Strategy to minimise the load shedding amount for voltage collapse

Comments

Transcription

Strategy to minimise the load shedding amount for voltage collapse
www.ietdl.org
Published in IET Generation, Transmission & Distribution
Received on 12th May 2010
Revised on 23rd September 2010
doi: 10.1049/iet-gtd.2010.0341
ISSN 1751-8687
Strategy to minimise the load shedding amount
for voltage collapse prevention
Y. Wang1 I.R. Pordanjani1 W. Li1 W. Xu1 E. Vaahedi2
1
Department of Electrical and Computer Engineering, University of Alberta, Edmonton, Alberta, Canada T6G 2V4
British Columbia Transmission Corporation, Vancouver, BC, Canada
E-mail: [email protected]
2
Abstract: This study presents a practical approach for determining the best location and the minimum amount of the load to be
shed for the event-driven-based load shedding schemes. In order to find the above key parameters, a non-linear optimisation
problem needs to be solved. A multistage method is proposed to solve this non-linear problem. The main idea of this method
is to solve the optimisation problem stage by stage and to limit the load shedding to a small amount at each stage. Using this
approach, the non-linear optimisation problem will be converted into a series of linear optimisation problems. By solving
these linear optimisation problems stage by stage, the optimal solution to the original non-linear problem is obtained.
Furthermore, in order to quickly identify the candidate load shedding locations in the multistage method, a novel multiport
network model is proposed. Based on the multiport network model, fast ranking of the load locations and of the generators’
participation factors can be done with little calculation efforts. Details of the problem formulation and the solution strategy
are presented here. The proposed strategy is illustrated and verified by using the IEEE 14-bus system, IEEE 118-bus system
and a real 2038-bus power system.
1
Introduction
With the increasing demand for electrical power and due
to economic and environmental constraints, power systems
are currently being operated closer to their limits than
they were previously. This has led to an ever-increasing
risk of voltage instability, which is the most important
limiting factor for power transmissions. Among different
countermeasures for the prevention of the voltage
instability, load shedding is the last line of defence when
there is no other alternative to stop an approaching voltage
collapse [1].
The growing concern on voltage instability incidents has
attracted a great deal of attentions. Significant progress has
been made in the research on the implementation of the
load shedding schemes over the past few decades [2 –8].
Undervoltage load shedding scheme is normally the
primary choice for most of the utilities due to its simplicity
[9 – 14]. However, it has been proven that the bus voltage
level alone is not a good indicator to assess the security of
the operating conditions, especially when the shunt
compensation and/or some other voltage control devices are
heavily used in the modern power systems [10]. Moreover,
the load shedding amount is difficult to be minimised only
based on the voltage levels at some particular buses.
In order to optimise the load shedding schemes, several
methods which are aimed at minimising the load shedding
amount have been proposed in recent years [9 – 11]. The
sensitivities of the load-ability margin and the sensitivities
of voltage with respect to the load parameters are often
IET Gener. Transm. Distrib., 2011, Vol. 5, Iss. 3, pp. 307– 313
doi: 10.1049/iet-gtd.2010.0341
used to determine the optimum load locations. By using the
sensitivities information, an optimisation problem is usually
formed and the minimum load shedding amount is
determined by solving it. However, since these sensitivities
vary significantly when the operating condition changes, the
load shedding amount which is computed based on the
sensitivities obtained before the load shedding is applied
might not be optimal. At the same time, associated with the
load shedding, the system also needs to shed the same
amount of generation to maintain the power balance.
However, the problem of how to distribute the amount of
generation shedding has rarely been discussed in the
literature. Although the modal analysis method [8] is
normally used to calculate the generators’ participation
factors, it is difficult to directly use these participation
factors to shed the generations.
In this paper, the variation in these sensitivities with respect
to the load shedding amount is first investigated.
This investigation reveals that a non-linear optimisation
problem needs to be solved in order to obtain the best
locations and the minimum amount for the load shedding.
