Lecture
If calculations of electromagnetic transient processes are performed in per-unit values, then the reduction of the calculation-scheme parameters is combined with expressing them in per-unit values. The corresponding formulas are derived according to the scheme:
The formulas obtained in this way are summarized in Table 1.3.
Table 1.3. Formulas for calculation in per-unit values
|
No. |
Parameter |
Form of specification |
Form of reduction |
|
1 |
Voltages and EMF |
In named units
|
|
|
In per-unit values relative to rated values |
|
||
|
2 |
Currents |
In named units
|
|
|
In per-unit values relative to rated values |
|
||
|
3 |
Reactances |
In named units
|
|
|
In per-unit values relative to rated values |
|
Similarly, formulas have been obtained for reducing the parameters of scheme elements (reactances) in per-unit values, taking into account the difference in their rated parameters (Table 1.4).
Table I.4. Formulas for reducing the reactances of scheme elements for calculation in per-unit values
|
No. |
Element of the power supply system |
Given parameters |
Calculation formula |
|
1 |
System (source of constant voltage) |
Voltage Un behind reactancexc in named units |
|
|
2 |
Same |
Voltage Un and short-circuit currentIk in named units |
|
|
3 |
—//— |
Voltage Un and short-circuit powerSkin named units |
|
|
4 |
—//— |
Power Snand voltageUc in named units and reactancexc(n) in per-unit values |
|
|
5 |
Current-limiting reactor |
Voltage Un, currentIn in named units, reactancexr(n) in per-unit values |
|
|
6 |
Loads accounted for by an equivalent reactance |
Power Sn in named units |
|
When connecting synchronous generators, compensators and motors at voltage stage n with base voltageUbn = Unom or Ubn = Uavg.
; (1.7)
at stage 
, (1.8)
where 
- the direct-axis component of the reactance at the initial instant of short circuit.
For synchronous motors 
, where
–the starting-current multiple when starting at full voltage. For induction motors
.
When connecting three-phase two-winding transformers at voltage stage nwith base voltageUbn = Unom or
Ubt = Uavg
, (1.9)
at voltage stage 
. (1.10)
In the case of three-phase three-winding transformers or autotransformers
When connecting three-phase two-winding transformers with a split LV winding, with the LV1, LV2 windings operating separately
(1.12)
where Kspl- the splitting coefficient. WhenKspl= 3.5
(1.13)
In the case of parallel operation of the LV1 and LV2 windings, a transformer with a split winding can be regarded as two two-winding transformers.
+The active resistance of the transformer is determined through the active-loss power at short circuit ΔPSC
. (1.14)
[[b8446]]
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