Improved control of current supply to transformer rectifier flux pumps

Abstract

The present technology relates to the field of superconducting transformer rectifier flux pumps and the field of controlling the supply of alternating current to the transformer rectifier flux pump to charge a load. A response of the transformer rectifier flux pump to a characterization current source is determined, which may include determining a value of the flux pump corresponding to a value of the applied current. A current supply value is calculated for each of a plurality of target values ​​of load current to be supplied to the load. The current supply to the flux pump is controlled accordingly. The supply may be varied based on feedback received from the flux pump, such as a sensor measuring a value on the secondary side of the transformer.

Description

[Technical Field]

[0001] The present technology relates generally to the field of superconductors, and more particularly to superconducting transformer rectifier flux pumps. More particularly, the present technology relates to methods and apparatus for controlling the supply of alternating current to a transformer rectifier flux pump for charging a load. [Background technology]

[0002] Superconducting circuits are used in a wide range of applications. Examples of applications for systems containing superconducting circuits include, but are not limited to, superconducting magnets, flux pumps, fault current limiters, magnetic energy storage systems, space propulsion, nuclear fusion, nuclear magnetic resonance (NMR), magnetic resonance imaging (MRI), levitation, water purification, and induction heating.

[0003] Many applications involving superconducting circuits require low-voltage, high-current power supplies, such as powerful high-temperature superconducting (HTS) magnets for applications like nuclear fusion. Meeting these requirements requires vast amounts of space with conventional power supplies, posing significant infrastructure challenges. Furthermore, connecting normal-conducting circuits to superconducting circuits housed in cryostats creates significant heat loads on the cryostat through physical contact, making cooling difficult. This requires sophisticated thermal design and imposes a significant thermal penalty on the cryostat and cooling system. Furthermore, large voltage drops across normal-conducting circuit components necessitate a power supply much higher than that required just to energize the superconducting coils.

[0004] Superconducting power supplies help solve these problems. Higher current densities allow power supplies to be more compact, and HTS flux pumps can be used to magnetically couple alternating current (AC) circuits without physical contact, avoiding cooling issues. Flux pumps can be used to induce current in superconducting materials without direct electrical contact, using electrolytic flux. This allows current to flow through HTS circuits without the need for a normally conductive electrical connection.

[0005] To power HTS magnets, large direct currents (DC) are required, which require rectification to convert AC (current that periodically reverses direction) into DC (current that flows in only one direction). Thus, one type of flux pump is the transformer-rectifier flux pump (TRFP), which typically uses a non-superconducting transformer primary coil magnetically coupled to a superconducting secondary coil, and a rectifier circuit coupled to the secondary coil.

[0006] There are some known issues with TRFPs. For example, residual flux during the charging process can gradually offset the transformer core. This offset limits the absolute current generated in the secondary circuit, changing the output of the flux pump. In addition, the amount of power generated can vary depending on the load current level. This can result in the TRFP being unable to effectively charge the load coil. Summary of the Invention [Problem to be solved by the invention]

[0007] An object of the present technology is to provide an improved method of controlling the supply of applied current to a transformer rectifier flux pump to charge a load, or an improved apparatus for controlling the supply of applied current to a transformer rectifier flux pump to charge a load, or an improved transformer rectifier flux pump.

[0008] Alternatively, the purpose of this technology is to at least provide the public with useful options. [Means for solving the problem]

[0009] In accordance with certain aspects of the present technology, methods and / or apparatus are provided for determining how to provide an applied current to a transformer rectifier flux pump to charge a load. In other aspects of the technology, methods and / or apparatus are provided for controlling the provision of applied current to a transformer rectifier flux pump to charge a load, e.g., controlling the provision based on a determination. Determining how to provide the applied current may include determining expected operation of the transformer rectifier flux pump.

[0010] In certain forms, determining how to supply the applied current to the transformer rectifier flux pump includes characterizing a response of the transformer rectifier flux pump to a characterization source of the applied current. Characterizing the response of the transformer rectifier flux pump may include determining a plurality of values ​​of the applied current at the transformer rectifier flux pump corresponding to a respective plurality of values ​​of the applied current supplied to the transformer rectifier flux pump. One or more steps in determining how to supply the applied current to the transformer rectifier flux pump may occur during a charging process, i.e., after charging of the load has begun.

[0011] In certain embodiments, determining how to supply the applied current to the transformer rectifier flux pump includes calculating one or more waveform values ​​for supplying the alternating current to the transformer rectifier flux pump for each of a plurality of target values ​​of load current supplied to the load. In certain embodiments, the target values ​​of load current may be calculated in one or more preselected increments up to a preselected target value of the load current.

[0012] In certain embodiments, the plurality of values ​​determined in the step of characterizing the response of the transformer rectifier flux pump to the characterizing source of applied current may be used to calculate a plurality of target values ​​of the load current, respectively.

[0013] In certain forms, controlling the supply of applied current to the transformer rectifier flux pump includes varying the supply of applied current to the transformer rectifier flux pump during the process of charging the load. The supply of applied current may be varied based on feedback received from the transformer rectifier flux pump, for example, feedback received from one or more sensors configured to measure a value of the transformer rectifier flux pump. The sensor may measure a value on a secondary side of the transformer rectifier flux pump.

[0014] According to one aspect of the present technology, a method for controlling a supply of an applied current to a transformer rectifier flux pump to charge a load is provided. The transformer rectifier flux pump may include a transformer including a primary coil and a secondary coil. The transformer rectifier flux pump may further include a rectifier connected to the secondary coil and configured to supply a load current to the load. The secondary coil, the rectifier, and the load may include one or more superconducting materials. The method may include calculating one or more waveform values ​​of an applied current supplied to the transformer rectifier flux pump for each of a plurality of target values ​​of the load current supplied to the load. The method may further include controlling the supply of the applied current to charge the load based on the one or more waveform values ​​of the supply of the applied current.

[0015] In certain forms, the method may include calculating one or more waveform values ​​of a supply of applied current to the transformer rectifier flux pump for target values ​​of the load current at one or more preselected increments up to the preselected target value of the load current.

[0016] In certain forms, the one or more waveform values ​​of the supply of applied current to the transformer rectifier flux pump may include a peak value of the supply of applied current when flowing in a first direction and a peak value of the supply of applied current when flowing in a second direction, the second direction being opposite to the first direction.

[0017] In certain forms, a method for calculating one or more waveform values ​​of a supply of an applied current to a transformer rectifier flux pump may include calculating one or more target voltage values ​​of the transformer rectifier flux pump for each of a plurality of target values ​​of a load current supplied to a load. The method may further include calculating one or more waveform values ​​of the supply of the applied current to the transformer rectifier flux pump from the one or more target voltage values.

[0018] In certain embodiments, the one or more target voltage values ​​may include a target value for a voltage output to a load. In certain embodiments, the target value for a voltage output to a load may include a target value for a voltage across a switch connected in parallel with the load.

[0019] In certain forms, the one or more target voltage values ​​may include a first target value of a voltage output to the load when the rectifier is in a first configuration in which current generated in the secondary coil is supplied to the load, and the one or more target voltage values ​​may further include a second target value of a voltage output to the load when the rectifier is in a second configuration in which no current is supplied to the load from the secondary coil.

[0020] In certain forms, the method may include providing a characterization source of impressed current to the transformer rectifier flux pump. The method may further include characterizing a response of the rectifier and / or the load to the characterization source. The method may further include controlling the supply of impressed current to charge the load based on the characterized response.

[0021] In certain forms, the method may include providing a characterization power supply and characterizing a response to the characterization power supply before commencing supplying an applied current to the transformer rectifier flux pump to charge the load.

[0022] In certain forms, the step of providing a characterization power supply includes providing a first characterization power supply of impressed current to the transformer rectifier flux pump when the rectifier is in a first configuration in which current generated in the secondary coil is supplied to the load, and characterizing a first response of the rectifier and / or the load to the first characterization power supply. The method may further include providing a second characterization power supply of impressed current to the transformer rectifier flux pump when the rectifier is in a second configuration in which no current is supplied from the secondary coil to the load, and characterizing a second response of the rectifier and / or the load to the second characterization power supply.

[0023] In certain embodiments, characterizing the response of the rectifier and / or the load to the characterized power source may include determining a plurality of voltage values ​​in the rectifier corresponding to a plurality of values ​​of applied current supplied to the primary coil. The plurality of voltage values ​​in the rectifier may include a voltage value output to the load. The voltage value output to the load may include a voltage value across a switch connected in parallel with the load.

[0024] In certain embodiments, the method may further include varying a supply of applied current to the transformer rectifier flux pump during the process of charging the load. In certain embodiments, the supply of applied current may be varied based on feedback received from one or more sensors configured to measure a value of the transformer rectifier flux pump. In certain embodiments, the feedback may include comparing the measured value with a target value of the transformer rectifier flux pump. In certain embodiments, varying the supply of applied current may include using a PID loop.

[0025] In certain embodiments, the one or more waveform values ​​may be values ​​of a current supplied to the primary coil. In certain embodiments, the transformer-rectifier flux pump may include a magnetic field generator for applying a magnetic field to one of the lengths of Type II superconducting material. The one or more waveform values ​​may be values ​​of a current supplied to the magnetic field generator.

[0026] According to another aspect of the present technology, a method for controlling a supply of an applied current to a transformer rectifier flux pump to charge a load is provided. The transformer rectifier flux pump may include a transformer including a primary coil and a secondary coil. The transformer rectifier flux pump may further include a rectifier connected to the secondary coil and configured to supply a load current to the load. The secondary coil, the rectifier, and the load may include one or more superconducting materials. The method may include providing a characterization power source of the applied current to the transformer rectifier flux pump. The method may further include characterizing a response of the rectifier and / or the load to the characterization power source. The method may further include controlling the supply of the applied current to charge the load based on the response of the characterization power source.

[0027] According to one aspect of the present technology, there is provided a method for controlling the supply of an applied current to a transformer rectifier flux pump to charge a load. The transformer rectifier flux pump may include a transformer including a primary coil and a secondary coil. The transformer rectifier flux pump may further include a rectifier connected to the secondary coil and configured to supply a load current to the load. The secondary coil, the rectifier, and the load may include one or more superconducting materials. The method may include controlling the supply of the applied current such that a voltage generated in the secondary coil of the transformer is substantially zero when integrated over one cycle.

[0028] According to another aspect of the present technology, a method for controlling a supply of applied current to a transformer rectifier flux pump to charge a load is provided. The transformer rectifier flux pump may include a transformer including a primary coil and a secondary coil. The transformer rectifier flux pump may further include a rectifier connected to the secondary coil and configured to supply a load current to the load. The secondary coil, the rectifier, and the load may include one or more superconducting materials. The method may include modifying the supply of applied current to the transformer rectifier flux pump based on feedback received from the transformer rectifier flux pump, for example, one or more sensors configured to measure a value of the transformer rectifier flux pump. The sensor measures a value on the secondary side of the transformer rectifier flux pump.

[0029] In accordance with another aspect of the present technology, there is provided an apparatus for controlling the supply of applied current to a transformer rectifier flux pump to charge a load, the apparatus may include a processor configured to perform the method of any one of the other aspects of the present technology.

[0030] According to another aspect of the present technology, there is provided a transformer rectifier flux pump including a transformer including a primary coil and a secondary coil. The transformer rectifier flux pump may further include a rectifier connected to the secondary coil and configured to supply a load current to a load. The secondary coil, the rectifier, and the load may include one or more superconducting materials. The transformer rectifier flux pump may further include a current control mechanism for controlling the supply of applied current to the primary coil. The current control mechanism may be configured to perform any of the methods of other aspects of the present technology.

[0031] In certain embodiments, the rectifier may include a switching assembly including one or more switches. In certain embodiments, each switch comprises a length of superconducting material configured to conduct a switch current, the length of superconducting material having a critical current. The transformer rectifier flux pump may further include one or more magnetic field generators, each configured to apply a magnetic field to the length of superconducting material of each switch. Each magnetic field generator may be configured to be selectively controlled to switch the length of superconducting material between a low resistance state and a high resistance state.

[0032] In certain configurations, in a low resistance state, the magnetic field strength is relatively low and the switch current may be substantially less than the critical current, and in a high resistance state, the magnetic field strength is relatively high and the critical current is reduced and the switch current may approach, be substantially equal to, or be greater than the critical current for the length of superconducting material.

[0033] In certain forms, the current control mechanism may be configured to control the supply of applied current to one or more magnetic field generators.

[0034] According to another aspect of the present technology, a transformer rectifier flux pump is provided, including a transformer including a primary coil and a secondary coil. The transformer rectifier flux pump may further include a rectifier connected to the secondary coil and configured to supply a load current to a load. The secondary coil, the rectifier, and the load may include one or more superconducting materials. The rectifier may include a switching assembly including one or more switches. In a particular embodiment, each switch includes a length of superconducting material configured to conduct a switch current, the superconducting material length having a critical current. The transformer rectifier flux pump may further include one or more magnetic field generators, each configured to apply a magnetic field to the superconducting material length of each switch. Each magnetic field generator may be configured to be selectively controlled to switch the superconducting material length between a low resistance state and a high resistance state. The transformer rectifier flux pump may further include a current control mechanism for controlling the supply of applied current to the primary coil and / or the one or more magnetic field generators. The current control mechanism may be configured to carry out the methods of any of the other aspects of the present invention.

