Patent Publication Number: US-2023137629-A1

Title: Pulse power drilling assembly transformer with a core having a non-conductive material

Description:
BACKGROUND 
     The disclosure generally relates to pulse power drilling and, more particularly, to transformers for pulse power drilling assemblies. 
     In drilling for oil and gas, kinetic energy of drilling fluid flowing through a drill string can be used to power downhole operations. However, in some instances, the power is not at the correct voltage to operate the components of a drilling assembly during downhole. In these instances, a transformer can be used to increase or decrease the voltage to a desired level to operate these components. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Aspects of the disclosure may be better understood by referencing the accompanying drawings. 
         FIG.  1    depicts a pulse power drilling assembly with a transformer, according to some embodiments. 
         FIG.  2 A  illustrates a schematic diagram of a portion of a pulse power drilling apparatus including a transformer, according to some embodiments. 
         FIG.  2 B  illustrates a schematic diagram of a portion of a pulse power drilling apparatus including a transformer, according to some embodiments. 
         FIG.  3    illustrates a cut-away side view of a sub-section of an assembly that includes a transformer, according to various embodiments. 
         FIG.  4    illustrates a cross-sectional view of the transformer of  FIG.  3   , viewed along section line  4 - 4  in  FIG.  3   . 
         FIG.  5 A  illustrates embodiments of a core, including one or more insulative breaks, which may be utilized in a transformer of a pulse power drilling assembly, according to some embodiments. 
         FIG.  5 B  illustrates embodiments of a core including radial laminate non-magnetic plates, which may be utilized in a transformer of a pulse power drilling assembly, according to some embodiments. 
         FIG.  5 C  illustrates embodiments of a core including straight laminate non-magnetic plates, which may be utilized in a transformer of a pulse power drilling assembly, according to some embodiments. 
         FIG.  5 D  illustrates embodiments of a core including a non-magnetic powder coated with non-conductive material, which may be utilized in a transformer of a pulse power drilling assembly, according to some embodiments. 
         FIG.  5 E  illustrates a core having a first example spiral configuration (having an insulative layer outside of an electrically conductive layer) that is part of a transformer of a pulse power drilling assembly, according to some embodiments. 
         FIG.  5 F  illustrates a core having a second example spiral configuration (having an insulative layer inside of an electrically conductive layer) that is part of a transformer of a pulse power drilling assembly, according to some embodiments. 
         FIG.  5 G  illustrates a core having a third example spiral configuration (having a first insulative layer outside of the electrically conductive layer and a second insulative layer inside of the electrically conductive layer) that is part of a transformer of a pulse power drilling assembly, according to some embodiments. 
         FIG.  6    depicts a flowchart of operations for powering a pulse power drilling assembly using a transformer, according to some embodiments. 
         FIG.  7    depicts an example computer for a pulse power drilling assembly with a transformer, according to some embodiments. 
     
    
    
     DESCRIPTION 
     The description that follows includes example systems, methods, techniques, and program flows that embody aspects of the disclosure. However, it is understood that this disclosure may be practiced without these specific details. For instance, this disclosure refers to a set of primary and secondary windings of a transformer in illustrative examples. Aspects of this disclosure can be also applied to a transformer with more than two sets of windings. In other instances, well-known instruction instances, protocols, structures and techniques have not been shown in detail in order not to obfuscate the description. 
     The electrical devices that may be utilized by a pulsed power drilling assembly (hereinafter “assembly”), may include a power transformer. The power transformer (hereinafter “transformer”) may be used in order to step-up voltages originally generated by other devices of the assembly, such as a turbine and an alternator combination, to one or more higher voltage levels that are ultimately delivered to electrodes being used by the assembly to perform drilling operations based on periodic pulses of electrical discharges into the subsurface formation. 
     Example pulse power drilling assemblies can have size and space restrictions imposed by a diameter of the borehole being drilled. These restrictions can introduce challenges to pulse power drilling because of the large amount of power and the operational requirements needed for pulse power operations. Some example embodiments include a transformer of the pulse power drilling assembly that is configured to meet the size and space restrictions while also satisfying the power and operational requirements needed for pulse power drilling. 
     In various examples, the transformer includes one or more primary windings that are arranged in electromagnetic coupling with one or more secondary windings of the transformer. The transformer provides a higher voltage level output at the secondary windings when electrical energy having lower voltage levels compared to the output voltage levels of the secondary windings is applied to the primary winding(s) of the transformer. The lower voltage levels applied to the primary winding may comprise a pulsed voltage waveform having switching time(s) at speeds up to 100 microseconds, and current levels of several hundred amperes. Due to the high switching rates, normal iron core type transformers would typical saturate, or have an inherent hysteresis that would not allow for the switching times required by the operating parameters needed for use in assembly. 
     Example embodiments of the transformer can include a core for the transformer formed from a solid ceramic tube separating the primary windings of the transformer from the secondary winding(s) of the transformer, while allowing close electromagnetic coupling between these sets of windings. Some embodiments of the core can include variations that include some portion of the core being formed from a metallic and conductive material, but arranged so that there is no continuous path for a flow of current within the metallic/conductive material that might be induced by the electromagnetic fields generated by either the primary or the secondary windings of the transformer during operation of the transformer. 
     Example Drilling Assembly 
       FIG.  1    depicts an example pulse power drilling assembly, according to some embodiments.  FIG.  1    illustrates an example drilling apparatus  100 . The example pulse power drilling apparatus  100  can include a pulse power drilling assembly (hereinafter “assembly”)  150  positioned in a borehole  106  and secured to a length of drill pipe  102  coupled to a drilling platform  160  and a derrick  164 . While depicted on the land  104  as an onshore drilling operation, example embodiments can also be performed as an offshore drilling operation. The assembly  150  can be configured to further the advancement of the borehole  106  using pulse electrical power generated by the assembly  150  and provided to electrodes  144  in a controlled manner to emit an electrical discharge through the formation material of a subsurface formation along the bottom face of the borehole  106  and in the nearby proximity to the electrodes  144 . This discharge can create high internal pressure to destroy the formation material from the inside. In other words, the electrical discharge can create a superheated condition in the fluid in the formation material—resulting in micro-explosions in the formation material. Thus, the formation material can break from tension from within caused by the emitted electrical discharge. 
     As illustrated in  FIG.  1   , the assembly  150  includes multiple sub-assemblies, including, in some embodiments, a turbine  116  at a top of the assembly  150  where the top of the assembly is a face of the assembly  150  furthest from a drilling face of the assembly  150  (which contains the electrodes  144 ). The turbine  116  is coupled to multiple additional sub-sections or components. These additional sub-sections or components may include various combinations of an alternator sub-section or component of the assembly (hereinafter “alternator”)  118 , a rectifier  120 , a rectifier controller  122 , a direct current (DC) link  124 , a voltage booster  126 , a voltage boost controller  128 , a pulse power controller  130 , the sensor  129 , one or more primary capacitor(s)  136 , a switch bank  134  (including one or more switches  138 ), a transformer  140 , one or more secondary capacitors  142 , and the electrodes  144 . 
     The assembly  150  can be divided into a generator  152  and a pulse power section  154 . The generator  152  can include the turbine  116 , the alternator  118 , the rectifier  120 , the rectifier controller  122 , the DC link  124 , the voltage booster  126 , and the voltage boost controller  128 . The pulse power section  154  can include the pulse power controller  130 , the sensor  129 , the one or more primary capacitor(s)  136 , the switch bank  134 , the switches  138 , the transformer  140 , the one or more secondary capacitors  142 , and the electrodes  144 . Components can be divided between the generator  152  and the pulse power section  154  in other arrangements, and the order of the components can be other than shown. 
     In some embodiments, the rectifier  120 , the DC link  124 , and the voltage booster  126  may be referred to as a “power conditioning system”, or PCS. These additional sub-assemblies of the PCS may be electrically coupled to receive the electrical power output generated by the alternator  118  and to provide further processing of the received electrical power in order to provide a conditioned electrical power output comprising conditioned electrical power. This further processing of the electrical power output received at the PCS may include rectification, voltage boosting, and frequency and/or waveform smoothing or regulating of the received electrical power. In operation, the rectifier controller  122  may control rectification functions performed by the PCS, while the voltage boost controller  128  may control voltage boosting functions being performed by the PCS. 
