Effect of State Feedback Coupling on the Design of Voltage Source Inverters for Standalone Applications

This Ph.D. thesis aims at investigating the effect of state feedback cross‐coupling decoupling of the capacitor voltage on the dynamics performance of Voltage Source Inverters for standalone microgrids/Uninterruptible Power Supply systems. Computation and PWM delays are the main factors which limit the achievable bandwidth of current regulators in digital implementations. In particular, the performance of state feedback decoupling is degraded because of these delays. Two decoupling techniques aimed at improving the transient response of voltage and current regulators are investigated, named nonideal and ideal capacitor voltage decoupling respectively. In particular, the latter solution consists in leading the capacitor voltage on the state feedback decoupling path in order to compensate for system delays. Practical implementation issues are discussed with reference to both the decoupling techniques. Moreover, different resonant regulators structures for the inner current loop are analysed and compared to investigate which is the most suitable for standalone microgrid applications. A design methodology for the voltage loop, which considers the closed loop transfer functions developed for the inner current loop, is also provided. Proportional resonant voltage controllers tuned at specific harmonic frequencies are designed according to the Nyquist criterion taking into account application requirements. For this purpose, a mathematical expression based on root locus analysis is proposed to find the minimum value of the resonant gain at the fundamental frequency. The exact model of the output LC filter of a three‐phase inverter is derived in the z‐domain. The devised formulation allows the comparison of two techniques based on a lead compensator and Smith predictor structure. These solutions permit the bandwidth of the current regulator to be widened while still achieving good dynamic performance. As a consequence, the voltage regulator can be designed for a wide bandwidth and even mitigates odd harmonics arising with unbalance loads supply. Discrete‐time domain implementation issues of an anti‐wind up scheme are discussed as well, highlighting the limitations of some discretization methods. Experimental tests performed in accordance to Uninterruptible Power Supply standards verify the theoretical analysis

Numerical methods for queues with shared service

A queueing system is a mathematical abstraction of a situation where elements, called customers, arrive in a system and wait until they receive some kind of service. Queueing systems are omnipresent in real life. Prime examples include people waiting at a counter to be served, airplanes waiting to take off, traffic jams during rush hour etc. Queueing theory is the mathematical study of queueing phenomena. As often neither the arrival instants of the customers nor their service times are known in advance, queueing theory most often assumes that these processes are random variables. The queueing process itself is then a stochastic process and most often also a Markov process, provided a proper description of the state of the queueing process is introduced. This dissertation investigates numerical methods for a particular type of Markovian queueing systems, namely queueing systems with shared service. These queueing systems differ from traditional queueing systems in that there is simultaneous service of the head-of-line customers of all queues and in that there is no service if there are no customers in one of the queues. The absence of service whenever one of the queues is empty yields particular dynamics which are not found in traditional queueing systems. These queueing systems with shared service are not only beautiful mathematical objects in their own right, but are also motivated by an extensive range of applications. The original motivation for studying queueing systems with shared service came from a particular process in inventory management called kitting. A kitting process collects the necessary parts for an end product in a box prior to sending it to the assembly area. The parts and their inventories being the customers and queues, we get ``shared service'' as kitting cannot proceed if some parts are absent. Still in the area of inventory management, the decoupling inventory of a hybrid make-to-stock/make-to-order system exhibits shared service. The production process prior to the decoupling inventory is make-to-stock and driven by demand forecasts. In contrast, the production process after the decoupling inventory is make-to-order and driven by actual demand as items from the decoupling inventory are customised according to customer specifications. At the decoupling point, the decoupling inventory is complemented with a queue of outstanding orders. As customisation only starts when the decoupling inventory is nonempty and there is at least one order, there is again shared service. Moving to applications in telecommunications, shared service applies to energy harvesting sensor nodes. Such a sensor node scavenges energy from its environment to meet its energy expenditure or to prolong its lifetime. A rechargeable battery operates very much like a queue, customers being discretised as chunks of energy. As a sensor node requires both sensed data and energy for transmission, shared service can again be identified. In the Markovian framework, "solving" a queueing system corresponds to finding the steady-state solution of the Markov process that describes the queueing system at hand. Indeed, most performance measures of interest of the queueing system can be expressed in terms of the steady-state solution of the underlying Markov process. For a finite ergodic Markov process, the steady-state solution is the unique solution of $N-1$ balance equations complemented with the normalisation condition, $N$ being the size of the state space. For the queueing systems with shared service, the size of the state space of the Markov processes grows exponentially with the number of queues involved. Hence, even if only a moderate number of queues are considered, the size of the state space is huge. This is the state-space explosion problem. As direct solution methods for such Markov processes are computationally infeasible, this dissertation aims at exploiting structural properties of the Markov processes, as to speed up computation of the steady-state solution. The first property that can be exploited is sparsity of the generator matrix of the Markov process. Indeed, the number of events that can occur in any state --- or equivalently, the number of transitions to other states --- is far smaller than the size of the state space. This means that the generator matrix of the Markov process is mainly filled with zeroes. Iterative methods for sparse linear systems --- in particular the Krylov subspace solver GMRES --- were found to be computationally efficient for studying kitting processes only if the number of queues is limited. For more queues (or a larger state space), the methods cannot calculate the steady-state performance measures sufficiently fast. The applications related to the decoupling inventory and the energy harvesting sensor node involve only two queues. In this case, the generator matrix exhibits a homogene block-tridiagonal structure. Such Markov processes can be solved efficiently by means of matrix-geometric methods, both in the case that the process has finite size and --- even more efficiently --- in the case that it has an infinite size and a finite block size. Neither of the former exact solution methods allows for investigating systems with many queues. Therefore we developed an approximate numerical solution method, based on Maclaurin series expansions. Rather than focussing on structural properties of the Markov process for any parameter setting, the series expansion technique exploits structural properties of the Markov process when some parameter is sent to zero. For the queues with shared exponential service and the service rate sent to zero, the resulting process has a single absorbing state and the states can be ordered such that the generator matrix is upper-diagonal. In this case, the solution at zero is trivial and the calculation of the higher order terms in the series expansion around zero has a computational complexity proportional to the size of the state space. This is a case of regular perturbation of the parameter and contrasts to singular perturbation which is applied when the service times of the kitting process are phase-type distributed. For singular perturbation, the Markov process has no unique steady-state solution when the parameter is sent to zero. However, similar techniques still apply, albeit at a higher computational cost. Finally we note that the numerical series expansion technique is not limited to evaluating queues with shared service. Resembling shared queueing systems in that a Markov process with multidimensional state space is considered, it is shown that the regular series expansion technique can be applied on an epidemic model for opinion propagation in a social network. Interestingly, we find that the series expansion technique complements the usual fluid approach of the epidemic literature

