D-q Impedance Identification In Three Phase Systems Using Multi-tone .
D-q impedance identification in three phase systemsusing multi-tone perturbationBo ZhouThesis submitted to the Faculty of the Virginia Polytechnic Institute and StateUniversity in partial fulfillment of the requirements for the degree ofMaster of ScienceinElectrical EngineeringPaolo Mattavelli, Co-ChairDushan Boroyevich, Co-ChairRolando BurgosJan 30, 2013Blacksburg, VirginiaKeywords: AC stability, d-q impedances, multi-tone, diode bridge rectifier
D-q impedance identification in three phase systemsusing multi-tone perturbationBo ZhouAbstractIn electric power systems, the existence of constant power loads such as output-regulatedpower converters may bring instability problem to AC or DC distributed systems. Impedancebased stability criteria has been proven a good tool for small-signal stability analysis.This works focuses on the developing of a comprehensive software tool which can extract DCor three phase AC impedances, and apply stability analysis. An algorithm is designed to selectFFT window and adjust perturbation frequencies. This feature enables the software to accuratelymeasure impedances even in existence of system line harmonics. Furthermore, multi-toneapproach is developed to improve simulation time. The complete software tool is tested withsimulation models and experiment results, to show the effectiveness.When multi-tone approach is applied on nonlinear loads, it gives incorrect results. The reasonis that perturbation frequency will have overlapping with side-band harmonics. An algorithm isdesigned to avoid this problem. The algorithm is tested with 12-pulse diode rectifier simulationmodel, and 6-pulse diode rectifier simulation model and experimental test bed. Both simulationand experiment results verifies the concept.
Acknowledgements1First of all, I would like to express my sincere gratitude to my advisor, Dr Paolo Mattavelli,for his patient guidance and kind help throughout all my years at Virginia Tech. It is him wholeads me step by step into the world of power electronics. He is generous to answer mynumerous questions and give me suggestions, which push me forward to progress. I still keep allthe notes he wrote for me during our personal meetings, which encourage me to dig intounknown problems. His rigorous attitude to the science will always be my best example to learnfrom. I would like to wish him all the best in his life.I am also grateful to my committee members Dr Dushan Boroyevich and Dr Rolando Burgos,for all the discussions during the weekly meetings and their valuable suggestions. I gained a lotfrom Dr Boroyevich’s overview of the research and his humorous personality. Dr Burgos’research habits also helped me a lot.I would like also to thank all the CPES team members: Ms. Teresa Shaw, Ms. MarianneHawthorne, Ms. Linda Gallagher, Ms. Teresa Rose, Ms. Linda Long, Mr. Bob Martin and MrDavid Gilham. Their support helps me to achieve my academic goal.I would likt also to thank my CPES friends and colleagues. It is my honor to know you andwork together with you: Mr. Zhiyu Shen, Mr. Bo Wen, Mr. Marko Jaksic, Mr. Igor Cvetkovic,Dr. Sara Ahmad, Dr. Qiang Li, Dr. Fang Luo, Dr. Pengju Kong, Dr. Dong Dong, Dr. Ruxi Wang,Mr. Doug Sterk, Mr. David Reusch, Mr. Xiao Cao, Mr. Shu Ji, Mr. Pengjie Lai, Mr. Qian Li, Mr.Daocheng Huang, Mr. Zijian Wang, Mr. Zheng Chen, Mr. Haoran Wu, Mr. Mingkai Mu, Mr.Feng Yu, Mr. Yingyi Yan, Mr. Chanwit Prasantanakorn, Ms. Yiying Yao, Mr. Yipeng Su, Mr.Milisav Danilovic, Mr. Hemant Bishnoi, Mr. Weiyi Feng, Mr. Wei Zhang, Mr. Shuilin Tian, Mr.Li Jiang (F.C.Lee), Mr. Li Jiang (K.Ngo), Mr Xuning Zhang, Mr. Jin Li, Mr. Pei-Hsin Liu, Mr.Yin Wang, Mr. Lingxiao Xue, Mr. Zhemin Zhang, Mr. Tao Tao, Mr. Di Xu, Mr. HanguangZheng, Mr. Zhiqiang Wang, Mr. Xiucheng Huang, Mr. Yang Jiao, Mr. Zhengyang Liu, Mr.Yucheng Yang, Mr Dongbing Hou, Miss. Han Cui, Mr. Jun Wang, Mr. Qiong Wang, Mr.Xuebing Chen, Mr. Chi Li, Mr. Chao Fei, Mr. Fang Chen, Miss. Yincan Mao, Mr Ming Lv.Without your help, this thesis would be impossible.1This work was sponsored by the Boeing Company.III
