2382 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 50, NO. 4, JULY/AUGUST 2014

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1 2382 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 50, NO. 4, JULY/AUGUST 2014 Power Transfer Capability of HVAC Cables for Subsea Transmission and Distribution Systems Joseph Song-Manguelle, Senior Member, IEEE, Maja Harfman Todorovic, Senior Member, IEEE, Song Chi, Member, IEEE, Satish K. Gunturi, Senior Member, IEEE, and Rajib Datta Abstract This paper provides a methodology to estimate power versus distance envelops of high voltage alternating current (HVAC) transmission systems for subsea applications. Alternating current (AC) technology is mature and is proven for land-based applications and relatively short offshore tiebacks. However, for long tiebacks, due to increased conductor capacitance, large reactive power needs to be supplied, leading to higher cable current rating, losses, and expensive umbilical. Subsea ac cables are limited in their capability to transmit power beyond a certain distance, depending on cable characteristics, installation conditions, and system operating mode. Power transfer boundary charts for ac technology based on analytical methods are presented. Analytical calculations and computer simulations of HVAC power cables were performed on more than 30 cables with rated voltage between 35 and 150 kv and cable cross sections between 95 and 400 mm 2. Effects of reactive compensation on system tieback distance have been analyzed, as well as low-frequency transmission and different modes of system operation. Cable models employing multiple pi sections and distributed parameters were used. Well-known power flow and simulation tools were used for validation. AC transmission boundaries were estimated based on the voltage and current limits for various cables under various operating modes. Index Terms High-voltage alternating current (HVAC), highvoltage direct current, oil and gas, subsea power, transmission and distribution (T&D). I. INTRODUCTION WITH the depletion of existing oil and gas reserves, there is a growing demand for deepwater oil and gas production, which requires long-distance power transmission and distribution (T&D) to multiple subsea electrical loads. Electric power can be transmitted and distributed over long distances Manuscript received July 15, 2013; accepted October 14, Date of publication November 20, 2013; date of current version July 15, Paper 2013-PCIC-476, presented at the 2013 IEEE Petroleum and Chemical Industry Technical Conference, Chicago, IL, USA, September 23 25, and approved for publication in the IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS by the Petroleum and Chemical Industry Committee of the IEEE Industry Applications Society. This work was supported in part by the Research Partnership to Secure Energy for America through the Ultra-Deepwater and Unconventional Natural Gas and Other Petroleum Resources program authorized by the U.S. Energy Policy Act of 2005 and in part by GE Global Research. J. Song-Manguelle is with ExxonMobil, Houston, TX USA ( joseph.m.song@exxonmobil.com). M. Harfman Todorovic, S. Chi, and R. Datta are with GE Global Research, Niskayuna, NY USA ( harfmanm@ge.com; chis@ge.com; datta@ge.com). S. K. Gunturi was with GE Global Research, Niskayuna, NY USA. He is now with GE Energy Storage, Schenectady, NY USA ( gunturi@ge.com). Color versions of one or more of the figures in this paper are available online at Digital Object Identifier /TIA Fig. 1. Subsea T&D system with conventional ac technology. either by alternating current (ac) or direct current. Subsea electrification is a key enabler and an integral part of processing and control for deepwater oil and gas production. Subsea processing (pumping, compression, and separation) requires the deployment of equipment such as variable speed drives, motors, switchgear, and power supplies in close proximity to the loads, which are connected via dry and wet mate connectors. Subsea control requires electric actuators and valves for all-electric trees and highly reliable power supply for communication and control at long step-out distances. This equipment requires easy and reliable installation and retrieval to increase production availability. The goal of subsea power T&D is to provide reliable power down to the seabed for production, processing, and control. Fig. 1 shows a typical subsea T&D system using conventional ac technology. The ac transmission system is a mature and proven technology for land-based applications and relatively short offshore tiebacks. However, due to cable capacitance, a large amount of reactive power needs to be supplied, in addition to the active power needed by the loads. This leads to larger cables with higher current rating and losses and, consequently, more expensive umbilical [1], [2]. The issue is particularly severe for longer step outs. For example, to supply approximately 60 MW of active power loads on the seabed with 75-mi step out, it is required to provide approximately 70-Mvar reactive power and 2-MW power loss under no-load condition and approximately 50-Mvar reactive power and 4-MW power loss under full-load condition. In this paper, a methodology is provided to estimate power versus distance envelops for a given high voltage ac (HVAC) cable. Analyses were performed on more than 30 power cables, with rated voltage between 35 and 150 kv and cable cross sections between 95 and 400 mm 2. Effects of reactive compensation and transmission frequency on system tieback IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See for more information.

