4.3 External Network Modelling

8/14/2019 4.3 External Network Modelling

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4.3.14.3 External network modelling

The interconnected system of Europe in 1995


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Observable network

External network

Externalnetwork

Externalnetwork

Internal network


Line outage


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Generator outage Observable network



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b) Outage of ageneration unit

Deviation of frequency Net tie line interchanges

a) Normal operation


Frequency and power deviation in the UCPTE network


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Real-time security analysis

4.3 External network modelling 4.3.5

State

Estimation

Modelof

external system

Security

analysis

Security constraints: met not met

Networkequivalent

State vector

Location ofbad data

J(x), E{J(x)}

Network topology

Measurements

Variance of mea-surement errors

Network parameter

Contingency set lines transformers generation units

Exeeding limits:

Ith

Vmin, Vmax

Imax


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Observable network

External network

External

network

External

networkInternal network

Network region Available information

Observable network:- Internal nodes- Boundery nodes

Measurements, on-off status quantities, transformator

tap-settings, network parameter, Vi, i (via stateestimation)

External network:- External nodes

Network topology (standard topology),network parameter

Available information



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[ ][ ] [ ] [ ]SVYVdiag =

E: external; B: boundary; I: internal

=

I

B

E

I

B

E

IIIB

BIBBBE

EBEE

I

B

E

S

S

S

V

V

V

YY0

YYY

0YY

V

V

V

diag

[ ][ ] [ ]

[ ][ ] [ ]

[ ][ ] [ ] )3.1(SVYVYVdiag

)2.1(SVYVYVYVdiag

)1.1(SVYVYVdiag

IIIIBIBI

BIBIBBBEBEB

EBEBEEEE

=+

=++

=+



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[ ] [ ] [ ]

[ ] [ ] [ ] [ ]

[ ] [ ] [ ] [ ] [ ]{ }

[ ] [ ] [ ] [ ] [ ]{ }BEB*

E

*

E1

1

EEE

BEBEE

11

EEE

BEBEE

1

EEE

EE

1

BEBEEE

VYSVdiagYV

VYSVdiagYV

VYSVdiagVY

SVdiagVYVY

=

=

=

=+

Elimination of [VE] using eq. (1.1)

Introducing [VE] in eq. (1.2)

[ ] [ ] [ ] [ ][ ] [ ] [ ]

[ ] [ ] [ ] [ ] } [ ]B

*

I

*

BI

*

B

*

BB

B

*

EBEE

11

EE

*

BEB

SVYVY

VYSVdiagYYVdiag

=++



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[ ] [ ]{ [ ] [ ] [ ] [ ] [ ] [ ] [ ]

[ ] [ ][ ] [ ] [ ][ ]EE

11

EE

*

BEBB

*

I

*

BI

*

B

*

EB

1

EE

*

BE

*

B

*

BBB

SVdiagYYVdiagS

VYVYYYVYVdiag

=

+

[ ] [ ] [ ] [ ] [ ] [ ]eqBIBIB

eq

BBB SVYVYVdiag =+

[ ] [ ] [ ][ ] [ ]

[ ] [ ] [ ][ ] [ ] [ ][ ]EE

11

EE

*

BEBB

eq

B

EB

1

EEBEBB

eq

BB

SVdiagYYVdiagSS

YYYYY

=

=

we can write:

With the definitions



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[ ] [ ] [ ][ ] [ ]

[ ] [ ] [ ] [ ] [ ] [ ][ ] )4.2(SVdiagYYVdiagSS

)3.2(YYYYY

EE

11*

EEBEBB

eq

B

EB

1

EEBEBB

eq

BB

=

=

Power flow equations after transformation:

)2.2(

)1.2(

S

S

V

V

YY

YY

V

V

diag I

eq

B

I

B

IIIB

BI

eq

BB

I

B

=

With definitions:



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[ ] [ ] [ ] [ ] [ ] [ ]*I

*

BI

*

B

*eq

BBB

eq

B VYVYVdiagS +=

On-line application:

Topology and network parameters of external, boundary and

internal network are known; so can be determined

using Eq. (2.3):

eq

BBY

[ ] [ ] [ ][ ] [ ]EB

1

EEBEBB

eq

BB YYYYY

=

of boundary and internal network are known as a

result of state estimation; therefore can be determined

using Eq. (2.1):

IB V,V eqBS

of external network are unknown; so the calculation

of with the use of Eq. (2.4) is not possible.

EE V,S

[ ]eqBS

[ ] [ ] [ ] [ ] [ ] [ ][ ]EE11*

EEBEBBeqB SVdiagYYVdiagSS

=



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passive part:equivalent branchesequivaltent shunts

active part:equivalent injections

Internal network

eqi

eqi jQP +

eq

iky

eq0iy

eqi

eqi jQP +

eqikyeq0iy


Equivalent representation of the external network


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German system with external network


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German system with equivalent for external network

Equivalentbranches

Equivalentinjections


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Variation in time of Peq

in boundary nodes (January 9th

1979)



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Bus admittance matrix:

Elimination of external nodes:

E: ExternalB: BounderyI: Internal


Reduction of the external network


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Internal network

2359.0j0890.0Z17 +=

2691.0j0973.0Z27 +=

1847.0j0387.0Z25 +=

2807.0j1068.0Z18 +=

2372.0j0497.0Z58 +=

1465.0j0529.0Z45 +=

2196.0j0460.0Z38 +=

1736.0j0364.0Z43 +=

2442.0j0511.0Z46 +=

2763.0j0579.0Z56 +=

Example of external network reduction



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Busadmittancematrix

Example



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1st stepExample



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2nd stepExample



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3rd stepExample



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4th stepExample



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5th stepExample



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Example of external network reduction

Internal network

3520.0jZ eq78 =

3213.0jZeq68 =

0380.1jZ eq67 =

Equivalent branches(Reactance reduced)


Documents

4.3 External Network Modelling