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Large-scale power system controlled islanding based on Backward

Elimination Method and Primary Maximum Expansion Areas

considering static voltage stability

Farkhondeh Jabari a,, Heresh Seyedi a, Sajad Najafi Ravadanegh b

a Faculty of Electrical and Computer Engineering, University of Tabriz, Tabriz, Iranb Smart Distribution Grid Research Lab, Department of Electrical Engineering, Azarbaijan Shahid Madani University, Tabriz, Iran

a r t i c l e i n f o

Article history:

Received 21 September 2014

Received in revised form 26 November 2014

Accepted 1 December 2014

Keywords:

Backward Elimination Method (BEM)

Binary Imperialistic Competitive Algorithm

(BICA)

Boundary network

Primary Maximum Expansion Area (PMEA)

Slow coherency

Static voltage stability

a b s t r a c t

This paper proposes a novel approach for separation of bulk power system into several stable subsystems

following a severe disturbance. An interconnected power system may become unstable due to wide area

contingency when it is operated close to the stability boundaries as a result of increased demand, power

industry restructuring and competition in the deregulated electricity markets. Meanwhile, large-scale

power system controlled splitting is the last resort to prevent catastrophic cascading outages and wide

area blackout. The proposed method of this paper reduces the huge initial search space of the islanding

strategy to only interface boundary network by clustering the coherent generators and simplifying the

network graph. Then, Backward Elimination Method (BEM) based on Primary Maximum Expansion Areas

(PMEAs) has been proposed to generate all proper islanding scenarios in the simplified graph. The New-

tonRaphson power flow method and QV modal analysis have been used to evaluate the steady state

stability of the islands in each generated scenario. Binary Imperialistic Competitive Algorithm (BICA)

has then been applied to minimize total load-generation mismatch considering no-isolated bus, voltage

permitted range and static voltage stability constraints. Comprehensive discussions have been provided

using the simulations on NPCC 68-bus test system. The results demonstrate the speed, effectiveness andcapability of the proposed strategy to generate fast feasible splitting solutions considering static and

dynamic stability.

2014 Elsevier Ltd. All rights reserved.

Introduction

Power industry restructuring and competition in the deregu-

lated electricity markets in order to provide increased consump-

tion causes operation of large power systems close to their

stability margins. Although an interconnected power system may

be stable against small disturbances, wide area contingencies

may cause the system to lose stability and lead to the catastrophic

wide area blackouts. Hence, splitting is the final action to preventcascading failures. Power system islanding procedures will have to

determine two important issues[1]:

1. When to split

Islanding starts exactly after separating detection. In recent

years, many different techniques have been proposed to detect

the interconnected power system splitting.

2. Where to split

Many wide area blackouts such as 2003 Italy [2], 2003 Sweden

Denmark[3], 2003 United States and Canada [4], 2005 JavaBali

[5], 2009 Brazil and Paraguay [6], July 2012 India blackout [7]

may have been prevented and load-generation mismatch may

have been reduced by fast, accurate, feasible controlled splitting

strategies[811]. Controlled intentional islanding separates a bulk

power system into a number of stable islands by tripping selectedtransmission lines according to the minimum load-generation mis-

match [12]. Hence, once separation is detected, the most important

step is to find the optimal splitting points. In the literature, several

approaches have been proposed to split a large power system into

several stable sections following a wide area contingency. These

procedures can be divided into two general categories. The first

one is based on the coherent generators clustering and the second

one is based on the network graph theory.

http://dx.doi.org/10.1016/j.ijepes.2014.12.008

0142-0615/ 2014 Elsevier Ltd. All rights reserved.

Corresponding author. Tel.: +98 41 33393732.

E-mail addresses: [email protected] (F. Jabari), [email protected]

(H. Seyedi),[email protected](S. Najafi Ravadanegh).

Electrical Power and Energy Systems 67 (2015) 368380

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Electrical Power and Energy Systems

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Islanding based on coherent generators clustering

In the literature, there are mainly two clustering methodology:

The first one identifies coherent machines through a time-domain

simulation according to the dynamic behavior of each generator

due to specific disturbance. Hence, the machines with similar rotor

angle or speed curves are assumed to be coherent. Slow coherency

theory as a two-time-scale method is a driven force behind the first

procedure. It is based on the power system oscillations which can

be classified into two modes; local or intra-area modes in the 1

3 Hz range and inter-area modes less than 1 Hz [13]. The machines

with the same inter-area mode swing together and they are called

coherent in the selected inter-area modes[14]. In[15], the coher-

ent groups are determined through the Empirical Mode Decompo-

sition (EMD) and Stochastic Subspace Identification (SSI) method.

