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13th International Conference on ICTPE-2017 “Technical and Physical Problems of Electrical Engineering” ICTPE Conference 21-23 September 2017 www.iotpe.com Yuzuncu Yil University Van, Turkey [email protected] [email protected] Number 1 Code 01PES01 Pages 1-6 PAPER TITLE N.M. Author 1 H.A. Author 2,3 B. Author 3 S. Author 4 R.T. Author 4 1. Electrical Engineering Department, … University of …, City, Country, [email protected]. Center of …, Faculty of Engineering, … University of …, City, Country, [email protected]. Department of …, Organization of …, City, Country, [email protected]. … Company, City, Country, [email protected], [email protected] Abstract- Permanent magnet synchronous motor (PMSM) have a wide range of applications, such as electric drives and machine ……………………………… ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………… to ensure stability and tracking. Simulations is carried out to verify the theoretical results. II. NONLINEAR MOTOR DYNAMICS A mathematical model of three-phase, two-pole permanent-magnet synchronous motors should be developed. Three-phase, two-pole permanent-magnet synchronous motor is illustrated in Figure 1. A. Motor Modeling For the magnetically coupled abc stator windings, we apply the Kirchhoff voltage law to find a set of the following differential equations: d as (1) u as rs i as dt d bs (2) u bs rs ibs dt d cs (3) u cs rs i cs dt ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. d bs rs i bs u bs (5) dt d cs rs i cs u cs (6) dt where the flux linkages are: Keywords: PMSM, Modeling, Saturation, ……………, …………., ……………., Lyapunov Stability. I. INTRODUCTION A broad spectrum of electric machines is widely used in electromechanical systems. In addition to the required …………………………………………………………… ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. primary issues are studied in this paper. In particular, we perform nonlinear modeling and analysis, controllers design, and validate the theoretical results [1]. 1 13th International Conference on “Technical and Physical Problems of Electrical Engineering” (ICTPE-2017) Van, Turkey, 21-23 September 2017 1 L1s L m 2 L m as 1 Lm L L m 1s bs 2 cs 1 1 Lm Lm 2 2 sin r 2 m sin( r ) 3 sin( r 2 ) 3 ias i bs ics L1s L m B.2. Different Sample Materials Depending upon different materials used in the insulation model the apparent charge varies. Parameters in Table 1 are simulated using MATLAB to observe the variation of Partial Discharge with different materials used in the sample model. Each material has different dielectric constants. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. 1 Lm 2 1 Lm 2 (7) C. Park Transformation Applying the Park transformation, we have the following expression for the electromagnetic torque: P m 2 Te iab cos r ibs cos( r ) 2 3 (14) 3 P 2 m r ics cos( r ) iqs 3 4 Using Equation (11) and the park transformation, one obtains the following differential equation to model permanent-magnet synchronous motors in the rotor reference frame: r diqs rs m r i r qs wr i ds r 3 3 dt L1s L m L1s L m 2 2 (15) 1 r u qs 3 L1s L m 2 r dids rs 1 r r r (16) i ds i qs r u ds 3 3 dt L1s L m L1s L m 2 2 where rs is the stator resistance, L1s and L m are the 3 Lm 2 and m is the amplitude of the flux linkages established by the permanent magnet. leakage and magnetizing inductances Lss L1s Figure 1. Two-pole permanent-magnet synchronous motor ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. di0r s r 1 r s i0r s u 0s dt L1s L1s (17) dwr 3 p 2 m r Bm P i qs r TL dt 8J J 2J (18) r r r where, iqs , ids , i0rs and uds , uqsr , u0r s are the quadrature, direct, and zero-axis current and voltage components. The analysis of permanent-magnet synchronous motors in the arbitrary reference frame using the quadrature, direct, and zero-quantities is simple. The electromagnetic torque is a function of the quadrature r current iqs and differential equation for the zero current B. Factors Affecting Partial Discharge Partial discharge activity in a solid dielectric material depends upon applying voltage, dielectric constant of the material and the size of the void. These are considered as the important factors affecting Partial Discharge in solid dielectrics. i0rs can be omitted from the analysis. We have: ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. That is, the total derivative of a positive-definite r r , ids , r ) is negative. Hence, an quadratic function V (iqs B.1. Applied Voltage When the applied high voltage is increased, the electric field is enhanced and the liberation electron rate is increased. As a result more Partial Discharges will occur. High voltage ranging from 4 KV to 20 KV is applied to the simulation model to observe the various activities due to the presence of void, which is done with the help of a laboratory experiment setup. open-loop system is uniformly asymptotically stable [3]. 