Renewable Energy Systems. Renewable Energy Systems

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1 Renewable Energy Systems 1

2 Σχ. 1 Χρήση γεννήτριας στην ηλεκτροπαραγωγή από αιολική ενέργεια 2

3 Σχ. 2 Χρήση γεννήτριας στην ηλεκτροπαραγωγή από υδατοπτώσεις 3

4 Σχ. 3 Χρήση γεννήτριας στην ηλεκτροπαραγωγή από θαλάσσια ενέργεια 4

5 Σχ. 4 Χρήση φωτοβολταϊκών στην ηλεκτροπαραγωγή 5

6 Bασικά προβλήματα στη διαχείριση και λειτουργία συστημάτων Έλεγχος των χαρακτηριστικών της παραγόμενης ηλεκτρικής ενέργειας Έλεγχος στροφικής κίνησης γεννητριών Έλεγχος του παραγόμενου ηλεκτρομαγνητικού πεδίου Έλεγχος της ενεργού και της αέργου ηλεκτρικής ισχύος Συντήρηση και διαγνωστική βλαβών στα συστήματα Παρακαλούθηση της κατάστασης λειτουργίας μονάδων ηλεκτροπαραγωής Παρακολούθηση της καταάστασης λειτουργίας του συστήματος μεταφοράς και διανομής Ανίχνευση βλαβών με επεξεργασία μετρήσεων αισθητήρων στο πεδίο του χρόνου Ανίχνευση βλαβών με επεξεργασία μετρήσεων αισθητήρων στο πεδίο της συχνότητας Διασύνδεση και συγχρονισμός με το υπόλοιπο ηλεκτρικό δίκτυο Converters AC/DC για σύνδεση AC μονάδων ηλεκτροπαραγωγής προς DC δίκτυο Ιnverters DC/AC για σύνδεση DC μονάδων ηλεκτροπαραγωγής προς AC δίκτυο Συγχρονισμός και ευστάθεια κατανεμημένων μονάδων ηλεκτροπαραγωγής Οικονομική εκμετάλλευση των 6

7 Έλεγχος των χαρακτηριστικών της παραγόμενης ηλεκτρικής ενέργειας Έλεγχος λειτουργίας γεννητριών DFIG Field orientted (vector) control Flatness-based control σε διαδοχικούς βρόχους Flatness-based control με μετασχηματισμό στη γραμμική κανονική μορφή Differential geometry-based control με μετασχηματισμό στη γραμμική κανονική μορφή H-infinity nonlinear control Έλεγχος λειτουργίας γεννητριών PMSG Έλεγχος σε s-frequency domain μετά από τοπική γραμμικοποίηση Flatness-based control λειτουργίας γεννητριών PMSG Συντήρηση και διαγνωστική βλαβών στα συστήματα Διαγνωστική βλαβών για γεννήτριες με χρήση νευρωνικών δικτύων Διαγνωστική βλαβών για μετασχηματιστές με χρήση νευρωνικών δικτύων Διαγνωστική βλαβών για το σύστημα μεταφοράς / διανομής με χρήση μη-γραμμικών φίλτρων Διαγνωστική βλαβών για ηλεκτρικές γεννήτριες με ανάλυση αρμονικών φάσματος 7

8 Διασύνδεση και συγχρονισμός με το υπόλοιπο ηλεκτρικό δίκτυο Flatness-based control για: Έλεγχο converters Έλεγχο inverters Συγχρονισμό και ευσταθή λειτουργία κατανεμημένων γεννητριών ΑC ρεύματος Συγχρονισμό και ευσταθή λειτουργία κατανεμημένων μονάδων DC ρεύματος Οικονομική εκμετάλλευση των Μέθοδοι στοχαστικής εκτίμησης για την αξιοπίστία μοντέλων τιμολόγησης ενέργειας Μέθοδοι φασματικής ανάλυσυης για την αξιοπίστία μοντέλων τιμολόγησης ενέργειας 8

9 Έλεγχος των χαρακτηριστικών της παραγόμενης ηλεκτρικής ενέργειας Έλεγχος λειτουργίας γεννητριών DFIG Field orientted (vector) control Flatness-based control σε διαδοχικούς βρόχους Flatness-based control με μετασχηματισμό στη γραμμική κανονική μορφή Differential geometry-based control με μετασχηματισμό στη γραμμική κανονική μορφή H-infinity nonlinear control Έλεγχος λειτουργίας γεννητριών PMSG Flatness-based control λειτουργίας γεννητριών PMSG Έλεγχος σε s-frequency domain μετά από τοπική γραμμικοποίηση 9