In this method, the generator rotor speed prepared from the Wide

Area Measurement System (WAMS) is only used to cluster the

coherent machines. In[16], a novel approach based on the correla-

tion characteristics of the generator rotor angle oscillation is pre-

sented to identify the coherent machines. In proposed scheme,

the correlation coefficients of generators are assessed by online

measurement of rotor angle oscillations. In[1720], a slow coher-

ency method has been applied to cluster the coherent generators of

an interconnected power network. The mathematical background

of slow coherency theory and selective modal analysis can be

found in[21].

In[12], the slow coherency theory is used to obtain the desired

generator groups. Angle Modulated Particle Swarm Optimization

(AMPSO) is then used to find a number of candidate scenarios that

provide optimal static and dynamic characteristics. In[2123], the

coherent machines have been clustered by the slow coherency the-

ory. A spanning tree based Breadth First Search (BFS) algorithm is

then used to find all proper islanding scenarios. This method

reduces the large initial search space of the integrated power sys-

tems islanding to the boundary branches. The proposed islanding

strategy determines the best separating points according to the

minimum load shedding. In[25,26],the Krylov projection methodhas been used to cluster the coherent machines. A spanning tree

based Depth First Search (DFS) algorithm has then been used to

find all candidate solutions in reduced search space. In [27], the

slow coherency based grouping is used to provide the primary

dynamic criteria. An automatic islanding program is then applied

to find the optimal cutsets to form the isolated stable islands con-

sidering minimum load-generation mismatch. All generators clus-

tering techniques reduce the large search space of the islanding

from the entire system to the boundary interface network signifi-

cantly. The slow coherency based islanding has two important

advantages [2124,27].

1. Slow coherency based clustering is independent of the size,

type and location of the disturbance. Hence, it is possible todesign a defensive splitting strategy before a wide area

disturbance.

2. Slow coherency based clustering is independent of the genera-

tor model details. So, the classical model can be used.

Islanding based on network graph theory

An interconnected power system can be interpreted as a simple

two-dimensional graph. The inputs are nodes and branches. In real

power system,the numberof nodes andbranches increaseconsider-

ably. Hence, the bulk power system splitting will have a large initial

search space. In some literature, the scenario reduction techniques

based on graph simplification have been proposed. In [1], Source

Node Expansion (SNE) algorithm based on slowcoherency has beenproposed to split a simplified power network. The SNE initiates

expansion from a source node to the connect loads until desired

power balance be met. When all sources were expanded, optimal

cutsets can be determined using the adjacency matrix. In[28], an

OBDD-based three-phase method has been proposed to find proper

islanding solutions of interconnected power systems. A time-based

layered structure has then been introduced to demonstrate the

capability of the proposed strategy. The feasibility of this method

has been studied by means of power system transient simulations

in [29]. In [30], a novel approach based on the minimal cutsets with

minimum net flow has been proposed to split the large power sys-

tem into several stable sections following a severe disturbance. In

[31],a three-phase multilevel partitioning scheme has been used

to split the entire network graph. The Greedy growing and KL algo-

rithm have then been applied to find the optimal scenario. In[32],

the slow coherency algorithm has been applied to cluster coherent

generators. Then, a multi-level graph partitioning has been pro-

posed to split the reduced network graph into desired islands with

minimum generation-load mismatch. In [33], an Ant SearchMecha-

nism (ASM) based on linear programming and DC power flow has

been proposed to identify proper splitting pointsconsidering power

balance and line overloading constraints. In[34], a Mixed Integer

Linear Programming (MILP) algorithm has been proposed to deter-

mine optimal islanding scenario. The steady-state DC power flow

equations and operating limits such as line losses, transmission

capacity constraint and generation limits have been considered to

minimize total load shedding. Then, an AC optimal load shedding

problem has been solved in islanded system to provide a scenario

that satisfies AC power flow.

