Lane Coburn & Associates, LLC. 
"Working With The Design Team To Provide The Client With Superior Design, Value Engineering And Constructability." 
12900 NE 180th Street, Suite 201 
Bothell, Washington 98011 
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"Working With The Design Team To Provide The Client With Superior Design, Value Engineering And Constructability." LANE COBURN & ASSOCIATES Home LANE COBURN & ASSOCIATES Profile LANE COBURN & ASSOCIATES Resume LANE COBURN & ASSOCIATES Services LANE COBURN & ASSOCIATES Referrals Certifications/Memberships: RCDD, LC, LEED, IESNA, NFPA, WSSHE, 7x24 Prof. Lic: Washington, Alaska, California, Hawaii, Oregon, Idaho, Montana, Arizona, Utah, Nevada, Pennsylvania, Virginia ©Lane Coburn & Associates, LLC. 4253684848 Keith Lane, P.E., RCDD/NTS, TPM, LC, IESNA, LEED A.P., President/Chief Engineer Scott Coburn  Principal / Partner
Lane Coburn & Associates, LLC. is an electrical engineering firm located in Bothell, Washington. We offer electrical engineering consulting services for the construction industry. We will also provide electrical engineering services for fast paced projects as a key member of your dynamic design build team. DESING BUILD DESING BUILD DESING BUILD DESING BUILD DESING BUILD DESING BUILD Seattle WA Seattle WA Seattle WA Seattle WA Seattle WA Seattle WA
Complete Engineering / Design Services LANE COBURN & ASSOCIATESLANE COBURN & ASSOCIATES SERVICES OVERVIEW Seattle WA Lane Coburn & Associates sets the highest standards for design/engineering services. These services include complete design of your project's electrical system. These services include but are not limited to the following: conceptual design, utility coordination, power system design, lighting system design, mechanical coordination, fire alarm design/coordination, special systems design/coordination, specifications, power studies, energy audits, cost estimating, utility rebate coordination, plan review coordination, peer review & construction administration. DESIGN COORDINATION Initial communications with the client is used to establish conceptual design requirements during the schematic phase of each project. Lane Coburn & Associates will make recommendations and assist the client in making decisions that may impact the electrical system, including future system capacity. Typical schematic level documentation includes preliminary load calculations, a oneline diagram, performance specifications, and a preliminary design narrative. Continued coordination with the design team is critical during design development, permit and construction documentation phases to ensure that all aspects of the electrical system are considered. Lane Coburn & Associates will coordinate with product vendors as required to provide accurate information and ensure constructability of the project. Calculations and electrical systems design will be documented based on design criteria, sound design/engineering practice, the National Electrical Code, and all local codes. Lane Coburn & Associates believes that the combination of sound engineering practices and active communication with other members of the design and construction teams will provide a well coordinated project with the greatest value for the owner. Lane Coburn & Associates QUALITY CONTROL PROCESS Lane Coburn & Associates holds inhouse Quality Assurance/Quality Control (QA/QC) meetings during the course of each project to ensure that all aspects of the design meet code requirements and client expectations. These reviews typically occur at the startup, 25%, 75% and 100% design stages. Lane Coburn & Associates utilizes the experience of all of key members to provide superior contract documents. POWER STUDIES Lane Coburn & Associates can provide a complete Power Systems Study. These studies can include; fuse/breaker coordination studies, ground fault studies, fault current calculations, asymmetric fault current calculations, voltage drop analysis, load flow analysis, relay protection setting analysis, time current curve analysis, generator sizing analysis and harmonics analysis. We utilize our experience, knowledge and a number of sophisticated software programs and spreadsheets to provide a comprehensive analysis of your system. FORENSIC ENGINEERING Keith Lane has a significant amount of experience in the design and troubleshooting of critical facilities. Keith has been the Engineer of Record for many data centers, call centers, collocation facilities, communication facilities and medical facilities. In addition, Keith has been asked to provide his professional opinion and analysis of several system failures. Keith has participated as an expert speaker on building design in a national telecast web cast. In addition, Keith has written numerous articles published nationally in Electrical Design, Maintenance and Construction Magazine, Consulting Specifying Engineering Magazine, Pure Power Magazine and BICSI Magazine. See Published Articles Section
Lane Coburn & Associates Offers Complete Power Systems Studies Including: Fuse/Breaker Coordination Studies Ground Fault Protection Analysis Studies Arc Flash Studies Fault Current Calculations Asymmetric Fault Current Calculations With Complete X/R Analysis Voltage Drop Analysis Load Flow Analysis Relay Protection Setting Analysis Complete Time Current Curve Analysis Generator Sizing Analysis Harmonics Analysis Lane Coburn & Associates Utilizes State of the Art Power Systems Software: SKM Software AMTECH  Protective Coordination Software Extensive Fault Current Programs and Spreadsheets Extensive Voltage Drop Spreadsheets and Software Programs Generator Sizing Software Harmonics Analysis Software Other Proprietary Software Keith Lane has completed many electrical system protective coordination studies over the past 13 years. These studies have included fault current analysis; power coordination study, ground fault study and arc flash study analysis. Some of these projects have included the following: Tacoma Convention Center Stevens Medical Office Building Rainier Medical Office Building Gig Harbor Medical Office Building AT&T Data Center Phase I AT&T Data Center Phase V University Village Shopping Center AAA Building Westin Hi rise Data Center Building Disney Data Center Network OS Data Center Switch and Data Data Center One Rincon Hill – 64 Story High Rise Residential Project University of Washington Research and Technology Building LBNL Fault Current Study, Power Coordination Study and Arc Flash
Telecommunication Design Lane Coburn & Associates, will not only provide a product that combines both a completely engineered and coordinated electrical system, but will also provide synergy with the telecommunication system. Lane Coburn & Associates has Professional Engineering Licenses holds a professional registration as a Registered Communications Distribution Designer and a Network Transport System Specialist. Our experience and expertise will provide the building infrastructure that will most effectively meet your telecommunication needs for today and for the future. Please read the "Why Hire and RCDD" below to gain a full understanding of what this professional credential can provide for your project. See attached link to information on Keith's participation on Consulting Specifying Engineers Magazine Industry Leaders Webcast. Why Hire an RCDD®? horizontal rule A registered professional in the field of telecommunications distribution design WHAT IS AN RCDD? An RCDD is a Registered Communications Distribution Designer who has attained the status of exceptional excellence in the field. The RCDD designation is recognized industrywide as indicating superior design expertise. Those holding the professional RCDD designation include architects, electrical engineers, telecommunications consultants, interior designers, telco personnel (from both the regulated and the deregulated sectors), data network designers, and many other industry specialists. RCDDs are accomplished professionals. WHAT IS BICSI®? BICSI is a professional notforprofit telecommunications association, founded in 1974 to serve the telephone company building industry consultants (BICs). BICs were responsible for the design and distribution of telecommunications wiring for commercial and multifamily buildings. BICSI has become a worldwide association with more than 12,000 members. Our programs and interests cover the broad spectrum of the voice, data, and video technologies. BICSI offers courses, conferences, publications, and registration programs for telecommunications cabling distribution designers and installers. 10 compelling reasons why you should hire a proven professional . . . an RCDD . . . to achieve your telecommunications design objectives When you hire a Registered Communications Distribution Designer (RCDD), you immediately add a unique level of knowledge to your organization. You take on an individual who has completed a rigorous, indepth program. It is a program designed to single out and present those individuals who are recognized as having demonstrable skills and professionalism in this highly specialized, demanding field. These outstanding individuals maintain their high status through an organized program of continuing education. It is the educational program that keeps them on the leading edge of rapidly developing technologies. 1. RCDDs have demonstrated a wide range of knowledge. Every RCDD professional has successfully completed and passed an extensive examination on the fundamentals of telecommunications distribution design. You know that the RCDD who has just joined your team has accomplished proven qualifications by meeting rigid standards. 2. The BICSI RCDD program is the standard of the industry. The cornerstone of the RCDD program is the BICSI Telecommunications Distribution Methods Manual. This publication contains more than 1,500 pages of information relating to low voltage wiring. As updates occur, they are added to the manual, assuring that the RCDD is fully informed on new developments and changes. Every RCDD is encouraged to be familiar with the contents of the manual. The RCDD professional possesses a solid foundation of knowledge, helping to assure steady control of projects and programs. 3. RCDDs exemplify professional conduct and integrity. Professional conduct and integrity of work completed mark the RCDD expert. A relationship of trust and honor is established with you and your RCDD. The BICSI RCDD program is designed with integrity in mind. All RCDD professionals are expected to exemplify these principles. 4. RCDDs must complete a structured program of continuing education. RCDD registration renewal is required every three years. A continuing education agenda requires all active RCDDs to participate as a prerequisite to understanding and meeting all current renewal specifications. RCDDs must confirm to you that their registration is current and in keeping with all of the requirements set forth by BICSI. 5. RCDDs have ready access to telecommunications resources. Through membership in BICSI, RCDDs have the capability of accessing more than 12,000 telecommunications professionals in all facets of the industry. This capability is distinguished by the wide choice of directions and alternatives it affords both the RCDD and the employer of the RCDD. RCDDs are often noted for the aggressive interest and active participation in the industry of their choice, the telecommunications industry. Networking and interaction enhance their knowledge and information resources. 