ELECTRICAL DIAGRAMS - PART – 03 - DIFFERENCE BETWEEN BLOCK AND LAYOUT DIAGRAM

BLOCK DIAGRAM - It is a functional drawing which shows and describes the main operating principles of the equipment or devices. It consists of principle functions or parts represented by blocks and is connected through lines that show the relationship between the blocks.

LAYOUT DIAGRAM - A drawing meant to show the physical arrangement of the wires and the components they connect is called layout design. 

ELECTRICAL DIAGRAMS PART – 02 - DIFFERENCE BETWEEN PICTORIAL AND SCHEMATIC DIAGRAM

ELECTRIC CIRCUIT – An electrical circuit is a path through which an electrical current flows. A closed circuit makes electrical current flow possible. An open circuit does not allow electrical current to flow.

An electric circuit made up of the basic elements resistance, inductance, and capacitance in a simple arrangement such that its performance would duplicate that of a more complicated circuit or network.

PICTORIAL CIRCUIT DIAGRAM - A pictorial circuit diagram uses simple images of components.

SCHEMATIC CIRCUIT DIAGRAM - A schematic circuit diagram is used to give a visual representation of an electrical circuit to an electrician.

ELECTRICAL DIAGRAMS PART – 01 - DIFFERENCE BETWEEN VECTOR AND PHASOR DIAGRAM

VECTOR - A quantity having direction as well as magnitude, especially as determining the position of one point in space relative to another.

VECTOR DIAGRAM - Vector diagram shows the direction and relative magnitude of a vector quantity by a vector arrow. Vector diagrams can be used to describe the velocity of a moving object during its motion. Vector diagrams can be used to represent any vector quantity. For example, acceleration, force, and momentum.

PHASOR - A phasor is a line whose direction represents the phase angle in electrical degrees and whose length represents, the magnitude and of the electrical quantity.

PHASOR DIAGRAM - The graphic representation of the phasors of sinusoidal quantities taken all at the same frequency and with proper phase relationships with respect to each other is called a phasor diagrams. The relative position of the phasors or phase difference which is important in a.c. calculations. 

UNSYMMETRICAL FAULT CALCULATIONS – PART – 32 – DOUBLE LINE TO GROUND AND LINE TO LINE FAULT - PROBLEM

A 33 kV bus bar has a three phase fault level of 1000 MVA. The negative and zero sequence source reactances are 2/3 and 1/3 of positive sequence reactance. The zero sequence resistance of the source is 50 ohms. A 30 MVA, 33 / 132 kV solidly grounded delta/star transformer having a reactance of 0.2 per unit. Is fed from 33 kV bus. Find fault current and fault MVA at 132 kV bus for the following faults. (a) Double line-to-ground fault and (b) Line to Line fault.

UNSYMMETRICAL FAULT CALCULATIONS – PART – 31 – THREE PHASE FAULT AND SINGLE LINE TO GROUND FAULT - PROBLEM

A 33 kV bus bar has a three-phase fault level of 1000 MVA. The negative and zero sequence source reactances are 2/3 and 1/3 of positive sequence reactance. The zero sequence resistance of the source is 50 ohms. A 30 MVA, 33 / 132 kV solidly grounded delta/star transformer having a reactance of 0.2 per unit. Is fed from 33 kV bus. Find fault current and fault MVA at 132 kV bus for the following faults. (a) Three phase fault and (b) Single line to ground fault.

UNSYMMETRICAL FAULT CALCULATIONS – PART – 30 – LINE-TO-LINE FAULT - PROBLEM

A 25 MVA, 11 kV, three-phase, 50Hz generator has Z1 = j0.25 p,u., Z2 = j0.35 p,u., Z0 = j0.1 p.u. and Zn = 0.3 ohms. If a line to line fault occurs on Y and B phases. Calculate the fault current and per phase voltages.

