Abstract
The paper is an attempt of an application of the fractional order derivative in modeling of power system elements.
The electrical part of the generating unit contains, first of all, the power generator equipped with an excitation system. Three other components may be identified, when the electromachine excitation system is considered. This type of excitation uses an AC electric machine as an exciting device.
The mathematical model of high frequency AC exciter with additional regulator, being one of three possible submodels of electromagnetic excitation system model, was chosen intentionally and used as a simulation platform. The presented model in its simplicity includes all elements that characterise far more advanced and extended models, for example power generators. It contains gain factors and time constants as well as saturation components. Another important factor is that this particular model operates only using positive signals developed by an additional regulator. The paper presents the method and exemplary results of parameter estimation of the fractional model of the high frequency AC exciter with an additional regulator. To preserve full reliability of the computations, true waveforms measured in a power plant were used as input and output signals of the model. The advantages of applying fractional order calculus were verified by comparing measured and computed model output waveforms. Both integer and fractional order models were used in computations.
The aspect of filtering the recorded measurement signals is also presented in the paper.
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References
General Electric, Energy Management System â PSLF â GE Energy Consulting (2018). https://www.geenergyconsulting.com/practice-area/software-products/pslf
Siemens, PSSÂźSINCAL All-in-one Simulation Software for the Analysis and Planning of Power Networks (2018). www.siemens.com/global/en/home/products/energy/services/transmission-distribution-smart-grid/consulting-and-planning/pss-software/pss-sincal.html
Majka, Ć., Paszek, S.: Mathematical model parameter estimation of a generating unit operating in the Polish National Power System. Bull. Pol. Acad. Sci. Tech. Sci. 64(2), 409â416 (2016)
Prastyaningrum, I., Handhika, J.: Mathematically analysis to improve efficiency of simple AC generator in term of special relativity. In: AIP Conference Proceedings 2014, p. 020124-1:6. AIP Publishing (2018)
Lewandowski, M., Majka, Ć., Ćwietlicka, A.: Effective estimation of angular speed of synchronous generator based on stator voltage measurement. Int. J. Electr. Power Energy Syst. 100, 391â399 (2018)
Singh, A.K., Pal, B.C.: Dynamic Estimation and Control of Power Systems, 1st edn. Academic Press, London (2018)
Paszek, S., NocoĆ, A.: Optimisation and Polyoptimisation of Power System Stabilizer Parameters. LAP LAMBERT Academic Publishing, SaarbrĂŒcken (2014)
BuĆa, D., Lewandowski, M.: Steady state simulation of a distributed power supplying system using a simple hybrid time-frequency model. Appl. Math. Comput. 319, 195â202 (2018)
BuĆa, D., Lewandowski, M.: Comparison of frequency domain and time domain model of a distributed power supplying system with active power filters (APFs). Appl. Math. Comput. 267, 771â779 (2015)
IEEE Standard Definitions for Excitation Systems for Synchronous Machines. In: IEEE Std 421.1-2007 (Revision of IEEE Std 421.1-1986), pp. 1â33 (2007). https://doi.org/10.1109/IEEESTD.2007.385319
IEEE Guide for Identification, Testing, and Evaluation of the Dynamic Performance of Excitation Control Systems. In: IEEE Std 421.2-2014 (Revision of IEEE Std 421.2-1990), pp. 1â63 (2014). https://doi.org/10.1109/IEEESTD.2014.6845300
IEEE Recommended Practice for Excitation System Models for Power System Stability Studies. In: IEEE Std 421.5-2016 (Revision of IEEE Std 421.5-2005), pp. 1â207 (2016). https://doi.org/10.1109/IEEESTD.2016.7553421
