Fractional Order Identification Method and Control: Development of Control for Non-Minimum Phase Fractional Order System

The increasing use of renewable energy has resulted in the need for improved a dc-dc converters. This type of electronic-based equipment is needed to interface the dc voltages normally encountered with solar arrays and battery systems to voltage levels suitable for connecting three phase inverters to distribution level networks. As grid-connected solar power levels continue to increase, there is a corresponding need for improved modeling and control of power electronic converters. In particular, higher levels of boost ratios are needed to connect low voltage circuits (less than 1000 V) to medium voltage levels in the range of 13 kV to 34 kV. With boost ratios now exceeding a factor of 10, the inherent nonlinearities of boost converter circuits become more prominent and thereby lead to stability concerns under variable load conditions. This dissertation presents a new method for analyzing dc-dc converters using fractional order calculus. This provides control systems designers the ability to analyze converter frequency response with Bode plots that have pole-zero contributions other than +/- 20 dB/decade. This dissertation details a systematic method of deriving the optimal frequency-domain fit of nonlinear dc-dc converter operation by use of a modified describing function technique. Results are presented by comparing a conventional linearization technique (i.e., integer-order transfer functions) to the describing-function derived equivalent fractional-order model. The benefits of this approach in achieving improved stability margins with high-ratio dc-dc converters are presented

Multifrequency Averaging in Power Electronic Systems

Power electronic systems have been widely used in the electrical power processing for applications with power levels ranging from less than one watt in battery-operated portable devices to more than megawatts in the converters, inverters and rectifiers of the utility power systems. These systems typically involve the passive elements such as inductors, capacitors, and resistors, the switching electronic components such as IGBTs, MOSFETS, and diodes, and other electronic circuits. Multifrequency averaging is one of the widely used modeling and simulation techniques today for the analysis and design of power electronic systems. This technique is capable of providing the average behavior as well as the ripple behavior of power electronic systems. This work begins with the extension of multifrequency averaging to represent uniformly sampled PWM converters. A new multifrequency averaging method of solving an observed issue with model stability is proposed and validated. Multifrequency averaging can also be applied to study the instability phenomenon in power electronic systems. In particular, a reduced-order multifrequency averaging method, along with a genetic algorithm based procedure, is proposed in this work to estimate the regions of attraction of power electronic converters. The performance of this method is shown by comparing the accuracy and efficiency with the existing methods. Finally, a new continuous-time multifrequency averaging method of representing discrete-time systems is proposed. The proposed method is applied to model digitally controlled PWM converters. Simulation and hardware results show that the proposed method is capable of predicting the average behavior as well as the ripple behavior of the closed-loop systems. Future research in the area of multifrequency averaging is proposed

Design and Control of Power Converters 2019

In this book, 20 papers focused on different fields of power electronics are gathered. Approximately half of the papers are focused on different control issues and techniques, ranging from the computer-aided design of digital compensators to more specific approaches such as fuzzy or sliding control techniques. The rest of the papers are focused on the design of novel topologies. The fields in which these controls and topologies are applied are varied: MMCs, photovoltaic systems, supercapacitors and traction systems, LEDs, wireless power transfer, etc

