D
Dt
k
K R
R
n
o
x
or
n
a
θ
τ
θ θ θ
0
11
2
0 1
1
1
( )
−
( )
=
⋅
( )
⋅
+ ⋅
( )
+
⋅ ∆ − −
(Equation 322)
Where
θ
0(n)
Top oil temperature in the tank at n
th
time step
θ
a
Ambient temperature [°C]
Δθ
or
Top oil temperature rise over ambient temperature at rated load, given by the
setting
Top oil Tmp rise
R Ratio of losses at rated current to no load losses, given by the setting
Ratio of
losses
k
11
, Շ
0
, K and x are as defined in the Parameter selection module in
Figure 789
.
The D operator implies a difference in the associated variable that corresponds to
each time step Dt. At each time step, the n
th
value of Dθ
0(n)
is calculated from the
(n-1)
th
value.
The initial conditions are calculated by setting the time derivative equal to zero in
Dθ
0(n)
equation, resulting in the following equations.
θ θ θ
0 0
2
1
1
( )
=
+ ⋅
( )
+
⋅ ∆ +
K R
R
x
or a
(Equation 323)
The top oil temperature at the n
th
time step is calculated as shown below.
TOPOIL TEMP D
n n
_ = +
−
( ) ( )
θ θ
0 1 0
(Equation 324)
The measured/calculated top oil temperature TOPOIL_TEMP is available in the
Monitored data view.
If the top oil temperature sensor is valid, the TOPOIL_TEMP output is
equal to the measured top oil temperature TOIL_TEMP input.
7.3.5.3 Hot-spot temp calculation
Winding hot-spot temperature depends on the winding temperature rise due to the
load factor and oil flow. These two factors act complimentary to each other in the
influence of temperature rise.
The differential equations for hot-spot temperature rise above top oil temperature
is solved as the sum of two differential equations.
∆ = ∆ − ∆
( ) ( ) ( )
θ θ θ
h n h n h n1 2
(Equation 325)
1MRS759142 F
Condition monitoring functions
REX640
Technical Manual
1387
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