0 95/30266 ~ ~ 8 8 ,~ 7 8, ,, r_".J~ s ~72s to allow power 8h; 1 across their trAn~"ics;on system by ;nA~l-Q~ ent power ~L.JdU~,~L~ or other utilities, and dQterring c.,.._LLu-i~ion of needed transmission neL .Lks, to namQ a few.
A slow-spreading, u~ Lullable decline in voltage, known a5 voltage collapse, is a specific type of trAn~; C~ n 5y5tem voltage instability. Voltage col 1 ~r~o results when generators reach their f ield current limits which causes a .1; 5Ahl; n~ of their exci-tation voltage control systems. Yoltage coll ~rse has recently caused major blackout5 in a number of different countries around the world.
In order to reduce the pogcih; l; ty of voltage col l~p-e in a power system, and more generally, improve the Dtability of the power system, system planning is per~ormed by many utility ~~;~. First, a mathemat-ical model repre5entative of the ba5ic el~ o~ the power system, and their inteL-.v--~ ion, is ~o--L.u~.~ad.
ThQse basic el~ - include generating stations, transformers, transmission line5, and sources of reac-tive ~;ese.~ such as Dyll~l~L~-uu voltage c~n~l~nC~rs and capacitor }~anks. Next, various computational te~hn;-~_es ~or an~lyzing system 5tability are performed using a ~uitably ~L~L - ~ computer. Based on this analysis, ~ os~d ~nh~r ~5 are formulated in an ad-hoc manner ~or improving voltage stability security. The m~ll` t-ical model can be updated based upon these ~Lu~ose~
so that the resulting system stability security can be analyzed. Fnh~ s which attain pr~A~t~rm;n~A design objectives are then physically impl~ ed in the actual ~ower system. The process Or wo ssr30266 218 8 6 7 8 r~ 725 system plAnn;n~ is continual in that it must be regular-ly perfor~ed in light of changing circumstances.
In mathematical terms, voltage collapse occurs 5 when equilibrium equations associated with the mathemat-ical model of the tr~n-micsi~n system do not have unique local solutions. Thi5 result5 either when a local solution does not exist or when multiple solutions exist. ~he point at which the equilibrium equations no 10 longer have a solution or a unique solution is often as_ociated with some physical or control cAr~hil ity limit o~ the power system.
Current methods for AecPe5;nq proximity to classic voltage instability are based on some measure of 15 how close a load ~low Jacobian is to a s;n~lArity cpndition, since a sin~ll~r load flow Jacobi~n implies that there is not a unique sol lt; ~n . These proximity measures include: (i) the smallest eigenvalue ~y~ ~ol.ing zero, (ii) the minimum c;nr~lAr value, (iii) 20 various sensitivity matrices, (iv) the reactive power flow-voltage level (Q-V) curve margin, (v) the real power ~low-voltage level (P-V) curve margin, and (vi) eigenvalue approximation ~ 3 of load flow Jacobian ~; nq-- 1 A rity .
The eigenvalue and minimum s;n~Ul~r value methods are disadvantageous in their lacking an indi-cation of the actual locations and causes of voltage instability. IIJLt:~V~ these methods have been known to produce micleA~;n~ results with respect to causes of voltage instability as well as the locations and types of Dnh~-- -~ necessAry to improve voltage stability security. Fur~h~ ~, the computational requirements Wo 9~/30266 2 1 g 8 ~ 7 8 ~ t ~
( for the eigenvalue and minimum singular value methods ~re relatively high. The sensitivity matrix methods have many of the same difficulties as the eigenvalue and ~ln~-lAr value methods resulting from being linear S ir._-- Al measures for a highly-nri~ni ;n~Ar ,l;ccr~rlt;
uous procefis.
Regardless of the method e~ployed f or as-sessing proximity to classic voltage instability, exi5ting methods employed by many utility r n; ~'S
10 assume that there is only one voltage instability problem. Purther, it is assumed that one distributed rQactive power loading pattern test detects the one voltage instability problem.
It is known that a voltagQ control area may be 15 defined as an electrically isolated bus group in a power ~ystem. RQactive L eS~=L veS in each voltage control area may be distributed via ~e~ y voltage control so that no ~ ~tur or station would exhaust I ~ L ~I ~S bef ore ~ll the other generators in the voltage control area.
20 Although this s~on~3Ary voltage control is effective in preventlng classic voltage instability, previously defined voltage control areas are no longer valid the originally existing transmission grid is ~r,hJ~r..~ o that bus groups are no longer as isolated.
25 A ~urther disadvantage of this approach is that the rR_ctive L~ 5 for controlling each voltage control area are limited to be within the voltage control area.
Methods are also known which employ a voltage zone def ined as a group of one or more tightly-coupled 30 g~nerator P-V buses together with the union of the sets of load buses they mutually support. In such methods, Wo 95/30266 2 1 8 8 6 7 8 r~l, r o47~

