Heating bundle with virtual sensing for thermal gradient compensation
The heating system with independently controlled heating regions and a controller addresses moisture-induced failures in cartridge heaters by ensuring optimal heat distribution and temperature control, enhancing reliability and safety.
Patent Information
- Authority / Receiving Office
- JP · JP
- Patent Type
- Patents
- Current Assignee / Owner
- WATLOW ELECTRIC MANUFACTURING CO
- Filing Date
- 2022-03-10
- Publication Date
- 2026-04-20
AI Technical Summary
Cartridge heaters used in heat exchangers are prone to failure due to moisture ingress, leading to dielectric breakdown and short circuits, resulting in costly downtime.
A heating system with independently controlled heating regions and a controller that modulates power based on temperature calculations and various inputs, including fluid parameters, to maintain optimal heat distribution and prevent overheating.
The system enhances reliability by allowing individual heating units to operate independently, reducing the risk of failure and enabling precise temperature control, thus minimizing downtime and improving safety.
Smart Images

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Abstract
Description
Technical Field
[0005] ,
[0001] Cross - Reference to Related Applications This application is a continuation - in - part of U.S. Patent Application No. 16 / 272,668, filed on February 11, 2019, entitled "Heater Bundle for Adaptive Control", which is a continuation of U.S. Patent Application No. 15 / 058,838, filed on March 2, 2016, now U.S. Patent No. 10,247,445. The entire content of the above disclosure is incorporated herein by reference.
[0002] The present disclosure relates to electric heaters, and more particularly to heaters for heating fluids such as fluids within heat exchangers.
Background Art
[0003] The description in this section only provides background information related to the present disclosure and does not constitute prior art.
[0004] The fluid heater may be in the form of a cartridge heater having a rod configuration for heating a fluid flowing along or through the outer surface of the cartridge heater. The cartridge heater may be disposed inside a heat exchanger for heating a fluid flowing through the heat exchanger. If the cartridge heater is not properly sealed, moisture and fluid can enter the cartridge heater, contaminating the insulating material that electrically insulates the resistive heating element from the metal sheath of the cartridge heater, resulting in dielectric breakdown and, consequently, heater failure. Moisture can also cause a short - circuit between the power conductor and the outer metal sheath. Failure of the cartridge heater can cause costly downtime of the device using the cartridge heater.
Summary of the Invention
Problems to be Solved by the Invention
[0005] [Means for solving the problem]
[0006] This section provides a general overview of this disclosure and is not a comprehensive disclosure of its entire scope or all of its features.
[0007] This disclosure provides a heating system comprising a heating bundle having at least one heating assembly having a plurality of heating units, at least one of which defines at least one independently controlled heating region. A plurality of power conductors are electrically connected to the heating units, and the power supply includes a controller configured to modulate power to at least one independently controlled heating region via the power conductors. The controller is configured to calculate the temperature in at least one heating unit based on a predetermined model and at least one input, and the controller modulates power to at least one heating unit based on the calculated temperature.
[0008] In a variation of this heating system, which can be implemented individually or in any combination, at least one heating unit is an end heating unit, at least one input includes the temperature of another location in the heating bundle, at least one input includes the temperature of at least one of the multiple heating units, at least one input includes the power consumption of the heating bundle, at least one input includes the average power consumption of the heating bundle over a given period, at least one input includes the voltage of the heating bundle and / or at least one voltage of the heating unit, at least one input includes the current of the heating bundle and / or at least one current of the heating bundle and / or heating unit, and at least one input includes the current of the heating bundle. The input includes leakage, at least one input includes insulation resistance of a heating bundle, at least one input includes at least one of fluid temperature, fluid velocity, fluid speed, and fluid mass flow rate, the controller supplies known currents to multiple heating units, measures the voltage of at least one independently controlled heating region, and calculates the temperature by comparing the measured voltage to a nominal voltage associated with the known current and identifying the voltage deviation and / or corresponding resistance deviation, the controller supplies known voltages to multiple heating units, measures the current of at least one independently controlled heating region, and calculates the temperature by comparing the measured current to a nominal current associated with the known voltage and identifying the current deviation and / or corresponding resistance deviation.
[0009] In a modified version of this heating system, the device for heating a fluid comprises a sealed housing defining an internal chamber and having a fluid inlet and a fluid outlet, and at least one heating assembly is located within the internal chamber of the housing. The at least one heating assembly is adapted to provide a responsive heat distribution to the fluid within the housing. The heat distribution is "responsive" based on the implementation of virtual sensing as described herein.
[0010] In another embodiment of the present disclosure, the heating system comprises a heating assembly including a plurality of heating units, the at least one heating unit defining at least one independently controlled heating region. A plurality of power conductors are electrically connected to the heating units, and the power supply includes a controller configured to modulate power to at least one independently controlled heating region via the power conductors. The controller is configured to calculate the temperature in at least one heating unit based on a given model and at least one input, and the controller modulates power to at least one heating unit based on the calculated temperature.
[0011] In variations of this heating system, which can be implemented individually or in any combination, at least one heating unit is an end heating unit, and a controller supplies a known current to multiple heating units, measures the voltage in at least one independently controlled heating region, and calculates the temperature by comparing the measured voltage to a nominal voltage associated with the known current and identifying the voltage deviation and / or corresponding resistance deviation. Furthermore, an apparatus having these variations of the heating system includes a sealed housing that defines an internal chamber and has a fluid inlet and a fluid outlet. The heating assembly is located within the internal chamber of the housing and is adapted to provide a responsive heat distribution to the fluid within the housing.
[0012] In yet another embodiment, the heating system includes a heating assembly comprising a plurality of heating units, two or more of which define at least one independently controlled heating region. A plurality of power conductors are electrically connected to the heating units, and the power supply includes a controller configured to modulate power to the independently controlled heating region via the power conductors. The controller is configured to calculate the temperature in two or more heating units based on a given model and at least one input, and the controller modulates power to the two or more heating units based on the calculated temperatures.
[0013] In a variation of this heating system, which can be implemented individually or in any combination, at least one heating unit is an end heating unit, and the controller supplies known currents to multiple heating units, measures the voltage of at least one independently controlled heating region, and calculates the temperature by comparing the measured voltage with a known current and associated nominal voltage to identify the voltage deviation and / or the corresponding resistance deviation.
[0014] Further areas of application will become apparent from the descriptions provided herein. It should be understood that the descriptions and specific examples are for illustrative purposes only and are not intended to limit the scope of this disclosure.
