# Improving voltage stability by reactive power reserve management

**ABSTRACT** The amount of reactive reserves at generating stations is a measure of the degree of voltage stability. With this perspective, an optimized reactive reserve management scheme based on the optimal power flow is proposed. Detailed models of generator limiters, such as those for armature and field current limiting must be considered in order to utilize the maximum reactive power capability of generators, so as to meet reactive power demands during voltage emergencies. Participation factors for each generator in the management scheme are predetermined based on the voltage-var (V-Q) curve methodology. The Bender's decomposition methodology is applied to the reactive reserve management problem. The resulting effective reserves and the impact on voltage stability are studied on a reduced Western Electric Coordinating Council system. Results prove that the proposed method can improve both static and dynamic voltage stability.

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**ABSTRACT:**Proposing the optimal AVC coordinating parameters and comparing effects of different grid planning for reactive balance in an scientific manner is one of the functional characteristics of smart AVC. In this paper Optimization Parameter (OP) system is developed in Hebei low voltage grid for this purpose. The data are taken from EMS. The state estimation is carried out periodically after obtaining real-time data. Taking state estimation results as the basic power flow and simulating AVC operations, the voltage variations and line loss analysis can be calculated for comparison. The system can compare optimization parameters for the real grid or the virtual grid. It's depending on whether considering the actual capacity of reactive power compensation equipments. The structure, hardware configuration and data exchange of the system are illustrated. Finally, several analysis tools of the OP system are introduced. With the system, it can be evaluated that effects of reducing line loss benefited from the AVC operations. It can propose coordinating priority of capacitors or on-load regulating transformers. Also it can provide the optimal AVC coordinating parameters and the optimal grid plans, which lead to better voltage control and better layout of reactive power compensation equipments.Journal of International Council on Electrical Engineering. 01/2014; 4(1). - SourceAvailable from: ocean.kisti.re.kr[Show abstract] [Hide abstract]

**ABSTRACT:**This paper presents target operation voltage guidelines of each voltage control area considering both voltage stability and economical efficiency in real power system. EMS(Energy Management System) data, Real-time simulator, shows not only voltage level but lots of information about real power system. Also this paper performs optimal power flow calculation of three objective functions to propose the best target operation voltage. objective function of interchange power flow maximum and active power loss minimization stand for economical efficiency index and reactive power reserve maximum objective unction represents stability index. Then through simulation result using optimazation technique, the most effective objective function is chosen. To sum up, this paper divides voltage control area into twelve considering electric distance characteristics and estimate or voltage level by the passage of time of EMS peak data. And through optimization technique target operation voltage of each voltage control area is estimated and compare heir result. Then it is proposed that the best scenario to keep up voltage stability and maximize economical efficiency in real power system.Transactions of the Korean Institute of Electrical Engineers 01/2009; 58(4). -
##### Conference Paper: Reactive power reserve management: Preventive countermeasure for improving voltage stability margin

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**ABSTRACT:**Voltage stability imposes important limitations on the power systems operation. The system should be operated with an adequate voltage stability margin by the appropriate scheduling of reactive power resources and voltage profile. The main countermeasures against voltage instability are distinctly classified into preventive and corrective control actions. The management of the reactive power generation and its reserve are the main preventive actions against voltage instability. In this paper a Benders' decomposition method is proposed to improve the voltage stability margin through management of reactive power and its reserve. The voltage and reactive power management is studied from the generator's point of view which so far less attention is paid rather than the load's perspective. The proposed optimization procedure is applied on 6 bus test system to illustrate the effectiveness of the method.Power and Energy Society General Meeting, 2012 IEEE; 01/2012

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338IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 20, NO. 1, FEBRUARY 2005

Improving Voltage Stability by Reactive

Power Reserve Management

Feng Dong, Student Member, IEEE, Badrul H. Chowdhury, Senior Member, IEEE,

Mariesa L. Crow, Senior Member, IEEE, and Levent Acar, Senior Member, IEEE

Abstract—The amount of reactive reserves at generating sta-

tions is a measure of the degree of voltage stability. With this

perspective, an optimized reactive reserve management scheme

based on the optimal power flow is proposed. Detailed models of

generator limiters, such as those for armature and field current

limiting must be considered in order to utilize the maximum

reactive power capability of generators, so as to meet reactive

power demands during voltage emergencies. Participation factors

for each generator in the management scheme are predetermined

based on the voltage-var (V-Q) curve methodology. The Bender’s

decomposition methodology is applied to the reactive reserve man-

agement problem. The resulting effective reserves and the impact

on voltage stability are studied on a reduced Western Electric

Coordinating Council system. Results prove that the proposed

method can improve both static and dynamic voltage stability.

