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Mathematical Model of Multi-Phase Power Converter for Parallel Computation

  • Vladimir Belov , Peter Leisner , Anders Mannikoff and Ilja Belov EMAIL logo
Published/Copyright: February 3, 2018

Abstract

Abstract — A mathematical model of a multi-phase power conversion system composed of modified bridge-elements (B-system) capable for parallel computation has been developed. Experimental validation on the example of a power system including a synchronous generator and an AC-DC rectifier has been performed. A mathematical algorithm for B-system assembly and steps to obtain mathematical model of the B-system have been developed. Integration of mathematical models of conversion system into the complete model of a multi-phase power system has been explained and evaluation of computational efficiency of parallel computation techniques for the developed model of an AC-DC-AC converter has been performed. The presented modelling method can be employed in the design phase of smart grids, for power quality and conducted emission analysis.

A Derivation of eqs (17)–(19) from eqs (15) and (16)

Expanding and collecting terms in eqs (15) and (16) results in the following equations:

(CL1L1CL1TCL1L12CL2TCL1L13CL3TCL2L21CL1TCL2L2CL2TCL2L23CL3TCL3L31CL1TCL3L32CL2TCL3L3CL3T)ddtIL+(CL1000CL2000CL3)NU+
+(CL1R1CL1TCL1R12CL2TCL1R13CL3TCL2R21CL1TCL2R2CL2TCL2R23CL3TCL3R31CL1TCL3R32CL2TCL3R3CL3T)IL+(CL1000CL2000CL3)MUC=0,
(CO1L1CO1TCO1L12CO2TCO1L13CO3TCO2L21CL1TCO2L2CO2TCO2L23CO3TCO3L31CO1TCO3L32CO2TCO3L3CO3T)ddtIL+(CO1000CO2000CO3)US+
+(CO1R1CO1TCO1R12CO2TCO1R13CO3TCO2R21CL1TCO2R2CO2TCO2R23CO3TCO3R31CO1TCO3R32CO2TCO3R3CO3T)IL+(CO1000CO2000CO3)NU+
+(CO1000CO2000CO3)MUC=0.

Let us now further develop the equations provided above, in order to arrive at the equations describing the currents related to each B-element:

(CL1L1CL1T)ddtIL1+(CL1L12CL2T)ddtIL2+(CL1L13CL3T)ddtIL3+
+(CL1R1CL1T)IL1+(CL1R12CL2T)IL2+(CL1R13CL3T)IL3+
+CL1N1U1+CL1M1UC1=0,
(CL2L21CL1T)ddtIL1+(CL2L2CL2T)ddtIL2+(CL2L23CL3T)ddtIL3+
+(CL2R21CL1T)IL1+(CL2R2CL2T)IL2+(CL2R23CL3T)IL3+
+CL2N2U2+CL2M2UC2=0,
(CL3L31CL1T)ddtIL1+(CL3L32CL2T)ddtIL2+(CL3L3CL3T)ddtIL3+
+(CL3R31CL1T)IL1+(CL3R32CL2T)IL2+(CL3R3CL3T)IL3+
+CL3N3U3+CL3M3UC3=0

In the compact form, these equations are written as eqs (17)–(19).

References

[1] Nagaraj V, Asmus P, Energy micro grids growing globally, Electric Energy T&D Magazine, Jul.-Aug. 2012: 38–40.Search in Google Scholar

[2] Blaabjerg F, Ionel DM. Renewable energy devices and systems – state-of-the-art technology, research and development, challenges and future trends. Electr Power Compon Syst. 2015;43(12):1319–28.10.1080/15325008.2015.1062819Search in Google Scholar

[3] Open Smart Grid Protocol (OSGP), ETSI GS OSG 001 V1.1.1 (2012-01), 2012.Search in Google Scholar

[4] Kraus R, Turkes P, Sigg J, Physics-based models of power semiconductor devices for the circuit simulator SPICE, Record. 29th Annual IEEE PESC 98 (Vol. 2), 17–22 May 1998: 1726–31.Search in Google Scholar

[5] Ammous A, Ammous K, Ayedi M, Sellami F. An advanced PWM-Switch Model including semiconductor device nonlinearities. IEEE Trans Power Electron. 2003;18(5):1230–3710.1109/TPEL.2003.816195Search in Google Scholar

[6] Liqiang Y, Zhengming Z, Hua B, Chongjian L, Yaohua L, The IGCT test platform for voltage source inverters. In: Proc. of 5th International Conference on Power Electronics and Drive Systems, 2003. PEDS 2003 (Vol.2), 17–20 Nov. 2003: 1291–94.10.1109/PEDS.2003.1283165Search in Google Scholar

