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POWER SYSTEM STABILITY ASSESSMENTSApplication of modal analysis to the Finnish transmission system

SINTEF ENERGY RESEARCH

HELSINKI UNIVERSITY OF TECHNOLOGY

Study made for Fingrid Oyj, Helsinki

Stefan Elenius, Kjetil Uhlen

Ole Bjørn Gjøsæter, Ian Norheim

Workshop at

Trondheim 30-31.2002

Trondheim workshop 30-31.2002 2

CONTENTS

1. Introduction slide 3

2. Analysis slide 6

3. Stabilizer design for generators slide 17

4. Influence of stabilizers slide 18

5. Fennoskan slide 19

6. Concluding remarks slide 25

7. Further research work slide 26


1. Introduction

• Project on power system stability with emphasis on the Finnish transmission grid.

• A main objective and motivation for the project has been to introduce the program system PacDyn for small signal stability analysis.

• The aim of the stability analysis has been to identify possible low damped system modes, and assess the observability and controllability of these modes as a basis for later investigations on design of power system stabilizers for generators, HVDC links and FACTS devices.

• Another aim of the project has been to establish a co-operation between Fingrid, Helsinki University of Technology (HUT) and SINTEF on power system stability assessment and control.


1.1 Software tools

• PSS/E

- The PSS/E system models can be referred to as the ‘truth’ models. The modelling is detailed including non-linearities. The effects of non-linearities are included in the simulations.

- Non-linear controllers can be modeled and developed with the PSS/E.

• PacDyn

- The PacDyn sofware makes initially a linearisation of the PSS/E load flow and dynamic models.

- The linearisation makes it possible to take advantage of the sophisticated methods from the control theory for analysis of linear systems.


1.2 Configuration and implementation of the Finnish system model (Nordic model) in Pacdyn

• High (winter) load condition with moderate export of power from Finland to Sweden. Number of online generators 1132. Load in Finland 12200 MW.

• Low (summer) load condition with high export from Finland to Sweden. Number of online generators 784. Load in Finland 7266 MW.

• PacDyn recognizes the PSS/E load flow and the majority of the dynamic declarations in PSS/E format.

• Dynamic models in PSS/E format, that PacDyn do not recognize, have been replaced with other models or have just been removed.

• Models removed are supplementary signals for static var compensators, frequency dependent load models, and current compounding for voltage regulators.

• Initially all HVDC models were replaced with constant power loads.


2. Analysis

Main findings from the stability assessments. The following is described.

• Main load flow data of the two study cases (winter and summer load).

• Eigenvalues (Frequency and damping of low damped inter-area modes (0.3 Hz, 0.5 Hz) and some local modes with low damping).

• “Mode shapes” for the most interesting eigenvaluesidentified.

• Transfer function residues for controllability assessment (identify most efficient units for installation/retuning of power system stabilisers).

• Transfer functions to illustrate the design of power system stabilisers (frequency response)


2.1 Eigenvalues Summary of critical modes and their observability (winter load)Mode

# Eigenvalue Damping(%)

Frequency(Hz) Observability

1 -0.020423 + 2.055230j 0.99 0.33 Inter-area mode. Mostobservable in Finland.

2 -0.152992 + 3.023388j 5.05 0.48 Inter-area mode. Mostobservable in Southern Norway.

3 -0.208246 + 3.812073j 5.45 0.61Inter-area mode. Mostobservable in Nordland,Norway and Sjælland, Dk.

4 -0.226852 + 4.866985j 4.66 0.77 Local area mode. Observable inWestern Norway.

5 -0.146120 + 5.293235j 2.76 0.84 Local area mode. Mostobservable in Sweden (SKAB)

6 -0.024255 + 5.324048j 0.46 0.85 Local mode, Denmark (NESA)

7 -0.043377 + 5.427713j 0.80 0.86 Local mode, Denmark (SEAS)

8 -0.345223 + 6.921447j 4.98 1.10 Local mode, mainly observablein HAG1 (PIKKARALA)

Modes# 4,5,6 originates from GENCLS-models with zero damping


Figure 4.1. Mode # 1: Inter-area mode, 0.33 Hz. Mode-shape with respect to generator speed (ww). Generators in Finland oscillate in phase against the rest of the system. Most observable in Finland.

2.2 Mode-shapes


Table 4.2. Mode # 1: Inter-area mode, 0.33 Hz. Mode-shape with respect to generator terminal power (PT). Generators in Finland oscillate in phase against the rest of the system. Largest power oscillations observable in Olkiluoto and Meripori generators.


Figure 4.3. Mode # 2: Inter-area mode, 0.48 Hz. Mode-shape with respect to generator speed (ww). Generators in Southern Norway (and Finland) oscillate in phase against the rest of the system. Speed variations most observable in Southern Norway


Table 4.4. Mode # 2: Inter-area mode, 0.48 Hz. Mode-shape with respect to generator terminal power (PT). Generators in Southern Norway (and Finland) oscillate in phase against the rest of the system. Power oscillations are observable in most of the largest generators in Nordel.