2 13th International Conference on “Technical and Physical Problems of Electrical Engineering” (ICTPE-2017) Van, Turkey, 21-23 September 2017 III. FEEDBACK LINEARIZATION CONTROL As a first step toward the design, we mathematically set up the design problem. It is easy to verify that the linearizability condition is guaranteed. Let: ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. Remark. In pole-placement design, the specification of optimum (desired) transient responses in terms of system models and feedback coefficients is equivalent to the specification imposed on desired transfer functions of closed-loop systems. Clearly, the desired eigenvalues can be specified by the designer, and these eigenvalues are used to find the corresponding feedback gains. However, the pole-placement concept, while guaranteeing the desired location of the characteristic eigenvalues can lead to positive feedback coefficients and control constraints. Hence, the stability, robustness to parameter variations, and system performance are significantly degraded. Mathematically, feedback linearization reduces the complexity of the corresponding analysis and design. However, even from mathematical standpoints, the simplification and "optimum" performance would be achieved in expense of large control efforts required because of linearizing feedback (25). This leads to saturation. It must be emphasized that the need to linearize (19, 20, 21) does not exist because the openloop system is uniformly asympotically stable. The most critical problem is that the linearizing feedback: ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. Hence, the feedback linearizing controllers cannot be implemented to control synchronous machines. It is desirable, therefore, to develop other methods to solve the motion control problem, methods that do not entail the applied voltages to the saturation limits to cancel r beneficial nonlinearities ids r , and iqsr r ,and IV. THE LYAPUNOV-BASED APPROACH In this section, the design is approached using a nonlinear model. Using Equations (19), (20) and (21), we have the following matrix form: ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. The feedback coefficients k p , k i , and k d can be found by solving nonlinear matrix inequalities. Applying the Lyapunov stability theory and generalizing the results above, the stability of the resulting closed-loop system can be examined studying the criteria imposed on the Lyapunov function. For the bounded reference signal, using the positive-definite quadratic function ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. he given tracking controllers extend the applicability of the stabilizing algorithms, and allows one to solve the motion control problem for electromechanical systems driven by permanent-magnet synchronous motors. Using the inverse Park transformation, one derives the control laws in the machine (abc) variables. In particular, the bounded PID controller is given as: ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. V. SIMULATION RESULTS In this section, we design a tracking controller for a electromechanical system. We use a Kollmorgen fourpole permanent-magnet synchronous motors H-232 with the following rated data and parameters: 135 W, 434 rad/sec, 40 V, 0.42 N.m, 6.9 A, rs 0.5 , Lss 0.001 [H] , L1s 0.0001 [H], L m 0.0006[H], m 0.069 [V.sec/rad ] or m 0.069 [N.m/A] , Bm 0.0000115 [N.m.sec/r ad], and J 0.000017 [Kg.m2 ] ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. methods that do not lead to unbalanced motor operation . 3 13th International Conference on “Technical and Physical Problems of Electrical Engineering” (ICTPE-2017) Van, Turkey, 21-23 September 2017 ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. This controller is bounded. The sufficient criteria for stability are satisfied. To study the transient behavior, a controller is verified through comprehensive simulations. Different reference velocity , loads , and initial conditions The applied phase voltages and the resulting phase currents in the as bs and cs windings are illustrated in Figure 2. Figure 3 documents the motor mechanical angular velocity. The setting time for the motor angular velocity as motor starts from stall is 0.0025 sec. The disturbance attenuation features are evident. In particular, the assigned angular velocity with zero steady-state error has been guaranteed when the rated load torque was applied. Figures 2 and 3 illustrate the dynamics of the closed – loop drive for the following reference speed and load torque: ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. …………………………………………………………… ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. Figure 2. Radial-velocity profiles for different rates ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. 