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Chapter I Introduction Introduction General With growing industrialization the transmission and distribution of electric power has gained tremendous importance. The trend is towards an integrated power network that will be immune to most of the man made and natural disturbances. In other words the stability and speed of response are the two conflicting criteria being imposed on such systems. To improve the system stability (constant voltage, constant frequency) a fast power flow control scheme is highly essential. In the recent years the HVDC transmission technology has attracted a lot of attention in is this regard. It has the capability of fast power flow control along with other advantages like; a) Handling bulk power b) Power flow under asynchronous conditions c) Power flow under faulted conditions d) Can supply Reactive Power with forced commutation e) Can improve the stability being a part of the AC Network But the control and co-ordination of HVDC systems is still a challenge for the Design engineers. The point-to-point two terminal HVDC links are gaining popularity day-by-day. The trend is towards building two terminal and parallel AC-DC-links to enhance the power transmission capability. Still the research has to go a long way on the control aspects of DC links to exploit all its advantages. Many researchers have presented their contributions to the DC link control on various aspects. The following reviews the various control strategies for HVDC links to improve AC-DC system performance during normal and abnormal operating conditions. Introduction 1.2 HVDC Control As mentioned one of the major advantages of using an HVDC link is the rapid controllability of transmitted power by the control of firing angles of the converters. The system control in an HVDC link tends to be quite complex with a hierarchy of controller structures (Fig. 1.1). With the advent of very fast micro-processors the complexity of such schemes are being minimised. Elaborate literature available in DC link control [1.1] have established the following control schemes for some obvious reasons. However, the standard is to subject the rectifier end with constant current and the inverter with constant extinction angle control. Although the standard controllers of the HVDC systems are well documented, a brief review is presented here for the sake of completeness. Fig. 1.1 Hierarchial Control Structure of a DC link 1.2.1 Rectifier Control The pole controIler(Fig.l.2) at the rectifier has two control modes i.e. minimum firing angle control and constant current control. Minimum Firing Angle Control The minimum firing angle is selected on the basis of minimum reactive power demand Introduction and sufficient positive voltage across non-conducting valves to ensure successful commutation. Typical value of 'a' ranges between 10° to 18° [1.2]. This control mode operates for low voltage levels on the rectifier terminal. Fig. 1.2 Block diagram of Converter Control Current Control The rectifier generally operates in this control mode during steady-state. The current is kept constant by making appropriate changes in the firing angle for changes in system voltage. 1.2.2 Inverter Control The inverter may operate in one of the following control modes 1. Extinction Angie Control 2. Current Control Extinction Angle Control (Figl.2) The inverter normally operates with this control in steady state. The advantage of using this control is primarily to avoid commutation failure and to minimise reactive power requirement. Typical value of extinction angle (yref) used is approximately 18°. 4 Introduction Current Control During disturbances such as DC line faults, starting of the system and power reversal, both rectifier and inverter operate in the current control mode. It has been demonstrated [1.1] that this control works efficiently for power reversal. The probability of commutation failure is minimised in this control mode because the extinction angle is always greater than the minimum limit(around 5°). Normally, the inverter is provided with current margin of 10%-20% to allow the current controller to operate at both the rectifier and the inverter ends independently [1.1], 1.2.3 Auxiliary Controls Most of the existing HVDC system have been designed for the well known economic and practical reasons. When integrated into a larger network, the fast power flow control capability of the DC links also offer an attractive method for enhancing overall system performance in eliminating AC system dynamic oscillations and improving transient stability performance [1.1]. The Power in a DC link can be modulated by the quantities derived from the AC system (such as frequency) in order to improve the security of the overall system. This is achieved by an additional power (or current) order derived from an emergency power controller or auxiliary controller. Power/Frequency Control When the DC link is used as a tie between two power systems, the frequency bias can be used to adjust the power flow over the tie to assist the system in difficulty. It is to be noted that an HVDC link has no inherent sensitivity to system frequency unless it is deliberately introduced in the control system. Without it, a constant powerflow can overstep a receiving system which has become separated from part on all of its load, even if governors cut-off all primary energy flow to the local generation. Similarly, a sending system can be brought eventually to a halt, if more power is required from it than the collective generation can produce. Thus, although it would first appear that there is little benefit in the frequency control for DC link between two systems so large that the link cannot be expected to influence the Introduction frequency of either; it is prudent to incorporate an element of frequency control which in the event of a partial