the amount of reactive power supply to maintain an ~cceptable voltage level is controlled. A disadvantage of this approach, however, i5 that characterizing a - voltage stability margin in terms of voltage does not S protect ~against classic voltage col 1 ~r-e .
Current engineering methods of locating potential voltage instability problems ;nrl~A~ simula-ting all single line outage cont;nq~n~ i~C, and identi-rying those that do not solve as causing voltage insta-10 bility. However, the lack of a solution is not aguarantee of voltage instability; a lack o~ a solution can occur because: the load rlow ~le ~ u~ aphson-based algorithms are not guaranteed to ~ul~tLye from any particular starting solution, but cu,.vel~e only when the 15 starting point is su~riciently close to the solt~t ~ ~n;
the load rlOw Cù~lvéL~3el~Ce is not guaranteed even when the 5ystem is close to a solution if the solution is clofie to a bifurcation; ru-."d o~r error arfects the load rlOw ~.ull~L~e~ ; and discontinuous changes due to 20 switching Or shunt ~1- , or outages of ~-.leL~tUL:i or lines can have a dramatic ef f ect on whether the load flow algorithm will COI~Ve:LYè to a solut;^n. The con-verged 501~1~ ionC ror all single outages only indicates that there are no bifurcations. In order to attempt to 25 prov~ that the absence of a C~ V~:LYed 8O1~t~ i5 caused by voltage instability, substantial ~ L and comput-er proc~C;r~q time are required. In one such method, the absence of a c~ L~ed solution i8 d~t~rm;n~ to be due to voltage collapse if one can add a f ictitious 30 ,_~ ~UL with infinite reactive supply at some bus to obtain a cu,.veL4ed load flow sol~ n. This method is not foolproof, and furfh~ ~:, does not indicate the Wo 9~30266 2 1 8 8 6 7 8 P~1l.J~. '472s cause of voltage instability nor indicate where it occurs .
However, current methods are ;n~ArAhle of identifying all of the many diiferent voltage stability 5 problemfi th~t can occur in a tr~n~ inn system. A
very routine operating change or D~ C~ y insigniSi-cant rnnt;nq~ncy in a remote region of the system, ~ollowed by another contingency, can cause voltage instability. Furth~ ~, voltage instability may occur 10 in many different sub-regions of the system. Current methods lack diagnostic ~LoceduL~s for identifying causes of specif ic voltage stability problems, as well as D,~D~ tlc and int~lllgent ~nhAn~ L ~Loce-lu~s for preventing voltage instability problems.
~ of the ~n~ Liull For the foregoing reasons, the need exists for a method o~ identifying potential locations of voltage instability problems, and det~n~n;nq corrective mea-sures to reduce the l ikPl ihnod of voltage instability.
It is thus an object of the present invention to provide an i uv.:d method for ~ t~mlninq potential voltage instability problems in an electrical power tr~n-~C~ion system.
~nother object of the present invention i5 to provid~ a method of identifying single conti n~n~
that cause voltage instability in an electrical power L. i r~ lon system .

o 9~l30266 !- 2 1 8 8 6 7 8 P~ 72s , .

A further object is to provide a method of identi~ying multiple cont;n~Pn~ s, transfer patterns and levels, and loading patterns and levels that cause voltage instability in an electrical power transmission 5 system.
In carrying out the above objects, the present invention provides a method of perf orming a ~nnt; nqPnry analysiD for a region of an electric power transmission system having a plurality of buses and a plurality of 10 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 CULL. ~r -inq rcactive power versus voltage ~elat;c~nch~. A corre-15 ~rnntl~n~ reactive reserve basin for each o~ at least oneof the voltage control areas is detP~;n~d. Each reactive reserve basin comprises at least one of the sources of reactive reserves sP~Pct~d in ~ e upon a measure of the reactive ~e SeL v~s depleted at a prede-20 tP~m;nPd operating point o~ the power system. A singlecontingency analysis is performed by _ ,_ ;nq a corre-~rnn~nq quantity rOr each reactive reserve basin in r~ ul-De to each of a plurality of single ~ont;nqpn~-ipq.
The UULL~-lJ'"'~7;nq quantity is lc~L~se~.L~tive of a 25 r~ t j nn in the reactive ~-:S-:L ~._6 within the reactive reserve basin. A multiple contingency analysis is per-~ormed for each reactive reserve basin based upon the ~ingle con~;n7Pnl~ipc whose c~LL- ,L~ in~ quantity exceeds a predetPrmi ~Pd threshold.
~he present invention further provides a method Or performing a voltage stability A~ ' for a region of an electric power trAn--;qqion system having ~09sl30266 218~78 r~ s l72s ~

a plurality of buses and a plurality of sources of reac-tive Le3_L~,~s 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 5 area has a similar correcpnn~; nq reactive power versus voltrAge relat i nn_h; r . At least one of the voltage control areas whose buses therewith in have a voltage at th~ minimum of the CULL ~ ;nj reactive power versus voltage relat;~AnAh;p which exceeds a voltage threshold 10 i8 selected. A CuLL~ i nj reactive reserve ~asin is ':tDrm;n~d 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 L~ ~eS selected in darDr' e upon a measure of the 15 r~active LQse~s depleted at a predetDrm;n-~3 operating point of the electric power tran-~; C~inA system. A
single c^nt;nqDnAy analysis is performed by computing a nq yuantity for each reactive reserve basin in ,~ se to each of a plurality of single fault 20 cont. ;nqanAi~ae~ wherein the CVLL r~ ;nq quantity is r.~L~ Lative of a re~ rt j r~n in the reactive reserves within the reactive reserve basin, and wherein the pluraAlity of single Cont;nqenAiD~ inAl~ DA~ at least one ingle generator outage and at least one single line 2S outaAgQ. The single cont;nq~-~Aia- whose C~LL ~ .,.1;nq quantity exceeds a predet-~m;nD~ thre ` ~]~ are select-~.
Thc voltage stability for single ~nd multiple coAt;nAJDn-cie~ with a plurality of transfer and loading patterns ar~ ~c~ d, wherein the single and multiple contingen-30 cie~ are based upon the selected single cont;nq~n~ c.
These and other objects, features and advan-tages will be readily ~ ale"~ upon cnn~ Aration of the W0 95130266 2 1 8 8 ~ 7 8 ~ 5'~ 1725 _g_ following description, a~ ded claims, and n~ ,-nying drawings .
Brief Des~ ,lion Of The Drawi~c FIGURE 1 is a f low chart of perf orming a 5 ~nn~;n.~nry analysis according to the method o~ the present invention;
FIGURE 2 is a f low chart of grouping buses into voltage control areas according to the method of the present invention;
FIGURE 3 is a flow chart of detonnin;nq a reactive reserve basin according to the method of the present invention;
FIGURE 4 is a f low chart of performing a single contingency analysis according to the method of 15 the present invention;
FIGURE 5 is a f low chart of perf or~ing a multiple contingency analysis according to the method of the present invention;
FIGURE 6 is a flow chart of ~l~t~m;n;
20 voltage control areas according to the method of the present invention;
- FIGURE 7 is a flow chart of performiny a contingency ~^leot;nn according to the method o~ the present invention;

