APPLICABILITY AND SUITABILITY OF RADIAL BASIS FUNCTION NEURAL NETWORK IN EXCITATION CONTROL SYSTEM OF SYNCHRONOUS MACHINE.
ABSTRACT: The supply of stable reliable and economic electric energy is a major determinant of industrial progress and consequent rise in the standard of living the world over. The high gain and fast action of excitation system produces the negative damping torque to the rotor of the synchronous generator which is handled with the introduction of power system stabilizer (PSS). The PSSs mostly discussed/proposed in literature are useful for specified fixed operating conditions. The varying load conditions are a challenge for stability of power system operation. The demand of power system stability is increasing along with the popularity of electrical products. Therefore variant PSS is required which should possess self-learning and adaptation properties of handling the changes and uncertainties in the system.
To solve this problem radial basis function neural network (RBFNN) based PSS with single machine connected at infinite bus (SMIB) model is proposed by taking angular frequency as an input to improve the transient and dynamic stability of electrical power system at varying loads.
The simulations results using Matlab/Simulink and neural network toolbox are compared with conventional and proposed RBFNN PSS at varying load conditions. The applicability and suitability of the proposed PSS show the improvements in transient and dynamic state stability enhancement.
Keywords:Power system stability Synchronous machine Power system stabilizer Neural network Radial basis function Simulink/Neural network toolbox.
Modern electrical power system (EPS) is characterized by extensive interconnections and increasing dependence on control for optimum utilization of existing resources. The supply of stable reliable and economic electric energy is a major determinant of industrial progress and consequent rise in the standard of living the world over. The need for improved power availability and power quality has been increasing over the years. Stability of power systems has been and it will continue to be the major concern in power system operations.
The high gain and fast action of excitation system produces the negative damping torque to the rotor of the synchronous generator. The controller referred as power system stabilizer (PSS) is desired to be connected with synchronous generator to compensate the negative effect of fast action and high gain of automatic voltage regulator (AVR) and other sources of negative damping .
These high gain AVRs cause a large phase lag at low system frequencies which are greater than the excitation system frequency. Therefore AVR has an important effect of minimizing synchronizing torque during sudden disturbances but it affects the damping torque negatively . The unwanted impact of these regulators can be compensated by introducing additional signals in the feedback loop. These additional signals are mostly taken from angular speed by inserting an additional stabilizing signal into the reference voltage summing junction of the excitation system. The function of the PSS is to detect an oscillation and to generate an additional signal used to provide positive damping to the AVR loop of generation unit. The mostly used existing PSS focused in literature is known as lead-lag network [1 6] consists of three stages namely a phase compensation stage a signal washout stage and a gain block stage. It must produce electrical torque component on the rotor in phase with speed deviations
for compensating the rotor damping or oscillation. The input signal of PSS may be any one of the generator speed frequency or electrical power. For a given input signal the parameters of PSS must compensate the gain and phase characteristics of the excitation system of the synchronous generator [1 2 6 9-11]. The parameter gain settings of the conventional PSS are mostly constant and are determined at fixed particular operating or loading conditions. The performance of these PSS is better for those particular working conditions but in case of variable loading conditions their response is poor [1 2 10-11].
The PSSs mostly discussed/proposed in literature are useful for fixed working conditions. The gain settings of these PSSs are obtained at specified operating conditions which are a challenge for varying loading conditions. The problem of instability may be created if these loading conditions change from one value to another.
1.1. Literature Review (Power System Stabilizer)
In literature a considerable efforts are taken on the application of power system stabilizer to enhance the stability of the electrical power system. 1.1.1. Conventional PSS: Heffron and Phillips  were the pioneer of representing the small disturbance model with linearized parameters of a single synchronous machine connected to an infinite bus (SMIB) system. They investigated that the large turbo-generators under excited operation are affected due to modern amplidyne voltage regulators. The application of modern voltage regulators for excitation system much affects the dynamic stability of turbo-generators in the under-excited region.
De Mello et al  in this respect explored the small scale stability characteristics of a SMIB through external impedance by means of frequency response analyses showing effects of machine and system parameters AVR gain and stabilizing functions.
Chan and Hsu  presented an optimal variable structure power system stabilizer for improving the dynamic stability of the synchronous machine by providing the damping torque component to the generator.