break-up of a system, will prevent over-speed or under-speed [1.1]. Stabilization ofAC Ties When a DC link is connected to a system with weak AC ties to neighbouring systems, DC link power can be varied quickly and automatically, to balance the load flows and maintain stability if one of the AC ties trips. A DC tie used in parallel with an AC tie can be employed to damp the low frequency inter-area oscillations in the AC tie. The control signal used can be - the rate of change of AC tie line power (or current) or the phase angle difference across the AC tie. The DC tie can also provide frequency control for one end if the AC tie gets disconnected and can thus permit resynchronisation of the AC tie. Sub-Synchronous Damping Control A radial HVDC link connected to a thermal generating station can contribute to the negative damping of the torsional oscillations at subsynchronous frequency due to the interaction with the current controller. This problem usually surfaces when there are no parallel AC links. The power modulation controller mentioned earlier which is designed to damp low frequency rotor oscillations can aggravate the problem. However, a suitably designed subsynchronous damping controller (SSDC) with control signal derived from the rotor velocity can help to damp torsional frequency oscillations. Emergency Control An HVDC link employing the simplest of control strategies, buffers one system from the disturbances on the other. Power flow can continue unchanged in the worst-possible condition, but the option is available to vary power flow to assist the system in trouble to the extent to which the healthy system can be allowed without putting itself in difficulty, subject only to the rating of the link. In general, with suitable control, a disturbance originating in either system can be shared in a predetermined manner and the oscillations occurring in both the systems can be damped simultaneously. Substantial damping can be achieved with a very small amount of DC power modulation. 6 Introduction 1.3 The Problem As described, an HVDC system irrespective of point to point or multiterminal, is equipped with one or more of the complex control schemes. To overcome AC-system problems, a DC link is required to have fast power flow control, while on the other hand sharp rise and fall times may cause extensive stress on the converter valves and other associated equipments. Therefore, for enhancing the performance of the DC link controls it is often required to adapt alternative methods to conventional fixed gain PI/PID controllers to have an optimal compromise between the above requirements. It is a well known fact that, due to the high degree of non-linearity and uncertainty it is difficult to obtain any accurate mathematical description of the HVDC systems for designing any fixed gain controllers. Therefore, to obtain optimum system performance it is essential to go for some advanced control strategies, where the wide variations in the operating points and uncertain system configurations can be taken care of. Keeping the above factors in view extensive research has already been done in the area of DC link control. A number of HVDC control design.techniques have already been reported, which make use of optimal control theory. Alexandridis and Galanos [1.3] have proposed a Kaman filter based approach for an optimal current regulator for rectifier side. This approach leads to decentralized optimal control systems based on the decomposition of the initial system into interconnected and independent subsystems, and the design of a Kalman filter capable of reconstructing the states of each subsystem and the unknown inputs at the interconnection points. In essence the method tries to find out the control using some fast hand information regarding the plant model and disturbances. The performance of the plant when subjected to such control schemes is better as long as the plant model does not change appreciably. However, there is no guarantee as to the effectiveness of such schemes under more uncertain and large signal conditions. 7 Introduction Fig. 1.3 The Kalman Filter based optimal current regulator When integrated into a larger AC network, the fast power flow control capability of the DC link also offers an attractive method for enhancing overall system performance, for eliminating AC system dynamic oscillations or for improving transient stability performance. Fig. 1.4 Controlling the behaviour of generators by HVDC link To and David [1.5] have described a systematic investigation of the full potential of using HVDC link to ensure the stability of operation and enhance the performance of the interconnected AC systems [Fig. 1.4], Yet in another interesting application of adaptive control Alvis et al,[1.6] have described a microprocessor based self tuning control for the rectifier current regulator of an HVDC link. The main contribution of this paper is to choose the proportional, integral and derivative gains for the rectifier current regulator so as to maintain the damping factor for the dominant mode of the ac/dc system. The identification algorithm adopted was based on a recursive least-square 8 Introduction method with factorisation of the covariance matrix [Figl.5]. As a whole the control strategy comprises three distinct stages; the modeling of the ac/dc system, the choice of a recursive identification algorithm and a control design block. Plant Parameters Fig. 1.5 Self Tuning Regulator Scheme The main drawbacks of these type of controllers are • the identification procedure assumes a fixed plant model • this cannot accommodate large variations in the operating conditions • the noise rejection property is limited However, for some of the application particularly when the AC systems at both the ends are strong this type control is good enough. But it is difficult to use such schemes when either end of the dc link