Wo 95/30266 ~ r~ s ~ l725

2~88'67~

FIGI~RE 8 is a f low chart perf orming a reactive reserve basin security ~-s~~ according to the method of the present invention;
FIG~RE 9 is a f low chart ' LL c.ting ro-5 bustness of the reactive reserve basins according to themethod of the present invention; ~nd FIGURE 10 is a f low chart per~orming a sta-bility security A-g L according to the method of the present invention.
lo Best Modes For Ca~ryin~ Out The l.. ~ n The method of the present invention u ~ L ~ -the disadvantages of previous security methods and systems by intn~ nntly selecting single cont~n~nn~ used in performing a multiple contingency 15 analysis. Nore specifically, the single contin~nnci~s used in performing the multiple c~nt;n~r~nry analysis are selected based upon the rn~ t i l~n in reactive reserves in ~ region of the electrical power trAn~ irn system known as a reactive reserve basin. rlû- :uve:I, the method 20 of the present invention p~udu~ i a hierarchical control

3~LL~U~UL~: wherein a lack of controlli~h;lity provides ~vidence of a potential voltage instability problem.
In general, the method of the present inven-tion i8 capable of identifying totally inrl~L.~ ,L
25 voltage st~bility problems that affect ~airly isolated Le-' irn~ of one or more utilities. A unique voltage stAbility problem occurs when a Q-V curve computed at any bus in a suf~iciently coherent group has the same shape, minimum, and reactive reserve basin. The neigh-~ W<~ 9S~30266 218 ~ ~ ~7 8 r~, !'1 ~72S

boring voltage control areas with reactive supplydevices that exhaust nearly all reactive reserves upon I~-'' in-J the minimum of the Q-V curve computed in some critical voltage control area is a reactive reserve 5 basin for that critical voltage control area. A global voltage stability problem occurs when the reactive I L~ in a large number of voltage control areas are QYhausted. Global reactive reserve basins for different voltage stability problems do not contain any of the 10 same voltage control areas. Each global voltage stabil-ity problem is prevented by a unique and nu.. uv~llapping set of reactive supply devices belonging to its reactive reserve basin.
For each global stability problem, a large set 15 of local stability problems lie nested therewithin. In turn, eac~ local stability problem has a different reactive reserve ~asin associated therewith. However, these local reactive reserve basins overlap. As a result, the po~ih~lity exists that a generator, switch-20 able shunt capacitor or SVC belongs to several localreactive reserve basins.
When the reactive reserves in a voltage con-trol area are exhausted, all reactive reserve basins to which that voltage control area belongs eYperience a 25 significant step change toward voltage instability. The local reactive reserve basin that exhausts all reactive r~ in all voltage control areas due to contingen-cies or operating changes is the local reactive reserve basin that e2cperiences voltage instability, as long as 30 the cnnt ;n~an~ or operating changes directly impact the critical voltage control area where the Q-V curve is ~ to determine that reactive reserve basin. The ~o 95130266 ~ 18 8 6 7 8 r~ 1725 ~

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 s obtain all the reactive supply needed to cope with the c~nt~nqPn~-iP~ or operating changes. As used herein, a c~nt~n7Pn~y may be any unexpected discrete change in the tr~n~ ion system due to equipment 10s8 (such as a tULr tr~n~ sinn line, or transformer) or a short lO circuit ltypically 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 al~o belnnq1nq to a global reactive reserve basin. This lS locally most vulnerable reactive reserve basin ha6 relatively small res~Lv~s 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 20 reserve basin. Such locally most vulnerable reactive reserve basins should be the ~ocus of any system en-~ _ 1,5 It should be noted that local voltage sta-bility problems are those brought on by continqQnriPs or 25 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 ad~ Qd, not just the locally most vulnerable. This 30 is 80 because each local stability problem, inrl11~in~
the locally most vulnerable, may be brought on by dirrerent continqPr~riP~ or operating changes that caus~

. .! ' ~, ~ WO 95130266 218 g 6 7 8 r~ 725 reduction of, or partially cut off, the reactive re-serves associated with the critical voltaqe control area .
Nore specifically, the method of the present 5 invention employs Q-V curve tests for de~Qrm;nin~ a hierarchical control structure which indicates that voltage instability occurs when a lack of controlla-bility is evident . Perf orming a multiple contingency analysis i5 illustrated by the f low chart shown in 10 Figure 1. The multiple contingency analysis is to be performed for a region of a power system having a plurality o~ buses and a plurality of sources o~ reac-tive reserves coupled thereto.
In block 100, the plurality of buses are 15 grouped into voltage control areas in ~loron~lpnre upon a CULL-- L------1;n~ reactive power versus voltage rela~inn~ h;~
i~or each of the buses. More specifically, each voltage control area is def ined as a coherent bus group where adding a reactive load at any bus in the group ~L UdUCeS
20 nearly identical Q-V curves in both shape and magnitude.
AB A result, each voltage control area has a unique voltage ~ n~t~hi l; ty caused by a local ir.-_,, Lal r~active supply problem.
In block 102, ~otonm;n;nlJ a cGLL~~L ~ in ~
25 reactive reserve basin f or each o~ at least one of the voltage control areas is performed. Each reactive reserve basin comprises at least one source of reactive L~ qlocted in r3oron~onre upon a quantity repre-sentative of the reactive ~es~- v- s exhausted at a 30 predeto~m; nod operating point of the power system. The at least one source of reactive res~L v~:s c~nt:~; nod W0 95/3~266 2 1 8 8 ~ .7 8 ~ 5C l725 within the reactive reserve basin form a set of stabi-lizing controls for the cvLL~-~v~ ;n~ voltage control arQn. Prererably, the predetPrm;no~l operating point of the power system is the minimum of the Q-V curve. It i8 5 also preferred that the total reseL veS in a voltage control area be dêpleted by a certain percentage and/or below a certain level before the reactive 60urces in the voltage control area added to a reactive reserve basin.
A single contingency analysis is performed by 10 block 104. Nore specifically, a quantity r~res~..Ldtive of the reactive ~CS_~VèS depleted in response to each of a plurality of single cont;n~onr1~c is _ L-'. These ~ingle cnnt; nqon~-ioC include single line outages and ~ingle generator outages. Using the information comput_ 15 ed in the single contingency analysis, a multiple cnn~;n~ ry analysis is performed in block 106. The multiple contingencies solecto~ for analysis comprise at least two of the single cont;n~Pnc ios whose CVL~ ~VI~d ing reactive reserve deplet;~n guantity exceeds a 20 procle~orm;nod threshold. The multiple contingency analysis is performed for at least one reactive reserve basin.
In Figure 2, a flow chart illustrates grouping the buces into voltage control areas in accordance with 25 the present invention. Voltage control areas are def ined as coherent bus groups where the Q-V curve ' at any bus in that coh~ L group has virtually identical voltage and reactive margin at the Q-V curve m1n~ . Furthermore, the shape and slope of the Q-V
30 curve . _ e~ at any bus in the voltage control area should be nearly identical . Based on the above def ini-tion, the voltage control areas ~re deto-m;necl using a wo ssl30266 2 1 8 8 6 7 8 PC ., ~ ' 'D47~