     The assembly  150  may be comprised of multiple sub-sections, with a joint used to couple each of these sub-sections together in a desired arrangement to form the assembly  150 . Field joints  112 A-C can be used to couple the generator  152  and the pulse power section  154  to construct the assembly  150  and to couple the assembly  150  to the drill pipe  102 . In some embodiments, the assembly  150  may include one or more additional field joints coupling various components of the assembly  150  together. Field joints may be places where the assembly  150  is assembled or disassembled in the field, for example at the drill site. In addition, the assembly  150  may require one or more joints referred to as shop joints that are configured to allow various sub-sections of the assembly  150  to be coupled together (for example at an assembly plant or at a factory). For example, various components of the assembly  150  may be provided by different manufacturers, or assembled at different locations, which require assembly before being shipped to the field. 
     Regardless of whether a joint in the assembly  150  is referred to as a field joint or a shop joint, the center flow tubing  114  extends through any of the components that include the center flow tubing  114 . A joint between separate sections of the center flow tubing  114  or a hydraulic seal capable of sealing the flow of the drilling fluid within the center flow tubing  114  may be formed to prevent leaking at the joints. 
     A flow of drilling fluid (illustrated by the arrow  110 A pointing downward within the drill pipe  102 ) can be provided from the drilling platform  160 , and flow to and through the turbine  116 , exiting the turbine  116  and flowing on into other sub-sections or components of the assembly  150 , as indicated by the arrow  110 B. The flow of drilling fluid through the turbine  116  can cause the turbine  116  to be mechanically rotated. This mechanical rotation can be coupled to the alternator  118  in order to generate electrical power. The PCS can further process and controllably provide the electrical power to the rest of the downstream assembly  150 . The stored power can then be output from the electrodes  144  in order to perform the advancement of the borehole  106  via periodic electrical discharges. The flow of drilling fluid can then exit at the bottom of the assembly  150  and return to the surface of the borehole  106  via the annulus  108  (illustrated by the arrows  110 C and  110 D). 
     The drilling fluid can flow through the assembly  150 , as indicated by arrow  110 B, and flow out and away from the electrodes  144  and back toward the surface to aid in the removal of the debris generated by the breaking up of the formation material at and nearby the electrodes  144 . The fluid flow direction away from the electrodes  144  is indicated by arrows  110 C and  110 D. In addition, the flow of drilling fluid may provide cooling to one or more devices and to one or more portions of the assembly  150 . In various embodiments, it is not necessary for the assembly  150  to be rotated as part of the drilling process, but some degree of rotation or oscillations of the assembly  150  may be provided in various embodiments of drilling processes utilizing the assembly  150 , including internal rotations occurring at the turbine  116 , in the alternator sub-section, etc. 
     The flow of drilling fluid passing through the turbine  116  can continue to flow through one or more sections of a center flow tubing  114 , which thereby provides a flow path for the drilling fluid through one or more sub-sections or components of the assembly  150  positioned between the turbine  116  and the electrodes  144 , as indicated by the arrow  110 B pointing downward through the cavity of the sections of the center flow tubing  114 . Once arriving at the electrodes  144 , the flow of drilling fluid can be expelled out from one or more ports or nozzles located in or in proximity to the electrodes  144 . After being expelled from the assembly  150 , the drilling fluid can flow back upward toward the surface through an annulus  108  created between the assembly  150  and walls of the borehole  106 . 
     The center flow tubing  114  may be located along a central longitudinal axis of the assembly  150  and may have an overall outside diameter or outer shaped surface that is smaller in cross-section than the inside surface of a tool body  146  in cross-section. As such, one or more spaces can be created between the center flow tubing  114  and an inside wall of the tool body  146 . These one or more spaces may be used to house various components, such as components which make up the alternator  118 , the rectifier  120 , the rectifier controller  122 , the DC link  124 , the voltage booster  126 , the voltage boost controller  128 , the sensor  129 , the pulse power controller  130 , the one or more primary capacitor(s)  136 , the switch bank  134 , the one or more switches  138 , the transformer  140 , and the one or more secondary capacitors  142 , as shown in  FIG.  1   . The sensor  129  can be located in different locations within the assembly. In this example, the sensor  129  is positioned near the pulse power controller  130  but can be in any location within the assembly  150  (depending on the size and particular sensor measurement). Other components may be included in the spaces created between the center flow tubing  114  and the inside wall of the tool body  146 . 
     The transformer  140  may be referred to as a “tubular transformer” in that the windings of the transformer, including one or more primary windings and one or more secondary windings, are wound around a center flow tubing  114  extending through the windings of the transformer and along a longitudinal axis of the example drilling apparatus  100 . The windings form tubular shaped sets of windings having different diameters in cross-section for the primary versus secondary windings. In various embodiments, an inner set of windings comprising either the primary winding(s) or the second winding(s), are formed as coil(s) wound around and in contact with or in close proximity to an outer surface of the center flow tubing  114 , thus encircling a portion of the center flow tubing  114  along a longitudinal length of the center flow tube. 
     A corresponding set of outer set of winding(s), comprising either the secondary or primary windings of the transformer  140  not included as part of the inner set of windings, is/are formed as one or more coils wound to encircle a portion of the center flow tubing  114  and to also encircle the inner set of coils. The outer set of winding encircles at least some portion of the center flow tubing  114  along the longitudinal axis of the example drilling apparatus  100  that corresponds with the portion of the center flow tubing  114  encircled by the inner windings. 
     A core material may be provided in a space between the inner set of windings and the outer set of windings. In various embodiments, the core comprises a tubular shape formed of an electrically non-conductive material, such as a ceramic material, and encircling the center flow tube and the inner set of windings. In various embodiments, the core comprises a tubular shape formed in part from a conductive material, such as a metal, that is constructed to prevent an electrical path for any currents that might be generated in the conductive material during the operation of the transformer from having a completed electrical path to flow through. Thus, the conductive material may strengthen the electromagnetic coupling available between the inner set of windings and the outer set of windings of the transformer while preventing losses due to current flows induced into the conductive material provided as part of the core of the transformer. 
     The center flow tubing  114  can seal the flow of drilling fluid within the hollow passageways included within the center flow tubing  114  and at each joint coupling sections of the center flow tubing  114  together to prevent the drilling fluid from leaking into or otherwise gaining access to these spaces between the center flow tubing  114  and the inside wall of the tool body  146 . Leakage of the drilling fluid outside the center flow tubing  114  and within the assembly  150  may cause damage to the electrical components or other devices located in these spaces and/or may contaminate fluids, such as lubrication oils, contained within these spaces, which may impair or completely impede the operation of the assembly  150  with respect to drilling operations. 
     The example pulse power drilling apparatus  100  can include one or more logging tools  148 . The logging tools  148  are shown as being located on the drill pipe  102 , above the assembly  150 , but can also be included within the assembly  150  or joined via shop joint or field joint to assembly  150 . The logging tools  148  can include one or more logging with drilling (LWD) or measurement while drilling (MWD) tool, including resistivity, gamma-ray, nuclear magnetic resonance (NMR), etc. The logging tools  148  can include one or more sensors to collect data downhole. For example, the logging tools  148  can include pressure sensors, flowmeters, etc. The example pulse power drilling apparatus  100  can also include directional control, such as for geosteering or directional drilling, which can be part of the assembly  150 , the logging tools  148 , or located elsewhere on the drill pipe  102 . 
     Communication from the pulse power controller  130  to the voltage boost controller  128  allows the pulse power controller  130  to transmit data about and modifications for pulse power drilling to the generator  152 . Similar, communication from the voltage boost controller  128  to the pulse power controller  130  allows the generator  152  to transmit data about and modifications for pulse power drilling to the pulse power section  154 . The pulse power controller  130  can control the discharge of the pulse power stored for emissions out from the electrodes  144  and into the formation, into drilling mud, or into a combination of formation and drilling fluids. The pulse power controller  130  can measure data about the electrical characteristics of each of the electrical discharges—such as power, current, and voltage emitted by the electrodes  144 . Based on information measured for each discharge, the pulse power controller  130  can determine information about drilling and about the electrodes  144 , including whether or not the electrodes  144  are firing into the formation (i.e. drilling) or firing into the formation fluid (i.e. electrodes  144  are off bottom). The generator  152  can control the charge rate and charge voltage for each of the multiple pulse power electrical discharges. The PCS, together with the turbine  116  and alternator  118 , can create an electrical charge in the range of 16 kilovolts (kV) which the pulse power controller  130  delivers to the formation via the electrodes  144 . 
     When the pulse power controller  130  can communicate with the generator  152 , the generator  152  and the alternator  118  can ramp up and ramp down in response to changes or electrical discharge characteristics detected at the pulse power controller  130 . Because the load on the turbine  116 , the alternator  118 , and the generator  152  is large (due to the high voltage), ramping up and ramping down in response to the needs of the pulse power controller  130  can protect the generator  152  and associated components from load stress and can extend the lifetime of components of the pulse power drilling assembly. If the pulse power controller  130  cannot communicate with the generator  152 , then the generator  152  may apply a constant charge rate and charge voltage to the electrodes  144  or otherwise respond slowly to downhole changes—which would be the case if the generator  152  is controlled by the drilling mud flow rate adjusted at the surface or another surface control mechanism. 