Contributions to Control of Electronic Power Converters

This thesis deals with the control of electronic power converters. In its development two main parts have been differentiated. On the one hand, the problem of the voltage balance in the capacitors of the dc-link in a three-level NPC converter is addressed. On the other hand, given that the techniques used in the first part to model the converters need to make certain assumptions and, with the intention of avoiding averaged models, in the second part, switched affine models have been developed to design the control of the output voltage in DC-DC boost type converters. In this way, in the first part several control laws have been developed using an averaged model formulated by duty cycles for each level in each phase. This formulation allows to consider, in the controllers design stage, the degree of freedom associated with the homopolar voltage injection. Therefore, the controllers are designed as well as a part of the modulation, so that control and modulation are integrated in the same stage. In this way, three controllers have been designed where, apart from the objective of the voltage balance of the capacitors, other objectives such as the number of commutations or the quality of the output signal have also been improved. In the second part of the thesis, four methods have been developed for the design of control laws taking advantage of the modeling of converters as switched affine systems given their hybrid behaviour. Thus, the first two laws take advantage of this modeling using the delta operator to avoid numerical problems when using systems where the sampling time is very low. The first of these controllers is based on Lyapunov’s function while the second is independent of this function, thus obtaining less conservative results. The other two laws developed for switched affine systems use an alternative model to that performed in the first two controllers, so certain existing disadvantages are avoided using again a design not based on Lyapunov’s function. Thus, the first law presents a basic control but, even so, improves the results of other existing laws in the literature. Finally, a design method to deal with systems with variations in their parameters has been presented.La presente tesis trata sobre el control de convertidores electrónicos de potencia. En su desarrollo se han diferenciado dos partes principales. Por un lado, se trata el problema del balance de tensiones en los condensadores que forman el dc-link en un convertidor NPC de tres niveles. Por otro lado, dado que las técnicas utilizadas en la primera parte para modelar los convertidores necesitan realizar determinadas suposiciones y, con la intención de evitar modelos promediados, en la segunda parte se han desarrollado modelos afines conmutados para diseñar el control de la tensión de salida en convertidores DC-DC tipo boost. De esta forma, en la primera parte se han desarrollado varias leyes de control utilizando un modelo promediado formulado mediante ciclos de trabajo para cada nivel en cada fase. Esta formulación permite considerar en la fase de diseño de los controladores, un grado de libertad asociado a la inyección de tensión homopolar. Por lo tanto, se diseñan los controladores a la vez que una parte de la modulación, de forma que se integra control y modulación en una misma fase. De esta forma, se han diseñado tres controladores donde, a parte del objetivo de balancear la tensión de los condensadores, se ha ido buscando mejorar también otros objetivos como el número de conmutaciones o la calidad de la señal de salida. En la segunda parte de la tesis, se han desarrollado cuatro leyes de control aprovechando el modelado de convertidores como sistemas afines conmutados dada su naturaleza híbrida. De esta forma, las dos primeras leyes, aprovechan dicho modelado usando el operador delta para evitar problemas numéricos al utilizar sistemas donde el tiempo de muestreo es muy bajo. El primero de dichos controladores está basado en la función de Lyapunov mientras que el segundo es independiente de dicha función obteniendo así resultados menos conservadores. Las otras dos leyes desarrolladas para sistemas afines conmutados utilizan un modelado alternativo al realizado en las dos primeras, de forma que se evitan ciertas desventajas existentes y mantienen un diseño no basado en la función de Lyapunov. Así, la primera ley presenta un control más básico pero que, aun así, mejora los resultados de otras leyes existentes en la literatura. Por último, se ha presentado un procedimiento de diseño que hace frente a sistemas con variaciones en sus parámetros

Uncertainty and disturbance estimator design to shape and reduce the output impedance of inverter

Power inverters are becoming more and more common in the modern grid. Due to their switching nature, a passive filter is installed at the inverter output. This generates high output impedance which limits the inverter ability to maintain high power quality at the inverter output. This thesis deals with an impedance shaping approach to the design of power inverter control. The Uncertainty and Disturbance Estimator (UDE) is proposed as a candidate for direct formation of the inverter output impedance. The selection of UDE is motivated by the desire for the disturbance rejection control and the tracking controller to be decoupled. It is demonstrated in the thesis that due to this fact the UDE filter design directly influences the inverter output impedance and the reference model determines the inverter internal electromotive force. It was recently shown in the literature and further emphasized in this thesis that the classic low pass frequency design of the UDE cannot estimate periodical disturbances under the constraint of finite control bandwidth. Since for a power inverter both the reference signal and the disturbance signal are of periodical nature, the classic UDE lowpass filter design does not give optimal results. A new design approach is therefore needed. The thesis develops four novel designs of the UDE filter to significantly reduce the inverter output impedance and maintain low Total Harmonic Distortion (THD) of the inverter output voltage. The first design is the based on a frequency selective filter. This filter design shows superiority in both observing and rejecting periodical disturbances over the classic low pass filter design. The second design uses a multi-band stop design to reject periodical disturbances with some uncertainty in the frequency. The third solution uses a classic low pass filter design combined with a time delay to match zero phase estimation of the disturbance at the relevant spectrum. Furthermore, this solution is combined with a resonant tracking controller to reduce the tracking steady-state error in the output voltage. The fourth solution utilizes a low-pass filter combined with multiple delays to increase the frequency robustness. This method shows superior performance over the multi-band-stop and the time delayed filter in steady-state. All the proposed methods are validated through extensive simulation and experimental results

Modeling and control of power converters in weak and unbalanced electric grids

Grid converters increasingly affect power system operation due to the increasing share of renewable energy sources and less conventional power plants. This shift in power generation leads to converter-dominated weak grids, which show critical stability phenomena but also enable converters to contribute to grid stability and voltage support. This thesis presents critical parts of converter controls and describes models to assess their characteristics. These models are used to derive design criteria and dedicated stability analysis methods for grid converter controls