Benchmark System #1

&

Benchmark System #2

N. Martins

CEPEL

National Harbor, MD, July 27-31, 2014

2014 IEEE Power & Energy Society General Meeting

IEEE PES Task Force on Benchmark Systems for Stability Controls

2

Benchmark System #13-Machine Infinite Bus System

Outline

� Desirable features of the system

� System description

� Eigenanalysis

� PSS/E - ANATEM/PacDyn comparative results

� Conclusions

3

Desirable Features of 3MIB System� Effectiveness of PSS to simultaneously contribute to

the damping of three electromechanical modes.

�These are modes of different nature:

�Intraplant

�Interplant

�Inter-area

�A well-designed PSS should be able to:

� provide good to excellent intraplant and local

mode damping under practically all operating

conditions

�adequately contribute to the damping control of

inter-area modes.

4

3MIB System description (1/2)

Reactances given

on 100 MVA base

5

3MIB System description (2/2)� Synchronous machine models consider transient

and subtransient effects in d and q axes.

� First order AVR models (IEEEST1A).

� Generators #1 and #2: Typical hydro-generator parameters.

� Generator #3: typical turbine-generator parameters.

� Load types:

Bus Active power Reactive Power

#480% constant-I

20% constant-Z100% constant-Z

#5 100% constant-P 100% constant-Z

6

Rotor speed mode-shapes

-1 0 1-1

0

1Mode M1 (1.43 Hz)

#1

#2

-1 0 1-1

0

1Mode M2 (1.25 Hz)

#1

#2 #3

-1 0 1-1

0

1Mode M3 (0.39 Hz)

#1#2#3

-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2

0

2

4

6

8

10

12

14

1616

14

12

10

8

6

4

20.98

0.86

0.74

0.6

0.48 0.36 0.24 0.12 0.06

Mode M1

Mode M2

Mode M3

Real [1/s]

Imag

[ra

d/s]

7

Uncompensated 3MIB system

Four eigensolutions

produced by raising

the values of a pure

gain PSS at gen. #1.

-3 -2.5 -2 -1.5 -1 -0.5 0 0.50

2

4

6

8

10

1212

10

8

6

4

2

Real [1/s]

Imag

[ra

d/s]

8

Residues of Δω(s)/ΔVref(s) for Gen #1With (blue) and without (red) phase compensation.

-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2

0

2

4

6

8

10

12

14

1616

14

12

10

8

6

4

20.98

0.86

0.74

0.6

0.48 0.36 0.24 0.12 0.06

Real [1/s]

Imag

[ra

d/s]

9

Phase-Compensated 3MIB system

Six eigensolutions

produced by

raising the gains

of phase-advance

PSSs at gen. #1

and #2.

10

ANATEM vs PSS/E Validation (1/2)

0 2 4 6 8 10 12 14 16 18 20

1398

1400

1402

1404

1406

1408

CaseA-noPSS

Time (s)

Pe (

MW

) G

en #

1

ANATEM

PSS/E

50 MVAr Reactor at Bus #5, No PSS

11

ANATEM vs PSS/E Validation (2/2)Steps in the AVRs references, No PSS

0 2 4 6 8 10 12 14 16 18 20

1350

1400

1450

CaseB-noPSS

Time (s)

Pe (

MW

) G

en #

1

ANATEM

PSS/E

12

PacDyn vs PSS/E LSYSAN Validation (1/2)

-30 -25 -20 -15 -10 -5 00

5

10

15

a)

Real (1/s)

Imag

(ra

d/s)

ANATEM

PSS/E

-2 -1.5 -1 -0.5 0 0.50

1

2

3

4

5

6

7

8

9

10b)

Real (1/s)

Imag

(ra

d/s)

ANATEM

PSS/E

All modes Electromechanical modes

13

PacDyn vs PSS/E LSYSAN Validation (2/2)

-1 -0.5 0 0.5 1-1

-0.5

0

0.5

1a) 1.43 Hz

-1 -0.5 0 0.5 1-1

-0.5

0

0.5

1b) 1.22 Hz

-1 -0.5 0 0.5 1-1

-0.5

0

0.5

1c) 0.39 Hz

Rotor speed mode-shapes

(×) PSS/E LSYSAN

(○) PacDyn

14

Conclusions on the 3MIB System�The 3MIB results show that good PSS designs

simultaneously contribute to the damping of

electromechanical modes of different nature.

�Three electromechanical modes are clearly

identified from the system eigensolution:

�Intraplant, interplant and inter-area.

�The PSS/E and ANATEM/PacDyn datafiles can be

downloaded from the Task Force website:

�Time-domain simulations and eigenanalysis

from both software show good matching .

15

Benchmark System #2The Brazilian 7-Bus Equivalent Model

Outline

� Desirable features of the system

� System description

� Eigenanalysis

� PSS/E - ANATEM/PacDyn comparative results

� Conclusions

16

Desirable Features of the System�Poor controllability via single generator excitation

control loop over a critical inter-area mode.

�Presence of a poorly-damped complex-conjugate

pair of zeros in the Itaipu AVR transfer function:

�These zeros, through system changes, approach

the pole pair to be damped, reducing the

generator damping control.

�Negligible controllability when near pole-zero

cancellation.