Several difficulties are involved in solving this non-linear
optimisation problem. In order to overcome these
difficulties, a multistage method is proposed. The main idea
of the proposed method is to solve the optimisation
problem stage by stage, and limit the load shedding to a
small amount at each stage. Using this approach, the nonlinear optimisation problem will be converted into a series
of linear optimisation problems. By solving them stage by
stage, the optimal solution to the original non-linear
307
& The Institution of Engineering and Technology 2011
www.ietdl.org
problem can be obtained. A new multiport network model is
also proposed in this paper in order to be used for quick
identification of the most effective locations for load
shedding. Using this model, not only can the loads be
ranked with little calculation efforts, but also the required
generation shedding can be easily distributed among the
generators.
The rest of the paper is organised as follows. Section 2
investigates the sensitivities of load-ability margin with
respect to load parameters under different load shedding
amount. Based on the findings in Section 2, a multistage
method is proposed in Section 3. In Section 4, the multiport
network model is introduced to rank the loads and
generators. In Section 5, the proposed method is applied on
several power systems and its performance is verified.
Finally, Section 6 consists of the conclusion.
2 Sensitivites of load-ability margin with
respect to load shedding amount
The load-ability sensitivity with respect to load parameters
can be defined by (1), which is modified from the
sensitivity formula in [12].
Seni =
Dl
DSi
i = 1, 2, . . . , n
(1)
where DSi is the load shedding amount at load bus i, Dl is the
load-ability margin increment after the load shedding and n is
the total number of loads.
In order to achieve the required load-ability margin
increment Dlreq, the minimum load shedding amount is
determined by shedding loads from the most sensitive loads
until the achieved margin increase Dl∗ exceeds Dlreq.
The margin increment Dl∗ is calculated by (2) [9].
Dl∗ =
m
Seni × DSi
m≤n
(2)
i=1
where DSi ¼ f × Si , f is the shedding fraction of the selected
load, Si and DSi are the load demand and the shedding amount
at bus i, respectively.
As indicated in [9], the minimum amount of load shedding
obtained from (2) relies on the following two assumptions:
1. Linearity of (2): the load-ability margin increments from
any single load shedding can be added up.
Fig. 1 Actual and the expected load-ability margins
2. Constant sensitivities: the load-ability sensitivities remain
constant no matter how much load is shed at the selected
locations.
To investigate the validity and accuracy of the above two
assumptions, the load-ability sensitivities are studied by
using the IEEE 14-bus system. Equations (1) and (2) are
used in this study.
The investigation results on the linearity of (2) are shown in
Fig. 1. In this figure, Dl∗ is calculated by using (2) and Dlact
is obtained using the continuation power flow method in the
commercial software PSS/E. Fig. 1 clearly reveals that the
validity of the linearity assumption is doubtful.
To study the second concern, the load-ability sensitivities of
the six loads in the IEEE 14-bus system are studied. For this
purpose, two different operation conditions – with and
without considering the non-linear effects – are studied. The
non-linear effects are the reactive power limit, actions of the
switched shunts and the movements of the tap changers.
The margin increment results with different load shedding
amount are shown in Fig. 2. According to Fig. 2a, when the
non-linear effects are not considered, the relationship between
the margin increments and the load shedding amount is
almost linear. In other words, without considering the nonlinear effects in the system, the sensitivities remain relatively
constant. On the other hand, when the non-linear effects are
considered, these sensitivities vary significantly, as shown in
Fig. 2b. This figure also indicates that shedding more loads
does not necessarily lead to a higher margin increment.
According to what was explained above, none of the
assumptions considered in (2) can be confirmed in power
systems. Therefore the solution obtained by (2) may not be
even close to the optimal load shedding results. Many
strategies have been proposed to solve this problem in
recent years. In this paper, a practical strategy called the
multistage method is proposed.
Fig. 2 Variation of the sensitivities under different load shedding amount
a Margin increments with different load shedding amount (without considering the non-linear effects)
b Margin increments with different load shedding amount (with considering the non-linear effects)
308
& The Institution of Engineering and Technology 2011
IET Gener. Transm. Distrib., 2011, Vol. 5, Iss. 3, pp. 307 –313
doi: 10.1049/iet-gtd.2010.0341
www.ietdl.org
3
Proposed multistage method
The above analysis indicates that a non-linear optimisation
problem, as described by (3), needs to be solved to obtain
the best load shedding location and the minimum load
shedding amount.
min Sshed =
m
DSi
i=1
Dl∗ = f (DS1 , DS2 , . . . , DSm )
Dl∗ ≥ Dlreq
s.t.
power flowf(z, s) = 0
power system components limits
limits proposed by the load shedding providers
(3)
where Sshed is the total load shedding amount, m is the number
of available load shedding providers, z is the system state
vector and s is the vector of active and reactive powers
consumed by the loads.