To achieve a fast practical islanding solution which satisfies all

the steady state and dynamic constraints within the islands is an

arduous challenge. A fast scenario generator algorithm is necessary

due to the inherent real-time application of islanding strategies in

which a feasible solution is needed to guarantee the stable opera-

tion of islands. In the literature, there are remarkable efforts on

defensive separating of power systems. However, there are still

some unsolved problems to satisfy the static and dynamic voltage

stabilities of islands and reduce the risk of their partial blackouts.This paper develops a real-time strategy for fast, proper, accurate

and feasible islanding decision making which can guarantee the

voltage security margin, steady state and dynamic stabilities of

islands and prevent their partial blackout. Another unique feature

of proposed scenario generator algorithm is its capability of ana-

lyzing the steady state stability of each island independent of the

other islands, since the PMEA of each island has been considered

in primary line and bus data matrices. Therefore, if there are N

coherent independent clusters, it will be possible to break one

complex optimization process into N computationally efficient

problems and reduce the average calculation time, significantly.

In the current paper, the large initial search space of the sepa-

rating strategy has been reduced to only smaller interface network

by aggregating the coherent machines and simplifying the networkgraph. Backward Elimination Method (BEM) based on Primary

Maximum Expansion Areas (PMEAs) is then proposed to generate

all proper islanding scenarios in the simplified power network.

The NewtonRaphson power flow and QV modal analysis have

been used to assess the steady state stability of the islands in each

generated scenario. Binary Imperialistic Competitive Algorithm

(BICA) is applied to minimize total load-generation mismatch con-

sidering integrity, voltage permitted range and static voltage sta-

bility constraints.

The rest of the current paper is organized as follows: Section

Problem formulation presents the problem formulation. The pro-

posed splitting strategy has been provided in Section Proposed

controlled islanding strategy. Section Simulation results and dis-

cussions contains the simulation results and discussion. Finally,conclusion appears in Section Conclusion.

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Problem formulation

Objective function

The amount of power mismatch affects the network frequency.

If active generation increases, the frequency will be increased else

if active load increases, the frequency will be decreased. It will be

necessary to maintain the islands frequency in an acceptable limitby minimizing the active power imbalance between load and gen-

eration. Hence, the following objective function is defined to min-

imize total load-generation mismatch.

Objective Function MinXnislandi1

PGisland i PLisland i ! 1

where PGislandi is the total active generation of ith island, PLislandi

the total active load ofith island and nislandis the number of islands.

PGisland i XNGim1

PGim 2

PLisland i XNLin1

PLin 3

In relations (2) and (3), PGi m and PLi n are the active generation of

themth machine and the active consumption of thenth load inith

island, respectively.

Constraints

The criteria for finding proper stable islanding scenarios can be

summarized as follows [12,33].

No-isolated bus (integrity)

The islanding process must not eliminate any bus from primary

integrated power system. All buses inside each island must be con-

nected to each other to form some integrated areas.

Voltage permitted range

The voltage magnitude must be limited in an acceptable range

as following relation:

Vmini

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magnitude of the sensitivity cannot evaluate the voltage security

margin and stability degree. Hence, the QV modal analysis is used

to determine the voltage stability indices. Therefore:

JR nKg 10

In (10),nand g are the right and left eigenvector matrices of theJR, respectively. The K matrix consists of the eigenvalues of the

reduced Jacobian matrix. From Eq.(10):

J1R nK1g 11

Substituting in Eq. (9), the relation between incremental change

in bus voltage magnitude and incremental change in bus reactive

power injection can be rewritten as(12) and (13):

DV nK1gDQ 12

And

DVXi

nigiki

DQ 13

In(13),k i is theith eigenvalue, ni is the ith column of the right

eigenvector matrix and gi is the ith row of the left eigenvectormatrix. Since:

g n1 14

Therefore:

gDV K1gDQ 15

The vectors of the modal voltage variation and the modal reac-

tive power variation are defined as(16) and (17), respectively:

v gDV 16

q gDQ 17

Eq.(18)can be written as:

vi qi=ki 18

Ifk i > 0, the voltage and the reactive power variation of the ith

PQ bus are along the same direction and the system is stable. If

ki < 0, the voltage and the reactive power variation of the ith PQ

bus are along opposite directions and the system is unstable. If

ki 0, theith modal voltage collapses.