UNSYMMETRICAL FAULT CALCULATIONS – PART – 29 – LINE-TO-LINE FAULT (Zn & Zf)

UNSYMMETRICAL FAULT CALCULATIONS – PART – 29 – LINE-TO-LINE FAULT (Zn & Zf)

Consider a three-phase circuit diagram of an unloaded generator, the neutral is connected through impedance Zn and fault impedance is Zf. If a line-to-line fault between Y and B phases derive the fault current and per phase voltages.

UNSYMMETRICAL FAULT CALCULATIONS – PART – 28 – LINE-TO-LINE FAULT

Consider a three-phase circuit diagram of an unloaded generator, if a line-to-line fault between Y and B phases derive the fault current and per phase voltages.

UNSYMMETRICAL FAULT CALCULATIONS – PART – 27 – DOUBLE LINE-TO-GROUND FAULT - PROBLEM

Two generators A and B are of rating 50 MVA, 11kV, three-phase and 50 Hz are connected in parallel and supply a substation feeder.

Generator A and B positive, negative and zero sequence impedances are Z1= j0.6 ohms, Z2 = j0.4 ohms, Z0 = 0.2 ohms and neutral impedance Zn = j0.1 ohms.

Feeder positive, negative and zero sequence impedances are

Z1 = Z2 = (0.4 + j0.7) ohms, Z0 = (0.7 + j3.0) ohms.
If fault involves in Y and B phases, calculate the fault current.

UNSYMMETRICAL FAULT CALCULATIONS – PART – 26 – DOUBLE LINE-TO-GROUND FAULT - PROBLEM

A 25 MVA, 11 kV, 50 Hz and three-phase generator has Z1 = j0.25 p,u., Z2 = j0.35 p,u., Z0 = j0.1 p.u. and Zn = 0.3 ohms. If a double line to ground fault occurs on Y and B phases. Calculate the line current, fault current, line to neutral voltages and line to line voltages during the occurrence of fault conditions.

UNSYMMETRICAL FAULT CALCULATIONS – PART – 25 – DOUBLE LINE-TO-GROUND FAULT - PROBLEM

A 25 MVA, 11 kV, 50 Hz and three-phase generator has Z1 = j0.25 p,u., Z2 = j0.35 p,u. and Z0 = j0.1 p.u. If a double line to ground fault occurs on Y and B phases. Calculate the line current, fault current, line to neutral voltages and line to line voltages during the occurrence of fault conditions.

UNSYMMETRICAL FAULT CALCULATIONS – PART – 24 – DOUBLE LINE-TO-GROUND FAULT – PROBLEM

PROBLEM

A 25 MVA, 11 kV, 50 Hz and three-phase generator has Z1 = j0.2 p,u., Z2 = j0.2 p,u. and Z0 = j0.05 p.u. If a double line to ground fault occurs on Y and B phases. Calculate the line current, fault current and line to neutral voltages during the occurrence of fault conditions

UNSYMMETRICAL FAULT CALCULATIONS – PART – 23 – DOUBLE LINE-TO-GROUND FAULT (Zs & Zf)

An unloaded generator with a fault on phases Y and B through impedance Zf to ground. The neutral of the generator is grounded through an impedance. Assume the generator is initially under no load.

UNSYMMETRICAL FAULT CALCULATIONS – PART – 22 – DOUBLE LINE-TO-GROUND FAULT

Consider a double line-to-ground fault, calculate the fault current and phase voltages.

UNSYMMETRICAL FAULT CALCULATIONS - PART - 21 - SINGLE LINE TO GROUND FAULT - PROBLEM

PROBLEM

Two generators G1 and G2 are connected in parallel the rating of each generator is 25 MVA, 11kV, three-phase, 50 Hz generator has positive sequence reactance = X1 = 20%, negative sequence reactance = 10% and zero sequence reactance = 15%.

CASE – 01 – G1 is grounded through 5% reactance and G2 is ungrounded

CASE – 02 – G1 is grounded through 5% reactance G2 is grounded

CASE – 03 – G1 and G2 are grounded through 5% reactance

Calculate the fault current.

