Parameter estimation for transformer modeling

Large Power transformers, an aging and vulnerable part of our energy infrastructure, are at choke points in the grid and are key to reliability and security. Damage or destruction due to vandalism, misoperation, or other unexpected events is of great concern, given replacement costs upward of $2M and lead time of 12 months. Transient overvoltages can cause great damage and there is much interest in improving computer simulation models to correctly predict and avoid the consequences. EMTP (the Electromagnetic Transients Program) has been developed for computer simulation of power system transients. Component models for most equipment have been developed and benchmarked. Power transformers would appear to be simple. However, due to their nonlinear and frequency-dependent behaviors, they can be one of the most complex system components to model. It is imperative that the applied models be appropriate for the range of frequencies and excitation levels that the system experiences. Thus, transformer modeling is not a mature field and newer improved models must be made available. In this work, improved topologically-correct duality-based models are developed for three-phase autotransformers having five-legged, three-legged, and shell-form cores. The main problem in the implementation of detailed models is the lack of complete and reliable data, as no international standard suggests how to measure and calculate parameters. Therefore, parameter estimation methods are developed here to determine the parameters of a given model in cases where available information is incomplete. The transformer nameplate data is required and relative physical dimensions of the core are estimated. The models include a separate representation of each segment of the core, including hysteresis of the core, λ-i saturation characteristic, capacitive effects, and frequency dependency of winding resistance and core loss. Steady-state excitation, and de-energization and re-energization transients are simulated and compared with an earlier-developed BCTRAN-based model. Black start energization cases are also simulated as a means of model evaluation and compared with actual event records. The simulated results using the model developed here are reasonable and more correct than those of the BCTRAN-based model. Simulation accuracy is dependent on the accuracy of the equipment model and its parameters. This work is significant in that it advances existing parameter estimation methods in cases where the available data and measurements are incomplete. The accuracy of EMTP simulation for power systems including three-phase autotransformers is thus enhanced. Theoretical results obtained from this work provide a sound foundation for development of transformer parameter estimation methods using engineering optimization. In addition, it should be possible to refine which information and measurement data are necessary for complete duality-based transformer models. To further refine and develop the models and transformer parameter estimation methods developed here, iterative full-scale laboratory tests using high-voltage and high-power three-phase transformer would be helpful.

Adaptive control of sinusoidal brushless DC motor actuators

Electrical Power Assisted Steering system (EPAS) will likely be used on future automotive power steering systems. The sinusoidal brushless DC (BLDC) motor has been identified as one of the most suitable actuators for the EPAS application. Motor characteristic variations, which can be indicated by variations of the motor parameters such as the coil resistance and the torque constant, directly impart inaccuracies in the control scheme based on the nominal values of parameters and thus the whole system performance suffers. The motor controller must address the time-varying motor characteristics problem and maintain the performance in its long service life. In this dissertation, four adaptive control algorithms for brushless DC (BLDC) motors are explored. The first algorithm engages a simplified inverse dq-coordinate dynamics controller and solves for the parameter errors with the q-axis current (iq) feedback from several past sampling steps. The controller parameter values are updated by slow integration of the parameter errors. Improvement such as dynamic approximation, speed approximation and Gram-Schmidt orthonormalization are discussed for better estimation performance. The second algorithm is proposed to use both the d-axis current (id) and the q-axis current (iq) feedback for parameter estimation since id always accompanies iq. Stochastic conditions for unbiased estimation are shown through Monte Carlo simulations. Study of the first two adaptive algorithms indicates that the parameter estimation performance can be achieved by using more history data. The Extended Kalman Filter (EKF), a representative recursive estimation algorithm, is then investigated for the BLDC motor application. Simulation results validated the superior estimation performance with the EKF. However, the computation complexity and stability may be barriers for practical implementation of the EKF. The fourth algorithm is a model reference adaptive control (MRAC) that utilizes the desired motor characteristics as a reference model. Its stability is guaranteed by Lyapunov’s direct method. Simulation shows superior performance in terms of the convergence speed and current tracking. These algorithms are compared in closed loop simulation with an EPAS model and a motor speed control application. The MRAC is identified as the most promising candidate controller because of its combination of superior performance and low computational complexity. A BLDC motor controller developed with the dq-coordinate model cannot be implemented without several supplemental functions such as the coordinate transformation and a DC-to-AC current encoding scheme. A quasi-physical BLDC motor model is developed to study the practical implementation issues of the dq-coordinate control strategy, such as the initialization and rotor angle transducer resolution. This model can also be beneficial during first stage development in automotive BLDC motor applications.

