Improvements in control of current supply of transformer-rectifier flux pump

Abstract

The present technology relates to the field of superconducting transformer-rectifier flux pumps and controlling the supply of alternating current to transformer-rectifier flux pumps for charging loads. Determining a response of the transformer-rectifier flux pump to the characterization current supply may include determining a value in the flux pump that corresponds to a value of the applied current. A current supply value is calculated for each of a plurality of target values of a load current to be supplied to a load. The supply of current to the flux pump is controlled accordingly. The supply may be modified based on feedback received from the flux pump, such as a sensor that measures a value on the secondary side of the transformer.

Description

1. Field of the Technology

[0001] The present technology generally relates to the field of superconductors, and more particularly to a superconducting transformer-rectifier flux pump. More specifically, the present technology relates to methods and devices for controlling the supply of alternating current to a transformer-rectifier flux pump to charge a load. 2. Background Art

[0002] Superconducting circuits have a wide range of applications. Examples of applications of systems including superconducting circuits include (and 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 including superconducting circuits require low-voltage high-current power supplies, such as in strong high-temperature superconducting (HTS) magnets for applications such as fusion. To meet these requirements, traditional power supplies require a large amount of space, which leads to significant infrastructure challenges. Moreover, connecting a normal conducting circuit to a superconducting circuit housed in a cryostat introduces a large thermal load into the cryostat through physical contact, resulting in cooling challenges.

[0004] This requires complex thermal design and imposes significant heat losses on the cryostat and the cooling system. It also causes significant voltage drops across the normal conducting circuit components, thus requiring a power supply much higher than that required to power only the superconducting coil.

[0005] Superconducting power supplies help to address these problems. Higher current density allows the power supply to be more compact, and the ability to magnetically couple alternating current (AC) circuits without any physical contact using an HTS flux pump avoids cooling problems. The flux pump can be used to induce a current in a superconducting material without the need for direct electrical contact with the electromagnetic flux. This allows current to flow in the HTS circuit without the need for normal conducting electrical connections.

[0006] To power an HTS magnet, a large direct current (DC) is required, which needs to be rectified to convert AC (a current that periodically reverses direction) to direct current (a current that flows only in one direction). Thus, one type of flux pump is a transformer-rectifier flux pump (TRFP), which typically uses a non-superconducting transformer primary coil magnetically coupled to a superconducting secondary coil, and the superconducting secondary coil has a rectifying circuit coupled to the secondary coil.

[0007] TRFP has some known problems. For example, the residual flux during charging can gradually shift the transformer core. This shift limits the absolute current generated in the secondary circuit, thereby changing the output of the flux pump. In addition, the amount of power generated can vary according to the energization level of the load. This may cause the TRFP to not charge the load coil effectively.

[0008] 3. Technical Objectives

[0009] One objective of the present technology is to provide an improved method for controlling the supply of current applied to a transformer-rectifier flux pump to charge a load. Alternatively, one objective of the present technology is to provide an improved device for controlling the supply of current applied to a transformer-rectifier flux pump to charge a load. Alternatively, one objective of the present technology is to provide an improved transformer-rectifier flux pump.

[0010] Alternatively, the objective of the technology is to at least provide useful options to the public. 4. Summary of the Invention

[0011] According to certain aspects of the present technology, a method and / or device for determining how to supply the applied current to a transformer-rectifier flux pump to charge a load are provided. In other aspects of the technology, a method and / or device for controlling the supply of current applied to a transformer-rectifier flux pump to charge a load are provided, for example, controlling the supply based on this determination. The step of determining how to supply the applied current may include determining the expected behavior of the transformer-rectifier flux pump.

[0012] In certain forms, determining how to supply the applied current to the transformer-rectifier flux pump includes characterizing the response of the transformer-rectifier flux pump to the characterized supply of the applied current. The step of characterizing the response of the transformer-rectifier flux pump may include determining a plurality of values in the transformer-rectifier flux pump, the plurality of values corresponding to a respective plurality of values of the applied current supplied to the transformer-rectifier flux pump. During the charging process, that is, after the charging of the load has started, one or more of the steps of determining how to supply the applied current to the transformer-rectifier flux pump may occur.

[0013] In certain forms, determining how to supply the applied current to the transformer-rectifier flux pump includes: for each of a plurality of target values of the load current to be supplied to the load, calculating one or more waveform values of the alternating current supplied to the transformer-rectifier flux pump. In certain forms, each of the target values of the load current may be calculated in one or more preselected increments until a preselected target value of the load current.

[0014] In certain forms, each of the plurality of target values for the load current may be calculated using the plurality of values determined in the step of characterizing the response of the transformer-rectifier flux pump to the characterizing supply of applied current.

[0015] In certain forms, controlling the supply of current applied to the transformer-rectifier flux pump includes modifying the supply of current applied to the transformer-rectifier flux pump during the process of charging the load. The supply of applied current may be modified based on feedback received from the transformer-rectifier flux pump (e.g., from one or more sensors configured to measure values of the transformer-rectifier flux pump). The sensors may measure values on the secondary side of the transformer-rectifier flux pump.

[0016] According to one aspect of the present technology, a method for controlling the supply of current applied 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 also include a rectifier connected to the secondary coil and configured to provide a load current to the load. The secondary coil, the rectifier and the load may include one or more length superconducting materials. The method may include: for each of a plurality of target values of the load current to be supplied to the load, calculating one or more waveform values of the supply of current applied to the transformer-rectifier flux pump. 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.

[0017] In certain forms, the method may include calculating the one or more waveform values of the supply of current applied to the transformer-rectifier flux pump for a target value of load current reaching a preselected target value of the load current in one or more preselected increments.

[0018] In some forms, the one or more waveform values of the supply of current applied to the transformer-rectifier flux pump may include a peak value of the supply of current applied when flowing in a first direction, and a peak value of the supply of current applied when flowing in a second direction, the second direction being opposite to the first direction.

[0019] In certain forms, a method for calculating one or more waveform values for supplying current to a transformer-rectifier flux pump may include calculating one or more target voltage values for the transformer-rectifier flux pump for each of a plurality of target values of load current to be supplied to a load. The method may further include calculating the one or more waveform values for supplying current to the transformer-rectifier flux pump from the one or more target voltage values.

[0020] In some forms, the one or more target voltage values include a target value of the voltage output to the load. In some forms, the target value of the voltage output to the load includes a target value of the voltage across a switch connected in parallel across the load.

[0021] In some forms, the one or more target voltage values may include a first target value of the 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. The one or more target voltage values may also include a second target value of the 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.

[0022] In some forms, the method may include providing a characterization supply of the applied current to the transformer-rectifier flux pump. The method may also include characterizing the response of the rectifier and / or the load to the characterization supply. The method may also include controlling the supply of the applied current based on the characterized response to charge the load.

[0023] In some forms, the method may include supplying the characterization supply and characterizing the response to the characterization supply before beginning to supply the applied current to the transformer-rectifier flux pump to charge the load.

[0024] In some forms, the step of providing the characterization supply includes: when the rectifier is in a first configuration in which current generated in the secondary coil is supplied to the load, supplying a first characterization supply of the applied current to the transformer-rectifier flux pump and characterizing a first response of the rectifier and / or the load to the first characterization supply. The method may also include: when the rectifier is in a second configuration in which no current is supplied from the secondary coil to the load, supplying a second characterization supply of the applied current to the transformer-rectifier flux pump and characterizing a second response of the rectifier and / or the load to the second characterization supply.

[0025] In some forms, characterizing the response of the rectifier and / or the load to the characterization supply may include determining a plurality of voltage values in the rectifier corresponding to respective plurality of values of the applied current supplied to the primary coil. The plurality of voltage values in the rectifier may include the voltage value output to the load. The voltage value output to the load may include the voltage value across a switch connected in parallel across the load.

[0026] In some forms, the method may further include modifying the supply of current applied to the transformer-rectifier flux pump during the process of charging the load. In some forms, the supply of the applied current may be modified based on feedback received from one or more sensors configured to measure values of the transformer-rectifier flux pump. In some forms, the feedback may include a comparison of a target value and a measured value of the transformer-rectifier flux pump. In some forms, modifying the supply of the applied current may include using a PID loop.

[0027] In some forms, one or more waveform values may be the values of the current supplied to the primary coil. In some forms, the transformer-rectifier flux pump may include a magnetic field generator for applying a magnetic field to one of a plurality of lengths of type-II superconducting material. One or more waveform values may be the values of the current supplied to the magnetic field generator.

[0028] According to another aspect of the present technology, a method of controlling the supply of current applied to a transformer-rectifier flux pump to charge a load is provided. The transformer-rectifier flux pump may include a transformer having 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 provide a load current to the load. The secondary coil, the rectifier, and the load may include one or more lengths of superconducting material. The method may include providing a characterized supply of the applied current to the transformer-rectifier flux pump. The method may further include characterizing the response of the rectifier and / or the load to the characterized supply. The method may further include controlling the supply of the applied current based on the characterized response to charge the load.

[0029] According to one aspect of the present technology, a method of controlling the supply of current applied to a transformer-rectifier flux pump to charge a load is provided. The transformer-rectifier flux pump may include a transformer having 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 provide a load current to the load. The secondary coil, the rectifier, and the load may include one or more lengths of superconducting material. The method may include controlling the supply of the applied current such that when integrated over a cycle, the voltage generated across the secondary coil of the transformer is substantially zero.

[0030] According to another aspect of the present technology, there is provided a method for controlling the supply of current applied to a transformer-rectifier flux pump to charge a load. The transformer-rectifier flux pump may include a transformer that includes a primary coil and a secondary coil. The transformer-rectifier flux pump may further include a rectifier that is connected to the secondary coil and is configured to supply a load current to the load. The secondary coil, the rectifier, and the load may include one or more lengths of superconducting material. The method may include modifying the supply of current applied to the transformer-rectifier flux pump based on feedback received from the transformer-rectifier flux pump, such as feedback received from one or more sensors configured to measure values of the transformer-rectifier flux pump. The sensors may measure values on the secondary side of the transformer-rectifier flux pump.

[0031] According to another aspect of the present technology, there is provided an apparatus for controlling the supply of current applied 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 technology.

[0032] According to another aspect of the present technology, there is provided a transformer-rectifier flux pump that includes a transformer that includes a primary coil and a secondary coil. The transformer-rectifier flux pump may further include a rectifier that is connected to the secondary coil and is configured to supply a load current to the load. The secondary coil, the rectifier, and the load may include one or more lengths of superconducting material. The transformer-rectifier flux pump may further include a current control mechanism for controlling the supply of current applied to the primary coil. The current control mechanism may be configured to perform the method of any one of the other aspects of the technology.

[0033] In some forms, the rectifier may include a switching assembly that includes one or more switches. In some forms, each switch may include a length of superconducting material configured to carry a switching current, wherein the length of superconducting material has 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 a corresponding 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 higher-resistance state.

[0034] In some forms, in the low-resistance state, the magnitude of the magnetic field may be relatively low such that the switching current is substantially less than the critical current, while in the higher-resistance state, the magnitude of the magnetic field may be relatively high to reduce the critical current such that the switching current approaches, is substantially equal to, or is greater than the critical current of the length of superconducting material.

[0035] In some forms, the current control mechanism can be configured to control the supply of current applied to one or more magnetic field generators.

[0036] According to another aspect of the present technology, a transformer-rectifier flux pump is provided, which includes a transformer that includes a primary coil and a secondary coil. The transformer-rectifier flux pump may further include a rectifier that is connected to the secondary coil and is configured to supply a load current to a load. The secondary coil, the rectifier, and the load may include one or more lengths of superconducting material. The rectifier may include a switching assembly that includes one or more switches. In some forms, each switch may include a length of superconducting material that is configured to carry a switching current, wherein the length of superconducting material has a critical current. The transformer-rectifier flux pump may further include one or more magnetic field generators, each of which is configured to apply a magnetic field to the length of superconducting material of a corresponding 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 higher-resistance state. The transformer-rectifier flux pump may further include a current control mechanism for controlling the supply of current applied to the primary coil and / or one or more magnetic field generators. The current control mechanism may be configured to perform the method of any one of the other aspects of the present technology.

[0037] After reading the following description that provides at least one example of the practical application of the present technology, other aspects of the present technology (which should be considered in all its novel aspects) will become apparent to those skilled in the art. 5. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] With reference to the following drawings, one or more embodiments of the present technology will be described hereinafter by way of example only and not by way of limitation, in which:

[0039] Figure 1 A graph showing an exemplary electric field of a high-temperature superconductor versus current is shown;

[0040] Figure 2 A diagram of a graph showing the electric field of a superconducting material versus current when three different magnitudes of external magnetic fields are applied;

[0041] Figure 3A A schematic diagram of an exemplary half-wave transformer-rectifier flux pump according to one form of the present technology;

[0042] Figure 3B A circuit diagram of an exemplary half-wave transformer-rectifier flux pump according to one form of the present technology;

[0043] Figure 3C is Figure 3ACircuit diagram of an exemplary half-wave transformer-rectifier flux pump during the charging phase;

[0044] Figure 3D is Figure 3A Circuit diagram of an exemplary half-wave transformer-rectifier flux pump during the maintenance phase;

[0045] Figure 3E is represented by Figures 3A - 3C Illustration of a form of a half-wave transformer-rectifier flux pump represented by a circuit diagram;

[0046] Figure 4 Circuit diagram of an exemplary center-tapped full-wave transformer-rectifier flux pump according to a form of the present technology;

[0047] Figure 5 Schematic diagram of an exemplary processing system according to a form of the present technology;

[0048] Figure 6 Shows the simulated variation of magnetic flux over time in the magnetic core of a transformer of a conventional TRFP for transformers with magnetic cores of various cross-sectional areas;

[0049] Figure 7A 、 Figure 7B Is a graph showing the magnitude of the applied current supplied to the primary coil of a transformer-rectifier flux pump over time during multiple stages in the process of charging a load according to a form of the present technology during one current cycle; and

[0050] Figure 8 Is a flowchart of a process performed by a current control mechanism when implementing a method for implementing a PID loop according to certain forms of the present technology. 6. Detailed implementation

[0051] 6.1. Principle of superconductivity

[0052] A superconductor or superconducting material is a material that exhibits zero resistance at a certain temperature called the critical temperature T c . This zero-resistance state is usually referred to as the superconducting state. Below the critical temperature, when the material is in the superconducting state, a phenomenon called the Meissner Effect occurs, which is the complete expulsion of any magnetic field from the superconductor. A superconductor is a perfect diamagnetic material up to a specific magnetic field strength called the critical magnetic field H c1 . At this time, the superconductor cannot keep the magnetic field outside, so the magnetic field enters the superconductor, which transforms the superconductor from the superconducting state to a state that no longer has zero resistance. This critical field also means that there is a limit to the current that a superconductor can carry, called the critical current I c .

