Question # 1

Evaluate the selection of circuit breakers based on sub transient calculations and relay settings for
transient calculations?

Answer:

Short circuit study is one of the basic power system analysis problems. It is also known as fault analysis.
When a fault occurs in a power system, bus voltages reduces and large current flows in the lines. This
may cause damage to the equipments. Hence faulty section should be isolated from the rest of the
network immediately on the occurrence of a fault. This can be achieved by providing relays and circuit
breakers.

The calculation of currents in network elements for different types of faults occurring at different
locations is called SHORT CIRCUIT STUDY. The results obtained from the short circuit study are used to
find the relay settings and the circuit breaker ratings which are essential for power system protection.

Symmetrical short circuit on Synchronous Machine

The selection of a circuit breaker for a power system depends not only upon the current the breaker is
to carry under normal operating conditions but also upon the maximum current it may have to carry
momentarily and the current it may have to interrupt at the voltage of the line in which it is placed. In
order to approach the problem of calculating the initial current we need to study the behaviour of a
synchronous generator when it is short circuited.

When an ac voltage is applied suddenly across a series R-L circuit, the current which flows has two
components 1. a steady state sinusoidally varying component of constant amplitude and 2. a non-
periodic and exponentially decaying with a time constant of L/R. (which is also referred as the dc
component current). The initial value of the dc component of current depends on the magnitude of the
ac voltage when the circuit is closed.

A similar but more complex phenomenon occurs when a short circuit occurs suddenly across the
terminals of a synchronous machine. A good way to analyze the effect of a three-phase short circuit at
the terminals of a previously unloaded generator is to take an oscillogram of the current in one phase
upon the occurrence of such fault. Since the voltages generated in the phases of a three-phase machine
are displaced 120 electrical degrees from each other, the short circuit occurs at different points on the
voltage wave of each phase. For this reason the unidirectional or dc transient component of current is
different in each phase. If the dc component of current is eliminated from the current of each phase, the
short circuit current plotted versus time will be as shown in Fig. 3.1
In the synchronous generator, generally the reduction of the air gap flux is caused by the mmf of the
current in the armature which is known as the armature reaction effect. At the instant prior to short
circuit, the no load armature current is very small resulting negligible armature reaction effect and
maximum air gap flux. When there is a sudden increase of stator current on short circuit, the air gap flux
cannot change instantaneously due to eddy currents flowing in the rotor and damper circuits, which
oppose this change. Since, the stator mmf is unable to establish any armature reaction, the reactance
due to armature reaction is negligible and the initial reactance is very small and almost equal to
armature leakage reactance alone. This results in very large initial current as seen from Fig. 3.1. This
period is referred as subtransient period.

After a few cycles, the eddy current in the damper circuit and eventually in the field circuit decays to
some extent and the air gap flux reduces due to partial armature reaction effect resulting in reduction in
short circuit current as seen in Fig. 3.1 Now the machine said to function in the transient period.

The rms value of the current determined by the intercept of the current envelope with zero time is
called the subtransient current |I “ |. Direct axis subtransient reactance Xd ” is |Eg| / |I ” | where |Eg|
is the rms phase voltage at no load.

The rms value of the current determined by the intercept of the current envelope leaving first few cycles
with zero time is called the transient current |I ’ |. Direct axis transient reactance Xd ’ is |Eg| / |I ’ |.

The rms value of the steady state short circuit current is |I|. Direct axis reactance Xd is |Eg| / |I|. The
currents and reactances discussed above are defined by the following equations.
The sub transient current |I”| is much larger than the steady state current |I| because the decrease in
air gap flux caused by the armature current cannot take place immediately. So large voltage is induces in
the armature winding just after the fault occurs than exists after steady state is reached. However, we
account for the difference in induced voltage by using different reactance in series with the no load
voltage Eg to calculate currents for sub transient, transient, and steady state conditions.

Equations (3.1) to (3.3) indicate the method of determining fault current in a generator when its
reactance are known. If the generator is unloaded when the fault occurs, the machine is represented by
Eg in series with the proper reactance.

The resistance is taken into account if greater accuracy is desired. If there is impedance external to the
generator between its terminals and the short circuit, the external impedance must be included in the
circuit.

Selection of circuit breakers

Much study has been made to circuit-breaker ratings and applications. From the circuit breaker current
view point two factors that are to be considered are:

* Maximum instantaneous current which the breaker must withstand

* The total current when the breaker contacts part to interrupt the circuit.

Up to this point we have devoted most of our attention to the subtransient current called the initial
symmetrical current, which does not include the dc component of current. Inclusion of dc component of
current results in a rms value of current immediately after the fault, which will be higher than the
subtransient current. For the circuit breakers above 5 kV subtransient current multiplied by 1.6 is
considered to be the rms value of the current the circuit breaker must withstand during the first half
cycle after the fault occurs. This current is called the momentary current.

The interrupting rating of a circuit breaker is specified in kVA or MVA. Interrupting kVA = 3 x kV of the
bus to which the breaker is connected

x interrupting current when its contacts part

 This interrupting current is , of course, lower than the momentary current and depends on the speed of
the circuit breaker, such as 8, 5, 3, or 2 cycles, which is a measure of the time from the occurrence of the
fault to the extinction of the arc.

The current which a breaker must interrupt is usually asymmetrical since it still contains some of the
decaying dc component of current. We shall limit our discussion to a brief treatment symmetrical basis
of breaker selection.

Breakers are identified by:

i) nominal voltage class, such as 69 kV

ii) ii) rated continuous current
iii) iii) rated maximum voltage
iv) iv) voltage range factor, K
v) v) rated short circuit current at rated maximum voltage
vi)
vii) The rated maximum voltage of a circuit breaker is the highest rms voltage for which the circuit
breaker is designed.

Rated voltage range factor,

viii) K = lower limit of the range of operating voltage rated maximum voltage Value of K determines
the range of voltage over which the product {rated short circuit current x operating voltage} is
constant.
ix) In the application of circuit breakers it is important not to exceed the shortcircuit capabilities of
the breakers. A breaker is required to have a maximum symmetrical interrupting capability
equal to K x rated short circuit current.