coherent group clustering algorithm. An initial value of a control parameter, alpha, for the clustering algorithm is selected in block 120. The coherent group cluctering algorithm employed is based on eliminating 5 the weAkest cnnnDcti9nc from each network bus until the ~um of reactive ~ L v~,ltage Jacobian Dl~ Ls ~or eliminated branches is less than a parameter alpha ti_es the largest d i AqnnA l element of the reactive power-voltage Jacobian matrix. The isolated bus groups 10 identified for a particular alpha are the coherent bus groups for that alpha value. This step of isolating bus groups in dDrDn~lDn-e upon the alpha paL D-r is illus-trated by block 122.
For smaller values of alpha selected in block 15 120, the bus groups are contin~ cly split until each - bus group comprises a single bus. On the C~.IIILL-LY, ir alpha is sDI~DrtPd to be relatively large in block 120, all buses belong to one bus group. In block 124, a level of co~.e.ell- y within bus groups as well as a 20 concomitant incoherency between bus groups is DYAminDd based upon the Q-V curves. In particular, the Q-V
curves are ~YAm j nD~ to determine whether all buses in uach bus cluster have substantially the same Q-V curve minimum. If the Q-V curve minima are not substAntiA~ly 25 the ~ame, then flow of the routine is directed back up to block 120 where a new value of alpha is select~Dd. If the Q-V curve minima are substantially the same, then the routine is exited by return block 126.
DetDrminin~ the reactive reserve basin rOr 30 each of at least one of the voltage control areas is illustrated by the rlow chart in Figure 3. In block 140, a selt of test voltage control areas is selected.

W09~/30266 218~ 8 ~ l72S ~

The solec~oA 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 ~P; qhhoring test voltage control areas .
5 Line charging, shunt capacitive withdrawal, series I2X
series reactive loss, increased reactive inductive or capacitive shunts due to under load tap changers, or ~witchable shunt capacitors or reactors cause the increase in reactive loss or supply in a voltage control lO area. A Q-V curve is _ ~ed in each test voltage control area that has satis~ied these conditions as Q-V
curves were computed in other voltage control areas.
Reactive reserve basins are only Ao1 o~inod for those te~t voltage control areas, called critical voltage 15 control areas, with Q-V curves having a large voltage and a small reactive marqin 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 20 voltage control areas which experience a reduction in ~seL~ greater than a prodetorminod threshold at the Q-V curve minimum is selected in block 142. In prac-tice, the pred~oto~minoA threshold is ~ -- d on a relative scale and is sole~ted to be less than 100%. In 25 one o~hoAi- , the reactive reserve basin voltage control areas which experience greater than 75%
reAllrt~on in ~ eSel veS in computing the Q-V curve down to the Q-V curve minimum. This logic is aimed at guaran-teuing that every reactive reserve basin is robust in 30 the sense that no contingency or operating change that causes voltage instability on the test voltage control area can exhaust all o~ the reactive supply and voltage control reserve in a voltage control area outside those ~ Wo 95130266 ~ 2 1 8~ 6 7 B I ~ 72~

voltage control areas contained in the reactive reserve basin ~d.
In the ~low chart o~ Figure 3, the reactive reserve basins are computed only for the selected subset 5 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 10 areas having Q-V curve voltage minima greater than a threshold and reactive minima smaller than another threshold. IIJI è~ve~ ~ the use of reactive reserve ~Iuantities provides an a~- 1 Ative proximity measure that makes voltage stability ~ practical 15 because it is an exhaustible ~,u .;e 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 identif ied that have large 20 numbers of voltage control areas and are nearly dis-~oint. Most, if not all, voltage stability problems that ever occur are local. ~IOL~:G~ a multiplicity o~
local voltage stability problems are associated with e~ch global voltage stability problem. Indeed, local 25 voltage stability problems may be ~t~rm;n~d with a local reactive reserve basin that is substantially a subset of some global reactive reserve basin. Identify-ing critical voltage control areas for each local stability problem and their reactive reserve basins 30 identifies the location of each stability problem, what reactive Lese~ ~s prevent each local stability problem WO g5130266 r~ 1725 2~88678 ~
. .

from occurring, and why each local voltage instability occurs .
still further, the locally most vulnerable re~ctive reserve basin, may be ~7PtPnmi nPd that lies S within virtually every other local reactive reserve basin according to the Q-V curve with nearly the largest voltage maxima and nearly the ~mallest reactive minima.
Thereafter, its reserves are rapidly exhausted for the Q-V curve - _~ed in the critical voltage control areas 10 associated with the global and all nested local reactive reserve basins. ~lowever, 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 15 severe contin~pnripq that directly impact its critical voltage control area because it lies in a remote and low voltage part of the ~ystem. This leads to contingen~y a^l~ct~l~n for each local reactive reserve basin where in some utilities the same cont1n~nriPC affect the global 20 and all locals, and yet in other utilities different cnnt;ngenriPc affect different locals within a global rRactive reserve basin.
Performing a single contingency analysis is ill~z,LL~ted by the flow chart in Figure 4. This single 25 ront1n7Qnry analysis is performed for each critical voltage control area and its associated reactive reserve ba~in. In block 160, a single ~nntin~pnry is simulated.
SpPr~f~r- types of single cnntin~enripc include single generator outages and single line outages. ~rhe reactive 30 reserves in each reactive reserve basin are computed for the single contingency in block 162. Conditional block 164 ~YA~inPC whether there are more single contin~Pnri~c ~ Wo 95/30266 ~ ~ 1 8 8 6 ~ 8 P~ "72~