Modelling and control techniques for multiphase electric drives: a phase variable approach

Multiphase electric drives are today one of the most relevant research topics for the electrical engineering scientific community, thanks to the many advantages they offer over standard three-phase solutions (e.g., power segmentation, fault-tolerance, optimized performances, torque/power sharing strategies, etc...). They are considered promising solutions in many application areas, like industry, traction and renewable energy integration, and especially in presence of high-power or high-reliability requirements. However, contrarily to the three-phase counterparts, multiphase drives can assume a wider variety of different configurations, concerning both the electrical machine (e.g., symmetrical/asymmetrical windings disposition, concentrated/distributed windings, etc...) and the overall drive topology (e.g., single-star configuration, multiple-star configuration, open-end windings, etc…). This aspect, together with the higher number of variables of the system, can make their analysis and control more challenging, especially when dealing with reconfigurable systems (e.g., in post-fault scenarios). This Ph.D. thesis is focused on the mathematical modelling and on the control of multiphase electric drives. The aim of this research is to develop a generalized model-based approach that can be used in multiple configurations and scenarios, requiring minimal reconfigurations to deal with different machine designs and/or different converter topologies, and suitable both in healthy and in faulty operating conditions. Standard field-oriented approaches for the analysis and control of multiphase drives, directly derived as extensions of the three-phase equivalents, despite being relatively easy and convenient solutions to deal with symmetrical machines, may suffer some hurdles when applied to some asymmetrical configurations, including post-fault layouts. To address these issues, a different approach, completely derived in the phase variable domain, is here developed. The method does not require any vector space decomposition or rotational transformation but instead explicitly considers the mathematical properties of the multiphase machine and the effects of the drive topology (which typically introduces some constraints on the system variables). In this thesis work, the proposed approach is particularized for multiphase permanent magnet synchronous machines and for multiphase synchronous reluctance machines. All the results are obtained through rigorous mathematical derivations, and are supported and validated by both numerical analysis and experimental tests. As proven considering many different configurations and scenarios, the main benefits of the proposed methodology are its generality and flexibility, which make it a viable alternative to standard modelling and control algorithms

Modulation and Control Techniques for Performance Improvement of Micro Grid Tie Inverters

The concept of microgrids is a new building block of smart grid that acts as a single controllable entity which allows reliable interconnection of distributed energy resources and loads and provides alternative way of their integration into power system. Due to its specifics, microgrids require different control strategies and dynamics of regulation as compared to ones used in conventional utility grids. All types of power converters used in microgrid share commonalities which potentially affect high frequency modes of microgrid in same manner. There are numerous unique design requirements imposed on microgrid tie inverters, which are dictated by the nature of the microgrid system and bring major challenges that are reviewed and further analyzed in this work. This work introduces, performs a detailed study on, and implements nonconventional control and modulation techniques leading to performance improvement of microgrid tie inverters in respect to aforementioned challenges

