Tutorial on Harmonics Modeling & Simulation

Tutorial on Harmonics Modeling & Simulation
Organized by Task Force on Harmonics Modeling & Simulation Adapted and Presented by Paulo F Ribeiro AMSC May 28-29, 2008 中正--電力品質實驗室

Scope The purpose of this tutorial is to provide an review of subjects that have significant impacts on the areas of harmonic analysis, modeling, and simulation. The major contents of the tutorial include an overview of harmonics modeling and simulation, harmonics and interharmonics theories, modeling of linear and nonlinear loads as well as network components, the time- and frequency-domain harmonic analyses, real-time modeling and simulation, benchmark test systems, procedure of time-domain harmonics modeling and simulation, and case studies. 中正--電力品質實驗室

Scope In addition to including the new subjects of interharmonics theory and real-time simulations and applications, it is worth mentioning that the two chapters of step-by-step analysis procedure performed by the commonly used harmonic simulation tool and real-life study examples are offered to facilitate participants to learn the area. The tutorial offers a handy material that is convenient for the beginners as well as those who already know the subject and is expected to provide the readers with a general background knowledge and further understanding on the subject. 中正--電力品質實驗室

Introductory Remarks for AMSC Workshop
Background of Presenter Industrial railway electrification (1976) Specs for designing of an SVC for transmission application Harmonic propagation in transmission systems TV viewing impact on transmission systems Harmonic modeling and simulation (IEEE Task Force, Tutorial CD) Probabilistic Aspects of Harmonics (IEEE Task Force) Preparation of text on Time-Varying Harmonic Distortions IEEE 519 Working Group Harmonics on shipboard power systems 中正--電力品質實驗室

Chapter Titles and Contributors
Chapter 1: Overview of Harmonics Modeling & Simulation Contributors: W. Xu and S. Ranade Chapter 2: Harmonics and Interharmonics Theory Contributors: G. W. Chang and A. Testa Chapter 3: Modeling of Linear Loads and Network Components Contributors: T. Ortmeyer, C. Hatziadoniu, and P. Ribeiro Chapter 4: Modeling of Nonlinear Loads Contributors: S. Tsai, Y. Liu, and G. W. Chang Chapter 5: Harmonic Analysis in Frequency and Time Domains Contributors: A. Medina, N. R. Watson, P. Ribeiro, and C. Hatziadoniu 中正--電力品質實驗室

Chapter Titles and Contributors
Chapter 6: Real-time Harmonics Modeling and Simulation Contributors: L-F. Pak, V. Dinavahi, G. Chang, M. Steurer, S. Suryanarayanan, P. Ribeiro Chapter 7: Test Systems for Harmonics Modeling & Simulation Contributors: W. Xu, M. Halpin, and S. Ranade Chapter 8: Procedure of Time-domain Harmonic Modeling and Simulation Contributors: C. J. Hatziadoniu, W. Xu, and G. W. Chang Open Discussions and Applications 中正--電力品質實驗室

Chapter 1: An Overview of Power System Harmonic Analysis
Tutorial on Harmonics Modeling and Simulation Contributors: W. Xu and S. Ranade 中正--電力品質實驗室

Outline Status and methods of harmonic analysis
Chapter 1: An Overview of Power System Harmonic Analysis Outline Status and methods of harmonic analysis New challenges of harmonic analysis Summary Modeling of power system components Algorithms for harmonic analysis Analysis of systems with distributed harmonic sources Modes of harmonic resonance Analysis of interharmonics 中正--電力品質實驗室

Status and methods of harmonic analysis
Chapter 1: An Overview of Power System Harmonic Analysis Status and methods of harmonic analysis Methods: 1) Frequency scan 2) Harmonic power flow Models: 1) Harmonic source: current source model 2) Non H-source: linear impedance model Variations: 1) Single-phase versus multiphase 2) Iterative versus non-iterative H power flow Applications: Systems with limited number of H-sources and the sources are typically large in size 中正--電力品質實驗室

Modeling of harmonic loads as current sources
Chapter 1: An Overview of Power System Harmonic Analysis Modeling of harmonic loads as current sources VFD V I + - V1 I1 + - P+jQ Vh Ih + - h=2,H = + VFD model at 60Hz VFD model at harmonic freq. VFD load spc = given spectrum data

Example of source modeling
Chapter 1: An Overview of Power System Harmonic Analysis Example of source modeling 中正--電力品質實驗室

Harmonic analysis methods
Chapter 1: An Overview of Power System Harmonic Analysis Harmonic analysis methods Objectives Check if resonance exists Check harmonic distortion levels (safe equipment operation) Filter design Compliance with standards Two types of assessments: Frequency response check resonance (Frequency scan) filter design  Distortion level calculation compliance check (harmonic power flow) equipment operating conditions 中正--電力品質實驗室

Frequency scan analysis
Chapter 1: An Overview of Power System Harmonic Analysis Frequency scan analysis 1 Frequency Scan: Determine the frequency response of a network at a given bus Network Z f 中正--電力品質實驗室

Harmonic power flow analysis
Chapter 1: An Overview of Power System Harmonic Analysis Harmonic power flow analysis Objective: compute harmonic distortion levels for a given operating condition There are many harmonic power flow algorithms proposed. Here we discuss the most useful algorithm. Current source model for harmonic sources Frequency domain Non-iterative What is known for solving the problem Fundamental frequency power flow results (I1 and q1). Typical spectrum of harmonic sources (Ih-spc, qh-spc) System Y(h) matrix, h=harmonic number Current source model described earlier 中正--電力品質實驗室

Harmonic power flow analysis
Chapter 1: An Overview of Power System Harmonic Analysis Harmonic power flow analysis Solution steps 1) Compute 60Hz power flow 2) Determine drive current (I1 and q1) 3) Determine drive harmonic current I(h) using the formula and typical drive spectrum 4) With known Y(h) matrix and drive current I(h), compute nodal voltage V(h) and branch current IB(h) 5) Compute harmonic indices (THD, IHD) using the V(h), IB(h) results. 中正--電力品質實驗室

Harmonic power flow analysis - other algorithms
Chapter 1: An Overview of Power System Harmonic Analysis Harmonic power flow analysis - other algorithms Time domain algorithm (e.g. EMTP simulation) or hybrid algorithm Iterative algorithms (frequency domain) F( [V1], [V2],...,[Vn], [I1], [I2], ..., [In],C) =0 Newton method Harmonic iteration method (see the diagram below) Bus voltages Linear network (including power flow constraints) Harmonic Source (non-linear) Current source 中正--電力品質實驗室