2 SONG-MANGUELLE et al.: POWER TRANSFER CAPABILITY OF HVAC CABLES FOR SUBSEA T&D SYSTEMS 2383 distance have been analyzed. Two different modes of system operations have been investigated: constant sending end voltage and variable sending end voltage through a tap-changing transformer. Cable models employing multiple pi sections and distributed parameters were used to improve the accuracy of the results. Power flow analysis was performed using wellknown simulation tools [4], [5]. Power versus distance envelops were estimated based on system voltage and current limitation of each cable. The information and methods provided in this paper are useful for design engineers and companies interested in assessing the feasibility of supplying power to offshore long tiebacks involving multiple subsea electrical loads. II. SYSTEM ASSUMPTIONS FOR BOUNDARY ESTIMATION A. System Transmission Voltage It is assumed that for a given cable, the transmission voltage of the system is 80% of the cable rated voltage. The 20% voltage derating factor is applied to limit the electrical insulation stress 1 on the cable for subsea application. The transmission voltage (derated nominal voltage of the cable) is therefore considered as the reference voltage of the system and is taken as 1.0 per unit (p.u.). If the power cable is already designed for adequately high insulation stress, then the transmission voltage does not need to be derated. B. System Operating Mode Two modes of system operation are considered. 1) Mode 1: The sending end voltage is kept constant at 1.0 p.u. The acceptable voltage fluctuation is ±10% of its transmission voltage (derated nominal voltage). As a consequence, at no-load condition, the voltage at the receiving end of the cable is allowed to increase due to Ferranti effect, up to 1.1 p.u of the transmission voltage. When the cable is loaded, the voltage droop at the cable receiving end is limited to 0.9 p.u. 2) Mode 2: The receiving end voltage is kept constant at 1.0 p.u. Depending on the transmission distance and system loading conditions, the transmission voltage is selected and adjusted to match the 1.0-p.u. voltage at the cable receiving end. The voltage adjustment can be done through a tap-changing transformer with multiple taps located topside or onshore. The subsea transformer is therefore designed with an input voltage equal to the system transmission voltage and does not need to be redesigned for each site. C. Acceptable Transmission Current The nominal current rating of the cable is provided in cable datasheet. Due to significant variability in ambient conditions such as temperature and soil resistivity and cable installation 1 The voltage stress on the insulation of a given conductor can be calculated as follows E 0 = U/(r ln(r/r)) (kv/mm), whereu is the voltage applied to the conductor (e.g., phase-to-ground voltage), r is the radius of the copper conductor under the inner semiconductive layer of the cable, and R is the radius of the insulated conductor under the outer semiconductive layer [3]. Fig. 2. Simplified model of HVAC T&D system with a cable pi section. conditions, such as cable laying depth, umbilical length, and trefoil or flat cable, the cable current carrying capability needs to be derated. In this analysis, a 30% current derating factor has been applied. Therefore, a 1.0-p.u. cable current corresponds to 70% of the nominal current provided in the cable datasheet. D. Cable Model Cable model has been selected to simplify system load flow equations. For Mode 1 operation (constant sending end voltage), multiple pi sections are used as the cable model, with one pi section per kilometer (km) of transmission line. For Mode 2 operation, a distributed cable parameter model is used. These models are similar to the models implemented in wellknown simulation software [4], [5]. E. Transformer Impedance and Load Characteristics The impedance of the sending and receiving ends transformers is assumed to be 5%. Loads are assumed to be located on the seabed and connected to the transmission line at the secondary of a single subsea transformer. The primary of the subsea transformer is connected at the receiving end of the cable. Therefore, interspersed loads distributed along the transmission line are excluded in this analysis. It is also assumed that the subsea transformer is only supplying variable frequency drives (VFDs). VFDs are usually designed to operate near-unity power factor seeing from their input side, regardless of the motor power factor. Subsea processes require VFDs to run at different operating points. An overall 2% margin on the power factor is considered at the transformer secondary. Therefore, estimations are based on a lagging power factor of For topside drive systems where a single VFD is used for each load, the VFD is located topside or onshore and connected at the cable sending end. In that case, it is assumed that motor power factor is 0.85 lagging. The VFD is supposed to provide cable and load reactive power. Motor and VFD efficiencies are excluded in this investigation. Therefore, the estimated power transfer capability of the transmission line is not the same as shaft power rating. III. POWER TRANSFER BOUNDARY ESTIMATION METHOD A. Limiting Factors To Transmit Power With HVAC Cables 1) Receiving End Voltage Under No-Load Conditions: A simplified HVAC T&D model is shown in Fig. 2. The power generation unit (grid or topside turbo generator) is simplified as

