Full- & Reduced-Order State-Space Modeling of Wind Turbine Systems with Permanent-Magnet Synchronous Generator

Wind energy is an integral part of nowadays energy supply and one of the fastest growing sources of electricity in the world today. Accurate models for wind energy conversion systems (WECSs) are of key interest for the analysis and control design of present and future energy systems. Existing control-oriented WECSs models are subject to unstructured simplifications, which have not been discussed in literature so far. Thus, this technical note presents are thorough derivation of a physical state-space model for permanent magnet synchronous generator WECSs. The physical model considers all dynamic effects that significantly influence the system's power output, including the switching of the power electronics. Alternatively, the model is formulated in the $(a,b,c)$- and $(d,q)$-reference frame. Secondly, a complete control and operation management system for the wind regimes II and III and the transition between the regimes is presented. The control takes practical effects such as input saturation and integral windup into account. Thirdly, by a structured model reduction procedure, two state-space models of WECS with reduced complexity are derived: a non-switching model and a non-switching reduced-order model. The validity of the models is illustrated and compared through a numerical simulation study.Comment: 23 pages, 11 figure

Structured Power System Model Reduction of Non-Coherent Areas

Abstract-This paper demonstrates how structured model reduction can be used to reduce the order of power systems without the need to identify coherent groups of generators. To this end the Klein-Rogers-Kundur 2-area system is studied in detail. It is shown how different modes of the system are captured as the model order is varied, which is of interest in e.g. distributed controller design, where the objective is to damp these oscillations. The power system is divided into a study area and an external area and the proposed algorithm is used to reduce the external area to a low order linear system, while retaining the nonlinear description of the study area. It is shown that this approach permits greater deviations from the steady-state than if a reduced system that is entirely linear is used, while still yielding accurate simulation results. Index Terms-Model reduction of power systems, internal systems, structured model reduction, dynamic equivalent

Model Order Reduction Based on Semidefinite Programming

The main topic of this PhD thesis is complexity reduction of linear time-invariant models. The complexity in such systems is measured by the number of differential equations forming the dynamical system. This number is called the order of the system. Order reduction is typically used as a tool to model complex systems, the simulation of which takes considerable time and/or has overwhelming memory requirements. Any model reflects an approximation of a real world system. Therefore, it is reasonable to sacrifice some model accuracy in order to obtain a simpler representation. Once a low-order model is obtained, the simulation becomes computationally cheaper, which saves time and resources. A low-order model still has to be "similar" to the full order one in some sense. There are many ways of measuring "similarity" and, typically, such a measure is chosen depending on the application. Three different settings of model order reduction were investigated in the thesis. The first one is H infinity model order reduction, i.e., the distance between two models is measured by the H infinity norm. Although, the problem has been tackled by many researchers, all the optimal solutions are yet to be found. However, there are a large number of methods, which solve suboptimal problems and deliver accurate approximations. Recently, research community has devoted more attention to large-scale systems and computationally scalable extensions of existing model reduction techniques. The algorithm developed in the thesis is based on the frequency response samples matching. For a large class of systems the computation of the frequency response samples can be done very efficiently. Therefore, the developed algorithm is relatively computationally cheap. The proposed algorithm can be seen as a computationally scalable extension to the well-known Hankel model reduction, which is known to deliver very accurate solutions. One of the reasons for such an assessment is that the relaxation employed in the proposed algorithm is tightly related to the one used in Hankel model reduction. Numerical simulations also show that the accuracy of the method is comparable to the Hankel model reduction one. The second part of the thesis is devoted to parameterized model order reduction. A parameterized model is essentially a family of models which depend on certain design parameters. The model reduction goal in this setting is to approximate the whole family of models for all values of parameters. The main motivation for such a model reduction setting is design of a model with an appropriate set of parameters. In order to make a good choice of parameters, the models need to be simulated for a large set of parameters. After inspecting the simulation results a model can be picked with suitable frequency or step responses. Parameterized model reduction significantly simplifies this procedure. The proposed algorithm for parameterized model reduction is a straightforward extension of the one described above. The proposed algorithm is applicable to linear parameter-varying systems modeling as well. Finally, the third topic is modeling interconnections of systems. In this thesis an interconnection is a collection of systems (or subsystems) connected in a typical block-diagram. In order to avoid confusion, throughout the thesis the entire model is called a supersystem, as opposed to subsystems, which a supersystem consists of. One of the specific cases of structured model reduction is controller reduction. In this problem there are two subsystems: the plant and the controller. Two directions of model reduction of interconnected systems are considered: model reduction in the nu-gap metric and structured model reduction. To some extent, using the nu-gap metric makes it possible to model subsystems without considering the supersystem at all. This property can be exploited for extremely large supersystems for which some forms of analysis (evaluating stability, computing step response, etc.) are intractable. However, a more systematic way of modeling is structured model reduction. There, the objective is to approximate certain subsystems in such a way that crucial characteristics of the given supersystem, such as stability, structure of interconnections, frequency response, are preserved. In structured model reduction all subsystems are taken into account, not only the approximated ones. In order to address structured model reduction, the supersystem is represented in a coprime factor form, where its structure also appears in coprime factors. Using this representation the problem is reduced to H infinity model reduction, which is addressed by the presented framework. All the presented methods are validated on academic or known benchmark problems. Since all the methods are based on semidefinite programming, adding new constraints is a matter of formulating a constraint as a semidefinite one. A number of extensions are presented, which illustrate the power of the approach. Properties of the methods are discussed throughout the thesis while some remaining problems conclude the manuscript