New challenges Distributed harmonic sources
Chapter 1: An Overview of Power System Harmonic Analysis New challenges Distributed harmonic sources Fluctuation of harmonic distortions with time Concerns on interharmonics Need to identify system deficiency more efficiently Need to revisit some of the modeling assumptions 中正--電力品質實驗室

New challenges 1 - distributed harmonic sources
Chapter 1: An Overview of Power System Harmonic Analysis New challenges 1 - distributed harmonic sources The harmonic-production characteristics of the sources will affect each other. (attenuation and diversity effects) Actual results The harmonic sources may also vary randomly. 中正--電力品質實驗室

Harmonic attenuation effect
Chapter 1: An Overview of Power System Harmonic Analysis New challenges 1 - distributed harmonic sources Harmonic attenuation effect New harmonic analysis methods need to take into account the characteristics 中正--電力品質實驗室

New challenges 2 - analysis of harmonic resonance
Chapter 1: An Overview of Power System Harmonic Analysis New challenges 2 - analysis of harmonic resonance · Which bus can excite a particular resonance more easily? · Where the resonance can be observed more easily? · What are the components involved in the resonance? · How far the resonance can propagate in a system? 中正--電力品質實驗室

Chapter 1: An Overview of Power System Harmonic Analysis New challenges 2 - analysis of harmonic resonance XL XC V I If this term = 0 => Resonance Some elements of [Y]-1 are large (the extreme case is [Y]-1= ) Implies that [Y] approaches singularity (something like [Y]=0) The singularity of [Y] can only be caused by one or more eigenvalues of the [Y] matrix = 0. 中正--電力品質實驗室

Chapter 1: An Overview of Power System Harmonic Analysis New challenges 2 - analysis of harmonic resonance Eigen-decomposition of the Y matrix: Right eigenvector matrix Left eigenvector matrix Eigenvalue matrix [U]=[T][V] -- called modal voltage [J] =[T][I] -- called modal current [L] -- can be called modal Y matrix 中正--電力品質實驗室

Chapter 1: An Overview of Power System Harmonic Analysis New challenges 2 - analysis of harmonic resonance Assume l1 is the eigenvalue approaching zero modal current J1 will lead to a large modal voltage U1 Other modal voltages are not affected (since they are decoupled from l1) 中正--電力品質實驗室

Chapter 1: An Overview of Power System Harmonic Analysis New challenges 2 - analysis of harmonic resonance Physical domain Modal domain Summary: In the modal domain, it is much easier to find the ‘locations’ or ‘buses’ (i.e. the modes) that are related to a resonance Once we know the resonance mode, we can find the buses most affected by the reassurance - based on the eigenvector information 中正--電力品質實驗室

Chapter 1: An Overview of Power System Harmonic Analysis New challenges 2 - analysis of harmonic resonance Participation of components in a resonance Participation of buses in a resonance 中正--電力品質實驗室

New challenges 3 - analysis of interharmonics
Chapter 1: An Overview of Power System Harmonic Analysis New challenges 3 - analysis of interharmonics Interharmonics produce flicker Frequency of interharmonic varies with the drive operating condition 中正--電力品質實驗室

Chapter 1: An Overview of Power System Harmonic Analysis New challenges 3 - analysis of interharmonics An interharmonic-producing drive cannot be modeled as an interharmonic current source IDC2 Source Motor VDC2 Converter Inverter IAC2 60Hz 50Hz VDC2 has ripples associated with the motor frequency VDC2 produces IDC2 through some impedances (including supply system Z) IDC2 is rectified (or penetrate) into the AC side to produce IAC2 Therefore, interharmonic current of IAC2 is affected by some impedances

Chapter 1: An Overview of Power System Harmonic Analysis New challenges 3 - analysis of interharmonics Sequence characteristics of interharmonics 中正--電力品質實驗室

Chapter 1: An Overview of Power System Harmonic Analysis
Summary Harmonic analysis has become a relatively mature area. This tutorial will focus on the well-established methods It is important to note that there are still many subjects remaining to be explored. Three examples have been used to demonstrate the possible developments in the area 中正--電力品質實驗室

Chapter 2 Harmonics and Interharmonics Theory
Tutorial on Harmonics Modeling and Simulation Contributors: G. W. Chang and A. Testa 中正--電力品質實驗室

Outline Introduction Fourier Series and Analysis
Basic Definition of Harmonic and Interharmonic Quantities Harmonic and Interharmonic Indices Power Factor under Distorted Situation Power System Response to Harmonics and Interharmonics Solutions to Harmonics and Interharmonics Summary 中正--電力品質實驗室

Introduction With the widespread proliferation of nonlinear devices such as power electronics and arc furnace loads, significant amounts of harmonic and interharmonic currents are being injected into the power system. Harmonic and interharmonic currents not only disturb loads that are sensitive to waveform distortion, but also cause many undesirable effects on power system components. 中正--電力品質實驗室

Introduction Harmonic Sources（nonlinear loads）
Single-phase loads: fluorescent lights, personal computers Three-phase loads: arc furnaces, ac/dc converters 中正--電力品質實驗室

Introduction 中正--電力品質實驗室

Introduction Harmonics and interharmonics are usually defined as periodic steady-state distortions of voltage and/or current waveforms in the power system. In the harmonics and interharmonics polluted environment, the theory regarding harmonic and interharmonic quantities needs to be defined to distinguish from those quantities defined for the system fundamental frequency. 中正--電力品質實驗室

Fourier Series and Analysis
Periodic Function Orthogonal Function e.g. Period: T 中正--電力品質實驗室

By the use of orthogonal relations, we have 中正--電力品質實驗室

Fourier analysis is a process of the de-composition for any distorted period wave shape into a fundamental and a series of harmonics. Advantages of Fourier series and analysis: -Useful for studying electrical networks which contain non- sinusoidal voltages and currents - The frequency components are harmonics of the fundamental frequency - For linear networks, treat each harmonic separately by using phasor analysis (frequency domain), then combine the results and convert back to the time domain waveform 中正--電力品質實驗室

Complex Form Waveform Symmetry - Even function: (no sine terms) - Odd function: (no cosine terms) - Half-wave symmetry: (no even harmonics) 中正--電力品質實驗室

Fourier Transform Discrete Fourier Transform: T frequency-domain spectrum and the time-domain function are both periodic sampled functions with N samples per period, Fourier transform pair becomes is the so-called spectrum of which is assumed to be one cycle of a periodic signal. k, n = 0, 1, ..., N-1, 中正--電力品質實驗室

