Fast-response rotating brushless exciters for improved stability of synchronous generators

JONAS KRISTIANSEN NØLAND

UURIE 347-16LISSN 0349-8352

Division of ElectricityDepartment of Engineering SciencesLicentiate Thesis

Uppsala, 2016

Abstract The Norwegian Network Code FIKS from the Norwegian Transmission System Operator (TSO) Statnett, states that synchronous generators ≥ 25 MVA must have a static excitation system. It also includes requirements on the step time response and the available field winding ceiling voltage of the excitation system. An improved brushless excitation system is in operation in some pilot power plants. A rotating thyristor bridge is controlled via Bluetooth. The step time response is as fast as conventional static excitation systems. However, a ceiling voltage factor of 2 requires the thyristor bridge to operate at firing angles about 60 degrees. High torque pulsations, low power factor and low utilization of the exciter is the end result. New power electronic interfaces on the shaft results in a betterutilization of the designed exciter and improves the mechanical performance as well as the controllability of the generator field winding. Permanent magnet rotating exciters increase the field forcing strength of the synchronous generator, yielding improved transient stability (Fault Ride-Through req.). Brushless exciters also reduces regular maintenance of the generator. The thesis includes experiments on a state of the art synchronous generator test setup including constructed PM exciter and different power electronic solutions. Some investigations has been done on industrial power plants as well. Keywords: synchronous generators, permanent magnet machines, excitation systems, power electronic interfaces © Jonas Kristiansen Nøland 2016

To mymother

List of papers

This thesis is based on the following papers, which are referred to in the textby their Roman numerals.

I Nøland, J. K., Hjelmervik, K. B., Lundin, U., "Comparison ofThyristor-Controlled Rectification Topologies for a Six-Phase RotatingBrushless Permanent Magnet Exciter", IEEE Transactions on EnergyConversion, vol. 31, no. 1., March 2016.

II Nøland, J. K., Lundin, U., "Step time response evaluation of differentsynchronous generator excitation systems", 4th IEEE InternationalEnergy Conference (ENERGYCON’2016) in Leuven, Belgium, in April2016.

III Nøland, J. K., Evestedt, F., Perez-Loya, J. J., Abrahamsson, J.,Lundin, U., "Design and characterization of a rotating brushless PMexciter for a synchronous generator test setup", XXIIth InternationalConference on Electrical Machines (ICEM’2016) in Lausanne,Switzerland, in September 2016.

IV Nøland, J. K., Evestedt, F., Perez-Loya, J. J., Abrahamsson, J.,Lundin, U., "Evaluation of different power electronic interfaces forcontrol of a rotating brushless PM exciter", 42nd Annual Conference ofthe IEEE Industrial Electronics Society (IECON’2016) in Firenze,Italy, in October 2016.

Reprints were made with permission from the publishers.

Contents

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111.1 Project background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111.2 Outline of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2 Excitation systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.1 Excitation control system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.2 Open circuit characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.3 Ceiling voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.4 High initial response excitation system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.5 Different excitation systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.5.1 Static excitation systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.5.2 Rotating brushless excitation systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.6 Standards and technical requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.7 Implementation of modern power electronics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3 Analytical solutions of open-circuit dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.1 Terminal voltage buildup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.2 De-excitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243.3 Positive step response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.4 Negative step response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

4 Electromechanical modelling of synchronous generators . . . . . . . . . . . . . . . . . . . . . . 274.1 Equivalent circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274.2 Grid dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284.3 Mechanical dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294.4 Park transformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304.5 Steady state operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

5 Parameter exctraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325.1 Synchronous generator parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325.2 Field-wound exciter parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

6 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

8 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 448.1 Exciter armature winding design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 448.2 Power electronic interfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

8.3 Bang-bang excitation control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 458.4 Synchronous generator modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

9 Summary of papers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

10 Svensk sammanfattning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

11 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

List of symbols

Symbol Unit Descriptionf Hz Fundamental electrical frequnecyTU f

s Field voltage time constantα Firing delay angle of thyristor bridgeγ Ceiling voltage factorL f H Field winding self inductanceM f H Field winding mutual inductance to the statorR f Ω Field winding resistance (hot)U f V Rated steady state field voltageI f A Rated steady state field currentu f V Instantaneous field voltagei f A Instantaneous field currentT ′do s Field winding open circuit time constantT ′d s Field winding short circuit time constantTf s Field winding voltage buildup time constantT37% s Field winding de-excitiation time constantT+5% s Field winding positive step response timeT+5% s Field winding negative step response timeT ′′d s Subtransient short circuit time constant, d-axisT ′′do s Subtransient open circuit time constant, d-axisT ′′q s Subtransient short circuit time constant, q-axisT ′′qo s Subtransient open circuit time constant, q-axisXdu Ω Unsaturated synchronous reactance, d-axisXqu Ω Unsaturated synchronous reactance, q-axisXd Ω Saturated synchronous reactance, d-axisXq Ω Saturated synchronous reactance, q-axisX ′d Ω Transient reactance, d-axisX ′′d Ω Subtransient reactance, d-axisX ′′q Ω Subtransient reactance, q-axisXl Ω Stator leakage reactance

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Symbol Unit Descriptionu f d V Instantaneous field voltage in the equivalent circuiti f d A Instantaneous field current in the equivalent circuitud V d-axis voltage of the grid seen from the generator (line-to-line rms)uq V q-axis voltage of the grid seen from the generator (line-to-line rms)id A

√3/2 times the d-axis phase current amplitude the generator

iq A√

3/2 times the q-axis phase current amplitude the generatored V d-axis terminal voltage of the generator (line-to-line rms)eq V q-axis terminal voltage of the generator (line-to-line rms)L f d H Field winding leakage inductance in the equivalent circuitL1d H Damper winding d-axis leakage inductance in the equivalent circuitL1q H Damper winding q-axis leakage inductance in the equivalent circuitLl H Stator winding leakage inductance of the generatorLe H Equivalent leakage inductance of the grid (step-up transformer leakage)Lad H Main d-axis inductance of the generatorLaq H Main q-axis inductance of the generatorR f d Ω Field winding resistance in the equivalent circuitR1d Ω Damper winding d-axis resistance in the equivalent circuitR1q Ω Damper winding q-axis resistance in the equivalent circuitRa Ω Phase armature resistance of generatorRe Ω Equivalent grid resistanceTe Nm Electrical torque from the generatorTm Nm Mechanical torque from the turbinePe W Electrical power produced by the generatorPm W Mechanical power input from the turbineQe VA Reactive power produced by the generatorp Number of poles of generatorωr rad/s Electrical frequency of the rotorωs rad/s Electrical frequency of the gridδ Rotor angleϕ Load angle (power factor angle)

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1. Introduction

Hydropower still maintains its position as the most important source of renew-able power generation in the world. In these days, most European countriesgo through a phase of intense refurbishment and upgrading of their existingplants. This leads to new challenges and the engineers need to regain backthe knowledge that went lost twenty years ago. The trend in the hydropowerindustry today is more use of computerized tools and this has really revolu-tionized the whole design process.

The generator is one of the key components of a hydropower plant, since itis responsible for converting the mechanical energy from the turbine to mag-netic energy through rotor excitation and finally to electric power absorbed bythe stator windings, distributing the energy into the power grid. The gener-ators used in hydro power plants are mainly synchronous generators. Thosegenerators need to be fed with direct current into their rotating field winding.This is the role of the excitation system.

This thesis investigates the benefits of a fast-response brushless rotating ex-citer, intended to feed the synchronous generator with controllable field cur-rent.

1.1 Project backgroundThe project initially started with a master thesis in 2011 by Peter Butros, incooperation with industry. Johan Bladh (former PhD student) supervised thework. A brushless field-wound rotating exciter was studied, intended for usein a fast-response brushless excitation system, with Bluetooth communicationfor control of a thyristor bridge attached to the rotor. The work continuedand an exciter rotor was constructed at the Ångstöm Laboratory during thefollowing year.

Jonas Kristiansen Nøland (also author of this thesis) did his thesis on de-sign and simulation of a permanent magnet stator, intended to be fitted into tothe constructed rotor of the brushless exciter. Six phase topologies was inves-tigated since it seemed to be relevant for the hydro power industry. The wholesystem was planned to be fitted into a complete state of the art synchronousgenerator test rig at the Ångstöm Laboratory. The master thesis was presentedboth at Chalmers University of Technology and Uppsala University, in theend of Mai 2013. Representatives from Statkraft was invited to the masterthesis presentation at Uppsala University. The meeting with Statkraft opened

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up for a PhD-position at the Ångstöm Laboratory with further work on thefast-response brushless rotating exciter technology. Jonas Kristiansen Nølandstarted as a PhD-student part-time from the autumn 2013 and full-time (80%)from spring 2014.

