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

This chapter presents the calculation results of model (type XT) parameters of a synchronous generator (PN = 44 kW) operating in the laboratory obtained with the use of the measured waveforms after introducing a PRBS disturbance in the generator voltage regulation channel. Determination of model parameters of synchronous generators operating in power plants is also presented. Sample calculations of mathematical model parameters of synchronous generators were made on the basis of dynamic waveforms recorded at the Pątnow Power Plant (PN = 230 MW—GENROU model) and Halemba Combined Heat and Power Plant (PN = 50 MW—RL models, GENROU model). Determination of parameters of the excitation system models is described in the further part of this chapter. Sample calculations of mathematical model parameters of the excitation systems operating in the Polish PS were carried out based on the dynamic waveforms recorded in the Pątnow Power Plant (electromachine excitation system model) and Skawina Power Plant (static excitation system model). Conclusions drawn from the calculations of the synchronous generator and excitation circuit model parameters as well as some comments on the errors of parameter estimation of the generating unit element models are given at the end of the chapter.

The paper presents the two-dimensional, field-circuit model of a high power synchronous generator verified by measurements. The model enables determining the waveforms of electromagnetic quantities in steady and transient states. Verification of the model was based on comparison of the measured and calculated waveforms after a disturbance in the voltage regulation system of a TWW-200-2 generator operating in Połaniec Power Plant. There are also presented the field methods for determining electromagnetic parameters (synchronous reactances and time constants) when using the distributions of static and quasi-static, magnetic and electromagnetic fields calculated by the finite element method (FEM). The set of these parameters was used as the starting parameters of the optimization algorithm for estimation of electromagnetic parameters of the synchronous generator circuit model. The dynamic waveforms under the generator load conditions calculated by the finite element method are the basis of parameter estimation. The parameter estimation of the generator model was performed with the use of the least squares method.

In the present paper, a thermodynamic analysis of Al-Dura, Baghdad station type (K– 160–13.34–0.0068), power plant has been carried out. The power plant system was simulated and a detailed parametric study undertaken. This study can be helpful to identify the plant site conditions that cause losses of useful energy taken place and also helpful to resolve some problems encountered in steam turbine, capacity unit. Developing nonlinear mathematical models based on system identification approaches during normal operation without any external excitation or disruption is always a hard effort, assuming that parametric models are available. This study included on using soft computing methods that would be helpful in order to adjust model parameters over full range of input–output operational data. In this case, the model parameters are adjusted by applying genetic algorithms as optimization methods. Comparison between the responses of the turbine – generator model with the responses of real system validates the accuracy of the proposed model in steady state and transient conditions. Simulation results shows that the efficiencies and feasibility of the developed model in term of more accurate and less deviation with the responses of read system in the steady and transient conditions, and the error of proposed function is less than 0.37%. This study presents the usage of the Cycle – tempo and Matlab/Simulink package to implement the model of the power plant. Finally, many recommendations have been suggested for improved plant performance.

Mathematical modeling provides a rigorous way to quantify immunological processes and discriminate between alternative mechanisms driving specific biological phenomena. It is typical that mathematical models of immunological phenomena are developed by modelers to explain specific sets of experimental data after the data have been collected by experimental collaborators. Whether the available data are sufficient to accurately estimate model parameters or to discriminate between alternative models is not typically investigated. While previously collected data may be sufficient to guide development of alternative models and help estimating model parameters, such data often do not allow to discriminate between alternative models. As a case study, we develop a series of power analyses to determine optimal sample sizes that allow for accurate estimation of model parameters and for discrimination between alternative models describing clustering of CD8 T cells around Plasmodium liver stages. In our typical experiments, mice are infected intravenously with Plasmodium sporozoites that invade hepatocytes (liver cells), and then activated CD8 T cells are transferred into the infected mice. The number of T cells found in the vicinity of individual infected hepatocytes at different times after T cell transfer is counted using intravital microscopy. We previously developed a series of mathematical models aimed to explain highly variable number of T cells per parasite; one of such models, the density-dependent recruitment (DDR) model, fitted the data from preliminary experiments better than the alternative models, such as the density-independent exit (DIE) model. Here, we show that the ability to discriminate between these alternative models depends on the number of parasites imaged in the analysis; analysis of about [Formula: see text] parasites at 2, 4, and 8h after T cell transfer will allow for over 95% probability to select the correct model. The type of data collected also has an impact; following T cell clustering around individual parasites over time (called as longitudinal (LT) data) allows for a more precise and less biased estimates of the parameters of the DDR model than that generated from a more traditional way of imaging individual parasites in different liver areas/mice (cross-sectional (CS) data). However, LT imaging comes at a cost of a need to keep the mice alive under the microscope for hours which may be ethically unacceptable. We finally show that the number of time points at which the measurements are taken also impacts the precision of estimation of DDR model parameters; in particular, measuring T cell clustering at one time point does not allow accurately estimating all parameters of the DDR model. Using our case study, we propose a general framework on how mathematical modeling can be used to guide experimental designs and power analyses of complex biological processes.