Coherency criterion

All machines in each island should remain in synchronism to

increase the dynamic stability of the created islands. Two non-

coherent generators must not be connected to each other. As

shown inFig. 1, two independent coherent groups should be iso-

lated by trippingij transmission line.

Proposed controlled islanding strategy

Coherent generators grouping

In this paper, the slow coherency based aggregating has been

applied on NPCC 68-bus test system to guarantee the dynamic

Fig. 4. Concepts of Primary Maximum Expansion Areas in New England 39-bus test system.

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stability of the created islands following a severe disturbance.

Coherency analysis as a scenario reduction technique can reduce

the computational burden of the stability studies and limit the

huge initial search space of the intentional separating to only smal-

ler interface network.

Proposed network graph simplification

In an interconnected power system with thousands of busesand branches, the islanding search space grows exponentially.

However, the graph simplification without losing the useful infor-

mation can reduce the calculation time, significantly. In graph the-

ory, the degree of a bus is the number of the branches connected to

it. The bus type can be classified into three categories; load bus,

generation bus and transfer bus. The bus with load and no gener-

ator is called load bus. The bus with generator and no load is called

generation bus and the bus with no load and generator is called

transfer bus. As shown inFig. 2, C is a degree two transfer bus. If

AC transmission line is closed, x(i) will be equal to 1, else, it will

be zero. Similarly, if C-B transmission line is closed, x(j) will be

equal to 1, else, it will be zero. The number of islanding scenarios

can be reduced by consideringx(i) =x(j).

As shown in Fig. 3, the binary states of the parallel transmissionlines between A and B can be considered to be identical. In other

words, all parallel branches between A and B are either connected

(1) or disconnected (0).

Determination of interface boundary network

Following the aggregation of the coherent machines and the

simplification of the network graph, it is important to determine

the types of the branches and buses to obtain the interface bound-

ary network and limit the search space from entire system to the

boundaries. The interface network between each area with other

adjacent areas is called boundary or probabilistic network which

consists of boundary or probabilistic branches and buses. Hence,

the branches or buses that are not boundary are called non-bound-

ary or deterministic branches or buses, respectively. In a large

power network, the branches and buses are classified into two cat-

egories as fallows:

Deterministic or non-boundary areas

The branches which connect coherent generators should be

closed. In other words, the islanding strategy is not allowed toopen these branches. If multiple trajectories exist to connect two

coherent machines, a path will be selected that none of its

branches can be considered as a boundary line. If the generators

Gi andGj are not coherent, the ij branch must be opened. Also,

the faulted transmission lines must be tripped. These branches

have non-boundary or deterministic states in power system islan-

ding studies. The buses connected to non-boundary lines are called

deterministic buses.

Probabilistic or boundary area

All of the branches which are not deterministic are called prob-

abilistic branches. The buses that are connected to the probabilistic

lines are called boundary buses.

Principles of proposed Backward Elimination Method

In this section, a novel probabilistic search strategy denoted as

Backward Elimination Method based on Primary Maximum Expan-

sion Areas is proposed for generating all proper separating scenar-

ios according to coherent groups and simplified network graph.

The NewtonRaphson power flow method and QV modal analysis

have been used to evaluate the steady-state stability of the islands

in each generated scenario. Binary Imperialistic Competitive Algo-

rithm is then applied to minimize the load-generation active

power mismatch considering integrity; voltage permitted range

and static voltage stability as optimization problem constraints.

Fig. 5. PMEAs of three islands and boundary branches in New England 39-bus test system.

372 F. Jabari et al. / Electrical Power and Energy Systems 67 (2015) 368380

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In order to apply the BEM based on PMEAs as a defensive islanding

strategy, the following steps should be carried out sequentially.

Determination of the Primary Maximum Expansion Areas

The Primary Maximum Expansion Area of the island A consistsof deterministic buses of island A, deterministic branches of island

A and boundary network considering isolated islands constraint.

As shown in Fig. 4, there are three coherent groups named A, B

and C and colored by red, blue and green, respectively. The bound-

ary or probabilistic interface network has been shown with purple.

The Primary Maximum Expansion Area of the island A has been

determined as a gray area by considering the islands

independence.