[0015] To ensure that this disclosure can be fully understood, various forms thereof, given as examples, are described herein with reference to the attached drawings. [Brief explanation of the drawing]
[0016] [Figure 1] This is a perspective view of a heated bundle configured in accordance with the teachings of this disclosure. [Figure 2]Perspective view of the heating assembly of the heating bundle of FIG. 1 according to the teachings of the present disclosure. [Figure 3] Perspective view of a modified example of the heating assembly of the heating bundle of FIG. 1 according to the teachings of the present disclosure. [Figure 4] Perspective view of the heating assembly of FIG. 3 according to the teachings of the present disclosure, in which the outer sheath of the heating assembly is removed for clarity. [Figure 5] Perspective view of the core of the heating assembly of FIG. 3 according to the teachings of the present disclosure. [Figure 6] Perspective view of a heat exchanger including the heating bundle of FIG. 1 according to the teachings of the present disclosure, where the heating bundle is partially disassembled from the heat exchanger to expose the heating bundle for illustrative purposes. [Figure 7] Block diagram of a method for operating a heating system including a heating bundle configured according to the teachings of the present disclosure. [Figure 8] Perspective view of a heating assembly including a heat supply unit according to the teachings of the present disclosure. [Figure 9] Cross-sectional view of the heating assembly taken along line 9-9 of FIG. 8 according to the teachings of the present disclosure. [Figure 10] Cross-sectional view of the heating assembly taken along line 10-10 of FIG. 8 according to the teachings of the present disclosure. [Figure 11] Perspective view of a heating assembly including another heat supply unit according to the teachings of the present disclosure. [Figure 12] Cross-sectional view of the heating assembly taken along line 12-12 of FIG. 11 according to the teachings of the present disclosure. [Figure 13] Cross-sectional view of the heating assembly taken along line 13-13 of FIG. 11 according to the teachings of the present disclosure. [Figure 14] Perspective view of a heating assembly including another heat supply unit according to the teachings of the present disclosure. [Figure 15] Side view of the heat supply unit of the heating assembly of FIG. 14 according to the teachings of the present disclosure. [Figure 16] Perspective view of a heating assembly including a heat supply unit according to the teachings of the present disclosure. [Figure 17]Perspective view of a heating assembly including a heat supply unit according to the teachings of the present disclosure. [Figure 18] Cross-sectional view of the heating assembly taken along line 18-18 of FIG. 17 according to the teachings of the present disclosure. [Figure 19] Cross-sectional view of the heating assembly taken along line 19-19 of FIG. 17 according to the teachings of the present disclosure. [Figure 20] Perspective view of a heating assembly including a heat supply unit according to the teachings of the present disclosure. **DETAILED DESCRIPTION OF THE INVENTION**
[0017] The drawings described herein are for illustrative purposes only and are not intended to limit the scope of the present disclosure in any way.
[0018] The following description is merely exemplary in nature and is not intended to limit the present disclosure, its application, or uses.
[0019] Referring to FIG. 1, a heating system constructed in accordance with the teachings of the present disclosure is generally indicated by reference numeral 10. The heating system 10 includes a heating bundle 12 and a power supply 14 electrically connected to the heating bundle 12. The power supply 14 includes a controller 15 for controlling the power supply to the heating bundle 12. As used in the present disclosure, a "heating bundle" refers to a heating device that includes two or more physically separate heating devices that can be independently controlled. Thus, if one of the heating devices within the heating bundle fails or deteriorates, the remaining heating devices within the heating bundle 12 can continue to operate. [[ID= As further shown, the mounting flange 16 includes a plurality of mounting holes 22. By using screws or bolts (not shown) passing through the mounting holes 22, the mounting flange 16 can be mounted to the wall of a container or pipe (not shown) that carries the fluid to be heated. At least a portion of the heating assembly 18 is immersed in the fluid inside the container or pipe to heat the fluid in this form of the disclosure.
[0022] Referring to Figure 2, one embodiment of the heating assembly 18 may be in the form of a cartridge heater 30. The cartridge heater 30 is generally a tubular heater comprising a core 32, a resistive heating wire 34 wound around the core 32, a metal sheath 36 enclosing the core 32 and the resistive heating wire 34 internally, and an insulating material 38 filling the space within the metal sheath 36, which electrically insulates the resistive heating wire 34 from the metal sheath 36 and conducts heat from the resistive heating wire 34 to the metal sheath 36. The core 32 may be made of ceramic. The insulating material 38 may be compressed magnesium oxide (MgO). Multiple power conductors 42 penetrate the core 32 longitudinally and are electrically connected to the resistive heating wire 34. The power conductors 42 also extend through end pieces 44 that seal the metal sheath 36. The power conductors 42 are connected to a power supply 14 (shown in Figure 1), which supplies power to the resistive heating wire 34. Figure 2 shows only two power conductors 42 extending through the end piece 44, but three or more power conductors 42 may extend through the end piece 44. The power conductors 42 may also be in the form of conductive pins. Various structures of the cartridge heater, as well as further structural and electrical details, are described in detail in U.S. Patents 2,831,951 and 3,970,822, which are assigned in common with this application and whose entire contents are incorporated herein by reference. Therefore, it should be understood that the forms shown herein are merely illustrative and should not be construed as limiting the scope of this disclosure.
[0023] Alternatively, multiple pairs of resistive heating wires 34 and power conductors 42 can be used to form multiple heating circuits that can be independently controlled to enhance the reliability of the cartridge heater 30. Therefore, if one of the resistive heating wires 34 fails, the remaining resistive heating wires 34 can continue to generate heat without causing failure of the entire cartridge heater 30 and without incurring downtime for the expensive machine.
[0024] Referring to Figures 3 to 5, the heating assembly 50 may be in the form of a cartridge heater having the same configuration as in Figure 2, except for the number of cores and power conductors used. More specifically, each heating assembly 50 includes a plurality of heating units 52 and an outer metal sheath 54 enclosing the plurality of heating units 52, along with a plurality of power conductors 56. An insulating material (not shown in Figures 3 to 5) is provided between the plurality of heating units 52 and the outer metal sheath 54 to electrically insulate the heating units 52 from the outer metal sheath 54. Each of the plurality of heating units 52 includes a core 58 and a resistive heating element 60 surrounding the core 58. The resistive heating element 60 of each heating unit 52 can define one or more heating circuits for defining one or more heating regions 62.