     In instances where the assembly  150  is off bottom, electrical power input to the system can be absorbed (at least partially) by drilling fluid, which can be vaporized, boiled off, or destroyed because of the large power load transmitted in the electrical pulses. In instances where the assembly  150  is not operating correctly, such as when one or more switch experiences a fault or requires a reset, application of high power to the capacitors  136 / 142  or the electrodes  144  can damage circuitry and switches when applied at unexpected or incorrect times. In these and additional cases, communications or messages between the pulse power controller  130  and the generator  152  allow the entire assembly to vary charge rates and voltages, along with other adjustments further discussed below. In cases where the pulse power controller  130  and generator  152  are autonomous, i.e. not readily in communication with the surface, downhole control of the assembly  150  can improve pulse power drilling function. 
     Example Transformers 
       FIG.  2 A  illustrates a schematic diagram of a portion of a pulse power drilling apparatus  200  including a transformer  201 , according to some embodiments. The transformer  201  illustrated in  FIG.  2 A  in various embodiments may be transformer  140  utilized in assembly  100  as illustrated and described above with respect to  FIG.  1   . As shown in  FIG.  2 A , transformer  201  includes primary windings  201 A,  201 B,  201 C, a secondary winding  209 , and a core  207  positioned between the primary windings and the secondary winding. Primary winding  201 A is electrically coupled in series with primary winding  201 B through electrical connection  203 , and primary winding  201 B is electrically coupled in series with primary winding  201 C through electrical connection  205 . The series coupled primary windings  201 A,  201 B,  201 C are coupled in parallel with primary capacitor bank  220 , which includes one or more capacitor(s)  221 , and in parallel with input conductors configured to provide an input voltage V IN    225  across the primary capacitor(s)  221  and primary windings  201 A,  201 B,  201 C. 
     Primary windings  201 A,  201 B,  201 C are electrically isolated from secondary winding  209 , but are electromagnetically coupled to secondary winding  209  at least through core  207 . Secondary winding  209  is electrically coupled in parallel with secondary capacitor bank  230 , which includes one or more secondary capacitor(s)  231 , and in parallel with output conductors configured to provide an output voltage V OUT    235  across the secondary winding  209  and the secondary capacitor(s)  231 . In various embodiments, transformer  201  is configured to receive input voltage V IN    225  across the primary windings  201 A,  201 B,  201 C as a first voltage, and to provide an output voltage V OUT    235  across the secondary winding  209 , wherein the voltage level of V OUT    235  is higher than the voltage level V IN    225  provided across the primary windings  201 A,  201 B,  201 C. 
     In various embodiments, primary capacitor bank  220  may include primary switch  222  configured to electrically connect and disconnect input voltage V IN    225  to and from, respectively, primary windings  201 A,  201 B,  201 C. In various embodiments, primary switch  222  may be positioned so that operation of the switch connects or disconnects primary windings  201 A,  201 B,  201 C from primary capacitor(s)  221 . The operation of primary switch  222  may be utilized to control the overall power level provided to transformer  201 , and/or as a safety feature used to disconnect electrical power from the primary windings of transformer  201  when a fault condition, such as an electrical overload, electrical short, and/or an overtemperature condition is detected. 
     In various embodiments, secondary capacitor bank  230  may include secondary switch  232  configured to electrically connect and disconnect secondary winding  209  from the output conductors configured to provide output voltage V OUT    235  to additional portions of the pulse power drilling assembly. In various embodiments, secondary switch  232  may be positioned so that operation of the switch connects or disconnects secondary winding  209  from secondary capacitor(s)  231 . The operation of secondary switch  232  may be utilized to control the overall power level provided as an electrical output from transformer  201 , and/or as a safety feature used to disconnect any electrical output power generated by transformer  201  when a fault condition, such as an electrical overload, electrical short, and/or an overtemperature condition is detected. 
     As shown in  FIG.  2 A , primary switch  222  and secondary switch  232  are coupled to switch controller  240 . In various embodiments, switch controller  240  is configured to control the operation of primary switch  222  to connect and disconnect the primary windings  201 A,  201 B,  201 C to and from, respectively, input voltage V IN    225  and/or primary capacitor(s)  221 . In various embodiments, switch controller  240  is configured to control the operation of secondary switch  232  to connect and disconnect the secondary windings  209  to and from, respectively, the conductors providing output voltage V OUT    235  and/or secondary capacitor(s)  231 . Switch controller  240  is not limited to any particular kind of controller or control device, and in various embodiments may be a separate controller, such as computer device, as illustrated and described below with respect to  FIG.  7   , and/or may be provided by and incorporated into any of the controllers described throughout this disclosure, and/or any equivalents thereof. 
     In various embodiments, one or more sensors  241  are coupled to switch controller  240 . Sensors  241  are not limited to any particular type or types of sensors, and may include any type of sensor configured to provide an output signal, such as an electrical and/or an optical output signal, that corresponds to some parameter or parameters being detected and/or measured by the sensor. In various examples, sensors  241  may include one or more sensors configured to measure electrical parameters, such as voltage levels at V IN    225  and/or voltage levels present across primary windings  201 A,  201 B,  201 C, and provide an output signal to switch controller  240  indicative of the measured voltage level(s). In various examples, sensors  241  may include one or more sensors configured to measure electrical parameters, such as voltage levels at V OUT    235  and/or voltage levels present across secondary windings  209 , and provide one or more output signals to switch controller  240  indicative of the measured voltage level(s). In various embodiments, sensors  241  may include one or more sensors configured to measure one or more electrical current levels, such as current flow into or out of primary capacitors  221 , through primary windings  201 A,  201 B,  201 C, into or out of secondary capacitors  231 , and/or through secondary winding  209 , and provide one or more output signals to switch controller  240  indicative of the measured current level(s). In various embodiments, sensors  241  may include one or more sensors configured to measure temperature levels at one or more locations within apparatus  200 , such as the temperature level of the primary windings, the core, and/or the secondary windings of transformer  201 , primary capacitors  221 , secondary capacitors  231 , and/or area proximate to and/or surrounding transformer  201  and/or the capacitors banks  220 ,  230 , and to provide one or more output signals to switch controller  240  indicative of the measured temperature level(s). In various embodiments, switch controller  240  may be configured to control the operation of primary switch  222  and/or secondary switch  232  based at least in part on the signals provided to the switch controller by sensors  241 . 
     Although primary capacitors  221  are illustrated in  FIG.  2 A  as a single capacitor, primary capacitors  221  may comprise a number of series coupled capacitors, a number of parallel coupled capacitors, and/or a network of series/parallel coupled capacitors. The arrangement and electrical coupling of the primary capacitors may be configured to allow the primary capacitors to receive and safely store electrical energy provided as V IN    225 . Primary windings  201 A,  201 B,  201 C are also configured with respect to insulative properties and current carrying capacity to receive and safely operate within the electrical ranges for voltage and current provided to the primary windings as V IN    225  and from primary capacitor(s)  221 . In various embodiments, primary windings  201 A,  201 B,  201 C of transformer  201  are configured to operate within a voltage range of zero to 20,000 Volts (peak to peak), and carry current flow in a range of zero to 300,000 Amperes. In various embodiments, the secondary winding  209  of transformer  201  is configured to operate within a voltage range of zero to 160,000 Volts (peak to peak), and carry current flow in a range of zero to 200,000 Amperes. In various embodiments, transformer  201  is configured to have a power rating of between 100 and 300 kWatts. In various embodiments, transformer  201  is configured to operate within a frequency range from 0 to 500 kilo-Hertz, inclusive. In various embodiments, transformer  201  is configured to operate over a temperature range of 75 to 300 degrees F. (25 to 150 degrees C.). The above-listed ranges and dimensions are non-limiting examples, because such ranges and dimensions can have other values depending on the material and other design parameters. 
     In various implementations, transformer  201  is configured to be positioned and operate when at least partially or fully submersed in a fluid, such as an oil, wherein the fluid may be in contact with any or all of the primary windings, the core, and/or the secondary winding of transformer  201 , and in various implementations may provide cooling and/or temperature control for the transformer. The fluid may reside and/or circulate through the primary windings, around the core, and through the secondary winding of the transformer. In addition to or in the alternative to any cooling provided to the transformer through the fluid in which the transformer may be immersed, the transformer may be cooled through thermal transfer of heat from the transformer or the area(s) around the transformer through the center flow tube and to a flow of fluid, such as drilling fluid, passing through the center flow tube. 
