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None-Linear Loads – Power Electronics Circuits
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None-Linear Loads – Power Electronics Circuits
Example of Distortion current
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Explore the impact of harmonic content in modern electrical loads due to nonlinear characteristics, decomposition into Fourier series, effects on power systems, regulatory standards, and analysis of power supply systems. Discover the evolution from linear to nonlinear loads driven by semiconductor advancements.
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Presentation Transcript
EEL 5245 POWER ELECTRONICS I EEL 5245 POWER ELECTRONICS I Lecture Lecture #11 Ch 3:Non Ch 3:Non- -Sinusoidal Systems and Harmonics Sinusoidal Systems and Harmonics Overview Overview #11
Discussion Topics Discussion Topics Real World Power System Data Real World Power System Data What is its harmonic content? And why? What is its harmonic content? And why? Decomposition of non Decomposition of non- -sinusoidal waveforms into sinusoidal waveforms into Fourier Series Fourier Series Significant Effects of Harmonics on Power System Significant Effects of Harmonics on Power System Power Parameters for Non Power Parameters for Non- -sinusoidal Systems Harmonics in Three Phase Systems Harmonics in Three Phase Systems Regulatory Standards for Harmonic Content Regulatory Standards for Harmonic Content PC Power Supply Analysis PC Power Supply Analysis sinusoidal Systems
Nature of Modern Electrical Loads Nature of Modern Electrical Loads Historically, electrical loads in the power system were Historically, electrical loads in the power system were predominately linear (purely sinusoidal input voltage predominately linear (purely sinusoidal input voltage draws a sinusoidal current in a linear load) draws a sinusoidal current in a linear load) Incandescent lighting, motor loads (cooling) Incandescent lighting, motor loads (cooling) Semiconductor advances paved the way for boom in Semiconductor advances paved the way for boom in electronic equipment electronic equipment development development PC, laptops, iPhones, Audio/Video Equipment, PC, laptops, iPhones, Audio/Video Equipment, Lighting Controls, etc. Lighting Controls, etc. These electronic loads are generally nonlinear (purely These electronic loads are generally nonlinear (purely sinusoidal line voltage draws distorted, non sinusoidal line voltage draws distorted, non- -sinusoidal, line current) line current) The nonlinear load means the current waveform, while The nonlinear load means the current waveform, while periodic, is not sinusoidal and has harmonics periodic, is not sinusoidal and has harmonics Harmonic content is a result of proliferation of nonlinear Harmonic content is a result of proliferation of nonlinear loads in the modern power system. loads in the modern power system. sinusoidal,
Nature of Modern Electrical Loads Nature of Modern Electrical Loads Real Data Examples Real Data Examples Note Note- - Voltage nearly sinusoidal, Voltage nearly sinusoidal, Current moderately distorted Current moderately distorted
Harmonic Content of Harmonic Content of Full Full- -Wave Rectifier Wave Rectifier with Filtering Cap with Filtering Cap Most electronic loads Most electronic loads employ a employ a peak detection peak detection rectifier rectifier at their front end at their front end Source current present only Source current present only when input sinusoidal when input sinusoidal exceeds DC voltage across exceeds DC voltage across capacitor capacitor
Linear Loads RL Circuits (b) Phasor Diagram (a) Simple Liner RL
None-Linear Loads Power Electronics Circuits (a) Source voltage and current (b) Distortion current
None-Linear Loads Power Electronics Circuits Example of Distortion current
Fourier Analysis for Fourier Analysis for Harmonics Calculation Harmonics Calculation = = + + + ( ) ... + + f t ( ) ( ) ( ( ) F F f t 1 f t f t 0 1 2 n sin n t + n t cos ) a b 0 n n = n Where constant Fo and the coefficients an and bn given by, T 2 = T ( ) cos = 1,2,3,..., a f t n tdt n T n 1 0 = ( ) F f t dt 0 T 0 T 2 = T ( ) sin = 1,2,3,..., b f t n tdt n n 0 Periodic waveforms can be resolved into an infinite Periodic waveforms can be resolved into an infinite Fourier Series Fourier Series Series is comprised of a summation of pure sinusoids Series is comprised of a summation of pure sinusoids each with frequencies that are integer multiples of the each with frequencies that are integer multiples of the fundamental frequency of the periodic waveform fundamental frequency of the periodic waveform
