Estimating Synchronous Machine Electrical Parameters from Frequency Response Tests

A method of obtaining synchronous machine d and q axis impedances by test as a function of frequency of d,q components has recently been proposed by de Mello and Hannett [1]. Their proposal ends by determination of the numerical values for the operational inductances Ld(j2w), Lq(j2w) or impedances Zd(j2w), Zq(j2w) at different values of W, the speed of the machine at which the tests are conducted; however, they do not show how the values of actual parameters such as inductances and time constants are to be obtained from the curves of operational inductance versus frequency.     

Coupled finite-element/state-space modeling of turbogenerators inthe abc frame of reference-the no-load case

This first of two companion papers centers on applying a coupled finite-element/state-space technique to the determination of self and mutual winding inductances of a 733 MVA turbogenerator and computing its open-circuit characteristic, in the natural abc frame of reference. In this method, the apparent self and mutual inductance profiles of the armature and field windings, expressed as functions of rotor position angle, are computed from a series of magnetic field solutions performed at uniformly-distributed samples of rotor positions covering the entire 360° electrical cycle, using the energy perturbation method. These inductances, which are obtained at no-load for three different excitation levels, include the full effect of space harmonics introduced by the magnetic circuit geometry, winding layouts and magnetic circuit saturation. The abc-frame/finite-element computed open-circuit characteristic is in excellent agreement with the test results. This computed no-load set of parameters forms the initial data for simulation of the full-load performance given in the companion paper, including the full impact of space harmonics and saturation on the flux linkage, current and voltage waveforms, and other performance parameters     

Characterising the d-axis machine model of a turbogenerator usingfinite elements

An analysis of a long established fundamental assumption is presented. The assumption that superposition is valid in frequency response derived models is shown to be wrong, because eddy current losses in the solid rotor cannot be superimposed in the machine direct-axis. This implies that network theory is not valid in characterising the d-axis machine model. A machine model structure with one damper winding in the d-axis is derived from finite element analysis. Unequal mutual inductances in the machine d-axis are determined and hence the so-called differential leakage inductances are found and they are frequency dependent. The study is made on a 150 MVA turbine generator by simulating the standstill frequency response test with finite elements     

Short-circuit test based maximum likelihood estimation of stabilitymodel of large generators

This paper presents a time-domain statistical identification method for synchronous-machine linear parameters from the standard line-to-line short-circuit test. The measurements are recorded on a 13.75-MVA hydrogenerator at Hydro-Quebec's Rapide-des-Quinze generating station. A complete mathematical model for synchronous machine asymmetrical test analysis is proposed. An efficient algorithm is built to accurately calculate the standard equivalent circuit from time-constants and operational inductances. The maximum likelihood estimator derived from the generalized least-squares method is then used for parameter identification. Validation of the estimated model response against the measured running-time domain data confirms the effectiveness of the proposed estimation technique     

Identification of synchronous machine linear parameters fromstandstill step voltage input data

This paper presents the results of a time-domain identification procedure to estimate the linear parameters of a 15 kVA salient-pole synchronous machine at standstill. A step voltage input test is performed, and the parameters of the time constant models and equivalent circuit models are estimated. The maximum likelihood algorithm is used for the estimation, and the best-fit model is selected from a set of increasing order models. The initialization values for the parameters to be estimated are determined from the operational inductances derived directly from the measured time domain data. The simulated equivalent circuit model response is validated against the measured standstill time domain and frequency domain data. In addition, simulation of the model response to an on-line small disturbance test is compared to the measured dynamic response     

Measurement of Synchronous Machine Parameters by a Modified Frequency Response Method - Part I: Theory

De Mello and Hannett [1] have theoretically proposed a method for determining the operational inductances Ld(j2w), Lq(j2w) of a synchronous machine at low values of generator speeds. Eitelberg and Harley [2] extended these ideas to obtain the inductances and time constants from the Ld(j2w), Lq(j2w) curves by a numerical procedure which allows one to attach different levels of importance to either the magnitude or phase fitting of the operational inductance expressions to the computed curves. The first part of this two-part paper extends these ideas [1-2] by proposing an improved MODIFIED data-processing method which uses a Fourier analysis of the open-phase voltage and short-circuit current to compute the operational inductances Ld(j2w), Lq(j2w) and avoids integration of the d,q axes flux linkages; providing that the fundamental and the third harmonic present in the recorded waveforms are considered. The second part [3] of this paper applies the improved MODIFIED data-processing method to a 3 kVA, 220 V microalternator.     

