Detrimental Effects of Capacitance on 


High-Resistance-GroundedMine 


Distribution Systems 


Joseph Sottile, Senior Memb~l;IEE%: Steve J. Gnnpragnsam, Thomas Novak, Fellow, IEEE, and 


Jeffrey L. Kohler, Senior M~n?ber:IEEE 


Abstract-Modern underground coal mines can be very large, 

having a total connected Imd in excess OF 15 M0hp. These mines 

generidly have many miles aC high-power conveyorbelts and 15 or 

more miles of high-voltage power cables at distribntion voltages 

of 12.47, 13.2, 13.8, Or 14.4 kV. The sl~ieldedcahlcs used in mine 

power distribution systems have a significant level of'capaciisncc, 

on the order of 110 pWft. This lever d capacitance, in an extensive 

power distribution system at today's voltage levels, can cause 

significant charging currents during a ground fault. This paper 

addresses the potential detrimental effects ~Tcapacitance charging 

currents during line-to-ground faults in mine power distrihutia~n 

systems. A representative mine prtwer system is modeletl. and 

sirn~~lationswith faults at variults locations are conducted to evaluatc.the enects of this capacitance on the lcvcl of fnult current and 

relay selectivity. This paper also incl~tdesresults rrr capacitance 

rneasuren~entsmade on mine power feeder cables used tc~validate 

the simuiation model. 

THE PRIMARY goals of a power-system protection 

scheme are to prevent personnel injury, minimize damage 

to the power system, and minimize the extent and duration 

of the adverse condition during wsious types of faults. With 

respect to ground faults. the protectian system should limit the 

fault current and energy, quickly and reliably detect the fault. 

and deenergize only the offending section of the power system 

(selectivity). 

A high-resistance grounded system is defined as n system, 

in which RO 5 X,, where Ra is the per-phase zero-sequence 

J. Sortile is with rhe Universiry of Kentucky. Lexington. KY 40506-0107 

USA (e-mait:jsottileFiaee.org). 

S. I. Gnapwgasam was with the University or Kentucky. Lexington. KY 

405054107 USA. He is now with ADS Consulting Engineem. New Yark. NY 

IIX10 I USA (e-moil:Stcve.Gnapngwam@ad~ce.com). 

T. Novak is with Viginin Poly~echnicInslitute anti State University. Rli~cksburg, VA 2406 1 USA (e-mail: !ornnovak@vt.&u). 

J. L. Kohler is withtheNarional tnstitute for Occupational Safety andHealth. 

Pittshrgh, PA 15236 USA (c-mail: jtkJQcdc.gov: IKol~lcr@cdc.gov). 

Color versinns of Figs. 2,4. and 5 nre available a1 ht~p://ieecxplore.icec.og. 

D~gitalOhjccl Idenrzfier ICI. I 1 WfTIA.2f10h.X80844 

resistance of the system and X, is the distributed per-pl-tase 

system-to-ground capacitive reactance [ 1 1. In practical mine 

power systems, the zero-sequence resistance is dominated by 

the neutral grounding reqistor (NGR). so a high-resistance 

grounded system requires thnt RN 5 l/ldY,. where RN is ihe 

value of the NGR, 

Ungrounded systems have no intentional connection to 

ground. They am. of course, grouoded by the distributed capacitance of phase windings and power-system conductors. 

Ungrounded systems have the disadvantage of subjecting the 

system to severe overvoltages during certain types of ground 

Ihults by repetitive charging of !he system capacitance or 

by resonance between the system capacitance and equipment 

and system indz~ctance. Systems in which the value of the 

NGR exceeds the lirnit For high-resistance grounding begin to 

exhibit the disadvantageous characteristics of an unyrounded 

system 121. 