TERPENE AND TERPENOID EMISSIONS AND SECONDARY ORGANIC AEROSOL PRODUCTION

Approximately 90% of fine aerosol in the Midwestern United States has a regional component with a sizable fraction attributed to secondary production of organic aerosol (SOA). The Ozark Forest is an important source of biogenic SOA precursors like isoprene (> 150 mg m-2 d-1), monoterpenes (10-40 mg m-2 d-1), and sesquiterpenes (10-40 mg m-2d-1). Anthropogenic sources include secondary sulfate and nitrate and biomass burning (51-60%), vehicle emissions (17-26%), and industrial emissions (16-18%). Vehicle emissions are an important source of volatile and vapor-phase, semivolatile aliphatic and aromatic hydrocarbons that are important anthropogenic sources of SOA precursors. The short lifetime of SOA precursors and the complex mixture of functionalized oxidation products make rapid sampling, quantitative processing methods, and comprehensive organic molecular analysis essential elements of a comprehensive strategy to advance understanding of SOA formation pathways. Uncertainties in forecasting SOA production on regional scales are large and related to uncertainties in biogenic emission inventories and measurement of SOA yields under ambient conditions. This work presents a bottom-up approach to develop a conifer emission inventory based on foliar and cortical oleoresin composition, development of a model to estimate terpene and terpenoid signatures of foliar and bole emissions from conifers, development of processing and analytic techniques for comprehensive organic molecular characterization of SOA precursors and oxidation products, implementation of the high-volume sampling technique to measure OA and vapor-phase organic matter, and results from a 5 day field experiment conducted to evaluate temporal and diurnal trends in SOA precursors and oxidation products. A total of 98, 115, and 87 terpene and terpenoid species were identified and quantified in commercially available essential oils of Pinus sylvestris, Picea mariana, and Thuja occidentalis, respectively, by comprehensive, two-dimensional gas chromatography with time-of-flight mass spectrometric detection (GC × GC-ToF-MS). Analysis of the literature showed that cortical oleoresin composition was similar to foliar composition of the oldest branches. Our proposed conceptual model for estimation of signatures of terpene and terpenoid emissions from foliar and cortical oleoresin showed that emission potentials of the foliar and bole release pathways are dissimilar and should be considered for conifer species that develop resin blisters or are infested with herbivores or pathogens. Average derivatization efficiencies for Methods 1 and 2 were 87.9 and 114%, respectively. Despite the lower average derivatization efficiency of Method 1, distinct advantages included a greater certainty of derivatization yield for the entire suite of multi- and poly-functional species and fewer processing steps for sequential derivatization. Detection limits for Method 1 using GC × GC- ToF-MS were 0.09-1.89 ng μL-1. A theoretical retention index diagram was developed for a hypothetical GC × 2GC analysis of the complex mixture of SOA precursors and derivatized oxidation products. In general, species eluted (relative to the alkyl diester reference compounds) from the primary column (DB-210) in bands according to n and from the secondary columns (BPX90, SolGel-WAX) according to functionality, essentially making the GC × 2GC retention diagram a Carbon number-functionality grid. The species clustered into 35 groups by functionality and species within each group exhibited good separation by n. Average recoveries of n-alkanes and polyaromatic hydrocarbons (PAHs) by Soxhlet extraction of XAD-2 resin with dichloromethane were 80.1 ± 16.1 and 76.1 ± 17.5%, respectively. Vehicle emissions were the common source for HSVOCs [i.e., resolved alkanes, the unresolved complex mixture (UCM), alkylbenzenes, and 2- and 3-ring PAHs]. An absence of monoterpenes at 0600-1000 and high concentrations of monoterpenoids during the same period was indicative of substantial losses of monoterpenes overnight and the early morning hours. Post-collection, comprehensive organic molecular characterization of SOA precursors and products by GC × GC-ToFMS in ambient air collected with ~2 hr resolution is a promising method for determining biogenic and anthropogenic SOA yields that can be used to evaluate SOA formation models.

