Thytronic XMR-D - Calculated; Phase

FUNCTION CHARACTERISTICS
57
Calculated
By means vector addition of direct measures the following are calculated (RMS value of fundamen-
tal components):
• Phase-to-phase voltages: U
12
, U
23
, U
31
• Fundamental component of the calculated residual voltage U
EC
[1]
• Thermal image ∆θ
Phase
[2]
• Displacement angle of any phase current respect the corresponding phase-to-neutral voltage:
Phi
L1
, Phi
L2
, Phi
L3
,
• Displacement angle of any phase current respect the remaining phase-to-phase voltages: Alpha
L1
,
Alpha
L2
, Alpha
L3
,
• Displacement angle of the residual current respect the corresponding measured residual voltage
(positive with current in lagging direction in respect to voltage): Phi
E
(traditional VT inputs only),
• Displacement angle of the residual current respect the corresponding calculated residual voltage
(positive with current in lagging direction in respect to voltage): Phi
EC
Note 1 In versions with VT inputs, the residual voltage is available as a direct measure U
E
and computed measure U
EC
, while for versions with input from
ThySensor or when the input is employed for the synchrocheck function, the residual voltage is only available as a calculated measure U
EC
Note 2 The adjustment and display range of displacements are 0°... 359°
U12.ai
U
L1
U
12
= U
L1
- U
L2
U
12
U
23
U
31
U
23
= U
L2
- U
L3
U
31
= U
L3
- U
L1
U
L2
U
L2
U
L3
U
L1
U
L3
(U
n
)
(U
n
)
(U
n
)
U
L1
U
12
U
31
U
23
U
L3
U
L2
UEC.ai
U
L1
U
EC
= U
L1
+ U
L2
+ U
L3
U
EC
U
L3
U
L2
(U
En
)
Theta.ai
I
L1
I
2
I
2
= (I
L1
+ e
-j120°
I
L2
+ e
+j120°
I
L3
)
I
1
= (I
L1
+ e
+j120°
I
L2
+ e
-j120°
I
L3
)
I
L3
I
L2
I
1
I
th
= √(I
1
2
+ K
2
2
∙I
2
2
)
∆θ
(∆θ
B
)
2
d∆θ
dt
I
B
I
th
∆θ
T+ T+
( )
+ =
Fase.ai
ϕ
L1
= ∠I
L1
- ∠U
L1
Phi
L1
, Phi
L2
,Phi
L3
Phi
E
Phi
EC
(° )
(°
)
(°
)
(°
)
Alpha
L1
, Alpha
L2
,Alpha
L3
U
L1
ϕ
L2
= ∠I
L2
- ∠U
L2
ϕ
L3
= ∠I
L3
- ∠U
L3
ϕ
E
= ∠U
E
- ∠I
E
ϕ
E
= ∠U
EC
- ∠I
E
α
L1
= ∠I
L1
- ∠U
23
α
L2
= ∠I
L2
- ∠U
31
α
L3
= ∠I
L3
- ∠U
12
U
L2
U
L2
I
L1
I
L2
I
L3
U
E
U
EC
I
E
XMR-D EQUIPMENT MANUAL
Ed. 2.9 - 02/2021