[0025] In this embodiment, each heating unit 52 defines one heating region 62, and the multiple heating units 52 within each heating assembly 50 are aligned along the longitudinal direction X. Thus, each heating assembly 50 defines multiple heating regions 62 aligned along the longitudinal direction X. The core body 58 of each heating unit 52 defines multiple through holes / openings 64 to allow the power supply conductor 56 to pass through. The resistive heating elements 60 of the heating unit 52 are connected to the power supply conductor 56, which is connected to the power supply unit 14. The power supply conductor 56 supplies power from the power supply unit 14 to the multiple heating units 52. By properly connecting the power supply conductor 56 to the resistive heating elements 60, the resistive heating elements 60 of the multiple heating units 52 can be independently controlled by the controller 15 of the power supply unit 14. Thus, a failure of one resistive heating element 60 for a particular heating region 62 does not affect the proper functioning of the remaining resistive heating elements 60 for the remaining heating regions 62. Furthermore, the heating unit 52 and the heating assembly 50 may be replaceable to facilitate repair or assembly.
[0026] In this embodiment, six power conductors 56 are used for each heating assembly 50 to supply power to five independent electric heating circuits on five heating units 52. Alternatively, the six power conductors 56 may be connected to a resistive heating element 60 to define three completely independent circuits on the five heating units 52. It is possible to have any number of power conductors 56 to form any number of independently controlled heating circuits and independently controlled heating regions 62. For example, seven power conductors 56 can be used to provide six heating regions 62. Eight power conductors 56 can be used to provide seven heating regions 62.
[0027] The power conductor 56 may include multiple power and power return conductors, multiple power return conductors and a single power conductor, or multiple power conductors and a single power return conductor. If the number of heating regions is n, the number of power conductors and return conductors is n+1.
[0028] Alternatively, a greater number of electrically distinct heating regions 62 can be created by multiplexing, polarity-sensitive switching, and other circuit topologies by the controller 15 of the power supply unit 14. The use of multiplexing or various arrangements of thermal arrays to increase the number of heating regions in the cartridge heater 30 for a given number of power conductors (e.g., a cartridge heater having six power conductors for 15 or 30 regions) is disclosed in U.S. Patents 9,123,755, 9,123,756, 9,177,840, 9,196,513 and their related applications, which are assigned in common with this application and whose contents are incorporated herein by reference in their entirety.
[0029] This structure allows each heating assembly 50 to include multiple heating regions 62 that can be independently controlled to vary the power output or heat distribution along the length of the heating assembly 50. A heating bundle 12 includes multiple such heating assemblies 50. Thus, the heating bundle 12 provides multiple heating regions 62 and a tuned heat distribution for heating a fluid flowing through the heating bundle 12 to suit a particular application. The power supply 14 can be configured to modulate power to each of the independently controlled heating regions 62.
[0030] For example, a heating assembly 50 can define m heating regions, and a heating bundle may contain k heating assemblies 50. Thus, a heating bundle 12 can define m × k heating regions. The multiple heating regions 62 within the heating bundle 12 can be individually and dynamically controlled according to heating conditions and / or heating requirements, including but not limited to the lifespan and reliability of the individual heating units 52, the size and cost of the heating units 52, the local heater flux, the characteristics and operation of the heating units 52, and the total power output.
[0031] Each circuit is individually controlled at a desired temperature or power level so that the temperature and / or power distribution adapts to variations in system parameters (e.g., changes in inlet flow conditions such as manufacturing variability / tolerances, changes in environmental conditions, inlet temperature, inlet temperature distribution, flow velocity, velocity distribution, fluid composition, and fluid heat capacity). More specifically, the heating unit 52 may not produce the same thermal output when operating at the same power level due to manufacturing variability and changes in the degree of thermal degradation over time. The heating unit 52 may be independently controlled to adjust the thermal output according to the desired thermal distribution. The individual manufacturing tolerances of the components of the heating system and the assembly tolerances of the heating system are amplified as a function of the modulated power of the power supply; in other words, the manufacturing tolerances of the individual components do not need to be very tight / narrow due to the high fidelity of the heating control.
[0032] Each heating unit 52 may include a temperature sensor (not shown) for measuring the temperature of the heating unit 52. If a hot spot is detected in a heating unit 52, the power supply 14 may reduce or turn off power to the heating unit 52 in which the hot spot was detected in order to prevent overheating or failure of that heating unit 52. The power supply 14 may modulate power to heating units 52 adjacent to the disabled heating unit 52 in order to compensate for the reduced heat output from the heating unit 52.
[0033] The power supply unit 14 may include a multi-region algorithm for turning off or reducing the power level supplied to any specific region and increasing power to heating regions adjacent to a specific heating region that has been disabled and whose thermal output has been reduced. By carefully modulating the power to each heating region, the overall reliability of the system can be improved. The safety of the heating system 10 is improved by detecting hot spots and controlling the power supply accordingly.
[0034] A heating bundle 12 having multiple independently controlled heating regions 62 can achieve improved heating. For example, some circuits on the heating unit 52 can operate at a nominal (or "typical") duty cycle of less than 100% (or at an average power level, which is part of the power generated by the heater to which the line voltage is applied). Lower duty cycles allow the use of resistive heating wiring with a larger diameter, thereby improving reliability.
[0035] Typically, smaller regions use finer wire sizes to achieve a given resistance. Variable power control allows for the use of larger wire sizes, accommodating lower resistance values, while simultaneously protecting the heater from overload through duty cycle limitations tied to the heater's power dissipation capability.
[0036] The use of a scaling factor may relate to the capacity of the heating unit 52 or heating region 62. Multiple heating regions 62 allow for more precise determination and control of the heating bundle 12. By using a specific scaling factor for a particular heating circuit / region, more aggressive (i.e., higher) temperatures (or power levels) are possible in virtually all regions, resulting in a smaller and lower-cost design for the heating bundle 12. Such scaling factors and methods are disclosed in U.S. Patent No. 7,257,464, which is assigned in common with this application and is incorporated herein by reference in its entirety.
[0037] The sizes of the heating regions controlled by individual circuits may be equal or different in order to reduce the total number of regions required to control the temperature or power distribution with the desired precision.
[0038] Referring back to Figure 1, the heating assembly 18 is shown to be a single-end heater, i.e., the conductive pins extend through only one longitudinal end of the heating assembly 18. The heating assembly 18 may extend through a mounting flange 16 or a bulkhead (not shown) and be sealed to the flange 16 or bulkhead. Thus, the heating assembly 18 can be removed and replaced individually without removing the mounting flange 16 from the container or tube.
