Maths help on: Derivation & Statcom

1. Abstract

The report has been structured in order to put some light upon a device connected in derivation i.e. Statcom. The report majorly takes into consideration certain servers which would help in order to link the electrical power systems & control the overall voltage. This device helps in order to generate the voltage wave comparing it to the one of the electric system to realize the exchange of reactive power.

Some of the advantages which have been attached along this device i.e. Statcom refers to a quick response time (A STATCOM has a step response of 8 ms to 30 ms). This helps with compensation of negative phase current and with the reduction of voltage flicker. An active power control is possible with a STATCOM (with optional energy storage on dc circuit). This could further help with system stability control.

The next method which has been discussed within the report refers to a Genetic Algorithms. Genetic Algorithms (GA.s) are a stochastic global search method that mimics the process of natural evolution. It is one of the methods used for optimization. John Holland formally introduced this method in the United States in the 1970 at the University of Michigan.

In the end, MATLAB-based analysis algorithm developed to perform stability studies in power systems. The result obtained by the simulating in MATLAB which shows the characteristic of exponential decay in the output. As the system is change on slow parameters, PID is very useful in controlling the variation even very small change. The concept of gene algorithm is so strong which can control the small deviation and the flickering in the STATCOM.

IntroductionIt is a device connected in derivation, basically composed of a coupling transformer that serves of link between the electrical power systems (EPS) and the voltage synchronous controller (VSC) that generates the voltage wave comparing it to the one of the electric system to realize the exchange of reactive power (Hill & Mareels, 1990). The control system of the STATCOM adjusts at each moment the inverse voltage so that the current injected.

The second model which has been described in the report refers to the Genetic Algorithms (GA.s) are a stochastic global search method that mimics the process of natural evolution. It is one of the methods used for optimization. John Holland formally introduced this method in the United States in the 1970 at the University of Michigan. The continuing performance improvements of computational systems have made them attractive for some types of optimization (Hill & Mareels, 1990). Genetic Algorithms are search and optimization techniques inspired by two biological principles namely the process of natural selection and the mechanics of natural genetics. GAs manipulates not just one potential solution to a problem but a collection of potential solutions. This is known as population. The potential solution in the population is called chromosomes. These chromosomes are the encoded representations of all the parameters of the solution (Hill & Mareels, 1990). Each chromosomes is compared to other chromosomes in the population and awarded fitness rating that indicates how successful this chromosomes to the latter.In the end, it has been concluded that MATLAB-based analysis algorithm has been developed in order to perform stability studies in power systems. The result obtained by the simulating in MATLAB which shows the characteristic of exponential decay in the output. As the system is change on slow parameters, PID is very useful in controlling the variation even very small change. The concept of gene algorithm is so strong which can control the small deviation and the flickering in the STATCOM. The major advantage of the MATLAB matrix techniques can be used to speed up the computation and stabilize the result. The genetic algorithm solver handles linear constraints and bounds differently from nonlinear constraints (Hill & Mareels, 1990).

Project Goal

The goal of this project is to measure the “PERFORMANCE OF STATCOM WITH PID CONTROLLER BASED ON GENETIC ALGORITHM using MATLAB”.

Statcom

It is a device connected in derivation, basically composed of a coupling transformer that serves of link between the electrical power systems (EPS) and the voltage synchronous controller (VSC) that generates the voltage wave comparing it to the one of the electric system to realize the exchange of reactive power. The control system of the STATCOM adjusts at each moment the inverse voltage so that the current injected. In the network is in quadrature to the network voltage, in these conditions P=0 and Q=0. In its most general way, the STATCOM can be modeled as a regulated voltage source Vi connected to a voltage bar Vs through a transformer.

The STATic COMpensator (STATCOM) uses a VSC interfaced in shunt to a transmission line. In most cases the DC voltage support for the VSC will be provided by the DC capacitor of relatively small energy storage capability – hence, in steady state operation, active power exchanged with the line has to be maintained at zero, as shown symbolically in the Figure. With the active power constraint imposed, the control of the STATCOM is reduced to one degree of freedom, which is used to control the amount of reactive power exchanged with the line. Accordingly, a STATCOM is operated as a functional equivalent of a static VAR compensator; it provides faster control than an SVC and improved control range.

Each GTO converter generates a voltage that is stepped up by a line side- series-connected multi-stage converter transformer. The converter transformer enables the build-up of a sine-wave voltage in both magnitude and phase. Because STATCOMs with multi-stage converter transformers do not generate significant internal harmonics, they generally require minimal, or no, harmonic filtering. If the number of firing pulses for the GTOs is increased (i.e., pulse-width modulation (PWM) order), the harmonics are further decreased. High-side voltage is generally used as a controller input, as indicated in the figure above.