1.2 Outline of the thesisChapter 2 presents an overview of excitation systems. The chapter includesdifferent important terms, standards and types of systems. Chapter 3 derivesthe analytical solutions of the response times of the excitation system when thesynchronous generator is open-circuited. The obtained solutions are closelylinked to Paper II, where experimental data from a hydro power plant is in-vestigated. Paper II studies the open circuit step response with a conventionalfield-wound rotating exciter and compares it with the performance of a shaft-driven PM rotating exciter investigated in Paper I, III and IV.

In Chapter 4, a complete dq-equivalent circuit model of the synchronousgenerator is presented including both mechanical dynamics and grid dynam-ics. The model parameters are extracted from manufacturer data in Chapter 5.Chapter 6 extends the generator open-circuit step response given in Paper IIwith a field current step response during loaded operation for the same powerplant. The step response is acting against a voltage dip in the connection pointof the generator to the grid. In Chapter 7, the conclusions of the thesis aresummarized and discussed, and Chapter 8 outlines the work of the PhD thesisto come.

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2. Excitation systems

Fig. 2.1 shows a block diagram of the components included in an excitationcontrol system. The exciter generates the direct current for the field windingof the synchronous generator. The excitation system includes the synchronousmachine regulator with different control schemes and protective functions. In-teractions exists between the power system and the excitation control system,including the feedback dynamics of the synchronous generator.

Figure 2.1. Block diagram of the components of an excitation control system.c©IEEE2014 [1]

2.1 Excitation control systemA complete excitation control system is given in Fig. 2.2, including the mostimportant subsystems.

Figure 2.2. General block diagram for synchronous machine excitation control sys-tem. c©IEEE2005 [2]

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In the terminal voltage transducer, the terminal voltage is sensed and re-duced to a dc quantity. The load compensator measures the current fromthe generator terminals in order to account for the voltage drop in the step-up transformer connecting the generator to the grid. If multiple generatorsare connected in parallel, the load compensator acts as a artificial couplingimpedance for load sharing purposes. The excitation control system also in-cludes a power system stabilizer (PSS), over- and under-excitation limiters andan automatic voltage regulator (AVR). The PSS is an additional function to thevoltage regulator to improve the damping of power system oscillations.

The dynamic response to a step input is one of the most important fea-tures of an excitation system, giving the generator the ability to act againstdisturbances in the grid. Fig. 2.4 shows some of the most important qualitiescharacterizing such a response, including rise time, overshoot, peak time, andsettling time as indicated.

Figure 2.3. Typical dynamic step response of a feedback control system to a stepchange in input. c©IEEE2014 [1]

2.2 Open circuit characteristicsFig. 2.4 plots the relation between the terminal voltage of the generator andthe field current. The correlation is linear up to a certain point. The fully

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loaded generator would need extra field current to account for the armaturereaction with the load currents.

Figure 2.4. Determination of no-load field current and air-gap field current. Line1 plots the linearized air-gap line, whereas line 2 includes the saturation effect.c©IEC2011 [3]

2.3 Ceiling voltageThe ceiling voltage is the maximum field voltage available for the excitationsystem. The difference between the positive ceiling voltage and the rated fieldvoltage indicates the field forcing capability and tends to improve power sys-tem transient stability [1]. With a voltage-bidirectional excitation system, anegative ceiling voltage is possible. This is helpful for a rapid demagnetizingof the synchronous generator and for control of the generator during over-voltage conditions. A high ceiling voltage can force rapid change in fieldcurrent. The firing angle margins causes the magnitude of the negative ceilingvoltage to be lower than the positive ceiling voltage for thyristor-controlledexcitation systems. Bus-fed or transformer-fed potential-source exciters loosesome advantage by the fact that the available ceiling voltage is reduced dur-ing the actual fault period [4]. During the fault period, the terminal voltage isgreatly reduced, directly influencing the bus-fed excitation system. Exciterswith ceiling voltage less than 150% of rated field voltage are classified as lowceiling voltage exciters according to IEEE [5].

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2.4 High initial response excitation systemThe literature tend to distinguish between high-speed response and normalresponse excitation systems [6]. Excitation systems with a fast dynamic per-formance are classified as a high initial response excitation system. Thosesystems are able to reach 95 percent of the difference between the availableceiling voltage and the rated field voltage in less then 0.1 seconds. A 6-pulse thyristor bridge rectifier directly connected to the field winding is ableto change the voltage over the whole range in less than 10 milliseconds witha 50Hz ac input [7]. With six firing pulses per electrical period, the maximumtime delay in the voltage response is [8]

TUf=

16 f

. (2.1)

Fig. 2.5 shows the voltage response delay for a step change in the appliedfield voltage for a thyristor bridge rectifier. The thyristor bridge firing angleis changed from 75 to 0 and the voltage response delay is less than 3ms.Theoretically the thyristor bridge ceiling voltage is obtained with a 0 firingangle, but normally the minimum firing angle is in the range 7-10 to ensurepositive forward voltage when the thyristors are triggered.

Figure 2.5. DC voltage waveform applied over the field winding due to a step changein the firing angle. Effects of commutation is neglected. c©IEEE1968 [8]

Fig. 2.6 shows how the nominal voltage response of an excitation systemis characterized. This evaluation is mostly used for slow response brushlessexcitation systems with an uncontrollable rotating diode bridge in the rotor.

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Figure 2.6. Excitation system nominal response. c©IEEE2014 [1]

2.5 Different excitation systems2.5.1 Static excitation systemsPotential source bus-fed excitation systemFig. 2.7 shows a block diagram of the static exication system. All com-ponents in these systems are stationary. They feed the direct current to thefield winding through slip rings. The most common type is the potential-source controlled-rectifier excitation system. The excitation power is bus-fedor transformer-fed, generated from the synchronous generator terminals andfed to a controlled rectifier through a shunt-connected step-down power poten-tial transformer. The system has a fast inherent response, it is easy maintain-able and inexpensive. However, the available ceiling voltage is dependent onthe input ac voltage to the controlled rectifier. During system-fault conditions,the depressed terminal voltage reduces the available ceiling voltage. Now-days, the potential-source excitation system is usually designed with higherceiling voltage levels to ensure satisfactory fault-on field-forcing capability.The ceiling voltage requirement is typically 2 times the rated field voltage.As an example; With a 30 percent drop in terminal voltage, a ceiling volt-age of 1.4 times the rated field voltage is available for field forcing. For highpower synchronous generator excitation systems, the potential-source thyris-tor rectifier exciter is the dominant topology [9]. Recent studies has shownthat the implementation of modern power electronic interfaces in static excita-tion systems can improve the field-forcing capability during reduced terminalvoltages [10–12].

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Grid Transformer

StationaryRectifier

SynchronousGenerator Load

VoltageSensors

Reference+-

Controller

Figure 2.7. Diagram of the conventional static excitation system.

Compound-cource excitation systemCompound excitation systems were very popular in the early 1970s and before,since prior to that time, fault current could not be provided by other sources[13]. The cost of a compound system is approximately 2 times the cost of apotential source bus-fed system. Where excitation support is needed, a powercurrent transformer is included, yielding a compund-source static excitationsystem. When the generator produces an output current, some of the excitationpower is provided by series connected power current transformers, yielding anequivalent to the field forcing capability in a shaft driven excitation system. Allfield excitation power is supplied by the power potential transformer when thegenerator operates at no-load.

2.5.2 Rotating brushless excitation systemsBrushless synchronous machines became reality with the introduction of com-pact high-power silicon diodes during the 1950s [14]. In the beginning theywere introduced for aircraft applications, where special flameproofing in haz-ardous atmospheres were needed [15]. In rotating brushless excitation sys-tems, the excitation power for the generator field winding is generated physi-cally close to the utilization point.

With an armature core carrying alternating current, the rotor core shouldbe laminated to reduce core loss. Solid steel rotors offers better mechanicalstability, but laminated cores has been proven successful for large inductionmotors. Another challenge arises with wireless measurement and control sys-tem of field voltage and field current. However, the signals could also bedelivered through brushes to attain better redundancy.

