This essay has been submitted by a student. This is not an example of the work written by our professional essay writers.
Electricity is a form of energy. It is the flow of electrons. Electricity is a basic part of nature and it is one of our most widely used forms of energy. We get electricity, which is a secondary energy source, from the conversion of other sources of energy, like coal, natural gas, oil, nuclear power and other natural sources, which are called primary sources. (Mary Bellis inventor's guide [nodate])
A turbine is a rotary engine that extracts energy from a fluid flow and converts it into useful work. The simplest turbines have one moving part, a rotor assembly, which is a shaft or drum with blades attached. Moving fluid acts on the blades, or the blades react to the flow, so that they move and impart rotational energy to the rotor. Early turbine examples are windmills and water wheels. Below is an example of a simple windmill.
Fig 1.1 windmill
Almost all electrical power on Earth is produced with a turbine of some type. Very high efficiency steam turbines harness about 40% of the thermal energy, with the rest exhausted as waste heat.
Turbines are often part of a larger machine. A gas turbine, for example, may refer to an internal combustion machine that contains a turbine, ducts, compressor, combustor, heat-exchanger, fan and (in the case of one designed to produce electricity) an alternator. (http://en.wikipedia.org/wiki/Turbine)
1.3 GENERATION OF ELECTRICITY
An electric generator is a device for converting mechanical energy into electrical energy. The process is based on the relationship between magnetism and electricity. In the years of 1831-1832 Michael Faraday discovered the operating principle of electromagnetic generators. The principle, later called Faraday's law, is that a potential difference is generated between the ends of an electrical conductor moving through a magnetic field [Fig 1.2]. In other words when a wire or any other electrically conductive material moves across a magnetic field, an electric current occurs in the wire.
Fig 1.2 principle of electromagnetic induction
A generator consists of a stationary structure, which provides a constant magnetic field, and a set of rotating windings which turn within that field. On small machines the constant magnetic field may be provided by one or more permanent magnets; larger machines have the constant magnetic field provided by one or more electromagnets, which are usually called field coils. The figure below shows a dc generator, i.e. a dc current is generated.
An electric utility power station uses either a turbine, water wheel, or other similar machine to drive an electric generator. The dynamic behaviour of the generator within a power system is of fundamental importance to the overall quality supply. The synchronous generator converts mechanical power to electrical power at a specific voltage and frequency.
Fig 1.3 a dc generator
The commutator converts the ac current into a dc. Large power generators are now rarely seen due to the now nearly universal use of alternating current for power distribution and solid state electronic AC to DC power conversion.
An alternator is an electromechanical device that converts mechanical energy to electrical energy in the form of alternating current. Most alternators use a rotating magnetic field but linear alternators are occasionally used. In principle, any AC electrical generator can be called an alternator, but usually the word refers to small rotating machines driven by automotive and other internal combustion engines. Alternators in power stations driven by steam turbines are called turbo-alternators.
Alternators generate electricity by the same principle as DC generators, namely, when the magnetic field around a conductor changes, a current is induced in the conductor. Typically, a rotating magnet called the rotor turns within a stationary set of conductors wound in coils on an iron core, called the stator. The field cuts across the conductors, generating an induced EMF, as the mechanical input causes the rotor to turn.
The rotating magnetic field induces an AC voltage in the stator windings. Often there are three sets of stator windings, physically offset so that the rotating magnetic field produces three phase currents, displaced by one-third of a period with respect to each other. (Thompson, Sylvanus P., Dynamo-Electric Machinery, A Manual for Students of Electrotechnics, Part 1, Collier and Sons, New York, 1902) (White, Thomas H.,"Alternator-Transmitter Development (1891-1920)". EarlyRadioHistory.us)
1.4 LOAD FREQUENCY CONTROL
Load demand is never constant and almost continuously varying. A change in load leads to a change in shaft frequency, and hence frequency of electric power transmitted. It is important to keep frequency of electric power transmitted within some very limited range since clocks in electronic apparatus like the computer, which is fed by electric current are tuned to that frequency. a serious change in frequency of electric power may destabilise operation of these apparatus.