10 Έλεγχος των χαρακτηριστικών της παραγόμενης ηλεκτρικής ενέργειας Έλεγχος λειτουργίας γεννητριών DFIG Field orientted (vector) control G. Rigatos, P. Siano, C. Cecati and N. Zervos, Control and disturbances compensation for doubly-fed induction generators using the Derivative-Free Nonlinear Kalman Filter, IEEE Transactions on Power Electronics, 2014 The paper studies differential flatness properties and an input-output linearization procedure for doubly-fed induction generators (DFIGs). By defining flat outputs which are associated with the rotor's turn angle and the magnetic flux of the stator, an equivalent DFIG description in the Brunovksy (canonical) form is obtained. For the linearized canonical model of the generator a feedback controller is designed. Moreover, a comparison of the differential flatness theorybased control method against Lie algebra-based control is provided. At a second stage, a novel Kalman Filtering method (Derivative-free nonlinear Kalman Filtering) is introduced. The proposed Kalman Filter is redesigned as disturbance observer for estimating additive input disturbances to the DFIG model. These estimated disturbance terms are finally used by a feedback controller that enables the generator's state variables to track desirable setpoints. The efficiency of the proposed state estimation-based control scheme is tested through simulation experiments. 10

11 Έλεγχος των χαρακτηριστικών της παραγόμενης ηλεκτρικής ενέργειας Έλεγχος λειτουργίας γεννητριών DFIG Flatness-based control σε διαδοχικούς βρόχους G. Rigatos and P. Siano, DFIG control using Differential flatness theory and Extended Kalman Filtering, IFAC INCOM 2012, 14 th IFAC Intl. Conference on Information Control Problems in Manufacturing, Bucharest, Romania, May A sensorless control scheme for doubly-fed induction generators (DFIG) is developed using flatness-based control theory and a state estimation method that is based on Extended Kalman Filtering. The complete sixth-order model of the doubly-fed induction generator is derived with the use of the stator and rotor electrical equations. Since all state variables and control inputs of the doubly-fed induction generator can be written as functions of the flat output and of the associated derivatives it can be proven that the DFIG model is differentially flat. The property of differential flatness indicates that the design of a DFIG controller is possible using feed-forward control terms which are complemented by suitable error feedback terms. Next, sensorless control for the doubly-fed induction generator is implemented. The Extended Kalman Filter is proposed for estimating the non-measurable elements of the DFIG state vector (such as the rotation speed and the magnetic flux) through the processing of measurements of the rotor s angle and of the rotor currents. The efficiency of the considered state estimation-based nonlinear control scheme is evaluated through simulation experiments. 11

12 Έλεγχος των χαρακτηριστικών της παραγόμενης ηλεκτρικής ενέργειας Flatness-based control με μετασχηματισμό στη γραμμική κανονική μορφή G. Rigatos, P. Siano, C. Cecati and N. Zervos, Control and disturbances compensation for doubly-fed induction generators using the Derivative-Free Nonlinear Kalman Filter, IEEE Transactions on Power Electronics, 2014 The paper studies differential flatness properties and an input-output linearization procedure for doubly-fed induction generators (DFIGs). By defining flat outputs which are associated with the rotor's turn angle and the magnetic flux of the stator, an equivalent DFIG description in the Brunovksy (canonical) form is obtained. For the linearized canonical model of the generator a feedback controller is designed. Moreover, a comparison of the differential flatness theorybased control method against Lie algebra-based control is provided. At a second stage, a novel Kalman Filtering method (Derivative-free nonlinear Kalman Filtering) is introduced. The proposed Kalman Filter is redesigned as disturbance observer for estimating additive input disturbances to the DFIG model. These estimated disturbance terms are finally used by a feedback controller that enables the generator's state variables to track desirable setpoints. The efficiency of the proposed state estimation-based control scheme is tested through simulation experiments. 12