On a class of parameters estimators in linear models dominating the least squares one

To enhance power system dependability and efficiency, it is of great importance to obtain correct parameters of the models of key power system components such as a synchronous generator (SG). Technology of synchronized phasor measurements allows us to estimate the SG model parameters through measurements in power system steady states and transients states, without switching the SG off and conducting complex testing procedures. The theory of electric circuits and electric machines, theory of optimization and statistics, and matrix algebra are applied in this study. The developed parameter estimation method has been implemented in the MATLAB software. The method has been verified through real-world measurements captured by a phasor measurement unit installed at a large power plant in the United Power System. This paper presents an algorithm of the turbogenerator synchronous reactance estimation via a set of synchrophasor data taken under steady-state conditions. Also, the paper considers the criteria for an appropriate data array ensuring successful parameter estimation. An algorithm has been developed and implemented in MATLAB software package. To improve the parameter estimation accuracy, an algorithm has been proposed to modify a nominal value for the SG no-load excitation current depending on the heating of the field winding. The algorithm has been successfully tested out based on a set of steady state synchrophasor data captured for one of the turbogenerators in the Russian United Power System. The authors have developed and analyzed quantitative criteria to determine a set of measured parameters of steady-state modes, providing the most accurate results of the turbogenerator synchronous reactance. The developed algorithm allows accurate update of the turbogenerator synchronous parameters through synchrophasor measurements recorded in a steady state modes of electric power systems. Using the criteria for selecting phasor data, it seems possible to automate the process of generating a data array of measurement of various steady-state modes necessary for identification. The proposed procedure that considers the field winding temperature can be employed in math models to estimate SG transient and subtransient parameters based on phasor measurements in transient modes of electric power systems.

The lithium-ion batteries of an electric vehicle belong to a high-voltage direct-current system. The high-voltage insulation performance of electric vehicles is very important for their safe operation. To solve the problems of slow response and the poor estimation accuracy of the insulation resistance under complex vehicle working conditions, a real-time insulation resistance detection method based on the variable forgetting factor least squares algorithm is proposed in this paper. Based on the low-frequency signal injection method and considering the influence of the Y capacitor, the corresponding circuit model and the mathematical model of the reflected wave voltage are established, and the mathematical model is linearized by a first-order Taylor expansion. By analyzing the influence of the forgetting factor on model parameter identification and setting appropriate shutdown criteria, the least squares algorithm with a variable forgetting factor is designed to quickly and accurately estimate the insulation resistance and Y capacitance. The experimental test results show that the proposed method can quickly track the changes in the insulation resistance and Y capacitance under the condition of noise interference and that the root mean square error of the estimation resistor is within 0.012.

Error measures for fuzzy linear regression: Monte Carlo simulation approach

Model selection is an important part of any statistical analysis. Many tools are suggested for selecting the best model including frequentist and Bayesian perspectives. There is often a considerable uncertainty in the selection of a particular model to be the best approximating model. Model selection uncertainty arises when the data are used for both model selection and parameter estimation. Bias in estimators of model parameters often arise when data based selection has been done. Therefore, model averaging of the parameter estimators will be done to alleviate the bias in model selection in a set of candidate models, by combining the information from a set of candidate models. This paper is two-fold, new criteria of model selection are proposed based on different averages of AIC, BIC, AICc, and HQC. Also, model averaging is introduced to compare the parameter estimators in model averaging with the ones in model selection. Two Simulation studies are considered, the first is for model selection and showed that the new proposed criteria are lies between some of the known criteria such as AIC, BIC, AICc, and HQC, and so they can be used as new criteria of model selection. The second simulation study is for model averaging and showed that the parameter estimators have less bias and less predicted mean square error (PMSE) compared with the parameter estimators in model selection.