6. RCDDs have access to a steady flow of professional, technical, and industry information. Active RCDDs have continuous access to the latest information in the telecommunications design industry. By virtue of the status of active RCDD, the professional you hire knows the way around the maze of the everchanging world of industry codes and regulations. Changes, updates, and revisions in telecommunications industry standards are known to render programs, projects, and objectives obsolete. Armed with knowledge and information, your RCDD can minimize these impacts. 7. BICSI conferences enrich the knowledge and capabilities of the RCDD. BICSI conferences and workshops are cosponsored by major universities and leading corporations. Rapidly changing technology, new products, and the effects of critical issues and challenges constitute the primary focus of the BICSI conferences. Active RCDDs attend these conferences and, as a result, they can offer leadingedge capabilities to those who hire them. When you hire an accredited RCDD, you get a concentration of working knowledge, handson experience, and indepth perception. 8. BICSI provides a wide range of training courses. Professional training for telecommunications professionals is the objective of BICSI's courses. Every accredited, active RCDD has direct access to more than 100 training courses and seminars, including: Distribution Design, Wireless Networks, Fiber Optic Design, Grounding and Protection, Project Management, and more. A full curriculum is offered on each specialized subject. Your RCDD professional has access to levels of continuing education unparalleled in most disciplines. The twopronged objective is education for the industry and training for the workplace. 9. RCDD professionals are often required. The RCDD registration is recognized and mandated by many private and state organizations. More and more projects require that bids be submitted by an RCDD. RCDDs earn recognition through registration won by diligent effort. 10. RCDDs are tested from a generic perspective, giving them flexibility. RCDDs have been tested from a generic viewpoint. They are not inhibited by specific product criteria. They exhibit innovation, advanced techniques, and longterm thinking. Freedom to apply knowledge and training exemplifies the RCDD. NeherMcGrath Calculations NeherMcGrath Calculations NeherMcGrath Calculations NeherMcGrath Calculations NeherMcGrath Calculations NeherMcGrath Calculations NeherMcGrath Calculations NeherMcGrath Calculations NeherMcGrath Calculations NeherMcGrath Calculations NeherMcGrath Calculations NeherMcGrath Calculations NeherMcGrath Calculations NeherMcGrath Calculations NeherMcGrath Calculations NeherMcGrath Calculations Data center Data center Data center Data center Data center Data center Data center Data center Data center Data center Data center Data center Data center Data center Data center Data center Data center critical facilities critical facilities critical facilities critical facilities critical facilities critical facilities critical facilities critical facilities critical facilities critical facilities critical facilities critical facilities critical facilities critical facilities critical facilities critical facilities LANE COBURN & ASSOCIATES Duct Bank Heating Calculations are Essential for Critical Environments (Data Centers) Electrical heating calculations may need to be performed when large amounts electrical duct banks with significant amounts of conduits and conductors are routed below grade in the earth. These heating calculations are performed to determine if any de rating of the conductors is required. This de rating is based on many factors including but not limited to the following: 1. Number and size of conduits and conductors 2. Configuration of the conduits and conductors 3. Spacing between the conduits in both the horizontal and vertical dimensions 4. Amount of earth above the conductors 5. The RHO factor and the amount of the back fill material 6. Load factor of the conductors 7. The actual design load As in any situation, if the electrical conductors overheat past their rated use, the insulation protecting the conductor could burn off or degrade to a point where a short circuit condition could be precipitated. As defined in this article the Load Factor plays a major role in defining if an installation will have a problem with overheating. A data center environment will typically have a very high Load Factor value, which will lead to significant problems if not designed properly. At Lane Coburn & Associates, LLC, we are beginning to see existing data centers with significant overheating issues. The large underground feeders serving these data centers posed no problems before these critical environments were loaded up to the intended design loads. We are starting to see existing data centers that previously never achieved 50% of the design capacity, now running at or near capacity. Electrical conductor heating calculations can be very complicated based on many of the variables noted previously. There are various software programs available for determining the potential de rating of feeder conductors in large electrical duct banks. It is also critical to hire a Professional Electrical Engineer with expertise in both critical environments topology and on providing NeherMcGrath calculations. Definitions utilized in the calculation Load Factor  The ratio of the average load in kilowatts supplied during a designated period to the peak or maximum load in kilowatts taking place in that period. Load factor, in percent, also can be derived by multiplying the kilowatt hours (kWh) in the period by 100 and dividing by the product of the maximum demand in kilowatts and the number of hours in the period. Example: Load Factor Calculation  Load Factor = kilowatt hours/hours in period/kilowatts. Assume a 1 day billing period or 1 times 24 hours for a total of 24 hours. Assume a customer used 15,000 kWh and had a maximum demand of 1500 kW. The customer's load factor would be 41.6 percent ((15000 kWh/24 hours/1500 kW)*100). The 41.6 % load factor may be representative of a standard commercial building. The load factor in a data center with fairly constant load 24 hours of the day should be significantly higher. RHO – Thermal resistivity. Thermal resistivity, as used in the National Electrical Code annex, indicates the heat transfer capability through a substance in the trench by conduction. This value is the reciprocal of thermal conductivity and is typically expressed in the units Ccm/watt. Where an underground electrical duct bank installation utilizes the configurations identified in the National Electrical Code examples, the National Electrical Code indicates in section 31015 (b), that calculations can be accomplished to determine actual rating of the conductors. A formula is provided in the National Electrical Code that can be utilized under "Engineering Supervision" to provide these calculations. This formula is typically not sufficient because it does not include the effect of mutual heating between cables from other duct banks. For distinctive duct bank configurations, an electrical system design engineer must utilize the Neher McGrath calculation method. The NeherMcGrath calculations are very complex and involve many calculations and equations and can be exceedingly time consuming. In addition, many of the calculations build on each other, so an error in one part of the calculation can result in a significant error in the final outcome. The hand calculations become even more complex if cable in the duct bank are of different sizes. I have provided some of the pertinent information directly from the National Electrical Code below: National Electrical Code : B.310.15 (B) (1) Formula Application Information. This NEC annex provides application information for ampacities calculated under engineering supervision. The data in Anex B is based on the Neher McGrath method NEC B.310.15 (B) (2) Typical Applications Covered by Tables. Typical ampacities for conductors rated 0 through 2000 volts are shown in Table B.310.1 through Table B.310.10. Underground electrical duct bank configurations, as detailed in Figure B.310.3, Figure B.310.4, and Figure B.310.5, are utilized for conductors rated 0 through 5000 volts. In Figure B.310.2 through Figure B.310.5, where adjacent duct banks are used, a separation of 1.5 m (5 ft) between the centerlines of the closest ducts in each bank or 1.2 m (4 ft) between the extremities of the concrete envelopes is sufficient to prevent de rating of the conductors due to mutual heating. These ampacities were calculated as detailed in the basic ampacity paper, AIEE Paper 57660, The Calculation of the Temperature Rise and Load Capability of Cable Systems, by J. H. Neher and M. H. McGrath. For additional information concerning the application of these ampacities, see IEEE/ICEA Standard S135/P46426, Power Cable Ampacities, and IEEE Standard 8351994, Standard Power Cable Ampacity Tables. You can see that the tables in the National Electrical Code for underground duct banks are very limited. If the RHO or Load Factor values are different that what is stated in the tables, then the tables do not apply. If the configuration of the conduits exceed the 6 electrical ducts as illustrated on Table B.310.7 the tables do not apply. Additionally if other duct banks are closer that 5 feet, the mutual heating effect of those conductors will not be taken into account. As stated previously, a remedy to the complexity of these calculations is to utilize a software program. The software will make the math substantially easer but the data the soft input into the software and the calculated result need to be tureally analizedy by speciliced engineeres enperenced with this type of heating issue. 