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Design Article

# Selecting a solar energy conversion method

## 7/3/2012 10:15 AM EDT

3. Evolving from a cell to a panel
Individual cells are connected in series and parallel to form a panel. Panels are connected in series and parallel to form a photovoltaic array. Connecting cells in series increases the voltage. Connecting them in parallel increases the current. If an individual cell has a forward drop of 0.5V and with a given illumination produces 100mA, connecting 50 cells in series would produce a 25V string. Connecting 60 of the strings in parallel would produce a 25V, 6A panel. If each panel could deliver 150W, connecting 50 panels on a rooftop would deliver 7.5kW.

The four key parameters of a solar panel are:
Voc, the open circuit voltage where Iout = 0, Pout = 0
Isc, the short circuit current where Vout = 0, Pout = 0
Vmp, the output voltage at when the power extracted is maximum
Imp, the output current when the power extracted is maximum.

In Figure 6 the red curve is the current as a function of voltage and the green curve is the power as a function of voltage along with the location of the maximum power point.

Figure 6

In the solar cell (or panel) equivalent circuit the parallel resistor Rp affects the slope of the current vs. voltage curve at Vout = 0. For an ideal panel, Rp = ∞ and the slope is zero. Series resistor Rs affects the slope of the power vs. voltage curve at Vout = Voc. Ideally Rs = 0 and the slope is infinite.

4. Transferring maximum power from a panel
The objective is to find the maximum power point (MPP) and always operate the panel voltage and current at that point. The MPP will vary with irradiance and temperature. Decreasing irradiance is represented by a lower Isc. As Isc reduces, the MPP moves to a lower voltage. As temperature increases, Vmp reduces and the maximum power gets less. Voc, Isc, Vmp, Imp and the effects of temperature are shown in the panel manufacturer’s datasheets. A method is needed to dynamically track these changes as the panel environment changes and always operate the panel at the maximum power point, regardless of external factors.

Since the equivalent circuit of a solar panel is represented by a current source with parallel and series resistances, the Thevenin equivalent circuit can be shown as a voltage source with a single series resistance. To transfer maximum power from the voltage source to the load, the load resistance must equal the source resistance. Figure 7 shows the I-V curve and the load line R2 with the proper slope that intersects the I-V curve at the MPP.

Figure 7

This is easily accomplished with the STMicroelectronics SPV1020 boost converter with embedded maximum power point tracking (MPPT).

The SPV1020 DC-DC boost converter with embedded MPPT is an active power optimizer. Its purpose is to increase the output voltage from a panel while simultaneously adjusting the panel’s output voltage to Vmp. This optimizes or maximizes the power extracted from the panel. The converter’s output voltage is set by the user. The converter’s duty cycle is determined by the Perturb and Observe MPPT algorithm. The converter’s input voltage (or panel’s output voltage) is the dependent variable and is set by the formula:

Vin = Vout * (1-duty cycle)

In the SPV1020, the duty cycle starts out at a low value of 5 percent. The input voltage and input current are measured and power calculated. Then the duty cycle is increased. The new input voltage is measured and input power calculated. If the new power is greater than the old power the duty cycle is increased again. This process continues until the new power does not change or is less than the old power. If the new power does not change, that is the maximum power point. If the new power is less than the old power, the duty cycle DECREASES and the process is repeated, until the new power equals the old power, and the maximum power point has been determined. In this case the converter will be operating at the top of the power vs. voltage curve as shown in Figure 8.

This Perturb and Observe algorithm runs continuously, at 256 times the switching period. The switching frequency is by default 100 kHz. The switching period is 10 microseconds and the MPPT algorithm is updated every 2.56 milliseconds.

Figure 8

chrisrodgers

7/3/2012 4:06 PM EDT

A very interesting and article, thanks very much!

I have a question.

For a set of conditions, it seems that a given solar cell will have a finite amount of power to deliver. A fixed DC load connected directly to the solar cell will form a voltage divider from the Thevenin equiv. voltage source (E) between Rs and the load (RL), assuming Rp is very large.

Let's say RL is quite a bit less than Rs. So the loaded solar cell voltage will drop when connected directly. Ideally, you'd like a way to make RL appear to increase to accomplish Max. Power Transfer (MPP). This would result in raising the load voltage (VL) to a maximum of one half the open circuit Thevenin voltage (E/2).