The angular frequency resolution of the spectrum is determined by the length of the signal as Thus, if T is selected as one period of , the outcome spectrum will only show components that are integer multiples of the fundamental frequency, which are defined as harmonics. If the data length is selected as p cycles (p>1 and is an integer) of the fundamental, the frequency resolution will change to This implies that once we use more than one fundamental cycle to perform the DFT, it also becomes possible to obtain components at frequencies that are not integer multiples of the fundamental. 中正--電力品質實驗室

The non-integer order components, according to the IEC definition, are called interharmonics. The DFT is often used in harmonics and interharmonics measurement. Fast Fourier transform (FFT) algorithms are very fast methods for performing the DFT calculations. There are pitfalls of the aliasing, the spectral leakage, and the picket-fence effect, when applying FFT for harmonics and interharmonics computations. 中正--電力品質實驗室

Basic Definition of Harmonic and Interharmonic Quantities
The definition of a harmonic can be stated as: A sinusoidal component of a periodic wave having a frequency that is an integer multiple of the fundamental frequency. The interharmonics are defined as those components with frequencies between two consecutive harmonics or those components whose frequencies are not integer multiples of the fundamental power frequency. One special subset of interharmonics that have frequency values that are less than that of the fundamental frequency is called sub-harmonics. 中正--電力品質實驗室

One major source of harmonics in the power system is the static power converter. Under ideal operating conditions, the current harmonics generated by a p-pulse line-commutated converter can be characterized by and e.g. Such harmonics are usually termed as characteristic harmonics. Non-characteristic harmonics are typically categorized as those integer frequency components other than characteristic ones. 中正--電力品質實驗室

The power electronic equipment with double conversion systems that connects two AC systems with different frequencies through a DC link can be an interharmonic source. Variable speed drives, HVDC, and other static frequency converters are typical examples of this class of sources. Other sources of interharmonics include time-varying loads such as welder machines and arc furnaces. There are various causes that could lead to the interharmonic components. One example is a signal that actually contains in the frequency domain with a component whose frequency is non-integer multiples of the fundamental frequency. 中正--電力品質實驗室

There are cases where the interharmonic components are produced by the picket-fence effect when applying the FFT, due to sampling the signal with a spectral leakage. The picket-fence effect occurs when the analyzed waveform includes spectral components which are not an integer multiple of the FFT fundamental frequency (i.e. the reciprocal of the window length in time). Such effect may lead to a situation where the frequency resolution (i.e. the sampled frequency interval) of the spectrum is not observable for certain frequencies. A frequency component lying between two FFT consecutive harmonics will affect these two harmonic magnitudes and also may cause the spectral leakage. 中正--電力品質實驗室

Frequency resolution = 30 Hz 中正--電力品質實驗室

Interharmonics: p1: the pulse number of the rectifier section p2: the pulse number of the output section m and n: integers fs: the power frequency f0: the inverter output frequency 中正--電力品質實驗室

Sub-harmonics have frequency values that are less than that of the fundamental frequency. Lighting flicker is one indication of the presence of interharmonics around the fundamental power frequency (including sub-harmonics), which is due to the voltage fluctuations with frequencies being much less than the system fundamental frequency. A well-known source of the voltage fluctuations that cause light flicker is the arc furnace. 中正--電力品質實驗室

Electric Quantities Under Non-sinusoidal Situation
Instantaneous voltage and current Instantaneous power Average power RMS voltage and current Apparent power Reactive power Distortion power Total power factor 中正--電力品質實驗室

Instantaneous Voltage and Current Instantaneous and Average Power 中正--電力品質實驗室

RMS Voltage and Current Apparent, Reactive, and Distortion Power 中正--電力品質實驗室

Power at sinusoidal situation Total power factor No consensus in the definition and physical meaning on reactive and distortion power. 中正--電力品質實驗室

Phase Sequences of Harmonics and Interharmonics
For variable frequency drives and motors with fluctuating loads, interharmonics can have either positive or negative sequence and are rarely zero sequence. The general rule is that the sequence of the interharmonc component is the same as that of the supply system harmonic components being modulated. Harmonic Order Phase Sequence 1 + 2 - 3 4 5 6 . 3h-1 3h 3h+1 中正--電力品質實驗室

Phase Sequences of Harmonics and Interharmonics
Positive sequence Negative Zero 3h-1: negative sequence 3h: zero sequence 3h+1:positive sequence h = 1, 2,…

Harmonic Indices Total Harmonic Distortion (THD)
Total Demand Distortion (TDD) Telephone Influence Factor (TIF) VT and IT Products C-Message Weighted Index Transformer K-Factor and Harmonic Loss Factor Distortion Power Factor 中正--電力品質實驗室

Harmonic Indices Total Harmonic Distortion (THD)
Total Interharmonic Distortion (TIHD) Λ is the set of all interharmonics components under considerations. 中正--電力品質實驗室

Harmonic Indices Total Demand Distortion (TDD)
is the maximum demand load current (15 or 30 minute demand) at fundamental frequency at the point of common coupling (PCC), calculated as the average current of the maximum demands for the previous twelve months. 中正--電力品質實驗室

Harmonic Indices Telephone Influence Factor (TIF)
is a weighting accounting for audio and inductive coupling effects at the h-th harmonic frequency. VT and IT Products 中正--電力品質實驗室

Harmonic Indices C-Message Weighted Index
K-Factor and Harmonic Loss Factor 中正--電力品質實驗室

Harmonic Indices Distortion Power Factor (PFD) 中正--電力品質實驗室

Harmonic Indices THDI (%) PFD 10 0.995 30 0.958 50 0.894 70 0.819 100
0.707 125 0.625 150 0.555 中正--電力品質實驗室

Power System Response to Harmonics and Interharmonics
- Series resonance - Parallel resonance - Distributed resonance 中正--電力品質實驗室

Series resonance Parallel resonance Distributed resonance 中正--電力品質實驗室

Parallel Resonace 中正--電力品質實驗室

Series Resonance 中正--電力品質實驗室

Solutions to Harmonics and Interharmonics
Remedial methods - Passive Filters - Phase Multiplication - Special Designed Transformer (e.g. zig-zag) - Active Filters Preventive method - Harmonic Standards * IEEE * IEC 中正--電力品質實驗室

Remedial Methods Series filter – characterized as a parallel resonant and blocking type with a high impedance at its tuned frequency Parallel filter – characterized as a series resonant and trap type with a low impedance at its tuned frequency Series filter Parallel filter 中正--電力品質實驗室

Remedial Methods Passive filter 中正--電力品質實驗室

Remedial Methods Phase Multiplication 中正--電力品質實驗室

Remedial Methods Special Designed Transformer 中正--電力品質實驗室

Remedial Methods 中正--電力品質實驗室

Remedial Methods Active filter 中正--電力品質實驗室

Preventive Methods (Harmonic Standards)
IEEE Current Distortion Limits for General Distribution Systems 中正--電力品質實驗室

