Distributed Load Control in Multiphase Radial Networks

The current power grid is on the cusp of modernization due to the emergence of distributed generation and controllable loads, as well as renewable energy. On one hand, distributed and renewable generation is volatile and difficult to dispatch. On the other hand, controllable loads provide significant potential for compensating for the uncertainties. In a future grid where there are thousands or millions of controllable loads and a large portion of the generation comes from volatile sources like wind and solar, distributed control that shifts or reduces the power consumption of electric loads in a reliable and economic way would be highly valuable.

Load control needs to be conducted with network awareness. Otherwise, voltage violations and overloading of circuit devices are likely. To model these effects, network power flows and voltages have to be considered explicitly. However, the physical laws that determine power flows and voltages are nonlinear. Furthermore, while distributed generation and controllable loads are mostly located in distribution networks that are multiphase and radial, most of the power flow studies focus on single-phase networks.

This thesis focuses on distributed load control in multiphase radial distribution networks. In particular, we first study distributed load control without considering network constraints, and then consider network-aware distributed load control.

Distributed implementation of load control is the main challenge if network constraints can be ignored. In this case, we first ignore the uncertainties in renewable generation and load arrivals, and propose a distributed load control algorithm, Algorithm 1, that optimally schedules the deferrable loads to shape the net electricity demand. Deferrable loads refer to loads whose total energy consumption is fixed, but energy usage can be shifted over time in response to network conditions. Algorithm 1 is a distributed gradient decent algorithm, and empirically converges to optimal deferrable load schedules within 15 iterations.

We then extend Algorithm 1 to a real-time setup where deferrable loads arrive over time, and only imprecise predictions about future renewable generation and load are available at the time of decision making. The real-time algorithm Algorithm 2 is based on model-predictive control: Algorithm 2 uses updated predictions on renewable generation as the true values, and computes a pseudo load to simulate future deferrable load. The pseudo load consumes 0 power at the current time step, and its total energy consumption equals the expectation of future deferrable load total energy request.

Network constraints, e.g., transformer loading constraints and voltage regulation constraints, bring significant challenge to the load control problem since power flows and voltages are governed by nonlinear physical laws. Remarkably, distribution networks are usually multiphase and radial. Two approaches are explored to overcome this challenge: one based on convex relaxation and the other that seeks a locally optimal load schedule.

To explore the convex relaxation approach, a novel but equivalent power flow model, the branch flow model, is developed, and a semidefinite programming relaxation, called BFM-SDP, is obtained using the branch flow model. BFM-SDP is mathematically equivalent to a standard convex relaxation proposed in the literature, but numerically is much more stable. Empirical studies show that BFM-SDP is numerically exact for the IEEE 13-, 34-, 37-, 123-bus networks and a real-world 2065-bus network, while the standard convex relaxation is numerically exact for only two of these networks.

Theoretical guarantees on the exactness of convex relaxations are provided for two types of networks: single-phase radial alternative-current (AC) networks, and single-phase mesh direct-current (DC) networks. In particular, for single-phase radial AC networks, we prove that a second-order cone program (SOCP) relaxation is exact if voltage upper bounds are not binding; we also modify the optimal load control problem so that its SOCP relaxation is always exact. For single-phase mesh DC networks, we prove that an SOCP relaxation is exact if 1) voltage upper bounds are not binding, or 2) voltage upper bounds are uniform and power injection lower bounds are strictly negative; we also modify the optimal load control problem so that its SOCP relaxation is always exact.

To seek a locally optimal load schedule, a distributed gradient-decent algorithm, Algorithm 9, is proposed. The suboptimality gap of the algorithm is rigorously characterized and close to 0 for practical networks. Furthermore, unlike the convex relaxation approach, Algorithm 9 ensures a feasible solution. The gradients used in Algorithm 9 are estimated based on a linear approximation of the power flow, which is derived with the following assumptions: 1) line losses are negligible; and 2) voltages are reasonably balanced. Both assumptions are satisfied in practical distribution networks. Empirical results show that Algorithm 9 obtains 70+ times speed up over the convex relaxation approach, at the cost of a suboptimality within numerical precision.

A molecular dynamics study of the microscopic properties of simple dense fluids

The microscopic properties of a two-dimensional model dense fluid of Lennard-Jones disks have been studied using the so-called "molecular dynamics" method. Analyses of the computer-generated simulation data in terms of "conventional" thermodynamic and distribution functions verify the physical validity of the model and the simulation technique.

The radial distribution functions g(r) computed from the simulation data exhibit several subsidiary features rather similar to those appearing in some of the g(r) functions obtained by X-ray and thermal neutron diffraction measurements on real simple liquids. In the case of the model fluid, these "anomalous" features are thought to reflect the existence of two or more alternative configurations for local ordering.