3 2384 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 50, NO. 4, JULY/AUGUST 2014 a voltage source. Lumped impedance of the power generation unit and the sending transformer is replaced by the resistance R ST and the inductance L ST. In this case, only a single pi section of the cable is shown, with its lumped parameters R C, L C, and C. The impedance of the subsea transformer is given by R T and L T. Overall, subsea loads are represented as an equivalent impedance with its power factor. A more accurate model is used, with multiple pi sections or uniformly distributed line parameters. If a voltage V SE is applied at the cable sending end, the voltage V RE at the cable receiving end under no-load condition is given by V RE = V SE cos(dω LC) where d corresponds to the transmission distance, L in henries (H) and C in farads (F) are the cable inductance and capacitance per unit length (for example, kilometers or miles), ω (ω =2πf) corresponds to the transmission voltage pulsation (in radians per second), and f is the transmission voltage frequency (in hertzs). For a given cable, the maximum transmission distance is limited by the voltage rise at the cable receiving end d maxv based on assumption (see Section II-A) and is given by ( ) 1 d maxv = a cos k (1) 1 ω LC. (2) k =1.1is the coefficient defining acceptable margins on the voltage rise due to Ferranti effect; according to assumption (see Section II-A), maximum acceptable voltage rise at the receiving end is supposed to be no more than 110% of the nominal transmission voltage. The unit of d maxv is the same as the unit used to define the per unit length of L and C. 2) Cable Current Carrying Capability: Under no-load conditions, the cable mainly carries the reactive current for charging the line capacitance 2, which can be approximated by [6] I C = V SE ωc (A/unit length). (3) The line charging current depends on the transmission frequency, i.e., the lower the frequency, the smaller the charging current. In addition, the current increases with the line capacitance, which is distributed along the transmission line; therefore, it increases with the transmission distance; the longer the distance, the higher the charging current. Under loaded conditions, the cable carries the reactive current to charge the line, the active current for line losses 3, and the useful active and reactive currents for the load. This imposes limits on the current carrying capability of the cable. For a selected transmission distance, the current margin remaining after the line is charged corresponds to the useful current for the load. There is a cutoff distance where the cable is fully 2 There are other leakage currents, but the capacitive current has the largest magnitude. The active component of the charging current is a small fraction of the cable charging current and can be neglected for transfer capability estimation [1]. 3 There are mainly four types of losses: dielectric losses, conductor losses (due to conductor resistance), metallic shield losses, and armor losses [1]. All these losses are neglected in this estimation; they represent a small fraction of the cable nominal power capability. loaded with line charging current. In that case, no power can be transferred to the load. That cutoff distance corresponds to the transmission limit of the cable, based on the current limitation. B. Power Transmission Boundary Estimation For a given ac power cable, load flow equations of the system are solved with varying distance and for each loading condition, from no load to full load. The no-load power corresponds to 0 MW, and full load corresponds to the approximate maximum power that can be carried by that cable. This power is estimated as the product of the derated transmission voltage and the derated current carrying capability of the investigated cable, with a 98% power factor. The total power is divided into 50 equal steps, and the maximum transmission distance is estimated for each power step. The initial transmission distance is 1 km, which corresponds to a cable with one pi section. The distance is linearly increased by 1 km (i.e., by one pi section); load flow equations are then solved for that system (for all 50 power steps), at each bus of the system and at each distance step. For example, at the twentieth kilometer of a transmission line, load flow equations of the system are solved first for 1 km of the transmission distance. Voltage and current at each bus of the transmission line (grid bus, sending end bus, receiving end bus, and load bus) are calculated. Then the new set of load flow equations is solved for 2 km, i.e., with a cable having two pi sections for all 