Symmetrical Three-phase Fault o6b3w

Symmetrical Three-Phase Fault

Prepared by: Christian A. Cagayan

Course Outline: • • • • • • • •

Introduction to Power System Analysis Common Power System Studies Types of Fault Purpose of Short Circuit Calculation Short Circuit Contributors Characteristic of Short Circuit Current Short Circuit Calculation Times Symmetrical Fault Calculation

Introduction to Power System Analysis • It is the study of the behavior, reliability and stability of the electrical network or system, during different operating and loading conditions (i.e. Normal, Contingency, Steady-State and Transient). • It is used to the Power System design practicality and workability; the sizing of the major electrical equipment. • Power System Analysis is considered as the widest and most complicated study in the field of Electrical Engineering.

Common Power System Studies 1. 2. 3. 4. 5. 6. 7. 8.

Load Flow Analysis Short Circuit Study Motor Acceleration Cable Sizing Calculation Relay Coordination Harmonic Study Arc Flash Calculation Grounding Grid Calculation (Touch & Step Potential) 9. Temperature Rise Analysis etc.

Types of Fault • Shunt fault – unintentional connection between phases or between phase and ground. 1. 2. 3. 4.

Three Phase Fault Line to Ground Fault (L-G) Line to Line Fault (L-L) Double Line to Ground Fault (L-L-G)

Symmetrical fault Unsymmetrical fault

• Series fault – open circuits which may be caused by broken conductors.

Shunt fault

Symmetrical fault (Three-Phase fault) • The symmetrical fault occurs when all the three conductors of a 3-phase line are brought together simultaneously into a short circuit condition as shown in Fig. 13-4 (a) Schematic diagram (b) positive sequence network. • This type of fault gives rise to symmetrical currents i.e. equal fault currents with 120 deg. displacement. • This type of fault occurs infrequently in practices as majority of the faults are unsymmetrical nature.

Symmetrical fault

Basic Assumptions • An important assumption is that the fault is “bolted”, that is, it has zero impedance. • This assumption simplifies calculation, since the resulting calculated values are a maximum and equipment selected on this basis will always have an adequate rating. • Symmetrical fault (3-phase fault) results in the maximum short circuit current available in the system. In most systems the 3-phase fault is frequently the only one calculated.

Basic Assumptions • Bolted line to line (L-L) currents are about 87% of the 3-phase value. • Bolted line to ground (L-G) currents can range from about 25-125% of the 3-phase value, depending on system parameters. However, L-G currents more than 100% of the 3-phase value rarely occur in industrial and commercial system.

Unsymmetrical fault - On the occurrence of an unsymmetrical fault, the currents in the three lines become unequal and so is the phase displacement among them. - However, the system impedances and the source voltages are always symmetrical through its main elements such as generators, transmission lines, synchronous reactors etc. - There are three ways in which unsymmetrical faults may occur in a power system (see Fig. 135, Fig. 13-6 and Fig. 13-7).

Line to Ground fault through a fault impedance

Double-Line to Ground fault

Double-Line fault

Purpose of Short Circuit Calculation 1. Determine the duty rating of protective devices and bus bracing capability. 2. Determine the proper size of cables. 3. Determine the settings of relays. 4. Properly coordinate the protective devices. 5. Determine whether the short-circuit MVA is sufficient to start large motors without excessive voltage dip. 6. Study the effect of power system harmonics. 7. Arc Flash Study.

Short Circuit Contributors 1. 2. 3. 4.

Utility Generator Synchronous Motor Induction Motor

Short Circuit Contributors UTILITY

SYNCHRONOUS MOTOR

GENERATOR

INDUCTION MOTOR

Characteristic of Short Circuit Current

Characteristic of Short Circuit Current

Characteristic of Short Circuit Current

Characteristic of Short Circuit Current

Short Circuit Calculation Times 1.) First Cycle a. RMS Symmetrical – used in sizing the Short Circuit Rating of Low Voltage MCCB, and Switch-Fuse combination. b. Asymmetrical – used in sizing the Short Circuit Rating of MV Switch-Fuse combination, and Close and Latch rating of MV Power Circuit Breaker (Asymmetrical = 1.6 RMS Symmetrical; Peak = 2.6 RMS Symmetrical). Contributions: Consider Subtransient Impedances from all sources.