Preventive Method (Harmonic Standards)
IEEE Recommended Voltage Distortion Limits 中正--電力品質實驗室

IEC : Compatibility levels for harmonic voltages (in percent of the nominal voltage) in LV and MV power systems Odd harmonics non multiple of 3 Odd harmonics multiple of 3 Even harmonics Order h Harmonic voltage % 5 7 11 13 17 19 23 25 >25 6 3,5 3 2 1,5 0,2 + 1,3‧(25/h) 9 15 21 >21 0,3 0,2 4 8 10 12 >12 1 0,5 NOTE – Total harmonic distortion (THD): 8%. 中正--電力品質實驗室

IEC :Indicative values of planning levels for harmonic voltage (in percent of the nominal voltage) in MV, HV and EHV power systems Odd harmonics non multiple of 3 Odd harmonics multiple of 3 Even harmonics Order h Harmonic voltage % MV HV-EHV 5 7 11 13 17 19 23 25 >25 4 3 2,5 1,6 1,2 0,2 + 0,5(h/25) 2 1,5 1 0,7 9 15 21 >21 0,3 0,2 6 8 10 12 >12 0,5 0,4 NOTE – Total harmonic distortion (THD): 6,5% in MV networks 3% in HV networks. 中正--電力品質實驗室

IEC Illustration of basic voltage quality concepts with time statistics relevant to one site within the whole system Illustration of basic voltage quality concepts with time/location statistics covering whole system 中正--電力品質實驗室

Summary Fourier Series and Analysis
Basic Definition of Harmonic and Interharmonic Quantities Harmonic and Interharmonic Indices Power Factor under Distorted Situation Power System Response to Harmonics and Interharmonics Solutions to Harmonics and Interharmonics 中正--電力品質實驗室

Chapter 3 Harmonic Modeling of Networks
Tutorial on Harmonics Modeling and Simulation Contributors: T. Ortmyer, C. Hatziadoniu, and P. Ribeiro 中正--電力品質實驗室

Distribution System Modeling
The initial decisions: - Three phase or single phase modeling - The extent of the primary model - Secondary distribution modeling The NATURE of the issue and the GOAL of the study constrain these decisions. 中正--電力品質實驗室

A Typical Primary Distribution System
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Things to note Any large or unique loads Capacitor banks/ cables(?)
Transmission supply Any unusual operating conditions? 中正--電力品質實驗室

Decision 1: Per phase versus Three Phase Modeling
The three phase model is required when: Single phase or unbalanced capacitors are present Ground or residual currents are important in the study Significant unbalanced loading is present A combination of wye-wye and/or delta-wye transformers leads to harmonic cancellation* 中正--電力品質實驗室

The typical instances where a single phase model may be sufficient are:
A single large three phase harmonic source is the cause of the study The remaining system is well balanced Ground currents are not an issue 中正--電力品質實驗室

Decision 2: The extent of the system model
Model the entire primary system Transmission source can be modeled by the 60 Hertz short circuit impedance if no significant transmission capacitance is nearby– but check that the transmission system is not a source of harmonics Power factor capacitors and any distributed generation should be modeled in detail 中正--電力品質實驗室

Decision 3: Load and harmonic source modeling
Identify and model all significant harmonic sources Determine present levels through measurements- also determine if harmonic levels peak at full or light load conditions Develop aggregate load models based on measurements and load distribution Validate with measurements taken as harmonic sources/capacitor banks are switched in and out 中正--電力品質實驗室

Representative secondary distribution system

Characteristics of secondary studies
Different voltage levels Fewer capacitors, and more with tuning coils Load data is more accessible- and more important Measurements can be more economical 中正--電力品質實驗室

Modeling transformers
Model the transformer connection Neglect the transformer magnetizing branch (usually ignore the transformer magnetizing harmonics) Model the harmonic reactance as the product of short circuit leakage reactance and harmonic number Model the harmonic resistance as the short circuit resistance. Correct for skin effect if data or model available. Include stray capacitance for frequencies above the low khertz range. 中正--電力品質實驗室

Line Models Distribution lines and cables should be represented by an equivalent pi. An estimated correction factor for skin effect can be included Model ground path for zero sequence harmonics 中正--電力品質實驗室

Capacitors Capacitors– model as capacitive reactance– 60 hertz reactance divided by the harmonic number. Be sure to note those single phase capacitors, and model as such. Model the capacitor as either grounded wye, or ungrounded wye or delta. 中正--電力品質實驗室

Load Models Linear Loads Induction and Synchronous Machines
Non-linear Loads 中正--電力品質實驗室

Linear Passive Loads TYPES: Incandescent lamps, resistive heater, electric range, water heater, space heater, etc. CHARACTERISTICS: RL type loads with RL values independent of frequency. 中正--電力品質實驗室

Line Connected MOTOR/GENERATOR LOADS
Linear or Nonlinear? Induction Motor Fundamental Frequency Per Phase Equivalent Circuit 中正--電力品質實驗室

IM Per Phase Harmonic Model

For synchronous generators, the per phase model of the synchronous generator is similar– use a series combination of stator resistance and substransient reactance in the model. On all direct connected machines, make sure and account for the ground connection (or lack of one) in studies with zero sequence harmonics. 中正--電力品質實驗室

Nonlinear Loads Adjustable speed drives
fluorescent lamps, computers and other electronic loads arc furnaces and welders These loads generate harmonic currents, and are modeled as sources at the harmonic frequencies 中正--電力品質實驗室

Load Model 1: Series Passive Load

Load Model 2: Parallel Passive Load

Load Model 3. Skin Effect Parallel Load Model

Load Model 4. Induction Motor plus Resistive

Load Model 5. CIGRE/EDF 中正--電力品質實驗室

Load Model 6. Inclusion of Load Transformer and Motor Damping

I. Case Study 1: Load Impedance Frequency Study

Case Study 1 Parameters Linear Load=743 kW.
PF Cap.=741kVAr, (C=5.4mF). Injected Harmonic Currents (A): I5 = I7 = 0.601 I11=0.382 I13=0.323 中正--電力品質實驗室

Case Study 1: Load Model 1, 2, and 3 results

Case Study 1: Load Model 4, 5, and 6 Results

Sensitivity of Impedance to Motor Penetration Level (Load Model 6, fixed PFC)

Sensitivity of Impedance to IM Penetration– w/changing PFC

Summary Define study needs Determine the modeling needs Get the data
Validate the data Produce good results!! 中正--電力品質實驗室