Conventional bus-fed brushless excitation systemOne of the main problems associated with the conventional brushless excita-tion system (Fig. 2.8) was the slow step response of the generator field current.Because of a rotating uncontrolled diode bridge, the generator field voltage isnot directly controlled. It takes time to change the field voltage to attain theceiling voltage. It was proven that this problem could be solved by minimizingthe inductances of the exciter in the initial design [16]. The ac-exciter couldbe designed to be capable of extremely fast changes of flux [17]. However, the

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diode bridge could still not attain negative voltage for de-excitation purposes.This problem could be solved by a de-excitation resistor on the shaft [18].

Maintenance is a very important aspect for the operation of synchronousgenerators, since it can reduce the cost of the power production. The use ofslip-rings and carbon-brushes is one of the key contributors to the requiredmaintenance [19, 20]. The brushes needs to be replaced regularly as they getworn down during use. The use of a rotating brushless exciter can handle thisproblem and thereby reduce the maintenance cost. However, several problemsrelated to the conventional brushless excitation system in the past, made amarket driver for the static excitation instead [21].

Grid Transformer

StationaryRectifier

RotatingExciter

RotatingRectifier

SynchronousGenerator Load

+-

VoltageSensors

ReferenceController

Figure 2.8. Diagram of the conventional bus-fed brushless excitation system.

Improved bus-fed brushless excitation systemThe improved bus-fed brushless excitation system shown in Fig. 2.9 is inoperation on some pilot power plants. They are still not operated with thesame dynamic performance as the static excitation system. This is due to thedual control scheme, where the stationary thyristor bridge reduces the ceilingvoltage available for the rotating thyristor bridge. Operators tend to not letthe rotating thyristor bridge operate at higher firing angles during steady stateconditions. Keeping the firing angle low, reduces the steady state torque pul-sations caused by the rotating rectifier as well as keeping the power factor ofthe rotating armature currrents high.

Grid Transformer

StationaryRectifier

RotatingExciter

RotatingRectifier

SynchronousGenerator Load

+-

+-

VoltageSensors

ReferenceController 1Controller 2

Figure 2.9. Diagram of the dual control bus-fed brushless excitation system.

3-stage shaft-driven brushless excitation systemWith a permanent-magnet generator (PMG) overhung from the ac-exciter, thetotal excitation power requirements is obtained directly from the generator

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shaft [15]. Since all excitation power is derived directly from shaft rotation,this system is classified as a [?] or [?] exciter. The independence of power sys-tem disturbances provides improved reliability. Fig. 2.10 shows the schematicdiagram of the conventional PMG excitation system. Because of the uncon-trolled rotating diode bridge connected to the field-wound exciter, this excita-tion system lacks a fast dynamic response.

NS

Pre-exciterStationaryRectifier

StationaryChopper

RotatingExciter

RotatingRectifier

SynchronousGenerator Load

+-

Controller Reference

VoltageSensors

Figure 2.10. Diagram of the conventional shaft-driven brushless excitation system.

2-stage shaft-driven brushless excitation systemThe 2-stage shaft-driven excitation system utilizes the permanent magnet gen-erator as the main exciter in an outer pole PM topology. A wirelessly con-trolled power electronic interface is needed on the shaft. Fig. 2.11 and 2.12proposes two different power electronic interfaces suitable for the 2-stageshaft-driven brushless excitation system. The thyristor-based interface is in-vestigated in Paper I of this thesis. It includes even multiphase topologies.Paper III presents the complete design characterization of a designed outerpole PM exciter for a 2-stage configuration. Paper IV investigates modernpower electronic interfaces as shown in Fig. 2.12.

NS

RotatingExciter

RotatingRectifier

SynchronousGenerator Load

VoltageSensors

+-

ControllerReference

Figure 2.11. Diagram of the 2-stage shaft-driven brushless excitation system withrotating thyristor-based power electronic interface.

NS

RotatingExciter

RotatingRectifier

RotatingChopper

SynchronousGenerator Load

-+

VoltageSensors

ControllerReference

Figure 2.12. Schematic diagram of the 2-stage shaft-driven brushless excitation sys-tem with rotating PWM chopper-based power electronic interface.

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2.6 Standards and technical requirementsDifferent transmission system operators (TSO’s) operates their grids with dif-ferent standards related to the excitation system of synchronous generators.Table 2.1 compares standards for the step response and the field winding ceil-ing voltage from different standards.

Table 2.1. Performance of the different interfaces

Standard Owner OC step response test Requirement Ceiling voltage

FIKS Statnett 0.95pu −→ 1.00pu 0.5s 2.00puSvKFS Svenska Krafnat 1.00pu −→ 1.10pu 0.8s NANGTR Statkraft/Vattenfall 0.95pu −→ 1.05pu 0.5s 2.00puIEEE IEEE Std 421 1.00pu −→ 1.03pu NA 1.50pu

IEEE standard 421.4 defines no step response time requirement for the ex-citation system but prefers to require a high initial response type exciter forlarger generators. This is because a fast field voltage response is directly linkedto the response of the field current.

The TSO’s specifies requirements on the fault ride-through capability of thegrid connected generators. Fault ride-through means the capability of electri-cal devices to be able to remain connected to the network and operate throughperiods of low voltage at the connection point caused by secured faults. FIKSstates that synchronous generators should be able to withstand a fault in thegrid if the actual time-dependent voltage profile lies within a certain minimumrequirement ("worst case"). The generator should also be able to support thegrid during the whole low voltage ride-through. After the fault clearing, thegenerator should be able to operate with a lower voltage level as a result of aweaker grid. The time it takes to clear the fault will determine the real voltageprofile of the grid. Fig. 2.13 shows the time-dependent voltage profile requiredfor generators connected to a grid with 220kV operating voltage or higher.

t[ms]0 150 9000

10.9

U [pu]

Figure 2.13. Time-dependent fault ride-though voltage profile for generators con-nected to a grid with operating voltage above or equal to 220kV [22].

21

2.7 Implementation of modern power electronicsThe thyristor bridge rectifier was introduced by General Electric in 1957 [23].From then, a revolution in the control of power was initiated. It marks thebeginning of modern power electronics as we know it. The semi-controlledthyristor devices was able to rectify a controlled dc voltage by adjusting thedelay firing angle. However, the expense of the delayed firing angle causes alarger phase shift between voltage and current fed from the ac input. Espe-cially in the hydropower industry, where a high firing angle is required for anavailable ceiling voltage, a high firing angle causes low power factor for theexcitation power.

In Fig. 2.14, a step change in the dc output voltage is compared with athyristor bridge rectifier and a dc-dc step-down converter. The dc-dc converterchanges the voltage reference by adjusting the duty cycle. The dc input couldbe fed from an uncontrolled diode bridge rectifier with no delay angle, yieldinga higher power factor. For a shaft-driven exciter, less torque ripple is also theend result (Paper IV). With modern power electronics, the voltage responseis instead related to the switching frequency of the pulse-width modulation,yielding

TUf=

1fsw

, (2.2)

which causes a faster response of the field voltage compared to thyristor-controlled rectifiers. The voltage time response becomes independent of thefundamental electrical frequency in the exciter armature. The switching fre-quency tends to be much higher than the fundamental frequency.

Figure 2.14. Comparison of different voltage control techniques. (a) Step-down dc-dcconverter. (b) Three-phase thyristor rectifier. c©IEEE2015 [24]

22

3. Analytical solutions of open-circuitdynamics

An unloaded synchronous generator excitation system can be simplified as aclassical RL-circuit. The relation between the instantaneous field voltage (u f )and instantaneous field current (i f ), is given by

u f = L fdi f

dt+R f i f , (3.1)

or written in circuit form shown in Fig. 3.1.

+− u f

L f R f

i f

Figure 3.1. Simple equivalent circuit of the excitation system with unloaded generator.

At rated steady state conditions, the voltage-current relationship is given byohms law, yielding

U f = R f I f , (3.2)where U f is the rated mean steady state field voltage and I f is the rated fieldcurrent. If u f = γU f , the general solution for Eq. 3.1 yields

i f = γI f +Ke− t

T ′do , (3.3)

where T ′do =L fR f

.

