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# CAPACITOR CURRENT FORMULA

## CAPACITOR CURRENT FORMULA

(OP)
I HAVE TO INSTALL A 200 KVAR 480 VOLT 3 PHASE FIXED CAPACITOR BANK AND I WAS WONDERING IF ANYONE HAD THE FORMULA FOR CALCULATING THE LINE CURRENT TO THIS BANK. I CLEARLY UNDERSTAND THE N.E.C. ON THE SUBJECT BUT THIS FORMULA IS NO WHERE TO BE FOUND.  PLEASE HELP.

### RE: CAPACITOR CURRENT FORMULA

For the Star (Y) connection, no resistors (since you indicate kVAR only), the routine formula is:
Iy=(kVAR x 1000)/(sqrt3 x VL-L)=(200 x 1000)/(sqrt3 x 480)=240.56Amps
If capacitors are connected in Delta connection, then the line current through the capacitor(s) branch connected phase-to-phase is:
Id=Iy/sqrt3=240.56/sqrt3=138.9Amps

### RE: CAPACITOR CURRENT FORMULA

line current = current between source and load
phase current = current in a phase (leg) of source or load
wye connected: line current = phase current
delta connected: line current = sqrt3*phase current

The line current for your bank will be 240 amps at 480V regardless of the type of connection used in the bank. The phase currents within the bank will vary depending on connection as described by jbartos above.

Keep in mind that the KVAR rating of your bank and the calculated line current is based on the rated voltage of 480V. The actual KVAR output and line current will vary depending on the actual voltage at your facility.

### RE: CAPACITOR CURRENT FORMULA

Suggestion: Please, notice that IEEE Std 100-1984 "IEEE Standard Dictionary of Electrical and Electronics Terms" defines "Line Current (Thyristor) as the current in the lines of the supplying power system"; however, there is no definition of the phase current. Now, consider an expression "phase fault (current)." This current would actually be what you define as the "line current." It appears that a further clarification is needed.

### RE: CAPACITOR CURRENT FORMULA

First, to answer RDTDIRECT's question regarding installation of a capacitor bank, the current to be supplied to the bank from your power source (ie. switchgear)will be 240A at 480V. Conductors and overcurrent protection should be sized as such based on NEC recommendations.

With respect to whether this current is called line current or phase current, the basic conventions for 3 phase power can be found in any number of texts on the subject. I believe the IEEE reference for Power topics is referred to as the "Red Book". I do not have that book, but I can provide some regular text references for those who wish to pursue it beyond this discussion. In order to describe the convention a picture is necessary. Draw a wye (star) connection on a piece of paper which we will say is a generator. Label the points ABC and the center N. Attach a line to each point ABC connecting it to an undefined load (picture=box) with terminals labeled XYZ respectively. By basic convention for 3-phase power:

Vab = line-to-line voltage or line voltage
Van = line-to-neutral voltage or phase voltage
Ina = phase current
Iax = line current
Note that for a wye
Ina=Iax (phase current=line current always)
Vab=Van*sqrt3 (balanced 3 phase only)

Doing the same exercise with a delta generator yields the following:

Vab=line-to-line or line voltage
Iab=phase current
Iax=line current
Note that for a delta
no neutral:phase voltage=line voltage (always)
Iax=Iab*sqrt3 (balanced 3 phase only)

Loads are similarly named, with a wye being
Zan=phase impedance
Zab=line impedance
Ian=phase current....etc.

The basis for the terminology is founded in the fact that 3-phase voltages and currents are phasors (vectors) with both magnitude and phase. When you get into any type of detailed analysis, the significance of the names becomes apparent. Again, any good text on 3-phase power will go into great detail on this subject.

Anyway, back to the two pictures just drawn, the current Iax can be defined as both "the current between the source and load" and as "the current in the lines of the supplying power system" (it is implied that the supplying power sytem has an associated load downstream of it). It is not often that definitions from solid state devices can be adopted to discussions of 3-phase power systems, but in the case of a thryristor's "line current" apparently it is so. This can probably be attributed to the fact that it is a power switching device. It is not a surprise that the term "phase current" was not referenced in STD 100-1984. Similarly, the term "gate current" associated with the aforementioned thyristor will not be referenced in IEEE STD 242-1975.