[0053] There are two types of superconductors, called type-I and type-II. Type-I superconductors are usually pure metals and act as described above. Type-II superconductors behave differently. Below an applied magnetic field of a certain magnitude (the first critical magnetic field H c1 ), they expel magnetic flux in a manner similar to type-I superconductors. However, they also exhibit a second critical magnetic field (H c1 ) that is always greater than H c2 . In the field between H c1 and H c2 , the magnetic field can penetrate the type-II superconductor in the form of Abrikosov vortices. This gives rise to an intermediate phase in which the material can exhibit a finite small resistance while essentially remaining superconducting. Due to this property, type-II superconductors can carry much more current in an applied magnetic field compared to type-I superconductors, making them useful for practical applications.

[0054] The critical temperature of a superconductor is usually defined as the temperature below which the resistivity of the superconductor drops to zero or close to zero. In other words, when the temperature of a superconductor is below the critical temperature, the superconductor is said to be in its superconducting state, and when the temperature is above the critical temperature, the superconductor is said to be in a non-superconducting state. Many superconductors have critical temperatures close to absolute zero; for example, mercury is known to have a critical temperature of 4.1 K. However, it is also known that some materials can have much higher critical temperatures, such as 30 K to 125 K; for example, magnesium diboride has a critical temperature of approximately 39 K, while yttrium barium copper oxide (YBCO) has a critical temperature of approximately 92 K. These superconductors are generally referred to as high-temperature superconductors (HTS). HTS are type-II superconductors.

[0055] 6.1.1. Critical Current

[0056] The critical current of a high-temperature superconductor wire or tape is usually defined as the current flowing in the superconductor wire / tape that results in an electric field drop of 100 μV / m ( = 1 μV / cm) along the wire. The critical current is a function of the superconducting material used and the physical arrangement of the superconducting material. For example, a wider tape / wire can have a higher critical current compared to a thinner tape / wire made of the same material. However, throughout the specification, reference to the critical current of a superconductor / superconducting material is for the purpose of simplifying the discussion. s

[0057] In a superconductor, if the current I is approximately equal to the critical current I c , the resistance of the superconductor is non-zero but small. However, if I is much greater than the critical current I c, the resistance of the superconductor becomes large enough to cause heat dissipation, which can heat the superconductor to a temperature above its critical temperature, which in turn makes it no longer superconducting. This situation is sometimes referred to as a "quench" and can damage the superconductor itself.

[0058] Figure 1 An exemplary graph depicting the internal electric field of a high-temperature superconductor versus current is shown. The electric field shown in the graph is related to the resistance by the following equation:

[0059]

[0060] Where:

[0061] · E is the electric field;

[0062] · I is the current passing through the superconductor;

[0063] · R is the resistance of the wire; and

[0064] · L is the length of the wire.

[0065] Therefore, Figure 1 the curve of is related to the resistance per unit length of the superconductor, and since the curve depicted is non-linear, the final resistance of the superconductor is non-linear with current.

[0066] In Figure 1 it can be seen that the electric field strength in the superconductor is essentially zero below the critical current I c of the superconductor. When the current in the 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 results in a rapid increase in the electric field strength in the conductor.

[0067] The transition from the superconducting state to the normal state in HTS materials, as Figure 1 shown, can be described by an empirical law known as the E-J power law:

[0068]

[0069] Where E is the electric field in the conductor, J is the current density, and n is an experimentally defined dimensionless parameter that controls the steepness of the transition. In most superconductors, the value of n is between 25 - 30. The critical current density J c is defined by some arbitrarily chosen threshold electric field E0, which can be 100 μV / m (= 1 μV / cm), as explained above.

[0070] In this specification, the relative resistance of superconducting materials and components including superconducting materials can be referred to. More specifically, this specification relates to superconducting materials in a low-resistance or higher-resistance state. It can be understood that when in the superconducting state, a superconducting material can have zero or substantially zero resistance, and thus these resistances are typically represented by the electric field present across the superconducting material for a given current. However, throughout this specification, for simplicity of discussion, relative resistances are referred to, such as the low-resistance and higher-resistance states of superconducting materials.

[0071] The term "low-resistance state" can refer to when a superconducting material has near or substantially zero resistance in the superconducting state, or when the material has a low resistance in a partial superconducting state. The term "higher-resistance" state refers to a state in which the superconducting material has a resistance that is substantially greater than the resistance in the low-resistance state, such as a substantially non-zero resistance or a resistance that is close to zero but substantially greater than the resistance in the low-resistance state. For the avoidance of doubt, unless the context otherwise clearly indicates, the higher-resistance states referred to in this specification can include the superconducting state.

[0072] Similarly, in the case where a superconductor mentioned in this specification is in a higher-resistance state because the current carried by the superconductor exceeds the critical current, it should be understood that unless the context otherwise clearly indicates, a higher-resistance state can also be achieved if the current carried by the superconductor is close to or substantially equal to the critical current.

[0073] When describing the technologies in this specification, materials and components containing the material are referred to as "superconducting". This term is commonly used in the art for such materials and should not be taken to mean that the relevant materials are always in the superconducting state. Under certain conditions, the material and components including the material can be not in the superconducting state. That is, the material can be described as "superconducting".

[0074] 6.1.2. Superconducting Materials

[0075] Certain forms of the technology can involve components formed from type-II superconductors (such as high-temperature superconducting (HTS) materials). Exemplary HTS materials suitable for this form of the technology include cuprate superconductors, such as 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 have a strong interdependence between the critical current and the applied magnetic field, which can make them particularly suitable for some forms of the technology of the present invention.

[0076] 6.1.3. Superconducting Switches

[0077] The form of the technology involves the use of superconducting switches. A superconducting switch is a switch formed from a length of superconducting material that can transition between a low resistance state and a high resistance state, as described herein. These states are not the open / closed states common to traditional normally-on switches, and typically, even in the higher resistance state, the resistance can be considered low according to the standards of a normally-on switch, e.g., a few ohms or less. In some forms, when in the higher resistance state, the length of superconducting material forming the switch can be in a superconducting state.

[0078] When in the superconducting state, the superconducting material can have a resistance of zero or substantially zero, and such a resistance in the superconducting state is more commonly expressed in terms of the electric field present across the superconducting material for a given current. However, throughout this specification, for the sake of simplicity in the foregoing discussion, relative resistance, low resistance, and higher resistance states have been referred to.

[0079] This transition between the low resistance state and the high resistance state in a superconducting switch can be induced using thermally, self-field, or magnetic-field-driven switches. Forms of the technology can use self-field and magnetic-field-driven switches.

[0080] 6.1.3.1. Self-field switch

[0081] In a self-field switch, the length of superconducting material forming the switch and the waveform of the applied current supplied to the length of superconducting material can be selected such that during a portion of the waveform, the current exceeds the critical current I C in the switch. This causes the length of superconducting material to transition to a higher resistance state. In other portions of the applied waveform, the resulting current is below the critical current I C , causing the switch to remain in the low resistance state. This switching mechanism has been shown to produce the rectification required for flux pumping.

[0082] Although forms of the technology will be described below without using self-switches, it should be understood that other forms of the technology can use this method.

[0083] 6.1.3.2. Magnetic-field switch

[0084] The critical current in a superconductor depends on the external magnetic field applied to the superconductor. More specifically, when a higher external magnetic field is applied to the superconductor, the critical current decreases until the value of the critical magnetic field, beyond which the superconductor no longer remains in the superconducting (low resistance) state. This relationship is shown in Figure 2 , Figure 2 which is a graphical illustration of the electric field of a superconducting material relative to current when three different magnitudes of external magnetic field are applied. The highest magnitude B 施加1 of the external magnetic field results in the lowest critical current I c1. In some forms, an external magnetic field that achieves 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 in only one direction, which can be referred to as a DC field as compared to a directionally, for example, sinusoidally periodically time-varying magnetic field (which can be referred to as an AC field).

[0085] For all superconductors, the critical current drops sharply only under a small externally applied magnetic field. This means that a small change in the applied magnetic field can result in a large change in the critical current. This relationship depends on the superconducting material and the way the superconducting material of this length carrying the current is manufactured.

[0086] It should be understood that this mechanism of reducing or suppressing the critical current by applying an external magnetic field (such as a DC field) is different from the phenomenon of dynamic resistance. This occurs when a superconductor is exposed to a time-varying (e.g., AC) magnetic field while carrying a DC transport current. This generates a DC resistance in the superconductor, which can be large enough to cause the superconductor to transition to a higher resistance state.

[0087] Although the forms of this technology will be described with respect to a magnetic field applied relative to DC, it should be understood that other forms of this technology can use other types of critical current suppression, such as dynamic resistance, in their place.

[0088] 6.2. Transformer - Rectifier Flux Pump

[0089] Certain forms of this technology involve flux pumps, particularly transformer - rectifier flux pumps (TRFPs). Some exemplary forms of the TRFP will be described in detail in the following paragraphs, but it should be understood that the forms of this technology are not limited to the concepts of these forms described for or applicable to the TRFP, and other forms of the TRFP can also be used for other forms of this technology.

[0090] Figure 3A is a schematic diagram of a flux pump 100 according to certain forms of the present technology, and the flux pump 100 is a TRFP 100 in the example shown. Figures 3B - 3D is a circuit diagram of an example of such a flux pump 100 according to certain forms, Figure 3E is an illustration of one form of the TRFP100, the circuit diagram of which is in Figures 3B - 3D shown. For clarity, not all components are shown in all of these figures.

[0091] The TRFP 100 includes a primary side 200 and a secondary side 300, which will be described in more detail below. In use, the primary side 100 of the TRFP100 is supplied with an alternating primary current I P , and the TRFP 100 operates to supply a rectified, i.e., direct, load current I L。During multiple cycles of the primary current I P the load current I L increases because more current is “pumped” into the load 390 each cycle by the flux flow through the TRFP 100.

[0092] 6.2.1. Primary side

[0093] The primary side 200 of the TRFP 100 includes a primary coil 204 configured to receive the primary current I P from a current source 202. In some forms, the TRFP 100 may also include the current source 202. In some forms, the primary side 200 includes components formed of conventional (non-superconducting) conductors. The primary coil 204 may include one or more turns of conductor. A length of conductor may transmit the primary current I P to the primary coil 204.

[0094] The primary side 200 may include a primary magnetic core 206 formed of a material having a relatively high magnetic permeability (such as ferrite). The primary coil 204 may be wound around a portion of the primary magnetic core 206.

[0095] The current source 202 may be configured to supply a current having selected characteristics to the primary coil 204. Further description of these characterizations is provided below. The current I P provided by the current source 202 may be controlled by a current control mechanism 203. Any suitable form of current control mechanism 203 may be used, such as a processor operably connected to the current source 202. In some forms, the TRFP 100 may also include the current control mechanism 203.

[0096] 6.2.2. Secondary side

[0097] In some forms of the technology, the secondary side 300 of the TRFP 100 includes a secondary coil 304 and a rectifier 320. The secondary side 300 may be configured to deliver the load current I L to the load 390. The secondary side 300 of the TRFP 100 and the load 390 may be housed in a cryostat 310. Generally, the conductive components of the secondary side 300 of the TRFP 100 may be formed of one or more superconducting materials.

[0098] 6.2.2.1. Cryostat

[0099] In Figures 3A to 3EIn the form shown, the TRFP 100 can include a cryostat 310 to house the components of the secondary side 300 and maintain a temperature suitable for superconducting components to adopt a low-resistance or superconducting state (in the absence of other factors that can cause one or more superconducting components to adopt a higher resistance or non-superconducting state, such as a current exceeding the critical current of the superconducting material or a magnetic field exceeding the critical field of the superconducting material). For example, the cryostat 310 can maintain the secondary side 300 at a temperature below the critical temperature T C of the superconducting material in the secondary side 300. Any suitable form of cryostat or cooling mechanism can be used. In some forms, some or all of the components of the primary side 200 can be positioned within the cryostat 310. The cryostat is not shown in Figures 3B to 3E the figure.

[0100] 6.2.2.2. Secondary Coil

[0101] The secondary side 300 of the TRFP 100 includes a secondary coil 304. The secondary coil 304 can include one or more turns of a superconductor, such as HTS material. The secondary side 300 can include a secondary core 306, which is formed of a material having a relatively high magnetic permeability (such as ferrite). The secondary coil 304 can be wound around a portion of the secondary core 306.

[0102] In certain forms of the technology, the TRFP 100 can include a transformer 150. The transformer 150 can include a primary coil 204 and a secondary coil 304. The transformer 150 can include a core formed by a primary core 206 and a secondary core 306. The primary core 206 and the secondary core 306 can be magnetically coupled together to form a magnetic circuit. In some forms, the primary core 206 and the secondary core 306 can be integral parts of the same permeable material body. In other forms, the primary core 206 and the secondary core 306 can be physically and thermally separated. For example, the secondary core 306 can be placed inside the cryostat 310 and the primary core 206 can be placed outside the cryostat 310, but they are placed relatively so as to be magnetically coupled when carrying a magnetic field.

[0103] In operation, when a time-varying (e.g., alternating) current I P is supplied to the primary coil 204, a time-varying (e.g., alternating) current I S is induced in the secondary coil 304.

[0104] Certain forms of the TRFP 100 including the transformer 150 according to the present technology can be applicable to various applications, such as including superconducting magnets, superconducting motors / generators, space propulsion systems, fusion reactors, research magnets, NMR, MRI, levitation, water purification, and induction heating. Using the transformer 150 in the TRFP enables the two parts of the TRFP to be electrically separated. The suitable form of the TRFP for this application will depend on various factors, including physical size constraints, cryogenic thermal load, output power, efficiency, cost, and controllability.

