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3 - Phase Efficiency, Power Factor, and Harmonics
Sept, 2014
Richard Hutchins
R&D Specialist / Eng-Lab
La Marche Mfg. Co.
Des Plaines, IL 60018
Introduction
The goal of this paper is not to make engineers, but to help our sales rep partners understand some of the terminology that the end user may use in specifying La Marche equipment. In the first installment of “Efficiency/ Power Factor / Harmonics” from the 2012 La Marche Trade Fair, the basic principles of these quantities were introduced for single phase systems. The necessity for efficiency in power systems has a growing importance. The proliferation of new electricity demands compounded by decommissioning of older Nuclear and Fossil power generation facilities exacerbate the problem. Refer back to the first installment for a refreshment on the concepts and definitions. This second installment introduces 3 - phase systems and how the 3-phase devices prevalent in higher power applications have an advantage over single phase systems when it comes to efficiency, power factor and harmonics. As the original paper’s goal was to introduce these properties, the goal of this paper is to expand on the original content for 3-phase applications.
Table of Contents:
Introduction .............................................................................................................................................. 1 A brief history of poly-phase systems .......................................................................................................... 2 The basics of 3-phase; compare to single phase. .......................................................................................... 3 Does a La Marche Charger require a “Y” or a “Δ” supply? .............................................................................. 6 Common 3-Phase transformer configurations in use: .................................................................................... 7 Some common 3-Phase waveforms: ............................................................................................................ 9 Triplen Harmonic Elimination in Delta transformers. .................................................................................... 12 What are the advantages of 3-phase systems over single-phase? ................................................................ 12 When would you recommend a 3-phase or single-phase charger? ................................................................ 12 List of commonly used 3-Phase Power equations: ....................................................................................... 13 References .............................................................................................................................................. 14 Glossary.................................................................................................................................................. 15
A brief history of poly-phase systems You may be aware of the debate over which electrical power distribution technique was superior; Thomas Edison’s DC (direct current), or George Westinghouse’s AC (alternating current). This “War of Currents” goes as far back as the 1880’s. It wasn’t until Westinghouse purchased Nicola Tesla’s patents for 3-phase generators, motors and transformers, that the currents would shift from the dominant DC distribution of the day towards AC power. The biggest problem with DC mass distribution was distribution losses of the standard generating voltage over distance when measured at the load. Edison was locating small power plants within 1-2 miles of the load to combat the wire losses. The DC system was upgraded to 3 - wires; +110V, Neutral-Return, and - 110V, as a method of distributing the user’s 100V loads between two circuits and lowering the wire losses. With balanced DC load currents, the Neutral-Return wire current will cancel to zero, When the DC loads were not balanced about the + & - 110Vdc rails, the Neutral-Return wire will carry the un-balanced load current differential. AC power could use transformers to step-up the voltage to very high levels, requiring less current to flow over long transmission lines for low wire losses of the same power level. At the load-side, another transformer steps the voltage down to usable levels. This method has advantages of efficient transmission over long distances compared to DC at the time, could use fewer but larger power plants of lower operating expenses, and customized voltages could be provided to the end user. The Westinghouse original designs were single phase using only 2-wires. Even with step-up/step-down transmission strategies, the high transmission voltages generated were limited to the insulation properties of materials available at the time, which limited AC power’s benefit of higher transmission voltages. The only prevalent electrical loads at the time were incandescent light bulbs and motors, both could be efficiently utilized with DC or AC power. The cost and availability of wire and electrical components were a real premium at the time. Nicola Tesla envisioned 3-phase AC power distribution over single-phase AC power. With the addition of only 1 - more wire than a single phase AC system could almost double the total amount of power transmitted. Adding one more wire adds only 50% more cost than the original 2 wires, and yields 73% more power for the same voltage; a great cost/benefit ratio! 4, 5, or 6 phases could just as easily been introduced as well, but cost and added complexity diminished the benefit, with 3-phases being the most optimal solution.
Figure 3. basic wiring diagrams for 3-phase Figure 4. Concurrent Voltage waveforms for 3-phase offset by 120°.
In single phase AC systems or DC systems, most voltage measurements are referenced to a common node, sometimes called a “ground” or more properly “common”; sometimes this will be a Neutral. When referring to voltage measurements in 3 - phase systems, it may or may not be referenced to a common Neutral. Please see figure 3 & 5. Figure 5. Wye diagram & voltage nomenclature The voltage nomenclature for documenting measurements or specifications is strait forward. It is generally accepted that voltage measurements of 3-phase systems are the RMS values.