13 Έλεγχος των χαρακτηριστικών της παραγόμενης ηλεκτρικής ενέργειας Differential geometry-based control με μετασχηματισμό στη γραμμική κανονική μορφή G. Rigatos, P. Siano, C. Cecati and N. Zervos, Control and disturbances compensation for doubly-fed induction generators using the Derivative-Free Nonlinear Kalman Filter, IEEE Transactions on Power Electronics, 2014 The paper studies differential flatness properties and an input-output linearization procedure for doubly-fed induction generators (DFIGs). By defining flat outputs which are associated with the rotor's turn angle and the magnetic flux of the stator, an equivalent DFIG description in the Brunovksy (canonical) form is obtained. For the linearized canonical model of the generator a feedback controller is designed. Moreover, a comparison of the differential flatness theorybased control method against Lie algebra-based control is provided. At a second stage, a novel Kalman Filtering method (Derivative-free nonlinear Kalman Filtering) is introduced. The proposed Kalman Filter is redesigned as disturbance observer for estimating additive input disturbances to the DFIG model. These estimated disturbance terms are finally used by a feedback controller that enables the generator's state variables to track desirable setpoints. The efficiency of the proposed state estimation-based control scheme is tested through simulation experiments. 13

14 Έλεγχος των χαρακτηριστικών της παραγόμενης ηλεκτρικής ενέργειας H-infinity nonlinear control γεννητριών DFIG G: Rigatos and P. Siano, Nonlinear H-infinity feedback control for doubly-fed induction generators, IEEE ICCEP 2015, 5th International Conference on. CLEAN ELECTRICAL POWER Renewable Energy Resources, Taormina, Italy, June 105 A new method for feedback control of asynchronous electrical machines is introduced, with application example the problem of doubly-fed induction generators (DFIGs). The control method consists of a repetitive solution of an H-infinity control problem for the DFIG, that makes use of a locally linearized model of the generator and takes place at each iteration of the control algorithm. The asynchronous generator s model is locally linearized round its current operating point through the computation of the associated Jacobian matrices. Using the linearized model of the generator an H-infinity feedback control law is computed. The known robustness features of H-infinity control enable to compensate for the errors of the approximative linearization, as well as to eliminate the effects of external perturbations. The efficiency of the proposed control scheme is shown analytically and is confirmed through simulation experiments. 14

15 Έλεγχος των χαρακτηριστικών της παραγόμενης ηλεκτρικής ενέργειας Έλεγχος λειτουργίας γεννητριών PMSG Έλεγχος σε s-frequency domain μετά από τοπική γραμμικοποίηση G.G. Rigatos and P. Siano, Design of robust electric power system stabilizers using Kharitonov's theorem, Mathematics and Computers in Simulation, Elsevier, vol. 82, no 1, Pages A robust power system stabilizer (PSS) is proposed as an effective way to damp-out oscillations in electric power systems. Oscillations of small magnitude and low frequency, linked with the electromechanical models in power systems, often persist for long periods of time and in some cases present limitations on the power transfer capability. The proposed PSS is designed according to Kharitonov s extremal gain margin theory. It has the following advantages: (i) it is based on simultaneous stabilization of limited number of extreme plants, (ii) the control design can be based on frequency response analysis techniques (root locus diagrams or Nyquist plots) and (iii) the resulting controller is a low-order phase-lead compensator, which is robust to the change of operating points. The proposed power system stabilizer is tested through simulation experiments. 15

16 Έλεγχος των χαρακτηριστικών της παραγόμενης ηλεκτρικής ενέργειας Flatness-based control λειτουργίας γεννητριών PMSG G. Rigatos, P. Siano and N. Zervos, Derivative-free nonlinear Kalman filtering for PMSG sensorless control, In: Mechatronics Engineering: Research Development and Education (M. Habib Ed.), J. Wiley, 2012 A derivative-free nonlinear Kalman Filtering approach is introduced aiming at implementing sensorless control of the Permanent Magnet Synchronous Generator (PMSG). In the proposed derivative-free Kalman Filtering method the system is first subject to a linearization transformation that is based on the differential flatness theory and next state estimation is performed by applying the standard Kalman Filter recursion to the linearized model. Unlike the Lie algebra-based estimator design method, the proposed approach provides estimates of the state vector of the permanent magnet synchronous generator without the need for derivatives and Jacobians calculation. By avoiding linearization approximations, the proposed filtering method improves the accuracy of estimation of the system state variables, and results in smooth control signal variations and in minimization of the tracking error of the associated control loop. 16

