Energy-based modelling and simulation of the interconnection of a back-to-back converter and a doubly-fed induction machine

This paper describes the port interconnection of two subsystems: a power electronics subsystem (a back-to-back AC/AC converter (B2B), coupled to a phase of the power grid), and an electromechanical subsystem (a doubly-fed induction machine (DFIM). The B2B is a variable structure system (VSS), due to the presence of control-actuated switches; however, from a modelling and simulation, as well as a control-design, point of view, it is sensible to consider modulated transformers (MTF in the bond graph language) instead of the pairs of complementary switches. The port-Hamiltonian models of both subsystems are presented and, using a power-preserving interconnection, the Hamiltonian description of the whole system is obtained; detailed bond graphs of all subsystems and the complete system are also provided. Using passivity-based controllers computed in the Hamiltonian formalism for both subsystems, the whole model is simulated; simulations are run to test the correctness and efficiency of the Hamiltonian network modelling approach used in this work.Peer Reviewe

Modeling and control of electromechanical systems

The material presented in the these notes covers the sessions Modelling of electromechanical systems, Passive control theory I and Passive control theory II of the II EURON/GEOPLEX Summer School on Modelling and Control of Complex Dynamical Systems. We start with a general description of what an electromechanical system is from a network modelling point of view. Next, a general formulation in terms of PHDS is introduced, and some of the previous electromechanical systems are rewritten in this formalism. Power converters, which are variable structure systems (VSS), can also be given a PHDS form. We conclude the modelling part of these lectures with a rather complex example, showing the interconnection of subsystems from several domains, namely an arrangement to temporally store the surplus energy in a section of a metropolitan transportation system based on dc motor vehicles, using either arrays of supercapacitors or an electric powered flywheel. The second part of the lectures addresses control of PHD systems. We first present the idea of control as power connection of a plant and a controller. Next we discuss how to circumvent this obstacle and present the basic ideas of Interconnection and Damping Assignment (IDA) passivity-based control of PHD systems

Energy-based modelling and simulation of the interconnection of a back-to-back converter and a doubly-fed induction machine

This paper describes the port interconnection of two subsystems: a power electronics subsystem (a back-to-back AC/CA converter (B2B), coupled to a phase of the power grid), and an electromechanical subsystem (a doubly-fed induction machine (DFIM). The B2B is a variable structure system (VSS), due to presence of control-actuated switches: however, from a modelling simulation, as well as a control-design, point of view, it is sensible to consider modulated transformers (MTF in the bond graph language) instead of the pairs of complementary switches. The port-Hamiltonian models of both subsystems are presented and, using a power-preserving interconnection, the Hamiltonian description of the whole system is obtained; detailed bond graphs of all subsystems and the complete system are also provided. Using passivity-based controllers computed in the Hamiltonian formalism for both subsystems, the whole model is simulated; simulations are run to rest the correctness and efficiency of the Hamiltonian network modelling approach used in this work.Peer Reviewe

Extended Galilean symmetries of non-relativistic strings

We consider two non-relativistic strings and their Galilean symmetries. These strings are obtained as the two possible non-relativistic (NR) limits of a relativistic string. One of them is non-vibrating and represents a continuum of non-relativistic massless particles, and the other one is a non-relativistic vibrating string. For both cases we write the generator of the most general point transformation and impose the condition of Noether symmetry. As a result we obtain two sets of non-relativistic Killing equations for the vector fields that generate the symmetry transformations. Solving these equations shows that NR strings exhibit two extended, infinite dimensional space-time symmetries which contain, as a subset, the Galilean symmetries. For each case, we compute the associated conserved charges and discuss the existence of non-central extensions.Postprint (author's final draft

Balanced model order reduction method for systems depending on a parameter

We provide an analytical framework for balanced realization model order reduction of linear control systems which depend on an unknown parameter. Besides recovering known results for the first order corrections, we obtain explicit novel expressions for the form of second order corrections for singular values and singular vectors. The final result of our procedure is an order reduced model which incorporates the uncertain parameter. We apply our algorithm to a system of masses and springs with parameter dependent coefficients.Postprint (author's final draft