Last but most importantly, I would like to express my deepest gratitude to my parents JianZhou, Qiulin Gao, and my girlfriend Xiaoxiao Li. Their selfless love and support encourage meto overcome all the problems in my life and create a better future.Thank you all,BoIV
TABLE OF CONTENTSChapter 1. Introduction . 11.1. Background and motivation . 11.2. Synchronous rotating coordinate of 3 phase systems and impedance in d-qcoordinate . 21.3. Stability criteria for three phase systems . 41.4. Contents . 5Chapter 2. Stability analysis software suite . 62.1. Impedance measurement algorithm . 62.2. Perturbation methods review . 82.2.1. Perturbation in steady state operation point . 82.2.2. Perturbation based on transient response . 92.3. STability Analysis Software sUite(STASU) . 102.3.1. Review of existing software tools for d-q impedance extraction . 102.3.2. Introduction to STASU . 162.3.3. Impedance calculation tool implementation . 192.3.4. Algorithm explanation . 202.3.5. Stability analysis . 302.3.6. Simulation results and application examples . 342.4. Experimental verification of multi-tone approach . 402.4.1. System implementation . 402.4.2. Generating multi-tone signal. 412.4.3. Data acquisition . 432.4.4. Data back-calculation. 442.4.5. Experiment results on passive components . 452.5. Summary . 48Chapter 3. Low power impedance analyzer . 493.1. Introduction . 493.2. System implementation . 493.3. System protection. 51V
3.3.1. Grounding fault in series voltage . 513.3.2. Power up sequence fault . 533.3.3. Summary of protection . 553.4. Test results . 563.4.1. Shunt current injection test . 56Chapter 4. The application of Multi-tone approach on nonlinear load . 584.1. Introduction . 584.2. Harmonic transfer study. 594.2.1. Harmonic from d-q to abc . 604.2.2. Harmonic transfer from AC to DC . 614.2.3. Harmonic transfer from DC to AC . 634.2.4. Frequency selection algorithm for nonlinear load . 654.2.5. Other potentially applicable cases . 674.3. Simulation and experimental verification . 684.3.1. Simulation verification. 684.3.2. Twelve-pulse diode bridge rectifier . 704.3.3. Experimental verification. 724.4. Summary . 74Chapter 5. Summary and Future work . 745.1. Summary . 745.2. Future work . 74Appendix A. STASU Programmer’s Mannual . 74A.1.Introduction . 76A.2.Flowcharts . 79A.3.Impedance calculation blocks . 84A.4.Summary . 86Appendix B. Impedance Analyzer . 87B.1.Introduction . 87B.2.Instrument specs . 88B.2.1. Power amplifier AE7570 specs . 88B.2.2. Transformer specs . 89VI
B.2.3. Impedance analyzer specs . 89B.3.Wiring Diagram. 91B.3.1. Bus connections . 91B.3.2. Signal connections . 92B.4.Protection . 95B.4.1. Introduction . 95B.4.2. Power up sequence protection . 96B.4.3. Overvoltage protection. 98B.5.Operation procedure . 101B.6.Summary . 102References . 103VII
LIST OF FIGURESFig. 1-1 Three phase AC system diagram . 2Fig. 1-2 Three phase system diagram in d-q coordinate . 3Fig. 1-3 Multi-variable feedback configuration: a) closed-loop and b) open-loop. 4Fig. 2-1 Three phase system diagram in abc coordinates with shunt current perturbation . 6Fig. 2-2 Three phase system diagram in d-q coordinates with shunt current perturbation . 7Fig. 2-3: Injection connections . 8Fig. 2-4 Single phase injection diagram . 9Fig. 2-5 Current step test diagram. 10Fig. 2-6 Saber simulation tool . 11Fig. 2-7 Powersim software tool . 12Fig. 2-8 Plecs software tool . 13Fig. 2-9 SIMPLIS software tool. 14Fig. 2-10 Simpowersystems software tool . 15Fig. 2-11 Flow chart for impedance calculation . 17Fig. 2-12 d-q Source and load impedance measurement blocks . 19Fig. 2-13 Phase-Looked Loop in the Synchronous Reference Frame . 20Fig. 2-14 Second-order RLC circuit . 21Fig. 2-15 Input voltage waveform . 22Fig. 2-16 Output voltage waveform . 23Fig. 2-17 Aliasing effect in time domain . 24Fig. 2-18 Aliasing effect in frequency domain . 25Fig. 2-19 Choosing FFT window when fline fpert1 . 26Fig. 2-20 Choosing FFT window when fline fpert1 . 27Fig. 2-21 Multi-tone signal . 28Fig. 2-22 Time domain multi tone signal waveforms . 29Fig. 2-23 Flow chart of Matlab codes for stability analysis . 31Fig. 2-24 Flow chart of impedance over-plot . 33Fig. 2-25 Schematic of unbalanced voltage source example . 34Fig. 2-26 d-q Impedance of unbalanced voltage source example . 35VIII
