Cascade Multilevel Inverters for Large Hybrid-Electric Vehicle Applications with Varying dc Sources by Tim Cunnyngham
Discussion Topics Large Hybrid-Electric Vehicle Applications Cascade Multilevel Inverters Research Objective Introduction to Research Approach Research Analysis, Methods, and Results Conclusions and Future Strategy
Large Hybrid-Electric Vehicles (HEV HEVs that require an average or continuous power that exceeds 50 kw Common applications are the electric and hybrid-electric transit bus Other applications include recreational vehicles, heavy-duty trucks, school buses, and military vehicles
Problems with Conventional Power Electronics More expensive and less reliable because dv/dt is considerably higher Semiconductor devices dissipate more heat due to higher switching losses Increased electromagnetic interference (EMI due to high frequency switching of popular pulse width modulation (PWM
Cascade Multilevel Inverters An alternative to conventional power electronics using pulse width modulation Reduces EMI by switching at the fundamental frequency Utilizes the individual batteries in an HEV to allow battery management and redundant switching The series structure allows scalability
Cascade Multilevel S S V a ( m V dc S 3 S 4 V an Inverter/Waveform S S V a ( m V dc S 3 S 4 5 g e a V ol t 0 Approximate Multilevel Waveform Des ired Waveform V a a V a dc S b a S -5 0 0. 0. 0.3 0.4 0.5 0.6 0.7 0.8 0.9 S 3 S 4 V a a V a dc S S 3 n S S 4 n S = Switch Representation
f f s MLI/w varying dc (a v s d s An illustration of an s-step multilevel waveform with varying step sizes. f d v d v π v π... v s v s s (b An example of a stepped waveform with s steps. 3 3 π 3 3 π s Figure 3-: Multilevel Waveforms.
Multilevel Waveform Fourier Series Invariant (equal unity dc sources f ( t = 4V π dc h= odd [ cos( h + cos( h + + cos( h ] s sin( hωt h Variant (unequal dc sources f ( t = 4 π h= odd [ v cos( h + v cos( h + + v cos( h ] s s sin( hωt h
Research Objectives Determine if the switching angles can be solved in real-time using a DSP chip Expand previous research to include variant dc sources Determine a method to sort the varying dc sources to: minimize total harmonic distortion (THD help balance the individual battery voltages
Research Approach Switching Angle Solution Methods Invariant dc sources Variant dc sources Miminizing Harmonics Harmonic Elimination Method Fixed Angle Sorting Method Harmonic Elimination Method
Research Approach Invariant unity dc Sources Minimizing Harmonics Harmonic Elimination Method (HEM Variant dc Sources Fixed Angle Sorting Method (FASM Harmonic Elimination Method
Minimizing Harmonics (Invariant This was used to solve for the switching angles that minimized THD = [ f ( t ] [ f ( t ] The angles were determined so that the total harmonic distortion was minimized. No control over the magnitude of the fundamental frequency component rms rms
Harmonic Elimination Method (Invariant Harmonic Elimination Method - the switching angles were solved to eliminate the 5th, 7th, th, 3th, etc. harmonics Must be used with a low-pass filter to remove the unwanted harmonics Maintains control over the fundamental frequency component for adjustable speed drives
Fixed Angle Sorting Method (Variant Angles were fixed to the values determined from the invariant HEM using unity dc sources The dc sources were perturbed and arranged using all possible combinations and then sorted by increasing THD This illustrated the waveform s THD variation by perturbing the dc sources
Harmonic Elimination Method (Variant The angles were computed to eliminate the specified harmonics and the THD was compared to the Fixed Angle Sorting Method and Invariant cases The magnitude of the fundamentalfrequency component can be controlled
Research Analysis and Methods Provide a detailed explanation and reason for the analysis techniques and methods that were used in the thesis Invariant (unity dc sources Minimizing Harmonics Harmonic Elimination Method (HEM Variant (unequal dc sources Fixed Angle Sorting Method Harmonic Elimination Method
