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1 Server Technology Inc. Phase Balancing: The Last Few Inches Of a High-Efficiency Power System White Paper STI June-25 Headquarters Server Technology, Inc Sandhill Drive Reno, NV United States of America +001 (775) Tel +001 (775) Fax EMEA Server Technology Intl. Sienna Court The Broadway Maidenhead Berkshire SL6 1NJ United Kingdom +44 (0) Tel +44 (0) Fax APAC Server Technology, Inc. 37 th Floor, Singapore Land Tower 50 Raffles Place Singapore, (0) Tel +65 (0) Fax

2 Overview Within enterprise data centers, power used for operating the facility, lighting, running IT loads and cooling is the largest operational expense. Numerous papers and articles have been published by The Green Grid, The Uptime Institute, PG&E, Lawrence Berkeley Laboratories and others discussing ways to measure, monitor and increase efficiencies. This paper discusses the effect on efficiency of load balancing across phases in a 3-phase distribution system. Though it is well known that an attempt should be made to balance loads in a 3-phase system, losses attributed to the failure to balance are not typically discussed. As amperage delivered to the data center cabinet continues to increase from 30A to 60A to 100A+, losses in the feeder wiring should be considered. 2 Phase Balancing: The Last Few Inches Of a High-Efficiency

3 The Math: Joule s First Law Joule's first law describes the relationship between the heat generated within and the current flowing through an electrical conductor. It is named for James Prescott Joule who studied the phenomenon in the 1840s. It is expressed as: Q = I 2 R t where Q is the heat generated by a constant current I flowing through a conductor of electrical resistance R, for time t. When current, resistance and time are expressed in amperes, ohms, and seconds respectively, the unit of Q is the joule. Dividing both sides of the equation by t gives: P = I 2 R where P is power in watts. One watt equals one joule per second. For any conductor with a specific known resistance, as the current increases, the power loss through that conductor increases as the square. For instance, a doubling of current will quadruple the power loss and thus heating from that conductor. Feeder Cable Resistance This table provides a quick reference for solid copper wire resistance for a range of gauges. AWG Ohms / 1000 AWG Ohms / 1000 AWG Ohms / 1000 AWG Ohms / Highlighted are 12-gauge which is common for 20A circuits, 10-gauge which is common for 30A circuits, and 6-gauge which is common for 60A circuits. These are rule of thumb values. Slight variation in resistance will be seen due to tolerance in the wire diameter, ambient temperature, insulation, and self-heating effects. These variations can be ignored for this analysis. Phase Balancing: The Last Few Inches Of a High-Efficiency

4 Delta Loads When utilizing a 120/208V 3-phase circuit in North America and applying loads in a delta configuration for 208V, balancing reduces losses in the feeder cables to the distribution point in the cabinet. Example 1: A 60A 208V 3-phase circuit is loaded in a delta configuration such that 13A is plugged into each of the three outlet phases: XY, YZ, and ZX. The current on the input lines are calculated using the following equations. X 2 = XY 2 + ZX 2 + XY ZX Y 2 = YZ 2 + XY 2 + YZ XY Z 2 = ZX 2 + YZ 2 + ZX YZ Thus the current through the X, Y, and Z input lines equals 22.52A each. Losses can be calculated using Joule s Law. P/R = X 2 + Y 2 + Z 2 P/R = (22.52) 2 + (22.52) 2 + (22.52) 2 = 1521 watts/ohm or 61 watts/100 of cable Worst case out of balance would be that all 48A are plugged into one of the outlet phases. In this case losses are: P/R = (39) 2 + (39) 2 + (0) 2 = 3042 watts/ohm or 122 watts/100 of cable This result shows that power loss and heat generated in feeder cables on out-of-balance circuits can be as much as double that of balanced delta loaded circuits. 4 Phase Balancing: The Last Few Inches Of a High-Efficiency

5 Wye Loads and Neutral Current When utilizing a 415V 3-phase circuit in North America or elsewhere around the world and applying loads in a wye configuration for 240V, balancing reduces losses in the feeder cables to the distribution point in the cabinet just as in the case of delta loads. Additionally, with wye loads, the current through the neutral wire should be considered. Using vector math and assuming the phases are mutually 120 apart, the current N through the neutral wire in a 3-phase wye loaded circuit where X, Y, and Z are the currents through the three input phases is expressed as: N 2 = X 2 + Y 2 + Z 2 X Y Y Z Z X When all three input lines are balanced such that X = Y = Z, zero current flows through the neutral wire. Worst case for the amount of current through the neutral wire comes when one or two of the input lines are without load. For instance, if Y = Z = 0, then N = X ; and if X = Y and Z = 0, then N = X = Y. The neutral current will never exceed the highest input line current. Current flowing through the neutral wire results in pure loss per Joule s First Law. Example 2: A 30A 240/415V 3-phase circuit is loaded in a wye configuration such that 8A is plugged into each of the three outlet phases: XN, YN, and ZN. Simply, the current through each input phase is 8A and the current through the neutral is 0A. Losses are: P/R = X 2 + Y 2 + Z 2 + N 2 P/R = (8) 2 + (8) 2 + (8) 2 + (0) 2 = 192 watts/ohm or 19 watts/100 of cable Worst case out of balance would be that all 24A are plugged into one of the outlet phases. In this case losses are: P/R = (24) 2 + (0) 2 + (0) 2 + (24) 2 = 1152 watts/ohm or 115 watts/100 of cable This result shows that power loss and heat generated in feeder cables on out-of-balance circuits can be as much as 6 times that of balanced wye loaded circuits. In this example, supposing the end user had 100 feeder cables at 100 feet in length each and was paying 10 cents a kilowatt hour, the cost to the facility would be \$8410 per year. Phase Balancing: The Last Few Inches Of a High-Efficiency

7 Summary With large data centers operating in the tens of megawatts, incremental increases in efficiency translate into appreciable savings. Although the amount of power loss and excess heat due to imbalanced loading is small in comparison with other system inefficiencies, it can be noticeable once all other points have been optimized. Implementing 240/415V power, as discussed in STI white paper Power Efficiency Gains by Deploying 415 VAC Power Distribution in North American Data Centers, goes a long way toward highest efficiency design. But as amperage requirements continue to increase in the data center cabinet, balancing of loads for efficiency becomes more and more important, especially in the wye distribution chain. A thorough analysis of the load balancing on a cabinet by cabinet basis, with trending of consumption over time is the first step to determine if additional steps should be taken to more optimize the load distribution. As with any potential improvement in the data center, an ROI should be calculated to determine if action is warranted. Phase Balancing: The Last Few Inches Of a High-Efficiency

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