50 power steps. In this case, the system buses are the following: grid bus, sending end bus, first pi section bus, second pi section bus, receiving end bus, and load bus. This approach is repeated over the total transmission distance of 20 km. At each distance segment, computed voltages and currents at each bus are stored with the corresponding power and distance. For each distance segment and for each power increment, the voltage at each bus is controlled to be between 90% and 110% of its nominal derated value. The distance where one of the bus voltages reaches the upper or lower limits for the power level is considered as the maximum distance due to voltage limitation, i.e., d maxv. If none of the voltage is out of the limits, then the maximum distance is defined by the no-load conditions. The same approach is applied to the sending end current, which is limited to the maximum allowable current on the cable (derated nominal current). The distance at which the sending end current reaches 100% of derated current is considered as the maximum distance due to current limitation, i.e., d maxi. The overall transfer capability of the cable is the smaller of the two distances, i.e., d max =min(d maxv,d maxi ). (4) A power versus distance envelop is then plotted for that cable and corresponds to the power transfer capability of the selected cable. Fig. 3 shows the receiving end voltage of a given cable for increments of receiving end power by 25%. At noload condition, that voltage increases as the distance increases (Ferranti effect). The cable receiving end voltage drops as the load increases. The maximum transmissible distance

4 SONG-MANGUELLE et al.: POWER TRANSFER CAPABILITY OF HVAC CABLES FOR SUBSEA T&D SYSTEMS 2385 Fig. 3. Receiving end voltage versus distances of a given cable for receiving end power increments of 25%. Fig. 5. Power versus distance envelope summarizing the results based on voltage and current limitations. However, the actual limit comes from the current rating of the cable. At no-load condition, the cable current rating is reached at about 60 mi. The current rating of the cable is fully utilized in supplying the reactive power demand of the cable and resistive losses. As load increases, the load current gets added to the reactive power. Hence, the amount of reactive power that can be supplied with increasing load gets progressively limited, thereby limiting the distance of transmission. Therefore, from the distances corresponding to the voltage limit and the current limit, the lowest distance determines the power transmission capability of that cable. Selected results are discussed in the next sections. Fig. 4. Sending end current versus distances of a given cable for receiving end power increments of 25%. determined by the voltage limitation is defined as the distance where the no-load receiving end voltage reaches 1.1 p.u. For the remaining power steps, the voltage continues to drop, as compared with the no-load voltage. Given that subsea processes start with the no-load condition, that corresponding distance becomes the transmission capability of the cable, even if the transmission distance is longer under loaded conditions. Fig. 4 shows the corresponding sending end current for the same power steps. The current limitation for each power steps corresponds to the distance where the sending end current reaches 1 p.u. (derated nominal current of the cable). Fig. 5 shows the power versus distance envelope summarizing the results based on voltage and current limitations. The same methodology is applied to all cables used for subsea HVAC T&D. It is observed that the increase in receiving end voltage at no-load condition sets a limit to the maximum distance (approximately 70 mi). As the load increases, the voltage at the receiving end is reduced, and hence, the distance over which power can be transferred increases. IV. SELECTED RESULTS A. Convention HVAC T&D Without Compensation at 60 Hz The method described in the previous section has been applied to several HVAC cables. Some of the cable parameters used are provided in [3]. According to assumption (see Section II-A), the transmission voltage of a 110-kV cable class is 88 kv, 106 kv for a 132-kV cable class, and 120 kv for a 150-kV cable class. These voltages correspond to 1.0 p.u. of the system voltage. According to assumption (see Section II-C), the reference current of these cables are derated to 70% of the current value given in [3]. Figs. 6 8 show the power versus distance envelops of the 110-, 132-, and 150-kV cable classes. The following are observed. 1) Regardless of the cable cross section and the voltage rating of the cable, the power transfer limit of these three sets of cables is approximately 60 mi. 2) For low power loads (0 40 MW), the cable cross section has minor impact on the maximum transfer tieback distance. 3) For a given application, increasing the cross section of the cable mostly increases the maximum power that can be supplied to subsea loads. It has minor impact on the maximum transfer tieback distance.