As seen in (3), several power system operation constraints
including power flow equations, power system components
limits and the limits of load shedding providers are
considered in the optimisation problem. More factors, such
as generators’ cost functions and load characteristics, can
also be considered as long as they are properly represented
in (3). However, the principle of solving this non-linear
optimisation problem remains the same. In this paper, we
mainly focus on introducing the principles of the multistage
method using the constraints described in (3).
The analysis in Section 2 reveals that the relationship
between the margin increment and the load shedding
amounts is an unknown non-linear function, which is
represented as the function f. Therefore there is a big
challenge in solving this non-linear optimisation problem.
To overcome this difficulty, a practical multistage method
is proposed. It is called multistage because it is going to
solve (3) stage by stage. For each stage, two circumstances
are considered:
1. The load shedding is applied at only one location.
2. The load shedding amount is limited to a small value (say
10%) so that the sensitivities can be considered constant.
Considering the above conditions, (3) can be converted to a
series of linear optimisation problems by using the piecewise
linear method. At each stage, the linear optimisation problem
can be described by (4). By solving these linear optimisation
problems one by one, the load-ability margin is improved
stage by stage. Until the last stage, the desired load-ability
margin is obtained. The solution to the original problem is
the combination of the solutions to all these linear
optimisation problems.
Max{Dli }
s.t.
Dli = Seni × DSi ,
Fig. 3 Flowchart of the proposed multistage method
Fig. 3. As seen in this figure, the sensitivities are calculated
at each stage and the load with the highest sensitivity is
selected as the most effective location. The load shedding
is then applied at the selected location. After this load
shedding, a new operation case is constructed and the next
stage starts. This process will be repeated until the required
margin is obtained. The final load shedding rule is the
combination of the results from all stages. It is worthwhile
to mention that the term of ‘multistage’ is only to describe
the design procedure, not to reflect the load shedding stages
in implementation.
The load shedding sensitivities can be calculated by using
any existing method such as the method proposed in [12]. The
main problem in this kind of methods is that they are very
time-consuming. This problem becomes more important in
the proposed multistage method because the sensitivities
need to be calculated at each stage, and a high number of
stages might be necessary for a large system. Moreover,
after a load shedding is applied at each stage, an active
power shedding should be applied to the generators in order
to construct a new base case. In other words, a proper
generation shedding should be assigned for the selected
load shedding at each stage.
In order to make the proposed multistage method more
practical, a new algorithm is required which can not only
find the most effective location for the load shedding in a
fast manner, but also obtain a proper generation shedding
associated with the selected load shedding. For this
purpose, a new procedure based on a multiport network
model is proposed in the next section.
4
i = 1, 2, . . . , n
(4)
Since (4) is a linear optimisation problem, it is quite easy to
solve it. It suffices to calculate the sensitivities and select
the load with the highest sensitivity.
According to what was explained above, the procedure of
the proposed multistage method will be as depicted in
IET Gener. Transm. Distrib., 2011, Vol. 5, Iss. 3, pp. 307– 313
doi: 10.1049/iet-gtd.2010.0341
Multiport network model
Associated with the multistage load shedding method
proposed in the previous section, a new multiport network
model is presented in this section to solve the following
two problems with little calculation effort:
1. find the most effective location for the load shedding at
each stage;
309
& The Institution of Engineering and Technology 2011
www.ietdl.org
The impedance ratio Zratio, j is calculated by (9), where ZLj
is the impedance of load j.
Zratio,j
Z j
= ,
ZLj ZLj =
VLj
,
ILj
j = 1, 2, . . . , n
(9)
Fig. 4 Multiport network model
2. obtain the generators’ participations associated with the
selected load shedding in order to calculate the proper
generation shedding for each generator.