- VLL = Voltage Measured Line-to-Line; AKA Phase-to-Phase.
- VBA = Voltage Measured Line-to-Line; Specifically from Phase-B to Phase-A.
- VLN = Voltage Measured Line-to-Neutral; AKA Phase-to-Neutral.
- VCN = Voltage Measured Line-to-Neutral; Specifically from Phase-C to Neutral. If the voltage is listed as simply VPhase-A then it is implied to that it was measured from Phase to Neutral. Here is an ideal example of voltages in a 480V “Y” commercial power or generator output.
- VLL = 480V
- VLN = 277V In our ideal scenario, the voltages are balanced such that each of the three VLL measured equally, and each of the three phases to neutral measured equally as well. In the US, it is common that a “Y” output generator or a “Y” output distribution transformer gets the Neutral terminal connected to Earth Ground at a single point within the master breaker panel board. When the3-phase load equipment has a Neutral connection, there will be a total of 5-conductors ran to the load; Neutral, Ground, and all 3-phases. If you have been given the voltage in terms of Phase-to-Neutral, you can calculate the voltage from line-to-line. 𝑉𝐿𝐿 = 𝑉𝐿𝑁 × (^) √ 3 480 𝑉𝐿𝐿 ≈ 277 𝑉𝐿𝑁 × (^) √ 3 480 𝑉𝐿𝐿 ≈ 277 𝑉𝐿𝑁 × 1. 732
Common 3-Phase transformer configurations in use: 3 - Phase transformers can be wound in several different ways. There are pros/cons associated with each winding configuration looking at cost, weight, and several electrical performance parameters. The transformer primary winding can be configured for either “Δ” or “Y”, and the secondary winding can be configured for either “Δ” or “Y”. A transformer’s primary and secondary could be mixed “Δ” or “Y” in any order. The general nomenclature for designating how the transformer is configured is strait forward.
- Δ/Δ = a Delta primary and Delta secondary
- Δ/Y = a Delta primary and Wye secondary
- Y/Δ = a Wye primary and Delta secondary
- Y/Y = a Wye primary and Wye secondary. When at the site of charger installation, you generally don’t know if the voltage transformer on site is Δ/Δ, Δ/Y, Y/Δ, or Y/Y. The La Marche charger is indifferent to this. The La Marche A75DE 3-phase microprocessor controlled SCR battery charger uses an internal Δ/Y for reasons that will be explained shortly. As you can tell from Figure 7, the specific wiring of each phase starts adding complexity and cluttering a schematic sheet very quickly. Many end-users such as a power utility draw their substation wiring diagrams as “single-line-diagrams” to save thousands of connections in triplicate. The Delta/Wye (Δ/Y). transformer shown in figure 7 was chosen so you can see how both Δ and Y windings are actually connected in a 3-phase transformer. The Δ and Y connections are made outside the transformer by connecting the beginnings and the endings of each winding properly.
Figure 7. Delta / Wye Transformer diagrams
- Generally, single-line-diagrams are reserved for “outside the box” wiring. The single-line-diagram is obviously quicker and cleaner, but requires trained installation electricians to understand the implied connections in order to install the devices properly.
- Generally, detailed schematics showing each connection are reserved for “inside the box” wiring. While inside the equipment, such as a La Marche battery charger, the schematic shows all connections for consistent quality control and a clear understanding of every connection made. Installation electricians may need to refer to the equipment schematic diagram to be certain all their field wiring connections are correct. When measuring current in 3-phase systems with an oscilloscope or power analyzer, it is necessary that the current probe direction points in towards the load to obtain proper relationship with the voltage measured. Phase currents are documented as RMS values such as: 12AmpsPhase-A. The Neutral current should also be measured and documented in RMS terms. Figure 8 shows what typical dry laminated transformers look like for 3-phase applications with the primary and secondary wires protruding out of the coils. The transformers shown could be wired in any combination of “Δ” or “Y”. As you will see later, there is an advantage to using a single 3-phase transformer as opposed to using three separate single phase transformers.
Figure 9. Balanced System Neutral Current. Figure 10. Un-Balanced System results in Neutral Current
Figure 11 Shows typical Rectifier "Y" phase leg current Figure 12 shows typical rectifier "Delta" phase current
1Kwatt DC output, and we wouldn’t recommend a single phase charger for applications greater than 13Kwatts. Even though a single phase charger may generate Triplen harmonics, at small power levels, they may be insignificant. However, if the steady state DC load is greater than a few KW, and they have 3-phase power available, suggest a 3-phase charger. List of commonly used 3-Phase Power equations: When using the formulas below, it is assumed that the voltage balance is within 3% Per ANSI C84.