Formation of the probabilistic line and bus data matrices considering

PMEAs

The primary line data matrices of the islands will have probabi-

listic nature due to the boundary transmission lines. After number-

ing all buses and determining the slack bus in each island (Theslack bus must not belong to the set of the boundary buses)

considering PMEAs of the islands, the primary probabilistic line

data matrix will be formed for each island as follows. For the kth

boundary branch connectingith andjth buses of island A, we can

use:

Zi;j 1 xkMZ0i;j 19

xk 0 if thekth boundary branch has been opened

1 if thekth boundary branch has been closed

20

Z0i;j Ri;j jXi;j 21

Z(i,j) is the impedance of the transmission line i to j in primary

probabilistic line data matrix of island A. Mis a sufficiently large

constant. Z0(i,j), R(i,j) and X(i,j) are the impedance, resistance

and reactance of ij transmission line in per unit, respectively.

According to (20), x(k) shows the state of the kth probabilistic

branch. In a generated scenario, the primary probabilistic line datamatrix can be updated as follows. If x(k) = 0, the kth boundary

Fig. 6. The flowchart of the proposed optimal defensive islanding strategy.

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branch is opened andZ(i,j) ffi M. Ifx(k) = 1 thekth boundary branch

is closed and Z(i,j) =Z0(i,j).

Once all buses of each island have been numbered and the slack

buses of the islands have been determined (The slack bus must not

belong to the set of the boundary buses), the probabilistic bus data

matrix will be formed for each island according to PMEA of island.

In order to generate proper splitting solutions, it is necessary to

update the probabilistic bus data matrices of the islands in eachgenerated scenario. Hence, if the ith bus of the island A (that is a

boundary bus) is removed from island A to island B, the ith bus

of island A will be eliminated from the probabilistic bus data

matrix of this island through a Bus-Trajectory matrix. In other

words, for each generated scenario, the probabilistic bus datamatrix which is formed based on the PMEA of the island A will

be updated across the Bus-Trajectory matrix of this island. The

Bus-Trajectory matrix of the island A can be formed as follows. If

the ith bus of the island A is a deterministic or non-boundary

bus, the ith row of the Bus-Trajectory matrix of island A will be

equal to 1. In other words, BTAi 1. If the ith bus of island A is

a probabilistic or boundary bus, the ith row of the Bus-Trajectory

matrix of island A can be calculated via the following steps.

1. All probabilistic trajectories which connect theith probabilistic

bus of island A to the deterministic network of this island

should be determined.

2. A trajectory which connects theith bus of island A to the deter-

ministic network of this island through boundary branches can

be considered as the multiplication of the binary states of these

probabilistic branches.

Table 1

All modes, frequency and damping of NPCC 68-bus system.

No Modes Freq (Hz) Damping Inter-area modes No Modes Freq (Hz) Damping Inter-area modes

1 0.0001 0 1 Yes 17 0.2500 7.1908i 1.1444 0.0347 No

2 0.8203 0 1 Yes 18 0.2500 + 7.1908i 1.1444 0.0347 No

3 0.3591 2.3868i 0.3799 0.1488 Yes 19 0.2500 7.6827i 1.2227 0.0325 No

4 0.3591 + 2.3868i 0.3799 0.1488 Yes 20 0.2500 + 7.6827i 1.2227 0.0325 No

5 0.3801 3.0739i 0.4892 0.1227 Yes 21 0.2517 7.8977i 1.2570 0.0319 No

6 0.3801 + 3.0739i 0.4892 0.1227 Yes 22 0.2517 + 7.8977i 1.2570 0.0319 No7 0.3617 3.9378i 0.6267 0.0915 Yes 23 0.2500 8.4151i 1.3393 0.0297 No