A block-diagonal structured model reduction scheme for power grid networks

We propose a block-diagonal structured model order reduction (BDSM) scheme for fast power grid analysis. Compared with existing power grid model order reduction (MOR) methods, BDSM has several advantages. First, unlike many power grid reductions that are based on terminal reduction and thus error-prone, BDSM utilizes an exact column-by-column moment matching to provide higher numerical accuracy. Second, with similar accuracy and macromodel size, BDSM generates very sparse block-diagonal reduced-order models (ROMs) for massive-port systems at a lower cost, whereas traditional algorithms such as PRIMA produce full dense models inefficient for the subsequent simulation. Third, different from those MOR schemes based on extended Krylov subspace (EKS) technique, BDSM is input-signal independent, so the resulting ROM is reusable under different excitations. Finally, due to its blockdiagonal structure, the obtained ROM can be simulated very fast. The accuracy and efficiency of BDSM are verified by industrial power grid benchmarks. © 2011 EDAA.published_or_final_versionDesign, Automation and Test in Europe Conference and Exhibition (DATE 2011), Grenoble, France, 14-18 March 2011. In Design, Automation, and Test in Europe Conference and Exhibition Proceedings, 2011, p. 44-4

Beyond cost reduction: Improving the value of energy storage in electricity systems

An energy storage technology is valuable if it makes energy systems cheaper. Traditional ways to improve storage technologies are to reduce their costs; however, the cheapest energy storage is not always the most valuable in energy systems. Modern techno-economical evaluation methods try to address the cost and value situation but do not judge the competitiveness of multiple technologies simultaneously. This paper introduces the market potential method as a new complementary valuation method guiding innovation of multiple energy storage. The market potential method derives the value of technologies by examining common deployment signals from energy system model outputs in a structured way. We apply and compare this method to cost evaluation approaches in a renewables-based European power system model, covering diverse energy storage technologies. We find that characteristics of high-cost hydrogen storage can be more valuable than low-cost hydrogen storage. Additionally, we show that modifying the freedom of storage sizing and component interactions can make the energy system 10% cheaper and impact the value of technologies. The results suggest looking beyond the pure cost reduction paradigm and focus on developing technologies with suitable value approaches that can lead to cheaper electricity systems in future.Comment: 15 pages, 10 figure

Policies and Motivations for the CO2 Valorization through the Sabatier Reaction Using Structured Catalysts. A Review of the Most Recent Advances

The current scenario where the effects of global warming are more and more evident, has motivated different initiatives for facing this, such as the creation of global policies with a clear environmental guideline. Within these policies, the control of Greenhouse Gase (GHG) emissions has been defined as mandatory, but for carrying out this, a smart strategy is proposed. This is the application of a circular economy model, which seeks to minimize the generation of waste and maximize the efficient use of resources. From this point of view, CO2 recycling is an alternative to reduce emissions to the atmosphere, and we need to look for new business models which valorization this compound which now must be considered as a renewable carbon source. This has renewed the interest in known processes for the chemical transformation of CO2 but that have not been applied at industrial level because they do not offer evident profitability. For example, the methane produced in the Sabatier reaction has a great potential for application, but this depends on the existence of a sustainable supply of hydrogen and a greater efficiency during the process that allows maximizing energy efficiency and thermal control to maximize the methane yield. Regarding energy efficiency and thermal control of the process, the use of structured reactors is an appropriate strategy. The evolution of new technologies, such as 3D printing, and the consolidation of knowledge in the structing of catalysts has enabled the use of these reactors to develop a wide range of possibilities in the field. In this sense, the present review presents a brief description of the main policies that have motivated the transition to a circular economy model and within this, to CO2 recycling. This allows understanding, why efforts are being focused on the development of different reactions for CO2 valorization. Special attention to the case of the Sabatier reaction and in the application of structured reactors for such process is paid

Steady state simulation and exergy analysis of supercritical coal-fired power plant with CO₂ capture

Integrating a power plant with CO₂ capture incurs serious efficiency and energy penalty due to use of energy for solvent regeneration in the capture process. Reducing the exergy destruction and losses associated with the power plant systems can improve the rational efficiency of the system and thereby reducing energy penalties. This paper presents steady state simulation and exergy analysis of supercritical coal-fired power plant (SCPP) integrated with post-combustion CO₂ capture (PCC). The simulation was validated by comparing the results with a greenfield design case study based on a 550 MWe SCPP unit. The analyses show that the once-through boiler exhibits the highest exergy destruction but also has a limited influence on fuel-saving potentials of the system. The turbine subsystems show lower exergy destruction compared to the boiler subsystem but more significance in fuel-saving potentials of the system. Four cases of the integrated SCPP-CO2 capture configuration was considered for reducing thermodynamic irreversibilities in the system by reducing the driving forces responsible for the CO₂ capture process: conventional process, absorber intercooling (AIC), split-flow (SF), and a combination of absorber intercooling and split-flow (AIC + SF). The AIC + SF configuration shows the most significant reduction in exergy destruction when compared to the SCPP system with conventional CO₂ capture. This study shows that improvement in turbine performance design and the driving forces responsible for CO₂ capture (without compromising cost) can help improve the rational efficiency of the integrated system