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A
SEMINAR REPORT
ON
AVOIDING RISK OF VOLTAGE INSTABILITY IN A
POWER SYSTEM THROUGH REACTIVE POWER
RESCHEDULING AND LOAD SHEDDING
(SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENT FOR THE
AWARD OF THE DEGREE OF)
BACHELOR OF TECHNOLOGY
2010 2011
JAIPUR NATIONAL UNIVERSITY, JAIPUR
(A Venture of seedling group of institutions)
BY
MANISH KUMAR SHARMA
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AB T ACT
As th use of renewable energy sources (R s) increases worl wi e, there is a rising interest
on their im acts on power system operation and control. The important impacts of a large
penetration of variable generations in area of operation and control can be summarized in the
directions of regional overloading of transmission lines in normal operation as well as in
emergency conditions, reduction of available tie-line capacities due to large load flows,
frequency performance, grid congestions, increasing need for balance power and reserve
capacity, increasing power system losses, increasing reactive power compensation, and
impact on system security and economic issues. The distributed power fluctuation (due to
using of variable generations) negatively contributes to the power imbalance, frequency and
voltage deviations. Significant disturbance can cause under/over frequency/voltage relaying
and disconnect some lines, loads and generations. Under unfavourable conditions, this may
resultin a cascading failure and system collapse. Here we describe a procedure forimproving
voltage stability condition of a power system by reactive power rescheduling or load
shedding. For this purpose, a voltage stability index and its threshold value is used as the
basis. Sensitivity factors are derived to relate change in voltage stability index for changes in
reactive power at generation buses and changes in load atload buses. Using these sensitivity
factors, a procedure is proposed for avoiding risk of voltage instability in a power system by
applying reactive power rescheduling orload shedding.
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ACKNOWLE E ENT
I would like to convey my sincere thanks to Prof.DEVENDRA DODA (HOD, EE) for
giving us such a wonderful opportunity to enhance our skills throughthese seminars.
I would like to express my deep sense of gratitude, indebtedness to Mr. DUR
ESH
NANDAN PATHAK(lecturer, EE, JNU, Jai pur), and all the faculty mem bers fortheir
guidance, ever inspiring help, affectionate encouragement & motivation .They have been a
great source ofinspiration forme.Ive been receiving valuable suggestions fromthem.
I am also thankfulto Mrs. DEEPIKA CHAUHAN who helped me in my seminar withhis
fullinterest. The uphilltask for completing this seminar report would have been impossible
without support of all staffmember.
No words are sufficientto express my gratitude to colleagues fortheir
exemplary patience, understanding, co-operation & for creating congenial environment to
carry outthis work.
NAVEEN KUMARMEENA
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FIGURE INDEX
TOPICS PAGENO.
Figure1. Flow chart for reactive power rescheduling or/and load Shedding to improve
voltage stability condition of a power system.................... ....................................................19 Figure1 continued..................................................................................................................20
Figure1 continued.................................................. ................................................................22
Figure1 continued..................................................................................................................23 Figure2. IEEE30Bus system................................................................................................24
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INTRODUCTION
The problem related to voltage instability in a power systemis a major concern for power
system operation and planning. A major factor contributing to voltage instability is thevoltage drop that occurs when active and reactive power ow throughinductive reactance of
the transmission network; this limits the capability ofthe transmission network for power
transfer and voltage support. The powertransfer and voltage support are furtherlimited when
some ofthe generators hittheir eld or armature currenttime-over load capability limits.
Voltage stability is threatened when a disturbance increases the reactive power demand
beyond the sustainable capacity ofthe available reactive power resources. Voltage collapse is
characterized by a slow variation in system operating point, due to increase in the loads, in
such a way thatthe voltage magnitude gradually decreases until a sharp accelerated change
occurs.Ithas been observed that voltage magnitudes, in general, do not give a good
indication of proximity to voltage stability limit.In recentliterature, many voltage stabilityand voltage collapse prediction methods have been presented. Some ofthe important ones
are:
(1) Voltage collapse index based on a normalload ow solution (L-index);
(2) Voltage collapse index based on closely located power ow solution pairs;
(3) Voltage collapse index based on sensitivity analysis; and
(4) Minimum singular value of Newton-Raphson power ow Jacobian matrix.
