控制电缆烧损事故之分析改善与预防对策课件

1、控制电缆烧损事故之分析改善与预防对策,1,Chapter 4 Modeling of Nonlinear Load,Organized by Task Force on Harmonics Modeling & Simulation Adapted and Presented by Paulo F Ribeiro AMSC May 28-29, 2008,Contributors: S. Tsai, Y. Liu, and G. W. Chang,控制电缆烧损事故之分析改善与预防对策,2,Chapter outline,Introduction Nonlinear magnetic core

2、sources Arc furnace 3-phase line commuted converters Static var compensator Cycloconverter,控制电缆烧损事故之分析改善与预防对策,3,Introduction,The purpose of harmonic studies is to quantify the distortion in voltage and/or current waveforms at various locations in a power system. One important step in harmonic studie

3、s is to characterize and to model harmonic-generating sources. Causes of power system harmonics Nonlinear voltage-current characteristics Non-sinusoidal winding distribution Periodic or aperiodic switching devices Combinations of above,控制电缆烧损事故之分析改善与预防对策,4,Introduction (cont.,In the following, we wi

4、ll present the harmonics for each devices in the following sequence: Harmonic characteristics Harmonic models and assumptions Discussion of each model,控制电缆烧损事故之分析改善与预防对策,5,Chapter outline,Introduction Nonlinear magnetic core sources Arc furnace 3-phase line commuted converters Static var compensator

5、 Cycloconverter,控制电缆烧损事故之分析改善与预防对策,6,Nonlinear Magnetic Core Sources,Harmonics characteristics Harmonics model for transformers Harmonics model for rotating machines,控制电缆烧损事故之分析改善与预防对策,7,Harmonics characteristics of iron-core reactors and transformers,Causes of harmonics generation Saturation effect

6、s Over-excitation temporary over-voltage caused by reactive power unbalance unbalanced transformer load asymmetric saturation caused by low frequency magnetizing current transformer energization Symmetric core saturation generates odd harmonics Asymmetric core saturation generates both odd and even

7、harmonics The overall amount of harmonics generated depends on the saturation level of the magnetic core the structure and configuration of the transformer,控制电缆烧损事故之分析改善与预防对策,8,Harmonic models for transformers,Harmonic models for a transformer: equivalent circuit model differential equation model du

8、ality-based model GIC (geomagnetically induced currents) saturation model,控制电缆烧损事故之分析改善与预防对策,9,Equivalent circuit model (transformer,In time domain, a single phase transformer can be represented by an equivalent circuit referring all impedances to one side of the transformer The core saturation is m

9、odeled using a piecewise linear approximation of saturation This model is increasingly available in time domain circuit simulation packages,控制电缆烧损事故之分析改善与预防对策,10,Differential equation model (transformer,The differential equations describe the relationships between winding voltages winding currents w

10、inding resistance winding turns magneto-motive forces mutual fluxes leakage fluxes reluctances Saturation, hysteresis, and eddy current effects can be well modeled. The models are suitable for transient studies. They may also be used to simulate the harmonic generation behavior of power transformers

11、,控制电缆烧损事故之分析改善与预防对策,11,Duality-based model (transformer,Duality-based models are necessary to represent multi-legged transformers Its parameters may be derived from experiment data and a nonlinear inductance may be used to model the core saturation Duality-based models are suitable for simulation of

12、 power system low-frequency transients. They can also be used to study the harmonic generation behaviors,控制电缆烧损事故之分析改善与预防对策,12,GIC saturation model (transformer,Geomagnetically induced currents GIC bias can cause heavy half cycle saturation the flux paths in and between core, tank and air gaps shoul

13、d be accounted A detailed model based on 3D finite element calculation may be necessary. Simplified equivalent magnetic circuit model of a single-phase shell-type transformer is shown. An iterative program can be used to solve the circuitry so that nonlinearity of the circuitry components is conside

14、red,控制电缆烧损事故之分析改善与预防对策,13,Rotating machines,Harmonic models for synchronous machine Harmonic models for Induction machine,控制电缆烧损事故之分析改善与预防对策,14,Synchronous machines,Harmonics origins: Non-sinusoidal flux distribution The resulting voltage harmonics are odd and usually minimized in the machines desig

15、n stage and can be negligible. Frequency conversion process Caused under unbalanced conditions Saturation Saturation occurs in the stator and rotor core, and in the stator and rotor teeth. In large generator, this can be neglected. Harmonic models under balanced condition, a single-phase inductance

16、is sufficient under unbalanced conditions, a impedance matrix is necessary,控制电缆烧损事故之分析改善与预防对策,15,Balanced harmonic analysis,For balanced (single phase) harmonic analysis, a synchronous machine was often represented by a single approximation of inductance h: harmonic order : direct sub-transient indu