[0039] Alternatively, the heating assembly 18 may be a "double-ended" heater. In a double-ended heater, the metal sheath is bent into a hairpin shape, and the power conductors pass through both longitudinal ends of the metal sheath, thereby sealing both longitudinal ends of the metal sheath through flanges or bulkheads. In this configuration, the flanges or bulkheads must be removed from the housing or container before the individual heating assemblies 18 can be replaced.
[0040] Referring to Figure 6, the heating bundle 12 is incorporated into the heat exchanger 70. The heat exchanger 70 includes a sealed housing 72 defining an internal chamber (not shown) and the heating bundle 12 positioned within the internal chamber of the housing 72. The sealed housing 72 includes a fluid inlet 76 and a fluid outlet 78 through which the fluid is guided in and out of the internal chamber of the sealed housing 72. The fluid is heated by the heating bundle 12 positioned within the sealed housing 72. The heating bundle 12 may be positioned for either cross-flow or flow parallel to their lengths.
[0041] The heating bundle 12 is connected to a power supply unit 14 which may include power modulation means such as switching means or a variable transformer to modulate the power supplied to individual regions. Power modulation may be performed as a function of time or based on the detected temperature of each heating region.
[0042] The resistive heating wiring can also function as a sensor that measures the temperature of the resistive wiring using the resistance of the wiring and transmits the temperature measurement information to the power supply unit 14 using the same power conductor. The means for sensing the temperature of each region allows for temperature control along the length of each heating assembly 18 in the heating bundle 12 (to the resolution of the individual regions). Thus, additional temperature sensing circuits and sensing means can be omitted, thereby reducing manufacturing costs. Direct measurement of the heating circuit temperature is a clear advantage when seeking to maximize the heat flux in a given circuit while maintaining a desired level of reliability of the system, as it eliminates or minimizes many of the measurement errors associated with the use of separate sensors. The heating element temperature is the characteristic that has the strongest impact on heating reliability. The use of resistive elements to function as both heaters and sensors is disclosed in U.S. Patent No. 7,196,295, which is assigned in common with this application and whose entire contents are incorporated herein by reference.
[0043] Alternatively, the power conductor 56 may be made of dissimilar metals so that the power conductor 56 of dissimilar metals can form a thermocouple for measuring the temperature of the resistive heating element. For example, at least one set of power and power return conductors may include different materials so that a junction is formed between the different materials and the resistive heating element of the heating unit, which is used to determine the temperature of one or more areas. Using “integrated” and “highly thermally coupled” sensing, such as using different metals in the heater, generates a thermocouple-like signal. The use of integrated and coupled power conductors for temperature measurement is disclosed in U.S. Patent Application No. 14 / 725,537, which is assigned in common with this application and whose entire contents are incorporated herein by reference.
[0044] The controller 15 for modulating the power supplied to each region may be a closed-loop automatic control system. The closed-loop automatic control system receives temperature feedback from each region and automatically and dynamically controls the power supply to each region, thereby automatically and dynamically controlling the power distribution and temperature along the length of each heating assembly 18 in the heating bundle 12 without continuous or frequent human monitoring and adjustment.
[0045] The heating units 52 disclosed herein may also be calibrated using a variety of methods, including, but not limited to, energizing and sampling each heating unit 52 to calculate its resistance. The calculated resistance can then be compared to the calibrated resistance to determine the resistance ratio, or a value that determines the actual heating unit temperature. Exemplary methods are disclosed in U.S. Patents 5,280,422 and 5,552,998, which are assigned in common with this application and incorporated herein by reference in their entirety.
[0046] One form of calibration includes operating the heating system 10 in at least one operating mode, controlling the heating system 10 to produce a desired temperature for at least one of the independently controlled heating regions 62, collecting and recording data for at least one independently controlled heating region 62 for the operating mode, then accessing the recorded data to determine the operating specifications of the heating system with a reduced number of independently controlled heating regions, and then using the heating system with a reduced number of independently controlled heating regions. The data may include, for example, power level and / or temperature information, among other operating data from the heating system 10 having collected and recorded data.
[0047] In a modified version of the present disclosure, the heating system may include a single heating assembly 18 instead of multiple heating assemblies within a heating bundle 12. The single heating assembly 18 comprises multiple heating units 52, each heating unit 52 defining at least one independently controlled heating region. Similarly, a power conductor 56 is electrically connected to each of the independently controlled heating regions 62 within each heating unit 52, and the power supply is configured to modulate power to each of the independently controlled heating regions 62 of the heating units via the power conductor 56.
[0048] Referring to Figure 7, the method 100 for controlling a heating system includes, in step 102, providing a heating bundle comprising a plurality of heating assemblies. Each heating assembly comprises a plurality of heating units. Each heating unit defines at least one independently controlled heating circuit (and thus a heating region). In step 104, power to each heating unit is supplied via power conductors electrically connected to each of the independently controlled heating regions within each heating unit. The temperature within each region is detected in step 106. The temperature may be determined using a change in the resistance of a resistive heating element in at least one heating unit. The region temperature can first be determined by measuring the region resistance (or, if appropriate materials are used, by measuring the circuit voltage).
[0049] The temperature values may be digitized. The signal may be communicated to a microprocessor. The measured (detected) temperature values can be compared to the target (desired) temperature of each region in step 108. In step 110, the power supplied to each heating unit can be modulated based on the measured temperature to achieve the target temperature.
[0050] Optionally, the method may further include adjusting the modulated power using a scaling factor. The scaling factor may be a function of the heating capacity of each heating region. The controller 15 may include an algorithm that potentially includes a scaling factor and / or mathematical model of the system's dynamic behavior (including knowledge of the system's update time) to determine the amount of power to be supplied to each region (via duty cycle, phase angle emission, voltage modulation, or similar techniques) until the next update. The desired power may be converted into a signal sent to a switch or other power modulator to control the power output to individual heating regions.
[0051] In this embodiment, if at least one heating region is turned off due to an abnormal condition, the remaining regions continue to provide the desired wattage without failure. Power is modulated to the functional heating regions to provide the desired wattage when an abnormal condition is detected within at least one heating region. If at least one heating region is turned off based on a determined temperature, the remaining regions continue to provide the desired wattage. Power is modulated to each heating region as a function of at least one of the following: received signal, model, and time.