2.3 Transfer function residues

Table 4.4. Summary of the transfer function residue computations

Mode#

Damping(%)

Frequency(Hz) Description:

1 0.99 0.33Inter-area mode. Highestcontrollability in Meripori andOlkiluoto.

2 5.05 0.48

Inter-area mode. Highestcontrollability in Forsmark,Oskarshamn, Ringhals andgenerators in Southwest ofNorway.

4 4.66 0.77Local area mode. Highestcontrollability in WesternNorway.


2.4 Frequency response computation

Figure 4.30 Transfer function frequency response for the VuosaariVSRKT1 generator with the generator voltage reference as input and generator electrical power as output.


2.5 Model validation


2.5 Model validation (cont.)

PSS/E modified means same dynamic setup as used for PacDyn.

Conditions: Summer load configuration with the network intact.

Verification of damping ratios


2.5 Model validation (cont.)

• The mode shapes from PacDyn calculations and those obtained by PSS/E modal analysis are quite close.

• The modal frequencies are very close.

• PacDyn generally shows lower damping ratios thanthe PSS/E simulations.


3. Stabilizer design for generators

• Transfer function frequency response from the generator voltage reference to generator terminal power used to determine the characteristics for stabilizers using generator active power as input signal.

• Stabilizer which has a gain of 1 p.u. and a good phase compensation at the inter-area oscillation frequency (2 rad/s), while maintaining a gain of 0.5 p.u. and a reasonable phase shift at the generator characteristic oscillation frequency.

• The stabilizer has low gain in the turbine resonance frequency range.

Gain

Phase

Design criteria


4. Influence of stabilizers• Stabilizers on strategic generators may improve the inter-area transfer

capacity

• With small signal analysis in PacDyn the damping of dominant oscillation modes were calculated as a function of the export from Northern Finland to Sweden in a typical summer load situation

• The export between Northern Finland and Sweden was calculated inPSS-E and controlled by complementary changing the production in Sweden and Finland

• The flow in the Fennoskan link was constant

• The case including new stabilizers on certain generators in Finland was computed and showed large improvement in the damping of the 0.35Hz oscillation mode and significant improvement in the damping of the 0.57 Hz oscillation mode.


4.1 Influence of new stabilizers at Olkiluoto and Loviisa

6 0 0 7 0 0 8 0 0 9 0 0 1 0 0 0 1 1 0 0 1 2 0 0-1

0

1

2

3

4

5

6

F lo w F I-S E (MW )

Dam

ping

(%)

0.35 Hz modeExisting PSSs

0.35 Hz modeNew PSSs

0.57 Hz mode


5. Fennoskan

• The Fennoskan HVDC link has a power system stabilizer installed.

• The inputs to the stabilizer are the bus frequencies from both converter stations.

Fennoskan’s PSS/E HVDC stabilizer model:

• The frequency difference between the stations is calculated and band-pass filtered with a center frequency at 3 rad/s.

• When the frequency difference after the band-pass filtering varies more than ± 25 mHz, the the stabilizer output is activated.

• The stabilizer works as a bang-bang controller with the output limited to ± 100 MW. The control action is pulse width modulated.


5.1 No HVDC stabilizer at generator trip in Sweden

Winter load. Trip of Forsmark2G. No HVDC stabilizer at Fennoskan.

Fin-Swe line power

Fin-Swe line power

OLG1 speedAC power from Rauma converter station

Stabilizer outputOLG1 power


5.2 HVDC stabilizer active at generator trip in Sweden

Stabilizer outputOLG1 power

OLG1 speed

Fin-Swe line powerFin-Swe line power

AC power from Rauma converter station

Winter load: Trip of Forsmark2G. HVDC stabilizer active at Fennoskan.


5.3 Transfer function, bus angle difference/DC current order

rad/s

rad/s

Gain(dB)

Phase

TETA = Angles at Rauma and Dannebo converter AC buses


5.4 Transfer function, Fin-Swe AC power/DC current order

rad/s

rad/s

Gain(dB)

Phase

PIJ = Active power in a Finland-Sweden 400 kV line


6. Concluding remarks• Linear analysis software is a powerful tool to use in parallel with

standard nonlinear power system simulation programs.

• The PacDyn computations and PSS/E simulations with modal analysis show almost identical modal frequencies. Mode shapes also agree quite well.

• There is a larger difference between the damping ratios obtainedby PacDyn computations and PSS/E simulations/modal analysis. PacDyn generally gives lower damping ratios the the PSS/E for the lowest oscillation modes.

• Power system stabilizer redesign and retuning at generating stations and converter stations can be a cost effective way to increase the transfer capacity of existing AC interconnections.

• Computations show that new stabilizers that will be taken into service at Olkiluoto and Loviisa in Finland, have a strong impact on the damping of the 0.35 Hz mode and a moderate impact on the 0.57 Hz mode.


7. Further research work

• The studies related to stabilizers on HVDC will continue.

• An international paper about the application of modal analysis to the Finnish transmission system will be written.

• Identify good locations for potential FACTS devices.

• Find control concepts for FACTS devices.

• Interactions between FACTS, HVDC and generator controllers.

• An international paper about the findings from our FACTS research.

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