IN DEGREE PROJECT MASTER'S PROGRAMME, ELECTRIC POWER, SECOND CYCLEENGINEERING 120 CREDITS

, STOCKHOLM SWEDEN 2015

Frequency Stability Analysis of theNordic Power System with NewHydropower Governor Settings

JIANGNAN XI

KTH ROYAL INSTITUTE OF TECHNOLOGY

SCHOOL OF ELECTRICAL ENGINEERING

Abstract

The Nordic power system is under continuous development. New productionsources and loads are installed at a high rate and old ones are taken out of opera-tion. This development gradually alters the power system dynamics. The NordicTransmission System Operators (TSOs) have observed that the frequency qual-ity is gradually decreasing and recognized a number of reasons for this. Theautomatic frequency containment reserve (FCR-N) is in place to keep the elec-tric frequency within the interval 50 +/- 0.1 Hz during normal operation. Thisfunction is mainly provided by a number of hydropower plants where the turbinegovernor is set to control the discharge in proportion to the measured frequencydeviation. In later years it has been shown that the disturbance damping is verylow in an interval around 1/60 Hz and it is believed that proper tuning of theturbine governors that provide FCR-N can help mitigating this problem. Newregulator settings have been suggested in a recent study performed at Vattenfalland Uppsala University to improve the performance of the FCR-N, yet keepingthe system robust and the wear on participating units at a minimum. It is nowdesired to investigate the possible effects of new governor settings on the overallpower system stability.

This thesis work consists of three main parts. First of all, a reduced Nordicpower system model is constructed in Simpow and validated with PMU datafrom the TSO. Secondly, the frequency responses with the newly suggestedgovernor settings have been investigated when introducing a disturbance into thesystem. Thirdly, the effects of the new governor settings on electro-mechanicaloscillations are investigated. In a word, the overall performance for new governorsettings are tested in a large scale power system model in this thesis work.

Sammanfattning

Det nordiska kraftsystemet ar under standig forandring. Nya produktionskalloroch laster ansluts och gamla tas ur bruk. Detta paverkar gradvis kraftsystemetsdynamik. De nordiska systemoperatorerna (TSOerna) har erfarit att frekven-skvaliteten gradvis forsamras, och att det kan finnas flera orsaker till detta.Den automatiska primarregleringsreserven (FCR-N) ska halla frekvensen inomintervallet 50 +/-0,1 Hz under normaldrift. Reserven levereras av ett stort antalvattenkraftverk, dar turbinregulatorn reglerar vattenflodet genom turbinen pro-portionellt mot den uppmatta frekvensavvikelsen. Pasenare ar har man kunnatvisa att dampningen av storningar med periodtider runt 60 sekunder ar dalig,och man tror att problemet skulle kunna avhjalpas med battre intrimning avturbinregulatorparametrarna. En studie utford paVattenfall och Uppsala Uni-versitet har tagit fram ett forslag panya turbinregulatorinstallningar som skaforbattra prestandan i regleringen utan att forsamra systemets robusthet elleroka slitaget pavattenkraftaggregaten. Nu vill man undersoka om de foreslagnainstallningarna kan ha nagon negativ inverkan pakraftsystemets stabilitet.

Det har examensarbetet bestar av tre delar. I den forsta delen satts en reduceradmodell av det nordiska elnatet upp i programmet Simpow, och en validering avmodellen gors med hjalp av PMU-data. I den andra delen undersoks frekvenss-varet fran den nya modellen med de foreslagna turbinregulatorinstallningarna.I den tredje delen undersoks de nya turbinregulatorinstallningarnas inverkanpasystemets elektromekaniska oscillationer. Med andra ord satestas i dettaexamensarbete nya turbinregulatorinstallningar i en detaljerad och storskaligkraftsystemmodell.

Acknowledgment

In full gratitude I would like to acknowledge the following individuals who en-couraged, inspired, supported, assisted, and sacrificed themselves to help mypursuit of my master degree.

Firstly I want to express my gratitude to my supervisors at Vattenfall and KTH,Dr. Johan Bladh, Dr. Jonas Persson, Mr. Daniel Wall and Linn Saarinenwho had guided me and helped through my project and Professor MehrdadGhandhari Alavijh and Harold Rene Chamorro Vera who had given me supportwhen I met the problem. Besides, Dr. Kenneth Walve, a very kind old man,gave me suggestions and helped not only on technical aspects but also the futurecareer.

My thesis work would not be possibly finished without help from the people Imentioned above.

My stay at Vattenfall has been a wonderful experience most because of mycolleagues who embraced me into their social group on the first day. JoakimLonnberg, Gaelle Ryckebusch, Elin Dalhborg and Gudjon Vesteinsson, they giveme warm help and encouragement when I met obstacles during the work.

Most importantly my family who has supported me in good and bad, althoughthey are in China.

To all of you, I really appreciate what you have done for me. Thanks a lot andall the best!

List of Figures

2.1 The Nordic power system divided in ten areas. . . . . . . . . . . 62.2 Nordic 32 model in Aristo . . . . . . . . . . . . . . . . . . . . . . 72.3 Extended Nordic test system. In the simulation, the northern

part of Norway is not included. . . . . . . . . . . . . . . . . . . . 82.4 π-Link Model of Transmission Lines. . . . . . . . . . . . . . . . . 102.5 Two-windings Transformer Model . . . . . . . . . . . . . . . . . . 112.6 Illustration of a Generating Unit [1]. . . . . . . . . . . . . . . . . 112.7 The representation of a synchronous machine. . . . . . . . . . . . 122.8 Phasor Measurement Units Operation in the power system. . . . 152.9 Extended Nordic Test System . . . . . . . . . . . . . . . . . . . . 162.10 Fourier transformation mathematical process . . . . . . . . . . . 182.11 The Bode plot example . . . . . . . . . . . . . . . . . . . . . . . 192.12 Governor system with steady state gain . . . . . . . . . . . . . . 212.13 New governor model configuration connecting to the grid. . . . . 222.14 Hydro power unit with new governor model in Simpow. . . . . . 242.15 Backlash in Mechanism . . . . . . . . . . . . . . . . . . . . . . . 242.16 Mathematical expression . . . . . . . . . . . . . . . . . . . . . . . 252.17 The test result of backlash function block in Simpow. A time

delay on the signals’ transfer illustrates the backlash effects inthe real mechanical system. . . . . . . . . . . . . . . . . . . . . . 26

3.1 The Single Line Diagram of extended Nordic power system inSimpow. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

3.2 A Comparison between the Nordic system models in PSS/E andin Simpow. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3.3 Old Governor model in Simpow with sinusoidal signals introducedto the system. The sinusoidal oscillation of power can arise thefrequency oscillation. . . . . . . . . . . . . . . . . . . . . . . . . 35

3.4 The sinusoidal signals injection to old governor model in Simpow. 363.5 Example of the measured power oscillations in Messaure during

the fullscale test. . . . . . . . . . . . . . . . . . . . . . . . . . . . 363.6 The system response in real test in Messaure. The system reso-

nance point are observed as 60 s. . . . . . . . . . . . . . . . . . . 373.7 The comparison of the Messaure test result between real test and

Simpow test. The result are from practical one and simulatedsystem, which explains the different system response time. . . . 38

3.8 The comparison of system response when perform the same dis-turbance in new governors. . . . . . . . . . . . . . . . . . . . . . 39

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3.9 Comparison of the system response measured during the full-scaletest (blue), the response of the old governor model in Simpow(black) and the response of the new governor model with theEp0 setting (red). . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

3.10 The comparison of system response when perform the same dis-turbance in new governors. The responses are from PMU datafrom real test in Messaure and simulated model with new gover-nor model equipped with new suggested settings. . . . . . . . . . 40

3.11 The comparison of system response when perform the same dis-turbance in new governors. The responses are from PMU datafrom real test in Messaure, simulated model with old governorsequipped and simulated model with new governor model equippedwith rescaled settings. . . . . . . . . . . . . . . . . . . . . . . . . 42

3.12 The comparison of system response when perform the same dis-turbance in new governors. The responses are from PMU datafrom real test in Messaure and simulated model with new gover-nor model equipped with new rescaled suggested settings. . . . . 42

3.13 The Comparison of frequency response with different new rescaledgovernor settings involved and without frequency dependent loadafter a generator tripped. The overshot value and recovery timeare chosen to evaluate the performance. . . . . . . . . . . . . . . 43

3.14 The Comparison of frequency response with different new rescaledgovernor settings involved and with frequency dependent load af-ter a generator tripped. The overshot value and recovery timeare chosen to evaluate the performance. . . . . . . . . . . . . . . 44

3.15 The impact of Backlash for governor performance. . . . . . . . . 453.16 The impact of new governor settings on inter-area modes. Several

groups of inter-area modes are observed with frequencies are f =0.33Hz, 0.57Hz, 0.60Hz, 0.78Hz, 0.80Hz. . . . . . . . . . . . . . 46

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List of Tables

2.1 Buses and generators of the New Nordic Test System. . . . . . . 52.2 Power lines and voltage levels in the New Nordic Test System. . 52.3 Signals explanation in governor. . . . . . . . . . . . . . . . . . . . 232.4 Per unit bases. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272.5 System and controller parameters presented with nominal values. 27

3.1 Different groups of settings . . . . . . . . . . . . . . . . . . . . . 393.2 The goals for different groups of settings according to previous

research. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393.3 Different groups of rescaled settings . . . . . . . . . . . . . . . . 41

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Contents

1 Introduction 11.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Previous Research . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Problem Definition . . . . . . . . . . . . . . . . . . . . . . . . . . 21.4 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Theory and Methodology 42.1 System Model Extension . . . . . . . . . . . . . . . . . . . . . . . 4

2.1.1 Model Description and Configuration . . . . . . . . . . . . 42.1.2 Modelling in Simpow . . . . . . . . . . . . . . . . . . . . . 9

2.2 Phasor Measurement Units Data Analysis . . . . . . . . . . . . . 152.2.1 Phasor Measurement Units in Power System . . . . . . . 152.2.2 Full Scale Frequency Response Tests . . . . . . . . . . . . 172.2.3 Fourier Analysis — Bode Plots . . . . . . . . . . . . . . . 17

2.3 Vattenfall New Hydro Turbine Governor Model Test . . . . . . . 212.3.1 New Governor Model Introduction . . . . . . . . . . . . . 212.3.2 New Governor Model Developed in Simpow . . . . . . . . 232.3.3 Parameter Validation . . . . . . . . . . . . . . . . . . . . 26

