scholarly journals Mathematical model parameter estimation of a generating unit operating in the Polish National Power System

2016 ◽  
Vol 64 (2) ◽  
pp. 409-416
Author(s):  
Ł. Majka ◽  
S. Paszek
Keyword(s):  
Mathematical Model ◽  
Parameter Estimation ◽  
Power System ◽  
Objective Function ◽  
Model Parameters ◽  
Gradient Algorithms ◽  
Hybrid Optimization Algorithm ◽  
National Power ◽  
The Mathematical Model ◽  
Paper Method

Abstract In the paper, a method and results of parameter estimation of the mathematical model of a generating unit operating in the Polish National Power System are presented. Computations of the parameters were carried out based on measurement and simulation of dynamic waveforms of selected quantities of the generating unit. The problem of parameter identification was brought to minimization of the objective function determined by the vector of deviations between the approximated and approximating waveforms computed on the basis of the models expressed by the searched parameters. A hybrid optimization algorithm, being a serial combination of genetic and gradient algorithms, was used for minimization of the objective function. A methodology for filtering the recorded measurement signals is proposed in the paper. Method and results calculation of the sensitivity to changes of the model parameters of selected dynamic waveforms are also presented.

scholarly journals Set-membership identifiability of nonlinear models and related parameter estimation properties

2016 ◽  
Vol 26 (4) ◽  
pp. 803-813 ◽  
Author(s):  
Carine Jauberthie ◽  
Louise Travé-MassuyèEs ◽  
Nathalie Verdière
Keyword(s):  
Mathematical Model ◽  
Parameter Estimation ◽  
Dynamic System ◽  
Nonlinear Models ◽  
Differential Algebra ◽  
Related Parameter ◽  
Set Membership ◽  
Estimation Problems ◽  
The Mathematical Model

Abstract Identifiability guarantees that the mathematical model of a dynamic system is well defined in the sense that it maps unambiguously its parameters to the output trajectories. This paper casts identifiability in a set-membership (SM) framework and relates recently introduced properties, namely, SM-identifiability, μ-SM-identifiability, and ε-SM-identifiability, to the properties of parameter estimation problems. Soundness and ε-consistency are proposed to characterize these problems and the solution returned by the algorithm used to solve them. This paper also contributes by carefully motivating and comparing SM-identifiability, μ-SM-identifiability and ε-SM-identifiability with related properties found in the literature, and by providing a method based on differential algebra to check these properties.

scholarly journals Determination of synchronous generator nonlinear model parameters based on power rejection tests using a gradient optimization algorithm

2017 ◽  
Vol 65 (4) ◽  
pp. 479-488 ◽  
Author(s):  
A. Boboń ◽  
A. Nocoń ◽  
S. Paszek ◽  
P. Pruski
Keyword(s):  
Parameter Estimation ◽  
Objective Function ◽  
Optimization Algorithm ◽  
Least Squares Method ◽  
Synchronous Generator ◽  
Operating Conditions ◽  
Model Parameters ◽  
State Variables ◽  
Starting Point ◽  
Gradient Optimization

AbstractThe paper presents a method for determining electromagnetic parameters of different synchronous generator models based on dynamic waveforms measured at power rejection. Such a test can be performed safely under normal operating conditions of a generator working in a power plant. A generator model was investigated, expressed by reactances and time constants of steady, transient, and subtransient state in the d and q axes, as well as the circuit models (type (3,3) and (2,2)) expressed by resistances and inductances of stator, excitation, and equivalent rotor damping circuits windings. All these models approximately take into account the influence of magnetic core saturation. The least squares method was used for parameter estimation. There was minimized the objective function defined as the mean square error between the measured waveforms and the waveforms calculated based on the mathematical models. A method of determining the initial values of those state variables which also depend on the searched parameters is presented. To minimize the objective function, a gradient optimization algorithm finding local minima for a selected starting point was used. To get closer to the global minimum, calculations were repeated many times, taking into account the inequality constraints for the searched parameters. The paper presents the parameter estimation results and a comparison of the waveforms measured and calculated based on the final parameters for 200 MW and 50 MW turbogenerators.

Optimization Research on Dynamic Balance of Spatial Engine under Limiting Shaking Moment

2009 ◽  
Vol 626-627 ◽  
pp. 693-698
Author(s):  
Yong Yong Zhu ◽  
S.Y. Gao
Keyword(s):  
Mathematical Model ◽  
Objective Function ◽  
Kinetic Analysis ◽  
Optimization Design ◽  
Design Method ◽  
Dynamic Balance ◽  
Optimized Design ◽  
Design Variables ◽  
The Mathematical Model ◽  
Shaking Moment

Dynamic balance of the spatial engine is researched. By considering the special wobble-plate engine as the model of spatial RRSSC linkages, design variables on the engine structure are confirmed based on the configuration characters and kinetic analysis of wobble-plate engine. In order to control the vibration of the engine frame and to decrease noise caused by the spatial engine, objective function is choosed as the dimensionless combinations of the various shaking forces and moments, the restriction condition of which presents limiting the percent of shaking moment. Then the optimization design is investigated by the mathematical model for dynamic balance. By use of the optimization design method to a type of wobble-plate engine, the optimization process as an example is demonstrated, it shows that the optimized design method benefits to control vibration and noise on the engines and improve the performance practically and theoretically.

