1. Power Generation from Renewable Energy Sources Fall 2012 Instructor: Xiaodong Chu Email ： chuxd@sdu.edu.cn chuxd@sdu.edu.cn Office Tel.: 81696127

2. Flashbacks of Last Lecture The output of a PV module can be reduced dramatically when even a small portion of it is shaded External diodes can help preserve the performance of PV modules – The main purpose for such diodes is to mitigate the impacts of shading on PV I –V curves – Such diodes are usually added in parallel with modules or blocks of cells within a module

3. Flashbacks of Last Lecture Consider the case when the bottom n − 1 cells still have full sun and still carry their original current I so they will still produce their original voltage V n−1 The output voltage of the entire module V SH with one cell shaded will drop to The voltage of the bottom n − 1 cells will be Then

4. Flashbacks of Last Lecture Crystalline silicon technologies Thin-film technologies Multiple junction technologies Concentrated photovoltaic (CPV) technologies

5. Photovoltaic Systems–Current– Voltage Curves for Loads Three most commonly configurations of PV systems – Systems that feed power directly into the utility grid – Stand-alone systems that charge batteries – Applications in which the load is directly connected to the PVs

6. Photovoltaic Systems–Current– Voltage Curves for Loads The photovoltaics in a grid-connected system deliver dc power to a power conditioning unit (PCU) that converts dc to ac and sends power to the building – If the PVs supply less than the immediate demand of the building, the PCU draws supplementary power from the utility grid, so demand is always satisfied – If the PVs supply more power than is needed, the excess is sent back onto the grid – The power-conditioning unit also helps keep the PVs operating at the most efficient point on their I –V curves as conditions change

7. Photovoltaic Systems–Current– Voltage Curves for Loads Grid-connected PV systems have a number of desirable attributes – Their relative simplicity can result in high reliability – Their maximum-power-tracking unit assures high PV efficiency – Their potential to be integrated into the structure of the building means that there are no additional costs for land – Their ability to deliver power during the middle of the day, when utility rates are highest, increases the economic value of their kilowatt-hours

8. Photovoltaic Systems–Current– Voltage Curves for Loads In the stand-alone system, an inverter converts battery dc voltages into ac for conventional household electricity, but in very simple systems everything may be run on dc and no inverter may be necessary The charging function of the inverter allows the generator to top up the batteries when solar is insufficient

9. Photovoltaic Systems–Current– Voltage Curves for Loads Stand-alone PV systems can be very cost effective in remote locations where the only alternatives may be high- maintenance generators burning relatively expensive fuel, or extending the existing utility grid to the site, which can cost much more These systems suffer from several inefficiencies including battery losses and the fact that the PVs usually operate well off of the their most efficient operating point Inefficiencies are often increased by mounting the array at a steep tilt angle to supply relatively uniform amounts of energy through the seasons, rather than picking an angle that results in the maximum possible annual energy delivery

10. Photovoltaic Systems–Current– Voltage Curves for Loads The third system type has photovoltaics directly coupled to their loads, without any batteries or major power conditioning equipment The most common example is PV water pumping in which the wires from the array are connected directly to the motor running a pump and when the sun shines, water is pumped There is no electric energy storage, but potential energy may be stored in a tank of water up the hill for use whenever it is needed These systems need to be carefully designed to be efficient

11. Photovoltaic Systems–Current– Voltage Curves for Loads While the I –V curve for a photovoltaic cell, module, or array defines the combinations of voltage and current that are permissible under the existing ambient conditions, it does not tell us anything about where on that curve the system will actually be operating This determination is a function of the load into which the PVs deliver their power Just as PVs have an I –V curve, so do loads

12. Photovoltaic Systems–Current– Voltage Curves for Loads The same voltage is across both the PVs and load, and the same current runs through the PVs and load When the I –V curve for the load is plotted onto the same graph that has the I –V curve for the PVs, the intersection point is the one spot at which both the PVs and load are satisfied, which is called the operating point

13. Photovoltaic Systems–Current– Voltage Curves for Loads Consider a simple resistive load or which, when plotted on current versus voltage axes, is a straight line with slope 1/R As R increases, the operating point where the PV and resistance I –V curves intersect moves along the PV I –V curve from left to right

14. Photovoltaic Systems–Current– Voltage Curves for Loads By using a variable resistance, called a potentiometer, or pot, as the load, and then varying its resistance, pairs of current and voltage can be obtained, which can be plotted to give the module I –V curve

15. Photovoltaic Systems–Current– Voltage Curves for Loads Since power delivered to any load is the product of current and voltage, there will be one particular value of resistance that will result in maximum power where V m and I m are the voltage and current at the maximum power point (MPP) Under the special conditions at which modules are tested, the MPP corresponds to the rated voltage V R and current I R of the module

16. Photovoltaic Systems–Current– Voltage Curves for Loads The dc motors, such as those often used in PV-water-pumping systems, exhibit a current–voltage relationship that is quite similar to that of a resistor Most are permanent-magnet dc motors As the motor spins, it develops a back electromotive force e, which is a voltage proportional to the speed of the motor (ω) that opposes the voltage supplied by the photovoltaics

