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Center-tapped delta transformer voltages

High-leg delta (also known as wild-leg or red-leg delta) is a type of electrical service connection. It is delta configured transformer windings with grounded center tap on one of the phases. This arrangement provides split-phase single-phase, and three phase, supply voltages.

Supply

A transformer having four wires coming out of the secondary, the three phases, plus a neutral connected as a center-tap on one of the windings.

The voltage magnitudes between the three phases are the same, however the voltage between the high-leg phase and the neutral is different. The phase-to-neutral voltage of two of the phases will be half of the phase-to-phase voltages. The high-leg phase-to-neutral voltage will be √3 times half the phase-to-phase voltage.

Example

Phasor diagram showing common North American voltages.

Consider the low voltage side of a 120/240 V high leg delta connected transformer, where the 'b' phase is the 'high' leg. The line-to-line voltages are all the same magnitude:

V_{ab}=V_{bc}=V_{ac}=240V

Because the winding between the 'a' and 'c' phases is center-tapped, the line-to-neutral voltages for these phases are as follows:

V_{an}=V_{cn}=V_{ac}/2=120V

But the phase-neutral voltage for the 'b' phase is different:

V_{bn}=V_{ab}*cos(30)\approx 208\ V

This can be proven by writing a KVL equation starting from the grounded neutral:

0+120\angle 0^{\circ }+240\angle 120^{\circ }=120{\sqrt {3}}\angle 90^{\circ }

Characteristics

The voltage between the center tap neutral and the ends of the transformer where the neutral originates is 50% of phase-to-phase voltage, however the voltage between neutral and the third leg, "high leg" is about 86.6% the phase-to-phase voltage.

Overall, configuration provide three relative voltages: 2x between phases,1.73x center tap to high-leg and 1x center tap to either ends.

Advantages

An advantage of delta arrangement in general is redundancy. If one of the transformers fail, the system can continue to carry three phase loads up to 58% of the total capacity.

Where the three-phase load is small relative to the total load, two individual transformers may be used instead of the three for a "full delta" or a three-phase transformer. This is called "open-delta high-leg", and has a reduced capacity relative to a full delta.^[1]^[2]^[3]

Disadvantages

A limitation with this design is that center tap to phase loads can not be balanced across the system. One transformer manufacturer limits the center tap to phase load to 5% of transformers rating ^[4]

Usage

North America

According to Schneider Electric, high-leg delta setup was commonly installed in industrial and factory applications in 1950s.^[5] Separate services for single-phase and three-phase loads, e.g., 120 V split-phase and 240 V to 600 V three-phase (for large^[quantify] motors) may be^[vague] a modern^[when?] solution where permitted in some^[where?] areas according to Ontario Electrical Safety Association^[6] The National Electric Code requires that panelboards connected to this type of transformer explicitly identify the high leg (usually the B phase), preferably by coloring it orange. ^[7].

References

^ "Transformer Basics Chapter 3". Federalpacific.com. Retrieved 2012-07-30.
^ Electrician's Calculations Manual - Nick Fowler - Google Boeken. Books.google.com. Retrieved 2012-07-30.
^ Illustrated Guide to the 1999 National Electrical Code - John E. Traister, Bradford Maher - Google Boeken. Books.google.com. Retrieved 2012-07-30.
^ Jefferson Electric
^ PDF
^ Ontario Electrical Safety Association 23nd Edition/2002 Comprising CSA Standard C22.1-02. Electrical Safety Association of Ontario. 2002. pp. Para 6-102 Appendix 'B'. ISBN 1-55324-570-9.
^ Article 110.15 of the 2005 National Electric Code (US)|National Electrical Code

sea.siemens.com
NFPA 70: National Electrical Code, 2005 Ed.

[fedpac-1] "Transformer Basics Chapter 3". Federalpacific.com. Retrieved 2012-07-30.

[2] Electrician's Calculations Manual - Nick Fowler - Google Boeken. Books.google.com. Retrieved 2012-07-30.

[3] Illustrated Guide to the 1999 National Electrical Code - John E. Traister, Bradford Maher - Google Boeken. Books.google.com. Retrieved 2012-07-30.

[4] Jefferson Electric

[5] PDF

[6] Ontario Electrical Safety Association 23nd Edition/2002 Comprising CSA Standard C22.1-02. Electrical Safety Association of Ontario. 2002. pp. Para 6-102 Appendix 'B'. ISBN 1-55324-570-9.

