Applications of perturbation theory to power electronic converters

Power Electronic converters usually require complex controllers, involving large numbers of state-space variables; their models, moreover, tend to include multiple nonlinearities. These characteristics make assessing the stability of systems dominated by power electronics converters particularly challenging. This work concerns the application of mathematical methods (in particular, attention focused on Singular Perturbation Theory) to power electronic systems, in order to model effectively their behaviour, reduce the size of their state-space systems, and assess their operating stability using simplified methods. Some preliminary work was performed on the ripple modelling of a DC-DC boost converter and a single-phase full-bridge inverter; second-order approximations of the ripple and average behaviour, computed by applying Singular Perturbation methods, were found to agree very well to the solutions computed for the initial-value problem ODEs. Singular Perturbation theory was subsequently applied to perform model reductions of power-electronic-based systems. First, a single-phase rectifier was considered, then AC microgrids. From a mathematical point of view, a similar approach was adopted in both cases to achieve the model reduction, but, given the different technical nature of such systems, they required separate literature reviews and preparatory work. The reductions were performed gradually, and several stages are here presented; results were tested in simulations, and stability analyses were compared to analogous analyses performed on the non-reduced full-sized systems

Applications of perturbation theory to power electronic converters

Power Electronic converters usually require complex controllers, involving large numbers of state-space variables; their models, moreover, tend to include multiple nonlinearities. These characteristics make assessing the stability of systems dominated by power electronics converters particularly challenging. This work concerns the application of mathematical methods (in particular, attention focused on Singular Perturbation Theory) to power electronic systems, in order to model effectively their behaviour, reduce the size of their state-space systems, and assess their operating stability using simplified methods. Some preliminary work was performed on the ripple modelling of a DC-DC boost converter and a single-phase full-bridge inverter; second-order approximations of the ripple and average behaviour, computed by applying Singular Perturbation methods, were found to agree very well to the solutions computed for the initial-value problem ODEs. Singular Perturbation theory was subsequently applied to perform model reductions of power-electronic-based systems. First, a single-phase rectifier was considered, then AC microgrids. From a mathematical point of view, a similar approach was adopted in both cases to achieve the model reduction, but, given the different technical nature of such systems, they required separate literature reviews and preparatory work. The reductions were performed gradually, and several stages are here presented; results were tested in simulations, and stability analyses were compared to analogous analyses performed on the non-reduced full-sized systems

Small signal modeling and analysis of microgrid systems

This dissertation focuses on small-signal modeling and analysis of inverter based microgrid systems. The proposed microgrid consists of two microsources placed on two different buses. The buses are connected using a distribution feeder with some impedance. The proposed microgrid can operate with the grid support, or without the grid support. When operated without the grid support, the standalone system’s microsources participate in controlling the system voltage and frequency. For a non-inertia source, such as the inverter, the load perturbations play an important role in system dynamics. In paper-I, such complex system was studied. In the grid-tied mode, the microsources share the load demand with other sources that are present in the main grid. The control algorithm for such system is much simpler than that of the islanded system. However, when aggregated in multi-bus system, prohibitively higher order state-space models are formed. In paper-II, a reduced order modeling of such systems was considered. Singular perturbation method was applied to identify the two time-scale property of the system. In paper-III, a similar approach was taken to develop a reduced order model of the islanded system that was developed in paper-I. Application of such reduced order models were illustrated by using them to simulate a modified IEEE-37 bus microgrid system. The islanded microgrids system’s stability is characterized in paper-IV by the Markov Jump Linear System Analysis. Conservative bounds on the expected value of the state were determined from a combination of the Markov process parameters, the dynamics of each linear system, and the magnitude of the impulses. The conclusions were verified with the simulation results. --Abstract, page iii

LHC Beam Stability and Feedback Control - Orbit and Energy -

This report presents the stability and control of the Large Hadron Collider's (LHC) two beam orbits and their particle momenta using beam-based feedback systems. The LHC, presently being built at CERN, will store, accelerate and provide particle collisions with a maximum particle momentum of 7TeV/c and a nominal luminosity of L = 10^34 cm^â2s^â1. The presence of two beams, with both high intensity as well as high particle energies, requires excellent control of particle losses inside a superconducting environment, which will be provided by the LHC Cleaning and Machine Protection System. The performance and function of this and other systems depends critically on the stability of the beam and may eventually limit the LHC performance. Environmental and accelerator-inherent sources as well as failure of magnets and their power converters may perturb and reduce beam stability and may consequently lead to an increase of particle loss inside the cryogenic mass. In order to counteract these disturbances, control of the key beam parameters â orbit, tune, energy, coupling and chromaticity â will be an integral part of LHC operation. Since manual correction of these parameters may reach its limit with respect to required precision and expected time-scales, the LHC is the first proton collider that requires automatic feedback control systems for safe and reliable machine operation. The aim of this report is to help and contribute towards these efforts

