Abstract:
Induction motor stator windings are described. An electric submersible pump apparatus comprises an induction motor rotatably coupled to a multi-stage centrifugal pump, the induction motor comprising a stator frame, the stator frame comprising a plurality of slots, and a squircle-shaped magnet wire windingly inserted into the plurality of slots, the magnet wire comprising a conductor comprising a squircular-shaped cross-sectional area, and an insulation layer coating an outer surface of the squircular-shaped conductor.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application claims the benefit of U.S. Provisional Application No. 61/862,326 to Hall et al., filed Aug. 5, 2013 and entitled “SYSTEM AND METHOD FOR OPTIMIZING SLOT FILL PERCENTAGE IN ELECTRIC MOTOR STATOR FRAMES,” which is hereby incorporated by reference in its entirety. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     Embodiments of the invention described herein pertain to the field of electric motors. More particularly, but not by way of limitation, one or more embodiments of the invention enable induction motor stator windings. 
     2. Description of the Related Art 
     Electric motors convert electrical energy into mechanical energy to produce linear force or torque and are used in many applications requiring mechanical power, such as pumps, power tools, household appliances and ship propulsion units. In the case of an electric submersible pump (ESP), for example, a two-pole, three phase, squirrel cage induction motor is typically used to turn a centrifugal pump for purposes of lifting fluid to the surface of a well. These electric motors include a stationary component known as a stator, and a rotating component known as the motor shaft. In ESP applications, the stator is energized by a power source located at the well surface and connected to the stator with an electric cable. The electricity flowing through the stator windings causes a magnetic field, and the motor shaft rotates in response to the magnetic field created in the energized stator. 
     The stator windings are a composition of stator laminations, magnet wire and one or more types of insulating material. Thin steel laminations are pressed together inside the stator housing. These laminations contain a series of insulated slots that allow magnet wire to be strung from one end of the stator to the other in a pattern that, when energized, creates the magnetic field. The magnetic field produced by the stator windings is a function of the amount of steel laminations in the stator, the type of steel utilized in the manufacture of the laminations, the quality of the insulation on the slots and on the magnet wire, and the amount of conductive material in the magnet wire that is woven into the slots. 
     Typically, conventional magnet wire includes a conductive material, such as copper or aluminum, which conductor is surrounded by a layer of insulating material, such as a polyimide film or a thermoplastic with high dielectric capabilities. Magnet wire is conventionally round in cross section and is available in several different wire gauge sizes. The gauge size (or diameter of the wire), and the number of times that the wire passes through the lamination stack dictate how much conductive material in the magnet wire is included in the stator winding. The more conductive material included in the stator winding, the better the magnetic field. 
       FIG. 1  illustrates a cross section of a conventional stator slot that contains windings of conventional round magnet wire. As shown in  FIG. 1 , the conventional slot contains empty space that is not filled by insulation or the magnet wire. The “slot fill” refers to the amount of space in the lamination slots that are occupied by wire or insulating materials, and is usually expressed as a percentage of the available slot area. If the slot fill percentage is too low, the quantity of conductive material from magnet wire will be low. This may cause the magnetic field created by the motor to suffer, and the motor may not operate efficiently or fail to perform as desired. On the other hand, care must be taken not to wind the wire too tightly in the slots. Doing so can cause damage to the wire in the winding process. 
     Currently, induction motor stator windings are not optimized, since inserting a series of round wires into a slot leaves an excessive amount of empty space in the slot, at least a portion of which could otherwise be filled with conductive material. Therefore, there is a need for additional induction motor stator windings. 
     BRIEF SUMMARY OF THE INVENTION 
     One or more embodiments of the invention enable induction motor stator windings. 