4 Figure #1 The diagram above is of a standard trench detail. Electrical heating becomes more of an issue when multiple rows of conduits are stacked on top of each other. Additionally, the separation of the conduits in both the vertical and horizontal planes as well as the total cover above the top row will all affect the potential de rating of the conductors. As stated above, both the load factor and the RHO value of the back fill also play large roles in determining the potential de rating of the conductors in the duct bank. See examples below. The actual configuration of the conduits within a duct bank can be manipulated to reduce any potential de rating. By placing the conduits with the most amount of heat dissipation at certain locations within they duct bank or separating the conduits that will emanate the most heat from each other, total de rating can be reduced. Some of the software programs offered today will provide information on the optimum method of layering your conduits within your duct bank to reduce the total heating effect. Fourier Law described the effects of heat transferred by conduction. The heat flux is proportional to the ratio of temperature over space. The air space within the conduit is the only area within a duct bank that does not conduct heat. In the air space convection occurs in lieu of conduction. The main method of heat transfer within a duct bank is conduction; therefore the air within the conduit will have less of an effect of heating. One of the major components of this calculation is the RHO (See definitions previously). Selected backfill material can be utilized to manipulate the RHO value. The following are typical RHO values for various materials: Typical ( reference ) values of thermal resistivity (RHO) are as follows: 1. Average soil (90 percent of USA) = 90 2. Concrete = 55 3. Damp soil (coastal areas, high water table) = 60 4. Paper insulation = 550 5. Polyethylene (PE) = 450 6. Polyvinyl chloride (PVC) = 650 7. Rubber and rubberlike = 500 8. Very dry soil (rocky or sandy) = 120 There are methods of analyzing the actual thermal characteristics of the soil in lieu of just estimating these values based on common typical numbers. A thermal property analyzer can be utilized to measure the actual thermal characteristics of the soil. Additionally, the duct bank installer can utilize engineered backfill where these characteristics are specifically designed and known. All of the heat created by an underground electrical cable must be dissipated through the adjacent soil. This is identified by the soil thermal resistivity coefficient (or thermal RHO, °Ccm/W). This value can typically fluctuate between 30 to 500°Ccm/W. Electrical engineers typically understand the characteristics of the electrical cable reasonably well. For the most part electrical engineers do not understand the behavior of soils. Generally, the electrical engineer will assume conservative values for RHO when performing these heating calculations. The use of a soil thermal RHO of 90°C cm per W has become embedded in electrical engineering design practices. Soil studies performed many years ago have found that this was a conservative RHO value for the majority of moist soils in the United States. This RHO value is commonly utilized for electrical distribution cables when the native soil is reused as the backfill for the trench. When select backfill is utilized in lieu of the native backfill for the immediate area around the electrical conduits this backfill will generally have a lower RHO than the native soil. The ability of the soil in the direct area around the electrical conduits to transmit the heat from the electrical cables establishes whether an electrical cable overheats or keeps cool. Over heating can lead to insulation failure or deterioration. Enhancing the peripheral thermal surroundings and precisely defining the soil and backfill thermal RHO values can result in a 10% to 15% increase in cable ampacity, with 30% improvements noted in some cases (3). Most damp soils have a RHO of less than 90°C cm/W. Moist sands, which are frequently positioned around electrical distribution conduits, may even have a RHO of less than 50°Ccm/W. The dilemma is that many soils, particularly homogeneous sands, may dry considerably when heated from the electrical cables. On the other hand, the thermal RHO of a dry soil can exceed 150°Ccm/W, and possibly reach levels of 300°Ccm/W. The dry thermal RHO of a properly designed and installed thermal backfill should be less than 100°Ccm/W and potentially as low as 75°Ccm/W. Soils found in barren areas are, as you would expect are very dry. The assumption of a moist soil in your calculations is certainly not conservative. In certain parts of the country, the soils have a high inherent thermal RHO. Soil that is not properly compacted in the cable trench will be less dense and have a significantly elevated thermal RHO. Even your typical 480 volt electrical distribution or low voltage cables that are continuously under full load may dry the soil. Inadequately compacted trench backfill can be an important issue. The thermal RHO of soil that is not compacted correctly can be much higher than soil that is correctly compacted. In addition, loose soil will dry more easily. The same effect can be developed when other cables are in close proximity. This effect is known as mutual heating. I have provided a few examples below. As you can see, the duct configuration is the same in all of the examples. I have however changed the Load factor and the RHO factor. Modifying these values changes the amount of current that can be pushed through the electrical conductors without exceeding their temperature limits. As you can see, the amount of de rating can be significant. Example #1 & Example #2 below In this example, a 4,000 amperes duct bank with a design load of 3,600 amperes is simulated based on an Earth RHO factor of 90, **dirt RHO factor of 90 and a load factor of 100. In this analysis, 16 sets of 4" conduits with 3 #600 MCM copper conductors is required to feed the 3,600 ampere load. Each set of conductors is locked in at 225 amperes each (16 * 225 = 3,600). This essentially is a 60% de rating. 16 sets of 600 MCM conductors with no de rating would equate to 6,720 amperes. (4,000 / 6,720 = 60%). As you can see below, the maximum temperature of the hottest conductor is 66.73 degree Celsius. Per the National Electrical Code, the feeders need to stay below 75.0 degree Celsius. As you can see in Example #2, if we try to reduce the number of conductors to 14 in lieu of the 16, the temperature rises to 79.67 degree Celsius. As the temperature could rise above 75 degree Celsius, this example is not code compliant. ** The dirt RHO is same as the earth RHO (typically 90) if native backfill is utilized to fill the area directly around the conduits. If select backfill is utilized around the conduits the dirt RHO could be less than the earth RHO. A dirt RHO of less than 90 can lead to less heating and less potential de rating. There is typically some discussion about utilizing the 90 degree Celsius rating of the conductors. Per National Electrical Code, section 110. 14 (C): "Conductors with temperature ratings higher than specified for terminations shall be permitted to be used for ampacity adjustments, corrections or both". This application is not typically applicable for 100% rated breakers. In fact, with most 100% rated circuit breakers, 90 Degree Celsius Cable is required, but it must be sized per the 75 Degree Celsius ampacity. These 100% rated breakers utilized the wire as a heat sync to be able to serve continuous loads at the full rating of the breaker. By evaluating the actual temperature of the conductors from the printout below, you can analyze the heat flow and determine the areas that will experience the most heating. which increases the possibility of thermal runaway. This is kind of a domino effect. Cables that are in close proximity to heat producing equipment and infrastructure will experience elevated ambient temperatures and can operate at a hotter temperature. LANE COBURN & ASSOCIATES, LLC ELECTRICAL ENGINEERING D/B TEAM MEMBER LIGHTING DESIGN CONSULTING LEED A.P 8 Example #1 Example #2 Example #3 below In this next example, a 4,000 amperes duct bank with a design load of 3,600 amperes is simulated based on an Earth RHO factor of 90, dirt RHO factor of 90 and a load factor of 75. In this example, the load factor was reduced from 100 to 75, all other values are the same as in example #1. In this analysis, 12 sets of 4" conduits with 3 #600 MCM conductors is required to feed the 3,600 ampere load. Each set of conductors is locked in at 300 amperes each (12 * 300 = 3,600). By reducing the load factor to 75, 4 – 4" conduits each with 3 #600 MCM conductors are not required. This is a very graphic example of how the assumption of load factor in the electrical system can have a significant effect on the total number of conduits and conductors that are required in your electrical distribution system. This essentially is a 79% de rating, example #1 above requires a 60% de rating. 12 sets of 600 MCM conductors with no de rating would equate to 5,040 amperes. (4,000 / 5,040 = 79%). As you can see below, the maximum temperature of the hottest conductor is 72.02 degree Celsius. The feeders need to stay below 75 degree Celsius. By evaluating the actual temperature of the conductors, you can analyze the heat flow and determine the areas that will experience the most heating. The hottest conductors are very close to the maximum 75 degree rating (72.02 degrees Celsius). Example #4 below In this example, a 4,000 amperes duct bank with a design load of 3,600 amperes is simulated based on an assumption that select backfill with an RHO of 75 is utilized. In this example, the load factor was reduced from 100 to 75 and the RHO of the concrete around the duct bank was reduced from 90 to 75. In this analysis, 12 sets of 4" conduits with 3 #600 MCM conductors is still required to feed the 4,000 ampere load (Same as in example #3). Each set of conductors is locked in at 300 amperes each (12 * 300 = 3,600). By reducing the load factor to 75, 4 – 4" conduits each with 3 #600 MCM conductors are not required. This essentially is a 79% de rating. 12 sets of 600 MCM conductors with no de rating would equate to 5,040 amperes. (4,000 / 5,040 = 79%). As you can see below, the maximum temperature of the hottest conductor is reduced to less than 65 degree Celsius (In example #3, the hottest conductors are at 72.02 degrees Celsius, this accounts for a drop of over 7 degrees Celsius). The feeders need to stay below 75 degree Celsius. The change from the dirt RHO from 90 to 75, in this case, did not change the total number of conductors required to carry the 3,600 amperes of load. By evaluating the actual temperature of the conductors, you can analyze the heat flow and determine the areas that will experience the most heating. Additionally, these programs will calculate the total loss of energy due to heating and the voltage drop of the conductor. The energy wasted through the conductors due to heat loss can be a significant number and should be considered with any evaluation of these type of electrical duct banks. The next example illustrates a situation that can occur when below grade electrical conductors with high usage and load factor are not sized in light of these heating calculations. Example #5 below A standard feeder schedule for a 4,000 ampere feeder based on the National Electrical Code section 310.16 would include 10 sets of 600 MCM copper conductors (10 x 420 amperes = 4,200). This does not include any de rating. The example below illustrates 10 sets of 600 MCM copper conductors with an Earth RHO factor of 90, dirt RHO factor of 90 and a load factor of 100%. As you can see, if 3,600 amperes is required (360 amperes running through each of 10 conductors), the conductors will heat up to approximately 133.6 degrees Celsius. After prolonged heating, this could cause serious damage to the insulation. These are the temperatures that can be reached in a data center that reached design loads that has not been designed based on heating calculations. This example is based on a conservative situation where the actual load is 3,600 amperes (86% of the rating of the conductors) and the load factor is 100 %. Actual current draw is typically significantly less than National electrical Code demand calculated load in most installation except data centers. In