to be simulated. If so, flow of the routine is directed back up to block 160 where another single contingency is simulated. I~ no further contingencies are to be simulated, then the con~;n~nri~ in each reactive S reserve basin are ranked from smallest to largest ba6ed upon the reactive reserves exhausted by block 166. In block 168, the single line outages which exhaust more than a pr~ et~-m;n~d pc--,c~ ge of the L~-LVCS in each voltage control area ~re listed.
In block 170, the two largest reactive ca-pacity generators in each reactive reserve basin which exhaust more than a ~r-'~ - ";n^~ pe~v~..L~tc of its reserve for some c~n~inq~n~y are 5~ rt~rl. These generators are placed on a y_.~creLtuL~, list. The two lists formed in blocks 168 and 170 are used in forming multiple con~in~nl-ies in a suLs~u_..~ multiple contin-gency analysis.
Per~orming multiple c-lnt;n~Qnry analysis is illustrated by the flow chart in Figure 5. Using the list Or single confin~n~ formed in block 168, a list of double line outages is ~ormed in block 180. Similar-ly, using the list of generators ~ormed in block 170, a list of double y~ e~ ~tUL outages is formed in block 182.
In block 184, a combination of line and g_~,_r c~toL
outages from the list5 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 ~-vducc~ in blocks 180, 182, and 184, is illustrated by block 1860 Software for det~rmining the voltage control areas is llustrated by the f low chart in Figure 6 . In Wo 95/30266 218 8 6 7 8 F~ l725 . - ;r ~

block 200, an initialization step is performed wherein a ~eed bus, a number of br~}ches, and a minimum voltage lQvel are 6P~ectP~ in ';order to define a region of inter~5t. Next, th;e Q-V curves are run and reactive 5 reserve basins are dPtarminP~l at all buses in the region o~ interest in block 202. In block 204, a voting ~JLOC:~duL~ is employed to select alpha where the Q-V
curves computed at all buses in each bus cluster has ~ubstantially the same Q-V curve minimum and reactive 10 reserve basin. The parameter alpha decides the size of the ~ -,t bus clusters which form voltage control areas. As alpha decreases, the size of the ~ul~elc ..l. bus clusters increases through a~ yc-tion of coherent bus clusters identi~ied for larger alpha values. Thi6 15 ~earch ~ lu,~ eliminates the need for a user to make a J, '_ ~ on where the differences in voltage changes at buses within coherent bus groups increases from very ~mall values, and the voltage change differences between buses in different bus groups for a di-,Lu,Lance suddenly 20 increase to large values as alpha decreases.
In the search ~Loc~-lu,~ for alpha, a bounded interval of potential values of alpha is first sQ~Pcted.
me ~LOC~luL~ places a dist~rh~n~-e, namely a voltage change at some ~eed bus, and calculates the changes in 25 voltage and angle at each bus due to the di~uLl,e,nce.
The ~Loc6.1uL-: finds bus clusters for ten e~ually-spaced alpha values in this bounded interval, and then f inds the smallest alpha value where the voltage and angle ch7~nqes within the bus group satisfy the following 30 equations:
-Wo 95130266 2 ~ 8 8 ~ ~ 8 P~ l725 ~'V,~ V~ s 1~ AV
S ~Ca ~l where ~V is a voltage change, ~ i5 an angle change, iand j are indices representing two buses within a bus group, and kl and k2 are f ixed p~-L ~S .
The results are conf irmed as voltage control 5 areas by running Q-V curves at all buses in the voltage control areas to establish if alpha was selected proper-ly 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 wa6 chosen 10 correctly so that the Q-V curve minima and reactive reserve basins computed at every bus in the bus clusters selected are id~n~i CA l, the user has obtained the voltage control areas and proper alpha value for obtain-ing these voltage control areas. If the alpha value was 15 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 C~Y Im; n~
until bus clusters which have nearly identical Q-V curve 20 minima and reactive reserve basins are found. Hence, computing voltage control areas in this manner i5 based on both the level o~ coherency within bus clusters and the level of incoherency across bus clusters.
Alternative rmho~ can be formed which 25 explicitly use the definition of voltage control area in order to find alpha. ~ore specifically, an alternative - . -'; L would search for the value of alpha that is as small as possible, i . e . which yL u luces the largest bus cluster, and yet assures that the Q-V curves comput-Wo 95130266 2 ~ 8 ~ 6 7 8 - P~ 0~72~ ~

ed at every bus in each bus cluster has nearly identical Q-V curve minima and reactive reserve basins. The search for alpha would only,~u~ .LLate on bus clusters in some region of intere5t, which are buses nbove a 5 cOEtain voltage rating and at most three circuit branch-es from ~ome seed bus.
Turning now to Pigure 7, a f low chart of a crmt ;n~erlry selection program is illustrated. As seen therein, a contingency selection and ranking for con-10 tingencies and operating changes that bring a particulartest voltage control area and its reactive reserve basin closest to voltage instability is performed. The cr~ntimJonry gelection and rankings are peLL~ --' for each critical voltage control area and associated 15 reactive reserve basin.
In block 210, a single line outage cnnt~nqonry i8 simulated. The reserves in each reactive reserve basin are computed for that contingency in block 212.
In conditional block 214, it is detormi nPd whether or 20 not there arQ àny other contin~onriPC to be simulated.
~r there are further con~in~Pnri~os to be simulated, then flow of the method is L-:LuL-Ied back to block 210. If th~re are no additional r~nt;n~onrio~ to be simulated, then ~low o~ the routine advances to block 216.
In block 216, the continr~onriP~ are ranked in ~ach reactive reserve ba5in based upon reactive re-serves. In block 218, the line outages that exhaust more than P9~ of the reserves in each voltage control area nre 5P1 ectP~ and placed in a list. Further, the lnrgest two reactive capacity ~ cLatUL~, in each reac-tive reserve basin that ~xhausts P% of its reserve f or ~vo 9sl30266 2 1 g 8 ~ 7 8 P~ 472~

