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Quality-Factor Considerations for Single Layer Solenoid Reactors

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Quality-Factor Considerations for Single Layer Solenoid Reactors Quality-factor considerations for single layer solenoid reactors M. Nagel1*, M. Hochlehnert1 and T. Leibfried1 1University of Karlsruhe, Institute of Electrical Energy Systems and High-Voltage Technology Engesserstr. 11, 76131 Karlsruhe, Germany *Email: [email protected] Abstract: As it is commonly known, rating and build- are affecting the performance of existing equipment. ing a reactor is not the easiest thing to do. Numerical High frequency noise is subjected to components, pre- solutions of complex magnetic field distributions need viously only fed with clean sine waves of 50/60Hz. to be calculated to verify the design. This is getting even This noise, mainly superimposed by power elec- more challenging, when the quality-factor (Q-factor) of tronic equipment like used in Flexible AC transmission a resonator is of major importance. This problem is for systems (FACTS) build with IGBT valves, is thereby a example appearing, when building resonance circuits new stress to the equipment and poorly investigated yet. with low losses for high voltage and high frequency While in the above mentioned case, the large slew rates (HF) experiments. Coreless, one layer solenoid, or like- of the switching pulses is generating the noise, more wise, reactors are needed there to meet both frequency longer known is high frequent noise to arise by trans- and voltage requirements. Coreless because of the hys- former switching over longer lines. teresis losses of magnetic materials at high frequency In common for all the cases of high frequency noise and only one layer, due to the maximum applicable field at standard equipment is the present lack of knowledge strength per winding, which is dropping significantly at about the performance of the insulation system. In par- high frequency voltage stress. ticular oil or paper insulations of power transformers, Several considerations on the design of the reactor were being the main cause for investigations in that field [2]. done and compared with real implementations of those The first step in any consideration about testing ma- solenoid reactors. Initial boundary conditions are a fixed terials is the building of a suitable source. In this case reactance needed and the length of the wire that needs to this means Voltage amplitudes up to 100kV at frequen- be as short as possible. Still variable are the diameter cies between 10kHz and 250kHz. The higher the fre- and length of the coil, the conductor thickness and type quency can be driven, the better and the more results are of wire, meaning normal enamelled- or special HF-litz possible to obtain. wire. While the latter influence is easy to determine, the higher the frequency, the more it is advised to cope with 2 REACTOR IN TEST SETUP the skin-effect and to use HF-litz, all other factors are bound to the magnetic induction of the construction. To For the tests described above, concerning high fre- avoid complex field simulations, a close observation of quency and high voltage testing of dielectric materials, the magnetic field at discrete positions is derived into a different basic setups of the power supply can be con- normalized Q-factor-curve for the evaluation of differ- sidered. The only one suitable for the tasks of producing ent configurations. Measurements of several model re- a constant sine wave with variable amplitude is a series actors were used, either to assess the found influences resonating circuit. This namely consisting of a capacitor and to verify the gathered curve. A close prediction of and a reactor connected in series with an excitation the Q-factor to be measured at a newly build solenoid at source as it can be seen in Fig. 1. a fixed frequency could thereby be performed. The re- sult of these considerations is an optimum sizing of a solenoid reactor and an estimate on the possible loss of RESONANCE quality for a deviant design. DC L 1 INTRODUCTION = AC C Driven by the continuing rise of energy consumption in the industrial centres of modern cities, the need for VALVE CONTROL more long range transportation of energy is getting more 1-250kHz urgent. Along side with the prospect of decentralised Fig. 1: Resonance circuit in the basic test setup generation, e.g. by solar, wind and wave generation the need for transportation capability is gaining more and Hereby the excitation voltage is provoking the oscil- more priority, not to mention the grid connection of lating circuit to work at its natural frequency. By the those generation plants. As already discussed, for ex- driven current in the circuit, a voltage drop-of over the ample by cigré [1], those changes in existing networks reactance is producing the desired amplitude for the quality factors seem to be valid for different designs and measurements. The specimen under investigation is put even between them as well. between the electrodes of the capacitor and stressed with that same voltage, which is also recorded. 