It is a common practice in modern mine power systems to 

size the NGR to limit the ncutnl current to 25 A and to use 

a pickup setting of 40% of this current limit, i.e.. 10 A. This 

is done to comply wirh Part 75.801 of Title 30 of the Code of 

Federal Re$ul:ktions. which requires that the NGR be of proper 

ohmic value to limit the voltage drop in the grounding circuit 

external to the resistor to not more than 100 V dtiring fnult 

~wndi~ions[3]. Because modern mine power systems can bc 

ver), exrensive. with 15 or more mi!el; of shielded high-voltage 

distri hut ion cahle, the distributed capacitance of these power 

systems combined with the low limit on neutral ground current 

can create situations in which the debnition of a Iligh-resistance 

grounded sysrem is violated and the system begins to exhibit 

[he characteristics of an ungrounded sysrem. 

This paper examines the nlodern grounding practice cornmonIy employed in underground coal mines and studies Ihe 

potential ror adverse effecls caused by distributed system capacitance. The analysis conducted involves the use of a Spice 

software to n~odrlan underground coal mine distribution system. Ground F~~i~lts are sintutnted at various points ant1 the 

effects or distributed sysrem capacitance on fault curren! levels, 

relay selectivity. and overvoltages are examitled. 

11, POWER-SYSTEMSIMULATION MODEL 

The mine power system thnt has been simulated is a 

12.47-kVexpanded rntIial distribution system supplying two 
TABLE I 

SUMMARY OF MAJORELECTRICALLOADS 


TABLE 11 


SUMMARY OF DlSTRlBUTlON SYSTEM 


continuous-miner (CM)sections and one longwall (LW) face. 

The borehole cable is 500-kcmil MP-GC,and the remainder of 

the distribution system consists of 4/0 MP-GC. Typical loading 

requirements for conveyor belt drive motors, LW, and CM 

equipment were used to develop the model. Tables 1 and I1 

summarize the relevant information about the distribution system and Fig. I shows a one-line diagram of the power system. 

Note that only major loads have been included in the system 

model. 

B, Model Developmenf 

Because interest was focused on studying the effects of 

distribution-system ground faults, several simplifications were 

made in developing the system model for simulation in 

si spice. 

The utility supply is modeled as a three-phase wye-connected 

voltage source in series with resistance and inductance values 

determined from the nominal system voltage, short circuit 

capacity, and X/Rratio (listed in Table 11). 

Load modeling was simplified by combining the power requirements of the individual loads at each production section 

into one equivalent load (as listed in Table I). The resulting Toads were modeled as three wye-connected resistance 

and inductance values determined from the total rated power, 

nominal system voltage, and assumed values for power factor 

(0.90 lagging), efficiency (90%), and load factor (0.85). 

A1 though this method of modeling line., modeling motor loads 

as constant impedance values instead of constant power values) 

would not be preferred for detailed load flow analysis, it is adequate for modeling ground faults in high-resistance grounded 

systems. 

Rather than modeling the conveyor belt and production 

section transformers as coupled coils, they were modeled as 

series resistance and inductance elements connected between 

the cables and the loads. The resistance and inductance values 

were determined by converting the transformer per unit impedances to the t 2.47-kV distribution voltage. Fig. 2 shows the 

portion of the simulation model for a 150-kVA transformer 

supplying a 1350-hp CM sect~on. Table 111 summarizes the 

transformer data for each size of transformer. Note that, while 

there are only three different sizes of transformers listed in this 

table, there are 12 transformers in the system. 

Mine distribution cables are represented as lumped parameter elements connected in a nominal-7i configuration. Several 

sources were consulted for resistance and 60-Hz reactance 

values for 500 kcmil and 410 mine power feeder, and it was 

determined that the values differed very slightly, if at all. 

Therefore, typical 90 "Cresistance values (per 1000ft) of 0.027 

and 0.063 I;t, and 60-Hz reactance values of 0.031 and 0.035 R 

for 500 kcmil and 410, respectively, for 15-kV MP-GCcables 

were used [4]. 