Tools Required for Analysis Fourier Series: f 4Vdc ( t = π h= odd [ cos( h + cos( h + + cos( h ] s sin( hωt h h - odd harmonic order s - number of dc sources, or steps
Tools Required for Analysis RMS value of a multilevel waveform: π [ f ( t ] rms = Vdc s s k= (k k Fundamental RMS value: s V cos( k π k= dc [ f ( t ] rms =
Minimizing Harmonics (Invariant Total harmonic distortion: THD% = 00 [ f ( t ] [ f ( t ] Taking the partial derivative: rms rms THD n = (n s cos( + k k= k= s (k k πs sin( n n = 0 n is the n th switching angle
Minimizing Harmonics (Invariant Found the angles that minimized the total harmonic distortion Provided faster solutions using an iterative process for calculating the THD for a large number of steps
Minimizing Harmonics (Invariant The number of steps used to synthesize the multilevel waveform were increased and the THD calculated : 30 5 0 D v H T 5 0 5 0 0 5 0 5 0 5 30 35 40 steps
Harmonic Elimination Method (Invariant The system of equations were solved to eliminate the lower dominant harmonics: cos(7 cos( cos(3 cos(5 cos( + cos(5 + cos(7 + cos( + cos(3 + cos( + cos( + cos(5 + cos(7 + cos( + cos(3 3 + cos( + cos(5 + cos(7 + cos( + cos(3 + cos( + cos(5 + cos(7 + cos( + cos(3 = 0 = 0 = 0 = 0 V p is the peak magnitude of the fundamental frequency component 3 3 3 3 4 4 4 4 4 5 5 5 5 5 π = 4 V p
Harmonic Elimination Method (Invariant The nonlinear transcendental equations were solved using an iterative process The magnitude of the fundamental frequency component can be controlled by adjusting V p and determining the corresponding set of switching angles. Desired method when used with a low-pass filter
Comparison of the Two Methods (Invariant Minimizing Harmonics minimizes the total harmonic distortion magnitude of the fundamental component cannot be controlled Harmonic Elimination Method eliminates selected harmonics magnitude of the fundamental component can be controlled
Comparison of the Two Methods (Invariant 5-step waveform Minimizing Harmonics THD = 7.6% (without filtering V p = 5.973 (not adjustable Harmonic Elimination Method THD = 8.9% (without filtering V p = 5.973 (adjusted for comparison Switching angles < 5 degree difference
Fixed Angle Sorting Method (Variant The switching angles remained fixed The dc voltage sources were perturbed from unity to [ 0.90 0.95.00.05.0] volts The perturbed voltages were combined all possible ways which produced 0 different permutations Each permutation was sorted by increasing THD
Fixed Angle Sorting Method (Variant 0 THD vs. Sorted Permutations 9.5 9 D % TH 8.5 8 Des ired Arrangement 7.5 0 0 40 60 80 00 0 Sorted Permutations
Fixed Angle Sorting Method (Variant The THD actually decreased from 8.48% to 7.8% The desired arrangement for balancing the battery voltages: [.0.05.00 0.95 0.90] the batteries with the higher voltage would be assigned the longer duty cycles, and the batteries with the lower voltages, would assigned the shorter duty cycles
Harmonic Elimination Method (Variant The system of equations were solved to eliminate the lower dominant harmonics and help balance the battery voltage [v v v 3 v 4 v 5 ] = [.0.05.00 0.95 0.90] 0 cos(3 cos(3 cos(3 cos(3 cos(3 0 cos( cos( cos( cos( cos( 0 cos(7 cos(7 cos(7 cos(7 cos(7 0 cos(5 cos(5 cos(5 cos(5 cos(5 4 cos( cos( cos( cos( cos( 5 5 4 4 3 3 5 5 4 4 3 3 5 5 4 4 3 3 5 5 4 4 3 3 5 5 4 4 3 3 = + + + + = + + + + = + + + + = + + + + π = + + + + v v v v v v v v v v v v v v v v v v v v V v v v v v p
Switching Angles vs. V p 70 Switching Angles vs. V p 60 5 50 e s D egre - (s 40 30 4 A ngle 0 3 0 0 4.8 4.9 5 5. 5. 5.3 5.4 5.5 5.6 V p Varying V p from 4.85V to 5.45 V
Total Harmonic Distortion vs. V p 4 THD vs. V p 3 D H T 0 9 8 7 4.8 4.9 5 5. 5. 5.3 5.4 5.5 5.6 V p Varying V p from 4.85V to 5.45 V
Harmonic Elimination Method (Variant A good initial guess is required to find a solution for V p For a wide range of V p, another guess is required because some switching angles converge at the endpoints and the THD increases significantly Specified harmonics can be eliminated and when combined with a low-pass filter and three-phase systems results in a low THD