(Adia J.Issop 2006 load frequency control, a survey of different methodologies cited Prabha 1994, p.124)
To optimize the performance of electrical equipments, it is important to ensure the quality of the electric power. A good quality of the electric power system requires both the frequency and the voltage to remain at standard values during operation. However the users of the electric power change the loads randomly and momentarily. It will be impossible to maintain the balances of both the active and reactive power without control. As a result of the imbalance, the frequency and voltage levels will be varying with the change of the loads. Thus a control system is essential to cancel the effects of the random load changes and keep the frequency and voltage level at standard values. (Yao Zhang, load frequency control of multiple area system, 2007)
1.5 CONTROL SYSTEM
A control system is usually defined as a combination of components (electrical, mechanical, thermal, or hydraulic) that act together to maintain actual system performance close to a desired set of performance specifications.
Open-loop control systems are those in which the output has no effect on the input. An open loop control system uses a controller or control actuator in order to obtain the desired output. The diagram below shows an open loop system.
Fig 1.5 Open loop control system
Closed-loop control systems are those in which the output has an effect on the input in such a way as to maintain the desired output value [Fig 1.6]. A closed-loop system includes some way to measure its output to sense changes so that corrective action can be taken.
Fig 1.6 closed loop control system
The speed with which a simple closed-loop control system moves to correct its output is described by its damping ratio and natural frequency. A system with a small damping ratio is characterized by overshooting the desired output before settling down. Systems with larger damping ratios do not overshoot the desired output, but respond more slowly. The figure below shows the output response of an underdamped, critically damped and overdamped system with respect to time.
Fig 1.7 underdamped, critically damped and overdamped output.
A feedback control system often uses a function of a prescribed relationship between the output and reference input to control the process. Often, the difference between the output of the process under control and the reference input is amplified and used to control the process so that the difference is continually reduced. The feedback concept has been the foundation for control system analysis and design. The figure below shows an ideal feedback model. Feedback can be either positive or negative.
Fig 1.8 Ideal feedback model. It is negative if B is less than zero.
1.7 LINEAR CONTROL
Linear control systems use linear negative feedback to produce a control signal mathematically based on other variables, with a view to maintaining the controlled process within an acceptable operating range.
The output from a linear control system into the controlled process may be in the form of a directly variable signal, such as a valve that may be 0 or 100% open or anywhere in between.
1.8 PID CONTROL
A Proportional integral and derivative controller is the most commonly used feedback controller. A PID controller calculates an "error" value as the difference between a measured process variable and a desired setpoint. The controller attempts to minimize the error by adjusting the process control inputs. In the absence of knowledge of the underlying process, a PID controller is the best controller. However, for best performance, the PID parameters used must be tuned according to the nature of the system - while the design is generic, the parameters depend on the specific system. The figure below shows a PID controller in a system.
By tuning the three constants in the PID controller algorithm, the controller can provide control action designed for specific process requirements. The response of the controller can be described in terms of the responsiveness of the controller to an error, the degree to which the controller overshoots the setpoint and the degree of system oscillation. However the use of the PID algorithm for control does not guarantee optimal control of the system or system stability.
Some applications may require using only one or two modes to provide the appropriate system control. This is achieved by setting the gain of undesired control outputs to zero. A PID controller will be called a PI, PD, P or I controller in the absence of the respective control actions.
Fig 1.9 PID controller
Simple PID controllers do not have the ability to learn and must be set up correctly. Selecting the correct gains for effective control is known as tuning the controller. PID controllers often provide acceptable control even in the absence of tuning, but performance can generally be improved by careful tuning, and performance may be unacceptable with poor tuning.
Some tuning methods include:
Manual method, ziegler nichols method, software based simulation methods or cohen coon method.
1.9.2 LIMITATIONS OF PID
PID controllers, when used alone, can give poor performance when the PID loop gains must be reduced so that the control system does not overshoot, oscillate or hunt about the control setpoint value. They also have difficulties in the presence of non-linearities, may trade off regulation versus response time, do not react to changing process behavior and have lag in responding to large disturbances.
Hence, very often, PID controllers are coupled with intelligent controllers to overcome these deficiencies. Intelligent control is described in further detail in the next chapter.
2.1 LOAD FREQUENCY CONTROL
The main objective of LFC is to maintain reasonably uniform frequency. The frequency of a power system is dependent entirely upon the speed at which the generators are rotated by their prime movers. Therefore, frequency control is basically a matter of speed control of the machines in the generating stations. All prime movers, whether they are steam or hydraulic turbines are equipped with speed governors, which almost without exception are purely mechanical speed sensitive devices.