Transient stability constrained optimal power flow considering fourth-order synchronous generator model and controls

Synthetic genetic circuits are the core research objects in synthetic biology, and the programming of cell behavior is achieved through the combination of engineered gene elements. Mathematical modeling provides crucial support for understanding and designing synthetic genetic circuits, enabling researchers to predict the dynamic behavior of the circuits and guide experimental optimization. This study reviews the categories of synthetic genetic circuits (such as gene switches, oscillators, feedback circuits, etc.) and their biological mechanisms, with a focus on the application of ordinary differential equation (ODE) models, stochastic modeling, and network topology dynamics models in circuit modeling. We expounded on the estimation of model parameters, sensitivity analysis, and the integration methods of experimental data and models, and compared the characteristics of numerical simulation algorithms and commonly used software tools (such as MATLAB, COPASI, BioNetGen, etc.). Through the discussion of the steady-state, oscillation behavior, multiple steady-state and bifurcation analysis of system dynamics, the understanding of the influence of positive and negative feedback mechanisms on system stability is deepened. In addition, we took the classic synthetic gene oscillator Repressilator as a case to conduct modeling and simulation analysis, and compared the model predictions with the experimental data. Finally, the application prospects of synthetic genetic circuits in the fields of bioengineering and medicine were summarized, and the future directions of promoting the design of synthetic circuits with the help of model optimization and artificial intelligence-assisted design were prospected. Research shows that mathematical modeling and computational simulation have become key tools for the study and design of synthetic genetic circuits, providing a theoretical basis and practical guidance for the engineering transformation of complex biological systems.

Excessive groundwater exploitation in Sirjan plain, located in south of Iran, has caused severe land subsidence. The main purpose of this paper is to determine the hydrogeological parameters of the aquifer system in Sirjan plain. To this end, the groundwater flow was simulated in both steady and transient states using the United States Geological Survey Modular Three-Dimensional Finite-Difference Groundwater Flow Model, MODFLOW. The hydraulic conductivity parameter of the aquifer system was first estimated and calibrated in the steady state by simulating the hydraulic head at 63 piezometric wells. The specific yield and recharge parameters were then calibrated in the transient state by simulating the drawdown within a period of interest, i.e. 23 September 2004 to 22 September 2005. The main innovation of this paper, however, is to use the potential of Synthetic Aperture Radar (SAR) interferometry time-series analysis in the last step of the proposed algorithm. Small Baseline Subset (SBAS) time-series analysis was applied using Envisat Advanced SAR (ASAR) images acquired from 1 June 2004 to 28 September 2010. The merit of SBAS time series is that it enables us to calculate the amount of subsidence in each period of interest while minimizing the temporal decorrelation effect. In the last step, the SBAS time-series analysis results were obtained to extract the accumulated subsidence from 19 October 2004 to 30 August 2005. The aquifer compaction due to this period was calculated in the Interbed Storage Package (IBS1) for MODFLOW in order to calibrate storage coefficient in a trial-and-error manner so as the calculated subsidence and the observed one by SAR interferometry be in a good agreement. The Root Mean Square Error (RMSE) between the simulated subsidence and the observed one is calculated as 0.019 m which is an indication of the high performance of modelling.

the important issue in the extraction of the unknown parameters in the photovoltaic model is the mathematical models.Therefore, a five equivalent circuit is analyzed in this work.The unknown parameters are five for single diode model, seven for double-diode model, eight for modified double-diode, and nine for three-diode model and ten for modified three-diode parameters.The performance of the modified three-diode model and three-diode model after estimate all parameters without assumption for any variable are compared with the performance of the both single diode model, double-diode model and also the modified double-diode of the same solar cell.Cuckoo search optimization algorithm (CSOA) is proposed for the estimation of the unknown parameters for the five solar cell equivalent models.The root mean square error, the absolute error for current and power, and the maximum power point absolute error are analyzed to the performance of the five solar cell models.