3.1 Terminal voltage buildupIf the excitation system initially starts with zero excitation current, i f (0) = 0,then K =−γI f in Eq. 3.3 , yielding

i f = γI f

(1− e

− tT ′do

), (3.4)

23

with u f = γU f as the applied field voltage. The time it takes to reach thenominal field current becomes

Tf = T ′do ln[

γ

γ−1

]. (3.5)

Fig. 3.2 shows how the terminal voltage buildup of a generic unloaded syn-chronous generator depends on the applied field voltage. With γ = 2, thegenerator reaches the terminal voltage in Tf

T ′do= ln(2) ≈ 0.693. The voltage

buildup time Tf will then become smaller than the generator d-axis transienttime constant. The positive ceiling factor (γ) improves the dynamic response.

Time [pu]0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Cu

rre

nt

[pu

]

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

γ = 3.0

γ = 2.8

γ = 2.6

γ = 2.4

γ = 2.2

γ = 2.0

γ = 1.8

γ = 1.6

γ = 1.4

γ = 1.2

γ = 1.0

Figure 3.2. No-load terminal voltage buildup: Field current, i fI f

, as a function of time,t

T ′do, with different applied field voltages, u f = γU f .

3.2 De-excitationDe-excitation starting with rated excitation current, i f (0) = I f , leads to K =(1− γI f ) in Eq. 3.3 , yielding

i f = γI f +(1− γ)I f e− t

T ′do , (3.6)

with u f = γU f as the applied field voltage. The time it takes to reach 37 percentof the nominal terminal voltage yields

T37% = T ′do

[1− γ

1e − γ

](3.7)

at no-load operation. There exists certain requirements in the NGTR of howfast the system should be demagnetized. If the generator time constant T ′do=7.5s,

24

the requierement is T37%T ′do≤ 1

5 = 0.2. The requirement should be met fromnominal load. Fig. 3.3 shows the benefit of applying a negative field voltageduring de-excitation of the generator. Notice that it takes T ′do to reach 1

e I f ifthe applied field voltage is zero during de-excitaiton. During balanced shortcircuit of the synchronous generator terminals, the subtransient short-circuittime constant, T ′d , should be used for calculation of T37%.

Time [pu]0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Cu

rre

nt

[pu

]

0.4

0.5

0.6

0.7

0.8

0.9

1

γ = -3.0

γ = -2.8

γ = -2.6

γ = -2.4

γ = -2.2

γ = -2.0

γ = -1.8

γ = -1.6

γ = -1.4

γ = -1.2

γ = -1.0

γ = -0.8

γ = -0.6

γ = -0.4

γ = -0.2

γ = 0.0

Figure 3.3. No-load de-excitation response: Field current, i fI f

, as a function of time,t

T ′do, with different applied field voltages, u f = γU f .

3.3 Positive step responseGiven that i f (0) = 0.95I f initially, leads to K = (0.95− γ)I f in Eq. 3.3, yield-ing

i f = γI f +(0.95− γ)I f e− t

T ′do . (3.8)

With a field current step change from 0.95pu to 1.00pu, 90% is reached wheni f (t) = 0.995I f , yielding

T+5% = T ′do ln[

0.95− γ

0.995− γ

]. (3.9)

According to FIKS, T+5%≤ 0.5s. If the generator time constant T ′do=7.5s, thenT+5%T ′do≤ 1

15 ≈ 0.067. A positive ceiling factor (γ) is needed for fast postive stepresponse. FIKS requirement is gamma equal to 2.

25

3.4 Negative step responseGiven that i f (0) = I f initially, leads to K = (1− γ)I f in Eq. 3.3, yielding

i f = γI f +(1− γ)I f e− t

T ′do . (3.10)

With a field current step change from 1.00pu to 0.95pu, 90% is reached wheni f (t) = 0.955I f , yielding

T−5% = T ′do ln[

1− γ

0.955− γ

](3.11)

With a six pulse thyristor bridge, a negative value of γ is possible. With thepositive ceiling factor (γ) of 2 at a firing angle of 10 degrees, a negative ceil-ing factor (γ) of about -1.75 is obtainable at 150 degrees firing angle duringunloaded operation. A large difference applies between the nominal field volt-age and the actual negative ceiling voltage during a negative step response. Incomparison to the positive step response, the negative step response is usuallyfaster for fully controlled thyristor rectifiers.

26

4. Electromechanical modelling ofsynchronous generators

During transient simulation of the synchronous generator, the rotor speed willno longer be constant as in the steady state model. The rotor speed depen-dent voltage terms in the equivalent circuit model leads to a non-linear set ofdifferential equations to be solved.

If one assumes that the synchronous generator feeds a balanced set of sourcevoltages through an equivalent inductance Le and an equivalent resistanceRe, those components needs to be included in the equivalent circuit equa-tions [25].

4.1 Equivalent circuitThe final equivalent circuit model is given in Fig. 4.1 and Fig. 4.2. The circuitsare magnetically cross-coupled. The generator terminal voltages are denoteded and eq, whereas the grid voltages are denoted ud and uq.

+− u f d

L f d

R f d

i f d

i1d

L1d

R1d

id+−

ωrψq

Lad

Ra Ll

Re

Le

+− ud

−

+

ed

Figure 4.1. Synchronous machine d-axis equivalent circuit

27

i1q

L1q

R1q

iq+ −

ωrψd

Laq

Ra Ll

Re

Le

+− uq

−

+

eq

Figure 4.2. Synchronous machine q-axis equivalent circuit

The d- and q-axis flux linkages are calculated from the d- and q-axis cur-rents, yielding

ψd = Lad(−id + i1d + i f d)− (Ll +Le)id (4.1)

ψq = Laq(−iq + i1q)− (Ll +Le)iq, (4.2)

where the equivalent inductance (Le) is added to the stator leakage inductance(Ll) of the synchronous generator. With the modified d- and q-axis flux link-ages, the grid-side d- and q-axis voltages equals

ud =−(Ra +Re)id−ωrψq +dψd

dt(4.3)

uq =−(Ra +Re)iq +ωrψd +dψq

dt, (4.4)

where the equivalent resistance (Re) is added to the stator armature resistance(Ra) of the synchronous generator.

4.2 Grid dynamicsSince all electrical components between the generator and the infinite bus isnow included in the equivalent circuit, the d- and q-axis voltages can be ob-tained from the instantaneous rotor angle (δ ), yielding

ud =U sinδ (4.5)

28

uq =U cosδ . (4.6)

For modelling of static exciation systems, the available field voltage is pro-portional to the voltage on the generator terminals. The generator terminalvoltage can be calculated from the infinite bus voltages, yielding

ed = ud +Reid−ωrLeiq +Lediddt

(4.7)

eq = ud +Reid +ωrLeid +Lediqdt

. (4.8)

Note that the mutual coupling between the d-axis circuit and the q-axis circuitis a function of the instantaneous rotor electrical angular speed (ωr) and not thesynchronous electrical angular speed of the grid (ωs). In steady state operation,ωr = ωs.

4.3 Mechanical dynamicsThe deviations in the rotor speed is found from

Tm−Te =2Jp

dωr

dt, (4.9)

where Tm is the applied mechanical torque and the electrical torque is calcu-lated from

Te =p2[ψd iq−ψqid ] . (4.10)

The assumption of a constant mechanical torque is not fully valid in reality.To account for the turbine effect on the torque as a result of speed deviations,another model [26] equals the turbine torque

Tm =p2

Pm

ωr, (4.11)

where the turbine power, Pm, is assumed to be constant instead. With an in-crease in the rotor speed, the turbine will react with a slightly lower torque,causing a damping effect.

