2024-10-18 Share: EE-464 Statics Power Conversion-II other PWM Techniques
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<!DOCTYPE html> <html> <head> <title>EE464-Static Power Conversion-II</title> <meta http-equiv="Content-Type" content="text/html; charset=UTF-8"/> <style type="text/css"> @import url(https://fonts.googleapis.com/css?family=Yanone+Kaffeesatz); @import url(https://fonts.googleapis.com/css?family=Droid+Serif:400,700,400italic); @import url(https://fonts.googleapis.com/css?family=Ubuntu+Mono:400,700,400italic); body { font-family: 'Droid Serif'; } h1, h2, h3 { font-family: 'Yanone Kaffeesatz'; font-weight: normal; } .remark-code, .remark-inline-code { font-family: 'Ubuntu Mono'; } </style> </head> <body> <textarea id="source"> class: center, middle # EE-464 STATIC POWER CONVERSION-II # Other PWM Techniques ## Ozan Keysan ## [keysan.me](http://keysan.me) ### Office: C-113 <span class="meta">•</span> Tel: 210 7586 --- # Hysteresis (Bang-Bang) PWM -- ## You already implemented in the first semester <img src="./images/ee464/hysteresis_pwm.png" alt="Drawing" style="width: 600px;"> --- # Hysteresis (Bang-Bang) PWM ### If your current is higher than your reference, reduce the current (switch off), if not increase the current (Switch ON) <img src="./images/ee464/hysteresis_pwm.png" alt="Drawing" style="width: 600px;"> --- # Hysteresis (Bang-Bang) PWM ### For an inverter, just change your reference current to a sinusoidal waveform instead of a constant reference. <img src="./images/ee464/hysteresis_pwm2.png" alt="Drawing" style="width: 500px;"> --- # Hysteresis (Bang-Bang) PWM -- - ## The switching frequency is varying -- - ## Difficult to design filter (because of varying fs) -- - ## Can induce side-band harmonics -- - ## Simple control and implementation --- # Hysteresis (Bang-Bang) PWM <img src="https://www.researchgate.net/profile/Michal_Knapczyk/publication/228659032/figure/fig3/AS:393882949963776@1470920421181/The-idea-and-control-signals-of-Hysteresis-Band-PWM.png" alt="Drawing" style="width: 550px;"> --- # Field Oriented Control (FOC) -- <img src="https://www.roboteq.com/images/article-images/how-to/image014.png" alt="Drawing" style="width: 550px;"> - ### [What is FOC?](https://www.youtube.com/watch?v=Nhy6g9wGHow) - ### [Field oriented Control of PM Motors](https://www.youtube.com/watch?v=cdiZUszYLiA) --- ## How to aim to a moving target? -- <img src="https://cdn.shopify.com/s/files/1/0264/5540/8674/files/carrot_and_donkey_large.jpg" alt="Drawing" style="width: 600px;"> --- # A Few Useful Mathematical Tools -- - ## Clarke Transformation - ## Park Transformation --- # [Clarke](https://en.wikipedia.org/wiki/Edith_Clarke) Transformation ## (a-b-c) to \\(\alpha \beta \\) Transformation ## From three-phase to two orthogonal phase transformation -- ### Main Idea: In a balanced three-phase system, \\(I_a + I_b + I_c =0\\) so there is redundant information and system can be reduced to two variables. --- ##How do you define the resultant (black) phasor? <img src="./images/rotating_mmf_phasor2.gif" alt="Drawing" style="width: 800px;"> --- # Clarke Transformation <img src="https://www.keil.com/pack/doc/CMSIS/DSP/html/clarke.gif" alt="Drawing" style="width: 600px;"/> --- # Clarke Transformation <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/36e05ba56ec15de753eb9f3c60983bc874e31370" alt="Drawing" style="width: 750px;"/> --- # Park Transformation ## (or D-Q Transformation) --- # Park Transformation in Space <iframe width="700" height="400" src="https://www.youtube-nocookie.com/embed/c4tPQYNpW9k" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe> ### i.e. [Interstellar - Docking Scene](https://www.youtube.com/watch?v=c4tPQYNpW9k) --- # Park Transformation -- ## From rotating frame to stationary frame -- ## Instead