[7] Article 110.15 of the 2005 National Electric Code (US)|National Electrical Code

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[2]

[3]

[4]

[5]

[6]

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@@ Line 1: / Line 1: @@
-'''High-leg delta''' (also known as wild-leg or red-leg delta) is a type of electrical service connection often found in older [[three-phase electric power]] installations. It is used where both lighting and three-phase motor loads are fed from the same distribution system.
 [[Image:CenterTappedTransformer.svg|thumb|Center-tapped delta transformer]]
 [[Image:CenterTappedTransformer Voltages.svg|thumb|Center-tapped delta transformer voltages]]
+'''High-leg delta''' (also known as wild-leg or red-leg delta) is a type of electrical service connection. It is delta configured transformer windings with grounded center tap on one of the phases. This arrangement provides [[Split-phase electric power|split-phase single-phase]], and three phase, supply voltages.
 ==Supply==
+{{unreferenced|section|date=December 2012}}{{original research|section|date=December 2012}}
-This type of service is supplied in one of two ways. One is by a transformer having four wires coming out of the secondary, the three phases, plus a neutral connected as a center-tap on one of the windings.  Another commonly used method requires two transformers. One transformer is connected to one phase of the overhead primary distribution circuit to provide the 'lighting' side of the circuit (this will be the larger of the two transformers), and a second transformer is connected to another phase on the circuit and its secondary is connected to one side of the 'lighting' transformer secondary, and the other side of this transformer is brought out as the 'high leg'. The voltages between the three phases are the same in magnitude, however the voltage magnitudes between a particular phase and the neutral vary.  The phase-to-neutral voltage of two of the phases will be half of the phase-to-phase voltage.  The remaining phase-to-neutral voltage will be √3 times half the phase-to-phase voltage.  Typically, the transformer is connected such that the 'B' phase is the 'high' leg.
+<!-- Prose here was pulled aside to talk page for culling  -->A transformer having four wires coming out of the secondary, the three phases, plus a neutral connected as a center-tap on one of the windings.
+The voltage magnitudes between the three phases are the same, however the voltage between the high-leg phase and the neutral is different. The phase-to-neutral voltage of two of the phases will be half of the phase-to-phase voltages. The high-leg phase-to-neutral voltage will be √3 times half the phase-to-phase voltage.
-In the United States, according to Article 110.15 of the 2005 [[National Electric Code (US)|National Electrical Code]], panelboards connected to this type of transformer must explicitly identify the high leg, preferably by coloring it orange.
-==Comparison==
-The system is a delta with a "mid-point" level added. Alternatives are symmetrical delta where the three phases have the same voltage to ground, and corner-grounded delta. Where the system is grounded has little effect on basic operation. The voltage is such that phase-to-phase voltages are 60 and 120 degrees apart, thus compatible with three-phase equipment.
 ==Example==
-[[File:High leg delta.svg|thumb|[[Phasor]] diagram showing three 240V phases, and center-tapped 120V lines.]]
+[[File:High leg delta.svg|thumb|[[Phasor]] diagram showing common North American voltages.]]
+Consider the low voltage side of a 120/240&nbsp;V high leg delta connected transformer, where the 'b' phase is the 'high' leg. The line-to-line voltages are all the same magnitude:
+:<math>V_{ab} = V_{bc} = V_{ac} = 240V</math>
-Consider the low voltage side of a 120/240&nbsp;V high leg delta connected transformer, where the 'B' phase is the 'high' leg.  The line-to-line voltages are all the same:
+Because the winding between the 'a' and 'c' phases is center-tapped, the line-to-neutral voltages for these phases are as follows:
+:<math>V_{an} = V_{cn} = V_{ac}/2 = 120V</math>
+But the phase-neutral voltage for the 'b' phase is different:
-:<math>V_{ab} = V_{bc} = V_{ac} = 240 V</math>
+:<math>V_{bn} = V_{ab} * cos(30) \approx 208\ V</math>
-Because the winding between the 'A' and 'C' phases is center-tapped, the line-to-neutral voltages for these phases are as follows:
-:<math>V_{an} = V_{cn} = 120 V</math>
-But the phase-neutral voltage for the 'B' phase is different:
-:<math>V_{bn} = 120\sqrt{3}\ V \approx 208\ V</math>
 This can be proven by writing a [[KVL]] equation starting from the grounded neutral:
 :<math>0 + 120 \angle 0^\circ + 240 \angle 120^\circ = 120\sqrt{3} \angle 90^\circ</math>
+{{clear}}
-'''Note:''' Writing the KVL equation going the other way, the same magnitude is found, though the phase angle will of course be different.
-==Advantages==
+==Characteristics==
+The voltage between the center tap neutral and the ends of the transformer where the neutral originates is 50% of phase-to-phase voltage, however the voltage between neutral and the third leg, "high leg" is about 86.6% the phase-to-phase voltage.
-This type of service is usually supplied using 240&nbsp;V line-to-line and 120&nbsp;V line-to-neutral.  In some ways, the high leg delta service provides the best of both worlds: a line-to-line voltage that is higher than the usual 208&nbsp;V that most three-phase services have, and a line-to-neutral voltage (on two of the phases) sufficient for connecting appliances and lighting. Thus, large pieces of equipment will draw less current than with 208&nbsp;V, requiring smaller wire and breaker sizes. Lights and appliances requiring 120&nbsp;V can be connected to phases 'A' and 'C' without requiring an additional step-down transformer.