Graphical display techniques have been used extensively to provide some intuitive insight into the various microscopic phenomena occurring in the model. For example, "snapshots" of the instantaneous system configurations for different times show that the "excess" area allotted to the fluid is collected into relatively large, irregular, and surprisingly persistent "holes". Plots of the particle trajectories over intervals of 2.0 to 6.0 x 10^-12 sec indicate that the mechanism for diffusion in the dense model fluid is "cooperative" in nature, and that extensive diffusive migration is generally restricted to groups of particles in the vicinity of a hole.

A quantitative analysis of diffusion in the model fluid shows that the cooperative mechanism is not inconsistent with the statistical predictions of existing theories of singlet, or self-diffusion in liquids. The relative diffusion of proximate particles is, however, found to be retarded by short-range dynamic correlations associated with the cooperative mechanism--a result of some importance from the standpoint of bimolecular reaction kinetics in solution.

A new, semi-empirical treatment for relative diffusion in liquids is developed, and is shown to reproduce the relative diffusion phenomena observed in the model fluid quite accurately. When incorporated into the standard Smoluchowski theory of diffusion-controlled reaction kinetics, the more exact treatment of relative diffusion is found to lower the predicted rate of reaction appreciably.

Finally, an entirely new approach to an understanding of the liquid state is suggested. Our experience in dealing with the simulation data--and especially, graphical displays of the simulation data--has led us to conclude that many of the more frustrating scientific problems involving the liquid state would be simplified considerably, were it possible to describe the microscopic structures characteristic of liquids in a concise and precise manner. To this end, we propose that the development of a formal language of partially-ordered structures be investigated.

An alternative management strategy for Lake Victoria (Kenya)

In Kenya, fisheries resource management has been based on the top-down centralized approach since the colonial days. Stakeholders have never been consulted concerning management decisions. The 4-beaches Study was undertaken to investigate the potential for an alternative management system for Lake Victoria.

Investigations in the theory of electromagnetic scattering from expanding dielectric obstacles

An equation for the reflection which results when an expanding dielectric slab scatters normally incident plane electromagnetic waves is derived using the invariant imbedding concept. The equation is solved approximately and the character of the solution is investigated. Also, an equation for the radiation transmitted through such a slab is similarly obtained. An alternative formulation of the slab problem is presented which is applicable to the analogous problem in spherical geometry. The form of an equation for the modal reflections from a nonrelativistically expanding sphere is obtained and some salient features of the solution are described. In all cases the material is assumed to be a nondispersive, nonmagnetic dielectric whose rest frame properties are slowly varying.

I. Numerical solution of exact pair equations. II. Numerical solution of first-order pair equations

Part I

Numerical solutions to the S-limit equations for the helium ground state and excited triplet state and the hydride ion ground state are obtained with the second and fourth difference approximations. The results for the ground states are superior to previously reported values. The coupled equations resulting from the partial wave expansion of the exact helium atom wavefunction were solved giving accurate S-, P-, D-, F-, and G-limits. The G-limit is -2.90351 a.u. compared to the exact value of the energy of -2.90372 a.u.

Part II

The pair functions which determine the exact first-order wavefunction for the ground state of the three-electron atom are found with the matrix finite difference method. The second- and third-order energies for the (1s1s)¹S, (1s2s)³S, and (1s2s)¹S states of the two-electron atom are presented along with contour and perspective plots of the pair functions. The total energy for the three-electron atom with a nuclear charge Z is found to be E(Z) = -1.125•Z² +1.022805•Z-0.408138-0.025515•(1/Z)+O(1/Z²)a.u.

Co-incineração de pneus com resíduos sólidos urbanos

O aumento da população, o crescimento das grandes cidades, da industrialização e do consumo, tem trazido preocupação com relação a sustentabilidade quanto à disponibilidade energética e quanto à destinação dos resíduos sólidos urbanos gerados. Dessa forma, é fundamental realizarem-se os estudos visando novas formas de reutilização dos resíduos gerados pelas atividades industriais. Os resíduos sólidos urbanos e os pneus inservíveis gerados trazem conseqüências ao meio ambiente e às populações quando destinados inadequadamente. A destinação final dos resíduos sólidos urbanos é complexa, sendo sempre um grande desafio para as administrações públicas. Com a Política Nacional de Resíduos Sólidos (instituída pela Lei n 12.305/2010), tem-se um marco da preservação ambiental, coma a gestão e gerenciamento de resíduos sólidos, com a ordem de prioridade: não geração, redução, reutilização, reciclagem, tratamento dos resíduos sólidos e disposição final ambientalmente adequada dos rejeitos e prevê, de forma inteligente, a atribuição aos fabricantes de responsabilidade pelo retorno de produtos descartados pelos consumidores. Uma alternativa para minimizar estes aspectos e impactos ambientais é o tratamento térmico com aproveitamento energético. Este processo contribui para mais uma solução de destinação dos resíduos, proporcionado uma redução das áreas a serem utilizadas nos aterros sanitários e contribuindo como uma fonte de geração de energia elétrica

Análise de viabilidade técnica e econômica da geração de energia através do biogás de lixo em aterros sanitários.