2.4 Stability Analysis of Nordic Power System in Simpow . . . . . . 282.4.1 Frequency stability analysis . . . . . . . . . . . . . . . . . 282.4.2 Small-signal stability Analysis . . . . . . . . . . . . . . . . 302.4.3 Analysis method in Simpow . . . . . . . . . . . . . . . . . 31

3 Simulation and Results 323.1 Model Comparison with PSS/E . . . . . . . . . . . . . . . . . . . 323.2 Model Validation with PMU Data . . . . . . . . . . . . . . . . . 35

3.2.1 Validation with Old Governor Model in Simpow . . . . . 353.2.2 Validation with New Governor Model in Simpow . . . . . 38

3.3 The New Governor Model Test results . . . . . . . . . . . . . . . 433.3.1 Frequency Response Comparisons . . . . . . . . . . . . . 433.3.2 Comparison with Backlash . . . . . . . . . . . . . . . . . 45

3.4 Effects on Inter-area modes . . . . . . . . . . . . . . . . . . . . . 46

4 Discussions and Conclusions 474.1 Nordic power system development . . . . . . . . . . . . . . . . . 474.2 New Governor Model Performance . . . . . . . . . . . . . . . . . 47

5 Future Work 49

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Appendix A Tables 52A.0.1 System Data of Extended Nordic 32 Model in PSS/E. . . 53A.0.2 Power Flow Result Comparison of Simpow and PSS/E. . 55

Appendix B Scripts 56B.0.3 Matlab-Fast Fourier Analysis . . . . . . . . . . . . . . . . 56

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Chapter 1

Introduction

1.1 Background

The interconnected synchronous Nordic power system comprises of Sweden, Nor-way, Finland and Eastern part of Denmark (Zealand). It includes a large amountof producers and consumers in the Nordic electricity market. To maintain thepower system stability especially the frequency quality, the electric power shouldbe kept in balance from production part and consumption part. Moreover, withthe development of renewable energy, more and more flexible generation is in-jected to the power grid, which might introduce fluctuations of power transferand alter the system dynamics. Thus, frequency control is of great importanceto keep the frequency within nominal range and guarantee the safe operation ofthe Nordic power system.

There are various types of generation sources in the Nordic power system in-cluding hydropower, wind power, nuclear power and thermal power. Sweden hasmore than 50% generation relying on hydropower and even Norway has almostthe entire generation coming from hydropower.

Since Vattenfall holds a majority of hydropower plants in Sweden, they have astrong interest on improvement of frequency control in the hydropower turbines.The automatic Frequency Containment Reserve (FCR-N) is the primary controlwhich is in place to keep the electric frequency within the interval 50.0 ± 0.1Hz during normal operation. This function is mainly provided by a number ofhydropower plants where the turbine governor is set to control the discharge inproportion to the measured frequency deviation. The governor’s performancebecomes one of the key factor in frequency control.

One new type of hydro turbine governor model has been developed by VattenfallResearch and Development, and see Saarinen [2], to consider more non-linearityas well as new governor settings that may have positive effects on mitigatingthe frequency variations in the power grid.

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1.2 Previous Research

In the latest years, it has been observed that the Nordic power system hasa frequency oscillation with a period time from 40 s to 90 s which will havea negative impact on the grid [3]. Full scale frequency response tests havebeen performed in Messaure hydropower station by introducing sinusoidal poweroscillation with amplitudes of up to more than 70 MW. They obtain a resonancepeak in the frequency amplitude for period times around 60 s. Moreover, itshows that small periodic power oscillations may cause big frequency oscillationsin the power grid [4].

In order to improve the quality of the grid frequency, Vattenfall has done someresearch on developing a new hydro turbine governor model and has performedsome related tests and experiments [2]. The new governor model includes Pro-portional and Integration part (PI Controller) and consider the hydropowerplants dynamics as well as backlashes in the servo and guide vane regulatingmechanism, both before and after the feedback to the controller. Vattenfallhas tested the governor performance and discovered some trade-off among thefunctionality aspects of the governor [5]. For example, a trade-off has been de-tected between the actuator work and frequency control performance as well asa trade-off between the performance of frequency control in the low-frequencyrange and the mid-frequency range [2] [5].

Besides, in Vanfretti [6], a research on implementation of the Nordic powersystem in an open source software (PSAT) and test of a newly developed hydroturbine governor has been done. In [6], it has been emphasized the importancefor small signal stability to introduce an appropriate model of hydro turbinegovernors. In Kundur [7], some related research has been done on detectingthe effects of governor settings for eigenvalues movements. His research focusedon three governor settings which are dashpot reset time, the temporary droopand the gate servomotor system gain. The dashpot is applied in mechanical-hydraulic governor system to provide the transient droop compensation [8]. Itdemonstrated that it can be neglected for the decrease in the damping ratiowith increase in reset time and gate servomotor system gain, comparing to suitfor their value selection [7].

1.3 Problem Definition

According to previous research, it is important for Vattenfall to test the newlydeveloped hydro turbine governor model in a large scale power system whichis similar to the real Nordic power system. New regulator settings have beensuggested in a recent study performed at Vattenfall and Uppsala University toimprove the performance of the FCR-N, yet keeping the system robust and thewear on participating units at a minimum [2]. It is now desired to investigate thepossible effects of new governor settings on the overall power system stability,especially the electro-mechanical oscillation. Modelling in the software Simpowof the Nordic power system and validation with real time data from PhasorMeasurement Units (PMU) has been made.

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This thesis work objectives can be summarized as following:

� Validate the Nordic system model in Simpow with PMU data.

� Analyse the frequency response effects on new turbine governor settingstuning.

� Detect the effects on electro-mechanical oscillation in the power grid witha new governor model.

1.4 Outline

Chapter 2 describes the theory and methodology have been referred in thisthesis work. It includes the Nordic system modelling, Phasor MeasurementUnit data analysis, new governor description and stability analysis of powersystem. Chapter 3 introduces the simulation and results based on chapter 2.Chapter 4 contains the discussion according to results obtained in chapter 3. Abrief conclusion is also drawn when it comes to end as well as with future workmentioned.

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Chapter 2

Theory and Methodology

2.1 System Model Extension

2.1.1 Model Description and Configuration

In the real Nordic power system, according to Figure 2.1 [9], the grid has beendivided into ten areas. With the geographical breakdown, it is here meantthat every country in the Nordic synchronous system is divided into at leastone area, because each country is responsible for the power balance withintheir own country. The other factor that has been taken into account is thetransmission capacity between the different areas, both within a country andbetween countries. As shown in Figure 2.1, the areas are connected together [9].

In order to test the governor’s performance in a real power system, the selectedtest system is Nordic 32 model proposed by Cigre task force 38-02-08 [10]. Thistest system which consists of 32 buses is a representation of the Swedish trans-mission system as well as small parts of the Norwegian and Finnish transmissionsystems. Most of the modelled plants are hydropower plants but it also includessome nuclear power plants and thermal power plants. The system is suitable forsimulations of transient stability and long term dynamics [10]. As can be seenin Figure 2.2, it shows the Nordic 32 model modelled in Aristo. It has 400 kV,220 kV and 130 kV lines. The system consists of four major parts: a large hydroproduction and some loads in the northern part, a heavy load and substantialthermal generation located in the central part, some thermal generation andsome load in the south west part, and a high load and generation in externalpart. They represents northern part of Sweden, central and southern part ofSweden, Danish Island Zealand and Finland part respectively. It indicates asignificant power transfer in the Nordic Power grid.

Since hydropower plants have covered almost 90% power generation in Norwayand 50% in Sweden, it is important to test the new governor performance in-cluding most of them. In this way, the Norway part should be extended. Ascan be seen from Figure 2.3, the Norwegian part has been extended focusingon south and middle part comparing to the previous model. A more detailedNorwegian power grid has been connected with Swedish grid. Except for theextension on the grid configuration, a step-up transformer has been added on

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each generator bus in the new test model in order to consider the reactive powerconsumed on it, which will be mentioned in the following part. The networkdata for the new test system are coming from Svenska Kraftnat [11].

The new governor model developed by Vattenfall Research and Development isadded to the hydropower plant model in the extended Nordic 32 model. Thesettings of new governor model for Sweden, Finland and Norway are differentaccording to their operation requirements.

Table 2.1 and 2.2 summarizes the buses, generators and lines of the new testsystem shown in Figure 2.3.

Countries& Number of Elements

Buses Generators Hydropower Generators

Sweden 40 22 11 (50%)Norway 18 7 7 (100%)Finland 6 6 2 (33.33%)Total 64 35 20 (57.14%)

Table 2.1: Buses and generators of the New Nordic Test System.

Countries & Elements 400kV 300kV 220kV 130kVSweden 35 0 2 17Norway 9 9 0 0Finland 10 0 0 0

Table 2.2: Power lines and voltage levels in the New Nordic Test System.

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Figure 2.1: The Nordic power system divided in ten areas.

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Figure 2.2: Nordic 32 model in Aristo

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Figure 2.3: Extended Nordic test system. In the simulation, the northern part ofNorway is not included.

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2.1.2 Modelling in Simpow

Simpow Introduction

The software used to model the system and test the new governor model in thisthesis work is Simpow. It is a software which can be used to perform digitalsimulation and electrical power system analysis and it is owned by Solvina.Power system models can be represented as static model and dynamic model,which are available for load-flow calculations, fault analysis and time-domainsimulations related to short-term dynamics both in fundamental frequency modeand momentaneous value mode. Besides, functions like linear analysis and singleline diagram can also be accessed in Simpow. The user can develop their ownprocesses and models in the Dynamic Simulation Language, DSL [12].

According to the standard of Simpow and the system dynamic of the new NordicTest system, each element will be represented both in static and dynamic modelin the following part.

Nodes representation

Nodes are an essential part of power system modelling. They are substations tolink up other elements in the model.

The static definitionThe static definition of a node in Simpow includes the voltage level of eachbus, such as 400 kV, 300 kV, 220 kV and 130 kV, which is summarized asTable 2.1 and Table 2.2 Then, the type of the node is defined either an ACnode or a DC node. In this model, all nodes are defined as three-phase ACnodes and their initial values for voltage magnitude in per unit of the basevoltage(Voltage Level) and phase angle in degrees will be clarified as well [12].Besides, the model has been divided into different areas and regions in orderto access the data of each area easily. Moreover, in order to insert a step uptransformer for each production bus, several generator buses have been definedfor each production bus to connect with step-up transformers. They are namedas BUSXGGXXX related to the bus that they are connected to. For example,BUS4GG011 represents the generator bus connected with Bus 4011.

