ABB RELION REX640 - Page 1388

The two differential equations are shown in Equation 326 and Equation 327 .
D
Dt
K
h n
w
hr
y
h n
k
k
∆ =
⋅
( )
⋅ ⋅ ∆ ⋅ − ∆
( )
( )
−
( )
θ θ θ
τ
1
22
21
1 1
(Equation 326)
D
Dt
K
h n
o
hr
y
h n
k
k
∆ =
⋅










⋅ −
( )
⋅ ∆ ⋅ − ∆
( )
−






θ θ θ
τ
2
21
2 1
1
22
1
(( )
( )
(Equation 327)
Where
Δθ
hr
Hot-spot-to-top-oil gradient at rated current [°C]
The constants Շ
w
, k
21
, k
22
and y are varying according to the Cooling mode setting
and are obtained from the Load factor calculation and parameter selection module.
The rated hot-spot to top oil gradient, HS_TOIL_GRA (Δθ
hr
), is calculated using the
formula as shown in Equation 328 .
∆ =
−
θ
hr
rated
Hotspot Tmp rise Top oil Tmprise
Current typetest
I






y
(Equation 328)
Where
I
rated
Rated current of the transformer
Hotspot Tmp rise Hot-spot temperature rise over ambient at rated load
Top oil Tmp rise Top oil temperature rise over ambient at rated load
Current type test Current applied in type testing to reach rated hot-spot temperature
At each time step, the n
th
value of DΔθ
h1(n)
and DΔθ
h2(n)
are calculated from the
(n-1) value; the solutions of which are combined in accordance with the hot-spot
temperature rise equation.
∆ = ∆ + ∆
( )
−
( ) ( )
θ θ θ
h n h n h n
D
1 1 1 1
(Equation 329)
∆ = ∆ + ∆
( )
−
( ) ( )
θ θ θ
h n h n h n
D
2 2 1 2
(Equation 330)
The initial conditions are calculated by setting the time derivative equal to zero
inDΔθ
h1(n)
and DΔθ
h2(n)
equations, resulting in the following equations.
Condition monitoring functions
1MRS759142 F
1388 REX640
Technical Manual