Analytical Study of Hydro-Pneumatic Processes for Gorlov's Power System

1994 ◽  
Vol 208 (1) ◽  
pp. 67-70
Author(s):  
A I Ryazanov
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Power System ◽  
Analytical Study ◽  
Model Tests ◽  
Air Pressure ◽  
Pneumatic Power ◽  
Time Required ◽  
The Mathematical Model

This paper describes the aerohydrodvnamics of processes in chambers of Gorlov's hydro-pneumatic power system. The mathematical model is developed to determine the main parameters of the processes: water and air velocities, air pressure in the chamber, the periods of time required to fill and empty the chambers and the output of energy during the cycle. The results obtained are in agreement with experimental data and model tests.

scholarly journals The identification of a device based on a Peltier element by the least squares method

2020 ◽  
pp. 17-27
Author(s):  
Vladimir Grinkevich ◽  
Keyword(s):  
Mathematical Model ◽  
Least Squares ◽  
Least Squares Method ◽  
Control Object ◽  
Object Identification ◽  
Model Parameters ◽  
Peltier Element ◽  
Transport Delay ◽  
Non Linear ◽  
The Mathematical Model

The evaluation of the mathematical model parameters of a non-linear object with a transport delay is considered in this paper. A temperature controlled stage based on a Peltier element is an identification object in the paper. Several input signal implementations are applied to the input of the identification object. The least squares method is applied for the calculation of the non-linear differential equitation parameters which describe the identification object. The least squares method is used due to its simplicity and the possibility of identification non-linear objects. The parameters values obtained in the process of identification are provided. The plots of temperature changes in the temperature control system with a controller designed based on the mathematical model of the control object obtained as a result of identification are shown. It is found that the mathematical model obtained in the process of identification may be applied to design controllers for non-linear systems, in particular for a temperature stage based on a Peltier element, and for self-tuning controllers. However, the least square method proposed in the paper cannot estimate the transport delay time. Therefore it is required to evaluate the time delay by temperature transient processes. Dynamic object identification is applied when it is required to obtain a mathematical model structure and evaluate the parameters by an input and output control object signal. Also, identification is applied for auto tuning of controllers. A mathematical model of a control object is required to design the controller which is used to provide the required accuracy and stability of control systems. Peltier elements are applied to design low-power and small- size temperature stage . Hot benches based on a Peltier element can provide the desired temperature above and below ambient temperature.

scholarly journals METHODS OF FORMULATING AND SOLVING OPTIMIZATION PROBLEMS OF CUTTING LOGS OF LARGE SIZE BY BAR-SAWING METHOD WITH CUTTING OUT ONE BAR AND FIVE PAIRS OF SIDE EDGING BOARDS WITH SUBSEQUENT SAWING LUMBER FOR EDGED BOARDS

2017 ◽  
Vol 7 (1) ◽  
pp. 137-150
Author(s):  
Агапов ◽  
Aleksandr Agapov
Keyword(s):  
Mathematical Model ◽  
Objective Function ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Target Function ◽  
Cross Sectional ◽  
Optimization Task ◽  
Cutting Out ◽  
The Mathematical Model ◽  
The Relationship

For the first time the mathematical model of task optimization for this scheme of cutting logs, including the objective function and six equations of connection. The article discusses Pythagorean area of the logs. Therefore, the target function is represented as the sum of the cross-sectional areas of edging boards. Equation of the relationship represents the relationship of the diameter of the logs in the vertex end with the size of the resulting edging boards. This relationship is described through the use of the Pythagorean Theorem. Such a representation of the mathematical model of optimization task is considered a classic one. However, the solution of this mathematical model by the classic method is proved to be problematic. For the solution of the mathematical model we used the method of Lagrange multipliers. Solution algorithm to determine the optimal dimensions of the beams and side edging boards taking into account the width of cut is suggested. Using a numerical method, optimal dimensions of the beams and planks are determined, in which the objective function takes the maximum value. It turned out that with the increase of the width of the cut, thickness of the beam increases and the dimensions of the side edging boards reduce. Dimensions of the extreme side planks to increase the width of cut is reduced to a greater extent than the side boards, which are located closer to the center of the log. The algorithm for solving the optimization problem is recommended to use for calculation and preparation of sawing schedule in the design and operation of sawmill lines for timber production. When using the proposed algorithm for solving the optimization problem the output of lumber can be increased to 3-5 %.

scholarly journals A mathematical model of common-cold epidemics on Tristan da Cunha