is a weak system. In this case the weaker AC system demands additional attention pertaining to the voltage instability and reactive power requirement at the converter bus. In its new role as a major element embedded in the AC network, an HVDC scheme must actively participate in the instantaneous scheduling of power according to the network conditions, which is a feature inherent to the AC systems. To and David[1.7] have presented a bang-bang-optimal control scheme to take care of the first swing instability and the subsequent instability caused by poor damping. The recursive least square algorithm with a variable 9 Introduction forgetting factor has been used for on-line identification of the AC/DC system parameters. A bang-bang optimal controller is used for resetting the optimal control except for a bang-bang action during the first swing for certain categories of faults, has been introduced. The decision when to implement the bang action and the timing of its duration are an important consideration for the controller design. From the above literature, it is apparent that, the HVDC transmission link is a non linear system that poses a difficult control problem because of the following reasons : • Presence of non-linear system components such as power transformers, converters and surge arrestors. • Variable nature and topology of the power system • Insufficient knowledge and data about the system • Presence of AC/DC filters which can often form resonant circuits with the power system • Generation of harmonics by the converters, which can interact with the controllers • Control strategy employed that has many operational modes due to system protection requirements Microprocessor-based adaptive controllers are increasingly being used within the industry to adapt controller parameters as functions of operating angle, system topology, and prior knowledge of system dynamics. However, there is scope for further improvement since very little on-line adaptation has been performed. In the brief literature review presented, it is found that most of the researchers have tried a number of schemes based on various optimal and adaptive control methods. And in all of them the model of the plant has been presumed to be fixed or only the parameters are identified (the order remaining same). But as mentioned, the HVDC system along with the associated AC systems is highly non-linear and uncertain. 10 Introduction Therefore, the design of controllers can not be carried out with any of the standard mathematical procedures. Rather a more intelligent human like control method which uses the approximate I/O inference methods should be developed and tested for its effectiveness. 1.4 Necessity of Intelligent Control Recently a lot of research in the application of knowledge based and Intelligent techniques to the control problems hints their effectiveness in HVDC links. Changes in environments and performance criteria, unmeasurable disturbances and component failures are some of the characteristics which necessitate intelligent control. Adaptive controller is the only choice when parameters uncertainty exists. However, adaptive controllers do not have long term memory and hence do not remember the optimal control parameters corresponding to various configurations of the plant. In such cases pattern recognizers have been used to classify the plant and choose the corresponding control parameters. Learning controllers can be used to choose between different adaptive algorithms, reference models or performance criteria. As more intelligent control systems are designed, it becomes more necessary to combine adaptation, learning and pattern recognition in novel ways to make decisions at various levels. On one hand one may use deep knowledge perhaps in the form of quantitative models along with qualitative reasoning for decision making and on the other hand, a simple rule-base derived from the experience of the process operator can also be used. The only requirement is that the decision making is automated so that the KBS system does not give advice on what action is best suited but actually goes ahead and implements the decision without checking with an operator. Control systems based on knowledge based systems, neural networks, genetic algorithms are all viable alternatives to those derived from conventional control theory. The Fuzzy controller is one such simple rule-based control system. The knowledge used for this are derived not only from an expert operator, but also from the designer of the systems. One of the main advantages of using a Fuzzy approach that the Fuzzy logic provides the best technique for knowledge representation that could possibly be devised for encoding knowledge about continuous variables. 11 Introduction On the other hand Artificial Neural Networks with its massive parallelism and ability to learn any kind of nonlinearity are used to address some of the very practical control problems. A neuro-controller (neural networks based control system) in general, performs a specific form of adaptive control, with the controller taking the form of a multilayer network and the adaptable parameters being defined as the adjustable weights. In general, neural networks represent parallel and distributed processing structures, which make them prime candidates for use in multivariable control systems. The neural network approach defines the problem of control as the mapping of measured signals and control actions. Thus, there are primarily two concepts prevailing over the domain of Intelligent Control and they are; 1. Fuzzy Logic based Control 2. Neural Network based Control In the first case, the controller is represented as a set of rules which accepts the input in the form of linguistic variables and gives the output in the form of linguistic variables. The advantages of such a controller are, • The approximate knowledge about the