These methods assess the closeness to the critical loading by looking in to the voltage
stability sensitivity indices orthe smallest Eigen value or singular value ofload ow Jacobian
matrix. Index presented in gives a scalar number to each load bus, called the L-index, to
indicate the proximity of voltage collapse for a power system. The index value ranges from0
to 1. The bus with largest value of L is the most vulnerable bus in the system. In the
procedure for calculation of L has been simplied using some acceptable approximations;
this reduces the computational burden considerably. A reliable voltage stability index Iihas
been proposed, whose threshold value is found to be varying marginally between 0.43to 0.52
as againstthe theoreticalthreshold value of0.5. The decrements ofthis index are rapid with
respectto load variation as it approaches the proximity of voltage collapse. Therefore, index
nearto 0.7is an alarming situation so far as voltage stability of a power systemis concerned.
For a voltage stability index to be effective and useful, it should possess the following
qualities: (1) Indicator/index should be related to the controllable parameters of a power
system through a simple function; and (2) some corrective measures could be derived from
the indices. The proposed procedure aims atinvolving only sensitive generation buses and/or
load buses for reactive power rescheduling and/or load shedding, respectively, to improve
voltage stability condition of a power system. Load shedding option is undertaken whenreactive power rescheduling of generation buses cannot improve voltage stability index of a
bus to a desired value.
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2.CLASSIFICATIONOF INSTABILIT MECHANISMS
The objective ofthis section is to relate the above concepts oflarge disturbance and time
scale decomposition to power system phenomena and models. We provide a classication of
loss of stability mechanisms relevantto voltage phenomena. State approximation to be used
and the overall systeminstability to be decomposed in several well dened categories. Let us
assume a large disturbance and considerthe possible unstable system responses thatmight
result.
2.1 Transient Period
In the transient period immediately following the disturbance the slow variables do not
respond yet and may be considered constant. The three majorinstability mechanisms are
T1: loss of equilibrium ofthe fast dynamics.
T2: lack of attraction towards the stable post-disturbance equilibrium ofthe fast dynamics.
T3: post-disturbance equilibrium oscillatory unstable. The transient period is the usualtime
frame of angular stability studies. Forinstance, the loss of synchronism following too slow a
fault clearing is a typical T2mechanism. This is also the time frame oftransient voltage
stability, which results fromloads trying to restore their powerin the transienttime frame.
Typical examples are induction motorloads and HVDC components.An example of T1voltage instability is the stalling of an induction motor fed through a long transmission line,
after some circuittripping makes the transmission impedance too large.Motor stalling causes
the voltage to collapse. The motormechanical and electricaltorque curves do notintersect
any longer, leaving the system without a post-disturbance equilibrium. An example of T2
voltage instability is the stalling ofinduction motors after a short-circuit.In heavily loaded
motor and/or slowly cleared fault conditions, the motor cannot reaccelerate afterthe fault.The mechanical and electricaltorque curves intersect but at fault clearing, the motor slip is
largerthan the unstable equilibrium value.
2.2 Power System Stability
Power system stability is the ability of an electric power system, for a given initial operating
condition, to regain a state of operating equilibrium after being subjected to a physical
disturbance, withmost system variables bounded so that practically the entire system remains
intact.