     Electric motor stator windings are described. In combination with an electric submersible pump system of the type wherein an induction motor is provided to operate a multi-stage centrifugal pump so as to turn the centrifugal pump, wherein the induction motor includes a stator frame and at least one slot in the stator frame, the improvement of an illustrative embodiment comprises a squircle-shaped magnet wire windingly inserted into the at least one slot to create a winding configuration, the magnet wire comprising a conductor with approximately a squircular cross-sectional shape, and an insulation layer coating an outer surface of the conductor, wherein a slot fill percentage of the at least one slot in the stator frame containing the squircular-shaped magnet wire in the winding configuration is at least 10% greater than a slot fill percentage of the at least one slot containing a round wire of about the same diameter in the winding configuration. 
     An illustrative embodiment of a magnet wire for an induction motor comprises a squircle-shaped magnet wire, the magnet wire comprising a copper wire comprising a squircular cross-sectional area, and an insulative coating fixedly coupled to an outer surface of the copper wire, the insulative coating forming a squircular-shaped surface of the magnet wire. In some embodiments, the magnet wire is windingly wrapped into at least one slot in a stator frame to form a stator winding. 
     An illustrative embodiment of an electric submersible pump apparatus comprises an induction motor rotatably coupled to a multi-stage centrifugal pump, the induction motor comprising a stator frame, the stator frame comprising a plurality of slots, and a squircle-shaped magnet wire windingly inserted into the plurality of slots, the magnet wire comprising a conductor comprising a squircular-shaped cross-sectional area, and an insulation layer coating an outer surface of the squircular-shaped conductor. 
     The induction motor of the system of an illustrative embodiment may comprise a variety of types of motors known in the art for use as electric submersible motors. For example, a three phase “squirrel cage” induction motor well known in the art, as well as wound type motors. Both these and other motors suitable for use with an ESP assembly may benefit from the induction motor stator windings of illustrative embodiments. 
     In further embodiments, features from specific embodiments may be combined with features from other embodiments. For example, features from one embodiment may be combined with features from any of the other embodiments. In further embodiments, additional features may be added to the specific embodiments described herein. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The above and other aspects, features and advantages of the invention will be more apparent from the following more particular description thereof, presented in conjunction with the following drawings wherein: 
         FIG. 1  is a stator slot containing conventional magnet wire windings of the prior art. 
         FIG. 2A  illustrates a cross sectional view taken along line  2 A- 2 A of  FIG. 3  of an ESP motor containing a number of slots comprising the magnet wire of illustrative embodiments. 
         FIG. 2B  shows an enlarged single slot of  FIG. 2A  comprising exemplary squircular magnet wire. 
         FIG. 2C  shows a cross sectional view taken along line  2 C- 2 C of  FIG. 2B  illustrating an exemplary magnet wire. 
         FIG. 2D  illustrates a single slot comprising exemplary triangular magnet wire. 
         FIG. 3  illustrates an exemplary three-phase induction motor for use in one or more embodiments of the system of the invention. 
         FIG. 4  is an elevation view of an exemplary electric submersible pump (ESP) assembly deployed underground, the ESP assembly comprising an induction motor including the magnet wire of an illustrative embodiment. 
         FIG. 5  is a flowchart illustrating an exemplary method of optimizing the slot fill percentage in induction motor stator windings. 
         FIG. 6A  is a cross sectional view of a squircular wire of an illustrative embodiment. 
         FIG. 6B  is a cross sectional view of a squircular wire of the rounded square type of an illustrative embodiment. 
         FIG. 6C  is a cross sectional view of an illustrative embodiment of a square wire. 
         FIG. 6D  is a cross sectional view of a rectircle wire of an illustrative embodiment. 
         FIG. 6E  is a cross sectional view of a triangular wire with rounded corners of an illustrative embodiment. 
         FIG. 7  illustrates a single slot comprising exemplary squircular wire of an illustrative embodiment. 
     