17、ctance : quadrature sub-transient inductance A more complex model a: 0.5-1.5 (accounting for skin effect and eddy current losses) Rneg and Xneg are the negative sequence resistance and reactance at fundamental frequency,控制电缆烧损事故之分析改善与预防对策,16,Unbalanced harmonic analysis,The balanced three-phase coup

18、led matrix model can be used for unbalanced network analysis Zs=(Zo+2Zneg)/3 Zm=(ZoZneg)/3 Zo and Zneg are zero and negative sequence impedance at hth harmonic order If the synchronous machine stator is not precisely balanced, the self and/or mutual impedance will be unequal,控制电缆烧损事故之分析改善与预防对策,17,In

19、duction motors,Harmonics can be generated from Non-sinusoidal stator winding distribution Can be minimized during the design stage Transients Harmonics are induced during cold-start or load changing The above-mentioned phenomenon can generally be neglected The primary contribution of induction motor

20、s is to act as impedances to harmonic excitation The motor can be modeled as impedance for balanced systems, or a three-phase coupled matrix for unbalanced systems,控制电缆烧损事故之分析改善与预防对策,18,Harmonic models for induction motor,Balanced Condition Generalized Double Cage Model Equivalent T Model Unbalanced

21、 Condition,控制电缆烧损事故之分析改善与预防对策,19,Generalized Double Cage Model for Induction Motor,Stator,Excitation branch,At the h-th harmonic order, the equivalent circuit can be obtained by multiplying h with each of the reactance,mutual reactance of the 2 rotor cages,2 rotor cages,控制电缆烧损事故之分析改善与预防对策,20,Equival

22、ent T model for Induction Motor,s is the full load slip at fundamental frequency, and h is the harmonic order - is taken for positive sequence models + is taken for negative sequence models,控制电缆烧损事故之分析改善与预防对策,21,Unbalanced model for Induction Motor,The balanced three-phase coupled matrix model can b

23、e used for unbalanced network analysis Zs=(Zo+2Zpos)/3 Zm=(ZoZpos)/3 Zo and Zpos are zero and positive sequence impedance at hth harmonic order Z0 can be determined from,控制电缆烧损事故之分析改善与预防对策,22,Chapter outline,Introduction Nonlinear magnetic core sources Arc furnace 3-phase line commuted converters St

24、atic var compensator Cycloconverter,控制电缆烧损事故之分析改善与预防对策,23,Arc furnace harmonic sources,Types: AC furnace DC furnace DC arc furnace are mostly determined by its AC/DC converter and the characteristic is more predictable, here we only focus on AC arc furnaces,控制电缆烧损事故之分析改善与预防对策,24,Characteristics of H

25、armonics Generated by Arc Furnaces,The nature of the steel melting process is uncontrollable, current harmonics generated by arc furnaces are unpredictable and random. Current chopping and igniting in each half cycle of the supply voltage, arc furnaces generate a wide range of harmonic frequencies,控

26、制电缆烧损事故之分析改善与预防对策,25,Harmonics Models for Arc Furnace,Nonlinear resistance model Current source model Voltage source model Nonlinear time varying voltage source model Nonlinear time varying resistance models Frequency domain models Power balance model,控制电缆烧损事故之分析改善与预防对策,26,Nonlinear resistance model

27、,simplified to,R1 is a positive resistor R2 is a negative resistor AC clamper is a current-controlled switch It is a primitive model and does not consider the time-varying characteristic of arc furnaces,modeled as,控制电缆烧损事故之分析改善与预防对策,27,Current source model,Typically, an EAF is modeled as a current s

28、ource for harmonic studies. The source current can be represented by its Fourier series an and bn can be selected as a function of measurement probability distributions proportion of the reactive power fluctuations to the active power fluctuations. This model can be used to size filter components an

29、d evaluate the voltage distortions resulting from the harmonic current injected into the system,控制电缆烧损事故之分析改善与预防对策,28,Voltage source model,The voltage source model for arc furnaces is a Thevenin equivalent circuit. The equivalent impedance is the furnace load impedance (including the electrodes) The

30、 voltage source is modeled in different ways: form it by major harmonic components that are known empirically account for stochastic characteristics of the arc furnace and model the voltage source as square waves with modulated amplitude. A new value for the voltage amplitude is generated after ever

31、y zero-crossings of the arc current when the arc reignites,控制电缆烧损事故之分析改善与预防对策,29,Nonlinear time varying voltage source model,This model is actually a voltage source model The arc voltage is defined as a function of the arc length Vao :arc voltage corresponding to the reference arc length lo, k(t): a

32、rc length time variations The time variation of the arc length is modeled with deterministic or stochastic laws. Deterministic: Stochastic,控制电缆烧损事故之分析改善与预防对策,30,Nonlinear time varying resistance models,During normal operation, the arc resistance can be modeled to follow an approximate Gaussian distr