[0035] Further aspects of the present technology, which should be considered in all its novel aspects, will become apparent to those skilled in the art upon reading the following description, which sets forth at least one example of a practical application of the technology. One or more embodiments of the present technology will now be described, by way of example only and not by way of limitation, with reference to the drawings. [Brief explanation of the drawings]

[0036] [Figure 1] 1 shows an example of a graph of electric field versus current for a high temperature superconductor. [Figure 2] 1 is a graph showing the relationship between electric field and current in a superconducting material when three external magnetic fields of different magnitudes are applied. [Figure 3A] FIG. 1 is a schematic diagram of an example half-wave transformer rectifier flux pump in accordance with one aspect of the present invention. [Figure 3B] FIG. 1 is a circuit diagram of an example half-wave transformer rectifier flux pump in accordance with one aspect of the present invention. [Figure 3C] FIG. 3B is a circuit diagram of the example half-wave transformer rectifier flux pump shown in FIG. 3A during the charging phase. [Figure 3D] FIG. 3B is a circuit diagram of the example half-wave transformer rectifier flux pump shown in FIG. 3A during a maintenance phase. [Figure 3E] FIG. 3B illustrates one embodiment of a half-wave transformer rectifier flux pump represented in the circuit diagram of FIGS. 3A-3C. [Figure 4] FIG. 1 is a circuit diagram of an example of a center-tapped full-wave transformer rectifier flux pump in accordance with one aspect of the present invention. [Figure 5] 1 is a schematic diagram of an example of a processing system according to an embodiment of the present invention. [Figure 6] Simulations show the change in flux over time in the core of a conventional TRFP transformer with different core cross-sectional areas. [Figure 7A] 1 is a graph illustrating the magnitude of applied current supplied to a primary coil of a transformer rectifier flux pump versus the elapsed time of one cycle of the current during various phases in the process of charging a load, in accordance with one aspect of the present technology; [Figure 7B] 1 is a graph illustrating the magnitude of applied current supplied to a primary coil of a transformer rectifier flux pump versus the elapsed time of one cycle of the current during various phases in the process of charging a load, in accordance with one aspect of the present technology; [Figure 8] 1 is a flowchart of a process performed by a current control mechanism when performing a method for implementing a PID loop in accordance with a particular embodiment of the technology. DETAILED DESCRIPTION OF THE INVENTION

[0037] 6.1. Principles of superconductivity

[0038] A superconductor or superconducting material has a critical temperature, T cA material has zero electrical resistance below a certain temperature called the critical magnetic field H. This state of zero electrical resistance is often called the superconducting state. When a material is in the superconducting state below the critical temperature, a phenomenon called the Meissner effect occurs. This is a phenomenon in which all magnetic fields are completely excluded from the superconductor. A superconductor is a material that has zero electrical resistance below a critical magnetic field H c1 It is a perfect diamagnetic material up to a certain magnetic field strength, called the critical field. At this point, the superconductor cannot block the magnetic field, and the field penetrates the superconductor, causing it to transition from a superconducting state to a state where it no longer has zero electrical resistance. This critical magnetic field also implies a limit to the electrical current that the superconductor can carry, known as the critical current I c It is known as.

[0039] There are two types of superconductors: Type I and Type II. Type I superconductors are typically pure metals and exhibit the behavior described above. Type II superconductors behave differently. Below a certain magnetic field (the first critical magnetic field H c1 ) is applied, it emits flux like a Type I superconductor, but at the second critical magnetic field (H c2 ), which is always H c1 It is larger than H c1 and H c2 In magnetic fields between , the magnetic field can penetrate type II superconductors in the form of Abrikosov vortices. This creates an intermediate phase in which the material remains essentially superconducting but can exhibit a finitely small resistance. This behavior allows type II superconductors to carry much more current in an applied magnetic field than type I superconductors, making them useful for practical applications.

[0040] The critical temperature of a superconductor is typically defined as the temperature below which the resistivity of the superconductor is zero or near zero. In other words, when a superconductor's temperature is below the critical temperature, it is said to be in a superconducting state; when a superconductor's temperature is above the critical temperature, it is said to be in a non-superconducting state. Many superconductors have critical temperatures near absolute zero; for example, the critical temperature of mercury is known to be 4.1 K. However, some materials are known to have much higher critical temperatures, such as 30 K to 125 K. For example, the critical temperature of magnesium diboride is approximately 39 K, while the critical temperature of yttrium barium copper oxide (YBCO) is approximately 92 K. These superconductors are commonly referred to as high-temperature superconductors (HTS). HTS are Type II superconductors.

[0041] 6.1.1.Critical current

[0042] The critical current of a high-temperature superconducting wire or tape is typically defined as the current flowing through the superconducting wire / tape that produces a field drop of 100 μV / m (=1 μV / cm) along the wire. The critical current is a function of both the superconducting material used and the physical arrangement of the superconducting material. For example, a wider tape / wire may have a higher critical current than a narrower tape / wire made of the same material. However, for simplicity of discussion, throughout this specification, we refer to the critical current of the superconductor / material.

[0043] In a superconductor, the current I reaches the critical current I c When I is approximately equal to the critical current I, the resistance of the superconductor is small, but not zero. c If the temperature is much higher than 0.05°C, the resistance of the superconductor becomes so great that heat dissipation occurs, heating it above its critical temperature and causing it to cease to be superconducting, a condition sometimes called a "quench" and potentially damaging to the superconductor itself.

[0044] An exemplary graph of the internal electric field versus current in a high temperature superconductor is shown in Figure 1. The electric field shown in this graph is related to the resistance by the following equation:

number

[0045] Thus, the graph in Figure 1 relates the resistance per unit length of the superconductor, and since the curve shown is nonlinear, the resulting resistance of the superconductor will be nonlinear with respect to current.

[0046] In Figure 1, the critical current I of a superconductor c Below we see that the electric field strength within a superconductor is essentially zero. As the current in a superconductor approaches the critical current, the electric field in the superconductor begins to increase. At the critical current, the electric field in the superconductor is 100 μV / m. Further increasing the current in the superconductor above the critical current causes a rapid increase in the electric field strength within the conductor.

[0047] The transition from the superconducting state to the normal conducting state in HTS materials, such as those shown in Figure 1, can be described by an empirical law known as the EJ power law.

number

[0048] Reference may be made herein to the relative resistance of superconducting materials and components that include superconducting materials. More specifically, this specification refers to superconducting materials in a low or high resistance state. It is understood that when in a superconducting state, superconducting materials can have zero or substantially zero resistance, and thus these resistances are often expressed in terms of the electric field that exists across the superconducting material for a given current. However, for ease of discussion, reference will be made throughout this specification to relative resistances, e.g., low and high resistance states of a superconducting material.

[0049] The term "low resistance state" may refer to when a superconducting material has near-zero resistance in a superconducting state, or when the material has low resistance in a partially superconducting state. The term "high resistance state" refers to a state in which a superconducting material has a resistance substantially greater than that of the low resistance state, e.g., a resistance that is substantially non-zero, or a resistance that is near zero but substantially greater than that of the low resistance state. For the avoidance of doubt, the high resistance state referred to herein may include a superconducting state, unless the context clearly indicates otherwise.

[0050] Similarly, when this specification refers to a superconductor being in a high resistance state as a result of the current carried by the superconductor exceeding the critical current, it should be understood that the high resistance state may also be achieved when the current carried by the superconductor approaches or substantially equals the critical current, unless the context clearly indicates otherwise.

[0051] In describing the technology herein, materials and components that make up the materials will be referred to as "superconducting." This term is used commonly in the art for such materials and should not be interpreted to mean that the materials are always in a superconducting state. Under certain conditions, the materials and components that make up the materials may not be in a superconducting state; that is, the materials are said to be "superconducting."

[0052] 6.1.2.Superconducting Materials

[0053] Certain forms of the technology may include components formed of Type II superconductors, such as high-temperature superconducting (HTS) materials. Exemplary HTS materials suitable for use in the described forms of the technology include copper oxide superconductors, e.g., rare-earth barium copper oxides (ReBCO) such as yttrium barium copper oxide, gadolinium barium copper oxide or bismuth strontium calcium copper oxide (BSCCO) superconductors, and iron-based superconductors. BSCCO superconductors typically exhibit a strong interdependence between critical current and applied magnetic field, which may make them particularly suitable for some forms of the current technology.

[0054] 6.1.3.Superconducting Switch

[0055] Some of the present technology uses superconducting switches. A superconducting switch, as described herein, is a switch formed from a length of superconducting material that can transition between low and high resistance states. These states are not the open / closed circuit states typical of conventional normally conductive switches, but rather may be considered low resistance (a few ohms or less) by the standards of normally conductive switches, even in the higher resistance states. In certain configurations, the length of superconducting material forming the switch may be in a superconducting state when in the high resistance state.

[0056] When in the superconducting state, a superconducting material can have zero or substantially zero resistance, and so the resistance in the superconducting state is more generally represented by the electric field that exists across the superconducting material for a given current. However, throughout this specification, to simplify the foregoing discussion, reference is made to relative resistance, low resistance states, and high resistance states.

[0057] This transition between low and high resistance states in a superconducting switch can be induced using thermal, self-field, or magnetic field driven switching. Forms of this technique can be used: self-field switching and magnetic field switching.

[0058] 6.1.3.1. Self-Field Switching

[0059] In self-field switching, the length of superconducting material forming the switch and the waveform of the applied current supplied to that superconducting material are such that during a portion of the waveform the current exceeds the critical current I of the switch. C This causes the length of the superconducting material to transition to a higher resistance state. During other portions of the applied waveform, the current produced exceeds the critical current I C , the switch remains in a low-resistance state. This switching mechanism has been demonstrated to produce the rectifying effect required for flux pumping.

[0060] The following describes a form of technology that does not use self-switching, but it should be understood that other forms of technology may also use the method.

[0061] 6.1.3.2. Magnetic Field Switching

[0062] The critical current of a superconductor depends on the external magnetic field applied to the superconductor. More specifically, as a higher external magnetic field is applied to the superconductor, the critical current decreases to the critical magnetic field value, beyond which the superconductor is no longer in a superconducting (low resistance) state. This relationship is illustrated in Figure 2, which is a graph showing the relationship between the electric field and current in a superconducting material when three external magnetic fields of different magnitudes are applied. The maximum external magnetic field B 印加1 So, the critical current I c1 In some configurations, an external magnetic field to achieve this effect can be applied perpendicular to the surface of the superconductor along the length where the critical current is reduced or suppressed. The applied magnetic field can be unidirectional and can be called a DC magnetic field. Alternatively, in a time-varying magnetic field, the direction changes periodically, for example, as a sinusoidal wave, and can be called an AC magnetic field.

[0063] In all superconductors, the application of a small magnetic field causes a rapid decrease in the critical current. This means that small changes in the applied magnetic field can result in large changes in the critical current. This relationship depends on the superconducting material and the manufacturing method of the length of superconducting material carrying the current.

[0064] It should be noted that this mechanism of reducing or suppressing the critical current by applying an external magnetic field (e.g., a DC magnetic field) is different from the phenomenon of dynamic resistance, which occurs when a superconductor is exposed to a time-varying magnetic field (e.g., an AC magnetic field) while carrying a DC current. This creates a DC electrical resistance in the superconductor, and if that resistance becomes large enough, the superconductor can switch to a more highly resistive state.

[0065] Although forms of the present technology are described in relation to a DC applied magnetic field, it should be understood that in other forms of the technology, other types of critical current suppression, such as dynamic resistance, may be used instead.

[0066] 6.2. Transformer Rectifier Flux Pump

[0067] Portions of the present technology relate to flux pumps, particularly transformer rectifier flux pumps (TRFPs). Certain exemplary forms of TRFPs are described in detail in the following documents, but it should be understood that forms of the present technology are not limited to the concepts described as being used in or applicable to these forms of TRFPs, and that other forms of TRFPs may be used with other forms of the present technology.

[0068] Figure 3A is a schematic diagram of a flux pump 100 in accordance with certain aspects of the present technology, with the illustrated example being a TRFP 100. Figures 3B-3D are circuit diagrams of one example of such a flux pump 100 in accordance with certain aspects, and Figure 3E is a diagram of one form of TRFP 100 whose circuit diagram is shown in Figures 3B-3D. For clarity, not all components are shown in these figures.

[0069] The TRFP 100 includes a primary side 200 and a secondary side 300, as described in more detail below. In use, an alternating primary current I is applied to the primary side 100 of the TRFP 100. P is supplied, and the TRFP 100 receives a rectified, or DC, load current I L to the load 390. P Over multiple cycles of the load current I, the flux flow through the TRFP 100 "injects" more and more current into the load 390 each cycle. L increases.

[0070] 6.2.1.Primary side

[0071] The primary side 200 of the TRFP 100 receives a primary current I from a current source 202. P In certain embodiments, the TRFP 100 may also include a current source 202. In certain embodiments, the primary 200 includes components formed from conventional (non-superconducting) conductors. The primary coil 204 may include one or more turns of conductor. A length of conductor may be configured to receive a primary current I P may be transported to the primary coil 204.

[0072] The primary side 200 may include a primary magnetic core 206 formed from a material having a relatively high magnetic permeability, such as ferrite. A primary coil 204 may be wound around a portion of the primary magnetic core 206.

[0073] The current source 202 may be configured to supply a current having selected characteristics to the primary coil 204. Further description of these characteristics is provided below. The current I supplied by the current source 202 P may be controlled by a current control mechanism 203. The current control mechanism 203 may take any suitable form, such as a processor operatively connected to the current source 202. In certain forms, the TRFP 100 may also include a current control mechanism 203.

[0074] 6.2.2 Secondary Side

[0075] In a particular form of the present technology, the secondary 300 of the TRFP 100 includes a secondary coil 304 and a rectifier 320. The secondary 300 supplies a load 390 with a load current I L The secondary 300 of the TRFP 100 and the load 390 may be housed within a cryostat 310. Generally speaking, the conductive components of the secondary 300 of the TRFP 100 may be formed from one or more superconducting materials.

[0076] Cryostat

[0077] 3A-3E, TRFP 100 may include a cryostat 310 for housing the components of secondary side 300 and maintaining a temperature suitable for the superconducting components to assume a low resistance, i.e., superconducting state (in the absence of other factors that may cause one or more of the superconducting components to assume a high resistance, i.e., non-superconducting state, such as a current exceeding the critical current of the superconducting material or a magnetic field exceeding the critical magnetic field of the superconducting material). For example, cryostat 310 may be configured to maintain secondary side 300 at a temperature above the critical temperature T of the superconducting material within secondary side 300. C The primary side 200 may be maintained at a temperature below 1000 K. Any suitable form of cryostat or cooling mechanism may be used. In some forms, some or all of the components of the primary side 200 may be located within the cryostat 310. The cryostat is not shown in Figures 3B-3E.

[0078] 6.2.2.2. Secondary Coil

[0079] The secondary side 300 of the TRFP 100 includes a secondary coil 304. The secondary coil 304 may include one or more turns of a superconductor, such as an HTS material. The secondary side 300 may include a secondary magnetic core 306 formed from a material having a relatively high magnetic permeability, such as ferrite. The secondary coil 304 may be wound around a portion of the secondary magnetic core 306.

[0080] In certain embodiments of the present technology, the TRFP 100 may include a transformer 150. The transformer 150 may include a primary coil 204 and a secondary coil 304. The transformer 150 may include a magnetic core formed from a primary magnetic core 206 and a secondary magnetic core 306. The primary magnetic core 206 and the secondary magnetic core 306 may be magnetically coupled to form a magnetic circuit. In some embodiments, the primary magnetic core 206 and the secondary magnetic core 306 may be integral parts of the same body of magnetically permeable material. In other embodiments, the primary magnetic core 206 and the secondary magnetic core 306 may be physically and thermally separated, e.g., the secondary magnetic core 306 may be located inside the cryostat 310 and the primary magnetic core 206 may be located outside the cryostat 310, but may be positioned relative to each other such that they are magnetically coupled to carry a magnetic field.