For the power control in static data, each generator bus is required to be definedas slack bus, PV bus or PQ bus. Exactly one slack bus with known voltagemagnitude and phase is required to be defined in each AC network [12].If thebus is defined as PV bus, voltage magnitude and active power production arefixed and must be given. Reactive power limitation can be defined to controlthe voltage. If the bus is defined as PQ bus, the active and reactive productionare fixed and must be given.The voltage magnitude limitation can be defined tocontrol the reactive power [12].

The dynamic definitionIn this model, there is no specific dynamic definition for each node which hasbeen defined in static data. The only dynamic definition for nodes will bedefined when it connecting to its corresponding synchronous machine.

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Lines representation

Transmission lines are very crucial parts of power system modelling. Its repre-sentation are of great importance to be accurate. Power system’s admittanceand impedance matrices will be built by referring to the parameters definitionof transmission line. Power system analysis and fault analysis can also be per-formed based on the data [13]. Lines in the new Nordic power system modelin Simpow are described only by static data. First of all, the voltage level ofeach line should be defined in static data as summarized in Table 2.2. Thenaccording to the modelling type of lines, which are a line with zero impedance,an impedance, a π-link or a DC-line, will be defined to show its impedance andadmittance.

In this model, lines are defined with a π-link as shown in Figure 2.4. The mosttypical characteristic of this line model is dividing the total shunt admittanceinto two equal parts placed at the sending and receiving ends of the line in orderto consider the shunt effect. In term of the short and medium length lines, thisrepresentation is adopted for its good approximation [13]. The line’s impedanceis written as R + jX and admittance is represented as B. The conductance Gis omitted for the lines in Nordic 32 model.

R+jX

G+jB G+jB

Figure 2.4: π-Link Model of Transmission Lines.

Transformers representation

Transformers are used for adjusting the voltage in electrical power system, whichare available for transferring electrical energy among circuits in the power grid.In Simpow, the transformer is represented as two ideal two-windings trans-former, which is linear and perfectly coupled. Its data is all defined in staticpart including the participating buses, tap sides and reference winding.

As can be seen from Figure 2.5, two-windings transformer is modelled as anideal transformer with the complex ratio [12].

UN2

UN1= TAU · ejFI (2.1)

where TAU is the actual turns ratios in per unit of nominal voltage level. FIis the phase shift for delta-coupled transformers must be specified which side isthe tapped side [12]. Besides, in Simpow, the tap side base power is in MVAand nominal voltages on both sides are supposed to be specified. Moreover,

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1 2

Figure 2.5: Two-windings Transformer Model

short circuit resistance and reactance between two windings can be given aswell. As for the power control of transformer, there are 6 type of transformerdefinitions.• TAUFI: Turn ratio and phase shift angle are fixed and must be given.• TAUP : Turn ratio and active power through the transformer are fixed andmust be given.• UFI: Voltage on the reference node and phase shift angle are fixed and mustbe given.• UP : Voltage on the reference node and active power through the transformerare fixed and must be given.• QFI: Reactive power through the transformer and phase shift angle are fixedand must be given.• QP : Reactive power through the transformer and active power through thetransformer are fixed and must be given.

Synchronous Generators representation

The synchronous generator is of great importance for power system since itconverts mechanical power to electrical power and feeds it into the transmissionsystem. In power system analysis, there are several ways to modelling thesynchronous machine in order to simulate its dynamic responses of it. [8]. Figure2.6 shows a basic model for a generating unit which indicates the transitionbetween the electrical part (generator) and the mechanical part (turbine andshaft).

Figure 2.6: Illustration of a Generating Unit [1].

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The generator part can be divided into two parts including the stator partand the rotor part. The stator has an armature winding which comprise ofthree identical windings which are named as a, b, and c which corresponds thethree phases in electrical system. They are 120 electrical degrees apart fromeach other during symmetrical circumstances. The rotor has a field windingwhich holds a direct currents to generate a magnetic flux. As can be observedin Figure 2.7, in order to represent the generator model into mathematical axes,the stator has been described in three magnetic axes a, b, and c correspond-ing to the three phases, while the rotor has been modelled by direct axis andquadrature axis. The q axis is positioned 90 electrical degrees behind the daxis. Moreover, short-circuited damper windings are of great importance to beequipped to reduce the mechanical oscillations of the rotor [1].

if

cb’

a a’

c’ b

a

cb

d q

Figure 2.7: The representation of a synchronous machine.

According to the definition above, the generator model can be defined as follow-ing. Assuming a power system comprise of N generators, the dynamic relationsof the i− th generator can be expressed as [14]:

δi = 2πf(ωi − 1)

ωi = Pmi−Pei−Di(ωi−1)2Hi

T ′d0iE′qi = Efi − E′qi − (Xdi −X ′di)(1−

T ′′d0i

T ′d0i

X′′di

X′di

)idi

T ′q0iE′di = −E′di − (Xqi −X ′qi)(1−

T ′′q0i

T ′q0i

X′′qi

X′qi

)iqi

T ′′d0iE′′qi = −E′′qi+ E′qi − [(X ′di −X ′′di)−

T ′′d0i

T ′d0i

X′′di

X′di (Xdi−X ′di)]idiT ′′q0iE

′′di = −E′′di+ E′qi − [(X ′qi −X ′′qi)−

T ′′q0i

T ′q0i

X′′qi

X′qi (Xqi−X ′qi)]iqi

(2.2)

12

where, the δi and ωi are representing the rotor angle and rotor speed of generatori. In Equation 2.2, the generator model of sixth order is described. In Simpow,there are four different synchronous machine models in fundamental frequencymode as well as 2nd, 3rd, 5th, and 6th order. In Johansson [15], an overviewof models is given. The Pmi and Pei are the mechanical power and electricalpower for generator i. The Di and Hi are the damping ratio and inertia atgenerator i. Xdi,X

′di and X ′′di as well as Xqi,X

′qi and X ′′qi are synchronous

machine reactance, transient and sub-transient reactance at d axis and q axis.As for the time constants, T ′d0i,T

′′d0i and T ′q0i, T

′′q0i are representing open circuit

transient and sub-transient time constants on d and q axis respectively. Besides,the E′di,E

′′di and E′qi, E

′′qi are indicating the transient and sub-transient voltages

on generator i, while the Efi represents the excitation drived field voltage [14].

In Simpow, the synchronous generators are only defined in dynamic parts. Onlysome generator buses productions have been defined in the static file which areready to connect with generators in dynamic part. According the model ex-pression equation(2.2),in the dynamic file of Simpow, synchronous machines aremodelled as one field winding, one damper winding in d axis and two damperwindings in q axis with saturation [12]. Thus, a specific data group is going todescribe the synchronous generators with different parameters including reac-tances for different windings in steady-state and transient-state and some timeconstants of different windings, the transient and open circuit condition. Be-sides, some connection parameters to exciters and governors will also be definedin dynamic part to clarify for each generator. Several importance parametersare explained as in the followings [12]. All other parameters can be checked inthe appendix dynpow file.

• XD&XQ: Direct- and quadrature-axis synchronous reactance in per unit.• XDP&XQP : Direct- and quadrature-axis transient reactance in per unit.• XDB&XQB: Direct- and quadrature-axis sub-transient reactance in perunit.• TD0P&TQ0P : Direct- and quadrature-axis transient open-circuit time con-stant.• TD0B&TQ0B: Direct- and quadrature-axis sub-transient open-circuit timeconstant.• V REG: Identification number of voltage regulator.• TURB: Identification number of turbine.• TAB: Identification number of saturation table for the resulting air-gap flux.

Load representation

Load is an important part for power system operation since it affects the balancewith electrical power generation.The load models are sorted as two basic types:static models and dynamic models [8].

In the Simpow, static models are stated with its initial values for both activeand reactive power. They are expressed as exponential model to represent the

13

voltage dependent and frequency dependent load in dynamic model, which aredescribed as following .

PL = PEXP = PL0 · (UL

UL0)mp QL = PEXP = QL0 · (

UL

UL0)mq (2.3)

PL = PEXP = PL0 · (f

f0)np QL = PEXP = QL0 · (

f

f0)nq (2.4)

where, UL0 is the base voltage of the node, and PL0 and QL0 are active powerand reactive powers when the voltage is at UL0 (PL0 and QL0 are given by theuser in the load flow file). UL is the actual value of voltage and voltage exponentsmp and mq describe the characteristics of this model.f is the actual frequencyof the power grid, andf0 is the nominal value of the frequency of the Nordicpower system which is 50 Hz. The frequency exponents np and nq describe thecharacteristic of the load changing with frequency varied in the grid operation.

• With mp = mq = 0, the model describes constant power characteristic.• With mp = mq = 1, the model describes constant current characteristic.• With mp = mq = 2, the model describes constant impedance characteristic.

In Nordic 32 model in Simpow, all the loads are represented as constant powercharacteristic. All settings of mp and mq are set to value zero, and active andreactive power of each load are set to a constant [1]. However, in order to as-similate to the real system the loads are represented by frequency dependentload in this thesis work as well.

14

2.2 Phasor Measurement Units Data Analysis

2.2.1 Phasor Measurement Units in Power System

The Phasor Measurement Unit is a monitoring device to measure the electricaldata in system operation relying on a same time source for synchronization [16].

As can been observed in Figure 2.8, the Phasor Measurement Unit (PMU)installed in power system significantly improves the monitoring of system re-sponses and analysing system dynamics. It can collect a lot of AlternativeCurrent quantities in each installation in the power grid, including voltage mag-nitude and phase angle, active and reactive power, and system frequency. Allthese data can be obtained in real time operation [17]. After all the data havebeen collected to Phasor Data Concentrators (PDC) and sent to SupervisoryControl and Data Acquisition (SCADA) system for analysis and decision canbe made for actions in the operation of the power system [18].

Power station

Transformer

Transmisson

lines

Transmisson

substation

Distribution

Substation

Co

mm

un

icatio

n N

etwo

rk

Phasor measurement data

gathering

Synchronized

timing

Data Acquisition

and

Accumulation

Smart-Automatic

Analysis and

Determination

Control Center

Automatic Actions

Operator Actions

Figure 2.8: Phasor Measurement Units Operation in the power system.

During the operation of the power system, faults and disturbances are common.The real time data collection for these events are valuable for future researchon protection of the power system. Moreover, measurements data can be usedas power system model validation and optimization of the system control [19].Besides, some other applications can be achieved including improvement on stateestimation, Oscillation detection and control, voltage stability monitoring andcontrol and system restoration and events analysis [16].As introduced in Chapter2.1, the Nordic power system is the interconnection of Sweden, Norway, Finland

15

and eastern Denmark. PMUs have been installed into different locations in theNordic Power Grid, marked with red dots in Figure 2.9. In this thesis work,active power and frequency data from Messaure power station has been used.