Although the active power and the reactive power have combined effects on the frequency and voltage, the control problem of the frequency and voltage can be decoupled. The frequency is highly dependent on the active power and the voltage is highly dependent on the reactive power. Thus, they can be considered separately. The active power and frequency control is referred to as load frequency control LFC, and the automatic voltage regulator (AVR) regulates the reactive power and voltage magnitude.(H. Saadat's Power system analysis Tata McGrawhill edition 2002)
Fig 1.6 schematic diagram of LFC and AVR of a synchronous generator.
Automatic voltage control
2.2 TRADITIONAL CONTROL SCHEMES
The most common type of traditional control schemes is the proportional, integral and derivative control scheme commonly used as PID control scheme. PID control is usually combined with logic, sequential machines, selectors, and simple function blocks. PID control scheme can be considered one of the easiest control strategy to be used due to its flexible implementation in different field in control engineering. However, before a PID controller can be used properly, a process called tuning is vital. In fact, proportional, integral and derivative control schemes can be implemented separately as controllers depending on the system under control. There are actually, different combination of these control schemes namely proportional controller, integral controller, derivative controller, proportional and derivative PD controller, proportional and integral PI controller, and proportional integral and derivative PID controller. Actually, there are also other traditional control schemes like feedback controllers using feedback loops (Roomaldawo W, load frequency control of wind turbine using PID and supervised NN control scheme,2009, cited Tzafestas 1997, p.3)
2.3 INTELLIGENT CONTROL SCHEMES
Since pure traditional control was proved to be unsuccessful in dealing with complex, strongly non linear and uncertain systems, that is where intelligent control schemes come into play.
The field of intelligent control was founded by Fu (1971 cited Tzafestas 1997,p.3) as an intersection of artificial intelligence and automatic control. Actually, intelligent control is an enhancement of traditional control to include the ability to sense and reason consequently about the environment with inexact and incomplete "a priori" knowledge and executing commands and controls in a flexible, adaptive and robust way.
Intelligent Control methods are actually classified in the following categories:
Model-Based Intelligent Control Methods
Knowledge-Based Intelligent Control Methods
Fuzzy Logic Intelligent Control Methods
Neural Network Intelligent Control Methods
Hybrid Intelligent Control Methods
2.3.1 Model-Based Intelligent Control Methods
In these methods, a mathematical model of the system under control must be knows in advance or derived from knows equations. In addition, the intelligent control needs to be produced using some kind of numerical learning-estimation and adaptation algorithms. Unfortunately, the model-based (numerical) learning algorithms suffer from serious problems when facing unmodelled dynamics and nonlinearities (Roomaldawo W, load frequency control of wind turbine using PID and supervised NN control scheme,2009, cited Tzafestas 1997, p/7).
2.3.2 Knowledge-Based Intelligent Control Methods
Here, these methods employ symbolic, i.e. non numerical/linguistic knowledge and models of the system under control and they have a knowledge base (facts, rules and events), an inference engine of how to draw conclusions from the knowledge base, and finally a system interface, i.e. a facility for passing the conclusions to the system. Though no global classification of knowledge-based controllers exists, most of these expert controllers may be classified into these two categories namely direct and indirect expert controllers (Tzafestas 1997, p.8).
2.3.3 Fuzzy Logic Intelligent Control Methods
Zadeh, the father of fuzzy control theory, was the one who first wrote a paper in fuzzy set theory. In that work, Zadeh explained the concept of human approximate reasoning to effectively make decisions on the basis of available imprecise linguistic information (Zadeh 1965, p. 338).
Fuzzy controllers are also knows as linguistic controllers, represent a class of adaptive controllers that do not require the mathematical model of the system under control. So instead of being described by mathematical equations, they are described by fuzzy (linguistic) rules. A fuzzy logic controller (FLC) normally produces a non linear mapping of an input data vector into a scalar output.
Fuzzy controllers have two important features:
1. Linguistic expressions to describe the behavior of the system or the control actions, and thus they mimic the actions of human users.
2. they are inherently nonlinear and so they have the ability to do control actions usually not possible with purely linear controllers.
(Roomaldawo W, load frequency control of wind turbine using PID and supervised NN control scheme,2009, cited Tzafestas 1997, p/9).
