## Welcome to the world of Optimizations

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

## Sunday, October 31, 2010

### Improvement of Maximum Load-ability of Power system by FACTS devices:Part 3

In the previous posts the Maximum load-ability problem without FACTS devices was discussed and modeled as an optimization problem.The problem has to modified to include the effect of FACTS devices. A brief introduction is given on the different FACTS devices.

A flexible alternating current transmission system (FACTS)

It is a system composed of static equipment used for the AC transmission of electrical energy. It is meant to enhance controllability and increase power transfer capability of the network. It is generally a power electronics-based system. There are two types of FACTS devices series and shuunt connected devies.

### Series compensation

In series compensation, the FACTS is connected in series with the power system. It works as a controllable voltage source. Series occurs in long transmission lines, and when a large current flow causes a large voltage drop. To compensate, series capacitors are connected.

### Shunt compensation

In shunt compensation, power system is connected in shunt (parallel) with the FACTS. It works as a controllable current source. Shunt compensation is of two types:
Shunt capacitive compensation
This method is used to improve the power factor. Whenever an inductive load is connected to the transmission line, power factor lags because of lagging load current. To compensate, a shunt capacitor is connected which draws current leading the source voltage. The net result is improvement in power factor.
Shunt inductive compensation
This method is used either when charging the transmission line, or, when there is very low load at the receiving end. Due to very low, or no load – very low current flows through the transmission line. Shunt capacitance in the transmission line causes voltage amplification (Ferranti Effect). The receiving end voltage may become double the sending end voltage (generally in case of very long transmission lines). To compensate, shunt inductors are connected across the transmission line.

## Series compensation devices

• Static synchronous series compensator (SSSC)
• Thyristor-controlled series capacitor (TCSC): a series capacitor bank is shunted by a thyristor-controlled reactor
• Thyristor-controlled series reactor (TCSR): a series reactor bank is shunted by a thyristor-controlled reactor
• Thyristor-switched series capacitor (TSSC): a series capacitor bank is shunted by a thyristor-switched reactor
• Thyristor-switched series reactor (TSSR): a series reactor bank is shunted by a thyristor-switched reactor

## Static synchronous compensator (STATCOM); previously known as a static condenser (STATCON)

### Improvement of Maximum Load-ability of Power system by FACTS devices:Part 2

In the last part some fundamentals of this problem was discussed.In this part the modelling of the the problem is to be completed.

Pli- Scheduled real power load of ‘i’th bus
Qli- Scheduled reactive power load of ‘i’th bus
Pgi- Generated real power of ‘i’th bus
Qli- Generated real power of ‘i’th bus
Vi-Voltage of ‘i’th bus
LFij-Line Flow (MVA)of transmission line connecting buses ‘i’ and ‘j’
If a power system has 'm' generator buses, 'n' load buses and 'k' transmission lines.
The number of parameters to be determined is 'm+1'
The number of equality constraints are 2*(n+m-1)
The number of inequality constraints are 2*m+n+k
In the figure the equations are clearly written. It can be solved by any conventional or unconventional optimization algorithm.

## 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.