[0081] During operation, a time-varying (e.g., alternating) current I flows through the primary coil 204. P is supplied to the secondary coil 304, a time-varying (e.g., alternating) current I S is induced.

[0082] The TRFP 100, including the transformer 150 in a particular form of technology, may be suitable for a variety of applications, such as superconducting magnets, superconducting motors / generators, space propulsion systems, fusion reactors, research magnets, NMR, MRI, levitation, water purification, and induction heating. The use of a transformer 150 in a TRFP allows for electrical isolation of the two parts of the TRFP. The form of TRFP suitable for an application depends on various factors, including physical size constraints, cryogenic heat load, output power, efficiency, cost, and controllability.

[0083] 6.2.2.3. Rectifier

[0084] In certain forms of the present technology, the secondary 300 of the TRFP 100 is connected to a secondary coil 304 via an AC current I induced in the secondary coil 304. S DC load current I to supply to load 390 L3B-3E and described in detail below, although rectifier 320 may include other arrangements of components in other forms of technology.

[0085] A rectifier 320 according to aspects of the present technology may include parts such as a switching assembly 330, a magnetic field generator assembly 340, and a control mechanism 350. These functional parts are described in further detail below, along with descriptions of exemplary forms of each functional part. Specific examples of rectifier 320 with exemplary forms of each functional part are also described. Other combinations of exemplary forms of each functional part are also provided in some aspects of the present technology, and it should be understood that the present technology is not limited to the specific examples shown and / or described.

[0086] In a particular embodiment, the secondary coil 304 supplies an AC current I to the switching assembly 330. S The switching assembly 330 includes an arrangement of one or more electrical switches 332 for rectifying and supplying a DC load current I to a load 390. L The magnetic field generator assembly 340 includes one or more magnetic field generators 342, each configured to apply a magnetic field to one or more electrical switches 332. A control mechanism 350 controls the magnetic field generator assemblies 342 to switch the electrical switches 332 of the switching assembly 330. The magnetic field generator assembly 340 and the control mechanism 350 are not shown in the circuit diagrams of Figures 3B-3D. The magnetic field generator assembly 340 and the control mechanism 350 are not shown in the circuit diagrams of Figures 3B-3D.

[0087] 6.2.2.3.1. Switching Assembly

[0088] In certain forms of the present technology, a switching assembly 330 includes an arrangement of one or more electrical switches 332 to rectify the AC current and convert it into a load current I for supply to a load 390. LThe arrangement of the electrical switches 332 within the switching assembly 330 determines the type of rectification performed by the rectifier 320, as described below. Various forms of technology may use one or more electrical switches 332 in any configuration to produce the rectifying effect. The following description describes examples of suitable configurations of electrical switches, but it should be understood that other configurations may be used in other forms of technology.

[0089] In a particular embodiment of the present technology, as shown in Figures 3B-3E, for example, rectifier 320 is a half-wave rectifier. In the embodiment shown in Figures 3B-3E, the switching assembly includes two superconducting switches 332a and 332b. The two switches 332a and 332b are connected in series, and a load 390 is connected in parallel to one of switches 332b. The length of superconducting material to which load 390 is connected may be referred to as a "bridge," and switch 332b may be referred to as a bridge switch. The other switch may be referred to as series switch 332a.

[0090] In the configurations shown in FIGS. 3B-3D, the non-zero resistance R J is used to connect in parallel the length of superconducting material forming electrical switch 332b between the superconducting material connected to secondary coil 304. In addition, the junction connecting rectifier 320 to load 390 has a non-zero resistance R L , where . For example, each joint can be a solder joint. As described below, for purposes of modeling the operation of the resulting circuit, the joint connecting the bridge and the length of superconducting material connecting to secondary coil 304 is shown as resistor 334, and the joint connecting load 390 to rectifier 320 is shown as resistor 392.

[0091] AC current I S is supplied from the secondary coil 304 to the switching assembly 330. The switching assembly 330 converts the AC current I SFor example, the control mechanism 350 may be configured to control the state of each switch 332 to rectify the alternating current I S Each switch 332 is controlled based on the direction of flow of the AC current I S Since the direction of flow of the AC current I depends on the phase of the current, in this configuration, the control mechanism 350 S For example, the state of each switch 332 is controlled in a timely manner based on the phase of the AC current I S is flowing in a first direction (i.e., when current flow is positive), first switch 332a is in a low resistance state and second switch 332b is in a high resistance state. This creates a low resistance path around the outside of the loop through switch 210a and across load 600. This is the configuration of rectifier 320 shown in FIG. 3C, where switch 332a is shown as a closed switch and switch 332b is shown as a variable resistor, and current I L is supplied to the load 390, this is sometimes referred to as the "charging phase."

[0092] When the polarity of the current changes (e.g., from positive to negative), control mechanism 350 may transition switch 332a to a high-resistance state and switch 332b to a low-resistance state. The high-resistance state of 332a prevents current flow from the transformer, partially blocking negative current flow. At the same time, the low-resistance state of 332b provides a path for current in the load to continue flowing, while exponentially decreasing with a time constant L / R (this means that if the entire load loop is superconducting, the load current will remain constant). This is the configuration of rectifier 320 shown in FIG. 3D, where switch 332a is shown as a variable resistor and switch 332b is shown as a closed switch, and may be referred to as the "maintenance phase" because the current in load 390 is generally maintained during this phase of the cycle. Thus, the current through load 390 is half-wave rectified. Additionally, the control mechanism 350 may open and close the switches 332a and 332b (ie, increase or decrease the resistance of the switches 332a and 332b) at the appropriate times to increase or decrease the current in the load 390 as needed.

[0093] In some forms of the present technology, the control mechanism 350 may control both the switches 332a and 332b to be in a low resistance state simultaneously for a period during the AC cycle. S can be in a high resistance state only part of the time that I is positive, and switch 332a S can be in a high resistance state only part of the time that I is negative, and the rest of the time, I S Whether t is positive or negative, both switches are in a low-resistance state. This can be used as a practical control strategy to ensure that the switches are in an open configuration (i.e., a high-resistance state) when current through the switches is in the desired direction. Control mechanism 350 may control the rectifier switches of any form of technology described herein in this manner, even if not explicitly stated. In some forms, control mechanism 350 may control switches 332a and 332b in this manner in a sustain mode, as described below.

[0094] 3B-3E show an example arrangement of two switches 332 in the switching assembly 330 forming a half-wave rectifier, it should be understood that other switching assemblies 330 in other forms of the present technology have other arrangements of switches 332 for rectifying alternating current. Additionally, switching assemblies 330 in other forms of the present technology may have other numbers of switches 332. For example, in some forms of the technology in which the rectifier 320 functions as a half-wave rectifier, the switching assembly 330 may include a single superconducting switch 332.

[0095] Additionally, in some forms of the present technology, the rectifier may function as a full-wave rectifier. In some such forms, the rectifier may include a switching assembly 330 including an arrangement of two switches 332. In other forms, the rectifier may include a switching assembly 330 including an arrangement of four switches 332. An exemplary form of a center-tapped full-wave transformer rectifier is shown in FIG. 4.

[0096] Suitable placement of switch 332 in switching assembly 330 included as part of rectifier 320 is described in more detail in PCT Application No. PCT / NZ2022 / 050009, published as International Publication No. WO2022 / 164330, the contents of which are incorporated herein by reference.

[0097] SWITCH

[0098] This aspect of the technology involves the use of one or more superconducting switches 332 that utilize the principle that the critical current of a superconducting material decreases when a high external magnetic field is applied to it, i.e., the aforementioned magnetic field switching. An example of such electrical switches 332a and 332b is shown in Figures 3A-3E. For reasons that will be explained later, switches 332a and 332b are shown in Figure 3B as variable resistors.

[0099] The electrical switch 332 includes a length of high temperature superconducting (HTS) material, such as any of the types of HTS material described above. The HTS material has a critical current I c and critical temperature T c HTS materials have a critical temperature T c The HTS material is placed in a cryostat 310 configured to maintain the HTS material at a temperature below 1000 K.

[0100] External magnetic field B 印加 When a magnetic field B is applied to the entire length of the HTS material, the critical current decreases as shown in Figure 2. Therefore, 印加 By applying a magnetic field B, the entire length of the HTS material can be made to function as a switch. 印加 When the magnitude of the magnetic field B is at a particular value, the HTS material is in a low resistance state if it conducts a switch current (i.e., a current through the electrical switch 332) that is less than the critical current. 印加 If the magnitude of increases from that value to a magnitude high enough that the critical current decreases to a value close to or below the magnitude of the current carried by the HTS material, the HTS material will enter a more highly resistive state.

[0101] The low resistance state of the HTS material can be considered equivalent to a closed state of switch 332, while the high resistance state is similar to an open state of switch 332. However, it is important to note that the high resistance state does not represent an electrical open circuit, as is common in mechanical switches, but rather a highly resistive conductive state. In this highly resistive conductive state, the HTS material can become highly resistive while remaining superconducting, or it can become non-superconducting.

[0102] The magnetic field B between the low and high resistance states of the switch 印加 The difference in magnitude between the magnetic field B and the magnetic field B can be varied in magnitude, including a continuous difference or a difference between two magnitudes. 印加 The magnitude of can be zero or a non-zero value.

[0103] In some forms, the magnetic field B applied to the HTS material 印加 It is understood that any magnitude of can be less than the magnitude of the critical magnetic field, where the critical magnetic field is the magnitude of the external magnetic field applied to the HTS material that causes the HTS material to transition to a high resistance state.

[0104] Energy losses in a superconducting switch are related to the critical current of the switch during switching. Because electrical switch 332 operates by reducing the value of the critical current during switching, electrical switch 332 (and devices including electrical switch 332) has lower losses and therefore higher efficiency than conventional superconducting switches.

[0105] In other forms of the present technology, the switching assembly 330 of the rectifier 320 may include one or more switches 332 that operate according to one or more different principles. Examples of alternative principles on which the switches 332 may operate are described in more detail in PCT Application No. PCT / NZ2022 / 050008, published as International Publication No. WO2022 / 164329, the contents of which are incorporated herein by reference. In particular forms, the switching assembly 330 may include multiple switches 332 that operate according to any combination of one or more of the above principles.

[0106] In some embodiments, one or more of the switches 332 may operate based on the principle of self-field switching, as described above. In some embodiments, one or more of the switches 332 may operate based on the principle of dynamic resistance. This occurs when a superconductor is subjected to a time-varying magnetic field while a direct current (DC) is passing through it. This creates a DC electrical resistance in the superconductor, which, if sufficiently large, can switch the superconductor to a more highly resistive state. The time-varying magnetic field that causes the dynamic resistance phenomenon can be an AC magnetic field, such as a sinusoidally varying magnetic field. For superconducting materials (e.g., wires or tapes) with a length significantly greater than their width or depth, the dynamic resistance can be primarily due to the component of the time-varying magnetic field applied to the superconducting material that is perpendicular to the length of the material.

[0107] 6.2.2.3.3. Magnetic Field Generator Assembly

[0108] In particular forms of the present technology, the magnetic field generator assembly 340 includes one or more magnetic field generators 342, each configured to apply a magnetic field to one or more electrical switches 332 of the switching assembly 330, and in particular to one or more superconducting materials comprising each electrical switch 332.

[0109] Exemplary configurations of the magnetic field generator assembly 340 are shown in FIGS. 3A-3E. In these configurations, the magnetic field generator assembly 340 includes one or more magnetic field generators 342. Exemplary configurations of the magnetic field generator assembly 340 are shown in FIGS. 3A-3E. In these configurations, the magnetic field generator assembly 340 includes one or more magnetic field generators 342. Each magnetic field generator 342 may include a magnetic core 344. The magnetic core 344 may be a high-permeability magnetic core, such as a ferrite core (e.g., an iron core) or a laminated steel core. In other configurations, other types of high-permeability magnetic cores at the operating frequency may be used, as well as non-magnetic cores or air cores. An air core may advantageously reduce the size, weight, and cost of the electrical switch 332 and may also provide the ability to drive higher currents without saturating the core. In the illustrated configuration, the magnetic core 344 is a substantially ring-shaped solid core, such as a square-shaped ring with rounded corners.

[0110] In an exemplary embodiment, the magnetic core 344 forms a gap 346. The gap 346 can be a space within the solid magnetic core 344, such as the space on one side of a square ring core. Any portion of the air core can be considered a gap 346.

[0111] In an exemplary embodiment, a conductor is wound around a portion of the magnetic core 344 within the coil 348. For example, the coil 348 formed by the conductor may be wound around one side of a square ring core, e.g., the side opposite the side where the gap 346 is formed. In the case of an air core, the coil 348 defines a volume within the core, which can be considered to be the air core and include the gap 346. In use, an applied current may flow through the conductor, sometimes referred to as a generator current. The flow of the generator current through the coil 348 generates a magnetic field within the core 344 and across the gap 346. In a particular embodiment of the present technology, a length of HTS material comprising the electrical switch 332 is positioned in the gap 346, and the magnetic field generated by the magnetic field generator 342 across the gap 346 is coupled to an external magnetic field B applied to the switch 332. 印加 This becomes:

[0112] In certain embodiments, the generator current carried by the conductors is supplied by a current source, e.g., an AC current source, such that the generator current is an AC generator current. In certain embodiments, the current source may be any of the current sources described in PCT Application No. PCT / NZ2022 / 050009, published as International Publication No. WO2022 / 164330, the contents of which are incorporated herein by reference. The generator current may be controlled by a current control mechanism, such as control mechanism 350, described below.

[0113] The strength of the magnetic field generated by magnetic field generator(s) 342 may vary continuously. Alternatively, the strength of the magnetic field generated by magnetic field generator(s) 310 may vary between two constant values. In certain forms, one of the constant values ​​may be zero.

[0114] An example of a TRFP 100 in accordance with one aspect of the present technology is shown in FIG. 3E. While the cryostat 310 is not shown in FIG. 3E, it should be understood that all superconducting components are housed within the cryostat 310. In one aspect of such a TRFP 100, the magnetic core of each of the transformer 150 and the first and second magnetic field generators 342 is divided into two core portions, with one core portion of each magnetic core located inside the cryostat 310 and the other core portion located outside the cryostat 310; for example, the secondary magnetic core 306 of the transformer 150 is located inside the cryostat 310 and the primary magnetic core 206 is located outside the cryostat 310. The two portions of each magnetic core are magnetically coupled. The interior of the cryostat 310 is maintained at a temperature low enough to allow superconducting materials located within the cryostat 310 (including those forming the electrical switch 332) to operate in a low-resistance, i.e., superconducting, state.