Brief Summary Switching Angle Solution Methods Invariant dc sources Variant dc sources Miminizing Harmonics Harmonic Elimination Method Fixed Angle Sorting Method Harmonic Elimination Method
Reducing the Number of Steps Reduces the number of steps used to synthesize the multilevel waveform Advantages Increases the range of operation while helping to balance and manage the battery voltages Increases system flexibility by allowing redundant operation and independent battery management Disadvantages The THD increases as the number of steps decreases
Reducing the Number of Steps The number of steps were reduced from 5 to 4, 3,, and using the invariant methods of analysis Fixed Angle Sorting Method Harmonic Elimination Method
Reducing the Number of Steps 0 THD v vs. V p 00 80 -step D v H T 60 3-step Alternative 4-step Alternative 5-step 40 4-step 5-step 0 -step 0 0.5.5.5 3 3.5 4 4.5 5 5.5 V p
Reducing the Number of Steps The transition points occur where the THD is the least for an overlapping region THD increased as the number of steps used to synthesize the waveform decreased When using 3 steps or less an alternative switching scheme like PWM can be used to keep the THD small
Three-Phase Analysis The triplin harmonics (3 rd, 9 th, 5 th, etc. are eliminated because each triplin harmonic forms three phasors of equal magnitude located at 0, 0, and 40 degrees. The nontriplin harmonics (5 th, 7 th, th, 3 th are eliminated by solving the system of equations for the switching angles
Three-Phase Analysis The line-to-line THD is very small when used with a low-pass filter to remove the upper harmonics and retain only the fundamental-frequency component Three independent multilevel inverters are required to produce the three phase-toneutral multilevel waveforms
Three-Phase Analysis (Assumptions Three five-step multilevel waveforms were used in a balanced three-phase system An ideal low-pass filter was used to remove all the harmonics above its cutoff frequency f c = hf s
Three-Phase Analysis 0 8 6 Phase and Line Voltages with an Ideal Low-Pass Filter v ab v a v b v c 4 g e a V ol t 0 - -4-6 -8-0 0 0. 0.4 0.6 0.8..4.6.8 t/π shown for h >3 th harmonic completely filtered
Three-Phase Analysis 0 8 6 Phase and Line Voltages with an Ideal Low-Pass Filter v ab v a v b v c 4 g e a V ol t 0 - -4-6 -8-0 0 0. 0.4 0.6 0.8..4.6.8 t/π h > st harmonic completely filtered
Three-Phase Analysis 6 Phase Voltage Ripple 4 Actual Des ired Sinusoid Voltage Ripple g e a V ol t 0 - -4-6 0 0. 0.4 0.6 0.8..4.6.8 t/π Ripple in the phase-to-neutral voltage (v an
Three-Phase Analysis 0 Line Voltage Ripple 8 6 4 Voltage Ripple g e a V ol t 0 - -4-6 -8-0 0 0. 0.4 0.6 0.8..4.6.8 t/π Ripple in the line-to-line voltage (v ab
THD Comparison Harmonics phase-neutral line-line THD THD 3.74 0 5.74 0 7.74 0 9 4.5386 0 4.5386 0 3 4.5386 0 5 4.59 0 7 4.7006.0043 9 5.639.369 5.373.369 3 5.3047.5079 5 6.304 4.300 7 6.6638 4.300 9 6.6688 4.377 3 6.7333 4.3386 33 6.8534 4.3386 35 7.805 4.9859 37 7.360 5.05 39 7.39 5.05
Conclusions A combination of multilevel-pulse-widthmodulated control was the method of choice for implementing the cascade multilevel inverter into large HEV drivetrains The batteries can be used balanced by assigning the higher battery voltages the longer duty cycle and the lower battery voltage the shorter duty cycles
Conclusions (Restatement of Research Objectives The switching angles cannot be solved in real-time using a DSP chip The previous research was expanded to include variant dc source analysis A method to sort the varying dc sources to ( minimize the THD, and ( help balance the individual battery voltages was developed
Future Research Suggestions Analyze the solution space for the switching angles over the range of variant dc sources Investigate an integrated control scheme to include a battery management system Explore a real-time implementation of the multilevel-pulse-width-modulated inverter
Summary Large Hybrid-Electric Vehicle Applications Cascade Multilevel Inverters Research Objective Introduction to Research Approach Research Analysis, Methods, and Results Conclusions and Future Strategy
Questions