The ESP power cable transmits the required surface power to the ESP motors. Typically, it is banded or clamped to the production tubing from below the wellhead to the ESP unit because it is not designed to support its own weight. It is a specially constructed three-phase power cable designed specifically for downhole well environments.
The cable design must be small in diameter, protected from mechanical abuse, and impervious to physical and electrical deterioration because of aggressive well environments. They are available in a wide range of conductor sizes or gauges. They can be manufactured in either round or flat configurations, using several different insulation and metal armor materials for different hostile well environments. Cross-sectional views of flat and round cable construction are shown in Figs. 1 and 2. There are two very good documents that fully describe the design, application, and testing of ESP submersible power cables—API RP11S5 and RP11S6.  This page will repeat some of the basic information and add supplemental information.
Conductors are copper wires that can be either a single solid configuration or multiple smaller strands. Solid conductors offer more advantages than their stranded counterpart. They are smaller, easier to clean and splice, do not adsorb gases, have a smoother surface to the insulation, which reduces electrical stress, and they are less expensive. Stranded cable offers more mechanical flexibility, but this is usually not an over-riding benefit. Also, unless the voids in the strand are filled, gases can migrate up or down the cable more easily.
The copper conductor is generally tinned or coated with a tin/lead alloy when it is insulated with polypropylene. In certain well environments, direct contact between copper and polypropylene can cause "copper poisoning" of the insulation, which reduces its electrical strength and degrades its physical properties. Synthetic-rubber insulation does not react with copper, so the vast majority of all rubber-insulated ESP cables are made with bare copper conductors.
There are two basic types of insulation used in ESP cable: polypropylene and ethylene propylene diene monomer (EPDM) synthetic rubber. Polypropylene or "poly" is the lower-temperature-rated insulation, a tougher material than rubber, and generally more cost effective. The insulation temperature rating for poly is 205°F (96°C), but it can be increased to 225°F (107°C) with the addition of an extruded protective layer of lead.  Above these temperatures, a rubber insulation is always required. The EPDM is the insulation of choice for synthetic-rubber-insulation cables. The compounding of the rubber, with more than twenty other ingredients, allows for it to be designed to have low oil swell, fairly low elongation, and a high modulus. By contrast, the EPDM formulated for surface power cable is not suitable for downhole oilwell service because of its excessive swell characteristic. Most high-quality EPDM-based insulation is rated for conductor temperatures up to 450°F (232°C). 
The EPDM-insulated conductors need protection from the oilwell environment because of swelling in the oil. To provide protection from the oil and to control swelling, different types of protective layers are applied over the insulation. Starting from the lowest level of protection to the highest, these layers are discussed next.
Tapes and braids. Thin tapes of polyvinyl fluoride are wrapped over the EPDM-insulated single conductors. The limitation of the tape is that it has an overlap that allows oil to seep through. To make the tapes more effective, a 50% overlap can be used. To add some additional containment, braids can be put over the tape. Common braid materials are nylon and polyester, which have temperature limits in water of about 250°F (121°C). More expensive engineered filaments can be used to extend this temperature rating to 300 to 400°F (149 to 205°C).
Extruded barrier. The next level of protection is a continuous extrusion of a high-temperature plastic layer over the insulation. The extruded barrier has no overlaps to let the oil contact the insulation. In addition, it increases the electrical strength of the insulation system. It also increases the chemical resistance of the cable, and in gassy wells, it regulates the rate of decompression of wellbore gases that have saturated into the insulation. Extruded barriers are made from fluoropolymers, such as polyvinylidene fluoride (PVDF) rated up to 320°F (160°C) and fluorinated ethylene propylene (FEP) (Teflon®) rated up to 400°F.
Lead barrier. In wells that have a damaging amount of hydrogen sulfide gas, the copper conductors can be attacked and destroyed. To protect against this, a thin layer of lead is extruded over the insulation. For poly insulation, the lead increases the maximum operating temperature of the cable. For EPDM insulation, fabric tape or a braid is placed over the lead as a manufacturing aid to minimize distortion of the lead during armoring. This step is not required for poly, because it is harder and more difficult to distort during the armoring process. Generally, lead cables are manufactured in flat configurations but can be made in round configurations for added containment and protection.