of dealing with sinusoidal signals, just use the magnitudes. -- ## When re-constructing signals use the rotor position information --- # Park Transformation <img src="https://static1.squarespace.com/static/584729023e00bebf8abd6ba0/t/58664f0f2994ca78b5145f29/1483099927549/?format=750w" alt="Drawing" style="width: 750px;"/> --- # Park Transformation -- <img src="./images/ee462/park_transform.png" alt="Drawing" style="width: 400px;"/> -- ## \\(I\_d = I\_\alpha cos(\theta) + I\_\beta sin (\theta)\\) -- ## \\(I\_q = I\_\beta cos(\theta) - I\_\alpha sin (\theta)\\) -- --- ## Reference Frames <img src="./images/ee462/reference_frames.png" alt="Drawing" style="width: 750px;"/> --- ## Clarke and Park Transformations <img src="https://static1.squarespace.com/static/584729023e00bebf8abd6ba0/t/5866535e414fb5c4d35ed4cb/1483101083243/ClarkePark_Animation?format=500w" alt="Drawing" style="width: 500px;"/> --- # Torque and Flux Control # Id: Proportional to flux in the air-gap # Iq: Proportional to torque generated --- # Inverse Transforms -- ## Required to apply reference voltage and current waveforms (sinusoidals) -- - ## Inverse Park Transform - ## Inverse Clarke Transform --- # Inverse Park Transform -- ## From rotation frame to stationary frame -- ## \\(I\_\alpha = I\_d cos(\theta) - I\_q sin (\theta)\\) -- ## \\(I\_\beta = I\_q cos(\theta) + I\_d sin (\theta)\\) --- ## Inverse Clarke Transform ### From two-axis orthogonal plane to 3-phase stationary frame. <img src="http://e2e.ti.com/cfs-file/__key/communityserver-discussions-components-files/171/3750._F764D653_.JPG" alt="Drawing" style="width: 500px;"/> --- ## Whole Workflow <img src="https://static1.squarespace.com/static/584729023e00bebf8abd6ba0/t/58c88acd579fb3efb64797c9/1489537751460/?format=1000w" alt="Drawing" style="width: 750px;"/> <img src="./images/ee464/foc_workflow.png" alt="Drawing" style="width: 600px;"/> --- # Classical Vector Control Diagram <img src="https://www.ednasia.com/wp-content/uploads/sites/3/2021/07/FOC2_photos_v2_x2_colored-e1624401752113.png" alt="Drawing" style="width: 700px;"/> --- # Vector Control in PMSM <img src="http://www.mdpi.com/sensors/sensors-17-00973/article_deploy/html/images/sensors-17-00973-g007.png" alt="Drawing" style="width: 750px;"/> --- # Vector Control in Induction Motors <img src="https://in.mathworks.com/help/sps/powersys/ug/electric_drives223.gif" alt="Drawing" style="width: 600px;"/> --- # Summary <img src="./images/ee464/donkey.png" alt="Drawing" style="width: 600px;"/> --- # Further Reading ### [Vector Control for Dummies](https://www.switchcraft.org/learning/2016/12/16/vector-control-for-dummies) ### [What is Field Oriented Control?](https://www.eetimes.com/document.asp?doc_id=1279321) ### [Field Oriented Control](http://mycourses.aalto.fi/pluginfile.php/1055633/mod_resource/content/12/Lecture10.pdf) ### [Field Oriented Control of AC Motors](http://www.ti.com/lit/an/bpra073/bpra073.pdf) ### [Sensorless PMSM Field Oriented Control](http://cache.nxp.com/assets/documents/data/en/reference-manuals/DRM148.pdf) ### [Space Vector PWM](https://www.switchcraft.org/learning/2017/3/15/space-vector-pwm-intro) --- # 3-Phase Two-Level Inverter -- <img src="./images/ee464/two_level_vsi.png" alt="Drawing" style="width: 800px;"> ### Anti-parallel diodes are not shown. --- # 3-Phase Two-Level Inverter <img src="./images/ee464/two_level_vsi_simple.png" alt="Drawing" style="width: 800px;"> ## Each leg has two positions: -- top switch closed (1) --- # 3-Phase Two-Level Inverter <img src="./images/ee464/two_level_vsi_simple.png" alt="Drawing" style="width: 800px;"> ## Each leg has two positions: -- bottom switch closed (0) --- # [Voltage Vectors](https://www.switchcraft.org/learning/2017/3/15/space-vector-pwm-intro) -- <img