17 Συντήρηση και διαγνωστική βλαβών στα συστήματα Διαγνωστική βλαβών για γεννήτριες με χρήση νευρωνικών δικτύων G.G. Rigatos, P. Siano and A. Piccolo, A neural network-based approach for early detection of cascading events in electric power systems, IET Journal on Generation Transmission and Distribution, vol.3, no. 7, pp , This paper proposes neural modelling and fault diagnosis methods for the early detection of cascading events in electric power systems. A neural-fuzzy network is used to model the dynamics of the power transmission system in fault-free conditions. The output of the neural-fuzzy network is compared to measurements from the power system and the obtained residuals undergo statistical processing according to a fault detection and isolation algorithm. If a fault threshold, de ned by the FDI algorithm, is exceeded then deviation from normal operation can be detected at its early stages and an alarm can be launched. In several cases fault isolation can be also performed, i.e. the sources of fault in the power transmission system can be also identi ed. The performance of the proposed methodology is tested through simulation experiments. 17

18 Συντήρηση και διαγνωστική βλαβών στα συστήματα Διαγνωστική βλαβών για μετασχηματιστές με χρήση νευρωνικών δικτύων G. Rigatos, P. Siano and A. Piccolo, Incipient fault detection for electric power transformers using neural modeling and the local statistical approach to fault diagnosis, IEEE SAS 2012, 2012 IEEE Sensors Applications Symposium, University of Brescia, Italy, Feb This paper proposes neural modelling and the local statistical approach to fault diagnosis for the detection of incipient faults in critical components of the electric power grid, such as power transformers. A neural-fuzzy network is used to model the thermal condition of the power transformer in fault-free operation (the thermal condition is associated to a temperature variable known as hot-spot temperature). The output of the neural-fuzzy network is compared to measurements from the power transformer and the obtained residuals undergo statistical processing according to a fault detection and isolation algorithm. If a fault threshold (that is optimally defined according to detection theory) is exceeded, then deviation from normal operation can be detected at its early stages and an alarm can be launched. In several cases fault isolation can be also performed, i.e. the sources of fault in the power transformer model can be also identified. The performance of the proposed methodology is tested through simulation experiments. 18

19 Συντήρηση και διαγνωστική βλαβών στα συστήματα Διαγνωστική βλαβών για το σύστημα μεταφοράς / διανομής με χρήση μη-γραμμικών φίλτρων G. Rigatos, P. Siano and N. Zervos, A Distributed State Estimation Approach to Condition Monitoring of Nonlinear Electric Power Systems", Asian Journal of Control, J. Wiley, The paper analyzes distributed state estimation methods for condition monitoring of electric power transmission and distribution systems. When a fault occurs in such large-scale systems, it is usually difficult to detect it and to determine its exact position. Moreover, due to the cost of installation and maintenance of measurement devices and due to the excessive size of the electric power grid, the complete monitoring of the associated infrastructure is impractical. Therefore, to monitor the condition of the power grid, some form of estimation is required. As suitable approaches for distributed state estimation the paper proposes the Extended Information Filter (EIF) and the Unscented Information Filter (UIF). The Extended Information Filter is actually an implementation of distributed Extended Kalman Filtering while the Unscented Information Filter is an implementation of distributed Unscented Kalman Filtering. With the use of the aforementioned filtering algorithms on processing units located at different parts of the power grid, one can produce local estimates of the system s state vector which in turn can be fused into an aggregate state estimation. The produced global state estimate enables continuous monitoring of the condition of the electric power system and early fault diagnosis if used by a suitable fault detection and isolation algorithm. 19

20 Συντήρηση και διαγνωστική βλαβών στα συστήματα Διαγνωστική βλαβών για ηλεκτρικές γεννήτριες με ανάλυση αρμονικών φάσματος G. Rigatos and P. Siano, An approach to fault diagnosis of nonlinear systems using neural networks with invariance to Fourier transform, Journal of Ambient Intelligence and Humanized Computing, Springer, A neural network with Gauss-Hermite polynomial activation functions is used for approximating the nonlinear system s dynamics out of a set of input-output data. Thus the output of the neural network provides a series expansion that takes the form of a weighted sum of Gauss-Hermite basis functions. Knowing that the Gauss-Hermite basis functions satisfy the orthogonality property and remain unchanged under the Fourier transform, subjected only to a change of scale, one has that the considered neural network provides the spectral analysis of the output of the monitored system. Actually, the squares of the weights of the output layer of the neural network denote the distribution of energy into the associated spectral components for the output signal of the monitored nonlinear system. By observing changes in the amplitude of the aforementioned spectral components of the nonlinear system one can have also an indication about malfunctioning of the monitored system and can detect the existence of failures. Moreover, since specific faults are associated with amplitude changes of specific spectral components of the system fault isolation can be also performed. 20