Identification of armature, field, and saturated parameters of alarge steam turbine-generator from operating data

This paper presents a step by step identification procedure of armature, field and saturated parameters of a large steam turbine-generator from real time operating data. First, data from a small excitation disturbance is utilized to estimate armature circuit parameters of the machine. Subsequently, for each set of steady state operating data, saturable mutual inductances L_ads and L_aqs are estimated. The recursive maximum likelihood estimation technique is employed for identification in these first two stages. An artificial neural network (ANN) based estimator is used to model these saturated inductances based on the generator operating conditions. Finally, using the estimates of the armature circuit parameters, the field winding and some damper winding parameters are estimated using an output error method (OEM) of estimation. The developed models are validated with measurements not used in the training of ANN and with large disturbance responses     

Measurement of Synchronous Machine Parameters by a Modified Frequency Response Method - Part II: Measured Results

De Mello and Hannett [1] have proposed a theoretical method for determining the operational inductances of a synchronous machine at low values of generator speeds. Eitelberg and Harley [2] extended these ideas to obtain the inductances and time constants from the Ld(j2w), Lq(j2w) curves by a numerical curve fitting procedure. Part I [3] of this paper broadens these ideas [1-2] by proposing an improved MODIFIED data-processing method which avoids the tedious integration of the d,q axes flux linkages [1]. Part II continues by performing a line-to-line short-circuit test on a 3 kVA, 220 V microalternator at different speeds covering the range which is of interest to subsynchronous resonance (SSR) studies [4]. Measured results illustrate the practical feasibility of this proposed frequency response method [1-3]. Practical problems associated with this test are also mentioned.     

Applicability of electrical short circuit current decay for solar cell characterization: limits and comparison to other methods

The electrical short-circuit current decay (ESCCD) method for determination of the bulk diffusion length L and the effective rear surface recombination velocity S is investigated with regard to application in solar cell development. To solve the major experimental problem, the fairly damped oscillations caused by parasitic capacitances and inductances, we introduced a calculation technique that fits the exponential decay plus three damped oscillations to the experimental curve. The measured effective diffusion lengths are compared to the results of an open-circuit voltage decay (OCVD) measurement and an evaluation of the spectral response of the solar cell, showing that only the ESCCD results are exclusively related to the base of the cell. The validity of the method is confirmed by the good agreement of the measured diffusion lengths and surface recombination velocities with those from two comparative measurements — determination of the bulk diffusion length performed on the unprocessed wafers using photoluminescence profile measurement and determination of L and S by evaluating the asymptotic decay time constants of the short-circuit current and the open-circuit voltage decay after optical excitation. Applying the method to electron-irradiated cells, decreasing diffusion lengths and increasing rear surface recombination velocities with increasing fluences could be observed. A discussion of the errors related to the ESCCD method shows that the accuracy in L and S depends critically on the knowledge of the device parameters.     

Calculation of two-axis induction motor model parameters usingfinite elements

The paper presents the use of the finite element method for determining the parameters of a two-axis model of a three-phase cage induction machine. The model parameters are obtained from the finite element field solutions. The saturation of the motor is taken into account in calculation of the flux distribution by using a static nonlinear vector potential solution. The linear time harmonic vector potential field solution is used for the inductances determination. All the inductances are determined as functions of the magnetizing current. Rotor skew is also taken into account. The accuracy of the described identification procedure is verified through laboratory measurements of the parameters     