5 2386 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 50, NO. 4, JULY/AUGUST 2014 Fig. 6. Mode 1 operation. Power transfer capability of a 110-kV cable class (uncompensated 60-Hz transmission). Fig. 9. cable. Mode 1 operation. Example of receiving end voltage of a 35-kV XLPE Fig. 7. Mode 1 operation. Power transfer capability of a 132-kV cable class (uncompensated 60-Hz transmission). Fig. 10. cable. Mode 1 operation. Example of sending end current of a 35-kV XLPE Fig. 8. Mode 1 operation. Power transfer capability of a 150-kV cable class (uncompensated 60-Hz transmission). B. Low-Voltage XLPE and EPR Cables Without Compensation at 60 Hz Low-voltage cross-linked polyethylene (XLPE) and ethylene propylene rubber (EPR) cables have been also investigated. The cables have been designed specifically for subsea applications; hence, they have high insulation capabilities. Their electrical insulation stress is between 3 and 4 kv/mm. Therefore, the transmission voltage used is not derated. Three sets of cables have been used: 35-kV XLPE and 35- and 69-kV EPR. A derating factor has been only applied to their current rating, according to assumption (see Section II-C). The method described in the previous section has been also used. Fig. 9 shows an example of the cable receiving voltage. Both the upper (1.1 p.u.) and lower (0.9 p.u.) limits are used to set the cable power transfer capability limits. The corresponding sending current is shown in Fig. 10. The cable transfer limitation is mainly determined by the voltage limitation. Therefore, the derating factor applied to the cable current has only a minor

6 SONG-MANGUELLE et al.: POWER TRANSFER CAPABILITY OF HVAC CABLES FOR SUBSEA T&D SYSTEMS 2387 Fig. 11. Mode 1 operation. Power transfer capability of a 35-kV XLPE 107 mm 2 cable (uncompensated 60-Hz transmission). Fig. 13. class. Mode 1 operation. Power transfer capability of a 35-kV EPR cable Fig. 12. Mode 1 operation. Power transfer capability of a 35-kV XLPE cable class (uncompensated 60-Hz transmission). impact on the maximum tieback distance, as shown in Fig. 11. A summary of the results is shown in Fig. 12 for different cable cross sections. Low power loads (5 8 MW with approximately 1 2 subsea VFDs for motor rating of MVA) can be supplied with these cables for a tieback distance up to 85 mi. A similar analysis has been performed for EPR cables with 35- and 69-kV transmission voltages. The results are summarized in Figs. 13 and 14. As explained in the previous sections, the transmission capability of ac cables is limited due to voltage rise at no-load (Ferranti effect) condition and cable charging current, which reduces the margin of load current that can be transmitted. The line charging current is the sum of currents flowing through line capacitances. With a simplified single pi section, as shown in Fig. 2, the line charging current corresponds to the sum of the two currents flowing through the two capacitors. C. Conventional HVAC T&D With Compensation at 60 Hz For HVAC systems where loads are supplied by VFD, the power factor at the receiving end is near unity. In that case, Fig. 14. class. Mode 1 operation. Power transfer capability of a 69-kV EPR cable there is negligible compensation from the load. However, an inductive compensation may be connected at the end of the line capacitor, to reduce the amount of charging current [see Fig. 15(b)]. Assume that an inductance is connected in parallel to the receiving end right-hand side capacitor. The current i 0 through the new branch is then reduced. The current through the capacitor located at the right of the pi section can be calculated as follows: Without compensation, i 0 = i c2 + i xre. (5) i 0 = jv RE ( c 2 ωd ). (6) With compensation, ( ) c i 0 = jv RE 2 ωd 1. (7) ωdl RE

7 2388 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 50, NO. 4, JULY/AUGUST 2014 Fig. 15. Basic principle of line capacitance compensation at cable receiving end. (a) Fixed compensation. (b) Line model with fixed compensation. Fig. 17. Mode 1 operation. Power transfer boundary of 35-kV XLPE class cables with compensation at 60 Hz. transfer tieback distance increases from 60 mi to approximately 90 mi with a fixed inductive compensation of 20 Mvar. The rating of the compensation only depends on the transmission distance, not on the maximum load installed at a given distance. This statement is consistent because the transmission distance is limited by the Ferranti effect at the cable receiving end at no-load conditions. Similar results are shown in Fig. 17 for XLPE cables, which shows a distance increase from 80 mi (uncompensated system at 60 Hz shown in Fig. 13) to approximately 110 mi. Fig. 16. Mode 1 operation. Power transfer boundary of 150-kV class cables with compensation at 60 Hz. Equation (7) shows that if an inductance is connected at the receiving end of the cable, the magnitude of the line charging current will be reduced compared with its initial value without compensation [see (6)]. That current