plant is required (not an accurate model like other optimal and adaptive control strategies) • Knowledge representation and inference is relatively simple and easy • Real time implementation is easier. In the second case, the controller is represented as a mapping between the inputs and outputs. Depending on a specific plant the map in the form of a network can be trained to implement any kind of control strategy. The network can' also be trained on-line to adapt to the changing conditions of the plant. The advantages of this controller are, • Parallel architecture makes faster implementation • Any kind of non-linear mapping is possible 12 Introduction • Training possible for various operating conditions, therefore, it can be adaptable to situations. The simple Fuzz1/ controller though represents a good non-linear controller cannot adapt its structure if the situation demands. Sometimes the Fuzzy controllers with fixed structures, fail to stabilise the plant under wide variations in the operating conditions. These type of controllers also lack the parallelism of Neural Controllers. On the other hand the Neural networks are very much adaptive to situations by adjusting their weights accordingly. The parallel architecture enables faster implementation of the control algorithm. However, in the presence of noise and other uncertainties the performance may deteriorate. Sometimes, in certain Neural Controller structures the model of the plant is required. But in case of plants whose model becomes highly uncertain it is difficult to use neural networks with fixed structure. In both the type of controllers the greatest advantage is the non-linearity which, if properly expanded (for a simple case) serves as a very good non-linear self tuning PI controller. To extract advantages of both the types of controllers it is wiser to use the combination of both, which leads to Fuzzy-Neural controllers. The new hybrid structure can be named as an Adaptive Fuzzy Controller. There are many structures of the aforesaid controllers used in practice. Some of them will be discussed in the following paragraphs. However, most of the above find wide use in small plants. For large-non-linear dynamic systems they are yet to be tested. In case of HVDC links as discussed, the situation demands such type controllers. The literature available in the Application of Intelligent Controllers to HVDC links is limited. V.K.Sood et al.[1.8] attempted to replace the rectifier side current regulator by a Neural Network based Controller [Fig. 1.6]. The paper discusses the feasibility and effectiveness of the controller and gives a comparative picture with the conventional controller. Here the rectifier side current controller has been completely replaced by a pair of Neural networks. One of them represents the fixed structure controller with a fixed set of weights. It is trained offline to adjust the weights for optimum system performance. The other 13 Introduction network is adaptable to the dynamic conditions of the plant and the v/eights automatically adjust themselves for various operating conditions, on-line. The results obtained for large and small signal disturbances are encouraging. 1.4.1 Intelligent Control Structures The failure of conventional fixed gain controllers in large non-linear dynamic systems has urged researchers to find alternate methodologies. Adaptive control is one such method where the changing conditions of the plants are taken into account to adjust the effective PID (proportional, derivative and integral) gains of the controllers. However, due to nonavailability of sufficient knowledge about the system the controllers do not work efficiently. Even some times the adaptive control degrades the performance if the plant model is incorrect. These are the reasons for finding more intelligent human like controllers for the plants described above. HVDC link is one such plant which needs efficient, fault tolerant, robust control strategies for reliable operation under normal and abnormal conditions. As discussed Neural networks and Fuzzy logic are the modem tools being used for control purposes. Several structures of the above controllers have been proposed in the literature . Some of them are in fact in use for controlling small systems. Extensive research can only tell the feasibility of such controllers in large systems. 1.4.2 Neural Controllers Models of dynamic systems and their inverses have immediate usage for control. In the literature on neural network architectures for control a large number of structures have been 14 Introduction proposed and used. Some of the well-established and well analysed structures are presented here. Supervised Control [1.9] (Fig. 1.7) ■ In some situations it may be desirable to design an automatic controller which mimics the action of the human operator. This has been called as supervised control. A neural network provides one possibility for this. Training the network is similar in principle to learning a system model. In this case however, the network inputs correspond to the sensory input information received by the human. The network target outputs used for training correspond to the human control input to the system. TrainedNeural Network Direct Inverse Control [1.10] (Fig.1.8) Neural Net based This utilises an inverse system model. The inverse model is simply cascaded with the controlled system in order that the composed system results in an identity mapping between desired response (i.e. the network inputs) and the controlled system output. Thus the network 15 Introduction £Cts directly as the controller in such a configuration. This is very common in robotics applications. However, this model clearly relies on the fidelity of the inverse model used as the controller. Model Reference Control [1.11] (Fig. 1.9) Here, the desired performance of the closed loop system is specified through a stable reference model M, which is defined by its input-output pair {r{t),yr (t)}. The control system attempts to make the plant output yp(t) match the reference model output asymptotically ; finally r(/) - .