[0105] 6.2.2.3. Rectifier

[0106] In certain forms of the technology, the secondary side 300 of the TRFP 100 includes a rectifier 320 for rectifying the alternating current I induced in the secondary coil 304 S into a direct load current I for supplying to the load 390. L Exemplary forms of the rectifier 320 are shown in Figures 3B - 3E and will be described in detail below, but the rectifier 320 can include other arrangements of components in other forms of the present technology.

[0107] The rectifier 320 according to forms of the present technology can include the following functional components: a switch assembly 330; a magnetic field generator assembly 340; and a control mechanism 350. These functional components will be described in more detail below, where exemplary forms of each functional component are described. Specific examples of the rectifier 320 including exemplary forms of each functional component will also be described. It should be understood that other combinations of exemplary forms of each functional component are also provided in some forms of the present technology, and the present technology is not limited to the specific examples shown and / or described.

[0108] In certain forms, the secondary coil 304 supplies the alternating current I S to the switch assembly 330. The switch assembly 330 includes an arrangement of one or more electrical switches 332 and is configured to rectify the alternating current to produce a direct load current I for supplying to the load 390. L The magnetic field generator assembly 340 includes one or more magnetic field generators 342, each magnetic field generator 342 being configured to apply a magnetic field to one or more of the electrical switches 332. The control mechanism 350 controls the magnetic field generator assembly 342 so as to switch the electrical switches 332 of the switch assembly 330. The magnetic field generator assembly 340 and the control mechanism 350 are not shown in the circuit diagram of Figures 3B to 3D .

[0109] 6.2.2.3.1. Switch Assembly

[0110] In some forms of the technology, the switching assembly 330 includes an arrangement of one or more electrical switches 332 and is configured to rectify an alternating current to produce a direct current output, such as a load current I for supply to a load 390. L The arrangement of the electrical switches 332 in the switching assembly 330 determines the type of rectification performed by the rectifier 320, as will be described below. Different forms of the technology may utilize one or more electrical switches 332 in any configuration to produce a rectification effect. In the following description, examples of suitable configurations of the electrical switches are described, but it should be understood that other configurations may be used in other forms of the present technology.

[0111] In some forms of the technology, such as Figures 3B to 3E shown, the rectifier 320 is a half-wave rectifier. In Figures 3B to 3E the form shown, the switching assembly includes two superconducting switches 332a and 332b. The two switches 332a and 332b are connected in series, and the load 390 is connected in parallel across one of the switches 332b. The length of superconducting material connecting the load 390 may be referred to as a "bridge", and the switch 332b may be referred to as the bridge switch. The other switch may be referred to as the series switch 332a.

[0112] In Figures 3B to 3D the form shown, it is assumed that a joint having a non-zero resistance R J is used to connect the length of superconducting material forming the electrical switch 332b, which is connected in parallel between the lengths of superconducting material connected to the secondary coil 304. In addition, the joint connecting the rectifier 320 to the load 390 is assumed to have a non-zero resistance R L . For example, the corresponding joint may be a welded joint. To model the resulting behavior of the circuit, as will be explained later, the joint connecting the bridge to the length of superconducting material connected to the secondary coil 304 is shown as a resistor 334, and the joint connecting the load 390 to the rectifier 320 is shown as a resistor 392.

[0113] An alternating current I S is supplied from the secondary coil 304 to the switching assembly 330. The switching assembly 330 is controlled by a control mechanism 350 that is configured to control the state of each of these switches 332 to rectify the alternating current I S . For example, the control mechanism 350 controls each switch 332 such that the state of each switch is based on the direction of flow of the alternating current I S . Since the direction of flow of the alternating current I S depends on the phase of the current, in this form, the control mechanism 350 is based on the alternating current I SThe phase controls the state of each switch 332 in a timed manner. For example, when the alternating current I S flows in the first direction (i.e., the current is positive), the first switch 332a is placed in its low-resistance state, while the second switch 332b is placed in its high-resistance state. In this way, a low-resistance path is formed around the outside of the loop through switch 332a and across the load 390. This is Figure 3C the configuration of the rectifier 320 shown in, where switch 332a is depicted as a closed switch and switch 332b is depicted as a variable resistor, and can be referred to as the "charging phase" because current I<^ L is supplied to the load 390 during this phase of the cycle.

[0114] When the polarity of the current changes (e.g., from positive to negative), the control mechanism 350 can cause switch 332a to transition to its high-resistance state and switch 332b to transition to its low-resistance state. The higher resistance state of 332a blocks the flow of current from the transformer, providing a measure to block the flow of negative-polarity current. At the same time, the low-resistance state of 332b provides a path for the current in the load to continue flowing, although this path decays exponentially with a time constant L / R (which would mean that if the entire load loop were superconducting, the load current would remain constant). This is Figure 3D the configuration of the rectifier 320 shown in, where switch 332a is depicted as a variable resistor and switch 332b is depicted as a closed switch, and can be referred to as the "maintenance phase" because the current in the load 390 is typically maintained during this phase of the cycle. Thus, the current flowing through the load 390 can be half-wave rectified. In addition, the control mechanism 350 can open and close switches 332a and 332b at appropriate times (i.e., increase and decrease the resistance of switches 332a and 332b) to increase and decrease the current in the load 390 as needed.

[0115] In some forms of the present technology, the control mechanism 350 can control switches 332a and 332b to be in the low-resistance state simultaneously for a certain period within the alternating current cycle. That is, switch 332b can be in the higher resistance state only for a part of the time when I S is positive, and switch 332a can be in the higher resistance state only for a part of the time when I S is negative, and for the remaining time, both switches are in the low-resistance state, regardless of I SWhether it is positive or negative. This can be used as an actual control strategy to ensure that when the current passing through the switch is in the desired direction, the switch is in the off configuration (i.e., the higher resistance state). The control mechanism 350 can control the switches of the rectifiers of any form of technology described herein in this manner, even if not explicitly stated. In some forms, the control mechanism 350 can control the switches 332a and 332b in the persistent mode in this manner, which will be further described below.

[0116] While Figures 3B to 3E An exemplary arrangement of two switches 332 in the switch assembly 330 forming a half-wave rectifier is shown, but it should be understood that other switch assemblies 330 of other forms of the present technology have other arrangements of switches 332 for rectifying alternating current. In addition, switch assemblies 330 of other forms of the present technology can have other numbers of switches 332. For example, in some forms of the technology where the rectifier 320 is used as a half-wave rectifier, the switch assembly 330 can include a single superconducting switch 332.

[0117] In addition, in some forms of this technology, the rectifier can act as a full-wave rectifier. In some such forms, the rectifier can include a switch assembly 330 that includes an arrangement of two switches 332. In other forms, the rectifier can include a switch assembly 330 that includes an arrangement of four switches 332. In Figure 4 An exemplary form of a center-tapped full-wave transformer rectifier is shown.

[0118] A suitable arrangement of the switches 332 in the switch assembly 330 that is part of the rectifier 320 is described in more detail in PCT Application No. PCT / NZ20 2 / 050009, published as International Publication No. WO2022 / 164330, the content of which is incorporated herein by reference.

[0119] 6.2.2.3.2. Switches

[0120] Forms of this technology include using one or more superconducting switches 332 that utilize the principle that the critical current of a superconducting material decreases when a higher external magnetic field is applied to the material, i.e., a magnetic field switch as explained previously. In Figures 3A to 3E Exemplary such electrical switches 332a and 332b are shown. For obvious reasons, the switches 332a and 332b are shown as variable resistors in Figure 3B

[0121] The electrical switch 332 includes a length of high-temperature superconducting (HTS) material, such as any of the types of HTS materials described above. The HTS material has a critical current I c and a critical temperature T c ​. The HTS material is located inside the cryostat 310, which is configured to maintain the HTS material at a temperature below the critical temperature T c .

[0122] When an external magnetic field B 施加 is applied to the length of the HTS material, the critical current decreases, as Figure 2 shown. Thus, the application of the magnetic field B 施加 can be used to make the length of the HTS material function as a switch. If when the magnitude of the magnetic field B 施加 has a certain value, the HTS material carries a switching current (i.e., the current flowing through the electrical switch 332) that is less than the critical current, then the HTS material will be in a low-resistance state. If the magnitude of the magnetic field B 施加 increases from this value to a relatively high magnitude that is high enough to reduce the critical current to a value closer to or below the magnitude of the current carried by the HTS material, then the HTS material will be in a higher-resistance state.

[0123] It can be considered that the low-resistance state of the HTS material is equivalent to the closed state of the switch 332, while the higher-resistance state is similar to the open state of the switch 332. However, it should be understood that the higher-resistance state is not an electrical open circuit as is common for mechanical switches, but rather represents a conductive state with a higher resistance. In this higher-resistance conductive state, the HTS material can remain in the superconducting state but with a higher resistance level, or it can be in a non-superconducting state.

[0124] The magnitude difference of the magnetic field B 施加 between the low-resistance state and the high-resistance state of the switch can vary to multiple magnitudes, including continuously varying magnitudes, and including changing it between two magnitudes. In the low-resistance state, the magnitude of the magnetic field B 施加 can be zero or non-zero.

[0125] It should be understood that in some forms, any magnitude of the magnetic field B 施加 applied to the HTS material can be below 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 move to a higher-resistance state.

[0126] The energy loss in the superconducting switch is related to the critical current in the switch during switching. Since the electrical switch 332 operates by reducing the critical current value during switching, the electrical switch 332 (and the device including the electrical switch 332) has lower losses than a conventional superconducting switch and thus higher efficiency.

[0127] In other forms of the technology, the switching assembly 330 of the rectifier 320 may include one or more switches 332 that operate on one or more different principles. Examples of alternative principles by which the switches 332 may operate in other forms are described in more detail in PCT Application No. PCT / NZ2022 / 050008, published as International Publication No. WO 2022 / 164329, the content of which is hereby incorporated by reference. In some forms, the switching assembly 330 may include multiple switches 332 that operate according to any combination of one or more of the aforementioned principles.

[0128] In some forms, one or more of the switches 332 may operate according to the principle of a self-field switch, as previously explained. In some forms, one or more of the switches 332 may operate according to the principle of dynamic resistance. This occurs when a superconductor is exposed to a time-varying magnetic field while carrying a DC transport current. This creates a DC resistance in the superconductor that can be large enough to cause the superconductor to transition to a higher resistance state. The time-varying magnetic field that causes the dynamic resistance phenomenon may be an alternating magnetic field, such as a sinusoidally varying magnetic field. In the case where the superconducting material has a length that is significantly greater than its width or depth (e.g., a wire or strip), the dynamic resistance may be mainly caused by the component of the time-varying magnetic field applied to the superconducting material that is perpendicular to the direction along the length of the material.

[0129] 6.2.2.3.3. Magnetic field generator assembly

[0130] In certain forms of the 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 lengths of superconducting material including each electrical switch 332.

[0131] In Figures 3A to 3E an exemplary form of the magnetic field generator assembly 340 is shown. In these forms, the magnetic generator assembly 340 includes one or more magnetic field generators 342. Each of the magnetic field generators 342 may include a magnetic core 344. The magnetic core 344 may be a high-permeability magnetic core, such as a ferrite magnetic core (e.g., an iron core) or a laminated steel / iron core. In other forms, other types of high relative permeability at the operating frequency may also be used, or a non-magnetic core or air core may be used. 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 form shown, the magnetic core 344 is a substantially toroidal solid core, such as a square ring with rounded corners.

[0132] In an exemplary form, the magnetic core 344 forms a gap 346. The gap 346 can be a space in the solid magnetic core 344, such as a space in one side of a square toroidal core. Any portion of an air core can be considered as the gap 346.

[0133] In an exemplary form, a conductor is wound around a portion of the magnetic core 344 in the form of a coil 348. For example, the coil 348 formed by the conductor can be wound around one side of a square toroidal core, such as the side opposite to the side on which the gap 346 is formed. In an air core, the coil 348 defines a space region inside it, and this space region can be considered as the air core and contains the gap 346. In use, the conductor can carry an applied current, which can be referred to as the generator current. The flow of the generator current through the coil 348 generates a magnetic field, including in the core 344 and across the gap 346. In some forms of the technique, the length of the HTS material including the electrical switch 332 is positioned in the gap 346 such that the magnetic field across the gap 346 generated by the magnetic field generator 342 is an external magnetic field B applied to the switch 332 施加 。

[0134] In some forms, the generator current carried by the conductor can be provided by a current source (such as an alternating current source) such that the generator current is an alternating generator current. In some forms, the current source can be any current source described in PCT Application No. PCT / NZ2022 / 050009, which is published as International Publication No. WO 2022 / 164330, the content of which is incorporated herein by reference. The generator current can be controlled by a current control mechanism, such as the control mechanism 350 described below.

[0135] The magnitude of the magnetic field generated by the magnetic field generator 342 can vary continuously. Alternatively, the magnitude of the magnetic field generated by the magnetic field generator 310 can vary between two constant values. In some forms, one of the constant values can be zero.

[0136] In Figure 3E an example of a TRFP 100 in accordance with one form of the present technique is shown. In Figure 3EThe cryostat 310 is not shown, but it should be understood that all superconducting components are housed within the cryostat 310. In one form of this TRFP100, the core of each of the transformer 150 and the first and second magnetic field generators 342 is divided into two core portions, where each core has one of the core portions located inside the cryostat 310 and another core portion located outside the cryostat 310. For example, the secondary core 306 of the transformer 150 is located inside the cryostat 310, while the primary core 206 is located outside the cryostat 310. The two parts of each core are magnetically coupled together. The interior of the cryostat 310 is maintained at a sufficiently low temperature to enable the superconducting material of this length located inside the cryostat 310, including those forming the electrical switch 332, to operate in a low resistance or superconducting state.

[0137] In another form of this TRFP 100, all of the cores 344, 206, and 306 of the magnetic field generator 342 and the transformer 150 are located inside the cryostat 310. The core of each of the transformer 150 and the first and second magnetic field generators 342 and 310 is divided into two core portions, where the two core portions in each core are separated by a thermal break. The two parts of each core are magnetically coupled together. Conductors connected to the primary coil 204 of the transformer and the coil 348 connected to the magnetic field generator 342 pass through the wall of the cryostat 310.