The proposed multiport network model is to equivalent the
power system by a model shown in Fig. 4. All the generator
and load buses are separated from the transmission network,
which is converted to an equivalent impedance matrix Z.
The equation to describe the above multiport network
model can be written as
V L = KE − ZI L
n
ZLLji ILi = Eeqj − Zj ILj
(6)
i=1,i=j
Zj =
ZLLjj ILj + Sni=1,i=j ZLLji ILi
ILj
Eeqj = [KE]j
(7)
(8)
where Zj is the Thevenin impedance of the network at bus
j and Eeq j is the Thevenin equivalent voltage seen at bus j.
The Thevenin equivalent parameter Eeq j represents the
contributions from all the generators. As well, the Thevenin
equivalent parameter Zj represents the impacts from all the
other loads. Using these parameters, the power system can
be converted into an equivalent circuit shown in Fig. 5.
For each load bus, the impedance matching theory can be
applied in order to find the weakest load bus. In other
words, the load with the highest impedance ratio value is
the weakest load [13]. The weakest load is obviously the
most effective location for the load shedding.
Fig. 5 Multiport network equivalent circuit
310
& The Institution of Engineering and Technology 2011
Eeqj = Kj1 E1 + Kj2 E2 + · · · + Kjm Em
(10)
Equation (10) shows the composition of the Thevenin
equivalent voltage. Based on (10), the contribution of each
generator on the selected load j can be defined by (11).
Cji =
(5)
where
T
E = E1 E2 . . . Em , V L = VL1 VL2 . . . VLn ]T ,
T
I L = IL1 IL2 . . . ILn , K is an n × m matrix obtained
from system admittance matrix, and Z is an n × n system
impedance matrix.
For the jth load bus, we can obtain
VLj = [KE]j − ZLLjj ILj −
Furthermore, the generators’ participations for the selected
load shedding can also be calculated based on the
contribution of each generator on this selected load. From
(6), we obtain an expanded expression of the Thevenin
equivalent voltage by (10).
|Kji Ei |
cos(uji )
|Eeq j |
(11)
where Cji is the contribution of generator i on the load j and uji
is the angle difference between the Thevenin equivalent
voltage Eeqj and the generator voltage KjiEi .
Thus, the participation of each generator on the selected
load shedding amount DSj will be calculated by (11). The
generation shedding of each generator associated with this
load shedding can then be obtained by (12). Meanwhile, the
capacity of the automatic frequency control of each
generator has to be taken into account in order not to
introduce any other problem, such as angular stability
problem. For this purpose, the amount of generation
shedding for each generator needs to be limited by its
corresponding control capacity DGi,max . If the calculated
generation shedding (DGji) is over DGi,max , the shedding is
fixed at DGi,max . The leftover (DGji 2 DGi,max) will be
distributed to the other generators based on the same ratio
provided by (12).
DGji =
Cji
k
Si=1 Cji
DPj
i = 1, 2, . . . , k
(12)
where DGji is the active power shedding of generator i, DPj is
the real part of the load shedding amount DSj and k is the total
number of generation plants in the systems.
In order to verify the performance of the proposed method,
the method is applied to different power systems.
IEEE 14-bus system: This case study is the stressed version
of IEEE 14-bus system. The studied case has 1.85 times more
load demand than the base case which can be found in [15].
After an N 2 2 contingency (the loss of the line between bus 2
and bus 4, and the line between bus 2 and bus 5), the system
power flow diverges. Both the modal analysis method [8] and
the proposed method are used to find the top five critical
(weakest) load buses. The results are listed in Table 1,
which reveals that both the methods lead to bus 14 as the
weakest bus in the system. As well, the generators’
contributions Cji associated with the load shedding at load
bus 14 are shown in Table 2.
IEEE 118-bus system: The studied power system is the
stressed IEEE 118-bus system. The studied case has two
times more load demand than the base case which can also
be found in [15]. After an N 2 1 contingency (the loss of
the line between bus 74 and bus 75), the system margin
IET Gener. Transm. Distrib., 2011, Vol. 5, Iss. 3, pp. 307 –313
doi: 10.1049/iet-gtd.2010.0341
www.ietdl.org
Table 1
Results of the bus ranking for IEEE 14-bus system
No.