src="./images/ee464/voltage_vectors.png" alt="Drawing" style="width: 600px;"> --- ### 000 - \\(v_0\\) (zero vector) ### 001 - \\(v_1\\) (Phase +U) ### 010 - \\(v_2\\) (Phase +V) ### 011 - \\(v_3\\) (Phase -W) ### 100 - \\(v_4\\) (Phase +W) ### 101 - \\(v_5\\) (Phase -V) ### 110 - \\(v_6\\) (Phase -U) ### 111 - \\(v_7\\) (zero vector) --- # Voltage Vectors: V0 <img src="./images/ee464/v0.png" alt="Drawing" style="width: 750px;"> --- # Voltage Vectors: V1 <img src="./images/ee464/v1.png" alt="Drawing" style="width: 750px;"> --- # Voltage Vectors: V2 <img src="./images/ee464/v2.png" alt="Drawing" style="width: 750px;"> --- # Voltage Vectors: V3 <img src="./images/ee464/v3.png" alt="Drawing" style="width: 750px;"> --- # Voltage Vectors: V4 <img src="./images/ee464/v4.png" alt="Drawing" style="width: 750px;"> --- # Voltage Vectors: V5 <img src="./images/ee464/v5.png" alt="Drawing" style="width: 750px;"> --- # Voltage Vectors: V6 <img src="./images/ee464/v6.png" alt="Drawing" style="width: 750px;"> --- # Voltage Vectors: V7 <img src="./images/ee464/v7.png" alt="Drawing" style="width: 750px;"> --- # Square Wave Operation <img src="https://media.giphy.com/media/aFdKsSmSHbLtC/giphy.gif" alt="Drawing" style="width: 800px;"> ### [BLDC Drive with square wave](https://www.youtube.com/watch?v=IiY01xIKg28) --- ## What about the vectors in between? -- <img src="./images/rotating_mmf_sine.gif" alt="Drawing" style="width: 750px;"> --- ## What about the vectors in between? <img src="./images/rotating_mmf_phasor.gif" alt="Drawing" style="width: 600px;"> --- ## What about the vectors in between? <img src="./images/rotating_mmf_phasor2.gif" alt="Drawing" style="width: 800px;"> --- # Voltage Synthesizing <img src="https://static1.squarespace.com/static/584729023e00bebf8abd6ba0/t/58fea6c8ebbd1a25ce89c905/1494287982183/Basic-Vectors-with-reference.png?format=500w" alt="Drawing" style="width: 500px;"/> --- # Voltage Synthesizing <img src="https://static1.squarespace.com/static/584729023e00bebf8abd6ba0/58fea923197aea4f7f28f61a/58fea9286a49632401d63e94/1493084598485/SVPWM-1.png?format=1000w" alt="Drawing" style="width: 700px;"/> --- # PWM Generation <img src="https://static1.squarespace.com/static/584729023e00bebf8abd6ba0/t/59110ff0ebbd1a1c7143886d/1494290426838/?format=1000w" alt="Drawing" style="width: 700px;"/> --- # PWM Generation <img src="https://static1.squarespace.com/static/584729023e00bebf8abd6ba0/t/59111028c534a5947d523098/1494290481944/?format=1000w" alt="Drawing" style="width: 550px;"/> ### Switching Sequence: 000-001-011-111 --- # PWM Generation ## Switching Sequence: - ## Zero Vector (000) -- - ## Basic Vector (i.e. 001) -- - ## Basic Vector (i.e. 011) -- - ## Zero Vector (i.e. 111) -- ## Only one switch position is changed at each step! --- # PWM Generation <img src="https://static1.squarespace.com/static/584729023e00bebf8abd6ba0/t/58feacf5d482e9da38497463/1493085606567/?format=1000w" alt="Drawing" style="width: 700px;"/> --- ## SPWM vs SVPWM -- <img src="./images/ee464/spwm_svpwm.png" alt="Drawing" style="width: 450px;"> #### Phase Voltages --- ## SPWM vs SVPWM -- - ## Space Vector PWM generates less harmonic distortion -- - ## Space Vector PWM utilizes input voltage more \\(1/2\\) vs \\(1/\sqrt{3}\\) (15% more) --- ### What is the max. possible phase voltage with SPWM (Sinusoidal PWM)? -- <img src="./images/ee464/spwm.jpg" alt="Drawing" style="width: 400px;"/> -- ### \\(\hat{V}\_{p-n}=\dfrac{V\_{DC}}{2}\\) --- ### What is the max. possible phase voltage with SPWM (Sinusoidal PWM)? -- ### The inverter is connected to 400 \\(V\_{l-l}\\) grid with a 3-ph diode rectifier: <img src="./images/ee464/vfd.jpg" alt="Drawing" style="width: 500px;"/> -- ### \\(V\_{DC}=\\) -- \\(\dfrac{3\sqrt{2}}{\pi} V\_{l-l} \\) -- \\(= 1.35 V\_{l-l} = 540 V\\) --- ### What is the max. possible