8 0.3617 + 3.9378i 0.6267 0.0915 Yes 24 0.2500 + 8.4151i 1.3393 0.0297 No

9 0.4302 4.9073i 0.7810 0.0873 Yes 25 0.2500 9.2183i 1.4671 0.0271 No

10 0.4302 + 4.9073i 0.7810 0.0873 Yes 26 0.2500 + 9.2183i 1.4671 0.0271 No

11 0.2500 5.9666i 0.9496 0.0419 Yes 27 0.2500 9.4569i 1.5051 0.0264 No

12 0.2500 + 5.9666i 0.9496 0.0419 Yes 28 0.2500 + 9.4569i 1.5051 0.0264 No

13 0.2550 6.4568i 1.0276 0.0395 No 29 0.2520 10.9986i 1.7505 0.0229 No

14 0.2550 + 6.4568i 1.0276 0.0395 No 30 0.2520 + 10.9986i 1.7505 0.0229 No

15 0.2906 7.0406i 1.1205 0.0412 No 31 0.2500 14.3598i 2.2854 0.0174 No

16 0.2906 + 7.0406i 1.1205 0.0412 No 32 0.2500 + 14.3598i 2.2854 0.0174 No

Table 2

Inter-area modes, frequency and damping of NPCC 68-bus system.

No Modes Freq (Hz) Damping

1 0.8203 0 1.0000

2 0.3591 2.3868i 0.3799 0.1488

3 0.3801 3.0739i 0.4892 0.1227

4 0.3617 3.9378i 0.6267 0.0915

5 0.4302 4.9073i 0.7810 0.0873

6 0.2500 5.9666i 0.9496 0.0419

Fig. 8. Voltage profile under given disturbances.

0.2

0.4

0.6

0.8

1

30

210

60

240

90

270

120

300

150

330

180 0

G14 rotor angle

0.05

0.1

0.15

0.2

30

210

60

240

90

270

120

300

150

330

180 0

G15 rotor angle

0.2

0.4

0.6

0.8

1

30

210

60

240

90

270

120

300

150

330

180 0

G16 rotor angle

0.1

0.2

0.3

30

210

60

240

90

270

120

300

150

330

180 0

G10,G11,G12,G13 rotor angles

0.05

0.1

0.15

0.2

0.25

30

210

60

240

90

270

120

300

150

330

180 0

G1,G2,G3,G4,G5,G6,G7,G8,G9 rotor angles

Fig. 7. Compass plot of rotor angle terms of 3rd inter-area mode eigenvector.


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3. The sum of the obtained expressions for all of the probabilistic

trajectories in previous step (which connect the ith probabilistic

bus of island A to the deterministic network of this island) is

calculated as theith row of the Bus-Trajectory matrix of island

A.

InFig. 5, there are three coherent groups named A, B and C. The3rd and 7th buses of island C are deterministic and probabilistic

buses, respectively. Therefore, the 3rd and 7th rows of Bus-

Trajectory matrix of island C will be equal to 1 and

x4 x6zfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflffl{

T1

x4 x5 x7 x8zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{

T2

x4 x5 x7 x9zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{

T3

,

respectively. The primary probabilistic bus data matrix of island A

can be updated as fallows. IfBTA(i) = 0, theith bus of island A will

be removed from this island. IfBTA(i) 0, the ith bus of island A

will belong to this island.

BEM, PMEAs and BICA based optimization

The BEM, PMEAs and BICA based optimization program is

applied to minimize total load-generation mismatch. The steadystate stability can be evaluated in each island using Newton

Raphson power flow program and QV modal analysis for each

generated scenario. The integrity, voltage permitted range andsteady-state voltage stability constraints have been considered in

the optimization process.

The coherent generators should be clustered based on the slow

coherency theory. The proposed graph simplification is then

performed. The deterministic areas and the interface boundary

network have then been determined according to the coherent

machines, deterministic and probabilistic buses and branches.

The PMEAs of the islands can be determined to form the

primary probabilistic line and bus data matrices. For each

generated scenario, the primary probabilistic line and bus data

matrices are updated through the Bus-Trajectory matrices. Then,

NewtonRaphson power flow and QV modal analysis have been

performed based on the updated line and bus data matrices in each

island. All of the controlled islanding constraints are then checked.If one of them is not met, the new scenario will be generated;

otherwise the load-generation power mismatch will be calculated

to find the best solution vector. The flowchart of the proposed opti-

mal intentional islanding strategy has been shown inFig. 6.

Simulation results and discussions

In order to demonstrate the speed, effectiveness and capability

of the proposed strategy, the NPCC 68-bus test system is used. One

line diagram and initial operating point of this system has been

given in[37].

The NewtonRaphson power flow has been performed undernormal operating condition. Total active load and generation are

Fig. 9. Simplified graph and boundary network of NPCC 68-bus test system.