UNSYMMETRICAL FAULT CALCULATIONS - PART - 20 - SINGLE LINE TO GROUND FAULT - PROBLEM

PROBLEM

Two generators G1 and G2 are connected in parallel the rating of each generator is 25 MVA, 11kV, three-phase, 50 Hz generator has positive sequence reactance = X1 = 20%, negative sequence reactance = 10% and zero sequence reactance = 15%.

CASE – 01 – ungrounded neutral

CASE – 02 – grounded neutral

CASE – 03 – G1 is grounded and G2 is ungrounded. Calculate the fault current.

UNSYMMETRICAL FAULT CALCULATIONS – PART – 19 - SINGLE LINE TO GROUND FAULT – TWO PROBLEMS

PROBLEM – 01

A star point of a 3 kV, 3 MVA three phase synchronous generator is solidly grounded. It's positive, negative and zero sequence impedances are 2.4, 0.45 and 0.3 ohms. The generator operating unloaded sustains a resistive fault between the R phase and ground. This fault has a resistance of 1.2 ohms. Calculate the fault current and the voltage to ground of the R phase.

PROBLEM – 02

A three phase 30 MVA, 33 kV alternator having X1 = 0.18 pu and X2 = 0.12 pu and X0 = 0.10 pu, based on its rating, is connected to a 33 kV overhead line having X1 = 6.3 ohms and X2 = 6.3 ohms and X0 = 12.5 ohms per phase. A single line to ground fault occurs at the remote end of the line. The alternator neutral is solidly grounded. Calculate the fault current.

UNSYMMETRICAL FAULT CALCULATIONS – PART – 18 – SINGLE LINE TO GROUND FAULT – TWO PROBLEMS

PROBLEM – 01

A star connected alternator with earthed neutral. A single line to ground fault occurs near the generator terminal of phase R. The fault current is 300 A. Calculate the sequence currents in the other phases and also calculate the if a reactance of 0.3 ohms is connected to the neutral calculate the fault current.
PROBLEM – 02

A three phase 10 MVA, 13.2 kV generator with earthed neutral supplied a feeder. The sequence impedances of generator and feeder are mentioned below. If a single line to ground fault occurs at the far end of the feeder, calculate the fault current.

UNSYMMETRICAL FAULT CALCULATIONS – PART – 17 – SINGLE LINE TO GROUND FAULT – PROBLEM

PROBLEM

A three-phase generator rated 25 MVA, 13.2 kV has a solidly grounded neutral. It's positive, negative and zero sequence impedances are 30%, 40%, and 5% respectively. Resistances are negligible.

(i) What value of reactance must be placed in the generator neutral so that the fault current for a line to a ground fault of zero fault impedance shall not exceed the rated line current?

(ii) What value of resistance in the neutral will serve the same purpose?

UNSYMMETRICAL FAULT CALCULATIONS – PART – 16 – SINGLE LINE TO GROUND FAULT – PROBLEM

PROBLEM

Calculate the shunt fault current and also determine the fault current when Xn = j0.15 p.u, Xn = j0.3 p.u and Xn = j0.6 p.u and also compare the results.

UNSYMMETRICAL FAULT CALCULATIONS – PART – 15 – SINGLE LINE TO GROUND FAULT – PROBLEM

PROBLEM

A 25 MVA, 11 kV three-phase generator has a direct sub-transient reactance of 0.25 pu, negative sequence reactance on 0.35 pu and zero sequence reactance of 0.1 pu. The neutral is grounded solidly grounded. Determine the fault current and the line to line voltages for sub-transient conditions when the single line to ground fault occurs on phase R. The generator operating unloaded at rated voltage.

UNSYMMETRICAL FAULT CALCULATIONS – PART – 14 – SINGLE LINE TO GROUND FAULT – PROBLEM

PROBLEM

A 25 MVA, 11 kV synchronous generator has Z1= 0.2, Z2 = 0.2 and Z0 = 0.05 p.u. A single line to ground fault occurs on the phase R of the generator. Find the fault current and line to line voltages during the fault condition. Assume that the generator neutral is solidly grounded and the generator is operating at no load and at rated voltage at the occurrence of a fault.