reduction consequently lowers the amount of current to flow through the cable. Therefore, system transmission distance may be increased for the same load, or higher load may be supplied at the same distance. The cable power transfer capability is improved with the compensation. The amount of compensation can be selected to reduce a given percentage of the cable capacitance; the higher that percentage, the bigger the inductance. This method has been used to highlight effects of compensation on cable transfer capability. It has been assumed that a fixed inductive compensation is installed on the receiving end of the cable, to compensate for 20% of the total cable capacitance. The fraction of the cable capacitance to be compensated should be defined based on an acceptable size of inductance to be marinized. This aspect is out of the scope of this estimation. Selected results are shown in Fig. 16, with the corresponding reactive power to be installed subsea. Compared with the uncompensated results with the same cable (Fig. 8), the maximum D. Effects of Frequency on the Transmission Line Assuming a lumped model of the transmission line, as shown in Fig. 2, if a voltage V SE is applied at the cable sending end, the receiving end voltage at the subsea cable end under no-load conditions can be calculated as given in (1), and (8) shows that the maximum transmission distance increases as the transmission frequency decreases, i.e., ( ) 1 1 d maxv = a cos k 2π LC 1 f. (8) With the same approximation, (9) shows that the maximum transmission distance due to current limitation also increases when the frequency decreases, i.e., d maxi = 2 2πCV SE 1 f. (9) Based on (8) and (9), for a given transmission voltage, the maximum transmission distance of a power cable increases if the transmission frequency decreases. However, physical sizes of the passive components such as topside transformer, subsea distribution transformer, and input transformers for each VFD will also increase. For a transmission frequency of 20 Hz, their size and weight will be approximately three times the size of 60-Hz transformers. This may be a limitation to expending low-frequency power transmission lines. The size and weight increase of

8 SONG-MANGUELLE et al.: POWER TRANSFER CAPABILITY OF HVAC CABLES FOR SUBSEA T&D SYSTEMS 2389 Fig. 18. system. Sending end configuration for a low-frequency transmission T&D subsea transformers also increases the installation complexity and cost. Low-frequency systems incur additional complexities, i.e., system interfaces such as sending end switchgear and subsea switchgear; dry and wet connectors should be designed for low-frequency operation because they are not available in the present subsea systems. An additional power conversion station (see Fig. 18) is also required to reduce the transmission frequency from 50/60 Hz to a lower frequency (e.g., 20 Hz). Therefore, this low-frequency subsea system may not be a promising alternative to an existing ac system. Fig. 19. Mode 2 operation. Sending end voltages that produce constant receiving end voltages at different loading conditions and different tieback distances. V. A LTERNATE APPROACH: CONSTANT RECEIVING END VOLTAGE METHOD A. Preliminary Considerations Results presented in the previous sections are based on Mode 1 operation according to assumption (see Section II-B). In that operating mode, the sending end voltage is kept constant and the receiving end voltage is allowed to fluctuate according to the transmission distance and the system loading conditions. Such system operation has the disadvantage that the subsea distribution transformer is required to be qualified for a wider range of voltage. Therefore, it may be beneficial to design a T&D system where the voltage at the receiving end is kept constant at the transformer nominal voltage, regardless of the step-out distance or subsea load power level (from no load to full load). One solution to fulfill the requirement of constant receiving end voltage is to use a tap-changing transformer at the sending end. In this case, the sending end voltage can be adjusted to keep the receiving end voltage constant with fluctuations in load or changes in tieback distance. Fig. 19 shows the sending end voltage variation, which produces a constant receiving end voltage (1.0 p.u.) regardless of load level and distance, for a 150-kV cable with 400 mm 2 cross section. It has been assumed that the sending end voltage can fluctuate between 0.85 and 1.1 p.u of the cable nominal derated voltage. For a given distance, it is assumed that the sending end voltage is linearly varied with change in the load, as shown in Fig. 22. The chosen transmission distance corresponds to the distance where the no-load sending end voltage is set to 0.85 p.u., as shown by the red dots in Fig. 20. B. Line Model and Analysis Method A two-terminal passive components model of a transmission line has been used, with its distributed parameters R C, L C, and C [7]. The sending end voltage V SE has