2.3 Voltage Stability
Voltage stability refers to the ability of a power systemto maintain steady voltages at all
buses in the system after being subjected to a disturbance from a given initial operating
condition. Characterized by loss of a stable operating point as well as by the deterioration of
voltage levels in and around the electrical centre ofthe region undergoing voltage collapse
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T e c ange in bus voltage vector [ V ] wit respect to c ange in reactive power
injection vector [Q] can be expressed as:
Substituting [V ] in Eq ( ) fro Eq ( ), we ave
T e sensitivity factors [] relate c ange in t e index value for kt
bus wit respect to c ange
in reactive power injections at t e buses, but reactive power resc eduling can becarried outonly in t e generation buses, as suc , representing Eq ( ) only for generationbuses we ave
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T e Jacobian atrix of NR load ow analysis relates c ange in real and reactive power
injections wit respect to c ange in bus voltage angles and bus voltage agnitudes asfollows:-
Substituting [ V ] in Eq ( ) fro Eq ( ) we ave
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T e above equation can be expressed as:
w ere [ ] and [] are t e sensitivity factors (SFs) relating [P] and [Q] to t e c ange in t e
index value of kt bus Assu ing load power factors do not c ange wit c ange in load
values, Eq ( 5) can be written as:
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3.Determination ofSuitable Value of MG, ML, and Solution Procedure:-
The proposed procedure aims at involving sensitive generation buses and/or load buses for
reactive power rescheduling and/or load shedding, respectively, to improve the voltage
stability condition of a power system. Load shedding option is undertaken when reactive
power rescheduling of generation buses cannot improve the voltage stability index of avulnerable load bus to its desired value. To ensure participation of sensitive generation buses
and/orload buses, buses having SF values more than cut off values cut and cut are selected
for reactive power rescheduling and/or load shedding, respectively. A factor (KM > 1) is
included for the purpose of ensuring that sufficient num ber of buses are included during
improvement of the value of Ik and all the rescheduled (reactive power) generators or load
shedding buses do no get xed at their limits. A value of KM 1.1 1.2 has been found to
work well formost ofthe systems. The procedure adopted for the selection of participating
buses is as follows:
1. Store the bus number in arrays BRj and BLj for j = 1. . .N according to descendingorder of the sensitivity factor associated with each bus for reactive power rescheduling and
load shedding, respectively (buses having highest sensitivity factor are ranked as one, bus
with nexthighest sensitivity ranked two, and so on) and setM = 0.
2. Set j = 1 and Iach = 0.3. i = BRj.4. Ifith bus is not a generation bus; go to step 6.5. If Iach > KMIk go to 15
M = M + 1
Iach = Iach + iQilimit
6. j = j + 1.
7. If j N; go to step 3.
8. Set j = 1 and ML = 0.
9.i = BLj.
10.Ifith bus is not a load bus; go to 13.
11.If j < 0 go to step 13.
12.If Iach > KMIk go to 15.
ML = ML + 1Iach = Iach + i PDi
limit
13. j = j + 1.
14.If j N; go to step 9.
15. Stop.
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5.Simulations Results and Discussion
To verify the applicability of the proposed procedure, simulations were carried out on
IEEE30 bus system shown in Figure 2. To demonstrate the effectiveness of the procedure,
both reactive power rescheduling and load shedding were carried out according to the
requirements to improve the value ofthe indexIk ofmost vulnerable bus to its desired value
Idesk . The system loading is adjusted in such a way that voltage stability indices of a few
buses ofthe system falls below 0.75. Table 1 shows the generations, loads, and voltage
conditions at these generation buses. Table 2 presents the loads, voltage condition, and
voltage stability index of load buses of the system. It shows the minimum value of voltage
stability index is appearing at load bus 19, the value is I19 = 0.718003. From voltage
instability point of view, this bus is the most vulnerable bus. Simulations were carried outto
improve this index to different desired value with different reactive power limits on the
generation buses.Minimum value ofload, which cannot be shed atload bus, is taken as 20%
ofthe initialload atthe bus. Table 3 presents the two different reactive powerlimits applied
to the generation buses for simulation purpose. Power limits on the generation buses.
Minimum value ofload, which cannot be shed atload bus, is taken as 20% ofthe initialload
atthe bus. Table 3 presents the two different reactive powerlimits applied to the generation
buses for simulation purpose.