[0052] For safety or process control reasons, typical heaters are generally operated to keep a certain point in the heater below a given temperature to prevent undesirable chemical or physical reactions at that location, such as combustion / ignition / oxidation or coke boiling. Therefore, this is usually addressed by a conservative heating design (e.g., a large heater with low power density and a much lower heat flux than is possible for the majority of its surface area).
[0053] However, using the heating bundle of this disclosure, it is possible to measure and limit the temperature at any location within the heater to a resolution of the size of the individual heating regions. Hot spots large enough to affect the temperature of individual circuits can be detected.
[0054] The ability to automatically adjust and consequently limit the temperature of individual heating regions ensures that the dynamic and automatic temperature limiting of each region keeps this region and all others operating at optimal power / heat flux levels without risking exceeding the desired temperature limit of any given region. This offers advantages in higher limit temperature measurement accuracy than current implementations that clamp separate thermocouples to the sheath of one of the elements in the bundle. The reduced margin and the ability to modulate power to individual regions can be applied selectively and individually to heating regions rather than to the entire heating assembly, thereby reducing the risk of exceeding a given temperature limit.
[0055] The characteristics of a cartridge heater can change over time. This time-varying characteristic would otherwise require the cartridge heater to be designed for a single, selected (worst-case) flow mode, and therefore, to operate in a suboptimal state for other flow conditions.
[0056] However, dynamic control of the power distribution across the entire bundle to the resolution of the core size by multiple heating units provided in the heating assembly makes it possible to achieve optimized power distributions for various flow conditions, in contrast to the single power distribution corresponding to only one flow condition in a typical cartridge heater. Thus, the heating bundle of this application enables an increase in total heat flux for all other flow conditions.
[0057] Furthermore, variable power control can increase the flexibility of heating design. Voltage can be isolated (to a considerable extent) from resistance in the heating design, and the heater can be designed with the largest wire diameter that can be mated to the heater. This allows for an increase in the capacity of power dissipation for a given heating size and reliability level (or heater lifespan), and a decrease in the size of the bundle for a given overall power level. The power in this configuration can be modulated by a variable duty cycle, which is part of a variable wattage controller currently available or under development. The heating bundle can be protected by programmable (or pre-programmed as needed) limits on the duty cycle in a given area to prevent "overloading" of the heating bundle.
[0058] Referring to Figure 8, a perspective view of a heating assembly 50 equipped with a heat supply unit is shown. Generally, the heat supply unit is configured to change the thermal conductance along the length of at least one heating assembly in order to compensate for non-uniform temperatures within at least one heating unit. This heat supply unit can take various forms, as will be described in more detail below.
[0059] Thus, each heating assembly 50 comprises a plurality of heating units 52. Each heating unit 52 defines either an end heating unit 52-1 or an adjacent heating unit 52-2. As shown in Figures 9 to 10, each of the end heating unit 52-1 and the adjacent heating unit 52-2 includes a core body 58 and a resistance heating element 60 surrounding the core body 58. The resistance heating element 60 of each end heating unit 52-1 defines one or more end heating regions 62-1, and the resistance heating element 60 of each adjacent heating unit 52-2 defines one or more adjacent heating regions 62-2.
[0060] The resistance heating elements 60 of the end heating unit 52-1 and the adjacent heating unit 52-2 are connected to a power conductor 56, which is connected to a power supply unit 14. The power conductor 56 supplies power from the power supply unit 14 to the end heating unit 52-1 and the adjacent heating unit 52-2. By selectively connecting the power conductor 56 to the resistance heating elements 60, the resistance heating elements 60 of the end heating unit 52-1 and the adjacent heating unit 52-2 can be independently controlled by the controller 15 of the power supply unit 14.
[0061] In one embodiment, the heat supply section of the heating assembly 50 is implemented by a conductive sleeve 120. As an example, referring to Figure 10, the conductive sleeve 120 is positioned close to the resistance heating element 60 of the end heating unit 52-1. In one embodiment, the conductive sleeve 120 surrounds the resistance heating element 60 and the core body 58, and is positioned between the outer metal sheath 54 and the resistance heating element 60. It should be understood that in other embodiments, the conductive sleeve 120 does not have to completely surround the resistance heating element 60 and the core body 58. It should also be understood that in other embodiments, the conductive sleeve 120 does not have to be positioned between the outer metal sheath 54 and the resistance heating element 60.
[0062] In one embodiment, the conductive sleeve 120 has a greater thermal conductivity than the outer metal sheath 54. Thus, the conductive sleeve 120 is configured to increase the conductance of the end heating unit 52-1 relative to the adjacent heating unit 52-2, thereby suppressing an undesirable temperature gradient along the heating assembly 50.
[0063] Referring to Figure 11, a perspective view of a heating assembly 50 having another exemplary heat supply unit is shown. In one embodiment, the heat supply unit of the heating assembly 50 is implemented by an outer sheath heat supply unit 130. Referring to Figures 12-13 in more detail, the heating assembly 50 includes an end outer metal sheath 54-1 and an adjacent outer metal sheath 54-2, respectively. The end outer metal sheath 54-1 and the adjacent outer metal sheath 54-2 collectively form an outer metal sheath 54, and the outer sheath heat supply unit 130 is implemented by the end outer metal sheath 54-2.
[0064] In one embodiment, the end outer metal sheath 54-1 and the adjacent outer metal sheath 54-2 have different thicknesses and / or thermal conductivity. As an example, the end outer metal sheath 54-1 has a greater thickness and higher thermal conductivity than the adjacent outer metal sheath 54-2. Thus, the end outer metal sheath 54-1 is configured to increase the conductance of the end heating unit 52-1 relative to the adjacent heating unit 52-2, thereby suppressing an undesirable temperature gradient along the heating assembly 50. It should be understood that the end outer metal sheath 54-1 and the adjacent outer metal sheath 54-2 can have different thicknesses and / or thermal conductivity in other variants to selectively control the temperature gradient along the heating assembly 50.
[0065] Referring to Figure 14, a perspective view of a heating assembly 50 having another exemplary heat supply unit is shown. In this embodiment, the heat supply unit of the heating assembly 50 is implemented by a power conductor heat supply unit 140. The power conductor heat supply unit 140 is implemented by an end power conductor 56-1 and an adjacent power conductor 56-2. In one embodiment, the end power conductor 56-1 and the adjacent power conductor 56-2 collectively form a plurality of power conductors 56. The end power conductor 56-1 is connected to the resistance heating element 60 of the end heating unit 52-1, and the adjacent power conductor 56-2 is connected to the resistance heating element 60 of the adjacent heating unit 52-2.