Control of AC/DC microgrids with renewables in the context of smart grids including ancillary services and electric mobility

Microgrids are a very good solution for current problems raised by the constant growth of load demand and high penetration of renewable energy sources, that results in grid modernization through “Smart-Grids” concept. The impact of distributed energy sources based on power electronics is an important concern for power systems, where natural frequency regulation for the system is hindered because of inertia reduction. In this context, Direct Current (DC) grids are considered a relevant solution, since the DC nature of power electronic devices bring technological and economical advantages compared to Alternative Current (AC). The thesis proposes the design and control of a hybrid AC/DC Microgrid to integrate different renewable sources, including solar power and braking energy recovery from trains, to energy storage systems as batteries and supercapacitors and to loads like electric vehicles or another grids (either AC or DC), for reliable operation and stability. The stabilization of the Microgrid buses’ voltages and the provision of ancillary services is assured by the proposed control strategy, where a rigorous stability study is made. A low-level distributed nonlinear controller, based on “System-of-Systems” approach is developed for proper operation of the whole Microgrid. A supercapacitor is applied to deal with transients, balancing the DC bus of the Microgrid and absorbing the energy injected by intermittent and possibly strong energy sources as energy recovery from the braking of trains and subways, while the battery realizes the power flow in long term. Dynamical feedback control based on singular perturbation analysis is developed for supercapacitor and train. A Lyapunov function is built considering the interconnected devices of the Microgrid to ensure the stability of the whole system. Simulations highlight the performance of the proposed control with parametric robustness tests and a comparison with traditional linear controller. The Virtual Synchronous Machine (VSM) approach is implemented in the Microgrid for power sharing and frequency stability improvement. An adaptive virtual inertia is proposed, then the inertia constant becomes a system’s state variable that can be designed to improve frequency stability and inertial support, where stability analysis is carried out. Therefore, the VSM is the link between DC and AC side of the Microgrid, regarding the available power in DC grid, applied for ancillary services in the AC Microgrid. Simulation results show the effectiveness of the proposed adaptive inertia, where a comparison with droop and standard control techniques is conducted.As Microrredes são uma ótima solução para os problemas atuais gerados pelo constante crescimento da demanda de carga e alta penetração de fontes de energia renováveis, que resulta na modernização da rede através do conceito “Smart-Grids”. O impacto das fontes de energia distribuídas baseados em eletrônica de potência é uma preocupação importante para o sistemas de potência, onde a regulação natural da frequência do sistema é prejudicada devido à redução da inércia. Nesse contexto, as redes de corrente contínua (CC) são consideradas um progresso, já que a natureza CC dos dispositivos eletrônicos traz vantagens tecnológicas e econômicas em comparação com a corrente alternada (CA). A tese propõe o controle de uma Microrrede híbrida CA/CC para integrar diferentes fontes renováveis, incluindo geração solar e frenagem regenerativa de trens, sistemas de armazenamento de energia como baterias e supercapacitores e cargas como veículos elétricos ou outras (CA ou CC) para confiabilidade da operação e estabilidade. A regulação das tensões dos barramentos da Microrrede e a prestação de serviços anciliares são garantidas pela estratégia de controle proposta, onde é realizado um rigoroso estudo de estabilidade. Um controlador não linear distribuído de baixo nível, baseado na abordagem “System-of-Systems”, é desenvolvido para a operação adequada de toda a rede elétrica. Um supercapacitor é aplicado para lidar com os transitórios, equilibrando o barramento CC da Microrrede, absorvendo a energia injetada por fontes de energia intermitentes e possivelmente fortes como recuperação de energia da frenagem de trens e metrôs, enquanto a bateria realiza o fluxo de potência a longo prazo. O controle por dynamical feedback baseado numa análise de singular perturbation é desenvolvido para o supercapacitor e o trem. Funções de Lyapunov são construídas considerando os dispositivos interconectados da Microrrede para garantir a estabilidade de todo o sistema. As simulações destacam o desempenho do controle proposto com testes de robustez paramétricos e uma comparação com o controlador linear tradicional. O esquema de máquina síncrona virtual (VSM) é implementado na Microrrede para compartilhamento de potência e melhoria da estabilidade de frequência. Então é proposto o uso de inércia virtual adaptativa, no qual a constante de inércia se torna variável de estado do sistema, projetada para melhorar a estabilidade da frequência e prover suporte inercial. Portanto, o VSM realiza a conexão entre lado CC e CA da Microrrede, onde a energia disponível na rede CC é usada para prestar serviços anciliares no lado CA da Microrrede. Os resultados da simulação mostram a eficácia da inércia adaptativa proposta, sendo realizada uma comparação entre o controle droop e outras técnicas de controle convencionais