Load bus ranking
1
2
3
4
5
Table 2
Modal analysis based
on the critical mode
Proposed method
14
10
9
4
5
14
9
10
4
5
0.01237
0.0
Results of the bus ranking of IEEE 118-bus system
No.
Load bus ranking
1
2
3
4
5
Table 4
Modal analysis based
on the critical mode
Proposed method
44
45
43
22
21
44
45
43
95
21
Generators’ contribution on the load bus 44
No.
generator 49
generator 54
Modal analysis based on
the critical mode
Proposed method
4220
4219
19 314
4361
19 388
4220
4219
4361
19 314
18 393
Generators’ contribution on the load bus 4220
No.
shrinks to 4%. Table 3 shows the top five critical load buses
for this case. According to this table, both the proposed
method and modal analysis method result in the load 44 as
the weakest load in the system. As well, the non-zero
generators’ contributions associated with the load shedding
at the load bus 44 are shown in Table 4.
Real 2038-bus power system: A real large system (the
Alberta Interconnected Electric System) is considered as the
last case study. It consists of 208 PV buses, 688 load buses
and 2366 branches. The total load demand is 10222.4 MW
and 3349.3 MVar. After an N 2 1 contingency or loss of
the line between bus 74 and bus 814, the system loses its
power flow solvability. The bus ranking results obtained
from the modal analysis method and the proposed method
are listed in Table 5. It can be seen that both of the
methods result in the same weakest load. Also, the top five
contributed generators associated with the load shedding at
load bus 4220 are shown in Table 6.
The above case studies clearly verify the performance of
the proposed method in terms of the identification of the
most sensitive load. The results from modal analysis and
those from the proposed method are perfectly consistent
with each other.
Therefore the proposed multiport network model can be
used in the procedure of the multistage method. For this
purpose, the procedure which was previously shown in
Table 3
Load bus ranking
1
2
3
4
5
Table 6
Generators’ contribution
generator 1
generator 2
Results of the bus ranking of the real power system
No.
Generators’ contribution on the load bus 14
No.
Table 5
Generators’ contribution
0.4518
0.3172
IET Gener. Transm. Distrib., 2011, Vol. 5, Iss. 3, pp. 307– 313
doi: 10.1049/iet-gtd.2010.0341
Generators’ contribution
generator 1495
generator 1497
generator 1496
generator 3248
generator 2248
0.1058
0.1044
0.0965
0.0430
0.0429
Fig. 6 Flowchart of the proposed strategy
Fig. 3 can be modified to the one depicted in Fig. 6. In the
new procedure, multiport network model is used at each
stage of the multistage method to find the most effective
location for the load shedding and the associated generation
shedding.
In the next section, the procedure described in Fig. 6 will be
demonstrated by the IEEE 14-bus system, the IEEE 118-bus
system and the real 2038-bus power system.
5 Illustration studies on the selected
power systems
The proposed strategy is applied to several test power
systems and the results are investigated in this section.
Both the proposed method and the conventional method
described by (2) are tested. The results are compared with
311
& The Institution of Engineering and Technology 2011
www.ietdl.org
As seen in this table, in order to restore the system, the
proposed method shed 0.43 MW less active power and
2.28 MVar less reactive power.
IEEE 118-bus system: The test system is the stressed IEEE
118-bus system. The studied case has two times more load
demand than the base IEEE 118-bus system. The stability
margin of the studied case is 6%. After the N 2 1
contingency, that is, the loss of the line between bus 74 and
bus 75, the system load-ability margin shrinks to 4%. The
results for the load shedding rules are listed in Table 8. In
this case, the results of the proposed strategy are the same
as the conventional method. The reason is that this
contingency is not severe and very small amount of load
shedding is enough to restore the system. As a result, as
seen in Table 8, the proposed strategy is completed in only
one stage. In this situation, the performance of the proposed
strategy might be improved by reducing the size of the load
shedding amount at each stage.
Real 2038-bus power system: The real power system used
in Section 4 is studied here. After the N 2 1 contingency, that
is, loss of the line between bus 74 and bus 814, the system
each other. The detailed information of the conventional
method can be found in [9]. The load shedding step size is
considered as 10% of the selected load for both of the two
methods.
