ABB 615 series Technical Manual page 284

Section 4
Protection functions
278
Thermal counter
49T applies the thermal model of two time constants for temperature measurement. The
temperature rise in degrees Celsius (°C) is calculated from the highest of the three-phase
currents according to the expression:
2
 
 
I
 
p * * T
∆Θ = ⋅
 
ref
  I  
ref
 
 
 
GUID-27A879A9-AF94-4BC3-BAA1-501189F6DE0C V2 EN
ΔΘ calculated temperature rise (°C) in transformer
I measured phase current with the highest TRMS value
Current reference setting (rated current of the protected object)
Iref the set value of the
Temperature rise setting (temperature rise setting (°C) with the steady-state current
Tref the set value of the
I )
ref
Weighting factor p setting (weighting factor for the short time constant)
p the set value of the
Δt time step between the calculation of the actual temperature
Short time constant setting (the short heating / cooling time constant)
the set value of the
t
1
Long time constant setting (the long heating / cooling time constant)
the set value of the
t
2
The warming and cooling following the two time-constant thermal curve is a
characteristic of transformers. The thermal time constants of the protected transformer are
given in seconds with the Short time constant and Long time constant settings. The Short
time constant setting describes the warming of the transformer with respect to windings.
The Long time constant setting describes the warming of the transformer with respect to
the oil. Using the two time-constant model, the protection relay is able to follow both fast
and slow changes in the temperature of the protected object.
The Weighting factor p setting is the weighting factor between Short time constant τ
Long time constant τ . The higher the value of the Weighting factor p setting, the larger is
2
the share of the steep part of the heating curve. When Weighting factor p =1, only Short-
time constant is used. When Weighting factor p = 0, only Long time constant is used.
t
∆ 
 

− I I

 1 
1 e τ 1 p
( )
− + − ⋅

  I
 
ref


 

1MAC059074-MB A
2
t
 ∆
 

−

 2 
T 1 e τ
⋅ ⋅ −

ref
 
 


 

Technical Manual
(Equation 14)
and
1
615 series ANSI