The jacket is designed to protect the insulation from physical damage. Also, in round cables, the jacket fills the space between the insulated conductors and the inside of the armor so that the armor can effectively contain the whole cable from oil and decompression swelling. Typical jacket materials include nitrile and EPDM rubber. Nitrile rubber has an operating temperature of 280°F (138°C) and is very resistant to oil swelling. As discussed above, the EPDM rubber’s properties can be varied by its compounding but is rated up to 400°F (205°C), and it swells in oil.
The metal armor that is wound around the three insulated conductors (flat cable) or the jacketed conductors (round cable) has a primary function of providing mechanical protection to the insulated conductors. On round cable, it has the added function of providing additional containment protection for oil swelling and gas decompression. The armor is usually made of mild galvanized steel, which is applicable to non- to mildly-corrosive wells. The galvanized armor is usually offered in several thicknesses, which increases the mechanical and corrosion protection. In more-corrosive applications, specialty metals are available, such as stainless steel and other alloys.
The typical construction and geometry of the ESP flat power cable is shown in Fig. 1. It has the three insulated conductors laying parallel with armor wrapped around them, providing a lower profile when the clearance between the casing inside diameter (ID) and production-tubing outside diameter (OD) is limited. Flat cable is not suitable for containing oil swell or gas decompression forces because of the interstices between the single conductors. If the insulation or jacket expands on a flat cable, it will deform the armor, bending it apart over its long axis and allowing the conductors to slide over one another. Insulation and jacket expansion can cause insulation splitting, leading to potential electrical failure. Flat cables, by virtue of their parallel conductor configuration, have an inherently induced imbalance. Flat-cable induced voltage and current imbalance is usually not a practical consideration in lengths less than 10,000 ft, unless the well is very hot and is pushing the thermal limits of the motor.
Round cable is superior to flat cable because it provides more protection to the conductors. Its typical construction and geometry are shown in Fig. 2. Round cable provides superior containment to the cable core, enabling it to better withstand decompression and oil swell forces without damage. Because pressure is naturally contained in a round shape and the space between the insulation and the inside of the cable armor is filled with jacket material, the cable armor acts to restrain and prevent any insulation expansion because of oil swell or gas-decompression expansion. Round cable is also naturally impedance balanced because of the equidistant spacing between the conductors. Therefore, there are no voltage or current imbalance issues affecting the motor.
The motor lead extension cable, also referred to as the motor flat, is a specially constructed, low-profile, flat cable. It is spliced to the lower end of the round or flat main power cable, banded to the side of the ESP pump and seal-chamber section, and has the male termination for plugging or splicing into the motor electrical connection. Because of its need for low profile, it requires compact construction. It generally has a thin layer of high-dielectric-strength polyamide material wrapped or bonded directly to the copper conductors. This allows for a thinner layer of insulation material, allowing for a lower profile. The MLE is generally selected on the basis of equipment: casing clearance and the voltage capacity requirement.
The cable materials for the wellbore application should be selected from the guidelines already provided and by the cable manufacturer. These guidelines include:
Insulation up to 205°F (96°C) uses polypropylene insulated cables. Over 205°F and up to 450°F (232°C), it utilizes synthetic rubber insulated cables.
Gassy wellbores use a cable that provides protection from decompression damage. This is a construction that adds hoop strength to the insulation to contain the insulation from expanding and rupturing. Generally, tapes and braids, as well as extruded barriers, provide this protection.
Hydrogen sulfide (H2S)—generally lead barrier cables are used to protect the copper conductor from damage.
Once the proper cable materials have been determined for the wellbore environment, the only remaining variable is the conductor size. The conductor size can be optimized on the basis of motor voltage/amperage rating and the casing clearance. Because there are several motor voltage/amperage combinations available for the HP required for the application, the selection of the cable to match the motor can be based on either the surface switchgear and transformer available or the most favorable economic evaluation. The testing methods and acceptance criteria are discussed and provided in Standard 1018, Recommended Practice for Field Testing Electric Submersible Pump Cable.