4 13th International Conference on “Technical and Physical Problems of Electrical Engineering” (ICTPE-2017) Van, Turkey, 21-23 September 2017 Table 11. Construction cost of 400 kV Number of Line Circuits Fix Cost of Line Construction (×103 dollars) Variable Cost of Line Construction (×103 dollars) 1 2 1748.6 1748.6 92.9 120.2 Table 12. Characteristics of 230 kV lines ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. ……………………………………………………………. 546.5 546.5 45.9 63.4 230 400 397 750 3.85e-4 1.24e-4 1.22e-4 3.5e-5 B. Symbols / Parameters I : The number of gas and heat units J : The number of water units C : The whole production expense Cti ( Pti (t )) : The fuel expense of its unit Pd (t ) : The load of net in t moment Pr (t ) : The cycling reserve load Pti (t ) : The production power of i heat unit Phj (t ) : The production power of j water unit rti ( Pti (t )) : The reserve power of i water unit rhj ( Phj (t )) : The reserve power of j water unit S ti (t ) : The starting expense of i heat unit S hj (t ) : The starting expense of j water unit t : The subtitle related to interval T : The time of a complete period under consideration ACKNOWLEDGEMENTS The great work of Mr. Eabcd Nancd that was a doctoral thesis and other parts for power research at the University of Cabcd, Iabcd, was a great help for developing this paper. With the cooperation of my Ph.D. thesis’s supervisor Prof. Sabcd Kabcd that spent a valuable part of his time for the paper. Table 10. Construction cost of 230 kV 1 2 Resistance (p.u/Km) A. Acronyms CHCP Combined Heat, Cooling and Power CHP Combined Heat and Power COP Coefficient of Performance DG Distributed Generation APPENDICES Appendix 1. Construction Cost and Characteristics of 230 and 400 kV Lines Tables 8 and 9 show the construction costs of 230 and 400 kV lines. Also, characteristics of these lines are listed in Table 10. Variable Cost of Line Construction (×103 dollars) Reactance (p.u/Km) NOMENCLATURES VI. CONCLUSIONS Permanent-magnet synchronous motors are used in a wide range of electromechanical systems because they are simple and can be easily controlled. The steady-state torque-speed characteristics fulfil the controllability criteria over an entire envelope of operation. In this paper a bounded controller is designed and sufficient criteria for stability are satisfied. Different reference velocity, loads, and initial conditions are studied to analyze the tracking performance of the resulting system. ……………………………………………………………. ……………………………………………………………. Fix Cost of Line Construction (×103 dollars) Maximum Loading (MVA) Appendix 2. GA and Other Required Data Load growth coefficient = 1.08; Inflation coefficient for loss = 1.15; Loss cost in now = 36.1 ($/MWh); Number of initial population = 5; End condition: 3500 iteration after obtaining best fitness (N=3500); LLmax = 30%. Figure 9. Source side voltage and current of phase (2) Number of Line Circuits Voltage Level REFERENCES [1] G.A. Taylor, M. Rashidinejad, Y.H. Song, M.R. Irving, M.E. Bradley, T.G. Williams, “Algorithmic Techniques for Transition Optimized Voltage and 5 13th International Conference on “Technical and Physical Problems of Electrical Engineering” (ICTPE-2017) Van, Turkey, 21-23 September 2017 Reactive Power Control”, International Conference on Power System Technology, Vol. 3, No. 2, pp. 1660-1664, 13-17 Oct. 2002. [2] J. Zhong, E. Nobile, A. Bose, K. Bhattacharya, “Localized Reactive Power Markets Using the Concept of Voltage Control Areas”, IEEE Transactions on Power Systems, Vol. 19, Issue 3, pp. 1555-1561, Aug. 2004. [3] A.B. Author1, “Title of the Book”, Ghijk Press, City, Country, Month Year. [4] A. Author1, C.D Author2, “Title of the Conference Paper”, 8th International Conference on Technical and Physical Problems of Electrical Engineering (ICTPE2013), No. 10, Code 01CPE05, pp. 42-48, City, Country, 9-11 September 2013. [5] A.B. Author1, C. Author2, D.E.F. Author3, “Title of the Journal Paper”, International Journal on Technical and Physical Problems of Engineering (IJTPE), Issue 12, Vol. 