[0138] Although certain exemplary arrangements of the magnetic field generator 300 in the magnetic field generator assembly 340 have been described, it should be understood that other magnetic field generators 342 in other forms of the present technology may take other forms, such as those described in PCT Application No. PCT / NZ2022 / 050009, published as International Publication No. WO 2022 / 164330, the content of which is incorporated herein by reference.

[0139] 6.2.2.3.4. Control mechanism

[0140] The rectifier 320 according to certain forms of the present technology includes a control mechanism 350 configured to control the magnetic field generator assembly 340 to switch the electrical switch 332 of the switch assembly 330.

[0141] In certain forms of this technology, the control mechanism 350 is configured to control the magnetic field generator 342 of the magnetic field generator assembly 340 such that the magnitude of the magnetic field generated by each magnetic field generator 342 is based on the phase of the current I in the primary coil 204 P of. For example, the magnitude of the magnetic field generated by each magnetic field generator 342 can vary with the primary current I PThe phase varies with a phase having a fixed phase difference. In one example, the fixed phase difference can be zero, in which case the magnetic field generated by each magnetic field generator 342 is in phase with the primary current I P and varies. In some examples, the magnitude of the magnetic field generated by each magnetic field generator 342 can be a first value for a portion of each cycle of the primary current I P and a second value for another portion of each cycle of the primary current I P . One of the first value or the second value can be zero.

[0142] In other forms of the technique, the rectifier 320 can include a control mechanism 350 as described in PCT application No. PCT / NZ2022 / 050009, which PCT application is published as International Publication No. WO 2022 / 164330, the content of which is incorporated herein by reference.

[0143] 6.2.2.4. Load

[0144] The load 390 is connected to the rectifier 320, and the rectifier supplies a direct load current I L to the load 390. In some forms, the load 390 can be considered part of the TRFP 100, i.e., part of the secondary side 300, while in other forms, the load 390 can be considered separate from the TRFP 100, and the TRFP 100 is configured to supply a load current to the load 390.

[0145] The forms of the technique can be unrestricted by the nature of the load 390. However, in some examples, the load 390 can include an HTS magnet, which can include a superconducting material coil and a core. Typical examples of the load 390 can have a relatively large inductance. In Figures 3B to 3D the forms of the technique shown, the load 390 is represented as an inductor having an inductance L coil .

[0146] 6.3. Current Source and Current Control Mechanism

[0147] It has been explained that the current source 202 can be configured to supply the applied current I to the primary coil 204 having selected characteristics P , and the current I PIt can be controlled by the current control mechanism 203. Although some aspects of the present technology relate to the manner of controlling the current supplied to the primary coil 204, as will be further explained below, in some forms, the present technology is not limited to the type of devices and systems for supplying current to the primary coil 204, and any suitable form of current source 202 and current control mechanism 203 can be used. Some aspects of the technology relate to the manner of controlling the current supplied to the magnetic field generator assembly 340, and similarly, the technology is not limited to the type of devices and systems for supplying current to the magnetic field generator assembly 340, and any suitable form of current source and control mechanism 350 can be used.

[0148] In some forms, the current control mechanism 203 can include a waveform generator, such as an arbitrary waveform generator (AWG) or a function generator. In some forms, the waveform generator can be implemented by a device dedicated to the waveform generation function through its operation. In some forms, the waveform generator can include any processing system or computing device configured to run waveform generator software, including devices not dedicated to this purpose, such as general-purpose computing or processing devices.

[0149] Figure 5 is a schematic diagram of an exemplary processing system 400 according to one form of the present technology. In some forms, the current control mechanism 203 can include a processing system 400 configured to operate as a waveform generator.

[0150] The processing system 400 includes a hardware platform 402 that manages the collection and processing of data from one or more devices, which can include sensors and user devices. The hardware platform 402 has a processor 404, a memory 406, and other components typically present in such computing devices. The hardware platform 402 can be local to the devices, or it can be remote from the devices and receive data through an appropriate communication link. In an exemplary form of the illustrated technology, the memory 406 stores information accessible by the processor 404, which includes instructions 408 executable by the processor 404 and data 410 retrievable, manipulable, or storable by the processor 404. The memory 406 can be any suitable device known in the art capable of storing information in a manner accessible by the processor 404, including computer-readable media, or other media that store data readable by an electronic device.

[0151] The processor 404 can be any suitable device known to those skilled in the art. Although the processor 404 and the memory 406 are shown within a single unit, it should be understood that this is not intended to be restrictive, and the functions of each processor and memory described herein can be performed by multiple processors and memories, which may or may not be physically separated from each other or from the processing system 400. The instructions 408 can include any set of instructions suitable for execution by the processor 404. For example, the instructions 408 can be stored as computer code on a computer-readable medium. These instructions can be stored in any suitable computer language or format. The data 410 can be retrieved, stored, or modified by the processor 404 according to the instructions 410. The data 410 can also be formatted in any suitable computer-readable format. Similarly, although the data is shown as being contained in a single location, it should be understood that this is not intended to be limiting and the data can be stored in multiple memories or locations. The data 410 can also include a record 412 of control routines for various aspects of the system 400.

[0152] The hardware platform 402 can communicate with a display device 414 to display the results of data processing. The hardware platform 402 can communicate via a network 416 with one or more other devices (such as user devices, such as a tablet computer 418a, a personal computer 418b, or a smart phone 418c, or other devices including sensors, such as current sensors and voltage sensors, and a current source 202), or one or more server devices 320 having an associated memory 322 for storing and processing data collected by the local hardware platform 402. It should be understood that the server 320 and the memory 322 can take any suitable form known in the art, such as a "cloud-based" distributed server architecture. The network 416 can include various configurations and protocols, including the Internet, an intranet, a virtual private network, a wide area network, a local area network, a private network using one or more company-proprietary communication protocols, whether wired or wireless, or a combination thereof.

[0153] The hardware platform 402 can be configured to run software that is configured to enable an inputter to input a desired waveform of the current I that will be supplied by the current source 202 to the primary coil 204. The inputter can be a user who can interact with the software through any one or more user devices (such as the display device 414 and / or the personal computer 418b). The hardware platform 402 can be configured to, for example, run any conventional waveform generator software known in the art. The software run by the hardware platform 402 can also be configured to cause the current I P The software run by the hardware platform 402 can also be configured to cause the current I PThe waveform of can be determined by the hardware platform 402 itself, for example, by the processor 404, which can be configured to run one or more algorithms for determining the desired current waveform, as further described below. In such a form, the inputter can include the hardware platform 402, such as the processor 404.

[0154] The hardware platform 402 can be configured to communicate with the current source 202 and control the current source 202 to deliver the current I to the primary coil 204 according to the desired waveform selected by the user and / or the processor 404, specifically the waveform of the current I P , that is, the current I P how it changes over time. The hardware platform 402 can communicate with the current source 202 through a wired and / or wireless communication link to control the current source 202. P

[0155] In some forms, the TRFP 100 includes the current source 202 and the current control mechanism 203. In other forms, the current source 202 and the current control mechanism 203 are separated from the TRFP 100, and the current source 202 is configured to supply current to the TRFP 100.

[0156] 6.4. Control of the primary current supplied to the TRFP

[0157] As previously described, the current source 202 on the primary side 200 can be configured to provide the applied current I to the primary coil 204 with selected characteristics P so as to charge the load 390 in a desired manner. In some forms of this technique, these characteristics are determined based on the load current to be supplied to the load 390 at the end of the load charging process and the required rate of increase of the load current.

[0158] 6.4.1. Previous research and development

[0159] Previous studies of the superconducting TRFP have focused on demonstrating its operating principle in a laboratory environment, and there has been little research on how the TRFP operates in real-world applications. For example, in laboratory experiments, the TRFP is used to charge a load 390 that includes a relatively small load coil (e.g., a load coil with a relatively small inductance). In some practical applications of the superconducting TRFP, load coils with significantly higher inductance can be used. HTS magnets for many applications can have an inductance of several hundred mH or more, which contrasts with the few mH ranges considered in many existing documents. The inductance of the load coil is a key parameter that defines the charging rate of the TRFP, and another is the voltage generated across the load coil during each cycle. The charging rate is inversely proportional to the load coil inductance, which means that as the inductance increases, the number of charging cycles required to reach a specified current increases proportionally. Thus, a TRFP with a load coil having an inductance of several hundred mH may require the TRFP to operate thousands of cycles to generate the same current as a TRFP with a load coil having an inductance of a few mH, as typically discussed in the existing literature. Additionally, the load coil in a real-world application may require a load current greater than about 10 kA, while conventional TRFPs typically achieve values in the range of 2 - 3 kA using a 10 μH load coil. Combining these two effects, for a TRFP with an equivalent voltage output, 10,000 more cycles may be required to achieve the same output current in a 100 mH load coil.

[0160] In developing certain forms of the technology described in this specification, consider how the TRFP operates when used with parameters in certain real-world applications that the technology may be used for. In doing so, certain improvements on how to operate the TRFP have been identified.

[0161] It should be understood that unless otherwise specified, the operating principle of the TRFP described in this document is not limited to the case where its application to the parameters of the system is as described above. That is, certain forms of the technology can be applied to any form of TRFP, regardless of their size, parameters, and application.

[0162] 6.4.2. Secondary Net Voltage

[0163] Previous studies have concluded that it is desirable to control the alternating applied current I supplied to the primary coil 204 P , such that there is a net zero current when integrated over a current cycle. However, it has been recognized that in some cases, such as when the TRFP is used to charge a load coil with a relatively high inductance, this method may have problems, such as inconsistent charging and / or inability to charge to the desired current level. This problem will be briefly illustrated by discussing the mechanism for achieving correction in the TRFP.

[0164] InFigures 3A - 3E In the example of the TRFP 100 shown, the alternating current primary current I P is rectified by the voltage V generated across the bridge switch 332b B . This voltage is determined by two factors: the critical current I of this length of superconducting material in the bridge switch 332b at the applied magnetic field and temperature C and the current I flowing through the switch B . In the TRFP 100, rectification is achieved by controlling the currents I C and I B over time to produce the desired voltage V output to the load 390 B . Some existing studies do not consider the dynamic characteristics of I B throughout the charging process. In fact, two factors affect the variation of I B over time: 1) the absolute amount of the secondary current I s induced in the secondary coil 304; and 2) the distribution of the secondary current I S around the secondary side 300 of the TRFP 100.

[0165] In the case where the TRFP 100 includes a rectifier 320 in the form of a half-wave rectifier, if the alternating current primary current I P has a constant waveform over each cycle (as in the case of a conventional HTS flux pump), then 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 S in the secondary coil 304 will remain consistent throughout the charging period. In both cases, this itself manifests as a change in the power transfer behavior from the waveform of the primary current I P applied throughout the charging process to the resulting secondary current I S . In existing HTS TRFPs, a DC offset is observed, and thus the secondary current I S changes throughout the charging cycle. When the secondary current I S changes, the voltage V B changes jointly, which changes and limits the charging rate.

[0166] For a selected transformer with a peak primary current I P matched to its size, the transformer 150 may initially be unsaturated. However, if the primary waveform does not have suitable characteristics, it may saturate. The simulation of the saturation of the transformer 150 is shown in Figure 6 . This behavior matches the changes measured experimentally. It can be observed that due to the dynamic characteristics of the flux pump behavior, the flux in the core changes significantly over time in both magnitude and direction. The effect of this change in flux is to inherently change the secondary current IS The absolute magnitude. For any DC offset, the secondary current I S of the absolute value is shifted, which will result in a change in the charging curve of the load 390.

[0167] Having considered factor 1) as above, we now discuss factor 2): the distribution of the secondary current I around the secondary side 300 of the TRFP 100. S When the increasing current I L is supplied to the load 390, less current I B will flow through the bridge switch 332b (since I S = I B + I L ). Since the voltage V B is related to the magnitude of I B , the voltage will also drop. However, although the voltage V B drops throughout the charging cycle, the voltage V B,M generated during the hold phase remains constant (since the distribution of I S does not affect this voltage). In fact, this charging balance between the voltage V B and the voltage V B,M shapes the transformer flux in the drive Figure 6 . Initially V B > V B,M , so the remaining flux in the same direction as the load current I L remains in the transformer core. As I L increases, V B drops until V B,M becomes larger. At this point, before saturating in the direction opposite to the load current, the flux in the transformer core will cross zero. This can be seen in Figure 6 . This saturation will occur regardless of the size of the transformer core or the magnitude of I L ; it is only related to the choice of the primary waveform. These observations are contrary to many conventional explanations for the origin of the DC offset in a half-wave rectifier flux pump.

[0168] Although the above discussion separates the two factors 1) and 2), in fact the relative strength of each element will affect the other. In fact, it is this correlation between these factors that contributes to the observations leading to certain aspects of the present technology.

[0169] The presence of the previously described DC offset is well established in the literature and has traditionally been considered an inevitable part of the charging cycle. Previous studies have understood the importance of DC offset in limiting performance. For example, previous work has considered how passive components (such as resistors) or built-in DC offsets within the primary waveform can improve the performance of the TRFP. However, that research was predicated on the assumption that DC offset is a fundamental aspect of flux pump operation.

[0170] Certain aspects of the present technology contemplate substantially avoiding (or at least reducing) DC offset. In some forms, this can ensure that the performance of transformer 150 remains constant throughout the charging of load 390. It can also facilitate dealing with the effects of the redistribution of current I S . The substantial avoidance of DC offset can allow high-temperature superconducting TRFPs to achieve higher load currents in certain forms and can also enable the TRFP to have consistent performance.

[0171] To substantially avoid DC offset as described above, it has been determined that the integral voltage V generated in secondary coil 304 of transformer in the entire cycle should be substantially zero. Accordingly, some forms of the technology include a current control mechanism 203 configured to control the supply of alternating current to the primary coil 204 of the primary side 200 of the TRFP 100 (such as the TRFP 100) such that when integrated over one cycle, the voltage V generated across secondary coil 304 of transformer 150 is S substantially zero. In the case of the half-wave rectifier 320 of the technology form shown, this is equivalent 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. S In Figures 3B - 3E the case of the half-wave rectifier 320 of the technology form shown, this is equivalent 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.