In additions, a fuzzy logic controller contains basically four vital components which are namely (Nelson and Marcelo 2002, p.9):
The controller's behaviors are defined by rules using IF-ELSE statements.
The Fuzzifier maps crisp values into input fuzzy sets to activate rules/
The inference engine maps input fuzzy sets by applying the rules.
The defuzzifier then maps the output fuzzy values into crisp values.
2.3.4 Artificial neural network Intelligent control methods
The science of artificial neural networks is based on the neuron. Neurons are the fundamental elements in the central nervous system. For many decades, engineers and scientists wanted to develop a machine that mimics the behavior of the human brain.
Neural network based intelligent controllers are also known as neuro- controllers. They represent a class of adaptive controllers which like fuzzy controllers, do not need the knowledge of a mathematical model of the system under control. In NN intelligent control, the NN is trained so as to optimize a criterion. Neuro controllers perform in general as a particular kind of adaptive control where the controller takes the form of a neural network. Learning process is then accomplished throught the adaptation of network's weights.
Neural neuro controller methods are normally categorized in three types:
direct neuro - control methods where the neuro controller is used as a signal based controller without a model of the system
methods using traditional controller in combination with a neural network.
Methods using both a neural model and a neurocontroller.
2.3.5 Hybrid Intelligent Control Methods
These methods use a mixture of at least two different classes for the above controllers. Model-based merged with knowledge-based control, knowledge-based with neural control,fuzzy with neural control, neural-expert system and so on are typical examples of the different hybrid control methods that can be implemented. These hybrid controllers actually allow a better control of the systems under investigation, and can generate more precise results as compared with single controllers used independently. However, the most common and one of the most powerful hybrid controller is the neural-fuzzy controller (Roomaldawo W, load frequency control of wind turbine using PID and supervised NN control scheme,2009, cited Tzafesta 1997, p. 10).
Logically, it can be said that the artificial neural networks try to emulate the "hardware" of the human brain, while the adaptive fuzzy systems try to emulate the "software" in the human brain.
2.4 LITERATURE REIVEW
Below some of the past works done in the topic under investigation are presented, studied and analysed so that important information can be extracted and used for the realization of this project.
2.4.1 ARTIFICIAL NEURAL NETWORK BASED DESIGN OF GOVERNOR CONTROLLER
(Dr. N. Rengarajan, C.S.Ravichandran, Dr.S.Palani 2007)
This paper deals with the design of Artificial neural network (ANN) based PID controller, to realize fast governor action in a power plant. The design technique is applied to single area, two area systems, to tune the parameters of the PID controller. (Emulation process)
The single area and two area system modeling are based on transfer function approach in H. Saadat's Power system analysis Tata McGrawhill edition 2002.
Normal PID controller work with fixed values of constant Kp, Ki, Kd. Parameter values have been chosen based on Routh Hurwith criterion. However the choice of the parameters are limited by the system specifications.
However, in a system, if inputs and the corresponding targets are identified, it can be implemented using ANN for the input - target pair.
Feed forward neural network architecture is chosen for the design of the controller, which is trained by a back propagation algorithm, Levenberg-Marquardt method. This method is applied for its superiority in convergence. Training has been carried out using NNTOOL box in MATLAB. TANSIG is employed as transfer function in the hidden layer and PURELIN in the output layer. Then the obtained weights and biases are chosen as the initial weights and biases.
The range over which error signal is in transient state, is observed. Corresponding values of the proportional, integral and derivative constants are set. This set is kept as target. Range of error signal is taken as the input. This input - target pair is fed and new neural network is formed using "nntool" in the MATLAB Simulink software. Updated weights and biases are given to a fresh neural network. Now the neural network is ready for operation.
The error signal is given as input to the neural network using MATLAB function. Desired target for each input value is obtained. The fresh neural network is written as program and is incorporated in the MATLAB function tool, in simulink diagram. Thus for each error signal fed as input, trained PID controller parameters KP, KI, KD are given back as output to called MATLAB function tool in simulink diagram.
As the neural network developed is purely dependent on the area control error signal, the network trained can be used for both single and two area systems. Further as the neural network is independent of the time instant, the trained network is more reliable for all disturbances which may occur at different time instances.