风电叶片疲劳加载试验电磁激振特性研究

提出一种基于电磁力驱动的风电叶片疲劳加载新方法。为进一步得到电磁机构参数对激振力特性的影响规律,首先,以螺线管式电磁铁为加载装置,采用解析法构建电磁疲劳加载系统数学模型;其次,设计多阶段电磁激振力并通过能量守恒定律得到电磁力与叶片振幅和频率的关系;最后,利用ANSYS Maxwell软件建立磁场仿真模型,验证电磁激振力设计的合理性,并分析电磁铁结构参数对加载力及速度的影响,得出在给定的叶片规格下满足测试要求的电磁机构的线圈匝数、形状参数、铁心长度、铁心外径的优选范围,可为后续电磁式疲劳加载试验台的开发奠定理论基础。     

An improved solar cell circuit model for organic solar cells

The validity of conventional circuit model for interpreting results obtained using organic solar cells is examined. It is shown that the central assumption in the model that photo-generated current remains constant from short-circuit to open-circuit condition may not hold for organic cells. An improved model based on the photovoltaic response of organic solar cells is proposed and a method of extracting the parameters of the model is presented.     

Effects of toothless stator design on dynamic model parameters ofpermanent magnet generators

The effects of toothless stator design on the dynamic model parameters of permanent magnet (PM) generators are presented. These parameters, which include inductances and induced back EMFs, are determined for a 75 kVA, 208 V, 400 Hz, two-pole, permanent magnet generator. Two particular stator designs, a toothless stator, and a conventional type stator (with iron teeth), are considered. The method which is used to determine these parameters is general in nature and is based on the use of a series of magnetic field solutions. A validation of the computed EMF and inductance values based on experimentally obtained data is given. The results of using these parameters in a state space model in the abc frame of reference to study the effects of a toothless stator design on the PM generator synchronous inductances are presented. Based on that, it is demonstrated that the effects of rotor saliency and armature loading on the machine parameters are minimized in the case of the toothless design     

Generalized generator model for transformer transfer voltage studies

Surge tests were performed to derive a generator model considering its frequency characteristics. Impulse voltages were applied to one terminal of the generators after placing a variable capacitor at the same terminal. The inductances and the core-loss resistances of a generator model can be determined from the measured oscillating voltages. This paper presents a generalization of the method aimed at deriving these generator parameters. The accuracy of the proposed method is confirmed to be satisfactory after comparing measured and simulated transfer voltages.     

Integrated Nonlinear Magnetic Field-Network Simulation of an Electronically Commutated Permanent Magnet Motor System under Normal Operation

An integrated magnetic field-network computer-aided method is presented, and is verified here by applying it in the determination of the performance of an electronically commutated permanent magnet motor system, and comparing the results with test results at rated operating conditions. Test results were found to be in very good agreement with numerical simulation data. At the core of this method are the instantaneous calculation of the magnetic field distribution within the machine, using the finite element method, and the determination of the winding inductances from these field solutions with the aid of an energy perturbation technique. The armature induced emfs are also obtained from these field solutions. These winding parameters, which are load dependent, are used in a nonlinear time domain network model of first order differential equations governing the dynamic performance of the motor to solve for the instantaneous phase currents. These new currents are then used at every time instant to determine the corresponding machine winding parameters, and the above process is repeated at successive time instants until the complete analysis period is covered. Though the validity of this method of analysis is verified in this paper by applying it to a 15 hp (11.2kw), 120 volt electronically commutated brushless dc motor system operating under normal and balanced conditions, the real utility of the method lies in its ability to analyze these motor systems under unbalanced partial or total component failure (fault) in the windings and associated conditioners. This type of application is given in a companion paper.     

Nonlinear system identification for model-based condition monitoring of wind turbines

This paper proposes a data driven model-based condition monitoring scheme that is applied to wind turbines. The scheme is based upon a non-linear data-based modelling approach in which the model parameters vary as functions of the system variables. The model structure and parameters are identified directly from the input and output data of the process. The proposed method is demonstrated with data obtained from a simulation of a grid-connected wind turbine where it is used to detect grid and power electronic faults. The method is evaluated further with SCADA data obtained from an operational wind farm where it is employed to identify gearbox and generator faults. In contrast to artificial intelligence methods, such as artificial neural network-based models, the method employed in this paper provides a parametrically efficient representation of non-linear processes. Consequently, it is relatively straightforward to implement the proposed model-based method on-line using a field-programmable gate array.     