With respect to the term "phase fault current", it is used in discussions of faults on 3 phase power systems and is described in a number of texts as well, including IEEE Std 242-1975 "Standard Practices for Protection Coordination of Industial and Commercial Power Systems".  A brief description of the terminology follows. A fault occurring line-to-line is referred to as a phase fault and will result in "phase fault current" flow. This is meant to distinguish that type of fault from a line-to-ground fault, or ground fault which results in "ground fault current" flow. Another term used in these discussions is "three phase fault current", which is that resulting from a line-line-line fault. In any case, fault currents will flow from the power source through the lines to the fault. Ground fault current is equal to the line curent of the grounded leg. Phase fault current is equal to the phasor sum of the line currents of the two affected phases.

### RE: CAPACITOR CURRENT FORMULA

Suggestion: More recent Reference (however, not current):
1. IEEE Std 100-1992 "The New IEEE Standard Dictionary of Electrical and Electronics Terms" Fifth Edition, 1992
2. IEEE Std 428-1981 "IEEE Standard Definitions and Requirements for Thyristor ac Power Controllers"
preserves the same definition as the 1984 edition. It provides traceability over IEEE Std 428-1981, Reference 2.
Also, Reference 1 defines "Phase Voltage of a Winding (Machine or Apparatus)" as "The potential difference across one phase of the machine or apparatus. The traceability is provided over:
1. IEEE Power Engineering Society Committee on Rotating Machinery
2. IEC - International Electrotechnical Commission
There appears to be a problem in one of the statement above:
Van = line-to-neutral voltage or phase voltage
namely, what if there is no neutral? There would be a phase but no phase voltage according to the above definitions. What if there is one-phase source without any neutral identification? Then, it appears that its voltage is appropriately called "phase voltage" rather than the line to neutral voltage. Some of the above terminology is very frequently appearing in textbooks. It means that the main focus is on understanding and education rather than on practicality and associated standards, cost, safety, etc. The above posting is lacking an expression "phase-to-phase voltage" which is very frequently used since many buses are identified as phase A, phase B, phase C, for example.
Another item in Reference 1 is "Phase-undervoltage relay (power switchgear)," which is defined as "A relay that operates when one or more phase voltages in a normally balanced polyphase circuit is less than a predetermined value." Traceability is over C37.100-1981 and C37.90-1978. There is no elaboration whether the phase voltages are phase-to-phase or phase-to-neutral. In some applications, this make very little difference; especially, if Ephase=Sqrt3 x Ephase-neutral is valid.

### RE: CAPACITOR CURRENT FORMULA

More recent references only appear to support my orginal points.

1. With respect to your referenced definition: phase voltage of a winding (machine or apparatus): "The potential difference across one phase of the machine or apparatus". That reference supports my definition as described above. If you did not read my previous post and follow the instructions on constructing a diagram representing the naming conventions for 3 phase power, please do so now. You will note on the first example (3phase wye generator) that the voltage Van is named as the phase voltage and the current Ian as the phase current. Please note that between the points A and N exists the "A" phase winding of the generator. As such, Van is the voltage across that winding and and Ian is the current through it. They are therefore referred to as "phase voltage and current".

2. Next, the statement that : "There appears to be a problem in one of the statement above:
Van = line-to-neutral voltage or phase voltage
namely, what if there is no neutral?"
If you still have not read the previous post, do so now. You will note that in the case of the Delta connected generator described above, the voltage Vab is labeled as line voltage and is noted to be equal to (synonymous with) the phase voltage. It was also noted that there was (obviously) no neutral in this case. Again, between A and B is a phase winding of the delta generator. Using your definition, Vab is "The potential difference across one phase of the machine or apparatus (generator in this case)", also known as phase voltage.

3. Suggestion: Read and understand a post before responding. Also, fully understand the nature of any materials you a citing and their relevance (if any) to the post you are responding to.

4. Considering that the original posted question has been answered, further discussion of terminology probably should be brought up in a separate posting so that the forum can recognize the topic of discussion for what it is and participate.