Index Terms—Bender’s decomposition methodology, optimal

power flow, reactive power management, voltage collapse.

I. INTRODUCTION

V

by a disruption, but is usually characterized by shortage of

fast-acting reactive reserves. Voltage collapse often involves

specific areas of the power system, although the entire system

may also be involved. Many system variables may participate

in this phenomenon. However, some physical insight into the

nature of voltage collapse may be gained by examining the

production, transmission and consumption of reactive power.

Voltage collapse is associated with reactive power demands

not being met because of limitations on the production and

transmission of reactive power [1]. Reactive power demand

generally increases with a load increase, motors stalling, or a

change in load composition such as an increased proportion

of compressor load. The fast reactive sources are generators,

synchronous condensers and power electronics-based flexible

ac transmissionsystems(FACTS).During voltageemergencies,

reactive resources should activate to boost transmission voltage

levels. This action reduces reactive losses of transmission

lines and transformers, and increases line charging and shunt

capacitor outputs. In the mid-term time scale, a voltage collapse

usually does not happen until most of the large reactive power

OLTAGE collapse typically occurs on power systems

which are heavily stressed. It may or may not be initiated

Manuscript received May 26, 2004. Paper no. TPWRS-00134-2004.

The authors are with the Electrical and Computer Engineering De-

partment, University of Missouri-Rolla, Rolla, MO 65409 USA (e-mail:

bchow@ece.umr.edu).

Digital Object Identifier 10.1109/TPWRS.2004.841241

resources reach their respective reactive power limits. Gen-

erally, one or two critical resources reaching their limits can

spawn cascading limiting effects at neighboring units. Hence it

is wise to keep enough reserves in order to improve the voltage

stability margin.

Reactivepowermarginshavealwaysbeenlinkedwithvoltage

stability. The Western Electric Coordinating Council (WECC)

specifies the voltage stability criteria in terms of real and reac-

tive power margins [1]. The minimum reactive power margin is

determined by the voltage-var (V-Q) curve method. The V-Q

method has been well studied [1]–[3]. Reference [4] discusses a

reactivemanagementprogramforapracticalpowersystem.The

authorsdiscussaplanninggoalofsupplyingsystemreactivede-

mands by installation of properly sized and properly located ca-

pacitor banks which will allow generating units to operate at or

near unity power factor. However, it is a cost-intensive proposi-

tion. Besides, this strategy is not always very effective since not

all the shunt capacitors are fully utilized. Reference [5] uses the

reactive power margins to evaluate voltage instability problems

forcoherentbusgroups.Thesemarginsarebasedonthereactive

reserves of generators and static var compensators (SVCs) that

exhaustreservesinthe processof computinga V-Q curve atany

bus in a coherent group or voltage control area. The authors in

[6] discuss a hierarchical optimization scheme which optimizes

asetofcorrectivecontrolssuchthatthesolutionsatisfiesagiven

voltage stability margin. Bender’s decomposition is employed

to handle stressed cases. In [7], the authors introduce a method-

ology to reschedule the reactive injection from generators and

synchronous condensers with the aim of improving the voltage

stability margin. Their method is formulated based on modal

participations factors and an optimal power flow (OPF) wherein

thevoltagestabilitymargin,ascomputedfrom eigenvectorsofa

reduced Jacobian, is maximized by reactive rescheduling. How-

ever, theauthors avoidusing a security-constrained OPF formu-

lation and thus the computed voltage stability margin from the

Jacobianwould nottruly represent the situationunder a stressed

condition.