     In various embodiments, the number of primary windings included in the transformer  201  may be determined at least in part based on the arrangement and the electrical parameters, such as voltage and current carrying requirements, associated with the banks of capacitors included in the primary capacitor(s)  221  coupled to the primary windings  201 A,  201 B,  201 C. In various examples, the current carrying reequipments for the primary capacitor(s)  221  may dictate that the capacitor banks be divided into two or more electrically separate banks of capacitors, each bank electrically coupled to an individual and separate coil windings of the primary windings  201 A,  201 B,  201 C of the transformer  201  in order to safely handle the current levels required to provide the overall power needed to be provided to and transferred through the transformer, an example of which is further illustrated and described below with respect to  FIG.  2 B . 
     Referring again to  FIG.  2 A , in operation electrical energy provided to the primary windings  201 A,  201 B,  201 C of the transformer  201  generates an electromagnetic field that induces electrical currents in the secondary winding  209  of the transformer. The electrical energy associated with these induced currents is then controllably stored into a secondary capacitor(s)  231  that is electrically coupled to the secondary winding  209 , and may be provided as output voltage V OUT    235 . 
     Core  207  as shown in  FIG.  2 A  may provide both the function of physical support for physical conductors, such as a wire, used to form the primary windings and/or the secondary winding of the transformer, and in some embodiments allows for more efficient coupling of the electromagnetic fields generated by the primary windings and utilized to induce currents in the secondary winding. In various embodiments, the core  207  is formed of an electrically insulative material, such as a ceramic. In various embodiments, the core  207  may be formed, at least in part, from an electrically conductive material, such as a metal. The core  207  in various embodiments allows the distance between the primary windings  201 A,  201 B,  201 C and the secondary winding  209  to be smaller compared to instances where no core or an air core would be utilized, and thus helps reduce the overall amount of space required within the apparatus  200  needed to house the transformer  201 . Further, embodiments of the core  207  may be tube shaped and allow for accommodation of a center flow tube configured to carry drilling fluid passing through a fluid passageway that is encircled by the transformer  201 . The primary windings  201 A,  201 B,  201 C and the secondary winding  209  of the transformer  201  may be arranged to encircle the center flow tube and maintain a separation between these windings using the core as the separating means. 
       FIG.  2 B  illustrates a schematic diagram of a portion of a pulse power drilling apparatus  250  including a transformer  260 , according to some embodiments. Apparatus  250  as illustrated in  FIG.  2 B  may include the same components and/or electrical connections arranged in a same or similar manner as illustrated and described above with respect to apparatus  200  and transformer  201 , with differences between apparatus  200  and  250  as described below. Components that relate to a same or similar device in FIGS.  2 A and  2 B retain the same reference number in both figures and may provide the same features and perform the same or similar functions in each of these apparatuses. 
     A shown in  FIG.  2 B , transformer  260  includes three primary windings  201 A,  201 B,  201 C, a secondary winding  209 , and a core  207  positioned between the primary and secondary windings. As further illustrated in  FIG.  2 B , each of the primary windings  201 A,  201 B,  201 C, is coupled to a respective and separate set of primary capacitor(s). Embodiments of transformer  260  are not limed to having three primary windings, and may have a plurality of primary windings more or less than three in number, wherein each of the primary windings may be individually coupled to a separate set of primary capacitors in a manner the same or similar to that illustrated in  FIG.  2 B . 
     For example, primary winding  201 A may be coupled in parallel with primary capacitor(s)  251 , wherein primary capacitor(s)  251  may include a number of series connected capacitors, a number of parallel connected capacitor(s), and/or a number of series/parallel connected capacitors. A switch  252  may be connected between primary winding  201 A and configured to connect and disconnect primary winding  201 A to and from, respectively, primary capacitor(s)  251 . Primary winding  201 B may be coupled in parallel with primary capacitor(s)  253 , wherein primary capacitor(s)  253  may include a number of series connected capacitor(s), a number of parallel connected capacitor(s), and/or a number of series/parallel connected capacitors. A switch  254  may be connected between primary winding  201 B and configured to connect and disconnect primary winding  201 B to and from, respectively, primary capacitor(s)  253 . Primary winding  201 C may be coupled in parallel with primary capacitor(s)  255 , wherein primary capacitor(s)  255  may include a number of series connected capacitor(s), a number of parallel connected capacitor(s), and/or a number of series/parallel connected capacitors. A switch  256  may be connected between primary winding  201 C and configured to connect and disconnect primary winding  201 C to and from, respectively, primary capacitor(s)  255 . 
     In various embodiments, the arrangement of the capacitors(s) within each one of the sets of primary capacitor(s)  251 ,  253 ,  255  is a same arrangement with respect to series and/or parallel coupling of the capacitors within the set. In various embodiments, the arrangement of the capacitors(s) within one or more of the sets of primary capacitor(s)  251 ,  253 ,  255  is a different arrangement of the capacitor(s) with respect to series and/or parallel coupling of the capacitors within at least one other of the sets of primary capacitor(s). 
     Based on the arrangements of the primary capacitor(s)  251 ,  253 ,  255 , each of these sets or primary capacitors may be configured to impress a respective voltage level across the respective one of primary windings  201 A,  201 B,  201 C to which that set of primary capacitors is coupled in parallel with. In various embodiments, each of primary capacitor(s)  251 ,  253 ,  255  may be coupled together in series with one another and in parallel with the input conductors providing the input voltage V IN    225  so that each of the primary capacitor(s) has a voltage level across the capacitors in that set of primary capacitors that is less than the total voltage level provided at V IN    225 . For example, primary capacitor(s)  251 ,  253 ,  255  may be configured so that each of these sets of primary capacitor(s) has an amount equal to approximately one third of the input voltage V IN    225  applied across the respective capacitor(s) included in that set of primary capacitors. In various embodiments, primary capacitor(s)  251 ,  253 ,  255  may be configured so that each of these sets of primary capacitor(s) has a different voltage level applied across the capacitor(s) including in a particular one of sets of primary capacitor(s) compared to a voltage level or voltage levels applied across other capacitors of a different one or ones of the primary capacitor(s). 
     In various embodiments, each of switches  252 ,  254 ,  256  may be controlled by switch controller  240  in order to control the coupling of the primary windings  201 A,  201 B,  201 C with the respective ones of the primary capacitor(s)  251 ,  253 ,  255 . Switches  252 ,  254 ,  256  are not limited to any particular type of switching device, and may be any switching device configured to provide electrical coupling between primary winding  201 A,  201 B,  201 C and the capacitor(s) included in capacitor bank  220 , including a solid state switching device, such as a MOSFET device. By separately coupling each of the primary windings  201 A,  201 B,  201 C to individual sets of primary capacitor(s), the overall voltage rating level, and thus the voltage rating for insulation used for insulating the windings of the primary windings may be reduced, while still allowing transformer  260  to provide a higher level of overall power passing through the primary circuitry of the transformer. In various embodiments, by individually switching on and off individual ones of the primary windings  201 A,  201 B,  201 C while maintaining voltage(s) on one or more of the primary windings but not on all of the primary windings, the overall power levels passing through the transformers may also be controlled. 
       FIG.  3    illustrates a cut-away side view of a sub-section  300  of a pulse power drilling assembly that includes a transformer  301 , according to various embodiments. As shown in  FIG.  3   , the cut-away view of sub-section  300  extends along the longitudinal axis  303  of the assembly. As shown in  FIG.  3   , sub-section  300  includes a center flow tube  310  positioned inside tool body  302 . The center flow tube  310  includes a fluid passageway  312  that extends along the longitudinal axis  303  of the tool body  302 . The center flow tube  310  in some embodiments is formed from an electrically non-conductive material, such as a ceramic. In some embodiments, the fluid passageway  312  extends through the entirety of the center flow tube  310  and provides a flow path for a drilling fluid to pass through the sub-section  300  including the transformer  301  when the sub-section  300  including the transformer  301  is coupled to adjoining sub-sections of the assembly. 
     One more primary windings  301 A,  301 B,  301 C formed from electrical conductors such as wires, are formed as coil windings that encircle the center flow tube  310 . The electrical conductors are not limited to comprising a particular type of material, and may comprise a metal or metallic compound or metal alloy, such as copper, aluminum, a compound of iron, or a non-metallic electrically conductive material, such as a carbon based material. As shown in  FIG.  3   , there are three primary windings encircling the center flow tube  310 , although embodiments of the transformer  301  may have more or a fewer number of primary windings. Although shown in  FIG.  3    as being circular in cross-section, the cross-sectional shape of the electrical conductors forming primary windings  301 A,  301 B,  301 C are not limited to being circular. In various embodiments, the electrical conductors forming primary windings  301 A,  301 B,  301 C may have any closed shape in cross-section, including square, rectangular, triangular, elliptical, oval shapes. In various embodiments, the areas of each of the conductors forming the primary windings  301 A,  301 B,  301 C may be in a range of 0.030 to 0.5 square inches, inclusive. The above-listed range is a non-limiting example, because this range can have other values depending on the material and other design parameters. 