Power Flow Control of a Doubly-Fed Induction Machine Coupled to a Flywheel

We consider a doubly–fed induction machine controlled through the rotor voltage and connected to a variable local load—that acts as an energy–switching device between a local prime mover (a flywheel) and the electrical power network. The control objective is to optimally regulate the power flow, and this is achieved by commuting between different steady–state regimes. We first show that the zero dynamics of the system is only marginally stable, thus complicating its control via feedback linearization. Instead, we apply the energy–based Interconnection and Damping Assignment Passivity–Based Control technique that does not require stable invertibility. It is shown that the partial differential equation that appears in this method can be circumvented by fixing the desired closed-loop total energy and adding new terms to the interconnection structure. Furthermore, to obtain a globally defined control law we introduce a state–dependent damping term that has the nice interpretation of effectively decoupling the electrical and mechanical parts of the system. This results in a globally convergent controller parameterized by two degrees of freedom, which can be used to implement the power management policy. The controller is simulated and shown to work satisfactorily for various realistic load changes.Peer Reviewe

A stator voltage oriented PI controller for the doubly-fed induction machine

In this paper we propose a new control scheme for the doubly–fed induction machine (DFIM) that offers significant advantages, and is considerably simpler, than the classical vector control method. In contrast with the latter, where the DFIM is represented in a stator flux–oriented frame, we propose here a model with orientation of the stator voltage. This allows for an easy decomposition of the active and reactive powers on the stator side and their regulation—acting on the rotor voltage—via stator current control. Our main contribution is the proof that a linear PI control around the stator currents ensures global stability for a feedback linearized DFIM, provided the gains are suitably selected. The feedback linearization stage requires only measurement of the rotor and stator currents, hence is easily implementable. Furthermore, to improve the robustness, an adaptive version that estimates the rotor resistance is proposed. Tuning rules for the PI gains are also provided. Finally, an outer loop control for the mechanical speed is introduced. The complete control system is tested both in simulations and experiments, showing good transient performance and robustness properties.Peer Reviewe

Power flow control of a doubly-fed induction machine coupled to a flywheel

We consider a doubly-fed induction machine –controlled through the rotor voltage and connected to a variable local load- that acts as an energy-switching device between a local prime mover (a flywheel) and the electrical power network. The control objective is to optimally regulate the power flow which is achieved commuting between two different steady-state regimes. We first show that zero dynamics of the system is only marginally stable complicating its control via feedback linearization. Instead, we apply the energy-based Interconnection and Damping Assignment Passivity-Based Control technique that does not require stable invertibility. It is shown that the partial differential equation that appears in this method can be obviated fixing the desired closed-loop total energy and adding new terms to the interconnection structure. Furthermore, to obtain a globally defined control law we introduce a state-dependent damping term that has the nice interpretation of effectively decoupling the electrical and mechanical parts of the system. This results in a globally asymptotically stabilizing controller parameterized by two degrees of freedom, which can be used to implement the power management policy. An indirect adaptive scheme for the rotor and stator resistances is also introduced. The controller is simulated and shown to work satisfactorily for various realistic load changes

Robust Hamiltonian passive control for higher relative degree outpus

We present an improvement of the well-know Interconnection and Damping Assignment-Passivity-based Control (IDA-PBC) technique. The IDA-PBC method is based on the Port –controlled Hamiltonian Systems description and requires the knowledge of the full energy (or Hamiltonian) function. This is a problem because, in general, the equilibrium point which is to be regulated depends on uncertain parameters. In this paper, we show how select the target port-Hamiltonian structure so that this dependence is reduced. This new approach allows to improve the robustness for higher relative degree outputs, and, for illustration purposes, is applied to a simple academic nonlinear syste

GeoPlex experimental setup: generator and converter

The experimental setup of the Flywhell Energy Storage System is presented. The system is made of a doubly-fed induction machine coupled to a flywheel and a back-to-back converte