[0115] In another version of this TRFP 100, the magnetic cores 344, 206, 306 of the magnetic field generator 342 and the transformer 150 are all located within the cryostat 310. The transformer 150 and each of the magnetic cores of the first and second magnetic field generators 342 and 310 are split into two core sections, with the two core sections within each magnetic core separated by a thermal break. The two sections of each magnetic core are magnetically coupled. Conductors connecting the primary coil 204 of the transformer and the coil 348 of the magnetic field generator 342 pass through the wall of the cryostat 310.

[0116] Although a particular exemplary arrangement of magnetic field generators 300 in magnetic field generator assembly 340 has been described, it should be understood that other magnetic field generators 342 in other forms of technology may take other forms, for example, as described in PCT Application No. PCT / NZ2022 / 050009, published as International Publication No. WO2022 / 164330, the contents of which are incorporated herein by reference.

[0117] 6.2.2.3.4. Control Mechanism

[0118] A rectifier 320 according to certain forms of the present technology includes a control mechanism 350 configured to control a magnetic field generator assembly 340 to switch an electrical switch 332 of a switching assembly 330 .

[0119] In certain forms of the present technology, a control mechanism 350 is configured to control the magnetic field generator(s) 342 of the magnetic field generator assembly 340, such that the magnitude of the magnetic field generated by each magnetic field generator 342 is controlled by the current I in the primary coil 204. P For example, the magnitude of the magnetic field generated by each magnetic field generator 342 is based on the phase of the primary current I P In one example, the fixed phase difference may be zero, in which case the magnetic field generated by each magnetic field generator 342 varies with the phase of the primary current I P In a particular example, the magnitude of the magnetic field generated by each magnetic field generator 342 varies with the primary current I P, which is the first value for part of each cycle, and the primary current I P and the second value for another portion of each cycle of the time series. Either the first value or the second value can be zero.

[0120] In another form of the present technology, the rectifier 320 may include a control mechanism 350 as described in PCT Application No. PCT / NZ2022 / 050009, published as International Publication No. WO2022 / 164330, the contents of which are incorporated herein by reference.

[0121] Load

[0122] A load 390 is connected to the rectifier 320, which supplies a DC load current I L In some forms, the load 390 may be considered to be part of the TRFP 100, i.e., part of the secondary side 300, while in other forms, the load 390 may be considered to be separate from the TRFP 100, which is configured to supply a load current to the load 390.

[0123] The form of the technology may not be limited by the nature of the load 390. However, in some examples, the load 390 may include an HTS magnet, which may include a coil and core of superconducting material. A typical example of the load 390 may have a large inductance. In the form of the technology shown in Figures 3B-3D, the load 390 has an inductance L コイル is expressed as an inductor.

[0124] 6.3. Current Source and Current Control Mechanism

[0125] A current source 202 applies a current I to a primary coil 204 having selected characteristics. P and may be configured to supply a current I Pis described as being controlled by current control mechanism 203. Certain aspects of the present technology relate to methods of controlling the current supplied to primary coil 204, as described further below, although in certain forms the technology is not limited by the type of device and system used to supply current to primary coil 204 and may use any suitable form of current source 202 and current control mechanism 203. Certain aspects of the present technology relate to methods of controlling the current supplied to magnetic field generator assembly 340 and also the technology is not limited by the type of device and system used to supply current to magnetic field generator assembly 340 and may use any suitable form of current source and control mechanism 350.

[0126] In certain embodiments, the current control mechanism 203 may include a waveform generator, such as an arbitrary waveform generator (AWG) or a function generator. In certain embodiments, the waveform generator may be implemented through a device whose operations are dedicated to the function of waveform generation. In certain embodiments, the waveform generator may include any processing system or computing device configured to execute waveform generator software, including devices not dedicated to this purpose (e.g., general-purpose computing or processing devices).

[0127] 5 is a schematic diagram of an exemplary processing system 400 in accordance with one aspect of the present technology. In particular aspects, the current control mechanism 203 may include the processing system 400 configured to operate as a waveform generator.

[0128] The processing system 400 includes a hardware platform 402 that manages the collection and processing of data from one or more devices, which may include sensors, user devices, etc. The hardware platform 402 includes a processor 404, memory 406, and other components typically included in such computing devices. The hardware platform 402 may be located locally with respect to the device(s) or remotely from the device(s) and may receive data via an appropriate communications link. In the illustrated embodiment of the technology, the memory 406 stores information accessible by the processor 404, including instructions 408 that can be executed by the processor 404 and data 410 that can be retrieved, manipulated, or stored by the processor 404. The memory 406 may be any suitable means known in the art for storing information in a manner accessible by the processor 404, including a computer-readable medium or other medium for storing data that can be read with the aid of an electronic device.

[0129] The processor 404 may be any suitable device known to those skilled in the art. While the processor 404 and memory 406 are illustrated as being within a single unit, this is not intended to be limiting, and it should be understood that each function described herein can be performed by multiple processors and memories that may or may not be separate from each other or separate from the processing system 400. The instructions 408 include any set of instructions suitable for execution by the processor 404. For example, the instructions 408 may be stored as computer code on a computer-readable medium. The instructions may be stored in any suitable computer language or format. The data 410 may be retrieved, stored, or modified by the processor 404 in accordance with the instructions 410. The data 410 may be formatted in any suitable computer-readable form. Again, while the data is shown stored in a single location, this is not intended to be limiting, and the data may be stored in multiple memories or locations. The data 410 may also include a record 412 of a control routine related to aspects of the system 400.

[0130] The hardware platform 402 may communicate with a display device 414 to display the results of processing the data. The hardware platform 402 may communicate via a network 416 with one or more other devices (e.g., user devices such as a tablet computer 418a, a personal computer 418b, a smartphone 418c, or other devices including sensors such as current sensors and voltage sensors and current sources 202), or with one or more server devices 320 with associated memory 322 for storing and processing data collected by the local hardware platform 402. It should be noted that the server 320 and memory 322 can take any suitable form known in the art, such as, for example, a “cloud-based” distributed server architecture. The network 416 may include a variety of configurations and protocols, including the Internet, an intranet, a virtual private network, a wide area network, a local network, a private network (wired or wireless) using one or more company-proprietary communication protocols, or a combination thereof.

[0131] The hardware platform 402 is configured such that the input is a current I supplied to the primary coil 204 by the current source 202. P The hardware platform 402 may be configured to execute software configured to allow input of a desired waveform of the current I. The input may be a user, who may interact with the software via one or more user devices, such as the display device 414 and / or the personal computer 418b. The hardware platform 402 may be configured to execute conventional waveform generation software known in the art, for example. The software executed by the hardware platform 402 may generate a waveform of the current I. PThe waveform of the desired current may be determined by the hardware platform 402 itself, e.g., by the processor 404. The processor 404 may be configured to execute one or more algorithms for determining the desired current waveform, as described further below. In such an embodiment, the input may include the hardware platform 402, e.g., the processor 404.

[0132] The hardware platform 402 communicates with and controls the current source 202 to generate a desired waveform, specifically the current I, selected by a user and / or a processor 404. P The waveform of the current I P changes over time, the current I flows through the primary coil 204. P The hardware platform 402 may be configured to provide the current source 202 via a wired and / or wireless communication link to control the current source 202.

[0133] In certain embodiments, the TRFP 100 includes a current source 202 and a current control mechanism 203. In other embodiments, the current source 202 and the current control mechanism 203 are separate from the TRFP 100, and the current source 202 is configured to supply current to the TRFP 100.

[0134] 6.4. Control of the primary current supplied to the TRFP

[0135] As previously mentioned, the current source 202 on the primary side 200 supplies an applied current I having selected characteristics to charge the load 390 in a desired manner. P to the primary coil 204. In certain forms of technology, these characteristics are determined based on the load current delivered to the load 390 at the end of the load charging process and the rate of increase of the required load current.

[0136] 6.4.1. Development of previous research

[0137] Previous research on superconducting TRFPs has focused on demonstrating the principles of operation in laboratory environments, with little research on how TRFPs would perform in practical applications. For example, in laboratory experiments, TRFPs are used to charge loads that include relatively small load coils, e.g., load coils with relatively small inductances. In practical applications of superconducting TRFPs, load coils with much higher inductances may be used. HTS magnets for many applications may have inductances of hundreds of millihels or more, as opposed to the several-millihelometer range assumed in much of the existing literature. The inductance of the load coil is a key parameter that defines the charging rate of a TRFP; another key parameter is the voltage generated across the load coil during each cycle. The charging rate is inversely proportional to the inductance of the load coil; that is, as the inductance increases, the number of charging cycles to reach a specified current increases proportionally. Therefore, a TRFP with a load coil with an inductance of hundreds of millihels may need to operate for thousands of cycles to generate the same current as a TRFP with a load coil with an inductance of several millihels, as commonly discussed in the existing literature. In addition, load currents in practical applications can exceed approximately 10 kA, whereas conventional TRFPs typically achieve values ​​in the 2-3 kA range using a 10 μH load coil. Combining these two effects, a TRFP with comparable voltage output may require an additional 10,000 cycles to achieve the same output current with a 100 mH load coil.

[0138] In developing the particular form of the technology described herein, consideration was given to how the TRFP would operate using parameters that would likely be used in a practical application of the technology, so that certain improvements in how the TRFP operates could be identified.

[0139] Unless otherwise specified, it should be understood that the principles of operation of the TRFP described herein are not limited to application in situations where the system parameters are as described above, and that certain aspects of the technology may be applicable to any form of TRFP, regardless of size, parameters, or application.

[0140] 6.4.2. Secondary Net Voltage

[0141] In previous studies, the AC applied current I supplied to the primary coil 204 P It is concluded that it is desirable to control the current so that the net current is zero when integrated over a current cycle. However, in some situations, for example when using a TRFP to charge a load coil with a relatively high inductance, this method has been found to cause problems such as unstable charging or inability to charge to the required current level. This issue will be briefly addressed by explaining the mechanism that achieves rectification in a TRFP.

[0142] In the example of the TRFP 100 shown in FIGS. 3A-3E, the AC primary current I P The rectification of the voltage V B This voltage is determined by the critical current I of the length of superconducting material in bridge switch 332b at the applied magnetic field and temperature. C and the current flowing through this switch I B In the TRFP 100, the current I C and I B Rectification is achieved by controlling the voltage V over time, and the desired voltage V is output to the load 390. B In the existing research, I B In reality, the dynamic nature of I over time is not taken into account. B The change in is affected by two factors: 1) the secondary current I induced in the secondary coil 304 S and 2) the secondary current I around the secondary side 300 of the TRFP 100.S Distribution of

[0143] For a TRFP 100 including a rectifier 320 in the form of a half-wave rectifier, the AC primary current I P has a constant waveform over each cycle, if the core of the transformer 150 does not saturate during operation, and / or if no DC offset is generated during charging, the secondary current I in the secondary coil 304 S remains constant during charging. In both cases, this means that the primary current I P The secondary current I generated from the applied waveform S In existing HTS TRFPs, a DC offset is observed, resulting in a change in the secondary current I throughout the charging cycle. S changes. Secondary current I S When changes occur, the voltage V B The charge rate also changes accordingly, changing and limiting the charge speed.

[0144] The transformer 150 is dimensioned to provide a peak primary current I P In a properly selected transformer with a primary waveform, saturation may not occur initially. However, if the primary waveform does not have the appropriate characteristics, saturation may occur. A simulation of the saturation of a transformer 150 is shown in Figure 6. This behavior is consistent with the experimentally measured changes. Due to the dynamic nature of the flux pumping behavior, the flux in the core was observed to vary significantly over time, both in magnitude and direction. The effect of this flux change is seen in the secondary current I S When a DC offset occurs, the secondary current I S The absolute value of ΔV shifts, causing a change in the charging profile of the load 390.

[0145] After factoring in factor 1) as above, and then factor 2), the secondary current I around the secondary side 300 of the TRFP 100 S The distribution of the current I supplied to the load 390 will be explained. L As increases, (I S =IB +I L ) the current I flowing through the bridge switch 332b. B The voltage V B I B However, since it is related to the magnitude of the voltage I B decreases over the entire charging cycle, while (I S The voltage V generated during the maintenance phase (since the distribution of B,M remains constant. In fact, the voltage V B and voltage V B,M This charge balance between the two determines the shape of the transformer flux in Figure 6. Initially, V B >V B,M , and therefore the load current I L A residual flux in the same direction as I remains in the transformer core. L As increases, V B decreases, and finally V B,M At this point, the flux in the transformer core passes through zero and then saturates in the opposite direction to the load current. This is shown in Figure 6. This saturation is dependent on the size of the transformer core and the I L These observations contradict many previous explanations for the origin of the DC offset in half-wave rectified flux pumps.

[0146] Although the above discussion has treated the two factors 1) and 2) separately, in reality, the relative strengths of each factor influence the other. In fact, it is this correlation between these factors that has contributed to the observations that have led to certain aspects of current technology.

[0147] The existence of the aforementioned DC offset is well established in the literature and has traditionally been considered an unavoidable factor in the charging cycle. Previous studies have recognized that DC offset is important in limiting performance. For example, previous studies have examined how passive components (e.g., resistors) or built-in DC offsets in the primary waveform can improve TRFP performance. However, this work was based on the assumption that DC offset is a fundamental factor in the operation of flux pumps.

[0148] Certain aspects of the present technology allow for the significant avoidance (or at least reduction) of DC offset. In some forms, this may ensure that the performance of the transformer 150 remains constant while the load 390 is charging. Also, the current I S By significantly avoiding DC offsets, high-Tc superconducting TRFPs may be able to achieve higher load currents in some configurations, potentially leading to more stable TRFP performance.

[0149] To substantially avoid the DC offset described above, the integrated voltage V generated over one cycle in the secondary coil 304 of the transformer 150 is S It has been determined that should be substantially zero. As a result, some forms of the present technology include a current control mechanism 203 configured to control the supply of AC current to the TRFP 100, e.g., to the primary coil 204 of the primary side 200 of the TRFP 100, such that the voltage V generated across the secondary coil 304 of the transformer 150 S becomes substantially zero when integrated over one cycle. For half-wave rectifier 320 in the form of the technology shown in Figures 3B-3E, this corresponds to the voltage across bridge switch 332b during the charging phase of the circuit being equal to the voltage across switch 332a during the maintenance phase.