     In various embodiments, a center point of each winding of the primary windings  301 A,  301 B, and  301 C may align with the center points of each of the other windings of the primary windings so that the center points fall along a line that is parallel to longitudinal axis  303 . In various embodiments, a center point of a winding of the primary windings may be staggered with respect to a distance between the center point and longitudinal axis  303  so that the conductors forming the primary windings do not align along a single line parallel to longitudinal axis  303 , but, for example, may have adjacent windings formed at a different distance from the longitudinal axis  303 . In various embodiments, each of the primary windings includes a single layer of electrical conductors forming each winding. In various embodiments, each of the primary windings incudes multiple layers, for example, two layers of electrical conductors, wherein a layer of winding is formed to encircle the inner winding(s) forming the primary windings. 
     In various embodiments, the inner most portion of each of the primary windings  301 A,  301 B,  301 C may be formed to be in direct contact with an outer surface  311  of the center flow tube  310 . The outer surface  311  of the center flow tube  310  may be circular in cross-section perpendicular to longitudinal axis  303  and completely encircling and enclosing a length of longitudinal axis  303 , thus forming a cylindrical shaped coil winding surface for positioning primary windings  301 A,  301 B,  301 C of the transformer  301 . 
     A core  307  may be formed in a tubular shape that encircles both the outer surface  311  of the center flow tube  310  and the primary windings  301 A,  301 B,  301 C of the transformer  301 , and extends laterally along the longitudinal axis  303  of the sub-section  300  at least over the same length that includes the primary windings  301 A,  301 B,  301 C. The core  307  may be formed from an electrically non-conductive material, such as ceramic. In some embodiments, the core  307  may be formed, at least in part, from an electrically conductive material, such as a metal, as further described below. 
     In addition to the primary windings  301 A,  301 B,  301 C, transformer  301  includes at least one set of coils forming secondary winding  309 . Secondary winding  309  may include a set of windings formed around and encircling the core  307  of the transformer  301 . The secondary winding  309  may be formed from an electrical conductor, such as a wire and is formed as a coil winding that encircles the center flow tube  310 , primary windings  301 A,  301 B,  301 C, and the core  307  of the transformer. In various embodiments, the coil winding forming the secondary winding  309  of the transformer may be positioned to be in direct contact with the outer most surface of the core  307 . 
     Although shown in  FIG.  3    as being circular in cross-section, the cross-sectional shape of the electrical conductors forming secondary winding  309  is not limited to being circular. In various embodiments, the electrical conductors forming secondary winding  309  may have any closed shape in cross-section, including square, rectangular, triangular, elliptical, and/or oval shapes. In various embodiments, the area of each of the conductors forming secondary winding  309  may be in a range of 0.05 to 0.5 square inches, inclusive. The above-listed range is a non-limiting example, because this range can have other values depending on the material and other design parameters. 
     In various embodiments, a center point of each winding of the secondary winding may align with the center points of each of the other windings of the secondary winding so that the center points fall along a line that is parallel to longitudinal axis  303 . In various embodiments, the center points of one or more windings of the secondary winding may be staggered with respect to a distance between the center point and longitudinal axis  303 , so that the conductors forming the secondary winding do not align along a single line parallel to longitudinal axis  303 , but for example may have adjacent windings formed at different distances from the longitudinal axis  303 . In various embodiments, the windings of the secondary winding  309  includes a single layer of electrical conductors forming the secondary winding. In various embodiments, the windings forming the secondary winding incudes multiple layers, for example, two layers of electrical conductors, wherein a layer of windings is formed to encircle another inner layer or layers of winding(s) forming the secondary winding. 
     The entire assembly, including the center flow tube  310 , the primary windings  301 A,  301 B,  301 C, the core  307 , and the secondary winding  309 , may be included within a space encircled by a section of the tool body  302 . In various embodiments, the tool body  302  is formed from a metal, and thus may be electrically conductive. As such, in various embodiments a space  318  between the secondary winding  309 , which may include an insulative material provided in the space, may be included with the transformer to help eliminate possible electrical shorts between the secondary winding  309  and the tool body  302 . This spacing may also aid in reducing eddy currents that may be generated in the tool body  302  due to the electromagnetic fields surrounding the secondary winding  309  during operation of the transformer. In addition, positioning the primary windings  301 A,  301 B,  301 C closest to the center flow tube  310 , and thus farther away from the tool body  302  compared to the secondary winding  309 , may further reduce the eddy current issue that may occur in the tool body  302 , as the primary windings  301 A,  301 B,  301 C may carry larger currents compared to the current carried by secondary winding  309  of the transformer. 
     Dimensionally, the transformer  301  including the primary and secondary windings and the core must fit within the space defined between the outer surface  311  of the center flow tube (having outer dimension  313 ) and the inner surface of the tool body  302 , or in other words having an outer most dimension  315 , while also having a longitudinal (length) dimension  317  that does not exceed the space allocated for the transformer. By designing the transformer  301  in a compact manner, for example using the core  307 , the distance included in the space  318  between the inner surface of the tool body and the outer most dimension  315  of the transformer may allow for minimizing the losses, such as eddy current losses, that may be attributed to the metal material used to form the tool body of the sub-section of the assembly where the transformer is positioned. By also positioning the secondary winding of the transformer closest to the tool body as described above, the losses, such as eddy current losses, may be further reduced, while providing an arrangement for transformer that can still accommodate a center flow tube passing through the sub-section of the assembly where the transformer is also located. 
     Because of the size restraints downhole (e.g., the width or diameter of the borehole) and the large amount of power that needs to be transformed in order to effectively perform pulse power operations, example embodiments include a transformer configured to satisfy these size restraints while being able to transform the large amount of power necessary for proper pulse power operations. In some embodiments, a length of the transformer is to extend along a longitudinal axis of the pulse power drilling assembly (as depicted). Also, in some embodiments, the length of the transformer is greater than a width of the transformer. For example, a length of the transformer is at least two times, five times, or 10 times greater than a width of the transformer. 
       FIG.  4    illustrates a cross-sectional view of the transformer  301  of  FIG.  3   , viewed along section line  4 - 4  in  FIG.  3   . As shown in  FIG.  4   , a center flow tube  310  encircles the longitudinal axis  303  of the assembly, and includes the fluid passageway  312  that extends through the entirety of the center flow tube  310  along the longitudinal axis  303  within the sub-section that includes the transformer  301 . The primary windings (illustratively represented as primary winding  301 A) of the transformer encircle the outer surface of the center flow tube  310 . In various embodiments, the primary windings are formed to be in direct physical contact with the outer surface of the center flow tube  310 . 
     The core  307  encircles both the center flow tube  310  and the primary windings  301 A of the transformer  301 . The secondary winding  309  of the transformer  301  are formed around and encircle the core  307 , and therefore, also encircle both the center flow tube  310  and the primary windings  301 A of the transformer  301 . The tool body  302  encircles the transformer  301  along the longitudinal axis  303  of the assembly, and is configured to couple with additional tool bodies of sub-sections of the assembly that are adjoined to the sub-section housing the transformer  301 . 
     In various embodiments, the core  307  is formed from a non-conductive material, such as a ceramic material, and is formed in a tubular shape at least partially enclosing a hollow cylindrical space encircled by the inner wall of the core  307  and having the center flow tube  310  and the primary windings  301 A positioned within the hollow cylindrical shape. The secondary winding  309  is formed around the outer surface of the core  307 . As such the core  307  may provide some of the physical structure for supporting the primary windings  301 A and the secondary winding  309  while also forcing a separation distance between the primary windings and the secondary winding based on the wall thickness and diameter in the cross-section of the outer diameter of the core itself. Other variations of the core are further illustrated and described below with respect to  FIGS.  5 A- 5 C . 
       FIG.  5 A  illustrates embodiments of a core  510 , including one or more insulative breaks, which may be utilized in a transformer of a pulse power drilling assembly, according to various embodiments. As shown in  FIG.  5 A , core  510  is viewed in cross-section, for example as illustrated in  FIG.  4    by section line  4 - 4 . Core  510  may be an embodiment of a core included as part of any of the transformers illustrated and described throughout this disclosure, and in any equivalents thereof. As shown in  FIG.  5 A , the core  510  may be formed from a tubular section  511 , which may comprise a metallic material, such as an iron or ferrous based metal, and which partially encircles a hollow passageway  520  extending along a longitudinal axis  518  of the core. 