Chapter 5: Harmonic Analysis in Frequency and Time Domains
Tutorial on Harmonics Modeling and Simulation Presenter: Paulo F Ribeiro Contributors: A. Medina, N. R. Watson, P. Ribeiro, and C. Hatziadoniu 中正--電力品質實驗室

Techniques for harmonic analysis Conclusions
Overview Introduction Techniques for harmonic analysis Conclusions 中正--電力品質實驗室

Introduction Ideal operation conditions in power networks:
Perfectly balanced Unique and constant frequency Sinusoidal voltage and current waveforms Constant amplitude 中正--電力品質實驗室

However,network components (nonlinear and time-varying components and loads),distort the ideal sinusoidal waveform this distorting effect is known as harmonic distortion. 中正--電力品質實驗室

Digital Harmonic Analysis
Harmonic detection Real time monitoring of harmonic content Harmonic prediction Harmonic simulation techniques 中正--電力品質實驗室

Harmonic Simulation Techniques
Frequency domain methods Time domain methods Hybrid time and frequency domain methods 中正--電力品質實驗室

Techniques for Harmonic Analysis
Frequency Domain. Direct method Iterative harmonic analysis Harmonic power flow method 中正--電力品質實驗室

Direct Method The frequency response of the power network, as seen by a particular bus, is obtained injecting a one per unit current or voltage at the bus of interest with discrete frequency steps for the particular range of frequencies. The process is based on the solution of the network equation, (1) 中正--電力品質實驗室

Table 1. Power network harmonic representation

Hybrid voltage and current excitations
Most power system nonlinearities manifest themselves as harmonic current sources, but sometimes harmonic voltage sources are used to represent the distortion background present in the network prior to the installation of the new nonlinear load. 中正--電力品質實驗室

A system containing harmonic voltages at some busbars and harmonic current injections at other busbars is solved by partitioning the admittance matrix and performing a partial inversion. This hybrid solution procedure allows the unknown busbar voltages and unknown harmonic currents to be found. 中正--電力品質實驗室

Partitioning the matrix equation to separate the two types of busbars gives:
(2) 中正--電力品質實驗室

The unknown voltage vector Vi is found by solving,

The harmonic currents injected by the harmonic voltage sources are found as,

Iterative Harmonic Analysis (IHA)
The IHA is based on sequential substitutions of the Gauss type. The harmonic producing device is modeled as a supply voltage-dependent current source, represented by a fixed harmonic current source at each iteration. The harmonic currents are obtained by first solving the problem using an estimated supply voltage. 中正--電力品質實驗室

The harmonic currents are then used to obtain the harmonic voltages.
These harmonic voltages in turn allow the computation of more accurate harmonic currents. The solution process stops once the changes in harmonic currents are sufficiently small. 中正--電力品質實驗室

Harmonic Power Flow Method (HPF)
The HPF method takes into account the voltage-dependent nature of power components. In general, the voltage and current harmonic equations are solved simultaneously using Newton-type algorithms. The harmonics produced by nonlinear and time-varying components are cross-coupled. 中正--電力品質實驗室

(5) The unified iterative solution for the system has the form,

where ΔI is the vector of incremental currents having the contribution of nonlinear components, ΔV is the vector of incremental voltages and [ΔYJ] is the admittance matrix of linear and nonlinear components. 中正--電力品質實驗室

Time Domain In principle, the periodic behavior of an electric network can be obtained directly in the time domain by integration of the differential equations describing the dynamics of the system, once the transient response has died-out and the periodic steady state obtained. 中正--電力品質實驗室

This Brute Force (BF) procedure may require of the integration over considerable periods of time until the transient decreases to negligible proportions. It has been suggested only for the cases where the periodic steady state can be obtained rapidly in a few cycles. 中正--電力品質實驗室

In this formulation, the general description of nonlinear and time-varying elements is achieved in terms of the following differential equation, where x is the state vector of n elements (6) 中正--電力品質實驗室

Practical nonlinear power systems can be appropriately solved in the time domain with a state space matrix equation representation based on non-autonomous ordinary differential equations having the form, where [A] is the square state matrix of size n×n, [B] is the control or input matrix of size n×r and u is the input vector of dimension r. (7) 中正--電力品質實驗室

Widely accepted digital simulators for electromagnetic transient analysis, such as EMTP and PSCAD/EMTDCTM can be used for steady state analysis. However, the solution process can be potentially inefficient, as detailed before. 中正--電力品質實驗室

Here, a discrete time domain solution for any integration step length h is adopted, where the basic elements of the power network, e.g. R, L and C are represented with Norton equivalents depending on h. 中正--電力品質實驗室

Other power network elements are formed with the adequate combination of R, L and C, which are in turn combined together for a unified solution of the entire network in the time domain, e.g. 中正--電力品質實驗室

Where [G] is the conductance matrix, v(t) the unknown voltages at time t, i(t) the vector of nodal current sources and iH the vector of past history current sources. (8) 中正--電力品質實驗室

Fast Periodic Steady State Solutions
A technique has been used to obtain the periodic steady state of the systems without the computation of the complete transient [Aprille and Trick, 1972]. This method is based on a solution process for the system based on Newton iterations. In a later contribution [Semlyen and Medina, 1995], techniques for the acceleration of the convergence of state variables to the Limit Cycle based on Newton methods in the time domain have been introduced. 中正--電力品質實驗室

Fundamentally, to derive these Newton methods it is assumed that the steady state solution of (6) is T-periodic and can be represented as a Limit Cycle for in terms of other periodic element of or in terms of an arbitrary T-periodic function, to form an orbit. 中正--電力品質實驗室

Before reaching the Limit Cycle the cycles of the transient orbit are very close to it. The location of these transient orbits are appropriately described by their individual position in the Poincaré Plane. 中正--電力品質實驗室

Extrapolation to the Limit Cycle
x 1 + D i P Transient Orbit Limit Cycle A Cycle

It is possible to take advantage on the linearity taking place in the neighborhood of a Base Cycle if (6) is linearized around a solution x(t) from ti to ti+T, yielding the variational problem, where is the T-periodic Jacobian matrix. (9) 中正--電力品質實驗室

Note that (9) allows the application of Newton type algorithms to extrapolate the solution to the Limit Cycle, obtained as [53], where, (10) (11) 中正--電力品質實驗室

In (10) , and are the vectors of state variables at the Limit Cycle, beginning and end of the Base Cycle respectively, and in (11) C, I and are the iteration, unit and identification matrices, respectively. 中正--電力品質實驗室