Stability Analysis of Converter Control Strategies for Power Electronics-Dominated Power Systems

The electric power system, whose well-established structure consolidated over decades of studies is composed of large centralized generating units, transmission systems, and distributed loads, is currently experiencing a significant transformation, posing new challenges for its safe operation in the near future. The increasing amount of grid-connected power electronics-based converters associated with renewable energy sources, is reducing the amount of energy produced by means of conventional generating units, generally represented by large synchronous machines (SMs) directly connected to the grid. As a consequence, declining system inertia, as well as reduced fault currents affecting short-circuit level and retained voltage under fault conditions, are expected. This has caused concerns among system operators (SOs) worldwide about the stability of the future power system, triggering discussions in different countries about the need for new converter control strategies, which would allow safe system operation under the expected grid configuration. In this scenario, the concept of ”grid-forming (GFM) converters” has been recently proposed as a possible solution allowing high-penetration of power electronics-based generation. Initially introduced in the context of microgrids, the concept of GFM converters needs to be reviewed for applications in wide interconnected systems. Indeed, at the present time, a well-established formulation is still missing in the literature, and several committees worldwide are currently working on a definition for identifying the characteristics of such converters. Due to the initial concern of SOs related to declining system inertia, the concept of GFM converters has been often associated with the idea of virtual inertia, and namely the emulation of a synthetic inertial response by means of a power electronics-based converter. Yet, this is only one aspect related to the increase of power electronics-based generation, and the concept of a GFM converter includes other features, which, however, need to be properly specified in order to provide clear guidelines for manufacturers aiming to the development of suitable converter control strategies. This thesis addresses the topic of GFM converters from a control perspective, and aims to characterize potential features, as well as the relevant issues related to this technology. First, the characteristics of a GFM converter are identified according to an extensive literature overview, so that by reviewing international practice on this technology, a general formulation for a GFM converter control structure is identified. Particular emphasis is given to the synchronization principle adopted by the converter which, contrary to state-of-the-art grid-connected converters adopting a dedicated unit for grid synchronization purposes, is generally achieved in a GFM converter by reproducing the power-synchronization mechanism of a SM. An extensive small-signal stability analysis is performed in order to identify the implications of the identified converter behaviour on converter stability, as well as the effects due to the interactions between converters operating nearby. Finally, potential issues related to the implementation of a GFM converter are highlighted, and possible solutions are proposed, whose effectiveness is validated by means of hardware-in-the-loop (HIL) simulations, as well as experimental tests in a laboratory environment, by adopting power-HIL (PHIL) test benches

PSO Based reduced order modelling of autonomous AC microgrid considering state perturbation

Reduced order modelling of complex autonomous microgrid system is crucial to its small signal modelling and stability concerns. To reduce the storage requirements and computational time, the order of such microgrids can be reduced by Model Order Reduction (MOR) techniques. This paper presents an optimal reduction technique, which retains dominant poles of the original system and achieves subsequent error minimization through the Particle Swarm Optimization algorithm (PSO). The 36th order complex microgrid system is reduced to 9th order approximant, which retains the significant dynamics of the original system. The simulation results reflect the superiority of the proposed method as compared to the balanced truncation method in terms of the time and frequency domain analysis of the reduced order equivalents. State perturbation in the state space model has also been considered in full as well as reduced order system dynamics and eigenvalue analysis for system stability