     The core  510  may be formed as a tubular shape extending along a length of longitudinal axis  518  and comprising a core wall having at least one break  512  in the circular shape of the core. The break may also extend along the length of the longitudinal axis  518 , thus separating a section of the core wall of the core along a section of the core running parallel to the longitudinal axis. The break  512  may be formed from an electrically insulative material, such as ceramic, and extending between a first end  513  and a second end  514  of the core wall of the core, wherein first end  513  and second end  514  are positioned proximate to each other with a space between the ends having a dimension  517  in a range from 0.1 to 1 inches, inclusive. In various embodiments, break  512  extends from inner surface  523  to outer surface  524  of core  510  along the entirety of the length of the core relative to the length dimension of the core extending along longitudinal axis  518 . Core  510  may have a circular shape in cross-section, wherein an overall diameter  515  for the outer surface of core  510  may be in a range from 1 to 15 inches, inclusive. In various embodiments, a core wall thickness  521  for core  510  may in a range from 0.25 to 3 inches, inclusive. The above-listed ranges and dimensions are non-limiting examples, because such ranges and dimensions can have other values depending on the material and other design parameters. 
     As shown in  FIG.  5 A , the core  510  may have just one break, such as break  512 , or may include additional break(s) formed from an insulative material, such as break  516 , illustratively represented by the dashed lines at the bottom portion of the core  510 . Break  516  may comprise a same or similar material used to form break  512  and may have physical dimensions the same as or similar to break  512 . In various embodiments that include a second break, such as break  516 , core  510  comprises a second tubular or curved section  519 , which is separated from tubular section  511  by both break  512  and break  516 . Second section  519  may be formed of a same material used to form section  511  in various embodiments. Embodiments of core  510  may include more than two separate breaks, wherein each of the breaks is positioned apart from one in a radial fashion around the core wall, each break separating two ends of the core wall from one another by the dimensions of the break. By including metallic material, core  510  may provide electromagnetic coupling between one or more primary windings of a transformer, for example on one side of the core wall (e.g., inside inner surface  523  of the core wall), and a secondary winding fore on the opposite side of the core wall (e.g. around or proximate to the outside surface  524  of the core wall of the core), while the one or more breaks function to reduce eddy current, and thus eddy current losses, in the core itself, during times when the transformer is powered. 
       FIG.  5 B  illustrates embodiments of a core  530  including radial laminate non-magnetic plates  532 , which may be utilized in a transformer of a pulse power drilling assembly, according to some embodiments. As shown in  FIG.  5 B , core  530  is viewed in cross-section, for example as illustrated in  FIG.  4    by section line  4 - 4 . Core  530  may be an embodiment of a core included as part of any of the transformers illustrated and described throughout this disclosure, and in any equivalents thereof. As shown in  FIG.  5 B , the core  530  may be formed from in a tubular shape, having an inner surface  533  encircling the longitudinal axis  538  of the core and spaced at a radial distance away from the longitudinal axis  538 , forming a tubular shaped hollow passageway  540 . An outer surface  534  encircles the inner surface  533  at a radial distance away from the longitudinal axis that is greater than the distance between the longitudinal axis and the inner wall, thus forming the core wall between the inner surface  533  and the outer surface  534 . The core wall may have a thickness dimension  535  in a range from 0.25 to 3 inches, inclusive. The above-listed range is a non-limiting example, because this range can have other values depending on the material and other design parameters. In various embodiments of core  530 , the core wall comprises a non-conductive or insulative material  531 , such as a high temperature epoxy. The insulative material  531  is embedded with a series of non-magnetic plates  532 . These non-magnetic plates  532  may be straight sections which are embedded in a radial arrangement within the insulative material forming core  530 . The non-magnetic plates may also have different configurations, such as interlocking shapes from which the tube is constructed. Each of the non-magnetic plates  532  in some embodiments extend throughout the tubular shape of the core wall along the length dimension of the core that is parallel to longitudinal axis  538 , and where each of the non-magnetic plates  532  are separated from one and other and electrically insulated from one another by the insulative material forming the core wall. In various embodiments, non-magnetic plates  532  do not extend to inner surface  533 , and/or do not extend to outer surface  534 , so that the non-magnetic plates are not exposed at least at the inner surface and/or at the outer surface. 
     Core  530  may have a circular shape with respect to outer surface  534 , and an outer diameter  536  in a range from 1 to 15 inches, inclusive. The above-listed range is a non-limiting example, because this range can have other values depending on the material and other design parameters. By including non-magnetic plates  532  embedded within the insulative material forming core  530 , core  530  may provide electromagnetic coupling between one or more primary windings of a transformer for example on one side of the core wall (e.g., inside inner surface  533  of the core wall), and a secondary winding formed on the opposite side of the core wall (e.g. around or proximate to the outer surface  534  of the core wall of the core), while the non-magnetic plates function to reduce eddy current, and thus eddy current losses, in the core itself, during times when the transformer is powered. 
       FIG.  5 C  illustrates embodiments of a core including straight laminate non-magnetic plates, which may be utilized in a transformer of a pulse power drilling assembly, according to some embodiments. As shown in  FIG.  5 C , core  570  is viewed in cross-section, for example as illustrated in  FIG.  4    by section line  4 - 4 . Core  570  may be substantially similar in dimension and configuration to the core  530  of  FIG.  5 B . In various embodiments of core  570 , the core comprises horizontal alternating layers of materials. The alternating layers may comprise layers of non-magnetic plates  571  separated by layers of non-conductive laminate materials  572 . The thickness of the non-magnetic plates  571  and the non-conductive laminate materials  572  illustrated in  FIG.  5 C  are for example purposes only. While the non-magnetic plates  571  are depicted as thicker than the layers of non-conductive laminate materials  572 , the alternating layer may be equal, or the layers of non-conductive laminate materials  572  may be thicker than the non-magnetic plates  571 . For example, each plate of the non-magnetic plates  571  may have a thickness in a range from 0.1 to 0.5 inches, inclusive. Each layer of the non-conductive laminate materials  572  may have a thickness in a range from 0.05 to 0.5 inches, inclusive. The above-listed ranges and dimensions are non-limiting examples, because such ranges and dimensions can have other values depending on the material and other design parameters. 
       FIG.  5 D  illustrates embodiments of a core including a non-magnetic powder coated with non-conductive material, which may be utilized in a transformer of a pulse power drilling assembly, according to some embodiments. As shown in  FIG.  5 D , core  580  is viewed in cross-section, for example as illustrated in  FIG.  4    by section line  4 - 4 . Core  580  may be substantially similar in dimension and configuration to the core  530  of  FIG.  5 B . Core  580  may be substantially similar in dimension and configuration to the core  530  of  FIG.  5 B . In various embodiments of the core  580 , the core  580  may be a core comprised of powder core  581 . A call out  582 , indicated by a dashed line circle, illustrates a close-up detail of the powder core  581 . The powder core  581  may comprise units of powder  583  surrounded by and/or coated with a non-conductive material  584 . While the units of powder  583  and the non-conductive material  584  are depicted in a uniform, circular pattern in  FIG.  5 D , the pattern may be irregular and/or the units of powder may comprise different shapes. The powder  583  coated with the non-conductive material  584  may prevent current flow in the core  580 . 
       FIG.  5 E  illustrates a core having a first example spiral configuration (having an insulative layer outside of an electrically conductive layer) that is part of a transformer of a pulse power drilling assembly, according to some embodiments.  FIG.  5 E  depicts a cross-sectional view of a core  550 , which can be an example of the cross-section of section line  4 - 4  of  FIG.  3   . 
     The core  550  may be an embodiment of a core included as part of any of the transformers illustrated and described throughout this disclosure, and in any equivalents thereof. As shown in  FIG.  5 E , the core  550  may be formed in a tubular shape. The core  550  may circumferentially surround an outer surface of a flow tube  590 . The core  550  may encircle a longitudinal axis  558  of a tool body and may be spaced at a radial distance away from the longitudinal axis  558 . A tool body  591  encircles the core  550  at a radial distance away from the longitudinal axis that is greater than the distance between the longitudinal axis  558  and the flow tube  590 . 