Feltes, J.W., Orero, S., Fardanesh, B., Uzunovic, E., Zelingher, S., Abi-Samra, N.: Deriving model parameters from field test measurements. IEEE Comput. Appl. Power 15(4), 30â36 (2002)
Hannett, L.N., Feltes, J.W.: Testing and model validation for combined-cycle power plants. In: In: Conference Proceedings on IEEE Power Engineering Society Winter Meeting, vol. 3, pp. 664â670 (2001)
Majka, Ć., Paszek, S.: Algorithms for estimation of model parameters of excitation system of an electrical machine. Acta Tech. CSAV (Ces. Akad. Ved) 55(2), 179â194 (2010)
Paszek, S., NocoĆ, A.: Parameter polyoptimization of PSS2A power system stabilizers operating in a multi-machine power system including the uncertainty of model parameters. Appl. Math. Comput. 267, 750â757 (2015)
Sierociuk, D., Malesza, W.: Fractional variable order anti-windup control strategy. Bull. Pol. Acad. Sci.: Tech. Sci. 66(4), 427â432 (2018)
Domansky, O., Sotner, R., Langhammer, L., Jerabek, J., Psychalinos, C., Tsirimokou, G.: Practical design of RC approximants of constant phase elements and their implementation in fractional-order PID regulators using CMOS voltage differencing current conveyors. In: Circuits, Systems, and Signal Processing, pp. 1â27. Springer, Heidelberg (2018). https://doi.org/10.1007/s00034-018-0944-z
SpaĆek, D.: Model generatora synchronicznego z uĆamkowym regulatorem napiÈ©cia PIbDa. In: Conference Aktualne problemy w elektroenergetyce APE 2015, pp. 51â59 (2015)
Sowa, M.: A harmonic balance methodology for circuits with fractional and nonlinear elements. Circ. Syst. Sig. Process. 37(11), 4695â4727 (2018)
Czuczwara, W., Latawiec, K.J., Stanislawski, R., Ćukaniszyn, M., Kopka, R., Rydel, M.: Modeling of a supercapacitor charging circuit using two equivalent RC circuits and forward vs. backward fractional-order differences. In: Progress in Applied Electrical Engineering (PAEE) (2018). https://doi.org/10.1109/PAEE.2018.8441060
Kapouleaa, S., Psychalinos, C., Elwakil, A.S.: Single active element implementation of fractional-order differentiators and integrators. AEU-Int. J. Electron. Commun. 97, 6â15 (2018)
Jakubowska-Ciszek, A., Walczak, J.: Analysis of the transient state in a parallel circuit of the class RLbCa. Appl. Math. Comput. 319, 287â300 (2018)
Jakubowska, A., Walczak, J.: Analysis of the transient state in a series circuit of the class RLbCa. Circ. Syst. Sig. Process. Spec. Issue: Fract.-Order Circ. Syst.: Theory Des. Appl. 35(6), 1831â1853 (2016)
Carvalho, A.R., Pinto, C.M., Baleanu, D.: HIV/HCV coinfection model: a fractional-order perspective for the effect of the HIV viral load. AAdv. Differ. Equ. 2018, 2 (2018). https://doi.org/10.1186/s13662-017-1456-z
Baranowski, J., Pia̧tek, P., Kawala-Janik, A., ZagĂłrowska, M., Bauer, W., DziwiĆski, T.: Non-integer order filtration of electromyographic signals. In: Latawiec, K., Ćukaniszyn, M., StanisĆawski, R. (eds.) Advances in Modelling and Control of Non-integer-Order Systems. Lecture Notes in Electrical Engineering, vol. 320, pp. 231â237. Springer, Cham (2015)
Kawala-Janik, A., et al.: Implementation of low-pass fractional filtering for the purpose of analysis of electroencephalographic signals. In: Ostalczyk, P., Sankowski, D., Nowakowski, J. (eds.) Non-integer Order Calculus and its Applications. RRNR 2017. Lecture Notes in Electrical Engineering, vol. 496, pp. 63â73. Springer, Cham (2019)
Voyiadjis, G.Z., Sumelka, W.: Brain modelling in the framework of anisotropic hyperelasticity with time fractional damage evolution governed by the Caputo-Almeida fractional derivative. J. Mech. Behav. Biomed. Mater. 89, 209â216 (2019)
Bia, P., Mescia, L., Caratelli, D.: Fractional calculus-based modeling of electromagnetic field propagation in arbitrary biological tissue. Math. Probl. Eng. 2016, 11 (2016)