^(Oll ^ £ >f°r some specified constant e> 0. In this structure the error defined above is used to train the network acting as the controller. Clearly, this approach is related to the training of inverse plant model. In the case, when the reference model is the identity mapping the two approaches coincide. In general, the training procedure will force the controller to be a "detuned" inverse, in a sense defined by the reference model. NN based Reference Model Internal Model Control (IMC) [1.12] (Fig. 1.10) In this case the role of the system forward and inverse models is emphasised. The system 16 Introduction forward and inverse model are used directly as elements within the feedback loop. IMC has been thoroughly examined and shown to yield transparently to robustness and stability analysis. In internal model control a system model is placed in parallel with the real system. The difference between the system and model outputs is used for feedback purposes. This feedback signal is then processed by a controller subsystem in the forward path; the properties of IMC dictate that this part of the controller should be related to the system inverse. Given network models for the system forward and inverse dynamics the realization of IMC using neural networks is straight forward; the system model and the controller are realised using the neural network model. Predictive Control [1.13] (Fig. 1.11) In the realm of optimal and predictive control methods, the receding horizon technique has been introduced as a natural and computationally feasible feedback law. In this approach a neural network provides prediction of future plant response over the specified horizon. The predictions supplied by the network are passed to a numerical optimization routine which attempts to minimize a specified performance criteria in the calculation of a suitable control signal. 17 Introduction Fig. 1.12 Structure for Optimal Control In this application, the state space is partitioned into regions (feature space) corresponding to various control situations (pattern classes). The realisation of the control surface is accomplished through a training procedure. Since the time-optimal surface in general is non-linear, it is necessary to use an architecture capable of approximating a non-linear surface. One possibility is to first quantize the state space into elementary hyper-cubes in which the control action is assumed to be constant. This process can be carried out with an LVQ(Leaming Vector Quantisation) architecture. It is then necessary to have another network 18 Introduction acting as a classifier. If continuous signals are required a standard back-propagation architecture can be used. Adaptive Linear Control [1.15] (Fig. 1.13) The eonneetionist approach can be used in nonlinear control but also as a part of a controller for linear plants. The Hopfield network may be utilised as a dynamic controller for linear systems. In this case, elements of variable structure theory were utilised to construct the controller, and as a result the proposed controller is characterised by its robustness. It is also possible to include adaptation using some standard method. Fig. 1.13 Structure for Feedback Networks as Controllers The Hopfield network can also be used as a part of the adaptation mechanism. In this case the network is induced in the adaptation path and is used to minimize simultaneously square error rates of all the states. Here, the output of the network represents the parameters of a linear model for the plant. Reinforcement Learning Control [1:16] This kind of network makes use of low quality (plant error) feedback signal. While the performance measure for a supervised system is defined in terms of a set of target by means of a known error, reinforcement learning addresses the problem using any measure whose value can be supplied to the learning algorithm. Instead of trying to determine target controller outputs from target plant responses, one tries to determine target controller output that would lead to increase in a measure of plant performance. The "critic" block is capable of evaluating the plant performance and generates an "evaluation signal" which is used by the reinforcement 19 Introduction learning algorithm. This approach is appropriate when there is a genuine lack of knowledge required for applying more specialized learning methods. Gain Scheduling [1.17] (Fig. 1.14) This is an old control engineering technique which uses process variables related with its dynamics to compensate the effect of working in different operating regions. Here the neural network is used as an associative memory that relates the parameters of the controller with the state of the plant. The Hopfield network, and other connectionist architectures can be used for this purpose. 1.4.3 Fuzzy Controllers Two approaches are extensively followed for designing fuzzy controllers: Direct Fuzzy control and Indirect Fuzzy control. In Direct Fuzz}' control the conventional controller is completely replaced; while in Indirect control the conventional control parameters (Proportional, Integral and derivative gains) are adjusted with an inference method based on Fuzz}' logic. The structure of the Fuzzy controller largely depends on the input and output classifications. Some of the common and well understood models will be discussed here. 20 Introduction Fuzzy PID Controllers [1.18] (Fig. 1.15) Here the error and the rate of change of error are fuzzified and then fed to the Fuzzy decision block. The Fuzzy inference block refers to the rule-base to generate output Fuzzy sets and their membership grades. Then a defuzzification scheme is used to derive the normalised values of the output