    
    
     While the invention is susceptible to various modifications and alternative forms, specific embodiments thereof are shown by way of example in the drawings and may herein be described in detail. The drawings may not be to scale. It should be understood, however, that the drawings and detailed description thereto are not intended to limit the invention to the particular form disclosed, but on the contrary, the intention is to cover all modifications, equivalents and alternatives falling within the spirit and scope of the present invention as defined by the appended claims. 
     DETAILED DESCRIPTION 
     Induction motor stator windings will now be described. In the following exemplary description, numerous specific details are set forth in order to provide a more thorough understanding of embodiments of the invention. It will be apparent, however, to an artisan of ordinary skill that the present invention may be practiced without incorporating all aspects of the specific details described herein. In other instances, specific features, quantities, or measurements well known to those of ordinary skill in the art have not been described in detail so as not to obscure the invention. Readers should note that although examples of the invention are set forth herein, the claims, and the full scope of any equivalents, are what define the metes and bounds of the invention. 
     As used in this specification and the appended claims, the singular forms “a”, “an” and “the” include plural referents unless the context clearly dictates otherwise. Thus, for example, reference to a wire includes one or more wires. 
     As used in this specification and the appended claims, the cross section of a wire refers to a cross section taken at a right angle to the length of the wire. 
     As used in this specification and the appended claims, reference to a “shape” of a wire, means the cross-sectional shape unless the context clearly dictates otherwise. 
     There are two known, yet incompatible, mathematical definitions of a squircle. As used in this specification and the appended claims, a “squircle” or “squircular” shape means approximately a mathematical shape with properties between those of a square and those of circle characterized by the equation x 4 +y 4 =r 4 , in a Cartesian coordinate system with the squircle centered at the origin of the x and y axis, where r is the radius of the squircle. In this definition, a squircle is a special case of a superellipse, with a=b (the semi-major and semi-minor axes are equal). The area of the squircle, as used herein, is defined by the equation: 
               A   =       8   ⁢     r   2     ⁢       Γ   ⁡     (     5   4     )       2         π         ,         
which may be approximated as: A=3.70815r 2 .
 