21 Διασύνδεση και συγχρονισμός με το υπόλοιπο ηλεκτρικό δίκτυο Flatness-based control για: Έλεγχο converters G. Rigatos, P. Siano, N. Zervos and C. Cecati, Derivative-free nonlinear Kalman Filtering for control of three-phase voltage source converters, IEEE IECON 2013, 39 th IEEE Conference on Industrial Electronics, Vienna, Austria, Nov The paper is concerned with proving differential flatness of the three-phase voltage source converter (VSC) model and its resulting description in the Brunovksy (canonical) form. For the linearized canonical model of the converter a feedback controller is designed. At a second stage, a novel Kalman Filtering method (derivative-free nonlinear Kalman Filtering) is introduced. The proposed Kalman Filter is redesigned as disturbance observer for estimating perturbations in the VSC model. These estimated disturbance terms are finally used by a feedback controller that enables the DC output voltage to track desirable setpoints. The efficiency of the proposed state estimation-based control scheme is tested through simulation experiments. 21

22 Διασύνδεση και συγχρονισμός με το υπόλοιπο ηλεκτρικό δίκτυο H-infinty control για: Έλεγχο converters G. Rigatos, P. Siano and C. Cecati, An H-infinity feedback control approach for three-phase voltage source converters, IEEE IECON 2014, Dallas, Texas, Oct This research work introduces a new control method for feedback control of nonlinear dynamical systems with application example the problem of multi-source voltage source converters. The control method consists of a repetitive solution of an H-infinity control problem for the voltage source converter, that makes use of a locally linearized model of the converter and takes place at each iteration of the control algorithm. The converter s model is locally linearized round its current operating point through the computation of the associated Jacobian matrices. Using the linearized model of the converter an H-infinity feedback control law is computed. The known robustness features of H-infinity control enable to compensate for the errors of the approximative linearization, as well as to eliminate the effects of external perturbations. The efficiency of the proposed control scheme is shown analytically and is confirmed through simulation experiments. The method can be applied to a wide class of nonlinear dynamical systems 22

23 Διασύνδεση και συγχρονισμός με το υπόλοιπο ηλεκτρικό δίκτυο Flatness-based control για: Έλεγχο inverters G. Rigatos, P. Siano, N. Zervos and C. Cecati, Nonlinear feedback control of three-phase inverter systems using the Derivative-free nonlinear Kalman Filter, IET ACDC 2015 International Conference, Birmingham UK, Feb The use of three-phase voltage inverters (DC to AC converters) is frequently met in the electric power system, such as in the connection of photovoltaics with the rest of the grid. The paper proposes a nonlinear feedback control method for three-phase inverters, which is based on differential flatness theory and a new nonlinear filtering method under the name Derivative-free nonlinear Kalman Filter. First, it is shown that the inverter s dynamic model is a differentially flat one. This means that all its state variables and the control inputs can be written as functions of a single algebraic variable which is the flat output. By exploiting differential flatness properties it is shown that the inverter s model can be transformed to the linear canonical (Brunovsky s) form. For the latter description the design of a state feedback controller becomes possible, e.g. using pole placement methods. Moreover, to estimate the non-measurable state variables of the linearized equivalent of the inverter, the Derivative-free nonlinear Kalman Filter is used. This consists of the Kalman Filter recursion applied on the linearized inverter s model and of an inverse transformation that is based on differential flatness theory, which enables to compute estimates of the state variables of the initial nonlinear system. Furthermore, by redesigning the aforementioned filter as a disturbance observer it becomes also possible to estimate disturbance terms that affect the inverter and subsequently to compensate for them. 23

24 Διασύνδεση και συγχρονισμός με το υπόλοιπο ηλεκτρικό δίκτυο Flatness-based control για: Συγχρονισμό και ευσταθή λειτουργία κατανεμημένων μονάδων DC ρεύματος G. Rigatos, Decentralized control of parallel inverters connected to microgrid using the Derivative-free nonlinear Kalman Filter, ISI Internal Report 2014 Decentralized control for parallel inverters connected to the power grid is developed using differential flatness theory and the Derivative-free nonlinear Kalman Filter. The problem is of elevated difficulty comparing to the control of stand-alone inverters because in this case in the dynamics of each inverter one has also to compensate for interaction terms which are due to the coupling with other inverters. It is proven that the model of the inverters, is a differentially flat one. This means that all its state variables and the control inputs can be written as functions of a single algebraic variable which is the flat output. By exploiting differential flatness properties it is shown that the multiple inverters model can be transformed into a set of local inverter models which are decoupled and linearized. For each local inverter the design of a state feedback controller becomes possible, e.g. using pole placement methods. Such a controller processes measurements not only coming from the individual inverter but also coming from other inverters which are connected to the grid. Moreover, to estimate the non-measurable state variables of each local inverter, the Derivative-free nonlinear Kalman Filter is used. This consists of the Kalman Filter recursion applied to the local linearized model of the inverter and of an inverse transformation that is based on differential flatness theory, which enables to compute estimates of the state variables of the initial nonlinear model of the inverter. Furthermore, by redesigning the aforementioned filter as a disturbance observer it becomes also possible to estimate and compensate for disturbance terms that affect each local inverter. 24

