V+

-

IR2

IS1 IP1

. . .

VR2 = ZR2 IR2

VR2 InPhase IR2

VR2 - ZR2 - IR2 = 0

. . .

2

1R L IC

CRS1

P1

S2

ConfluencesPhase AngleOrder of Magnitude

AlgebraicValue

Constraints

. . . VS1 - ZS1 - IS1 = 0VS1 = ZS1 IS1

. . .

. . .

VC = ZC IC

IC Ahead VCVALUE Angle(ZC) = 90

VC - ZC - IC = 0

VS1 = VR1 + VL

. . .VR1 > VL

IS1

VS1VS2

I

VLIC

VR1

VR2 P1

VS1 P1< V S1 P1V = V VS1 P1< V

VR1< VL VR1 L= V VR1 L< V

PCM

V+

-

IR2

2

1R L

R

I S1

IS1

VS1 VS2

VR1

VP1IR2

VL

IC

IR2

2R

IC

RF

-

+

VP1

VS1+ -

IS1

1R

V+

-

S1

L

C

S

1P

2

PSInterface

AutomaticConstraintGeneration

(Tree)

InterfaceQPA

Constr.Circ. Tree

CircuitModification

CircuitSolver

CircuitClustering

BSOCGeneration

Circ.

PS

ModelingPS

Circ.Circuit

Tree

PSAD

QPA

HRCP

Constraints

Constraints

Design

Diagnosis

Circuit

Constraints

+DecompositionConstraints

CircuitCircuit

Clustering

Constraints

Clustering

PS TreeConstraints

Power System

Constraint Sets

C tt+

Im

Cb

aRe

C ejtt

V+

-

IR2 IC

I S1

IP1

1R

2R

1P

1S

2S

-

+

+ -V

L

VC

S1

P1

IS1

VS1VS2

I

VLIC

VR1

VR2 P1

XLXR ILIR

I

+V-

IR

IL I

V

e

XLXR ILIR XC IC

I

+V-

IR

IL

IC

I

V

e

2_

1_

a b

V

25

2

34

1

6

8

57

4_

3_

2_

1_V

V2

1

ba

c

d

V1R+V2R

V2R

V1

V1+V2

V2

V1+V2

V1R

4_

3_

2_

1_

VV

2

V1

5

8

7 6

34

21

38

25

V

V2

1

2

4

V1

8

7

5

1

3

27

V2

6

18

36

35

46

45

minimummagnitude’s

-y Cos e

y

x x x

21

3

4

V1

78

6

5V2

36

38a

d

q

2_e

V1

2

3

1

4

56

7

8

1e

2e

V2

V1

V2

V1

V2

V1

V2

36

3

38

6

8

1

16

18

’e ’q

_

d

a

a

d q

Y

X

Z Y

X

Z

Z

X

Y

0 e 1 e (1+e)(1+e)-1 -1

8

<< >>

< >

~< = >~-< >-

15 1500B

750 300

8

190015 A

A<<B

V+

-

IR2 IC

I S1

IP1

1R

2R

1P

1S

2S

-

+

+ -V

L

VC

S1

P1

I C

I R2

P1I

CircuitCirc.

AutomaticConstraintGeneration

(Tree)

InterfaceQPA

CircuitModification

CircuitSolver

CircuitClustering

BSOCGeneration

Tree

QPA

HRCP

Constraints

Constraints

Design

Diagnosis

Circuit

Constraints

+DecompositionConstraints

CircuitCircuit

Clustering

Constraints

Clustering

Constraint Sets

Circuit TreeConstr.

V+

-

IR2 IC

I S1

IP1

1R

2R

1P

1S

2S

-

+

+ -V

L

VC

S1

P1

e1 e2

Rf S1

Rf

I Rf

Co

C

Zc < Zco

Zc > Zco

IcIco

Vc

PSInterface

AutomaticConstraintGeneration

(Tree)

InterfaceQPA

Constr.Circ. Tree

CircuitModification

CircuitSolver

CircuitClustering

BSOCGeneration

Circ.

PS

ModelingPS

Circ.Circuit

Tree

PSAD

QPA

HRCP

Constraints

Constraints

Design

Diagnosis

Circuit

Constraints

+DecompositionConstraints

CircuitCircuit

Clustering

Constraints

Clustering

PS TreeConstraints

Power System

Constraint Sets

T TL L

1 2 3

G

n n

GXgVg

+ -ng

Xt

Vct+- Xct

nct

Xtl

L nl

Rl Xl

Xc

Capacitor BankC

ComponentPower System Circuit

Equivalent ComponentPower System Circuit

Equivalent

Bus

Generator

TransformerT

Load

TControl Transf.

Transm. Line

I

+

-Vg

Xg

ng

Xt Xtl

Rl

Xl

nl

1 2 3

S1

I

+

-Vg

Xg

ng

Xt Xtl1 2 3

Rl

Xl

nl

S1

C

G

1 2 3

T TL

L

C

LG

1 2Ia

Ib

VL

VLo

VT

I Lo I L

TCT L

VLo VL

I L

VT I Lo

LPST

Xa

X C X b

Ib

I a

IL

+

-Vg

LZ

IL

Z L

Ia

Ib

a

b

Z

Z- +VtVg+

-

-

+Vg

Z L

aZ

bZ

IbVg

IaVg

ILVg

Z L

bZ

-

+Vt

Ibt Iat ILt

aZ

V2Ia

Ib

IbIb

IL

Ia

Ia Ib=

PSTCapacitor

TCT

bZ

Z LaZ-

+VT

I I IbVT aVT LVT