Electro-Mechanical Actuators for HVDC Breakers
ARA BISSAL
PhD Thesis
Stockholm, Sweden 2015
ISBN 978-91-7595-480-6 SWEDEN Akademisk avhandling som med tillstånd av Kungl Tekniska högskolan framlägges till offentlig granskning för avläggande av teknologie doktorexamen onsdagen den 22 maj 2015 klockan 10.00 i F3, Kungl Tekniska högskolan, Lindstedtsvägen 26, Stockholm.
© Ara Bissal, May 2015
Abstract
The continuously increasing demand for clean renewable energy has rekin-dled interest in multi-terminal high voltage direct current (HVDC) grids. Although such grids have several advantages and a great potential, their materialization has been thwarted due to the absence of HVDC breakers. In comparison with traditional alternating current (AC) breakers, they should operate and interrupt fault currents in a time frame of a few milliseconds. The aim of this thesis is focused on the design of ultra-fast electro-mechanical actuator systems suitable for such HVDC breakers.
Initially, holistic multi-physics and hybrid models with different levels of complexity and computation time were developed to simulate the entire switch. These models were validated by laboratory experiments. Following a generalized analysis, in depth investigations involving simulations comple-mented with experiments were carried out on two of the sub-components of the switch: the ultra-fast actuator and the damper. The actuator efficiency, final speed, peak current, and maximum force were explored for different design data.
The results show that models with different levels of complexity should be used to model the entire switch based on the magnitude of the impulsive forces. Deformations in the form of bending or elongation may deteriorate the efficiency of the actuator losing as much as 35 %. If that cannot be avoided, then the developed first order hybrid model should be used since it can simulate the behaviour of the mechanical switch with a very good accuracy. Otherwise, a model comprising of an electric circuit coupled to an electromagnetic FEM model with a simple mechanics model, is sufficient.
It has been shown that using a housing made of magnetic material such as Permedyn, can boost the efficiency of an actuator by as much as 80 %. In light of further optimizing the ultra-fast actuator, a robust optimization algorithm was developed and parallelized. In total, 20520 FEM models were computed successfully for a total simulation time of 7 weeks. One output from this optimization was that a capacitance of 2 mF, a charging voltage of 1100 V, and 40 turns yields the highest efficiency (15 %) if the desired velocity is between 10 m/s and 12 m/s.
The performed studies on the passive magnetic damper showed that the Halbach arrangement gives a damping force that is two and a half times larger than oppositely oriented axially magnetized magnets. Furthermore, the 2D optimization model showed that a copper thickness of 1.5 mm and an iron tube that is 2 mm thick is the optimum damper configuration.
Keywords: Actuators, Armature, Capacitors, Circuit breakers, Coils, Damp-ing, Eddy currents, Elasticity, Electro-mechanical devices, Electromagnetic forces, Finite element methods, HVDC transmission, Image motion analy-sis, Magnetic domains, Magnetic flux, Magnetic forces, Magnetic materials, Magnets, Thermal analysis.
intresset för högspänd likström (HVDC) i elnät med fler än två ändstationer. Trots att dessa nät har flera fördelar och en stor potential har förverk-ligandet förhindrats på grund av frånvaron av HVDC-brytare. I jämförelse med en brytare av växelström (AC) måste en HVDC-brytare kunna bryta en felström inom loppet av ett fåtal millisekunder.
Syftet med denna avhandling är inriktat på utformningen av ultrasnabba elektromekaniska aktuatorsystem som lämpar sig för sådana brytare. Dessa är baserade på så kallade Thomsonspolar vilka består av en platt spiralformad lindning vilken är kopplad till en uppladdad kondensator som sedan laddas ur genom spolen som därvid alstrar en kraftimpuls.
Initialt utvecklades multifysik- och hybridmodeller med olika komplexitet och erforderlig beräkningstid för att simulera dessa aktuatorsystem.
Dessa validerades sedan med laboratorieexperiment. Därefter genomfördes en ingående modelleringsstudie av aktuatorsystemets ingående komponenter, den ultrasnabba aktuatorn och magnetiska dämparen. Aktuatorn verknings-grad, sluthastighet, toppström och maximala kraft utforskades bl a för olika designdata.
Resultaten visar att modeller av olika grad av komplexitet bör använ-das för att modellera hela aktuatorn beroende på storleken av den alstrade kraftimpulsen. Deformationer i form av böjning eller töjning kan försämra verkningsgraden så mycket som 35 %.
Om dessa effekter inte kan undvikas, bör den fullständiga hybridmodellen användas eftersom den kan simulera aktuatorns beteende med en mycket god noggrannhet. Annars är en modell bestående av en elektrisk krets med en enkel mekanikmodell kopplad till en elektromagnetisk FEM modell tillräcklig. Utförda studier visar att användning av en aktuatorfixtur gjord av mag-netiskt material, exempel Permedyn, kan öka verkningsgraden hos aktuatorn med upp till 80 %.
Med syfte att ytterligare optimera den ultrasnabba aktuatorn utvecklades en robust optimeringsalgoritm för användning av parallella kärnor. Med denna genomfördes under 7 veckors tid totalt 20520 FEM-beräkningar. Ett resultat från denna optimering var att en kapacitans på 2 mF, en laddningspänning av 1100 V och 40 lindningsvarv ger en högsta verkningsgrad (15%) om den önskade sluthastigheten ligger mellan 10 m/s och 12 m/s.
Genomförda studier av den magnetiska dämparen visar bl.a. att om de an-vända permanentmagneterna utförs i form av ett Halbacharrangemang medför detta en dämpande kraft som är två och en halv gånger större än om motsatt axiellt orienterad magnetiserade magneter används.
Acknowledgements
Firstly, I would like to express my gratitude to my supervisor, Prof. Göran Engdahl, for his guidance, innovative ideas, and numerous comments throughout this PhD thesis. Special thanks goes to Prof. Rajeev Thottappillil for his continuous support, and to Dr. Nathaniel Taylor for being one of the reviewers of this thesis. I’d also like to thank Prof. Anders Eriksson, for being my pillar in mechanics.
A lot of this thesis work was made possible thanks to the collaborative and fruitful working atmosphere at ABB AB Corporate Research. Therefore, I would like to thank Dr. Mikael Dahlgren and Magnus Backman for trusting in me and giving me the opportunity to work with Dr. Thomas Eriksson, Dr. Ener Salinas, and Dr. Lars Liljestrand. Their advice and guidance was very beneficial especially when it came to answering a lot of my technical questions. I was fortunate to get to meet people like Dr. David Schaeffer, Dr. Zichi Zhang, Stephan Halen, Lars Jonsson, Ola Jeppsson, Dr. Elisabeth Lindell, and Dr. Roberto Alves at ABB AB Corporate Research. In my opinion, a nice working environment strongly depends on the people whom you work with.
During my PhD studies, I also had the privilege of working at ABB DE Corpo-rate Research in Ladenburg, Germany, for a mobility of six months. I learned a lot from this experience and had the chance to work with many competent professionals with different backgrounds such as Dr. Octavian Craciun, Dr. Veronica Biagini, Dr. Christian Simonidis, Dr. Jörg Gebhadrt. Also, I would like to thank Dr. Markus Schneider, Wolfgang Waldi, Dr. Guenther Mechler, Dr. Gregor Stengel, Dr. Alexander Horch, and Dr. Ulf Ahrend. Last but not least, I would like to express my gratitude to Dr. Andreas Decker, Dr. Arne Wharburg, Dr. Kim Listmann, Dr. Jan Schlake, Andreas Schader, and Dietmar Post with whom I have had very interesting discussions on the train from Darmstadt to Ladenburg. In general, the hospitality and kindness of all my newfound German colleagues knew no limits.