OprzÈ©dkiewicz, K., Mitkowski, W., Gawin, E., Dziedzic, K.: The Caputo vs. Caputo-Fabrizio operators in modeling of heat transfer process. Bull. Pol. Acad. Sci. Tech. Sci. 66(4), 501â507 (2018)
Lewandowski, M., Walczak, J.: Optimal base frequency estimation of an electrical signal based on Pronyâs estimator and a FIR filter. Appl. Math. Comput. 319, 551â561 (2018)
Lewandowski, M., Walczak, J.: Current spectrum estimation using Pronyâs estimator and coherent resampling. COMPEL 33(3), 989â997 (2014)
WrĂłbel, T.: Pra̧dnice zwiÈ©kszonej czÈ©stotliwoĆci. Wydawnictwo Ministerstwa Obrony Narodowej, Poland, Warsaw (1972)
Walker, J.H.: High frequency alternators. J. Inst. Electr. Eng. London 31, 67â80 (1946)
Li, P., Chen, L., Wu, R., Tenreiro Machado, J.A., Lopes, A.M., Yuan, L.: Robust asymptotic stability of interval fractional-order nonlinear systems with time-delay. J. Frankl. Inst. 355(15), 7749â7763 (2018)
Dassios, I.K., Baleanu, D.I.: Caputo and related fractional derivatives in singular systems. Appl. Math. Comput. 337, 591â606 (2018)
Brociek, R., SĆota, D., WituĆa, R.: Reconstruction of the thermal conductivity coefficient in the time fractional diffusion equation. In: Latawiec, K., Ćukaniszyn, M., StanisĆawski, R. (eds.) Advances in Modelling and Control of Non-integer-Order Systems. Lecture Notes in Electrical Engineering, vl. 320, pp. 239â247. Springer, Cham (2015)
www.mathworks.com/help/signal/ref/filtfilt.html?searchHighlight=filtfilt (2018)
Oppenheim, A.V., Lim, J.S.: The importance of phase in signals. Proc. IEEE 69(5), 529â541 (1981). https://doi.org/10.1109/PROC.1981.12022
www.mathworks.com/help/matlab/math/solve-differential-algebraic-equations-daes.html (2018)
Sowa, M., Kawala-Janik, A., Bauer, W.: Fractional differential equation solvers in octave/Matlab. In: 2018 23rd International Conference on Methods & Models in Automation & Robotics (MMAR) (2018)
Garrappa, R.: Numerical solution of fractional differential equations: a survey and a software tutorial. Mathematics 6, 16 (2018)
Sowa, M.: Application of a SubIval numerical solver for fractional circuits. In: Proceedings of the 20th International Research Conference, New York, USA, 27â28 August 2018, pp. 2560â2564 (2018)
Sowa, M.: A local truncation error estimation for a SubIval solver. Bull. Pol. Acad. Sci.: Tech. Sci. 66(4), 475â484 (2018)
Sowa, M.: Application of SubIval in solving initial value problems with fractional derivatives. Appl. Math. Comput. 319, 86â103 (2018)
Sowa, M.: Application of SubIval, a method for fractional-order derivative computations in IVPs. In: Babiarz, A., Czornik, A., Klamka, J., Niezabitowski, M. (eds.) Theory and Applications of Non-integer Order Systems. Lecture Notes in Electrical Engineering, vol. 407, pp. 489â499. Springer, Cham (2017)
Sowa, M.: Solutions of circuits with fractional, nonlinear elements by means of a SubIval solver. In: Ostalczyk, P., Sankowski, D., Nowakowski, J. (eds.) Non-integer Order Calculus and its Applications. Lecture Notes in Electrical Engineering, vol. 496, pp. 217â228. Springer, Cham (2019)
Sowa, M.: A subinterval-based method for circuits with fractional order elements. Bull. Pol. Acad. Sci. Tech. Sci. 62(3), 449â454 (2014)
http://msowascience.com (2018)
http://octave.org/doc/v4.2.1/Nonlinear-Programming.html (2018)
Nocedal, J., Wright, S.J.: Numerical Optimization. Springer Series in Operations Research and Financial Engineering. Springer, Heidelberg (2006)
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Majka, Ć. (2020). Using Fractional Calculus in an Attempt at Modeling a High Frequency AC Exciter. In: Malinowska, A., Mozyrska, D., Sajewski, Ć. (eds) Advances in Non-Integer Order Calculus and Its Applications. RRNR 2018. Lecture Notes in Electrical Engineering, vol 559. Springer, Cham. https://doi.org/10.1007/978-3-030-17344-9_5
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