1. Power Electronics and Power Conversion, Assiut University 1 Photovoltaic Systems Ahmed G. Abo-Khalil

2. Power Electronics and Power Conversion, Assiut University 2 Components of PV Systems

3. Power Electronics and Power Conversion, Assiut University 3 Electrical Equivalent Circuit PV Cells

4. Power Electronics and Power Conversion, Assiut University 4 I-V and P-V Characteristics

5. Power Electronics and Power Conversion, Assiut University 5 Stand-alone PV System

6. Power Electronics and Power Conversion, Assiut University 6 Introduction to DC−DC Buck Converter

7. Power Electronics and Power Conversion, Assiut University 7 DC-DC Converter DC−DC Buck Converter + V in − + V out − I out I in Lossless objective: P in = P out, which means that V in I in = V out I out and The DC equivalent of an AC transformer

8. Power Electronics and Power Conversion, Assiut University 8 Example of an inefficient DC−DC converter + V in − + V out − R1R1 R2R2 If V in = 39V, and V out = 13V, efficiency η is only 0.33 The load Unacceptable except in very low power applications

9. Power Electronics and Power Conversion, Assiut University 9 Another method – lossless conversion of 39Vd c to average 13Vdc If the duty cycle D of the switch is 0.33, then the average voltag e to the expensive car stereo is 39 ● 0.33 = 13Vdc. This is lossl ess conversion, but is it acceptable? R stereo + 39Vdc – Switch state Closed, 39Vdc Open, 0Vdc Switch open Stereo voltage 39 0 Switch closed DT T

10. Power Electronics and Power Conversion, Assiut University 10 Convert 39Vdc to 13Vdc, cont. Try adding a large C in parallel with the load to control ripple. But if the C has 13Vdc, then when the switch closes, the source current spikes to a huge value and burns out the switch. R stereo + 39Vdc – C Try adding an L to prevent the huge current spike. But now, if the L has current when the switch attempts to open, the inductor’s current momentum and resulting Ldi/dt burns out the switch. By adding a “free wheeling” diode, the switch can open and the inductor current can continue to flow. With high- frequency switching, the load voltage ripple can be reduced to a small value. R stereo + 39Vdc – C L R stereo + 39Vdc – C L A DC-DC Buck Converter lossless

11. Power Electronics and Power Conversion, Assiut University 11 C’s and L’s operating in periodic steady-state Examine the current passing through a capacitor that is operating in periodic steady state. The governing equation is which leads to Since the capacitor is in periodic steady state, then the voltage at time t o is the same as the voltage one period T later, so The conclusion is that or the average current through a capacitor operating in periodic ste ady state is zero which means that

12. Power Electronics and Power Conversion, Assiut University 12 Now, an inductor Examine the voltage across an inductor that is operating in period ic steady state. The governing equation is which leads to Since the inductor is in periodic steady state, then the current at t ime t o is the same as the current one period T later, so The conclusion is that or the average voltage across an inductor operating in periodic stea dy state is zero which means that

13. Power Electronics and Power Conversion, Assiut University 13 KVL and KCL in periodic steady-state Since KVL and KCL apply at any instance, then they must also be valid in averages. Consider KVL, The same reasoning applies to KCL KVL applies in the average sense KCL applies in the average sense

14. Power Electronics and Power Conversion, Assiut University 14 V in + V out – i L L C i C I i in Buck converter + v L – V in + V out – L C I i in + 0 V – What do we learn from inductor voltage and capacitor current in the average sense? I out 0 A Assume large C so that V out has very low ripple Since V out has very low ripple, then assume I out has very low ripple

15. Power Electronics and Power Conversion, Assiut University 15 The input/output equation for DC-DC converters usually comes by examining inductor voltages V in + V out – L C I i in + (V in – V out ) – i L (i L – I out ) Reverse biased, thus the diode is open for DT seconds Note – if the switch stays closed, then V out = V in Switch closed for DT seconds

16. Power Electronics and Power Conversion, Assiut University 16 V in + V out – L C I – V out + i L (i L – I out ) Switch open for (1 − D)T seconds i L continues to flow, thus the diode is closed. This is the assumption of “continuous conduction” in the inductor which is the normal operating condition. for (1−D)T seconds