IEEE 14-bus system: This test power system is a stressed
system from the IEEE 14-bus system. The studied case has
1.85 times more load demand than the base IEEE 14-bus
system. The voltage stability margin of the studied case is
42%. After the selected N 2 2 contingency, that is, the
two transmission lines outages (the branch between bus 2
and bus 4, and the branch between bus 2 and bus 5), the
system loses its power flow solvability. The load shedding
strategy is then applied to ensure that the load-ability
margin is no less than the required 5% (WSCC standard
[14]).
Based on the results from Table 1, load bus 14 will be
chosen at the first stage and the load shedding amount is
10% for this stage. This procedure is then repeated until the
required voltage stability margin is obtained. Table 7 shows
the load shedding results obtained from the proposed
strategy and those obtained by the conventional strategy.
Table 7
Results of the load shedding rules for IEEE 14-bus system
Methods
Load shedding rules
Stage
the proposed strategy
1
2
3
4
5
6
7
8
9
10
11
12
13
the conventional method
Table 8
Margin after shedding, %
Location
Amt, %
14
14
9
9
9
14
14
9
14
10
14
9
4
10
10
10
10
10
10
10
10
10
10
10
10
10
29.36 MW,
11.84 MVar
5
14
10
9
100
100
20
29.79 MW,
14.12 MVar
6
Results of the load shedding rules for IEEE 118-bus system
Methods
Load shedding rules
the proposed strategy
the conventional method
Table 9
Total shedding amount
Location
Amt, %
Total shedding amount
Margin after shedding, %
bus 44
bus 44
10
10
1.6 MW, 1.2 MVar
1.6 MW, 1.2 MVar
5
5
Results of the load shedding rules for the real large system (outage of the line 74 –814)
Methods
the proposed strategy
the conventional method
Load shedding rules
Location
Amt, %
Total shedding amount
Margin after shedding, %
4220
4219
99 393
100
30
10
34.89 MW, 15.49 MVar
5
4220
4219
100
40
36.56 MW, 16.54 MVar
6
312
& The Institution of Engineering and Technology 2011
IET Gener. Transm. Distrib., 2011, Vol. 5, Iss. 3, pp. 307 –313
doi: 10.1049/iet-gtd.2010.0341
www.ietdl.org
Table 10 Results of the load shedding rules for the real large system (outage of the line 1164–1165)
Methods
Load shedding rules
Location
the proposed strategy
the conventional method
Amt, %
Total shedding amount
Margin after shedding, %
1169
19 185
60
10
6.85 MW, 2.4 MVar
8
1169
100
9.5 MW, 3.7 MVar
8
loses its power flow solvability. To save space, only the final
results of the load shedding rules are listed in Table 9, which
shows that the proposed method shed 1.67 MW less active
power and 1.05 MVar less reactive power.
In order to further verify the advantage of the proposed
multistage method, another N 2 1 contingency which is the
loss of the line between bus 1164 and bus 1165 is studied.
After this contingency, the system again loses its power
flow solvability. The top five weakest load buses for this
case are the buses 1169, 19 156, 19 185, 4590 and 19 371.
Both the conventional method and the proposed multistage
method are studied to determine the optimal load shedding
rules. The results are listed in Table 10. As seen in this
table, the proposed method shed 38.6% less active power
and 54.1% less reactive power.
The above case study results clearly confirm the
advantages of the proposed multistage method. According
to the above results, the important features of the proposed
strategy can be summarised as follows:
1. The proposed multiport network model accurately
identifies the best load shedding locations with little
calculation effort. This model also enables us to find a
proper generation shedding associated with the selected
load shedding.
2. In order to restore the power system from an emergency
operating condition, the proposed multistage strategy
provides the optimal solution. Compared to the
conventional method, the proposed method needs less
amount of load reduction.
6
Conclusions
Because of the non-linearity that exists in the relationship
between the load-ability margin and the load shedding
amount, a non-linear optimisation problem needs to be
solved for optimising the load shedding rules, which
includes the best load shedding locations, the minimum
load shedding amount and the corresponding generation
reduction. In order to solve this non-linear programming
problem, a practical multistage method was proposed in this
paper. By using the piecewise linear method, the multistage
method converts the original non-linear problem into a
series of linear programming problems and solves these
linear problems one by one. At each stage, the load-ability
margin is improved and the desired margin is obtained at
the last stage. The solution to the original non-linear
optimisation problems is the combination of the solutions to
all these linear programming problems.