Parameter identification of a copper-zeolite SCR catalyst model using reactor data

The selective catalytic reduction system is a well established technology for NOx emissions control in diesel engines. A one dimensional, single channel selective catalytic reduction (SCR) model was previously developed using Oak Ridge National Laboratory (ORNL) generated reactor data for an iron-zeolite catalyst system. Calibration of this model to fit the experimental reactor data collected at ORNL for a copper-zeolite SCR catalyst is presented. Initially a test protocol was developed in order to investigate the different phenomena responsible for the SCR system response. A SCR model with two distinct types of storage sites was used. The calibration process was started with storage capacity calculations for the catalyst sample. Then the chemical kinetics occurring at each segment of the protocol was investigated. The reactions included in this model were adsorption, desorption, standard SCR, fast SCR, slow SCR, NH3 Oxidation, NO oxidation and N2O formation. The reaction rates were identified for each temperature using a time domain optimization approach. Assuming an Arrhenius form of the reaction rates, activation energies and pre-exponential parameters were fit to the reaction rates. The results indicate that the Arrhenius form is appropriate and the reaction scheme used allows the model to fit to the experimental data and also for use in real world engine studies.

DYNAMIC MODEL BASED STATE ESTIMATION IN A HEAVY DUTY DIESEL AFTERTREATMENT SYSTEM FOR ONBOARD DIAGNOSTICS AND CONTROLS

Estimating un-measurable states is an important component for onboard diagnostics (OBD) and control strategy development in diesel exhaust aftertreatment systems. This research focuses on the development of an Extended Kalman Filter (EKF) based state estimator for two of the main components in a diesel engine aftertreatment system: the Diesel Oxidation Catalyst (DOC) and the Selective Catalytic Reduction (SCR) catalyst. One of the key areas of interest is the performance of these estimators when the catalyzed particulate filter (CPF) is being actively regenerated. In this study, model reduction techniques were developed and used to develop reduced order models from the 1D models used to simulate the DOC and SCR. As a result of order reduction, the number of states in the estimator is reduced from 12 to 1 per element for the DOC and 12 to 2 per element for the SCR. The reduced order models were simulated on the experimental data and compared to the high fidelity model and the experimental data. The results show that the effect of eliminating the heat transfer and mass transfer coefficients are not significant on the performance of the reduced order models. This is shown by an insignificant change in the kinetic parameters between the reduced order and 1D model for simulating the experimental data. An EKF based estimator to estimate the internal states of the DOC and SCR was developed. The DOC and SCR estimators were simulated on the experimental data to show that the estimator provides improved estimation of states compared to a reduced order model. The results showed that using the temperature measurement at the DOC outlet improved the estimates of the CO , NO , NO2 and HC concentrations from the DOC. The SCR estimator was used to evaluate the effect of NH3 and NOX sensors on state estimation quality. Three sensor combinations of NOX sensor only, NH3 sensor only and both NOX and NH3 sensors were evaluated. The NOX only configuration had the worst performance, the NH3 sensor only configuration was in the middle and both the NOX and NH3 sensor combination provided the best performance.