3 INDUCTANCE AND QUALITY There are three major boundaries in this whole setup. First, the resonance frequency of the series circuit When looking at the investigated reactance we need needs to be the one being under test. A task not too easy to focus on the actual inductivity of it and its calcula- to fulfil, concerning the dielectric constant of the used tion. According with that, it is broadly known, that a material and the impact on the electric field in the ca- simple formula for each design is not available, nor any- pacitor. A tuning of the circuit is therefore absolutely thing usable available. All considerations on that matter, necessary. This can either be done by varying the reac- suitable for simple working formulas are given and de- tance, a suggestion which is practically not easily done rived by [3]. Main focus for any of those calculations is for low frequency increments, or by adding or subtract- always a given setup of windings, finally leading to a ing more capacitance. inductivity L. Anything of that is done by using differ- Secondly and surely the most annoying in the design ent boundary considerations, only usable in that particu- process is the constant use of materials, that are not in- lar case. This is neglecting the fact of any quality of the vestigated for the kind of stress being subjected to them. designed dimensions. For example is a reactor in use, for which you need to Considerations on any criteria of the design is done design the number of turns, layers, insulation and thick- for transformer and converter cases, or for radio fre- ness. Some of the limitations are easy to make. A quency considerations in how to obtain the largest in- roughly calculated reactance, corresponding to the mini- ductance value possible with a given wire. mum capacitance, will give basic clues. The test voltage Solving ways like those are not feasible in our case. rising up to 100kV will result in the same voltage ampli- Given by the resonance circuit, a fixed value is needed tude between the ports of the reactance. If not using a crucially. Starting from there we need to build the best single layer, this voltage is present in a winding next to reactance possible. Only boundary there is the building another. This can be mastered by shaping the insulation of it. type and thickness. At least as long as standard AC or So what is influencing the quality of a reactor, given DC stress is used. Calculating thicknesses, amounts and by (2) with the used frequency f of investigation. behaviours with unknown values is simply waste of 2⋅⋅⋅π f L paper and time. QReactor = (2) Thirdly, and initially causing this presentation, is the RL reachable amplitude in the circuit, directly bound to the Since, as stated above, the frequency and Inductivity quality factor Q of the elements the higher the fre- are not changeable, only by reduction of the real Resis- quency gets. tance of the reactor, a rise in quality-factor is possible. 1 L So it is absolutely needed to think about what is in total Q = (1) RC R C causing RL. First to mention there is the wire itself. The used ma- The actual resistance R, compared to the inductive terial, copper in most cases, has a real resistance. While (L) and capacitive (C) part is dampening and limiting we are not changing the material or distributor this the reachable resonance amplitude. Given a fixed exci- value is unchangeable either. In any case this effect is tation voltage. The above stated problems are concern- present. Which means equally for either DC or AC phe- ing both elements equally. Yet the capacitor consists in nomenon. a large amount of the specimen under investigation At high currents the skin effect will also influence which can not be changed. Tuning is done by adding the resistance of the wire. Any conducted current will ceramic capacitors, connected in series for not exceed- see a displacement towards the surface. This is leading ing their estimated breakdown strength. No shaping of to a higher current density in the hull and less to none in quality factor can be done in either of the capacitors. the middle. Even more displacement is occurring when Only by the design and shape of the built reactance, any the frequency of the used current rises. Ultimately, the positive change in the quality factor can be achieved. higher the surface area of any used conductor is, the Cores inside the reactor are totally neglected here, lower will be its resistance and vice versa. since only ferrite materials could handle such high fre- Not only are we solely looking at the wire itself, but quencies, but being priceless for such big diameters and to the linking of the windings to one another.
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