Interposing the SPV1020 boost converter between the solar cell and RL will make the load impedance appear matched to the solar cell (RL = Rs), boosting VL and hence the load current.

Maybe I'm not seeing something here, but doesn't this violate conservation of energy? Or is MPP accomplished only "piece-wise", during each PWM pulse of the boost converter?

Thanks for any light you can shed on this.

sudhakar_amberroot

7/3/2012 11:54 PM EDT

Thevenin cannot be applied here because of the nonlinear device being present which is the parallel diode array. So the maximum point will not be E/2 but much higher since the current through the diode will come down with reduction of the terminal diode.

chrisrodgers

7/4/2012 7:22 PM EDT

In the article it states "Since the equivalent circuit of a solar panel is represented by a current source with parallel and series resistances, the Thevenin equivalent circuit can be shown as a voltage source with a single series res." This seems to say that Thevenin is indeed applicable here. But my point is not about Thevenin per se, nor about the maximum achievable load voltage, but rather the question of conservation of energy. As you say, as the load voltage rises, "the current through the diode will come down". This is a result of P=EI. You can change the voltage, but the power from the solar cell does not change. So I still wonder how, for a fixed DC load resistance, it's possible to increase the load voltage using a boost converter. More load voltage will result in more load current, and therefore more load power. Any comment on this, Ed?

twarner250

7/5/2012 10:19 AM EDT

The power delivered by the cell (or array) is function of its output voltage, it is not fixed. As the cell voltage rises, the current in the internal diode rises, leaving less of the photo current for the load.

Any power not taken by the load will be converted to heat.

HarrisMarcus

7/9/2012 4:36 PM EDT

You have stated “As the cell voltage rises, the current in the internal diode rises, leaving less of the photo current for the load”. This is not so. If you follow the panel I-V curve shown in Figure 6 when the cell voltage increases the cell current decreases. The maximum cell voltage is the open circuit voltage, Voc, where the current is zero.

jg_

7/5/2012 6:30 PM EDT

Thevenin is a poor approach, a better model is a current source, with a parallel clamp diode, and better curves would include constant power profiles (V*I = constants) which makes the MPPT seeking easier to visualize.

HarrisMarcus

7/9/2012 4:35 PM EDT

The maximum power available from the panel does not change but the power that is actually extracted from the panel does change and it is a function of the load resistance RL. This maximum power point occurs when RL = Rs. The boost converter decreases the value of RL by adjusting its duty cycle. The input resistance seen by the panel is RL x (1-du)^2 where du is the duty cycle internally set by the SPV1020. The SPV1020 duty cycle is internally adjusted so that RL x (1-du)^2 equals the panel output resistance Rs.

HarrisMarcus

7/12/2012 1:38 PM EDT

The maximum power available from the panel does not change but the power that is actually extracted from the panel does change and it is a function of the load resistance RL. This maximum power point occurs when RL = Rs. The boost converter decreases the value of RL by adjusting its duty cycle. The input resistance seen by the panel is RL x (1-du)^2 where du is the duty cycle internally set by the SPV1020. The SPV1020 duty cycle is internally adjusted so that RL x (1-du)^2 equals the panel output resistance Rs.

Brakeshoe

7/6/2012 4:14 PM EDT

Yes, the Thevenin model applies in figure 2, as you are looking back into the terminals of the source. What's more, if you apply a variable resistive load, you will get a linear graph of voltage vs current.

chrisrodgers

7/7/2012 10:40 AM EDT

I see that my understanding is slowly beginning to clear. I found the found Fig. 3.7 on pg. 24 of the following article to be helpful:

https://digital.library.txstate.edu/bitstream/handle/10877/3171/fulltext.pdf

I think what was bothering me was that the boost converter cannot increase the load voltage to any arbitrarily high level. It is necessarily limited by the PV maximum power curve for a given set of conditions (illumination, temp., etc.) This Fig. (3.7) seems to bear that out that.

HarrisMarcus

7/9/2012 4:37 PM EDT

The article you provided is very thorough and detailed. Thank you. You cannot get more power out than you have coming in.

HarrisMarcus

7/9/2012 4:34 PM EDT

You are correct. The intent of using the Thevenin equivalent is to show that whatever the value Rs even though non-linear, RL must match it to provide maximum power transfer.