     As used herein, a “rectircle” is the rectangular counterpart to a squircle. 
     As used herein, a square has a comparably sized diameter to a circle when a length of a side of the square is equal to the diameter of the circle. 
     “Coupled” refers to either a direct connection or an indirect connection (e.g., at least one intervening connection) between one or more objects or components. The phrase “directly attached” means a direct connection between objects or components. 
     One or more embodiments of the invention provide induction motor stator windings for use in electric submersible pump (ESP) applications. While the invention is described in terms of an oil or gas pumping embodiment, nothing herein is intended to limit the invention to that embodiment. 
     The system of the invention comprises an electric submersible pump (ESP) assembly.  FIG. 4  illustrates an exemplary ESP assembly  400  arranged underground to pump gas or oil and making use of the induction motor stator windings of illustrative embodiments. As illustrated, ESP assembly  400  comprises a multistage centrifugal pump  420  to lift well fluid to the surface through production string  410 . Fluid enters the centrifugal pump  420  through ESP intake  430 , which intake  430  may be bolted-on or integral to the centrifugal pump  420 . In order to function properly, electrical motor  300  must be protected from well fluid ingress, and seal section  440  provides a fluid barrier between the well fluid and motor oil. Motor oil resides within seal section  440 , which is kept separated from the well fluid. In addition, seal section  440  supplies oil to electrical motor  300 , provides pressure equalization to counteract expansion of motor oil in the well bore and carries the thrust of centrifugal pump  420 . Downhole sensors  460  may allow an operator to monitor the operation of electrical motor  300 , for example the temperature and/or speed of electrical motor  300  utilizing magnet wire  220 . Casing sizes for the ESP assembly illustrated may range from about 4.5 inches to 9 inches outer diameter, though the invention is not limited to these exemplary embodiments. A power cable (not shown) may connect motor  300  to a power source near the surface of the well. 
     The ESP system of an illustrative embodiment may comprise electrical motor  300 . In some embodiments, electric motor  300  may be a three phase “squirrel cage” induction motor or a wound type motor used in the system of the invention to enhance the advantages of the stator windings of illustrative embodiments employing magnet wire  220  (shown in  FIG. 2B ). An illustrative embodiment of electric motor  300  is shown in  FIG. 3 . As shown in  FIG. 3 , electric motor  300  may include stator frame  310 . Stator frame  310  may be comprised of steel laminations and include bore  330  to accommodate the rotating member (shaft) of motor  300 . In some embodiments, magnet wire  220  may be hand-wound on motor  300  or the winding may be automated. Motor  300  of the system of illustrative embodiments may operate from 15 to 1,000 horsepower, though the invention is not limited to this example. End coils  340  and main lead wire  350  are also shown. Main lead wire  350  connects to a power cable for motor  300 , to energize stator frame  310 . 
     Stator frame  310  comprises a plurality of steel slots  200 , as shown in  FIG. 2A . Slots  200  may be insulated as is well known to those of skill in the art. Slots  200  include wire windings of one or more magnet wire  220  shown in  FIGS. 2A-2C . As illustrated in  FIG. 2B , the cross-sectional area of magnet wire  220  passed through slot  200  is squircular shaped. Squircular shaped magnet wire  220  is also illustrated in  FIG. 6A . Squircular shaped magnet wire  220  of the rounded square type is illustrated in  FIG. 6B . In other embodiments, magnet wire  220  wire may be square, as illustrated in  FIG. 6C , rectircle shaped as illustrated in  FIG. 6D , or equilateral triangle in shape with rounded corners, as illustrated in  FIG. 2D  and  FIG. 6E . Magnet wire  220 , as illustrated in  FIGS. 6A-6E , is comprised of conductor  250  and insulation. In illustrative embodiments, conductor  250  may be shaped in the form of the selected shape (i.e., squircle, rectircle, square), and insulative layer  230  may take the shape of underlying conductor  250 . In the example shown in  FIGS. 2A-2C , conductor  250  is squircle shaped, and insulation layer  230  includes a squircle-shaped surface area that maintains the squircle shape of conductor  250  and/or magnet wire  220 . 
     In some embodiments, for example squircle, rectircle, squircle of the rounded square type, or triangular, corner  245  of magnet wire  220  may be rounded. Rounding the corners of magnet wire  220  may reduce stresses on the wire insulation and reduce the overall profile of wire  220 . A quadrilateral shape such as a square, or a triangle, may include sharp corners that may pierce or wear away magnet wire  220 &#39;s insulation. Rounding corners  245  may reduce the sharpness of corner  245 , protecting wire insulation  230  from damage. In addition, rounded corners  245  may protect wire insulation  230  from wear during the winding process. Rounded corners  245  may provide just enough space to avoid damage to magnet wire  220  whilst still increasing slot fill as compared to a round wire. 
       FIG. 2C  shows a cross section across line  2 C- 2 C of  FIG. 2B  of magnet wire  220 . As shown in  FIGS. 2B and 2C , conductor  250  is squircle shaped and encased in insulation  230 . In some embodiments, conductor  250  may be copper or aluminum, for example copper wire or aluminum wire. Insulation  230  may be polyimide tape, extruded polymer thermoplastic, other wire insulation well known to those of skill in the art, or a combination of one or more layers of any of the foregoing.  FIGS. 6A-6E  show additional embodiments of magnet wire  220  with conductor  250  and insulation  230 . 
     Magnet wire  220  of illustrative embodiments substantially increases the slot fill percentage of electric induction motor  300 , as compared to the slot fill percentage of a motor having identical slots, and the same number of turns per slot, but making use of a conventional round wire. The increase in slot fill percentage may be illustrated with the following conceptual example: 
     The slot fill of slot  200 , expressed as a percentage, may be represented with the formula: 
               SF   =         A   ×   N     S     ×   100       ;         
where SF is the slot fill percentage, A is the cross sectional area of the wire, N is the of number of turns in slot  200 , and S is the area of slot  200 . Thus, if one were to take a slot including turns of a conventional round wire, the slot fill percentage of such a slot may be expressed as:
 
                 SF   Round     =             π   ⁢           ⁢     d   2       4     ×   N     S     ×   100       ;         
where SF is the slot fill percentage, d is the diameter of the wire, N is the number of turns in the slot and S is the area of slot  200 .
 
     If one were to take slot  200 , including turns of magnet wire  220  where magnet wire  220  is a square, the slot fill percentage of such a slot may be expressed as: 
                 SF   Square     =           d   2     ×   N     S     ×   100       ;         
where SF is the slot fill percentage, d is the length of a side of square magnet wire  220 , N is the number of turns in the slot and S is the area of slot  200 .
 
