Mathematical Model Of Plant Research Articles

Mathematical Modeling and Optimal Control of the Process of Hydrogen Adsorption Production

The paper considers the structure of the mathematical model for 6-bed plant for hydrogen production. The adapting optimal control system for technological process is proposed. The results of numerical imitating calculations of dynamic operating modes of the system are given.

Data-driven control for multi-rate multi-input/single-output systems

For the next generation of manufacturing, represented by Industrie 4.0, a multi-input controller is designed directly from controlled data, without using the mathematical plant model, where the ratio between the D/A conversion of multiple inputs and the A/D conversion of a single output is non-uniquely. With the proposed method, the fixed-structured controller is optimally designed by solving a model reference problem using one-shot data. Furthermore, to eliminate inter-sample ripples emerged by input oscillation, the deviation of the control inputs is also evaluated using the proposed method. As a result, a non-ripple data-driven controller is achieved. Numerical examples show that the proposed multi-rate data-driven method is superior than the conventional single-rate method.

Dynamic simulation of high-purity twin-bed N2-PSA plants

At present, nitrogen production from air by pressure swing adsorption (PSA) is simulated almost exclusively at low product purity levels (< 99% N2). However, with increasing global demand for highly purified gases provided by energy-efficient separation processes the requirement for either extensive experimental research in the high-purity range or predictive computer simulations arises. This paper presents a mathematical model of a twin-bed PSA plant equipped with a carbon molecular sieve (Shirasagi MSC CT-350) for the generation of high-purity nitrogen (99.9–99.999% N2). The model is implemented in the process simulator Aspen Adsorption™. The influence of operating conditions as well as the cycle organisation on the process performance is validated, especially the influence of pressure, temperature, half-cycle time, purge flow rate, and cutting time. The precision of the performance prediction by numerical simulations is critically discussed. Based on the new insights efficiency improvement strategies with a focus on reduced energy consumption are introduced and discussed by means of radar charts.

Evaluación de control y filtros fraccionales en la reducción de la interacción del acoplamiento cruzado en el modelo no lineal de una estación hidroeléctrica

En este artículo, un modelo matemático multivariable no lineal de una central hidroeléctrica reversible, desarrollado en Matlab-Simulink, es empleado para evaluar el desempeño de un controlador Proporcional Integral Derivativo (pseudo derivativo) con anti-windup, donde las acciones integral y derivativa son de orden fraccional. Este control se muestra robusto, manteniendo su rendimiento tanto en el caso de respuesta directa como en la respuesta de acoplamiento cruzado. De igual forma, se muestra la ventaja de usar un filtro para reducir la interacción de acoplamiento cruzado de este sistema. El efecto de este filtro, de orden fraccional, en el desempeño del sistema, se muestra mediante la reducción de la integral del error cuadrático.

Critical stable sectional area of downstream surge tank of hydropower plant with sloping ceiling tailrace tunnel

AbstractThis paper investigates the critical stable sectional area (CSSA) of downstream surge tank (DST) of hydropower plant with sloping ceiling tailrace tunnel (SCTT). Firstly, two types of nonlinear mathematical model of hydropower plant with SCTT during transient process are established. Then, the criterion of operation stability of hydropower plant is obtained based on nonlinear stability theory. Formulae for CSSAs of DST under two types of mathematical model are derived. Finally, the similarities, differences, and relationships of different CSSAs are clarified. The effect mechanisms of the assumption of steady power output of hydro‐turbine and the SCTT on CSSA of DST are revealed. The recommended use conditions of different CSSAs are explained. The results indicate that, under the assumption of steady power output of hydro‐turbine, the formula for CSSA of DST of hydropower plant with SCTT is analytical and has a simple expression. Under the complete model, the formula for CSSA of DST of hydropower plant with SCTT is not analytical and has a complicated expression. The former formula is suggested to be given the priority of use because of good precision and concise expression. SCTT can improve the stability of hydropower plant and decrease the CSSA of DST.