variables. It can be multiplied by a scaling factor to generate the actual input to the plant. These are of two types i.e. linear and non-linear. The symmetrical rule table is a characteristic of a linear Fuzz}' controller. However, very often the situations demand asymmetrical configurations and therefore the rule table is asymmetrical leading, to non-linear Fuzzy controllers. Also the method of defuzzification sometimes characterise a controller to be linear or non-linear. Fig. 1.15 Structure of the Fuzzy PID Controller Hybrid Fuzzy Controller [1.19] (Fig. 1.16) Often Fuzzy controllers have inputs generated by a conventional controller (e.g. combinations of integrators and differentiators). Typically the error is the input to the conventional controller. These types of controllers are robust and need a less complicated rule base. The lead/lag times can also be adjusted by choosing proper time constants for the conventional controller. Fig. 1.16 An Hybrid Fuzzy Controller 21 Introduction Fuzzy Adaptive Controller [1.20] (Fig. 1.17) Here the structure is same as that of Fuzzy PID controller. But the slope of the input membership functions are adjusted to adapt with the error. In this case since the membership function becomes adaptable, the controller becomes robust and insensitive to plant parameter variations. In addition to the slope of the membership functions the following parameters of the Fuzzy controller can also be adapted according to, • The set of rules and knowledge base • A finite set of values describing the universe of discourse. Fig. 1.17 Block Diagram for the Adaptive Fuzz}-' Controller Fuzzy Sliding Mode Controller [1.21] Although Fuzzy control is very successful especially for non-linear systems, there is a lack in design of such controllers with respect to performance and stability. The success behind the Fuzzy controlled plants is that it is similar to the sliding model control (SMC) which is, for a specific class of non-linear systems an appropriate robust control method. SMC can be applied especially in the presence of model uncertainties, parameter fluctuations and disturbances provided that the upper bounds of their absolute values are known. For the FSC (Fuzz}' Sliding mode Controller) whose input is an error vector e and whose output is a scalar control value u, the general design rules may be formulated as: 22 Introduction R\ :Tne normalised control value UN (controller output) should be negative above the switching line and positive below it. R2 '.Normalised states (Controller inputs) eN,eN.... that fall out of the phase plane should produce maximum value |max respective sign of UN . i?3; jt/_y | should increase as the distance 'd' between the actual state and the line perpendicular to the switching line grows, for the following reasons : • Normalised state eN,eN.... that are situated at the boundaries inside the phase plane produce maximum values with respective sign of UN so that discontinuities at the boundaries of the phase plane can be avoided. • The central domain of the phase plane can be arrived at very quickly. This controller has been successfully applied to small plants and the results obtained are better than the sliding mode conu-oller. The sliding mode controller shows chattering effects whereas, the Fuzzy sliding mode controller is smooth. Fuzzy Model Following Controller [1.22] (Fig. 1.18) Fig. 1.18 Fuzzy-model Following Control System For a conventional Fuzzy control system, the resulting performance is difficult to predict. In order to have the advantages of a Fuzzy logic controller with desired performance, a Fuzzy adaptive controller is introduced to a model-following control system. Fig. 1.18 shows the basic structure of the model following controller. The error between the plant output and the 23 Introduction reference model output is used to adjust the membership functions of the Fuzzy controller. It has been demonstrated [1.22] that the proposed controller displays good performance. Hierarchical Fuzzy Controller [1.23] (Fig. 1.19) In an hierarchical Fuzzy controller the structure is divided into different levels. Similar to tuning a radio set by coarse and fine adjustments the hierarchical controller gives an approximate output at the first level which is then modified by the second level rule set. This process is repeated in succeeding level of hierarchy. Fig. 1.19 The Configuration of Adaptive Hierarchial Fuzzy Control System The rules in the first level are of following form if ( x{ is ax, x2 is a12,....*„i ls a\,n\) then (output yl is bx) The rules in the ith (i>l) level are of the form. if ( *y.+I is aNji.... xN.+n. is aN_) and(yM is A_,)then(output y-is b() » The number of rules in such kind of controllers are drastically reduced. In addition the controller action is more human like and therefore is easy to formulate the rule base. Such type of controllers can also be made adaptable by changing the membership functions according the performance index of the plant. 24 Introduction 1.4.4 Self Organising Controllers These controllers are more or less similar to adaptive Fuzzy controllers. But in this case the rule base, and membership functions are tuned with the plant operating conditions. These controllers have the self-learning capability. Therefore the rule base is automatically formulated with little or no intervention of the human expert. By using certain strategy the controller can be made to start from an empty rule base. Control rules are generated and modified by the learning algorithm evaluating the performance enhancement matrix. And after several runs (on several changes in the reference signal) the controller can give a good performance. 