5. "Possessing a great library is a matter of wealth, understanding a great library is a matter of achievement." Anonymous

### RE: CAPACITOR CURRENT FORMULA

Suggestion: It appears that relevant references are needed or required in practical situations. In some cases, the textbook approach is allowed in others industry standards, military standards, safety codes, etc. must be followed or preferred.
The rhatcher postings above may be supplemented/corrected (marked by >>) as follows:
Vab = line-to-line voltage or line voltage
>>or phase-to-phase voltage
Van = line-to-neutral voltage or phase voltage
>>or phase-to-neutral voltage
Ina = phase current
>>or phase-to-neutral (line-to-neutral) current
Iax = line current
Note that for a wye
Ina=Iax (phase current=line current always)
Vab=Van*sqrt3 (balanced 3 phase only)
>>Addition: In case of phase-to-phase (or synonymously, line-to-line) fault, there is phase-to-phase (line-to-line) fault current
Doing the same exercise with a delta generator yields the following:
Vab=line-to-line or line voltage
>> or phase-to-phase voltage
Iab=phase current
>>Correction: Phase-to-phase (or line-to-line) current
Iax=line current
>>or phase current
Note that for a delta
no neutral:phase voltage=line voltage (always)
>>phase-to-phase voltage=line-to-line voltage (since there may be considered a fictitious neutral for analyses, etc.
Iax=Iab*sqrt3 (balanced 3 phase only)

Loads are similarly named, with a wye being
Zan=phase impedance
>>phase-to-neutral (or line-to-neutral) impedance
Zab=line impedance
>>or phase-to-phase (or line-to-line) impedance
Ian=phase current....etc.
>>or phase-to-neutral (line-to-neutral) current
Reference:
1. ANSI/IEEE Std 242-1986 "An American National Standard IEEE Recommended Practice for Protection and Coordination of Industrial and Commercial Power Systems"

Reference 1, page 115 states that "A current transformer transforms line current into values suitable for standard protective relays...." Since the current transformers may be connected in delta- or y-connection, as needed or required, then the line is interpreted as the line-to-neutral (phase-to-neutral) current for y-connection and line-to-line (phase-to-phase) current for the delta-connection. This agrees with my first posting and does not contradict the Reference 1 intent. Good references tend to remove a lot of subjectivity in postings. Also, the ground fault current subject is more involved, e.g. there are line-to-line-to-ground faults that are different from line-to-ground faults.

### RE: CAPACITOR CURRENT FORMULA

For jbartos:

In reviewing your "supplement" to my terminology, I agree that the terms you provided for the wye case are somewhat synonymous, but I don't agree with all of the terms in the delta case. Either way, I am not familiar with the fact that the reference you cited (STD 242) establishes, or makes any attempt to establish, any standard or convention in terminology for the naming of three phase voltages and currents in the context of three phase power analysis. You have stated that "good references tend to remove a lot of subjectivity in postings." Let's put that to the test. Please give the specific citation from the listed reference supporting your supplemental definitions. Do not provide references to other devices (ie. thyristors, phase undervoltage relays, current transformers, widgets) and do not provide quotations, but instead provide the citation (ie. chapter, section, paragraph) where the the definitions you stated above are given in the context of three phase power and wye or delta connected sources and/or loads. I anxiously await the opportunity to review those citations in my copy of the same reference.

Anyway, I entered into the discussion of terminology that followed because of a desire to share my understanding of the topic, because I thought you were genuinely interested, and because I thought I could possibly learn a little in the process. However, it is disheartening to come to the realization that this is probably not an academic exchange of ideas but instead a pissing contest. Come on...Do you really want me to explain to you what the definition you gave for current transformers means, or have you brought this up to believing that the presented definition discredits one or more of the definitions I have previously stated? If you think the latter case is true, you are sadly mistaken. Suggestion: If you haven't figured it out by now, I work with three phase power...I was touching a set of wye connected CT's on Friday,  a troubleshooting job. I am a BSEE EIT also. I have direct (ie.hands-on) experience with UV relays, SCR's , switchgear, generators, motors, starters, etc....With respect to the original post, I have specified, purchased, and installed a 13.8kV power factor correction bank (actually, contractors installed it to my specs, but hey...I don't do shovels.)