     Thus for a given slot area, and a number of turns, N, and where the diameter of a round wire is the same as the length of a side of a square magnet wire  220 , the percentage increase in slot fill by moving from a conventional round wire to square magnet wire  220  of comparable diameter may be expressed as: 
     
       
         
           
             
               
                 ( 
                 
                   
                     
                       SF 
                       Square 
                     
                     
                       SF 
                       Round 
                     
                   
                   - 
                   1 
                 
                 ) 
               
               × 
               100 
             
             = 
             
               27.32 
               ⁢ 
               % 
             
           
         
       
     
     The calculation for percent increase in slot fill by moving from a circle to a squircle may be approximated in much the same way. The cross sectional area, A, of a squircular wire may be approximated as: 
     A=3.70815 r 2 , while that of a circle is A=πr 2 . As 3.70815 is greater than it (approximately 3.14159.), the cross-sectional area of a squircle of radius r is greater than the cross-sectional area of a circle of radius r by approximately 18%. Thus, the percentage increase in slot fill by moving from a conventional round wire to a squircular wire of same diameter is about 18%. 
     An increase in slot fill percentage translates into a greater amount of space in the slot being filled by conductive wire as opposed to empty space. Thus, as illustrated by the previous example, the use of the same number of turns in a stator slot configuration, such as the slot configuration of slot  200  illustrated in  FIG. 2B , when square, squircular, squircular of the rounded square type, or rectircle magnet wire  220  of comparable diameter is utilized, increases the amount of conductor  250  (e.g., copper or aluminum) in a given slot  200  where round wire has conventionally been utilized. This additional amount of conductor  250  can substantially improve the performance of stator frame  310  by improving the ratio of conductor  250  to steel in stator frame  310 ; the steel creating the magnet field that is responsible for the rotational force of electric motor  300  once stator frame  310  is energized. More conductor  250  in slot  200  may achieve the same horsepower with a shorter stator frame  310  or make the same stator frame  310  have higher horsepower. 
     In the illustrated example, the increase in slot fill percentage is about 25% for a square wire and 18% for a squircle wire, although not all of the increase is attributable to additional conductor  250 , since wire insulation  230  also takes up space in slot  200 . Other increases in slot fill percentage are also contemplated depending upon the shape of a cross section of magnet wire  220 , which may be square, squircle, squircle of the rounded corner type, rectangular, rectircle, trapezoidal, a parallelogram, triangular or other four-sided or poly-sided shape (for example a pentagon or octagon), and which may have rounded corners  245 . In triangular embodiments, the triangle may be equilateral, isosceles or scalene type. In some embodiments, the increase in slot fill percentage may be between about 10% and about 20%. 
     The previously discussed examples of slot fill percentage have assumed that in replacing a traditional round wire with differently shaped magnet wire  220  of comparable diameter, the number of turns in slot  200  remains constant. However, depending upon the selected shape of magnet wire  220 , and the type of winding method employed, the number of turns in slot  200  may also be increased due to the more efficient nesting of magnet wire  220  in slot  200  with respect to adjacent magnet wires  220 . For example, as shown in  FIG. 2D , triangular magnet wire  220  may be wound in slot  200  with less empty space in between adjacent magnet wires  220  than with round wire. Additional turns in slot  200  may also contribute to increasing slot fill percentage by increasing the amount of conductor  250  in slot  200 . This increase may come at the expense of higher resistance due to the longer length of the wire—although in many embodiments the gain in efficiency from additional conductor material may outweigh any losses due to resistance. 
     In other embodiments, slot fill percentage may be increased despite a reduction in the number of turns per slot  200 , due to the substantial gain in cross-sectional area of conductive material in slot  200 , while also reducing the resistance, because the wire has greater cross sectional area and so can carry more current, and yet is shorter due to the ability to use a reduced number of turns. These benefits are achieved through the use of magnet wire  220  of illustrative embodiments in place of traditional round wire. 