The figure shows the equivalent circuit of a STATCOM system. The GTO converter with a dc voltage source and the power system are illustrated as variable ac voltages in this figure. These two voltages are connected by a reactance representing the transformer leakage inductance.

Using the classical equations that describe the active and reactive power flow in a line in terms of Vi and Vs, the transformer impedance (which can be assumed as ideal) and the angle difference between both bars, we can defined P and Q. The angle between the Vs and Vi in the system is d. When the STATCOM operates with d=0 we can see how the active power send to the system device becomes zero while the reactive power will mainly depend on the voltage module. This operation condition means that the current that goes through the transformer must have a +/-90º phase difference to Vs. In other words, if Vi is bigger than Vs, the reactive will be send to the STATCOM of the system (capacitive operation), originating a current flow in this direction (Sen, 1999). In the contrary case, the reactive will be absorbed from the system through the STATCOM (inductive operation) and the current will flow in the opposite direction. Finally if the modules of Vs and Vi are equal, there won´t be nor current nor reactive flow in the system. Thus, we can say that in a stationary state Q only depends on the module difference between Vs and Vi voltages. The amount of the reactive power is proportional to the voltage difference between Vs and Vi.

There can be a little active power exchange between the STATCOM and the EPS. The exchange between the inverter and the AC system can be controlled adjusting the output voltage angle from the inverter to the voltage angle of the AC system. This means that the inverter can not provide active power to the AC system form the DC (Koterev, Taylor & Mittelstadt, 1999) accumulated energy if the output voltage of the inverter goes before the voltage of the AC system. On the other hand, the inverter can absorb the active power of the AC system if its voltage is delayed in respect to the AC system voltage.

The STATCOM smoothly and continuously controls voltage from V1 to V2. However, if the system voltage exceeds a low-voltage (V1) or high-voltage limit (V2), the STATCOM acts as a constant current source by controlling the converter voltage (Vi) appropriately. Thus, when operating at its voltage limits, the amount of reactive power compensation provided by the STATCOM (Sen, 1999) is more than the most-common competing FACTS controller, namely the Static Var Compensator (SVC). This is because at a low voltage limit, the reactive power drops off as the square of the voltage for the SVC, where Mvar=f(BV2), but drops off linearly with the STATCOM, there Mvar=f(VI). This makes the reactive power controllability of the STATCOM superior to that of the SVC, particularly during times of system distress (Koterev, Taylor & Mittelstadt, 1999).

In addition the STATCOM has other advantages compared to an SVC, such as:

• Quicker response time (A STATCOM has a step response of 8 ms to 30 ms). This helps with compensation of negative phase current and with the reduction of voltage flicker.

• Active power control is possible with a STATCOM (with optional energy storage on dc circuit). This could further help with system stability control.

• No potential for creating a resonance point. This is because no capacitor banks or reactors are required to generate the reactive power for a STATCOM.

• The STATCOM has a smaller installation space due to no capacitors or reactors required to generate M-var, minimal or no filtering, and the availability of high capacity power semiconductor devices. Designs of systems of equal dynamic ranges have shown the STATCOM to be as much as 1/3 the area and 1/5 the volume of an SVC.

• A modular design of the STATCOM allows for high availability (i.e., one or more modules of the STATCOM can be out-of-service without the loss of the entire compensation system).

PID

PID (proportional integral derivative) control is one of the earlier control strategies. Its early implementation was in pneumatic devices, followed by vacuum and solid state analog electronics, before arriving at today’s digital implementation of microprocessors. It has a simple control structure which was understood by plant operators and which they found relatively easy to tune. Since many control systems using PID control have proved satisfactory, it still has a wide range of applications in industrial control. According to a survey for process control systems conducted in 1989 (Koterev, Taylor & Mittelstadt, 1999), more than 90 of the control loops were of the PID type. PID control has been an active research topic for many years; see the monographs. Since many process plants controlled by PID controllers have similar dynamics it has been found possible to set satisfactory controller parameters from less plant information than a complete mathematical model. These techniques came about because of the desire to adjust controller parameters in situ with a minimum of effort, and also because of the possible difficulty and poor cost benefit of obtaining mathematical models. The two most popular PID techniques were the step reaction curve experiment, and a closed-loop “cycling” experiment under proportional control around the nominal operating point. In this chapter, several useful PID-type controller design techniques will be presented, and implementation issues for the algorithms will also be discussed.The PID Actions (Introduction)

A typical structure of a PID control system is shown in figure below , where it can be seen that in a PID controller, the error signal e(t) is used to generate the proportional, integral, and derivative actions, with the resulting signals weighted and summed to form the control signal u(t) applied to the plant model. A mathematical description of the PID controller is

Where is the input signal to the plant model, the error signal e(t) is defined as e(t) = r(t) − y(t), and r(t) is the reference input signal.