In [8], the authors employ a security-constrained OPF for

optimal var expansion planning design. The OPF is solved

twice—once with simply the voltage profile constraint and then

with a pre-selected voltage stability margin criterion. The larger

of the two solution is then selected for the combined solution.

In this paper, a reactive reserve management program

(RRMP) based on an optimal power flow is proposed to

manage critical reactive power reserves. A multi-objective

function specifically for this purpose is introduced. This

0885-8950/$20.00 © 2005 IEEE

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DONG et al.: IMPROVING VOLTAGE STABILITY BY REACTIVE POWER RESERVE MANAGEMENT339

function is used in a mixed-integer nonlinear optimization

formulation. Various generators are assigned different weights

in order to maintain maximum reactive reserves within the

areas that are most vulnerable to voltage instability problem. A

decomposition technique is adopted to formulate subproblems

with various stress levels. The nonlinear interior point method

(NIP) is then used to solve the separate subproblems. The ad-

vantage in this formulation is that the system is able to maintain

a specified voltage stability margin, and at the same time, raise

its level of voltage stability. The proposed method is tested on

a reduced WECC system with 283 buses and 29 generators.

II. OPTIMIZATION FRAMEWORK

A. Reactive Reserves

The reactive power sources consist of synchronous gener-

ators and shunt capacitors and reactors on the transmission

network. During a disturbance, the real power component

of line loadings does not change significantly, whereas the

reactive power flow can change dramatically. The reason is

that the voltage drops resulting from the contingency decreases

the reactive power generation from line charging and shunt

capacitors, thereby increasing reactive power losses. Sufficient

reactive reserves should be available to meet the var changes

following a disturbance. Simply speaking, the reactive power

reserve is the ability of the generators to support bus voltages

under increased load condition or system disturbances. How

much more reactive power the system can deliver depends on

the operating condition and the location of the reserves, as well

as the nature of the impending change.

The reserves of reactive sources can be considered a measure

of the degree of voltage stability. As a matter of fact, BPA—a

transmission provider in the western United States—considers

reactive reserves at major generating plants to be a critical in-

dicator of voltage stability and, consequently, the agency has

installed a reactive power monitor [9] at critical hydroelectric

power stations that serve its service area.

The available reactive power reserve of a generator is deter-

mined by its capability curves [10]. It is worth noting that for a

givenrealpoweroutput,thereactivepowergenerationislimited

by both armature and field heating limits.

The active and reactive power generation output at a syn-

chronous generator may be represented as [10]

(1)

(2)

where

perunitsystemand

order to write an analytical model to relate the reactive power

limit to the maximum field current, we use a cylindrical rotor

model with

. Thus, from (1) and (2), the maximum

is the terminal voltage of the generator based on the

,whereisthefieldcurrent.In

reactive power with respect to the field current limit may be

obtained as

(3)

Thus, the maximum reactive power

determined by the maximum field current

tionship also shows that the maximum reactive generation is a

function of the terminal voltage. The maximum reactive power

output should also satisfy the armature current limitation as

follows:

of the generator is

. The rela-

(4)

The reactive power reserve of the th generator is then repre-

sented as

(5)

where

and (4) and

ating conditions. A generator’s reactive reserve is calculated by

(5) if

is lower than. However, if

the reactive reserve is set to zero and

the terminal voltage.

is the smaller of the two values obtained from (3)

is the reactive power output under normal oper-

reaches its limit,

varies as a function of

B. Mathematical Formulation

The RRMP is formulated as an optimal search problem

whose primary objective is to maximize the effective reactive

reserves under normal operating conditions to ensure higher

voltage stability margin. A secondary objective is to minimize

losses subject to various operational constraints. The dual-ob-

jective RRMP is therefore formulated as follows.

Objective function

(6)

where

be optimized, that is,

the reactive power reserve of the gth generator;

factor of the th generator and is discussed in the following sec-

tion,and

representsthetransmissionlosses.Sincewehave

adualobjectiveofmaximizingreactivereservesandminimizing

transmission losses, we pick

The constraints to the above optimization are

is the sum of reactive reserves of the system to

is

is weight

. and.