[0172] However, the magnitude of the voltage in the secondary side 300 of the TRFP 100 is determined by the non-linear resistivity of the superconducting material in the electrical switch 332. This makes it difficult to calculate the parameters of the desired primary waveform to achieve the necessary charging, especially when charging occurs and the current in load 390 gradually increases. Accordingly, in certain forms of the technology, the waveform of the primary current I P is feedback-controlled during the charging of load 390. Exemplary forms of such feedback control will be described below.

[0173] While some forms of the technology described below involve using a rectifier 320 in the form of a dual-switch half-wave rectifier, in other forms, other configurations of the rectifier 320 in the TRFP 100 can be used, and equivalent analysis and structures can be generated for such other forms.

[0174] In other forms of the technology, it may be desirable for the DC offset to be non-zero, or the DC offset may be inevitable, such as in the case of a center-tapped full-wave rectifier as described below. In such forms, the TRFP 100 may be configured such that the DC offset is non-zero but predetermined, and optionally has the same DC offset over a plurality of consecutive periods. This can enable precise management of the DC offset during charging of the load. Thus, in some forms, the TRFP 100 may include a current control mechanism 203 configured to control the supply of alternating current to the TRFP 100 (e.g., the primary coil 204 of the primary side 200 of the TRFP 100) to produce a predetermined DC offset in the secondary current. In some forms, the predetermined DC offset may be produced over a plurality of periods, such as a plurality of consecutive periods. In some forms, the predetermined DC offset may be zero.

[0175] 6.4.3. Waveform of Primary Current

[0176] In certain forms of the technology, the current control mechanism 203 is configured to control the current source 202 to supply the applied current I to the primary coil 204. P . The applied current I P may be an alternating current. In certain forms, the waveform of the applied current I P , i.e., the variation of the current I P over time, may be as shown in Figure 7A , Figure 7A which is a graph showing the relationship between the magnitude of the alternating current I supplied to the primary coil 204 of the TRFP 100 and time during multiple stages in the process of charging the load 390 over one current cycle. The waveform of the applied current I P may be characterized by one or more values, which are referred to as waveform values in this specification. The nomenclature of exemplary waveform values as shown in P and Figure 7A and Figure 7B (and the following description) will now be explained.

[0177] In the first part of the cycle, which may be the first half of the cycle, the current flows through the primary coil 204 in a first direction, which is represented as a current with a positive value in Figure 7A and Figure 7B . During the first time period, the current increases from a first value, which may be zero, to a maximum value. As shown in Figure 7A and Figure 7B , the rate of increase of the current may be substantially linear during this first time period. During the second time period, the current may remain at a substantially constant value, as shown in Figure 7A and Figure 7B for I P,CAs shown. This value may be referred to as the peak positive current. The duration of the second period is as shown in Figure 7A and Figure 7B where t 充电 is shown. Subsequently, during the third period, the current decreases from the maximum value to a lower value, which may be zero. As shown in Figure 7A and Figure 7B the rate of increase of the current during this third period may be substantially linear.

[0178] Subsequently, during the second part of the cycle, which may be the second half of the cycle, the current flows through the primary coil 204 in a second direction opposite to the first direction, and this second direction is represented as a current with a negative value in Figure 7A and Figure 7B During the fourth period, the current decreases from a value that may be zero (i.e., becomes more negative, but increases in magnitude in the negative direction) to the maximum value. As shown in Figure 7A and Figure 7B the rate of increase of the current may be substantially linear during this first period. During the fifth period, the current may remain at a substantially constant value, as shown in Figure 7A and Figure 7B where I P,M is shown. This value may be referred to as the peak negative current. The duration of the second period is as shown in Figure 7A and Figure 7B where t 维持 is shown. Subsequently, during the sixth period, the current increases from the maximum negative value to a higher value, which may be zero. As shown in Figure 7A [[ID=3�]]and Figure 7B the rate of increase of the current may be substantially linear during this sixth period.

[0179] Figure 7A and Figure 7B The waveforms shown in may be considered an approximation of the square-wave primary current I P . In some forms, for the second and fifth periods, i.e., the values of t 充电 and t 维持 , it may be advantageous to make them as small as possible. Thus, in some forms, the waveform of the primary current I P supplied to the primary coil 204 may be approximated as a triangular waveform. In some forms, the values of t 充电 and t 维持 may be equal or substantially equal. For simplicity, all periods except t 维持 and t 充电 may be neglected, and this approach will be adopted in the following discussion.

[0180] Figure 7A and Figure 7B The examples of the waveforms shown in may be used to provideFigures 3A to 3E The primary coil 204 of any one or more exemplary forms of the TRFP 100 shown in. The TRFP 100 includes a rectifier 320 that operates as a half-wave rectifier. In this form of the TRFP 100, when current flows in one direction in the primary coil 204, the rectifier 320 is in such a configuration that current is supplied from the secondary coil 304 to the load 390, and the load 390 is charged. And when current flows in the opposite direction in the primary coil 204, the rectifier 320 is in a different configuration such that no current is supplied from the secondary coil 304 to the load 390, but rather the current in the load 390 is maintained by means of a superconducting loop through the bridge switch 332b. Thus, Figure 7A and Figure 7B The first part of the period of the waveform shown, i.e., the first, second, and third time periods when the current is positive, can be referred to as the "charging phase", while Figure 7A and Figure 7B The second part of the period of the waveform shown, i.e., the fourth, fifth, and sixth time periods when the current is negative, can be referred to as the "maintaining phase". This is the reason for the subscripts "C" and "M" in Notes I P,C and I P,M below.

[0181] In Figure 7A and Figure 7B are shown a plurality of different primary current waveforms 602, 604, 606 having different magnitudes of peak positive and negative currents. Each primary current waveform 602, 604, 606 can represent the waveform of the primary current I P of different periods. As will be explained later, certain characteristics of the primary current I P waveform can change during the course of a period in order to charge the load 390 in a desired manner. In some forms, the characteristics can change after each period, while in other forms, the characteristics can remain the same for a certain number of periods and then change in subsequent periods.

[0182] In certain forms, the value of the peak positive current I P,C and / or the value of the peak negative current I P,M can be adjusted through a series of periods. The value of the peak positive current in the k-th period is and the value of the peak negative current in the k-th period is In Figure 7A and Figure 7B , the waveform 602 represents the first current period, and thus the corresponding peak positive current value and negative current value are and The waveform 606 indicates that once the load current in the load 390 has reached the desired level and the corresponding peak positive and negative current values in this period are and the current at can be greater than and can be greater than

[0183] In the forms of the techniques discussed above and below, the peak current value is described as an exemplary waveform value that varies between cycles to regulate the output voltage generated. However, in other forms, other waveform values may vary between cycles. Examples include changing the magnitude of t 维持 and t 充电 . In other forms, the strength and / or direction of the applied magnetic field may vary between cycles. In some forms, one or more of these values may vary. The process for integrating these methods may be similar to the method outlined below and may thus be modified to include a range of waveform variations in addition to or instead of peak current modification. For reasons of simplicity of description, forms involving peak current variations are described herein.

[0184] 6.4.4. Other Nomenclature

[0185] In addition to the terms already introduced, the following terms will be used in the subsequent description:

[0186] · is the load current supplied to the load 390 at the start of the k-th cycle;

[0187] · ΔI L is the change in the load current supplied to the load 390 during the current cycle. In some forms, this value may be constant for the process of charging the load 390, while in other forms, this value may change over time, for example if a change in the ramp rate is desired;

[0188] · is the change in the load current supplied to the load 390 during the charging phase of the k-th cycle;

[0189] · is the change in the load current supplied to the load 390 during the maintenance phase of the k-th cycle;

[0190] · is the peak current generated in the secondary coil 304 during the charging phase of the k-th cycle;

[0191] · is the peak current generated in the secondary coil 304 during the maintenance phase of the k-th cycle;

[0192] · N1 is the number of turns in the primary coil 204 of transformer 150;

[0193] · N2 is the number of turns in the secondary coil 304 of transformer 150;

[0194] · t 周期 is the time of the total 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 to sixth time intervals as described above);

[0195] · is the time-averaged voltage generated across the load 390 (which can be a coil) during the charging phase of the k-th period;

[0196] · is the time-averaged voltage generated across the bridge (e.g., Figures 3B - 3E the bridge switch 332b in the form shown) during the charging phase of the k-th period;

[0197] · is the time-averaged voltage generated across the Figures 3B - 3E series switch 332a in the form shown in

[0198] · is the voltage across the bridge (e.g., across the Figures 3B - 3E bridge switch 332b in the form shown) during the charging phase of the k-th period required to achieve the desired charging of the load 390;

[0199] · is Figures 3B - 3E the voltage across the series switch 332a in the form shown in

[0200] · is the current through the bridge (e.g., through the Figures 3B - 3E bridge switch 332b in the form shown) during the charging phase of the k-th period.

[0201] 6.4.5. Characterization of the supply response

[0202] It has been explained that, in some forms, the supply of the applied current I supplied to the primary coil 204 P is controlled so as to charge the load 390 in a desired manner. For example, the load 390 can be charged by increasing the magnitude of the load current I supplied to the load in a stepwise manner L such that the load current I LIts magnitude increases incrementally after a certain number of cycles (e.g., after each cycle). In some forms, the applied current I supplied to the primary coil 204 can be controlled P such that the load current I is incrementally increased by substantially the same amount at each increment. This can be referred to as a "linear ramp" of the load 390. L Due to the non-linear resistivity of the superconducting material in the TRFP 100, precise control and management of the electromagnetic state of the flux pump is difficult. Thus, in some forms of the technology, the response of the TRFP 100 is characterized experimentally before charging the load 390, i.e., before starting to supply an alternating current to the TRFP 100 for charging the load 390 to a desired level.

[0203] In some forms of the technology, the characterization phase may not be implemented, and the control can be determined by only analyzing the TRFP 100, e.g., by solving or approximating analytical equations derived directly from considerations of the topology and construction of the TRFP 100.

[0204] In some forms, the response of the TRFP 100 can be characterized at least partially experimentally while the load 390 is being charged. For example, some steps of characterizing the response of the TRFP 100 can occur while the load 390 is being partially charged to the desired charge level.

[0205] Characterizing the response of the TRFP 100 can include characterizing the response of the rectifier 320 and / or the load 390.

[0206] Characterizing the response of the TRFP 100 can include providing a characterized supply of the applied current to the primary coil 204 of the transformer 150. The current source 202 and the current control mechanism 203 can be used to provide the characterized supply of current, but in other forms, a current source and a current control mechanism different from those that will ultimately be used for charging the load 390 can be used. In some forms, the characterized supply of the applied current has a waveform that is the same as or substantially similar to the waveform of the applied current supply that will be supplied to the primary coil 204 when charging the load 390. For example, the duration of each part of the cycle of the characterized supply can be the same as that of the charging supply. Additionally, the duration of each period of the cycle of the characterized supply can be the same (or substantially the same) as that of the charging supply, including the t

[0207] values of the characterized supply being the same (or substantially the same) as the t 充电 and t 维持 values of the charging supply. The values of the positive and negative peak currents can vary for both the characterized supply of current and the charging supply, as will be explained. 充电 and t 维持 ​

[0208] In certain forms of the technology, any one or more of the plurality of parameters of the TRFP 100 can be determined as part of characterizing the response of the TRFP 100 to a characterization supply. In certain forms, one or more voltage values in the rectifier 320 corresponding to a given current value supplied to the primary coil 204 are determined. For example, the voltage value output to the load 390 can be determined. In Figures 3B - 3E the form of the half-wave rectifier 320 shown, the voltage output to the load 390 can be the voltage V across the bridge B , i.e., the voltage across the bridge switch 332b. Additionally, the current I flowing through the bridge (i.e., through the bridge switch 332b) B can be determined, and this value corresponds to each determined voltage value. In certain forms, a value corresponding to the peak of the current in the waveform supplied to the primary coil 204 (I P,C or I P,M , depending on whether it is the charging phase or the sustaining phase) is determined.

[0209] In certain forms of the technology, the necessary measuring devices for directly measuring these parameters or measuring other parameters are provided, and these parameters can be determined indirectly, for example, by calculation from these parameters. The measuring devices can include one or more voltage sensors and one or more current sensors. It should be understood that any determination of the parameters of the TRFP 100 necessary for the subsequent description, but without explicitly mentioning the measuring device for determining the parameter, can be achieved by using appropriate sensors.

[0210] The correspondence between multiple values of one parameter and multiple values of another parameter, such as the voltage value in the rectifier corresponding to the primary current value, can be stored in a data storage device in an appropriate form, such as stored in a data array or a look-up table.

[0211] In an operable TRFP 100, the characterization of the response can be performed periodically or frequently, for example, every few hours, days, or weeks, depending on the nature of the TRFP 100 and its use.

[0212] More specific details of the characterization of the response of the TRFP 100 in certain forms of the technology will now be described. In particular, in the case where the TRFP 100 includes certain types of rectifiers 320 (such as Figures 3B - 3E the half-wave rectifier 320), the characterization of the response of the TRFP 100 can include characterizing the response of the TRFP 100 in the charging phase and characterizing the response of the TRFP 100 in the sustaining phase. It should be understood that in the case of a rectifier (such as a full-wave rectifier) where both phases of the waveform correspond to charging, the description of characterizing the response in the charging phase can be applied only.

[0213] 6.4.5.1.Characterization during the Charging Phase - Characterization Table

[0214] In some forms of this technology, the TRFP 100 may be characterized during the charging phase, e.g., when Figures 3B - 3E When the rectifier 320 is in a configuration to supply the current generated in the secondary winding to the load 390, the voltage value in the rectifier 320, for example, the voltage value V across the bridge switch 332b and output to the load 390 is determined. B , which corresponds to the AC current value supplied to the primary coil 204, such as the peak current value I in the positive direction P,C .

[0215] In an exemplary form, Figures 3A - 3E The TRFP 100 is shown assembled and the load 390 is connected as described above. In addition, the rectifier 320 is placed in a configuration where the current generated in the secondary winding 304 is supplied to the load 390, e.g. Figures 3B - 3E In the case of the half-wave rectifier 320, the bridge switch 332b is placed in a higher resistance state and the switch 332a is placed in a lower resistance state. As described above, a magnetic field can be applied to the bridge switch 332b by a magnetic field generator to achieve this.