I will always cherish my time at KTH especially because of outstanding friends such as Dr. Samer Sisha, Dr. Andreas Krings, Dr. Shuang Zhao, Dr. Respi-cius Kiiza, David Fernando Ariza González, Cong-Toan Pham, and Dr. Antonios Antonopoulos. A very special thanks goes to my friend and colleague Jesper Magnusson, with whom I have worked the most with throughout my PhD. I would also like to thank Peter Lönn not only for his help in IT matters at KTH, but also
for his jolly character.
I deeply appreciate having invaluable friends like Rami Bou Hadir, Hani Dakhil, Joseph Noufaily, Anthony Saliba, and Elie Karaa who have travelled all the way from Lebanon to Sweden to support me for my PhD defense.
I would also like to thank my sister for her sweetness, love, and support. Special thanks goes to my mother for sacrificing her life to raise and support me every step of the way. I hope one day I can make you as proud of me as I am of you.
Last but certainly not least, I would like to thank Silvia Lohfink for her extreme kindness and never ending love. She was like a candle in the midst of darkness, illuminating the countless winter nights I spent writing this PhD thesis.
Ara Bissal
Contents viii
1 Introduction 1
1.1 Background . . . 1
1.1.1 Why HVDC? . . . 2
1.1.2 Limitations of Multi-terminal HVDC Grids . . . 2
1.1.3 HVDC Breakers . . . 3
1.2 Objectives of the Thesis . . . 4
1.3 Thesis Outline . . . 5
1.4 Scientific Contributions . . . 6
1.5 List of Publications . . . 6
2 The Mechanical Switch 9 2.1 Requirements of the Mechanical Switch . . . 9
2.2 Switch Design . . . 10
2.3 Modeling . . . 12
2.3.1 Electromagnetic Modeling . . . 13
2.3.2 Thermal Modeling . . . 17
2.3.3 Mechanical Modeling . . . 18
2.4 Model Validations by Experiments . . . 22
2.5 Results and Discussion . . . 27
2.5.1 Models With Finer Segmentations . . . 32
3 The Ultra-Fast Actuator 35 3.1 State of the art . . . 35
3.1.1 Applications . . . 35
3.1.2 Modeling . . . 36
3.2 Modeling . . . 36
3.3 Experimental Validation . . . 38
3.3.1 The Experimental Setups . . . 38
3.3.2 Results and Discussion . . . 41
3.4 Sensitivity Analysis . . . 44
3.4.1 The Electrical Circuit . . . 44 viii
3.4.2 The Magnetic Circuit . . . 51
3.4.3 The Shape of the Actuator . . . 59
3.5 Brute Force Optimization . . . 72
3.5.1 Setup of the optimization model . . . 74
3.5.2 Results and Discussion . . . 75
4 The Composite Magnetic Damper 97 4.1 State of the Art . . . 97
4.2 Theory . . . 97
4.3 Methodology . . . 98
4.4 Modeling . . . 99
4.4.1 Static modeling . . . 99
4.4.2 Transient Modeling . . . 99
4.5 Model and Concept Verification . . . 100
4.5.1 Small Scale Prototypes . . . 100
4.5.2 Large Scale Prototype . . . 103
4.6 Optimal Damper Design . . . 105
5 Conclusions and Future Work 111 5.1 Conclusions . . . 111
5.2 Future Work . . . 112
A Math Operators 113
B Symbols and Acronyms 115
Bibliography 119
Introduction
This section provides the background, motivation, and objectives of this research study. Furthermore, the thesis outline, the scientific contributions, and list of publications are given.
1.1
Background
The world has seen a steady increase in population since the beginning of mankind. Their needs and expectations in life have been constantly increasing. The standard of living has increased dramatically especially with the advancement of mankind. Nowadays, their insatiable desire for electric energy is mostly met with non renew-able sources of power generation such as power plants based on fossil fuels. These power plants are harmful to the environment and contribute to global warming because they release large amounts of green house gases.
The Kyoto Protocol, a treaty with currently 192 parties, binds all of its par-ticipants to fight global warming by reducing the emission of green house gases. A post-Kyoto protocol agreement, will be discussed at the 21st United Nations Climate Change Conference, which will be held in Paris, France in 2015. For the first time in over twenty years, the objective of this conference is to establish binding targets for the reduction of green house gas emissions in all nations.
Consequently, countries have initiated a lot of initiatives and subsidies to en-courage clean, green, and renewable technologies. One such technology is offshore wind turbines cable of transforming wind into renewable energy. Another example is photovoltaics, a method that transforms solar energy into electric energy by making use of semiconducting material exhibiting the photovoltaic effect. Due to these incentives, a lot of research has been conducted towards increasing their efficiency. One factor that hinders adoption of renewable energy is the transportation of this energy over long distances to consumers.
Power generation and consumption are usually separated by large geographic distances. Offshore wind power is one such example. Wind turbines are installed
far out in the sea. The generated energy has to be transported over long distances before reaching local grids. Another such example are solar panels installed in remote deserts such as the Mongolian desert. Such forsaken areas are attractive due to the presence of large amounts of solar energy and vast areas of land.
One of the main challenges in harnessing the potential of renewable energy is to be able to transport it with minimum transmission losses [1–3]. Thus, a lot of research has been conducted on high voltage direct current (HVDC), as an efficient solution to transport power efficiently [4–13].
The European HVDC study group is putting a lot of effort to define “Technical guidelines for first HVDC grids” [14]. A new coming trend in HVDC is the transition from traditional point to point interconnections into terminal and multi-vendor HVDC systems. Compared to point to point connections, a multi-terminal HVDC grid has fewer terminals, hence a lower cost and lower losses. Moreover, the failure of a DC line at a terminal does not interrupt the power flow between other terminals. Each terminal can operate with different current and power ratings in a fully controllable manner.
All these initiatives have rekindled interest in multi-terminal high voltage direct current grids. Integrating renewable energy in local grids to meet the increasing demands of electricity significantly decreases the release of green house gases. One recent project that is estimated to be commissioned in 2015 is BorWin1 [15]. In this project, HVDC cables connect the German grid to an offshore cluster of wind farms 130 km out to sea. The power rating of this wind farm is 400 MW. Once operational, 1.5 million households will receive clean renewable energy avoiding the emission of more than 150 thousand tons of carbon dioxide per annum.
1.1.1
Why HVDC?
Alternating current (AC) cables are limited in their transmission capability depend-ing on the length of the cable among other cable characteristics [16]. The longer the cable, the larger is the capacitance, that constantly needs charging when subjected to an AC voltage. The charging current will be equal to the transmitted current at some critical cable length. This hinders power transmission and can be avoided by using a direct current (DC) system.
At some break-even distance, a DC system will be less costly than an AC system. For distances below 600 km it is cheaper to use an AC system. An HVDC system will be more expensive since AC-DC conversion and vice versa is required.
One very large advantage of HVDC is that it allows asynchronous intercon-nections [17]. Furthermore, it has significantly lower losses, a lower environmental impact, and is highly controllable.
1.1.2
Limitations of Multi-terminal HVDC Grids
Although HVDC technology has major advantages over traditional high voltage alternating current (HVAC), it has not been accepted due to the absence of an
HVDC breaker. The adoption of this technology relies entirely on the existence of a HVDC breaker [18, 19]. A conventional HVAC breaker cannot be used for an HVDC breaker due to the absence of a current zero crossing. Unlike an AC system, a DC system has a constant current. Moreover, DC systems have a very small impedance, thus fault currents increase quickly in magnitude and attain dangerously high levels [20]. Large currents can destroy all components connected in the network unless circuit breakers intervene promptly and interrupt these fault currents. If a slow breaker is used, then it should be dimensioned also for such large currents, complicating its design [21]. Moreover, it will be large and bulky, and in some cases would need even extra cooling. Thus, it is of crucial importance to have a fast breaker to avoid these complications.
