The document discusses inverse-time overcurrent protection relays and their time-current curves. It describes the standard inverse, very inverse, extremely inverse, and long time inverse curves defined by IEC 60255 with their corresponding K and E values. It then provides examples of calculating the operating times for different relay types and settings based on the inverse-time equations, for short circuit currents of 2, 4, 6, 10, and 20 times the pickup setting.

1. characteristic of IDMT curves for overcurrent
relays
• There are many types of IDMT
curve as shown in the figure
below.
• Long time inverse type
• IEC inverse type
• IEC very inverse type
• IEC extremely inverse

2. Equations of IDMT curves
•T= 𝑇𝑀𝑆(
𝐾
(
𝐼𝑠.𝑐
𝐼𝑠𝑒𝑡
) 𝐸−1
)
• These standard according to IEC
60255 standard characteristics for
constant parameters (K and E)
•Isetis pickup setting of the current.
•Is.cis a value of short circuit current
No Relay characteristics K E
1 Standard inverse 0.14 0.02
2 Very inverse 13.5 1
3 Extremely inverse 80 2
4 Long time inverse 120 1

3. Calculate and Comparison between times
according to curve, TMS, Iset, and Is.c.
• If the TMS is equal to 0.1 and CT is
equal to 300/5 and Iset is equal to
5A as a secondary value.
• Is.c = 2 times of Iset
•Is.c = 4 times of Iset
•Is.c = 6 times of Iset
•Is.c = 10 times of Iset
•Is.c = 20 times of Iset

4. Type of curve Iset
value
Is.c value K & E
value
equations Result of
time
Standard inverse
300
300
300
300
300
2T=600
4T=1200
6T=1800
10T=3000
20T=6000
K=0.14
E=0.02
T= 𝑇𝑀𝑆(
𝐾
(
𝐼𝑠𝑒𝑡
𝐼𝑠.𝑐
) 𝐸−1
) 1.002
0.4979
0.3837
0.2970
0.2267
Very inverse
300
300
300
300
300
2T=600
4T=1200
6T=1800
10T=3000
20T=6000
K=13.5
E=1
T= 𝑇𝑀𝑆(
𝐾
(
𝐼𝑠𝑒𝑡
𝐼𝑠.𝑐
) 𝐸−1
) 1.35
0.45
0.27
0.15
0.0710
Extremely inverse
300
300
300
300
300
2T=600
4T=1200
6T=1800
10T=3000
20T=6000
K=80
E=2
T= 𝑇𝑀𝑆(
𝐾
(
𝐼𝑠𝑒𝑡
𝐼𝑠.𝑐
) 𝐸−1
) 2.666
0.5333
0.2285
0.0808
0.020
Long time inverse
300
300
300
300
300
2T=600
4T=1200
6T=1800
10T=3000
20T=6000
K=120
E=1
T= 𝑇𝑀𝑆(
𝐾
(
𝐼𝑠𝑒𝑡
𝐼𝑠.𝑐
) 𝐸−1
) 12
4
2.4
1.3333
0.6315

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