Reactance Transient

Cuncnt imiisieiits A similar situation will arise wheti a switching ON operation of the rectifier unit occurs hen it is a thyristor rectifier. Under load conditions, the stored magnetic energy in the incoming supply system, which can be the feeding transformer and the line reactances similar to a fault condition discussed earlier, may cause a current transient which can be expressed by... 

Since the interrupter will take at least three or four cycles to operate from the instant of fault initiation, it is this transient reactance that is more relevant for the purpose of short-circuit calculations. 

When the rotor poles are coincident with the stator coils axis the armature reaction is a maximum and the reactance is called the direct axis transient reactance X . 

The situation is different when the rotor poles are at right angles to the stator coils. There is no induction in the fleld circuit and the reluctance is high, being almost the same as for the steady state condition. In this situation the corresponding quadrature axis transient reactance X approximately equals the reactance Xq. Cylindrical rotors of two-pole high speed generators have a nearly uniform rotor diameter and almost constant air gap all around the periphery. Hence the reactance X is almost equal to X. ... 

During this transient condition, or more appropriately called a sub-transient condition, the additional flux is forced to occupy a region consisting of air and the surface of the rotor poles. This is a high reluctance condition which gives rise to reactances of low values. 

By the same reasoning as for the transient reactances so the sub-transient reactances are derived, and are called the direct axis sub-transient reactance X and the quadrature axis subtransient reactance X" . 

Figure 3.2 D-axis transient reactance versus field leakage reactance.

The damper bars or winding act in a manner very similar to an induction motor and provide a breaking torque against the transient disturbances in shaft speed. To be effective the damper needs to have a steep torque versus shp characteristic in the region near synchronous speed. The equivalent impedance of the damper requires a low resistance and a high reactance. High conductivity copper bars are embedded into the pole face to provide a low reluctance path for the leakage flux. 

Figure 3.9 D-axis sub-transient reactance versus generator MVA rating.

Constraint i) will need the sub-transient reactances of the generators to be higher than for a standard design. It may also require the starting impedance of the motors to be higher than normal in order to reduce their sub-transient currents. 

Constraint ii) requires the transient reactances of the generator to be kept as small as practically possible. At the same time the starting current of the motors should be kept as low as possible, without unduly increasing their run-up time. 

These two constraints counteract in the design of the generator, because the physical dimensions of items such as rotor and stator conductor slots affect the sub-transient and transient reactances differently. In general fixing one of these reactances will limit the choice available for the other. 

Tables 5.1-5.4 show the approximate resistance and reactance values in per-unit for two-pole and four-pole low voltage induction motors that are generally of the Design D type. Tables 5.5-5.8 show the approximate resistance and reactance values in per-unit for two-pole and four-pole high voltage induction motors that are of the reduced starting current type. In the absence of exact data from a manufacturer these data can be used for system studies such as starting motors, transient stability and fault current contribution. The data from a manufacturer should be used for calculations and system studies that are to be carried out during the detailed design phase of a project.

Equation (7.2) can be used to calculate the situation at the time given for the breaking duty. Usually the sub-transient time decay term has fallen to zero, and the solution is in the transient period. When an external impedance is present its resistance can be included in the Ta time constant and its reactance added to the appropriate machine reactances. References 5 and 6 explain how the derived reactances and time constants are calculated and affected by the addition of the external impedance. 

Figure 7.2 Functions pertaining to the calcnlation of the critical switching time of circuit breaker that disconnects a generator from a switchboard. The generator has low values of sub-transient and transient reactances. The sensitivity of the time constant Ta is shown.

The peak value of the fault current dnring the first cycle of instantaneons cnrrent. This valne determines the peak asymmetrical dnty of the switchgear connected to the generator. This valne is determined by the sub-transient reactance. 

Since the peak value of the fault current reduces in time due to the effects of the sub-transient and transient reactances, it is necessary to establish a driving voltage suitable for each part of the process and calculation. The concept used is one which assigns an emf behind an appropriate impedance of, in the case of generators, an appropriate reactance. 

E" denotes the sub-transient emf behind the sub-transient reactance X. Used to calculate the... 

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