17. Power Electronics and Power Conversion, Assiut University 17 Since the average voltage across L is zero From power balance,, so The input/output equation becomes Note – even though i in is not constant (i.e., i in has harmonics), the input power is still simply V in I in because V in has no harmonics

18. Power Electronics and Power Conversion, Assiut University 18 Examine the inductor current Switch closed, Switch open, DT(1 − D)T T I max I min I avg = I out From geometry, I avg = I out is halfway between I max and I min ΔIΔI iLiL Periodic – finishes a period where it started

19. Power Electronics and Power Conversion, Assiut University 19 Effect of raising and lowering I out while holding V in, V out, f, and L constant iLiL ΔIΔI ΔIΔI Raise I out ΔIΔI Lower I out ΔI is unchanged Lowering I out (and, therefore, P out ) moves the circuit toward discontinuous operation

20. Power Electronics and Power Conversion, Assiut University 20 Effect of raising and lowering f while holding V in, V out, I out, and L constant iLiL Raise f Lower f Slopes of i L are unchanged Lowering f increases ΔI and moves the circuit toward discontinuous operation

21. Power Electronics and Power Conversion, Assiut University 21 iLiL Effect of raising and lowering L while holding V in, V out, I out and f constant Raise L Lower L Lowering L increases ΔI and moves the circuit toward discontinuous operation

22. Power Electronics and Power Conversion, Assiut University 22 Inductor current rating Max impact of ΔI on the rms current occurs at the boundary of continuous/discontinuous conduction, where ΔI =2I out 2I out 0 I avg = I out ΔIΔI iLiL Use max

23. Power Electronics and Power Conversion, Assiut University 23 V in + V out – i L L C i C I V in + V out – i L L C i C I i in Voltage ratings Diode sees V in MOSFET sees V in C sees V out Diode and MOSFET, use 2V in Capacitor, use 1.5V out Switch Closed Switch Open

24. Power Electronics and Power Conversion, Assiut University 24 Impedance matching DC−DC Buck Converter + V in − + V out = DV in − I out = I in / D I in + V in − I in Equivalent from source perspective Source So, the buck converter makes the load resistance look larger to the source

25. Power Electronics and Power Conversion, Assiut University 25 Example of drawing maximum power from sola r panel I sc V oc P max is approx. 130W (occurs at 29V, 4.5A) For max power from panels at this solar intensity level, attach I-V characteristic of 6.44Ω resistor But as the sun conditions change, the “max power resistance” must also change

26. Power Electronics and Power Conversion, Assiut University 26 Connect a 2Ω resistor directly, extract only 55W 130W 6.44Ω resistor 2Ω resistor 55W To draw maximum power (130W), connect a buck converter between the panel and the load resistor, and use D to modify the equivalent load resistance seen by the source so that maximum power is transferred

27. Power Electronics and Power Conversion, Assiut University 27 V panel + V out – i L L C i C I i panel Buck converter for solar applications + v L – Put a capacitor here to provide the ripple current required by the opening and closing of the MOSFET The panel needs a ripple-free current to stay on the max power point. Wiring inductance reacts to the current switching with large voltage spikes. In that way, the panel current can be ripple free and the voltage spikes can be controlled

28. Power Electronics and Power Conversion, Assiut University 28 DC−DC Boost Converter

29. Power Electronics and Power Conversion, Assiut University 29 V in + V out – C i C I i in Buck converter i L L + v L – Boost converter V in + V out – C i C I i in i L L + v L –

30. Power Electronics and Power Conversion, Assiut University 30 Boost converter This is a much more unforgiving circuit than the buck converter V in + V out – C i C I i in i L L + v L – i D If the MOSFET gate driver sticks in the “on” position, then there is a short circuit through the MOSFET – blow MOSFET! If the load is disconnected during operation, so that I out = 0, then L continues to push power to the right and very quickly charges C up to a high value (  250V) – blow diode and MOSFET! Before applying power, make sure that your D is at the minimum, and that a load is solidly connected