Comparison of responses with conventional intergral and PID controller show that the neural network controller has quite satisfactory generalization capability, feasibility and reliability as well as accuracy in both single area and two area system.
2.4.2 LOAD FREQUENCY CONTROL FOR A TWO AREA INTERCONNECTED POWER SYSTEM USING A ROBUST GENETIC ALGORITHM CONTROLLER
( B. Venkata Prasanth, Dr S.V. Jayaram Kumar [no date] )
In this paper a new robust load frequency controller for a two area interconnected power system is presented to quench the deviations in frequency and tie line power due to different load disturbances using genetic algorithm which is also an adaptive control method. The dynamic model of the system is developed without the integral control. The area control error is also not included.
The power system is represented using frequency deviation, rate of frequency deviation and its derivative as variables namely âˆ†f1, âˆ† f1 and âˆ†f1 and âˆ†f2, âˆ†f2 and âˆ†f2 of the two areas concerned.
The system frequency deviations are zero before any disturbance in the power system. Assuming a step load change, the system behavior is observed when the GA is incorporated in area 1, or area 2, or both areas.
In this work, the optimum adjustment of the classical AGC is investigated using genetic algorithms and performance indices, namely the integral of time - multiplied absolute value of error
S = âˆ« t|e(t)| dt
In this study, the optimal values of the parameters âˆ†f1 or âˆ†f2, and âˆ†f1 or âˆ†f2 which minimize an array of different performance indices are easily and accurately computed using a genetic algorithm.
In a typical run of the GA, an initial population is randomly generated. It is referred to as the 0th generation. Each individual has an associated performance index value. Using the performance index information, the GA then produces an new population.
The application of the GA involves repetitively two steps:
The calculation of the performance index for each of the individuals in the current population. To do this, the system must be simulated.
The genetic algorithm then produces the next generation of individuals using the reproduction, cross over and mutation operators.
The case study with GA controllers in both areas for a load change in area 1 gives the best results. Although the responses are oscillatory, the magnitude of the overshoot is less than that of other cases. It is also observed that the values of the maximum overshoots are increasing with increase in load changes. Settling times for frequency deviation and tie line power deviations is less as compared to the other schemes.
2.4.3 FUZZY LOGIC BASED AUTOMATIC LOAD FREQUENCY CONTROL OF TWO AREA POWER SYSTEM WITH GRC
(P.Aravindan and M.Y. Sanavullah [no date])
This paper describes the automatic generation control of interconnected reheat thermal system using
Proportional- Integral (PI)
Extended Proportional - Integral (extended PI)
Fuzzy logic controller (FLC)
System investigation has been carried out on two area reheat power system considering GRC. Dynamic response of change in frequencies âˆ†F1, âˆ†f2 and âˆ†Ptie for 1% step load perturbation is obtained using MATLAB. Proper assumptions and approximations are made to linearise the mathematical equations which describe the system and transfer function model
GRC of 3% p.u MW/min are usually applied to reheat turbines.
126.96.36.199 Conventional PI controller
Gain Kp and Ki has been optimized using Integral Square Error ISE criterion. For ISE technique, the objective function used is
J = âˆ«(âˆ†Ptie² + âˆ†Fi²) âˆ†T
where, âˆ†F = change in frequency and
âˆ†Ptie = change in tie line power
The two area thermal system is simulated with PI controllers.
188.8.131.52 Conventional Extended PI controller
In this control scheme an exponential decaying factor (Î») is chosen as follows,
h(t) = e -Î»t u(t)
the extended integral control is given by
âˆ« e -Î»(t-Æ®) âˆ†(Æ®) d Æ®
With its s-domain function of
The decaying factor of extended PI varies in proportion to the degree of deviation of feedback signals. For large overshoot, large value of decaying factor should be selected to reduce the effects of the error,while small decaying factor for small error.
184.108.40.206 Fuzzy logic controller
The design of FLC can be normally divided into three areas namely allocation of area of inputs, determination of rules and deffuzifying of output into a real value.
In this paper the proposed fuzzy logic controller takes the input as ACE and ACE.
ACE is given as
ACEi = âˆ†FiBi + âˆ†Ptie
7 membership functions have been used to explore the best settling time, namely Negative Big NB, Negative Medium NM, Negative Small NS, Zero ZO, Positive Small PS, Positive Medium PM, Positive Big PB.
