Harmonic Model For Nonlinear Power Electronic Circuits And Its Application To Harmonic Analysis

Distortion of sinusoidal voltage and current waveforms caused by harmonics generated by power electronic devices is one of the major power quality concerns in electric industry. In recent years, power electronic devices have been widely used, making the harmonic pollution problem more serious than ever before. Most countries are beginning to pay more attention to the harmonic related research. Problems caused by harmonics can be summarized as follows: it can cause heating and vibration to the rotary motors and cause additional power loss to the motors, transformers and power lines. If the addition of capacitors tunes the system to resonate near a harmonic frequency present in the load current or system voltage, large currents or voltages at that frequency will be produced, and the capacitors may be destroyed. Waveform distortion affects the performance of protective relays and may cause relays to operate improperly or to not operate when required. There is also some evidence that harmonic distortion of the current can affect the proper functioning of the automatic control devices. The juxtaposition of telephone and power lines on utility poles creates opportunities for power frequency interference with telephone communication.Harmonic source model analysis is the basis of all harmonic studies. With the help of the harmonic source model, the harmonic generation mechanism of the harmonic sources can be revealed, which will be useful for the development of harmonic control measures. The harmonic current source model is the most widely used harmonic source models in the practical engineering. In this method, the nonlinear loads are represented using harmonic current spectra of known magnitudes and phase angles, which prevents an adequate assessment of cases involving distributed harmonic sources. Research on a fast, accurate and easy to use harmonic source model is of both theoretical and practical significances.If one needs to find the harmonic distortion levels for a system, a harmonic power flow analysis is needed to be conducted. The harmonic power flow can be solved with a suitable calculation algorithm on the basis of the network connections and device parameters. Since the harmonic measurement instrument can not be installed on each branch or each bus in the system, an accurate and fast harmonic power flow method becomes necessary in order to acquire the necessary harmonic distortion information in the power system and design proper filters.In this dissertation, the harmonic source characteristics are analyzed in the frequency domain, and a novel model is proposed to analyze the harmonic generation of the nonlinear power electronic devices. The proposed harmonic source model transforms the time domain non-linear characteristics of the power electronic devices into a frequency domain linear matrix model. A new non-iterative harmonic power flow algorithm has been proposed based on the model, which can calculate the harmonic condition of systems containing distributed harmonic sources fast and accurately. The contributions of the dissertation are summarized as follows:(1) A novel harmonically coupled admittance matrix model is proposed for the single phase and three phase AC/DC converters. The model can consider the impact of following factors to the generation of harmonic currents: the fundamental frequency voltage phase angle, the thyristor firing angle, the supply voltage side harmonic voltages, direct voltage electromotive force and the thyristor commutation angle. The matrix represents the coupling among the converter AC side harmonic voltages and currents accurately and it does not vary with the harmonic conditions of the system. Morever, the model has the following important characteristics:a. The model is analytical; it will enable one to investigate the harmonic coupling characteristics of the converters much more thoroughly. Each harmonic voltage will generate every order of harmonic currents.b. The harmonic currents are not only functions of the supply side harmonic voltages, they are also functions of the harmonic conjugates.c. The model is developed for a wide range of operating conditions. Unlike the linearized model, the proposed model is operating point independent.(2) With the matrix model, it becomes possible to analyze the interactions of various harmonic components of the converters.a. The first columns elements of Y⁺ represents the impact of fundamental frequency voltage on the generation of converter harmonic currents, the contribution of the fundamental frequency voltage is more significant than the harmonic voltages.b. The fundamental frequency current is produced mainly through the fundamental frequency voltages.c. The diagonal elements of Y⁺ represent the impact of h^th harmonic voltage on the h^th harmonic current. So these elements are effectively the self harmonic admittance of the converter. The mutual coupling is modeled by the off-diagonal elements of the Y⁺and Y^-matrices. They make the analysis of harmonic power flow one harmonic at a time impossible. For the single phase converter, the self coupling effect is more significant than the harmonic mutual coupling effect; the mutual coupling and self coupling effect both reduce with the increasing of the harmonic order. However, for the three phase converter, there are no significant differences between the self coupling and mutual coupling effects.d. Fundamental frequency voltage phase angle only lead to the harmonic current waveform shift on the time axis, whereas the enlarging of the firing angle will reduce the contribution of harmonic voltage to the generation of harmonic current.e. Each matrix element is in a convergent infite series form.(3) A new non-iterative harmonic power flow calculation algorithm is proposed based on the harmonically coupled admittance matrix model. For the fundamental frequency power flow, the harmonic sources are treated as constant PQ loads. With the fundamental frequency voltage results, the control variables of the harmonic source can be obtained, and then the harmonic matrix model can be calculated. By solving the system matrix equations and the harmonic source model equations together, the system harmonic results can be get non-iteratively. The harmonic power flow method has the following characteristics:a. The method is non-iterative; the system admittance matrix equations and the harmonic source model equations are both linear, by solving these equations, the whole system harmonic conditions can be obtained in one step.b. The method is suitable to the systems with distributed harmonic sources, the attenuation and diversity effects can be taken into account.c. It is a decoupled harmonic power flow analysis method; the fundamental frequency power flow is solved first by treating the harmonic sources as constant PQ load, the harmonic power flow is calculated after the fundamental frequency power flow results are known. The algorithm is illustrated with the AC/DC converters as the main harmonic sources inthe power system. Simulation results on several cases reveal that the harmonic power flowmethod is fast, accurate and is suitable for the system with distributed harmonic sources.(1) Based on the harmonic matrix model of the single phase and three phase thyristorcontrolled reactors (TCRs), the harmonic generating characteristics of the TCRs havebeen investigated using the model. A TCR produces harmonics through threecomponents: the fundamental frequency voltage, the harmonic voltages that have thesame orders as the harmonic currents and the cross-coupling of one harmonic voltagewith another harmonic current. With the help of equivalent circuit model, the impact ofeach component is quantified.a. If the supply voltage contains no harmonics, the TCR harmonics drop much faster than that of converters when the harmonic number increases. For a TCR, the fundamentalfrequency current is produced mainly through Y^<sub>1.1⁺ which is the equivalent 50Hzadmittance of the device.b. The contribution of harmonic voltages to the generation of fundamental frequencycurrent reduces in the order of1/h.c. The harmonic admittance of the TCR isÏ€L/(?)(Ï€-2α), which can be used as theformulas for the TCRs Norton equivalent circuit.d. For h^th TCR harmonic current, it has the same coupling with the (h-n)^th harmonic voltage as that with the (h+n)^th harmonic voltage. The self admittance plays the most important role in the generation of the corresponding harmonic current. The coupling is significant among the near-diagonal components in the mutual coupling relations.e. The contribution of the harmonic voltage conjugates is much less than the harmonic voltages to the generation of harmonic currents.