4ITAIPU

1.03948.5

1 62.6

24.3

6500.0

1957.9R

1 0.0

-39.7

6IVAIPORA

0.98921.4

-4.9

79.81

0.0

-2097.2

6437.3

1973.4

-6315.6

1109.0

1

5IVAIPORA

0.99821.2

845.8

-9.2

1 0.0

-32.9

1.0000

1.0000

109.3

-224.8

7EQUIVALENT

0.9660.0

1 2884.0

-196.0

1 -3164.3

952.3R

1 0.0

-39.2

6211.2

1133.1

-6048.3

1187.61

227.3

1

1FOZ AREIA

1.03024.5

2405.0

-467.0

1 1658.0

-412.3R

1 0.0

-190.1252.9

120.5

-251.5

-102.4

2S. SANTIAGO

1.03027.2

1 692.3

-184.0

1 1332.0

-200.3R

1 0.0

488.6

137.5

-484.9

-82.8

3S. SEGREDO

1.029

688.2

-235.01

1540.0

-446.7R

1 0.0

-120.9

151.1

4.4

-151.0

-2.8

-999.9

124.3

1002.8

-88.0

-158.2

1

1

-109.3

IEEE BENCHMARK SYSTEMBRAZILIAN 7-BUS EQUIVALENT SYSTEMTUE, OCT 01 2013 10:16

17

System description (1/2)

Red: 500 kV

Black: 765 kV

18

System description (2/2)

� Synchronous machine models:

� consider transient and subtransient effects in d and q axes.

� salient-pole rotor.

� All machines with identical AVR models (IEEEST1A).

� Δω-PSS in all machines except generator #7 (EQUIVALENT).

� Line chargings represented by shunt capacitors.

� Load model: 100%I for P and 100%Z for Q.

19

Interarea modes

� Mode 1 (unstable): oscillation of the Itaipu power plant against the Southern and Southeastern systems.

� Mode 2: oscillation of the Southern system (Salto Santiago (#2), Salto Segredo (#3) and Foz do Areia (#1) power plants) against the Southeastern system and the Itaipu power plant combined.

20

Mode 1 Mode 2

Rotor speed mode-shapes

21

Pt/Vref Residues� Pt_i/Vref_i transfer function residues for the

unstable pole:

� First approach: stabilize the system with PSS only at Itaipu.

Generator Residue

Itaipu 6.70 ∟31.6°

Equivalent 5.55 ∟165°

F. Areia 0.044 ∟162°

S. Segredo 0.042 ∟160°

S. Santiago 0.027 ∟144°

22

Stabilization with one PSS (1/2)

� The zeros with positive real part in the stabilization loop of Itaipu attract the unstable poles as the PSS gain is increased.

(*) Poles (○) Zeros

23

Stabilization with one PSS (2/2)

� The unstable root locus branch tends to the RHP zero as the PSS gain is increased.

24

Stabilization with two PSS (1/2)

� The system can be stabilized by the addition of ∆ω-PSSs to Itaipu and Segredo generators.

(*) Poles (○) Zeros

25

Stabilization with two PSS (2/2)

26

Stabilization with three PSS

� The addition of PSSs to Segredo, Areia and Santiago generators is not sufficient to stabilize the system.

� There exists a complex pair of zeros closely located to the unstable pole pair.

� By combining local and remote signals to the input of the Itaipu generator, the system can be stabilized with two PSS.

27

ANATEM vs PSS/E Validation (1/2)50 MVAr Reactor at Bus #6, PSS only at Itaipu

0 2 4 6 8 10 12 14 16 18 20

1657

1657.5

1658

1658.5

1659

CaseA-PSSita - Gen #1

Time (s)

Pe (

MW

)

ANATEM

PSS/E

CaseA-allPSS - Gen #1

28

ANATEM vs PSS/E Validation (2/2)Step in the AVR reference of Itaipu, PSS only at Itaipu

0 2 4 6 8 10 12 14 16 18 20

1654

1656

1658

1660

1662

CaseB-PSSita - Gen #1

Time (s)

Pe (

MW

)

ANATEM

PSS/E

CaseB-allPSS - Gen #1

29

PacDyn vs PSS/E PSSLT Validation (1/2)

All modes Electromechanical modes

-25 -20 -15 -10 -5 00

1

2

3

4

5

6

7

8

9

a)

Real (1/s)

Imag

(ra

d/s)

ANATEM

PSS/E

-2 -1.5 -1 -0.5 0 0.50

1

2

3

4

5

6

7

8

9

10b)

Real (1/s)

Imag

(ra

d/s)

ANATEM

PSS/E

System without PSS

30

PacDyn vs PSS/E PSSLT Validation (1/2)

All modes Electromechanical modes

System with PSS at all generators

-70 -60 -50 -40 -30 -20 -10 00

10

20

30

40

50

a)

Real (1/s)

Imag

(ra

d/s)

ANATEM

PSS/E

-5 -4 -3 -2 -1 00

5

10

15b)

Real (1/s)

Imag

(ra

d/s)

ANATEM

PSS/E

31

Conclusions�Pole-zero analysis shows the inherent modal

controllability problem (TF zeros in the vicinity of

the electromechanical mode to be damped).

�Test system needs 2 PSSs to be stabilized.

�The PSS/E and ANATEM/PacDyn datafiles can be

downloaded from the Task Force website:

�Verified differences in the time-domain

simulations are under investigation.

�Higher mismatch in the eigenvalue calculation

for the well damped system.

32

Thank you!