An electrical interpretation of mechanical systems via the pseudo-inductor in the Brayton-Moser equations

In this paper an analogy between mechanical and electrical systems is presented, where, in contrast to the traditional analogy, position dependence of the mass inertia matrix is allowed. In order to interpret the mechanical system in an electrical manner, a pseudo-inductor element is introduced to cope with inductor elements with voltage-dependent electromagnetic coupling. The starting point of this paper is given by systems described in terms of the Euler-Lagrange equations. Then, via the introduction of the pseudo-inductor, the Brayton-Moser equations are determined for the mechanical system. © 2005 IEEE.

Passivity voltage based control of the boost power converter used in photovoltaic system

Introduction. This paper presents a robust nonlinear control of the DC-DC boost converter feeding by a photovoltaic system based on the passivity control. The control law design uses the passivity approach. Novelty. The novelty consists in designing a control law for a photovoltaic system using a passivity approach based on energy shaping and associated with damping injection. Purpose. The purpose consists to develop a tool for design and optimize a control law of the photovoltaic system in order to improve its efficiency under some conditions such as the variations of the temperature, the irradiation and the parameters. Also, the control law design should be simple with a lower overshoot and a shorter settling time. Methods. This work uses the port Hamiltonian mathematical approach with minimization of the energy dissipation in boost converter of the photovoltaic system to illustrate the modification of energy and generate a specify duty cycle applied to the converter. Results. The results with MATLAB/SimPowerToolbox® have proven the robustness against parameter variations and effectiveness of the proposed control. Practical value. The experimental results, carried out using a dSPACE DS1104 system, are presented to show the feasibility and the robustness of the proposed control strategy against parameter variations.Вступ. У статті представлено надійне нелінійне керування живленням перетворювача постійного струму, що підвищує, фотоелектричною системою на основі керування пасивністю. У створенні закону управління використовується пасивний підхід. Новизна. Новизна полягає у розробці закону управління фотоелектричною системою з використанням пасивного підходу, заснованого на формуванні енергії та пов'язаного з упорскуванням демпфування. Мета. Мета полягає в тому, щоб розробити інструмент для проектування та оптимізації закону керування фотогальванічною системою для підвищення її ефективності за деяких умов, таких як зміни температури, опромінення та параметрів. Крім того, будова закону управління має бути простою, з меншим перерегулюванням і коротшим часом встановлення. Методи. У роботі використовується математичний підхід Гамільтона до порту з мінімізацією розсіювання енергії у перетворювачі фотоелектричної системи, що підвищує, щоб проілюструвати зміну енергії і створити заданий робочий цикл, що застосовується до перетворювача. Результати. Результати з використанням MATLAB/SimPowerToolbox® довели стійкість до змін параметрів та ефективність запропонованого керування. Практична цінність. Представлені експериментальні результати, отримані з використанням системи dSPACE DS1104, щоб показати здійсненність та стійкість запропонованої стратегії управління при  зміні параметрів

A port-Hamiltonian formulation of physical swithching systems with varying constraints

International audienceThis paper extends a generic method to design a port-Hamiltonian formulation modeling all geometric interconnection structures of a physical switching system with varying constraints. A non-minimal kernel representation of this family of structures (named Dirac structures) is presented. It is derived from the parameterized incidence matrices which are a mathematical representation of the primal and dual dynamic network graphs associated with the system. This representation has the advantage of making it possible to model complex physical switching systems with varying constraints and to fall within the framework of passivitybased control

Differentiation and Passivity for Control of Brayton-Moser Systems

This paper deals with a class of Resistive-Inductive-Capacitive (RLC) circuits and switched RLC (s-RLC) circuits modeled in Brayton Moser framework. For this class of systems, new passivity properties using a Krasovskii's type Lyapunov function as storage function are presented. Consequently, the supply-rate is a function of the system states, inputs and their first time-derivatives. Moreover, after showing the integrability property of the port-variables, two simple control methodologies called output shaping and input shaping are proposed for regulating the voltage in RLC and s-RLC circuits. Global asymptotic convergence to the desired operating point is theoretically proved for both proposed control methodologies. Moreover, robustness with respect to load uncertainty is ensured by the input shaping methodology. The applicability of the proposed methodologies is illustrated by designing voltage controllers for DC-DC converters and DC networks

Energy Shaping Control for Stabilization of Interconnected Voltage Source Converters in Weakly-Connected AC Microgrid Systems

With the ubiquitous installations of renewable energy resources such as solar and wind, for decentralized power applications across the United States, microgrids are being viewed as an avenue for achieving this goal. Various independent system operators and regional transmission operators such as Southwest Power Pool (SPP), Midcontinent System Operator (MISO), PJM Interconnection and Electric Reliability Council of Texas (ERCOT) manage the transmission and generation systems that host the distributed energy resources (DERs). Voltage source converters typically interconnect the DERs to the utility system and used in High voltage dc (HVDC) systems for transmitting power throughout the United States. A microgrid configuration is built at the 13.8kV 4.75MVA National Center for Reliable Energy Transmission (NCREPT) testing facility for performing grid-connected and islanded operation of interconnected voltage source converters. The interconnected voltage source converters consist of a variable voltage variable frequency (VVVF) drive, which powers a regenerative (REGEN) load bench acting as a distributed energy resource emulator. Due to the weak-grid interface in islanded mode testing, a voltage instability occurs on the VVVF dc link voltage causing the system to collapse. This dissertation presents a new stability theorem for stabilizing interconnected voltage source converters in microgrid systems with weak-grid interfaces. The new stability theorem is derived using the concepts of Dirac composition in Port-Hamiltonian systems, passivity in physical systems, eigenvalue analysis and robust analysis based on the edge theorem for parametric uncertainty. The novel stability theorem aims to prove that all members of the classes of voltage source converter-based microgrid systems can be stabilized using an energy-shaping control methodology. The proposed theorems and stability analysis justifies the development of the Modified Interconnection and Damping Assignment Passivity-Based Control (Modified IDA-PBC) method to be utilized in stabilizing the microgrid configuration at NCREPT for mitigating system instabilities. The system is simulated in MATLAB/SimulinkTM using the Simpower toolbox to observe the system’s performance of the designed controller in comparison to the decoupled proportional intergral controller. The simulation results verify that the Modified-IDA-PBC is a viable option for dc bus voltage control of interconnected voltage source converters in microgrid systems

Lagrangian modeling of switching electrical networks

In this paper, a general and systematic method is presented to model topologically complete electrical networks, with or without multiple or single switches, within the Euler–Lagrange framework. Apart from the physical insight that can be obtained in this way, the framework has proven to be useful for the application of passivity-based control techniques, which on a case by case basis already has shown to be useful for the control of power converters within the class of switching electrical networks. The switches are assumed to be ideal, and pulse-width modulation is taken into account. Magnetic coupling of inductive elements is also included in the framework.