some line outage are also selected. These generators are placed in another list. The list of generators is uLed to produce a set of 6evere single and double L~tUL outage cont;n~n~ ies. The list of line 5 outages are used to produce a set of severe single and double line outage cont;n~J~nri.~e. The list of genera-tors and line outages is used to produce a set of combination line outage and loss of generation contin-gencies .
In block 220, the severe single and multiple cont-;n~n~i~C are simulated and ranked based upon the reactive reserve in a reactive reserve basin. The ~nnt-; ngrnry selection routine can be run several times in 6~ to obtain all of the information on why 15 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 zone6 or areas where voltage instability is to be studied, or in the entire system model.
In a preferred o~ho~ , the contingency E~ql~c~;on routine would output a report summari~ing the effects of the worst five cont;n~nri~C for each criti-c~l reactive reserve basin. The output for each reac-tive reserve basin has an initial summary Or the status in the ~L~ ingency case, ;nrll~3;ng the bus names and numbers for all buses in each of the reactive reserve basin voltage control areas, the reactive supply capaci-- ty and L~_3~LVC:S for yclleL-tuL~ y~ lrv.. ~,us u~ c_.
and switchable shunt capacitors at the bus where the 30 L is located.

Wo 9s/3026~ 218 8 6 7 8 - r~l" ~ ~725 ~1 - ~ --24--After the initial status of a reactive reserve basin i5 provided, the five worst contin~onril~ for that reactive reserve basin are given. Each contingency i5 described and the reac,tive supply reserves at all 5 generators and switchable shunt capacitors in each reactive re6erve basin voltage control area are given.
The order of voltage control areas in the report of voltage control area reactive supply les~. v~:5 for a particular reactive reserve basin is based on the 10 ~ e of re6erve exhaustion during _Lation of the Q-Y 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 Cr~ntin~JPnriPC presentQd 15 in the output report for a reactive reserve basin is ba~ed on the p~ agQ of ~lL ~ ingency reactive reserve~ exhausted witn the contingency causling the largQst peL.e..~ye reduction reported first. The order of the reactive reserve basins presented in the output 20 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 conti -, ~ are reported f irst .
The contin~onry selection routine assists the user in ~PtPrm~"~"7 the reactive reserve basins that experience voltage instability because they would be the f irst to be reported . If no reactive reserve basin ~erience voltage instability, the reporting of the reactive reserve basins in the order of the largest PeL~ aY-; reduction in total reserves gives only a partial indic~tion of the reactive reserve basin with the most severe contin~Pnripc. FtL~ ayt: reduction in WO 95/30266 2 1 ~ 8 ~ 7 ~ P~./. 5'~ '7~S ' total reactive L~5~v~5 of a reactive reserve basin is ~n e~YI-Ql 1 qn~ indicator of the worst contingency in a reactive reserve basin and the most vulnerable reactive reserve basin when the system is experiencing or is 5 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 r~active r~6_L~,_s are exhausted on voltage control areas listed at the end of the list given for that reactive 10 reserve basin are effective indicators in judging proYimity to voltage instability when the contingency does not bring a reactive reserve basin close to voltage instability. The reason for utilizing both indicators ~or voltage collapse proximity rather than peL~ .,Lage 15 reactive reserve re~ tinn is tha~ the system experien~l-es a quantum step toward voltage instability after each ~;llrcP-five voltage control area experiences reserve exhaustion, and experience indicates voltage control areas that exhaust res L v~s near the Q-V curve minimum 20 for the llL~ ;n~nry case are near the Q-V curve minimum for most contingencies.
An alternative ~"~ho~ 1 L of the contingency r-~rtion routine would further include modifying the ~et of reactive reserve basin voltage control areas 25 reserve level for con~in~Pnrif~C 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 ~6 c~ Lingency reserve basin voltage control area 30 that is totally or partially rl~ ccnnn~cted from the test voltage control area by the line outage cnnt; n7~ncy .
cont ~ n~Dn~ C that have a modif ied reactive reserve basin and the voltage control area that should be WO9~/30266 2188678 r~ 0~725 ~

deleted from the pre-contingency reactive reserve basin both can be detected by looking f or cont i "g~nries where a reactive reserve basin voltage control area experienc-es little reduction in reserve co~mpared to other severe 5 cont~n~P~ C. The deletion ~of these voltage control areas from reactive reserve bàsins for those contingen-cies will make the contingency ranking based on reactive re~erve basin reactive reserves more accurate without reguLring the user to make judgments.
In Figure 8, perf orming a reactive reserve basin security :.cc~- L is illustrated by a flow chart. An initialization step is performed in block 230 wherein sPl ected data is retrieved . This data i n~ C
base case 6imulation data, values of alpha, values of a 15 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 20 area iB specified along with its test bus. The lists of ~ingle line outage, double line outage, single loss of generation, double loss of generation, and combination con~in~pnripc are read in block 234.
In block 2 3 6, the Q-V curves are computed f or 25 each r-~ntin~Pnry 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 PY~rllt j nn of the routine is ~topped. If there are no positive Q-V curve 3 o minima, then execution of the routine proceeds to block 240 .

Wo95/3~266 T~~ 725 ~8867~

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 eYecution o~ the routine is stopped. Otherwise, the tr~ns~er 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 contin-gency and voltage control area. I~ there is a Q-V curve with a positive minimum as detected by conditional block 250, then execution of the routine is stopped. Other-wise, 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 o~ the routine is directed back up to block 248.
Ir no additional transfer patterns need evaluation, then --CUti r n of the routine is completed.
Ideally, the computed reactive reserve basins are robust. Rubu:,L~ess 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 ~ u..Lingency case can experience exhaustion of reserves at the Q-V curve ro~ rse point after: any single contingency, transfer, 30 or loading pattern change; or after any combination line outage and loss o~ reactive esuuru~ r~nt;ng nry; or after any combination line outage/ loss o~ reactive lerJuL-,e contingency and any trans~er or loading change W095/30266 21886~8 ~ F,725 ~

