Panel Session: IEEE PES Task Force on Benchmark

Systems for Stability Controls Simplified 14-generator model of the

southern and eastern Australian power system

David Vowles & Mike Gibbard Power Systems Dynamics Group

School of Electrical and Electronic Engineering The University of Adelaide, South Australia

(david.vowles@adelaide.edu.au michael.gibbard@adelaide.edu.au)

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Outline • Objective • Simplified 14-generator model of the

Australian system • Benchmark tuning of conventional PSSs • Damping performance • Transient performance • Model implementation & validation • Model report and data

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Objective

• Validated longitudinal multi-machine test system for benchmarking the tuning and performance assessment of PSSs and other controls in a multi-machine power system

• Provide basis for well tuned ‘conventional’ PSSs • Provide ‘conventionally’ tuned PSSs for the system to

serve as a benchmark against which other ‘advanced’ PSS tuning methodologies can be assessed.

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AU14GEN system: • Longitudinal 50 Hz system prone to

small-signal instability • Unstable without PSSs

• Multiple identical generators within each of 14 power plants are aggregated • 5th order (2 d- and 1-q-axis wdg.) • 6th order (2 d- and 2-q-axis wdg.) • Generator saturation neglected • IEEE Std. 421.5 AVR/exciters:

• AC1A (3) & ST1A (11) • Turbine / governors not represented

• Five SVCs • Constant impedance loads • Four main regions interconnected by

relatively weak transmission corridors • Three inter-area modes • Ten local modes

• System unstable without PSSs …

AU14GEN – Operating Conditions Encompassing set of six base case scenarios

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Damping performance without PSSs 6

Benchmark ‘Conventional’ PSS Tuning • Provide PSSs tuned according to a ‘conventional’

methodology to serve as a benchmark against which alternative ‘advanced’ design methodologies can be assessed – Speed input PSSs tuned for each of the 14 generators – ‘Conventional’ P-Vr PSS tuning method employed – Show that ‘conventional’ tuning effectively improves

damping over encompassing set of six base case scenarios • Near ‘pure’ left shift in both local and inter-area modes • PSSs introduce uniform damping torque coefficients over range of

electromechanical modal frequencies

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Basis for ‘conventional’ PSS tuning (1) 8

Linearized model of multi-machine system showing shaft-dynamics, AVR/exciter and speed-input PSS of a generator.

Basis for ‘conventional’ PSS tuning (2) 9

Torque coefficients of electromagnetic origin introduced by PSS: DAMP(s) Disable shaft dynamics of all machines in the system:

( ) ( )s SS

s

DDDD

PDA V PMP SSV

sP rs PVω ω

∆= = × = ×∆ ∆

∆∆

∆

Basis for ‘conventional’ PSS tuning (3) We specify DAMP(s) De Damping torque coefficient Tw Washout filter time constant Tl Lowpass filter time constant

Objective is to introduce ‘pure’ damping torque coefficient of De pu

on machine MVA rating over the range of electromechanical modal

frequencies (e.g. 1 to 15 rad/s)

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( ) 11 1

w ln nw

ew l

sTDAMP s DsT sT

= + +

Basis for ‘conventional’ PSS tuning (4) PVr characteristics computed for encompassing set of operating conditions for each generator (e.g. for generator VPS_2 in figure). For given generator tend to find: • mag. xtics have similar shape, though

steady-state gain tends to increase with P & Q output

• phase xtics. are coherent Synthesize low order transfer-function PVR(s) to fit representative PVr xtic.

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( ) ( )( )3.5

1 0.0292 1 0.0708PVR s

s s=

+ +

Basis for ‘conventional’ PSS tuning (5) Recall torque-coefficients of electromagnetic origin introduced by PSS are:

We have specified DAMP(s) and synthesised a TF PVR(s) that is representative of the family of generator PVr xtics. Thus, we have the basis for determining the PSS TF PSS(s):

For the example of the VPS_2 generator we have:

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( ) ( )s SS

s

DDDD

PDA V PMP SSV

sP rs PVω ω

∆= = × = ×∆ ∆

∆∆

∆

( ) ( ) ( )11 1

w ln nw

ew l

sTDAMP s D PSsT sT

PVR s S s

= = × + +

( ) ( )( ) ( )

( )

27.5 11 7.5 1 0.00667

1 7.51 7.5 1 0.00667 1 0.00

3.51 0.0292 1 0

6

.0708

1 0.0292 1 0.06

7083 7.5

e

e

sDAMP s Ds s

s

PSS s

PSS Ds s

s s

s ss

s

= = × + +

∴ = × × × × + + +

+ +

+

+

Summary of shifts in inter-area modes due to PSSs for 6 cases

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Legend: • Cases 1, 2, 3, 4, 5, & 6 • k, l, m – Three inter-area modes

with PSSs out-of-service • K, L, M – corresponding inter-area

modes with PSSs in-service with all PSS damping gains De = 20 pu on machine MVA rating.

