SYMMETRICAL FAULT CALCULATIONS – PART – 04 – CALCULATION OF FAULT CURRENT & PROBLEM

PROBLEM
The reactance diagram of the system shown in the figure. If a balanced three phase fault occurs at bus 2 and bus 2, calculate the fault current and also find the post-fault voltages at bus 1, 2 and 3. All the bus voltage magnitudes are one and zero degrees.

SYMMETRICAL FAULT CALCULATIONS – PART – 03 – CALCULATION OF SHORT CIRCUIT kVA & ONE PROBLEM

PROBLEM

SYMMETRICAL FAULT CALCULATIONS – PART – 02 – CALCULATION OF SHORT CIRCUIT kVA & ONE PROBLEM

PROBLEM – 01
A three phase transmission line operating at 10 kV and having a resistance of 1 ohms and reactance of 4 ohms is connected to the generating station bus-bars through 5 MVA step-up transformer having a reactance of 5%. The bus bars are supplied by a 10 MVA alternator having 10% reactance. 
Calculate the short-circuit kVA fed to the symmetrical fault between phases if it occurs (i) at bus one (ii) at bus two (iii) at bus three.

SYMMETRICAL FAULT CALCULATIONS – PART – 01 – IMPORTANCE OF FAULT CALCULATIONS

AIM OF SHORT CIRCUIT STUDY

The aim of short circuit study is to determine fault current, bus voltages and line currents under the fault condition. It is also used to determine ratings of CB and Power transformers and other power systems equipment (CT and PT).

CLASSIFICATION OF FAULTS

1. Shunt fault (short circuits) – Shunt faults involve power conductor or conductors-to-ground or short circuit between conductors. Shunt faults are characterized by the increase in current and fall in voltage and frequency.

2. Series faults (open circuits) – When circuits are controlled by fuses or any device which does not open all three phases, one or two phases of the circuit may be opened while the other phases or phase is closed. Series faults are characterized by the increase in voltage and frequency and fall in current in the faulted phases.

CAUSES OF FAULTS

Lightning, heavy winds, trees falling across lines, vehicles colliding with towers or poles, line breaks, failure of insulation etc. are the causes of faults.

ILL EFFECTS OF SHORT-CIRCUIT FAULTS

Most of the faults on the power systems lead to a short-circuit condition. When such a conditions occur, a heavy current flows through the equipment, causing considerable damage to the equipment and interruptions of service to the consumers.

IMPORTANCE OF STUDYING FAULT CALCULATIONS

Fault calculations involve finding the voltage and current distribution throughout the system during the fault condition so that the protective devices may be set to detect the fault and isolate the faulty portion of the system so as to minimize the harmful effects of such contingencies.

SYMMETRICAL FAULT

The fault on the power system which gives rise to symmetrical currents (i.e. equal fault current in the lines with 1200 displacement) is called a symmetrical fault.

UNSYMMETRICAL FAULTS

Those faults on the power system which give rise to symmetrical currents (i.e. unequal fault currents in the lines with unequal displacement) are known as unsymmetrical faults. 

Generally, the fault currents are much larger than load current and, therefore, the load currents can be neglected during fault calculation.

ASSUMPTIONS ARE MADE IN FAULT CALCULATIONS

1. The emf of all the generators is assumed to be 1 per unit

2. Shunt elements in the transformer model that account for magnetizing current and core loss is neglected.

3. Shunt capacitances of the transmission lines are neglected.

4. System resistance is neglected only inductive reactance of the system is taken into account.

THEOREM USED IN FAULT CALCULATIONS

The fault calculation of the fault current can be very easily calculated by applying Thevenin’s theorem. It is only necessary to find the open circuit emf and network impedance as seen from the fault point. In most of the calculations, the open circuit emf can be assumed to be 1pu.

STEPS INVOLVING IN FAULT CALCULATIONS

1. Draw a single line diagram of the system

2. Select a common base and find out the per unit reactance of all generators, transformers, lines etc., as referred to the common base.

3. Indicate all the reactance values in the reactance diagram.

4. Find the reactance of the system as seen from the fault point.

5. Find the fault current and fault MVA in per unit values.

6. Convert the per unit values into actual values.

7. Retrace the steps in the calculation to find the current and voltage distribution throughout the network.

BUS IMPEDANCE MATRIX – PART – 10 - MUTUALLY COUPLED BRANCHES IN Z-BUS AND ONE PROBLEM

Transmission lines have the mutual coupling with other transmission lines. It is necessary to incorporate mutually coupled branches in Z-bus.

PROBLEM – For the system shown in the figure, form bus impedance matrix.