(7)

(8)

(9)

(10)

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340IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 20, NO. 1, FEBRUARY 2005

where

voltage magnitude at load bus ;

voltage angle difference between bus

and bus ;

elements of the admittance matrices;

active/reactive power injected into net-

work at bus ;

total number of transformers, generators,

shunt capacitive/reactive installations,

and loads, respectively;

control variables;

limits of tap setting of transformer

branch ;

limits of voltage at generator bus ;

compensation capacity limits at bus ;

limits of voltage at load bus ;

reactive power capacity limits at gen bus

.

The voltage stability constraints may be written as

(11)

where

set “C”,

cases;

is the reactive load for the th stressed case in the

, andis the total number of stressed

is the reactive load under normal condition;

is a direction of load increase;

reactive load under normal condition;

reactive margin. For example,

load at bus

with respect to the system load increase, where

.

A power system can be stressed from the current operating

point to the collapse point by increasing the reactive loads in

several directions. In some directions, the system may have in-

sufficient reactive power margin to guarantee voltage security.

These cases are grouped into one set, which will be called “C”.

These critical cases are determined in the third step during as-

signment of weight factors of participating generators, as dis-

cussed at the end of Section II. By satisfying constraint (11),

the system has a minimum reactive margin required for secure

operation. Ensuring all voltage control areas to have the min-

imum reactive margin is equivalent to all stressed cases being

feasible under the operation constraints.

The intent in the above formulation is not only to satisfy

the voltage stability criteria but also to improve voltage sta-

bility. Thus, if (11) is satisfied in the optimization, the system

is guaranteed to be voltage stable and optimizing var reserve in

(6) would not be needed if stability was not to be improved.

Without the aforementioned objective function, it is possible

that some strong areas in the system may rob weaker areas of

the much-needed reactive reserves.

is the total

is the specified

is the relative increase in the

C. Determination of Area Weights

Under an ideal operating condition, all generators operate at

unity power factor so the system possesses the maximum reac-

tivereservepossible.However,it isextremelydifficulttoimple-

ment such an operating condition in real power systems. Sec-

ondly, given all generators are equally weighted, maximizing

the reactive reserves for the entire system is both inefficient and

inadequate. Attempting to maximize reactive reserves at gen-

erators as an operational optimization measure with equal par-

ticipation throughout a system may lead to undesirable conse-

quences such as depleting reserves at generators which are crit-

icaltomaintainingvoltagestabilityintheeventofadisturbance.

It is well known that the voltage instability phenomenon is

essentially a local problem, wherein some weak areas become

prone to voltage collapse because of shortage of reactive power.

These areas need higher reactive power reserves than others

when subjected to the same voltage emergency. In [5], the au-

thor discusses the importance of dividing the power network

into voltage control areas because each area exhibits vulnera-

bility to a disturbance in a different way. With the same objec-

tive in mind, we have separated the entire network into voltage

control areas with the basic idea being that the weakest trans-

mission element connected to each bus is identified by a scalar

parameter

. The parameter is determined such that the V-Q

curve minima in computing the V-Q curve minimum at a bus

are almost identical for all buses in one voltage control area.

The groups of buses that remain interconnected, after the weak

transmission elements are eliminated, define the voltage con-

trol areas. The reactive power-voltage relationship given by the

Jacobian matrix element

is used to measure electrical dis-

tance between any two nodes. The off diagonal Jacobian ma-

trixelementswiththesmallestabsolutevaluesindicatetheweak

connections or long electrical distances between corresponding

buses and are therefore eliminated from each row until the sum

of the elements eliminated is less than or equal to

. The buses corresponding to the remaining

elements in the Jacobian are grouped into one voltage control

area. Then, the V-Q curve at any bus within each control area is

computed to find the reactive margin of this area.

The bottom of the V-Q curve is the maximum reactive load

that a system can sustain. The distance from this point to the

operating point is usually considered the reactive power margin

at the bus [3]. Using this method, we can reliably claim that the

area that has the smallest reactive margin is the most vulnerable

to voltage instability. At the minima of the V-Q curve, the re-

active reserves of generators that are depleted are the effective

reservesforthisareaand,thereby,determinethereactivemargin

in the area. The amount of effective reserves is a key index in

voltage stability assessment. Therefore, an objective of the pro-

posed RRMP is to maximize the effective reactive reserves in

the system. These reserves associated with each voltage control

area are assigned a weight according to

, where

(12)

where

To summarize, the procedure for weight factors is as follows.