Gupta et al  proposed a criterion for designing a PSS to cancel the negative damping torque produced in a synchronous machine and AVR.
Yuan and Chang  investigated digital and analog stabilization of power system using a proportional-integral (PI) PSS by the root-locus method for obtaining the optimal stabilizer gains of the PI stabilizer.
Hsu and Liou  proposed a self-tuning proportionalintegral-derivative (PID) PSS for improving the dynamic stability of a single synchronous generator over a wide range of loading conditions. They proposed that the self-tuning PID-PSS can enhance both the transient stability and the dynamic stability of the generator.
Wu and Hsu  proposed a self-tuning PID-PSS for multimachine system. P. Kundur  discussed the stability criterion with respect to synchronous equilibrium and introduced the mathematical expressions for the dynamic stability as a set of linear time invariant differential equations.
1.1.2 Classification based on artificial intelligent (AI) techniques: Recently researchers are concerned with artificial intelligence techniques as an effective tool to resolve many power system stability problems and to develop an efficient PSS that could be more effective when properly joined together with conventional mathematical approaches. These techniques include artificial neural network (ANN) Fuzzy logic and intelligent optimization and hybrid artificial intelligent techniques discussed by Lokman .
184.108.40.206. Artificial neural network and fuzzy logic based PSS: Wu and Hsu  investigated tuning of proportional integral (PI) type PSS using an artificial neural network (ANN) by taking active power (P) and power factor (PF) as the input signals to the ANN. They proposed that the ANN based PSS provides good damping over a wide range of loading conditions. Zhang et al  suggested adaptive ANN PSS and Liu et al  designed an indirect adaptive neural network based PSS (INDC) consisting of a neuroidentifier and a neuro-controller.
Majid et al  replaced a PSS with a fuzzy logic controller in which frequency deviation and acceleration of synchronous generator rotor were taken as input signals to the controllers. Hariri and Malik  proposed a fuzzy logic based PSS with learning ability that combines the advantages of both nueral network and fuzzy logic control schemes. Nallathambi and Neelakantan  proposed fuzzy logic based PSS for increasing stability of two area four machine system.
220.127.116.11 Optimization based intelligent techniques: These techniques include genetic algorithm (GA) particle swarm optimization (PSO) Tabu search (TS) etc. Abido et al  proposed the Tabu search algorithm for SMIB and multimachine power systems for various loading conditions to find optimal parameters of conventional lead-lag PSS. AlHinai  proposed the particle swarm optimization based PSS for self-tuning of parameters of PSS. Haddin et al  proposed PSO based coordination of AVR-PSS and AGC for improving the dynamic stability of the generator and in addition Hemmati et al  proposed PID-PSS based hybrid genetic algorithm for SMIB.
18.104.22.168 Hybrid artificial intelligent techniques: Two or more artificial intelligent techniques applied simultaneously in series or in integration to obtain successful results are known as hybrid AI techniques. Djukanovic et al  presented adaptive fuzzy logic controller based on unsupervised learning neural nets for increasing the transient stability of a hydropower system. To avoid these drawbacks Abido and Abdel-Magid  proposed a fuzzy basis function network (FBFN) to develop PSS where the strengths of both fuzzy logic and neural networks were combined by emerging the learning abilities of ANN to fuzzy logic systems. Afzalian and et al  proposed the tuning optimal parameter of neuro-fuzzy PSS technique with genetic algorithm on SMIB.
2.PROBLEM STATEMENT AND SUGGESTED SOLUTIONS
The power system stabilizers mostly discussed in literature are useful for fixed working conditions [30-32]. The gain settings of these PSS are obtained at specified operating conditions and hence there is a challenge for light medium and heavy loading conditions. These gain settings are useful for those operating conditions at which they are designed. The problem of instability may be created if these loading conditions change from one value to another value.
The demand of power system stability is increasing along with the popularity of electrical products. An AVR is used to maintain changes in the output voltage avoiding the malfunction of the electrical load terminals. Many synchronous machines are manufactured with high gain fast acting voltage regulators for increasing the dynamic stability to keep the generator in synchronism with the interconnected power system during sudden disturbances. The high gain and fast action of excitation system produces the negative damping torque to the rotor of the generator. Therefore a controller referred as power system stabilizer is needed to be connected with synchronous generator to compensate the negative effect of fast action and high gain of AVR and other sources of negative damping [31-32].