[0066] In some configurations, referring to Figures 14-15, the end power conductor 56-1 and the adjacent power conductor 56-2 have different thicknesses, cross-sectional areas, and / or thermal conductivity. As an example, the end power conductor 56-1 has a greater thickness (T1) and cross-sectional area (proportional to the thickness T1 in this configuration) than the thickness (T2) and cross-sectional area (proportional to the thickness T2 in this configuration) of the adjacent power conductor 56-2. Thus, the end power conductor 56-1 is configured to increase the conductance of the end heating unit 52-1 relative to the adjacent heating unit 52-2, thereby suppressing an undesirable temperature gradient along the heating assembly 50. It should be understood that the end power conductor 56-1 and the adjacent power conductor 56-2 can have different thicknesses, cross-sectional areas, and / or thermal conductivity in other configurations in order to selectively control the temperature gradient along the heating assembly 50.
[0067] Referring to Figure 16, a perspective view of a heating assembly 50 having another exemplary heat supply section is shown. In one embodiment, the heating assembly 50 includes an end spacing 150 and an adjacent spacing 152, and the heat supply section of the heating assembly 50 is defined by the end spacing 150. As used herein, “spacing” refers to the gap between consecutive heating units 52. For example, the end spacing 150 refers to the gap between an end heating unit 52-1 and an adjacent heating unit 52-2, and the adjacent spacing 152 refers to the gap between adjacent heating units 52-2. In one embodiment, the width in the longitudinal direction X of the end spacing 150 (W1) is greater than the width in the longitudinal direction X of the adjacent spacing 152 (W2).
[0068] In Figure 16, the widths of the end spacing 150 (W1) are equal, but in other embodiments, the widths of the end spacing 150 (W1) do not have to be equal. Similarly, in Figure 15, the widths of the adjacent spacing 152 (W2) are equal, but in other embodiments, the widths of the adjacent spacing 152 (W2) do not have to be equal. In one embodiment, the width of the end spacing 150 (W1) is less than or equal to the width of the adjacent spacing 152 (W2). By selectively specifying the widths of the end spacing 150 (W1) and the adjacent spacing 152 (W2), the conductance of the end heating unit 52-1 relative to the adjacent heating unit 52-2 can be increased, thereby suppressing undesirable temperature gradients along the length of the heating assembly 50.
[0069] Referring to Figure 17, a perspective view of a heating assembly 50 having another exemplary heat supply unit is shown. In some embodiments, the heating assembly 50 includes an end spacer 160 and adjacent spacers 162, and the heat supply unit of the heating assembly 50 is implemented by the end spacer 160. The end spacer 160 is positioned between an end heating unit 52-1 and an adjacent heating unit 52-2, and the adjacent spacers 162 are positioned between the adjacent heating units 52-2. The end spacer 160 and adjacent spacers 162 can be implemented from a variety of materials having lower thermal conductivity, such as ceramic materials (e.g., aluminum nitride, boron nitride, polyurethane, and glass-based materials such as borosilicate glass, acrylic glass, and glass fiber, among others).
[0070] In some configurations, the longitudinal width X of the end spacer 160 (W3) is greater than the longitudinal width X of the adjacent spacer 162 (W4). While the widths of the end spacers 160 (W3) are equal in Figure 17, it should be understood that in other configurations, the widths of the end spacers 160 (W3) may not be equal. Similarly, while the widths of the adjacent spacers 162 (W4) are equal in Figure 17, it should be understood that in other configurations, the widths of the adjacent spacers 162 (W4) may not be equal. In one configuration, the width of the end spacer 160 (W3) is less than or equal to the width of the adjacent spacer 162 (W4). By selectively specifying the widths of the end spacer 160 (W3) and the adjacent spacer 162 (W4), the conductance of the end heating unit 52-1 relative to the adjacent heating unit 52-2 can be increased to suppress undesirable temperature gradients along the heating assembly 50.
[0071] In one embodiment, the power conductor heat supply section 140 and end spacers 160 described above are combined to form a heat supply section, referring to Figures 14 to 17. As an example, as shown in Figures 18 to 19, an end power conductor 56-1 extends longitudinally X along the heating assembly 50 so that the end power conductor 56-1 is located within the corresponding end spacer 160 and within the corresponding end heating unit 52-1 (not shown). Similarly, an adjacent power conductor 56-2 extends longitudinally X along the heating assembly 50 so that the adjacent power conductor 56-2 is located within the corresponding adjacent spacer 162 and within the corresponding adjacent heating unit 52-2 (not shown). In some embodiments, an end power conductor 56-1 located within an end spacer 160 has a larger cross-sectional area than an adjacent power conductor 56-2 located within an adjacent spacer 162. It should be understood that the end power conductor 56-1 placed within the end spacer 160 may have a cross-sectional area less than or equal to the cross-sectional area of the adjacent power conductor 56-2 placed within the adjacent spacer 162 in other configurations.
[0072] Referring to Figure 20, a perspective view of a heating assembly 50 having another exemplary heat supply is shown. In one embodiment, the heat supply of the heating assembly 50 is implemented by a variable-width heat supply unit 170. The variable-width heat supply unit 170 includes at least one of the end heating units 52-1. In some embodiments, the longitudinal width X of the end heating unit 52-1 (W5) is greater than the longitudinal width X of the adjacent heating unit 52-2 (W6). It should be noted that in other embodiments, the width of the end heating unit 52-1 (W5) may be less than or equal to the width of the adjacent heating unit 52-2 (W6). By selectively specifying the width (W5) of the end heating unit 52-1 and the width (W6) of the adjacent heating unit 52-2, the conductance of the end heating unit 52-1 relative to the adjacent heating unit 52-2 can be increased to suppress undesirable temperature gradients along the heating assembly 50. Although not shown in the diagram, it should be easily understood that the power conductor for heating unit 52 extends between the end heating unit 52-1 and the adjacent heating unit 52-2.