     The core includes an insulative layer  551  and an electrically conductive layer  552  such that the insulative layer positioned outside the electrically conductive layer  552 . The electrically conductive layer  552  may comprise a sheet of electrically conductive material, such as copper or aluminum, and which may be wound into a spiral shape that encircles the outer surface of the flow tube  590  and extends in a spiral routing out toward the tool body  591 . In various embodiments, the insulative layer  551  is placed in the spaces between the individual layers of the electrically conductive layer  552  to provide electrical isolation between the individual layers relative to the adjacently positioned portions of the electrically conductive layer  552 , for example relative to a radial  555  extending from the longitudinal axis to the tool body  591 . In addition, the edge of the electrically conductive layer  552  extending along the core  550  closest to the flow tube  590  may not extend to the flow tube  590  and may not be coupled to any other electrical conductor. The edge of the electrically conductive layer  552  extending along or closest the tool body  591  may not extend to the tool body  591 , and also may not be coupled to any other electrical conductor. As such, there is no path for a flow of current that may be generated in the core  550  as a result of the exposure of the electrically conductive layer  552  to electromagnetic fields that may be generated during the operation of the transformer where the core  550  is located. As such, the electrically conductive layer  552  may not result in a loss of efficiency of the transformer due, for example, to eddy current losses. 
       FIG.  5 F  illustrates a core having a second example spiral configuration (having an insulative layer inside of an electrically conductive layer) that is part of a transformer of a pulse power drilling assembly, according to some embodiments.  FIG.  5 F  depicts a cross-sectional view of a core  560 , which can be an example of the cross-section of section line  4 - 4  of  FIG.  3   . The core  560  is similar to the core  550  of  FIG.  5 E  except for the relative positions of the insulative layer and the electrically conductive layer. In particular, an insulative layer  553  is positioned inside of the electrically conductive layer  552 . 
     The core  560  may be an embodiment of a core included as part of any of the transformers illustrated and described throughout this disclosure, and in any equivalents thereof. As shown in  FIG.  5 F , the core  560  may be formed in a tubular shape. The core  560  may circumferentially surround an outer surface of the flow tube  590 . The core  560  may encircle the longitudinal axis  558  of a tool body and may be spaced at a radial distance away from the longitudinal axis  558 . The tool body  591  encircles the core  560  at a radial distance away from the longitudinal axis that is greater than the distance between the longitudinal axis  558  and the flow tube  590 . 
       FIG.  5 G  illustrates a core having a third example spiral configuration (having a first insulative layer outside of the electrically conductive layer and a second insulative layer inside of the electrically conductive layer) that is part of a transformer of a pulse power drilling assembly, according to some embodiments.  FIG.  5 G  depicts a cross-sectional view of a core  562 , which can be an example of the cross-section of section line  4 - 4  of  FIG.  3   . The core  562  is similar to the core  550  of  FIG.  5 E  except for a second insulative layer (an insulative layer  555 ) that is positioned inside of the electrically conductive layer  552 . This is in addition to the insulative layer  551  that is positioned on the outside of the electrically conductive layer  552 . 
     The core  562  may be an embodiment of a core included as part of any of the transformers illustrated and described throughout this disclosure, and in any equivalents thereof. As shown in  FIG.  5 G , the core  562  may be formed in a tubular shape. The core  562  may circumferentially surround an outer surface of the flow tube  590 . The core  562  may encircle the longitudinal axis  558  of a tool body and may be spaced at a radial distance away from the longitudinal axis  558 . The tool body  591  encircles the core  562  at a radial distance away from the longitudinal axis that is greater than the distance between the longitudinal axis  558  and the flow tube  590 . 
     While  FIG.  5 A- 5 G  are described with respect to a core, the configuration of the core may be applied to other parts of the transformer, such as the outer tool body and the center flow tube. For example, in one embodiment the outer tool body may comprise a spiral configuration, as depicted in  FIG.  5 E . In this example embodiment, the spiral configuration of the outer tool body encircles the center flow tube and the core. In some embodiments, the center flow tube, the core, and the outer tool body may all exhibit a similar configuration. For example, each component may exhibit a spiral configuration as depicted in  FIG.  5 E . In other embodiments, the components may each have a different configuration. The configuration of the center flow tube, the core, and the outer tool body may exhibit any combination of configurations as depicted in  FIGS.  5 A- 5 G . Other possible configurations may also be used. 
     Example Operations 
       FIG.  6    depicts a flowchart of operations for powering a pulse power drilling assembly using a transformer, according to some embodiments. The pulse power drilling assembly may be substantially similar to the assembly of  FIG.  1   . The transformer may be substantially the same or similar to any of the transformers or portions of the transformer illustrated and described with respect to  FIGS.  1 - 5 C . Operations of a flowchart  600  of  FIG.  6    begin at block  601 . 
     At block  601 , a turbine and an alternator combination generates power in a pulse power drilling assembly, such as the assembly of  FIG.  1   . Drilling fluid from the surface flows through the drill string of the assembly to the turbine and alternator combination. The moving drilling fluid moves blades of the turbine which in turn imparts rotational energy to a rotor of the turbine. The turbine extracts the energy from the moving fluid and converts the energy into work. When the turbine is combined with a power generator, such as an alternator, the alternator convert the work into electrical power. The turbine may be an impulse turbine, a reaction turbine, or any other type of turbine. 
     At block  602 , a transformer (“transformer”) transforms the power generated by the turbine and alternator combination into a power that can be used by the electrodes of the assembly. The transformer may be the same or similar to any of the transformers described with respect to  FIGS.  2 - 5 C . The transformer includes a primary and secondary set of windings would around a center flow tube extending through the windings along a longitudinal axis of the tool. The primary windings and secondary windings have different inductances that allow the transformer to convert the power generated power from a lower voltage into a higher voltage. The secondary windings have a greater number of turns than the primary windings to step-up or increase the voltage. The ratio of turns between the primary and secondary windings partially determines the increase in voltage. The current in the primary windings also impacts the voltage. 
     The primary and secondary windings are wound around a core. When a voltage is applied to the primary windings, current flows through the primary windings which in turn generates a magnetic field that surrounds the primary windings according to Faraday&#39;s law of electromagnetic induction. The strength of the magnetic field builds as the current flow rises to its maximum value. As the magnetic field expands outward from the primary windings, the core forms a path for and concentrates a magnetic flux in response to the magnetic field. The magnetic flux links the turns of the primary and secondary windings. When the magnetic lines of flux flow around the core, they pass through the turns of the secondary windings, causing a voltage to be induced in the secondary windings. As a result, the total induced voltage in each winding is directly proportional to the number of turns in the secondary winding. However, the peak amplitude of the output voltage available on the secondary windings will be reduced if the magnetic losses of the core are high. Embodiments of the core described in  FIGS.  5 A-C  can be used to reduce the magnetic losses of the core. The electrical energy produced from the transformer is controllably stored in a second capacitor of the transformer. 
     At block  603 , the transformer transfers power to the electrodes of the assembly. A pulse power control unit electrically couples the transformer to the electrodes. The pulse power control unit further processes and controllably provides the electrical power from the transformer to the electrodes. The pulse power control unit extracts or releases the power sored in the second capacitor of the transformer to power the electrodes during pulse power drilling operations. 
     At block  604 , the electrodes emit the power into the formation. The electrodes emit a form of pulsed power plasma that deteriorates the formation surrounding the electrodes. The circulation of drilling fluid out of the assembly and back toward the surface removes any lose formation substance from the emission of power. This process of deteriorating the formation and removing the deteriorated substance from the borehole advances the drilling of the borehole. 
       FIG.  6    is annotated with a series of numbers. These numbers represent stages of operations. Although these stages are ordered for this example, the stages illustrate one example to aid in understanding this disclosure and should not be used to limit the claims. Subject matter falling within the scope of the claims can vary with respect to the order and some of the operations. 
     The flowcharts are provided to aid in understanding the illustrations and are not to be used to limit scope of the claims. The flowcharts depict example operations that can vary within the scope of the claims. Additional operations may be performed; fewer operations may be performed; the operations may be performed in parallel; and the operations may be performed in a different order. It will be understood that each block of the flowchart illustrations and/or block diagrams, and combinations of blocks in the flowchart illustrations and/or block diagrams, can be implemented by program code. The program code may be provided to a processor of a general-purpose computer, special purpose computer, or other programmable machine or apparatus. 
     As will be appreciated, aspects of the disclosure may be embodied as a system, method or program code/instructions stored in one or more machine-readable media. Accordingly, aspects may take the form of hardware, software (including firmware, resident software, micro-code, etc.), or a combination of software and hardware aspects that may all generally be referred to herein as a “circuit,” “module” or “system.” The functionality presented as individual modules/units in the example illustrations can be organized differently in accordance with any one of platform (operating system and/or hardware), application ecosystem, interfaces, programmer preferences, programming language, administrator preferences, etc. 