From this detailed discussions a power system stabilizer is required which should possess self-learning and adaptation properties of handling the changes and uncertainties in the system. Hence due to these problems an artificial neural network based PSS is proposed by taking angular frequency as an input to improve the transient and dynamic stability of electrical power system.
The neural network (NN) possesses great prospective capabilities because they have been developed on logical mathematical formulation and versatile and well-known mathematical back grounds . The easily modeling of complex system is the superiority of neural networks to conventional controller system; they require a precise information and knowledge with mathematical models. Sometimes this information and knowledge is missing for conventional controllers; hence the problem becomes more crucial. The NN does not require such conditions and can handle such complex systems very relatively easier. They require input-output mapping relationships and their data to learn. They can learn and train during on line and off line situation of the process of system [34-36]. They do not require mathematical modeling computer programming and deeply understanding of the system. They are naturally generalized and parallel distributed in their architecture structures [31-36].
Feedforward neural network based PSS is p research work. Popular type of FFNN known function" (RBF) network with orthogonal lea learning algorithm is proposed. The simulatio Matlab/Simulink and neural network toolbo and discussed in detail with conventional PI RBFNN power system stabilizer.
3.MODELOFPOWERSY PROPOSED METHODOLOGY The synchronous generator connected to a bu transmission line can be represented equivalent circuit with external impedance ( 31-32] popularly known as single synchr (generator) connected to an infinite bus ( Figure 1 shows the equivalent circuit of SMI
The linearized model of synchronous excitation system developed based on the he linearized equations for the synchronou given by (the subscripts are dropped for co briefly explained in [1-8 31-32].
The complete state-space model of the synchronous generator with excitation system with state variables and VREF and Tm are the driving functions by assuming that VS is zero. For all operating conditions the power system dynamics and PSS can be modeled by a set of nonlinear differential equation as [1-8 31-32]:Equation
The voltage regulator is often assumed to introduce negative damping and to compensate the damping and to improve the system dynamic stability in general artificial signals for generating damping torque in phase with the angular frequency are produced which are known as "supplementary stabilizing signals (power system stabilizers) network" [1 31-32]. To obtain the error fed to the AVR controller stabilizing signals of PSSs are injected in excitation systems at the summing point where terminal voltage and reference voltage are added. Such PSS signal Vs generally obtained from speed/frequency deviation and is processed through a suitable network to obtain the desired phase relationship. the terminal voltage for a prolonged error in a frequency such as might be in an overload condition. The second component shown in equation (7) represents a lead compensation pair used to improve the phase-lag through the network from VREF to at the power system frequency of oscillation.
The phase characteristics f the power system stabilizer depend upon the system parameters and the loading condition. The required phase-lead at any loading condition can be obtained by choosing the suitable values of t1 t2 t3 and t4 time constants. The PSS produces positive component of damping torque that is in phase with the frequency deviation and used to compensate negative damping in rotor which requires a phase-lead circuit for compensating the phase-lag between exciter input and the resulting electrical torque. For this purpose a high-pass filter the field exciter voltage [1 31 32].
The complete linearized block model of synchronous generator including automatic voltage regulator and PSS is shown in Figure 3 and 4 (two prevalent perspectives) with the parameters and numerical values mentioned in [1 31 32]. The input to the proposed power system stabilizer is speed/frequency and output is applied at the summing junction of the reference voltage.
4.DESIGNING METHODOLOGY OF RBF NEURAL NETWORK
In this methodology an orthogonal least squares (OLS) algorithm of RBF automatically chooses a suitable number of neurons in the hidden layer of a RBF network from a set of input data. The RBF networks are not only universal approximators but they also have the best approximation property.
For a particular application RBF networks are mostly faster than other types of feedforward neural networks.
A radial basis function network can be utilized to approximate a function. The neurons are attached to the hidden layer until it meets the precise mean square error goal. In case of training of RBF network the below steps in MATLAB software are repeated until the network's mean square error falls below the goal .
To find the input vector with the greatest error.
A radial basis (radbas) transfer function neuron is added with weights equal to the vector of step 2.
The linear (pureline) transfer function layer weights are redesigned to minimize error.
It is found that Nineteen (19) neurons are created in the hidden layer.
One (01) neuron or node with linear transfer function is used in the output layer.
