# Time-Current Curves Using Excel

Time-Current Curves Using Excel – Part 1
In these articles, I have discussed the methodology on how to create time-current curves using excel. 1. 2. 3. 4. Creating Coordination Curves with Excel Time-Current Curves with Excel II Time-Current Curves with Excel III Time-Current Curves with Excel IV

Creating Coordination Curves with Excel
As electrical engineers, doing protective devices coordination is always a part of our tasks. You may say that I could always use ETAP or EDSA or SKM Power Tools to do the job.

If your company has the money to buy all these software, then you are right. The most important thing however is, do you know how to use the sophisticated power system analysis software.

At the end of this tutorial, the electrical engineer will be able to create coordination graphs for any particular application. This tutorial also aims to provide tips during the process.

The requirements of this tutorial are the following

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You have MS Excel - at least MS Excel 2003 - lower versions may do as well. You know how to use MS Excel You know how to create graphs.

This is a sample of coordination curve we shall be doing on the next part of the tutorial.

Time-Current Curves with Excel II
In this part of the tutorial, we shall be able to produce a Normal Inverse time-current curve. Given the values below, we will be plotting the values on an XY Scatter graph with data points connected without markers.

Normal Inverse Curve 400A Setting I (A) 600 800 1200 1600 1600 1600 4800 4800 t (s) 2.75 1.60 1.01 0.80 0.80 0.14 0.14 0.10

Try plotting the values and I presume that you will be getting a graph similar to Figure 1.

Figure 1

To plot a graph similar to Figure 2, the technique is to chunk the data into separate data series.

Data Series 1 I (A) 600 800 1200 1600 t (s) 2.75 1.60 1.01 0.80

Data Series 2 I (A) 1600 1600 t (s) 0.80 0.14

Data Series 3 I (A) 1600 4800 t (s) 0.14 0.14

Data Series 4 I (A) 4800 4800 t (s) 0.14 0.10

Figure 2

As I have said in the first part of this tutorial, I presume that you know how to use MS Excel. In the next part, we shall be learning about how to calculate curves for normal inverse, very inverse, extreme inverse and long time inverse

Time-Current Curves with Excel III
In this tutorial, we shall be able to create Normal Inverse curves from the formula given below (IEC). This formula has been used in so many coordination studies world wide. You can actually use it to coordinate your protection settings with your power supplier. Normally the time setting for the network protection will be provided by the power supplier. We shall be discussing this on the next tutorial.

Time-Current Formula where

k = time, s α, β = constants, see table below I = Input Current IO = Pickup setting

The curve constants for the different response curves are as follows.

Curve Constants α Normal Inverse (Type A) Very Inverse (Type B) 0.02 1.00 β 0.14 13.5 80.0 120

Extremely Inverse (Type C) 2.00 Long Time Inverse 1.00

Using the formula above, the resulting values will be the following table. You could copy the whole table and paste it into your worksheet or create the values yourself using the above formula. Remember that this curve is for Normal Inverse curve.

500 A CT Rating (Normal Inverse) 0.05 0.10 0.20 0.25 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 I/IO I (A) Time, s 1.5 750 0.86 1.72 3.44 4.30 5.16 6.88 8.60 10.32 12.04 13.76 15.47 17.19

2.0 1000 0.50 1.00 2.01 2.51 3.01 4.01 5.01 6.02 7.02 8.02 9.03 10.03 3.0 1500 0.32 0.63 1.26 1.58 1.89 2.52 3.15 3.78 4.41 5.04 5.67 6.30 4.0 2000 0.25 0.50 1.00 1.24 1.49 1.99 2.49 2.99 3.49 3.98 4.48 4.98 5.0 2500 0.21 0.43 0.86 1.07 1.28 1.71 2.14 2.57 3.00 3.42 3.85 4.28 6.0 3000 0.19 0.38 0.77 0.96 1.15 1.53 1.92 2.30 2.69 3.07 3.45 3.84 7.0 3500 0.18 0.35 0.71 0.88 1.06 1.41 1.76 2.12 2.47 2.82 3.17 3.53 8.0 4000 0.16 0.33 0.66 0.82 0.99 1.32 1.65 1.98 2.31 2.64 2.97 3.30 9.0 4500 0.16 0.31 0.62 0.78 0.93 1.25 1.56 1.87 2.18 2.49 2.80 3.12 10 5000 0.15 0.30 0.59 0.74 0.89 1.19 1.49 1.78 2.08 2.38 2.67 2.97 20 10000 0.11 0.23 0.45 0.57 0.68 0.91 1.13 1.36 1.59 1.81 2.04 2.27
With the values above, We shall be using the 2003 version of Excel to draw the chart. If you have 2007 version, it is not a problem, the steps would just be different but the resulting graph will still be the same.