Although general approximations can be used to estimate 

the cable capacitance, it was decided that the capacitance 

values used in the simulation model should be based on a 

representative cable used commonly In undergraund coal mine 

distribution systems. By doing this, comparisons could be made 

with capacitance measurements on the same type of cable. The 

brand and type of cable selected for this paper is an AmerCabIe 

Tiger Brand TB2-604, Type MP-GC,3/C, 15-kV cable. This 

cable was chosen because: it is widely used in distribution systems, and the dimensions required for calculating capacitance 

were available. 

The per-phase capacitance from line to ground can be calculated from the following reEationship [4]: 

where 

E dielectric constant of the insulation; 

f thickness of the conductor insu tation; 

d diameter under the insulation. 

For ethylene propytene rubber (EPR) insulation at this voltage class, the typicnl SIC value is 3.2, and the ~nnximumvalue is 

4.0. The typical value of 3.2 was used because it is what would 

be expected in the field, although using a value of 4.0 would 

he more conservative because it would predict the maximum 

expected capacitance. The strand diameter, extruded strand 

shield, and insulation thickness values used for calculating 

capacitance of this cable are listed in Table IV [5]. 

The extntded strand shield is a semiconductor surrounding 

the power conductor and is added to provide a uniform radial voltage stress distribution by filling interstices along the 

perimeter of the power conductor. When the strand shield is 

added, the conductor is placed in tension, and lthe conductor 

diameter is reduced by approximately two mils below the 

nominal value. As a result, the diameter under the insuiation for 

a 410 cable is 

cl= (0.510)f (2 x 0.018) = 0.546 in. 

As an example, the resulting per-phase capacitance per foot 

for a 410 cable is 
t2.47 kV Feed 

Short Circuit CapaCjty = 126.9 MVd 


XlR = 14.41 


Borehole Cable 


500 MCM, 15 kV 


MP-GC 

410 

700 fi 


13,000ft 12.47 kVI 


1040-600 v 


I000 kVA 
 G3 


12.47 kV1 410 

4160-600 V 6000 ft 

1500 kVA @ 

12.47 kVI 12.47kVI 4m 


41 60-600 V Motor Pit 4160600V
 400 hp 1500 kVA --@ 

Belt Drive 72.47 kVI 

5800 R 1400 hp 4160-600 V 


1500 kVA 


Belt Drive 


1000 hp 


410 Belt Drive 


200 fl 1000 hp
 0 


1040-600 

12.47 kVI 

V 

4M @

7250R 4H) 


1000 kVA 0 200ft 


1 2.47 kVI 410 

I-

@

1040-600V 7250 fi 12.47 kVI 410 

5000 t 

Belt Drive 1OOOkVA 

@ 725 hp 12.47 kVI 

1000 kVA @

wWdJ 1040-800 V T2.47 kVI 

1040-600 v 410 Belt Drive I000 ~VA
 $800R 725 hp 


4ED 


0 CM Sedion Belt Drive 

5000 R 

410 Total Connected hp: 

1350 hp 725 hp 410 1800 fl 


200 ft 


0 


12.47 kVI 4M 

't04@600v 7250ft 


1000 kVA 64 


12.47 kVI 4m 

300hp 300 hp 300hp 350 MCM 

104bHI0V 7250 fi 

725 hp -= @12.47 kVI 

Hydraul~cPumps 1000 R 

63 

Belt Drive I000 kVA 

1040-600V 210 210 210 210 210 

CM Sedion 

Total Connected hp: Shearer Headgab Headgate Tailgate Stage Stage Crusher 

1350 hp 1400 hp 703hp 700 hp 700 hp Loader Loader 300 hp 

200hp 200hp 

Fig. I. Oiie-tinediag~mo~minedistributionqs~em. 
Transformer 

$1257 $4257 $257 5% ~~~~$(pr~mary) XIR = 4

CM Section 

1350hp 

0.90laggingpf 

0.90efficien~r 

0.85load factor 

Fig. 2. Portion of si~nulntion model represenrill; 1500-kVA 1mn5Former 

supplying a 1.150-hp CM ~ectinn. 