Defuzzification to obtain crisp value of LFC output is done by center of area method.
The system is simulated for a step load disturbance of 1% on either area.
The system performance is observed on the basis of dynamic parameter (i.e) settling time.
The results show that the FLC yields much improved control performance when compared to PI and extended PI.
The first step in the analysis and design of a control system is mathematical modeling of the system. Two methods are generally used, the transfer function method and the state variable approach. Here, since the transfer function method is used, the system is first linearised by making use of proper assumptions and approximations.
3.1 GENERATOR MODEL
One of the essential components of power systems is the three phase ac generator known as synchronous generator or alternator.
Î”Pm(s) 1/2Hs Î”â„¦(s)
Figure 2.1 Transfer function model for generator model
3.2 LOAD MODEL
The load on a power system consists of a variety of electrical devices. For resistive loads, such as lighting and heating loads, the electrical power is independent of frequency. Motor loads are sensitive to changes in frequency. How sensitive it is to frequency depends on the composite of the speed-load characteristics of all the driven devices.
Î”Pm(s) 1/(2Hs+D) Î”â„¦(s)
Figure 2.2 Transfer function model for load model
3.3 PRIME MOVER MODEL
The source of mechanical power is commonly known as prime mover. The model of the turbines relates change in mechanical power output Î”Pm to changes in say steam valve position Î”Pv for a steam turbine. Different types of turbines vary widely in characteristics. The simplest prime mover model for the non-reheat steam turbine can be approximated with a single time constant TT. The time constant TT is in the range of 0.2 to 2.0 seconds.
Î”PV(s) 1/(1+TTs) Î”Pm(s)
Figure 2.3 block diagram for a simple non-reheat steam turbine
3.4 GOVERNOR MODEL
When the generator electrical load is suddenly increased, the electrical power exceeds the mechanical power input. This power deficiency is supplied by the kinetic energy stored in the rotating system. The reduction in kinetic energy causes the turbine speed and, consequently, the generator frequency to fall. The change in speed is sensed by the turbine governor which acts to adjust the turbine input valve to change the mechanical power output to bring the speed to a new steady-state.
Figure 2.4 Speed governing system
Combining all the components involved in the power system gives the following model:
Î”Pref(s) Î”Pg Î”PV Î”Pm
1/(1+Tgs) 1/(1+TTs) 1/(2Hs+D)
Governor Turbine Rotating mass
Figure 2.5 LFC block diagram of an isolated system
3.5 AUTOMATIC GENERATION CONTROL
When the load on the system is increased, the turbine speed drops before the governor can adjust the input of the steam to the new load. As the change in the value of speed diminishes, the error signal becomes smaller and position of the governor falls gets closer to the point required to maintain a constant speed. However the constant speed will not be the set point, and there will be offset. One way to restore the speed or frequency to its nominal value is to add an integrator.
The integral unit monitors the average error over a period of time and will overcome the offset. Because of its ability to return a system to its set point, integral action is known as the rest action. Thus, as the system load change continuously, the generation is adjusted automatically to restore the frequency to the nominal value .This scheme is known as the "automatic generation control" (AGC).
In an interconnected system consisting of several pools, the role of the automatic generation control (AGC) is to divide the loads among system, station generators so as to achieve maximum economy and correctly control the scheduled interchanges of tie-line power while maintaining a reasonably uniform frequency.
(H. Saadat's Power system analysis Tata McGrawhill edition 2002)
3.6 AGC IN A SINGLE AREA SYSTEM
With the primary LFC loop, a change in the system load will result in a steady-state frequency deviation, depending on the governor speed regulation. In order to reduce the frequency deviation to zero, we must provide a reset action. The rest action can be achieved by introducing an integral controller to act on the load reference setting to change the speed set point. The integral controller increases the system type by one which forces the final frequency deviation to zero. See figure below. The integral controller gain KI must be adjusted for a satisfactory transient response.