K_p: Proportional gain, a tuning parameter

K_i: Integral gain, a tuning parameter

K_d: Derivative gain, a tuning parameter

t: Time or instantaneous time (the present)

1. Genetic Algorithm (Introduction)

Genetic Algorithms (GA.s) are a stochastic global search method that mimics the process of natural evolution. It is one of the methods used for optimization. John Holland formally introduced this method in the United States in the 1970 at the University of Michigan. The continuing performance improvements of computational systems have made them attractive for some types of optimization (Koterev, Taylor & Mittelstadt, 1999). The genetic algorithm starts with no knowledge of the correct solution and depends entirely on responses from its environment and evolution operators such 10 as reproduction, crossover and mutation to arrive at the best solution. By starting at several independent points and searching in parallel, the algorithm avoids local minima and converging to sub optimal solutions. In this way, GAs have been shown to be capable of locating high performance areas in complex domains without experiencing the difficulties associated with high dimensionality, as may occur with gradient decent techniques or methods that rely on derivative information .

2. Characteristics of Genetic Algorithm

Genetic Algorithms are search and optimization techniques inspired by two biological principles namely the process of natural selection and the mechanics of natural genetics. GAs manipulates not just one potential solution to a problem but a collection of potential solutions. This is known as population (Koterev, Taylor & Mittelstadt, 1999). The potential solution in the population is called chromosomes. These chromosomes are the encoded representations of all the parameters of the solution. Each chromosomes is compared to other chromosomes in the population and awarded fitness rating that indicates how successful this chromosomes to the latter. To encode better solutions, the GA will use genetic operators or evolution operators. such as crossover and mutation for the creation of new chromosomes from the existing ones in the population. This is achieved by either merging the existing ones in the population or by modifying an existing chromosome (Sen, 1999). The selection mechanism for parent chromosomes takes the fitness of the parent into account. This will ensure that the better solution will have a higher chance to procreate and donate their beneficial characteristic to their offspring. A genetic algorithm is typically initialized with a random population consisting of between 20-100 individuals. This population or also known as mating pool is usually represented by a real-valued number or a binary string called a chromosome. For illustrative purposes, the rest of this section represents each chromosome as a binary string. How well an individual performs a task is measured and assessed by the objective function. The objective function assigns each individual a corresponding number called its fitness. The fitness of each chromosome is assessed and a survival of the fittest strategy is applied.

There are three main stages of a genetic algorithm; these are known as reproduction, crossover and mutation. This will be explained in details in the following section.

Population Size

Determining the number of population is the one of the important step in GA. There are many research papers that dwell in the subject. Many theories have been documented and experiments recorded. However the matter of the fact is that more and more theories and experiments are conducted and tested and there is no (Koterev, Taylor & Mittelstadt, 1999) fast and thumb rule with regards to which is the best method to adopt. For a long time the decision on the population size is based on trial and error. In this project the approach in determining the population is rather unscientific. From my reading of various papers, it suggested that the safe population size is from 30 to 100. In this project an initial population of 20 was used and the result observed. The result was not promising. Hence an initiative of 40, 60, 80 and 90 size of population was experimented. It was observed that the population of 80 seems to be a good guess. Population of 90 and above does not results in any further optimization.

Reproduction

During the reproduction phase the fitness value of each chromosome is assessed. This value is used in the selection process to provide bias towards fitter individuals. Just like in natural evolution, a fit chromosome has a higher probability of being selected for reproduction. An example of a common selection technique is the Roulette Wheel selection method. Each individual in the population is allocated a section of a roulette wheel. The size of the section is proportional to the fitness of the individual. A pointer is spun and the individual to whom it points is selected (Koterev, Taylor & Mittelstadt, 1999). This continues until the selection criterion has been met. The probability of an individual being selected is thus related to its fitness, ensuring that fitter individuals are more likely to leave offspring. Multiple copies of the same string may be selected for reproduction and the fitter strings should begin to dominate.

Four common methods for selection are:

1. Roulette Wheel selection

2. Stochastic Universal sampling

3. Normalized geometric selection

4. Tournament selection

Due to the complexities of the other methods, the Roulette Wheel methods is preferred

Crossover

Once the selection process is completed, the crossover algorithm is initiated. The crossover operations swap certain parts of the two selected strings in a bid to capture the good parts of old chromosomes and create better new ones. Genetic operators manipulate the characters of a chromosome directly, using the assumption that certain individuals’ gene codes, on average, produce fitter individuals. The crossover probability indicates how often crossover is performed. A probability of 0% means that the offspring will be exact replicas of their parents and a probability of 100% means that each generation (Kundur, 1994) will be composed of entirely new offspring. The simplest crossover technique is the Single Point Crossover. There are two stages involved in single point crossover:

1. Members of the newly reproduced strings in the mating pool are mated (paired) at random.

2. Each pair of strings undergoes a crossover as follows: An integer k is randomly selected between one and the length of the string less one, [1,L-1]. Swapping all the characters between positions k+1 and L inclusively creates two new strings.