Transient simulation model and process simulation analysis of fast cut back process in thermal power plant

Fast Cut Back (FCB) technology of large thermal power plant can maintain the isolated operation of auxiliary power after the units are disconnected from the power grid. FCB unit can immediately cut off all external loads without turbine or boiler shutdown in case of large power grid failure, and supply power immediately as the external power grid fault eliminated, which has a very important impact on improving the stability and the recovery speed of the power grid system. Therefore, it is necessary to establish a dynamic mathematical model of thermal power plant to simulate FCB process. According to the principle of mass and energy balance, a dynamic mathematical model of 1050 MW thermal power unit was established. The model considered the change trends of main steam pressure and temperature caused by the action of main steam valve and high-pressure (HP) bypass valve in FCB process, and the action characteristics of safety valve and pressure control valve (PCV) valve in FCB system. This model provides a reference for the simulation and control of FCB process in thermal power unit.

A new reference model-based fixed-structure controller for industrial applications

This paper introduces a new approach to design a fixed-structure controller for those industrial applications, where mathematical model of the plant is not known. The design methodology is composed of two steps. First, black-box system identification is used to obtain a mathematical model of plant and second, a fixed-structure controller is designed based on reference model defined by closed-loop performance. For controller identification, prediction error method (PEM) is considered, which uses the off-line generated input-output inherently noise free data using the reference model. Due to fixed design structure, the controller is independent of plant's order. The proposed approach is tested on a lab-based real-time magnetic levitation system (MLS). The results show effectiveness of the proposed approach with good reference tracking and robustness properties. The proposed approach emerged a lower order controller which is computationally efficient and easy to implement. Compare to other data-driven techniques, inverse mapping of the reference model is not required and the performance versus design/tuning time comparison with conventional proportional integral derivative (PID) controller is also improved.

Комплексная модель автономной энергетической установки на основе стабилизирующих преобразователей напряжения

Improving the fuel, economic and environmental indicators of the process of generating electrical energy is an urgent problem of small-scale power generation, due to a significant share of traditional solutions based on diesel generator sets, which are not highly efficient in the overall structure of primary fuel use (including the stages of production, transportation and final transformation). At the same time, the modern development of technologies in the field of promising energy sources and power electronics contributes to the sustainable diversification of energy resources, strengthening the position of environmentally friendly renewable energy. However, the use of alternative types of fuels for variable speed engine generators, photovoltaic and wind power plants is associated with the need to use additional devices for converting electrical energy – stabilizing voltage converters. This article is devoted to issues related to the design of autonomous power systems based on these voltage converters using mathematical modeling tools. The paper describes a complex mathematical model of an autonomous power plant with a variable speed motor-generator and an electric energy storage device, presents a mathematical description of the main components of such a system, and also provides examples of the model implementation in a specialized software environment. A distinctive feature of the proposed model is an approach to modeling the operating modes of an engine-generator set, which is a synthesis of multi-parameter characteristics of an internal combustion engine, analytical expressions for energy storage and conversion systems. The presented complex model makes it possible to determine the electrical, energy and environmental indicators of autonomous power plants when the power of the electrical load changes. The article provides an example of the nature of the results obtained in computer modeling.

Assessment of the Efficiency of Wind Energy Use in Russia

The constant increase in the requirements for the generation of electricity forces the search for new means of generating energy. It is not the first year that technologies for the development of alternative energy sources have been considered and introduced in the largest countries of the world. Wind power occupies a special place in this direction. In Russia, this industry is still not sufficiently developed to provide a significant share of energy consumption, but the industrial potential with the proper level of technological support can radically correct this situation. This article discusses the perspectives for using wind power plants in Russia. A mathematical model of a wind power plant was built in this study, taking into account the parameters of a WH6.4-5000W type wind generator and consisting of a virtual synchronous generator, which is an element of the SimPowerSystem library, and blocks from the Simulink application of the Matlab software package that simulates the effect of wind and the movement of the mechanical part of the wind generator. An assessment of the economic efficiency of the use of wind turbines in Russia was carried out using the constructed model.