BUS IMPEDANCE MATRIX – PART – 09 - MUTUALLY COUPLED BRANCHES IN Z-BUS AND ONE PROBLEM

Transmission lines have the mutual coupling with other transmission lines. It is necessary to incorporate mutually coupled branches in Z-bus.

PROBLEM - 01 - For the system shown in the figure, form bus impedance matrix.

BUS IMPEDANCE MATRIX - PART – 08 - FORMULATION OF Z-BUS AND ONE PROBLEM

For the system shown in the figure, form bus impedance matrix.

BUS IMPEDANCE MATRIX - PART – 07 - FORMULATION OF Z-BUS AND ONE PROBLEM

For the system shown in the figure, form bus impedance matrix.

BUS IMPEDANCE MATRIX - PART – 06 –FORMATION OF Z-BUS MATRIX AND ONE PROBLEM

For the system shown in the figure. Form bus impedance matrix.

BUS IMPEDANCE MATRIX - PART – 05 - FORMATION OF Z-BUS MATRIX AND ONE PROBLEM

PROBLEM - 01

For the system shown in the figure, form bus impedance matrix.

BUS IMPEDANCE MATRIX - PART – 04 - Z-BUS FORMATION AND ONE PROBLEM

PROBLEM - 01

For the system shown in the figure, form bus impedance matrix.

BUS IMPEDANCE MATRIX - PART – 03 - TYPE FOUR MODIFICATION AND ONE PROBLEM

PROBLEM - 01
For the system shown in the figure, form bus impedance matrix.

BUS IMPEDANCE MATRIX - PART – 02 - ALGORITHM FOR FORMULATION OF Z-BUS AND ONE PROBLEM

PROPERTIES OF BUS IMPEDANCE MATRIX

1. Bus impedance matrix is symmetric when bus admittance matrix is symmetric.

2. Bus impedance matrix is a full matrix.

3. in bus admittance some of the elements are zero but in bus impedance matrix zero elements of bus admittance matrix becomes non-zero elements.

Bus impedance can be found in two ways:

1. Inverse of bus admittance matrix

2. Directly found from the reactance diagram.

ALGORITHM FOR FORMULATION BUS IMPEDANCE MATRIX

Type - 01 - Adding Zs from a new bus to the reference bus.

Type - 02 - Adding Zs from new bus to the reference bus.

Type - 03 - Adding Zs from new bus to the old bus.

Type - 04 - Adding Zs between two old buses.

PROBLEM - 01

The figure shows a three bus system. Assuming bus 1 to be the reference bus fine [Zbus]

BUS IMPEDANCE MATRIX - PART – 01 – DRIVING POINT IMPEDANCE AND TRANSFER IMPEDANCE AND ONE PROBLEM

BUS IMPEDANCE MATRIX IS VERY USEFUL FOR FAULT ANALYSIS

DRIVING POINT IMPEDANCE

The input or driving point impedance of an active network is defined as the impedance presented by the network to the specified terminals when all internal sources are shorted but their internal impedances retained.

TRANSFER IMPEDANCE

The ratio of the driving voltage in one mesh of a network to the resulting current in another mesh, all other sources being set to zero.

BUS ADMITTANCE MATRIX - PART – 20 – ONE PROBLEM - PHASE SHIFTING TRANSFORMER

PROBLEM
Formulate Y-bus matrix for the system shown in the figure. The phase shifting is connected between the bus 1 and 2.

BUS ADMITTANCE MATRIX - PART – 19 - MODELLING OF PHASE SHIFTING TRANSFORMER

The Phase shifting transformer is commonly used to control real power flow in the multiline power network.

Phase shifting transformer has a complex turns ratio having magnitude and phase angle.

The phase angle depends on the position of tap position of the transformer.

BUS ADMITTANCE MATRIX - PART – 18 - EQUIVALENT CIRCUIT MODEL OF SINGLE PHASE UNIT - DELTA-DELTA TRANSFORMER

The equivalent circuit model of the single phase unit can be derived by connecting a Delta-Delta transformer as comprising a Delta-Star transformer connected in series (Back to Back) via a zero impedance link to a Star-Delta transformer.

BUS ADMITTANCE MATRIX - PART – 17 - ONE PROBLEM - INCLUSION OF OFF-NOMINAL TAP SETTING TRANSFORMER IN A LINE

PROBLEM ONE

Formulate Y-Bus matrix for a network shown in fig. The line series admittance of the lines and line charging admittance are mentioned in the figure. An off-nominal tap setting transformer is connected between the lines 1-3 and its ratio is 1.05:1.