Table 3Best scenario for islanding of NPCC 68-bus test system.

x(1) x(2) x(3) x(4) x(5) x(6) x(7) x(8) x(9) x(10) x(11)

1 1 0 1 1 1 1 1 0 0 1

x(12) x(13) x(14) x(15) x(16) x(17) x(18) x(19) x(20) x(21)

1 1 1 0 0 1 1 1 1 1

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equal to 184.0873 and 182.3390 per unit, respectively. The simula-

tion results consist of three sections.

Slow coherency based clustering

Under normal operating condition, the coherent generators can

be identified based on the slow coherency scheme. InTable 1, all

modes, frequency and damping of the NPCC 68-bus system have

been shown. According toTable 2, there are five inter-area modes

in this system.

A compass plot of the rotor angle terms of the eigenvectors in

the 3rd inter-area mode is shown in Fig. 7. According to rotor angle

terms, five coherent groups {G1,G2,G3,G4,G5,G6,G7,G8,G9},

{G10,G11,G12,G13}, {G14}, {G15}, {G16}, have been formed.

Graph simplification and determination of interface boundary network

A solid three-phase fault occurs on one of transmission lines

connecting bus 930 close to bus 9 at t= 1.0 s and is cleared after

0.3 s by removing the transmission lines 930. Another contin-

gency is occurred on the branch 127 at t= 1.3 s and this branch

will be opened. The voltage profile following given contingencies

and the simplified network graph with boundary network have

been shown inFigs. 8 and 9, respectively.

BEM, PMEA and BICA based optimization

The search space will have 221 = 2, 097, 152 possible solutions.

The best solution vector and load-generation mismatch in five

areas have been reported in Tables 3 and 4, respectively. According

to Table 4, the total generation (201.207 per unit) is larger than the

total load (182.689 per unit), thus load shedding is not necessary.

The total minimum power mismatch is 18.5188 per unit which lost

in transmission systems. The optimal islanded NPCC 68-bus power

system has been shown inFig. 10.

Voltage profiles of five islands have been shown inFigs. 11 and

12. The static voltage stability indices of islands have been shown

Fig. 10. Optimal islanded NPCC 68-bus test system.

Table 4

Load, generation and power mismatch of islands in per unit.

Active power in per unit Area 1 Area 2 Area 3 Area 4 Area 5 Total

Total active generation 17.4697 11.5000 33.1888 81.6431 57.4062 201.2078

Total active load 13.0683 11.5000 32.2170 74.1237 51.7800 182.689

Total active imbalance 4.4014 0.000 0.9718 7.5194 5.6262 18.5188


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Fig. 12. Voltage profile in island 4 and 5.

Fig. 13. Voltage stability indices in island 1 and 3.

Fig. 14. Voltage stability indices in island 4 and 5.

Fig. 11. Voltage profile in island 1, 2 and 3.

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in Figs.13and14. Basedon the optimalscenario,the5th,6thand 7th

busesof area 1 whichare similar to the 22nd, 21st and 20thbuses of

area 4 and 39th, 38thand42ndbusesof area 5,belongto the island 4.

The 3rd, 4th,5th and 6th buses ofthe area3 which are similarto the

26th, 25th, 28th and 27th buses of the area 4 belongto the island 3.

The 17th, 18th and 19th buses of the area 4 which are similar

to the 37th, 36th and 35th buses of the area 5 belong to the

island 5. According to Fig. 9, the PQ buses in island 1, 3, 4, 5

are {3, 4, 5, 6, 7}, {3, 4, 5, 6}, {4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 17, 18,

19, 20, 21, 22, 23, 24, 25, 26, 27, 28} and {3, 6, 7, 9, 10, 11, 12, 13,

14, 15, 16, 17, 19, 21, 22, 23, 24, 25, 26, 28, 29, 30, 31, 33, 35, 36, 37,

38, 39, 40, 41, 42}, respectively. All stabilityindicesare positive and

the static voltage stability has been satisfied in each island.

As mentioned in the introduction section, the optimum separat-

ing points can be found by solving four optimization problems in

islands 1, 3, 4 and 5, sequentially or simultaneously. In this study,

the sequential method has been applied as follows.