a data center environment, the actual loads and load factor can be very high. It is critical to determine if your existing data center was designed based on these NeherMcGrath calculations. Example #6 below In this example, I utilized a design load of 3,600 A and reduced the load factor to 60%. The earth and dirt RHO is set at the standard 90. In this example, the standard feeder schedule for a 4,000 ampere service (10 sets of 600 MCM copper conductors (10 x 420 amperes = 4,200)) will not heat up to more than 75 degree Celsius. This example illustrates that most electrical duct bank installations will typically not require any de rating based on the heating calculations. It has been our experience that most data center applications run above a 90% load factor. Example #7 In this final example, I have utilized a 4,000 ampere duct bank with a design load of 3,200 amperes and increased the load factor to approximately 90%. The earth and dirt RHO are again set at the standard 90. In this example, the standard feeder schedule for a 4,000 ampere service (10 sets of 600 MCM copper conductors (10 x 420 amperes = 4,200)) will heat up to more than 75 degree Celsius. Many data center installation may require de rating, these heating calculations may be critical to ensure that the designed electrical duct bank is adequate to serve the anticipated loads based on the assumed load factor, RHO factor and duct bank configurations. It is important to note that not all feeders routed in electrical duct banks are going to require de rating, in fact, most will not require de rating. If the "design load" is less than the rating of the conductors and/or if the load factor is lower than 100, in many cases, de rating may not be required. The reality is that most commercial installations have a load profile with a load factor of less than 50% and an actual current draw of somewhat less than the full rating of the conductors. Many data centers have actual measured loads that are 70% to 100% of the rating of the conductors and very high load factors. With all of these factors and criteria involved, it is important to evaluate each electrical duct bank to determine if heating calculations are required and if any de rating will apply. Because of the complexity of these analysis, it is important to acquire the services of a qualified electrical design professional that utilizes the appropriate electrical design software. Additionally, as stated in the National Electrical code, the calculations should be performed under "Engineering Supervision" and should require the approval of a licensed professional engineer. References 1. National Electrical Code 2005 2. AmpCalc from Calcware 3. Underground Cables Need a Proper Burial Apr 1, 2003 12:00 PM By Deepak Parmar and Jan Steinmanis, Geotherm Inc. End of Article Written By: Keith Lane, P.E., RCDD/NTS Specialist, LC, LEED A.P. Principal  Lane Coburn and Associates, LLC Scott Coburn Principal  Lane Coburn and Associates, LLC Understanding the NeherMcGrath Calculation and the Ampacity of Conductors Heat Transfer The key to understanding ampacity is to learn about heat transfer. The definition of ampacity is given in the National Electrical Code (NEC) as "the current in amperes a conductor can carry continuously under the conditions of use without exceeding its temperature rating." To better understand ampacity we need to examine how heat is transferred and thermal circuits in respect to a current carrying conductor. When current is carried by a conductor it must pass through the electrical resistance of the conductor. When this happens heat is generated. One unit of heat, watts, can be calculated by I squared times R, where R equals the electrical resistance of the conductor in ohms and I equals the current in amperes. The heat generated in the conductor passes through several thermal barriers by convection, conduction, and radiation and dissipates into the air. Possible thermal barriers are the conductor insulation, the air inside a duct, the duct wall, the soil surrounding an underground duct, and any additional thermal insulation applied such as polyurethane. The transfer of heat follows a fundamental law in physics, and heat always flows from the warmer object to the colder object, much like heat flowing from the inside of a house through the walls to the outside on a cold day. The rate of heat transfer is dependent on several variables and can be described by a thermal equation that closely resembles ohms law (E=IxR), substituting heat for current and thermal resistance for electrical resistance. In a heat transfer equation the rate of heat transfer is directly dependent on the difference in temperature between the conductor called TC and the ambient temperature called TA. In a heat transfer equation TCTA = (IxIxR) x RCA, where I is current in amperes, R is electrical resistance in ohms, and RCA is thermal resistance in degrees Centigradecm/watt usually called thermalohmfeet. TC is the maximum permissible operating temperature in degrees Centigrade of the conductor. TA is the ambient temperature of the air or soil for underground installations. Solving for I: Letting heat, IxIxR in this case, be represented by W and thermal resistance, RCA, by R with a line over it, we can draw a thermal circuit that is similar to an electrical circuit. NeherMcGrath equation Founded by a man named Fourier in the 1850's, Equation No. 1 is sometimes called the Fourier heat transfer equation. The equation in section 31015(b) of the NEC, called the NeherMcGrath equation, is a more complex version of the Fourier heat transfer equation. The NeherMcGrath equation was discovered by two cable engineers in 1957. In the NeherMcGrath (NM) equation, Delta TD, is a term added to the ambient temperature, TA, to compensate for heat generated in the jacket and insulation for higher voltages. Delta TD is called the dielectric loss temperature rise and is insignificant for voltages below 2000. Another term in the NM equation, (1+YC), is a multiplier used to convert direct current resistance (RDC) to alternating current resistance or impedance. For wire sizes smaller than No. 2 this term becomes insignificant. Of course, we must remember that the NM equation was developed using the standard power frequency of 60 hertz and sinusoidal wave forms for current and voltage. There are many equations used to calculate the various thermal resistances for the conductor insulation, the air space between a conductor and the inside of a conduit, the conduit or duct wall, and the thermal resistance outside the conduit. Like electrical resistors, thermal resistances in series are added and the total equals RCA. Ambient temperature, TA, varies but usually 30 or 40 degrees Centigrade is used for above ground installations. For underground installations TA is universally 20 degrees Centigrade. Civil engineers working for the State of Alaska Department of Transportation state that the actual measured temperature 30 inches beneath the surface is 19.3 degrees Centigrade near Fairbanks, Alaska. This of course, is during the summer months. The conductor temperature, TC, for most 600 volt building wire is 60, 75, or 90 degrees Centigrade. The maximum insulation temperature for conductors is determined by conducting aging and enlongation tests in environmental chambers. In the NM calculation there are many variables in the 30 to 40 equations used to account for the number of conductors, number and size of adjacent conduits, number and size of adjacent duct banks, coefficient of surface emissivity, number of cables, axial spacing between cables, extraneous heat sources, and wind velocity. All these factors and more effect the calculation of ampacity. An analysis of the NM calculation reveals many details about ampacity: for instance, the ampacity of conductors in a bright and shiny conduit in free air is higher then the ampacity in a dull and dark conduit because of the coefficient of surface emissivity and its effect on the radiation of heat. Also, one of the most criticized faults of the NM calculation is revealed: The calculation is based on one single linear foot of a conductor that may be several hundred feet long where the conditions vary dramatically along the entire length. There are ampacity tables in the National Electrical Code that are sufficient for most installations. However, the tables in the NEC are very crude approximations and therefore include a substantial safety margin. There are instances where the application of the ampacity tables including the safety margins are insufficient requiring engineers, installers, and inspectors to perform actual NM calculations using one of the several software packages available. For instance, there are no requirements in the NEC to address the problem of excessive thermal insulation around cables and conduits. What happens if there are several inches of polyurethane foam around a conduit? There are no derating tables in the NEC for this kind of situation. Yet, the addition of excessive thermal insulation will effect the ampacity of a conductor, especially polyurethane foam that has three times the insulation value of fiberglass. To address this problem we must remember that the NM equation is a radial heat transfer equation and that the NM calculation is performed on one typical foot of an installation that may be several hundred feet long. Radial heat transfer means that heat flows outward at ninety degrees to the length of the conductor as opposed to axial heat transfer where heat flows along the length of the conductor. In the real world there is axial and radial heat transfer. But the NM equation and the NEC assume that a conductor and surrounding thermal barriers are infinitely long and uniform where no axial heat transfer takes place. There are, however, some allowances in the NEC for axial heat transfer. For instance, there are no derating for over three current carrying conductors in a nipple if the nipple is not over 24 inches long. Also, bundled cables are not required to be derated if the bundles are not longer than 24 inches. There is also the ten per cent rule given in section 31015(c). These are situations where there is enough axial heat transfer to prevent the conductors from overheating. It would also be prudent to assume that where there is excessive thermal insulation not over 24 inches long, the ampacity of the applicable conductors would not be effected because of axial heat transfer. NeherMcGrath Calculations The NeherMcGrath Calculations provide a method for calculating underground cable temperatures or ampacity ratings and are derived from the following technical paper: J. H. Neher and M. H. McGrath,"The Calculation of the Temperature Rise and Load Capability of Cable Systems", AIEE Transactions, Part III, Volume 76, pp 752772, October, 1957. This paper considers the complicated heat transfer issues associated with the determination of underground system ampacities. The paper cites the following basic equation for calculation of a cable ampacity: However, this single equation masks the great complexity involved in these procedures. There are scores of complicated equations involved in developing the terms in this equation and those required for temperature calculations. (The paper defines