[7] Maksimovic D, Stankovic AM, Thottuvelil VJ, Verghese GC. Modeling and simulation of power electronic converters. Proc IEEE. 2001;89(6):898–912.10.1109/5.931486Search in Google Scholar

[8] Luo Y, Dougal R, Santi E, Multi-resolution modeling of power converter using waveform reconstruction. In: Proc. of 33rd Annual Simulation Symposium, 2000 (SS 2000), 16–20 Apr 2000: 165–74.10.1109/SIMSYM.2000.844913Search in Google Scholar

[9] Fankhauser HR, Aneros K, Edris -A-A, Torseng S. Advanced simulation techniques for the analysis of power system dynamics. IEEE Comput Appl Power. 1990;3(4):31–36.10.1109/67.60751Search in Google Scholar

[10] Watson N, Arrillaga J. Harmonic assessment using electromagnetic transient simulation and frequency-dependent network equivalents. IEE Proc. On Generation, Transmission and Distribution. 2003;150(6):641–50.10.1049/ip-gtd:20030944Search in Google Scholar

[11] Xiong X, Ouyang J. Modeling and transient behavior analysis of an Inverter-based microgrid. Electric Power Compon Syst. 2011;40(1):112–30.10.1080/15325008.2011.621926Search in Google Scholar

[12] Yang T, Bozhko S, Le-Peuvedic JM, Asher G, Hill CI. Dynamic phasor modeling of multi-generator variable frequency electrical power systems. IEEE Trans Power Syst. 2016 Jan;31(1):563–71.10.1109/TPWRS.2015.2399371Search in Google Scholar

[13] Raghuwanshi SS, Singh A, Mokhariwale Y. A Comparison & performance of simulation tools MATLAB/SIMULINK, PSIM & PSPICE for power electronics circuits. Int J Advanced Res Comput Sci Software Eng. 2012;2(3):187–91.Search in Google Scholar

[14] Mendoza-Araya PA, Venkataramanan G. Stability analysis of AC microgrids using incremental phasor impedance matching. Electric Power Compon Syst. 2015;43(4):473–84.10.1080/15325008.2014.985346Search in Google Scholar

[15] Belov V, Belov I, Nemoykin V, Johansson A, Leisner P, Computer modelling and analysis of EMC in a multi-phase electrical system. In: Proc. of 3rd Nat. conference EMB04, Göteborg, Sweden, 2004: 294–301.Search in Google Scholar

[16] Belov V, Paldyaev N, Shamaev A, Johansson A, Leisner P, Belov I, A Complete mathematical model of an independent multi-phase power supply system based on multi-phase bridge-element concept. WSEAS Trans. on Circuits and Systems. 2005;4:1009–18.Search in Google Scholar

[17] Belov V, Leisner P, Johansson A, Paldyaev N, Shamaev A, Belov I. Mathematical modelling of a wind power system with an integrated active filter. J Electric Power Syst Res. 2009;79(1):117–25.10.1016/j.epsr.2008.05.007Search in Google Scholar

[18] Generator type ECO 3-2S/4. Datasheet DS041A/1 issue 003, 22/01/2004. www.elektromotoren.at. Access 08 March 2017.Search in Google Scholar

[19] Pacheco PS. Parallel programming with MPI. San Francisco, California: Morgan Kaufmann, 1997.Search in Google Scholar

[20] The OpenMP® API specification for parallel programming, http://openmp.org. Access 05 February 2017.Search in Google Scholar

[21] Liu C, Wu H, Feng L, Yang A. Parallel fourth-order Runge-Kutta method to solve differential equations In: Proc. of 2nd Int. Conf. on Information Computing and Applications (ICICA 2011), Qinhuangdao, China, October 28–31, 2011: 192–99.10.1007/978-3-642-25255-6_25Search in Google Scholar

[22] Korch M, Rauber T. Comparison of parallel implementations of Runge-Kutta solvers: message passing vs. threads. In: Joubert GR, Nagel WE, Peters FJ, Walter WV, editor(s). Parallel Computing Software Technology, Algorithms, Architectures and Applications. Advances in Parallel Computing. Vol. 13, 2004:209–16.Search in Google Scholar

[23] Van Der Houwen PJ, Sommeijer BP. Parallel iteration of high-order Runge-Kutta methods with stepsize control. J Comput Appl Math. 1990;29(1): 111–27. ISSN 0377-0427.10.1016/0377-0427(90)90200-JSearch in Google Scholar

Received: 2017-6-11
Accepted: 2018-1-13
Published Online: 2018-2-3

© 2018 Walter de Gruyter GmbH, Berlin/Boston

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