Theory, Simulation, and Implementation of Grid Connected Back to Back Converters Utilizing Voltage Oriented Control

This work presents a back to back converter topology with the ability to connect two power systems of different voltages and frequencies for the exchange of power. By utilizing indirect AC/AC conversion decoupling is achieved between the power systems with one of the three-phase, two-level voltage source converters performing the AC/DC conversion that maintains the required DC bus voltage level at unity power factor while the other converter operates in all four quadrants supplying/consuming active and/or reactive power with the other power system. The prototype implementation resides at UW-Milwaukee’s USR Building microgrid test bed facility. A possible application topology would be the converter that maintains the DC bus voltage to be connected to the microgrid’s electrical bus of distributed energy sources while the other converter is connected to the utility in order to supply the required active and/or reactive power to support the needs of the grid

Five-Level Flying Capacitor Converter used as a Static Compensator for Current Unbalances in Three-Phase Distribution Systems

This thesis presents and evaluates a solution for unbalanced current loading in three-phase distribution systems. The proposed solution uses the flying capacitor multilevel converter as its main topology for an application known as Unbalanced Current Static Compensator. The fundamental theory, controller design and prototype construction will be presented along with the experimental results. The Unbalanced Current Static Compensator main objective is the balancing of the up-stream currents from the installation point to eliminate the negative- and zero-sequence currents originated by unbalanced single-phase loads. Three separate single-phase flying capacitor converters are controlled independently using a d-q rotating reference frame algorithm to allow easier compensation of reactive power. Simulations of the system were developed in MATLAB/SIMULINK™ in order to validate the design parameters; then, testing of the UCSC prototype was performed to confirm the control algorithm functionality. Finally, experimental result are presented and analyzed

Modular Multilevel Cascaded Flying Capacitor STATCOM for Balanced and Unbalanced Load Compensation

Voltage and current unbalance are major problems in distribution networks, particularly with the integration of distributed generation systems. One way of mitigating these issues is by injecting negative sequence current into the distribution network using a Static Synchronous Compensator (STATCOM) which normally also regulates the voltage and power factor. The benefits of modularity and scalability offered by Modular Multilevel Cascaded Converters (MMCC) make them suitable for STATCOM application. A number of different types of MMCC may be used, classified according to the sub-module circuit topology used. Their performance features and operational ranges for unbalanced load compensation are evaluated and quantified in this research. This thesis investigates the use of both single star and single delta configured five-level Flying Capacitor (FC) converter MMCC based STATCOMs for unbalanced load compensation. A detailed study is carried out to compare this type of sub-module with several other types namely: half bridge, 3-L H-bridge and 3-L FC half bridge, and reveals the one best suited to STATCOM operation. With the choice of 5-L FC H-bridge as the sub-module for STATCOM operation, a detailed investigation is also performed to decide which pulse width modulation technique is the best. This was based on the assessment of total harmonic distortion, power loss, sub-module switch utilization and natural balancing of inner flying capacitors. Two new modulation techniques of swapped-carrier PWM (SC-PWM) along with phase disposed and phase shifted PWM (PS-PWM) are analyzed under these four performance metrics. A novel contribution of this research is the development of a new space vector modulation technique using an overlapping hexagon technique. This space vector strategy offers benefits of eliminating control complexity and improving waveform quality, unlike the case of multilevel space vector technique. The simulation and experimental results show that this method provides superior performance and is applicable for other MMCC sub-modules. Another contribution is the analysis and quantification of operating ranges of both single star and delta MMCCs in rating the cluster dc-link voltage (star) and current (delta) for unbalanced load compensation. A novel method of extending the operating capabilities of both configurations uses a third harmonic injection method. An experimental investigation validates the operating range extension compared to the pure sinusoidal zero sequence voltage and current injection. Also, the superiority of the single delta configured MMCC for unbalanced loading compensation is validated

Stabilised Control of Converter Interfaced DERs for Reliable Operation of Microgrid and Microgrid Clusters

This thesis aims to achieve a stabilised control of converter interfaced DER for the reliable and resilient operation of microgrid and microgrid clusters. The suitability of voltage and current control for VSCs is evaluated and corrective measures are proposed to stabilise converter operation. Furthermore, the accurate power demand distribution in islanded MGs and interconnected MGs are ensured by advanced control strategies. The proposal presented in the thesis is verified both through simulation and experimental work