over 80 variables and contains in excess of 70 formulas excluding appendices.) To solve for unique ampacities or temperatures at each cable position, a multiple set of equations must be developed to take into account interference heating from every position in the system, and a matrix solution technique for simultaneous equations utilized. AmpCalc handles all the complexity and allows the user to quickly and easily determine ampacities for virtually any underground ductbank or direct burial arrangement. Abstract—This paper introduces the heat transfer mechanisms in underground cable installations and analyzes the available solution methods of the diffusion equation. The heat sources and thermal resistances of the different layers of a cable installation are described. The basic concepts behind the NeherMcGrath method (IEEE) are discussed, along with its differences with the IEC standards for underground cable installations. The available commercial computer programs, designed to perform ampacity calculations are listed along with a description of the modeling capabilities of CYME's CYMCAP. Index Terms—Ampacity. Underground Cables. NeherMcGrath. IEC Standards. CYMCAP. Cables. I. INTRODUCTION TO CABLE AMPACITY MPACITY is a term given by Del Mar in 1951 to the currentcarrying capacity of a cable. Ampacity in an underground cable system is determined by the capacity of the installation to extract heat from the cable and dissipate it in the surrounding soil and atmosphere. The maximum operating temperature of a cable is a function of the damage that the insulation can suffer as a consequence of high operating temperatures. The insulation withstands different temperatures as function of the duration of the current circulating in the conductors. There are three standardized ampacity ratings: steady state, transient (or emergency) and shortcircuit. Only steady state ampacity ratings are discussed in this paper. Ampacity calculation techniques are as old as the cables themselves. Anders has summarized the history of ampacity calculations in his 1997 book [1]. There are analytical and numerical approaches to calculate cable ampacity. The two major international standard associations, the IEEE and the IEC, have adopted the analytical methods as the basis for their standards [2], [39]. The numerical approaches are mainly based on finite differences or finite elements techniques. The finite elements technique is better suited for cable ampacity because of the round geometry of cables. This paper focuses on the analytical techniques for the computation of cable ampacity in steadystate through the use of assumptions that simplify the problem. For transient (or emergency) calculations the reader is referred to [1], [8], [9], [12] and [13]. Calculation of shortcircuit ratings is described in [14] for both adiabatic and nonadiabatic conditions. II. AN OVERVIEW OF HEAT FLOW There are three physical mechanisms for heat transfer: • Conduction • Convection • Radiation Fourier Law describes the heat transferred by conduction. In very simple terms, the heat flux is proportional to the ratio of temperature over space. In an underground cable installation heat conduction occurs everywhere except in the air space in the conduit. Convection of heat occurs in moving fluids (air, water, etc.) and obeys Newton's Law. The flow of heat is proportional to the temperature difference. In an underground cable installation convection takes place in the air space inside the ducts and at the surface of the earth. The StefanBoltzmann Law describes the radiation of heat phenomenon as being proportional to the difference the temperatures at the power of four (tf 4 –t0 4). In underground cables radiation of heat occurs from the cable(s) to the ducts. Figure 1 show a typical temperature distribution for a duct bank installation using an engineered backfill on top of the duct bank. From the figure one can appreciate the diffusion of heat that occurs in underground cable systems. Diffusion is a process by which heat is transferred for one region to another in a slow, spacelimited fashion described by decaying exponentials. Therefore, there is a practical distance, away from the heat source, beyond which the heating effects are not felt. Figure 1. Typical temperature distribution of an underground cable installation Calculation of Underground Cable Ampacity III. HEAT SOURCES IN CABLE SYSTEMS The heat sources in cable installations can be divided into two generic groups: heat generated in conductors and heat generated in insulators. Figure 2 shows a complex cable construction, for illustration purposes, containing many of the possible layers in a cable. The losses in the metallic (conductors) elements are by far the most significant losses in a cable and they are caused by: (a) Joule losses due to impressed currents, circulating currents or induced (eddy current) losses; (b) Hysteresis losses in conductors that are also magnetic. The following metallic components of a cable system will produce heat: • Core conductors • Sheaths • Concentric neutrals • Armors • Skid wires • Pipes/ducts The losses in those components are functions of the frequency (f.) and the temperature (t) of operation and proportional to the square of the current (I). Customarily, the dependency with temperature and frequency is included in an equivalent ac resistance to express Joule law as: (1) Insulating materials also produce heat. The heat produced in the insulating layers is only important under certain high voltage conditions. The following components could be considered: • Main insulation • Shields • Screens • Jackets • Beddings/servings The loss relationship is given by: (2) where C is the capacitance, V is the voltage applied and δ is the loss angle. Figure 2. Illustration of a complex cable construction IV. HEAT FLOW IN UNDERGROUND CABLE INSTALLATIONS In an underground cable system the main heat transfer mechanism is by conduction. With the exception of the air inside the conduits in duct banks or buried ducts installations all the heat is transferred by conduction. Since the longitudinal dimension of a cable is always much larger than the depth of the installation, the problem becomes a twodimensional heat conduction problem. In Cartesian coordinates one must solve the diffusion equation given by [1]: (3) where: ρ = Thermal conductivity of the material c = Volumetric thermal capacity of the material W = Rate of energy (heat) generated Equation (3) cannot be solved in closed form for the complicated geometry of an underground cable arrangement (see Figure 1). Additionally, numerical solutions could not be obtained in the precomputer era (before 1950's). However, cables are being installed since the 1890's. Furthermore, since numerical solutions, considering all particularities of the installation, require of the solution of a large number of linear (or nonlinear) equations only with the powerful computers available nowadays, it is becoming practical to get numerical solutions for cable rating purposes. In view of the complications of the ampacity problem, engineers found practical solutions by combining analytical solutions to simplified geometries with heuristic results. In particular the use of thermalelectrical analogies with empirical work has been very popular with cable engineers. To that effect, the paper published by Neher and McGrath in 1957 [10] is remarkable; they summarized the knowledge on the ampacity calculation field to that date, and today (2005), the NeherMcGrath method is still being used and it is the base for the IEEE and the IEC standards. V. THE NEHERMCGRATH METHOD The technique known as the NeherMcGrath method for ampacity calculations is based on a thermalelectrical analogy method due to Pashkis and Baker (1942) [11]. The basic idea is to subdivide the study area in layers. Then one substitutes the heat sources by current sources, the thermal resistances by electrical resistances and the thermal capacitances by electrical capacitances. Figure 3 shows the correspondence between the cable installation components and the electric circuit elements for steady state ampacity calculations. Note that the capacitances play no part in steady state ratings. To find the ampacity we first note that the potential of every node in the circuit is analog to the temperature of the regions between the layers. Thus, the potential difference between the terminals of the circuits and the innermost current source represents the temperature rise of the core of the cable with respect to the ambient temperature. Therefore the temperature of the cable's core is the ambient temperature plus Δ t; see F To derive an expression from where the ampacity can be computed directly, the heat sources (electrical losses) W 's are expressed as proportion of the conductor losses (Wc). The conductor losses are computed using the ac resistance and the current. Thus, by substituting the following expressions: one can compute the ampacity of a cable. Of paramount importance for cable rating is the accurate calculation of the thermal resistances T, the loss factors λ and the ac resistance Rac of the core of the cable. The loss factors λ take into account eddy losses induced and circulating currents, while Rac considers the temperature dependency of the resistances. Calculation of Thermal Resistances In the NeherMcGrath method, the thermal resistances are either computed from basic principles or from heuristics. One can appreciate, from Figure 3, that some of the internal layers of a cable can be considered as tubular geometries. The following expression is used for the computation of the thermal resistance of tubular geometries: is applicable for most internal to the cable layers (T1, T2, T3). For complicated geometries and for the layers external to the cable, such as threecore cables, duct banks, etc., heuristics are used. For uniformity with (7) the following expression has been proposed: G is called the geometrical factor because it is a function of the shape and dimensions of the particular geometry under analysis. There are a number heuristics used in the calculation of thermal resistances. For example, there are expressions for: equally or unequally loaded cables, for touching or not touching cables, for flat or triangular formations, trefoils, backfills, duct banks, etc. There are too many possibilities to be considered in this paper, the interested reader can find all the details in list references of this paper. Numerical methods (finite elements) have been used to determine extensions to the geometrical factors when heuristics do not exist. The external to the cable thermal resistivity is commonly computed assuming that the surface of the earth in the neighborhood of the cable installation is an isothermal. Kennelly made this assumption in 1893 and it is still being used. This assumption allows for the application of the image method to compute the external to the cable thermal resistance (T4). The following expression results from the image method: The thermal resistance of the layers external to the cable (T4) must also include the duct when present, and the air inside. The duct itself is of tubular geometry and it very easy to model, however, the treatment of the air inside of a duct is a complex