## Welcome to the world of Optimizations

In this blog concepts of conventional and unconventional optimization techniques are discussed.

## Saturday, October 30, 2010

### Improvement of Maximum Load-ability of Power system by FACTS devices:Part 1

Now days lot of research is going on FACTS and its application on power system performance enhancement.

In this post let us try to understand the problem of Maximizing the loadability of the power system with and without incorporating the FACTS devices.

i) Maximum loadability without FACTS devices

If a problem is to be understood the title should be understood in the realistic way.

A Power System comprises of generators,loads , transmission lines and other devices ( circuit breakers ,capacitors. and lightning arrestors).

1.The generators have real and reactive power limits and a better voltage voltage profile is to be maintained.

2.The loads have to receive the scheduled power at a better voltage. The load voltage voltage should be within the allowable range . Normally it is between 90% to 110% of the base(rated) voltage.

3.The transmission lines have the MVA power flow rating .

It is known that the load on a power system is not certain and subject to change with time. The variation of demand with time is called the Load duration curve.

All the Load centers are having Maximum demand indicators which record the maximum demand on a day/week and year. From this the importance of the maximum load-ability can be understood.

The term Maximum load-ability can be defined as the maximum load that can be served by the power network without violating the voltage,power and line flow constraints.

This is an offline study done on the power system data to determine the maximum load supplied by the power system without violating the constraints.

A) what is the data is required to carry out this analysis.?

busdata,generator and linedata ( same like matpower data format)

MATPOWER is a package of MATLAB® M-files for solving power flow and optimal power flow problems. It is intended as a simulation tool for researchers and educators that is easy to use and modify. MATPOWER is designed to give the best performance possible while keeping the code simple to understand and modify. It was initially developed as part of the PowerWeb project.

B) Problem Formulation

Let us put the points in the following way.
• The loads are to be increased.In the literature the method followed is to increase the loads by the same amount .
• The generators are optimally allocated to meet the new demand and losses .
• The load voltage limits ,power limits of generators and the line flow limits are checked.
• The maximum amount of load that can be supplied by the power system is maximum load-ability.
C) Mathematical Modelling

In this problem the control variables are the loadability parameter and the real power of the generation.

The problem is modeled as a optimization(Maximization or Minimization) an problem.

The objective function

The constraints are
equality constraints: Power flow equations

In equality constraints : real and reactive power limits of generators and line flow limits. of the transmission line.

In the next part let us see how to model this problem with FACTS devices.

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