1.1.3
HVDC Breakers
Recent research is devoted to understanding, designing, modeling, and testing of HVDC breakers [22–37]. To interrupt a HVDC current, three different HVDC breaker topologies could be used: a power electronic topology, a purely mechanical topology, or a combination of both, also known as a hybrid topology.
The power electronic or solid state breaker may consist of any active turn-off high power semiconductor such as an insulated gate bipolar transistors (IGBTs), in parallel with a metal oxide varistor (MOV). In a normally conducting mode, the IGBTs conduct the nominal current in the main path. IGBTs are placed in series and parallel such that they can withstand the voltage and current ratings respectively. If bidirectional current conduction is a requirement, then the number of components have to be doubled. Once a fault current emerges, the IGBTs are turned off and the current commutates to the MOV branch. The MOV starts to conduct and starts to absorb the energy in the circuit. The voltage drop across the MOV must be equal to or larger than the system voltage to ensure that the fault current decays to zero. The state of the art for interrupting a fault current with a power electronic breaker is 1 µs, 5 kA, and 640 kV [37].
The main advantages of using a solid state breaker are the absence of mechanical parts and extremely fast turn-off times. The major disadvantage is that it has very high on-state losses. Thus, its operating cost is very high. Excessive losses overheat the breaker, requiring a cooling system. This increased complexity increases the cost of such a topology even more.
The relatively high costs and high on-state losses of a solid state breaker mo-tivate the search for other methods with lower losses. One other method is a pure mechanical breaker composed of three parallel branches. In the first branch, an ultra-fast mechanical switch is located. In a normally conducting mode, the current passes through the metallic contacts of the mechanical switch. Depending on the system voltage, the contacts might be inserted in a vacuum bottle or in any other type of gas to increase the dielectric strength of the medium. The second branch consists of a resonance circuit. A capacitor in series with an inductor is connected in parallel with the mechanical switch. At the instant a fault current
is detected, the mechanical switch is activated. As the contacts open, an arc is established. Once the contacts have separated with a minimum distance such that the mechanical switch can withstand the reverse recovery voltage, the capacitor bank generates a high frequency oscillating current that forces a current zero in the mechanical switch. Thus, the current is interrupted and commutates to the third and last parallel branch, the branch containing the MOV. Finally, the MOV absorbs the magnetic energy stored in the circuit. The fault current starts to decay until it is completely interrupted.
With such a scheme, the losses in the main path are minimized. However, the state of the art mechanical breakers in 2009 have an operational time of 60 ms. This is quite slow and will result in relatively large fault currents before they are interrupted. One way of limiting the current rise is by installing an inductor in the main circuit path such that when a fault occurs, it limits the di
dt. The major
disadvantage of this scheme is arcing. The arc will erode the contacts significantly decreasing their lifetime. Hence, they should be maintained more frequently.
The advantages of both schemes are combined in a third topology, the hybrid HVDC breaker. The hybrid breaker also consists of three parallel stages. In a normally conducting mode, the ultra-fast mechanical switch conducts the nominal current. In case of a fault, the solid state breaker sitting in the second stage is triggered so that it starts conducting. Afterwards, the mechanical switch is activated such that its contacts open to commutate the current to the second stage. Once the mechanical switch is fully open, the solid state breaker is turned off to interrupt the current. The current then commutates to the third and final branch, the one containing the MOV. The MOV limits the current which starts to decay until it reaches zero. The world’s first hybrid HVDC breaker was released by ABB in the year of 2012. It has an operation time of 5 ms [20].
This scheme has very low on-state losses, is relatively fast, and has less arcing time than a purely mechanical breaker. Another advantage is that the demands on the power electronic switch will be reduced since it does not have to conduct the nominal current continuously. One disadvantage is that it is still orders of magnitude slower than a pure solid state solution.
1.2
Objectives of the Thesis
Grid operators introduce a series inductance to limit fault currents in HVDC girds. This however is not an optimum solution since the inductor is costly, results in unnecessary losses, may introduce voltage fluctuations, and might also require an additional cooling system. Moreover, arcing significantly reduces lifetime and reliability increasing maintenance costs. All these drawbacks can be mitigated by decreasing the operational time of the electro-mechanical switch.
Increasing the speed of the electro-mechanical switch by designing high per-formance high efficiency actuators can improve the functionality, reliability, and lifetime of the breaker. These high performance switches can be installed in both
the purely mechanical and the hybrid topologies.
The objective of the thesis is to firstly develop multi-physics simulation models with different levels of accuracy and computation time. Such models can help to understand the behaviour of these devices in which electromagnetics, mechanics, and thermal aspects must be considered. Secondly, another objective is to carry out a sensitivity analysis to identify the sensitivity of the actuator to all involved parameters. This opens the door to study the influence of critical materials and key components that can significantly boost the efficiency and performance of the actuator. Thirdly, another objective is to design a generic, robust, optimization model to optimize these ultra fast actuators and boost their performance and efficiency. Finally, the last objective is to model, design, and build a passive magnetic damper that can be used for decelerating the actuator in a controllable manner.
1.3
Thesis Outline
The main focus of this thesis is the study and design of ultra-fast electro-mechanical switches. This thesis is presented using the general-to-specific pattern. Initially, simulations and experiments are done on a holistic perspective, that is, on the entire mechanical switch. They are then followed with simulations of and experiments on the detailed components. The thesis is divide into the following five chapters:
Chapter 1:
This chapter is the current chapter. It presents the background, motivation, and the objectives of the work.Chapter 2:
This chapter provides a holistic description of the mechanical switch and its sub-components; the actuator, the push/pull rod, the contacts, and the damper. Finite element method based multi-physics models are derived with dif-ferent levels of complexity and are validated by experiments.Chapter 3:
In this chapter, one of the most important sub-components of the mechanical switch is studied, the ultra-fast actuator. The state of the art is investigated. A sensitivity analysis is carried out using experimentally validated multi-physics models. Finally, an optimization scheme is presented.Chapter 4:
In this chapter, another switch sub-component is studied, the damper. A passive magnetic damper is designed, modeled, and experimentally validated.Chapter 5:
This chapter concludes the thesis with a summary of the main findings and touches on future work that can be valuable in this field.1.4
Scientific Contributions
The work of the author has resulted in the following contributions to the state of the art:
• A comprehensive description of the required physics for modeling large im-pulsive forces in large structures within small time scales.
• A detailed description of an ultra-fast switch and necessary requirements to boost its efficiency.
• Experimentally validated multi-physics models with different levels of com-plexity and computation time.
• Sensitivity analysis of an ultra-fast actuator.
• A novel method to boost the efficiency of ultra-fast actuators.
• A robust generic brute force optimization algorithm to optimize ultra-fast actuators with variable objectives and constraints.
• Experimentally validated magnetic damper simulation models. • The design of an optimal passive composite magnetic damper.
1.5
List of Publications
The work presented in this thesis has resulted in a mix of conference publications, journal publications, and patents. The first author is the main corresponding author and has sole responsibility for the paper. All publications are listed in reverse chronological order.
Conference Publications
• A. Bissal, E. Salinas, J. Magnusson, G. Engdahl, “Magnetic Flux Conductors for Ultra-Fast Actuators,” submitted for review to IEEE Energy Conversion
Congress an Exposition (ECCE), Montreal, Canada, September 2015.