1) Divide the network into voltage control areas as specified

above.

is the reactive margin of the area.

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DONG et al.: IMPROVING VOLTAGE STABILITY BY REACTIVE POWER RESERVE MANAGEMENT341

2) Determine the reactive margin for each area by the V-Q

method.

3) Determine the weights for each generator based on the

specific margins in each area.

III. STRESSED CASE SUBPROBLEM

By considering the reactive margin constraints of (11), the

constrained optimization problem (6)–(11) becomes one of re-

active reserve management with dynamic security constraints.

At the optimal point, the system has the maximum reactive

reserves under normal operation condition, and each case in

set C is feasible. It can be hierarchically decomposed into two

parts, a base case subproblem and a stressed case subproblem

that can be solved by the Bender’s cuts decomposition method

[11]–[13]. For some stressed cases, the power flow may be-

come infeasible. However, in order to apply a decomposition

methodology, there is a need to have some measure of this in-

feasibility. Since this kind of infeasibility is caused by reactive

power load increase, fictitious reactive injections are used as

slack variables and added to the constraints corresponding to

the reactive power balance equation at a bus. Therefore, the

objective function for the stressed cases is to minimize the sum

of the fictitious injections of reactive power. If the fictitious

injections are equal to zero, then we claim that the stressed case

is feasible. The stressed case subproblem may then be stated

as shown in the equation at the bottom of the page, where

andare fictitious capacitive and inductive power injection,

respectively, at bus . Although, theoretically, fictitious reactive

power can be injected at any bus, since the set “C” of critical

load directions is given, we select only those buses in this

critical set for a load increase. In the above formulation,

the vector of control variables and

case problem.

is

is determined by the base

IV. ALGORITHM IMPLEMENTATION

The procedure for the two level Bender’s decomposition

is presented in Fig. 1. The base case subproblem (master

Fig. 1.Two-level hierarchical structure for optimization.

problem) is the optimization problem given by (6). Thus, the

master problem is formulated as follows:

(19)

(20)

(21)

(22)

Eachsubproblem(13)–(18)(shownatthebottomofthepage)

at the second level minimizes the fictitious reactive injections

for the given values of

and returns to the master problem,

information about the optimal objective function and its sensi-

tivitieswithrespectto

—calledBender’scuts.Theprocedure

is briefly discussed below.

An initial guess of control variables

the master problem (19)–(22) with

With the given

, the stressed cases are sequentially formulated

and solved, and the optimal result of each stressed case is used

to update the Bender’s cuts. For example, for the th stressed

case subproblem, thevalue of the objective function

means that the system has sufficient reactive margin required

and that the stressed case is feasible. Alternately,

means that the stressed case is infeasible with the current con-

trol variables. Thus, the more accurate Bender’s cuts

is obtained by solving

.

(13)

(14)

(15)

(16)

(17)

(18)

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342IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 20, NO. 1, FEBRUARY 2005

in the master problem based on the op-

are theLagrangemultipliers as-

timal results are built,where

sociated with the th stressed case. The Bender’s cuts return to

the master problem, the information to remediate infeasibility

of the stressed case. The two-stage process is repeated until a

is found for which all

the fictitious injections of reactive power are equal to zero in all

stressed case subproblems.

Each subproblem is solved through a NIP. The foundation

for interior point methods consist of three building blocks:

barrier method for optimization with inequality constraints,

Lagrange’s method for optimization with equality constraints,

and Newton’s method for solving nonlinear equations. The

master problem is taken as an example to show the application

of the NIP. By using slack variables, the problem (19)–(22) is

rewritten as

. That is,

(23)

(24)

(25)

(26)

(27)

where

primary nonnegative slack variables used to transform the in-

equality constraints to equalities. The inequality constraints are

incorporated into the objective function as a logarithmic bar-

rier function. So, barrier functions

introduced with respect to (27). The Lagrange function for the

problem (23)–(27) is defined as

is the vector of state variables, and are the

and are

(28)

where , andare the Lagrange multipliers, andand

are the barrier parameter. At the optimal point, barrier pa-

rameters

and reach zero. The set of nonlinear equa-

tions are derived following optimality conditions and solved

by Newton’s methods. For the interested reader, [14] and [15]

present the interior point method in more detail.