UNSYMMETRICAL FAULT CALCULATIONS – PART – 13 – SINGLE LINE TO GROUND FAULT CURRENT USING MATRIX MANIPULATION

POSITIVE SEQUENCE IMPEDANCE (Z1)

The impedance offered by an equipment or circuit to positive sequence current is called positive sequence impedance.

NEGATIVE SEQUENCE IMPEDANCE (Z2)

The impedance offered by an equipment or circuit to negative sequence current is called negative sequence impedance.

ZERO SEQUENCE IMPEDANCE (Z0)

The impedance offered by an equipment or circuit to zero sequence current is called zero sequence impedance.

UNSYMMETRICAL FAULT CALCULATIONS – PART – 12 PART – 12 – SINGLE LINE TO GROUND FAULT

In a balanced three phase system negative and zero sequence currents are zero.

In a three phase, four wire system the magnitude sequence current is one-third of the current in the neutral.

The neutral is not earthed the zero sequence impedance is infinity, hence the fault current is zero.

The most common type of three phase fault is the single line to ground fault (70%).

ASSUMPTIONS

1. The impedance of the fault is zero.

2. Load currents are neglected.

3. The generated e.m.f. the system is of positive sequence only.

UNSYMMETRICAL FAULT CALCULATIONS – PART – 11

DELTA-CONNECTED WINDING

In delta connected winding no zero sequence currents flow in the lines because there is no return path for these currents.

STAR-CONNECTED WITHOUT NEUTRAL WINDING

In a three-phase, a three-wire system without a neutral network, the zero sequence line currents are zero.

STAR-CONNECTED WITH NEUTRAL GROUNDED

Three phase with neutral return zero sequence currents can flow both in the phase and windings as well as in the lines.

If the neutral is solidly grounded Zn = 0.

Total zero sequence impedance from point Ground to P is equal to the Total zero sequence impedance from Neutral to P.

The voltage to neutral or voltage to ground is the same in the case of positive and negative sequence systems.

For solidly grounded system zero sequence impedance is infinity.

UNSYMMETRICAL FAULT CALCULATIONS – PART – 10 – PROBLEM

PROBLEM

A star connected load consists of three equal resistance of 1 ohms. The load is assumed to be connected to an Unsymmetrical three-phase supply, the line voltages are 220V, 385V and 400 V. Find the symmetrical three-phase current in the R phase by the symmetrical component method.

UNSYMMETRICAL FAULT CALCULATIONS – PART – 09 – PROBLEMS

PROBLEM

An unbalanced three phase network of pure resistance draws currents of 10. 10 and 14.14 amperes respectively from the R, Y and B lines of a three phase balanced supply. Find the symmetrical components of the line currents, if the load is delta connected.

PROBLEM

Prove that (i) positive sequence of the line component is equal to [(a – 1) / a ] x positive sequence of the phase voltage.

Prove that (i) negative sequence of the line component is equal to [(a^2 – 1) / a^2 ] x positive sequence of the phase voltage.

UNSYMMETRICAL FAULT CALCULATIONS – PART – 08 – PROBLEMS

PROBLEM

The line currents in R, Y and B phases are given referred to the same reference vector. Find the symmetrical components of currents.

PROBLEM

The current in the neutral to ground connection is 18 A. Calculate the zero phase sequence components in the phases.

UNSYMMETRICAL FAULT CALCULATIONS – PART – 07 - PROBLEMS

PROBLEM

A delta connected balanced resistive load is connected across an unbalanced three-phase supply shown in the figure. Current in R and Y phases are specified. Determine the symmetrical components of the current.

PROBLEM

A delta connected load is supplied from a three-phase supply. The fuse in the blue is removed and the current in the other two lines are specified. Find the symmetrical components of currents.