been kept constant Fig. 20. Mode 2 operation. Sending end current based on a constant receiving end voltage method. to 1.0 p.u., and the cable has been increasingly loaded from no load to its full load capability with 50 power steps. The receiving end current I RE has been calculated according to the load variation. Then the sending end voltage and current have been calculated according to (8) [7]. Examples of results are shown in Figs. 20 and 21. The sending and receiving ends voltages and currents are related as follows: [ ] [ ][ ] VSE cos h(λd) ZW sin h(λd) VRE = (10) Y W sin h(λd) cos h(λd) I SE I RE where γ = LC is the propagation constant of the line, and d is the transmission distance. The cable impedance Z C is given by Z C = R C + jx C, Y C = jωc, and the cable is given by Z W = Z C /Y C Y W =1/Z W. (11)

9 2390 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 50, NO. 4, JULY/AUGUST 2014 Fig. 21. Mode 2 operation. Example of power transfer boundary. Fig. 22. Sending end voltage adjustment as a function of cable loads, for all tieback distances. VI. CONCLUSION A methodology to estimate power versus distance envelops for subsea power T&D systems has been presented considering various system assumptions, practical operating conditions, and cable models. The power transfer capability of a given HVAC cable is affected by cable voltage and current limitations. Cable voltage is limited by acceptable transmission voltage increase under no-load conditions due to Ferranti effects (upper margin) and voltage droop under loaded conditions (lower margin). Current carrying capability of a cable is influenced by installation conditions. Current cable limitation is dictated by the system transmission frequency and reactive charging current for the line capacitance. Based on various system assumptions, calculation and simulation results discussed in this paper have shown that most of the investigated HVAC cables have comparable cutoff transmission distance where the cable is fully loaded with the capacitive charging current of the line. For noncompensated systems, this distance is around mi, with the constant sending end operating mode, regardless of the cable cross section. Investigated cables include 110-, 132-, and 150-kV nominal voltage classes, with cross sections between 185 and 400 mm 2. This distance can be increased by around 5 mi if a tap-changing transformer is used to keep the receiving end voltage constant, regardless of the cable loading conditions. On the other hand, this transmission distance can be also increased by mi if a fixed inductive reactance is installed subsea to compensate up to 20% of the total cable capacitance. For 35-kV (XLPE and EPR) and 69-kV EPR cables specifically designed for the subsea transmission, the cutoff distance is approximately between 80 and 90 mi without compensation and around 110 mi with 20% compensation. However, electrical power that can be transmitted up to such distance is approximately 6 MW; taking into account system efficiency, only a single load (e.g., pump load) can be supplied. These cables are therefore suitable for a topside drive application. The methodology presented in this paper can be extended to subsea T&D systems with variable compensation or combined fixed (inductive or capacitive) and variable compensation. The transmission distance is then swept from 1 km to a very long distance (e.g., 300 mi). Then the maximum transfer capability based on current limitation d maxi is defined whenever the sending end current reaches its derated value. The maximum transfer capability d maxv based on voltage limitation is defined whenever the sending end voltage is out of its upper (1.1 p.u.) or lower (0.85 p.u.) limits. The cable power transfer capability is taken as the minimum between d maxi and d maxv. An example of sending end voltage versus power is shown in Fig. 22. For a given transmission distance, the sending end tap-changing transformer plots are defined as the calculated sending end voltages at that distance for each loading conditions. An example of results is shown in Fig. 21. For this particular cable, Mode 2 operation without compensation increases the transmission distance about 5 mi compared with Mode 1 operation (see Fig. 8). ACKNOWLEDGMENT Research Partnership to Secure Energy for America (RPSEA) ( is a nonprofit corporation whose mission is to provide a stewardship role in ensuring the focused research, development, and deployment of safe and environmentally responsible technology that can effectively deliver hydrocarbons from domestic resources to the citizens of the United States. RPSEA, operating as a consortium of premier U.S. energy research universities, industry, and independent research organizations, manages the program under a contract with the U.S. Department of Energy s National Energy Technology Laboratory. The authors would also like to thank the RPSEA working group for valuable suggestions and the GE Global Research Center for facilities for this investigation.

