California State Professional Engineer Registration Examination

The following problem is taken from Easypower Demo 7.0 Protection-1.dez sample file. The problem will be solved using the MVA method implemented in the online short circuit calculator presented on this web-site. Fault current values at nodes a) to j) need to be calculated. The resulting short circuit current values will be compared with the respective values produced by ESA Easypower 7.0.

MVA sequence diagram below shows positive and zero sequence networks for the above power system. Since the positive and negative sequence impedances are the same in a static symmetrical system, conversion of a positive sequence network to a negative sequence network is accomplished by changing if necessary only the impedances that represent rotating machinery and by omitting emfs. Three phase synchronous generators and motors have internal voltages of positive sequence only, since they are designed to generate balanced voltages. Electromotive forces are omitted on the assumption of balanced generated voltages and the absence of negative sequence voltages induces from outside sources. In our example, negative sequence network is identical to positive sequence with emf sources removed.

Full scale short circuit study requires analysis of positive, negative and zero sequence networks. The table below shows entry data required for the analysis. RES MVA and RES X/R columns show the resulting MVA and X/R quantities for the respective sequences.

POSITIVE SEQUENCE NETWORK
IDLABELSC MVAX/RDESCRIPTIONP A R E N TRES MVARES X/RN O D E
1PSE20007PSE-SOUTH 2000MVA S.E.020177.03a
2TX-125022.3TX-1 20 MVA Z=8% D-YRG1240.6717.4b
3C-4110500.91-1/C-4/0 AWG 210 FEET CU2237.114.4c
4C-542050.61-1/C-2/0 AWG 400 FEET CU222911.9d
5C-177350.91-1/C-4/0 AWG 300 FEET CU2235.113.1e
6TX-383.312.6TX-3 5 MVA Z=6% D-YRG377.914.54f
7TX-47.53.7TX-4 0.3 MVA Z=4% D-YG47.273.8g
8TX-216.675.7TX-2 1 MVA Z=6% D-YG521.045.7h
9M-22.3817.6398KVA 16.7%Z 17.62X/R6
10M-35.9625996KVA 16.7%Z 24.97X/R6
11M-48.9428.41494KVA 16.7%Z 28.43X/R6
12PNL-1000 SCMVA 480V PANEL7
13C-366.812-1/C-350 MCM 125 FEET CU817.63.43I
14C-266.812-1/C-350 MCM 125 FEET CU817.13.26j
15MCC-12.674.5446KVA 16.7%Z 4.5X/R13
16M-11.4714.2247KVA 16.7%Z 14.21X/R8
17MCC-21.484.5247KVA 16.7%Z 4.5X/R14
NEGATIVE SEQUENCE NETWORK
IDLABELSC MVAX/RDESCRIPTIONP A R E N TRES MVARES X/RN O D E
1PSE20007PSE-SOUTH 2000MVA S.E.020177.03a
2TX-125022.3TX-1 20 MVA Z=8% D-YRG1240.6717.4b
3C-4110500.91-1/C-4/0 AWG 210 FEET CU2237.114.4c
4C-542050.61-1/C-2/0 AWG 400 FEET CU222911.9d
5C-177350.91-1/C-4/0 AWG 300 FEET CU2235.113.1e
6TX-383.312.6TX-3 5 MVA Z=6% D-YRG377.914.54f
7TX-47.53.7TX-4 0.3 MVA Z=4% D-YG47.273.8g
8TX-216.675.7TX-2 1 MVA Z=6% D-YG521.045.7h
9M-22.3817.6398KVA 16.7%Z 17.62X/R6
10M-35.9625996KVA 16.7%Z 24.97X/R6
11M-48.9428.41494KVA 16.7%Z 28.43X/R6
12PNL-1000 SCMVA 480V PANEL7
13C-366.812-1/C-350 MCM 125 FEET CU817.63.43I
14C-266.812-1/C-350 MCM 125 FEET CU817.13.26j
15MCC-12.674.5446KVA 16.7%Z 4.5X/R13
16M-11.4714.2247KVA 16.7%Z 14.21X/R8
17MCC-21.484.5247KVA 16.7%Z 4.5X/R14
ZERO SEQUENCE NETWORK
IDLABELSC MVAX/RDESCRIPTIONP A R E N TRES MVARES X/RN O D E
1PSE15009PSE-SOUTH 1500 ZS MVA S.E.015009a
2TX-1 D022.3TX-1 20 MVA DELTA SIDE1
1TX-1 RY3.17019.9 OHM GROUND RESISTANCE0
2TX-1 Y29422.25TX-1 20 MVA Z0=6.8% WYE SIDE13.180.06b
3C-4121011-1/C-4/0 AWG 210 FEET CU23.170.07c
4C-54631.61-1/C-2/0 AWG 400 FEET CU23.150.09d
5C-184611-1/C-4/0 AWG 300 FEET CU23.170.08e
6TX-3 D00TX-3 5 MVA DELTA SIDE3
7TX-4 D00TX-4 0.3 MVA DELTA SIDE4
8TX-2 D00TX-2 1 MVA DELTA SIDE5
 