HarrisMarcus

7/9/2012 4:33 PM EDT

RL will normally be much greater than Rs.

Interposing the SPV1020 boost converter between the panel and RL decreases the load resistance seen by the panel. The load resistance seen by the panel Rin = RL x (1-du)^2 where du is the duty cycle internally set by SPV1020. The duty cycle is set by the SPV1020 so that RL x (1-du)^2 = Rs, the source resistance of the panel.

HarrisMarcus

7/12/2012 1:37 PM EDT

RL will normally be much greater than Rs.

Interposing the SPV1020 boost converter between the panel and RL decreases the load resistance seen by the panel. The load resistance seen by the panel Rin = RL x (1-du)^2 where du is the duty cycle internally set by SPV1020. The duty cycle is set by the SPV1020 so that RL x (1-du)^2 = Rs, the source resistance of the panel.

dafi

7/3/2012 8:29 PM EDT

Yes an interesting article indeed. Thank you.

I have two questions:
1. what level of monitoring is needed to detect a failure in one panel/optimizer? It would seem that without some monitoring a failure could occur in one optimizer and you would not know about it at teh central inverter.
2. how applicable is the use of optimizers for an off grid (battery) system? I am assuming they would still serve their purpose by delivering more power to a DC-DC inverter/battery charger.

HarrisMarcus

7/9/2012 4:39 PM EDT

You would need to monitor the panel output voltage and input voltage.. This can be done through the SPI bus in the SPV1020. The SPI bus provides a direct measurement of input voltage, input current and duty cycle. Output voltage can be computed by Vout = Vin/(1-du).

HarrisMarcus

7/9/2012 4:40 PM EDT

Optimizers can be used for batteries as well as AC grid systems. STMicroelectronics has an evaluation board with P/N STEVAL-ISV005V1 that uses the SPV1020 and SEA05 constant voltage constant current controller to charge a 240W lead acid battery.

dave_dne

7/3/2012 9:16 PM EDT

The enphase M215 data sheet shows 208/240VAC output. But in this article "Power loss due to wiring" analysis indicates 115VAC output from the M215. Ed are we looking at the same thing here?

And the M215 has remote monitoring features.

On the 'cons' side - the M215 is does have a narrow min/max start voltage of 22/45VDC. I don't work for enphase but I did give their micro inverters a detailed review for a home PV system.

And lastly, what about potential problems with DC arc faults using a 350VDC voltage to the central inverter? Thought I read somewhere that NFPA/NEC was now addressing this issue? Anyway, I'd like to see something mentioned about any future NEC code requirements for high (~300VDC+) DC voltages to a central inverter.

HarrisMarcus

7/9/2012 5:45 PM EDT

We are looking at the same thing. The article compared a microinverter delivering 115VAC, not necessarily Enphase which delivers a higher voltage, to a higher voltage, lower current DC system.

The SPV1020 has performance monitoring features available through its SPI bus that include input voltage, input current and duty cycle. Output voltage can be computed from input voltage and duty cycle.

dave_dne

7/10/2012 12:33 PM EDT

twarner250

7/5/2012 10:18 AM EDT

The power delivered by the cell (or array) is function of its output voltage, it is not fixed. As the cell voltage rises, the current in the internal diode rises, leaving less of the photo current for the load.

Any power not taken by the load will be converted to heat.

HarrisMarcus

7/12/2012 1:42 PM EDT

You have stated “As the cell voltage rises, the current in the internal diode rises, leaving less of the photo current for the load”. This is not so. If you follow the panel I-V curve shown in Figure 6 when the cell voltage increases the cell current decreases. The maximum cell voltage is the open circuit voltage, Voc, where the current is zero.

green_is_now

1/23/2013 4:44 PM EST

you misinterpreted him you are both saying the same thing.

rroy22520

7/5/2012 11:08 AM EDT

What about delivering solar power not to the AC grid but to the local loads? MPPT absolutely must be considered for moving and non moving cells and reflector. But also the infrastructure for intelligent load switching/engagement to optimize the local loads so they put less demand on the grid. Solar in the desert is great if you can build a factory (a suitable load) underneath the arrays so the transmission distance is not the issue, getting the raw materials in and the finished product out.

http://www.lulu.com/spotlight/poconoarmchairreview

7/6/2012 1:12 AM EDT

Doesn't maximum power output fall drastically over the first few months? That means, it seems to me, that the control circuits have to be designed to handle outputs that are achievable for only a small percentage of the array's life, and only early on. After that, isn't it true that the control circuits will never see that level of output again?

http://www.lulu.com/spotlight/poconoarmchairreview

7/6/2012 1:14 AM EDT

It would be nice if solar panels could be sold "broken in" so that their initial degradation would not complicate array designs.