• A. Bissal, E. Salinas, J. Magnusson, G. Engdahl, “On the Design of a Linear Composite Magnetic Damper,” accepted for publication in IEEE
Interna-tional Magnetics Conference (INTERMAG), Beijing, China, May 2015.
• A. Bissal, J. Magnusson, E. Salinas, G. Engdahl, “Electrical to Mechanical Energy Conversion of Linear Ultra-Fast Electro-Mechanical Actuators Based on Stroke Requirements,” in International Conference of Electrical Machines
• C. Chen, A. Bissal, E. Salinas, “Numerical Modeling and Experimental Testing of Eddy-Current Dampers” in 14th International Conference on New
Actuators, Bremen, Germany, 2014.
• A. Bissal, J. Magnusson, and G. Engdahl, “The influence of the Velocity Term and Thermal Effects in Force Impulse Generator Simulations,” IEEE
Conference on Electromagnetic Field Computation CEFC 2012, Oita, Japan,
November 2012.
• A. Bissal, J. Magnusson, E. Salinas, G. Engdahl, A. Eriksson, “On the Design of Ultra-Fast Electromechanical Actuators: A Comprehensive Multi-Physical Simulation Model,” Electromagnetic Field Problems and Applications
(ICEF), 2012 Sixth International Conference on, pp.1-4, June 2012.
• A. Bissal, J. Magnusson, G. Engdahl, E. Salinas, “Loadability and Scal-ing Aspects of Thomson Based Ultra-Fast Actuators,” in 13th Internation
Conference on New Actuators, Bremen, Germany, June 2012.
Journal Publications
• A. Bissal, J. Magnusson, M. Backman, E. Salinas, G. Engdahl, “Electrical to Mechanical Energy Conversion of Linear Ultra-Fast Electro-Mechanical Actuators Based on Stroke Requirements,” accepted for publication in IEEE
Transactions on Industrial Applications, 2014.
• A. Bissal, A. Eriksson, J. Magnusson, G. Engdahl, “Hybrid Multiphysics Modeling of an Ultra-Fast Electro-Mechanical Actuator,” submitted for re-view to The international journal of Electric Power Systems Research, 2014. • A. Bissal, J. Magnusson, G. Engdahl, “Multi-physics Modeling and experi-mental verification of Ultra-Fast Electro-Mechanical Actuators,” submitted for review to The International Journal of Applied Electromagnetics and
Mechanics, 2014.
• A. Bissal, J. Magnusson, and G. Engdahl, “Comparison of Two Ultra-Fast Actuator Concepts,” IEEE Transactions on Magnetics, vol.48, no.11, pp.3315-3318, November 2012.
Other Publications
The author has also done minor contributions in the following publications listed below.
• J. Magnusson, J. Martinez-Velasco, A. Bissal, G. Engdahl, “Optimal De-sign of a Medium Voltage Hybrid Fault Current Limiter” Energy Conference
• J. Magnusson, A. Bissal, G. Engdahl, R. Saers, Z. Zhang, L. Liljestrand, “On the Use of Metal Oxide Varistors as a Snubber Circuit in Solid-State Breakers,” in Innovative Smart Grid Technologies Europe (ISGT EUROPE), 2013 4th IEEE/PES.
• J. Magnusson, A. Bissal, G. Engdahl, J.A. Martinez-Velasco, “Design As-pects of a Medium Voltage Hybrid DC Breaker ,” in Innovative Smart Grid
Technologies Europe (ISGT EUROPE), 2013 4th IEEE/PES.
• S. Mousavi, A. Krings, G. Engdahl, A. Bissal, “Novel Method for Measure-ment of Anhysteritic Magnetization Curves,” Conference on the Computation
of Electromagnetic Fields, Compumag 2013.
Licentiate Thesis Publication
• A. Bissal “On the Design of Ultra-Fast Electro-Mechanical Actuators,” Li-centiate Thesis at "The Royal Institute of Technology (KTH)", Stockholm, Sweden, May 2013.
Patents
• P.O. Karlström, E. Salinas, T.R. Eriksson, A. Bissal, “A High Voltage Current Interrupter and an Actuator System for a High Voltage Current Interrupter”, Patent Number: WO2014000790, June, 2012.
Some parts of the listed publications are included and elaborated more in detail in this thesis. Materials based on publications in conferences or journals are copyrighted by their respective associations.
The Mechanical Switch
This chapter provides a holistic description of the mechanical switch and its sub-components; the actuator, the push/pull rod, the contacts, and the damper. The entire switch is modeled and validated by laboratory experiments.
2.1
Requirements of the Mechanical Switch
The mechanical switch of an HVDC breaker normally consists of an ultra fast actuator, a damper, bi-stables, a push/pull rod, contacts, and springs.
Due to the low impedance in an HVDC grid, fault currents can increase quickly in magnitude, attaining large values in a matter of milliseconds. Therefore, a circuit breaker should be able to operate within this time scale such that it is able to interrupt these fault currents promptly before they become large and harder to interrupt.
An example of a typical HVDC breaker located in a 320 kV grid would be to interrupt a fault current within 2 ms. Assuming a maximum over voltage of 10 %, this breaker should ideally be able to withstand 350 kV. If sulfur hexafluoride is used as an insulating medium with a dielectric breakdown strength that is roughly two and a half times that of air, i.e. 7.5 kV/mm, then the contacts should be separated by 50 mm. If the contacts are subjected to a constant acceleration of 25,000 m/s2, then they would attain a speed 50 m/s and travel 50 mm in 2 ms.
Assuming a total moving mass of 3 kg, including the armature, the push/pull rod, and one end of the contact, then a constant force of 75 kN is required. In reality, since the contacts start from rest, then the actuator has to be able to generate a peak force of 150 kN after 1 ms. Such a combination involving large forces, short time scales, and a length scale set by the length of the push/pull rod, usually in the order of several hundreds of millimeters, poses a mechanical challenge.
(a) TC (b) DSC Figure 2.1: Sketches of the drives
2.2
Switch Design
To be able to generate such impulsive forces, an ultra fast electromagnetic actuator is required. Two topologies that are able to generate such forces are considered, the Thomson coil (TC), and the double sided coil (DSC) (see Fig. 2.1). The TC is composed of a flat spirally shaped coil consisting of several turns, with an electrically conducting armature in its proximity. The armature has a flat profile and can be situated directly on top or at the bottom of the coil, as close as possible to minimize the air gap. To generate such large currents, capacitors are connected in series and in parallel to increase the charging voltage and increase the capacitance respectively. Such a unit is charged using a DC power supply and is referred to as a capacitor bank. Upon the discharge of the capacitor bank through the coil, a large current surge is generated. This current generates a time varying magnetic field that will be mostly confined in the air gap between the coil and the armature. A voltage, proportional to the time derivative of the axial component of the field generated by the coil is induced in the armature. Thus, azimuthally directed eddy currents appear directly in close proximity of the coil within the armature. The product of these currents with the radial component of the field generated by the coil and penetrating the armature causes large repulsive forces.