The maximum reactive power generation is calculated to de-

termine whether the limit is reached in each iteration during the

subproblem optimal search. If the limit is exceeded, the corre-

sponding generator node is changed to a PQ node, where the

reactive power generation becomes a function of the terminal

voltage as given by (3)–(4). The generator’s reactive reserve is

made equal to zero.

V. CASE STUDY

A. Reduced WECC System

A reduced WECC system, geographically representing the

western United States, is used to test the RRMP. This system,

TABLE I

REACTIVE MARGIN IN AREAS BEFORE AND AFTER OPTIMIZATION

shownintheAppendix,consistsof283buses.Theentiresystem

is divided into several subareas administratively. These are BC,

WA, MT, ID, WY, UT, OR, CO, NM, NV, AZ, and CA. The

heavy load area is located in the CA region. Some subareas

such as WA, MT etc. are responsible for supplying power to

CA via long-distance high-voltage lines. Under normal condi-

tions, there are no operating constraint violations. However, a

preliminary analysis shows that there are several weak areas

prone to voltage instability. The system is divided into sev-

eral different voltage control areas using the method discussed

in Section II-C. A bus in each area is selected for conducting

the V-Q analysis. Table I shows the reactive margins in the

nine areas before optimization. It is noted that there are two

weak areas—areas 8 and 9 with insufficient reactive margin,

vis-à-vis 350 and 200 MVAr, respectively. Both areas are in the

Northern CA area. The required reactive margin is specified as

450 MVAr, which is 5% of the total reactive load Thus, using

MVAr in (12), we determine the weight fac-

tors of effective reserves at each generator as shown in Table I.

Assuming a dual objective of maximizing reactive reserves

and minimizing system losses,

and, respectively thereby giving ten times more priority

tomaximizingthereservesthanminimizingthelosses.Thecon-

trol variables include voltage set points of 12 out of 28 gen-

erators, ten ULTCs, and six shunt capacitors. The set “C” in-

cludes five stressed cases. The optimal search starts with the

master problem before consideration of the stressed cases. The

set points are then sent to the subproblems. e.g., one stressed

case is that the total reactive loads in northern CA area are in-

creased by 450 MVAr. The increased reactive demands are pro-

portionally distributed among all loads in this area to each re-

active load under normal condition. The value of the objective

function of this stressed case is 108.3 MVAr, which means that

this stressed case is not feasible. With Bender’s cuts, the base

case is resolved to calculate a set of control variables. After just

one iteration between the master problem and the subproblems,

the overall procedure converges and the new set points ensure

feasibility for all stressed cases.

The specified reactive margin

fect on the results and computation time. An unreasonably high

reactive margin specified may lead to a null solution set for the

optimization problem and necessitate additional reactive com-

pensationdevicestomeetthereactivemargin.Thus,thereactive

margin for a system must be determined carefully. Usually, the

andin (6) are selected as

has a significant ef-

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DONG et al.: IMPROVING VOLTAGE STABILITY BY REACTIVE POWER RESERVE MANAGEMENT343

Fig. 2. Voltage profile before and after optimization.

TABLE II

REACTIVE POWER OUTPUT AND VOLTAGE SHCEDULE

TABLE III

SHUNT CAPACTIOR AND ULTC SHCEDULE

NERC-recommended reactive power criteria for area reliability

is a good starting point.

After optimization, the control variables activated include

nine generation voltage settings, two shunt capacitors, and two

ULTCs. In Tables II and III, voltage, shunt capacitors and tap

changer reschedules are listed respectively. In Table II, the

fourth and fifth columns are the reactive power outputs and

voltages at the generator terminal buses after optimization.