matter. The heat transfer is dominated by convection and radiation and not by conduction. There exist simple formulas, which have been obtained experimentally and that work fine for the conditions tested. Loss Factors (λ) Loss factors in equation (5) relate to the losses that metallic layers (sheaths, armors, etc.) produce in proportion to the losses of the cable core. These losses include circulating currents and induced currents (eddy currents). The geometrical arrangements are diverse and some are quite complicated. The bonding used for sheaths (or concentric neutrals) plays a very important role in the current intensity that circulates in them. Thus the losses are very much dependent on the bonding type and the geometrical arrangement of the cables (flat or triangular formation). The possibilities are too many to be discussed in this paper; the interested reader can see all the details in references [1], [3] and [4]. Currently, even finite elements ampacity programs use analytical expressions to compute the losses produced in every layer of the cable installation. AC Resistance The operating resistance of a cable is a function of the temperature and the frequency. The temperature variation is described by: ( ) [1 ( )] 0 0 R t =R +α t − t (10) where: R0 = Resistance at a base temperature (t0 = 20°C) α = Coefficient of variation with temperature Although there exists an analytical expression, using Bessel functions, for the modeling of eddy current effects in cables, for low frequencies (50 and 60 Hz), there are very simple and accurate formulas adequate for ampacity calculations. The eddy current effects are included by two factors. One considers the skin effect (ys) and the other, the proximity effect (yp). The mathematical expression to account for these losses is: ( ) (1 ) DC s p R f = R + y + y (11) Combining (10) and (11) we have: ( , ) [1 ( )](1 ) ac 0 0 s p R t f = R +α t − t + y + y (12) The values for ys and yp are computed from simplified analytical expressions particular to each cable core construction (solid, stranded, segmented, etc.). VI. IEC VERSUS NEHERMCGRATH A detailed description of the difference between the two methods can be found in Appendix F of [1]. For steady state ampacity simulations the two approaches are virtually the same. The greatest difference is that the IEC equations use the metric system while NeherMcGrath use the imperial system. Thus equations look very different, but the two methods are equivalent. In the NeherMcGrath method, there are explicit equations for the transient rating, while in the IEC, detailed methodologies are given. In general, IEC methods are more up to date and consider more cases than the NeherMcGrath method. Following is a description of the most important modeling differences: Eddy Losses • In the NeherMcGrath approach only the eddy losses for triangular configurations are computed. IEC includes flat formations as well. • In the IEC standards the magnetic armors are considered, while they are not in the NeherMcGrath method. Thermal Resistances • IEC gives expressions for geometric factors of threecore, oilfilled, belted, etc., cables. • IEC considers more insulation materials than Neher McGrath. • IEC makes a distinction between trefoil and flat configurations (touching and not touching) for T4. • IEC considers in detail unequally loaded cables. • Soil dryout is considered in IEC. VII. COMMERCIAL AMPACITY PROGRAMS The first and most advanced commercial program for cable ampacity calculations is CYMCAP. Its development started in the 1980's jointly by Ontario Hydro (Hydro One), McMaster University and CYME International, under the auspices of the Canadian Electricity Association (CEATI). CYMCAP is based on the IEC Standards and features a very friendly GUI (Graphical User Interface). Over 100 companies in close to 50 countries use CYMCAP. This program can compute steady state ampacities and transient ampacities. CYMCAP features a duct bank optimizer and the possibility to handle several duct banks with different thermal resistivities in the same installation. USAmp is next in the development ladder. It is based on the NeherMcGrath method for steady state ampacity calculations. It supports transients based on the CIGRE report [13]. It has a GUI, but data is entered and displayed mostly in tabular form. USAmp has been used to obtain the IEEE Standard tables published in [2]. ETAP is another tabular program based on the Neher McGrath method. It does not support transient ampacity calculations. There are other smaller programs such as: PCORP, Underground Cable Ampacity Calculator, etc. with rudimentary GUI's and calculation engines. Some are royalty free, with no documentation or technical support. VIII. CYMCAP CYMCAP is a dedicated computer program for performing ampacity and temperature rise calculations for power cable installations. A description of its main features is given below. Analytical Capabilities • Iterative techniques based on the IEC Standards. • A detailed graphical representation of virtually any type of power cable. This facility can be used to modify existing cables and enrich the program's cable library with new ones, including singlecore, threecore, belted, pipetype, submarine, sheathed, and armored cables. • Different cable installation conditions such as directly buried, thermal backfill, underground ducts, duct banks and multiple soil layers with different thermal resistivity. • Cables in pipes with the pipe directly buried or in a thermal backfill. • Independent libraries and databases for cables, ductbanks, load curves, heat sources and installations. • Simulation of cables on riser poles, groups of cables in air, moisture migration, nearby heat sources and heat sinks, etc. • Different cable types within one installation. • Nonisothermal earth surface modeling. • Cyclic loading patterns as per IEC60853. • Multiple cables per phase with proper modeling of the sheath mutual inductances, which greatly © CYME International T&D, 2005 5 influence circulating current losses, and thus derating. • All bonding arrangements for flat and triangular formations are supported with explicit modeling of minor section lengths, unequal cable spacing, etc. Figure 5 presents a typical graphical display screen of a duct bank installation containing trefoil arrangements, threecore cables and singlephase circuits. Also, any of its cables can be displayed and edited simultaneously. Figure 5. Typical CYMCAP Screen Transient Analysis The program supports transient thermal analyses including the following: • Ampacity given time and temperature. • Temperature analysis given time and ampacity. • Time to reach a given temperature, given the ampacity • Ampacity and temperature analysis as a function of time. • Userdefined load profiles per circuit. • Multiple cables per installation. • Circuits can be loaded simultaneously or one at a time. Figure 6. Typical transient simulation report Figure 6 shows a graphical display of the results of a transient simulation. In CYMCAP one can display the temperature as a function of time simultaneously with the load curve, the installation arrangement and the cables used. D uct Bank Optimizer The Duct Bank Optimizer is an addon module to CYMCAP that allows the user to determine the optimal placement of several circuits within a duct bank. More specifically, the module can recommend the various circuit dispositions within the duct bank in order that: • The duct bank overall ampacity, i.e. the sum of the ampacities for all circuits, is maximized. • The duct bank overall ampacity, i.e. the sum of the ampacities for all circuits, is minimized. • The ampacity of any given circuit is maximized. • The ampacity of any given circuit is minimized. 1520 A 1590 A OPT 110,000 + Combinations Figure 7. Results of a duct bank optimization simulation Figure 7 presents a 3 by 4 duct bank with three trefoils and one threephase circuit (one phase per conduit). There are over 110,000 possible combinations. However, CYMCAP has an elaborated mathematical algorithm that prevents the repetitive calculation of equivalent cases, therefore the solution is obtained very efficiently. The left hand side condition in Figure 7 shows the cables placed automatically. On the righthand side one can see the optimal cable location that maximizes ampacity. Multiple Duct Banks The Multiple Duct Banks module (MDB) is the extension to CYMCAP designed to determine the steady state ampacity of cables installed in several neighboring duct banks and/or backfills with different thermal resistivity. The module presents a unique solution combining standard and nonstandard calculation methods. The module computes the values of T4 (the external to the cable thermal resistance) using finite elements and then the ampacity (or operating temperature) of the cable system is obtained using the IEC standardized solution method. The following capabilities can be highlighted: • Modeling up to eleven rectangular areas with different thermal resistivity. • Modeling up to three duct banks in a single installation. • Modeling one heat source or sink in the installation. • Computation of the steady state ampacity or temperature. © CYME International T&D, 2005 6 Figure 8 exemplifies two of the many possibilities that the MDB (Multiple Duck Bank) modeling facilities of CYMCAP can handle. Figure 8. Illustration of the MDB module of CYMCAP Validation CYMCAP has been validated against field tests. In Figure 9 a comparison between time simulations and field tests is presented. One can appreciate that the simulated and measured results match with reasonable accuracy. Figure 9. CYMCAP simulations versus field tests CYME offers the very best customer support with the commitment of answering support questions within 24 hours. Additionally, CYME holds a oneday CYMCAP seminar during its yearly User's Group in Montreal. IX. SUMMARY An introduction to the heat transfer mechanisms in underground cable installations was given. An analysis of the possible solution methods of the diffusion equations was presented. A description of the heat sources and thermal resistances of the different layers of a cable installation has been offered. The basic concepts behind the NeherMcGrath method were discussed together with the differences between the IEEE (NeherMcGrath method) and the IEC standards for underground cable installations. A description of the modeling capabilities CYMCAP, CYME's cable ampacity program, was presented. X. REFERENCES [1] George J. Anders, "Rating of Electric Power Cables: Ampacity Computations for Transmission, Distribution, and Industrial Applications, IEEE Press / McGraw Hill, 1997. [2] IEEE Standard Power Cable Ampacity Tables, IEEE Std. 8351994. [3] Electric Cables – Calculation of the current rating – Part 1: Current rating equations (100% load factor) and calculation of losses – Section 1: General. IEC Standard 28711 (199412). [4] Electric Cables – Calculation of the current rating – Part 1: Current rating equations (100% load factor) and calculation of losses – Section 2: Sheath eddy current loss factors for two circuits in flat formation. IEC Standard 28712 (199311). [5] Electric Cables – Calculation of the current rating – Part 2: Thermal resistance – Section 1: Calculation of the thermal