It has been concluded from the analyzed case studies that the Newton methods based on a Numerical Differentiation (ND) and a Direct Approach (DA) process, respectively, require less than 43% of the total number of periods of time needed by the BF approach, substantially reducing the computation effort required by the ND and DA methods to obtain the periodic steady state solution. 中正--電力品質實驗室

Hybrid Methods The fundamental advantages of the frequency and time domains are used in the hybrid methodology [53], where the power components are represented in their natural frames of reference, e.g., the linear in the frequency domain and the nonlinear and time-varying in the time domain. 中正--電力品質實驗室

Fig. 1 System seen from load nodes.
The Fig. 1 illustrates the conceptual representation of the hybrid methodology. Fig. 1 System seen from load nodes. 中正--電力品質實驗室

(12) The iterative solution for the entire system has the form,

3. Conclusions A description has been given on the fundamentals of the techniques for the harmonic analysis in power systems, developed in the frames of reference of frequency, time and hybrid time-frequency domain, respectively. The details on their formulation, potential and iterative process have been given. 中正--電力品質實驗室

In general Harmonic Power Flow methods are numerically robust and have good convergence properties. However, their application to obtain the non-sinusoidal periodic solution of the power system may require the iterative process of a matrix equation problem of very high dimensions. 中正--電力品質實驗室

Conventional Brute Force methodologies in the time domain for the computation of the periodic steady state in the power system are in general an inefficient alternative which, in addition, may not be sufficiently reliable, in particular for the solution of poorly damped systems. 中正--電力品質實驗室

The potential of the Newton techniques for the convergence to the Limit Cycle has been illustrated.
Their application yields efficient time domain periodic steady state solutions. 中正--電力品質實驗室

Presenter: Paulo F RIbeiro
Chapter 6: Real-Time Digital Time-Varying Harmonics Modeling and Simulation Techniques Tutorial on Harmonics Modeling and Simulation Presenter: Paulo F RIbeiro Contributors: L-F. Pak, V. Dinavahi, G. Chang, M. Steurer, S. Suryanarayanan, P. Ribeiro 中正--電力品質實驗室

Need for Sophisticated Tools for Power Quality (PQ) Studies
Proliferation of nonlinear and time-varying loads has led to significant power quality concerns. Traditionally, time-varying harmonics were studies using statistical and probabilistic methods for periodic harmonics. Cannot describe random characteristics Cannot capture the reality of physical phenomena. A time-dependent spectrum is needed to compute the local power-frequency distribution at each instant. Significant advances in equipment for PQ monitoring, waveform generation, disturbance detection, and mitigation. Digital signal processing is widely used. Sophisticated power electronic controllers are used for PQ mitigation. Need for testing and validation of such equipment. Real-time digital simulation as an advanced tool for PQ analysis and mitigation. 中正--電力品質實驗室

Real-Time Harmonic Modeling and Simulation Techniques
Wave Digital Filters Discrete Wavelet Transform Real-Time Electromagnetic Transient Network Solution Real-Time Digital Simulators RTDS PC-Cluster Based Simulators HYPERSIM DSPACE 中正--電力品質實驗室

Wave Digital Filters Digital Signal Processing tool that transforms analog networks into topologically equivalent digital filters Synthesis is based on wave network characterization Designed to attain low-sensitivity structures to quantization errors in digital filter coefficients Powerful technique for simulating power system harmonics and transients 中正--電力品質實驗室

Discrete Wavelet Transform
Time-Frequency representation of time varying signals. Wavelet analysis starts by adopting a prototype function. Time Analysis is done with a contracted high-frequency prototype. Frequency analysis is done using a dilated low- frequency prototype. Operator representation theory is used to model electrical componenets in discrete wavelet domain 中正--電力品質實驗室

PC-Cluster Based Real-Time Digital Simulator
Real-Time eXperimental LABoratory (RTX-LAB) at the University of Alberta. 中正--電力品質實驗室

Features of the RTX-LAB Simulator
Fully Flexible and scalable Fast FPGA based analog and digital I/O and high intra-node communication speed Varity of synchronization options Compatible with MATLAB/SIMULINK and other programming languages 中正--電力品質實驗室

Hardware Architecture of the RTX-LAB Simulator
Two types of computers- Targets and Hosts Targets are dual CPU based 3.0 GHZ Xeon, work as the main simulation engine and facilitates FPGA based I/Os Hosts are 3.00 GHZ Pentium IV, used for model development, compilation and loading of the model to the cluster 中正--電力品質實驗室

Software Architecture of the RTX-LAB Simulator
Target OS- RedHawk Linux Host OS- Windows XP Model Development- MATLAB/SIMULINK Other programming Languages C, C++ 中正--電力品質實驗室

Communication Links in the RTX-LAB Simulator
InfiniBand Link Maximum Throughput- 10Gbps Shared Memory bus speed – 2.67Gbps Signal Wire Link Data Transfer rate-1.2Gbps Gigabit Ethernet link Transfer Rate- Up to 1Gbps I/O signals from real-hardware are connected through FPGA based I/Os Xilinx Virtex-II Pro is used 100 MHZ operation speed 中正--電力品質實驗室

Subsystems and Synchronization in the RTX-LAB Simulator

Single-line Diagram of the Arc Furnace Installation
Case Study 1: Time-Varying Harmonic Analysis on the RTX-LAB Real-Time Digital Simulator Single-line Diagram of the Arc Furnace Installation 中正--電力品質實驗室

Schematic of the Arc Furnace Model
Case Study 1: Time-Varying Harmonic Analysis on the RTX-LAB Real-Time Digital Simulator Schematic of the Arc Furnace Model 中正--電力品質實驗室

Voltage and Current for the Arc Furnace
Case Study 1: Time-Varying Harmonic Analysis on the RTX-LAB Real-Time Digital Simulator Voltage and Current for the Arc Furnace 中正--電力品質實驗室

Voltage at the Primary Winding of the MV/LV Transformer
Case Study 1: Time-Varying Harmonic Analysis on the RTX-LAB Real-Time Digital Simulator Voltage at the Primary Winding of the MV/LV Transformer 中正--電力品質實驗室

Current in the Primary Winding of the MV/LV Transformer
Case Study 1: Time-Varying Harmonic Analysis on the RTX-LAB Real-Time Digital Simulator Current in the Primary Winding of the MV/LV Transformer 中正--電力品質實驗室