CT 1

2C

T 11

2

FT 41

FT 61

FT 62

FT 63

CT 3

2

FT 43

FT 44

FT 45

FT 47

CT 2

1

FT 51

CT 1

1C

T 11

1

CT 2

2C

T 12

2

CT 3

1C

T 23

1

FT 42

FT 14

2

FT 50

FT 15

1

CT 7

1

CT 7

2

CT 7

3CT 7

4

AT 1

11

AT 1

21

AT 1

31

RT 1

31

RT 1

33

RT 1

32

AT 2

41

Luleå river

Gru

nd

forsen

Storn

orrfo

rs

Kilfo

rsen

HjältaSto

ckho

lm

Forsm

ark

Oskarh

amn

Go

theb

erg

Rin

ghals

Sou

th

Swed

en an

d

Sjaelland

Kem

inm

aa

Petäjäsko

ski

Pyh

änselkä

Therm

al P

ow

er p

lants

Finlan

dSw

eden

Bo

rgvik0

10

02

00

30

04

00

km

40

0 kV

30

0 kV

22

0 kV

Test System o

f No

rdic

Po

wer G

rid

13

0 kV

51

00

51

01

51035102

5301

5300

60

01

5501

5401

56

02 5402

56

01

5400

5500

56

03

56

00

6000

6100

51

04

51

05

60

02

52

01

52

02

52

03

52

04

62

00

No

rth p

art (Fin

nm

ark & Tro

ms)

Ofo

ten

Salten

Ro

ssåga

Sun

dalso

raM

öre o

g Ro

msd

al

Hassle O

sloA

kershu

s

Telemark

Ho

rdalan

d

Ro

galand

No

rway

Figure 2.9: Extended Nordic Test System

16

2.2.2 Full Scale Frequency Response Tests

In order to solve the problem of degrading of frequency quality in the Nordicpower system, more and more studies related to frequency control have beenperformed. Full scale frequency response tests in the Nordic synchronized areahave been applied in the Messaure hydropower station which is located nearLulea river [4] [3]. Sinusoidal power with different periods and magnitudes havebeen applied by three turbine governors in the power station. The magnitudeof the sinusoidal power oscillations were up to 70 MW and the periods were 15s, 25 s, 40 s, 60 s, 100 s, 150 s, and 250 s. The aim of the full scale test is todetect if rather small periodic power oscillations from load or generation cancreate the frequency oscillations in the power system. [4] It has been observedduring the test that there is a resonance peak in the frequency amplitude forperiod times around 60 s [3].

With the power oscillations injection to the Nordic Synchronized Network, thesystem has oscillation phenomenon indicated in many quantities which are ob-served by phasor measurement units distributed in the whole Nordic system.The data from different stations have been collected for analysis the systembehaviours after this experiment, especially the data from Messaure station. Inorder to validate the reduced Nordic power system model constructed in Chap-ter 1 in Simpow, the same sinusoidal test has been performed in computer modeas well. By comparing the system resonance point obtained from Simpow andfrom PMU data from Messaure Station, the system validation is verified.

The way to detect the dynamic responses from full scale tests is to investigatethe transfer function from the turbine governor with the input as frequencydeviation ∆f and the output as the active power. If the input is superimposedsinusoidal signal with certain frequencies, the output of the signal will also holdthe same frequencies. For each of the frequency, the output signal will havea specific amplitude and a phase shift corresponding to the input. Bode plotsbased on Fast Fourier Transformation(FFT) is a good tool to look into thesystem dynamic responses in frequency domain for a certain pair of input andoutput, which will be described in the following section.

2.2.3 Fourier Analysis — Bode Plots

Fourier transform is a technique to analyse aperiodic as well as periodic signals,it is a transform from time domain to frequency domain as shown in Figure2.10 [20].The Fourier transform is termed as frequency domain representationof the original signal. The Fourier Transform is defined as:

F (jω) = F [f(t)] =

∫ ∞0

f(t)e−jωtdt (2.5)

As the time domain signal, the frequency domain signal has a real part and

17

imaginary part. The absolute value of this complex number shows the powerof a certain frequency present in the original function, and the phase of thecomplex number represents the phase offset with the basic sinusoidal frequency.

Time

Fourier Transformation

Frequency

Figure 2.10: Fourier transformation mathematical process

Also bode plot is also a graph which can show the frequency response of asystem. It always comes to a combination of magnitude plot indicating theamplitude of the frequency response and a phase plot indicating the phase ofthe frequency response. The bode plot of a transfer function shows the gain andphase shift from input to output signal.

The magnitude axis of the Bode plot is usually expressed as decibels of power.However in this thesis work, the magnitude axis is expressed by the ratio ofthe absolute values of input and output signals in order to discover the relationbetween them.

A Bode phase plot is a graph of phase versus frequency, also plotted on a log-frequency axis, usually used in conjunction with the magnitude plot, to evaluatehow much a signal will be phase-shifted. For example a signal described by:A sin(ωt) may be attenuated but also phase-shifted. If the system attenuates

18

it by a factor x and phase shifts it by -Φ the signal out of the system will be(Ax ) sin(ωt − Φ). The phase shift Φ is generally a function of frequency. An

exmaple for a bode plots are shown in Figure 2.11.

−20

0

20

Mag

nitu

de (

abs

ratio

)

10−1

100

101

102

103

−135

−90

−45

0

45

Pha

se (

deg)

Bode Diagram

Frequency (rad/s)

Figure 2.11: The Bode plot example

By applying the two methods mentioned above, the phasor measurement datacollected at Messaure station can be analysed. Interests has been highly focusedon the relations between frequency and active power. Thus, the active powerand frequency is defined with fourier transformation:

Pf =

∞∑−∞

P · ejωt ff =

∞∑−∞

f · ejωt (2.6)

Where, ω is equal to 2π/T and T varies from 250 s, 150 s, 100 s, 60 s, 40 s, 25 sand 15 s. For each of the period time, the magnitude and phase difference canbe calculated as following:

| G(jω) |= | f(jω) || P (jω) |

(2.7)

φ(jω) = φf (jω)− φP (jω) (2.8)

Where, φ represents the phase angle for each signal in frequency domain. Thensubstitute period times into ω = 2π/T . Then a corresponding point for eachtime periods come up in both magnitude and phase plot. It is an approximate

19

way to get this system behaviour with only raw data, but it still provide uswith evidence to look into the system response when exposed to sinusoidaldisturbances. The result is achieved in Matlab by using FFT function.

20

2.3 Vattenfall New Hydro Turbine Governor ModelTest

In hydropower stations, the original source of electrical energy distributed inpractice is the potential energy stored in the water. In order to ensure a goodperformance of between electrical power and frequency in the real power grid,the turbine governor for the hydropower plant has been developed to balancethe power generation and consumption so as to maintain the grid frequency ina safe range. With the information from grid frequency, the turbine governorcontrol the gate opening of the valve to limit the flow of the water to control theoutput power.The original Simpow governor model is depicted in Figure 2.12.The generator speed is the input signal to the governor and the gate position isthe output signal from the governor. [8].

∑

∑

∑ 1

𝑇𝐹𝑠 + 1

1 + 𝑇𝑅𝑠

𝑟𝑇𝑅

1

𝑠

1

𝑇𝐺𝑠 + 1

𝑅

+

-

+

+

+

1.

-

+

𝜔

∆𝜔

𝑅𝐸𝐹

𝑉𝐸𝐿𝑀

−𝑉𝐸𝐿𝑀

𝑌

Sinusoidal

Power

Figure 2.12: Governor system with steady state gain

The Nordic power system has a lot of hydropower, and frequency control arepredominately performed by hydropower plants. Since Vattenfall is one of themain hydropower plants owners in Nordic power system, a high quality hydroturbine governor is of great importance to ensure the safe operation of thesystem and economic profits.

2.3.1 New Governor Model Introduction

A detailed hydro turbine governor model which involves both governing systemand plant dynamics has been shown in Figure 2.13. this controller structure isemployed in the hydropower plants belongs to Vattenfall VattenKraft AB [2].Two backlash blocks have been added to the new governor model to involvemore non-linearity into the model, which make it get closer to real model incurrent system. The signals definition is clarified in Table 2.3.

21

The controller part is usually described as a PI controller which can be modifiedmanually to get better response. In the governor part, servo is always modelledas a first order lag filter called Gs(s) [2].

Gs(s) =1

Tys+ 1e−sTdel (2.9)

Water dynamic of hydropower plant is of great necessity to consider when de-veloping a governing system. The water in the penstock is accelerated when theguide vane opening is altered. The relation between guide vane opening andpower output is concludes as a transfer function Gt(s) [2].

Gt(s) = K−Y0Tws+ 1

0.5Y0Tws+ 1(2.10)

𝑓𝑑𝑒𝑣.𝑟𝑒𝑓 u

𝑌 𝑢𝑝

𝑃𝑑𝑖𝑠𝑡 𝑓𝑑𝑖𝑠𝑡

y

Controller

+

+

-

+

-

+

+

+ +

+ +

+

n

+

∑ ∑ ∑ ∑ ∑

∑

1

𝑇𝑓𝑠 + 1

𝐾𝑝

𝐾𝐼𝑠

1

𝑇𝑦𝑠 + 1 𝐾

−𝑇𝑤𝑠 + 1

0.5𝑇𝑤𝑠 + 1

1

𝑀𝑠 + 𝐷

𝐸𝑝

Plant Grid

Figure 2.13: New governor model configuration connecting to the grid.

22

Signal Variable Name Units

fdev.ref Grid frequency deviation reference (=0) Hzy Grid frequency deviation from 50 Hz Hzu Plant control signal, guide vane opening dev. %Y Plant guide vane opening position dev. %up Plant output power deviation MWPdist Load disturbance (Positive if power is added) MWfdist Grid frequency disturbance Hz

n Measurement disturbance Hz

Table 2.3: Signals explanation in governor.

The governor can be expressed as a first order low-pass input signal filter withthe transfer function as [2]:

C(s) =Kps+Ki

(Tfs+ 1)(Tys2 + (EpKp + 1)s+ EpKi)(2.11)

In the previous research, this governor has been studied when connected to asimplified system which is only described by 1/(Ms+D), where M is the systeminertia and D is the frequency dependence of the load. In this thesis work, asystem model much closer to the real Nordic power system is developed to studythe governor performance in a large scale power system. Thus, a governor shouldbe developed in Simpow.

2.3.2 New Governor Model Developed in Simpow

Since the extended Nordic 32 model has been developed in Simpow, this targetVattenfall new governor model is supposed to be built in Simpow in order toevaluate its performance. The biggest challenge is that there is not a blockdiagram to represent the backlash in the model in Simpow.