TABLE 111 

TRANSFORMERSUMMARY 

TABLE 1V 

CABLEPARAMETERS FOR CALCIIL,\TING CAPACITANCE

TABLE V 

RESISTANCF. IYDUCTAVCE, AND CAPACITANCEVALUESFOR MINE 

DlSTRIRUTIoN CABLES 

Pcr-Phasc 

Conductor Resistance Inductance Capacitance 

500 kcmil 0.027 0.U821 0.1520 

410 aw~ 0.063 0.0928 0.1094 

Table V provides n summary of the resistance, inductance, and 

capacitance values used for the 500-kcmil borehole cable and 

4JO distribution cables used in the m~ne simulation model. 

Although the capacitance calculations are relatively straightforward, the authors believe that, considering the nature of 

this paper, it is important to provide verification by comparing 

calculations with measurements. Therefore, an experiment was 

conducted, in which the capacitance of a piece of mine power 

feeder was measured. The selected cable was a 500-ft section of 

-' Co~rductor 

ing 

Conductor 

Fig.1. Experimental setup for mensuritig capaci~ance. 

15-kV 4/0 MP-GC mine power feeder manufactured by AmerCable, which is the same size and type used in the capacitance 

calculations. 

The experimental procedure consisted of energizing the 

open-circuited cable from line to grouud and measuring the 

voltage and current. These values were then used to compute 

the 60-Hz reactance, from which the capacitance could be 

determined. The cable was also hi-pot tested prior to making 

the measurements to ensure if had no insulation defects that 

would cause nbnortnally high leakage current. 

Power for the tests was obtained from a standard 120-V outlet 

and fed into a 120-V variac that was connected to a 120 :480 V 

step-up transformer. Although the variac was specified as 

1 20 V, the actual output range was approxinlately 0-1 34 V. This 

provided a variable ac voltage range of approximazely 0-536 V 

for the tests. Five feet of insulated # I2 awg conductor was used 

as lead wire to connect the transformer to the cable power and 

grounding conductors. Fig. 3 illustrates rhe experimental setup. 

Measurements were acquired by connecting n Tektronix 

P6009 low-input-capacitance. high-voltage probe between tine 

and ground and clamping an AEMC Model Kt 10 DC/AC 

MicroProbe current probe nmund the #I2 awg lead wire. Signals were acquired by a Fluke 123 ScopeMeter. During the 

experiments. some harmonic distortion of the current waveform 

was observed. Although this distortion was not large compared 

to the 60-Hz signal, it caused difficulties in accurately determining the phase shift between voltage and current. Notwithstanding. observations indicated that the current led the voltage 

by npproxin~ately80". Because this phase shift was difficult 

to determine accurately, and the reaczive co~nponenzof current 

leading voltage by approximately XU0 is nearly equal to a. purely 

reactive current. no attempt was made to separate the real and 

reactive components. and the total measured current was used 

to determine capacitance. 

Voltage and current measurernetlts were based on the true 

rms value indicated by the Fluke ScopeMeter. These values 

were also verified by connecting the probes to a Fluke Model 

87 Mul2imeter. In addition, because the Fluke 87 Multimefer 

has a capacitance meter, it was used to measure capacitance to 

provide additional verification. The insulation was discharged 

before connecting the cnpacitancc rnecer to the cable to eliminate the possibility of having a residual charge on the insulafion. 

Table YI provides a su~ninnry of the capacitance measurements 

made fin the 15-kVcable. 