Crossover is a critical feature of genetic algorithms:

It greatly accelerates search early in evolution of a population
It leads to effective combination of schemata (sub solutions on different chromosomes)

3. Mutation

Using selection and crossover on their own will generate a large amount of different strings. However there are two main problems with this:

1. Depending on the initial population chosen, there may not be enough diversity in the initial strings to ensure the Genetic Algorithm searches the entire problem space.

2. The Genetic Algorithm may converge on sub-optimum strings due to a bad choice of initial population. These problems may be overcome by the introduction of a mutation operator into the Genetic Algorithm. Mutation is the occasional random alteration of a value of a string position. It is considered a background operator in the genetic algorithm (Kundur, 1994). The probability of mutation is normally low because a high mutation rate would destroy fit strings and degenerate the genetic algorithm into a random search.

The steps involved in creating and implementing a genetic algorithm:

1. Generate an initial, random population of individuals for a fixed size.

2. Evaluate their fitness.

3. Select the fittest members of the population.

4. Reproduce using a probabilistic method (e.g., roulette wheel).

5. Implement crossover operation on the reproduced chromosomes

(Choosing probabilistically both the crossover site and the mates.).

6. Execute mutation operation with low probability.

7. Repeat step 2 until a predefined convergence criterion is met.

The convergence criterion of a genetic algorithm is a user-specified conditions for example the maximum number of generations or when the string fitness value exceeds a certain threshold.

Select Fittest

Fittest define the probability of selection of a suitable chromosomes. The new chromosomes or the offspring is always hoped to be better than the parents one, hence the more suitable more the chance of their reproduction. All the offspring is generated into the form of genetic algorithm which is aligned and arranged into the matrix of best suited and reproductive chromosomes. Parents are selected at random with selection chances biased on relation to chromosome evaluations (Kundur, 1994).

Optimum solution

The deviation action of the control output has a relation with the rate in change of the measurement of the error. PID stands for the proportional, integral and derivative of the design to eliminate the need for continuous operator action. Integral or reset action is set in either repeat/time or time/repeat and hence the reproduction phase the fitness value of each crossover is assessed. The PID controller is capable to provide the satisfactory closed loop operation. This is used for the unstable and non-minimal performance of the offspring which is useful in multiple distributions of the crossover (Kundur, 1994).

1. OSCILLATION CONTROL USING PID

Even though it is a costly option when compared to the use of GTO for oscillation control, there are additional benefits of PID controllers. Besides oscillation control, PID local voltage control capabilities allow an increase in system load ability which is not possible at all with GTO. The main issues to control PID are based on:

Arrangement issues
Controlling the inputs

All the facts are depends on the analysis of Eigen value of the matrix related to the operating voltage and its limits. The introduction of SVC and STATCOM controllers at an appropriate location, by itself does not provide adequate damping, as the primary task of the controllers is to control voltage (Koterev, Taylor & Mittelstadt, 1999). Hence, in order to increase the system damping, it is necessary to add an additional control block with an appropriate input signal. Hence PID controllers are used as it has

K_i: Integral gain, a tuning parameter;
K_d: Derivative gain, a tuning parameter;
t: Time or instantaneous time (the present)

Now we have the controlling ability to check the variation of the operating voltage which is used in the realization of the exchange of reactive power in STATCOM. As the three modes in the PID are used such as, mode observability was employed to determine the best input signal which is going to be controlled. The main purpose of this experiment is to obtain the stable voltage output and to avoid voltage flicking. The negative current in the system is control by providing the feedback with instantaneous time controlled PID (Kundur, 1994). To control the SVC bus voltage, with an additional control block and signals to damp oscillations. The basic electronic block of a STATCOM is the voltage source converter (VSC), which in general converts an input dc voltage into a three-phase output voltage at fundamental frequency, with rapidly controllable amplitude and phase angle. In addition to this, the controller has a coupling transformer and a dc capacitor. The control system can be designed to maintain the magnitude of the bus voltage constant by controlling the magnitude and/or phase shift of the VSC output voltage (Kundur, 1994).

10. Result

MATLAB-based analysis algorithm developed to perform stability studies in power systems. The result obtained by the simulating in MATLAB which shows the characteristic of exponential decay in the output. As the system is change on slow parameters, PID is very useful in controlling the variation even very small change. The concept of gene algorithm is so strong which can control the small deviation and the flickering in the STATCOM. The major advantage of the MATLAB matrix techniques can be used to speed up the computation and stabilize the result. The genetic algorithm solver handles linear constraints and bounds differently from nonlinear constraints.

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