Sun Intensity

The magnitude of the photocurrent is maximum under full bright sun (1.0 sun). On a partially sunny day, the photocurrent diminishes in direct proportion to the sun intensity. The i-v characteristic shifts downward at a lower sun

FIGURE 8-9

i-v characteristic of 22 watts pv module at full and half sun intensities. (Source: United Solar Systems Corporation, San Diego, California. With permission.)

FIGURE 8-9

i-v characteristic of 22 watts pv module at full and half sun intensities. (Source: United Solar Systems Corporation, San Diego, California. With permission.)

Intensity

1.0 Sun

0.5 Sun

FIGURE 8-10

i-v characteristic of pv module shifts down at lower sun intensity, with small reduction in voltage.

0 100 200 300 400 500 600 700 800 900 100

Solar radiation W/m2 o

FIGURE 8-11

Photoconversion efficiency versus solar radiation. The efficiency is practically constant over a wide range of radiation.

intensity as shown in Figure 8-10. On a cloudy day, therefore, the short circuit current decreases significantly. The reduction in the open-circuit voltage, however, is small.

The photoconversion efficiency of the cell is insensitive to the solar radiation in the practical working range. For example, Figure 8-11 shows that the efficiency is practically the same at 500 watts/m2 and 1,000 watts/m2. This means that the conversion efficiency is the same on a bright sunny day and a cloudy day. We get lower power output on a cloudy day only because of the lower solar energy impinging the cell.

8.6.2 Sun Angle

The cell output current is given by I = 10 cos 0, where Io is the current with normal sun (reference), and 0 is the angle of the sunline measured from the normal. This cosine law holds well for sun angles ranging from 0 to about 50°.

Sun incidence angle (degrees)

FIGURE 8-12

Kelley cosine curve for pv cell at sun angles from 0 to 90°.

TABLE 8-1

The Kelley Cosine Values of the Photocurrent in Silicon Cells

TABLE 8-1

The Kelley Cosine Values of the Photocurrent in Silicon Cells

Sun Angle

Mathematical

Kelly

Degrees

Cosine Value

Cosine Value

30

0.866

0.866

50

0.643

0.635

60

0.500

0.450

80

0.174

0.100

85

0.087

0

Beyond 50°, the electrical output deviates significantly from the cosine law, and the cell generates no power beyond 85°, although the mathematical cosine law predicts 7.5 percent power generation. The actual power-angle curve of the pv cell is called Kelly cosine, and is shown in Figure 8-12 and Table 8-1.

8.6.3 Shadow Effect

The array may consist of many parallel strings of series-connected cells. Two such strings are shown in Figure 8-13. A large array may get partially shadowed due to a structure interfering with the sunline. If a cell in a long-series string gets completely shadowed, it will lose the photovoltage, but still must carry the string current by virtue of its being in series with the other fully operating cells. Without internally generated voltage, it cannot produce power. Instead, it acts as a load, producing local I2R loss and heat. The remaining cells in the string must work at higher voltage to make up the loss of the shadowed cell voltage. Higher voltage in healthy cells means lower string current as per the i-v characteristic of the string. This is shown in the bottom left of Figure 8-13. The current loss is not proportional to the shadowed area, and may go unnoticed for mild shadow on a small area. However, if more cells are shadowed beyond the critical limit, the i-v curve

Sun incidence angle (degrees)

Shade Effect String

FIGURE 8-13

Shadow effect on one long pv string of an array. The power degradation is small until shadow exceeds the critical limit.

FIGURE 8-13

Shadow effect on one long pv string of an array. The power degradation is small until shadow exceeds the critical limit.

Bypass Yot

FIGURE 8-14

Bypass diode in pv string minimizes the power loss under heavy shadow.

FIGURE 8-14

Bypass diode in pv string minimizes the power loss under heavy shadow.

gets below operating voltage of the string, making the string current fall to zero, losing all power of the string.

The commonly used method to eliminate the loss of string due to shadow effect is to subdivide the circuit length in several segments with bypass diodes (Figure 8-14). The diode across the shadowed segment bypasses only that segment of the string. This causes a proportionate loss of the string voltage and current, without losing the whole string power. Some modern pv modules come with such internally embedded bypass diodes.

FIGURE 8-15

Effect of temperature on the i-v characteristic. The cell produces less current but greater voltage, with net gain in the power output at cold temperature.

FIGURE 8-15

Effect of temperature on the i-v characteristic. The cell produces less current but greater voltage, with net gain in the power output at cold temperature.

8.6.4 Temperature Effect

With increasing temperature, the short-circuit current of the cell increases, whereas the open-circuit voltage decreases (Figure 8-15). The effect of temperature on the power is quantitatively evaluated by examining the effects on the current and the voltage separately. Say Io and Vo are the short-circuit current and the open-circuit voltage at the reference temperature T, and a and P are their respective temperature coefficients. If the operating temperature is increased by AT, then the new current and voltage are given by the following:

Isc = Io (1 + a • AT) and ^ = Vo (1 - p • AT) (8-6)

Since the operating current and the voltage change approximately in the same proportion as the short-circuit current and open-circuit voltage, respectively, the new power is as follows:

P = V • I = Io (1 + a • AT) • Vo (1 - P • AT) (8-7)

This can be simplified in the following expression by ignoring a small term:

For typical single crystal silicon cells, a is 500 pu per °C and P is 5 mu per °C. The power is therefore:

P = po • [1 + (500pu - 5mu) • AT] or Po • [1 - .0045AT] (8-9)

Voltage

High Temperature —- Low Temperature

FIGURE 8-16

Effect of temperature on the p-v characteristic. The cell produces more power at cold temperature.

