# DC short circuit calculations example

Annotation: The example below shows how to create single line diagram of mine power system, pre-assign a single short circuit MVA factor to each basic component within the power system based on the impedance it adds to the system, program the one line diagram into short circuit calculator, run the analysis, interpret the results, calculate ac and dc short circuit current values on ac and dc side of transformer rectifier combination.

### Create One Line Diagram of Distribution System

Develop a comprehensive one-line radial diagram of the power system being analyzed. It is recommended that you use a copy of the same one-line diagram which is applied when laying out the distribution system ( Figure 1 a).  Figure 1a
Figure 1b

Each basic component within the industrial electrical distribution system is pre-assigned a single short circuit MVA factor (SC MVA) based on the impedance it adds to the system ( Figure 1 b). Generators, motors, transformers are normally given their own rated MVA, X/R ratios and impedance ratings [typical X/R and impedance ratings].The short circuit MVA of each is equal to its MVA rating divided by its own per unit impedance. For instance, a 2000KVA, 5.75%Z transformer has a SC MVA = Rated MVA / Z = 2 / 0.0575 = 34.8MVA, where Z is the transformer impedance in p.u. For a feeder where the voltage is given and its impedance or reactance is known, its short circuit MVA is equal to kV^2 divided by its impedance in ohms. For example, the 14000 feet long copper cable connecting 4160V rated secondary of the 2000kVA transformer with primary side of the transformer/rectifier combination impedance equals to 0.99 Ohms ( based on X = 4.53 mOhm/100ft and R = 5.43 mOhm/100ft copper conductor cable reactance and resistance data ). The cable SCMVA rating is therefore equal to 4.160^2 / 0.99 = 17.5 SCMVA. Typical 300kW 300V transformer rectifier combination impedance equals to 10% , and it's short circuit MVA ratings would be equal to 0.3MVA / 0.1 = 3.0 SCMVA. Loads not contributing to system's short circuit current are assigned a SC MVA value of 0.

### Develop a hierarchical tree in terms of database records

 ID * Label SC MVA Error, % X/R Error, % Description Par- ent ? 1 Utility 500.00 1 12.00 5 500MVA 22kV Utility System 0 2 TRSFRM 1 34.80 1 12.00 5 2MVA 5.75%Z, 4.16kV Secondary 1 3 CABLE 1 17.50 1 0.83 5 14000 ft 4/0 Cu Cable, Mag duct 2 4 TRSF/REC 3.00 1 6.00 5 300kW Transformer/Rectifie 10%Z 3 5 CABLE 2 0.76 1 0.46 5 1000 ft 1/0 Cu Cable, Mag duct 4 6 TROLLEY 0.00 1 0.00 5 Trolley System contributes 0 MVA 5

% columns list margin of error for values from SC MVA and X/R columns.
p_id column lists parent ID (id of the upstream equipment)

The system equipment tree should be broken into levels, with each level being more focused than the last. The tree consists of nodes connected to each other by branches. Please note that a node may have one or more children, but can have only one parent. Equipment parent id equals the id of the upstream device feeding the equipment. TRSFRM 1 is fed from Utility. The TRSFRM 1 is assigned parent id of "1" which equals the Utility id value. Utility is a root feeding the system, its parent id is assigned "0" by default. You will need the reference table similar to the one above to input your system information required for AC / DC short circuit analysis using ARCAD Online Short Circuit Calculator.

### Run the program and observe the results

The program will output the hierarchical system equipment tree with short circuit MVA calculated at each node.

The Results of SC MVA Calculations:
• Utility[ 500(12X/R) +  0 =  500 (12X/R) ]
• TRSFRM 1[ 32.9(12X/R) +  0 =  32.9 (12X/R) ]
• CABLE 1[ 12.3(1X/R) +  0 =  12.3 (1X/R) ]
• TRSF/REC[ 2.46(4X/R) +  0 =  2.46 (4X/R) ]
• CABLE 2[ 0.62(0.8X/R) +  0.00 =  0.62 (0.8X/R) ]
• TROLLEY[0.00]

Short circuits contributed by upstream (red color) and downstream (blue color) equipment are listed across each node. Upstream and downstream values above contain one more significant digit than required by error analysis rules. This digit is dropped off the final result (in green color). In this manner, phenomenon known as "round-off error" is effectively avoided. Figure 2 below shows calculated short circuit MVA transferred onto the original one-line diagram. Figure 2

Divide total SC MVA values by 1.73 * kVLL to get 3 phase short circuit current values in kA on AC side. For example, to calculate short circuit current value on line side of the transformer rectifier combination, take calculated 12.3 SCMVA value, divide it by 4.160kV and divide it by 1.73. The resulting ac short circuit current is equal to 1.71kA.

Divide total SC MVA value by system voltage in kV to get short circuit current value in kA on DC side. For example, to calculate short circuit current value on load side of the transformer rectifier combination, take calculated 2.46 SCMVA value and divide it by 0.30kV. The resulting dc short circuit current is equal to 8.20kA.

 Instantaneous circuit breaker settings for the short-circuit protection of direct current 300 and 500 volt trailing cables, by W. Vilcheck and Co. U.S. Department of Labor.

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