The main difference between a DSC and a TC is the currents in the armature. The armature of a DSC consists of yet another coil that is connected in series with the primary coil such that currents of the opposite direction flow. Currents in prox-imity to each other flowing in opposite directions cause a repulsive force similar to the phenomenon explain above. However, the DSC has several advantages. It does not rely on a time varying field to induce currents in its armature. Furthermore, the generated force is less sensitive to the linearly expanding air gap, causing it to have a higher efficiency than the TC. One major disadvantage limiting its use is due to
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5
6a
7
6b
Figure 2.2: A sketch of a DC breaker showing the current carrying contacts (2), the push/pull rod (4), the armature (5), the coils (6), and the bistables (7).
the required flexible copper cable connecting the primary coil with the armature. This connection is quite sensitive and can break easily severely diminishing the lifetime of the actuator. Yet another difficulty with the DSC is to wind a coil and attach it firmly to the push/pull rod ensuring it does not deform. As for the TC, an aluminum alloy can be manufactured out of one solid piece that generates the forces and can be easily incorporated in the insulating push/pull rod.
This actuator cannot be directly connected to the metallic contacts. One strict requirement of a HVDC breaker is to actuate its contacts using an electrically insulating material to prevent the fault currents to flow elsewhere. An insulating material that electrically isolates the contacts from the armature and yet allows the transmission of forces between them is required. This component is the above-mentioned push/pull rod ((4) in Fig. 2.2) and is usually made of composite materials or ceramics. The impulsive forces are generated in the armature and have to be first transmitted through the push/pull rod before they arrive to the desired location, i.e. the metal contacts. The main part of the body forces are generated within the first few millimeters inside the armature which is located directly on top of the coil. Depending on the system voltage level, the push/pull rod has to have a certain minimum length denoted by LPr. The usual length of such push/pull rods
is around 600 mm. The time it takes for a wave to propagate through the armature to the contacts denoted by ttravelcan be estimated using the velocity of waves (vp)
in a homogeneous isotropic medium with ttravel= LPr vp , (2.1) vp= s K + 4G/3 ρ , (2.2)
where K , G, and ρ are the bulk modulus, shear modulus, and density of the medium.
In this study, a push/pull rod manufactured of fiberglass reinforced epoxy (FR4) is investigated since its properties are significantly superior to the traditional material used for such applications. It is electrically insulating and mechanically very strong with a Young’s modulus of 24 GPa and a yield tensile stress exceeding 310 MPa. It has a shear modulus of 11 GPa and a density of 1850 kg/m3.
Fur-thermore, it can be machined in any desired shape and size even if smoothness in shape should be strived for. If the travel time in the aluminium armature is neglected, then the time it takes for the wave to travel from one end of the push/pull rod to the other is around 160 µs, which is in the time scale of the HVDC breaker operation. This time may be even longer if a longer push/pull rod is used or the push/pull rod is manufactured of a material with a lower Young’s modulus. Therefore, in the following sections, different models are examined in order to study the influence of the push/pull rod mechanics on the force generation mechanism and the displacement of the armature.
2.3
Modeling
From this section on, the TC actuator is studied since it is more robust than the DSC. Modeling such an actuator is quite challenging since large deformations, large displacements, and high currents are involved. This constitutes a multi-physics transient problem, whereby electromagnetics, mechanics, and thermal equations may be needed to be able to accurately predict the behaviour of the actuator.
The modeling of the actuator is divided into two parts, a circuit model and a finite element method (FEM) model that are implemented in the software Comsol Multiphysics (version 4.3b, Comsol AB, Stockholm, Sweden) as shown in Fig. 2.3. An electrical source consisting of series and parallel connected capacitors, a thyris-tor, and cable leads connecting to a Thomson coil (TC) is modeled as a lumped circuit. On the other hand, the TC actuator that comprises a primary stationary coil and a mobile conductive armature, is modeled using a FEM model. These two models are then coupled together and solved simultaneously. To generate a large impulsive current, several parallel and series connected capacitors are charged to a voltage denoted VC. The capacitor bank can be modeled as an effective capacitance
in series with its effective resistance denoted by RC. As for the thyristor and the
V
cR
strayR
TCL
strayL
TCA
rm
a
tu
re
R
cFigure 2.3: A SPICE circuit coupled to a FEM model for a Thomson coil. The coil and the armature are modeled using FEM, since the resistance and inductance of the coil and armature, RTC and LTC, are nonlinear and changing dynamically as
the armature moves away. The capacitor, diode, thyristor, and cables are modeled by lumped parameters.
together and designated by Rstray and Lstray, respectively. A free-wheeling diode
is furthermore placed in parallel with the capacitor bank to prevent the build up of a negative voltage, since an electrolytic capacitor must be charged with only one polarity.
The finite element method is used to model the spiral coil and the armature, solving the electromagnetic and mechanical equations at every time step. In the model, concentric rectangles representing the width and depth of each coil conduc-tor turn are drawn in a two dimensional axi-symmetric geometry, avoiding the need to use 3D simulations, and significantly reducing computation time.
2.3.1
Electromagnetic Modeling
The inputs to the electromagnetic models are the capacitance and the charging voltage of the capacitor bank. The voltage (Vcoil) across the spiral coil in the FEM
model, serves as the connecting point to the circuit model. The total voltage at the terminals of the coil is divided into the different concentric turns such that,
Jen= σeVn 2πrn , (2.3) Vcoil= n X i=1 |Vi| , (2.4) In= Z Jn.ds , (2.5) Icir= I1= I2= ... = In , (2.6)
J(A/m )
Figure 2.4: The current density 100 µs after the discharge of the capacitor bank is distributed in only small portions of the geometry. Positive current densities appear in the top part of the coil conductors, while negative currents are induced in a piece of the armature situated directly above the coil.
which ensures that the current (In) flowing through each and every turn (n) is the
same. Here, the externally applied current density is denoted by Jen and is due
to the voltage across each coil turn Vn. The electrical conductivity is denoted by
σe, the current density by Jn, and the surface area of each conductor by s. The
average radius of each turn is denoted by rn and is given by rin+r2out, the average
of the inner and outer radii of every turn.
The current density induced in a moving conductive armature Ji,arm, is given
by
Ji,arm = σe(E + v × B) , (2.7)
where, v is the velocity of the moving object, E is the electric field and B the magnetic flux density. The currents in a primary coil are simpler since it is stationary. The induced current density is given by
Ji,coil= σeE . (2.8)
by
Jcoil= Je+ Ji,coil , (2.9)
Jarm = Ji,arm , (2.10)
respectively, where Je, is the externally applied current density. An example of
the current densities in the coil and the armature of a TC can be seen in Fig. 2.4. Based on Maxwell’s equations,
∇ × H = J , (2.11)
∇ × E = −∂B∂t , (2.12)
B = ∇ × A , (2.13)
the magnetic equation for the primary coil, TCp, is written as
σe
∂A ∂t +
1
µ∇ × (∇ × A) = Je , (2.14)
where A is the magnetic vector potential, H the magnetic field intensity, J the current density, ∇ the nabla operator, and µ the magnetic permeability. The magnetic equation for the mobile armature, is given by
σe
∂A ∂t +
1
µ∇ × (∇ × A) − σev × (∇ × A) = 0 . (2.15)
The magnetic flux density upon the discharge of the capacitor bank can be seen in Fig. 2.5. A current in the presence of a perpendicularly oriented magnetic field results in a body force fem, also know as a Lorentz force (see Fig. 2.6).
fem= J × B . (2.16)
Similar to the current density distribution, the force density in the armature is inhomogeneous (see Fig. 2.6). It is highest in the domains that have the large product of the current density and the magnetic flux density. Thus, since the field cannot penetrate deep in the armature, the force density is largest close to the surface of the armature located directly on top of the coil. At the center of the armature, there is very little force. This creates a torque which might be destructive to the armature. If the armature is not strong enough, it might bend and deform plastically.
To be able to resolve such small skin depths, second order triangular elements are used to mesh the surface. The maximum allowed element size is limited to half a millimeter to catch these gradients. Although setting such small mesh ele-ments increases memory demand and computation time, it is necessary to increase accuracy and ensure stability and convergence.