This expression indicates that for every °C rise in the operating temperature above the reference temperature, the silicon cell power output decreases by 0.45 percent. Since the increase in the current is much less than the decrease in the voltage, the net effect is the decrease in power at high operating temperatures.

The effect of varying temperature on the power output is shown in the power versus voltage characteristics at two operating temperatures in Figure 8-16. The figure shows that the maximum power available at lower temperature is higher than that at higher temperature. Thus, cold temperature is actually better for the pv cell, as it generates more power. However, the two Pmax points are not at the same voltage. In order to extract maximum power at all temperatures, the pv system must be designed such that the module output voltage can increase to V2 for capturing Pmax2 at lower temperature and can decrease to V1 for capturing Pmax1 at higher temperature.

8.6.5 Effect of Climate

On a partly cloudy day, the pv module can produce up to 80 percent of their full sun power. Even on an extremely overcast day, it can produce about 30 percent power. Snow does not usually collect on the modules, because they are angled to catch the sun. If snow does collect, it quickly melts. Mechanically, modules are designed to withstand golf ball size hail.

8.6.6 Electrical Load Matching

The operating point of any power system is the intersection of the source line and the load line. If the pv source having the i-v and p-v characteristics

Characteristics

FIGURE 8-17

Operating stability and electrical load matching with resistive load and constant power load.

FIGURE 8-17

Operating stability and electrical load matching with resistive load and constant power load.

shown in Figure 8-17 (a) is supplying the power to the resistive load R17 it will operate at point A1. If the load resistance increases to R2 or R3, the operating point moves to A2 or A3, respectively. The maximum power is extracted from the module when the load resistance is R2 (Figure 8-17b). Such load matching with the source is always necessary for maximum power extraction from the pv module.

The operation with constant power loads is shown in Figure 8-17(c) and (d). The constant power load line has two points of intersection with the source line, denoted by B1 and B2. Only point B2 is stable, as any perturbation from it will generate a restoring power to take the operation back to B2. Therefore, the system will operate at B2.

The necessary condition for the electrical operating stability of the solar array is as follows:

_ dP ~

>

" dP ~

_ dV _

load

_ dV _

source

Some loads such as heaters have constant resistance, with power varying with the voltage squared. On the other hand, some loads such as induction motors behave more like constant power loads, drawing more current at lower voltage. In most large systems with mix loads, the power varies approximately in linear proportion with voltage.

8.6.7 Sun Tracking

More energy is collected by the end of the day if the pv module is installed on a tracker, with an actuator that follows the sun like a sunflower. There are two types of sun trackers:

Solar Energy Follows Sun

FIGURE 8-18

Dual-axis suntracker follows the sun like a sunflower around the year. (Source: American Sun Company, Blue Hill, Maine. With permission.)

• one-axis tracker, which follows the sun from east to west during the day.

• two-axis tracker tracks the sun from east to west during the day, and from north to south during the seasons of the year (Figure 8-18). A sun tracking design can increase the energy yield up to 40 percent over the year compared to the fixed-array design. The dual-axis tracking is done by two linear actuator motors, which aim the sun within one degree of accuracy (Figure 8-19). During the day, it tracks the sun east to west. At night it turns east to position itself for the next morning sun. Old trackers did this after the sunset using a small nickel-cadmium battery. The new designs eliminate the battery requirement by doing it in the weak light of the dusk and/or d awn. The Kelley cosine presented in is useful to assess, accurately, the power available from sun at the evening angles.

FIGURE 8-19

Actuator motor of the suntracker. (Source: American Sun Company, Blue Hill, Maine. With permission.)

Golf Condition Sun Intensity Sensor

FIGURE 8-20

Sun tracking actuator principle. The two differentially connected sensors at 45° generate signal proportional to the pointing error.

FIGURE 8-20

Sun tracking actuator principle. The two differentially connected sensors at 45° generate signal proportional to the pointing error.

When the sun is obscured by a dark cloud, the tracker may aim at the next brightest object, which is generally the edge of the cloud. When the cloud is gone, the tracker aims at the sun once again. Such sun-hunting is eliminated in newer suntracker design.