in any pattern. Demonstrating that the reactive reserve basins are robust based on the above def inition is illustrated by the f low chart in Figure 9 .
In block 260, a~`set of line outage contin-5 gencies, loss of L~SOllL-_ contingencies, transfers, real power loading pattern changes, operating changes, and combination line outage/loss of resource cont ;nqPnrip~
that are known to exhau5t reactive reserves in one or more specified reactive reserve basins as well as test o 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 n~;ng to a specified reactive reserve basin are ' ; n~-d by computing the Q-V curve and its minimum ror each single or double contingency or operating change specified. The reactive reserve basins of the Q-20 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 i8 u~ed to confirm that con~;nqPn~iPR or operating 25 chAnges do not exhaust reseLvt:s on volt~ge control areas where all rêactive supply and voltage control reseL vt:S
are not nearly or completely exhausted when a Q-V curve is computed for the p ~æ ~ ;n~Pnry case at a test bus in a critical voltage control area.
Performing an intelligent voltage stability 8ecurity: RRP- t is illustrated by the flow chart in Wo 9~/30266 ~ 1 ~ 8 ~ 7 ~ P~ o l725 Flgure 10. The ~LOCeduL-3 involves det~rmin;n~, 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 5 reserve basin. These bus clusters are found based on .O~_L~I~UY~ in other words, the same voltage and angle changes are exhibited at all buses in the voltage control area due to any distl~rh~n-~. Alternatively, the bus clusters are found based on controllability, observ-10 ability, or modal properties.
Next, the subset of all of the reactive supplyL~ ~8 within voltage control areas that exhaust all o~ their re~ctive supply at the minimum Or the Q-V curve at any bus in the test voltag~ control area is 15 d~t~ n~d at block 272. The minimum of the Q-V curve can generally be obtained using a normal Newt~l. Raphr~"~
algorithm using a standard ~LùcelluLe: that will obtain the minimum when the direct application of the Newton-Raphson alqorithm would stop obtaining solutions short 20 of the minimum.
A ~econd condition f or buses to belong to a voltage control area is that the Q-V curve computed at ach bus in a test voltage control area exhausts the same reactive supply ~ _80uL ues in the same set of 25 voltage control areas at the Q-V curve mini - The subset of reactive supply resuuL~ eS in a system ex-hausted at the Q-V curve minimum is called the reactive reserve basin for that voltage control area. T h e l~lope of the Q-V curve deuL se ~ discont i n~ Ucly each 30 time all of the reactive supply res~Lv~s in one of the voltage control areas in the reactive reserve basin is exhausted. The reactive supply from a reactive reserve Wo 95130266 2 ~ 8 8 ~ ~ 8 ~ 72s ~ I .

basin voltage control area to the test voltage control area is r-; n1-~ i nP~ as long as one of the voltage con-trols associated with reac~t~ ive supply devices in a voltage control area is ac~e and holds the voltage in 5 th~t voltage control ar~ba.
The discontinuity in the slope of the Q-V
curve occurs not only due to 10s8 0~ reactive supply rrom the reactive reserve basin voltage control area, but occurs due to the increased rate of increase in 10 reactive losses with voltage decline that ~- ,-nieS
loss of all voltage control in a voltage control area.
The reactive reserve basins are computed for only 6^1 ected 6ubsets of voltage control areas that are predicted to be vulnerable to voltage instability. The 15 voltage control areas that can experience voltage coll~rse are predicted by detorm;n;n~ those that have large shunt capacitive supply or experience large reactive network loss change ~or Q-V curves computed to dat a~m~ nP the reactive reserve }~asin for a ~ ~oighhr~ring 20 voltage control area.
A further step entails detorr;n;n~, at block 274, those reactive reserve basins and their associated test voltage control areas that are most vulnerable to ~lngle or multiple con~;n7onoiPc, The ~ive worst 25 cont;n~onrio^~ which either cause voltage collapse by exhausting all reactive L~se.ves in the reactive reserve basin or bring the reactive reserve basin closest to voltage instability by exhausting the largest pe~ ,g-es of the reactive reserves in that reactive reserve 30 basin, are also found at block 276.

W095l30266 ~ l g 8 ~ 7 ~ ,. s~: l7~s A file of single worst line outage contin-gencies 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 5 which is also ~Lv-luced, at block 280, by identifying the two largest capacity generators from each reactive reserve basin where one or more line outage contingen-cies exhaust P% or more of the reactive reserve basin Lt:-~L V~8. These two contingency lists are used to 10 produce, at block 282, a list of all single line outag-es, 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 15 .. SeL ~_3 were exhausted by single line outages is ~L v~uc~d .
These files are used to compute Q-V curve minima and reactive res~rve basin voltage control are~-s with reactive ~ S_L V~:S f or every contingency in the 20 li~its for each reactive reserve basin test voltage control area specif ied . Although the number of con-t; n7r-lr~ ~c in the list6 is pref erably limited to the projected ten worst c~ntin~enri~S~ a user may be allowed to run all of the other contin7en~ C.
In block 284, a security ~-9~C t for single and multiple contingencies with different transfer and loading patterns is performed. Transfer limits are deto-min~d for each anticipated transfer pattern (speci-fied by a group of generators with increasing generation in some percent~ge of the total transfer level and a group Or generators with decreasing generation in some ~c~.,L~.ge of the total transfer level). The transfer Wo 95/30266 2 ~ 8 8 6 7 8 . ~11. l72s level is increased in incL~ ~s and Q-V curves are computed for all reactive reserve basin critical voltage control areas and all single and multiple conti"~en~iec.
If all Q-V curves for all single and multiple contin-5 gencies in every critical voltage control area havenegative Q-V reactive minlma ~implyin~ voltage stabil-ity~ the total transfer level is ir-,L~ ' e~'i again and nll Q-V curves are ~ Led. This process is repeated until one Q-V curve has Q-V curve positive minima 10 (implying voltage instability). The total transfer level limit for the transfer pattern is thus determined.
A transfer pattern level limit is computed for each l~n~;~;r~ted transfer pattern and the reactive reserve basin where the Q-V curve is positive for one or more 15 single or multiple contl"qD"riP is noted.
The fiame process is repeated f or loading patterns to find those reactive reserve basins that have po~itive Q-V curve minima for one or more con~ Pn--iec.
The reactive reserve basins that constrain each transfer 20 (or loading pattern) and the contingpn~ipc that cause the voltage instability for that transfer (or loading pattern) are used as the basis of dpcignin~ Pnh~n~ Ls that prevent voltage instability in that reactive ruserve basin ~or those cont; nqPn~ c and a desired 25 level of transfer ~possibly larger than the current transfer limit). It should be noted that the general pll~nn;n~ design criterion for voltage instability only rQquires that a power system survive a worst combination ~tu~ and line outage and does not require that a 30 system survive a double line outage contingency.
If the load flow wilL not solve for some contingency, transfer pattern and level, or loading ~ Wo 95130266 ~! 1 8 8 6 7 ~ P~l/u_ "25 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 ~ome global reactive reserve basin allows a Q-V curve 5 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 ba~in. This feature allows on to ~t~Prm;nP whether a contingency, or tran6fer or loading 10 pattern causes a voltage instability in some other global reactive reserve basin than the one being stud-ied .
If one has performed the above ACSP ~ of transfer limits for each anticipated transfer pattern 15 and loading limits for each anticipated loading pattern, one can ~1P1 PrminP the transfer pattern limits that need to be increased and the desired level, as well as the loaaing pattern limits that need to be increased and their desired levels. For each transfer tor loading) 20 pattern where the design criterion is not satisfied out to the de5ired limit, one knows the local reactive reserve basin or basins and the contin~enripc that cause voltage instability in that reactive reserve basin or basins .
The previously described . ' ';- - of the present invention have many advantages. By d~tPrm; n; ng single con~;n~rnriPC which exhaust more that ~)L~ _,eci-fied p~L~ L~ge of reactive reserves, a ~ tionally efficient method of performing multiple contingency analysis results. The resulting method is capable of ~-ler~t;n~ multiple loss of reactive ~3~uL.es, line outages, and combinations thereof, for performing an WO 95130266 ~ ~ 8 8 6 ~ 8 P~/u~. .72~ ~