RTDS at CAPS Provides time domain solution in real time with typical time step sizes around 50 μs using the Dommel (EMTP) algorithm Features dual time step (<2 μs) capability for PE simulations Allows up to 54 electrical nodes per rack, but subsystems can be connected through cross-rack elements (transmission lines, etc.) Large library of power system and control component models (like EMTDC) > 350 parallel DSPs > 2500 analog outputs and over 200 digital inputs and outputs RPC – Network Solution IRC – Inter-rack Communication WIF – Workstation Interface 3PC – Controls, system dynamics GPC – Network solution, fast-switching converters 中正--電力品質實驗室

14 Rack RTDS Installation at CAPS
Largest RT simulator installation in any university worldwide Systems of up to 250 three-phase buses Sufficient high-speed I/O to enable realistic HIL and PHIL experiments 中正--電力品質實驗室

(Controller) hardware in loop (HIL) and power hardware in loop PHIL
Simulated rest of system 中正--電力品質實驗室

Schematic of the Industrial Distribution System and Rectifier Load
Case Study 2: Power Quality Sensitivity Study of a Controller on the RTDS Schematic of the Industrial Distribution System and Rectifier Load 中正--電力品質實驗室

Case Study 2: Power Quality Sensitivity Study of a Controller on the RTDS
Single-phase Voltage Sag (40% reduction, no phase shift) and its Impact on Rectifier DC Output 中正--電力品質實驗室

Case Study 2: Power Quality Sensitivity Study of a Controller on the RTDS
Phase-Shifted Single-phase Voltage Sag (40% reduction) and its Impact on Rectifier DC Output 中正--電力品質實驗室

Case Study 3: Harmonic Distortion on the RTDS Shipboard Power System
Voltage (kV) 中正--電力品質實驗室

Case Study 4: A HIL Simulation for Studying the Transient Behavior of Wind DG

Conclusions With rising number of time-varying and nonlinear loads sophisticated harmonics modeling and simulation tools are needed. A combination of fast topological methods and powerful real-time simulators can overcome limitations of off-line simulation tools. A general review of current off-line harmonic modeling and simulation tools is presented. Currently available real-time simulation techniques are discussed. Two real-time case studies: arc furnace modeling and power quality sensitivity of a controller, are presented. 中正--電力品質實驗室

Chapter 7: Test Systems for Harmonics Modeling and Simulation
2007 IEEE PES Tutorial on Power System Harmonics Presenter: Paulo F Ribeiro Contributors: W. Xu, M. Halpin, and S. Ranade 中正--電力品質實驗室

Outline Utility transmission system Utility distribution system
Chapter 7: Test systems for harmonics modeling and simulation Outline Utility transmission system Utility distribution system Industrial distribution system Commercial distribution system 中正--電力品質實驗室

System 1: Utility transmission system
Chapter 7: Test systems for harmonics modeling and simulation System 1: Utility transmission system Balanced system, single-phase analysis is sufficient 中正--電力品質實驗室

Chapter 7: Test systems for harmonics modeling and simulation System 1: Utility transmission system Branch data Sample Data Harmonic source data 中正--電力品質實驗室

Chapter 7: Test systems for harmonics modeling and simulation System 1: Utility transmission system Sample Results 中正--電力品質實驗室

System 2: Utility distribution system
Chapter 7: Test systems for harmonics modeling and simulation System 2: Utility distribution system Unbalanced system, three-phase harmonic analysis is needed 中正--電力品質實驗室

Chapter 7: Test systems for harmonics modeling and simulation System 2: Utility distribution system Load data Sample Data Harmonic source data 中正--電力品質實驗室

Chapter 7: Test systems for harmonics modeling and simulation System 2: Utility distribution system Sample Results 中正--電力品質實驗室

System 3: Industrial distribution system
Chapter 7: Test systems for harmonics modeling and simulation System 3: Industrial distribution system Balanced system, single-phase analysis is sufficient 中正--電力品質實驗室

Chapter 7: Test systems for harmonics modeling and simulation System 3: Industrial distribution system Sample Data Branch data Harmonic source data 中正--電力品質實驗室

Chapter 7: Test systems for harmonics modeling and simulation System 3: Industrial distribution system Sample Results 中正--電力品質實驗室

System 4: Commercial distribution system
Chapter 7: Test systems for harmonics modeling and simulation System 4: Commercial distribution system Unbalanced system, three-phase harmonic analysis is needed 中正--電力品質實驗室

System 4: Commercial distribution system
Chapter 7: Test systems for harmonics modeling and simulation System 4: Commercial distribution system Sample Data Load and branch data Harmonic source data Filter data 中正--電力品質實驗室

Filter winding current
Chapter 7: Test systems for harmonics modeling and simulation System 4: Commercial distribution system Sample Results Filter winding current 中正--電力品質實驗室

Chapter 7: Test systems for harmonics modeling and simulation
Summary Four test systems covering typical situations where harmonic analysis is needed. It also covers two types of systems, balanced and unbalanced In all cases, harmonic sources are modeled as current sources 中正--電力品質實驗室

Chapter 8: Procedure of Time-Domain Harmonics Modeling and Simulation
Tutorial on Harmonics Modeling and Simulation Presenter: Paulo F Ribeiro Contributors: C. J. Hatziadoniu, W. Xu, and G. W. Chang 中正--電力品質實驗室

OUTLINE Introduction: Relevance of the Time Solution Procedures
The Modeling Approach Harmonic Sources in the Time Domain Apparatus Modeling Formulation of the Network State Equation Harmonic Solution Procedure Software Demonstration of Harmonic Simulation Summary and Conclusion 中正--電力品質實驗室

INTRODUCTION Why Time Domain Solution?
When is Time Domain Solution Appropriate? How Accurate is Time Domain Solution Compared to Direct Methods? What are the General Characteristics of a Time Domain Solution Procedure? 中正--電力品質實驗室

Why Time Domain Solution?
“Time Domain Simulation is preferable to direct methods in certain line varying conditions involving power converters and non-linear devices.” It allows detail modeling, especially of non-linear network elements; It allows the assessment of non-linear feedback loops onto the harmonic output (e.g. study of harmonic instability in line commutated converters). Example of Direct Methods PCFLOH; SuperHarm. 中正--電力品質實驗室

When is Time Domain Solution Appropriate?
Calculations of non-characteristic harmonics from power converters. Calculation of harmonic instability and harmonic interactions between power converters and the converter control. Harmonic filter design and harmonic mitigation studies. The effect of harmonics on equipment and protection devices. Real time digital simulations-RTDS of harmonics such as hardware-in-loop simulations. 中正--電力品質實驗室

Accuracy of Time Domain Simulation v. Direct Methods
The time response of the system must arrive at a periodic steady state. Quasi periodic or aperiodic response possible under non-linear feedback control. Sampling and integration errors. The sampling step is dictated by the highest harmonic order of interest. Modeling errors approximating the non-linear characteristic of certain apparatuses (e.g. transformer magnetization and arrester v-i characteristics) 中正--電力品質實驗室

