The results obtained from the faults at the terminals of an unloaded synchronous generator can also be used in the analysis of faults in power systems.
Consider a short section of a transmission line in which phase is grounded. Only for theoretical purpose (for convenience of representation of fault currents), think of the fault as occurring on a short stub line, built out from the line at the fault point, as illustrated in Fig. 5.11. Let Ia Ib and Ic be currents in three phases of the stub line.
Assuming that the power system consists of linear elements, the whole system can be reduced to a single generator (Fig. 5.12) with an equivalent internal impedance by using Thevenin’s theorem. The emfs Ea1, Ea2, Ea0 are the symmetrical components of the open-circuit voltage to ground before the fault occurred.
In the usual case the pre-fault voltages are balanced and therefore, Ea1 = Ea; Ea2 = 0 and Ea0 = 0. The impedances Z1, Z2 and Z0 are the positive-, negative- and zero-sequence impedances, viewed from the fault point. For illustration of the application of Thevenin’s theorem for determining the equivalent sequence networks, consider a simple power system shown in Fig. 5.13.
On occurrence of fault, say at point F in Fig. 5.13, unbalanced conditions will be introduced.
For analysis following assumptions are made:
ADVERTISEMENTS:
1. The impedances are all constant and independent of currents.
2. The synchronous generator is a salient pole type which may generate under fault condition, negative- and zero-sequence emfs which are small and are negligible. Thus for all purposes the machine is assumed to generate only positive phase sequence emfs.
The network under such conditions can be represented by three independent single phase sequence networks as follows:
Sequence networks of the system are shown in Fig. 5.14. The point where a fault is assumed to occur is marked F on the single line diagram and on the sequence networks. Sequence networks are drawn. Each of the networks can be replaced by its Thevenin’s equivalent between the two terminals composed of its reference bus and the point of occurrence of the fault.
ADVERTISEMENTS:
The Thevenin’s equivalent circuit of each sequence network is given below the corresponding network in Fig. 5.14.
Thevenin’s equivalent of positive-sequence network is shown in Fig. 5.14 (d). The internal voltage Vf of the single generator of the equivalent circuit for the positive-sequence network is the pre-fault voltage to neutral at the fault point, Z1 is the impedance measured between fault point F and the reference bus of the positive-sequence network with all internal emfs short circuited.
Similarly, the Thevenin’s equivalent negative- and zero-sequence networks are obtained from the negative- and zero-sequence networks respectively. Since the system is balanced, no negative- or zero- sequence currents are flowing before the occurrence of the fault. So no emfs appear in the Thevenin’s equivalent circuit. The impedances Z2 and Z0 are measured between the fault point F and the reference bus in their respective networks.
ADVERTISEMENTS:
In the positive-sequence network, the currents throughout the system due to fault can be added to the load currents before the fault to obtain the total positive-sequence current during the fault. The net fault current is the fault current considering the system under no load condition plus the load current super-imposed over the fault currents.
Fault through an Impedance:
Sometimes the fault occurring may not be a dead short circuit between the line (or lines) and ground but may result in a fault impedance Zf to be introduced between them, as illustrated in Fig. 5.15.
In order to afford for the ground fault through impedance, 3 Zf is to be added in series with the zero-sequence of network.
ADVERTISEMENTS:
Procedure for Fault Calculation:
The procedure to be followed for computation of fault currents etc., is given below:
1. Draw sequence impedance diagrams by inspection of single line diagram of the power system. Zero-sequence impedance diagram is required to be drawn only if there is an earth fault also.
2. Set the values of sequence impedances in each network.
3. Reduce the networks into their equivalent impedances Z1, Z2 and Z0.
4. Connect the equivalent networks, as given in Table 5.1.
5. Obtain the sequence components of currents and voltages using equations given in Table 5.1.
6. Obtain the currents in different phases from sequence-components of currents using equations given in Table 5.1.
7. Voltage, if required, can be obtained from knowledge of impedances and sequence currents.