The oscillations in the rotor angle (δ ) are obtained by integrating the differ-ence between rotor speed and synchronous speed, yielding

ωr−ωs =dδ

dt. (4.12)

The instantaneous power factor angle seen from the connection point to thegrid, could be calculated from the instantaneous rotor angle, yielding

ϕ = tan−1(

idiq

)−δ . (4.13)

29

4.4 Park transformationThe real time-dependent phase voltages are found from power-invariant trans-formation, yieldingua

ubuc

=

√23

−cos(θ) sin(θ) 1−cos(θ − 2π

3 ) sin(θ − 2π

3 ) 1−cos(θ + 2π

3 ) sin(θ + 2π

3 ) 1

uduqu0

, (4.14)

similarly for the phase currentsiaibic

=

√23

−cos(θ) sin(θ) 1−cos(θ − 2π

3 ) sin(θ − 2π

3 ) 1−cos(θ + 2π

3 ) sin(θ + 2π

3 ) 1

idiqi0

. (4.15)

As a result of the power-invariant transformation, ud and uq displays a vectorwith magnitude equal to the line-to-line rms voltage. The magnitude of thecurrent vector composed of id and iq is equal to

√3/2 times the rms phase

current. The power delivered to the grid equals

Pe = ud id +uqiq, (4.16)

and the reactive power production equals

Qe = uqid−ud iq. (4.17)

4.5 Steady state operationBy applying KVL rule on the d- and q-axis equivalent circuits, steady stateoperation yields

−RaId−U sin(δ )+ωsLqIq = 0 (4.18)

−RaIq−U cos(δ )+ωsLadI f d−ωsLdId = 0. (4.19)

Equation 4.18 could be expressed as

RaI sin(δ +ϕ)+U sin(δ ) = XqI cos(δ +ϕ). (4.20)

The solution with respect to the rotor angle yields

tan(δ ) =XqI cos(ϕ)−RaI sin(ϕ)

U +RaI cos(φ)+XqI sin(ϕ). (4.21)

The rotor angle at rated apparent power, power factor and terminal voltage canbe obtained with Ra and Xq in per unit quantities, yielding

tan(δ ) =Xq,pu cos(ϕ)−Ra,pu sin(ϕ)

1+Ra,pu cos(φ)+Xq,pu sin(ϕ). (4.22)

30

Also, the required steady state field current given from 4.19, yielding

I f d =U cos(δ )+XdI sin(δ +ϕ)+RaI cos(δ +ϕ)

Xad. (4.23)

The field current in real quantities is equal to

I f =U cos(δ )+XdI sin(δ +ϕ)+RaI cos(δ +ϕ)√

32 ωsM f

, (4.24)

where the factor√

3/2 comes from the fact that the mutual inductance in theequivalent circuit model is scaled up as a result of power invariant transforma-tion. The field winding reduction factor k f is equal to

√2Lad/

√3M f .

31

5. Parameter exctraction

5.1 Synchronous generator parametersTable 5.1 compares the re-specification of the Svante generator with the orig-inal specification (generator in the lab). The major change is the increasedlength of the air gap from 4mm to 8.3mm. Studies of the generator has al-ready been made in [26–28]. Table 5.2 compares the rating of four differ-ent larger generators. Generator G4 has already been investigated extensivelyin [29, 30]. The collection of generators show the variations in terminal volt-age, mechanical speed and apparent power. G2 and G3 are installed with abrushless rotating exciter with rotating thyristor bridge and wireless trigger-ing.

Table 5.1. Specification of the test generator in the labDescription Symbol G1 G1* UnitApparent power S 75 185 kVAPower factor cos(ϕ) 0.90 0.90Rotor angle, rated load δ 24.2 21.7

Terminal voltage U 156 380 VRated current I 278 281 AField voltage, rated load U f 64.5 107.2 VField current, rated load I f 20.8 34.5 AField current, ceiling limit IF 50.0 50.0 AField current, rated no load IFNL 12.4 27.5 AField current, rated short circuit IFSC 11.7 21.3 AField current, air gap line IFAG 9.6 21.1 AFrequency f 50 50 HzNumber of poles p 12 12Air gap length g 8.3 4 mmMechanical speed n 500 500 rpmMoment of inertia J 55 75 kgm2

Inertia constant H 1.01 0.56 s

32

Table 5.2. Specification comparing four different synchronous generators in operationin nordic countries

Symbol G2 G3 G4 G5 UnitS 36.00 52.00 206.00 320.00 MVA

cos(ϕ) 0.85 0.90 0.90 0.86δ 20.87 23.87 20.57 23.90

U 11.00 11.00 21.00 18.00 kVI 1.89 2.73 5.66 10.26 kA

UF 161 183 188 340 VIF 806 1156 1766 1570 A

IFNL 479 594 1245 527 AIFSC 452 569 970 617 AIFAG 461 545 1110 493 A

f 50.00 50.00 50.00 50.00 Hzp 64.00 32.00 52.00 16.00n 93.75 166.67 115.38 375.00 rpmJ 1950.00 865.50 9877.50 1651.00 tm2

H 2.61 2.54 3.50 3.98 s

Additionally to the generator rating, also a proper design specification liesbehind. Table 5.3 shows the design chosen to fulfill the ratings given in Table5.1 and 5.2.

Table 5.3. Comparing the design specification of the four different industrial genera-tors with the generator in the lab

Description Symbol G1 G2 G3 G4 G5 UnitStator inner diam. Dsi 0.725 8.03 6.42 10.50 5.60 mActive length la 0.303 0.89 0.87 1.835 2.65 mAir gap length g 8.3 (4) 15.5 18 25 30 mmNumber of slots Qs 108 432 240 390 288Slots per pole per phase qs 3 2 1/4 2 1/2 2 1/2 6Coil pitch qs,coil 9 6 NA NA 15Circuits per phase cs 1 1 1 4 4Conductors per slot ns 2 2 2 2 2Dampers per pole nD 3 4 4 5 9Field turns per pole NF 162 24 1/2 26 1/2 18 1/2 42 1/2

There exists rough analytical estimates which relates the design specifica-tion to the ratings. The general generator formula

U = k1

√32

qsns

cs2π f DsilaBδ , (5.1)

estimates the terminal voltage. Bδ is the fundamental air gap flux density(normally slightly above 1T) and k1 is the fundamental winding factor. The

33

fundamental winding factor is calculated from [31]

k1 =sin(

π

6

)qs sin

(π

6qs

) sin(

qs,coilπ

6qs

). (5.2)

An important parameter for exciation systems is the reduction factor, relatingthe field current and field voltage in the equivalent circuit to the real ones. Ananalytical estimation in [32] states that the field winding reduction factor isequal to

k f =

√6

π

qsns

N f csk1kc, (5.3)

where kc is a correction factor related to the longitudinal reaction of the ma-chine. The relation between the stator referred and the rotor referred fieldvoltage is

u f d = k f u f (5.4)

i f d =i f

k f, (5.5)

used in the equivalent circuit of the synchronous generator. Also the fieldwinding parameters in real quantities yields

R f =R f

k2f

(5.6)

L f =Lad +L f d

k2f

. (5.7)

M f =

√23

Lad

k f. (5.8)

The equivalent circuit parameters can be extracted from the standard param-eters in Table 5.4. G1WD corresponds to the experimental generator withoutdamper bars, whereas G1CD shows the standard parameters with continuousdamper bar connection.

34

Table 5.4. Standard parameters comparing the test rig generator with four differentindustrial generators

Symbol G1WD G1CD G2 G3 G4 G5 UnitXl 0.0880 0.0880 0.170 0.170 0.147 0.150 pu

Xdu 1.2130 1.2130 0.980 0.959 0.874 1.250 puXqu 0.9100 0.9100 0.620 0.687 0.574 0.750 puXd 0.9430 0.9430 0.943 0.959 0.768 1.170 puXq 0.7130 0.7130 0.597 0.687 0.512 0.702 puX ′d 0.4090 0.4173 0.320 0.299 0.253 0.270 puX ′′d 0.2851 0.3749 0.240 0.198 0.188 0.170 puX ′′q 0.5362 0.3192 0.190 0.243 0.218 0.190 puT ′do 0.6233 0.6336 2.700 5.309 7.440 12.570 sT ′d 0.2703 0.2803 1.000 1.614 1.796 2.916 sT ′′do 0.0005 0.0024 0.053 0.058 0.092 0.086 sT ′′d 0.0003 0.0021 0.040 0.047 0.068 0.054 sT ′′qo 0.0003 0.0057 0.137 0.120 0.028 0.233 sT ′′q 0.0002 0.0025 0.042 0.055 0.012 0.063 sTa 0.0191 0.0171 0.090 0.210 0.239 0.319 s

From the synchronous generator standard parameters, the main inductancesare obtained from simply subtracting the leakage (Lad = Ld − Ll and Laq =Lq− Ll). The other equivalent circuit parameters are obtained according to[29, 33], yielding

L f d = LadL′d−Ll

Ld−L′d(5.9)

L1d = (L′d−Ll)L′′d−Ll

L′d−L′′d(5.10)

L1q = LaqL′′q−Ll

Lq−L′′q(5.11)

R f d =Lad +L f d

ωbaseT ′do(5.12)

R1d =L1d +L′d−Ll

ωbaseT ′′do(5.13)

R1q =Laq +L1q

ωbaseT ′′qo(5.14)

Ra =2L′′dL′′q

Ta(L′′d +L′′q)(5.15)

The following relations exists between the open circuit time constants and theshort circuit time constants

T ′do =Xd

X ′dT ′d , (5.16)

35

T ′′do =X ′dX ′′d

T ′′d , (5.17)

T ′′qo =Xq

X ′′qT ′′q . (5.18)

Table 5.5 shows the standard parameter in per unit quantities, whereas Table5.5 outputs the parameters in actual quantities for the power-invariant recipro-cal dq-system. The real rotor-referred quantities are given in Table 5.7.