The PMEA of the island 1 has been shown in Fig. 15. There are

five probabilistic branches and 32 scenarios in optimization pro-

cess of island 1. Therefore, the number of required initial countries,

imperialists and decades of the BICA and calculation time will be

decreased. In the obtained best scenario shown inFig. 15, the volt-

age permitted range and SVS criteria have not been satisfied for the

5th, 6th and 7th buses of the island 1. Hence, they are transferred

from island 1 to area 4. If in optimization process of area 4, the

voltage constraints are not satisfied for 20th, 21st and 22nd buses,they will again be transferred from island 4 to area 5.

The PMEA and the optimum separating point of the area 3 with

16 solutions have been shown inFig. 16. It is not necessary to trip

any boundary branch for optimal isolation of Section Proposed

controlled islanding strategy. According to the best solutions of

the islands 1 and 3, the reduced interface network of the subsys-

tem 4 will have 256 possible solutions. As shown in Fig. 17,it will

optimally become an isolated area by tripping the 217 transmis-

sion lines based on the obtained optimal solution. Finally, the 5th

island will have 32 possible scenarios. Based on the obtained best

scenario shown in Fig. 18, it is not necessary to trip any probabilis-

tic branch for defensive separation of Section Conclusion. All con-

straints in the optimization process of the island 5 have been met.

Hence, the optimization problems have been implemented in avery short time as a result of the fast convergence of each process

within first iteration.

As shown inFigs. 1518, total search space will have 336 pos-

sible scenarios in five optimization problems. In order to prove

the practicability of the proposed fast strategy, the calculation time

has been compared with OBDD, ASM and ST-BFS methods in

Table 5.

According to above table, the proposed algorithm is computa-

tionally efficient and fast.

Similar to the previous scheme, the four optimization programs

can be implemented considering Primary Maximum Expansion

Areas of islands instead of their reduced interface boundary net-

works in simultaneous method. There are 32, 16, 214 = 16,384

and 210

= 1024 scenarios in four splitting search spaces,respectively.

Fig. 15. PMEA of island 1.

Fig. 16. PMEA of island 3.

Fig. 17. Reduced interface network of island 4.


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Conclusion

Power industry restructuring and competition in the deregu-lated electricity markets in order to provide increased consump-

tion causes operation of large power systems close to their

stability margins. If there is no emergency corrective control to

resynchronize all generators and prevent fault spreading, occur-

rence of large disturbance may cause the system to lose stability

and even lead to the wide area blackout. Hence, defensive

Separation of bulk power system as a comprehensive real-time

decision making is the last defense line against passive collapse

of system.

This paper introduces a novel strategy for separation of inter-

connected power systems following severe disturbances. In this

paper, the slow coherency based aggregation and graph simplifica-

tion as two scenario reduction techniques have been used to

reduce the large initial search space of the islanding strategy from

entire network to only smaller interface boundary network. Then,

Backward Elimination Method (BEM) based on Primary Maximum

Expansion Areas (PMEAs) has been proposed to generate all fast,

proper and feasible islanding scenarios in the simplified systemby transferring some of the boundary buses in one island to

another island such that total mismatch is minimized. The New-

tonRaphson power flow method and QV modal analysis have

been used to evaluate the steady-state stability of the islands in

each generated scenario. The Binary Imperialistic Competitive

Algorithm (BICA) has then been applied to minimize total load-

generation mismatch considering integrity, voltage permitted

range and static voltage stability constraints. The proposed sce-

nario generator algorithm generates each possible islanding solu-

tion in an average calculation time less than 0.1 s and evaluates

the static voltage stability of the PQ buses based on QV modal

analysis in each generated solution. The results demonstrate the

speed, effectiveness and capability of the proposed scheme to gen-

erate fast practical splitting solutions considering static and

dynamic stability.

Fig. 18. Reduced interface network of island 5.

Table 5

Calculation times of fast strategies.

Calculation time PMEAs, BEM and BICA based optimization(on a Lenovo with 2.10 GHz CPU, 4 GB RAM)

OBDD (on a PC Pentium IV-1.4GCPU and 256M DDRAM)

ASM (PC with 2.26GHzCPU, 2 GB RAM, 3 MB

Cache)

ST-BFS

For finding each

scenario

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