B(T)
Figure 2.5: The magnetic flux density, in (T), 100 µs after the discharge of the capacitor bank reaches 5 T and is highest in the air gap separating the coil and the armature.
A variable time step is implemented such that the model uses very small time steps only when needed. Nonlinear components, such as the diode model in the circuit, require a very small time step down to 50 ns. Such a small time step should only be used when the free-wheeling diode is activated. The diode is activated when the voltage across the capacitor bank becomes zero. Although this small time step does not improve the accuracy in the computation of the magnetic field, it is necessary for the diode model to ensure convergence. Otherwise, time steps as large as 10 µs can be used without sacrificing accuracy.
The generated forces accelerate the armature, dynamically changing the size of the air gap. Thus the computed displacement is used to implement a moving mesh based on the Arbitrary Lagrangian-Euler method. If the movement is not accounted for, then unrealistically large forces will be computed. Furthermore, the system resistance and inductance are highly dependent on the size of the air gap. As the air gap increases in size, inductance increases since the field from the primary coil is not cancelled as effectively by the armature. A large inductance limits the
di
dt. A slower current rise results in a larger skin depth. Thus the current diffuses
more into the material, decreasing resistance.
Once the mesh is distorted and violates a mesh criterion, the simulation is paused and the geometry is re-meshed. Prior to re-meshing, the results are ex-tracted from the mesh, interpolated, and set in the newly generated mesh. A stop criterion can be the mesh quality or the maximum allowed elongation of the
Fem(Pa)
Figure 2.6: The force density, in (Pa), 100 µs after the discharge of the capacitor bank. The coil is subjected to compressive forces while the armature is subjected to an axially directed body force that is mostly concentrated in the first few millimeters closest to the coil.
element.
2.3.2
Thermal Modeling
Inrush currents with large current densities and small skin depths may lead to a temperature increase. The temperature rise in a stationary current-conducting coil can be expressed by,
ρCp
∂T
∂t = ∇ · (k∇T ) + Q , (2.17)
where ρ is the density of the material, Cpis its heat capacity, T is the temperature,
k is its thermal conductivity, and Q is the heat source density. The heat source
density is equal to the resistive losses and can be calculated by
Q = J
2
σe
. (2.18)
To simulate the temperature distribution in a moving object, a velocity term should be added if the system of equations is solved using a stationary reference frame. Thus the temperature equation in the armature of a TC or a DSC moving with a velocity v is given by,
ρCp
∂T
∂t + v · ∇T
If a large temperature rise exists, then the electrical conductivity in the domains exposed to these high temperatures deteriorate. This deterioration is a function of temperature and can be quantified by
σe= σe0[1 + α(T − T0)]−1 . (2.20)
If special attention is invested in the dimensioning of the coil conductor, and high current densities with small skin depths do not appear for a long time, then the thermal equations can be disregarded. To avoid high temperatures, a rectangular coil is used whereby the depth of the coil can be dimensioned such that it can act as a heat reservoir. The larger the depth of the conductor, the larger the mass, and the larger is the energy required to increase its temperature. However, the length of the conductor cannot be increased indefinitely as it will affect the generated force. Although increasing the depth of the conductor does decrease the net resistance and limits the temperature rise, it also results in less current densities and longer path for the magnetic field, increasing the reluctance. Therefore, there exists an optimum conductor size. A more detailed study on the influence of temperature on the actuator can be found in [38].
2.3.3
Mechanical Modeling
The developed electromagnetic model and the following mechanical models are co-simulated such that the generated electromagnetic force is used as an input to the mechanical models. The mechanical behaviour of the actuator has a significant influence on the generation of the electromagnetic forces. Several FEM based mechanical models are developed with different levels of complexity. Model 1 is the most detailed and accurate model. Although it is too computationally demanding, it has a very high accuracy and hence is used as a benchmark model. Other less computationally demanding models are developed and investigated to determine if simpler models can be used without compromising accuracy.
Model 1: Full multi-physics model
The full mutli-physics model simulates the behaviour of the breaker when subjected to an impulsive force. All components, i.e. the actuator comprising of the coil and the armature, and the push/pull rod that is at one end attached to the armature and the other to the copper contacts are meshed and simulated. Due to the existence of moderate strains and large displacements, the second Piola-Kirchhoff stress tensor
S and the Green Lagrange strain tensor Emare implemented [39]. Although these
might somewhat collide with the electromagnetic symbols described earlier, they are used nonetheless. Cauchy’s first equation of motion can be expressed by
DivP + Fem = ρ0
D2U
where P is the first Piola-Kirchhoff stress tensor,
DivP = FS , (2.22)
F the deformation gradient, and D is the total derivative. The electromagnetic
forces described in the material reference frame,
Fem= Jfem , (2.23)
are computed by multiplying the calculated electromagnetic forces in the spatial coordinates fem by
J = detF , (2.24) the determinant of F. In Eq. 2.21, ρ0 is the density of the reference material and
U is the displacement vector given by
U = x − X , (2.25)
where x and X are position vectors in the current and reference configurations, respectively. The deformation gradient and the Green Lagrange strain tensor can be computed by
F = GradU + I , (2.26)
Em=
1 2(Grad
TU + GradU + GradTUGradU) , (2.27)
where I is the identity matrix, and GradT is the gradient transpose operator with respect to the material reference frame.
To avoid deformations of any kind, the armature is manufactured out of a material that is mechanically strong, yet electrically conductive at the same time. The material is classified as the aluminum alloy 7075 T651. Such a material is used since it has both a high Young’s modulus and a relatively high electrical conductivity compared to steel alloys. This material is represented by a linear elastic model
S = C : Em , (2.28)
where C is the fourth order stiffness tensor and ":" is the double contraction operator (see Appendix A for more details). These derived equations are also used for the push/pull rod.
These equations are only valid as long as the material remains in the elastic region. If the material deforms plastically, then they are no longer valid. Modeling plastic material is not of interest in this chapter since all components integrated in a HVDC breaker should have a high reliability. They should be able to successfully survive at least ten thousand operations.
Finally, this switch is modeled as an axi-symmetric continuum problem, us-ing Comsol Multiphysics. The developed model consists of 26,000 quadratically interpolated elements.
Model 2: Hybrid multi-physics first order model
A hybrid model is defined as a model consisting of FEM based modeling and analytical equations. The armature and the coil are modeled using FEM i.e. by (Eq. 2.21-Eq. 2.28) since it is very difficult to compute the electromagnetic forces using another method. The push/pull rod on the other hand is modeled using a simplified version of the Kelvin-Voigt model [40]. It is modeled as a first order spring-mass model. This spring has a stiffness k and is bounded by a mass at each side. The first mass, denoted m1, equals half the mass of the push/pull rod
(m1= m/2). On the other hand, the other mass connected at the lower terminal
of the spring is equal to the sum of the masses of half of the push/pull rod and
M , the mass of the attached contact system (m2= m/2 + M ). The sketch of the
model is shown in Fig. 2.7.
If the stresses in the material are assumed to be purely axial, then the stiffness of the push/pull rod can be computed by the linear stress-strain relation
σ = S11= Eǫ =
F
A , (2.29)
where E is the Young’s modulus, ǫ is the strain in the material, F the force acting on the push/pull rod, and A is the push/pull rod’s cross sectional area. The force generated by a elongating a spring by δx is given by,
Fspring= kδx , (2.30)
where k is the stiffness. The axial stiffness of a push/pull rod having a length L, can be represented by
k = EA
L , (2.31)
using the reference geometry.