[0150] However, the magnitude of the voltage on the secondary side 300 of the TRFP 100 is determined by the nonlinear resistance of the superconducting material(s) in the electrical switch 332. This makes it difficult to calculate the parameters of the desired primary waveform to achieve the required charging, especially as charging occurs and the current in the load 390 is gradually increasing. As a result, in certain forms of the present technology, the primary current I P The waveform of the signal is feedback-controlled. An exemplary form of such feedback control is described below.

[0151] In some embodiments of the technology described below, a rectifier 320 in the form of a two-switch half-wave rectifier is used, although in other embodiments, other configurations of rectifier 320 in TRFP 100 may be used, and equivalent analyses and structures may be generated for such other embodiments.

[0152] In other embodiments of the present technology, a non-zero DC offset may be desirable or unavoidable, such as in the case of a center-tapped full-wave rectifier described below. In such embodiments, the TRFP 100 may be configured so that the DC offset is not zero, but rather predetermined and optionally the same over multiple consecutive cycles. This allows the DC offset to be precisely managed during charging of a load. Accordingly, in some embodiments, the TRFP 100 may include a current control mechanism 203 configured to control the supply of alternating current, such as to the primary coil 204 of the primary side 200 of the TRFP 100, to create a predetermined DC offset in the secondary current. In some embodiments, the predetermined DC offset may be created over multiple cycles, e.g., multiple consecutive cycles. In some embodiments, the predetermined DC offset may be zero.

[0153] 6.4.3. Primary Current Waveform

[0154] In certain forms of the present technology, a current control mechanism 203 controls the current source 202 to apply a current I Pto the primary coil 204. The applied current I P can be an alternating current. In a specific form, the applied current I P The waveform of the current I P The time variation of the AC current I supplied to the primary coil 204 of the TRFP 100 during various phases of the process of charging the load 390 may be as shown in FIG. 7A. P 1 is a graph showing the magnitude of the applied current I versus time over one cycle of the current. P The waveform of may be characterized by one or more values, referred to herein as waveform values. We will now describe the nomenclature of the exemplary waveform values ​​shown in Figures 7A and 7B (and in the following discussion).

[0155] During a first portion of the cycle (which may be the first half of the cycle), current flows through the primary coil 204 in a first direction, which is shown in FIGS. 7A and 7B as a current having a positive value. The current increases from a first value (which may be zero) to a maximum value over a first period of time. As shown in FIGS. 7A and 7B, the rate of increase of the current over this first period of time may be substantially linear. Over a second period of time, the current increases to I in FIGS. 7A and 7B. P,C The duration of the second period may be held at a substantially constant value, as shown in FIGS. 7A and 7B as t 充電 The current then decreases from the maximum value to a lower value (which may be zero) over a third period of time. As shown in Figures 7A and 7B, the rate of increase of the current over this third period of time may be approximately linear.

[0156] Then, during a second portion of the cycle (which may be later in the cycle), current flows through the primary coil 204 in a second direction opposite the first direction, which is shown in FIGS. 7A and 7B as a current having a negative value. The current decreases from one value, which may be zero, to a maximum value (i.e., approaching a negative value but increasing in magnitude in a negative direction) over a fourth period of time. As shown in FIGS. 7A and 7B, the rate of increase of the current is substantially linear over this first period of time. Over a fifth period of time, the current decreases to I in FIGS. 7A and 7B. P,M The duration of the second period may be held at a substantially constant value, as shown in Figures 7A and 7B, as t メンテナンス The current then increases from the most negative value to a higher value (which may be zero) over a sixth time period. As shown in Figures 7A and 7B, the rate of increase of the current over this sixth time period may be substantially linear.

[0157] The waveforms shown in Figures 7A and 7B are square wave primary currents I P In certain embodiments, the second and fifth periods, i.e., t 充電 and t メンテナンス It may be advantageous for the value of I to be as small as possible. Therefore, in some configurations, the primary current I supplied to the primary coil 204 P The waveform of t can approximate a triangular waveform. 充電 and t メンテナンス The values ​​of t may be equal or substantially equal. For simplicity, メンテナンス and t 充電 All periods other than can be considered negligible, and this approach will be adopted in the rest of the discussion.

[0158] The example waveforms shown in Figures 7A and 7B may be used to power one or more primary coils 204 of the exemplary configuration of the TRFP 100 shown in Figures 3A-3E. The TRFP 100 includes a rectifier 320 operating as a half-wave rectifier. In this configuration of the TRFP 100, when current flows in one direction through the primary coil 204, the rectifier 320 is configured such that current is supplied from the secondary coil 304 to the load 390, charging the load 390. When current flows in the reverse direction through the primary coil 204, the rectifier 320 is configured differently, and no current is supplied from the secondary coil 304 to the load 390; instead, the current in the load 390 is maintained by a superconducting loop via the bridge switch 332b. Thus, the first portion of the cycle of the waveforms shown in Figures 7A and 7B, i.e., the first, second, and third periods when the current is positive, can be referred to as the "charging phase," and the second portion of the cycle of the waveforms shown in Figures 7A and 7B, i.e., the fourth, fifth, and sixth periods when the current is negative, can be referred to as the "maintenance phase." This is what is referred to in the notation I P,C and I P,M This is why the subscripts "C" and "M" are added to the

[0159] 7A and 7B show several different primary current waveforms 602, 604, 606 with different positive and negative peak current magnitudes. Each primary current waveform 602, 604, 606 represents the primary current I in different cycles. P As will be described later, the primary current I P The particular characteristics of the waveform may be changed over the course of a cycle in order to charge the load 390 in a desired manner. In some forms, the characteristics change after each cycle, while in other forms, the characteristics may remain the same for a certain number of cycles and then change in subsequent cycles.

[0160] In certain configurations, the peak positive current I P,C and / or the value of the peak negative current I P,M The value of can be adjusted over a series of cycles. The value of the peak positive current in the kth cycle is TIFF2025540060000004.tif77, and the value of the peak negative current at the kth cycle is 7A and 7B, waveform 602 shows the first current cycle, with peak positive and negative current values ​​of TIFF2025540060000006.tif77 and TIFF2025540060000007.tif77. Waveform 606 shows the current after the load current in load 390 reaches the desired level, with the peak positive and negative current values ​​for this cycle being: TIFF2025540060000008.tif78 and TIFF2025540060000009.tif79. In certain configurations, the positive and negative peak current values ​​in the primary current waveform may generally increase over time, i.e., as the number of cycles increases. For example, TIFF2025540060000010.tif77 is TIFF2025540060000011.tif78 is larger than TIFF2025540060000012.tif67 Can be larger than TIFF2025540060000013.tif66.

[0161] In the embodiments of the technique described above and below, the peak current value is described as an exemplary waveform value that is varied from cycle to cycle to adjust the output voltage generated. However, in other embodiments, other waveform values ​​may be varied from cycle to cycle. Examples include t メンテナンス and t 充電In yet other embodiments, the strength and / or direction of the applied magnetic field may be varied between cycles. In some embodiments, one or more of these values ​​may be varied. The process of integrating these approaches may be similar to the methodology outlined below and, therefore, may be modified to include various waveform modifications in addition to or instead of peak current modifications. For ease of explanation, embodiments including peak current modifications will be described herein.

[0162] 6.4.4. Other Nomenclature

[0163] In addition to the nomenclature already introduced, the following terms will be used in the following description:

[0164] ● TIFF2025540060000014.tif65 is the load current supplied to load 390 at the start of the kth cycle. ●△I L is the change in load current delivered to load 390 during a current cycle. In some forms, this value is constant for the process of charging load 390, but in other forms, the value may change over time, for example, if a varying ramp rate is required. ● TIFF2025540060000015.tif68 is the change in load current supplied to load 390 during the charging phase of the kth cycle. ● TIFF2025540060000016.tif610 is the change in load current supplied to load 390 during the maintenance phase of the kth cycle. ● TIFF2025540060000017.tif56 is the peak current generated in the secondary coil 304 during the charging phase of the kth cycle. ● TIFF2025540060000018.tif67 is the peak current generated in the secondary coil 304 during the maintenance phase of the kth cycle. N1 is the number of turns in the primary coil 204 of the transformer 150. N2 is the number of turns in the secondary coil 304 of the transformer 150. ●t サイクル is the time of the entire period (i.e., the sum of the durations of the first and second parts of the period, or the sum of the durations of the first through sixth periods mentioned above). ● JPEG2025540060000019.jpg812 is the time-averaged voltage developed across the load 390 (which may be a coil) during the charging phase of the kth cycle. ● TIFF2025540060000020.tif75 is the time-averaged voltage developed across the bridge (eg, bridge switch 332b of the type shown in Figures 3B-3E) during the charging phase of the kth cycle. ● TIFF2025540060000021.tif77 is the time-averaged voltage generated across series switch 332a in the maintenance phase of the kth cycle in the form shown in FIGS. 3B-3E. ● JPEG2025540060000022.jpg915 is the voltage across the bridge (e.g., the voltage across bridge switch 332b in the configuration shown in FIGS. 3B-3E) during the charging phase of the kth cycle required to achieve the desired charging of load 390. ● JPEG2025540060000023.jpg715 is the voltage across series switch 332a of the type shown in FIGS. 3B-3E during the maintenance phase of the kth cycle required to achieve the desired charging of load 390. ● TIFF2025540060000024.tif64 is the current through the bridge (eg, bridge switch 332b in the configuration shown in FIGS. 3B-3E) during the charging phase of the kth cycle.

[0165] 6.4.5. Characterization of response to power supply

[0166] In some embodiments, the applied current I supplied to the primary coil 204 P It has been described that the supply of the load current I is controlled to charge the load 390 in a desired manner. For example, the load 390 may be configured to supply a load current I L , so that after a certain number of cycles, e.g., after each cycle, the load current I L In some embodiments, the magnitude of the applied current I supplied to the primary coil 204 P The supply of load current I L may be controlled to increase stepwise by substantially the same amount. This is sometimes referred to as a "linear ramp" of the load 390.

[0167] The electromagnetic state of the flux pump is difficult to precisely control and manage due to the nonlinear resistance of the superconducting material of the TRFP 100. As a result, in some forms of the technique, the response of the TRFP 100 is experimentally characterized prior to charging the load 390, i.e., prior to commencing the supply of alternating current to the TRFP 100 that serves to charge the load 390 to a desired level.

[0168] In certain forms of the present technology, a characterization phase is not implemented and control may be determined solely by analysis of the TRFP 100, for example, by solving analytical equations derived directly taking into account the topology and structure of the TRFP 100, or by approximating the solution of analytical equations.

[0169] In some forms, the response of the TRFP 100 may be experimentally characterized, at least in part, while charging of the load 390 is in progress, e.g., some steps of experimentally characterizing the response of the TRFP 100 may be performed while the load 390 is partially charged toward a desired charge level.

[0170] Characterizing the response of the TRFP 100 may include characterizing the response of the rectifier 320 and / or the load 390 .

[0171] Characterizing the response of the TRFP 100 may include supplying a characterization source of impressed current to the primary coil 204 of the transformer 150. A current source 202 and current control mechanism 203 may be used to provide the characterization source of current, although in other embodiments, a different current source and current control mechanism may be used than those ultimately used to charge the load 390. In certain embodiments, the characterization source of impressed current has a waveform that is the same as or substantially similar to the waveform of the supply of impressed current supplied to the primary coil 204 when charging the load 390. For example, the duration of each portion of the cycle of the characterization source may be the same as the charging source. In addition, the duration of each period of the cycle of the characterization source may be the same (or substantially the same) as the charging source, and the t 充電 and t メンテナンス The values ​​of peak positive and negative currents may vary in both the current characteristics and the charging supply, as described below.

[0172] In certain forms of the present technology, one or more of a plurality of parameters of the TRFP 100 may be determined as part of characterizing the response of the TRFP 100 to a characterization power supply. In certain forms, one or more voltage values ​​within the rectifier 320 corresponding to a predetermined value of current supplied to the primary coil 204 may be determined. For example, a voltage value output to the load 390 may be determined. In the form of the half-wave rectifier 320 shown in FIGS. 3B-3E, the voltage output to the load 390 is determined by the voltage V across the bridge, i.e., bridge switch 332b. B In addition, the current I flowing through the bridge, i.e., the bridge switch 332b, corresponding to each of the determined voltage values ​​can be calculated. B In certain embodiments, a value corresponding to the peak value of the current of the waveform supplied to the primary coil 204 (I depending on whether it is the charging phase or the maintenance phase) may be determined. P,C or I P,M The following is determined:

[0173] Certain forms of the present technology provide the necessary measurement equipment used to measure these parameters directly or to measure other parameters from which these parameters may be determined indirectly, such as by calculation. The measurement devices may include one or more voltage sensors and one or more current sensors. It should be noted that the determination of the parameters of the TRFP 100, while necessary for the following description, can be performed using appropriate sensors, even if no measurement equipment is explicitly mentioned for determining that parameter.

[0174] The correspondence between multiple values ​​of one parameter and multiple values ​​of another parameter, for example, rectifier voltage values ​​corresponding to primary current values, may be stored in a data storage device in a suitable format such as a data array or look-up table.

[0175] With the TRFP 100 in operation, response characterization may be performed periodically or frequently, for example, every few hours, days, or weeks, depending on the nature of the TRFP 100 and its application.

[0176] More specific details of the response characteristics of the TRFP 100 in certain forms of the present technology will now be described. In particular, for a TRFP 100 including a particular type of rectifier 320, such as the half-wave rectifier 320 of Figures 3B-3E, characterizing the response of the TRFP 100 may include characterizing the response of the TRFP 100 in a charging phase and characterizing the response of the TRFP 100 in a maintenance phase. It will be understood that in the case of a rectifier in which both phases of the waveform correspond to charging (e.g., a full-wave rectifier), only the description of the response characteristics in the charging phase applies.

[0177] 6.4.5.1.Charging Phase Characterization - Characterization Table

[0178] In a particular form of technology, the TRFP 100 may be characterized during a charging phase, e.g., when the rectifier 320 of FIGS. 3B-3E is in a configuration where the current generated in the secondary coil is supplied to the load 390, and the voltage value of the rectifier 320, e.g., the voltage V across the bridge switch 332b, is measured. B The value of the AC current supplied to the primary coil 204, e.g., the positive current I P,C A value corresponding to the peak value of can be determined.

[0179] As an example, TRFP 100 may be assembled as shown in Figures 3A-3E, with load 390 connected as described above. Additionally, rectifier 320 may be configured such that current generated in secondary coil 304 is supplied to load 390; for example, in the case of half-wave rectifier 320 of Figures 3B-3E, bridge switch 332b is in a high resistance state and switch 332a is in a low resistance state. As explained above, a magnetic field may be applied to bridge switch 332b by a magnetic field generator to achieve this.