Торрефикация — ресурсосберегающее направление термохимической переработки биомассы

Significant scales in which biomass accumulates have prompted specialists to search ways of efficiently using its energy potential at the background of the crisis of non-renewable energy sources. One of such ways is torrefaction – thermochemical pyrolysis of biomass by subjecting it to slow heating and holding at a temperature of 200–300°C to obtain a solid carbon-containing product. Investigations carried out in the biomass torrefaction field are reviewed and analyzed. Biomass properties and various ways of processing it for use as power-generating fuel are considered. The properties of non-torrefied and torrefied pellets are compared. The latter, in comparison with the source ones, feature an increased heating value, low hygroscopicity, sufficient bulk density, and good grindability. The main torrefaction technologies and types of torrefaction reactors are considered. A mathematical model of a wood waste torrefaction plant was developed in the Aspen Plus software environment. The study results have revealed the effect the specific heat admission to the torrefaction reactor and the initial moisture content in the material have on the process operating parameters: the mass fraction of carbon transferred into solid torrefaction products and the pyrolysis gas specific yield, composition, heating value, and temperature. The possibility to arrange autonomous heating of the reactor using the chemical heat of pyrolysis gas has been shown. The reactor heating requires 44% of the gas waste from the torrefaction process; the other 56% can be used as an energy source in related technologies. The obtained results can be used in studying and designing the reactor and torrefaction plant.

Modelling the Combined Heat and Power Plants with Steam Turbines in the Study of Energy Security Problems

Abstract The paper considers the development of mathematical models of combined heat and power plants that are to be used while modelling the fuel and energy complex. Consideration is given to three methods of combined heat and power plant (CHP) modelling: The first method provides for the simplified modelling based on CHP aggregation in one energy zone; the second method is based on modelling the individual CHP using the accurate parameters of their equipment operation; the third method is based on the use of standard regime diagrams for modelling individual CHP. Analysis of the presented methods of CHP modelling revealed that the third method out of the three methods proposed is most appropriate for mathematical models of fuel and energy complex for studying the fuel and power supply reliability. The experimental part of the paper describes the process of deriving the analytical dependencies of electricity and heat generation versus fuel used by CHP that is obtained by the third method proposed.

Obtaining a Neural Network Mathematical Model That Takes Into Account Various Power Supply Schemes

Gas turbine units are widely used as a drive for a synchronous generator in a gas turbine power plant. The main problem here lies in the fact that the control systems of such gas turbine plants are transferred practically unchanged from their aviation counterparts. This situation leads to inefficient operation of the gas turbine power plant, which affects the quality of electricity generation. To solve this problem, it is necessary to improve the control algorithms for the automatic control systems of gas turbine plants. When solving this problem, gas turbine plants should be considered in interaction with other subsystems and units; for gas turbine power plants, this is, first of all, an electric generator and the electric power system as a whole. Setting up a control system is one of the most costly stages of their production, both in terms of finance and time. Especially time-consuming operations are non-automated manual configuration management system for developmental and operational testing. Therefore, it is proposed to use a software-modeling complex, on the basis of which it is possible to obtain a neural network mathematical model of a gas turbine power plant and conduct its tests.

Potreba za navodnjavanjem kukuruza na zemunskom černozemu u poslednjih pola veka

The aim of this paper is to examine the water regime of chernozem under maize crops in the last half century (1966-2019) and to determine whether during that period and to what extent, there was an increase or decrease in maize irrigation requirements. The mathematical plant model FAO CROPWAT 8.0 was used for the calculation. The calculation was performed on the basis of monthly values of reference evapotranspiration (ETo) for the period 1966-2019, calculated by the modified Hargreaves method, daily values of precipitation from the meteorological station Surcin, data on the selected plant, which are in accordance with FAO56. The soil is chernozem on the Zemun les terrace. The analysis was performed by dividing the research period into three subperiods: the first twenty (1966-1985), the second twenty (1986-2005) and the last fourteen (2006-2019) years. It was found that the average values of potential evapotranspiration of maize were increasing, starting from the first (500mm) to the third (562mm) subperiod, while the average values of actual evapotranspiration, as well as the average amount of effective precipitation in the vegetation period of maize, decreased. Consequently, the average water deficit, i.e. maize irrigation requirements was increased by 56%, starting from the first (205mm) to the third (319mm) subperiod of the research. The increase in the water deficit also caused an increase in the projected reduction in maize yield related to its genetic capasity, which averaged 31% in the first subperiod and 47% in the third. Analysis of the results on a monthly and decadal level showed that maize irrigation requirements lasts from June to August, with a maximum in the second decade of July. In all three summer months, an increase in maize irrigation requirements was registered from the first to the third subperiod of the research, with the maximum increase during July. The conducted research, which generally gives an insight into the state of the water regime of Zemun chernozem in the last half century, shows that the conditions of maize production in the natural rain regime are deteriorating and that the irrigation requirement is increasing.

