1.)Classify the different buses used in load flow study. Discuss briefly.
Ans: In the load flow studies, two variable are known, and two are to be
determined. Depends on the quantity to be specified the buses are
classified into three categories generation bus, load bus and slack bus.
Generation Bus or Voltage control bus
This bus is also called the P-V bus, and on this bus, the voltage
magnitude corresponding to generate voltage and true or active power
P corresponding to its rating are specified. Voltage magnitude is
maintained constant at a specified value by injection of reactive power.
The reactive power generation Q and phase angle δ of the voltage are
to be computed.
Load Bus
This is also called the P-Q bus and at this bus, the active and reactive
power is injected into the network. Magnitude and phase angle of the
voltage are to be computed. Here the active power P and reactive
power Q are specified, and the load bus voltage can be permitted
within a tolerable value, i.e., 5 %. The phase angle of the voltage , i.e.δ
is not very important for the load.
Slack, Swing or Reference Bus
Slack bus in a power system absorb or emit the active or reactive power
from the power system. The slack bus does not carry any load. At this
bus, the magnitude and phase angle of the voltage are specified. The
phase angle of the voltage is usually set equal to zero. The active and
reactive power of this bus is usually determined through the solution of
equations.
The slack bus is a fictional concept in load flow studies and arises
because the I2R losses of the system are not known accurately in
advance for the load flow calculation. Therefore, the total injected
power cannot be specified at every bus. The phase angle of the voltage
at the slack bus is usually taken as reference or zero
2.) What are the advantages of bus admittance matrix over bus impedance matrix?
Ans: The following are the advantages of the bus admittance matrix.
1. The data preparation of the bus admittance matrix is very simple.
2. The formation of the bus admittance matrix and its modification is
easy.
3. The bus admittance matrix is a sparse matrix thus the computer
memory requirement is less.
3.) Why is one of the buses taken as slack bus in load flow studies?
Ans: The slack bus is crucial to a load flow problem since it will
account for transmission line losses. In a load flow problem,
conservation of energy results in the total generation equaling to the
sum of the loads.
4.) Explain all the methods to improve transient stability limit of a power system.
Ans: The methods often employed in practice to improve
system stability are:
1. Increasing System Voltage:
Transient stability is improved by raising the system voltage
profile, (i.e., raising E and V). Increase in system voltage means
the higher value of maximum power, P max that can be transferred
over the lines. Since shaft power, P s = Pmax sin δ, therefore, for a
given shaft power initial load angle δ 0 reduces with the increase
in Pmax and thereby increasing difference between the critical
clearing angle and initial load angle.
2. Reduction in Transfer Reactance:
Transient stability can also be improved by reducing the transfer
reactance,. The effect of reducing the transfer reactance means
increase of Pmax resulting in increase in transient stability
3. Using High Speed Circuit Breaker:
The quicker a breaker operates, the faster the fault is removed
from the system and better is the tendency of the system to
restore to normal operating conditions.
4. Automatic Reclosing:
As the majority of faults on the transmission lines are transient in
nature and are self-clearing, rapid switching and isolation of
faulty lines followed by reclosing are quite helpful in maintaining
stability.
5.) Describe the equal area criterion of stability for a sudden change in mechanical input in a single
machine infinite bus bar system.
Ans : The equal area criterion is a simple graphical method for
concluding the transient stability of two-machine systems or a single
machine against an infinite bus. This principle does not require the
swing equation for the determination of stability conditions. The
stability conditions are recognized by equating the areas of segments
on the power angle diagram between the p-curve and the new power
transfer line of the given curve.
The principle of this method consists on the basis that when δ oscillates
around the equilibrium point with constant amplitude, transient stability
will be maintained.
6.) Derive and plot the power angle equation for a synchronous machine connected to infinite bus.
Ans : Consider a synchronous machine connected to an infinite bus
through a transmission line of reactance Xl shown in a figure below. Let
us assume that the resistance and capacitance are neglected.
Let,
V = V<0⁰ – voltage of infinite bus
E = E<δ – voltage behind the direct axis synchronous reactance of the
machine.
Xd = synchronous / transient resistance of the machine
The complex power delivered by the generator to the system is
S = VI
Let,
the system
Active power transferred to
The reactive power transferred to the system
The maximum steady-state power transfers occur when δ = 0
The graphical representation of Pe and the
load angle δ is called the power angle curve. It is widely used in power
system stability studies. The power angle curve is shown below
8)Solution:
(a) Find the stored energy in the rotor at synchronous speed.
The stored energy is given by
Where G represents complex rated power and H is the inertia constant of
turbo-generator.
(b) If the mechanical input is suddenly raised to 80 MW for an electrical
load of 50 MW, find rotor acceleration, neglecting mechanical and electrical
losses.
The rotor acceleration is given by
Where M is given by
So, the rotor acceleration is
(c) If the acceleration calculated in part(b) is maintained for 10 cycles, find
the change in torque angle and rotor speed in revolutions per minute at the
end of this period.
The change in torque angle is given by
Where t is given by
So,
The change in torque in rpm/s is given by
The rotor speed in revolutions per minute at the end of this period (10
cycles) is given by
Where P is the number of poles of the turbo-generator.
7.) State and explain Equal area criterion of stability. Derive expression for critical clearing
angle and critical clearing time when three phase fault occurs on a power system.
Ans:
The critical clearing angle is defined as the maximum change in the load
angle curve before clearing the fault without loss of synchronism. In
other words, when the fault occurs in the system the load angle curve
begin to increase, and the system becomes unstable. The angle at
which the fault becomes clear and the system becomes stable is called
critical clearing angle.
When the initial load is given, then there is a critical clearing angle, and
if the actual clearing angle exceeds a critical clearing angle, the system
becomes unstable otherwise it is stable. Let the curve A represents the
power angle curve for a healthy condition; curve B represents the
power angle curve for faulty condition and curve C represents the
power angle curve after isolation of fault as shown below.
Where γ1 is the ratio of system reactance in healthy condition to that of
during the fault and γ2 is the ratio of steady state limit of the system
after the isolation of fault and that of system under the initial condition.
For transient stability limit, two areas A1 = A2 or in other words the area
under curve adec (rectangle) is equal to the area under the
curve da’b’bce.
Now substituting,
we have,
or
Also from the curves
or
Thus if γ1, γ2, and δ0 are known, the critical
clearing angle δc can be determined.