resistance. IEC Standard 28721 (199412). [6] Electric Cables – Calculation of the current rating – Part 2: Thermal resistance – Section 2A: A method for calculating reduction factors for groups of cables in free air, protected from solar radiation. IEC Standard 28722 (199505). [7] Electric Cables – Calculation of the current rating – Part 3: Sections on operating conditions – Section 1: Reference operating conditions and selection of cable type. IEC Standard 28731 (199507). [8] Calculation of the cyclic and emergency current rating of cables – Part 1: Cyclic rating factor for cables up to and including 18/30 (36) kV. IEC Publication 8531 (1985). [9] Calculation of the cyclic and emergency current rating of cables – Part 2: Cyclic rating of cables greater than 18/30 (36) kV and emergency ratings for cables of all voltages. IEC Publication 8532 (198907). [10] J.H. Neher and M.H. McGrath, "The Calculation of the Temperature Rise and Load Capability of Cable Systems", AIEE Transactions Part III  Power Apparatus and Systems, Vol. 76, October 1957, pp. 752772. [11] V. Pashkis and H. Baker, "A method for determining the steadystate heat transfer by means of an electrical analogy", ASME Transactions, Vol. 104, pp. 105110, 1942. [12] J.H. Neher, "The Transient Temperature Rise of Buried Cable Systems", IEEE Transactions on Power Apparatus and Systems, Vol. PAS83, February 1964, pp. 102114. See also the Discussion by McGrath. [13] CIGRE, "Current Ratings of Cables for Cycling and Emergency Loads. Part 1. Cyclic Rating (load factor less than 100%) and Response to a Step Function", Electra No. 24, pp. 6396. [14] Calculation of Thermally Permissible ShortCircuit Currents, Taking into Account NonAdiabatic Heating Effects, IEC Standard 949, 1988. XI. BIOGRAPHY Francisco de León was born in Mexico City in 1959. He received the B.Sc. and the M.Sc. (summa cum laude) degrees in Electrical Engineering from the National Polytechnic Institute (Mexico), in 1983 and 1986 respectively, and obtained his Ph.D. degree from the University of Toronto, Canada, in 1992. He has held several academic positions in Mexico and has worked for the Canadian electric industry. Currently working with CYME International T&D in St. Bruno (Quebec, Canada), he develops professional grade software for power and distribution systems and is the leading technical support of CYMCAP, CYME's cable ampacity program. He has published over a dozen papers in refereed journals (IEEE/IEE), which have been cited over 100 times in journals listed in the Science Citation Index. Francisco is a Senior Member of the IEEE. 282 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 28, NO. 2, MARCHIAPRIL 1992 Correlations of Submersible Cable Performance to NeherMcGrath Ampacity Calculations Gordon C. Baker and Marcus 0. Durham, Senior Member, ZEEE AbstractThe configuration and application of electric submersible pump cable demands careful consideration of temperature effects on the cable materials. Tests were conducted to develop correlation factors and modifications to the NeherMc Grath thermal model. These disclose the unique features of the cable. A series of equations are presented. Application charts are provided to assist the user in proper selection of the cable. NOMENCLATURE 17.0 cross sectional area of copper in a conductor (circular mil) (see Table I) 3.6 0.029 diameter of conductor (inches) (see Table I) diameter over the armor (inches) NOTE: round and flat cables use different equations to calculate the Oar diameter over the jacket NOTE: round and flat cables use different equations to calculate the Djk thermal resistivity of insulation, constraining coverings, and jacket 500°C cm/Watt cable lay factor, for round cables = 1.02 conductor resistance at conductor temperature (ohms per foot) thickness of armor (inches) insulation thickness (inches) 0.090 for 5000 volt insulation rating jacket thickness (inches) 0.060 for submersible cable restraining covering thickness (inches) 0.010 for these calculations temperature of ambient surroundings ( " C) temperature of the conductor ("C) the mean temperature across the gas area ("C) temperature coefficient of zero resistance for copper 10.371 circular mil ohms per foot @20"C thermal resistance of the gas zone between the cable surface and the surrounding casing pipe Paper PID 9115, approved by the Petroleum and Chemical Industry Committee for presentation at the 1990 Petroleum and Chemical Industry Technical Conference, Houston, TX, September 10 12. Manuscript released for publication March 13, 1991. G. C. Baker is with Phillips Cables Ltd., Brockville, Canada K6V 5W4. M. 0. Durham is with Theway Corporation, and the University of Tulsa, IEEE Log Number 9104065. Tulsa, OK 74153. TABLE I CONDUCTOMRE ASUREMENTS Circular AWG Configuration mil Area Diameter #6 solid 26240 0.162" #2 stranded 66360 0.292" #1 stranded 83690 0.332" # 1 IO stranded 105600 0.373" #4 solid 41740 0.204" TR TR, thermal resistance of the insulation thermal resistance of the jacket. INTRODUCTION TH ERE ARE THREE IEEE Recommended Practices that cover the specification of electrical submersible pump cables. The Recommended Practices address polypropylene insulated cable, ethylenepropylene insulated cable, and field testing of the cable. These Recommended Practices have recently undergone a fiveyear review. In an attempt to provide more accurate data, a number of tests were conducted. The results of these tests were used to develop correlation factors for use in the NeherMcGrath relationship. AMPACITCYA LCULATIONS The useful working life of any cable is adversely affected by the operating temperature of the cable. Excessive conductor temperature may irreversibly damage the cable insulation and jacket. Submersible pump cables are applied in harsh environments with high ambient temperatures. The ambient in conjunction with conductor heat rise makes effective application of submersible cable a tedious process. This paper provides the cable user with a method to estimate the maximum conductor temperature for the submersible pump cable application. The ampacity calculations are developed from the Neher McGrath formula (see eq. 9 of [l]). Their equations were based on work derived in the early 1930's for highvoltage power cables. Nevertheless, their paper was first presented in 1957 at an IEEE (NEE) meeting in Montreal, Canada. Their equation for cable ampacity is identified: where Z conductor current (amperes) 00939994/92$03.00 0 1992 IEEE BAKER AND DURHAM: CORRELATIONS OF SUBMERSIBLE CABLE PERFORMANCE 283 Ta TC RdC 1 + Y, Td TR temperature of ambient surrounding cable ("C) temperature of conductor ("C) temperature rise of conductor due to dielectric dc resistance of conductor at conductor operating temperature T, (ohms per foot) ac/dc resistance ratio thermal resistance (per conductor) between the conductor and ambient (thermalohmfoot) . loss ("C) MODIFIECDA LCULATIONS The NeherMcGrath relationships are modified for submersible cable. Some of the calculations will be more complex. However, several assumptions can be made to simplify the ampacity calculations for pump cable applications. The 600to5000V range used in pump cables allows the removal of the dielectric loss portion of the original equation. The actual dielectric losses are very small. Therefore, the temperature rise due to dielectric Td may be neglected. Submersible cable conductors range in size from #6 to # 1/0 AWG. For this configuration, the ac/dc ratio is almost equal to one [4]. Thus, the (1 + Y,) term becomes unity. For submersible pump cables, the ampacity equation then simplifies as follows: I = sqrt[ (T,  To) / (R d, * TR) ]. (2) There are a number of terms and abbreviated symbols used in developing the relationship. The Appendix contains an alphabetic listing of these symbols. Numeric values are given where constant terms are employed. Each of the terms will be analyzed in detail. The most complex component of the equation is the thermal resistance (TR). This parameter incorporates the physical characteristics of the cable as well as the application configuration. TEMPERATUORFE C ONDUCTOR Since the surface of the metal conductor will be the hottest spot within the cable, the surface temperature of the conductor must be restricted to protect the insulation and jacket. The maximum rated conductor operating temperature T, is dependent on the submersible pump cable construction. Polypropylene (PP) insulated cables have a rated maximum operating conductor temperature of 96°C (205 OF) [61. Ethylene Propylene Diene Monomer (EPDM) is commonly referred to as EPR insulated cable. These designs may operate at much higher temperatures. An accepted maximum rated conductor operating temperature for EPDM insulated and nitrile jacketed cable is 140°C (284°F) [7]. CONDUCTORRE SISTANCE During the ampacity determinations, conductor resistance is calculated at the maximum conductor temperature. The conductor resistance relationships are based on uncoated copper. It is assumed that the increase in actual resistance due to coating of the conductors is negligible. For round cables, derivation of the conductor resistance must include corrections for length of wire. The twisting of the cable conductors effectively increases the actual length in the cable. To compensate, the conductor resistance is increased by 2 %. This inflation is incorporated into a cable lay factor (LF). The accepted factor for submersible cable is 1.02. The twisting and length increase does not apply to flat cables. Therefore, the lay factor is one. The modified conductor resistance may be expressed as follows (see eq. 10 and Table I in [l]). The resistance is measured in ohms per foot at the conductor temperature: (LF) * 10.371 * (234.5 + T,)  (4) A, * 254.5 where LF cable lay factor R,, resistivity of copper at 20°C Tzr temp coefficient of zero resistance for copper 234.5 T, conductor temperature ("C) A, cross sectional area of the conductor (circular mils). AMBIENTTE MPERATURES The ambient temperature surrounds the cable. The value of the ambient is often assumed to be the static bottom hole temperature. However, in a downhole environment, the ambient temperature depends not only on the bottom hole conditions but on a number of other factors. The temperature gradient from the perforations to the cable, the heat rise from the submersible equipment, and the heat generated from the cable all have an effect on the ambient temperature. For the ampacity calculations carried out in this project, T, may vary from 40°C (104°F) to 140°C (284°F). THERMARLE SISTANCE For submersible applications, the TR value consists of three parts. These components are the insulation TR,, jacket TR,, and the gas zone between the cable and pipe casting TR, PI. TR is expressed in thermalohmfeet (tof): TR = TR, + TR, + TU, ( 5 ) where TR, TR of the insulation TR, TR of the jacket TR, TR of gas zone between the cable surface and surrounding casing pipe. THERMARLE SISTANCOFE T HE GASZ ONE Cable that is installed within a metal conduit, such as a well casing, has some contact with the metal surface. However, much of the cable is exposed to the gas within the conduit. The heat transfer characteristics of the gas zone dramatically affects the ability of the cable to dispose of heat. From the