Fuzzy Monte Carlo mathematical model for load curtailment minimization in transmission power systems

This paper presents a methodology which is based on statistical failure and repair data of the transmission power system components and uses fuzzyprobabilistic modeling for system component outage parameters. Using statistical records allows developing the fuzzy membership functions of system component outage parameters. The proposed hybrid method of fuzzy set and Monte Carlo simulation based on the fuzzy-probabilistic models allows catching both randomness and fuzziness of component outage parameters. A network contingency analysis to identify any overloading or voltage violation in the network is performed once obtained the system states by Monte Carlo simulation. This is followed by a remedial action algorithm, based on optimal power flow, to reschedule generations and alleviate constraint violations and, at the same time, to avoid any load curtailment, if possible, or, otherwise, to minimize the total load curtailment, for the states identified by the contingency analysis. In order to illustrate the application of the proposed methodology to a practical case, the paper will include a case study for the Reliability Test System (RTS) 1996 IEEE 24 BUS.

Mathematical model for HIV dynamics in HIV-specific helper cells

In this paper we study a delay mathematical model for the dynamics of HIV in HIV-specific CD4 + T helper cells. We modify the model presented by Roy and Wodarz in 2012, where the HIV dynamics is studied, considering a single CD4 + T cell population. Non-specific helper cells are included as alternative target cell population, to account for macrophages and dendritic cells. In this paper, we include two types of delay: (1) a latent period between the time target cells are contacted by the virus particles and the time the virions enter the cells and; (2) virus production period for new virions to be produced within and released from the infected cells. We compute the reproduction number of the model, R0, and the local stability of the disease free equilibrium and of the endemic equilibrium. We find that for values of R0<1, the model approaches asymptotically the disease free equilibrium. For values of R0>1, the model approximates asymptotically the endemic equilibrium. We observe numerically the phenomenon of backward bifurcation for values of R0⪅1. This statement will be proved in future work. We also vary the values of the latent period and the production period of infected cells and free virus. We conclude that increasing these values translates in a decrease of the reproduction number. Thus, a good strategy to control the HIV virus should focus on drugs to prolong the latent period and/or slow down the virus production. These results suggest that the model is mathematically and epidemiologically well-posed.

A mathematical model for supermarket order picking

Order picking consists in retrieving products from storage locations to satisfy independent orders from multiple customers. It is generally recognized as one of the most significant activities in a warehouse (Koster et al, 2007). In fact, order picking accounts up to 50% (Frazelle, 2001) or even 80% (Van den Berg, 1999) of the total warehouse operating costs. The critical issue in today’s business environment is to simultaneously reduce the cost and increase the speed of order picking. In this paper, we address the order picking process in one of the Portuguese largest companies in the grocery business. This problem was proposed at the 92nd European Study Group with Industry (ESGI92). In this setting, each operator steers a trolley on the shop floor in order to select items for multiple customers. The objective is to improve their grocery e-commerce and bring it up to the level of the best international practices. In particular, the company wants to improve the routing tasks in order to decrease distances. For this purpose, a mathematical model for a faster open shop picking was developed. In this paper, we describe the problem, our proposed solution as well as some preliminary results and conclusions.

Scheduling aircraft’s engines repair process: a mathematical model

In this talk, we discuss a scheduling problem that originated at TAP - Maintenance & Engineering - the maintenance, repair and overhaul organization of Portugal’s leading airline. In the repair process of aircrafts’ engines, the operations to be scheduled may be executed on a certain workstation by any processor of a given set, and the objective is to minimize the total weighted tardiness. A mixed integer linear programming formulation, based on the flexible job shop scheduling, is presented here, along with computational experiment on a real instance, provided by TAP-ME, from a regular working week. The model was also tested using benchmarking instances available in literature.

Optimization model for medium term natural gas commitment

In this paper we study the optimal natural gas commitment for a known demand scenario. This study implies the best location of GSUs to supply all demands and the optimal allocation from sources to gas loads, through an appropriate transportation mode, in order to minimize total system costs. Our emphasis is on the formulation and use of a suitable optimization model, reflecting real-world operations and the constraints of natural gas systems. The mathematical model is based on a Lagrangean heuristic, using the Lagrangean relaxation, an efficient approach to solve the problem. Computational results are presented for Iberian and American natural gas systems, geographically organized in 65 and 88 load nodes, respectively. The location model results, supported by the computational application GasView, show the optimal location and allocation solution, system total costs and suggest a suitable gas transportation mode, presented in both numerical and graphic supports.

