Transformers phase voltage

Most power systems comprise several different three-phase voltage levels, e.g. 11,000 V, 6600 V and 440 V. They are isolated from one another by the use of transformers. Each isolated sub-section is invariably earthed or grounded at one or more points. (The term earthed will be used hereinafter.) The purpose of this is to ensure that the voltage difference between any condnctor and its casing cannot rise above a predetermined amount. The voltage difference can increase dne to several causes. 

The driving voltage is the phase voltage. The sonrce impedance Zs is fixed and is usually that of the upstream supply cables and transformers, or generators (or the output impedance of supplies such as a UPS). Zs can often but not always be neglected. The cable conductor impedance Z is easily calculated from the cable data for one phase conductor and its route length. Similarly the armouring impedance Z can be calculated from the data, which is predominantly resistive for most types of power cables. For typical cable data see the tables in Chapter 9. 

Electricity is taken from the National Grid by appropriately located substations which eventually transform the voltage down to 11 kV at a local substation. At the local substation the neutral conductor is formed for single-phase domestic supplies and three-phase supplies to shops, offices and garages. These supplies are usually underground radial supplies from the local substation, but in rural areas we still see transformers and overhead lines suspended on wooden poles. Figures 3.11 and 3.12 give an overview of the system from power-station to consumer. 

The phase voltage at the substation transformer will be a little higher than 230 V to allow for the inevitable voltage drop in the distribution cables. In urban areas, the line/neutral and the line/earth loop impedances will be comparable and will probably be only a small fraction of an ohm, whereas the victim s hand-to-hand impedance will be in the order of 2000 ohms. Under these circumstances the effects of the circuit impedances can be ignored. The victim s touch voltage will be about 230 V and, for a total body impedance of 2000 ohms, the shock current would be 230/2000 = 0.11 A. This is high enough to cause ventricular fibrillation in many people should the current flow for about 0.5 s. 

As is well known, all alternating current (AC) power systems are basically three-phase circuits. This fact makes voltage, current, and impedance a 3-D matrix form. A symmetrical component transformation (i.e., Fortescue and Clarke transformations) is well known to deal with three-phase voltages and currents. However, the transformation cannot diagonalize an n X n impedance/admittance matrix. In general, modal theory is necessary to deal with an untransposed transmission line. In this chapter, modal theory is explained. By adopting modal... 

Transforming these modal voltages to phase voltages by V = Av gives... 

This will generally be the nominal system voltage, except for transformers connected between a phase and the ground or between the neutral and the ground, when the primary voltage will be considered as / < limes the nominal systems voltage (Vd-... 

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. 

This is the difference in phase between the primary and the secondary voltage phasors (S). The direction of the phasors are so ehosen. that the angle is zero for i perfect transformation. Refer to Ihe phasor diagram. Figure 15.2. and Table 15.5 for measuring and Table 15.6 for protection VTs. 

When the primary of a three-phase two-winding transformer, having its secondary wound for a three-phase open delta, is connected across an unbalanced supply system, a residual voltage across the open delta will appear. This is the principle on which this transformer is based (Figure 15.4(a)). As discussed in Section 21.2.2, and illustrated in Figure 21.7, the phasor sum of all the three line to ground voltages in a three-phase balanced system is zero, i.e. 

When this balance is disturbed, due to either an unbalance in the loads or due to a ground fault, a residual or zero phase sequence voltage in the neutral circuit will appear. When one of the phases in the secondary of a three-phase transformer is open circuited and a three-phase supply is applied to its primary windings, there will appear... 

Nominal voltage ratio e.g. 6.6 kV/110 V for two phase or three phase transformers and -transformers 4 times this for line to neutral... 

Figure 18.13 A transformer as a capacitor voltage divider, drawn for one phase...

In single-phase bridge circuits for ac connections and for very low ac output voltages below 5 V, single-phase center tap circuits are used as rectifier circuits for CP transformer-rectifiers. They have an efficiency of 60 to 15% and a residual ripple of 48% with a frequency of 100 Hz. A three-phase bridge circuit for three-phase alternating current is more economical for outputs of about 2 kW. It has an efficiency of about 80 to 90% and a residual ripple of 4% with a frequency of 300 Hz. The residual ripple is not significant in the electrochemical effect of the protection current so that both circuits are equally valid. 

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