[0180] To characterize the TRFP 100, multiple characterization signals are applied with applied currents having waveforms identical or substantially similar to those used for charging over the expected range of applied currents. For example, multiple characterization signals are applied with different waveform values, e.g., peak positive values ​​I P,C may be sequentially applied to the primary coil 204 of the transformer 150. The level of the applied current characterization power supply may be set to a level that will not saturate the transformer 150. Each time the applied current characterization power supply is applied, the voltage V across the bridge switch 332b B (I B ) and the output value to the load 390 are measured and recorded. After each characterization current application, the load current I L may decay to zero, so that at the start of each characterization step, the current in the secondary coil 304 is equal to the current in the bridge switch 332b (i.e., I S,C =I B ) is ensured to be equal to V for TRFP 100. B (IB )=V S,C (I S,C ) is assumed, but variations from this equivalence can be quantified and integrated as needed.

[0181] V B (I B ) values ​​are based on the wide range of bridge currents, I, possible with a particular design of the TRFP 100. B As a result, a range of corresponding waveform values ​​of the applied current characteristic power supply is supplied to the primary coil 204.

[0182] In this way, the conditions for charging the load 390 are replicated during the characterization phase, including all potential actual variations from the modeled behavior of the TRFP 100, as described below. Additionally, this characterization process may also be useful in establishing the functionality of the TRFP 100.

[0183] In addition, in certain forms, V B (I B ) may be independent of the load current. In this configuration, △I L ∝V B (I B ), one characteristic may be assumed to hold for all possible experimental variables, regardless of load current. B (I B ) may depend on the load current or the ramp rate, which may change the effective voltage generated, for example, by AC losses or inductive coupling. To account for these effects, additional terms may be added to the relevant equations. Alternatively, such effects may be accounted for by a feedback loop, for example in the form of a PID loop, as will be explained below.

[0184] In certain embodiments, the process of supplying multiple characterization power sources to the primary coil 204 to characterize the behavior of the TRFP 100 may be performed only upon initial installation and before the start of the charging process, while in other embodiments, one or more subsequent characterization steps may occur in which one or more additional characterization power sources are supplied to the primary coil 204. For example, periodic checks of the characteristic operation of the TRFP 100 may be performed.

[0185] In a particular form, the result of the process of characterizing the TRFP 100 during the charging phase by sourcing and measuring parameters is the bridge current value I across the bridge of the TRFP 100 in question. B and its associated voltage value V B (I B ) In a particular embodiment, this sequence of values ​​can be, for example, V B (I B ) and I B The data may be stored or presented as a data array, such as a lookup table of: An example of a lookup table in one embodiment of the present technology is shown in Table 1.

[0186] [Table 1] Table 1 - Example look-up table showing TRFP 100 characteristics during charging phase

[0187] Bridge current I confirmed during the characterization process B The increments between values ​​of may be selected as needed. In particular embodiments, various increments may be used. For example, B is the critical current I of the bridge switch 332b. C,B If it is less than, then each value I B The intervals between currents I and I are reasonably wide (e.g., 10-20 A steps). Additional values ​​of current and corresponding voltage within this range can be generated by interpolation. B The interval between the values ​​of is determined by the time when the current is greater than or equal to the critical current I of the bridge switch 332b. C,B As the current approaches the critical current IC,B If the values ​​are within about 20-30% of the I B , which is the critical current I of the bridge switch 332b. C,B may exceed 1.5I, for example. C,B becomes.

[0188] At this stage, the current I in bridge 332b B Bridge V B (I B ) and that is supplied to the load 390 is established (e.g., Table 1). In a particular embodiment, the next step is to B and the input primary current (for example, the input primary current I P,C The goal is to calculate the correlation between the peak positive values ​​of the

[0189] Bridge current I B is the load current I L , the required current generated in the secondary coil 304 changes with increasing load current as follows:

[0190]

number

[0191]

number

[0192] Thus, a series of voltage values ​​V across the bridge (and / or provided to the load 390) B (I B ) and the corresponding peak positive current value I provided to the primary coil 304 P,C can be determined in the form of another look-up table, for example, as shown in Table 2.

[0193] [Table 2] Table 2 - Example look-up table showing characteristics of the TRFP 100 during the charging phase

[0194] 6.4.5.2. Characteristics in the Maintenance Phase

[0195] For configurations of the TRFP 100 where a maintenance phase exists in addition to the charging phase, such as the half-wave rectifier 320 shown in FIGS. 3B-3E, a similar process of characterizing the TRFP during the maintenance phase can be performed to measure the voltage value of the rectifier 320, e.g., the voltage V across the series switch 332a. M , which corresponds to the value of the alternating current supplied to the primary coil 204, e.g., the current I P,M corresponds to the negative peak value of

[0196] As an example, the TRFP 100 is assembled as shown in Figures 3A-3E. During this characterization step, the load 390 may or may not be connected. Additionally, the rectifier 320 is configured so that no current is supplied from the secondary coil to the load 390; for example, in the case of the half-wave rectifier 320 of Figures 3B-3E, bridge switch 332b is in a low resistance state and switch 332a is in a high resistance state. As explained above, a magnetic field may be applied to bridge switch 332a to achieve this.

[0197] Next, a voltage regulator having a waveform identical or substantially similar to that used for charging and having a negative peak value I P,M A plurality of characteristic power sources having different waveform values, such as , can be sequentially supplied to the primary coil 204 of the transformer 150. The level of the applied current characteristic power source can be set to a level that does not saturate the transformer 150. Each time an AC current characteristic power source is supplied, the voltage V across the series switch 332a M (I S ) is measured and recorded. Unlike the charging phase characterization, after each characterization current, the load current I Ldoes not need to decay to zero before the next characterization current is applied.

[0198] Similar to the characteristics of the charging phase, the current I through the series switch 332a is possible for a particular design of the TRFP 100. S For a wide range of V M (I S ) can be determined, resulting in a corresponding range of values ​​for the applied current characterizing power supply provided to the primary coil 204. B Similar to what was explained above for values ​​of current I S A number of values ​​and ranges (e.g., similar increments and maximum values) can be applied.

[0199] As described in connection with the charging phase, in certain embodiments, the process of supplying multiple characterization power sources to the primary coil 204 to characterize the operation of the TRFP 100 may be performed only during initial installation and before the start of the charging process, although in other embodiments, one or more subsequent characterization steps may occur in which the applied current of one or more characterization power sources is supplied to the primary coil 204. For example, periodic checks of the characteristic operation of the TRFP 100 may be performed.

[0200] In a particular embodiment, the result of the process of characterizing a TRFP 100 during the charging phase and measuring parameters is a series of currents I flowing through the series switch 332a of the TRFP 100 in question. S and the associated voltage value V across the series switch 332a. M (I S In a particular embodiment, the series of values ​​may be, for example, V M (I S ) and I S The data may be stored or presented as a data array, such as a lookup table of: Table 3 shows an example of a lookup table according to one embodiment of the present technology.

[0201] [Table 3] Table 3 - Example look-up table showing characteristics of TRFP 100 during the maintenance phase

[0202] In this phase, the current I S Switch V M (I S ) is found to produce a specific voltage across I (e.g., Table 3). In a specific configuration, the next step is to S and the input primary current (for example, the input primary current I P,M These are related based on the number of windings in transformer 150 as follows:

[0203]

number

[0204]

number

[0205] Thus, a series of voltage values ​​V across the series switch 332a (and / or secondary coil 304) M (I S ) and the corresponding peak negative current value I supplied to the primary coil 304. P,M can be determined in the form of another look-up table, for example as shown in Table 4.

[0206] [Table 4] Table 4 - Example look-up table showing characteristics of TRFP 100 during the maintenance phase

[0207] 6.4.6. Target value calculation

[0208] After the characterization phase, understand how the TRFP 100 responds to a specific supply current during each of the charging and, if applicable, maintenance phases. Another aspect is to create analytically derived target values ​​that account for the dynamic response of the flux pump, as outlined in Section 6.4.2. Specifically, the target value is the voltage required across the switch during the charging process. The target value may incorporate requirements for the charging process, such as DC offset control and ramp rate, into the system. Determining the target value requires skilled analysis to understand the physical mechanisms inherent in the TRFP and develop the equations necessary to generate the target value.

[0209] Another aspect of the control process in some forms of the present technology is taking a derived target value that represents a desired output and mapping it to a required input. The inputs in a typical TRFP are the applied primary current waveform and, in the case of field-driven switching, the waveform(s) of the electromagnet(s). Thus, the term "waveform value" is used to encompass changes in the input variables caused by the control process. Another way to describe a change in waveform is that it may be a change in the input that produces a desired target value. This unique combination of coefficients forms the basis of certain forms of the present technology.

[0210] In a common approach adopted in certain forms of technology, a target load current I supplied to the load 390 at the end of the charging process is 目標 , i.e., to what level the load 390 is charged. The rate at which the load 390 is charged is also determined, and the load current ΔI supplied to the load 390 over the current cycle is determined based on the period of the cycle of the applied current supplied to the primary coil 204. L As mentioned above, the change in load current △I L may vary during the charging process, but for a linear ramp, the load current ΔI LThe change in may be selected to be substantially constant over the course of the charging process. Based on the target load current and the target charge rate of the load 390, a waveform value for the current to be applied to the primary coil 204 in each cycle is calculated. In the following description, the waveform value is defined as the peak positive current I in each cycle delivered to the primary coil 204. P,C and peak negative current I P,M In other forms, different values, such as waveform values ​​of the applied current or values ​​characterizing the waveform of the strength and / or direction of the magnetic field generated by magnetic field generator 342, may be calculated and modified to achieve the same or a similar effect.

[0211] Target load current I L The waveform value of the applied current (for example, I P,C and I P,M ) is the desired target load current I L This is calculated by first calculating target values ​​for the voltages of the TRFP 100 that are expected to generate a voltage of . This can be accomplished before charging the flux pump, as the target values ​​can be analytically derived, as shown below. The method then includes calculating waveform values ​​for the applied current supplied to the primary coil 204 or the magnetic field generator 342 from the target voltage values ​​derived from a characteristic table or a separate numerical or analytical solution. In certain configurations, such as the configuration of the half-wave rectifier 320 shown in FIGS. 3B-3E, the target values ​​may include one or more target voltage values ​​when the rectifier 320 is in a configuration in which current is supplied from the secondary coil 304 to the load 390 (i.e., a charging phase) and one or more target voltage values ​​when the rectifier 320 is in a configuration in which current is not supplied from the secondary coil 304 to the load 390 (i.e., a maintenance phase). In certain configurations, the target voltage values ​​may include target values ​​for one or more voltages provided to the load 390, such as the voltage across the bridge switch 332b. JPEG2025540060000033.jpg711 and the voltage across the series switch 332a JPEG2025540060000034.jpg712 and one or more target values.

[0212] In certain embodiments, the waveform values ​​of the applied current are determined from the voltage values ​​using a lookup table, such as Table 2 or Table 4, to characterize the response of the TRFP 100.

[0213] In certain configurations, the waveform values ​​of the applied current may be determined using a numerical or analytical solution of the superconducting properties of the TRFP 100 and a detailed analysis of the TRFP 100 configuration, such as the configuration described in Section 6.4.7.1.

[0214] In certain configurations, the waveform values ​​may be modified by a feedback loop based on the measured response, as described in Section 6.4.7.

[0215] An exemplary process is now described in further detail for the TRFP 100 to determine the applied current delivery characteristics necessary to achieve a desired load current in the load 390. The exemplary process outlined below creates a set of target values ​​before charging begins, although in certain configurations, the same principles may be utilized to generate these target values ​​during charging.

[0216] 6.4.6.1. Modeling a Half-Wave Rectifier - Creating Target Values

[0217] The following sections describe how a rectifier 320 in the form of a half-wave rectifier 320, such as that shown in Figures 3B-3E, can be modeled in a particular technology form. It is expected that, after reading this description, a skilled recipient will be able to perform similar modeling for other forms of rectifiers, including other forms of half-wave rectifiers and full-wave rectifiers. Accordingly, while a brief overview of a center-tapped full-wave rectifier is further described below, a detailed analysis of other exemplary forms of rectifier 320 is not provided.

[0218] The following derivation focuses on two coefficients that determine the output voltage of a half-wave rectifier that includes a switch 332 that operates based on applying a magnetic field across a length of superconductor to change the superconductor's critical current. These are: 1) the nonlinear resistance caused by the combination of the applied magnetic field and current, and 2) the junction resistance introduced during assembly. In existing rectifiers of this type, these coefficients have indeed been found to dominate the voltage response. However, inductive coupling and AC loss mechanisms have been shown to affect the output voltage. In certain configurations, these mechanisms can cause output voltage fluctuations that cannot be mitigated by PID feedback control, as suggested in the discussion below. In these configurations, it may be necessary to incorporate these additional coefficients into the target value equation. Those skilled in the art can implement these additions by following the process outlined below. It is important to note that the overall methodology remains unchanged, regardless of the physical mechanism driving the commutation process in a Type II superconducting transformer rectifier flux pump.

[0219] As previously discussed, when deciding how to charge a load 390 using the TRFP 100, the charge rate (ΔI L ) and the target load current (I 目標 ) can be determined. In the TRFP 100, the charging rate is determined by the input current ( TIFF2025540060000035.tif831). When modeling the TRFP 100, the voltage across the load 390, V コイル The charging and maintenance phases are considered separately because the mechanism driving V is different for each cycle. In fact, during the maintenance phase, the voltage V コイル Since V is driven by losses rather than an external drive voltage, performance can be considered in terms of the current consumption of the RL circuit. コイル is exactly the same as the induced voltage across the coil. (Formula 1)

[0220]

number

[0221] where V コイル is the inductance of the load 390 only. The target value is generated by TRFP 100. コイル to generate a user-defined required As shown below, to satisfy the TRFP 100 example, where load 390 is charged with a gradually increasing load current and switching assembly 330 operates nonlinearly to ensure that a preferential net-zero flux is produced over each cycle, a single V コイル Instead, it requires changes in input parameters (waveform values) to accommodate dynamic changes in operation caused by charging, so V コイル For each cycle ( It may be necessary to change it for each image (JPEG2025540060000038.jpg79).

[0222] In certain forms of the present technology, Several assumptions can be made to find JPEG2025540060000039.jpg812. One assumption is that the charging of load 390 is コイル can be accurately characterized by simplifying to a time-averaged value. Experiments have shown that this approximation is very accurate. In other forms of control processes, The temporal response of JPEG2025540060000040.jpg714 can be directly considered.

