2008 IEEE T&D LA Conference, Aug. 2008

Equivalent Models of the Argentinian Electrical Power System for

Stability Analysis of the Uruguayan network

M. Artenstein, A. Giusto Instituto de Ingeniería Eléctrica

Facultad de Ingeniería Universidad de la República - Uruguay

Grant PDT 47/05 Ministerio de Educación y Cultura - Uruguay

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Plan

• Introduction• Basic concepts of the theory• Application to the Uruguayan case• Results • Conclusions

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Introduction

• Main idea: To build an equivalent, reduced, model of the contiguous system (i.e. the Argentinian) able to suitably describe the dynamic response to disturbances on the Uruguayan system.

• Static (power flow) and dynamic equivalent• Motivations:

- to hide complexity,- to reduce computation time,- at the least possible expense of accuracy.

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Basic Concepts of the Theory

• The technique is based on the Slow Coherency theory (Chow et al, 1990).

• In the occasion of a disturbance on the area of study, the external machines tend to gather in coherent groups.

• The oscillation frequencies of the external machines are typically low (less than 1 Hz); the frequencies associated

to local modes are higher.

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0 1 2 3 4 50 .4

0 .5

0 .6

0 .7

0 .8

0 .9

1

t i m e (s )

Swings of several Argentinian machines (Comahue) in the face of a fault on PALMAR A-500 kV, Uruguay.

Basic Concepts

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Basic Concepts

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Basic concepts

Power system model  ( swing equations)

(power flow) 

 

M d2dt 2

= f ,V

0=g ,V

M d2dt 2

=K1K 2V

0 =K3K 4V

: machine anglesV: node complex voltagesM: inertia matrix

Linear model (DAE) around the equilibrium:

Differential linear model: d 2dt 2

=K 1−K2 K 4−1K3 ⇒ d x

dt=AS x.

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Cluster identification through the mode shapes

       

       

     

       

       

Eigenvectors for the r slowest modes

1 2 r modesmachines

2

n

1

The machines that oscillate coherentlyin the r slowest modes exhibitesimilar rows in this matrix.

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Choice of the number of cluster “r”• r covers the number of inter-area frequencies (less than 1 Hz)• Not too small, to keep good accuracy• Iterative process

Machine aggregation• The machines are aggregated behind the transient reactance.• The equivalent machine has an inertia equal to the sum of the individual inertias, and• a null transient reactance.

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Basic conceptsCluster aggregation

If we substitute each by the position of the center of inertia ...

we get

the model that describes the slow

oscillation modes of the system.

M ad 2 ydt 2

= K 1 y K 2V

0 = K3 yK 4V

ya=∑ miiM a

; ma=∑ mi for each cluster.

M a=diag ma ; y=col ya .

i ya

11

Application to the Uruguayan power systemUruguay.• Max. distance 600 km• Population: 3.4 millions

• Annual generation 5400 GWh• Installed generation: 2.3 GW• Peak load: 1.4 GW

Transmission lines. • 500 kV: 770 km• 150 kV: 3 550 km (2006 data)

Interconnected Argentinian-Uruguayan system:• 1773 nodes• 192 machines

Area of study (Uruguay plus Salto Grande):• 294 nodes• 23 machines

Computation tools: • Siemens-PTI PSS/E, • PSAT (F. Milano, 2005)• MATLAB

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Application

Criteria for the clusters identification • Uruguayan network belonging to an unique cluster.

• Frequency upper limit = 1Hz.

• Check for accuracy.

Results

• 11 clusters

• The preserved area of study comprises the Uruguayan 23 machines plus 26 Argentinian ones.

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ResultsCluster # Mach Geographic Area

1 1 CENTRO

2 2 CBA

3 2 NE

4 1 NW

5 3 GBA

6 10 COMAHUE

7 20 NE+PARAGUAY

8 21 CUYO

9 48 CENTRO, NW

10 49 URUGUAY.GBA,BA

11 35 COMAHUE

CLUSTERS

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0,9889 0,9830 0,9259 0,9253 0,8714 0,9151 0,8615 0,8844 0,7635 0,8357 0,7465 0,7499 0,7233 0,7157 0,6776 0,6702 0,6148 0,5972 0,5117 0,4823 0 0

EquivalentOriginal

Frequencies of the slowest modes, Hz

• Quadratic error: 3.5%

• Final network after static reduction: 53 machines, 344 nodes.

• Static reduction led the error to 7.2 %

• Argentinian system was reduced from 1479 nodes, 169 machines to 50 nodes and 30 machines.

Summary

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Validation

• The original and reduced model were compared through the analysis of transient response to a fault at PALMAR station (triphasic short circuit, with line tripping).

• Complete generator model for original system, second order models for external reduced system.

• Excitation system and speed control not included.

• Three generation/load scenarios: hydro, thermal and reduced load.

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Results

0 1 2 3 4 5- 0 . 5

0

0 . 5

1

1 . 5

2

t i m e ( s )

Angle, BATLLE 6a.Hydro scenario

0 1 2 3 4 5- 0 . 1

0

0 . 1

0 . 2

0 . 3

0 . 4

0 . 5

0 . 6

0 . 7

0 . 8

t i m e ( s )

Angle, BATLLE 6a.Thermal scenario

OriginalReducedOriginal

Reduced

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Conclusions

• An equivalent model of the Argentinian system was computed, useful to analyze the dynamic behavior of the Uruguayan system.

• The model performs very well in the face of local disturbances.

• Future work: to extend the model to include excitation system and governor.

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Thanks for your attention

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