Comparison of these measurements with calculated values 

given in (3) shows very good agreement. The cnpiwitance calculation for 500ft of 15-kV4/0 MP-GC is 0.1094/2 = 0.0547{tF 

per phase. From Table VI, the average measured value is 
TABLE VI 

RESULTSOF TESTSON IS-kV 410MINEPOWER FEEDER 

I Voltage I Current I Capacitance I 

* Measurement 3 is the result of a Fluke 87 Multimeter 

used in capacitancemode. 

TABLE VII 

FAUI-TAND NEUTRAL GROUNDING RESISTORCURRENTS FOR VARIOUSGROUNDFAULTS 

0.050 pF, which is s difference of less than 10% from the 

calcul~tted value. 

3. Simulation Verification 

Because the model is relatively extensive (over 300 nodes, 

over 140resistors, over 140inductors, and over 100capacitors), 

it was important to verify it before simulating groltnd faults. 

This was accomplished by running the simulation and using 

peak values and zero-crossing times to determine individual 

phasor values. Phasors were computed for the loads, and in each 

case, the voltages and currents were balanced, and the power 

factor was 0.90 tagging. Because the loads were necessarily 

modeled as constant impedance elements instead of constant 

power loads, the total system power was less than the specified 

power requirements due to voltage drops in the branches. 

However, for the purposes of this paper, this difference was 

inconsequential. 

IV. RESULTS OF ANALYSES 

A series of ground-Fault simulations were conducted to determine the effect of distributed capacitance on the level of 

fault current and relay selectivity in high-resistance grounded 

distribution systems. In a13 simulations, an NGR current limit of 

25 A was used because this value is a common limit currently 

used in coal mines to comply with regulations. The pickup was 

assumed to be 40% oh the NGR current limit. 

The first set of simulations consisted of observing the level 

of fault current and NGR current for ground faults at various 

points in the distribution system. The fault locations included 

the service point, the bottom of the borehole, the distribution 

cable to one of the CM sections, the distribution cable to the 

LW, and the distribution cable to two main belt drives. Table VII 

lists the faulted branches, the current through the NGR, the fault 

current, and the prefault line voltage. Results indicate that the 

fault current exceeds the NGR current by a factor of nearIy three 

in all cases. The table also shows that the fault and NGR current 

decrease slightly with distance from the source due to reduction 

of the fault voltage with distance from the source. 

Becalrse the level of fault current significantly exceeds the 

NGR limit, simulations were conducted todetermine the impact 

on relay selectivity during a ground fault in the distribution 

system. The hrst case presented is a line-to-ground fault in the 

cable connecting bus 1.7 to bus 16. There is a tripIe-'breaker 

switchhouse at bus 13(i.e., bottom ofthe borehole) and all three 

outgoing circuits are protected by a relay and circuit breaker. 

A summary of the zero-sequence currents (31Ao)for each 

of the branch circuits is given in Fig. 4. (The Fault and NGR 

currents were given in Table VII.) This figure illustrates that 

the maximum zero-sequence current is in the faulted 'branch, 

and that very little zero-sequence current flows in the short 

circuit to the motor pit. However, the zero-sequence current in 

the branch circuit feeding the CM sections and LW exceeds the 

ground-fault pickup setting by a factor of five. Therefore, in 

this situation, selectivity is lest, and it is likely that the circuit 

breaker in this branch would trip when a ground fault occurs in 

the branch between bus 1 3 and 16, 

Fig. 5 shows another situation, in which the line-to-ground 

fault was located in branch 31-32, and the zero-sequence 

current in branch 31-38 (feeding the LW) was computed. 

In this case, the charging current is essentially equal to the 

pickup value of I O A; therefore, this is another siti~ation where 

selectivity would be lost. 