4, No. 3, pp. 79-86, September 2012. [6] http://www.abcd.efgh_ijk.LMN/.../opqr.pdf. Babcd Kabcd was born in Aabcd Mabcd, Rabcd, in February 1961. He received a five-year degree in electronic engineering from the University of Babcd, Rabcd, in 1986 and the Ph.D. degree in Automatic Systems and Control from the same university, in 1996. He is currently a Professor with the University of Pabcd, Rabcd. Previously, he was in hardware design with Dabcd Rabcd SA, Rabcd. He has authored of six books in Power Converter area, one in Theory and Control Systems, one in Fuzzy Control, one in Hardware topologies for PC and Devices, and one in Medical Electronics and Informatics. Also, he is co-authored of the book Fundamentals of Electromagnetic Compatibility, Theory and Practice and of a book chapter - “Iabcd Cabcd of the Eabcd Gabcd Sabcd, in the book “Iabcd Sabcd and Kabcd Mabcd for Eabcd”. His current research interests include the broad area of nonlinear systems, on both dynamics and control, and power electronics. He has authored or coauthored of several papers (over to 100) in journals (ISI/INSPEC or Rabcd Aabcd indexed) and international conference proceedings. He is an Associate Editor of scientific journal of the University of Pabcd “Eabcd and Cabcd Sabcd” and program chair and proceeding editor of the International Conference on “Eabcd, Cabcd and Aabcd Iabcd”, 2005, 2007 and 2009 editions. BIOGRAPHIES Nabcd Mabcd was born in Tacd, Iabcd, 1967. He received the B.Sc. and the M.Sc. degrees from University of Tabcd (Tabcd, Iabcd) and the Ph.D. degree from University of Sabcd (Tabcd, Iabcd), all in Power Electrical Engineering, in 1989, 1992, and 1997, respectively. Currently, he is a Professor of Power Electrical Engineering at University of Eabcd (Babcd, Aabcd). He is also an academic member of Power Electrical Engineering at University of Sabcd (Tabcd, Iabcd) and teaches Power System Analysis, Power System Operation, and Reactive Power Control. He is the secretary of International Conference on ABCD. His research interests are in the area of Power Quality, Energy Management Systems, ICT in Power Engineering and Virtual E-learning Educational Systems. He is a member of the International Electrical and Electronic Engineers. Sabcd Eabcd was born in Tabcd, Eabcd Aabcd, Iabcd in September 1940. He received the Dipl.-Ing. degree on Sabcd Tabcd from the Rabcd, Aabcd, Gabcd in 1969. From 1970 to 1971 he worked for Aabcd, Fabcd, Gabcd on electric distribution system planning. From 1972 to 1977 he was a lecturer of Electrical Engineering at University of Tabcd, Tabcd, Iabcd. From 1977 to 1979 he was as postgraduate student in Uabcd, Eabcd, where he received M.Sc. degree on Power System. From 1980 to 2007 he was a professor of Electrical Engineering of University of Tabcd. In February 2007 he was retired. During his working in University of Tabcd he was from 1988 to 1989 in Rabcd, Aabcd, Gabcd and 1996 to 1997 in Electrical Engineering Department of University of Sabcd, Cabcd in Sabbatical leave. His research interest is in electrical machines, modeling, parameter estimation and vector control. Habcd Sabcd was born in Zabcd, Iabcd, on January 23, 1951. He received the B.Sc. and M.S.E. degrees in Electrical Engineering in 1973 and 1979 and the Ph.D. degree in electrical engineering from Mabcd State University, Uabcd, in 1981. Currently, he is a full professor at electrical engineering department of University of Tabcd Tabcd, Iabcd. His research interests are in the application of artificial intelligence to power system control design, dynamic load modeling, power system observability studies and voltage collapse. He is a member of Mabcd Association of Electrical and Electronic Engineers and IEEE. Rabcd Tabcd was born in Sabcd, Nabcd, Abcd on 28 September 1949. He is professor of power engineering (1993); chief editor of scientific journal of “Pabcd Eabcd Pabcd” from 2000; director of Institute of Pabcd from 2002 up to 2009; academician and the first vicepresident of Aabcd Nabcd Aabcd of Sabcd from 2007. He is laureate of Aabcd State Prize (1978); Honored Scientist 6 13th International Conference on “Technical and Physical Problems of Electrical Engineering” (ICTPE-2017) Van, Turkey, 21-23 September 2017 of Aabcd (2005); co-chairman of International Conferences on “Tabcd and Pabcd Eabcd”. His research areas are theory of non-linear electrical chains with distributed parameters, neutral earthing and ferroresonant processes and alternative energy sources. His publications are more than 250 articles and patent and 5 monographs. 7