Î”Pref(s) Î”Pg Î”PV Î”Pm
1/(1+Tgs) 1/(1+TTs) 1/(2Hs+D)
Governor Turbine Rotating mass
Figure 2.6 AGC for an isolated power system
3.7 AGC IN MULTIAREA SYSTEM
In many cases, a group of generators are closely coupled internally and swing in unison. Furthermore, the generator turbines tend to have the same response characteristics. Such a group of generators are said to be coherent. Then it is possible to let the LFC loop represent the whole system, which is referred to as control area. The AGC of a multi-area system can be realized by studying first the AGC for a two-area system. Consider two areas represented by an equivalent by an equivalent generating unit interconnected by a lossless tie line with reactance Xtie. Each area is represented by a voltage source behind an equivalent reactance as shown in Figure 2.6
Figure 2.6 Equivalent network for two area power system
During normal operation, the real power transferred over the tie line is given by
P12 = |E1| |E2| sinÎ´12
Where X12 = X1+ Xtie+ X2, and Î´12= Î´1 - Î´2.
The tie line power deviation then takes on the form
Î”P12 = Ps(Î”Î´1 - Î”Î´2)
The tie line power flow appears as a load increase in one area and a load decrease in the other area, depending on the direction of the flow. The direction of the flow. The direction of flow is dictated by phase angle difference; if Î”Î´1 > Î”Î´2, the power flows from area 1 to area 2. A block diagram representation for the two-area system with LFC containing only the primary loop is shown in Figure 4.3.
Figure 2.7 Two area system with primary LFC loop
3.8 TIE-LINE BIAS CONTROL
In the normal operating state, the power system is operated so that the demands of the areas are satisfied at the nominal frequency. A simple control strategy for the normal mode is
Keep frequency approximately at nominal value.
Maintain the tie-line flow at about schedule.
Each area should absorb its own load charges.
Conventional LFC is based upon tie-line bias control, where each area tends to reduce the area control error (ACE) to zero. The control error for each area tends to consists of linear combination of frequency and tie-line error.
ACEi = Î£nj=1 Î”Pij +Ki Î”Ï‰
The area bias Ki determines the amount of interaction during a disturbance in the neighboring areas. An overall satisfactory performance is achieved when K is selected equal to the frequency bias factor of that area, i.e., Bi =1/Ri +Di . Thus, the ACEs for a two area systems are
ACE1 = Î”P12 +B1 Î”Ï‰1
ACE1 = Î”P21 +B2 Î”Ï‰2
Where Î”P12 and Î”P21 are departures from scheduled interchanges. ACEs are used as actuating signals to activate changes in the reference power set points, and when steady state is reached, Î”P12 and Î”Ï‰ will be zero. The integrator gain constant must be chosen small enough so as not cause the area to go into a chase mode. The block diagram of a simple AGC for two area system is shown in Figure 2.8.
Figure 2.8 AGC block diagram for two area system
3.9 LOAD FREQUENCY CONTROL WITH GENERATOR RATE CONSTRAINTS (GRC)
In practical steam turbine system due to thermodynamic and mechanical constraints, there is a limit to the rate at which its output power can be changed. This limit is referred to as GRC. Rate limits are imposed to avoid a wide variation in process variables like temperature and pressure for the safety of the equipments. Generally, GRC of 3%/p.uMW/min are usually applied to reheat turbines. Several methods have been proposed to consider the effect of GRC for the design of automatic generation controller. When GRC is considered, the system dynamic model becomes non linear and linear control techniques cannot be applied for optimization of the controller settings. (Adia Issop, load frequency control, a survey of different methodologies, 2006 cited Machowski and Balek 1998,p 310)
Fig 3.9 Non linear turbine model with GRC
ARTIFICIAL NEURAL NETWORK
The science of artificial neural networks is based on the neuron.
Neurons are the fundamental elements in the central nervous system. The diagram below (Fig.4.1) shows the components of a neuron.
Fig 4.1 component of a neuron
A neuron is made up of 3 main parts -dendrites, cell body and axon. The dendrites receive signals coming from the neighboring neurons. The dendrites send their signals to the body of the cell. The cell body contains the nucleus of the neuron. If the sum of the received signals is greater than a threshold value, the neuron fires by sending an electrical pulse along the axon to the next neuron. The following model is based on the components of the biological neuron (Fig. 4.2). The inputs X0-X3 represent the dendrites. Each input is multiplied by weights W0- W3. The output of the neuron model, Y is a function, F of the summation of the input signals
Fig 4.2 block diagram of a neuron network
4.2 ADVANTAGES OF ANN
1. The main advantage of neural networks is that it is possible to train a neural network to perform a particular function by adjusting the values of connections (weights) between elements. For example, if we wanted to train a neuron model to approximate a specific function, the weights that multiply each input signal will be updated until the output from the neuron is similar to the function.