In order to reduce the calculation efforts on the location
selection, a multiport network model was also proposed in
this paper. Using the multiport network model, the most
effective locations for the load shedding and proper
IET Gener. Transm. Distrib., 2011, Vol. 5, Iss. 3, pp. 307– 313
doi: 10.1049/iet-gtd.2010.0341
generation dispatching information can be easily obtained.
The results obtained from the multiport network model
were verified using the well-known modal analysis
method. Three test power systems including a real
power system have been used to examine the effectiveness
of the proposed algorithms. The results have verified
the advantages of the proposed method. Compared to the
traditional algorithm, the proposed multistage method needs
less load reductions to restore the system from emergency
conditions.
7
Acknowledgment
This work was supported in part by Natural Sciences and
Engineering Research Council of Canada (NSERC) and
China Scholarship Council under grant 20066035.
8
References
1 Cutsem, T.V.: ‘Voltage instability: phenomena, countermeasures, and
analysis methods’, Proc. IEEE, 2000, 88, pp. 208–227
2 Taylor, C.W., Erickson, E.C., Martin, K.E., Wilson, R.E.,
Venkatasubramanian, V.: ‘WACS—wide-area stability and voltage
control system: R&D and online demonstration’, Proc. IEEE, 2005,
93, pp. 892 –906
3 Sinha, A.K., Hazarika, D.: ‘A comparative study of voltage stability
indices in a power system’, Int. J. Electr. Power Energy Syst., 2000,
22, pp. 589 –596
4 Zarate, L.A.Ll., Castro, C.A.: ‘A critical evaluation of a maximum
loading point estimation method for voltage stability analysis’, Electr.
Power Syst. Res., 2004, 70, pp. 195 –202
5 Zambroni de Souza, A.C., Stacchini de Souza, J.C., Leite da Silva,
A.M.: ‘On-line voltage stability monitoring’, IEEE Trans. Power
Syst., 2000, 15, pp. 1300–1305
6 Haque, M.H.: ‘On-line monitoring of maximum permissible loading of a
power system within voltage stability limits’, IEE Proc. Gener. Transm.
Distrib., 2000, 150, pp. 107–112
7 Chebbo, A.M., Irving, M.R., Sterling, M.J.H.: ‘Voltage collapse
proximity indicator: behavior and implications’, IEE Proc. Gener.
Transm. Distrib., 1992, 139, pp. 241–252
8 Gao, B., Morison, G.K., Kundur, P.: ‘Voltage stability evaluation using
modal analysis’, IEEE Trans. Power Syst., 1992, 7, pp. 1529–1542
9 Nikolaidis, V.C., Vournas, C.D.: ‘Design strategies for load-shedding
schemes against voltage collapse in the Hellenic system’, IEEE Trans.
Power Syst., 2008, 23, (2), pp. 582– 591
10 Mozina, C.J.: ‘Undervoltage load shedding’. 60th Annual Conf. on
Protective Relay Engineers, March 2007, pp. 16–34
11 Cutsem, T.V.: ‘An approach to corrective control of voltage instability
using simulation and sensitivity’, IEEE Trans. Power Syst., 1995, 10,
(2), pp. 616– 622
12 Cutsem, T.V., Vournas, C.D.: ‘Voltage stability of electric power
systems’ (Springer, New York, 2007)
13 Vu, K., Begovic, M.M., Novosel, D., Mohan Saha, M.: ‘Use of local
measurements to estimate voltage-stability margin’, IEEE Trans.
Power Syst., 1999, 14, (3), pp. 1029–1035
14 Abed, A.M.: ‘WSCC voltage stability criteria, undervoltage load
shedding strategy, and reactive power reserve monitoring
methodology’. IEEE PES Summer Meeting, July 1999, vol. 1,
pp. 191–197
15 http://www.ee.washington.edu/research/pstca/
313
& The Institution of Engineering and Technology 2011

Similar documents