- Solve Voltage or imbalance according to ANSI C84.1_2011: (note, the percentage of current
imbalance uses the same formula; simply replace “VLL” with “CurrentPhase”.
𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑉𝑜𝑙𝑡𝑎𝑔𝑒𝐼𝑚𝑏𝑎𝑙𝑎𝑛𝑐𝑒 = 100 ∙ (
𝑀𝑎𝑥𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛𝐹𝑟𝑜𝑚𝐴𝑣𝑒𝑟𝑎𝑔𝑒𝑉𝐿𝐿
A. Note, IEEE has at least 2 different formulas specifying the percent imbalance in 3- phase systems that do not match ANSI C84.1. The IEEE formulas have about a 1% spread between different results as compared to the C84.1 formula. B. Note, NEMA PE 5 has yet another voltage imbalance formula with at least a 2-percent error from the ANSI C84.1 formula, and it will be revised shortly under IEEE-P2405 to the C84.1 formula shown above.
- Solve Watts when VoltageLL, CurrentPHZ, and PF are known: W = VLL APHZ PF 3
- Solve Individual line current when Input Wattage, PF, & VoltageLL are known (balanced
system):
3 _ ( ) = V PF Input Powerwatts I LL Phase
- Solve Individual line current when Rectifier DC output Wattage, PF, Efficiency & VoltageLL are
known (balanced system):
3 _ _ ( ) = V PF Eff DC Output Power watts I LL Phase
- Solve 3-phase PF when Watts, VLL, & APHZ are known (balanced system):
3 ( ) 3 = VLL A PHZ Powerwatts phzPF
- Solve KiloWatt (KW) when VLL, APHZ, and PF are known (balanced system): 1000 3 3 _ = V A PF phz KW LL PHZ
- Solve KVA when VLL & APHZ are known (balanced system): 1000 3 = VLL APHZ KVA
- Approximate PT secondary phase current in a “Y” circuit from the DC rectified output current
(balanced system):
A (^) Secondary PHZ Idc 3 2 _^0.^817 3 2 References INTERNATIONAL ENERGY OUTLOOK 2014 http://www.eia.gov/forecasts/ieo/world.cfm IAEA International Atomic Energy Agency: The World Outlook for Electricity Investment http://www.iaea.org/Publications/Magazines/Bulletin/Bull461/power_to_the_people.html Webster’s Wiley Encyclopedia of Electrical and Electronics Engineering Volume 17 1999 ISBN 0- 471 - 13946 - 7 Power Electronics Converter, Applications, and Design by Mohan, Undeland, and Robbins. Published by John Whiley & Sons. 2003 ISBN0- 471 - 22693 - 9 Power Electronics Course University of Wisconsin Madison School of Engineering. 2012 www.epd.engr.wisc.edu Handbook of Electric Power Calculations 3rd^ Ed by Wayne Beaty. Published by McGraw-Hill 2000 IEEE Chicago Section PES Group class: Harmonics on Power Systems Workshop presented by: Roger Dugan, Sr.Technical Executive for EPRI, Knoxville, TN www.epri.com http://my.epri.com/portal/server.pt/gateway/PTARGS_0_243352_317_205_776_43/http%3B/uspalecp604% B7087/publishedcontent/publish/epri_calculates_annual_cost_of_charging_an_ipad_at__1_36_da_855261.ht ml http://hyperphysics.phy-astr.gsu.edu/hbase/electric/powerac.html#c
PFC: Power Factor Correction, can be found on higher quality switch-mode power-supplies. A circuit that actively manipulates the input current wave shape and displacement to eliminate harmonics, and make the PF very close to a perfect “1”. This circuit will make a load appear as a purely resistive load. TCO = Total Cost of Ownership. THD: Total Harmonic Distortion is the measure of how distorted a signal is from the intended sine wave usually expressed as a percentage. Triplen-Harmonics: multiples of 3rd^ order harmonics, 3rd, 9th, 15th^27 th. Triplen harmonics have special properties when evaluating 3-phase power systems. VA: Volt Amp product; unit of Apparent Power VAR: Volt Amp product of Reactive circulating energy; unit of Reactive Power due to non perfect PF.