5.1.Desired Value of I19des
= 0.75
Case-I reactive power limits are applied to the generation buses for improving value ofthe
voltage stability index at bus 19. The results obtained from simulation are presented in Tables
4 and 5.
The simulation results show that the voltage stability index is improved to 0.744932 from
0.718003through reactive power rescheduling.In this case, load shedding is not required for
improvement ofthe voltage stability index.
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5.2. Desired Value of I19des
= 0.8
At rst, Case-I reactive power li its are applied to t e generation buses for i proving value
of t e voltage stability index at bus T e results obtained fro si ulation are presented in
Tables and
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6.CONCLUSIONThe proposed procedure for reactive power rescheduling or load shedding aims atimproving
voltage stability condition of a power system from proximity of voltage collapse.Index Ik, the
voltage stability index ofthe most vulnerable bus of a power system, is used as the basis for
the improvement of voltage stability condition of the system. Sensitivity factors are derivedto relate change in voltage stability index for change in reactive power at generation buses
and change in load at load buses. The sensitivity factors are used to determine the required
reactive power rescheduling and/orload shedding to im prove voltage stability condition of a
power system. The proposed procedure aims at involving only sensitive generation buses
and/or load buses for reactive power rescheduling and/or load shedding, respectively, to
im prove voltage stability condition of a power system. Load shedding option is undertaken
when reactive power rescheduling of generation buses cannotimprove voltage stability index
of a bus to its desired value. The proposed procedure for improving voltage stability
condition by reactive power rescheduling or load shedding can provide usefulinformation to
power system planner/operator to undertake corrective action to avoid risk of voltage
instability in a power system.
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7. APPENDICES
N Total number of buses in the system
NG Total number of generation buses in the system
NL Number ofload buses in the system
Pi Injected active power atith bus
Qi Injected reactive power atith bus
QGi(max) Maximumlimit of reactive power generation atith bus
QGi(min) Minimumlimit of reactive power generation atith bus
PDi(min) Limit on load shedding ofthe ithload bus
Si Pi + jQi
Vi Magnitude of voltage atith bus
i Angle ofthe bus voltage atith bus
Gi j + jBi j Element of Y -BUS matrix atith row and j th column
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8. REFERENCES
1.Kunder, P., Paserda, J., Ajjarapu, V., Anderson, G., Bose, A., Conizares, C., Haliziargyriou,
N.,Hill, D., Stamaoric, A., Taylor, C., Cutsen, T. V., and Vittal, V., Denition and
classication of power system stability, IEEE/CIGRE Joint Task Force on Stability Terms
and Denition, IEEE Trans. Power Syst., Vol.19, No.2, pp.1387 1401, May 2004.
2. Kessel, P., and Glavitsch, H., Estimating the voltage stability of a power system, IEEE
Trans. Power Del., Vol. PWRD-1, No.3, pp.346 354, July 1986.
3. Clark, H. K., New challenges: Voltage stability, IEEE Power Eng. Rev., pp. 33 37,
April1990.
4. Tamura, Y., Mori, H., and Lwanoto, S., Relationshi p between voltage instability and
multiple load ow solutions in electrical system, IEEE Trans., Vol. PAS-102, pp. 1115
1125, May 1983.
5. Crisan, O., and Liu, M., Voltage collapse prediction using an im proved sensitivity
approach, Elec. Power Syst.Res., pp.181190, 1984.
6. Lof, P. A., Anderson, G., and Hill, D. J., Voltage stability indices of stressed power
system, IEEE Trans. PWRS, Vol.8, No.1, pp.326335, 1993.
7. Tiranuchit, A., and Thomas, R. J., A posturing strategy against voltage instability in
electrical power systems, IEEE Trans. PWRS, Vol.3, No.1, pp.8793, 1989.
8. Tuan, T. Q., Fandino, J., Hadjsaid, N., and Sabonnadiere, J.C., Emergency load shedding
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pp.341351, Feb.1994.
9. Sinha, A. K., and Hazarika, D., Comparative study of voltage stability indices in a power
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