Question $2$

AIM: To write a MATLAB program for analyzing the small$-$signal stability of a single$-$machine$-$infinite bus system, assuming classical model of the generator $($constant voltage behind transient reactance$)$ THEORY: Power system stability may be broadly defined as that property of a power system that enables it to remain in a state of operating equilibrium under normal operating conditions and to regain an acceptable state of equilibrium after being subjected to a disturbance. Power system stability may be broadly classified as $($i$)$ rotor angle stability and $($ii$)$ voltage stability. Rotor angle stability is the ability of interconnected synchronous machines of a power system to remain in synchronism. Rotor angle stability can be further classified in to Transient stability and small signal stability depending on the type of disturbance. Transient stability is the rotor angle stability study of a system following large disturbances. Small signal $($or small disturbance$)$ stability is the ability of the power system to maintain synchronism under small disturbances. The disturbances are considered sufficiently small for linearization of system equations to be permissible for purpose of analysis. Instability that may result can be of two forms.

I. Steady increase in rotor angle due to lack of sufficient synchronizing torque.

II$.$ Rotor oscillations of increasing amplitude due to lack of sufficient damping torque. There are four modes of oscillations causing small signal instability in a power system. They are:

a$.$ Local Modes or Machine System Modes are associated with the swinging of ynitsat a generating station with respect to the rest of the power system. The freguencyrange of oscillation is $(0\mathrm{.}8to2)Hz.$

b$.$ Inter area Modes are associated with the swinging of many machines in one partef the system against machines in other parts. The frequency ranges for inter areamedes is to $0\mathrm{.}8$

$20$:$33$

PROJECT$4.$docx

Question $2$

AIM:

To write a MATLAB program for analyzing the small$-$signal stability of a single$-$machine$-$infinite bus system, assuming classical model of the generator $($constant voltage behind transient reactance$)$

I. Steady increase in rotor angle due to lack of sufficient synchronizing torque.

II$.$ Rotor oscillations of increasing amplitude due to lack of sufficient damping torque. There are four modes of oscillations causing small signal instability in a power system. They are:

a$.$ Local Modes or Machine System Modes are associated with the swinging of units at a generating station with respect to the rest of the power system. The frequency range of oscillation is $(0\mathrm{.}8$ to $2)$ Hz$.$

b$.$ Inter area Modes are associated with the swinging of many machines in one part of the system against machines in other parts. The frequency ranges for inter area modes is $(0\mathrm{.}2$ to $0\mathrm{.}8)$ Hz$.$

Numerical Example:

The test system considered for small signal stability analysis is the single machine infinite bus syst

Figure $1\mathrm{.}1$: Single line diagram of SMIB system

Figure $1\mathrm{.}1$ shows the system representation applicable to thermal generating station consist of four $555$MVA,$24kV,60Hz$ units. The network reactances shown in the figure are in per unit on $2220$MVA,$24kV$ base $($referred to the LT side of the step$-$up transformer$).$ Resistances are assumed to be negligible. The post fault system condition in per unit on the $2220$MVA,$24kV$ base is as follows:

$P=0\mathrm{.}9$

$Q=0\mathrm{.}3($ overexcited $)$

$Et=1\mathrm{.}036$

$E_B=\frac{0\mathrm{.}995}{{?}_0}$

The generators are to be modeled as a single equivalent generator represented by the classical model with the following parameters expressed in per unit of $2220$ MVA $24$ kV base

$x_d=0\mathrm{.}3$

$H=3\mathrm{.}5MW-\frac{s}{M}VA$