1TX-3 RY0.2706.9 OHM GROUND @ 2.4KV0
2TX-3 Y9812.58TX-3 5 MVA Z0=5.1% WYE SIDE10.270f
3M-200398KVA 16.7%Z IND MOTOR2
4M-300996KVA 16.7%Z IND MOTOR2
5M-4001494KVA 16.7%Z IND MOTOR2
 
1TX-4 Y8.823.68TX-4 .3 MVA Z0=3.4% WYE SIDE08.823.68g
2PNL-1000 SCMVA 480V PANEL1
 
1TX-2 Y19.65.68TX-2 1 MVA Z0=5.1% WYE SIDE019.65.7h
2C-37.412-1/C-350 MCM 125 FEET CU15.581.4I
3C-27.412-1/C-350 MCM 125 FEET CU15.581.4j
4MCC-100446KVA 16.7%Z 4.5X/R2
5M-100247KVA 16.7%Z 14.21X/R1
6MCC-200247KVA 16.7%Z 4.5X/R3

Table below is a compilation of the kA produced by the online short circuit calculator, system line to line voltages and Easypower 7.0 calculation results at potential fault points. The resulting short circuit current values in kA are obtained by running MVA to KA converter.

N O D ELABELVLL, kVMVA 1MVA 2MVA 0X/R 1X/R 2X/R 03 phase, kAEP 3 phase, kAL-G, kAEP L-G, kAL-L, kAEP L-L, kA
aPSE1152017201715007.037.039.0010.1410.127.55 *7.568.778.77
bTX-113.8240.67240.673.1817.417.40.0610.0810.060.400.408.728.72
cC-413.8237.1237.13.1714.414.40.079.939.920.400.398.598.59
dC-513.82292293.1511.911.90.099.599.720.390.398.308.42
eC-113.8235.1235.13.1713.113.10.089.859.840.400.408.518.52
fTX-32.477.977.90.2714.5414.540.0018.7618.750.200.2016.2316.24
gTX-40.487.277.278.823.83.83.688.758.759.309.307.577.57
hTX-20.4821.0421.0419.65.75.65.7025.3424.7224.6024.3021.8021.40
M-22.382.380.0017.6217.620.00
M-35.965.960.0025250.00
M-48.948.940.0028.428.40.00
PNL-10.480.000.000.000.000.000.00
IC-30.4817.617.65.583.43.41.4021.1920.6912.5012.2018.3017.90
jC-20.4817.117.15.583.33.31.420.5920.1812.3012.0017.8017.48
MCC-10.482.672.670.0014.214.20.00
M-10.481.4714.20.0014.214.20.00
MCC-20.481.471.470.004.54.50.00

* - Based on 1500 SCMVA utility line to ground short circuit MVA. This value is calculated using: MVASLG=SQRT(3)VLLI1ph [ESA Easypower]

Per unit method can be utilized in solving industrial power system short circuits. The figure below shows bus admittance positive and zero sequence per unit matrix for the above system. Negative sequence matrix equals the positive per unit matrix in this example. 2000 MVA and 115kV had been taken as base values.




The results of per unit calculations are within 5 percent margin of the MVA method values obtained by running the online calculator. Still, the MVA method does not require a common MVA base as required by the per unit method. Also, per unit method usually ends up with small decimals resulting from converting impedances from one voltage to another or from converting impedances to the same common base. This can easily lead to mistakes in the decimals with resulting wrong or inaccurate answers. Nonetheless, buss admittance sequence network per unit method is indispensable in more advanced short circuit study where voltage drops on other than faulted buss and power flow analysis are being investigated.

Following observation can be made from the performed study:

  • Short circuit current values derived from Easypower and the Online Short Circuit Calculator presented on this web-site are by all practical means equal;
  • Easypower zero sequence impedance for motors is taken as infinity (no ground return path). Apparently, there is no easy way to accurately calculate short circuits contributed by grounded motors in Easypower. There is no limitation like this when the online short circuit calculator is used for fault analysis.