Jun 16, 2018

Differential protection | Calculation of current distribution


EARTfelt Welcome dear friends of protection and control engineering, during the primary test of a differential protection commissioning, it may be necessary to carry out a so-called current test. In today's article, we show you a concrete example of how to calculate the current distribution step by step. Here we go!

To estimate the expected secondary current ratios, the current distribution needs to be calculated as part of the preparations for the test. Furthermore, the results of the calculation help us check the ampacity of our short-circuit equipment. It's important here to adhere to the thermal limit curve times so that the short circuit equipment we're using doesn't burn out.

The primary test

Current transformers of transformers and drives on medium voltage and distribution network level, we check with the so-called 400 volt test, the test current comes out of the socket (Hereis our article "400 volt test?"). But what if we are dealing with larger systems? Only large test transformers, power test runs with hand-operated power plant generators or circular current tests with short-circuit power from the grid can help us here. In our calculation example, we show an example of the test using a power plant generator. The differential protection systems of the three transformers BAT, BBT1 and BBT2 are to be tested. To carry out the current drive, three-phase short circuits are installed outside the protection zones of the differential protection functions. Our example shows a block with 2 internal power transformers and 5 short circuit locations (see cover picture above).

Simplification into the equivalent circuit diagram

The ratio of total resistance to individual resistance is the same ratio as individual (branch) current to total current.

The branch currents for the two auxiliary transformers are therefore:

The transformation of the unit transformer must also be taken into account when calculating the current I1-OS:

We need the equivalent impedances for the transformers before we can work with these formulas. These are derived from german DIN VDE 0102:

Equivalent impedance of unit transformer:

Equivalent impedance of auxiliary transformer:

We first have to break the three-winding transformer down into 3 two-winding transformers by conceptually leaving one side of each open.

The equivalent impedances of the delta connection result in:

Next, we transform the transformer into a star connection, but please do not use the traditional delta-star transformation. We are going to stick  with the technically clean transformation as set out in DIN VDE 0102 for 3-winding transformers.

The final step involves combining the star connection to create a common equivalent impedance:

The current divider rule can now be resolved and we are in a position to calculate the distribution of our primary currents.

We now convert the results into secondary values using the current transformer ratios and add them to a simple Excel spreadsheet in the test program.

It's a good idea to use an Excel spreadsheet for this calculation, as this will allow you to make any changes you want to the input values. In addition, you will then have everything you need for the next test and won't have to start over.

HEARTfelt Greetings Alexander Muth