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What is TSM and PSM of a relay and how to calculate

Relay Time Setting Multiplier and Plug Setting Multiplier calculation

How to calculate relay TSM and PSM

Relay time setting multiplier (TSM) and plug setting multiplier (PSM) are the two key parameters required to calculate the operating time of the relay. Having knowledge of these two is very important in order to understand the relay operation. 
Remember These two terms are related with the IDMT type relay, they are irrelevant for the definite type relays. 
So let's know about the relay TSM and PSM 

What is Time Setting Multiplier (TSM) :

TSM or Time Setting Multiplier of relay is defined as the ratio of actual operating time to the ideal operating time (operating time obtained from PSM vs Time graph).
Some time it is also written as Time multiplier or TMS.

What is Plug Setting Multiplier (PSM) 

PSM or Plug Setting Multiplier is defined as the ratio of fault current from CT secondary to the pickup current of the relay.

Remember : pickup current is the minimum current required to start the relay operation. 

For example; in case of disk type electro magnetic relay it is the minimum current from the secondary of Curren Transformer (CT) for which the disk just starts moving.

How to calculate the Relay PSM :

Calculation of relay plug setting is very simple . But before that you need know a little about your system. 

like whether your CT has a 1ampere or 5 ampere secondary.

For example it may be a 400/5 A or 400/1 ,250/1 .... So like that.

During any fault there is a huge current that flows through the CT primary. which also generates a current in the CT secondary circuit .

We measure this CT secondary current with a low range ammeter which shows the current by multiplying with the CT ratio and shows that on a properly calibrated scale.

For example: you have a 250/1A CT in your system, during a fault 1000A fault current is flowing through the CT primary and an ammeter of full scale 5 Ampere is used to measure this. 

That means when the 1000A fault current flows through the CT primary it will generate (1000*1/250) A = 4A to its secondary. 

And the ammeter is so calibrated that it shows 1000 ampere whenever it sence 4 A through it .

Now you have the Primary fault current , CT primary/secondary ratio and the pickup current of the relay (which can be manualy set by the operator depending upon the system requirements)
this is all you need to know to calculate PSM of the relay

The formula to calculate Relay PSM:

Now say 1000A Fault Current through CT primary 
ie, the secondary CT current I'=1000*1/250 =4A
(As we have assumed that the CT ratio is 250/1A)

And let the pickup current is set at 1A

Now the Plug Setting Multiplier or PSM =
(4/1) = 4

Now the Plug Setting Multiplier or PSM
= (4/1) = 4

NB: Most of the time the pickup current range lies between 50% to 200% of CT secondary ie, 0.5A to 2A for 1ampere CT and 2.5A to 10A for a 5ampere CT.

Remember: PSM is a unit less quantity as it is a ratio of two same unit.

How to calculate the Relay TSM :

In case of an IDMT relay, the operating time is always inverse in nature .

That means higher the fault Current the lesser the operating time.

In case of disk type electromagnetic relays There is a time setting dial scaled between 0 to 1 with an increment of 0.1
And in case of numerical relays there is no physical dial but you can set it by entering the value manually.

The actual operating time of a relay is obtained from the PSM vs Time graph 

This graph varies depending on which international standard it's following
It can be The IEEE standard or can be IEC standard.

Most of the safety relay follows the IEC standards.

The formula to calculate Relay TSM :

In practical cases we do not calculate the relay TSM but using TSM we calculate the actual operating time of the relay. 
Now you may think that how we will know the TSM and the ideal operating time 
The answer is there is a formula which guides the relation between all the relay parameters discussed above with the operating time 
Also the ideal operating time of operation is indicated by the manufacturer of the for a specific PSM and and TSM 
Now for example : let's say the ideal operating time is 10 seconds if the fault current becomes 2times the pickups current. 
And the TSM is set to 0.5 by the operator
Now the actual operating time would be, t = 10*0.5 = 5 seconds 
See how easy is that. 
Hope you have learned something from here 
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