• x, X – other modes with PSSs out-of-service and in-service respectively.

Summary of shifts in local modes due to PSSs for 6 cases

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Legend: • Cases 1, 2, 3, 4, 5, & 6 • a, b, … , j – 10 local modes with

PSSs out-of-service • A, B, … , J – corresponding local

modes with PSSs in-service with all PSS damping gains De = 20 pu on machine MVA rating.

Transient Stability (1) • AU14GEN model includes AVR/Exciter limits, PSS

output limits and SVC susceptance limits. – Exciter saturation neglected

• In the Australian NER two-phase to ground faults are considered to be the most severe credible contingency for voltages of 220 kV and higher. – Except under extraordinary conditions the risk of three

phase faults are considered to be so low as to be non-credible.

– Accordingly benchmark transient stability studies on the AU14GEN system are conducted for solid 2ph-g faults.

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Transient Stability (2) • Comprehensive set of transient-stability studies have

been performed with PSSs in-service – AU14GEN system is transiently stable for 2ph-g faults applied at either

terminal of each transmission line or transformer (excepting generator step-up transformers) and cleared by tripping the faulted element. • Clearance times: 100 ms for voltages of 330 kV and lower; 80 ms for 500 kV

– Loss of generation / load events not simulated because turbine / governor models not included in current version of AU14GEN.

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Model Implementation • Small-signal and large-signal representations of

AU14GEN implemented by model developers in Mudpack and PSS/E respectively.

• Independent implementations for model validation:

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Group Type of Analysis Software Package Status

Uni. Sao Paulo Small-Signal PacDyn (CEPEL) Validated

Uni. Sao Paulo Large-Signal ANATEM (CEPEL) Validated excepting for SVC controller limits

Uni. Waterloo Small-Signal PowerTech Tools (SSAT)

Uni. Waterloo Large-Signal PowerTech Tools (TSAT)

Small-signal Model Validation (1) Eigenanalysis: Compare electromechanical modes for 6 cases obtained with different software packages. e.g. Mudpack (MP)/ PacDyn (PD) comparison …

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Small-signal Model Validation (2) Small-disturbance voltage-reference step responses: Compare responses of key variables (P, W, Vt, Q, Efd, Ifd) from different packages due to small step-change in AVR voltage-reference for each generator in all 6 cases. Local modes are excited. • e.g. Mudpack / PSS/E comparison for BPS_2 in case 2 …

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Small-signal Model Validation (3) Small-disturbance mechanical power step responses: Compare responses of inter-regional power flow from different packages due to small step-changes in mechanical power input to widely separated generators in all 6 cases. Inter area modes excited. • e.g. Mudpack / PSS/E comparison for -10 MW step on Pm.NPS_5 & +10 MW step

on Pm.GPS_4

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Small-signal Model Validation (4)

PVr characteristics: Compare PVr characteristics computed with different packages for all generators in case 2 • e.g. Mudpack / PSS/E comparison

of PVr characteristic of LPS_3 Note: Frequency responses computed in PSS/E using an add-on tool developed at Adelaide University.

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Large-signal Model Validation (1) 2ph-g faults applied at network side of generator step-up transformers: • Compare responses in different packages (e.g. PSS/E and ANATEM)

– Key variables (P, W, Vt, Q, Efd, Vs) of the generator adjacent to the fault in different transient-stability packages. AVR/exciter & PSS variables limited.

– Power (P) and terminal voltage of other selected generators in the system. – SVC susceptance (B)

• Example: In case 2 a 2ph-g fault applied to the HV side of the TPS_4 step-up transformer (i.e. bus 410) and cleared in 100 ms by tripping #1 ckt to bus 413. Compare responses computed by PSS/E and ANATEM. – Note: SVC limits VMAX and VMIN not represented in this study.

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Large-signal Model Validation (2) 23

Large-signal Model Validation (3) 24

Large-signal Model Validation (4) 25

Large-signal Model Validation (5) 26

AU14GEN model report, data and results • Availability:

– http://www.eleceng.adelaide.edu.au/groups/PCON/PowerSystems/IEEE/AU14G/Ver04 – IEEE PSDP committee web-site (to be advised)

• Summary of content – AU14GEN model report – Model data

• Loadflow data in PSS/E format • Small-signal model in Mudpack format • Large-signal model in PSS/E format

– Results • State-space matrices & eigen-analysis results for cases 1 & 6 in Matlab format • Time-series data for small-disturbance step-responses in Matlab & CSV formats • Time-series data for transient-stability studies in Matlab & CSV formats

– Post-processing tools • Rudimentary Matlab tools for loading and plotting time-series data.

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