     In yet another example, squircular magnet wire  220  may be used in place of traditional circular wire in slot  200 . However, instead of keeping the diameter of squircular magnet wire  220  the same as traditional circular wire for the replacement, the cross sectional areas may be maintained for the replacement. In such an instance, more turns of squircular magnet wire  220  may fit in slot  200  due to differences in nesting of the squircular shape. Such an example is illustrated in  FIG. 7 . As shown in  FIG. 7 , thirty-one turns of squircular magnet wire  220  fit into slot  200 , where only about twenty-one turns of conventional round magnet wire of the same cross-sectional area would fit. Such an arrangement may be beneficial, for example in high temperature applications to combat wire insulation decay. In this example, there may be as much as a 40% gain in conductor  250  cross-sectional area in slot  200 . 
     The run life of an ESP system may be directly related to the quality and reliability of the power cable. Power cables for the system of the invention may be round or flat and configured to function in temperatures ranging from around −60° F. to about 450° F. Power cables of the system should provide extreme durability and reliability in conditions including resistance to decompression and fatigue with corrosion-resistant barriers that resist fluids and gas. Cables manufactured to ISO 9001 standards may be preferred in one or more embodiments of the invention. 
       FIG. 5  illustrates one or more methods of making magnet wire  220  for use in stator frame  310  of motor  300  of an ESP assembly. At step  100 , conductor  250  may be drawn to size and the selected shape (e.g., a squircle or square), annealed and cleaned using methods known in the art. In some embodiments, the corners of the shaped conductor  250  may be separately rounded at step  105 , for example in the instance the rounding has not previously been completed during step  100 . 
     In one example, if a squircle-shaped wire is selected, conductor  250  may be drawn in the shape of a square at step  100 . In such an example, at step  105 , the corners of conductor  250  may be rounded to create a squircle-shape conductor  250 . Rounding the corners may be accomplished by pulling conductor  250  through a series of progressively smaller dies until the desired rounded-corner shape has been reached. In instances where the corners are rounded at step  100  and/or in instances where a square shape has been selected, for example, step  105  may not be necessary. In another example, conductor  250  may be drawn to a squircle shape at step  100  and step  105  is not necessary. 
     At step  110 , conductor  250  may insulated. In some embodiments, conductor  250  may be pulled through a polyimide film (tape) wrap machine to wrap conductor  250  with insulation  230 . The polyimide tape may contain adhesive on its surface or the adhesive may be separately applied. This adhesive makes contact with the conductor  250  and may be heat activated, providing a bond to the wire. Using such a method, insulation  230  would take the quadrilateral or triangular shape of conductor  250 . One type of polyimide tape that may be used is poly(4,4′-oxydiphenylene-pyromellitimide), also known as Kapton®. Various types of polyimide tape may be suitable, such as Kapton® tape types FN, HN and HPP-ST, for example. Other polyimide tapes having similar chemical properties may also be used. In some embodiments, conductor  250  may be drawn through an extrusion mold (die) to apply an organic polymer thermoplastic, such as molten PEEK (polyetheretherketone) as insulation  230 . Other organic polymers thermoplastics having similar chemical properties as PEEK may also be employed. In embodiments where insulation  230  is PEEK, the PEEK die forces the molten organic polymer thermoplastic around the conductor  250 , also maintaining the selected quadrilateral or triangular shape. In certain embodiments, multiple layers of insulation  230  may be used, such as a layer of polyimide film surrounded by a layer of PEEK to form magnet wire  220  in a squircle, square, rectircle, square with rounded corners or other shape as described herein. 
     At step  120 , magnet wire  220  may now be wound onto motor  300  in a conventional fashion and used for ESP applications. In preferred embodiments, needle winding may be employed to prevent twist, undulation and drift of magnet wire  220  during winding. Needle winding may also assist in preventing rub or friction defects in insulation  230 . In other embodiments, machine random winding may be employed. In some embodiments, magnet wire  220  may be triangular in shape or triangular with rounded corners, as illustrated in  FIG. 2D  and  FIG. 6E . A triangular wire or triangular wire with rounded corners may be less likely to bend during winding since triangular wire may withstand more downward force for the same cross sectional area as a round wire. 
     When combined into a system with a three-phase induction, wound type or other motor for ESP applications, the magnet wire of illustrative embodiments optimizes the slot fill percentage of stator frames and creates an improved system and method for oil or gas well production. Other motors suitable for ESP applications may also be used as part of the system of the invention. 
     While the invention herein disclosed has been described by means of specific embodiments and applications thereof, numerous modifications and variations could be made thereto by those skilled in the art without departing from the scope of the invention set forth in the claims. The foregoing description is therefore considered in all respects to be illustrative and not restrictive. The scope of the invention is indicated by the appended claims, and all changes that come within the meaning and range of equivalents thereof are intended to be embraced therein.