Fractional model for malaria transmission under control strategies

We study a fractional model for malaria transmission under control strategies.Weconsider the integer order model proposed by Chiyaka et al. (2008) in [15] and modify it to become a fractional order model. We study numerically the model for variation of the values of the fractional derivative and of the parameter that models personal protection, b. From observation of the figures we conclude that as b is increased from 0 to 1 there is a corresponding decrease in the number of infectious humans and infectious mosquitoes, for all values of α. This means that this result is invariant for variation of fractional derivative, in the values tested. These results are in agreement with those obtained in Chiyaka et al.(2008) [15] for α = 1.0 and suggest that our fractional model is epidemiologically wellposed.

A coinfection model for HIV and HCV

We study a mathematical model for the human immunodeficiency virus (HIV) and hepatites C virus (HCV) coinfection. The model predicts four distinct equilibria: the disease free, the HIV endemic, the HCV endemic, and the full endemic equilibria. The local and global stability of the disease free equilibrium was calculated for the full model and the HIV and HCV submodels. We present numerical simulations of the full model where the distinct equilibria can be observed. We show simulations of the qualitative changes of the dynamical behavior of the full model for variation of relevant parameters. From the results of the model, we infer possible measures that could be implemented in order to reduce the number of infected individuals.

Modelling real solar cell using PSCAD/MATLAB

This paper presents the development of a solar photovoltaic (PV) model based on PSCAD/EMTDC - Power System Computer Aided Design – including a mathematical model study. An additional algorithm has been implemented in MATLAB software in order to calculate several parameters required by the PSCAD developed model. All the simulation study has been performed in PSCAD/MATLAB software simulation tool. A real data base concerning irradiance, cell temperature and PV power generation was used in order to support the evaluation of the implemented PV model.

Planeamento do consumo de energia eléctrica

O objectivo deste trabalho é optimizar o planeamento de produção tendo como meta a redução do custo total da energia eléctrica consumida. Este trabalho está dividido em 3 etapas distintas: na 1ª etapa foi feito um levantamento do problema, das restrições do mesmo e da escolha do modelo para a sua resolução. Na etapa seguinte, fez-se a escolha da ferramenta a usar, que foi o Xpress, e fez-se a implementação do problema nessa mesma ferramenta. E por fim, na 3ª etapa, foi feita a validação do modelo e análise das soluções obtidas com comparações com que o era feito antes. Recorrendo a programação inteira foi desenvolvido um modelo de optimização para atingir o objectivo em causa e consequentemente foi escrito o código que reflectisse o modelo matemático. Todos os passos necessários à sua implementação foram concluídos e validados com comparação com o que antes se fazia, notando-se assim melhorias ao nível de eficiência energética na ordem dos 8%, mas também uma melhoria no aproveitamento de recursos humanos e tempo que eram despendidos para desenvolver planos de produção de forma manual. Essa melhoria temporal que se compreende entre quatro a seis horas semanais pode ser aplicada noutras actividades da empresa com maior valor acrescentado.

Optimization of Cu(II) biosorption onto ascophyllum nodosum by factorial design methodology

A Box–Behnken factorial design coupled with surface response methodology was used to evaluate the effects of temperature, pH and initial concentration in the Cu(II) sorption process onto the marine macroalgae Ascophyllum nodosum. The effect of the operating variables on metal uptake capacitywas studied in a batch system and a mathematical model showing the influence of each variable and their interactions was obtained. Study ranges were 10–40ºC for temperature, 3.0–5.0 for pH and 50–150mgL−1 for initial Cu(II) concentration. Within these ranges, the biosorption capacity is slightly dependent on temperature but markedly increases with pH and initial concentration of Cu(II). The uptake capacities predicted by the model are in good agreement with the experimental values. Maximum biosorption capacity of Cu(II) by A. nodosum is 70mgg−1 and corresponds to the following values of those variables: temperature = 40ºC, pH= 5.0 and initial Cu(II) concentration = 150mgL−1.

Self-similarity principle: the reduced description of randomness

A new general fitting method based on the Self-Similar (SS) organization of random sequences is presented. The proposed analytical function helps to fit the response of many complex systems when their recorded data form a self-similar curve. The verified SS principle opens new possibilities for the fitting of economical, meteorological and other complex data when the mathematical model is absent but the reduced description in terms of some universal set of the fitting parameters is necessary. This fitting function is verified on economical (price of a commodity versus time) and weather (the Earth’s mean temperature surface data versus time) and for these nontrivial cases it becomes possible to receive a very good fit of initial data set. The general conditions of application of this fitting method describing the response of many complex systems and the forecast possibilities are discussed.