Decomposition of Decomposition of v v & & i i into Harmonic Components Harmonic Components into = n = + + ( ) sin( ) i t I I n t s DC sn ni 1 = n = + + + + sin( ) sin( ) I I t I n t 1 1 DC s i sn ni 2 DC DC Fundamental Fundamental Component Component Harmonic Harmonic Components Components Component Component = n = + + ( ) sin( ) v t V V n t s DC sn nv 1 = n = + + + + sin( ) sin( ) V V t V n t 1 1 DC s v sn nv 2
Most Significant Most Significant Effects Harmonics in the Power System Harmonics in the Power System Effects of of Harmonics reduced True Power Factor (add to RMS but do no real Harmonics reduced True Power Factor (add to RMS but do no real work) work) Less of power system capacity available with no benefit Less of power system capacity available with no benefit EMI Created interferes with other equipment operation such as EMI Created interferes with other equipment operation such as communications signals and control electronics in other devices communications signals and control electronics in other devices Comm equipment doesn Comm equipment doesn t work well near harmonic generators t work well near harmonic generators Neutral Current in 3 Phase Wye connected systems can be larger Neutral Current in 3 Phase Wye connected systems can be larger than phase current causing overloaded conductors than phase current causing overloaded conductors Historically neutral conductors had been design with smaller Historically neutral conductors had been design with smaller ampacity than phase conductors ampacity than phase conductors Only high end metering devices detect harmonic content Only high end metering devices detect harmonic content If it doesn If it doesn t say t say True RMS True RMS it will read incorrectly for most it will read incorrectly for most electronic loads electronic loads Transformers and motors are subjected to additional heating due Transformers and motors are subjected to additional heating due to harmonics to harmonics K K- -Factor rated equipment for additional I^2*R Losses Factor rated equipment for additional I^2*R Losses
Harmonics in the Power System Harmonics in the Power System
Real Power and Harmonics Real Power and Harmonics
Real Power and Harmonics Real Power and Harmonics
Power Transfer Power Transfer Different Harmonics Different Harmonics ? ? ? ??? ??????? ?? 3? ? ? ? :??????????? ?? ? ? ? :???????????? ????? ? ??? ??????? ?????
Power Transfer Power Transfer Same Harmonics Same Harmonics ? ? :? ??? ??????? ?? 3? ? ? :? ??? ??????? ?? 3? ? ? :???????????? ????? ??? ??????? ?????
Example Example Average power calculation Average power calculation
Example Example Average power calculation( Average power calculation(con d con d) )
RMS Value of Nonlinear Waveform RMS Value of Nonlinear Waveform
Power Factor Definition Power Factor Definition
True Power Factor Definition True Power Factor Definition
Distortion Factor and THD Distortion Factor and THD
DF vs. THD DF vs. THD
Harmonics in Three Phase Systems Harmonics in Three Phase Systems
Harmonics in Three Phase Systems Harmonics in Three Phase Systems
Harmonics in Three Phase Systems Harmonics in Three Phase Systems
Harmonics in Three Phase Systems Harmonics in Three Phase Systems
Neutral Currents in 3 Phase, Neutral Currents in 3 Phase, Wye Connected Systems Wye Connected Systems Assuming a balanced load with no phase shift (V and I in phase) Assuming a balanced load with no phase shift (V and I in phase) Assuming line current composed of fundamental, 60Hz, and third Assuming line current composed of fundamental, 60Hz, and third harmonic, 180 Hz only (In practice other harmonics would be present harmonic, 180 Hz only (In practice other harmonics would be present Third harmonic set at 33% of fundamental current amplitude Third harmonic set at 33% of fundamental current amplitude Assume power system fully loaded such that phase conductors are Assume power system fully loaded such that phase conductors are rated for 100 A rated for 100 ARMS RMS
Neutral Currents in 3 Phase, Neutral Currents in 3 Phase, Wye Connected Systems Wye Connected Systems
Harmonics in Three Phase Systems Harmonics in Three Phase Systems
Standards Regulating Standards Regulating Harmonic Content Harmonic Content US MIL- -STD STD- -461B 461B US Military Standard (Mandatory) US Military Standard (Mandatory) Harmonic limits now enforced by all US Armed Harmonic limits now enforced by all US Armed Forces Forces International Electro International Electro- -technical Commission technical Commission Standard 555 Standard 555 European Standard (Mandatory) European Standard (Mandatory) Limits based on actual current values specified Limits based on actual current values specified by harmonic number by class of equipment by harmonic number by class of equipment IEEE 519 IEEE 519 US Suggested Guidelines by IEEE US Suggested Guidelines by IEEE Harmonic limits are based on the ratio of Harmonic limits are based on the ratio of fundamental component of load current to short fundamental component of load current to short circuit current at the utility interface point circuit current at the utility interface point US MIL