1.4.5 Indirect Fuzzy Controllers Sometimes it is convenient to improve the existing conventional PI strategy rather than replacing the whole controller itself. From the stability point of view, there is not any particular method to design a direct Fuzzy controller which will be stable under all circumstances. Therefore, for plants where the operating conditions exhibit a wide range of variations, the design of a direct Fuzzy controller becomes difficult. However, the proportional and integral gains of the conventicnal controllers can be adjusted with the help of Fuzzy logic. ° 1.4.6 Neuro-Fuzzy Controllers In order to get a mapping with substantial flexibility and non-linearity Neural networks are used. To represent the abstract knowledge and to infer it like human brains Fuzzy logic is the best approach. However, it suffers from the absence, of learning and mapping. To get the advantage of the Fuzzy logic as well as Neural networks a number of network architectures employing the principle of Fuzzy logic have been proposed. These are termed as the Fuzzy Neural Networks(FNN). ; FNN1 [1.27] (Fig1.20) As shown in the Fig. 1.20 the neural network consists of two layers. The input layer (7j, /2_) fuzzifies the inputs into crisp sets. The connections from the inputs to outputs are made through the weights. At the output neurons the bias is combined (logically, by Zadeh AND, OR, Leukaswiecz OR) to produce outputs. 25 Introduction if, V = max A = min Vk = (**!»...... ,vhn) tk = InPuts .....>'**) desired outputs 0k = {0k i,.....,Okn) outputs of the network. given input Vk the output neurons first combine the incoming signals with their corresponding weights using V = max and A = min as follows Hi - VjAK,*)...... .{A{Kto>r„,}} fbrlS<S» Output neuron Oi now combines Wkl together with bias 0( to produce its output Oki = @i for 1 <i <n, all k. The difference of this network with the traditional one is that, here the min, max operations are used for multiplication and addition. A modified delta rule [1.27] has been proposed to adjust the weights and 0{. FNN2 [1.28] (Fig. 1.21) This type of network uses a typical Fuzzy neuron. The neuron sends a crisp signal xt to N, 1 < i < n . The weights for N are Fuzzy sets A-t, 1 </</?. The membership function of input xi is evaluated through At- (xt) and the results are combined into one number y inside 26 Introduction N . N then transforms y into (Crisp) output 0 which is then sent to some other (Fuzzy) neurons in the network. FNN3 [1.28] (Fig. 1.22) This uses another type of neuron which sends Fuzzy signal Xx towards N , 1 <i<n. In the process Xf is transformed, by some transformation 7), into X) = [(X)), 1 < i < n . N has Fuzzy weights A.: which are first combined with transformed signal into Wt = At * X] for some operator *, l <i<n, and these Wt- are combined into one Fuzzy set W inside N . Finally N transforms W to its output O . The training algorithm for such networks have been proposed in [1.28]. Fig. 1.22 Fuzzy Neural Net-Ill FNN4 [1.28] (Fig. 1.23) This type Neural Network uses neuron which sends Fuzzy signal Xi to N . There are no weights and N has a Fuzzy transfer relation R , so that its output 0 is (Xj,......,Xn)oR 27 Introduction for some type of composition operator "o". The network built-up from such type of Fuzzy neuron appears ideal for rule extraction from training data, in a Fuzzy expert system. ANFIS (Adaptive Network-based Fuzzy Inference Systems) [1.29] (Figl.24) An adaptive network is a multilayer feedforward network in which each node performs a particular function (node function) on incoming signals as well as a set of parameters pertaining to this node. The formulas for the node functions may vary from node to node, and the choice of each node function depends on the overall input-output function which the adaptive network is required to carry out. To reflect different adaptive capabilities, both circle and square nodes have been used. A square node (adaptive node) has parameters while a circle node (fixed node) has none. In order to achieve a desired input-output mapping, the parameters of all the square nodes are updated according to given training data and a gradient-based learning procedure can 28 Introduction be used. As described in [1.29] a Fuzzy controller can be easily made to fit into this. Thus it is equivalent to a typical Fuzzy inference system with an adaptive structure. A Self Tuning Neuro-Fuzzy Controller [1.30] (Fig. 1.25) Fig. 1.25 A Self Tuning Neuro-Fuzzy Controller This network is similar to CMAC ( Cerebellum Model Articulation Controller). Such type of controllers are very much similar to a Simple Fuzzy controller with an adaptive defuzzification procedure. As shown in the Fig. 1.25 the CMAC architecture represents the connectionist model cf a Fuzzy controller. The error between the reference and the plant output is trained to adjust the weights. This architecture is simple and well understood. The training procedure also needs the least number of calculations. This architecture is discussed in subsequent Chapters. In the literature a number of architectures have been proposed. Out of them only a few are applicable to the HVDC link control. The HVDC link is a very complicated and large system. Therefore to qualify for such systems the controller need to have the following essential properties. • It should be robust over a wide range of operating conditions. • It should adapt to all the transient and dynamic conditions • It should be easier to choose the parameters of the controllers on-line • The mathematical computations should be less such that it does not create any computational burden 29 Introduction Out of all the above described structures only a few satisfy these conditions. Therefore, only some of them have been tested for their feasibility and effectiveness in controlling HVDC systems. They will be discussed in detail in the following chapters. 1.5 Motivation and Problem Statement The motivations behind this thesis is work can be attributed to the following reasons: 1. The intelligent control techniques have found themselves successful in small plants where the number of control variables are less. 2. For large dynamic systems these techniques need extensive off line study for their feasibility and effectiveness. 