A simple approach to numerical modelling of propane combustion in fluidized beds

A mathematical model is proposed for the evolution of temperature, chemical composition, and energy release in bubbles, clouds, and emulsion phase during combustion of gaseous premixtures of air and propane in a bubbling fluidized bed. The analysis begins as the bubbles are formed at the orifices of the distributor, until they explode inside the bed or emerge at the free surface of the bed. The model also considers the freeboard region of the fluidized bed until the propane is thoroughly burned. It is essentially built upon the quasi-global mechanism of Hautman et al. (1981) and the mass and heat transfer equations from the two-phase model of Davidson and Harrison (1963). The focus is not on a new modeling approach, but on combining the classical models of the kinetics and other diffusional aspects to obtain a better insight into the events occurring inside a fluidized bed reactor. Experimental data are obtained to validate the model by testing the combustion of commercial propane, in a laboratory-scale fluidized bed, using four sand particle sizes: 400–500, 315–400, 250–315, and 200–250 µm. The mole fractions of CO2, CO, and O2 in the flue gases and the temperature of the fluidized bed are measured and compared with the numerical results.

Application of fractional controllers for quad rotor

This paper studies the application of fractional algorithms in the control of a quad-rotor rotorcraft. The development of a flight simulator provide the evaluation of the controller algorithm. Several basic maneuvers are investigated, namely the elevation and the position control.

A New Approach in the Design of Air Stripping Columns for the Treatment of Groundwater Contaminated With Volatile Organic Compounds

Volatile organic compounds are a common source of groundwater contamination that can be easily removed by air stripping in columns with random packing and using a counter-current flow between the phases. This work proposes a new methodology for column design for any type of packing and contaminant which avoids the necessity of an arbitrary chosen diameter. It also avoids the employment of the usual graphical Eckert correlations for pressure drop. The hydraulic features are previously chosen as a project criterion. The design procedure was translated into a convenient algorithm in C++ language. A column was built in order to test the design, the theoretical steady-state and dynamic behaviour. The experiments were conducted using a solution of chloroform in distilled water. The results allowed for a correction in the theoretical global mass transfer coefficient previously estimated by the Onda correlations, which depend on several parameters that are not easy to control in experiments. For best describe the column behaviour in stationary and dynamic conditions, an original mathematical model was developed. It consists in a system of two partial non linear differential equations (distributed parameters). Nevertheless, when flows are steady, the system became linear, although there is not an evident solution in analytical terms. In steady state the resulting ODE can be solved by analytical methods, and in dynamic state the discretization of the PDE by finite differences allows for the overcoming of this difficulty. To estimate the contaminant concentrations in both phases in the column, a numerical algorithm was used. The high number of resulting algebraic equations and the impossibility of generating a recursive procedure did not allow the construction of a generalized programme. But an iterative procedure developed in an electronic worksheet allowed for the simulation. The solution is stable only for similar discretizations values. If different values for time/space discretization parameters are used, the solution easily becomes unstable. The system dynamic behaviour was simulated for the common liquid phase perturbations: step, impulse, rectangular pulse and sinusoidal. The final results do not configure strange or non-predictable behaviours.

Modelação de um Sistema de AVAC, em Software LabVIEW

Na União Europeia, a energia utilizada nos edifícios é responsável por uma grande parte do consumo total, cerca de 40%, de toda a energia produzida, contribuindo em grande escala para as emissões de gases de efeito de estufa, como o CO2. [ADENE, 2014]. A minimização deste consumo, durante o período de ciclo de vida de um edifício, é um grande desafio associado ao ambiente e à economia. Na atualidade assistimos, cada vez mais, ao emergir de novas tecnologias. Faz parte dessa realidade, o crescimento e o desenvolvimento das UTA’s, que surgem como resposta do ser humano pela busca de otimização da sua zona de conforto, da qualidade de ar interior e da eficiência energética. Assim, para que não se sacrifique o conforto térmico, há que conciliar a qualidade de ar interior com a energia dispensada para climatizar os espaços. Para ajudar à minimização de CO2 em conjunto com uma eficiência energética e conforto térmico, traduzindo-se numa melhor qualidade de ar no interior de espaços climatizados, surge o objetivo de implementar uma aplicação através do software LabVIEW para prever uma experiência real. Como solução, recorreu-se a modelos matemáticos que traduzissem os vários balanços térmicos, balanços de massa e de CO2. As principais conclusões deste trabalho foram: validação do comportamento do modelo matemático da temperatura; validação do comportamento do modelo matemático de CO2; humidade relativa com 25% de registos válidos.