17. Photovoltaic Systems–Current– Voltage Curves for Loads From the equivalent circuit, the voltage–current relationship for the dc motor is where back emf e = kω and R a is the armature resistance A dc motor runs at nearly constant speed for any given applied voltage even though the torque requirement of its load may change

18. Photovoltaic Systems–Current– Voltage Curves for Loads Notice that at start-up, while ω = 0, the current rises rapidly with increasing voltage until current is sufficient to create enough starting torque to break the motor loose from static friction Once the motor starts to spin, back emf drops the current and thereafter I rises more slowly with increasing voltage

19. Photovoltaic Systems–Current– Voltage Curves for Loads The inefficiency of the simple PV–motor setup

20. Photovoltaic Systems–Current– Voltage Curves for Loads There is a device, called a linear current booster (LCB), that is designed to help overcome this loss of potentially usable insolation when current delivered to the motor is insufficient to overcome friction What an LCB does is to convert low-current, high-voltage power into high-current, low-voltage power The lower voltage means that the motor will spin at a slower rate

21. Photovoltaic Systems–Current– Voltage Curves for Loads Since PVs only provide power during the daylight hours and many applications require energy when the sun is not shining, some method of energy storage is often needed – For a water pumping system, this might be the potential energy of water stored in a tank – For grid-connected systems, the utility lines themselves can be thought of as the storage mechanism: PV energy is put onto the grid during the day and taken back at night – For most off-grid applications, energy is stored in batteries for use whenever it is needed

22. Photovoltaic Systems–Current– Voltage Curves for Loads An ideal battery is one in which the voltage remains constant no matter how much current is drawn, which means that it will have an I –V curve that is simply a straight up-and-down line

23. Photovoltaic Systems–Current– Voltage Curves for Loads A real battery has some internal resistance and is often modeled with an equivalent circuit consisting of an ideal battery of voltage V B in series with some internal resistance R i During the charge cycle, with positive current flow into the battery, we can write

24. Photovoltaic Systems–Current– Voltage Curves for Loads The simple equivalent circuit representation is complicated by a number of factors, including the fact that the open-circuit voltage (V B ) depends not only on the state of charge but also on battery temperature and how long it has been resting without any current flowing Internal resistance is also a function of temperature and state of charge, as well the age and condition of the battery

25. Example 9.1 of the textbook: you should master it! Photovoltaic Systems–Current– Voltage Curves for Loads

26. Significant efficiency gains could be realized if the operating points for resistive, dc motor, and battery loads could somehow be kept near the knee of the PV I –V curves throughout the ever-changing daily conditions Devices to do that, called maximum power trackers (MPPTs), are available and are a standard part of many PV systems— especially those that are grid-connected There are some very clever, quite simple circuits that are at the heart of not only MPPTs but also linear current boosters (LCBs) as well as a number of other important power devices The key is to be able to convert dc voltages from one level to another

27. Photovoltaic Systems–Current– Voltage Curves for Loads A boost converter is a commonly used circuit to step up the voltage from a dc source, while a buck converter is often used to step down voltage A buck-boost converter is capable of raising or lowering a dc voltage from its source to whatever dc voltage is needed by the load The transistor switch flips on and off at a rapid rate under control of some sensing and logic circuitry

28. Photovoltaic Systems–Current– Voltage Curves for Loads There are two situations to consider: the circuit with the switch closed and the circuit with the switch open The duty cycle D (0 < D < 1) is the fraction of the time that the switch is closed, which controls the relationship between the input and output voltages of the converter

29. Photovoltaic Systems–Current– Voltage Curves for Loads As a typical solar day progresses, ambient temperature and available insolation are constantly changing, which means that the I –V curve for a PV array is constantly shifting and the operating point for any given load is constantly moving around as well Manufacturers provide I –V curves for various temperatures and solar intensity, but there are times when hour-by-hour curves are helpful

30. Photovoltaic Systems–Current– Voltage Curves for Loads Over most of a PV I –V curve, current at any voltage is directly proportional to insolation, which suggests we can simply scale the 1-sun (1000 W/m 2 ) I –V curve by moving it up or down in proportion to the anticipated insolation This generalization is completely true for short-circuit current I SC (i.e., V = 0) Open-circuit voltage V OC decreases as insolation decreases, so the simple assumption of current being proportional to insolation breaks down near V OC Under most circumstances, however, the operating voltage of a system is around the knee, or even lower, where current is very close to being proportional to insolation

31. Photovoltaic Systems–Current– Voltage Curves for Loads

32. The simple assumption that current is proportional to insolation makes it easy to draw hour-by-hour I –V curves for clear days We need to do is scale the 1-sun (1 kW/m 2 ) I –V curve in direct proportion to those estimated hourly solar intensities Since the 1-sun I –V curve itself depends on cell temperature, and cell temperature depends on insolation and ambient temperature, we could imagine adjusting the 1-sun reference curve on an hour-by-hour basis

33. Photovoltaic Systems–Current– Voltage Curves for Loads