Short Circuit Calculation Times 2.) 1.5 to 4 Cycles – used in sizing the Interrupting Rating of MV Power Circuit Breakers. Contributions: a. Induction motors – NEGLECT b. Synchronous motors - X’d c. Generators – X”d d. Utility – X”d 3.) 30 Cycles – used in estimating the performance of Time Delay Relays and Fuses. Contributions: a. Utility – X”d b. All others - NEGLECT

Symmetrical Fault Calculation Short Circuit Calculation by: 1.) Thevenin Equivalent 2.) Network Reduction 3.) Bus ittance Matrix Steps for Fault Calculation: 1. Draw a single line diagram. 2. Choose base kVA and convert all percentage reactances (per unit) to this base value. 3. Draw reactance diagram showing one phase of the system and the neutral. Indicate the reactances in per unit. The transformer in the system should be represented by a reactance in series.

Symmetrical Fault Calculation Steps for Symmetrical Fault Calculation: 4. Find the total per unit reactance of the network up to the point of fault. 5. Find the full load current corresponding to the selected base kVA and the normal system voltage at the fault point. Short Circuit Formulas: 𝑨𝒄𝒕𝒖𝒂𝒍 𝑷𝒆𝒓 𝑼𝒏𝒊𝒕 =

𝑴𝑽𝑨𝒇 = 𝟑 𝑽𝑳𝑳 𝑰𝒇

𝑴𝑽𝑨𝒃 𝑴𝑽𝑨𝒇 = 𝒁𝒑𝒖 𝑽𝑳𝑳 𝟐 𝑴𝑽𝑨𝒇 = 𝒁𝑻𝑯

𝒁𝒏𝒆𝒘 = 𝒁𝒐𝒍𝒅

𝑩𝒂𝒔𝒆

𝑴𝑽𝑨𝒏𝒆𝒘 𝑴𝑽𝑨𝒐𝒍𝒅

𝒌𝑽𝒐𝒍𝒅 𝒌𝑽𝒏𝒆𝒘

𝑰𝒇(𝒂𝒄𝒕𝒖𝒂𝒍) = 𝑰𝒇(𝒑𝒖) 𝑰𝒃𝒂𝒔𝒆 𝑰𝒃𝒂𝒔𝒆 =

𝑴𝑽𝑨𝒃𝒂𝒔𝒆 𝟑 𝒌𝑽𝑳𝑳

𝟐

Three Phase Fault

Three Phase Fault

Three Phase Fault 𝑉𝑇𝐻 𝐼𝑎1 = = 𝐼𝑓(𝑝𝑢) 𝑍1 + 𝑍𝑓 𝐼𝑎 = 𝐼𝑎1 𝐼𝑎2 = 𝐼𝑎0 = 0 𝐼𝑎 = 𝐼𝑏 = 𝐼𝑐 𝑰𝒇(𝒂𝒄𝒕𝒖𝒂𝒍) = 𝑰𝒇(𝒑𝒖) 𝑰𝒃𝒂𝒔𝒆 • On a balanced three phase system, the same magnitude of fault currents will flow in each phase of the network if a three phase fault occurs. • Since faults currents are balanced, the faulted system can, therefore, be analyzed using the single phase representation.

Sample Problem 1

Sample Problem 2

Thevenin Equivalent • Thevenin’s Theorem states that, with respect to a given pair of terminals, any electric circuit can be represented by a single voltage source in series with a single impedance.

Thevenin Equivalent Fault MVA: • The short circuit current at any point in the power system is generally expressed in of a fault MVA. By definition,

Sample Problem 3

Sample Problem 4

Network Reduction 1.) Draw the Single Line Diagram. 2.) Draw the Impedance Diagram. 3.) Convert all parameters to per-unit. 4.) Reduce the network between the source(s) and the fault location. 5.) Calculate the fault current.

Sample Problem 5

Solution to Problem 5

Solution to Problem 5

Solution to Problem 5

Solution to Problem 5

Solution to Problem 5

Solution to Problem 5

Solution to Problem 5

Solution to Problem 5

Bus ittance Matrix

Bus ittance Matrix

NOTE: 𝑌𝑖𝑗 =

1 𝑍𝑖𝑗

=

1 𝑅𝑖𝑗 +𝑗𝑋𝑖𝑗

Bus ittance Matrix

Bus ittance Matrix

Bus ittance Matrix

Elements of 𝑌𝑏𝑢𝑠

Systematic Fault Analysis Using Bus Impedance Matrix

Systematic Fault Analysis Using Bus Impedance Matrix

Systematic Fault Analysis Using Bus Impedance Matrix

Sample Problem 6 • Fault at bus 1 and 2 in Fig. 7.3 are of interest. The pre-fault voltage is 1.05 per unit and pre-fault load current is neglected. • (a) Determine the 2 x 2 positive-sequence bus impedance matrix. • (b) For a bolted three-phase short circuit at bus 1, use 𝑍𝑏𝑢𝑠 to calculate the subtransient fault current and the contribution to the fault current from the transmission line. • (c) Repeat part (b) for a bolted three-phase short circuit at bus 2.