     Any combination of one or more machine readable medium(s) may be utilized. The machine-readable medium may be a machine-readable signal medium or a machine-readable storage medium. A machine readable storage medium may be, for example, but not limited to, a system, apparatus, or device, that employs any one of or combination of electronic, magnetic, optical, electromagnetic, infrared, or semiconductor technology to store program code. More specific examples (a non-exhaustive list) of the machine readable storage medium would include the following: a portable computer diskette, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or Flash memory), a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing. In the context of this document, a machine-readable storage medium may be any tangible medium that can contain or store a program for use by or in connection with an instruction execution system, apparatus, or device. A machine-readable storage medium is not a machine-readable signal medium. 
     A machine-readable signal medium may include a propagated data signal with machine readable program code embodied therein, for example, in baseband or as part of a carrier wave. Such a propagated signal may take any of a variety of forms, including, but not limited to, electro-magnetic, optical, or any suitable combination thereof. A machine readable signal medium may be any machine readable medium that is not a machine readable storage medium and that can communicate, propagate, or transport a program for use by or in connection with an instruction execution system, apparatus, or device. 
     Program code embodied on a machine-readable medium may be transmitted using any appropriate medium, including but not limited to wireless, wireline, optical fiber cable, RF, etc., or any suitable combination of the foregoing. The program code/instructions may also be stored in a machine readable medium that can direct a machine to function in a particular manner, such that the instructions stored in the machine readable medium produce an article of manufacture including instructions which implement the function/act specified in the flowchart and/or block diagram block or blocks. 
     Example Computer 
       FIG.  7    depicts an example computer for a pulse power drilling assembly with a transformer, according to some embodiments. A computer  700  includes a processor  701  (possibly including multiple processors, multiple cores, multiple nodes, and/or implementing multi-threading, etc.). The computer  700  includes a memory  707 . The memory  707  may be system memory or any one or more of the above already described possible realizations of machine-readable media. The computer  700  also includes a bus  703  and a network interface  705 . The computer  700  also includes a pulse power controller  711 . The pulse power controller  711  may perform operations as described in  FIG.  6   , and/or any of the other control operations, such as control of switching devices, as described throughout this disclosure and any equivalent thereof. Any one of the previously described functionalities may be partially (or entirely) implemented in hardware and/or on the processor  701 . For example, the functionality may be implemented with an application specific integrated circuit, in logic implemented in the processor  701 , in a co-processor on a peripheral device or card, etc. Further, realizations may include fewer or additional components not illustrated in  FIG.  7    (e.g., video cards, audio cards, additional network interfaces, peripheral devices, etc.). The processor  701  and the network interface  705  are coupled to the bus  703 . Although illustrated as being coupled to the bus  703 , the memory  707  may be coupled directly to the processor  701 . 
     While the aspects of the disclosure are described with reference to various implementations and exploitations, it will be understood that these aspects are illustrative and that the scope of the claims is not limited to them. In general, techniques for powering a pulsed power drilling assembly as described herein may be implemented with facilities consistent with any hardware system or hardware systems. Many variations, modifications, additions, and improvements are possible. 
     Plural instances may be provided for components, operations or structures described herein as a single instance. Finally, boundaries between various components, operations and data stores are somewhat arbitrary, and particular operations are illustrated in the context of specific illustrative configurations. Other allocations of functionality are envisioned and may fall within the scope of the disclosure. In general, structures and functionality presented as separate components in the example configurations may be implemented as a combined structure or component. Similarly, structures and functionality presented as a single component may be implemented as separate components. These and other variations, modifications, additions, and improvements may fall within the scope of the disclosure. 
     Example Embodiments 
     Embodiment 1: An apparatus comprising: a sub-section of a pulse power drilling assembly including a transformer encircling a center flow tube through which a drilling mud is to flow for drilling a borehole into a subsurface formation based on periodic pulses of electrical discharges from the pulse power drilling assembly, the transformer comprising, at least one primary winding that encircles the center flow tube; a core that encircles the at least one primary winding, wherein the core comprises an electrically non-conductive material; and at least one secondary winding that encircles the core. 
     Embodiment 2: The apparatus of Embodiment 1, wherein the transformer comprises a laminated tubular transformer. 
     Embodiment 3: The apparatus of Embodiment 1 or 2, wherein the transformer is to receive an electrical power at a first voltage and is transform the electrical power from the first voltage to a second voltage that is higher than the first voltage. 
     Embodiment 4: The apparatus of Embodiment 3, wherein the pulse power drilling assembly is to drill the borehole into the subsurface formation based on the periodic pulses of the electrical discharges are derived from the electrical power at the second voltage. 
     Embodiment 5: The apparatus of Embodiment 4, wherein the electrical power includes a level of current of at least 100 amperes. 
     Embodiment 6: The apparatus of any of Embodiments 1-5, wherein a length of the transformer is to extend along a longitudinal axis of the pulse power drilling assembly, wherein a length of the transformer is greater than a width of the transformer. 
     Embodiment 7: The apparatus of any of Embodiments 1-6, wherein a length of the transformer is to extend along a longitudinal axis of the pulse power drilling assembly, wherein a length of the transformer is at least five times greater than a width of the transformer. 
     Embodiment 8: The apparatus of any of Embodiments 1-7, wherein the transformer is housed in a conductive casing of the pulse power drilling assembly. 
     Embodiment 9: A method comprising: drilling a borehole into a subsurface formation based on periodic pulses of electrical discharges emitted from a pulse power drilling assembly into the subsurface formation, wherein the drilling comprises, flowing a drilling mud through a center flow tube of the pulse power drilling assembly; transforming, using a transformer in the pulse power drilling assembly, power from a first voltage to a second voltage that is higher than the first voltage, wherein the transformer comprises at least one primary winding that encircles the center flow tube, a core that encircles that encircles the at least one primary winding, and at least one secondary winding that encircles the core, wherein the core comprises an electrically non-conductive material; and transferring the power periodically to electrodes of the pulse power drilling assembly; and emitting, from the electrodes, the periodic pulses of the electrical discharges into the subsurface formation based on the power. 
     Embodiment 10: The method of Embodiment 9, wherein the transformer comprises a laminated tubular transformer. 
     Embodiment 11: The method of Embodiment 9 or 10, wherein the power includes a level of current of at least 100 amperes. 
     Embodiment 12: The method of any of Embodiments 9-11, wherein a length of the transformer is to extend along a longitudinal axis of the pulse power drilling assembly. 
     Embodiment 13: The method of Embodiment 12, wherein a length of the transformer is greater than a width of the transformer. 
     Embodiment 14: The method of Embodiment 12, wherein a length of the transformer is at least five times greater than a width of the transformer. 
     Embodiment 15: A system comprising: a pulse power drilling assembly to be positioned in a borehole formed in a subsurface formation, the pulse power drill assembly to drill the borehole based on periodic pulses of electrical discharges into the subsurface formation, the pulse power drilling assembly comprising, a center flow tube to through which a drilling mud is to flow for drilling the borehole; at least one primary capacitor to store electrical power at a first voltage, wherein, after at least one discharge criteria is satisfied, the at least one primary capacitor is to discharge the electrical power at the first voltage; a transformer coupled to the at least one primary capacitor and encircling the center flow tube, wherein the transformer comprises, at least one primary winding; a core encircling the at least one primary winding, wherein the core comprises an electrically non-conductive material; and a secondary winding encircling the core, wherein the transformer is to transform the electrical power from the first voltage to a second voltage that is higher than the first voltage; and at least one electrode to output a pulse of the periodic pulses of the electrical discharges into the subsurface formation based on the electrical power transformed to the second voltage. 
     Embodiment 16: The system of Embodiment 15, wherein the transformer comprises a laminated tubular transformer. 
     Embodiment 17: The system of Embodiment 15 or 16, wherein the electrical power includes a level of current at least greater than 100 amperes. 
     Embodiment 18: The system of any of Embodiments 15-17, wherein a length of the transformer is to extend along a longitudinal axis of the pulse power drilling assembly, wherein a length of the transformer is greater than a width of the transformer. 
     Embodiment 19: The system of any of Embodiments 15-18, wherein a length of the transformer is to extend along a longitudinal axis of the pulse power drilling assembly, wherein a length of the transformer is at least five times greater than a width of the transformer. 
     Embodiment 20: The system of any of Embodiments 15-19, wherein the pulse power drilling assembly comprises a conductive casing encasing the center flow tube, the at least one primary capacitor, the transformer, and the at least one electrode. 
     Use of the phrase “at least one of” preceding a list with the conjunction “and” should not be treated as an exclusive list and should not be construed as a list of categories with one item from each category, unless specifically stated otherwise. A clause that recites “at least one of A, B, and C” can be infringed with only one of the listed items, multiple of the listed items, and one or more of the items in the list and another item not listed.