{"id":868,"date":"2013-09-30T15:29:47","date_gmt":"2013-09-30T14:29:47","guid":{"rendered":"https:\/\/l2ep.univ-lille.fr\/?page_id=868"},"modified":"2018-10-26T13:59:21","modified_gmt":"2018-10-26T12:59:21","slug":"developpements","status":"publish","type":"page","link":"https:\/\/l2ep.univ-lille.fr\/en\/groupes-de-recherche\/equipe-commande\/developpements\/","title":{"rendered":"Generalized Vectorial Formalism (GVF)"},"content":{"rendered":"

Within of the study of multiphase electric drives (with more than two independent currents) an approach was developed [1] in order to generalize the formalism of the Space Phasor adapted to inverter-machine systems having only two independent currents.<\/p>\n

The GVF, Generalized Vectorial Formalism, thus makes it possible to model in a unified way the systems having multi-degrees of freedom. Here are some examples. An N-leg inverter is modelled by a vectorial polyhedron of dimension N (a hypercube) or an N-phase electric machine, by the eigenspaces and eigenvectors associated to eigenvalues of inductance matrix after a linear transformation. The machine supply is thus defined by a linear application between inverter space and machine space, with its core.<\/p>\n

Concretely, a complex machine is represented by an association of several equivalent di-phase or single-phase machines. Two chapters, published in Wiley, were devoted to a presentation of the multiphase electric drives by this formalism [2] [3]. This approach was extended to the multi-actuator systems of Gantry type and the piezoelectric multi-actuator systems. Associated with the EMR (Energetic Macroscopic Representation), the GVF allows to obtain a decoupled representation of the systems, leading to a control scheme by inversion.<\/p>\n

A relevant application of this approach, in addition to a real-time implementation of the optimal controls [4], consists to study multiphase drives in flux weakening mode where it is necessary to control the inverter very close to voltage saturation in order to exploit the DC-bus as well as possible. Thanks to the GVF, the machine voltage during flux weakening operation can be obtained according to a maximum given torque.<\/p>\n

Within the SOFRACI project financed by FUI (Fonds Unique Interminist\u00e9riel in French), the objective is to develop a motorization for electric vehicle with integrated fast charger using the same traction components (motor and power electronics). Based on analytical models of the machine, a flux weakening strategy has been developed. The 3rd harmonic injection of voltage by taking into account of the inverter saturation, allows to obtain a higher torque for a given maximum current [5]. A 3D-representation of the inverter makes it possible to visualize the space of available voltage (see Fig. 1).<\/p>\n

 <\/p>\n

\"formalisme<\/a><\/p>\n

Space of available voltage for a 6-leg Voltage Source Inverter feeding a 3-phase machine (3 independent currents) in flux weakening with voltage saturation<\/i><\/strong><\/span><\/p>\n

 <\/p>\n

A 48V, 10-15kW, 0-14000 rpm 5-phase machine has been also studied in the MHYGALE project funded by ADEME. With a speed range from 2000 rpm to 14000 rpm during the flux weakening operation, some control strategies, based on cartography approach, have been proposed [6] by injecting the 3rd and the 5th harmonic of voltage in steady state.<\/p>\n

Used to make easier the control of multiphase or multi-actuator systems, the GVF is also a powerful tool for multiphase machine design. Indeed, analyzing the characteristics of equivalent machines or sub-systems allow to define a conceptual specification suitable for the control of these sub-systems (inductance values of the machine for example).<\/p>\n

\"machine<\/a><\/p>\n

Example of a machine designed and controlled at the laboratory<\/em><\/strong><\/span><\/p>\n

 <\/p>\n

References :<\/strong><\/span><\/p>\n

[O1] E. Semail, \u00ab Outils et m\u00e9thodologie d\u2019\u00e9tude des syst\u00e8mes \u00e9lectriques polyphas\u00e9s. G\u00e9n\u00e9ralisation de la m\u00e9thode des vecteurs d\u2019espace<\/i>\u00bb, Th\u00e8se de doctorat en G\u00e9nie Electrique, 2000, Universit\u00e9 des Sciences et Technologie de LILLE
\nhttp:\/\/tel.archives-ouvertes.fr\/tel-00266256\/<\/span><\/a><\/span><\/strong><\/span><\/p>\n

[O2] X. Kestelyn, E. Semail, \u00ab\u00a0Multiphase Voltage Source Inverters\u201d chap 8 in book \u201cStatic Converters\u00a0\u00bb, ISBN. 978-1-84821-195-7. ISTE Ltd and John Wiley & Sons Inc, mars 2011, 27 pages.
\nhttp:\/\/eu.wiley.com\/WileyCDA\/WileyTitle\/productCd-1848211953.html<\/span><\/a><\/span><\/span><\/strong><\/p>\n