1971 ◽  
Vol 69 (3) ◽  
pp. 423-433 ◽  
Author(s):  
B. J. Hammond ◽  
D. A. J. Tyrrell
Keyword(s):  
Mathematical Model ◽  
Common Cold ◽  
Average Duration ◽  
Model Parameters ◽  
Epidemic Threshold ◽  
Tristan Da Cunha ◽  
Simulation Techniques ◽  
Time Courses ◽  
The Mathematical Model ◽  
Computer Simulation Techniques

SUMMARYRecords of seven common-cold outbreaks on the island of Tristan da Cunha are compared with the corresponding time courses given by the mathematical model of Kermack & McKendrick (1927) and with an alternative model that directly involves a constant average duration of individual infection. Using computer simulation techniques the latter model is shown to be preferred and is then closely matched to the field data to obtain values for the model parameters. Consideration is then given to the intensity of epidemics predicted by the model and to the distribution of the actual epidemics relative to the theoretical epidemic threshold.

scholarly journals The generation of a mathematical model of the biogas production process from organic municipal solid waste

2020 ◽  
Vol 180 ◽  
pp. 02019 ◽  
Author(s):  
Marzhan Temirbekova ◽  
Madina Aliyarova ◽  
Iliya Iliev ◽  
Aliya Yelemanova ◽  
Saule Sagintayeva
Keyword(s):  
Mathematical Model ◽  
Municipal Solid Waste ◽  
Solid Waste ◽  
Anaerobic Fermentation ◽  
Biogas Production ◽  
Biogas Plant ◽  
Model Parameters ◽  
Biochemical Processes ◽  
Biogas Plants ◽  
The Mathematical Model

This paper justifies the efficiency of the biogas collection and utilization at the MSW (municipal solid waste) landfill in Almaty with the installation of several modern biogas plants. The optimal mode of processes occurring in a biogas plant is determined by computer generated simulations. Mathematical model parameters were identified to describe biochemical processes occurring in a biogas plant. Two approaches are used to resolve the mathematical model: the finite-difference method for solving the system of differential equations and simulation modeling by using the Any Logic package. A program is written in the algorithmic language C ++. Numerous calculations were carried out, the results of which are presented in curves and their qualitative picture is consistent with the ongoing processes. The created computer program allows to make a preliminary forecast of anaerobic fermentation occurring in the bioreactor depending on volume of the substrate, methane microorganisms and temperature conditions.

A Universal Mathematical Model for a New Combined-Cycle, Fossil-Fuel Power System (LAJ Cycle): Part 1 — Static Model

2002 ◽  
Author(s):  
Roddie R. Judkins ◽  
Timothy R. Armstrong ◽  
Solomon D. Labinov
Keyword(s):  
Mathematical Model ◽  
Power System ◽  
Methane Conversion ◽  
Fossil Fuel ◽  
Dynamic Models ◽  
Static Model ◽  
Combined Cycle ◽  
Model Parameters ◽  
Lagrangian Multiplier ◽  
Molar Ratios

A universal mathematical model (UMM) has been developed and applied to the LAJ (for Labinov, Armstrong, and Judkins) cycle, a new combined-cycle, fossil-fuel power system. The UMM includes static and dynamic models of the system. The static model allows for thermodynamic and thermochemical analyses of the basic system components (reformer, turbine, membrane separator, fuel cell, air compressor, heat exchanger, and other components) and the entire system. Equilibrium compositions of reforming products are defined by minimizing Gibbs free energy of the mixtures using the Lagrangian multiplier method. The dependence of the main system parameters on pressure (P), temperature (T), and water-to-methane molar ratios (N) at the steam reformer have been evaluated. For selected reforming parameters, viz., P = 4.0 MPa and T = 1200 K, the degree of methane conversion is near 95% with N = 5. However, in view of mass and size limitations on equipment, a lower value of N = 3 is preferred, in which case the degree of methane conversion is 88%. The dependence of the system static model parameters on N has been investigated, and economic characteristics of the model have been evaluated for an output power of 250 kW. It is shown that when, N = 3, the fuel cost contribution to overall electricity costs is 1 cent/kWh.

Study on the Dynamic Models of Systems Biology from the View of Engineering

2012 ◽  
Vol 220-223 ◽  
pp. 952-957
Author(s):  
Chen Liu ◽  
Xiao Yan Liu
Keyword(s):  
Mathematical Model ◽  
Systems Biology ◽  
Dynamic Process ◽  
Biological System ◽  
Dynamic Models ◽  
Model Parameters ◽  
State Variables ◽  
Biochemical Pathway ◽  
The Right ◽  
The Mathematical Model

From the view of engineering, based on expatiating the features of systems biology, the paper discusses the workflows and the research emphasis of systems biology. It also explains how to model and analyze the dynamic process of signal transmitting network for a biological system by an example. Based on the complexity and uncertainty of the mathematical model, the right methods are chosen to realize the effective estimation of state variables and model parameters for the biochemical pathway.

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