Fig. 2-27 d-q Impedance of unbalanced voltage source example . 36Fig. 2-28 Schematic of DC/DC converter. 37Fig. 2-29 Closed-loop output impedance of DC/DC converter . 39Fig. 2-30 System diagram for multi-tone approach verification. 40Fig. 2-31 Flowchart of multi-tone signal generation . 42Fig. 2-32 MSO4054B oscilloscope . 43Fig. 2-33 Flowchart of multi-tone impedance calculation . 44Fig. 2-34 Resistive load multi-tone test diagram . 45Fig. 2-35 Resistive load multi-tone measurement . 46Fig. 2-36 RL multi-tone test diagram . 47Fig. 2-37 RL load multi-tone measurement . 48Fig. 3-1 System diagram of three phase impedance analyzer . 49Fig. 3-2 Switch of shunt current injection and series voltage injection . 50Fig. 3-3 Relay connection for shunt/series switch . 51Fig. 3-4 Overvoltage protection . 52Fig. 3-5 Overvoltage protection board . 53Fig. 3-6 Back control panel of Techron 7570 amplifier . 54Fig. 3-7 Power up sequence protection board . 54Fig. 3-8 Overview of protection for series voltage injection . 55Fig. 3-9 Overview of protection for shunt current injection . 56Fig. 3-10 VSI closed-loop output impedance measurement . 57Fig. 3-11 VSI closed-loop output impedance . 57Fig. 4-1 Schematic of six-pulse diode bridge rectifier . 58Fig. 4-2 Impedance results of the multi-tone and single-tone approaches . 59Fig. 4-3 Flowchart of impedance calculation process for diode bridge rectifier . 60Fig. 4-4 Spectrum of line current . 64Fig. 4-5 Flowchart of algorithm to avoid perturbation frequencies overlapping . 66Fig. 4-6 Impedance result comparison of improved multi-tone and single-tone approach . 67Fig. 4-7 6-pulse diode bridge rectifier impedance simulation measurement . 68Fig. 4-8 Result comparison for 6-pulse diode bridge rectifier input impedance . 69Fig. 4-9 12-pulse diode bridge rectifier impedance simulation measurement . 70IX
Fig. 4-10 Result comparison for 12-pulse diode bridge rectifier input impedance . 71Fig. 4-11 6 pulse diode rectifier input impedance measurement setup . 72Fig. 4-12 Input impedance comparison for 6 pulse diode bridge rectifier. 73Fig Apx. A-1 STASU file folders . 76Fig Apx. A-2 Flowchart of GUI . 79Fig Apx. A-3 Flowchart of 1st step of impedance calculation . 80Fig Apx. A-4 Flowchart of 2nd step of impedance calculation . 81Fig Apx. A-5 Flowchart of 3rd step of impedance calculation . 82Fig Apx. A-6 Flowchart of stability analysis . 83Fig Apx. A-7 Overview of impedance calculation blocks . 84Fig Apx. A-8 Block mask editing . 85Fig Apx. A-9 Impedance calculation block implementation . 85Fig Apx. B-1 Low-power impedance analyzer . 87Fig Apx. B-2 Output specs of AEtechron 7570 . 88Fig Apx. B-3 POWERTRAN transformer . 89Fig Apx. B-4 Shunt current configuration . 89Fig Apx. B-5 Series voltage configuration . 90Fig Apx. B-6 Bus connection diagram . 91Fig Apx. B-7 Wiring diagram for relay board . 92Fig Apx. B-8 Signal channels of UC . 93Fig Apx. B-9 BNC connector panel . 94Fig Apx. B-10 Summary of impedance analyzer protection . 95Fig Apx. B-11 Power up sequence protection board . 97Fig Apx. B-12 Over-voltage protection board . 99Fig Apx. B-13 Flowchart for operation procedure . 101X
LIST OF TABLESTable 2-1 Parameters of passive components . 34Table 2-2 Parameters of DC/DC converter . 37Table 2-3 Parameters for resistive load test . 45Table 2-4 Perturbation frequencies . 45Table 2-5 Parameters for RL load test . 47Table 2-6 Perturbation frequencies . 47Table 4-1 DIODE BRIDGE PARAMETERS . 58Table 4-2 Frequency parameter definitions . 65Table 4-3 Parameters of 6 pulse diode rectifier simulation model . 68Table 4-4 Parameters of 12-pulse diode rectifier simulation model . 70Table 4-5 Parameters of 6 pulse diode rectifier . 72Table 4-6 Perturbation frequencies of the first measurement . 72Table 4-7 Perturbation frequencies of the second measurement . 73Table Apx. A-1 Summary and classification of STASU files . 77Table Apx. B-1 Signal channels discription . 931