Table 5.5. Equivalent circuit parameters of the generators in per unitSymbol G1WD G1CD G2 G3 G4 G5 Unit

Ll 0.088 0.088 0.170 0.170 0.1470 0.1500 puLad 0.855 0.855 0.773 0.789 0.6210 1.0200 puLaq 0.625 0.625 0.427 0.459 0.3650 0.5520 puL f d 0.433 0.693 0.186 0.153 0.1254 0.1360 puL1d 0.511 2.290 0.131 0.035 0.0669 0.0240 puLpl 0.081 -0.161 NA NA NA NA puL1q 1.584 0.367 0.084 0.029 0.0462 0.0208 puR f d 0.007 0.007 0.001 0.001 0.0003 0.0003 puR1d 21.916 3.507 0.017 0.009 0.0060 0.0053 puR1q 1.584 0.556 0.012 0.013 0.0467 0.0078 puRa 0.062 0.062 0.008 0.003 0.0027 0.0018 pu

Table 5.6. Equivalent circuit parameters of the generatorsSymbol G1WD G1CD G2 G3 G4 G5 Unit

Ll 0.0909 0.0909 1.819 1.262 1.001 0.483 mHLad 0.8831 0.8831 8.270 5.843 4.232 3.287 mHLaq 0.6455 0.6455 4.568 3.402 2.487 1.779 mHL f d 0.4472 0.7158 1.991 1.135 0.853 0.438 mHL1d 0.5278 2.3652 1.404 0.261 0.456 0.077 mHLpl 0.0837 -0.1663 NA 1.135 NA NA mHL1q 1.6360 0.3791 0.896 0.218 0.315 0.067 mHR f d 2.2714 2.2714 3.800 1.316 0.683 0.296 mΩ

R1d 1904.7 1137.9 56.419 20.858 12.872 5.396 mΩ

R1q 514.0 119.1 41.962 30.312 100.070 7.930 mΩ

Ra 20.1178 20.1178 25.213 7.703 5.750 1.813 mΩ

Table 5.7. Real field winding parameters of the four different generatorsSymbol G1 G2 G3 G4 G5 Unit

k f 0.027 0.138 0.091 0.080 0.037L f 1.96 0.54 0.84 0.79 2.72 HM f 32.70 59.90 64.47 52.75 88.86 mHR f 3.1075 0.1993 0.1583 0.1062 0.2166 Ω

36

5.2 Field-wound exciter parametersDue to the small size and lower market value in comparison to a generator ora turbine, exciters have not been sufficiently focused upon [34]. All conven-tional exciters studied in this thesis have equal design parameters with slightmodifications (See Table 5.8).

Table 5.8. Generic design parameters for all excitersDescription Parameter Value UnitNumber of poles p 18Slots per pole per phase qr 3Number of parallel circuits cr 6Number of conductors per slot nr 8Number of field winding turns per pole n f 240Coil pitch in number of slots qr,coil 8Fundamental winding factor k1 0.9452Rotor outer diameter Dro 1.7 m

Table 5.9 compares the specification of three different exciters with equaldesign parameters given in Table 5.8. The behavior of exciter X1 with a ro-tating thyristor bridge is investigated in Paper II. Exciter X1 is in operationon an industrial power plant including a wireless communication system forthyristor triggering.

The different exciters are fitted into generators with different mechanicalspeeds, which results in slight variations in the electrical frequency of the ro-tor armature winding. For exciters with a rotating thyristor bridge, the fieldvoltage time response is directly proportional to the electrical frequency. Thisis because the thyristor bridge is triggered only 6 times per electrical period.

Table 5.9. Specification of three different exciters with generic design parametersDescription Parameter X1 X2 X3 UnitApparent power S 231 260 313 kVAPower factor cos(ϕ) 0.919 0.920 0.921Terminal voltage U 150 212 212 VRated I 888 708 853 ARated generator field voltage UF 183 260 260 VRated generator field current IF 1156 920 1110 ARated exciter field voltage U f 109 210 189 VRated exciter field current I f 21.42 22.87 20.58 AElectrical frequency f 25.00 14.07 17.31 HzMechanical speed n 166.70 93.80 115.38 rpmAir gap length g 5.3 5.0 5.3 mmActive length la 0.25 0.5 0.5 m

The power factor of the the different exciters are specified only for rotat-ing diode bridge operation. For the specification of a fast-response brushless

37

excitation system with a rotating thyristor bridge, this would not be a valid as-sumption. At higher firing angles, the commutation interval tends to be smallas a result of high commutation voltages. The phase currents in the rotor ar-mature have a square wave shape. The relation between the rms value of thearmature currents and the generator field current becomes then

I =

√23

I f . (5.19)

Including the both the effect of the displacement and distortion of the currents,the true power factor becomes

PF =1√

1+23 π2−6

6

· cos(α)≈ 0.955cos(α), (5.20)

where the firing angle (α) accounts for the displacement power factor. Nor-mally the ceiling voltage of a fast-response exciter is attained at 10 firingangle. For a ceiling voltage factor of 2, the steady state operating firing angletends to be about 60 (Paper II). This suggests the actual steady state powerfactor is about 0.48. The problem of a low power factor could be solved withother power electronic interfaces, like a rotating capacitor and a dual quadrantchopper (Paper IV).

In recommended exciter design, the direct axis synchronous reactance shouldbe about 1.22 per unit [34]. Also, the direct axis transient reactance is pro-posed to be 0.26 per unit. Among the exciters investigated in this thesis, X2have parameters close to this recommended practice (see Table 5.10). Pa-per III investigates the design of an outer pole PM exciter with a direct axissynchronous reactance of about 0.2 per unit. This is a general trend whencomparing field wound synchronous machines with permanent magnet ma-chines [35].

Table 5.10. Standard parameters of different excitersDescription Parameter X1 X2 X3 UnitLeakage reactance Xl 0.212 0.108 0.160 puCommutating reactance Xcom 0.410 0.250 0.378 puD-axis synchronous reactance Xd 1.912 1.242 1.751 puQ-axis synchronous reactance Xq 0.883 0.555 0.788 puD-axis transient reactance X ′d 0.410 0.227 0.339 puD-axis subtransient reactance X ′′d 0.390 0.216 0.322 puQ-axis subtransient reactance X ′′q 0.883 0.555 0.788 puOpen circuit time constant T ′do 2.113 2.453 2.314 sShort circuit time constant T ′d 0.453 0.451 0.448 sArmature time constant Ta 0.108 0.147 0.145 s

The final per unit equivalent circuit parameters are given in Table 5.11. Therotor of the exciters are solid, with no added damper bars. However a small

38

damping effect is seen due to the induced eddy currents in the rotor. How-ever, for modelling purposes, the effect of the damper winding could easily beneglected.

Table 5.11. Equivalent circuit parameters of different excitersDescription Parameter X1 X2 X3 UnitD-axis main inductance Lad 1.7000 1.1345 1.5920 puQ-axis main inductance Laq 0.6700 0.4475 0.6280 puField winding leakage inductance L f d 0.2241 0.1354 0.2017 puDamping leakage inductance L1d 1.7622 1.0377 1.7058 puField winding resistance R f d 0.0058 0.0059 0.0071 puArmature winding resistance Ra 0.0319 0.0240 0.0290 pu

For conversion of the equivalent circuit parameters into real measurableparameters, equations given in [36], yields

L f = T ′doR f (5.21)

M f =√

(T ′do−T ′d)R f Ld , (5.22)

where R f is the measured hot-field resistance. The rotor armature winding no-load terminal voltage (E) can be calculated from the mutual inductance (M f )and the no-load exciter field current (IFNL), according to

E =

√32

ωM f IFNL. (5.23)

The factor√

32 is included into equation 5.23 as a result of the power-invariant

dq-transformation in order to obtain reciprocal mutual inductance between thefield winding and the fictive d-axis armature winding. If the stator field wind-ing is replaced by permanent magnets (Paper I, III and IV), the no-load termi-nal voltage equals

E =

√32

ωψm, (5.24)

where the magnet flux linkage ψm replaces M f I f . All extracted parameters inreal units of the investigated field-wound exciters are given in Table 5.12.