A half diallel cross among six parents of wheat (Triticum aestivum L.) was achieved for combining ability under recommended irrigation and water stress at Etay EL-Baroud Agricultural Research Station, Agricultural Research Center, Egypt, during 2009/2010 and 2010/2011 seasons in RCBD with three replications. Data were recorded from F1 generation for days to heading, days to physiological maturity, plant height, flag leaf area, spike length, number of spikelets spike-1, number of kernels spike-1, number of spikes plant-1, 1000-kernel weight and grain yield plant-1. Mean squares for genotypes, parents, crosses and parent vs. crosses were significant for all the studied traits in both irrigation treatments. General combining ability (GCA) and specific combining ability (SCA) mean squares were significant for all the studied traits in both irrigation treatments. High GCA/SCA ratios which largely exceeded the unity were detected for all studied traits, except for grain yieldplant-1 under the study in both conditions. Wheat genotype Line 1 (P6) showed the maximum desirable GCA values for days to heading, days to physiological maturity, flag leaf area, spike length, under water stress, number of kernels spike-1and 1000-kernel weight under both conditions. For shortness, the cultivar Sakha 93 (P2) proved to be the best general combiner for plant height under both environments. Meanwhile, Sham 6 under normal conditions and Sahel 1 under water stress conditions were the best combiners for plant height concerning breeding for tallness. The cultivar Gemmeiza 9 proved to be a good general combiner for number of spikelets spike-1 under both conditions. The cultivar Misr 1 found to be the best general combiner for number of spikes plant-1 and grain yield plant-1 under normal condition, while the cultivar Sakha 93 found to be the best general combiner for number of spikes plant-1 and grain yield plant-1 under water stress condition. The cross (Sahel 1 x Sham 6) showed the maximum desirable SCA values for days to heading and days to physiological maturity under both water regime treatments. The cross (Misr 1 x Line 1) exhibited the maximum SCA for plant height under normal conditions, while (Sahel 1 x Gemmeiza 9) showed the maximum SCA for plant height under water stress condition. The cross (Sahel 1 x Misr 1) showed maximum SCA value for flag leaf area under both environments. The cross (Sham 6 x Line 1) was the best specific combiners for spike length under normal conditions, while (Sahel 1 x Sham 6) was the best for spike length under stress conditions. The best specific combiner for kernels spike-1 under both conditions was the cross (Misr 1 x Line 1). The cross (Sakha 93 x Misr 1) showed the best SCA for number of spikes plant-1 under normal conditions while the cross (Sakha 93 x Line 1) was the best one under water stress conditions. For 1000-kernel weight the cross (Gemmeiza 9 x Misr 1) was the best specific combiner under both irrigation conditions. The cross (Sakha 93 x Line 1) exhibited the maximum SCA for grain yield plant-1 under normal conditions while the cross (Sakha 93 x Gemmeiza 9) was the best one under water stress conditions. The crosses (Sakha 93 x Gemmeiza 9), (Sakha 93 x Line 1) and (Misr 1 x Line 1) were prospective in wheat breeding programs since they expressed significant and desirable (ŝij) effects for most traits.

Hepatitis B is transmitted through blood or body fluids contaminated with the virus from Hepatitis B sufferers (carriers). The factors that cause a person to contract Hepatitis B are sexual intercourse, blood contact, placental contact from the mother to the baby, and saliva. The incubation period for Hepatitis B Virus (HBV) ranges from 30 - 180 days with an average of 60 - 90 days. HBV can be detected 30 - 60 days after infection and persists for a certain period. Thus, the behaviour of infectious diseases can be observed and described using mathematical modelling. Mathematical modelling is a field of mathematics that represents and explains physical systems or problems that occur in the real world and are solved in mathematical statements. The mathematical model used to overcome uncertainty in variable values ​​is a stochastic model. These causal factors are not directly observed and form a Markov chain. The model that can be used for the uncertainty of an event is the Hidden Markov Model. The Hidden Markov Model (MHM) is a type of stochastic modelling that does not recognize the factors that trigger the problem being modelled. The Poisson Hidden Markov model is used to model Hepatitis B disease. Hepatitis B disease data is a series of observations that experience overdispersion and depend on the trigger of Hepatitis B disease, which is assumed not to be observed directly and forms a Markov chain. The aim to be achieved in this research is to model Hepatitis B disease at the Medan Haji Hospital using the Poisson Hidden Markov model and to find parameter estimates using the Expectation Maximization Algorithm. This type of research uses quantitative research methods. The conclusions that can be drawn based on the results and previous discussions are as follows: the method for determining the average number of patients in patient B can use the PHMM (Poisson Hidden Markov Model) method with the EiM (Expectation-Maximization Algorithm) algorithm, the best model for the number of Hepatitis B patients in Haji Hospital at this hospital is the model with three hidden cases with the parameter estimation value. The average number of Hepatitis B patients is 0.0324 in 1 month, and the average predicted results obtained by the hidden condition model 3 align with the original conditions in the previous months.