Compared with initial conditions, the results show improved

reactive power reserves. The voltage profile of the system is

also improved as shown in Fig. 2 and the transmission losses

are reduced by 45 MW, from 637 MW down to 592 MW.

B. Static Analysis and Dynamic Simulations

In this section, we verify the optimization results from two

aspects—static analysis (V-Q curves) and full dynamic simu-

lations. In Fig. 3, two V-Q curves are plotted. Curve “A” is the

V-Qcurveatbus112inarea9attheinitialoperatingstate.From

the figure, the reactive margin is 200 MVAr, which is also listed

Fig. 3. V-Q curves at bus 112 before and post optimization.

Fig. 4. Real power margin improvement with RRMP.

in Table I. After running the RRMP optimization, a V-Q anal-

ysis at the same bus reveals that the reactive margin is improved

to 500 MVAr, as shown by curve “B”. Similar conclusions were

drawn by analyzing reactive margins at other voltage control

areas.

The improvement in the real power margin after optimization

can be seen in Fig. 4. It shows two PV curves. P is the sum of

totalrealpowerloadsandVis theaveragevoltageinarea8.The

solidcurveAinthefigurecorrespondstothemarginattheinitial

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344IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 20, NO. 1, FEBRUARY 2005

Fig. 5.Voltage trajectory at bus 118.

condition and curve B corresponds to that after optimization. It

is obvious that the total real power margin has been extended by

3 p.u. or 300 MW.

We now see how the results of the RRMP impacts dynamic

voltage stability. We ran a full time domain simulation of the

system subject to the same disturbances both before and after

optimizationandcomparedtheresults.Dynamicmodelsinclude

OELs installedatGen #118,#148, #138, and#144, 108ULTCs,

as well as ten induction motors in addition to the usual models

associated with synchronous generators (exciters, turbine-gov-

ernors and PSS). In order to reduce simulation computation

time, the OEL time constants were deliberately reduced.

The disturbance consists of a sequence of an outage of Gen

#112 at 10 s, and outages of both circuits of the line 76–82 at

10 and 40 s, respectively. The software used for the dynamic

simulations was EUROSTAG [16].

In Fig. 5, the voltage trajectories at bus 118 are shown with

respect to the two cases. Curve "b" is with the optimal oper-

ating conditions and curve "a" is with the initial operating con-

ditions. The case with the initial conditions results in a faster

voltage collapse when subjected to the above mentioned distur-

bance. The reasons for the earlier collapse may be summarized

as follows: After the trip-off of the first circuit of the line 76–82

and the generator 112, the OEL at generator 118 is enforced

at 30 s. Hence, this generator loses voltage control. A large in-

duction motor load IND 119, connected to bus 1119—in close

proximity to generator 118, stalls. Then reactive power demand

increases rapidly, which eventually sets the collapse in motion.

In the other case, the OEL at the same generator 118 delays ac-

tivation until 35 s due to a higher system voltage profile. The

system is strong enough to survive from transient voltage in-

stability as well as the ensuing outage of the second circuit of

the line 76–82. After a time delay, ULTCs start to operate to

restore voltages on the load side and the system is stressed fur-

ther.Thebusvoltagesdecreasegraduallyandthereactivepower

generation from shunt capacitors and transmission lines reduce

drastically. Finally the system collapses at 130 s. The longer pe-

riod until collapse leaves some time for operator intervention

so as to initiate some control strategies to prevent the system

fromcollapsing.Thepropercorrectivecontrolinthiscasewould

Fig. 6. Reduced WECC System.

have been to block tap changers. By blocking tap changers, the

system is voltage stable, shown as curve "c" of Fig. 5. The com-

parison shows that reactive reserves are beneficial to improve

voltage stability.

Tocomparetheaboveresultswithasingleobjectiveofsimply

minimizing losses,

and

and 1.0, respectively, thereby ignoring the reactive reserves and

minimizing the losses. The constraints were kept the same, and

the reactive power margin was still 450 MVAr. In this case, the

global optimization problem failed to converge after ten itera-

tions. Two out of five stressed cases were found to be infeasible.