Develop model with Hidraw

Hidraw is a powerful tool to develop schematic block diagrams into computerlanguages. System modelling and calculations are all based on Dynamic Simu-lation Language(DSL). Thus the governor is re-modelled in Simpow as shownin Figure 2.14.

23

Figure 2.14: Hydro power unit with new governor model in Simpow.

Backlash Block in Simpow

The backlash is a non-linear part in the new governor model. It is a commonphenomenon which appears in most mechanical and hydraulic system. The deadband existing in the mechanism leads to a hysteresis phenomenon between inputand the output position. It can affect the system performance [21] or introduceoscillations.

The backlash mechanism is illustrated as in Figure 2.15. The Body1 tries totransmit the motion to Body2 via a dead zone of magnitude D. The trans-mission will be correct when the two bodies are in contact, in this case therepositions are identical. Out of the contact, the transmission will be delayed bythe presence of the dead zone where the relation between the bodies positionswill describe an hysteresis cycle behaviour [21].

In a mathematical way, the backlash can be interpreted as following:xout = xin, in contact

xout = 0, otherwise(2.12)

where xin is the input signal while xout is the output signal. ”incontact” meansif | xout−xin |> D and xin(xin−xout) > 0. D is the dead band of the backlash.

Velocity Position

Body 1

Body 2

D/2

D

Figure 2.15: Backlash in Mechanism

24

D

D xin

xout

Figure 2.16: Mathematical expression

According to mathematical explanation above, the backlash function can bedeveloped in Simpow. Since DSL has its own limitation when solving the dif-ferential equations, it is not that easy to use the expressions above to describebacklash. Thus, an approximate approach has been set up using much easiermathematical expression.

xout = xin −D, if (xin − xout) > D

xout = xin +D, if (xin − xout) < −D

xout = xin, if −D < (xin − xout) < D

(2.13)

Based on this algorithm, the backlash block can be developed in Simpow. Asinusoidal test has been executed to verify whether it works. The result is shownin Figure 2.17.

25

0 1 2 3 4 5 60.95

1

1.05

1.1Backlash Effect

Input signalOutput signal

0 2 4 6 8 10 12 14 16 18 200.95

1

1.05

1.1

1.15

Input signalOutput signal

Figure 2.17: The test result of backlash function block in Simpow. A time delay onthe signals’ transfer illustrates the backlash effects in the real mechanical system.

2.3.3 Parameter Validation

In the previous research, the settings for the Vattenfall new governor are setbased on its system specification. In this thesis work, the Vattenfall new gov-ernor is tested in Reduced Nordic power system model. Thus, the governorsetting should be rescaled according to the new system. As for the frequencycontrol, the most important parameter is the droop of the governor. To get theright dynamic behaviour of the Reduced Nordic power system model and thereal system, the relation between FCR and inertia has to be the same in bothsystems. The inertia of the real system varies depending on the number andtype of units connected to the grid. At the time of the full scale test, the systeminertia was estimated to be approximately 270000 MW·s [2]. According to theSimpow model, the inertia of the test system is 90883.76 MW·s.

Thus, the scaling factor between test system and new system is:

ScalingFactor : K =HTestsystem

HRealsystem=

90883.76MW · s270000MW · s

' 1

3(2.14)

26

The power base in real system is 37650 MW(the total participated power inprimary frequency control) [2], while the power base in the new system modelis 12550 MW based on the scaling factor K.

The Nordic TSO:s purchase a reserve of 600 MW FCR-N, which operates in thenormal band +-0.1 Hz. This gives a system FCR gain of 6000 MW/Hz. Nor-wegian hydropower plants are in some cases required to deliver some additionalFCR-N, and if this is included in the calculation, the system FCR-N gain isapproximately 7350 MW/Hz [2]. In this thesis, the lower value (6000 MW/Hz)will be assumed to be the real system FCR-N gain. In conformity with thescaling factor, the droop for the test system becomes 2000 MW/Hz. Besides,according to the data in Simpow, the power participated in primary frequencycontrol is 14695 MW. When transform droop into per unit, it is expressed as :

EpTest =1

2000MW/Hz×50Hz14695MW

= 0.147 (2.15)

since the frequency base of the grid is 50 Hz. Then EpTest is rescaled as 0.147.

In a conclusion, since the EpTestis rescaled based on the scaling factor, all ofother parameters of controller are supposed to be changed with the new droopsetting. The per unit bases used in this chapter is summarized as Table 2.4 andall system and controller parameters are listed in Table 2.5.

Variable type Value UnitsPbase 12550 MWfbase 50 Hz

Table 2.4: Per unit bases.

System & Controllerparameters

Nominal values Units

Tw 1.5 sK 1 p.u.Ty 0.2 s

Kp(Sweden) 0.68 p.u.Kp(Norway) 1.7 p.u.Kp(Finland) 0.34 p.u.

Ki 0.1134 s−1

Ep 0.147 p.u.Tf 1 sTi 60 s

Table 2.5: System and controller parameters presented with nominal values.

27

2.4 Stability Analysis of Nordic Power Systemin Simpow

Power system has to cope with different instability during the system operation,such as electro-mechanical oscillation caused by interconnected synchronousgenerators swing against each other and grid frequency oscillation due to imbal-ance of consumption and generation. With the scale of power system becominglarger, more and more approaches have been performed to maintain the powersystem stability [22]. Sometimes these new approached are highly interactedwith each other. In this master thesis, the involvement of new governor isto improve the frequency quality. However, it should not affect the inter-areamodes avoiding the electro-mechanical oscillation. Thus, these two terms havebeen taken out to explain more as following.

2.4.1 Frequency stability analysis

Frequency stability is a term to indicate the grid frequency performance whensuffering from a big imbalance of power generation and consumption [22]. Thefrequency is reduced once a load increases or a generation is lost during opera-tion. The reason is that the reduction of the power leads to deceleration of therotors in the generators contributing to the decrease of the system frequency.

In practical power system operation, the power consumption is varying andsometimes there are larger disturbances, for example due to tripping of produc-tion units. Thereby a regulation of active power to maintain the grid frequencywithin safe range is required. According to the criterion from European Net-work of Transmission System Operators (ENSTO-E), the frequency control isexecuted in three steps as:

� Frequency Containment Reserves (FCR)

The FCR is used to maintain the grid frequency after the occurrence of adisturbances within an acceptable maximum Steady State Frequency De-viation(SSFD). The FCR has been divided into two operation conditionswhich are FCR for Normal operation (FCR-N) and FCR for Disturbances(FCR-D)

FCR-N is fully activated when the acceptable maximum SSFD reaching±0.1Hz. The trigger time for a fully application of FCR-N is from 120 sto 180 s. FCR-D is activated for maximum SSFD reaching −0.5Hz andit takes 30 s to finish the full activation.

� Frequency Restoration Reserves (FRR)

The FRR is employed to restore the grid frequency back to the nominalvalue and replace the FCR. The automatic FRR takes 2 minutes to getfully activated while the manual way takes 15 minutes.

28

� Replacement Reserves (RR)

The RR means that a required level of operating reserves should be re-stored and to be well prepared for further frequency instability. The acti-vation time varies from 15 minutes up to hours [23].

Primary Frequency control

The primary control FCR-N is the focus of this thesis work. A permanentfrequency droop is applied in order to share the control of all participated gen-erators involved in FCR.

As introduced in last subsection, the governor controls the gate in order toachieve a desired power output. The governor output signal is the sum of theset-point of the unit, which is controlled manually and the FCR-N contribution.

The speed droop is termed as the percentage change in frequency required tomove the gate of guide vane from fully closed to fully opened.

Frequency Responses

There remains three stages after the generator is tripped. In the first few sec-onds, the frequency drops according to how big the system inertia is. Thenrotors start swinging in the generators. In the next several seconds, the pri-mary control which is controlled by turbine governor takes the responsibility torecover the frequency back to a value. Thus, the frequency response in timedomain can illustrate the performance of new governor.

29

2.4.2 Small-signal stability Analysis

Modal Analysis

In general, the multi-machine power system is a typical non-linear system whichcan be described by the following Differential-Algebraic-Equations.

x = f(x, y, u)

0 = g(x, y, u) (2.16)

In order to identify the oscillation modes of a multi-machine power system,linearising the dynamic of the power system based on modal analysis is of greatimportance. After the linearisation, the system which applies PSS and FACTSdevices can be used by

∆x = A∆x+B∆u

∆y = C∆x+D∆u (2.17)

Where, x is a vector of order nx×1 representing the state variables in the system.Y is a vector of order m×1 representing the outputs or measured variables inthe system. U is a vector of order r×1 representing the system inputs or controlvariables. Moreover, A is matrix defined as the state matrix of order nx×nx. Bis a matrix defined as the input matrix of order nx×r. C is a matrix defined asthe output of order m×nx. D is a feed forward matrix of order m×r.

The eigenvalues of A matrix are termed as a series of solutions λ = λ1 · · ·λnx

which has the size of nx. These solutions satisfy the following equation:

det(A− λ1) = 0 (2.18)

The eigenvalues of the system could be real or complex. It is convenient toassign each eigenvalue λi to each mode which can describe the system. A realeigenvalue corresponds to a non-oscillatory mode in the system. A negativereal eigenvalue corresponds to a decaying mode while a positive real eigenvaluemonotonic instability.

If matrix A is real, the complex eigenvalues of the system always occur inconjugate pairs. Each pairs represents to an oscillatory mode and expressedby (for the i-th mode):

λi = σi ± jωpi (2.19)

The real part of the eigenvalue gives the damping of the i-th mode. An eigen-value with a negative real part represents a damped oscillatory mode. Howevera positive σ represents an oscillatory instability. The imaginary component ωpi

gives the oscillation frequency of the i-th mode, and is expressed by:

fpi =ωpi

2π(2.20)

The damping ratio of the i-th mode is given by:

ζi =−σi

|σi ± jωpi|(2.21)

The damping ratio determines the decay rate of the oscillation amplitude.

30

Inter-area Modes for Nordic Power System

Based on the modal analysis performed above, the independent modes can beobserved and the interaction of generators in the power system can be studied[12]. One important phenomenon is inter-area oscillations. There are certainmodes where groups of generators in different areas of the power grid swingingagainst with each other which gives rise to undesired active power flow betweenareas [24]. In order to restrain the negative effects of the electro-mechanicaloscillation, power system stabilizer has been applied to the system to improvethe damping. Meanwhile, some other controllers, for example, the hydro turbinegovernor, when introduced into the power system, might affect the damping ofthe inter-area modes. The impact of governor tuning is the damping of theinter-area modes is investigated through linear analysis in Simpow. Each pairof eigenvalues stands for an oscillatory mode and inter-area modes are mainlyconcentrating on the frequency range from 0.1 to 0.8 Hz [25].