[0223] time average Using JPEG2025540060000041.jpg57, the required △I L necessary to achieve Consider how to calculate JPEG2025540060000042.jpg67. To do this, we need to consider the charging phase ( TIFF2025540060000043.tif710) and maintenance phase ( Calculate the change in current in both the ion beam and the ion beam (TIFF2025540060000044.tif67).

[0224] During the charging phase, the time-averaged voltage results in a linear ramp rate during the charging process, and in Equation 1 JPEG2025540060000045.jpg68 is represented as follows: (Formula 2)

[0225]

number

[0226] However, the loss of load current during the maintenance phase is more complicated. TIFF2025540060000047.tif710 JPEG2025540060000048.jpg718 is determined by JPEG2025540060000049.jpg611 is determined by the RL circuit in the load loop and, as will be described later, by the current generated by the transformer 150 during the maintenance phase. L,M Regarding the load current in (t) and Kirchhoff's loop law in the load loop, JPEG2025540060000050.jpg59 looks like this:

[0227]

number

[0228]

number

[0229]

number

[0230]

number

[0231]

number

[0232] In some configurations, the analysis may be able to explicitly account for this variation. However, in certain configurations, for simplicity, the voltage may be assumed to be constant throughout the maintenance phase. Experiments have shown that for 5Hz operation with a set of parameters comparable to a real system, the impact of this assumption is approximately 90µV, although this is highly system dependent. As will be seen below, these assumptions form part of a set of effects not directly handled by these analytical equations and may therefore be able to be managed with additional techniques. Regardless of this assumption, TIFF2025540060000061.tif1156 is defined above. (Formula 3)

[0233]

number

[0234] where: JPEG2025540060000063.jpg1446 and JPEG2025540060000064.jpg914 is a constant. This formula is used to calculate the maintenance phase loss for the maintenance phase ( TIFF2025540060000065.tif77). This leads to an unavoidable circularity in the calculation. To address this circularity, Assume that TIFF2025540060000066.tif66 does not change significantly between successive cycles. In an operating control process with a constant ramp rate, this is expected behavior. Therefore, TIFF2025540060000067.tif66 is the I S,M is the value of TIFF2025540060000068.tif78. Using this assumption, Equation 3 becomes: (Formula 4)

[0235]

number

[0236] Due to the nature of the control process, cycle (△I L ) matches the user-defined charge rate.

[0237]

number

[0238]

number

[0239]

number

[0240]

number

[0241]

number

[0242] Equation 5 is based on the known parameters for the first current cycle. The formula for TIFF2025540060000076.tif1013 is: The only variable you need to add is the This is a reasonable assumption for TIFF2025540060000077.tif87, and one example of how to achieve this is described below.

[0243] However, Equation 5 is the coil ( TIFF2025540060000078.tif812), but the voltage that is important for the TRFP 100 is the bridge TIFF2025540060000079.tif1035. So now we calculate the conversion between these two values. Using Figure 2, we get:

[0244]

number

[0245] where JPEG2025540060000081.jpg710 is the average in the kth cycle TIFF2025540060000082.tif84. Basically, the load loop (R L ) resistance is the required This means that more voltage needs to be generated across the bridge to produce JPEG2025540060000083.jpg926. Using the linear ramp rate assumption, JPEG2025540060000084.jpg913 can be calculated.

[0246]

number

[0247]

number

[0248] Note that all the resistances in the bridge are joint resistances R J , acting to charge the load coil 390. The required voltage can therefore be derived as follows:

[0249]

number

[0250]

number

[0251]

number

[0252] In certain forms, TIFF2025540060000090.tif65 and △I L These assumptions can be eliminated by a comprehensive characterization phase that characterizes all possible variations in . This results in the formation of large data arrays or look-up tables. Alternatively, in other forms, the control method handles these second-order effects by implementing a feedback mechanism, such as a PID loop, based on a comparison of the target value with the desired value, as described below. Currently, this potential difference is accounted for by the coefficients described below. Modeled by TIFF2025540060000091.tif724.

[0253] The desired target voltage ( Having established the critical current (TIFF2025540060000092.tif730), we now need to consider how voltages are generated in the TRFP 100. The TRFP 100 (referred to herein as a "J" or "J-J") includes a rectifier 320 with a switching assembly 330 that includes a switch 332 of a type that applies a magnetic field to suppress a critical current and, as a result of that suppression, effect switching. C (B) In the case of a TRFP, the voltage that charges the load 390 is TIFF2025540060000093.tif712. For example, in the circuit of Figures 3B-3D, all of the voltage generated across the bridge charges the load 390. This scenario can apply to many forms of TRFP 100, since there may be joints within the bridge. This result suggests that J C (B) In the case of TRFP, the secondary coil 304 ( It was found that the efficiency of converting the voltage generated by the load 390 (TIFF2025540060000094.tif728) into the voltage that charges the load 390 can be very high (for example, 100%).

[0254]

number

[0255]

number

[0256] As mentioned above, in certain forms, ΔI L To charge with TIFF2025540060000097.tif936 needs to be generated.

[0257]

number

[0258]

number

[0259]

number

[0260] Here, n determines the behavior of the superconductor in the nonlinear state and depends on the magnetic field and temperature of the superconductor. Note that at this point, the nonlinear behavior of the superconductor does not affect the modeling analysis. Therefore, the above considerations apply to any TRFP 100, regardless of the rectification mechanism. Currently, it is assumed that the TRFP 100 is J C (B) Only in the specific form of TRFP, J C (B) Using the mechanism, we obtain Equation 8, which has the following form: (Formula 9)

[0261]

number

[0262] where: TIFF2025540060000103.tif1352, TIFF2025540060000104.tif1316, and TIFF2025540060000105.tif1216 is a constant.

[0263] One option is to numerically solve Equation 9 using a defined n value. However, this method is highly susceptible to inaccuracy because the TRFP 100 heats up during commutation, changing n. Instead, certain configurations utilize experimentally generated relationships between specific parameters, such as the characteristic tables outlined in Section 6.4.5.1, in combination with calculated target values. This approach allows nonlinear superconducting characteristics and second-order effects (e.g., AC losses) to be incorporated into the control process. This requires specific relationships between parameters (e.g., characterization tables) generated from the characterization phase to provide the data necessary for applying the control process. As mentioned previously, two different characteristic tables are required for the charging and maintenance phases.

[0264] Now consider how to calculate the target value for the maintenance phase. Using Kirchhoff's loop law as before, the voltage generated by transformer 150 during the maintenance phase is: (Formula 10)

[0265]

number

[0266] In contrast to the charging phase, the maintenance phase may serve the sole purpose of preventing saturation of the transformer 150. In a particular form, this means requiring: (Formula 11)

[0267]

number

[0268]

number

[0269] When rearranged to a constant over a cycle, the term on the right is the voltage required to stop the core from saturating over a cycle.

[0270]

number

[0271]

number

[0272] It can be a little confusing to have two required voltages (Equation 8), even though we start with the assumption that the voltages are equal. However, it is important to understand that the required voltages are concentrated only across the superconducting switching element 332, and not the total voltage produced across the secondary coil 304 of the transformer 150 (which remains in Equation 10). Note that the required maintenance phase voltage increment ( TIFF2025540060000111.tif719TIFF2025540060000112.tif714) are R J These factors depend on how the current is distributed through the bridge, which is not likely to be obvious in advance.

[0273] Similar to the charging phase, once the desired target value is established, a process must be established to convert it into the actual input required for the TRFP. c (B) Assuming it is based on commutation, the voltage on switch 332a is determined using a power law.

[0274]

number

[0275]

number

[0276] where: JPEG2025540060000115.jpg1538, TIFF2025540060000116.tif78, and TIFF2025540060000117.tif830. As with the charging phase, this equation can be solved numerically, or the left-hand side of the equation can be characterized experimentally. Certain forms of the present technology may employ the latter approach.

[0277] 6.4.6.2. Calculation of Waveform Values ​​- Half-Wave Rectifier

[0278] We now describe how, in certain forms of the present technology, a pre-calculated set of waveform values ​​may be determined for the supply of current supplied to the primary coil 204 and / or magnetic field generator 342 of the TRFP 100. In other forms of the technology, some of these waveform values ​​may be generated during the charging process.

[0279] To overcome the aforementioned circularity problem, a predicted value of the peak current generated during the maintenance phase may be generated. In one form, this value is determined by the critical current value of the length of superconducting material forming the series switch 332a, i.e., TIFF2025540060000118.tif836. A more common approach is to add an additional component ( TIFF2025540060000119.tif34) to I C,M (B,T), where α can be determined by the required ramp rate. In either approach, with the initial values ​​chosen, we can use Eq. Calculate TIFF2025540060000120.tif850. This value is used to derive the required waveform changes. Note that no other estimates are required.

[0280] The next step is to use Equation 7 to calculate the known resistance and the user-defined TIFF2025540060000121.tif84 and △I L and TIFF2025540060000122.tif77 estimate is used to determine the target value of the voltage across the bridge (e.g., the voltage across bridge switch 332b in the configuration shown in FIGS. 3B-3E) during the charging phase of the first cycle required to achieve the desired charging of load 390, i.e., Calculate TIFF2025540060000123.tif851.

[0281] Then, the calculated TIFF2025540060000124.tif711 were compared with the corresponding voltage to current values ​​determined when characterizing the response of TRFP 100 using the characterization power supply (e.g., charge lookup table (Table 3)), and interpolated if necessary, to obtain Generate TIFF2025540060000125.tif711 P,C This value is the peak positive current value of the waveform of the current supplied to the primary coil 204 in the first cycle, i.e., Set as TIFF2025540060000126.tif77.

[0282] The next step is to calculate the target voltage across series switch 332a during the maintenance phase of the first cycle required to achieve the desired charging of load 390. For example, Equation 12 calculates the voltage across series switch 332a for the known resistance and user-defined TIFF2025540060000127.tif64 and △I L and Using the estimates from TIFF2025540060000128.tif55, TIFF2025540060000129.tif949 can be calculated.

[0283] Then, the calculated TIFF2025540060000130.tif610 is compared with the corresponding voltage to current values ​​determined when characterizing the response of the TRFP 100 using the characterization power supply (e.g., using the maintenance lookup table (Table 4)), interpolating if necessary, to obtain Generate TIFF2025540060000131.tif610 P,M This value is the peak negative current value of the waveform of the current supplied to the primary coil 204 in the first cycle, i.e., Set as TIFF2025540060000132.tif77.

[0284] The above steps (except the first step) are then repeated for the selected increment of load current △I L Based on the target load current I 目標 This may be repeated multiple times.

[0285] Table 5 below shows an example of this series of calculations being performed and the results entered into a look-up table.

[0286] [Table 5] Table 5 - Example of load charging targets using TRFP

[0287] To clarify how to fill out this table, the kth row reads: 1. The value of TIFF2025540060000134.tif54 is the difference between the previous value of the load current and △I L Add up the Determined by TIFF2025540060000135.tif723. 2. The value of TIFF2025540060000136.tif712 is the (k-1)th row The value is TIFF2025540060000137.tif69. 3. TIFF2025540060000138.tif714 and The value for TIFF2025540060000139.tif712 is determined using the formula shown in the table. 4. TIFF2025540060000140.tif69 and The value for TIFF2025540060000141.tif67 is TIFF2025540060000142.tif611 and Determined from the corresponding value in TIFF2025540060000143.tif712 using the appropriate lookup table (Table 2 or Table 4).

[0288] In certain embodiments, these steps may be performed before charging of load 390 begins to determine a target charging scheme, e.g., a scheme set in a data array of a look-up table such as Table 5. In other embodiments, the calculation or recalculation of the target value may occur dynamically during the charging process of load 390, i.e., after charging of load 390 begins, i.e., the above steps may be performed and repeated one or more times during charging of load 390, e.g., after the completion of one or more charging cycles.

[0289] 6.4.6.3. Modeling a Center-Tapped Full-Wave Rectifier

[0290] The detailed examples above relate to modeling a rectifier 320 in the form of a half-wave rectifier 320 as shown in Figures 3B-3E. It has been noted that the present technology may also include other types of rectifiers that may form part of the TRFP 100. This section describes an example current control method adaptation that may be used in the case of a rectifier 320 in the form of a full-wave rectifier.

[0291] In a full-wave rectifier, both the positive and negative portions of the waveform of the applied current supplied to the primary coil 204 serve to charge the load 390. This can be more energy efficient than a half-wave rectifier and can significantly reduce current ripple. Also, important to the control process, the asymmetry between the two portions of the cycle is significantly reduced and can be considered approximately insignificant. In practice, a DC offset may occur in the first portion of the cycle (e.g., the positive portion), resulting in a slight asymmetry between the positive and negative charging phases. This offset can cause variations in the charging rate between the positive and negative portions of the cycle and may be accounted for in some techniques. In some configurations, this offset may naturally correct, which may be considered in further analysis.

[0292] In addition to reducing asymmetry within the charging cycle, a center-tapped full-wave rectifier, unlike a half-wave rectifier, distributes the load current evenly among the transformer sections. This introduces an unavoidable DC offset into the secondary current. However, the nature of this offset differs from the behavior of a transformer, so an offset in one section of the transformer can be completely canceled by an offset in another section of the transformer. Thus, the distribution of the load current affects the current generated in the secondary circuit, but may not saturate the transformer. Because this offset is directly related to the load current, it is relatively easy to address. As shown below, in certain configurations, a target value table can be added to the target value table. This can be processed by adding the term TIFF2025540060000144.tif88.

[0293] A detailed analysis of a full-wave rectifier is not provided here, but can be determined by the skilled recipient by following the analysis provided above for the half-wave rectifier example. As an example, for a TRFP 100 with rectifier 320 in the form of a center-tapped full-wave rectifier, of the type shown in Figure 4 and Figures 16, 17, 21, 22, 26, 27, 29, and 30 of PCT Application No. PCT / NZ2022 / 050009, published as International Publication No. WO2022 / 164330, the contents of which are incorporated herein by reference.

[0294] To emphasize the generality and use of the target approach, the final target equation required for a center-tapped full-wave rectifier is presented without derivation. For simplicity, we focus on a series of assumptions that reduce the complexity of the target equation. These are: ●No-load resistance: R L O ●Constant △I L is not required, instead a constant voltage V is used to define the target value for each cycle. セット is used. There is no attempt to cancel out the DC offset. Both the positive and negative sections of the primary waveform are scaled identically, resulting in the same peak current, I S have. • No attempt is made to integrate additional physical components such as AC losses. Use analytical solutions rather than experimental comparison tables. For the above assumptions, analytical methods result in simple calculations without the need for numerical approaches. A look-up table approach can provide more robust control in some configurations, while analytical methods may suffice in others. Using these assumptions, The target value formula for the center-tapped full-wave flux pump in TIFF2025540060000145.tif64 is as follows:

[0295]

number

[0296] 6.4.7. Changing the primary current supply

[0297] For example, if the TRFP 100 is used to charge a load 390 based on the target value calculated as described above, the TRFP 100 may not perform exactly as modeled. The above analysis makes several assumptions and simplifications, and the target voltage may need to be adjusted to achieve the desired performance of the TRFP 100. TIFF2025540060000147.tif816 and TIFF2025540060000148.tif815, and as a result some modifications to the waveform values ​​of the applied current may be required, including △I L and achieving zero net flux throughout the cycle.

