PHASE TO PHASE SHORT CIRCUIT BASIC INFORMATION

Phase to phase short circuit is also known as line to line fault.

Faults involving abnormal conduction from one phase to another without involving ground may be represented using the interconnection of Figure below.

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Sequence interconnections for a phase-to-phase fault not involving ground

The zero-sequence network is not involved and may be ignored. As for the three-phase condition, Zf would normally be the fault impedance, but it could also be a phase-to-phase load impedance if the problem of interest is the response of the system to a phase-to-phase-connected single-phase load.

An interesting and often useful relationship develops from Figure.

In the special case of a zero-impedance phase-to-phase fault, if the negative-sequence impedance of nearby synchronous machines is approximately equal to the positive-sequence impedances of such machines or if no synchronous generators are nearby at all, then the phase-to-phase fault current will be 0.87 times the corresponding three-phase fault current.

This relationship can be proven by calculating sequence currents in Figure for the specified condition and then converting them to phase currents using symmetrical components equation.

HIGH VOLTAGE AC POWER CIRCUIT BREAKER SHORT CIRCUIT RATING

The short-circuit rating of a circuit breaker is established by the symmetrical component of short-circuit current in rms amperes, designated rated short-circuit current, to which all required short-circuit capabilities are related. All values apply to both grounded and ungrounded short circuits on predominantly inductive or resistive 3-phase circuits with a normal frequency phase-to-phase recovery voltage equal to the operating voltage.

Figure 1— Relation of Symmetrical Interrupting Capability, Closing Capability, Latching Capability,

and Carrying Capability to Rated Short-Circuit Current

Rated Short-Circuit Current.
The rated short-circuit current of a circuit breaker is the highest value of the symmetrical component of the polyphase or phase-to-phase short-circuit current in rms amperes measured from the envelope of the current wave at the instant of primary arcing contact separation which the circuit breaker shall be required to interrupt at rated maximum voltage and on the standard operating duty.

It also establishes, by fixed ratios, the highest currents which the breaker shall be required to close and latch against, to carry, and to interrupt. For numerical values of rated shortcircuit current, refer to the tables of preferred ratings in ANSI C37.06-1979.

The relationship of rated short-circuit current to the other required capabilities is illustrated graphically in Figs 1 and 2.

Figure 2— Ratio of Circuit Breaker Asymmetrical to Symmetrical Interrupting Capabilities

Related Required Capabilities.
The circuit breaker shall have the following related required capabilities which are based on a relay time of one-half cycle, but may be used with any permissible tripping delay.


Required Symmetrical Interrupting Capability for Polyphase and Phase-to-Phase Faults.
For polyphase and phase-to-phase faults, the required symmetrical interrupting capability of a circuit breaker is the highest value of the symmetrical component of the short-circuit current in rms amperes at the instant of primary arcing contact separation which the circuit breaker shall be required to interrupt at a specified operating voltage on the standard operating duty and irrespective of the direct current component of the total short-circuit current.

The numerical value at an operating voltage between 1/K times rated maximum voltage and rated maximum voltage shall be determined by the following formula: In no case shall the required symmetrical interrupting capability exceed K times short-circuit current.


The numerical value shall be equal to the product of a ratio S, specified below and illustrated in Fig 2, times the required symmetrical interrupting capability of the breaker determined for the operating voltage. The values of S shall be 1.4, 1.3, 1.2, 1.1, or 1.0 for breakers having primary arcing contact parting times of 1, 1.5, 2, 3, 4, or more cycles, respectively.

The values of S for primary arcing contact parting times between those given above shall be determined by linear interpolation. The primary arcing contact parting time shall be considered equal to the sum of one-half cycle (present practical minimum tripping delay) plus the lesser of:

1) The actual opening time of the particular breaker, or
2) 1.0, 1.5, 2.5, or 3.5 cycles for breakers having a rated interrupting time of 2, 3, 5, or 8 cycles, respectively.

NOTE — Any combination of symmetrical and direct current components is permissible, provided that the following conditions are met at the instant of primary arcing contact separation:

1) The symmetrical component does not exceed the required symmetrical interrupting capability
2) The degree of asymmetry does not exceed 100 percent
3) The total short-circuit current does not exceed the required asymmetrical interrupting capability

Required Interrupting Capability for Single Line-to-Ground Faults.
For single line-to-ground faults, the required symmetrical interrupting capability and the required asymmetrical interrupting capability of a circuit breaker shall be 1.15 times the corresponding values for polyphase and phase-to-phase faults. In no case are the capabilities for single line-to-ground faults required to exceed K times the symmetrical interrupting capability (that is, K times rated short-circuit current) and K times asymmetrical interrupting capability, respectively, determined at rated maximum voltage.

Required Closing-Latching-Carrying-Interrupting Capabilities.
The circuit breaker shall be capable of performing the following duties in immediate succession:

1) Closing and, immediately thereafter, latching any normal-frequency making current which does not exceed 1.6K times the rated short-circuit or whose maximum crest (peak making current) does not exceed 2.7K times the rated short-circuit current.

2) Carrying a short-circuit current I for any time up to the permissible tripping delay determined in accordance with 5.8.

3) Interrupting any short-circuit current which, at the instant of primary arcing contact separation, has a symmetrical value not exceeding the required asymmetrical interrupting capability.