In Nordic power system, it has been observed that several inter-area modes areexisting. A 0.33 Hz mode has been discovered between Finland and South ofNorway or sometimes it can be witnessed between southern Norway and Sweden.The poor damping of this mode results in the limitations of power flow on thetie line. Besides, a 0.48 Hz mode has been found between South of Norway andSweden or Denmark [19]. The new Vattenfall governor model’s impact on thesemodes will be studied in the following part.

2.4.3 Analysis method in Simpow

For the frequency stability analysis, since all variables in Simpow are definedin per unit, the frequency of the power grid has the same characteristic withthe rotor speed. The frequency in the network is a measure for the rotationspeed of the synchronized generators. By increasing the total demand, thesystem frequency will decrease and by decreasing the system demand, the systemfrequency will increase. Thus, the rotor speed in per unit is observed when asmall disturbance happened in the system to test the governor performance.

As for the small signal stability analysis, the modal analysis can be performedin Simpow so as to get the eigenvalues list. The inside functions contained inmodal analysis in Simpow is strong enough to take a deep look into even thegovernor participation for a specific mode and much more functions.

31

Chapter 3

Simulation and Results

The simulation procedures and results are summarized in the following chapter.Firstly, the extended model of Nordic power system has been developed in Sim-pow. With the comparison of the power flow results from the PSS/E model fromSvenska Kraftnat, the system model in Simpow is verified. System data andpower flow results are tabulated in Appendix A. Secondly, with the help of theTSO(Transmission System Operator), the PMU data when applying sinusoidaltest in Messaure station as mentioned in Chapter 2 has been collected. The sys-tem response in Simpow is compared to the result from PMU data to confirmthe system model further. Thirdly, the new governor parameters suggested bySaarinen [5] are tested and compared to the standard parameter setting (EP0)and to the performance of the old Simpow governor model. A sensitivity studyis also carried out, where the impact of different parameters on the performanceis shown. Finally, the impact on the inter-area modes by the new governorparameters is studied by eigenvalue analysis.

3.1 Model Comparison with PSS/E

According to the Nordic system model in the PSS/E from Svenska Kraftnat,a new model with Norwegian part extended as well as step-up transformersequipped with generator buses has been developed in Simpow. The new modelconsists of southern Norway, most of Sweden and a representative part of Fin-land. The result of a load flow calculation is presented in the single line diagramin Figure 3.1 and a table in Appendix A. Moreover, the comparison of the datafrom the PSS/E model with the data from Simpow are shown by the errors onactive and reactive productions in Figure 3.2 and 3.3. It can be seen that thereis only one bus for active power that has a significant difference than othersand three buses for reactive power. But they all keep the range not over ±10%,which can be treated as reasonable range. The reason for these differences arethe different bus definitions in two different software. First of all, in PSS/E,the swing bus is defined on the step-up transformer side inside the generatordefinition while the swing bus is defined on the generator side in Simpow. Thus,the swing bus voltage in Simpow must be adjusted to make the voltage afterthe transformer same as in the PSS/E. Thereby the reactive power has somefluctuations on some buses comparing to the PSS/E.

32

Figure 3.1: The Single Line Diagram of extended Nordic power system in Simpow.

33

-0.01

0

0.01

0.02

0.03

0.04

0.05

0 10 20 30 40

Erro

r(%

)

Bus

Active Power Production Errors on Each Bus

BUS 4011

(a) The errors on active production.

-8

-6

-4

-2

0

2

4

6

8

0 10 20 30 40

Err

or(

%)

Bus

Reactive Power Production Errors on

Each Bus

BUS 4041BUS 4031

BUS 5300

(b) The errors on reactive production.

Figure 3.2: A Comparison between the Nordic system models in PSS/E and inSimpow.

34

3.2 Model Validation with PMU Data

3.2.1 Validation with Old Governor Model in Simpow

For the sake of validating the system model further, the Messaure full scaletest is reproduced in the Simpow model. In order reduce the error during thesimulation, sinusoidal signals are injected in the governor of the generator on Bus4011 in the northern part of the model, which represents the Messaure stationin Nordic power grid. The sinusoidal signals are injected shown as Figure 3.3,while Figure 3.4 illustrates how it is developed in Simpow. Actually, as seenfrom the figure, the input is only a sinusoidal signals in per unit as a frequencyoscillation. However, this fake frequency to the governor can arise a sinusoidalpower injected to the system which reach the requirements of the real test inMessaure.

The governor model used in the Simpow has a simple structure. Several pa-rameters are defined as following. TR is the governor time constant.TF is thefilter time constant.TG is the servo time constant. besides, gate limits and gatevelocity limits are termed as GMAX , GMIN and ±V ELM [12]. The sinusoidalpower oscillations which are introduced in to the system are regarded as perunit value to meet the requirement of governor settings. Moreover, the PhasorMeasurement Unit in Messaure observes the power oscillations injected to thepower system as shown in Figure 3.5. The oscillation period times are 250 s,150 s, 100 s, 60 s, 40 s, 25 s, and 15 s. But in Figure 3.5, oscillation periodtimes shows only 100 s, 25 s and 15 s as an example.

∑

∑

∑ 1

𝑇𝐹𝑠 + 1

1 + 𝑇𝑅𝑠

𝑟𝑇𝑅

1

𝑠

1

𝑇𝐺𝑠 + 1

𝑅

+

-

+

+

+

1.

-

+

𝜔

∆𝜔

𝑅𝐸𝐹

𝑉𝐸𝐿𝑀

−𝑉𝐸𝐿𝑀

𝑌

Sinusoidal

Power

Figure 3.3: Old Governor model in Simpow with sinusoidal signals introduced to thesystem. The sinusoidal oscillation of power can arise the frequency oscillation.

35

Figure 3.4: The sinusoidal signals injection to old governor model in Simpow.

13:20 13:30 13:40 13:50300

350

400

450

500Power Oscillations in Messaure Station

Time [18−Mar−2014]

Figure 3.5: Example of the measured power oscillations in Messaure during thefullscale test.

36

Based on the fast fourier analysis and bode plots in Matlab, the data comingfrom Full Scale Frequency Response Test is analysed. The test is executed bothon day and night. The result is shown in Figure 3.6.

10−3

10−2

10−1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Frequency (Hz)

Gai

n (p

.u./p

.u.)

Day Test

Night Test

Figure 3.6: The system response in real test in Messaure. The system resonancepoint are observed as 60 s.

As can be seen from Figure 3.6, the points are representing the gain for each ofoscillation period times from 15 s to 250 s. The upper one are the gains at eachof period times. It is found that the resonance peak point are pointing at 60s which is well-matched with the known data [4]. Thus, it can be verified thatthe analysis tool for the system response is reliable.

As mentioned above, the extended system model is supposed to be tested in anidentical way. By the same mean of calculation, the model system response isshown in Figure 3.7 with the comparison with the Messaure one.

37

10−3

10−2

10−1

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Frequency (Hz)

Gai

n (p

.u./p

.u.)

Real test in MessaureOld governor model in Simpow

Figure 3.7: The comparison of the Messaure test result between real test and Simpowtest. The result are from practical one and simulated system, which explains thedifferent system response time.

As shown above, the blue curve represents the result from real test in Messaureholding a 60 s resonance peak, while the green curve illustrates the identicaltest performed in Simpow with a 40 s resonance peak. For the short timeperiods in the Simpow test, for example 15 s to 60 s, it holds a higher valuesince the Simpow has more sensitivity on the disturbance within this periodrange. However, since the governor type and settings are different and real powersystem has a higher level complexity, the system model in Simpow has a moresensitive response than real system when subject to a disturbance. Therefore itis of great necessity to involve new governor model into the test system to makethe system closer to the real one.

3.2.2 Validation with New Governor Model in Simpow

In order to validate the test system with new governor model, the same test issupposed to be performed again with the same approach as in Messaure test.However, it is also necessary to detect the effects of new governor model on theFull Scale test. It is important to observe if the resonance peak point of system ismoved with the new governor model applied and the with the controller settingrescaled. Besides, the backlash is considered in the system with 0.05% to get amuch accurate model for governor part. The sinusoidal signals has been injectedas shown in Figure 3.8. Sinusoidal signals have been applied with 250 s, 150 s,100 s,60 s,40 s and 25 s,15 s period time.

38

Previous research has suggested three different governor settings (C1, C2 andC3) which satisfies different goals on performance and disturbance sensitivity.These new settings have been tested in Simpow. The Ep0 setting is the nominalvalue which is currently used by Vattenfall. Each of new setting is shown inthe Table 3.1 [5] and the tuning goals are presented in Table 3.2. It is of greatimportance to detect if new settings can have a better response to system.The results are viewed in Figure 3.9 and Figure 3.10 with comparison with oldgovernor model and different settings performance.

∑ ∑ ∑

∑

1

𝑇𝑓𝑠 + 1

𝐾𝑝

𝐾𝐼𝑠

1

𝑇𝑦𝑠 + 1 𝐾

−𝑇𝑤𝑠 + 1

0.5𝑇𝑤𝑠 + 1

𝑓𝑑𝑒𝑣.𝑟𝑒𝑓

𝐸𝑝

u 𝑌 𝑢𝑝

𝑓𝑑𝑖𝑠𝑡

Controller

+

+

-

+

+

+

+

Plant

𝑓

-

𝑛 Sinusoidal

Frequency

Figure 3.8: The comparison of system response when perform the same disturbancein new governors.

Group Setting (p.u.) Kp KI Tf [s] Ep

Ep0 1.0 1/6 1.0 0.1C1 2.0 0.1786 0.83 0.1C2 2.6 0.244 0.1 0.1C3 2.7 0.0672 1.5 0.12

Table 3.1: Different groups of settings

Group Setting (p.u.) Goals

Ep0 The nominal setting of governorC1 Fulfil all optimization goals and constraintsC2 Allows more disturbance sensitivityC3 Allows more high steady state grid frequency deviation

Table 3.2: The goals for different groups of settings according to previous research.

39

10−3

10−2

10−1

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Frequency (Hz)

Gai

n (p

.u./p

.u.)

Real test in Messaure

Old governor model in Simpow

New governor model in Simpow with Ep0

Figure 3.9: Comparison of the system response measured during the full-scale test(blue), the response of the old governor model in Simpow (black) and the response ofthe new governor model with the Ep0 setting (red).

10−3

10−2

10−1

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Frequency (Hz)

Gai

n (p

.u./p

.u.)