[O3] X. Kestelyn, E. Semail , \u201cVectorial Modeling and Control of Multiphase Machines with Non-salient Poles Supplied by an Inverter\u201d, Chap7 in book \u201c Control of Non-conventional Synchronous Motors\u201d, ISTE Ltd and John Wiley & Sons Inc, ISBN: 9781848213319, 2012, 44 pages
\nhttp:\/\/eu.wiley.com\/WileyCDA\/WileyTitle\/productCd-184821331X.html<\/span><\/a><\/span><\/span><\/strong><\/p>\n

[O4] X.\u00a0 Kestelyn, E. Semail, \u201cA Vectorial Approach for Generation of Optimal Current References for Multiphase Permanent Magnet Synchronous Machines in Real-time\u201d, IEEE Transactions on Industrial Electronics, Vol 58, N\u00b011, pp5057-5065, Nov 2011. doi: 10.1109\/TIE.2011.2119454 (https:\/\/hal.archives-ouvertes.fr\/hal-00785154\/document<\/span><\/strong><\/a>)<\/p>\n

[O5] P. Sandulescu, F. Meinguet, X. Kestelyn, E. Semail, A. Bruyere, \u00ab\u00a0Flux-weakening operation of open-end winding drive integrating a cost effective high-power charger\u201d, IET Electrical Systems in Transportation (accept\u00e9 pour publication nov 2012), 6-2013, pp.12? <\/span><\/span><\/strong>doi: 10.1049\/iet-est.2012.0026\u00a0\u00a0(https:\/\/hal.archives-ouvertes.fr\/hal-00790157\/document<\/a><\/span><\/strong><\/span>)<\/span><\/p>\n

[O6] M. Trabelsi, N.K. Nguyen, E. Semail, \u201c<\/span>Real-time Switches Fault Diagnosis based on Typical Operating Characteristics of Five-Phase Permanent Magnet Synchronous Machines\u00a0\u00bb\u00a0 , IEEE Transactions on Industrial Electronics, Vol 63, N\u00b08, pp 4683-4694, August 2016, DOI 10.1109\/TIE.2016.2554540,\u00a0<\/span><\/span>\u00a0url (https:\/\/hal.archives-ouvertes.fr\/hal-01314309\/document<\/a><\/span><\/strong>)<\/p>\n

[O7] T.J. Dos Santos Moraes, N.K. Nguyen, E. Semail, F. Meinguet, M. Guerin,\u00a0<\/span><\/span>\u201cNew Electrical Inversed-Series Connection for Even-Phase Symmetrical\u00a0<\/span><\/span>PMSMs\u00a0<\/span>\u00ab\u00a0, Transaction on Power Electronics , Volume: 33, Issue 9, pp7938-7947, sept 2018,\u00a0<\/span><\/span>DOI : 10.1109\/TPEL.2017.2766359, 9\u00a0<\/span>\u00a0url (http:\/\/hdl.handle.net\/10985\/13796<\/a><\/span><\/strong><\/span>)\u00a0\u00a0<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

Within of the study of multiphase electric drives (with more than two independent currents) an approach was developed [1] in order to generalize the formalism of the Space Phasor adapted to inverter-machine systems having only two independent currents. The GVF, Generalized Vectorial Formalism, thus makes it possible to model in a unified way the systems […]<\/p>\n","protected":false},"author":3,"featured_media":0,"parent":568,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"_links":{"self":[{"href":"https:\/\/l2ep.univ-lille.fr\/en\/wp-json\/wp\/v2\/pages\/868"}],"collection":[{"href":"https:\/\/l2ep.univ-lille.fr\/en\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/l2ep.univ-lille.fr\/en\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/l2ep.univ-lille.fr\/en\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/l2ep.univ-lille.fr\/en\/wp-json\/wp\/v2\/comments?post=868"}],"version-history":[{"count":39,"href":"https:\/\/l2ep.univ-lille.fr\/en\/wp-json\/wp\/v2\/pages\/868\/revisions"}],"predecessor-version":[{"id":5257,"href":"https:\/\/l2ep.univ-lille.fr\/en\/wp-json\/wp\/v2\/pages\/868\/revisions\/5257"}],"up":[{"embeddable":true,"href":"https:\/\/l2ep.univ-lille.fr\/en\/wp-json\/wp\/v2\/pages\/568"}],"wp:attachment":[{"href":"https:\/\/l2ep.univ-lille.fr\/en\/wp-json\/wp\/v2\/media?parent=868"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}