Leakage reactances

The accuracy of a VT depends upon its leakage reactance and the winding resistance. It determines the voltage and the phase errors of a transformer and varies with the VA on the secondary side. With the use of better core material (for permeability) (Section 1.9) and better heat dissipation, one can limit the excitation cunent and reduce the error. A better core lamination can reduce the core size and improve heat dissipation. 

For ease of calculation, let us consider the impedance of the transformer as its leakage reactance, ignoring resistance and draw an equivalent circuit diagram as in Figures 24.25 (b) and (c) Assuming the length of the primary distribution line to be 15 km, the total line parameters will become... 

T) Leakage reactance of transmitter-end transformer. Resistance of overhead lines of section B-B. 

X, = Stator leakage reactance per phase at rated current. 

Example Figure 4.17 shows a 2000-kVA, 13.8-kV to 480/277-V transformer with a leakage reactance of 6.0% feeding a bus containing two 500-hp adjustable speed drives. A 750-kVAR Y-connected capacitor bank is installed on the 480-V bus for power factor correction. Perform an analysis to determine the conditions for resonance (consult Figure 4.18 for the transformer and capacitor connections and their respective voltages and currents) ... 

When the rotor pole axis coincides with the axis of the stator coils the magnetic circuit seen by the stator has minimum reluctance. The reactance corresponding to the armature reaction in this rotor position is called the direct axis synchronous reactance Xs/- If the stator winding leakage reactance, Xa, is deducted from Xgd the resulting reactance is called the direct axis reactance X/. 

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

A low armature leakage reactance Xa requires the number of stator slots per phase to be kept small, and a high utilisation of conductors per slot. Double layer slots are most often used for high voltage machines. 

The armature leakage reactance is very much dependent upon the stator slot dimensions. It can be shown that ... 

The field leakage reactance is dependent on the shape of the pole yoke. 

In practice Ri is much smaller than Xn and so the maximum torque is very dependent upon the value of the leakage reactances, especially the rotor leakage reactance X2. The maximum torque is also called the breakdown torque. 

Currents now exist in both windings. Therefore a volt-drop must exist in each winding due to its leakage reactance (due to leakage flux) and its conductor resistance. The equivalent circuit of a single-phase transformer can be represented as in Figure 6.2. 

Figure 6.3 Leakage reactance in percent versus the MVA rating 50 Hz transformers.

Assume the leakage reactance Xfg of each generator unit transformer to be 0.08 per unit, and ignore the resistance. 

All but the smaller ratings of inverters used in the oil industry require a sinusoidal ouqtut waveform. The quality of the waveform is typically defiued as, being that no greater than 5% total harmonic distortion should be present. In order to achieve a sinusoidal output it is uecessary to include a filter iu the output circuit. The output of the inverter usually has a double wouud transformer so that the required line voltage is obtained. The filter is placed on the load side of the transformer, its leakage reactance of the transformer contributes to the filteriug process. 

Mutual reactance between windings in the d-axis. Mutual reactance between windings in the g-axis. Leakage reactance of a stator winding. 

By referring to Chapter VI of Reference 3 sub-section 25, in particular, the algebraic substitutions and a sequence of approximations can be studied, from which the following results are most frequently used. In sub-section 20.2c herein the symbols for the leakage reactances are usually quoted slightly differently, Xia, Xnai, X q and Xi become Xg, X d, X q and Xf respectively. It should be remembered that these are leakage reactances, wherein the suffix 1 emphasises the fact. 

Zero phase sequence reactance Xg has a value lower than X and is a complex function of the slot pitching of the stator windings and the leakage reactance present in their end windings, see Reference 7, Chapter XII. 

X2 = Xl2 — Xm is the rotor leakage reactance, not to be confnsed with the negative seqnence reactance. 

Some motor designers apply the reactive change to the sum of the stator and rotor leakage reactances -... 

Another popular rectifier circuit is the full-controlled three-phase full wave rectifier. This circuit is more expensive because six thyristors are used. However, the form factor is much better, about 1.01, and the ripple current is 360 Hz. The higher frequency makes it easier to filter the ripple current. The half-controlled three-phase bridge rectifier circuit may require armature current smoothing reactors to reduce the ripple current. Another problem associated with the non-uniform DC input to the motor is the commutation. The motor must commutate under a relatively high degree of leakage reactance. 

The winding resistance is assumed to be 1% of the leakage reactance, that is, the resistive component is almost neglected in this simulation. The resistance referred to the high-voltage side is... 

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