IEC 555: IEC 555: Class A limits Class A limits
IEEE IEEE- -519 Current Limits, 519 Current Limits, Low Voltage Systems Low Voltage Systems
IEEE IEEE- -519 voltage limits 519 voltage limits
PC Power Supply Analysis PC Power Supply Analysis To investigate the nature of Harmonics in the modern power To investigate the nature of Harmonics in the modern power system, the personal computer load is representative system, the personal computer load is representative Quantity in service increasing in residential, commercial, Quantity in service increasing in residential, commercial, and industrial use and industrial use Not uncommon to have an office area with many PCs Not uncommon to have an office area with many PCs PC Power supply is Switch Mode Power Supply (SMPS) PC Power supply is Switch Mode Power Supply (SMPS) with peak detection rectifier at front end for rectification with peak detection rectifier at front end for rectification Moderate harmonic generator Moderate harmonic generator For this analysis, experimental data is collected on a For this analysis, experimental data is collected on a Pentium 4 Dell Machine, 80Gb Hard Drive, 250W Power Pentium 4 Dell Machine, 80Gb Hard Drive, 250W Power Supply, and 19 Supply, and 19 CRT Monitor CRT Monitor Data is collected with a Fluke 41, Power Harmonics Data is collected with a Fluke 41, Power Harmonics Analyzer Analyzer
PC Power Supply Analysis PC Power Supply Analysis
PC Power Supply Analysis PC Power Supply Analysis
PC Power Supply Analysis PC Power Supply Analysis
Fourier Analysis for Fourier Analysis for Harmonics Calculation ( Harmonics Calculation ( = = + + + ( ) ... + + f t ( ) ( ) ( ( ) F F f t 1 f t f t 0 1 2 n sin n t + n t cos ) a b 0 n n = n T 2 = T ( ) cos = 1,2,3,..., a f t n tdt n n T 1 0 0 = ( ) F f t dt 0 T T 2 = T ( ) sin = 1,2,3,..., b f t n tdt n n 0 Periodic waveforms can be resolved into an infinite Periodic waveforms can be resolved into an infinite Fourier Series Fourier Series Series is comprised of a summation of pure sinusoids Series is comprised of a summation of pure sinusoids each with frequencies that are integer multiples of the each with frequencies that are integer multiples of the fundamental frequency of the periodic waveform fundamental frequency of the periodic waveform
Fourier Analysis for Fourier Analysis for Harmonics Calculation Harmonics Calculation + + = 1 0 ) ( t f F Book Correctio n + + ( ) ( ) ... ( ) f t f t f t 2 n = n = + ( cos( ) C C n t 0 n o n T 1 0 1 = b ( ) C f t dt 2 2 = + 1 tan ( ) n a j b a b 0 T n n n n a n Pay attention to Quadrant Trigonometric Form often used Trigonometric Form often used industrial test equipment uses this format industrial test equipment uses this format FFT function gives complex form, angle derived assumes a FFT function gives complex form, angle derived assumes a cosine function is used to recreate f(t) so Sine and Cosine not cosine function is used to recreate f(t) so Sine and Cosine not interchangeable without proper shifting interchangeable without proper shifting Note if function either even or odd, A Note if function either even or odd, An n reduces to either a b bn n (odd) and Theta (odd) and Thetan n is either 0 (even) or is either 0 (even) or - -90 (odd) reduces to either an n (even) or 90 (odd) (even) or
Use of Symmetry in Fourier Analysis Use of Symmetry in Fourier Analysis odd symmetry f(T)=-f(-T) Even symmetry f(t)=f(-t) Half-wave symmetry f(t)=-f(t+T/2) an=0 (for all n) / 2 T 4 = n tdt f t ( )sin b n T 0 bn=0 (for all n) / 2 T 4 T 0 = ( ) cos a f t n tdt n / 2 / 2 T T 4 4 0 0 n tdt n tdt f t ( )cos f t ( )sin n odd n odd T T = = a b n n 0 0 n even n even Odd and Half-wave symmetry f(t)=-f(t+T/2), f(t)=-f(-t) / 4 T 8 0 n tdt f t ( )sin n odd T an=0 (for all n) = b n 0 n even Even and Half-wave symmetry f(t)=-f(t+T/2), f(t)=f(-t) / 4 T 8 0 n tdt f t ( )cos n odd T bn=0 (for all n) = a n 0 n even
Observations on Symmetry Observations on Symmetry Can save alot of time Can save alot of time Converter circuit waveforms often not symmetric Converter circuit waveforms often not symmetric Converter input current and voltage generally has Converter input current and voltage generally has symmetry symmetry Odd and Half Wave very common Odd and Half Wave very common Be able to recognize this combination and its effect Be able to recognize this combination and its effect on Fourier Components on sight on Fourier Components on sight In Industrial Power System (on AC side of things, In Industrial Power System (on AC side of things, most everything is odd with half wave symmetry, so most everything is odd with half wave symmetry, so no even harmonics and no DC value no even harmonics and no DC value