My point is....what is your point? Right now I intend to follow this thread solely to recieve your reference citations from the STD 242 supporting the supplements and corrections you have made in your previous post. Again, I anxiously wait those citations! Otherwise, if you are genuinely interested in discussing terminology for the sake of terminology or interested in pursuing a discussion of any of the devices you have brought up, please start a new post with a topic as such so that the other members of the forum can see the topic for what it is and join in accordingly. Otherwise, if this is what I think it is... I see no point in continuing.

### RE: CAPACITOR CURRENT FORMULA

Suggestion to the previous posting: Please, become familiar with large professional standards organization practices and prerogatives. The IEEE is in a position to establish a definition in its standard (including dictionary) and cite an origin of that definition. The correct definition may originate in various areas. There is no "patent" on right definition in "right area." That could be considered an "ideal way" to generate definitions. This is answer to your immediate above posting: "Do not provide references to other devices (ie. thyristors, phase undervoltage relays, current transformers, widgets) and do not provide citations, but instead provide the citation (ie. chapter, section, paragraph) where the the definitions you stated above are given in the context of three  phase power and wye or delta connected sources and/or loads. I anxiously await the opportunity to review those citations in my copy of the same reference."
The immediate above posting "You (jbartos) stated that it would be 240A if it is wye connected and 140A if it is delta. Perhaps you misunderstood the question, perhaps you misstated your answer (damn terminology!), perhaps you misunderstand the concepts involved." appears to be conflicting  rhatcher (Electrical) posting on Jan 18, 2001"line current = current between source and load
phase current = current in a phase (leg) of source or load
wye connected: line current = phase current
delta connected: line current = sqrt3*phase current"
which seems to be leading to a general confusion.
Also, please, notice that the IEEE has IEEE Std 100 (Dictionary) for definitions. Whatever is stated in other IEEE standards is supposed to be not to the contrary of IEEE Std 100, which in majority of cases is or meets the intent of IEEE Std 100. Please, notice that there are educated people around with more advanced education than BSEE and more practical education such as "Electrical Apprenticeship," or "Master Electrician."

### RE: CAPACITOR CURRENT FORMULA

Let's be clear on this - what is needed here to answer the original question is the current in each supply wire, so that the branch circuit protection can be properly selected.
Assuming that the 200 KVAR, 480 V rating is for the complete bank, it is immaterial whether the individual cans are connected in delta or wye - that is another question that speaks to to selection of the can voltage and kVAR ratings for the particular duty.
There are 3 wires supplying the capacitor bank.  The current in the supply leads will be (200/0.48xsqrt(3))= 240A, regardless of the can configuration.  This value should be stated on the bank nameplate or data sheet, which should be consulted as part of the engineering design of the circuit.

### RE: CAPACITOR CURRENT FORMULA

Suggestion: The previous posting appears to be the right answer to the posted original question; however, the line current in the original posting may be investigated for protective devices that may be placed in lines for y-connection and in delta branches for the delta-connection.

### RE: CAPACITOR CURRENT FORMULA

Thank you peterb! That is the correct answer. As has been the case before in this thread, it was followed with a response that was meaningless...

### RE: CAPACITOR CURRENT FORMULA

Suggestion: Consult Reference
1. NFPA 70-1999 Article 460 - "Capacitors"

460-2A(b) "Means of Discharge" since there shall be discharge circuits permanently connected to the terminals of the capacitor or capacitor bank (200kVAR, 3ph)...
Remark: The discharge circuits will add some smaller current to the line current depending how they are connected. There is no mention about these in the original posting. They will be different for y-connection of the capacitor bank and for delta-connection of the capacitor bank.

460-8 "Conductors" (c) "Disconnecting Means (4) The rating of the disconnecting means shall not be less than 135 percent of the rated current of the capacitor.
Remark: Now it depends how the capacitor bank is connected since there is a difference in the capacitor current connected in y-connection or delta-connection. Any reference to the capacitor bank seems to be missing.

Also, it appears that the capacitor bank is not off the shelf of some major capacitor manufacturer since those capacitor banks have the nameplates with the line current indicated.