original NeherMcGrath paper, an expression for calculating TR, may be obtained (see eq. 41 of [l]). The 284 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 28, NO. 2, MARCH/APRIL 1992 units are tof side primarily exposed to the gas zone: TRg=3*A/[1+ { ( B + (C*Tm))*Da,}] (6) Oar= [ d + (2*t;) + (2*t,)] + [2*Tj] + [4*t,,,]. where A, B, and C are constants. The article (see Table VI1 of [ l ] )p rovides numeric values for the A, B,C terms under some conditions. For example, a cable in an airfilled metal conduit has constants A = 17.0, B = 3.6, and C = 0.029. This configuration is most similar to a submersible cable operating above the fluid level of the well. Mean Temperature The parameter T, symbolizes the mean temperature across the gas area. The result is dependent on the temperature of the cable conductor T, and the ambient temperature T,. Many of the values used must be experimentally developed since each application is different. Tests were conducted by placing a thermocouple in the air space. The thermocouple was 1 in from the cable. An experimental factor of 0.3 was necessary to correct the mean temperature parameter. The mean temperature (T,) is now defined: T, = T, + [(T,  T,) *O.3]. (7) Diameter The parameter D,, depicts the diameter (in inches) over the armor. For PP and EPDM insulated cables, the insulation thickness t, is set at 0.090 in. This measurement is characteristic of 5OOOV rated cables. Calculations made with 0.075in cable, which is the insulation thickness of 3OOOV rated cables, do not appreciably alter the end result. Typically, submersible pump cable constructions include a constraining covering with a thickness t, over the insulation. It is assumed that this layer adds another 0.010 in to the insulation wall. For PP and EPDM insulated round and flat cables, the (9) THERMARLE SISTANCOFE THE INSULATION FOR ROUNDC ABLES An expression for calculating the thermal resistivity of the insulation TR, of round cables may be obtained from the NeherMcGrath paper (see eq. 39 of [l]). The reference assumed copper had a constant temperature coefficient. The relationship is modified for variations in the thermal resistivity: TR, = 0.0052 * * G, * TCF (10) where q thermal resistivity of insulation material 500 "C G, geometric factor TCF temperature correction factor. A mathematical formula for calculating the geometric factor is as follows (see [5] and eq. 8 of [l]): cm/W (see Table VI of [l] and see [3]) G, = 2.3010g,, [3 * (G, + l ) ] ( 1 1 ) [ ( 8 * ( t i + t , ) ) + t , ] * [ t , + t , + t , ] G, = 4 * d * ( t i + t,) . (12) A correction factor (TCF) has been developed to compensate for changes in the thermal resistivity with temperature. The factor is a mathematically derived number based on the positioning of the three conductors and the ratios of thickness of the insulation to the diameter of the conductors: TCF= (d*1000 + T,)/T, (13) jacket thickness ti is set at 0.060 in. The nominal armor strip thickness t,,, is 0.025 in for round cables. To compensate for the armor interlocking profile, an additional 0.060 in is where d is the diameter of the conductor (in inches), and T, is the temperature of the conductor ("cl. included in the summation. ~ Considering all these components, the diameter over round cable armor D,, may be calculated as follows. The dimensions are in inches: Oar = [d + (2*t,) + (2" t,)] *2.155 THERMARLE SISTANCOEF THE JACKETFO R ROUNDC ABLES From the original reference, an expression for calculating the thermal resistance of the jacket TR , for round cables may be obtained (see eq. 40 of [l]). Again, the TCF has been included to compensate for changes in the thermal resistivity with temperature: * 3 * [ t, / ( Djk  ti) ] * TCF ( 14) + (2 * t,) + (4 * tu,,) + 0.060" ( 8 ) where TR , = 0.0104 * t, insulation thickness t, restraining coverings thickness t, tu,, thickness of armor d diameter of conductor. A different procedure is used to determine the diameter over flat cable armor. Furthermore, there is a difference in the armor thickness. The nominal armor strip thickness t,,, diminishes to 0.020 in. The D,, measurement is taken in the flat direction. This orientation is used since the cable is mounted with the flat jacket thickness over the insulation where t, is the jacket thickness over the insulation, and Djk is the diameter of the jacket. The diameter over the jacket Dik for round cables may be represented by Djk= [ d + (2*t,) + (2*t,)] *2.155+ [ 2 * t j ] . (15) THERMARLE SISTANCOEF THE JACKETAN D INSULATION FOR FLAT CABLE The TR, and TR, values are different for flat and round cables. Neher and McGrath presented an expression for BAKER AND DURHAM: CORRELATIONS OF SUBMERSIBLE CABLE PERFORMANCE 285 I60 h v) W E 140 w a .U E 120 W c 100 w2 P: e: 80 2 80 b% 0 5 40 3 20 0 U . 120 130 140 I50 I60 170 180 190 200 210 MAXIMUM WELL TEMPERATURE (F) Fig. 1 . Ampacity for round cable, polypropylene, 205F conductor. calculating TRi and TR , of flat cables. It is assumed that the thermal resistivity of the insulation, jacket, and any reinforcing layers are equal. For flat cables, the thermal resistance of the insulation and jacket (TR, and TR,) are lumped together The referenced expression was derived for flat cable configurations used in highvoltage systems. These types of cables are not closely spaced like the three conductors in a flat pump cable. The thermal resistance would be different in For pump cable calculations, it has traditionally been assumed that thermal resistance for each conductor is equal. However, experimentation has proven that the center conductor does get slightly warmer than the outer two conductors. the jacket for flat cables may be calculated as follows (see eq. 38 of [l]): 160 2 140 2 into one equation. v z; loo g 5 ' 60 the center insulated conductor. 5 40 g 20 U 120 130 140 150 160 170 180 190 200 210 MAXIMUM WELL TEMPERATURE (F) The resistance (per conductor) Of the and Fig. 2, Ampacity for flat cable polypropylene, 205F conductor, TR,+ TR, = 0.012 * q *log (Djk/ d ) * TCF. (16) The value of Djk is calculated based on the insulation thickness, the overlying, constraining coverings or braids, and the jacket thickness. For flat cables, the diameter over the jacket Djk may be established: Djk = [ d + (2 * t i ) + (2 * t r ) ] + [2 * t,] . (17) AMPACITCYH ARTS Using the derived ampacity equations, a series of ampacity curves may be generated. Four such graphs are displayed. Figs. 1 and 2 are ampacity charts for round and for flat polypropylene insulatedpump cables, respectively. The plots exhibit the maximum current loading for different conductor sizes. These graphs were derived using a conductor temperature of 205°F. The ampacity curves for round and for flat EPDMinsulated, nitrile rubberjacketed pump cables are given in Figs. 3 and 4. The charts depict the maximum current loading for different conductor sizes. These plots were derived using a conductor temperature of 284°F. 160 h 0 wP: 140 w 3a 120 g BO W bz 100 w ' 60 e: 05 40 3 0 g 20 v o 110 130 I50 170 I90 210 230 250 270 290 MAXIMUM WELL TEMPERATURE (F) Fig. 3. Ampacity for round cable, EPDM, 284F conductor. original thermal model developed by Neher and McGrath. These test were conducted with thermocouples applied to conductors and placed in ambient gas. These tests provided the basis for the correction factor. CONCLUSIONS EXPERIMENTAL The procedures that have been introduced will provide the user with the method to estimate the conductor temperature of a submersible pump cable. Cable life can be extended by A series of experiments were conducted to verify the applicability of the correlation factors that were applied to the 286 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 28, NO. 2, MARCHIAPRIL 1992 I60 h UY W U 140 W 5a 120 g 80 v cz LOO W ' 60 U 50 40 5 0 g 20 U n 110 130 150 170 190 210 230 250 270 290 MAXIMUM WELL TEMPERATURE (F) Fig. 4. Ampacity for flat, EPDM, 284F conductor. not subjecting the materials to thermal abuse. A series of calculations and conversion factors are presented. These modify the NeherMcGrath equations for the unique configuration of electric submersible pump cable. From the correlations, a series of ampacity charts are arrayed. The curves and equations are a tool for the production or field engineer to assist in the proper selection and operation of an electrical submersible pump system. REFERENCES J. H. Neher and M. H. McGrath, "The calculation of the temperature rise and load capacity of cable systems,'' J. Power App. Syst., Oct. 1957. R. Beer and R. Trapp, "Proposed formula for oil well cable," Mar. 1985, personal communication. D. McAllister, Electrical Cables Handbook. London: Granada, 1982, Table 8.2. D. G. Fink and H. W. Beaty, Standard Handbook for Electrical Engineers (12th ed.). D. S. Simons, "Cable geometry and the calculation of current carrying capacity," AIEE Trans., June 1923. IEEE Recommended Practice for Specifying Electric Submersible Pump CablePolypropylene Insulation, IEEE STD 1019. New York: IEEE. IEEE Recommended Practice for Specifying Electric Submersible New York: McGraw Hill, Table 1819. Pump CableEthylene Polypropylene Rubber Insulation, IEEE STD 1018. New York, IEEE. Gordon C. Baker received an Honors Bachelor of Science degree in chemistry from Queens University, Kingston, Canada. He is an Applications Engineer for Phillips Cables Limited, Brockville, Canada. He has previously published four papers on mining and submersible cable applications. Mr. Baker is a Charter Chemist (CChem) in Canada. He is a past member of ASTM and the American Chemical Society. He has been active on the CSA Working Group M421 and CSA C22.2 #96. He is also a member of the Electrical Electronic Manufacturers Association of Canada and an alternate to ICEA. In addition, he is a member of the IEEE working group on electrical submersible pump cable. Marcus 0. Durham (S'64M'76SM'82) received the B.S. degree in electrical engineering from Louisiana Technical University, Ruston, the M.E. degree in engineering systems from the University of Tulsa, Tulsa, OK, and the Ph.D. degree in electrical engineering from Oklahoma State University, Stillwater. He is the Principal Engineer of Theway Corp., Tulsa, OK, which is an engineering, management, and operations group that conducts training, develops computer systems, and provides design and failure analysis of facilities and electrical installations. He is also an associate professor at the University of Tulsa, specializing in microcomputer applications and electrical/mechanical energy systems. He has developed a broad spectrum of electrical and facilities projects for both U.S. and international companies. Based on his extensive background, he has become a recognized author who has published numerous papers, articles, and manuals and has conducted training in such diverse topics as electrical power design, management, and microcomputer applications. Dr. Durham is a registered Professional Engineer, a state licensed electrical contractor, and a FCC licensed radiotelephone engineer. Professional affiliations include member of the Society of Petroleum Engineers. He has served on and been Chairman of many committees and standards groups within the IEEE, SPE, and API. Honorary affiliations include Phi Kapp Phi, Tau Beta Pi, and Eta Kappa Nu.