analysis Or the effect of multiple contingencies on each reactive reserve basin. Furthermore, P--ho~i- Ls of the present invention are capable of l~dentifying the specif-ic crltical voltage control area and reactive reserve 5 basin that is brought to voltage instability after some cnnt;nq~nry by a particular transfer or loading pattern change th~t can cause voltage instability in a voltage control area.
Another advantage is that the present inven-lO tion identif ies a global stability problem and eachlocal 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 reactiYe reserve basin in the critical voltage 15 control areas that maintain voltage and thereby prevent the reactive losses that consume and choke of f reactive supply ~rom outslde, as well as inside, the respective reactive reserve basin from reaching the critical voltage control area. A global voltage stability 20 problem generally has many individual local voltage stability problems and each can occur due to different continq~nri~ or in some cases due to the same severe continq~nriP~ that cause loss of local voltage stability for several critical voltage control areas by exhausting 25 their reactive reserve basin reserves. The advantages still further include detectinq each critical voltage control area, its reactive reserve basin, the severe ~ingle and multiple continq~nri~ that cause voltage instability in several local reactive reserve basins and 30 may even cause a global voltage instability.

wo 95~30266 ' ~ ~ 8 8 6 7 8 P~l/ J~472~

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 reCo~ni7e various alternative designs and ~mhoAir--lts 5 for pr~c~ icing the invention as defined by the following c~ai~e~

Claims

What Is Claimed Is:

1. 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 method comprising:
grouping the plurality of buses 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 relation-ship;
determining a corresponding reactive reserve basin for each of at least one of the voltage control areas, the reactive reserve basin comprising 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;
performing a single contingency analysis by computing a corresponding quantity for each reactive reserve basin in response to each of a plurality of single contingencies, wherein the corresponding quantity is representative of a reduction in the reactive re-serves within the reactive reserve basin; and performing a multiple contingency analysis, for each reactive reserve basin, based upon the single contingencies whose corresponding quantity exceeds a predetermined threshold.

2. The method of claim 1 wherein grouping a plurality of buses comprises:
determining whether each of the buses within each voltage control area has a substantially similar reactive margin at the minimum of the corresponding reactive power versus voltage relationship;
determining whether each of the buses within each voltage control area has a substantially similar voltage at the minimum of the corresponding reactive power versus voltage relationship; and ~ determining whether each of the buses within each voltage control area has a substantially similar reactive reserve basin at the minimum of the corre-sponding reactive power versus voltage relationship.

3. The method of claim 1 wherein determining a corresponding reactive reserve basin comprises:
selecting the 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;
and selecting the at least one of the voltage control areas whose buses therewithin have a reactive margin at the minimum of the corresponding reactive power versus voltage relationship which is less than a reactive margin threshold.

4. The method of claim 3 wherein determining a corresponding reactive reserve basin further comprises selecting the at least one source of reactive reserves from the voltage control areas whose reactive reserves therewithin are depleted beyond a predetermined thresh-old at the predetermined operating point.

5. The method of claim 1 wherein the pre-determined operating point is the minimum of the cor-responding reactive power versus voltage relationship.

6. The method of claim 1 wherein the plu-rality of single contingencies comprises a single generated outage.

7. The method of claim 1 wherein the plurality of single contingencies comprises a single line outage.

8 . The method of claim 1 wherein performing a multiple contingency analysis comprises:
varying a transfer pattern and level for the electric power transmission system; and varying a loading pattern and level for the electric power transmission system.

9. A method of performing a voltage sta-bility 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 method comprising:
grouping the plurality of buses into a plu-rality of voltage control areas such that each of the buses within each voltage control area has a similar corresponding reactive power versus voltage relation-ship;
selecting 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;
determining a corresponding reactive reserve basin for each of the at least one of the voltage control areas, the reactive reserve basin comprising 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;
performing a single contingency analysis by computing a corresponding quantity for each reactive reserve basin in response to each of a plurality of single contingencies, wherein the corresponding quantity is representative of a reduction in the reactive re-serves 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;
selecting the single contingencies whose corresponding quantity exceeds a predetermined thresh-old; and assessing the voltage stability for single and multiple fault contingencies with a plurality of trans-fer and loading patterns, wherein the single and multi-ple contingencies are based upon the selected single contingencies.