One method of designing the suntracker is to use two pv cells mounted on two 45° wedges (Figure 8-20), and connecting them differentially in series through an actuator motor. When the sun is perfectly normal, the current on both cells are equal to Io • cos 45°. Since they are connected in series opposition, the net current in the motor is zero, and the array stays put. On the other hand, if the array is not normal to the sun, the sun angles on the two cells are different, giving two different currents:

I1 = Io cos (45 + 5), and I2 = Io cos (45 - 5) The motor current is therefore:

Im = Ii-12 = Io cos(45 + 5)-Io cos(45-5) Using Taylor series expansion:

f (x + h) = f (x) + h • f '(x) + h^r f "(x) + -we can express the two currents as the following:

I1 = Io cos 45 - Io 5 sin 45, and L = I cos 45 -1 5 sin 45

The motor current is then Im = Ii -12 = 2 Io 5 sin45° (8-11)

I 5 if 5 is in radian

Small pole-mounted panels can use one pole-mounted suntracker. Large array, on the other hand, is divided into small modules, each mounted on its own single-axis or dual-axis tracker. This simplifies the structure and eliminates the problems related with large motion.

8.7 Peak Power Point Operation

The suntracker drives the module mechanically to face the sun to collect the maximum solar radiation. However, that, in itself, does not guarantee the maximum power output from the module. As was seen in Figure 8-16, the module must operate electrically at a certain voltage which corresponds to the peak power point under the given operating conditions. First we examine the electrical principle of the peak power operation.

If the array is operating at voltage V and current I on the i-v curve, the power generation is P = V ■ I watts. If the operation moves away from the above point, such that the current is now I + AI, and the voltage is V + AV, the new power is as follows:

Which, after ignoring a small term, simplifies to the following:

The AP should be zero at peak power point, which necessarily lies on a locally flat neighborhood. Therefore, at peak power point, the above expression in the limit becomes as follows:

dl I

We take note here that dV/dI is the dynamic impedance of the source, and V/I is the static impedance.

There are three electrical methods of extracting the peak power from the module, as described below:

(1) In the first method, a small signal current is periodically injected into the array bus and the dynamic bus impedance Zd = dV/dI and the static bus impedance Zs = V/I are measured. The operating voltage is then increased or decreased until Zd = - Zs. At this point, the maximum power is extracted from the source.

(2) In another electrical method, the operating voltage is increased as long as dP/dV is positive. That is, the voltage is increased as long as we get more power. If dP/dV is sensed negative, the operating voltage is decreased. The voltage is kept put if the dP/dV is near zero within a preset dead band.

(3) The third method makes use of the fact that for most pv cells, the ratio of the voltage at the maximum power point to the open circuit voltage (i.e., Vmp/Voc) is approximately constant, say K. For example, for high-quality crystalline silicon cells K = 0.72. An unloaded cell is installed on the array and kept in the same environment as the power-producing module, and its open circuit voltage is continuously measured. The operating voltage of the power-producing array is then set at KVoc, which will produce the maximum power.

8.8 pv System Components

The array by itself does not constitute the pv power system. We must also have a structure to mount it, point to the sun, and the components that accept the DC power produced by the array and condition the power in the form that is usable by the load. If the load is AC, the system needs an inverter to convert the DC power into AC, generally at 50 or 60 Hz.

switcliing regulator

DC to AC Inverter

DC to AC Inverter

Loads

Duty J Batter>' 2 i ratio I Charger

Loads

Peak power tracking controls

Solar panels

Peak power tracking controls

Charge current controller"^—Ah

Solar panels

Batteries

Batteries

FIGURE 8-21

Peak power tracking photovoltaic power system showing major components.

Figure 8-21 shows the necessary components of a stand-alone pv power system. The peak power tracker senses the voltage and current outputs of the array and continuously adjusts the operating point to extract the maximum power under the given climatic conditions. The output of the array goes to the inverter, which converts the DC into AC. The array output in excess of the load requirement is used to charge the battery. The battery charger is usually a DC-DC buck converter. If excess power is still available after fully charging the battery, it is shunted in dump heaters, which may be space or room heaters in a stand-alone system. When the sun is not available, the battery discharges to the inverter to power the loads. The battery discharge diode Db is to prevent the battery from being charged when the charger is opened after a full charge or for other reasons. The array diode Da is to isolate the array from the battery, thus keeping the array from acting as load on the battery at night. The mode controller collects the system signals, such as the array and the battery currents and voltages, keeps track of the battery state of charge by bookkeeping the charge/discharge ampere-hours, and commands the charger, discharge converter, and dump heaters on or off as needed. The mode controller is the central controller for the entire system.

In the grid-connected system, dump heaters are not required, as all excess power is fed to the grid lines. The battery is also eliminated, except for small critical loads, such as the start up controls and the computers. The DC power is first converted into AC by the inverter, ripples are filtered and then only the filtered power is fed into the grid lines.

For pv applications, the inverter is a critical component, which converts the array DC power into AC for supplying the loads or interfacing with the grid. A new product recently being introduced into the market is the AC-pv modules, which integrates an inverter directly in the module, and is presently available in a few hundred watts capacity. It provides utility grade 60 Hz power directly from the module junction box. This greatly simplifies the pv system design.

References

1. Cook, G., Billman, L. and Adcock R. 1995. "Photovoltaic Fundamental," DOE/Solar Energy Research Institute Report No. DE91015001, February 1995.

Getting Started With Solar

Getting Started With Solar

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