[0216] To characterize the TRFP 100, multiple characterizing signals of the applied current are applied that have waveforms that are the same as or substantially similar to the waveforms that will be used for charging across the expected range of applied current. For example, multiple characterizing signals with different waveform values (e.g., peak positive value I P,C ,) are sequentially supplied to the primary winding 204 of the transformer 150. The level of the applied current supply may be such that the transformer 150 is not saturated. When each supply of the applied current is provided, the voltage value V across the bridge switch 332b and output to the load 390 is measured and recorded. B (I B ). After each characterization supply of current, the load current I in the load 390 may be allowed to L This ensures that the current in the secondary winding 304 is equal to the bridge switch 332b (i.e., I ) at the beginning of each characterization step. S,C =I B ) current. In addition, it is assumed that for this form of TRFP 100, V B (I B )=V S,C (I S,C ), although deviations from this equivalence can be quantified and integrated if necessary.

[0217] A wide range of bridge currents I that are possible for a particular design of the TRFP 100 B are used to determine V B (I B ). Thus, a corresponding range of the waveform values of the supplied current representing the supply is supplied to the primary coil 204.

[0218] In this way, the conditions for charging the load 390 are replicated during the characterization phase, including all possible actual variations from the simulated behavior of the TRFP 100 described later. Additionally, this characterization process is also useful in establishing the capabilities of the TRFP 100.

[0219] It should be noted that in some forms, V B (I B ) may have no dependence on the load current. In such forms, as ΔI L ∝V B (I B ), it can be assumed that a characterization holds for all possible experimental variables, independent of the load current. In other forms, V B (I B ) may depend on the load current or the ramp rate. For example, AC losses and / or inductive coupling may change the effective voltage generated. Additional terms can be added to the relevant equations to account for these effects. Alternatively, as will be discussed, feedback loops, such as in the form of a PID loop, can account for such effects.

[0220] In some forms, the process of providing multiple characterization supplies to the primary coil 204 to characterize the behavior of the TRFP 100 can be performed only during initial installation and before the charging process begins. However, in other forms, one or more subsequent characterization steps can occur, where one or more additional characterization supplies of the applied current are provided to the primary coil 204. For example, a periodic check of the characterization behavior of the TRFP 100 can be performed.

[0221] In some forms, the result of the process of providing a characterization current supply and measuring the parameters of the TRFP 100 during the charging phase can be a series of values of the bridge current I B of the TRFP 100 under discussion and the associated voltage values V B (I B ) across the bridge. In some forms, this series of values can be stored or presented as a data array, such as a lookup table of V B (I B ) versus I B . An example of a lookup table in one form of the present technology is presented in Table 1:

[0222]

[0223] Table 1 - Exemplary Lookup Table Characterizing TRFP 100 During the Charging Phase

[0224] The bridge current value I determined during the characterization can be appropriately selected B for the increment between. In some forms, various increments can be used. For example, when the current I B is less than the critical current I of the bridge switch 332b C,B , I B the interval between each value of can be quite wide (e.g., 10 - 20A steps). The additional values of current and corresponding voltage within this range can be generated by interpolation. When the current approaches the critical current I of the bridge switch 332b C,B , the current value I B the interval between can be decreased, including significantly decreased. For example, if the current is within approximately 20 - 30% of the critical current I C,B , the interval between values can be decreased to approximately 1A. Measurements can be made until I B the maximum value, which can be higher than the critical current I of the bridge switch 332b C,B , e.g., 1.5I C,B .

[0225] At this stage, those currents I in the bridge 332b have been determined B to produce a specific voltage V across the bridge B (I B ) to be supplied to the load 390 (e.g., Table 1). In some forms, the next step is to calculate the correlation between I B and the input primary current, e.g., the peak positive value I of the input primary current P,C .

[0226] The bridge current I B will be reduced by the load current I L , so the required current generated in the secondary coil 304 scales with the increase in load current as follows:

[0227]

[0228] Based on the turns ratio of the transformer 150, this current is related to I P,C :

[0229]

[0230] Thus, a series of voltage values V across the bridge (and / or supplied to the load 390) B (I B ) and the corresponding peak positive current values I supplied to the primary coil 304PC It can be determined, for example, in the form of another look-up table such as that presented in Table 2:

[0231]

[0232] Table 2 - Exemplary look-up table characterizing TRFP 100 during the charging phase

[0233] 6.4.5.2. Characterization during the maintenance phase

[0234] In the case of the form of TRFP 100, where there is a maintenance phase in addition to the charging phase, for example, for a half-wave rectifier 320 such as Figures 3B - 3E shown, a similar process for characterizing TRFP during the maintenance phase can be performed in order to determine the voltage value in the rectifier 320, for example, the voltage value V across the series switch 332a M , which corresponds to the value of the alternating current supplied to the primary coil 204, for example, the current peak I in the negative direction P,M .

[0235] In an exemplary form, the TRFP 100 as Figures 3A - 3E shown is assembled. The load 390 can be connected or not connected for this characterization step. Additionally, the rectifier 320 is placed in a configuration where 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 , the bridge switch 332b is placed in a low-resistance state and the switch 332a is placed in a high-resistance state. As described above, a magnetic field can be applied to the bridge switch 332a in order to achieve this.

[0236] Then, multiple characterization supplies of the applied current having a waveform that is the same as or substantially similar to the waveform that will be used for charging, and multiple characterization supplies having different waveform values (for example, the peak negative value I P,M ,) can be sequentially supplied to the primary coil 204 of the transformer 150. The level of the characterization supply of the applied current can be such that the transformer 150 does not saturate. When each characterization supply of the alternating current is provided, the voltage value V across the series switch 332a is measured and recorded M (I S ). Different from the characterization of the charging phase, after each characterization supply of the current, the load current I in the load 390 L does not need to decay to zero before the next characterization supply is provided.

[0237] Similar to the characterization of the charging phase, for a wide range of currents I through the series switch 332a S the possible values of V for a particular design of TRFP100 can be determined M (IS )。Therefore, the corresponding range of values characterized by the applied current is supplied to the primary coil 204. Currents values I similar to those explained above for the charging phase can be applied B for the current value I S in terms of number and range, such as similar increments and maximum values.

[0238] As explained with respect to the charging phase, in some forms, the process of providing multiple characterizations of the supply to the primary coil 204 to characterize the behavior of the TRFP 100 can be performed only during initial installation and before the charging process begins, but in other forms, one or more subsequent characterization steps can occur, where one or more additional characterizations of the supply of the applied current to the primary coil 204 are provided. For example, a periodic check of the characterization behavior of the TRFP 100 can be performed.

[0239] In some forms, the result of the process of providing a characterization of the current supply and measuring the parameters of the TRFP 100 during the charging phase can be a series of current values I through the series switch 332a S and their associated voltage values V across the series switch 332a of the TRFP 100 being discussed M (I S ). In some forms, this series of values can be stored or presented as a data array, such as a look-up table of V M (I S ) versus I S . An example of a look-up table in one form of the present technology is presented in Table 3:

[0240] <![CDATA[I S (A)]]> <![CDATA[V M (I S )(V)]]> 0 0 1 0 … 0 1.5 1.165

[0241] Table 3 - Exemplary Look-up Table for Characterizing the TRFP 100 During the Characterization Maintenance Phase

[0242] At this stage, it has been determined that those currents I in the series switch 332a I S produce a specific voltage V across the switch S (I M )(e.g., Table 3). In some forms, the next step is to calculate the correlation between I S and the input primary current, such as the peak negative value I of the input primary current S . These are related based on the number of windings in the transformer 150, as: P,M

[0243]

[0244] And the result is:

[0245] ​

[0246] Thus, a series of voltage values V across the series switch 332a (and / or in the secondary coil 304) M (I S ) and the corresponding peak negative current values I supplied to the primary coil 304 P,M can be determined, for example, in the form of another look-up table such as presented in Table 4:

[0247]

[0248]

[0249] Table 4 - Exemplary Look-up Table Characterizing the TRFP 100 in the Hold Phase

[0250] 6.4.6. Target Value Calculation

[0251] After the characterization phase, it is understood how the TRFP 100 will respond to a particular supply current in each charging and hold phase (if applicable). Another aspect can be to generate an analytically derived target value that describes the dynamic response of the flux pump as outlined in Section 6.4.2. For clarity, the target value is the voltage required across the switch during the charging process. The target value can embed the requirements of the charging process (such as DC offset control and ramp rate) into the system. Determining the target values requires an understanding of the physical mechanisms inherent within the TRFP and skilled analysis to create the equations needed to generate them.

[0252] In some forms of the present technology, another aspect of the control process is to obtain the derived target values representing what needs to be output and map them to the required inputs. The input in a general TRFP is the applied primary current waveform, and in the case of a magnetic field driven switch, it is the electromagnet waveform. Thus, the term "waveform value" will be used to cover the variation of the input variables caused by the control process. Another way of describing the waveform variation is that they can be changes to the input that result in the required target values. It is this unique combination of these elements that forms the basis of certain forms of this technology.

[0253] In the general approach employed in certain forms of this technology, it is determined what the target load current I to be supplied to the load 390 at the end of the charging process is, 目标 i.e., to what level the load 390 should be charged. It is also determined at what rate the load 390 should be charged, and based on the period of the applied current to be supplied to the primary coil 204, this determines the change ΔI in the load current supplied to the load 390 over the current cycle L . As previously mentioned, the change ΔI in the load current LIt can vary during the charging process, although in the case of a linear ramp, the change in load current ΔI L can be selected to be substantially constant during the charging process. Based on the target load current and the target rate of charging the load 390, the waveform values of the current applied to the primary coil 204 for each cycle are calculated. In the following discussion, the waveform values take the form of the peak positive current I P,C and the peak negative current I P,M in each cycle supplied to the primary coil 204. In other forms, different values can be calculated and varied, such as other waveform values of the applied current or waveform values characterizing the magnetic field strength and / or direction generated by the magnetic field generator 342, to achieve the same or similar effects.

[0254] By initially calculating the target value of the voltage of the TRFP 100 expected to generate the desired target load current I L , the waveform values of the applied current to be supplied to the primary coil 204 for each value of the target load current I L (e.g., I P,C and I P,M ) are calculated. This can be achieved before flux pump charging, and as will be shown below, the target value can be derived analytically. Then, the method includes calculating the waveform values of the applied current to be supplied to the primary coil 204 or the magnetic field generator 342 based on the target values of the voltage obtained from a characterization table or separate numerical or analytical solutions. In some forms, such as in the form of the half-wave rectifier 320 shown in Figures 3B - 3E , the target values can include one or more voltage target values when the rectifier 320 is in the configuration of supplying current from the secondary coil 304 to the load 390 (i.e., the charging phase), and one or more voltage target values when the rectifier 320 is in the configuration of not supplying current from the secondary coil to the load 390 (i.e., the maintaining phase). In some forms, the target values of the voltage can include the target values of one or more voltages to be provided to the load 390, such as the voltage across the bridge switch 332b and one or more target values of the voltage across the series switch 332a

[0255] In some forms, using the results characterizing the response of the TRFP 100, such as using look-up tables such as Tables 2 and 4, the waveform values of the applied current are determined from the voltage values.

[0256] In some forms, the waveform values of the applied current can be determined by using numerical or analytical solutions of the superconducting properties of the TRFP 100 and a detailed analysis of the TRFP 100 configuration. An exemplary such form is discussed in Section 6.4.7.1.

[0257] In some forms, the waveform value can be modified through a feedback loop based on the measured response, as discussed in Section 6.4.7.

[0258] An exemplary process for determining the supply characteristics of the applied current required to achieve the desired load current in the load 390 by the TRFP 100 will now be described in more detail. Although the exemplary process outlined below creates a set of target values before the start of charging, in some forms, these target values can be generated during charging using the same principles.

[0259] 6.4.6.1. Modeling of the Half-Wave Rectifier - Creation of Target Values

[0260] The following section describes how a rectifier 320 in the form of a half-wave rectifier 320 as shown in Figures 3B - 3E can be modeled in some forms of the technology. It is expected that those skilled in the art will be able to perform similar modeling for other forms of rectifiers (including other forms of half-wave rectifiers and full-wave rectifiers) after reading this specification. Therefore, although a brief overview of a center-tapped full-wave rectifier is further discussed below, no detailed analysis of other exemplary forms of the rectifier 320 is provided.

[0261] In the following derivation, two factors are focused on determining the output voltage of a half-wave rectifier that includes a switch 332 that operates based on applying a magnetic field to a certain length of superconductor to change the critical current of the superconductor. These are: 1) the non-linear resistivity caused by the combination of the applied magnetic field and current; and 2) the connection resistance generated during the assembly process. For existing rectifiers of this type, it has been shown that these factors actually dominate the voltage response. However, it has been shown that inductive coupling and AC loss mechanisms affect the output voltage. In some forms, these mechanisms may cause variations in the voltage output that cannot be mitigated by using PID feedback control, as suggested in the following discussion. In these forms, it may be necessary to integrate these additional components into the target value equation. Those skilled in the art will be able to implement these additions according to the method outlined below. It is important to note that regardless of the physical mechanism driving the rectification process for a type-II superconducting transformer rectifier flux pump, the most basic method remains the same.

[0262] As described above, when deciding how to charge the load 390 using the TRFP 100, two characteristics can be determined: the charging rate (related to ΔI L ), and the target load current (I 目标 ) in the load 390. In the TRFP 100, the charging rate is determined by the input current defined by the voltage generated across the load 390 over the entire period. When modeling the TRFP 100, since the mechanism driving the voltage V across the load 390 is different in each period, the charging and sustaining phases are considered separately. In fact, during the sustaining phase, the performance can be considered based on the current dissipation in the RL circuit because the voltage V in this phase is driven by the losses rather than an external driving voltage. In this case, V is precisely the induced voltage across the coil: 线圈 Since the mechanism is different in each period, the charging and sustaining phases are considered separately. In fact, during the sustaining phase, the performance can be considered based on the current dissipation in the RL circuit because the voltage V in this phase is driven by the losses rather than an external driving voltage. 线圈 is driven by the losses rather than an external driving voltage. In this case, V 线圈 is precisely the induced voltage across the coil:

[0263] (Equation 1)

[0264]

[0265] where L 线圈 is only the inductance of the load 390. The generation of the target value is necessary to ensure that the TRFP 100 generates the correct V 线圈 to create the desired value defined by the user such as per period. As will be shown below, a single V 线圈 may not be sufficient to satisfy the example of the TRFP 100, in which the load 390 is charged with a gradually increasing load current, where the switching component 330 operates non-linearly, and it is ensured that a preferential net-zero flux is generated over each period. Instead, V 线圈 may need to be changed within each period to handle the dynamic changes in the behavior caused by the charging, which requires a change in the input parameters (waveform values).