3. The HVDC links are highly dynamic and non-linear. The plant conditions demand more efficient and robust control schemes for a wide range of operating points. 4. Extensive research need to be carried out in the application of Fuzzy and Neural controllers to the HVDC links. 5. Furthermore, in the study of AC-DC system interactions the HVDC control schemes need thorough investigations, for these controllers very often regulate some of the vital parameters of the AC system. Therefore, along with the applications of Neural and Fuzzy controllers some of the more advanced control schemes have been tested to establish the advantages of the proposed controllers in AC-DC system interaction. 6. In addition to the Fuzzy and Neural controllers some other advanced schemes should be tried to evaluated the relative merits and demerits. In the literature input-output linearising controllers have been applied successfully to control some of the practical systems. The potential of this method needs to be verified in case of the DC links relative to the conventional and Intelligent control. As a whole the thesis is devoted to the study of Intelligent controllers for HVDC converters. However, in the study of AC-DC system interaction, some of the advanced controllers along with the Intelligent controller has been tested. 30 Introduction 1.6 Thesis Outline The thesis has been primarily devoted to evaluate the performance of some of the Fuzzy and Neuro-Fuzzy controllers in point-to-point and Multi-terminal HVDC links. Before they are tested on bench-mark models, the Fuzzy controller has been tested as an auxiliary control in an AC-DC system with a quasi-steady-state model. Chapter-II discusses the application of Fuzzy controller to the auxiliary control loop of the PI current regultator. Here the DC link has been used to damp out the transient oscillations in the connected AC system. The firing angle to the rectifier has been modulated by an auxiliary signal derived from the system frequency deviation. Along with the Fuzzy controller, some of the advanced controllers have also been tested. The self-tuning and the variable structure sliding mode controllers are some of the very advanced non-linear controllers which in recent years have been proven to be very effective. These two controllers have been tested as the auxiliary controllers for the AC-DC system in Chapter-II. Finally, a comparative study has been taken up to prove the worth of the Fuzzy controllers. In Chapter-Ill some of the Fuzzy and Neuro-Fuzzy controllers have been tested on a two-terminal point-to-point HVDC benchmark model. The transformers, transmission lines and converters have been represented in detail in the simulation program. The simulation have been carried out in an EMTP type program known as EMTDC. Here the Fuzzy and the Neuro-Fuzzy controllers act as robust and self tuning controllers. Unlike Chapter-II here the main objective is to damp out the DC link transients. Therefore, the generators at either end are represented by simple voltage sources . There is no auxiliary control provided here. As robust controllers the conventional rectifier current regulator has been completely replaced by Fuzzy and NeuroFuzzy blocks. As self-tuning controller the proportional and the integral gains of the conventional controller have been tuned on-line by methods based on Fuzzy Logic. Five different robust and self-tuning Fuzzy and Neuro-Fuzzy controllers have been tested by subjecting the system to different normal and abnormal situations. In Chapter-IV the same benchmark model of Chapter-Ill has been used to evaluate the 31 Introduction performance of an Input-Output Linearising Controller, The Linearising Controllers are best known for their application to non-linear plants. The philosophy is to cancel out the plant nonlinearities thus making the design task easier. Substantial literature available tells the success of such controllers in large number of control problems. The simulation results pertaining to the proposed linearising controller has been compared with the Fuzzy and Neuro-Fuzzy controllers *of Chapter-Ill. Out of all the proposed controllers the better ones are chosen to be implemented as the rectifier current regulators in a Multi-terminal-DC system. The performance and design of these controllers for a 3-terminal DC system has been presented in Chapter-V. The study includes the transient response of the system under various kinds of faults. Much remains to be explored in designing suitable Fuzzy controllers for non-linear and uncertain plants. As these controllers are also highly non-linear, it leads to difficulty in the analysis and design of appropriate structures for a given plant. Chapter-VI gives an overall assessment and tells the future scope of this research work especially in the' area of design and analysis of these controllers. 1.7 Conclusion The thesis has been primarily devoted to the study of Intelligent controls for large systems. AC-DC systems in fact come under such systems. The wide spread non-linearity and high degree of uncertainty makes it difficult for the designer to choose the proper control strategy. Therefore while undertaking this work it was anticipated that the AI (Artificial Intelligent) based controllers would give a better solution. From the coincised literature review it is found that, a number of controllers based on Neural network and Fuzzy logic have proved themselves successful in controlling small-non linear plants. However, for large-non-linear plants it is yet to prove its worth. To investigate the possibility of their application in such plants this thesis work has been taken up. 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