### RE: CAPACITOR CURRENT FORMULA

First:

jbartos says ...
Suggestion: Consult Reference
1. NFPA 70-1999 Article 460 - "Capacitors"

460-2A(b) "Means of Discharge" since there shall be
discharge circuits.....
Remark: The discharge circuits will add some smaller
current to the line current.....

This is rich....do you not understand that discharge circuits are active only after the capacitor is disconnected from the source or supply? To do otherwise would intitiate a bolted three phase ground fault. And where does it say that this will be different for wye or delta connected 3 banks?......IT DOESN'T.

Next:

jbartos says:
460-8 "Conductors" (c) "Disconnecting Means (4) The
rating of the disconnecting means shall.......
Remark: Now it depends how the capacitor bank is
connected......

Hardly worthy of comment.....Again, where does it say that the line currents will be different?

Give a guy a couple of books and show him where the index is and voila (!), he is an expert...education, experience, understanding of the topic, and common sense are obviously optional.

### RE: CAPACITOR CURRENT FORMULA

Suggestion to the previous posting: Reference:
1. Fink D. G., Beaty H. W. "Standard Handbook for Electrical Engineers," 14th Ed, McGraw-Hill, 2000, Chapter10.5 "Power Capacitors"
2. NFPA 70-1999 National Electrical Code
Reference 1 indicates that "..delta and single-phase connections are usually made on low-voltage circuits." This means that one may select a disconnect switch and protection with rating related to 240A/3**0.5 rather than 240A. There appears to be significant savings. Also, the discharge resistors may be turned on after the capacitors are turned off or fixed with permanent connection to the capacitors that appears to be safer since no discharge resistor switching is needed. Reference 2 Article 460A(b) "Means of Discharge." The discharge circuits shall be either permanently connected to the terminals of the capacitor or capacitor bank, or provided with automatic means of connecting it to the terminals of the capacitor bank on removal of voltage from the line. Manual means of switching or connecting the discharge circuit shall not be used.

### RE: CAPACITOR CURRENT FORMULA

hi guys,
just for interest and of no bearing to your study of the NEC.

Aus. standard AS3000 calls for the protection device and the cabling to the bank to be 135% of the bank rating and that the contactors etc be specifically rated for capacitor duty. rules 4.16.1 ,2,3

regards
Don

### RE: CAPACITOR CURRENT FORMULA

NFPA 70-1999 in Article 460-8(b) "Overcurrent Protection" (2) "The rating or setting of the overcurrent device shall be as low as practicable." The ampacity rating of cables is in agreement with the AS3000 in the previous posting, namely 135% of the rated current of capacitor (which also implies the capacitor bank). The capacitor bank needs either a disconnect if its dedicated branch circuit is protected by fuses or circuit breaker if its dedicated branch circuit is protected by this circuit breaker, all for the minimum safety. The delta bank may have the more sensitive protection of the delta capacitor branches to protect a capacitor in each delta branch in addition to the safety code. In case that the capacitor bank is tied with other load, e.g. motor, additional safety restrictions apply.

### RE: CAPACITOR CURRENT FORMULA

Note that the individual capacitor cans within the bank can certainly be provided with individual fusing - this is quite standard.  That is a completely separate matter to the branch circuit protection, which takes the overall bank current into consideration.  If you try to fuse a 200 KVAR capacitor bank branch circuit for load current of (240/sqrt(3))= 138.5A, you will be blowing a lot of fuses, as the phase (line) load current will still be 240A, whether or not the bank (which is rated for a total of 200 KVAR) is internally connected wye or delta.

### RE: CAPACITOR CURRENT FORMULA

The line current 240A and the capacitor bank protection aligned with respect to the dedicated branch circuit for the capacitor bank has been evident from the first posting. However, the details and various alternatives seem to cause additional postings.
It appears that the capacitor bank may be attached to some existing branch circuit (load). In that case, the fundamental protection of delta-connected capacitor branches may be within the delta-connection and the short-circuit protection may be over the short-circuit protection of the branch circuit conductors (with necessary short circuit safety constraints) and remaining load attached to that branch circuit. NFPA 70-1999 Reference addresses it. Also, the protection within the delta-connected capacitor bank can be made more sensitive.

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