This model can be generalized into an n segment hybrid model as shown in Fig. 2.7 (C). Dividing the push/pull rod into n segments yields n springs and n + 1 masses. Each spring will have a stiffness of nk and each mass will be m
n+1, except
that the final mass, placed at the very end, will be equal to the mass of the contacts in addition to the mass of one of these partially distributed masses.
Model 3: Push/pull rod assumed infinitely stiff
Model 3 is a simpler model than model 2. In this model, the push/pull rod is assumed to be infinitely stiff. It can also handle the mechanical stresses. Thus, it is modeled as a lumped element having only a mass. The masses of the push/pull rod and the copper contacts are lumped together and attached to the armature. On the other hand, since the armature is exposed to bending moments, it is modelled using equations (2.21-2.28).
m/(n+1) + M
nk
m/(n+1)
m/(n+1)
nk
k
m/2
m/2 + M
(B)
(C)
(A)
Figure 2.7: A sketch showing the modeling of the armature (top, in silver), the push/pull rod (in green), and the contacts (in dark red), by a full multi-physics model in (A), by a first order hybrid model in (B), and by a generalized n segment hybrid model in (C). The push/pull rod’s total mass is represented by m and its stiffness along elongation by k. The mass of the copper contact is represented by
M .
Model 4: Armature and push/pull rod assumed infinitely stiff
Model 4 is the simplest and least computationally demanding model of them all. In this case, all components are modeled using simple mechanics. In other words, the stresses and strains are not computed and their influence on the generated electromagnetic forces is neglected. The developed electromagnetic equations are used to compute the repulsive body force. The axial component of this force, in the z direction (nz) is then integrated to compute the velocity and the position of
Figure 2.8: A picture showing the slim and large mushroom shaped armatures. Although both are designed to withstand the mechanical stresses, one is flexible and prone to bending while the other is more robust and stiffer.
the actuator as Z Z Z Fem· nzrdrdθdz = Mtot dv dt , (2.32) x = Z vdt , (2.33)
where Mtotis the lumped mass of the armature, the push/pull rod, and the metallic
contacts.
2.4
Model Validations by Experiments
Two experimental setups were built to study the validity of the developed models for different cases. The first experiment was done with a slim armature. If exposed to an impulsive force that is large enough for the intended operating speed, it is prone to bending. Even though it will survive, it will deform elastically. The main reason for designing such an armature was to study the influence of finite deformations and bending on the performance of the drive. In the second experiment the slim armature was replaced by a larger, more robust, and bulky armature. This was designed such that it can generate and deliver the electromagnetic forces to the destination with minimum bending. The slim and the large armatures can be seen side by side in Fig. 2.8. Using two differently dimensioned armatures paves the way to validate the full multi-physics model, model 1, and the infinitely stiff model, model 4.
The experimental setup showing the actuator and the steel frame can be seen in Fig. 2.9. In this figure, the mushroom shaped armature is lying on top of a spirally shaped coil. Eight markers are attached on the bakelite frame to center the armature after every operation. If the armature and the coil are not well aligned, then a larger force may be induced on only one side of the armature leading to a
Figure 2.9: A picture showing the experimental setup. The slim mushroom armature is sitting on a flat spiral coil that is connected with large cables to a capacitor bank. It is mounted with a 3.6 kg steel mass.
rotational moment. The stem of the armature has threads such that it can carry a load. This weight represents the mass of the metal contacts. Two cylindrically shaped steel masses, one weighing 3.6 kg and the other 1.5 kg, were attached firmly to the slim and large armatures, respectively. Two large black cables connect the terminals of the coil to the capacitor bank. A capacitor bank, having a capacitance of 33 mF and capable of being charged up to 500 V, was used to power the small armature. A capacitor bank, having a slightly larger electrical energy, was used to power the larger armature. This capacitor bank has a capacitance of 11 mF and is capable of being charged up to 900 V,
The actuator is installed in a large and bulky steel frame that weighs around 300 kg. This steel frame was clamped to a large two-ton steel table to avoid defor-mations and vibrations. To decelerate the armature smoothly without breaking the components, a Newton mass damper was implemented. The top of the armature collides with the damper and transfers its kinetic energy coming to a halt. The nitrogen-oil damper then slowly damps the energy.
The measured parameters were, the voltage of the capacitor bank, the delivered current pulse, the acceleration and the position of the armature. Once the thyristor was triggered, a sudden voltage rise could be measured across its cathode and ground. This was used to send a transistor-transistor logic (TTL) to trigger the
Time [ms] C u rr en t [k A ] exp 100 V sim 100 V exp 200 V sim 200 V exp 300 V sim 300 V exp 400 V sim 400 V exp 500 V sim 500 V 0 0.5 1 1.5 2 2.5 3 0 2 4 6 8 10
Figure 2.10: A picture showing the measured currents (solid lines) and the simulated currents (dashed lines) of the slim armature for increasing charging voltages in steps of 100 V.
high speed camera. The current pulse was measured using a Pearson probe and the armature’s acceleration was measured using accelerometers. These accelerometers however did not survive the high accelerations. After impact, the accelerometers were broken. Thus, the plan to measure the acceleration was abandoned. Instead, a high speed camera filming at a rate of 100,000 fps was used. The armatures were marked with high contrast markers and were filmed. Afterwards, the collected images were calibrated to track the motion of the armature. The velocity of the armature was computed by taking the time derivative of the measured positions.
With the help of the camera, different parts of the mushroom armature could be tracked. To be able to measure bending, the tip of the armature, i.e. the point of the armature having the largest radius was tracked. Another point that was marked and tracked was the top flat part of the armature. Tracking these two points enabled the bending of the armature to be computed.
The measured and simulated current pulses for the slim armature can be seen in Fig. 2.10. Model 1 was used to simulate the actuator since bending was expected. At low voltages, the current pulse looks smooth and normal. It has only one peak situated at 750 µs. However, when the charging voltage was ramped up, thereby increasing the initial energy, oscillations were introduced in the current pulse. This distortion increased with increasing charging voltages. Following the discharge of the capacitor bank charged with 500 V, two distinct peaks could be seen in the current pulse, one at 550 µs, and one at 850 µs. The second peak is even larger than the first. This observation is referred to as the camel hump effect.
To investigate the camel hump behaviour introduced in the current pulse, the bending of the mushroom armature was simulated and measured (see Fig. 2.11).
Time [ms] B en d in g [m m ] Measurement Simulation 0 0.2 0.4 0.6 0.8 0 0.2 0.4 0.6 0.8 1
Figure 2.11: Comparison of the measured and simulated bending of the mushroom armature upon the discharge of a capacitor bank charged with 500 V. The bending cannot be measured for longer time scales since the picture loses focus with large displacements rendering the tracking unreliable.
The focus of the camera was shifted to the head of the mushroom. The first point tracked was point A as indicated in Fig. 2.15. This point is situated at the wing of the armature. The second point that was marked and tracked was a point located at the top part of flat part of the armature. Both points were tracked with a high speed camera simultaneously. Bending is defined as the change in vertical position of one point with respect to another. If both points move vertically with the same distance, then no bending exists.