phase voltage with SPWM (Sinusoidal PWM)? -- <img src="./images/ee464/vfd.jpg" alt="Drawing" style="width: 500px;"/> -- ### Maximum motor phase voltage: -- ### \\( V\_{phase-rms} = \dfrac{V\_{DC}}{2 \sqrt{2}}= 190 V\\) ### which is quite low for standard motors! --- ## How can you increase the output voltage beyond the DC-link voltage limit? -- <img src="https://images3.memedroid.com/images/UPLOADED950/5bbcb4de55956.jpeg" alt="Drawing" style="width: 400px;"/> --- # Third Harmonic Injection (THIPWM) -- ### A sinusoidal reference voltage output: <img src="https://static1.squarespace.com/static/584729023e00bebf8abd6ba0/t/590687ddff7c50866d9f4f1d/1493600229378/?format=1000w" alt="Drawing" style="width: 800px;"/> --- # Third Harmonic Injection (THIPWM) ### Assume you apply a waveform like that: <img src="https://static1.squarespace.com/static/584729023e00bebf8abd6ba0/t/59068b67725e256add1f37f5/1493601135313/?format=1000w" alt="Drawing" style="width: 800px;"/> ### which composes of the fundamental and a third-harmonic component --- # Third Harmonic Injection (THIPWM) ### Such that \\(V = \dfrac{V\_{DC}}{2}\\) at \\(\pi/3\\) <img src="https://static1.squarespace.com/static/584729023e00bebf8abd6ba0/t/59068e15e6f2e142b4adbe4f/1493601820281/?format=1000w" alt="Drawing" style="width: 800px;"/> --- # Third Harmonic Injection (THIPWM) ### What is the phase voltage? <img src="https://static1.squarespace.com/static/584729023e00bebf8abd6ba0/t/590691aed1758ec4d7664141/1493602742473/ThirdHarmonics.png?format=500w" alt="Drawing" style="width: 500px;"/> #### Third harmonic cancels itself (common-mode voltage), the potential of the neutral votlage is oscillating, but the winding doesn't see this change and observe a pure sinusoidal. --- # Third Harmonic Injection (THIPWM) ### What is the phase voltage? ### THIPWM: \\( V\_{phase-rms} = \dfrac{V\_{DC}}{ \sqrt{6}}= 220 V\\) -- ### %15 higher than SPWM ### ( \\( V\_{phase-rms} = \dfrac{V\_{DC}}{2 \sqrt{2}}= 190 V\\)) --- # Third Harmonic Injection (THIPWM) <img src="./images/ee462/thipwm.gif" alt="Drawing" style="width: 800px;"/> --- ## How about SVPWM? -- ### What is the phase voltage for one of the SVPWM vectors? -- ### \\(\hat{V\_n} = \dfrac{2}{3}V\_{DC}\\) -- ### What if two adjacent vectors are applied for %50, %50? -- ### \\(= \dfrac{2}{3}V\_{DC} \dfrac{\sqrt{3}}{2} = \dfrac{1}{\sqrt{3}}V\_{DC}\\) ### Same with THIPWM: \\(V\_{ph,rms}= \dfrac{1}{\sqrt{6}}V\_{DC} = 220 V\\) --- ## How about SVPWM? ### Magnitude comparison of SPWM and SVPWM <img src="./images/ee464/svpwm_locus.png" alt="Drawing" style="width: 500px;"/> --- ### Magnitude comparison of SPWM and SVPWM ### Space Vector (SVPWM) ### Max. \\(V\_{l-l,rms} = \sqrt{3} \dfrac{\frac{V\_{dc}}{\sqrt{3}}}{\sqrt{2}}\\) -- \\(= \dfrac{V\_{dc}}{\sqrt{2}} = 0.707 V\_{dc}\\) -- ### Sinusoidal (SPWM) -- ### Max. \\(V\_{l-l,rms} = \sqrt{3} \dfrac{\frac{V\_{dc}}{2}}{\sqrt{2}}\\) -- \\(= \dfrac{ \sqrt{3} V\_{dc}}{2\sqrt{2}} = 0.612 V\_{dc}\\) ### SVPWM is %15 higher than SPWM --- ## You can download this presentation from: [keysan.me/ee464](http://keysan.me/ee464) </textarea> <script src="https://remarkjs.com/downloads/remark-latest.min.js" type="text/javascript"></script> <script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS_HTML&delayStartupUntil=configured" type="text/javascript"></script> <script type="text/javascript"> var slideshow = remark.create({countIncrementalSlides: false}); // Setup MathJax MathJax.Hub.Config({ tex2jax: { skipTags: ['script', 'noscript', 'style', 'textarea', 'pre'] } }); MathJax.Hub.Queue(function() { $(MathJax.Hub.getAllJax()).map(function(index, elem) { return(elem.SourceElement()); }).parent().addClass('has-jax'); }); MathJax.Hub.Configured(); </script> </body> </html>
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