Step 1 Select the cell range as shown.

Note: Do not include the I/IO, else you will be getting a different graph profile.

Step 2 Start chart wizard and select XY (Scatter) with data points connected by smoothed lines without marker.

Step 3 Select the data range with series in columns

Step 4 Type a title, make sure to put x-axis title as Current in amperes and y-axis values as time in seconds.

Step 5 Click the gridlines tab and tick all the major and minor gridlines for X and Y axis. Then click finish. If prompted about the location of the graph, select it as an object in the worksheet.

Step 6 The resulting graph will be

Step 7 Double click on the Y-axis values, the format Y-axis window will pop-up. Select Logarithmic scale. and values as shown. Do similar for the X-axis.

Step 8 The resulting graph will be as follows. As you could see, the graph scale now are logarithmic.

Step 9 Try format the graph, putting some additional values, removing the chart background, etc. The final graph may look like this.

Next time

Time-Current Curves with Excel IV

This is the final part of the tutorial creating for time-current current curves with Excel. We shall be able to attain a complete relay coordination similar to this following curve.

To understand better the coordination curve, here are the parameters. Please note that values are referred to the primary which is 11kV.

Utility Supply (0.2 time multiplier) Voltage : 11kV SC Capacity : 75MVA Protection: 250A set @ 5IN Supply Cable Size : 35 mm PVC/PVC Primary Circuit Breaker (0.16 time multiplier) Rating : 160A Setting 1 : 800A @ 5IN Setting 2 : 1120A @ 7IN Power Transformer Rating: 2500 kVA, 11/0.415kV, 6.25%Z
2

Secondary Circuit Breaker (0.12 time multiplier) Rating : 4000A (150A - referred to Primary) Setting 1 : 604A @ 4IN Setting 2 : 905A @ 6IN Motor Cable Size : 185 mm PVC/PVC Motor Circuit Breaker (0.1 time multiplier) Rating : 800A (30A - referred to Primary) Setting 1 : 483A @ 16IN Setting 2 : 604A @ 20IN
2

The utility time multiplier is normally provided by the power provider. Then, we need to work below it else, our protection is not time coordinated with the utility.

For the motor circuit breaker, we need to select a setting wherein the value protection will not trip during motor starting which is ideally 6 time the full load motor current and it should still be tripping below the secondary circuit breaker setting.

You may have noticed that I have included the damaged curve of the cables. These are correctly selected because they way above the protection setting of the utility.

This is the final part of the time-current curve with excel. If you have any queries, feel free to post a comment and we shall discuss

I would suggest that if you are not familiar with creating graphs in excel that you go to each of the tutorials listed above to be able to comprehend the foregoing how tos. In this series of tutorials, I will be discussing "HOW TOS" on relay coordination using excel. In each part of the tutorial, a methodology will be presented step-by-step.

It is expected that after the completed of the whole series of tutorials, readers will be able to demonstrate their acquired in relay coordination using excel.

Time-Current Curve Part 2 – Discrimination
In Part 1, I have discussed the basics of using excel in plotting time-current curves. In this tutorial, I will be presenting an example of a possible discrimination curve using the different curve types based on IEC 60255 (BS 142). 1. Standard Inverse (Normal Inverse) - this is the most commonly used curve for over-current protection. 2. Very Inverse - used where fault current decreases significantly between protection points. 3. Extremely Inverse - used when coordinating with fuses. IDMT Equation:

where:

Constants Values

Curve Type Standard Inverse 0.02 0.14 Very Inverse 1 13.5 80 Extremely Inverse 2

When doing relay coordination, take note that "?Inverse Over Current Relay" operating time is inversely proportional to the fault current which means it will have faster operating times at higher fault levels and for faults nearer to the source.

I have attached the excel in creating this curves but before downloading the excel file, please take time to read this instructions on using the worksheet. 1. The worksheet was created using Excel 2010 saved on compatibility mode with Excel 97-2003. There might be some functionality lost during the process due to backward compatibility. 2. Curve type can be selected using a drop down list.

3. This worksheets could be used for a three relays. 4. Curves on the graph: 1. Fault Current 2. Supply relay 3. Clearance curve 1 between supply relay and relay 1 down stream. 4. Relay 1 curve 5. Clearance curve 2 between supply relay and relay 1 down stream. 6. Relay 2 curve. 5. Downstream relay currents are plotted on the graph converted into the supply voltage base. 6. The worksheet have been formatted for easy printing.