Real Test in Messaure

New governor model in Simpow with Ep0

New governor model in Simpow with C1New governor model in Simpow with C2

New governor model in Simpow with C3

Figure 3.10: The comparison of system response when perform the same disturbancein new governors. The responses are from PMU data from real test in Messaure andsimulated model with new governor model equipped with new suggested settings.

Observing from Figure 3.9, the system resonance peak point is moved back

40

to 60 s since a more complicated new governor model which includes non-linearparts is involved in the system. The system response is much closer to the realone when owning the new governor model equipped in the system. However, thegains for each testing period points are higher than the given one. The new set-tings C1, C2 and C3 reduces the peak of the gain curve. This corresponds wellwith the results from the lumped model that was used in previous research [5].

Although the new governor model makes the model response more realistic inthe way that the system resonance peak occurs at the rigth frequency, there isa large discrepancy in the gain. There is a lot of uncertainty in many of theparameter values in the model. There is no detailed information available aboutthe water time constants or backlash of the units, and previous studies haveshown that the governor settings differ between different hydropower ownersand between the Nordic countries. There is also a great uncertainty in theamount of frequency dependent and voltage dependent load in the system.

As a first attempt to ”tune” the Simpow model parameters to make the modelfit the measurements, the loads of the system are made frequency dependent,by setting the frequency exponent NP=2. Secondly, the amount of FCR-N inthe system is decreased to achieve a more realistic balance between inertia andFCR in the model, as described in Chapter 2.3, and the governor parametersare rescaled accordingly. The rescaled parameters are shown in Table 3.3. Thesystem responses for rescaled setting are shown in Figure 3.11 and Figure 3.12.

Group Setting (p.u.) Kp KI Tf [s] Ep

Ep0 0.68 0.1134 1.0 0.147C1 1.36 0.1214 0.83 0.147C2 1.769 0.166 0.1 0.147C3 1.53 0.0457 1.5 0.1764

Table 3.3: Different groups of rescaled settings

41

10−3

10−2

10−1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Frequency (Hz)

Gai

n (p

.u./p

.u.)

Real test in Messaure

Old governor model in Simpow

New governor model in Simpow with Ep0with rescaled parametersand frequency dependent loads

Figure 3.11: The comparison of system response when perform the same disturbancein new governors. The responses are from PMU data from real test in Messaure,simulated model with old governors equipped and simulated model with new governormodel equipped with rescaled settings.

10−3

10−2

10−1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Frequency (Hz)

Gai

n (p

.u./p

.u.)

Real Test in MessaureLinnmodel in Simpow with Ep0with rescaled parametersand frequency dependent loads

Linnmodel in Simpow with C1with rescaled parameters and frequency dependent loadsLinnmodel in Simpow with C2with rescaled parameters and frequency dependent loadsLinnmodel in Simpow with C3with rescaled parameters and frequency dependent loads

Figure 3.12: The comparison of system response when perform the same disturbancein new governors. The responses are from PMU data from real test in Messaureand simulated model with new governor model equipped with new rescaled suggestedsettings.

42

In Figure 3.11 and Figure 3.12, with the rescaled parameters of governor model,the gain for each period point declines and is closer to real system behaviour,although the system resonance point is moved to 40 s. It can be concluded thatthe new settings decrease the gain resonance peak, which means that they aremore efficient in suppressing disturbances. The suppression of disturbances isimportant to the safe operation of the grid.

3.3 The New Governor Model Test results

In this section, the new governor’s performance is tested by introducing a smalldisturbance into the power system. In this thesis, one of the generator has beentripped on Bus 4063. The frequency response with different settings and differ-ent system dynamic included, such as frequency dependent load and backlash.

3.3.1 Frequency Response Comparisons

Comparison with Different New Rescaled Settings without FrequencyDependent Loads

In this part, the frequency responses when a generator is suddenly disconnectedfrom the system are illustrated. Different rescaled settings are tested and theresult is shown in 3.13. The frequency dependent loads are not included.

0 50 100 150 200 250 30000.5

149.8

49.85

49.9

49.95

50

50.05

Time (s)

Fre

quen

cy (

Hz)

New governor model with Ep0New governor model with C1New governor model with C2New governor model with C3

Figure 3.13: The Comparison of frequency response with different new rescaledgovernor settings involved and without frequency dependent load after a generatortripped. The overshot value and recovery time are chosen to evaluate the performance.

43

It can be observed that the new settings results have smaller overshot, smalleroscillation and faster recovery time than the nominal setting Ep0.

Comparison with Different New Rescaled Settings with FrequencyDependent Loads

Since the frequency dependent load indicates the real loads behaviour accordingto the frequency variation of the power grid, it is practical to consider it intothe test system.

0 50 100 150 200 250 30000.5

149.9

49.92

49.94

49.96

49.98

50

50.02

Time (s)

Fre

quen

cy (

Hz)

New governor model with Ep0with rescaled parametersand frequency dependent loads

New governor model with C1and frequency dependent loads

New governor model with C2and frequency dependent loads

New governor model with C3 and frequency dependent loads

Figure 3.14: The Comparison of frequency response with different new rescaled gov-ernor settings involved and with frequency dependent load after a generator tripped.The overshot value and recovery time are chosen to evaluate the performance.

As shown in Figure 3.14, the system responses show better results for newsettings from C1 to C3 comparing to Ep0 setting. The total frequency variationis decreased and oscillation is improved as well due to the frequency dependentloads. The loads with frequency components considered regulate it self withthe frequency varied after the disturbance. It makes the difference betweentotal generation and total loads in the test system smaller and keeps the systembalance better.

44

3.3.2 Comparison with Backlash

0 50 100 150 200 250 30000.5

1

49.7

49.75

49.8

49.85

49.9

49.95

50

50.05

Time (s)

Fre

quen

cy (

Hz)

Backlash 0.025%Backlash 0.05%Backlash 0.1%Backlash 0.5%

Figure 3.15: The impact of Backlash for governor performance.

As mentioned in Chapter 2.3, backlash exists in the turbine part as well asthe governor parts. According to the previous research, the backlash is onlyconsidered in the turbine part with the value varied from ±0.025% to ±0.5%.As shown in Figure 3.15, with the value of backlash increasing, the frequencyhas worse responses with bigger overshot. However, it can be observed that thesystem from ±0.1% to ±0.5% existing a big difference on the overshot, whilefrom ±0.025% to ±0.1% varies not much. It can be proposed there should belimits there to control the backlash not affecting the system a lot, which can beregarded as the protection limits on the turbine part.

45

3.4 Effects on Inter-area modes

As introduced in Chapter 2.4, the inter-area modes have been observed in Nordicpower system in order to ensure the small-signal stability of the power system.When testing the new governor model settings, the inter-area modes are notsupposed to be affected. The comparison for new settings and nominal settingswhich is used currently is shown in Figure 3.16. The horizontal axis representsthe frequency and vertical axis represents the damping of the modes.

−0.7 −0.6 −0.5 −0.4 −0.3 −0.2 −0.1 0

0.4

0.5

0.6

0.7

0.8

0.9

1

New Governor Ep0 Setting

New Governor C1 Setting

New Governor C2 Setting

New Governor C3 Setting

Figure 3.16: The impact of new governor settings on inter-area modes. Severalgroups of inter-area modes are observed with frequencies are f = 0.33Hz, 0.57Hz,0.60Hz, 0.78Hz, 0.80Hz.

There are five modes which have been observed in Simpow simulation as shownin Figure 3.16. Their corresponding frequencies are 0.33 Hz, 0.57 Hz, 0.60 Hz,0.78 Hz and 0.80 Hz. It can be seen from the figure that the inter-area modesare not affected with different controller settings changed. Therefore, the newgovernor settings are able to maintain the inter-area modes and improve thefrequency response.

46

Chapter 4

Discussions and Conclusions

4.1 Nordic power system development

Comparing to the old Nordic 32 model, the extend Nordic power system modelin Simpow is improved. The extension on the southern of Norway and Finlandpart includes a more detailed system. It has involved more non-linear parts intothe system and adding more inter-connections into the system, which is benefitfor further investigation on system behaviour.

Comparing to the PSS/E model [11], the step-up transformer is added on eachgenerator in Simpow in order to consider the reactive power consumed duringthe system operation in order to adjust the limits of reactive power of generatorsto make the system more accurate and closer to the real one.

4.2 New Governor Model Performance

The reduced Nordic power system model constructed in Simpow is partiallyvalidated with the PMU data from Nordic TSO since the 60 s resonance peakpoint is not achieved in the Simpow model. It is performed by applying thesame full scale test into the Simpow model and the parameters of the controllerare rescaled according to the inertias of real system and test system. In a word,model validation with new governor model is partially finished. The modelbehaves qualitatively as the real power system when subjects to a sinusoidaldisturbance.

Although it has a difference on the system resonance peak points, it shows goodresults on scaling down the gains for the injected oscillations when applying thenew governor setting of the controller. It indicates that the new settings areable reduce the oscillation when system subjects to disturbances and decreasethe sensitivity to the disturbance. The peak points can be moved by varying thecontroller parameters as well as the droop of the controller related to the howmuch primary frequency control is involved. Besides, the frequency responsesof new governor settings when a generator lost in the system have better resultsthan nominal value which is applied in the real system. Therefore, parameter

47

tuning of the governors seems to be a useful tool to affect the frequency stabilityin the range around 1/60 Hz.

For the electro-mechanical oscillation, parameters can be changed within certainlimits without negative impacts on inter-area modes.

The backlash existing in the governor introduces non-linear component into thesystem. It has more negative impact on the frequency response with increasingthe value of it. When controlling the backlash within a limited range, it will notaffect system response a lot. However, it is good to involve it into the powersystem model when performing the simulation so as to assimilate it to real one.

48

Chapter 5

Future Work

Model Modification

The model of Nordic power system is supposed to be extended more with north-ern part of Norway included. More inter-connections among Nordic countriesare good to be considered into the model in order to investigate the overallsystem behaviours. The parameters for the governor ought to be modified ac-cording to new system, and the validation with the PMU data from the fullscale test should be performed again to verify the new system.

Backlash Safety Range

The backlash safety range for huge impacts on system responses is supposed tobe discovered. It is a good reference for the turbine preventive maintenance.

Automatically Parameter Shift in Governor

In the system operation, the frequency deviation varies a lot with the fluctuationof production and consumption. It is good to have an automatically parametershift device in the governor. It can be used for detecting the amplitude of thefrequency deviation so as to shift governor settings with strong or soft control. Itwill make the system more intelligent during the daily operation. However, theoscillations generated when shifting the parameters should be carefully avoidedto keep the system stable.

49

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51

52

Appendix A

Tables

A.0.1 System Data of Extended Nordic 32 Model in PSS/E.