+Overall, configuration provide three relative voltages: 2x between phases,1.73x center tap to high-leg and 1x center tap to either ends.
-Where the three-phase load is small relative to the total load, two individual transformers may be used instead of the three for a "full delta" or a three-phase transformer, thus providing a variety of voltages at reduced cost. This is called "open-delta high-leg", and has a reduced capacity relative to a full delta.<ref>{{cite web|url=http://www.federalpacific.com/university/transbasics/chapter3.html |title=Transformer Basics Chapter 3 |publisher=Federalpacific.com |date= |accessdate=2012-07-30}}</ref><ref>{{cite book|url=http://books.google.com/books?id=HBSTWOl4V8IC&pg=PA58 |title=Electrician's Calculations Manual - Nick Fowler - Google Boeken |publisher=Books.google.com |date= |accessdate=2012-07-30}}</ref><ref>{{cite book|url=http://books.google.com/books?id=8cT8D9_WP7MC&pg=PA252 |title=Illustrated Guide to the 1999 National Electrical Code - John E. Traister, Bradford Maher - Google Boeken |publisher=Books.google.com |date= |accessdate=2012-07-30}}</ref>
-==Disadvantages==
+===Advantages===
-Since one phase-to-neutral voltage (phase 'B') is higher than the others, no single phase loads can be connected to this phase.  This eliminates the ability to use one third of the breakers in a panel for single-phase loads. Further, the lack of loading on the high leg will result in an unbalanced load. An autotransformer may be used to convert the 208&nbsp;V to 120&nbsp;V.
+An advantage of delta arrangement in general is redundancy. If one of the transformers fail, the system can continue to carry three phase loads up to 58% of the total capacity.
-==Usage==
+Where the three-phase load is small relative to the total load, two individual transformers may be used instead of the three for a "full delta" or a three-phase transformer. This is called "open-delta high-leg", and has a reduced capacity relative to a full delta.<ref name="fedpac">{{cite web|url=http://www.federalpacific.com/university/transbasics/chapter3.html |title=Transformer Basics Chapter 3 |publisher=Federalpacific.com |date= |accessdate=2012-07-30}}</ref><ref>{{cite book|url=http://books.google.com/books?id=HBSTWOl4V8IC&pg=PA58 |title=Electrician's Calculations Manual - Nick Fowler - Google Boeken |publisher=Books.google.com |date= |accessdate=2012-07-30}}</ref><ref>{{cite book|url=http://books.google.com/books?id=8cT8D9_WP7MC&pg=PA252 |title=Illustrated Guide to the 1999 National Electrical Code - John E. Traister, Bradford Maher - Google Boeken |publisher=Books.google.com |date= |accessdate=2012-07-30}}</ref>
-High-leg delta is commonly found in older systems. Current practice is to give separate services for single-phase and three-phase loads, e.g., 120&nbsp;V [[Split-phase electric power|split-phase]] (lighting ''et cetera'') and 240&nbsp;V to 600&nbsp;V [[Three-phase electric power|three-phase]] (for large motors).
+===Disadvantages===
-However, many jurisdictions forbid more than one class for a premises' service, and the choice may come down to 120/240 single-/three-phase (delta), 120/208 three-phase (wye), or 277/480 three-phase (wye).
+A limitation with this design is that center tap to phase loads can not be balanced across the system. One transformer manufacturer limits the center tap to phase load to 5% of transformers rating <ref>[http://www.jeffersonelectric.com/cgi-bin/site.pl?12201&id=423-7237-000&query=423-7237-000 Jefferson Electric]</ref>
+==Usage==
-The advantages for 208Y/120 volt systems (which can feed both single and three-phase loads) is all wiring methods and materials are "300 volt class".
+===North America===
+{{original research|section|date=December 2012}}
-The advantage for 480Y/277 volt three-phase system is is that 277 single-phase wiring methods and materials are "300 volt class", and lighting circuits can be fed at 277 volts without requiring a step-down dry-type transformer. However, 480 three-phase wiring methods and materials are "600 volt class".
+According to Schneider Electric, high-leg delta setup was commonly installed in industrial and factory applications in 1950s.<ref>[http://www.powerlogic.com/literature/70072-0168-02.pdf PDF]</ref> Separate services for single-phase and three-phase loads, e.g., 120&nbsp;V [[split-phase electric power|split-phase]]  and 240&nbsp;V to 600&nbsp;V [[three-phase electric power|three-phase]] (for large{{quantify|date=December 2012}} motors) may be{{vague|date=December 2012}} a modern{{when?|date=December 2012}} solution where permitted in some{{where?|date=December 2012}} areas according to [[Ontario, Canada|Ontario]] Electrical Safety Association<ref>{{cite book|title=Ontario Electrical Safety Association 23nd Edition/2002 Comprising CSA Standard C22.1-02|year=2002|publisher=Electrical Safety Association of Ontario|isbn=1-55324-570-9|pages=Para 6-102 Appendix 'B'}}</ref> The [[National Electric Code]] requires that panelboards connected to this type of transformer explicitly identify the high leg (usually the B phase), preferably by coloring it orange. <ref>Article 110.15 of the 2005 National Electric Code (US)|National Electrical Code</ref>.
 ==References==