Chapter 1. INTRODUCTION1.1. Background and motivationThe application of power electronic technology enables high-quality power conversion. Inmany cases there are requirements of output power regulation. As described in [1-4], the constantpower loads show negative incremental input impedance characteristic. For ideal source systemslike grids, the effect of constant power loads is very small. However there are some smallersystems like aircraft systems, electric vehicles, ships and renewable energy systems. When thesesystems operate in islanding mode, constant power loads may bring unstable issues.As these systems become more and more widely applied, it is important to guarantee safeoperation. It is shown that the stability of DC systems can be analyzed and predicted by studyingthe return ratio of source output impedance and load input impedance [5][6]. A few stabilitycriteria have also been proposed to define stability margin of DC systems [7-9].Like DC systems, the stability of 3 phase AC systems can be also analyzed by studying thesource and load impedances. General Nyquist Criterion (GNC) [10] is applied in multi-variablesystems like 3 phase AC systems. In [11], stability criteria for three phase system can be derivedby studying the eigenvalue loci of the multi-variable return ratio matrix. Moreover in somespecific applications when the power factor of load converter is high, the GNC can be simplified[12] by only studying the return ratio of Zdd impedances.It is shown that source and load impedances play a very important role in system stabilityprediction. Therefore there is a need to identify the source and load impedances of power systemat DC or AC interfaces. A lot of work has been devoted to measuring the impedance of DCsystems [13-15]. There are also attempts to identify impedance of AC systems [16-20]. Howevermost methods have been tested and verified for passive components. Few are verified forswitching converters. Even for software simulation, there are few available tools for ACimpedance identification.1
1.2. Synchronous rotating coordinate of 3 phase systemsand impedance in d-q coordinateElectrical source and load systems can be unstable when they are interconnected. The stabilitycan be analyzed by studying the source and load impedance at the interface. For DC systems thatis straight forward because it is easy to find the steady state operation point and identifyimpedances. However for 3 phase AC system, it is not that easy to find a steady state operationpoint. A typical 3 phase power system is shown in Fig. t)ZLcnSystem voltages are withrespect to neutral point nFig. 1-1 Three phase AC system diagramThe voltages at the AC interface are given by (1-1).The interface voltages and currents aretime-varying, which means there is no way to find steady state operation point.( )(( )(),( )(),),(1-1)The system is non-stationary with periodic tendencies. The three voltages could berepresented as a voltage vector, rotating in a three-dimensional space. If all the voltages followsthe expression (1-1), the vector will be rotating in a circle with an angular speed of. In order totransform the system to stationary, a rotating coordinate can be defined with the same angularspeed. The transformation matrices between two coordinates are defined by (1-2):2
( )( )( ) [( )(()) (())],(1-2) ( ),(1-3)This alignment will be applied for all the impedance extraction in this work.Applying the transformation to the voltages, we get:[((())])([ (())]) [](1-4),By doing this, we could transform the non-stationary 3-phase system in abc coordinates tostationary system in d-q0 coordinates. For balanced system, the 0-axis variables are always 0,which could be ignored. The d-q system diagram is shown in Fig. 1-2:ILdq(t)ZSdqVSdq(t)ZLdqVLdq(t)Fig. 1-2 Three phase system diagram in d-q coordinateBy transforming the three phase system into d-q coordinate, a steady state operation point canbe found. Thus the impedance measurement techniques can be applied also in three phasesystems.The load impedance in d-q coordinate can be defined:[( )]( )[( )( )( )][( )( )]( )The source impedance in d-q coordinate can be defined in the same way.3(1-5)