A geração de energia a partir do biogás do lixo em aterros sanitários é uma maneira de produzir energia elétrica renovável e limpa, reduzindo os impactos globais provocados pela queima dos resíduos sólidos urbanos. A contribuição ambiental mais relevante é a redução de emissões dos gases de efeito estufa (GEE), por meio da conversão do metano em dióxido de carbono, visto que o metano possui um potencial de aquecimento global cerca de 21 vezes maior, quando comparado ao dióxido de carbono (através da combustão do mesmo). De acordo com o Mecanismo de Desenvolvimento Limpo (MDL), os países ricos podem comprar créditos de carbono (CERs) dos países em desenvolvimento (que possuam projetos sustentáveis) para cumprir suas metas ambientais. O objetivo é transformar um passivo ambiental (destinação final dos resíduos sólidos urbanos) em um recurso energético, além do estudo da alternativa de obtenção de recursos financeiros através dos CERs. São analisadas as tecnologias de conversão energética (tecnologia de gás de lixo, incineração, entre outras), com a seleção da melhor alternativa para a geração de energia através do biogás de lixo em aterros sanitários. A metodologia utilizada é a recomendada pela Agência de Proteção Ambiental dos Estados Unidos - USEPA (2005). Serão apresentadas outras duas metodologias de cálculo da geração de metano: a do Banco Mundial e a do IPCC (Painel Intergovernamental sobre Mudanças Climáticas). São apresentados estudos comparativos demonstrando quando as turbinas a gás, motores de combustão interna (ciclos Otto ou Diesel) ou outras tecnologias de conversão energética serão viáveis na área técnica e econômica para implantação de Unidades Termoelétricas a biogás. No caso do Aterro de Gramacho, o projeto é viável com a utilização de motores a combustão interna e a obtenção de receitas com a venda da produção de energia e créditos de carbono. Por fim, será apresentada a alternativa do uso do biogás como substituto do gás natural para fins energéticos ou outros fins industriais.

Biossorção de tório com emprego de Sargassum filipendula

Com o aumento do rigor para descarte de efluentes contaminado com metais pesados, as pesquisas têm se intensificado na busca de métodos de remoção, que tragam bons resultados de captação dos metais, aliado a um baixo custo. O uso de biomassas como bactérias, fungos e algas marinhas como material adsorvente, tem se apresentado como uma alternativa, principalmente para soluções com baixo teor de metais. Neste trabalho, a alga marinha Sargassum filipendula foi avaliada na sua capacidade de remoção do metal tório de uma solução sintética e do efluente dos laboratórios de análises ambientais do IRD. A cinética desta biossorção foi estudada em regime de batelada e o equilíbrio foi alcançado com 180 min de reação. Dois modelos cinéticos foram utilizados nesta avaliação, um de primeira ordem e um modelo de pseudo segunda ordem, tendo o modelo de segunda ordem apresentado um melhor ajuste dos dados. Na avaliação da capacidade máxima de captação do tório pela biomassa marinha em regime de batelada, foi construída a isoterma que apresentou um perfil crescente na captação alcançando um máximo de 2,59 mol/g. Os modelos de Langmuir e Freundlich foram utilizados para ajustar os dados da isoterma, tendo apresentado maior correlação com os dados o modelo de Langmuir, resultando num valor de captação máxima calculado pelo modelo de 2,92 mol/g. A capacidade de remoção do metal tório da alga Sargassum filipendula também foi avaliada em regime contínuo. Um estudo de altura crítica de leito foi realizado preenchendo-se uma coluna com diferentes massas de alga correspondendo a diferentes alturas de leito. A concentração de tório residual foi quantificada na solução de saída e a menor concentração na saída foi alcançada com 40 cm de leito ou 96 g de biomassa. Após este estudo um sistema contínuo com duas colunas, com 96 g de biomassa cada, e uma bomba peristáltica foi utilizado para o tratamento do efluente real do IRD, contendo não apenas o metal tório, mas outros metais como urânio, cálcio, cromo, ferro, chumbo, etc. Cento e cinco litros de efluente foram tratados numa concentração de 6 mg/L, a concentração do efluente de saída foi de 3,75 mg/L. A caracterização do efluente quanto aos metais presentes foi realizada em ICP-MS, os resultados demonstraram que não houve competição pelos sítios ligantes da biomassa entre o tório e os demais metais. Além disso, alguns metais como cálcio, ferro e magnésio, tiveram um aumento na concentração de saída indicando a presença do mecanismo de troca iônica na biossorção do tório por Sargassum filipendula

