class: center, middle # EE-463 STATIC POWER CONVERSION-I # Diode Rectifiers ## Ozan Keysan ## [keysan.me](http://keysan.me) ### Office: C-113 <span class="meta">•</span> Tel: 210 7586 <!--- # Announcement ## Until next week: ### Please open a [GitHub](https://github.com/) account ### Read [basics](https://www.atlassian.com/git/tutorials/what-is-version-control) on version control ([and more](http://keysan.me/okst/)) ### Install Simulink (or any other program) and start practicing --> --- # Line Frequency Diode Rectifiers -- <img src="./images/ee463/rectifier_block.png" alt="Drawing" style="width: 800px;"/> --- # Line Frequency Diode Rectifiers ## Ideal Rectifier -- - ## Ripple free DC output -- - ## Sinusoidal (THD=0) input current -- - ## High Efficieny -- - ## Small Size (High Power Density) --- # Simplest Case: One diode with resistive load -- <img src="./images/ee463/one_diode_R.png" alt="Drawing" style="width: 600px;"/> ## Can you plot the voltage-current waveforms? -- ### What about the average voltage? --- # One Diode with R-L Load -- <img src="./images/ee463/one_diode_RL.png" alt="Drawing" style="width: 600px;"/> <!--- ## Let's plot the equivalent circuits --> --- # One Diode with R-L Load ## Diode continues to conduct for extended period <img src="./images/ee463/one_diode_RL_waveform.png" alt="Drawing" style="width: 600px;"/> --- # One Diode with R-L Load -- ## Diode continues to conduct for extended period: # Commutation! -- ## How does the average voltage change with commutation? -- ## It becomes smaller! --- # One Diode with back-emf (i.e. DC Motor) <img src="./images/ee463/one_diode_Ea.png" alt="Drawing" style="width: 600px;"/> ### Current starts flowing when vs > Ed --- # One Diode with back-emf (i.e. DC Motor) <img src="./images/ee463/one_diode_Ea_waveform.png" alt="Drawing" style="width: 600px;"/> --- # Single-Phase Diode Rectifier <img src="https://satkit.com/image/cache/catalog/products/einphasen-dioden-bruckengleichrichter-50a-1000v-kbpc5010-neu-electronic-tools-a5029-700x700.jpg" alt="Drawing" style="width: 300px;"/> <img src="https://cdn-reichelt.de/bilder/web/xxl_ws/A400/GENERAL-SEMICONDUCTORS-GBU8M.png" alt="Drawing" style="width: 200px;"/> ## Commercial Bridge Rectifiers --- # Single-Phase Diode Rectifier <img src="./images/ee463/single_phase_diode.png" alt="Drawing" style="width: 600px;"/> ## Let's assume ideal source (Ls=0) to start with --- # Single-Phase Diode Rectifier ### Also assume load draws constant current (id) -- <img src="./images/ee463/bridge_rectifier_id.png" alt="Drawing" style="width: 500px;"/> --- # Single-Phase Diode Rectifier ### You can redraw it as: <img src="./images/ee463/redrawn_single_phase_rectifier.png" alt="Drawing" style="width: 500px;"/> --- # Single-Phase Diode Rectifier ## Can you calculate the average output voltage? -- ## Can you plot the input current waveform? -- ## What about the THD of input current? --- # Single-Phase Diode Rectifier <img src="./images/ee463/bridge_rectifier_is.png" alt="Drawing" style="width: 800px;"/> ## THD of current (square waveform)= -- \\(\frac{\sqrt{1-\frac{2\sqrt{2}}{\pi}^2}}{\frac{2\sqrt{2}}{\pi}}\\) --- # Single-Phase Diode Rectifier <img src="./images/ee463/bridge_rectifier_is.png" alt="Drawing" style="width: 800px;"/> ## THD of current (square waveform)= \\(\frac{\sqrt{0.19}}{0.9}=0.484\\) --- # Short Review of Fourier Series -- > ## All waveforms, no matter what you scribble or observe in the universe, are actually just the sum of simple sinusoids of different frequencies. --- # Fourier Series <img src="./images/ee463/fourier.gif" alt="Drawing" style="width: 400px;"/> [Interactive Fourier Series](./fourier.html), [Complex Orbits](https://www.youtube.com/watch?v=QVuU2YCwHjw), [Singing Train](https://www.youtube.com/watch?v=tNxh2bMWPOQ), [Useful applets](http://www.falstad.com/fourier), [Fourier examples](http://ptolemy.eecs.berkeley.edu/eecs20/week8/examples.html), [Tone Generator](https://onlinetonegenerator.com/) [More Useful Links on Fourier Series](http://keysan.me/explained/) --- # Fourier Series ### \\( f(x)= a\_{0} + \sum\_{n=1 }^{\infty }a\_{n}\cos (n x) + \sum\_{n=1 }^{\infty }b\_{n}\sin (n x) \\) -- ### \\( a\_{0} = \dfrac{1}{2 \pi } \int\limits\_{- \pi}^{\pi} f(x) dx\\) ### \\( a\_{n} = \dfrac{1}{ \pi } \int\limits\_{- \pi}^{\pi} f(x)cos(nx) dx\\) ### \\( b\_{n} = \dfrac{1}{ \pi } \int\limits\_{- \pi}^{\pi} f(x)sin(nx) dx\\) --- # Some