The first infeasible stressed case was one where we increased

reactive power demand in area 8 by 450 MVAr uniformly dis-

tributing the load increase at area buses 113,114, 115, and so

on. The second infeasible stressed case was where we increased

reactive power demand in area 9 by 450 MVAr, uniformly dis-

tributing the load increase at area buses 13, 142, 150, 151, and

so on.

At this point, the required reactive margin was decreased

from 450 to 300 MVAr and the global optimization problem

converged. With the reduced reactive margin, power losses

decreased from 637 to 573 MW, which was to be expected.

However, three generators (buses 140, 148, and 159) from out-

side the weak area received additional reactive reserves, while

two generators (buses 116 and 118) in the weak area were left

unchanged. In addition, two additional ULTCs (

and

–

) that were outside the weak area were op-

timized and the output of one new shunt capacitor outside the

weak area was reduced. Additionally, the real power margin

was reduced to 120 MW.

in (6) were then selected as 0

–

Page 8

DONG et al.: IMPROVING VOLTAGE STABILITY BY REACTIVE POWER RESERVE MANAGEMENT345

VI. CONCLUSION

This paper discusses the management of dynamic reactive

powerreservesinordertoimprovevoltagestability.Themethod

is based onoptimal powerflow and theBender’s decomposition

technique. The proposed RRMP is decomposed into two parts

giving it a hierarchical structure that gives the optimal problem

addedflexibility.Botharmatureandfieldcurrentlimitingarein-

troduced into the optimization problem so as to make the model

more accurate for mid-term voltage stability analysis. The ro-

bust interior point method is utilized to solve the problem. De-

tailed generator models were considered in the optimization.

Since synchronous generators contain the most effective dy-

namic reactive reserves, a weighting scheme is designed to se-

lect the set of participating generators that have the most influ-

enceinstrengtheningaweakarea.Theweightsweredetermined

by V-Q curves. Both static and dynamic voltage stability mar-

gins are improved by managing the reactive reserves at these

participatinggenerators.Teststudiesshowthatreactivereserves

are beneficial for maintaining and improving voltage stability.

Theuniquenessinthesolutionstrategyproposedinthispaper

stems from the fact that when dealing with var optimization,

most optimization procedures described in the literature focus

upon reactive power rescheduling and not reactive reserve

margin optimization. In the realm of mid-term voltage stability,

the reactive reserve margin is extremely important at genera-

tors because it gives an advance indication of how close the

generator might be to its OEL becoming active. Conceivably,

a weak area could become weaker if a generator’s OEL would

operate in a stressed situation because of the simple reason that

its reactive capability would be exhausted. In turn, this would

lead to the area importing reactive power from neighboring

areas, thus creating an onerous situation for a collapse to occur.

APPENDIX

This Appendix shows the reduced WECC System, which is

shown in Fig. 6.

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Feng Dong (S’03) received the B.S. and M.S. degrees in electrical engineering

from Hohai University, Nanjing, China, in 1995 and 1999, respectively. He is

currently pursuing the Ph.D. degree in the Department of Electrical and Com-

puter Engineering, University of Missouri-Rolla.

Badrul H. Chowdhury (S’86–M’87–SM’92) received the M.S. and Ph.D. de-

grees in electrical engineering from Virginia Tech, Blacksburg, VA, in 1983 and

1987, respectively.

He is currently a Professor in the Electrical and Computer Engineering De-

partment, University of Missouri-Rolla.

Mariesa L. Crow (S’83–M’90–SM’94) received the B.S.E.E. degree from the

University of Michigan, Ann Arbor, and the Ph.D. degree from the University

of Illinois at Urbana–Champaign in 1989, both in electrical engineering.

She is currently Associate Dean for Graduate Studies and Research and a

ProfessorofElectricalandComputerEngineeringattheUniversityofMissouri-

Rolla.

Levent Acar (M’86–SM’88) received the M.S. and Ph.D. degrees in electrical

engineering from The Ohio State University, Columbus, OH, in 1984 and 1988,

respectively.

He is currently an Associate Professor in the Electrical and Computer Engi-

neering Department, University of Missouri-Rolla.