A Complete Time Domain Model of the Induction Motor for Efficiency Evaluation

The saturation of mutual and leakage inductances as well as the eddy currents effects are taken into account to represent an almost complete model of the induction motor. These effects are not trivial, when the stator voltage and/or frequency changes considerably. Therefore, the model is suitable for the motor performance studies under nonsinusoidal voltage waveform supplies. The effects of eddy currents are represented by a simple double cage model equivalent to the deep bar cage. A practical method for finding the double cage parameters is outlined and the results obtained were used in the simulation. The accuracy of the model is emphasized by comparing the simulation results with test results of the stator inrush current during starting under no-load conditions. The model is used for calculating the induction motor losses in the time domain, when the motor is fed from nonsinusoidal voltage waveform supplies. Samples of the obtained results from different voltage waveforms are given together with that of a pure sinusoidal voltage supply for comparison.     

Effects of temperature dependent properties in electromagnetic heating

Electromagnetic heating such as microwave processing and radio frequency heating becomes very popular because of its non-contact, pollution free and fast distribution of thermal energy within the object of interest. In electromagnetic heating, the temperature distribution within a sample greatly depends on the dielectric properties which are functions of electromagnetic frequency, temperature and the composition of the object. There are many experimental and numerical investigations on electromagnetic heating because of its widespread use in food and other industries, but only few researchers have looked at this problem from analytic point of view specifically for the temperature dependent properties. In this paper, we developed an analytic expression for temperature distribution in a three dimensional rectangular object under electromagnetic heating and presented a method to incorporate temperature dependent properties of the object in determining the temperature distribution at different times. A simplified Maxwell’s equation is solved for plane wave to obtain electric field distribution in the body, and the electromagnetic power absorption is computed from the electric field distribution which was then used as a source term in the energy equation. Next an unsteady, three dimensional, non-homogenous energy equation is solved by integral transform technique to obtain temperature distribution. Finally, this closed form analytical solution is used to study the effects of electromagnetic frequency, dielectric properties, and heat transfer coefficient on temperature distribution in a rectangular salmon fillet. It is found that incident frequency, sample thickness and processing time have significant influence on the heating pattern. For radio frequency heating, the temperature dependent dielectric properties influence the temperature distribution significantly, but the effect of temperature dependent dielectric properties is less dominant for the microwave frequency used in the household microwave oven. Our results also show that microwave heating provides heterogeneous temperature distribution with alternate hot and cold spots. On the other hand, the radio frequency heating allows almost uniform temperature distribution within the body, which makes it a better choice for quick and convenient heating process especially for commercial and industrial heating.     

Maximum likelihood estimation of synchronous machine parametersfrom standstill time response data

This paper presents a systematic approach for identification of a three-phase salient-pole synchronous machine rated at 5 kVA from standstill time-domain data. Machine time constant models and the equivalent circuit models are identified and their parameters are estimated. The initialization of the estimated parameters is achieved by the Laplace transformation of the recorded standstill time-response data and the derivation of the well-known operational inductances. The estimation is performed using the Maximum Likelihood algorithm. Based on the best estimated equivalent circuit models, simulation studies using the measured on-line dynamic responses are performed to validate the identified machine models     

Currents Induced in the Inner Stator Frame of Large Turbogenerators by the End-Zone Field

A method is described, based on 3-dimensional field calculations, for calculating the eddy-currents induced in the inner stator frame by the end-zone field; these currents are an order of magnitude greater than those caused there by yoke saturation, and their mechanism is explained through the calculation results for given alternative designs; it is based mainly on the shielding of the end-zone field. The eddy currents are limited mainly by the inductances; the effect of resistivity should be less than 15%. The design having the outer housing and inner frame electrically insulated from each other appears less satisfactory than the more usual design where the parts are electrically connected.