10 SONG-MANGUELLE et al.: POWER TRANSFER CAPABILITY OF HVAC CABLES FOR SUBSEA T&D SYSTEMS 2391 REFERENCES [1] W. A. Thue, Electrical Power Cable Engineering. New York, NY, USA: Marcel Dekker, [2] T. Worzyk, Submarine Power Cables. Berlin, Germany: Springer, [3] XLPE Cable Systems, rev. 1, ABB, Zurich, Switzerland, [4] Operation Technology Inc., ETAP, Power System Analysis Software, ETAP, Irvine, CA, USA, [5] EMTP, EMTP-RV ElectroMagnetic Transients Program User s Guide, EMTP, Middleton, WI, USA, [6] C. S. Schifrren and W. C. Marble, Charging current limitations in operation of high-voltage cable lines, IEEE Trans. Power App. Syst., vol. 75, no. 3, pp , Jan [7] A. Panosyan, Modeling of advanced power transmission system controllers, Ph.D. dissertation, Univ. Hannover, Hanover, Germany, Song Chi (S 04 M 07) received the Ph.D. degree in electrical engineering from The Ohio State University, Columbus, OH, USA. Since 2008, he has been an Electrical Engineer with GE Global Research, Niskayuna, NY, USA. Dr. Chi is a member of the Industrial Drives Committee of the IEEE Industry Applications Society. Joseph Song-Manguelle (M 07 SM 10) received the B.S. degree in pedagogical sciences and the M.S. degree in electrical engineering from the University of Douala, Douala, Cameroon, and the Ph.D. degree in electrical engineering from the Swiss Federal Institute of Technology, Lausanne, Switzerland. He held engineering positions with GE Global Research, Munich, Germany, and GE Oil and Gas, Le Creusot, France, where he was involved in the design and test of large variable-frequency drives (VFDs), as well as developing new solutions for solving torsional vibration issues resulting from VFDs. In 2008, he joined GE Global Research, Niskayuna, NY, USA, where he designed high-voltage direct current power transmission and distribution systems for future long tieback subsea applications. Since 2012, he has been a Senior Electrical Engineer with ExxonMobil Development, Houston, TX, USA, where he is focused on oil and gas facilities design, as well as technical qualification of subsea electrical components such as subsea power cables, subsea VFDs, subsea motors (induction and permanent magnet), subsea transformers, and subsea switchgears. Dr. Song-Manguelle is a member of the Petroleum and Chemical Industry Committee Standards and Marine Subcommittees, the Industrial Drives Committee, and the Power Electronics Committee of the IEEE Industry Applications Society. He currently serves as an Associate Editor of the Industrial Drives Committee for the IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS. Maja Harfman Todorovic (S 03 M 08 SM 13) received the Ph.D. degree in electrical engineering from Texas A&M University, College Station, TX, USA. Since 2008, she has been a Lead Power Engineer with GE Global Research, Niskayuna, NY, USA. Dr. Todorovic is a member of the Industrial Drives Committee and the Power Electronic Devices and Components Committee of the IEEE Industry Applications Society. Satish K. Gunturi (M 05 SM 12) received the Ph.D. degree in materials science and metallurgy from Cambridge University, Cambridge, U.K. He was a Principal Scientist with ABB Corporate Research, Zürich, Switzerland, dealing with power electronics packaging. He is currently a Senior Materials Technologist with GE Energy Storage, Schenectady, NY, USA. Prior to that, he was a Senior Engineer with GE Global Research, Niskayuna, NY, USA. Rajib Datta received the B.E. degree in electrical engineering from Jadavpur University, Calcutta, India, in 1992, the M.Tech. degree in electrical engineering from the Indian Institute of Technology, Kharagpur, India, in 1994, and the Ph.D. degree from the Indian Institute of Science (IISc), Bangalore, India. From 1995 to 2000, he was a Research Scholar with the Department of Electrical Engineering, IISc. From 2000 to 2001, he worked on converter topologies for large-scale wind parks with the ABB Corporate Research Center, Ladenburg, Germany. From 2001 to 2012, he was a Senior Engineer and Laboratory Manager in the power conversion organization with GE Global Research, Niskayuna, NY, USA. In 2013, he was an Associate Professor with Arizona State University, Phoenix, AZ, USA. Since 2014, he has been a Principal Engineer at GE Global Research.