Describing Arc Flash Incident Energy per Feeder Length in the Presence of Distributed Resources Tom R. Chambers, P.E. Power System Engineering, Inc. Madison, WI

Agenda Introduction Impedance Frame of Reference TCC Curve Equations Fault Analysis Arc Flash Analysis – Algorithm – Application to IEEE 1584 Arc Flash Calculator Case Studies Sources and Degree of Error Conclusions

Introduction Often, a utility will wish to know the maximum incident energy available on a specific feeder.

Fault current, clear time, and energy change per impedance There is, somewhere on this feeder, a maximum incident energy

Introduction We must calculate the incident energy at 3-4 key locations per feeder – Minimum fault current – 7.5 cal/cm 2 – 2 second cut-off current – 7.8 cal/cm 2 – Just behind instantaneous –6.0 cal/cm 2 – Maximum fault current – 1.1 cal/cm 2 Time consuming, but… – Protection characteristics per feeder are often the same per substation – Minimal calculation time

Far more complicated with distributed resources Two currents, two clear times

Introduction The point of maximum incident energy may be at the substation source… – High source current, but short arcing time – Low DG current, and long arcing time …or it may be at the terminals of the DG… – Low source current, long arcing time – High DG current, but short arcing time …or it may be somewhere in the middle… – Fairly high source and DG current – Fairly long source and DG arcing time

Introduction There is no rule of thumb Far too dependent on – Variable protection characteristics – Variable range of available fault current between sources As DG penetration increases, and arc flash studies become of greater and greater focus, the time to perform arc flash studies must be reduced

Methods Iterative Method (current) – Time consuming Must evaluate energy summation in 1 mile increments, 0.5 mile increments, 0.25 mile increments… to narrow in on highest energy – Prone to error The more often calculations are performed, the more chance for error is introduced Graphical Method (proposed) – Fast A few key pieces of information are required – More descriptive The energy in discrete feeder length increments is returned and plotted – Quickly updatable for multiple scenarios

Impedance Frame of Reference The most convenient frame of reference to describe position in electrical terms is impedance A reference point is chosen – The substation bus, if for no other reason, because transmission and transformer source impedance is known at this location – Example: The source impedance at the secondary bus is 1.6Ω Our “index” at this point is 1.6 The impedance at the DG is determined – Example: The Thevenin impedance (looking back to the substation source) at the DG terminals is 5.2Ω Our “index” at this point is 5.2

Impedance determined by engineering model Or, available fault current Determine Thevenin Impedance to Source

Time-Current Characteristic Curve The minimum and maximum Thevenin impedance is defined – The position between the substation and DG may now be described in terms of impedance (e.g. 3Ω from the reference 1.6Ω, or where our engineering model indicates 1,732A of source current only) As impedance (and more importantly, the ability to define current per position) is defined, only time is required – When will the protective device open when presented with any level of available fault current?

Time-Current Characteristic Curve

Many curves were created before this equation form was adopted – Based on the electromagnetic and mechanical characteristics of the original relay Manufacturers recognize that protection engineers often wish to continue using these old curve shapes Consequently, curve fitting is performed and A, B and P constants are derived to describe older curves Different manufacturers have derived equations for older curves to more or less accuracy. Comparisons to the original curve shapes are typically available.

Fault Current per Impedance Index The impedance range between the substation and DG is known The source and DG contribution per impedance increment can now be determined Define m as a factor indicating the percentage of total impedance – We may use m to define our position as percentage of total impedance

Fault Current per Impedance Index

Summary Thus Far At this point, for any location on the feeder, in between DG and substation source… – We know the impedance between the location and each source – We know the fault current contribution from each source at that location Because the TCC curve for each protective device has been expressed via an equation… – We are able to determine clear time for each value of current calculated

Arc Flash Hazard Analysis For a medium voltage system, these are the primary equations for arcing current and incident energy We have calculated I bf (bolted fault current) and t (time) – The remaining variables are global to a particular feeder Working distance, arc gap, etc. Arc flash incident energy may now be determined Arcing Current Incident Energy

Incident Energy from Multiple Sources First… the previous equations are valid for one source – Two different sources have two different protective characteristics Two sets of time and current combinations To add incident energy from two sources, we must divide the total contribution period into two distinct time periods

Incident Energy from Multiple Sources The first period (t 1 )… the time during which both source and DG current contributes (I A and I B ) The second period (t 2 )… the time during which only one source contributes (I B ), after the first protective device clears

Incident Energy from Multiple Sources Single Source Multiple Source

Incident Energy from Multiple Sources These series of equations leading to the final energy equation must be calculated in whatever increments considered appropriate For the sample program, arc flash incident energy is evaluated per increments of 1% of total Thevenin impedance range – (5.2Ω-1.6Ω)*1% = m = 0.36Ω – Fault current and incident energy are calculated at 0.36Ω 0.72Ω 1.08Ω Etc.

Modifications to IEEE 1584 Calculator It is most convenient to modify the existing IEEE 1584 Arc Flash calculator – Requires two additional data entry tabs (substation and DG) – Requires modification to the Data-Normal tab – Requires one additional tab for curve display

Modifications to IEEE 1584 Calculator

Ref Z – First two rows are substation Thevenin Impedance – From there, add impedance range in 1% increments C24 = Z_SOURCE C25 = Z_SOURCE C26 = C24 + Z_SCAN*0.01 C27 = C25 + Z_SCAN*0.01 C28 = C26 + Z_SCAN*0.01 C29 = C27 + Z_SCAN*0.01 …(etc)…

Modifications to IEEE 1584 Calculator Bolted fault current of bus in kA – t 1 … Determine substation fault current at corresponding Ref Z – t 2 … Determine DG fault current at corresponding Ref Z

Modifications to IEEE 1584 Calculator Opening Time – t 1 … Determine the shortest clear time and return. If greater than or equal to 2 seconds, return 2. – t 2 … Determine the longest and shortest clear time, and subtract the two. If longest time is greater than or equal to 2 seconds, return the difference between 2 and t 1. If shortest time is greater than or equal to 2 seconds, return 0.

Modifications to IEEE 1584 Calculator

Comparative Study I Source Midline DR

Comparative Study I – Iterative Method This series of calculations will need to be performed at every location you wish to determine incident energy, continually zeroing in on the actual maximum incident energy

Comparative Study I – Proposed Method Using our developed spreadsheet, we need only enter these known characteristics, and the answer is immediately determined

Comparative Study I

A comparison of both methods yields some error Typically acceptable – TCC curve has inherent 10% error Greater at lower pickups Due to manufacturer derived curves – Basler, SEL, Eaton (Cooper), etc. will all have slightly different curve shapes for a Kyle- 134, for example

Comparative Study II What if the curves in question were not derived for electromechanical shapes, but were created in accordance with the ANSI equation?

Comments on Error What’s the difference? – Comparative Study I Original curves published by Eaton used for traditional method Mathematically derived coefficients describing original curves used for proposed method – Comparative Study II Curves created specific to the ANSI equation were used These same coefficients and same equations were used in the proposed method Be aware that you’re using curves published by the actual manufacturer of the relay you’re using!

Conclusion We hope this presentation will serve as a useful guide for performing future arc flash hazard analyses There has been significant dialogue, which we believe has resulted in a study that everyone feels comfortable with and with which everyone has confidence in the approach and assumptions used We’re always available for questions and advice

Tom R. Chambers, P.E. System Engineer Power System Engineering