Last Updated: Feb 26, 2017

### Voltage Stability:

A power system is said to be voltage stable if it is able to maintain steady voltages at all its buses after a disturbance. In other words, one can say that voltage stability is the ability to maintain steady voltages at all the buses in the power system after being exposed to a disturbance. The disturbances may be:

- Line or Generator outages,
- Increase in loading,
- Generators, synchronous condensers and other reactive power sources inching close to their reactive power limits.

A power system is voltage stable if the magnitude of voltage at a bus increases as the reactive power injection (at the same bus) is increased. At a given operating condition, this is true for every bus in the system.

When the reactive power demand of the load is not fulfilled, voltage collapse occurs. Voltage stability of a power system is on the verge of collapse when a disturbance increases the reactive power demand beyond the available capacity of the system components. Voltage collapse is a usual phenomenon in a heavily loaded power system or a system having shortage of reactive power. The voltage drop in the line impedance during power flow is the main cause of voltage instability. This reduces the power transfer ability of the transmission system and also reduces voltage support ability.

A system is "voltage unstable" if the magnitude of voltage at one or more bus decreases when the reactive power injection at the very bus or buses is increased.

Thus, for a power system, if the V-Q sensitivity is positive for every bus, the system is voltage stable, otherwise for a negative V-Q sensitivity, the system is voltage unstable.

A system is "voltage unstable" if the magnitude of voltage at one or more bus decreases when the reactive power injection at the very bus or buses is increased.

Thus, for a power system, if the V-Q sensitivity is positive for every bus, the system is voltage stable, otherwise for a negative V-Q sensitivity, the system is voltage unstable.

### Voltage Stability Index:

Voltage stability analysis of a power system involves determination of an index called the “voltage stability index” which is used as a measure of inclination of Power system towards voltage collapse. These indices are helpful in determining the weak bus so that adequate reactive power allocation can be done.### Methods of determining the Voltage Stability Index:

There are few methods of determining the voltage stability index and “L-index method” is one such method.In L-index method, one has to partition the Y bus matrix as Y

_{GG}, Y

_{GL}, Y

_{LG}, and Y

_{LL}, where ‘G’ stands for generator and ‘L’ stands for Load. Matrix Y

_{LG}, and Y

_{LL}are required to calculate the matrix FLG needed for calculation of L-index. Detailed theory can be seen in many research papers.

### MATLAB coding for Y bus partition:

The
MATLAB coding for Y bus partition is as given below:

clear; clc;

% File gives the partition of Y
bus.

num=6; % specify the bus system if you to work with
many examples.

% a function file “volt_ang” gives the
admittance, magnitude and angle of bus voltage.

% This file is a part of the NR load flow code and not given here.

[Y, Vm, Va]= volt_ang(num)

linedt= line_data(num); % calling the line data for the system

busdt= bus_data(num); % calling the bus data for
the system

nb= max(busdt(:,1)) ; % gives the total number
of buses in the system

type =busdt(:,2) ; % identify the type
of bus i.e. ref., generator, and load

pv = find(type==2 l type==1); % identify the PV bus

npv = length(pv); % gives the number of PV buses

pq = find(type==3); % identify the PQ bus

npq = length(pq); % gives the number of PQ buses

pq = find(type==3); % identify the PQ bus

npq = length(pq); % gives the number of PQ buses

for m=1:npq,

for n= 1:npq,

Y

_{LL }(m,n) = Y (pq(m), pq(n));

end

end

for m=1:npq,

for n = 1:npv,

Y

_{LG}(m,n)= Y(pq(m), pv(n));

end

end

FLG
= (Y

_{LL})^-1*Y_{LG}