[0073] Referring to Figures 8 to 20, the controller 15 is configured to calculate the temperature in at least one of the heating units 52, such as the end heating unit 52-1, based on a predetermined model (e.g., a mathematical model representing, among other things, the various components and / or dynamic behavior of the heating system 10) and at least one input. (This common approach may also be called "virtual sensing" because the temperature is calculated rather than measured.) In one embodiment, the at least one input includes, but is not limited to, the temperature at another location within the heating bundle 12, the temperature of another heating unit 52, the temperature of any of the independently controlled heating regions 62 located on the heating assembly 18, the power consumption of either the heating bundle 12 and / or the heating unit 52, and / or the average power consumption of either the heating bundle 12 and / or the heating unit 52 over a predetermined period of time. In one embodiment, at least one input includes, but is not limited to, the voltage of either the heating bundle 12 and / or the heating unit 52, the current of either the heating bundle 12 and / or the heating unit 52, the current leakage of either the heating bundle 12 and / or the heating unit 52, and / or the insulation resistance of the heating bundle 12. To perform the functions described herein, the controller 15 includes one or more electrical circuits / components for acquiring at least one input (e.g., one or more sensing circuits for measuring the power of the heating unit 52).
[0074] As an example, the controller 15 is configured to calculate the temperature within the end heating unit 52-1 by first supplying a known current to the heating unit 52 and measuring the voltage across the end heating unit 52-1. The controller 15 then compares the measured voltage to a nominal voltage associated with the known current to identify a voltage deviation and / or a corresponding resistance deviation. Subsequently, the controller 15 calculates the temperature of the end heating unit 52-1 based on the voltage deviation and / or the corresponding resistance deviation using a predetermined model. As described above, the controller 15 then modulates power to the independently controlled heating region 62 via the power conductor 56 based on the temperature of the end heating unit 52-1. To perform the functions described herein, the controller 15 includes one or more processors configured to execute instructions stored in a non-temporary computer-readable medium such as random access memory (RAM) and / or read-only memory (ROM). Alternatively, the controller 15 supplies a known voltage to multiple heating units 52, measures the current in at least one independently controlled heating region 62, and calculates the temperature by comparing the measured current with a nominal current for a known voltage to identify the current deviation and / or the corresponding resistance deviation.
[0075] Unless otherwise expressly indicated herein, all numerical values indicating mechanical / thermal properties, compositional percentages, dimensions and / or tolerances, or other properties should be understood to be modified by the word “about” or “approximately” when describing the scope of this disclosure. This modification is desirable for a variety of reasons, including industrial implementation, material, manufacturing, and assembly tolerances, as well as test capability.
[0076] The spatial and functional relationships between elements are described using a variety of terms, including “connected,” “engaged,” “joined,” “adjacent,” “next to,” “above,” “above,” “below,” and “positioned.” Unless expressly stated to be “direct,” where a relationship between a first element and a second element is described in this disclosure, that relationship may be a direct relationship in which there are no other intervening elements between the first element and the second element, or an indirect relationship in which there are one or more intervening elements (spatially or functionally) between the first element and the second element. Where used herein, the phrase “at least one of A, B, and C” should be interpreted as meaning (A OR B OR C) using the non-exclusive logic OR, and not as “at least one of A, at least one of B, and at least one of C.”
[0077] The descriptions in this disclosure are essentially illustrative, and therefore, any modifications that do not deviate from the content of this disclosure are intended to be within the scope of this disclosure. Such modifications should not be considered a departure from the spirit and scope of this disclosure. Furthermore, various omissions, substitutions, combinations, and modifications of the forms of systems, apparatus, and methods described herein can be made without departing from the spirit and scope of this disclosure, even if such omissions, substitutions, combinations, and modifications are not expressly shown or illustrated in the figures of this disclosure. 。 The invention described in the original claims of this application is listed below. [1] A heating system, It is a heated bundle, A heating assembly comprising a plurality of heating units, wherein at least one of the plurality of heating units defines at least one independently controlled heating region, A heating bundle including a plurality of power conductors electrically connected to the heating unit, The power supply includes a controller configured to modulate power to the at least one independently controlled heating region via the power supply conductor, A heating system in which the controller is configured to calculate the temperature in the at least one heating unit based on a predetermined model and at least one input, and the controller modulates power to the at least one heating unit based on the calculated temperature. [2] The heating system according to [1], wherein the at least one heating unit is an end heating unit. [3] The heating system according to [1], wherein the at least one input includes the temperature at another location within the heating bundle. [4] The heating system according to [1], wherein the at least one input includes the temperature of at least one of the plurality of heating units. [5] The heating system according to claim 1, wherein the at least one input includes the power consumption of the heating bundle. [6] The heating system according to [1], wherein the at least one input includes the average power consumption of the heating bundle over a predetermined period of time. [7] The heating system according to [1], wherein the at least one input includes the voltage of the heating bundle and / or the voltage of at least one of the heating units. [8] The heating system according to [1], wherein the at least one input includes the current of the heating bundle and / or the current of at least one of the heating units. [9] The heating system according to [1], wherein the at least one input includes current leakage from the heating bundle.
[10] The heating system according to [1], wherein the at least one input includes the insulation resistance of the heating bundle.
[11] The heating system according to [1], wherein the at least one input includes at least one of fluid velocity, fluid speed, fluid rate, and fluid mass flow rate.
[12] The heating system according to [1], wherein the controller supplies known currents to the plurality of heating units, measures the voltage of the at least one independently controlled heating region, and calculates the temperature by comparing the measured voltage with a nominal voltage associated with the known current to identify a voltage deviation and / or a corresponding resistance deviation.
[13] The heating system according to [1], wherein the controller supplies known voltages to the plurality of heating units, measures the current in the at least one independently controlled heating region, and compares the measured current with a nominal current associated with the known voltage to identify current deviations and / or corresponding resistance deviations.
[14] A device for heating a fluid, A sealed housing having an internal chamber, a fluid inlet and a fluid outlet, The heating system according to claim 1, wherein the at least one heating assembly is located within the internal chamber of the housing, The apparatus wherein the at least one heating assembly is adapted to provide a responsive heat distribution to the fluid within the housing.
[15] A heating system, A heating assembly comprising multiple heating units, wherein at least one heating unit defines at least one independently controlled heating region, Multiple power conductors electrically connected to the heating unit, The power supply includes a controller configured to modulate power to the at least one independently controlled heating region via the power supply conductor, A heating system in which the controller is configured to calculate the temperature in the at least one heating unit based on a predetermined model and at least one input, and the controller modulates power to the at least one heating unit based on the calculated temperature.
[16] The heating system according to
[15] , wherein the at least one heating unit is an end heating unit.