25 Διασύνδεση και συγχρονισμός με το υπόλοιπο ηλεκτρικό δίκτυο Flatness-based control για: Συγχρονισμό και ευσταθή λειτουργία κατανεμημένων γεννητριών ΑC ρεύματος G. Rigatos, P. Siano and N. Zervos, Sensorless Control of Distributed Power Generator with the Derivative-free Nonlinear Kalman Filter, IEEE Transactions on Industrial Electronics, A control method for distributed interconnected power generation units is developed. The power system comprises Permanent Magnet Synchronous Generators (PMSGs) which are connected to each other through transformers and tielines. A derivative-free nonlinear Kalman Filtering approach is introduced aiming at implementing sensorless control of the distributed power generators. In the proposed derivative-free Kalman Filtering method the generator s model is first subjected to a linearization transformation that is based on differential flatness theory and next state estimation is performed by applying the standard Kalman Filter recursion to the linearized model. Unlike Lie algebra-based estimator design methods, the proposed approach provides estimates of the state vector of the permanent magnet synchronous generator without the need for derivatives and Jacobians calculation. Moreover, by redesigning the proposed derivative-free nonlinear Kalman Filter as a disturbance observer it is possible to estimate at the same time the non-measurable elements of each generator s state vector, the unknown input power (torque) and the disturbance terms induced by interarea oscillations. The efficient real-time estimation of the aggregate disturbance that affects each local generator makes possible to introduce a counter-disturbance control term thus maintaining the power system on its nominal operating conditions. 25

26 Οικονομική εκμετάλλευση των Μέθοδοι στοχαστικής εκτίμησης για την αξιοπίστία μοντέλων τιμολόγησης ενέργειας G. Rigatos, A Kalman Filtering approach to the detection of option mispricing in electric power markets, I EEE SSCI 2014, Orlando, Florida, USA, Dec Option pricing models are usually described with the use of stochastic differential equations and diffusion-type partial differential equations (e.g. Black-Scholes models). In case of electric power markets these models are complemented with integral terms which describe the effects of jumps and changes in the diffusion process and which are associated with variations in the production rates, condition of the transmission and distribution system, pay-off capability, etc. Considering the latter case, that is a partial integrodifferential equation for the option s price, a new filtering method is developed for estimating option prices variations without knowledge of initial conditions. The proposed filtering method is the so-called Derivative-free nonlinear Kalman Filter and is based on a transformation of the initial option price dynamics into a state-space model of the linear canonical form. The transformation is shown to be in accordance to differential flatness theory and finally provides a model of the option price dynamics for which state estimation is possible by applying the standard Kalman Filter recursion. Based on the provided state estimate, validation of the Black-Scholes partial integrodifferential equation can be performed and the existence of inconsistent parameters in the electricity market pricing model can be concluded. 26

27 Οικονομική εκμετάλλευση των Μέθοδοι φασματικής ανάλυσυης για την αξιοπίστία μοντέλων τιμολόγησης ενέργειας G. Rigatos, Parameter change detection in financial options models using neural networks with invariance to Fourier transform, ISI Internal Report, June 2014 In this paper, modeling of financial options dynamics is performed, using a neural network with 2D Gauss-Hermite basis functions that remain invariant to Fourier transform. Knowing that the Gauss- Hermite basis functions satisfy the orthogonality property and remain unchanged under the Fourier transform, subjected only to a change of scale, one has that the considered neural network provides the spectral analysis of the options dynamics model. Actually, the squares of the weights of the output layer of the neural network denote the spectral components for the monitored options dynamics. By observing changes in the amplitude of the aforementioned spectral components one can have also an indication about deviations from nominal values, for parameters that affect the options dynamics, such as interest rate, dividend payment and volatility. Moreover, since specific parametric changes are associated with amplitude changes of specific spectral components of the options model, isolation of the distorted parameters can be also performed. 27