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Table 5.12. Machine parameters in natural reference frame of different excitersDescription Parameter X1 X2 X3 UnitField winding inductance L f 10.7524 22.5261 21.2510 HMutual inductance M f 0.1004 0.2105 0.1986 HReduction factor of field winding k f 0.0106 0.0105 0.0105Field winding resistance, cold R f ,15C 4.0900 7.3900 7.3900 Ω

Field winding resistance, hot R f 5.0887 9.1837 9.1837 Ω

Armature winding resistance, cold Ra,15C 2.9500 4.0700 4.0700 mΩ

Armature winding resistance, hot Ra 3.1254 4.1479 4.1479 mΩ

The field inductances of the exciters are high, which explains the reasonwhy the dynamics of conventional brushless exciters are slow dynamically.The field inductances of exciter X2 and X3 are about two times higher thanthe field inductance of exciter X1. This is primarily a result of the scaling ofthe active length (la).

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6. Results

This chapter uses the model of the synchronous generator presented in Chapter4 and the parameter data given in Chapter 5. The field current step responsestudied in Paper II for for open circuit operation is extended with a study ofthe step response during loaded operation for the same generator and with alow voltage ride-through profile on the connection point to the grid. Firstly,the synchronous generator is simulated with an infinite bus directly connectedto the generator terminals. The study investigates the transient stability ofgenerator G3 with the 4 following excitation control approaches:• Case 1: No step response; field current is kept constant during the whole

fault ride-through and equal to the current needed to obtain zero powerfactor at rated turbine power during steady state conditions.• Case 2: No step response; field voltage is kept constant during the whole

fault ride-through and equal to the field voltage needed to obtain zeropower factor during steady state operation at rated turbine power.• Case 3: The field winding is fed with the available ceiling voltage during

the whole fault ride-through, but the available field voltage fed from thegenerator terminals, is directly dependent on the time-dependent LVRT-profile.• Case 4: Field voltage is independent of the fault and rated ceiling volt-

age is applied during the whole fault, yielding fastest step response pos-sible. This is the case if one applies a shaft-driven PM exciter, equivalentto the novel prototype analyzed in Paper I, III and IV. The details of thefast-response shaft-driven excitation system is presented in Chapter 2.

Another simulation is made with an equivalent grid inductance (Le) in order tomore correctly represent the behavior of the interaction between the generatorand the grid.

Final results are given on the next page. Fig. 6.1 shows that case 2, 3 and 4obtains synchronism during the fault ride-through. The field current reach highvalues during the fault as a result of the fact that the equivalent grid inductanceis neglected. Keeping the field current constant during the LVRT-profile is nota good idea in order to keep synchronism.

Fig 6.2 investigates case 3 and 4 with an equivalent grid inductance of 0.05in per unit. This is an approximation to account for the leakage reactanceof the step-up transformer in between the generator and the connection pointto the grid. The static potential source excitation system cannot keep syn-chronism since the available field voltage is reduced during the fault. Theshaft-driven excitation system is independent of the grid. Because of its fieldforcing strength, the synchronism is kept.

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-30

0

30

60

90

120

150

180

An

gle

[d

eg

]

Rotor angle

Case1

Case2

Case3

Case4

48

48.5

49

49.5

50

50.5

51

51.5

52

52.5

53

Fre

qu

en

cy [

Hz]

Rotor electrical frequency

Case1

Case2

Case3

Case4

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2

Time [s]

0

0.5

1

1.5

2

2.5

3

Cu

rren

t [p

u]

Field current

Case1

Case2

Case3

Case4

Figure 6.1. Low Voltage Ride-Through test following the profile of Fig. 2.13 withzero power factor and with different excitation control approaches. The equivalentinductance (Le) and equivalent resistance (Re) is set to zero.

-30

0

30

60

90

120

150

180

An

gle

[d

eg

]

Rotor angle

Case3

Case4

4848.5

4949.5

5050.5

5151.5

5252.5

5353.5

54

Fre

qu

en

cy [

Hz]

Rotor electrical frequency

Case3

Case4

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2

Time [s]

0

0.5

1

1.5

2

2.5

3

Vo

ltag

e [

pu

]

Field voltage

Case3

Case4

Figure 6.2. Low Voltage Ride-Through test following the profile of Fig. 2.13 with zeropower factor, comparing potential source static excitation with shaft driven exciation.The equivalent inductance (Le) is equal to 0.05 per unit and equivalent resistance (Re)is set to zero.

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7. Conclusion

The thesis includes many different disciplines within electrical power engi-neering. In exciter design, the power electronic design aspects is directlylinked to the electrical machine design. The performance of the excitationsystem determines the field forcing strength of the synchronous generator.

Traditionally, permanent magnets have not found its use in hydropower gen-erators. However, outer pole PM exciters are able to make the excitation sys-tem independent of the grid voltage.

Modern power electronic interfaces are able to improve the performance ofthe exciter. The end result is increased power factor, reduced torque pulsa-tions and improved controllability. The dual quadrant chopper, with a rotatingcapacitor on the rotating shaft, includes less active components compared toconventional thyristor based interfaces.

The step response of the field current in the synchronous generator is di-rectly linked to the available field winding ceiling voltage. The availabilityof the field voltage is more reliable on shaft-driven PM rotating exciters com-pared to conventional potential-source static exciters. Compound-source staticexciters is an alternative, but it includes more components, causing it to be lessattractive due to increased costs.

Simulations shown in Chapter 6 proves that field forcing during low volt-age ride-through improves the ability to keep the synchronous generator insynchronism to the grid. The shaft-driven PM excitation system has a goodability to keep the generator in synchronism during voltage dips. Even thebus-fed field-wound exciter used on some pilot plants will perform better thanthe conventional static excitation system. This is because the exciter fieldwinding has a very high self inductance. It takes time to change the exciterfield current, even during voltage dips.

The stabilizing effect of the fast-response available ceiling voltage has beendocumented in the literature [4, 6]. In [37], it is pointed out the problem ofthe reduced terminal voltage input to the bus-fed static and rotating excitationsystem during faults. This is the major benefit of the rotating shaft-driven PMexcitation system.

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8. Future work

The content of my future work is divided into four different branches; exciterdesign aspects, power electronic design aspects, controller design aspects andcomplete models that incorporates all aspects, including regulator, generatorand the grid.

8.1 Exciter armature winding designOur rotor armature winding design was based on conventional field-woundrotating exciters. Distributed windings are widely used in industry, but sin-gle layer concentrated winding design would lead to better fault tolerance ofthe exciter. Paper III shows that the per unit reactances of the designed ex-citer are small compared to conventional field-wound exciters. Short circuitcurrents are easier to suppress in field-wound exciters, which is as challengefor PM rotating exciters, especially since the armature currents flows in therotor. Fault tolerant design will make the phases less magnetically coupled toeach other. With a six phase system, one could obtain redundancy not onlyin the power electronics but also from the sources. Single layer concentratedwinding design tends to obtain higher values for the phase inductances, whichcould make the per unit reactances of the PM exciter closer to the conventionalfield-wound exciters.

8.2 Power electronic interfacesThe power electronic interfaces studied in Paper IV should be studied for mul-tiphase topologies as well. Some investigations has been made of the multi-phase topologies in Paper I, but not for the modern power electronic interfaces.The rotating diode bridge connected to a dc link capacitor is proven to reducetorque ripple and increase the power factor compared to the thyristor rectifier.Multiphase topologies with the diode bridge are expected to improve the per-formance further. Also the dynamics of the the rotating thin film capacitor andthe dual quadrant chopper should be compared with the controllability of thethyristor bridge rectifier. Earlier investigations shows that the controllabilityof the thyristor bridge is more sensitive to the size of the phase inductances ofthe exciter.

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8.3 Bang-bang excitation controlMost excitation systems uses a PID regulator in the automatic voltage regu-lator (AVR). The regulator adjusts the average field voltage by changing thedelay firing angle of a thyristor bridge rectifier. I order to obtain a fast stepresponse, a high gain of the regulator is required. This leads to overshoots inthe field current during step response. FIKS requires that the overshoot shouldbe less than 15 percent of the step change and non-oscillating [22]. Othertransmission system operators have requirements on the field current settlingtime instead [38].