1.3. Stability criteria for three phase systemsConstant power loads such as power converters with regulated output voltage have negativesmall-signal input impedance. In DC distributed systems, this phenomenon may result in smallsignal instability at the DC interface.( )( )( )( )(1-6)The transfer function between DC source voltage and interface voltage is given by (1-6). It isproposed in [5] that Nyquist criterion could be applied on the DC interface stability by studying( )the return ratio( ), where( ) stands for the source impedance and( ) stands forthe load impedance.On the other hand, three phase AC system is a multi-input multi-output (MIMO) system.Generalized Nyquist Criterion is proposed to extend the frequency response methods in singleinput single-output systems to MIMO systems.A multi-variable feedback system is shown in Fig. 1-3.a)u(s) G1(s)y(s)b)u(s) G2(s) ’L(s) G1(s)G2(s) G1(s)y(s)G2(s)Fig. 1-3 Multi-variable feedback configuration: a) closed-loop and b) open-loop.Theorem: The Generalized Nyquist Stability Criterion [10].Let the multivariable feedback system shown in Fig. 1-3 have no open-loop unobservable oruncontrollable modes whose corresponding characteristic frequencies lie in the right half plane.Then this configuration will be closed-loop stable if and only if the net sum of anticlockwiseencirclements of the critical point ( 1 j0) by the set of characteristic loci of L(s) is equal to thetotal number
Fig. 4-10 Result comparison for 12-pulse diode bridge rectifier input impedance . 71 Fig. 4-11 6 pulse diode rectifier input impedance measurement setup. 72 Fig. 4-12 Input impedance comparison for 6 pulse diode bridge rectifier. 73 Fig_Apx.
Odd-Mode Impedance: Z d Impedance seen by wave propagating through the coupled-line system when excitation is anti-symmetric (1, -1). Common-Mode Impedance: Z c 0.5Z e Impedance seen by a pair of line and a common return by a common signal. Differential Impedance: Z diff 2Z d Impedance seen across a pair of lines by differential mode signal .
Differential Impedance Differential Impedance: the impedance the difference signal sees ( ) ( ) 2 2( ) Z 0 small I V I V diff Z diff one one Differential impedance decreases as coupling increases 1v -1v I one x I two How will the capacitance matrix elements be affected by spacing? C 12 C 11 C 22 Eric Bogatin 2000 Slide -18 www .File Size: 1MBPage Count: 25
DiffZ0 (ohm) - Calculated differential impedance. Like Single Impedance you can change the value for impedance to the needed value. The tool calculates the necessary width. You can change all values of the white boxes to calculate your impedance. Note: If you want to change the material disable “Show Diff Impedance”.
2.2.3. Electrochemical impedance spectroscopy The electrical properties of the bigels were studied using computer controlled impedance analyzer (Phase sensitive multimeter, PSM1735, Numetriq, Japan) The impedance parameters such as impedance, phase angle, capacitance an
2.4. Electrochemical impedance spectroscopy studies Electrochemical impedance spectroscopy (EIS) can provide useful information on the impedance changes of the electrode surface. Lower impedance values indicate higher conductance. Therefore, electrochemical impedance spectroscopy wa
suring acoustic impedance and calibrating impedance heads and propose a general calibration technique for heads with multiple transducers. We consider the effect of transducer errors on impedance measurements and present a technique for distributing any measurement errors over the frequency range. To demonstrate the technique we use an impedance
1.2 Measuring impedance To find the impedance, we need to measure at least two values because impedance is a complex quantity. Many modern impedance measuring instruments measure the real and the imaginary parts
N. Sharma, M. P. Rai* Amity Institute of Biotechnology (J-3 block), Amity University Uttar Pradesh, Sector-125, Noida, India A B S T R A C T P A P E R I N F O Media requirement for microalgae cultivation adds most to the cost of biodiesel production at Paper history: Received 30 July 2015 Accepted in revised form 6 September 2015 Keywords: - Chlorella pyrenoidosa Cattle waste Lipid content .