2. Neural networks are composed of elements operating in parallel. Parallel processing allows increased speed of calculation compared to slower sequential processing.
3. Artificial neural networks (ANN) have memory. The memory in neural networks corresponds to the weights in the neurons. Neural networks can be trained offline and then transferred into a process where adaptive learning takes place. In our case, a neural network controller could be trained to control an inverted pendulum system offline say in the simulink environment. After training, the network weights are set. The ANN is placed in a feedback loop with the actual process. The network will adapt the weights to improve performance as it controls the pendulum system.
The main disadvantage of ANN is they operate as black boxes. The rules of operation in neural networks are completely unknown. It is not possible to convert the neural structure into known model structures such as ARMAX, etc. Another disadvantage is the amount of time taken to train networks. It can take considerable time to train an ANN for certain functions
4.3 TYPES OF LEARNING
Neural networks have 3 main modes of operation - supervised, reinforced and unsupervised learning.
In supervised learning the output from the neural network is compared with a set of targets, the error signal is used to update the weights in the neural network.
Reinforced learning is similar to supervised learning however there are no targets given, the algorithm is given a grade of the ANN performance.
Unsupervised learning updates the weights based on the input data only. The ANN learns to cluster different input patterns into different classes.
4.4 NEURAL NETWORK STRUCTURES
There are 3 main types of ANN structures
1.single layer feedforward networks
2. multi-layer feedforward networks
3. recurrent networks
The most common type of single layer feedforward network is the perceptron. Other types of single layer networks are based on the perceptron model. The details of the perceptron are shown below (Fig. 4.3).
Fig 4.3 block diagram of perceptron
Inputs to the perceptron are individually weighted and then summed. The perceptron computes the output as a function F of the sum. The activation function, F is needed to introduce nonlinearities into the network. This makes multi-layer networks powerful in representing nonlinear functions.
There are 3 main types of activation function
Different activation functions affect the performance of an ANN.
Log-sigmoid function Tan-sigmoid function Linear function
The output from the perceptron is
y[k] €½€ f (wT [k].x[k])
The weights are dynamically updated using the back propagation algorithm. The difference between the target output and the actual output (error) is calculated.
e[k] €½€ T[k] €€ y[k]
The errors are back propagated through the layers and the weight changes are made. The formula for adjusting the weights is
w[k €«1] €½€ w[k] €«€ m.e[k].x[k]
Once the weights are adjusted, the feed-forward process is repeated. The weights are adapted until the error between the target and actual output is low. The approximation of the function improves as the error decreases. Single-layer feedforward networks are useful when the data to be trained is linearly separable. If the data we are trying to model is not linearly separable or the function has complex mappings, the simple perceptron will have trouble trying to model the function adequately.
4.4.2 Multi-layered perceptrons
Neural networks can have several layers. There are 2 main types of multi-layer networks namely feedforward and recurrent.
In feedforward networks the direction of signals is from input to output, there is no feedback in the layers. The diagram below (Fig. 4.4) shows a 3-layered feedforward network.
Input layer Hidden layer Output layer
Fig. 4.4: Diagram of a multi-layered perceptron
Increasing the number of neurons in the hidden layer or adding more hidden layers to the network allows the network to deal with more complex functions.
The weights in MLP's are updated using the backpropagation learning.
There are two passes before the weights are updated.
In the first pass (forward pass) the outputs of all neurons are calculated by multiplying the input vector by the weights.
The error is calculated for each of the output layer neurons.
In the backward pass, the error is passed back through the network layer by layer. The weights are adjusted according to the gradient decent rule, so that the actual output of the MLP moves closer to the desired output. A momentum term could be added which increases the learning rate with stability.
The second type of multi-layer networks are recurrent (Fig.4.5). Recurrent networks have at least one feedback loop. This means an output of a layer feeds back to any proceeding layer.
Input layer Hidden layer Output layer
This gives the network partial memory due to the fact that the hidden layer receives data attime t but also at time t-1. This makes recurrent networks powerful in approximating functions depending on time.
(Tim Callinan Artificial Neural Network identification and control of the inverted pendulum Aug 2003)