[17] A device for heating a fluid, A sealed housing having an internal chamber, a fluid inlet and a fluid outlet, The heating assembly comprises the heating system described in
[15] , which is located within the internal chamber of the housing, The apparatus wherein the heating assembly is adapted to provide a responsive heat distribution to the fluid within the housing.
[18] The heating system according to
[15] , wherein the controller supplies known currents to the plurality of heating units, measures the voltage of the at least one independently controlled heating region, and calculates the temperature by comparing the measured voltage with a nominal voltage associated with the known current to identify a voltage deviation and / or a corresponding resistance deviation.
[19] The heating system according to
[15] , wherein the controller supplies known voltages to the plurality of heating units, measures the current in the at least one independently controlled heating region, and calculates the temperature by comparing the measured current with a nominal current associated with the known voltage to identify current deviations and / or corresponding resistance deviations.
[20] A heating system, A heating assembly comprising multiple heating units, wherein two or more of the multiple heating units define at least one independently controlled heating region, Multiple power conductors electrically connected to the heating unit, The power supply includes a controller configured to modulate power to the independently controlled heating region via the power supply conductor, A heating system in which the controller is configured to calculate the temperature in the two or more heating units based on a predetermined model and at least one input, and the controller modulates the power to the two or more heating units based on the calculated temperature.
[21] The heating system according to
[20] , wherein the at least one heating unit is an end heating unit.
[22] The heating system according to
[20] , wherein the controller supplies known currents to the plurality of heating units, measures the voltage of the at least one independently controlled heating region, and calculates the temperature by comparing the measured voltage with a nominal voltage associated with the known current to identify a voltage deviation and / or a corresponding resistance deviation.
[23] The heating system according to
[20] , wherein the controller supplies known voltages to the plurality of heating units, measures the current in the at least one independently controlled heating region, and calculates the temperature by comparing the measured current with a nominal current associated with the known voltage to identify current deviations and / or corresponding resistance deviations.
Claims
1. A heating system, A heated bundle, A heating assembly comprising a plurality of heating units, wherein at least one heating unit among the plurality of heating units defines at least one independently controlled heating region, and A heating bundle including a plurality of power conductors electrically connected to the heating unit, The power supply includes a controller configured to modulate power to the at least one independently controlled heating region via the power supply conductor, The aforementioned controller, The plurality of heating units are configured to supply at least one input, It is configured to measure the electrical characteristics associated with the at least one independently controlled heating region, The electrical characteristics are configured to be compared with nominal electrical characteristics associated with the at least one input in order to identify the deviation. A heating system configured to calculate the temperature in the at least one heating unit based on a predetermined model, the at least one input, and the deviation, wherein the controller modulates power to the at least one heating unit based on the calculated temperature.
2. The heating system according to claim 1, wherein the at least one heating unit is an end heating unit.
3. The heating system according to claim 1, wherein the at least one input includes the voltage of the heating bundle and / or the voltage of at least one of the heating units.
4. The heating system according to claim 1, wherein the at least one input includes the current of the heating bundle and / or the current of at least one of the heating units.
5. The heating system according to claim 1, wherein the at least one input is a known current, the electrical characteristic is a voltage, and the nominal electrical characteristic is a nominal voltage associated with the known current.
6. The heating system according to claim 1, wherein the at least one input is a known voltage, the electrical characteristic is a current, and the nominal electrical characteristic is a nominal current associated with the known voltage.
7. A device for heating a fluid, A sealed housing having an internal chamber, a fluid inlet and a fluid outlet, The heating system according to claim 1, wherein at least one heating assembly is located within the internal chamber of the housing, The apparatus wherein the at least one heating assembly is adapted to provide a responsive heat distribution to the fluid within the housing.
8. A heating system, A heating assembly comprising a plurality of heating units aligned along the longitudinal direction, wherein at least one of the plurality of heating units defines at least one independently controlled heating region, A plurality of power conductors electrically connected to the heating unit along the longitudinal direction, The power supply includes a controller configured to modulate power to the at least one independently controlled heating region via the power supply conductor, The aforementioned controller, The plurality of heating units are configured to supply at least one input, It is configured to measure the electrical characteristics associated with the at least one independently controlled heating region, The electrical characteristics are configured to be compared with nominal electrical characteristics associated with the at least one input in order to identify the deviation. It is configured to calculate the temperature in the at least one heating unit based on a predetermined model, the at least one input, and the deviation, A heating system configured to modulate power to at least one heating unit based on the calculated temperature.
9. The heating system according to claim 8, wherein the at least one heating unit is an end heating unit.
10. A device for heating a fluid, A sealed housing having an internal chamber, a fluid inlet and a fluid outlet, The heating system according to claim 8 comprises the heating assembly being located within the internal chamber of the housing, The heating assembly is adapted to provide a responsive heat distribution to the fluid within the housing of the apparatus.
11. The heating system according to claim 8, wherein the at least one input is a known current, the electrical characteristic is a voltage, and the nominal electrical characteristic is a nominal voltage associated with the known current.
12. The heating system according to claim 8, wherein the at least one input is a known voltage, the electrical characteristic is a current, and the nominal electrical characteristic is a nominal current associated with the known voltage.
13. A heating system, A heating assembly comprising a plurality of heating units aligned along the longitudinal direction, wherein two or more of the plurality of heating units define at least one independently controlled heating region, A plurality of power conductors electrically connected to the heating unit along the longitudinal direction, The power supply includes a controller configured to modulate power to the independently controlled heating region via the power supply conductor, The aforementioned controller, The plurality of heating units are configured to supply at least one input, It is configured to measure the electrical characteristics associated with the at least one independently controlled heating region, The electrical characteristics are configured to be compared with nominal electrical characteristics associated with the at least one input in order to identify the deviation. It is configured to calculate the temperature in the two or more heating units based on a predetermined model, the at least one input, and the deviation, A heating system configured to modulate power to two or more heating units based on the calculated temperature.
14. The heating system according to claim 13, wherein at least one of the plurality of heating units is an end heating unit.
15. The heating system according to claim 13, wherein the at least one input is a known current, the electrical characteristic is a voltage, and the nominal electrical characteristic is a nominal voltage associated with the known current.
16. The heating system according to claim 13, wherein the at least one input is a known voltage, the electrical characteristic is a current, and the nominal electrical characteristic is a nominal current associated with the known voltage.
17. The heating system according to claim 1, wherein the plurality of heating units are aligned along the longitudinal direction, and the plurality of power conductors are electrically connected to the heating units along the longitudinal direction.
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