It is n relatively straightforward process for mine operators 

to evaluate their particular system for situations where loss 

of relay selectivity is likely to occur. The process involves 

estimating the cable capacitance for the portion of the system 

in question and using that capacitance to estimate the charging 

current. To illustrate, consider the situation in which the fault is 

in branch 13-1 6,and the zero-sequence current in branch 13-22 

is to be predicted. The per-phase capacitance for the distribution 

cable is approximately 1 I0 pFlft, and thee are 62000 ft of 

cable in the distribution system for the remainder of the mine 

supplied through branch 13-22. The total per-phase capacitance 

is therefore 6.82 pF,which is a 60-Hz reactance of -389 !2 per 

phase. The three-phase zero-sequence current flowing in this 

branch can be estimated by dividing the line-to-neutral voltage 

by one-third of the per-phase reactance 

This value compares very well with the simulation result of 

54.6A. Repeating this calcuIation for the zero-sequence current 

in branch 31-38 for a ground fault in branch 31-32 yields an 

estimate of 9.7 A co~npared with the simulation result of 9.8 A. 

Note that in these examples the prefault voltage was used so 

that an accurate comparison with the simulation results could 

be made. However, in practical situations the nominal system 

voltage would be used. 

Another aspect of a power system in which the charging 

current exceeds the NGR current is the rise in voltage for a 

resonant fault condition. To examine this, n fal~lr with an inductive reactance equal to the capacitive reactance of the system 
0-0 


3EAO from bus I3 3IAD from bus $3 31AO from bus I3 

to 14 to 16 to 22 

Fig. 4. Zero-sequence current for a line-to-ground fault in branch connecting bus 13 40 bus 16. 

60.0 


0.0 


3lAO frombus 31 to 32 31AO from bus 31 to 38 

Fig. 5. Zero-sequence current for rline-to-ground fault in branch connpcring bus 3 1 to bus 32. 

Fig. 6. Line-to-ground voltages Tor a resonant bult condition. 

(not including the power factor correction capacitors) was through a 281-mH inductance, indicates that the system would 

introduced at bus 36, and the simulation was mn for approx- be subjected to a rise in voltage of approximately three times 

imately ten cycles. The result, shown In Fig. 6 for a fault the rated voltage for a resonant fault condition. 
Modern mine power systems can have a significant amount 

of distributed system capacitance. In certain cases. this cnpncitance and the practice of limiting the NGR current to 25 A can 

create situations that violate the definition of n high-resistance 

grounded system. For example, in the power systetn prcscntcd 

in this paper. which is based on an actual mine distribution 

system. the per-phase dislributed ctlpacilance is 8.36 pF. which 

has a 60-572reactance of -317.4 Q. Therefore, the value of 

the NGR should be less rhan 106 fi for this system to comply 

with the definition of high-resistance grounding. However, in 

practice, the resistor would be approximately 288 R in order to 

limit the NGR current to 25 A. Simulations have demonsrraled 

that the fault current is nearly three times the NGR current limit. 

the system is prone to loss of selectivity, and is also susceptible 

ta damage from overvottnges for a resonant fault condition. 

[ I 1 iEEE Rt~~~o~~~nrcrt~Ii~d Prfrr~icrJ)r Gn>ttndi/~g of ~trtf~~s~rinl OII~C<JIIIJ~~PW;(I/ 

So1vt.r S~sr~tn.~, IEEE Std. 142-1991. 1996.

121 IEEE Rt~cr,r~tm~~ei.~i I'rotricrfor Ptnrrt lion and Coodir~flriorrnf Jr~rirr,~rrinl 

(rrl(l Comr~rrrci~~l Pr~~wr S151tr1rs, lEEE Sfrt 242-2001, 2001.

131 	 30 CFR 75.801. 'rirle 30 af the Code ol' Fcdcnl Kcgulntinns." Mi81rrzrl 

Kr.~oirrres.Oftice Fcdera! Rcpister National Arcliives Records A(Inllnihtrittion. 21)03. 

141 Mittirrx Crrblr E11~irtrprln,q Hrrtrrl!>or>k, Tlic hlincoodo Colnpnliy. 

Anaconda. MT. 1975. 

151 M.Fuller, private c~~nrntin~~~ion. AmerCnbfr. MM.2004.