31. Power Electronics and Power Conversion, Assiut University 31 Boost converter V in + V out – C i C I i in i L L + v L – i D Modify your MOSFET firing circuit for Boost Converter operation (see the MOSFET Firing Circuit document)

32. Power Electronics and Power Conversion, Assiut University 32 Boost converter Using KVL and KCL in the average sense, the average values are + 0 V – I out V in + V out – C I L 0 A I in V + V out – C i C I i in i L L + v L – i D Find the input/output equation by examining the voltage across the inductor

33. Power Electronics and Power Conversion, Assiut University 33 Switch closed for DT seconds Reverse biased, thus the diode is open for DT seconds V in + V out – C I i in i L L I out Note – if the switch stays closed, the input is short circuited! + V in −

34. Power Electronics and Power Conversion, Assiut University 34 Switch open for (1 − D)T seconds Diode closed. Assume continuous conduction. V in + V out – C I i in i L L for (1−D)T seconds (i L – I out ) + (V in − V out ) −

35. Power Electronics and Power Conversion, Assiut University 35 Since the average voltage across L is zero The input/output equation becomes A realistic upper limit on boost is 5 times

36. Power Electronics and Power Conversion, Assiut University 36 Examine the inductor current Switch closed, Switch open, DT(1 − D)T T I max I min I avg = I in I avg = I in is half way between I max and I min ΔIΔI iLiL

37. Power Electronics and Power Conversion, Assiut University 37 Inductor current rating Max impact of ΔI on the rms current occurs at the boundary of continuous/discontinuous conduction, where ΔI =2I in 2I in 0 I avg = I in ΔIΔI iLiL Use max

38. Power Electronics and Power Conversion, Assiut University 38 Capacitor current and current rating 2I in −I out −I out 0 Max rms current occurs at the boundary of continuous/discontinuous conduction, where ΔI =2I out Use max i C = (i D – I out ) V in + V out – C i C I i in i L L i D

39. Power Electronics and Power Conversion, Assiut University 39 Worst-case load ripple voltage The worst case is where C provides I out for most of the period. Then, −I out 0 i C = (i D – I out )

40. Power Electronics and Power Conversion, Assiut University 40 Voltage ratings Diode sees V out MOSFET sees V out C sees V out Diode and MOSFET, use 2V out Capacitor, use 1.5V out V in + V out – C I i in i L L V + V out – C I i in i L L

41. Power Electronics and Power Conversion, Assiut University 41 Continuous current in L 2I in 0 I avg = I in iLiL (1 − D)T guarantees continuous conduction Then, considering the worst case (i.e., D → 1), use max use min

42. Power Electronics and Power Conversion, Assiut University 42 Impedance matching DC−DC Boost Converter + V in − +−+− I in + V in − I in Equivalent from source perspective Source

43. Power Electronics and Power Conversion, Assiut University 43 Example of drawing maximum power from sola r panel I sc V oc P max is approx. 130W (occurs at 29V, 4.5A) For max power from panels, attach I-V characteristic of 6.44Ω resistor But as the sun conditions change, the “max power resistance” must also change

44. Power Electronics and Power Conversion, Assiut University 44 Connect a 100Ω resistor directly, extract only 14W 130W 6.44Ω resistor 100Ω resistor 14W To extract maximum power (130W), connect a boost converter between the panel and the load resistor, and use D to modify the equivalent load resistance seen by the source so that maximum power is transferred So, the boost converter reflects a high load resistance to a low resistance on the source side

45. Power Electronics and Power Conversion, Assiut University 45 5A10A 120V Likely worst-case boost situation MOSFET. 250V, 20A L. 100µH, 9A C. 1500µF, 250V, 5.66A p-p Diode. 200V, 16A BOOST DESIGN

46. Power Electronics and Power Conversion, Assiut University 46 40V 2A50kHz 200µH BOOST DESIGN MOSFET. 250V, 20A L. 100µH, 9A C. 1500µF, 250V, 5.66A p-p Diode. 200V, 16A Minimum Inductance Values Needed to Guarantee Continuous Current Converter Type For Continuous Current in the Input Inductor Boost fI V L in 2 

47. Power Electronics and Power Conversion, Assiut University 47 Questions?