33、ibution is the variance which is determined by short-term perceptibility flicker index Pst Another time varying resistance model: R1: arc furnace positive resistance and R2 negative resistance P: short-term power consumed by the arc furnace Vig and Vex are arc ignition and extinction voltages,控制电缆烧损

34、事故之分析改善与预防对策,31,Power balance model,r is the arc radius exponent n is selected according to the arc cooling environment, n=0, 1, or 2 recommended values for exponent m are 0, 1 and 2 K1, K2 and K3 are constants,控制电缆烧损事故之分析改善与预防对策,32,Chapter outline,Introduction Nonlinear magnetic core sources Arc fu

35、rnace 3-phase line commuted converters Static var compensator Cycloconverter,控制电缆烧损事故之分析改善与预防对策,33,Three-phase line commuted converters,Line-commutated converter is mostly usual operated as a six-pulse converter or configured in parallel arrangements for high-pulse operations Typical applications of

36、 converters can be found in AC motor drive, DC motor drive and HVDC link,控制电缆烧损事故之分析改善与预防对策,34,Harmonics Characteristics,Under balanced condition with constant output current and assuming zero firing angle and no commutation overlap, phase a current is h = 1, 5, 7, 11, 13, . Characteristic harmonics

37、 generated by converters of any pulse number are in the order of n = 1, 2, and p is the pulse number of the converter For non-zero firing angle and non-zero commutation overlap, rms value of each characteristic harmonic current can be determined by F(,) is an overlap function,控制电缆烧损事故之分析改善与预防对策,35,H

38、armonic Models for the Three-Phase Line-Commutated Converter,Harmonic models can be categorized as frequency-domain based models current source model transfer function model Norton-equivalent circuit model harmonic-domain model three-pulse model time-domain based models models by differential equati

39、ons state-space model,控制电缆烧损事故之分析改善与预防对策,36,Current source model,The most commonly used model for converter is to treat it as known sources of harmonic currents with or without phase angle information Magnitudes of current harmonics injected into a bus are determined from the typical measured spectr

40、um and rated load current for the harmonic source (Irated) Harmonic phase angles need to be included when multiple sources are considered simultaneously for taking the harmonic cancellation effect into account. h, and a conventional load flow solution is needed for providing the fundamental frequenc

41、y phase angle, 1,控制电缆烧损事故之分析改善与预防对策,37,Transfer Function Model,The simplified schematic circuit can be used to describe the transfer function model of a converter G: the ideal transfer function without considering firing angle variation and commutation overlap G,dc and G,ac, relate the dc and ac sid

42、es of the converter Transfer functions can include the deviation terms of the firing angle and commutation overlap The effects of converter input voltage distortion or unbalance and harmonic contents in the output dc current can be modeled as well,控制电缆烧损事故之分析改善与预防对策,38,Norton-Equivalent Circuit Mode

43、l,The nonlinear relationship between converter input currents and its terminal voltages is I & V are harmonic vectors If the harmonic contents are small, one may linearize the dynamic relations about the base operating point and obtain: I = YJV + IN YJ is the Norton admittance matrix representing th

44、e linearization. It also represents an approximation of the converter response to variations in its terminal voltage harmonics or unbalance IN = Ib - YJVb (Norton equivalent,控制电缆烧损事故之分析改善与预防对策,39,Harmonic-Domain Model,Under normal operation, the overall state of the converter is specified by the ang

45、les of the state transition These angles are the switching instants corresponding to the 6 firing angles and the 6 ends of commutation angles The converter response to an applied terminal voltage is characterized via convolutions in the harmonic domain The overall dc voltage Vk,p: 12 voltage samples

46、 p: square pulse sampling functions H: the highest harmonic order under consideration The converter input currents are obtained in the same manner using the same sampling functions,控制电缆烧损事故之分析改善与预防对策,40,Chapter outline,Introduction Nonlinear magnetic core sources Arc furnace 3-phase line commuted co

47、nverters Static var compensator Cycloconverter,控制电缆烧损事故之分析改善与预防对策,41,Harmonics characteristics of TCR,Harmonic currents are generated for any conduction intervals within the two firing angles With the ideal supply voltage, the generated rms harmonic currents h = 3, 5, 7, , is the conduction angle, a

48、nd LR is the inductance of the reactor,控制电缆烧损事故之分析改善与预防对策,42,Harmonics characteristics of TCR (cont.,Three single-phase TCRs are usually in delta connection, the triplen currents circulate within the delta circuit and do not enter the power system that supplies the TCRs. When the single-phase TCR is

49、 supplied by a non-sinusoidal input voltage the current through the compensator is proved to be the discontinuous current,控制电缆烧损事故之分析改善与预防对策,43,Harmonic models for TCR,Harmonic models for TCR can be categorized as frequency-domain based models current source model transfer function model Norton-equivalent circuit model time-domain based models models by differential equations state-space model,控制电缆烧损事故之分析改善与预防对策,44,Current Source Model,by discrete Fourier analysis,控制电缆烧损事故