Performance Analysis of a Self-excited Induction Generator Mathematical Dynamic Model with Magnetic Saturation, Cross Saturation Effect and Iron Losses

Construction of appropriate mathematical model of plant (object to be modeled) has especially important meaning for designing controller. A reliable and good control performance requires more detailed model. Nevertheless, the latter must be established from at least two viewpoints of preciseness and compactness. In this paper, the considered plant is a self-excited induction generator (SEIG). In order to improve the accuracy, we take into consideration in the SEIG modeling: magnetic saturation phenomenon, cross saturation effect and iron losses. To our best knowledge, this is the first time that the three mentioned phenomena have been integrated into the same and single SEIG model which is presented in an inherent mathematical form. As we will see in the results, the contribution of these three phenomena in the accuracy improvement is really significant. In addition, to achieve compactness of the proposed model, a simpler configuration is obtained for the electrical equivalent circuit associated to the studied model by using Thevenin transformation. The proposed model is built in MATLAB-SIMULINK environment and used to study and analyze the performance of a SEIG under various operating point conditions. The obtained results are compared to measurements and also to the values obtained from models without the three discussed phenomena.

Consideration of Thermodynamic Processes Formation of Compressed-Air Foam in Design Compressed Air Foam Systems

The main problem with creating compressed air systems is to properly regulate the flow of water and the flow of air that is fed into the mixing chamber so as to continuously provide a foam that must have adequate fire-fighting properties and remain stable over time. The process of obtaining compression foam is a thermodynamic process, which depending on the specified technological factors can be both isothermal and adiabatic. The nature of the process determines both the geometric and physical properties of the foam, and its possible fluctuations can lead to changes in the physical characteristics of the foam. The work provides recommendations for determining the type of thermodynamic process, which makes it possible to improve the accuracy when creating mathematical models of mobile plants for the production of CAF.

Synchronization of a Network of Nonlinear Plants with Time Delay as in Condition Under Uncertainty

Robust algorithms for synchronizing a network of nonlinear plants with time delay are proposed. A network of control plants in the Lurie form with Lipshets nonlinearities is considered taking into account the time delay under the conditions of constantly operating external uncontrolled disturbances. Taking into account nonlinear and delayed components in mathematical models of plants makes the system close to real. In each local network plant, the input of the leading subsystem is monitored. Dynamic compensation of disturbances in each of the plants is carried out by extracting a signal that carries information about these disturbances, and then suppressing it using an auxiliary circuit and two observers of the system variables. The use of variable observers is due to the need to obtain estimates of the derivatives of the system variables, the measurement of which is not available. A numerical example of the synchronization of a network consisting of four nonlinear control plants with a delay in state under conditions of uncertainty of the parameters of their mathematical models and the action of external bounded disturbances is considered. For the network of plants, the proposed control algorithms are applied. The numerical simulation in the Simulink Matlab package was carried out, the graphs of transient processes for tracking errors for each of the four subsystems are presented. The simulation results confirmed the theoretical conclusions and showed good performance of the proposed synchronization algorithms in the conditions of constantly operating external and internal disturbances.

MATHEMATICAL MODELING OF THERMAL POWER PLANT'S BOILER AIR-GAS FLOW PATH REGULATION MODES

The paper presents a mathematical model for thermal power plant's boiler air-gas flow paths and auxiliaries. With application of production fans' and flue gas extractor fans' head-capacity curves and tables, equivalent relations for the net of the mechanisms are obtained. A problem of determining the optimal control parameters for a group of centrifugal mechanisms in the air-gas path is studied. The effect of the boiler furnace draft on its auxiliaries operation is analyzed. The results of mathematical modeling for typical serial and parallel connections of the mechanisms in the thermal power plant hydraulic network are given.