HarrisMarcus

7/9/2012 5:46 PM EDT

The power output of a solar panel changes a slight amount with time and this is specified in the panel manufacturer’s data sheet. This case the power optimizer can be used to very good advantage because as the Vmp and Imp points change with time, the SPV1020 dynamically tracks these changes and enables the maximum power available to be extracted from the panel.

Trinity51

7/6/2012 5:50 AM EDT

Rich - as far as I am aware the panel output is surprisingly constant with time. Most panels are guaranteed more than 90% rated output after 10 years and more than 80% output after 25 years (approx 100,000 hours of daylight use). Typical results are better than that, so degradation is just a fraction of 1% per year.

Mineyes

7/6/2012 3:39 PM EDT

"Southern Exposure is Obvious" That is true only in the Northern Hemisphere. A better statement, might be "Equatorial Exposure is required"

HarrisMarcus

7/9/2012 5:46 PM EDT

Yes you are correct. I should not be thinking only in terms of the northern hemisphere.

Robotics Developer

7/7/2012 2:29 PM EDT

A very nice article with good technical details! Very much appreciated, thank you! I am wondering if this level of complexity is needed when using solar power both locally and not at normal line voltages (ie. 12V or 24V DC lighting/systems)?

HarrisMarcus

7/9/2012 5:47 PM EDT

Using a power optimizer is not complicated and system design is straightforward. For a low voltage lighting application, the power optimizer will allow the maximum amount of power available to be extracted from the panel.

selinz

7/9/2012 4:46 PM EDT

Interestingly, a solar panel sales guy came by on the day that this article was published. I was astonished to find out that I could actually save money immediately. It turns out that we use double the "average" user and for anything beyond the norm, the 15 cents/kwh goes to about 30cents/kwh. Thank you PGE. This makes getting enough panels to knock our electricity useage in half has a quick payback period. (7-8 years).
If you are a do it yourselfer, it can be even less. see
http://www.wholesalesolar.com/enphase-solar-power-system.html
for example pricing. And no, I am in no way affiliated with these folks. They popped out of a simple google search. YMMV.

GREAT-Terry

7/11/2012 11:32 AM EDT

Very interesting MPPT control method. I like the micro-inverter idea as it is the most efficient way to dump energy to the grid. Managing multiple 200-300W power is much easier than a huge 10kW stuff. Great article!

HarrisMarcus

7/12/2012 1:35 PM EDT

Actually the microinverter method is less efficient than power optimizers and a large central inverter because 1) the voltage is higher and current lower which reduces I square R losses and 2) due to economies of scale there is less overhead and fewer number of components along with control circuits. The efficiency of the SPV1020 power optimizer is 98% and the efficiency of one large central inverter will be more than multiple microinverters.

green_is_now

1/23/2013 4:49 PM EST

until the cells get unbalanced and your 1% advatage quickly disapeers and micro inverters win on efficiency for both momentary cell inbalance (think clouds, bird droppings...) Or if a cell degrades or is mismatche power can actually drop in a cell in a series string.

green_is_now

1/23/2013 4:49 PM EST

Also there is no reason the 120 v cant be interleaved to give balanced 220Vac.

green_is_now

1/23/2013 4:51 PM EST

Large voltage ratio power coversion has lower and lower efficiencies as voltage ratios go up.
So its not just IR losses must also consider switching losses with respect to voltage ratio boost levels.

karan91

1/30/2013 5:05 AM EST

hi,any suggestion Solar Energy Conversion method for solar boat project??

LindaSF

4/1/2013 12:14 PM EDT

Your article is a little over my head but from the financial stand point there are 3 points that I always consider when debating between central inverters and micro inverters. Micro inverters are preferred when you need module level monitoring (monitoring the performance of each individual solar module), when partial array shading occurs, or when the design is constrained by locating modules sections of the roof with different orientation. If non of the above are true I usually recommend a central inverter. You can compare prices anywhere online: http://webosolar.com/store/en/80-microinverters