Error goal is 0.00001
Spread constant is 1.4 4.2PERFORMANCEWITHRADIALBASIS FUNCTION NETWORK
The transient responses of terminal voltage and dynamic response of frequency deviation with conventional PSS PID-PSS and RBF-PSS for synchronous generator are compared and discussed as shown in Figures 6-9.
Transient responses of terminal voltages (Vt)5 The transient performance of the proposed power system stabilizer is compared with the CPSS PID-PSS at normal4 loading conditions mentioned above in detail.3 Dynamic performance of speed/frequency deviation The performance of the proposed RBF power system stabilizer for speed/frequency deviation is investigated at1 normal loading conditions (P= 1.0 pu and Q= 0.62 pu).
5. COMPARISON OF RESULTS
From a detailed discussion on the results obtained by applying FFNN RBF network it is clear that the performance of the RBF networks is better than the conventional type PSSs. The RBF networks have favorable characteristics of the best approximation property and a compact network structure. The RBF networks have a faster training time than MLP networks as described in [new paper of JBASR]. However RBF networks require more hidden layer neurons than MLP networks . The architectures of RBF networks are shown in below Table 1.
Table 1: The architectures of RBF networks
Table 2: The rise time settling time and p. u overshoot comparisons of PSSs in case of frequency deviation responses
Type of PSS###Rise time###Settling###Overshoot
Tables 2 and 3 describe the comparisons of terminal voltage and frequency deviation in case of proposed types RBF network in terms of the rise settling times and per unit overshoot of all the types of PSSs.
In this work a simulation program technique has been developed that can narrowly analysis the operation of complete model of synchronous machine with AVR excitation LFC and PSS in the domain of transfer functions in order to determine the terminal voltage and speed/frequency responses of the model. With the help of this model we have focused on PID-PSS system of synchronous generator in order to replace with feedforward RBFPSS.
Table 3: The rise time settling time and p. u overshoot
comparisons of PSSs in case of Terminal voltage responses
Type of PSS###Rise time###Settling###Overshoot
Hence a PID-PSS system is developed then trained in parallel with RBF and compared the responses at trained data at operating conditions described in detail [1 31-32]. It is desired to design here a better controller for the power system stabilization system of synchronous generator in order to improve transient and dynamic stability of power system. This has been followed by some closing comments on the worth of this work.
The feedforward artificial neural network (FFANN) applications with promising performances in power system stability of synchronous generator excitation systems have been successfully implemented.
This work presents results concerning the use of feedforward neural networks to obtain a controller which incorporates the properties of a conventional PID controller. Popular type of feedforward neural networks namely radial basis function (RBF) networks has been proposed.
The simulation result indicates that the RBF-PSS control system ensures superior responses at normal as well as changing operating conditions. Comparisons of rise time settling time and p.u overshoot shown in Tables 2 and also specify the better performances of proposed technique.
FFNN controllers proffer improved performances in transient response of terminal voltages and good results of dynamic stability in case of angular speed/frequency.
As RBF NN yields dynamic presentation with the normal loading conditions at which they are trained and for other varying load conditions.
The particular conclusion concerned with the above architectures are outlined below A considerable shortcoming of MLP networks [JBASR plus other my paper references] are overcome with the application of proposed RBF-PSS. Due to its distinguishing properties simple network configuration proficient learning process and finest estimations which make the RBF networks most preferable in control applications.
In this research work RBF networks are trained by means of the orthogonal least squares (OLS) algorithm. This technique of OLS algorithm chooses proper number of the radial basis function centres from input information; for this reason the dilemma of selecting the most favorable number of first or hidden layer neurons is involuntarily resolved. For this work 25 neurons in the input layer with radial basis function as the activation function and one neuron with linear transfer function in the second or output layer are chosen for training.
Form the results it is obvious that the performance of radial basis function networks is as superior as can be accomplished and compared by all the types of PSSs. Furthermore RBF networks take faster training time than MLP networks. RBF networks require more number of hidden layer neurons than MLP networks for the solution of the same problem at the same time.
The small variations in the responses are not reflected clearly due to sturdy network stuck between the synchronous generator and the infinite bus system.
The understanding and familiarity which have been achieve from beginning to end of this research and its implementation has been enormously priceless. The work implicated in the exploration and analysis of this work has broadened our scale towards electrical power system control.
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