With the implementation of modern power electronic excitation control in-terfaces like the dual-quadrant chopper, new control strategies are possibleto implement. The field voltage can change from positive ceiling voltage tonegative ceiling voltage instantaneously, yielding a reduced the field currentovershoot. The switches are controlled based on a reference value of the fieldcurrent. By allowing a certain tolerance band for the field current, the switch-ing position of the chopper is changed every time the field current hits the edgeof the band. The switching frequency and the duty cycle happens naturally asa result of the specified reference and tolerance. Earlier work has shown thepossibility of rapid changes of field voltage in the bang-bang excitation controlscheme [39], which leads to improved damping of oscillations in the system.

8.4 Synchronous generator modellingThe impact of the excitation system on synchronous generator transient stabil-ity should be studied further. The synchronous generator model should includeaccurate models of the excitation system, the step-up transformer and and theautomatic voltage regulator including PSS. The electromechanical generatormodel presented in Chapter 4 should be validated with experimental measure-ments on industrial power plants. It is interesting to investigate if the applica-tion of fast-response brushless rotating exciters could increase the active powerutilization of the synchronous generator. Studies of low voltage ride-throughfor governor controlled prime mover driven generators are rarely found in theliterature [40].

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9. Summary of papers

Paper IComparison of Thyristor-Controlled Rectification Topologies for a Six-Phase Rotating Brushless Permanent Magnet Exciter. A preliminary de-sign of the outer pole PM exciter with a diametrical permanent magnet orien-tation is analyzed. Different thyristor rectification topologies of a multiphasePM exciter is investigated. Analytical models are compared with equivalentcircuit simulations and a FEM model. The results proves the benefit of amultiphase exciter with a thyristor based power electronic interface. The per-formance is evaluated with respect to torque ripple and excitation current con-trollability.

The article was published in IEEE Transactions on Energy Conversion, vol.31(1), pp. 314-322, March 2016.

Paper IIStep time response evaluation of different synchronous generator excita-tion systems. Different excitation system configurations are investigated withrespect to their dynamic performances. Experimental results from a real in-dustrial power plant with brushless excitation and wireless communication isused as input for a simulation study. The same exciter is simulated in differentconfigurations. The new brushless configurations all meet the step time re-sponse requirements for conventional static excitation systems set by StatnettSF.

E. Dahlen from Voith Hydro helped out with technical and experimentaldata.

The paper was presented by the author, who is the main author of the pa-per, at the 4th IEEE International Energy Conference (ENERGYCON’2016) inLeuven, Belgium, in April 2016. It was also selected for inclusion in the IEEEXplore database.

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Paper IIIDesign and characterization of a rotating brushless PM exciter for a syn-chronous generator test setup. The final design of the PM exciter with para-metrical permanent magnet orientation is analyzed. The construction and andfitting of the stator into the synchronous generator test rig is also discussed.Experimental measurements of coil voltages, phase voltages and line-to-linevoltages is made with a 166.67 rpm speed on the shaft. Comparison with FEMsimulations is done. Also simulated magnetic flux densities is validated withhall sensor measurements. An extensive analysis of the d- and q-axis induc-tances is made in the end of the paper, as well as a full specification of theexciter.

The paper was submitted to the XXIIth International Conference on Elec-trical Machines (ICEM’2016) in Lausanne, Switzerland, in September 2016.

Paper IVEvaluation of different power electronic interfaces for control of a rotat-ing brushless PM exciter. This paper investigates the performance of differ-ent power electronic interfaces on the PM exciter, designed for a synchronousgenerator test setup. Three different interface is studied with respect to avail-able field winding ceiling voltage and torque ripple pulsations. It is concludedthat a diode rectifier in the rotating frame makes the system simpler since itis self-commutated. It also reduces the torque ripple and improves the powerfactor compared to the thyristor bridge rectifier. Interface B is proven to be thebest compromise between complexity and performance.

The paper was submitted to the 42nd Annual Conference of the IEEE Indus-trial Electronics Society (IECON’2016) in Firenze, Italy, in October 2016.

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10. Svensk sammanfattning

Den norska elnätsstandarden FIKS från Statnett, uppger att synkrongenerato-rer med Installerad effekt över 25 MVA måste ha statisk magnetiseringsutrust-ning. Den innehåller också krav på stegsvar för fältströmmen och tillgängligtoppspänning för fältlindningen till synkrongeneratorn.

Ett förbättrat borstlöst magnetiseringssystem är i drift i vissa pilot kraftverk.En roterande tyristorbrygga styrs via Bluetooth. Stegsvarstiden är lika snabbtsom konventionella statiska excitationssystem. Men en toppspänningsfaktorpå två kräver att tyristorbryggan driver tändvinklarna på ungefär 60 grader.Resultatet av detta är högre vridmomentpulsationer, lägre effektfaktor och lågtutnyttjande av mataren.

Nya kraftelektroniska gränssnitt på axeln resulterar i en bättre utnyttjan-de av den designade mataren och förbättrar den mekaniska prestanda såvälsom bättrad styrbarhet av fältströmmen genom fältlindningen. Även perma-nentmagnetiserade roterande matare ökar styrkan at tvinga fältström hos densynkrona generator, vilket ger förbättring i transient stabilitet (det så kalladeLov Voltage Ride Through kravet). Borstlösa matare minskar också det regel-bundna underhållet av generatorn.

Avhandlingen ger experimentella mättningar på en testanläggning med syn-krongenerator och en konstruerad permanentmagnetiserad matare med olikakraftelektroniska lösningar. Den innehåller även mätningar på industrianlägg-ningar.

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11. Acknowledgements

The research presented in this thesis was carried out as a part of the Stat-kraft R&D-program: Future Hydro Power. Statkraft is a leading company inhydropower internationally and Europe’s largest generator of renewable ener-gy. The company supports hydropower research in both Sweden and Norway.Statkraft is a member of the Swedish Hydropower Centre (SVC), where Upp-sala University hosts the electromechanical research. They also supports theNorwegian Hydropower Centre, including the hydropower group at the Uni-versity College of Southeast Norway (USN), hosted by Norwegian Universityof Science and Technology in Trondheim.

Urban Lundin, my supervisor: Thank you for your support and for all theopportunities you have given me. Without you, I would never have been whereI am today. Thank you for all the exciting experiments we have set up the lastyears. It is an honor to have you as my main supervisor.

From Statkraft, Geir Aalvik and Jan Petter Haugli: Thank you for your greatfollow up on the project and your feedback. Also thanks to Stefan Ring, fromStatnett, for giving me insights into the grid requirements on the excitationsystems.

Special thanks to Fredrik Evestedt for all the help you have given me forrunning our experiments on the test rig and your work on the power electronicinterfaces. Also thanks to Johan Abrahamsson and J. Jose Perez-Loya, foryour extensive experimental knowledge and for all the help and supervisionyou have given me.

From Vattenfall R&D, Johan Bladh and Linn Saarinen: Thanks for all gre-at discussions and for our cooperation. And also thanks to my colleges PerNorrlund and Weijiia Yang, for the opportunity to get real insights into theturbine-generator interaction.

Thanks for good cooperation with Mats Wahlen at Svea Power and ErikDahlen from Voith Hydro. It is very motivating to get real industrial data toconfirm what you are working on.

From the University College of Southeast Norway (USN), Duy Tho Doand Tone Gran: Thank you for giving me the opportunity to do my PhD atUppsala University in cooperation with Statkraft. Thanks to Lars ChristianIversen, for initiation of the project. Also thanks to Roy Rasmussen, for theopporunity to give lectures on Electrical Machines and Power Electronics tosecond year engineering students. I have also had a good time cooperatingwith Per Åsmund Jørgensen.

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Special thanks to Karina Bakkeløkken Hjelmervik. Your supervision so farhas been very helpful. You have great skills in Matlab and Latex, which is pri-celess for publishing in journals. Also, thanks for your insights into analyticalmathematics and simulation methods.

I want to thank Einar Halvorsen, Medhi Azadmehr and Frank Karlsen, foryour interest and insights into energy conversion approaches. Thanks for thediscussions we have had. I would also like to thank Marius Stian Tannum andHelge Tor Kristiansen for giving me insights into maritime electrical powersystems, automation systems and electrical standards.

Thanks to Svein Thore Hagen for my opportunity to join USN’s hydropo-wer group. Special thanks to Thomas Øyvang, my friend and colleage, doing aPhD on hydropower generators as well. All our discussions have been very va-luable. And thanks for great feedback and discussions with Gunne J. Hegglid,Dietmar Winkler and Bernt Lie.

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