SYMMETRICAL COMPONENTS TUTORIALS FOR PROTECTIVE RELAYING

Symmetrical components are applied to calculations of unbalanced fault currents and voltages and in rotating machine analysis. Theory of symmetrical components can be briefly stated thus: a coplanar vector is defined by the position of its terminal and length and has 2 degrees of freedom.

A three-phase balanced system has 2 degrees of freedom because the current or voltage vectors (phasors) are displaced from each other by equal angles of separation of 120◦ and are of equal length. A three-phase unbalanced system of currents or voltages has 6 degrees of freedom because the vectors are of varying length at varying displacement angles from each other.

Such an unbalanced system can be resolved into three symmetrical systems, each system having three vectors with 2 degrees of freedom. Positive-sequence system is a set of balanced three-phase components of the same phase sequence as the original unbalanced set.

Negative-sequence system is a set of three-phase components of opposite phase sequence to the positive sequence system but vectors (phasors) of the same magnitude. Zero-sequence system consists of three single-phase components of the same magnitude and cophasial.

These are related by the following equations:

 

and

 

Where Va, Vb, and Vc are the original unbalanced voltages; a is a unit vector operator that rotates 120◦ in the counterclockwise direction; and V+a, V −a, and V0a are the positive, negative, and zero sequence components of the original unbalanced set.

Characteristics of Sequence Components

In a three-phase wye connected and ungrounded system, no zero sequence current flows. If the wye point is grounded, neutral carries the out-of-balance current. In a delta connection, no zero sequence currents can appear in the line currents.

In a balanced three-phase system with balanced loads, only positive sequence currents can flow. Negative sequence currents are set up in circuits of unbalanced impedances and voltages.

In symmetrical circuits, currents and voltages of different sequence do not affect each other (i.e., the positive sequence currents produce only positive sequence voltage drops and the theorem of superposition applies). Sequence impedance networks must be constructed for unbalanced fault current calculations and data input to digital computers.

As an example, the single-line-to-ground fault is given by the expression:

 

 

Where Ig is the single-line-to-ground fault current; E is the line-to-neutral voltage; and Z+, Z−, and Z0 are the positive, negative, and zero sequence impedances to the fault point.

THE NATURE OF SHORT CIRCUIT CURRENTS – PROTECTIVE RELAYING CONSIDERATION

Under normal system conditions, the equivalent circuit of Figure 2-1 may be used to calculate load currents. Three impedances determine the flow of current.

Zs and Zc are the impedances of the source and circuit, respectively, while Zl is the impedance of the load. The load impedance is generally the largest of the three, and it is the principle determinant of the current magnitude.

Load impedance is also predominantly resistive, with the result that load current tends to be nearly in phase with the driving voltage. A short circuit may be thought of as a conductor that shorts some of the impedances in the network while leaving others unchanged.

This situation is depicted in Figure 2-2. Because Zs and Zc become the only impedances that restrict the flow of current, the following observations may be made:

a) The short-circuit current is greater than load current.

b) Because Zs and Zc are predominately inductive, the short-circuit current lags the driving voltage by an angle approaching the theoretical maximum of 90°. 

 

The change in state from load current to short-circuit current occurs rapidly. Fundamental physics demonstrate that the magnitude of current in an inductor cannot change instantaneously. This conflict can be resolved by considering the short-circuit current to consist of two components:

— A symmetrical ac current with the higher magnitude of the short-circuit current

— An offsetting dc transient with an initial magnitude that is equal to the initial value of the ac current, but which decays rapidly

The initial magnitude of the dc transient is directly controlled by the point on the voltage wave at which the short circuit occurs. If the short circuit occurs at the natural zero crossing of the driving voltage sinusoid, the transient is maximized.

However, the transient is a minimum if the fault occurs at the crest of the voltage sinusoid. At any subsequent time, the magnitude of the dc transient is determined by the time constant of the decay of the dc, which is controlled by the ratio of reactance to resistance in the impedance limiting the fault.

Equation (2-2) can be used to calculate the instantaneous magnitude of current at any time. For the protection engineer, the worst case initial current includes the full dc transient.

The driving voltage depicted in Figure 2-1 and Figure 2-2 is the Thevenin equivalent opencircuit voltage at the fault point prior to application of the short circuit. This voltage includes sources such as remote generators with voltage regulators that maintain their value regardless of the presence of a short circuit on the system as well as nearby sources whose voltages decay when the short circuit is present.

The amount of decay is determined by the nature of the source. Nearby generators and synchronous motors with active excitation systems sustain some voltage, but because the short circuit causes their terminal voltage to drop, the current they produce is gradually reduced as the fault is allowed to persist.

At the same time, induction motors initially participate as short-circuit current sources, but their voltages decay rapidly as the trapped flux is rapidly drained. Figure 2-3 shows the generic tendencies of various kinds of short-circuit current sources and a composite waveform for the symmetrical ac current decay.  

 

Figure 2-4 depicts the most realistic case of the decaying symmetrical ac current combined with the decaying dc transient. From this figure, a generalized short-circuit current may be described in the following terms:

— High initial magnitude dc transient component of current, which decays with time

— High initial magnitude symmetrical ac current, which diminishes gradually with time

— Symmetrical ac current lags driving voltage by a significant angle, approaching 90°