[0266] In some forms of this technology, several assumptions may need to be made to find . One assumption is that the charging of the load 390 can be accurately characterized by reducing the dynamic V 线圈 to a time average. Experiments have shown that this approximation is highly accurate. Other forms of the control process can directly consider the time response of

[0267] Using the time average we consider how to calculate the desired to achieve the desired ΔI L . To this end, we calculate the current changes during the charging and sustaining phases.

[0268] For the charging phase, using the time-averaged voltage results in a linear ramp rate during the charging process, which means that the given by Equation 1 is:

[0269] (Equation 2)

[0270]

[0271] However, the loss of load current during the maintenance phase is more complex. It is now determined by but is determined by the RL circuit within the load loop, as shown, by the current generated by the transformer 150 during the maintenance phase. According to the load current (I L,M (t)) during the maintenance phase and Kirchhoff's loop law in the load loop, is:

[0272]

[0273] where the response originating from the load coil 390 is completely determined by the inductive behavior. This can be rearranged as:

[0274]

[0275] where and are constants. This enables the integral to become:

[0276]

[0277] Therefore, during the maintenance phase, the voltage in the load loop changes with time (even if is constant). As

[0278]

[0279] In some forms, the analysis can enable this change to be explicitly considered. However, in some forms, for simplicity, it can be assumed that the voltage is constant throughout the maintenance phase. Experiments have shown that for 5 Hz operation with a set of parameters comparable to a real system, the effect of this assumption is approximately 90 μV, although this is highly system-dependent. As will be discussed later, these assumptions form part of the range of effects not directly addressed by these analytical equations and can therefore be managed by additional techniques.

[0280] Disregarding this assumption, as defined above:

[0281] (Equation 3)

[0282]

[0283] where and is a constant. This equation represents the losses during the hold phase and the secondary current generated during the hold phase that has not yet been calculated. This introduces an inevitable circularity in the calculations. To counteract this circularity, we assume that does not change significantly between consecutive cycles. For an operating control process with a constant slope rate, this is the expected behavior. Therefore, it can be assumed that is i.e., the I of the previous cycle value. Using the assumption, Equation 3 becomes: S,M ) value. Using the assumption, Equation 3 becomes:

[0284] (Equation 4)

[0285]

[0286] For the nature of the control process, we are interested in ensuring that the total change in the load current (ΔI L ) over the entire cycle matches the user-defined charging rate:

[0287]

[0288] Using Equation 2:

[0289]

[0290] Now all the terms in the above equation are defined or determined by characterizing the existing experimental state. This means we can rearrange to find the required to generate the desired ΔI L :

[0291] (Equation 5)

[0292]

[0293] Equation 5 is an equation based on the known parameters of the first current cycle. The only variable that must be added is a reasonable assumption for in the first cycle, and an example of how to achieve this is discussed below. in the first cycle, and an example of how to achieve this is discussed below.

[0294] However, while Equation 5 deals with the voltage generated across the coil terminals, the voltage that is important for the TRFP 100 can be the voltage across the bridge Therefore, we now work out the conversion between these two values. Using Figure 2 , this is:

[0295]

[0296] where is the average over the k-th cycle In essence, the resistance of the load circuit (R L ) means that more voltage must be generated across the bridge to produce the required voltage Using the linear slew rate assumption, it can be calculated that:

[0297]

[0298] This means that:

[0299] (Equation 6)

[0300]

[0301] It should be noted that all the resistances in the bridge are used to charge the load coil 390 (including the connection resistance (R J ). Therefore, we can derive the required voltage as:

[0302]

[0303] (Equation 7)

[0304]

[0305] All of the above work is to determine how the required voltage changes over time to handle the charging of the load 390. Through three assumptions, this becomes a linear problem:

[0306] 1. The charging voltage generated can be characterized by the time-averaged voltage during the charging phase;

[0307] 2. The voltage change generated during the holding phase is minimal; and

[0308] 3. The secondary current generated during the holding phase does not change significantly between cycles.

[0309] In some forms, if all possible variations of and ΔI L are to be characterized, these assumptions may be eliminated by a comprehensive characterization phase. This forms a large data array or look-up table. Instead, in other forms, the control method handles these second-order effects through a feedback mechanism (such as a PID loop) based on the comparison of the target value and the required value, as discussed later. Now, the potential difference will be modeled by the factors as described below.

[0310] After establishing the required target voltage to be generated across the bridge switches during the charging phase After that, we must now consider how voltage is generated in the TRFP 100. For the TRFP 100 including the rectifier 320 with the switching component 330, the switching component 330 includes a switch 332 of the type in which a magnetic field is applied to suppress the critical current and as a result of this suppression, switching is achieved (for the purposes of this specification, it may be referred to as "J C (B)TRFP"), the voltage for charging the load 390 can be entirely determined by the voltage generated in the bridge . For example, for the circuit in Figures 3B to 3D , all the voltages generated in the bridge charge the load 390. This may be true for many forms of the TRFP 100 because the junctions may explicitly exist within the bridge. The corollary is that for the J C (B)TRFP, in terms of converting the voltage generated in the secondary coil 304 of the transformer 150 into the voltage for charging the load 390, it can be highly (e.g., 100%) efficient.

[0311]

[0312] For the exemplary case outlined above:

[0313]

[0314] As shown above, in some forms, for charging under ΔI L , the secondary coil 304 of the transformer 150 must generate

[0315]

[0316] resulting in:

[0317] (Equation 8)

[0318]

[0319] where is defined by the non-linear resistivity response of the superconductor within the bridge:

[0320]

[0321] where n determines the behavior of the superconductor in its non-linear state and depends on the magnetic field and temperature of the superconductor. Note that up to this point, the non-linear behavior of the superconductor has not interacted with the modeling analysis. Thus, the above considerations will be the case for any TRFP 100, regardless of the rectification mechanism. Now, only in some forms where the TRFP 100 is C (B)TRFP, do we utilize JC (B) mechanism, which results in Equation 8 in the following form:

[0322] (Equation 9)

[0323]

[0324] where and are constants.

[0325] One option is to numerically solve Equation 9 using the defined value of n. However, since the heating of the TRFP 100 during rectification causes n to change, this is likely to be inaccurate. Instead, in some forms, we utilize the experimentally generated relationships between certain parameters (such as the characterization table outlined in Section 6.4.5.1) and the calculated target values. This approach enables the embedding of the non-linear superconducting characteristics and second-order effects (such as AC losses) into the control process. This requires specific relationships between the parameters (such as the characterization table) generated from the characterization phase to provide the data needed for the application control process. As mentioned before, two different characterization tables are required for the charging and sustaining phases.

[0326] We now consider how to calculate the target value for the sustaining phase. As mentioned before, using Kirchhoff's loop law, the voltage generated by the transformer 150 during the sustaining phase is:

[0327] (Equation 10)

[0328]

[0329] In contrast to the charging phase, the sustaining phase can be used solely for the purpose of stopping the saturation of the transformer 150. In some forms, this means we require:

[0330] (Equation 11)

[0331]

[0332] Therefore:

[0333]

[0334] Rearranged as a constant in the cycle, the right-hand side becomes the voltage required to stop core saturation in the cycle:

[0335]

[0336] (Equation 12)

[0337]

[0338] Although starting from the assumption that the voltages should be equal (Equation 8), it may seem slightly confusing that we have two different required voltages. However, it is important to understand that the required voltage is only concentrated on the superconducting switch element 332, rather than on the total voltage generated in the secondary coil 304 of the transformer 150, which is maintained in Equation 10. Note that the required hold-phase voltage increases will be reduced due to the R J related factors. These in turn depend on how the current is distributed through the bridge. This is not considered clear a priori.

[0339] As in the charging phase, where the required target values have been established, we must establish the process for converting these values into the actual inputs required for the TRFP. We assume that the superconducting switch element is based on J c (B) rectification, so the voltage in switch 332a is determined using the power law:

[0340]

[0341] This means that Equation 10 has the following form:

[0342] (Equation 13)

[0343]

[0344] where and As in the charging phase, this equation can be solved numerically, or the left-hand side of the equation can be characterized experimentally. In some forms of the technology, the latter method can be employed.

[0345] 6.4.6.2. Calculation of Waveform Values - Half-Wave Rectifier

[0346] The following describes how, in some forms of the technology, a set of pre-calculated waveform values for the supply of current to the primary coil 204 of the TRFP 100 and / or the magnetic field generator 342 are determined. In other forms of the technology, some of these waveform values can be generated during the charging process.

[0347] To overcome the previously highlighted roundness problem, a predicted value for the peak current generated during the hold phase can be generated. In one form, this value is set equal to the critical current value of the superconducting material forming this length of the series switch 332a A more general method might be to add an additional component (α) in I C,M (B,T), where α can be determined by the required ramp rate. In either method, the selected initial value is used to calculate using Equation 12 This value is then used to derive the required waveform variations. It should be noted that no other estimations are required.

[0348] In a subsequent step, Equation 7 is used to calculate the target value of the voltage across the bridge (e.g., Figures 3B - 3E the bridge switch 332b in the form shown in during the charging phase of the first cycle, which is required to achieve the desired charging of the load 390, i.e., using known resistances and user-defined L and estimations.

[0349] Next, the calculated is compared with the current value of the corresponding voltage determined when characterizing the supply (e.g., using the charging look-up table (Table 3)) to characterize the response of the TRFP 100, and interpolation is performed if necessary to find the I that produces P,C . This value is set as the peak positive current value of the waveform of the current supplied to the primary coil 204 during the first cycle, i.e.,

[0350] The next step is to calculate the target value of the voltage across the series switch 332a during the hold phase of the first cycle, which is required to achieve the desired charging of the load 390. For example, using Equation 12, we can use known resistances and user-defined and ΔI L and estimations to calculate

[0351] Then, the calculated is compared with the current value of the corresponding voltage determined when characterizing the supply (e.g., using the hold look-up table (Table 4)) to characterize the response of the TRFP100, and interpolation is performed if necessary to find the I that produces P,M . This value is set as the peak negative current value of the waveform of the current supplied to the primary coil 204 during the first cycle, i.e.,

[0352] The above steps (except for the first step) can then be repeated multiple times based on a selected increment ΔI L of the load current until the target load current I 目标 is reached.

[0353] Table 5 below shows an example of this series of calculations being performed, and the results are populated in the look-up table.

[0354]

[0355]

[0356] Table 5 - Exemplary Table of Target Values for Charging a Load Using TRFP

[0357] To clarify how the table is filled, for row k:

[0358] 1. The value of is determined by adding the previous value of the load current and ΔI L i.e.,

[0359] 2. The value of is the value of in row (k - 1);

[0360] 3. and The values of are determined using the formulas shown in the table; and

[0361] 4. and The values of are determined by the corresponding values of and and in the same row, and using the appropriate look - up table (i.e., Table 2 or Table 4).

[0362] In some forms, these steps can be performed to determine a target charging scheme before starting to charge the load 390, e.g., the scheme stated in a data array of a look - up table such as Table 5. In other forms, the calculation or recalculation of the target values can occur dynamically during the process of charging the load 390, i.e., after starting to charge the load 390, the above steps can be performed and can be repeated one or more times during the charging of the load 390, e.g., after one or more charging cycles.

[0363] 6.4.6.3. Modeling of a Center - Tapped Full - Wave Rectifier

[0364] The detailed examples given in the above description relate to the modeling of the rectifier 320 in the form of the half - wave rectifier 320 as shown in Figures 3B - 3E It has been explained that in some forms of the present technology, other types of rectifiers can form part of the TRFP 100. In this section, we will discuss the modifications to an exemplary method of current control that can be used in the case of a rectifier 320 in the form of a full - wave rectifier.

[0365] ​In a full-wave rectifier, both the positive and negative portions of the waveform of the applied current supplied to the primary coil 204 are used to charge the load 390. This can be more energy-efficient than in the case of a half-wave rectifier and can also significantly reduce the current ripple. Also, and importantly for the control process, the asymmetry between the two parts of the cycle is significantly reduced and, as an approximation, it can be considered insignificant. In practice, the initial (e.g., positive) part of the cycle can produce a DC offset that causes a slight asymmetry between the positive and negative charging phases. This offset can lead to a variation in the charging rate between the positive and negative parts of the cycle and can be taken into account in some forms of the technique. In some forms, the offset can correct itself naturally, as will be assumed in the upcoming analysis.

[0366] In addition to the reduced asymmetry during the charging cycle, in a center-tapped full-wave rectifier, the load current can be evenly distributed between the transformer sections, which is different from in a half-wave rectifier. This results in an unavoidable DC offset in the secondary current. However, due to the nature of this offset being different from the action of the transformer, the offset in one part of the transformer can be completely cancelled out by the offset in another part of the transformer. Thus, when the load current distribution affects the current generated in the secondary circuit, it may not saturate the transformer. Since this offset is directly related to the load current, it can be cancelled out relatively directly. As shown below, in some forms, it can be handled by adding one term to the target value table.

[0367] A detailed analysis of the full-wave rectifier is not given here, but a person skilled in the art can determine it by following the analysis of the example of the half-wave rectifier given above. As an example, in the case where the TRFP 100 includes a rectifier 320 in the form of a center-tapped full-wave rectifier, such as the rectifiers of the type shown in Figures 16, 17, 21, 22, 26, 27, 29, and 30 of PCT Application No. PCT / NZ2022 / 050009, which is published as International Publication No. WO 2022 / 164330, the content of which is incorporated herein by reference. Figure 4 and Figures 16, 17, 21, 22, 26, 27, 29, and 30, the content of which is incorporated herein by reference.