[0298] In the above analysis, these assumptions / simplifications are This component is difficult to preprocess due to the potential for interaction between various parameters. Accordingly, in certain aspects of the present invention, a method for controlling the supply of applied current to a primary coil 204 includes modifying a target value for the supply of applied current during the charging process, i.e., after charging of the load 390 has begun, which may be referred to as dynamic control of the supply of applied current. In some aspects of the present technology, the supply of applied current may be modified based on feedback received from the TRFP 100, such as one or more sensors (e.g., the secondary 300) configured to measure a value of the TRFP 100. In certain aspects, the feedback for modifying the supply of applied current may include a comparison of one or more target values ​​to one or more experimentally measured values ​​of the TRFP 100.

[0299] In certain embodiments, one or both of the two comparisons may be used as a basis for modifying the supply of applied current.

[0300] 1. Applied current by TIFF2025540060000150.tif864 The peak positive value of the supply of TIFF2025540060000151.tif77 is modified. This step may help ensure that the desired ramp rate is achieved each time the modification is performed, e.g., every cycle.

[0301] 2. Applied current by TIFF2025540060000152.tif810 The peak negative value of the supply of TIFF2025540060000153.tif855 is modified. Based on this recalculated modified target value, the supply of applied current may be modified. This step helps prevent transformer 150 from saturating.

[0302] The alteration of the application of the applied current in the described manner may occur after each cycle of application of the applied current, or may occur periodically but less frequently, such as after a certain number of cycles, or the alteration may occur irregularly.

[0303] The changes resulting from the feedback can be implemented in different ways in different forms of the technology. For example, the following options may be used:

[0304] 1. Modify existing waveform values ​​based on analytically derived properties of TRFP. 2. Use a PID loop to modify existing waveform values, or 3. The target value is repeatedly (e.g., each cycle) recalculated to replace the waveform value. Each of these options will be explained in more detail below.

[0305] 6.4.7.1. Analytically Derived Properties

[0306] In certain forms of the present technology, certain assumptions simplify the above analysis and may be sufficient to apply an analytical approach to determine what modifications are needed to the supply of alternating current.

[0307] For example, in the case of a TRFP 100 with a rectifier 320 in the form of a full-wave rectifier, the joint resistance R J It may be assumed that the temperature dependence of the behavior of the superconductor and the temperature dependence of the superconductor's behavior can be cancelled, in which case Equation 9 simply becomes

[0308]

number

[0309]

number

[0310]

number

[0311] For example, analytically determining how to vary the supply of current applied to rectifier 320 in the form of a half-wave rectifier of the type shown in Figures 3B-3E may be considered too inaccurate for a practically implementable solution. The nonlinearity of superconducting switches means that changes in the physical properties of the superconducting element, such as temperature, can cause large variations in the output voltage, potentially resulting in large discrepancies between the calculated and measured response.

[0312] PID Loop

[0313] In certain forms, the current control mechanism 203 is configured to implement one or more PID loops, and modifying the supply of applied current may include using the PID loop(s) to provide feedback from the secondary side 300 to control the current.

[0314] In some forms of the present technology, for example, where rectifier 320 is in the form of a half-wave rectifier and the current cycle has a charging phase and a maintenance phase, current control mechanism 203 may be configured to implement two PID loops, one for each phase. In the first PID loop, current control mechanism 203 controls the applied current, as defined above. In the second PID loop, the current control mechanism 203 controls the applied current, as defined above. TIFF2025540060000162.tif88 may be configured to control the peak negative value of the supply relative to ε.

[0315] 8 is a flowchart of the process performed by the current control mechanism 203 when performing a method 700 that implements one or both of the PID loops in accordance with a particular form of technology. The method 700 may have two inputs: for example, the applied current vs. ω For the PID loop controlling the peak positive value of the supply of TIFF2025540060000163.tif66, the input is the value explained above. TIFF2025540060000164.tif512 and △I L (user defined). Applied current vs. ε For the PID loop controlling the peak negative value of the supply of TIFF2025540060000165.tif69, the input is the value explained above. TIFF2025540060000166.tif722 and TIFF2025540060000167.tif821. In step 701, a difference value 702 between the input values ​​is calculated, and for example, the values ​​ω and ε may be determined. In steps 703, 704, and 705, correction terms are determined from the difference value 702, which are the proportional, integral, and derivative terms, respectively. These terms are summed in steps 706 and 705 to determine the output of the PID loop (the applied current for the next cycle). TIFF2025540060000168.tif89 peak positive value of the applied current and the next cycle Determine the peak negative value of the supply of JPEG2025540060000169.jpg109, etc.

[0316] In certain configurations, the methods for calculating the proportional, integral, and derivative terms may be experimentally derived, for example, by the Ziegler-Nichols method or other suitable methods. The conditions may also be gain-scheduled.

[0317] Calculating waveform values ​​using the method described above accounts for the nonlinearity of the superconducting switch, so that the changes that need to be made through the PID control process are small and approximately linear.

[0318] To fully utilize PID loop control, it may be helpful to perform a detailed characterization of the response of TRFP 100, as described above. Once the characteristics of TRFP 100 have been characterized, it is expected that, for a particular configuration, the characteristics will remain consistent over time.

[0319] 6.4.7.3. Recalculating Waveform Values

[0320] In other embodiments, the target value for the delivery of the applied current to the primary coil 304 may be repeatedly recalculated, for example, periodically, e.g., every cycle. This approach may, in some embodiments, avoid the need to first pre-calculate a complete set of waveform values ​​for the delivery of the applied current. For example, a look-up table such as Table 5 above may not need to be generated, or may only need to be partially generated.

[0321] For example, in the case of a TRFP 100 with a rectifier 320 in the form of a half-wave rectifier, as shown in Figures 3B-3E, the results from the previous cycle can be re-entered into the above equations with modifications related to ω and ε. For ω, Equation 2 changes to:

[0322]

number

[0323] Performing the associated algebra, Equation 5 becomes:

[0324]

number

[0325] Therefore, in these configurations, feedback control of the positive peak value of the applied current supply is performed by determining the empirically derived ω TIFF2025540060000172.tif88 can be handled by delicately manipulating the values.

[0326] In the case of feedback control using ε, Eq. TIFF2025540060000173.tif732 is simply replaced by ε.

[0327]

number

[0328]

number

[0329] As indicated above, in this form of the technology, the waveform values ​​are TIFF2025540060000178.tif943 and The loop-up table is then calculated periodically, for example, during each cycle, using the formula in TIFF2025540060000179.tif833. Processing speed limitations may hinder the viability of this approach, especially as frequencies increase. However, calculations and interpolation from existing loop-up tables are relatively easy for processors to perform, and research has shown that this approach does not impose significant limitations on the time response of the control process.

[0330] Persistence Mode

[0331] In certain embodiments, once the load 390 is fully charged, for example, the load current decreases to load current I 目標 Once the target value of I is reached, the TRFP 100 may operate in sustain mode, where the charge on the load 390 is maintained and the load current is I 目標 can be maintained at

[0332] In sustain mode, the load current delivered to the load 390 does not increase (i.e., I L ). Therefore, from the above equation, we obtain

[0333]

number

[0334] In some forms, these equations are used to derive target values ​​for the voltage, and thus waveform values ​​for the primary current waveform (e.g., using a lookup table), to maintain the TRFP 100 in sustained mode.

[0335] 6.5. Other comments

[0336] Unless the context clearly dictates otherwise, throughout the description and claims, the words "comprise," "comprising," and the like are to be construed in their inclusive sense, i.e., "including, but not limited to," rather than in their exclusive or exhaustive sense.

[0337] The entire disclosures of all applications, patents and publications, cited above and below, are hereby incorporated by reference.

[0338] The reference herein to any prior art is not, and should not be construed as, an acknowledgment or in any way an indication that that prior art forms part of the common general knowledge in that field in any country in the world.

[0339] The technology may be broadly described as consisting of the components, elements and features referred to or shown in the specification of the application, individually or collectively, or any or all combinations of two or more of said components, elements or features.

[0340] Where reference is made in the foregoing description to components for which integers or their equivalents are known, those integers are incorporated herein as if individually set forth.

[0341] It should be noted that various changes and modifications to the presently preferred embodiments described herein will be apparent to those skilled in the art. Such changes and modifications can be made without departing from the spirit and scope of the present technology and without diminishing its attendant advantages. Accordingly, such changes and modifications are intended to be included within the present technology.

Claims

1. 1. A method of controlling the supply of applied current to a transformer rectifier flux pump for charging a load, comprising: The transformer rectifier flux pump comprises: a transformer having a primary coil and a secondary coil; a rectifier connected to the secondary coil and configured to supply a load current to a load; the secondary coil, the rectifier, and the load include one or more lengths of Type II superconducting material; The method comprises: calculating one or more waveform values ​​for a supply of an applied current to the transformer rectifier flux pump for each of a plurality of target values ​​of load current supplied to the load; and controlling a supply of an applied current to charge the load based on one or more of the waveform values.

2. 10. The method of claim 1, comprising calculating one or more waveform values ​​of a supply of applied current to a transformer rectifier flux pump in one or more preselected increments relative to the target value of the load current up to a preselected target value of the load current.

3. 3. The method of claim 1, wherein the one or more waveform values ​​of the supply of impressed current to the transformer rectifier flux pump include a peak value of the supply of impressed current when flowing in a first direction and a peak value of the supply of impressed current when flowing in a second direction, the second direction being opposite to the first direction.

4. The method for calculating waveform values ​​of the applied current supply to the transformer rectifier flux pump comprises: calculating one or more target voltage values ​​for the transformer rectifier flux pump for each of a plurality of target values ​​of load current supplied to the load; and calculating one or more waveform values ​​of a supply of applied current to the transformer rectifier flux pump from one or more of the target voltage values.

5. The method of claim 4 , wherein the one or more target voltage values ​​include a target value for a voltage output to the load.

6. The method of claim 5 , wherein the target value of the voltage output to the load comprises a target value of the voltage across a switch connected in parallel with the load.

7. The one or more target voltage values ​​are: a first target value of a voltage output to the load when the rectifier is in a first configuration in which a current generated in the secondary coil is supplied to the load; and a second target value of voltage output to the load when the rectifier is in a second configuration in which no current is supplied from the secondary coil to the load.

8. 8. The method of claim 1, comprising the steps of: supplying a characterization excitation current to the transformer rectifier flux pump; characterizing a response of the rectifier and / or the load to the characterization excitation current; and controlling the supply of an excitation current to charge the load based on the characterization response.

9. 9. The method of claim 8, further comprising the steps of: providing the characterization power supply before beginning to provide an impressed current to the transformer rectifier flux pump to charge the load; and characterizing a response to the characterization power supply.

10. The step of providing a characterization power supply comprises: providing a first characterization source of impressed current to the transformer rectifier flux pump when the rectifier is in a first configuration in which the current generated in the secondary coil is supplied to a load, and characterizing a first response of the rectifier and / or the load to the first characterization source; and providing a second characterization source of impressed current to the transformer rectifier flux pump when the rectifier is in a second configuration in which no current is supplied from the secondary coil to the load, and characterizing a second response of the rectifier and / or the load to the second characterization source.

11. 11. A method according to any one of claims 8 to 10, wherein characterising the response of the rectifier and / or the load to the characterised power supply comprises determining a plurality of voltage values ​​across the rectifier corresponding to a respective plurality of values ​​of the applied current supplied to the primary coil.

12. The method of claim 11 , wherein the plurality of voltage values ​​at the rectifier includes a voltage value output to the load.

13. 13. The method of claim 12, wherein the voltage value output to the load comprises a voltage value across a switch connected in parallel with the load.

14. The method of any one of claims 1 to 13, further comprising the step of varying the supply of applied current to the transformer rectifier flux pump during the process of charging the load.

15. 15. The method of claim 14, further comprising varying the supply of the applied current based on feedback received from one or more sensors configured to measure a value of the transformer rectifier flux pump.

16. The method of claim 15 , wherein the feedback comprises a comparison of a target value and a measured value of the transformer rectifier flux pump.

17. A method according to any preceding claim, wherein the one or more waveform values ​​are values ​​of current supplied to the primary coil.

18. 18. The method of any one of claims 1 to 17, wherein the transformer rectifier flux pump includes a magnetic field generator for applying a magnetic field to one length of Type II superconducting material, and the one or more waveform values ​​are values ​​of a current supplied to the magnetic field generator.

19. 19. Apparatus for controlling the supply of applied current to the transformer rectifier flux pump to charge the load, the apparatus comprising a processor configured to perform the method of any one of claims 1 to 18.

20. The transformer rectifier flux pump comprises: a transformer having a primary coil and a secondary coil; a rectifier coupled to the secondary coil and configured to supply a load current to the load; the secondary coil, the rectifier, and the load include one or more lengths of Type II superconducting material; Transformer rectifier flux pump 19. The apparatus further comprising a current control mechanism for controlling the supply of applied current to the primary coil, the current control mechanism being configured to perform the method of any one of claims 1 to 18.

21. 21. The transformer rectifier flux pump of claim 20, wherein the rectifier includes a switching assembly including one or more switches.

22. each said switch includes a length of type II superconducting material configured to carry a switch current, said length of type II superconducting material having a critical current; 22. The transformer rectifier flux pump of claim 20 or 21, further comprising one or more magnetic field generators each configured to apply a magnetic field to the length of Type II superconducting material of each of the switches, each magnetic field generator configured to be selectively controlled to switch the length of superconducting material between a low resistance state and a high resistance state.

23. 23. The transformer rectifier flux pump of claim 22, wherein in the low resistance state, the magnetic field strength is relatively low and the switch current is substantially less than the critical current, and in the high resistance state, the magnetic field strength is relatively high, the critical current is reduced, and the switch current approaches, substantially equals, or is greater than the critical current for the length of superconducting material.

24. A transformer rectifier flux pump according to any one of claims 22 to 23, wherein the current control mechanism is configured to control the supply of applied current to one or more magnetic field generators.

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