What are the General Characteristics of a Time Domain Solution Procedure?
Slow Transient Modeling. May use programs such as EMTP, PSCAD, and SIMULINK. May incorporate local controls of power converters. Describe a limited part of the system around the harmonic source. Run simulation until steady state  Use FFT within the last simulation cycle to compute harmonics. 中正--電力品質實驗室

Modeling Approach Harmonic Sources Power Converters Non-Linear Devices
Detail representation including grid control and, possibly, higher level control loops. Equivalency: Represent as rigid source. Non-Linear Devices Transformer magnetizing and inrush current. Arrester current in over-voltage operation. Background harmonics: Rigid source representation. 中正--電力品質實驗室

Power Converters: Detail Representation
Detail Valve model Surge arrester representation in studies of harmonic overvoltages Representation of the grid control 中正--電力品質實驗室

Power Converters: Switching Function
Voltage-Sourced inverters are more suitable for this representation. Switching function approach: Voltage: Current: 中正--電力品質實驗室

Non-Linear Devices: Transformer
Piece-wise Linear representation of the core inductance. Switching inductance model (flux controlled switches). 中正--電力品質實驗室

Formulation of the Network Equations
Pre-integrated Components: Algebraic Equations State Equations: Numerical Integration Piece-wise Linear Equations Time Varying Equations 中正--電力品質實驗室

Summary of The Time Domain Procedure

SIMULINK Demonstrations
Converter Simulation Using the Switching Function Non-Linear Resistor Rigid Harmonic Source Impedance Measurement Network Equivalency 中正--電力品質實驗室

Converter Simulation Through the Switching Function
Linear Network. Insert the converter as: Voltage source on ac side. Current source on dc side. Incorporate high level converter controls. 中正--電力品質實驗室

Example of Non-Linear Resistor Using User-Defined Functions
Voltage Controlled Element: Parasitic capacitance C’ User-defined function describing the i(v) function 中正--電力品質實驗室

Rigid Harmonic Source Using the s-Function
S-Function: Calculation of the harmonic current: Simulation time slows down with increasing order N 中正--電力品質實驗室

Impedance Scans Using Rigid Harmonic Sources
Basic assumptions: Linear Network Model. Single driving point (e.g. location of harmonic source). The harmonic source is represented by a rigid current source at pre-defined harmonic orders. Driving point impedance Transfer impedance Procedure: Inject positive, negative, or zero sequence current separately at unit amplitude; Arrive at steady state Obtain bus voltage Apply FFT Driving point impedance Transfer Impedance 中正--電力品質實驗室

Impedance Scan: Transfer Function Method
Basic Assumptions The impedance is defined as a current-to-voltage network (transfer) function: Network is driven by a signal-controlled current source. More than one inputs can be used. Procedure Define network as a subsystem; Define the controlling signals of the current sources as the inputs; Define the voltages at the buses of interest as the outputs; Use the LTI tool box to obtain the driving and transfer impedances. 中正--電力品質實驗室

Impedance Scan: Transfer Function Method—Example
Inputs: Signal node 1 (array input: number of input signals is three). Outputs: Voltage at network nodes 1, 2, and 3 (each is an array of three). Voltage is measured by the voltmeter or the multimeter block 中正--電力品質實驗室

Network Equivalency It is often desirable to represent a part of the network (referred to as the external network) by a reduced bus/element equivalent preserving the impedance characteristic at one or more buses (interface or interconnection buses). The part of the network that is of interest can be represented in detail. 中正--電力品質實驗室

Network Equivalency Using SIMULINK
The procedure replaces the external network by a TF block representing the driving point impedance at the interface bus. The TF block is embedded into the network of interest: Drive the block input by the interface bus voltage; Connect the block output to the input of a signal driven current source; Connect the current source to the interface bus; 中正--電力品質實驗室

Network Equivalency: Example
Method becomes cumbersome for multiple interface buses. Mutual phase impedances are omitted. 中正--電力品質實驗室

Summary Time domain harmonic computation is useful in cases where detail modeling of the harmonic source is required; The modeling approach is the same as the slow transient modeling approach; The size of the network simulated is limited to a few buses around the harmonic source; Software like SIMULINK combine several useful features that can provide insight into a problem, especially for educational purposes. 中正--電力品質實驗室

Chapter 9 Case Studies Presenter: Paulo F Ribeiro
Tutorial on Harmonics Modeling and Simulation Presenter: Paulo F Ribeiro Contributors: J. Wikston, E. Gunther, and M. Grady 中正--電力品質實驗室

Case 1 Simulation of the potential harmonic impacts caused by DC motor drives of ski lifts in a ski area 中正--電力品質實驗室

Single Line Diagram 中正--電力品質實驗室

Scenarios Scenario SKIA. No Corrections.
Scenario SKIB. 30° phase shifting transformers added at Apollo and BigBoss ASDs. Scenario SKIC. Case SKIB, plus 1800 kVAr of filters. 中正--電力品質實驗室

SKIA, Voltage Waveform and Spectrum at Bus #1, Substation 12
SKIA, Voltage Waveform and Spectrum at Bus #1, Substation 12.5 kV (THDV = 12.2%) 中正--電力品質實驗室

SKIB, Voltage Waveform and Spectrum at Bus #6, Base (THDV = 8.7%)

SKIC, Voltage Waveform and Spectrum at Bus #6, Base (THDV = 2.7%)

Case 2 Harmonics and interharmonics, the filter design, and design verification measurements associated with an industrial load 中正--電力品質實驗室

Introduction The load and compensation Measurements Filter design
Performance measurements 中正--電力品質實驗室

Load and Compensation 6 pulse load
Characteristic harmonic orders are n*p +/- 1 Initial design 5th and 7th on MV bus 中正--電力品質實驗室

Measurements - Voltage Distortion

Measurements – 200 ms window

Measurements - Interharmonics

Filter Design Type of filter Location of filter 中正--電力品質實驗室

Filter Types 中正--電力品質實驗室

Filter Location Utility bus Secondary of customers step-down
Fault level reduced to ½ Utility bus impedance 100% variation Secondary of customer step-down 50% 中正--電力品質實驗室

Performance Measurements

Case 3 Analysis of harmonic impacts of variable frequency drives to the system 中正--電力品質實驗室

SuperHarm model one-line diagram

Predicted voltage waveform distortion without filters

Predicted voltage waveform distortion at Bus I with power factor correction capacitors

Tutorial on Harmonics Modeling & Simulation

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