# Static Voltage Stability Enhancement Using FACTS Controller

2016 International Conference on Emerging Technological Trends [ICETT]

to compute the weak nodes where reactive power compensator can be placed. Comparative analysis of this approach is done with the existing power flow based L-index. All the techniques presented are tested on the IEEE 5 bus and the practical 26-bus test systems. The STATCOM FACTS device

is used as a reactive compensator device for voltage stability

enhancement in this paper. The remaining of this paper is

organized as follows: Section II gives the mathematical formulation of the suggested approach of the NSCPF and a brief note on the conventional power flow based L-Index technique, while a brief description of the STATCOM used is presented in Section III. Section IV present result and discussion of the work and the conclusion of the work is presented in Section V. II. PROBLEM FORMULATIONS

Mathematical formulations of NSCTPF start from the

basic law of circuit theory. It is derived by partitioning the Y-admittance matrix into four regions as shown in (1)

»¼

º«¬ª»¼º«¬ª=»¼º«¬ªL G LL LG GL GG L G V V Y Y Y Y I I (1) »¼

º

«

¬ª=LL LG GL GG Y Y Y Y Y (2)

If we further expand (1) and manipulate the resulting algebraic equations, we have;

»¼

º

«¬ª»¼º«¬ª=»¼º«¬ªL G LL LG GL GG L G V I D W H Z I V (3) where

[][]1?=GG GG Y Z

[][][]GL GG GL Y Y H 1??= [][][]1?=GG LG LG Y Y W

[][][][][]GL GG LG LL LL Y Z Y Y D ?=

The eigenvalue decomposition of matrix LL D is given by *

1

*i i

n

i i LL f f F F D ξ

ξ¦===

(4)

where

F is an orthonormal matrix with eigenvectors i f and ξis a diagonal matrix with eigenvalues i ξ.

Expanding (3) also results in:

[][][][]{}G LG L LL

L I W I D V ?=

?1

(5)

Substitution of (21) in (22)

[][][][]{}G LG L n i i i i L I W I v V ?¼

º

«¬ª=¦

=1*ξν (6)

From (5) and (6), it can be seen that large values of i

ξ

depicts small changes in the load voltage. However, as the

system is stressed, the value of i ξ becomes smaller and the

load voltage becomes weaker. If the magnitude of i ξis equal to zero, the corresponding load voltage collapses. The weak load bus is surrounded by lines with high impedances. The extent of whether the reactive elements are not enough or sufficient in power system is solely depends on the participation between network buses observable from the eigenvectors of the matrix F. In some occasions, the critical

bus, which is associated to the smallest eigenvalue may not be a more critical load bus.

Thus, this present work digs deep to further explore the

concept of structural based participation factor to determine

the most critical load bus, which contributes most to the

smallest eigenvalue as identified using (4) for voltage stability

enhancement. We termed this Network Structural Characteristics Theory-Participation Factor (NSCTPF) in this work. This is done by identifying the elements contributing

most in these modes. The bus participation factor measuring the contribution of the th i bus to the th

j mode is the product of right and left eigenvectors defined in (7) and it is given as

ji ij ij f f NSCTPF =

(7)

It follows that, the bus, which has large participation factors

corresponds to the most critical system buses which are liable to voltage collapse.

L-index proposed by [20] and the modal analysis of the reduced Jacobian matrix [11] are used in this work as benchmarks to test the effectiveness of the proposed approach of NSCTPF. With these techniques, the suitable locations for the STATCOM FACTS device are determined. Details of the mathematical formulations of the L-Index and the modal analysis techniques are reported in [20] and [11] respectively. The L index varies in a range between 0 (no load) and 1 (voltage collapse). The maximum of these indices gives the proximity of the system voltage collapse. For the modal analysis, the bus with the highest value of the Modal Analysis Participation Factor (MAPF) is usually considered the critical bus.

II STATCOM FACTS CONTROLLER

STATCOM is a shunt-connected device, which regulates the voltage at the connected bus to the reference value by controlling the voltage and angle of internal voltage source. The resulting STATCOM can inject or absorb reactive power to or from the bus to which it is connected and thus control the bus voltage magnitude. The STATCOM has the capacity to either inject or absorb the reactive power of the system, depending on the voltage magnitude to which it is connected into. When system voltage is low, the STATCOM injects

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