[0368] To highlight the generality and use of the target value method, we give the final required target value equation for a center-tapped full-wave rectifier without the need for differentiation. For simplicity, we focus on a set of assumptions that reduce the complexity of the target value equation. These are:

[0369] · No load resistance: R L = 0;

[0370] · For the constant ΔI LNo requirements: Instead, a constant voltage is used to define the target value in each period: V 设定 ;

[0371] · No attempt is made to cancel the DC offset: The positive and negative parts of the primary waveform are scaled equally and have the same peak current: I S ;

[0372] · No attempt is made to integrate other physical components, such as: AC losses;

[0373] · Use the analytical solution instead of comparing the look-up table by experimental methods. In the case of the above assumptions, the analytical method simplifies to simple calculations without the need for numerical methods. In some forms, the look-up table method may provide more robust control, and in other forms, the analytical method may be sufficient.

[0374] Using these assumptions, the target value equation of the center-tapped full-wave flux pump of

[0375]

[0376] 6.4.7. Modify the primary current supply

[0377] When the TRFP 100 is used to charge the load 390 based on the calculated target value, as described above, for example, the TRFP100 may not perform as precisely as the model. Many assumptions and simplifications are used in the above analysis, which may mean that the target voltage and need to be modified multiple times, thereby modifying the waveform value of the applied current to achieve the desired performance of the TRFP 100, which may include charging the load at a charging rate consistent with ΔI L and a net zero flux for the entire cycle.

[0378] In the above analysis, these assumptions / simplifications are incorporated into a single component . Due to the potential interaction between a series of parameters, this component is difficult to handle a priori. Therefore, in some forms of the present invention, the method of controlling the supply of the current applied to the primary coil 204 includes modifying the target value of the supply of the applied current during the charging process, that is, after the charging of the load 390 has started, which can be referred to as the dynamic control of the supply of the applied current. In some forms of this technique, the supply of the applied current can be modified based on feedback received from the TRFP 100 (for example, from one or more sensors configured to measure the value of the TRFP 100, such as the secondary side 300). In certain forms, the feedback for modifying the supply of the applied current can include the comparison of one or more target values of the TRFP 100 with one or more experimentally measured values.

[0379] In some forms, one or both of the two comparisons can be used as a basis for modifying the supply of the applied current:

[0380] 1. Due to modifying the positive peak value of the applied current This step can help ensure that the desired ramp rate is achieved each time the modification is performed (e.g., each cycle); and

[0381] 2. Due to modifying the negative peak value of the applied current Similarly, the supply of the applied current can thus be modified based on this recalculated, modified target value. This step can help prevent the transformer 150 from saturating.

[0382] Modifying the supply of the applied current in the described manner can occur after each cycle of the supply of the applied current. Alternatively, for example, after a certain number of cycles, it can occur regularly but less frequently. Alternatively, the modification can occur on an irregular basis.

[0383] The modifications resulting from the feedback can be implemented in different ways using different forms of technology. For example, the following options can be used:

[0384] 1. Modify the existing waveform value based on the analysis-derived characteristics of the TRFP;

[0385] 2. Modify the existing waveform value by using a PID loop; or

[0386] 3. Replace the waveform value by recalculating the target value on a cyclic basis (e.g., each cycle).

[0387] Each of these options will now be described in more detail.

[0388] 6.4.7.1. Analysis-derived characteristics

[0389] In some forms of this technique, certain assumptions can simplify the above analysis and are sufficiently valid such that they can be used to apply analysis methods to determine what modifications may be required to the supply of the alternating current.

[0390] For example, in the case where the TRFP 100 includes a rectifier 320 in the form of a full-wave rectifier, in some cases it can be assumed that the connection resistance R of the superconducting behavior J and the temperature dependence can be negated, in which case Equation 9 will simply become:

[0391]

[0392] where and This can be solved directly

[0393]

[0394] This can then be converted to determine the required peak AC supply current The following equation:

[0395]

[0396] It can be argued that for a practically achievable solution, it is necessary to analytically determine how to modify e.g. Figures 3B to 3E The supply of applied current to the rectifier 320 in the form of a half-wave rectifier of the type shown may be too inaccurate. The nonlinearity of the superconducting switch means that, for example, changes in the physical properties of the superconducting element (such as temperature) may lead to significant changes in the output voltage and thus to significant differences between the calculated and measured responses.

[0397] 6.4.7.2.PID loop

[0398] In some forms, the current control mechanism 203 may be configured to implement one or more PID loops, and modifying the supply of applied current may include using the PID loops to provide feedback from the secondary side 300 to control the current.

[0399] In some forms of the technology, such as those in which the rectifier 320 takes the form of a half-wave rectifier and there are charging and maintenance phases in the current cycle, the current control mechanism 203 can be configured to implement two PID loops, one for each phase. In the first PID loop, the current control mechanism 203 can be configured to control the supply of the applied current relative to the peak positive value of ω. As defined above. In the second PID loop, the current control mechanism 203 may be configured to control the supply of the applied current relative to the peak negative value of ε As defined above.

[0400] Figure 8 is a flow chart of the process performed by the current control mechanism 203 when executing method 700 to implement one or both of the PID loops according to some forms of the technology. Method 700 may have two inputs, for example, the peak positive value of the supply current applied relative to ω in the PID loop control. In the case of and ”. The applied current in the PID loop controls the supply relative to the peak negative value of ε In this case, the input can be as described above At step 701, the difference 702 between the input values can be calculated, for example, the values ω and ε can be determined. At steps 703, 704, and 705, correction terms are determined based on the difference 702, which are the proportional term, the integral term, and the derivative term, respectively. At steps 706 and 705, these terms are summed to determine the output of the PID loop, such as the peak positive value for the supply of the applied current for a subsequent period and the peak negative value for the supply of the applied current for a subsequent period

[0401] In some forms, the way of calculating the proportional term, the integral term, and the derivative term can be experimentally derived, for example, by the Ziegler-Natta method or any other suitable method. These terms can also be gain-scheduled.

[0402] The calculation of the waveform values using the above method can handle the non-linearity of the superconducting switch, such that the modifications required by the PID control process can be small and approximately linear.

[0403] To use the PID loop control satisfactorily, a broad characterization of the response of the TRFP 100 may be useful, as explained above. It is expected that once the TRFP 100 has been characterized, the characterization should remain consistent in some forms for a relatively long period of time.

[0404] 6.4.7.3. Recalculation of waveform values

[0405] In other forms, the target value of the supply of the current applied to the primary coil 304 can be recalculated on a cyclic basis, for example, periodically, such as in each cycle. In some forms, this method can avoid the need to pre-calculate the entire set of waveform values of the supply of the initially 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.

[0406] In the case where the TRFP 100 includes a rectifier 320 in the form of a half-wave rectifier, for example, as Figures 3B to 3E shown, the result of the previous cycle can be re-input into the above equation and modified in relation to ω and ε. For ω, this involves changing Equation 2 as follows:

[0407]

[0408] Throughout the relevant algebra, Equation 5 becomes:

[0409]

[0410] Thus, in these forms, the feedback control of the positive peak of the applied current supply can be subtly manipulated by the empirically derived ω in each cycle processed with a value.

[0411] For feedback control using ε, in Equation 13 can simply be replaced with ε:

[0412]

[0413] where and where:

[0414]

[0415] As described above, in this form of the present technology, for example, between each cycle, using the and updated above, the waveform values are regularly calculated by the equation. Limitations in processing speed may impede the feasibility of this method, especially when the frequency increases. However, for a processor, calculations and interpolation from a pre - existing cycle table are relatively simple, and studies have shown that this method should not be a major limitation on the time response of the control process.

[0416] 6.4.8. Persistent Mode

[0417] In some forms, once the load 390 has been fully charged, for example, the load current has reached the target value I 目标 of the load current, the TRFP 100 can operate in persistent mode. In this mode, the charging of the load 390 can be maintained, and the load current can be held at I 目标 .

[0418] In persistent mode, the load current supplied to the load 390 does not increase, i.e., ΔI L = 0, and thus, according to the previous equation:

[0419]

[0420] In some forms, these equations are used to derive the target value of the voltage and thus the waveform values for the primary current waveform (e.g., using a look - up table) to maintain the TRFP 100 in persistent mode.

[0421] 6.5. Other Remarks

[0422] Unless the context clearly requires otherwise, throughout the specification and claims, the words "comprise", "comprising", etc. shall be construed in an inclusive sense as opposed to an exclusive or exhaustive sense; that is, in the sense of "including but not limited to".

[0423] The entire disclosures of all applications, patents, and publications (if any) cited above and below are hereby incorporated by reference into this document.

[0424] The citation of any prior art in this specification is not and should not be taken as an admission or any form of suggestion that this prior art forms part of the common general knowledge in the field of endeavor in any country in the world.

[0425] The technology may also be broadly said to reside in the parts, elements, and features individually or jointly mentioned or indicated in this application's specification in any or all combinations of two or more of the said parts, elements, or features.

[0426] Where the foregoing description refers to components in general or having known equivalents thereof, such general components are hereby incorporated as if set forth individually.

[0427] 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 technology and without diminishing its attendant advantages. Accordingly, such changes and modifications are intended to be included within the technology.

Claims

1. A method for controlling the supply of current applied to a transformer-rectifier flux pump to charge a load, Among them, The transformer-rectifier flux pump includes: A transformer including a primary coil and a secondary coil; and A rectifier connected to the secondary coil and configured to supply a load current to the load; Wherein the secondary coil, the rectifier, and the load include one or more lengths of type-II superconducting material, Wherein the method includes: For each of a plurality of target values of the load current to be supplied to the load, calculating one or more waveform values of the supply of current applied to the transformer-rectifier flux pump; and Controlling the supply of the applied current based on the one or more waveform values to charge the load.

2. The method according to claim 1, wherein The method includes calculating the one or more waveform values of the supply of current applied to the transformer-rectifier flux pump for target values of the load current that reach a preselected target value of the load current in one or more preselected increments.

3. The method according to any one of claims 1 to 2, wherein The one or more waveform values of the supply of current applied to the transformer-rectifier flux pump include a peak of the supply of current applied when flowing in a first direction and a peak of the supply of current applied when flowing in a second direction opposite to the first direction.

4. The method according to any one of claims 1 to 3, wherein The method of calculating the waveform values of the supply of current applied to the transformer-rectifier flux pump includes: For each of a plurality of target values of the load current to be supplied to the load, calculating one or more target voltage values for the transformer-rectifier flux pump; and Calculating the one or more waveform values of the supply of current applied to the transformer-rectifier flux pump from the one or more target voltage values.

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

6. The method according to claim 5, wherein, The target voltage value output to the load includes a target voltage value across the switches connected in parallel across the load.

7. The method according to any one of claims 4 to 6, wherein, The one or more target voltage values include: A first target value of the voltage output to the load when the rectifier is in a first configuration, in which the current generated in the secondary coil is supplied to the load; and A second target value of the 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. The method according to any one of claims 1 to 7, wherein, The method includes supplying a characterization of the applied current to the transformer-rectifier flux pump, characterizing the response of the rectifier and / or the load to the characterization of the supply, and controlling the supply of the applied current based on the characterized response to charge the load.

9. According to the method of claim 8, wherein, The method includes supplying the characterization of the supply and characterizing the response to the characterization of the supply before starting to supply the applied current to the transformer-rectifier flux pump to charge the load.

10. The method according to claim 8 or 9, wherein, The step of supplying the characterization of the supply includes: When the rectifier is in a first configuration supplying the current generated in the secondary coil to the load, a first representation of the applied current is supplied to the transformer-rectifier flux pump and represents a first response of the rectifier and / or the load to the first representation of the supply; and When the rectifier is in a second configuration where no current is supplied from the secondary coil to the load, a second representation of the applied current is supplied to the transformer-rectifier flux pump and represents a second response of the rectifier and / or the load to the second representation of the supply.

11. The method according to any one of claims 8 to 10, wherein, Characterizing the response of the rectifier and / or the load to the representation of the supply includes determining a plurality of voltage values in the rectifier, the plurality of voltage values corresponding to respective plurality of values of the applied current supplied to the primary coil.

12. The method according to claim 11, wherein, The plurality of voltage values in the rectifier includes the voltage value output to the load.

13. The method according to claim 12, wherein, The voltage value output to the load includes the voltage value across the switches connected in parallel across the load.

14. The method according to any one of claims 1 to 13, wherein The method further includes modifying the supply of the current applied to the transformer-rectifier flux pump during the process of charging the load.

15. The method according to claim 14, wherein, Modifying the supply of the applied current based on feedback received from one or more sensors configured to measure values of the transformer-rectifier flux pump.

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

17. The method according to any one of claims 1 to 16, wherein, The one or more waveform values are current values supplied to the primary coil.

18. The method according to any one of claims 1 to 17, wherein The transform-rectifier flux pump includes a magnetic field generator for applying a magnetic field to one of a plurality of lengths of type-II superconducting material, and the one or more waveform values are current values supplied to the magnetic field generator.

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

20. A transformer-rectifier flux pump, comprising: A transformer including a primary coil and a secondary coil; and A rectifier connected to the secondary coil and configured to supply load current to a load, Wherein the secondary coil, the rectifier, and the load include one or more lengths of type-II superconducting material, Wherein the transformer-rectifier flux pump further includes: A current control mechanism for controlling the supply of current applied to the primary coil, wherein the current control mechanism is configured to perform the method according to any one of claims 1-18.

21. The transformer-rectifier flux pump according to claim 20, wherein, The rectifier includes a switch assembly including one or more switches.

22. The transformer-rectifier flux pump according to claim 20 or 21, wherein, Each switch includes a length of type-II superconducting material configured to carry switch current, wherein the length of type-II superconducting material has a critical current. Wherein, the transformer-rectifier flux pump further includes one or more magnetic field generators, each magnetic field generator being configured to apply a magnetic field to the type-II superconducting material of the corresponding switch over the length thereof, wherein each magnetic field generator is configured to be selectively controlled to switch the superconducting material of the length between a low-resistance state and a higher-resistance state.

23. The transformer-rectifier flux pump according to claim 22, wherein, In the low-resistance state, the magnitude of the magnetic field is relatively low such that the switching current is substantially less than the critical current, and wherein, in the higher-resistance state, the magnitude of the magnetic field is relatively high to reduce the critical current such that the switching current approaches the critical current, is substantially equal to the critical current or is greater than the critical current of the superconducting material of the length.

24. The 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 current applied to the one or more magnetic field generators.

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