The comparison of the simulated and observed bending is shown in Fig. 2.11. It can be seen that although there is a small discrepancy in absolute value, the trend shown by simulations and experiments matches very nicely. Some of the sources of error are due to filming with a small angle and loss of focus after 800 µs. This trend is also visible in the current pulse. This is yet another confirmation of how bending affects the current pulse. The second larger peak obtained at 850 µs is due to the smaller air gap caused when the wing of the armature bends back towards the coil. After the armature starts bending away from the coil, the internal elastic forces start to increase. Once these forces become larger than the electromagnetic force, the armature bends backwards towards the coil. This causes a smaller air gap and a sudden decrease in inductance. Reducing the inductance causes a large increase in current thus creating a second current peak that is larger in magnitude. The slim armature’s measured and simulated velocities, due to the discharge of the capacitor bank that is initially charged with different charging voltages are
V el o ci ty [m / s] Time [ms] exp 100 V sim 100 V exp 200 V sim 200 V exp 300 V sim 300 V exp 400 V sim 400 V exp 500 V sim 500 V 0 2 4 6 8 10 0 2 4 6 8 10 12
Figure 2.12: A picture showing the measured velocities (solid lines) and the simulated velocities (dashed lines) of the slim armature for increasing charging voltages in steps of 100 V.
shown in Fig. 2.12. The model predicts the behaviour of the armature nicely. The plots for the large armature’s simulated and measured current pulses are shown in Fig. 2.13. Model 4 was used for the simulation since this armature was designed such that deformations were minimized. Although this assumption fits perfectly for small charging voltages, the deviations between the simulations and the observed velocities increased with increasing charging voltages. The simulated current pulse following the discharge of a capacitor bank charged with 300 V almost coincides with the measured current pulse. However, for larger voltages, the simulated current pulse always peaks prior to the measured current pulses. This is an indication of less inductance in the simulations. Since deformations are not computed, then the total system inductance in the simulation model will be smaller. In reality, the armature bends slightly and moves away from the coil. Thus the magnetic field from the primary coil is not counteracted as efficiently, thereby resulting in a larger inductance. Finally, although some bending does exist, it is very small since all current pulses exhibit only one peak.
The large armature’s simulated and measured velocities are shown in Fig. 2.14. It was expected that the simulated armature velocities would be slightly larger than the measured values for large charging voltages. This is simply because the current peaks in the simulation are larger than those measured current peaks. This leads to larger induced forces. To sum up, for this design with such a bulky armature, model 4 can be used with high confidence. Although a small discrepancy does exist, it is still very accurate.
Time [ms] C u rr en t [k A ] exp 300 V sim 300 V exp 400 V sim 400 V exp 500 V sim 500 V exp 600 V sim 600 V exp 700 V sim 700 V exp 800 V sim 800 V exp 900 V sim 900 V 0 0.5 1 1.5 2 2.5 3 0 2 4 6 8 10 12
Figure 2.13: A picture showing the measured currents (solid lines) and the simulated currents (dashed lines) of the large armature for increasing charging voltages in steps of 100 V.
2.5
Results and Discussion
After validating the developed models with experiments, the entire switch including the push/pull rod is included in the simulations. The push/pull rod is much more elastic than the armature itself. As an initial start, model 1 is utilized to simulate the switch. The velocity distribution, following the discharge of a capacitor bank, can be seen in Fig. 2.15. As expected, 150 µs after discharge, the velocity in the wings of the armature attain 38 m/s. However, this time scale was not enough for the force to propagate to the contacts located at the bottom of the push/pull rod. This is a very large velocity gradient and is a big drawback for the operation of the switch. This result however was not a surprise and was expected initially from Eq. (2.1).
The displacement of the points A, B, and C computed by using model 1, can be seen in Fig. 2.16. The bending of the armature is defined as the difference
Time [ms] V el o ci ty [m / s] sim 300 V exp 300 V sim 400 V exp 400 V sim 500 V exp 500 V sim 600 V exp 600 V sim 700 V exp 700 V sim 800 V exp 800 V sim 900 V exp 900 V 0 1 2 3 4 5 0 2 4 6 8 10 12 14 16 18
Figure 2.14: A picture showing the measured velocities (solid lines) and the simulated velocities (dashed lines) of the large armature for increasing charging voltages in steps of 100 V. The simulation error increases with increasing impulsive forces since even the large armature is elastic and will therefore bend eventually.
between points A and B, while the elongation of the push/pull rod is defined by the difference between points B and C. Evidently, most of the bending occurs in the first 600 µs. The armature bends in the order of several millimeters. Although this does deteriorate the performance of the actuator, the elongation due the elasticity of the push/pull rod is much more severe. 300 µs after discharge, point A, located on the wing of the armature, is displaced by as far as 6 mm. In the mean time, the contacts are still stationary.
Following the simulations done using simulation model 1, it is important to investigate performance of each of the developed mechanical models. The current pulses, computed from models 1 to 4, can be seen in Fig. 2.17. Evidently, simulation model 4 gives the largest current peak, followed by model 3, and finally by models 1 and 2. Model 4 has the least inductance since the armature and the push/pull rod are assumed to be infinitely stiff. A lower inductance leads to a larger and earlier current peak. Model 3 gives a slightly smaller current pulse than model 4 that peaks at a later time. In model 3, the effect of the armature’s bending and elongation can be seen since the push/pull rod is modeled as infinitely stiff. Thus the decrease in the magnitude of the current pulse is not that severe as in the
v(m/s)
Figure 2.15: A 3D picture showing the velocity profile of the system in [m/s] after 150 µs. (B) is a zoom in of the entire actuator shown in (A). The armature, which is situated directly on top of the coil, is threaded into a push/pull rod and attached firmly. Point A is located at the outermost extremity of the mushroom armature. Point B is located at the top of the stem of the armature, i.e. just below the rounded corner joining the head of the mushroom to its stem. Point C is located on the bottom of the push/pull rod, i.e. where the copper contacts are attached.
following cases. Models 1 and 2 give a current pulse that is significantly smaller than the current pulse simulated by using model 4. In this case, taking into account the elastic behaviour of all components has a large impact on the current pulse. After subjecting the armature to an impulsive force, it is suddenly repelled before this force is felt by the contacts. Thus a premature air gap is created increasing system inductance. This sudden increase in inductance limits thedi
dt. Consequently,
Time [ms] P o in t p o si ti o n s [m m ] fr o m M o d el 1 ptA ptB ptC 0 1 2 3 4 0 20 40 60 80 100
Figure 2.16: The displacements of three different points characterizing the dynamic motion of the breaker. The bending of the head of the mushroom can be computed by subtracting the axial displacement of pt B from that of pt A. Similarly, the elongation of the push/pull rod and the stem of the mushroom armature can be computed by subtracting the displacement of pt C from that of pt B.
incorporated components, the larger is the impact on the current pulse due to higher inductances.
This not only negatively impacts the current pulse, but also the efficiency of the actuator. An infinitely stiff system will attain a velocity of 29 m/s while a deformable system will attain only 25 m/s keeping everything else constant. Thus, the efficiency of an infinitely stiff system is 35 % larger than the latter.
Evidently, the models that give lower currents will give smaller forces (see Fig. 2.18). In fact, the generated forces are inversely proportional to the square of the length of the air gap. Thus, the difference in force between all four models is much larger than their difference in the current pulses. Model 4 gives the largest peak force, followed by model 3 and finally by models 1 and 2. Although models 1 and 2 have identical force peaks, they seem to oscillate out of phase. An infinitely stiff system will result in the largest force impulse.
The displacements of the contacts versus time from all the developed models are given in Fig. 2.19. Models 1 and 2 have very similar displacements. However, they oscillate out of phase. Models 3 and 4 travel a longer distance for a given amount of time. Therefore, it can be clearly concluded that model 2 is able to predict the behaviours of the contacts with very good accuracy. The only noticeable difference is that model 1 and 2 oscillate out of phase. If the current pulse, the force impulse, and the displacements are used as judging criteria, then it can be clearly concluded that model 2 has similar results in comparison with model 1, the benchmark model. Model 3 is less accurate, and model 4 has the least accuracy. In this case, model