Bus Number Bus Name Base kV Area Num Voltage (pu) Angle (deg)

41 BUS41 130 8 0,9855 -47,69

42 BUS42 130 8 0,982 -46,68

43 BUS43 130 8 0,9747 -52,99

46 BUS46 130 8 0,9718 -53,03

47 BUS47 130 8 1,0012 -46,39

51 BUS51 130 8 1,0008 -55,04

61 BUS61 130 8 0,9641 -53,16

62 BUS62 130 8 0,9818 -49,03

63 BUS63 130 8 0,9511 -51,62

1011 BUS1011 130 1 1,1226 1,06

1012 BUS1012 130 1 1,13 3,51

1013 BUS1013 130 1 1,145 7,86

1014 BUS1014 130 1 1,16 10,26

1021 BUS1021 130 2 1,1 11,33

1022 BUS1022 130 2 1,0681 -9,21

1041 BUS1041 130 4 0,9708 -67,9

1042 BUS1042 130 4 1 -50,83

1043 BUS1043 130 4 0,9999 -62,54

1044 BUS1044 130 4 0,9909 -54,05

1045 BUS1045 130 4 0,9975 -57,36

2031 BUS2031 220 3 1,0518 -24,95

2032 BUS2032 220 3 1,1 -12,1

4011 BUS4011 400 1 1,01 0

4012 BUS4012 400 1 1,01 1,44

4021 BUS4021 400 2 1,0234 -24,28

4022 BUS4022 400 2 1,0002 -11,46

4031 BUS4031 400 3 1,01 -28,14

4032 BUS4032 400 3 1,0195 -32,51

4041 BUS4041 400 8 1 -44,55

4042 BUS4042 400 8 1 -43,65

4043 BUS4043 400 8 0,9939 -49,26

4044 BUS4044 400 8 0,9953 -50,79

4045 BUS4045 400 5 1,0031 -54,6

4046 BUS4046 400 8 0,9944 -48,88

4047 BUS4047 400 8 1,02 -44,14

4051 BUS4051 400 5 1,02 -51,9

4061 BUS4061 400 6 0,9815 -49,22

4062 BUS4062 400 6 1 -45,53

4063 BUS4063 400 6 0,98 -47,99

5100 300 21 1 -50,26

5101 NOR_1 400 21 1,0028 -49,37

5102 400 21 0,9998 -48,52

5103 400 21 0,9986 -47,73

5300 300 21 1 -36,6

5301 400 21 1,0001 -41,84

5400 300 21 1 -48,52

53

5401 400 21 0,9933 -50,82

5402 400 21 1,0002 -48,75

5500 300 21 1 -50,95

5501 400 21 1,002 -50,67

5600 300 21 1 -57,67

5601 400 21 0,9997 -57,4

5602 400 21 0,9328 -60,61

5603 300 21 0,9267 -61,94

6000 300 21 1 -49,38

6001 400 21 0,9994 -49,92

6100 300 21 1 -53,04

7100 BUS4071 400 7 1,01 0,68

7101 400 1 1,01 0,62

7102 400 1 1,0191 6,38

7200 BUS4072 400 7 1,0206 10,14

7201 400 1 1,01 12,31

7203 400 1 1,01 15,4

7204 400 1 1,01 11,02

7205 400 1 1,01 12,12

8001 LIT 400 1 1 -43

8002 LIT2 400 1 1 -43

8500 400 1 1,02 -48,59

54

A.0.2 Power Flow Result Comparison of Simpow and PSS/E.

Name DP(S-P) DQ(S-P) Base ErrorP(%) ErrorQ(%)

PROD BUS1GG012 0,8325 0,32 800 0,001040625 0,04

PROD BUS1GG013 0,6243 -1,5063 600 0,0010405 -0,25105

PROD BUS1GG014 -0,3553 0,0928 700 -0,000507571 0,013257

PROD BUS1GG021 0,8325 0,1727 600 0,0013875 0,028783

PROD BUS1GG022 -0,5838 6,859 250 -0,0023352 2,7436

PROD BUS1GG042 -0,2508 0,8973 400 -0,000627 0,224325

PROD BUS1GG043 -0,6254 4,043 200 -0,003127 2,0215

PROD BUS2GG032 -0,9391 -0,1777 850 -0,001104824 -0,02091

PROD BUS4GG011 44,6039 15,6545 1000 0,0446039 1,56545

PROD BUS4GG012 -0,9594 -0,2859 800 -0,00119925 -0,03574

PROD BUS4GG021 -0,9797 9,5891 300 -0,003265667 3,196367

PROD BUS4GG031 -0,8548 20,8637 350 -0,002442286 5,961057

PROD BUS4GG041 -1,2024E-08 21,7903 300 -4,00783E-11 7,263433

PROD BUS4GG042 -0,1889 12,9112 700 -0,000269857 1,844457

PROD BUS4GG4A7 -0,8762 1,9865 600 -0,001460333 0,331083

PROD BUS4GG4B7 -0,8762 1,9865 600 -0,001460333 0,331083

PROD BUS4GG5A1 -0,1675 9,3772 700 -0,000239286 1,3396

PROD BUS4GG5B1 -0,7513 -6,2292 700 -0,001073286 -0,88989

PROD BUS4GG6A2 -0,397 0,6841 600 -0,000661667 0,114017

PROD BUS4GG6B2 -0,397 0,6841 600 -0,000661667 0,114017

PROD BUS4GG6B3 0 -0,3155 150 0 -0,21033

PROD BUS5GG100 -0,0002 -5,7197 600 -3,33333E-07 -0,95328

PROD BUS5GG300 1E-04 -56,3674 916 1,0917E-07 -6,15365

PROD BUS5GG400 -0,0005 -11,9567 633 -7,89889E-07 -1,88889

PROD BUS5GG500 -0,0003 6,0646 333 -9,00901E-07 1,821201

PROD BUS5GG600 0,0005 26,4275 950 5,26316E-07 2,781842

PROD BUS6GG000 -0,0003 14,56238 466 -6,43777E-07 3,124974

PROD BUS6GG100 0,0002 10,732 966 2,07039E-07 1,110973

PROD BUS7GG100 0,0002 -0,658087 333 6,00601E-07 -0,19762

PROD BUS7GG101 0,0002 -0,0004 333 6,00601E-07 -0,00012

PROD BUS7GG201 -0,0003 0,0042 433 -6,92841E-07 0,00097

PROD BUS7GG203 0 -0,0002 866 0 -2,3E-05

PROD BUS7GG204 -0,0002 -0,001 475 -4,21053E-07 -0,00021

PROD BUS7GG205 -0,0002 -0,0035 475 -4,21053E-07 -0,00074

PROD BUS8GG500 0 0,0495 666 0 0,007432

2,3580169

55

Appendix B

Scripts

B.0.3 Matlab-Fast Fourier Analysis

clear allclose all hidden

Ts = 0.1;Pbase = 14695;% Pbase = 1000;fbase = 1;Data = load('AllLinnGov.mat');Check = load('CheckPoints.mat');format longperiodtid = [250;150;100;60;40;25;15];%% Checkp1 = [4806 4438 2988 1807 1218 768 637];% Checkp2 = [39797 22278 14987 12607 6018 3777 3946];% % Checkf1 = [4806 2728 2988 1807 1218 768 967];% % Checkf2 = [39797 22257 14987 12607 6018 3777 3946];% Checkf1 = [4437 2728 2858 1797 1288 1578 967];% Checkf2 = [39437 22257 14857 12597 5697 3837 3946];

% Ts = periodtid;% Tst = Ts';Name = {'Test250','Test150','Test100','Test60','Test40','Test25','Test15'};amp = zeros(length(Name),1);phase = zeros(length(Name),1);%%for j = 1:length(Name)

format long% Data = load(filename{1});

Test = Data.(Name{1,j});% ptemp = Test(2000:end,2);% ftemp = Test(2000:end,3);% % ptemp = Test(Checkp1(j):Checkp2(j),2);% % ftemp = Test(Checkf1(j):Checkf2(j),3);

ptemp = Test(Check.PL(j):Check.PR(j),2);ftemp = Test(Check.FL(j):Check.FR(j),3);

pnew = (ptemp-mean(ptemp))/Pbase;fnew = (ftemp-mean(ftemp))/fbase;

56

% figure(j)% plot(Test(2000:end,1),ptemp);% title('Power');% figure(j+7)% plot(Test(2000:end,3),ftemp);% title('Frequency');

% pnew = (ptemp-mean(ptemp))/Pbase;% fnew = (ftemp-mean(ftemp))/fbase;

% pnew = ptemp;% fnew = ftemp;L = length(pnew); %add some zero-paddingFs = 1/Ts;

NFFT = 2ˆnextpow2(L);

P = fft(pnew,NFFT);evalFreqs = Fs/2*linspace(0,1,NFFT/2+1);

F = fft(fnew,NFFT);

% figure(j),% plot(evalFreqs,2*abs(P(1:NFFT/2+1))),title('Power');% grid% xlabel('Frequency (Hz)'),ylabel('Magnitude')% axis([0 1 0 1])%% figure(j+7),% plot(evalFreqs,2*abs(F(1:NFFT/2+1))),title('Grid frequency')% axis([0 1 0 1])% grid% xlabel('Frequency (Hz)'),ylabel('Magnitude')

magP = 2.*abs(P(1:NFFT/2+1));magF = 2.*abs(F(1:NFFT/2+1));phP=angle(P(1:NFFT/2+1));phF=angle(F(1:NFFT/2+1));[ampP,fP] = max(magP);

amp(j) = magF(fP)./magP(fP);phase(j) = (phP(fP)-phF(fP))*180/pi;

% amp(j) = magP(fP)./magF(fP);% phase(j) = (phP(fP)-phF(fP))*180/pi;end

f=1./periodtid;[f,ind]=sort(f);f=f';amp=amp(ind)';phase=phase(ind)';

amparraySimLinnC3=amp;pharraySimLinnC3=phase;farraySimLinnC3=f;

%%

h=figure;

subplot(2,1,1),semilogx(farraySimLinnC3,amparraySimLinnC3,'*-b'),grid,

57

legend('day');xlabel('Frequency (Hz)'),ylabel('Gain (p.u./p.u.)')title('Test Result in BUS4GG011 with Linn Governors in all Nordic countries');subplot(2,1,2),semilogx(farraySimLinnC3,pharraySimLinnC3,'*-b'),gridxlabel('Frequency (Hz)'), ylabel('Phase (\circ)')

save('amparraySimLinnC3','amparraySimLinnC3');save('pharraySimLinnC3','pharraySimLinnC3');save('farraySimLinnC3','farraySimLinnC3');

58

TRITA EE 2015:93

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