Important Functions -- ### Even function: -- \\(f(-t)=f(t)\\) -- \\(\rightarrow b_h=0\\) -- ### Odd function: -- \\(f(-t)=-f(t)\\) -- \\(\rightarrow a_h=0\\) -- ### Half-wave symmetry: -- \\(f(t)=-f(t+T/2)\\) -- ### \\(\rightarrow a_h=b_h=0\\) for even harmonics -- ### Even quarter-wave: -- Even function and Half-wave symmetry -- ### \\(\rightarrow b_h=0\\) for all harmonics ### \\(\rightarrow a_h=0\\) for even harmonics --- # Effect of Line Inductance -- <img src="./images/ee463/bridge_rectifier_Ls.png" alt="Drawing" style="width: 500px;"/> ## Can you still draw square current from grid? -- ### There has to be finite time between +Id to -Id transition. --- # Let's start with a simple circuit -- <img src="./images/ee463/single_phase_commutation.png" alt="Drawing" style="width: 500px;"/> -- ### Draw the equivalent circuits at each interval --- ### Voltage Waveforms -- <img src="./images/ee463/commutation_2_diode.png" alt="Drawing" style="width: 800px;"/> --- ## How to calculate the commutation period (u)? -- ## \\(cos(u) = 1- \dfrac{\omega L_s I_d}{\sqrt{2} V_s}\\) -- - ## Ls, Id increases commutation time -- - ## Vs reduces commutation time --- ## How does the average voltage changes? -- ## \\(Vd= \dfrac{0.9 Vs}{2} - \dfrac{Au}{2\pi}\\) -- ## Reduction in average voltage ## \\(\Delta Vd= \dfrac{\omega Ls}{2\pi} Id\\) --- ## What about commutation in single phase rectifier? <img src="./images/ee463/bridge_rectifier_Ls.png" alt="Drawing" style="width: 500px;"/> --- ## Voltage-Current Waveforms <img src="./images/ee463/1ph_rectifier_commutation.png" alt="Drawing" style="width: 650px;"/> --- ## How does the average voltage changes? -- ## Similar to previous case,but: - ## Current goes from -Id to Id - ## Commutation happens twice (2Au) -- ## \\(Vd= 0.9 Vs - \dfrac{2 \omega Ls}{\pi} Id\\) --- # Rectifier with DC Side Voltage -- <img src="./images/ee463/rectifier_Vdc.png" alt="Drawing" style="width: 650px;"/> --- # Can you plot the voltage waveforms? -- <img src="./images/ee463/rectifier_Vdc_voltage.png" alt="Drawing" style="width: 700px;"/> --- # Average current ## \\(Id\_{av}= \dfrac{\int_b^f i(\theta) d \theta}{\pi} \\) -- ## What is the short circuit current (when Vd=0)? -- ## \\(Id\_{(short-circuit)} = \dfrac{Vs}{\omega Ls}\\) --- <!--- ## How does the average current changes with Vd? <img src="./images/ee463/rectifier_Vd_Id.png" alt="Drawing" style="width: 700px;"/> ## What about THD vs Id current? <img src="./images/ee463/rectifier_Id_THD.png" alt="Drawing" style="width: 750px;"/> ## Crest Factor vs Id current? <img src="./images/ee463/rectifier_Id_crest.png" alt="Drawing" style="width: 750px;"/> ---> # Some Alternative Topologies --- # Centre-Tap Rectifier -- <img src="https://instrumentationtools.com/wp-content/uploads/2016/07/instrumentationtools.com_center-tapped-full-wave-rectifier-operation.png" alt="Drawing" style="width: 800px;"/> --- # Centre-Tap Rectifier <img src="http://hyperphysics.phy-astr.gsu.edu/hbase/Electronic/ietron/rectct2.gif" alt="Drawing" style="width: 800px;"/> --- # Centre-Tap Rectifier ## Can you compare it with the full-bridge rectifier? #### in terms of: -- - ### Number of Diodes (and ratings) -- - ### Cost -- - ### Current Waveform --- ## Voltage Doubler Rectifier -- <img src="https://www.lifewire.com/thmb/uU0d3vCrHp2VupSwak7Du5Il0QI=/768x0/filters:no_upscale():max_bytes(150000):strip_icc()/sentey-xpp-series-psu-56a6fa135f9b58b7d0e5cdf5.jpg" alt="Drawing" style="width: 600px;"/> --- ## Voltage Doubler Rectifier -- <img src="./images/ee463/voltage_doubler.png" alt="Drawing" style="width: 750px;"/> --- #Quiz -- ### Many single-phase rectifiers are connected to three phase system. ### Can you plot the neutral line current? --- ## Effects of Single Phase Rectifiers -- - ## Voltage Waveform (Notching) -- - ## Neutral Line Current -- - ## THD --- ## Effects of Single Phase Rectifiers ## Current Distortion <img src="./images/ee463/current_distortion.png" alt="Drawing" style="width: 750px;"/> --- ## Effects of Single Phase Rectifiers ## Line Voltage Distortion <img src="./images/ee463/line_voltage_distortion.png" alt="Drawing" style="width: 750px;"/> --- ## Effects of Single Phase Rectifiers ## Neutral Line Current <img src="./images/ee463/neutral_line_current.png" alt="Drawing" style="width: 750px;"/> --- ## You can download this presentation from: [keysan.me/ee463](http://keysan.me/ee463)