Vectorial solution of Kukhtarev equations for doubly doped crystals and optimal choice of recording directions in nonvolatile holographic storage

Vectorial Kukhtarev equations modified for the nonvolatile holographic recording in doubly doped crystals are analyzed, in which the bulk photovoltaic effect and the external electrical field are both considered. On the basis of small modulation approximation, both the analytic solution to the space-charge field with time in the recording phase and in the readout phase are deduced. The analytic solutions can be easily simplified to adapt the one-center model, and they have the same analytic expressions given those when the grating vector is along the optical axis. Based on the vectorial analyses of the band transport model an optimal recording direction is given to maximize the refractive index change in doubly doped LiNbO3:Fe: Mn crystals. (c) 2007 Optical Society of America.

Advancements in jet turbulence and noise modeling: accurate one-way solutions and empirical evaluation of the nonlinear forcing of wavepackets

Jet noise reduction is an important goal within both commercial and military aviation. Although large-scale numerical simulations are now able to simultaneously compute turbulent jets and their radiated sound, lost-cost, physically-motivated models are needed to guide noise-reduction efforts. A particularly promising modeling approach centers around certain large-scale coherent structures, called wavepackets, that are observed in jets and their radiated sound. The typical approach to modeling wavepackets is to approximate them as linear modal solutions of the Euler or Navier-Stokes equations linearized about the long-time mean of the turbulent flow field. The near-field wavepackets obtained from these models show compelling agreement with those educed from experimental and simulation data for both subsonic and supersonic jets, but the acoustic radiation is severely under-predicted in the subsonic case. This thesis contributes to two aspects of these models. First, two new solution methods are developed that can be used to efficiently compute wavepackets and their acoustic radiation, reducing the computational cost of the model by more than an order of magnitude. The new techniques are spatial integration methods and constitute a well-posed, convergent alternative to the frequently used parabolized stability equations. Using concepts related to well-posed boundary conditions, the methods are formulated for general hyperbolic equations and thus have potential applications in many fields of physics and engineering. Second, the nonlinear and stochastic forcing of wavepackets is investigated with the goal of identifying and characterizing the missing dynamics responsible for the under-prediction of acoustic radiation by linear wavepacket models for subsonic jets. Specifically, we use ensembles of large-eddy-simulation flow and force data along with two data decomposition techniques to educe the actual nonlinear forcing experienced by wavepackets in a Mach 0.9 turbulent jet. Modes with high energy are extracted using proper orthogonal decomposition, while high gain modes are identified using a novel technique called empirical resolvent-mode decomposition. In contrast to the flow and acoustic fields, the forcing field is characterized by a lack of energetic coherent structures. Furthermore, the structures that do exist are largely uncorrelated with the acoustic field. Instead, the forces that most efficiently excite an acoustic response appear to take the form of random turbulent fluctuations, implying that direct feedback from nonlinear interactions amongst wavepackets is not an essential noise source mechanism. This suggests that the essential ingredients of sound generation in high Reynolds number jets are contained within the linearized Navier-Stokes operator rather than in the nonlinear forcing terms, a conclusion that has important implications for jet noise modeling.

Active reservoir management: a model solution

Steady-state procedures, of their very nature, cannot deal with dynamic situations. Statistical models require extensive calibration, and predictions often have to be made for environmental conditions which are often outside the original calibration conditions. In addition, the calibration requirement makes them difficult to transfer to other lakes. To date, no computer programs have been developed which will successfully predict changes in species of algae. The obvious solution to these limitations is to apply our limnological knowledge to the problem and develop functional models, so reducing the requirement for such rigorous calibration. Reynolds has proposed a model, based on fundamental principles of algal response to environmental events, which has successfully recreated the maximum observed biomass, the timing of events and a fair simulation of the species succession in several lakes. A forerunner of this model was developed jointly with Welsh Water under contract to Messrs. Wallace Evans and Partners, for use in the Cardiff Bay Barrage study. In this paper the authors test a much developed form of this original model against a more complex data-set and, using a simple example, show how it can be applied as an aid in the choice of management strategy for the reduction of problems caused by eutrophication. Some further developments of the model are indicated.