Parameter Self-Tuning of SISO Compact-Form Model-Free Adaptive Controller Based on Long Short-Term Memory Neural Network

Model-free adaptive controller (MFAC) is a novel data-driven control methodology that relies only on input/output (I/O) measurement data instead of classic mathematical models of actual controlled plants. The single-input single-output (SISO) compact-form MFAC (SISO-CFMFAC) is a promising method for controlling SISO nonlinear time-varying systems. The parameters in SISO-CFMFAC must be carefully tuned before use, as inappropriate parameters may lead to poor control performance. However, up to now, parameter tuning has been a time-consuming and laborious task. In this paper, a new approach called SISO-CFMFAC-LSTM is proposed for parameter self-tuning of SISO-CFMFAC based on long short-term memory (LSTM) neural network. To evaluate the performance of the proposed methodology, qualitative and quantitative comparisons with other existing control algorithms are carried out. Six individual performance indices, namely, the root mean square error (RMSE), the integral absolute error (IAE), the integral time-weighted absolute error (ITAE), the integral absolute variation of the control signal (IAVU), the maximum overshoot (MO), and the imprecise control ratio (ICR), are introduced for quantitative comparison. The experimental results demonstrate that the proposed SISO-CFMFAC-LSTM achieves the best performance in all indices, indicating that it is an effective control method for SISO nonlinear time-varying systems.

Використання технологій опріснення морської води для попереднього упарювання рідких радіоактивних відходів

Processing of liquid radioactive waste (LRW) includes evaporation followed by vitrification. Reducing the energy consumption of evaporation of LRW is an urgent task. In the article, an attention is paid to the fact that similar technical and economic problems are solved with the desalination of seawater. It is proposed to use well-developed seawater desalination technologies for preliminary evaporation of LRW. For a detailed analysis, desalination technology with mechanical vapor compression (MVC) was selected. This technology is energy-saving because it implements the heat pump principle. MVC technology is highly efficient, simple, and does not lead to the generation of secondary radioactive waste. A mathematical model of a single-stage desalination plant with MVC has been developed, taking into account that the thermodynamic cycle of this process is open. Since there are no data on the physical properties of LRW in the literature, the properties of sea water were used. The design and operational parameters were optimized in order to reduce the cost of 1 m3 of evaporated water. It has been established that the main design parameters affecting the cost of evaporated water are the degree of vapor compression in the compressor and the heat exchange surface area of the evaporatorcondenser. The influence of these parameters on capital and operating costs is shown. The optimal combinations of these parameters are determined. To ensure the optimal operating mode of the installation, it is necessary to maintain the optimum salt content of boiling brine, which is determined by the rate of consumption of the source water. The optimal values of these parameters are calculated in a wide range of salt content of the source water. It is shown that, at low salinity of the initial LRW, evaporation is advisable to be carried out in a multi-stage installation. As a result of the calculations, it was found that the specific cost of evaporation of liquid radioactive waste with an initial salt concentration of 10% to a salt content of 20% using the desalination technology with mechanical vapor compression is 0.843 USD/m3.

A control model of the operating head dynamics of Jebba hydropower system

Electricity availability in Nigeria has been very poor over the years, underscoring the need for a better approach for managing generating resources. This paper presents the development of a dynamical model of the operating head of Jebba hydroelectric power plants for system studies and control system design. The mathematical model of the plant was developed from flow continuity conditions, some model parameters were obtained from the source while others were estimated from observations and analysis of the measured data. The developed dynamical equation was validated by comparing the response produced with values obtained by measurement. Upon integrating the model equation in Microsoft EXCEL VBA® environment, a deviation of 2% from measured values was observed. Operators can therefore use the model as a decision support system, while control engineers can find the model directly applicable for optimal and robust control system design for the station.Keywords: Control, Dynamical model, Hydropower, Inflow, Operating head.