IMPROVING VOLTAGE STABILITY IN POWER SYSTEMS USING MODAL ANALYSIS

PROJECT PRESENTATION ON

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Voltage StabilityThe voltage stability of a power system refers to its ability to properly maintain steady, acceptable voltage levels at all buses in the network at all times, even after being subjected to a disturbance.

Reasons of instability1.Insufficient supply of increased demand in reactive power2.Load on transmission line is too high3.Voltage sources are too far from the load centre4.Source voltage are too low

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FACTS Devices

1)The term FACTS refers to alternating current transmission systems incorporating power electronic-based and other static controllers to enhance controllability and increase power transfer capability

2)Used in parallel with electro-mechanical devices

3)Effective response in operation, frequent variation in output and smoothly adjustable output

4)Various functions are :

a) Voltage control b) Short Circuit Current Limiting

c) Transient Stability d) Dynamic Stability

e) Active and Reactive Power Flow Control

5) Commonly used FACTS devices are:

SVC STATCOM SMES

BESS TCSC SSSC

UPFC IPC

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Modal analysis

Static method which involves computation of critical eigenvalue of the reduced power system steady state Jacobian matrix and the associated participation factors

Shows how close the current operating point of power system is to the voltage collapse point

At each operating point P was kept constant and evaluate voltage stability by considering the incremental relationship between Q and V

The linearized steady state system power voltage equations are given by.

To reduce (1), let ∆P =0,

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v = ∆V = the vector of modal voltage variationsq= ∆Q = vector of modal reactive power variations

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Relative participation of kth bus to ith mode is expressed by bus participation factor as

where ξki and hik are kth element of the right and left eigenvectors corresponding to i th eigenvalue of JR

for the ith mode

In the proposed method, for each contingency a probabilistic index is defined which evaluates the relative participation of each bus in voltage instability caused by all of the critical eigenvalues corresponding to that contingency

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the larger the magnitude of bus participation factor in critical modes, that bus is more effective in voltage instability. the smaller the magnitude of positive σj, that mode is more critical

the total participation in all critical modes (TPCM) for each bus

PCMi = contribution of bus i to voltage instability caused by critical modes under k th contingency state

Poutage = likelihood of kth contingency occurring corresponding to outage of line k

m = number of critical eigenvalues in kth contingency

Pij = participation factor of bus i to critical eigenvalue j

σj = critical eigenvalue j

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Steps of the proposed method1.Perform a power flow computation to establish conditions at the specific operating point and generate system Jacobian matrix.2.Perform modal analysis to obtain a relative measure of the system distance to bifurcation, identify the weakest system buses, and identify the weakest system branches.3.Generate V-P/Q-V curves at weak nodes identified in modal analysis.4.Placement of reactive compensation devices at critical buses identified.

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Case study

IEEE 14 Bus Power System

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Proposed method of prevention of voltage collapse

Assumption taken:1.σcritical=12.The failure probability of all lines is assumed to be 0.023.The load and generation of the system is scaled by the factor of 0.95

Choose bus with largest value of TPCM and minimum value of σ

Table 1- smallest eigen values for the three different contingencies

Table 2- The smallest eigen value associated with contingency after installation of STATCOM at Bus 12

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Table 5- The smallest eigen value associated with contingency after installation of STATCOM at Bus 7

Table 4- TPCM values of buses

Table 3- TPCM values of buses

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Targets achieved1.Studied about voltage stability problem, FACTS devices and load flow techniques.2.Studied MATLAB tools.3.Calculated the stability problem on 2 bus system using Modal Analysis.4.Studied IEEE-14 bus system and understood which one is the weakest bus and where compensations can be installed optimally.

Next steps1.Cross check the result on POWER WORLD simulator.2.Then finally will apply this method on 220KV transmission system.

THANK YOU !

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