Solar-array controller needs no multiplier to maximize power
Relying on the logarithmic behavior of transistor junctions to calculate power, this controller operates a photovoltaic array at its maximum power point.
W Stephen Woodward, Chapel Hill, NC; Edited by Martin Rowe and Fran Granville -- EDN, December 5, 2008
Solar-photovoltaic arrays are among the most efficient, cost-effective, and scalable “green” alternatives to fossil fuels, and researchers are almost daily announcing new advances in photovoltaic technology. But successful application of photovoltaics still depends on strict attention to power-conversion efficiency. Figure 1 shows one reason for this attention.
A photovoltaic array’s delivery of useful power to the load is a sensitive function of load-line voltage, which in turn depends on insolation—that is, sunlight intensity—and array temperature. Operation anywhere on the current/voltage curve except at the optimal maximum-power-point voltage results in lowered efficiency and a waste of valuable energy. Consequently, methods for maximum-power-point tracking are common features in advanced solar-power-management systems because they can boost practical power-usage efficiency—often by 30% or more.
Because of its generality, a popular maximum-power-point-tracking-control algorithm is perturb and observe, which periodically modulates, or perturbs, the load voltage; calculates, or observes, the instantaneous transferred power response; and uses the phase relationship between load modulation and calculated power as feedback to “climb the hill” of the current/voltage curve to the maximum-power-point optimum. The perturb-and-observe algorithm is the basis of the maximum-power-point-tracking-control circuit (Figure 2, in yellow) but with a twist (in blue), which achieves a feedback function equivalent to a current-times-voltage power calculation but without the complexity of a conventional multiplier. The idea relies on the well-known logarithmic behavior of transistor junctions, VBE=(kT/q)log(IC/IS)=(kT/q)[log(IC)–log(IS)], where VBE is the base-to-emitter voltage. It also relies on the fact that adding logarithms is mathematically equivalent to multiplication. Here’s how.
Capacitor C2 couples a 100-Hz, approximately 1V-p-p-modulation or 1V-p-p-perturbation square wave from the S2/S3 CMOS oscillator onto the photovoltaic-input voltage, V. The current/voltage curve of the array causes the input current, I, to reflect the V modulation with a corresponding voltage-times-current input-power modulation. IC1A forces IQ1 to equal I×x1, where I is the solar-array current and x1 is a gain constant. IC1B forces IQ2 to equal V/499 kΩ, where V is the solar-array voltage. Thus, VQ1=(kT1/q)1[log(I)–log(IS1)+log(x1)], and VQ2=(kT2/q)[log(V) –log(IS2)–log(499 kΩ)]. VQ1 is the base-to-emitter voltage of Q1; k is the Boltzman constant; T1 is the temperature of Q1; q is the elementary charge of the electron; I is the current input from the solar panel’s negative terminal; IS1 is the saturation current of Q1; x1 is the arbitrary gain constant, which IC3 determines; V is the voltage input from the solar panel’s positive terminal; IS2 is the saturation current of Q2; K is degrees Kelvin; VPF is the power-feedback signal; and VIP is the calculated power-input signal. Because k, q, IS1, IS2, x1, and 499 kΩ are all constants and T1=T2=T, however, for the purposes of the perturb-and-observe algorithm, which is interested only in observing the variation of current and voltage with perturbation, effectively, VQ1=(kT/q)log(I), and VQ2=(kT/q)log(V).
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The series connection of Q1 and Q2 yields VPF=VQ1+VQ2=(kT/q)[log(I)+log(V)]=(kT/q)log(VI), and, because of IC1B’s noninverting gain of three, VIP=3(kT/q)log(V I)≈765 µV/% of change in watts. The VIP log (power) signal couples through C1 to synchronous demodulator S1, and error integrator and control op amp IC1C integrates the rectified S1 output on C3. The IC1C integrated error signal closes the feedback loop around the IC3 regulator and results in the desired maximum-power-point-tracking behavior.
Using micropower parts and design techniques holds the total power consumption of the maximum-power-point-tracking circuit to approximately 1 mW, which avoids significantly eroding the efficiency advantage—the point of the circuit in the first place. Meanwhile, simplifying the interface between the maximum-power-point-tracking circuit and the regulator to only three connection nodes—I, V, and F—means that you can easily adapt the universal maximum-power-point-tracking circuit to most switching regulators and controllers. Therefore, this Design Idea offers the efficiency advantages of a maximum-power-point-tracking circuit to small solar-powered systems in which more complex, costly, and power-hungry implementations would be difficult to justify.
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Thank you for this great Design Idea!
I plan to take the central part of your circuit, the "power calculator" and to implement it to control an electronic load to monitor a solar panel's performance. I got it to work nicely today on a bread board. Since my load circuit is very different from your buck/boost-regulator, my modifications start at the integrator, and I also decided to use an opamp as relaxation oscillator to provide the square wave.
However, I have a question: could you enlighten me about the choice of the capacity of C2 and C3 in your circuit?
When it comes to Fig.1: you are wrong about the labeling of the axes in your answer from 12/13/2008. The abscissa (X) axis should be "VOLTAGE" (as it is) and the ordinate (Y) should be "CURRENT" and "POWER." Otherwise your the labeling "VMPP" wouldn't fit.
Thanks again from Sweden,
Uwe.
Uwe Zimmermann - 2009-4-5 12:35:00 PDT -
When the latest EDN arrives I immediately got to Design Ideas -- and am always excited to find a submission by W. Stephen Woodward. I have never communicated with Mr. Woodward, but if I were ever in Chapel Hill NC I would try to meet this genius.
I saw this DI last year, and it stuck in my brain when students came to see me about maximizing the power output from microbial fuel cells. I immediately referred them to EDN and Mr. Woodward''''s design.
I went back to find the article myself, and was shocked that anyone could attack Mr. Woodward''''s designs. Over the 15+ years of reading EDN and DIs I have always been overwhelmed by his creative and elegant circuit designs. I could only hope to get close to his expertise and creativity in my own designs.
I must agree that if one were to peruse the excellent designs published by Mr. Woodward over the years, one would recognize his genius!
If Mr. Woodward were to read this note, please invite me to visit your lab!
Christopher Gecik - 2009-15-4 13:33:00 PDT -
When the latest EDN arrives I immediately got to Design Ideas -- and am always excited to find a submission by W. Stephen Woodward. I have never communicated with Mr. Woodward, but if I were ever in Chapel Hill NC I would try to meet this genius.
I saw this DI last year, and it stuck in my brain when students came to see me about maximizing the power output from microbial fuel cells. I immediately referred them to EDN and Mr. Woodward''s design.
I went back to find the article myself, and was shocked that anyone could attack Mr. Woodward''s designs. Over the 15+ years of reading EDN and DIs I have always been overwhelmed by his creative and elegant circuit designs. I could only hope to get close to his expertise and creativity in my own designs.
I must agree that if one were to peruse the excellent designs published by Mr. Woodward over the years, one would recognize his genius!
If Mr. Woodward were to read this note, please invite me to visit your lab!
Christopher Gecik - 2009-15-4 13:19:00 PDT -
Mr. Woodward-
Don't worry about the whiny Brit, he should check other sources anyway or stick with things he's DEAD CERTAIN about to begin with.
Good circuit idea, timely and well thought out. I've searched and there are lots of hand wavers out there but it's either your MPP circuit(s) or buy a finished product.
I puzzled over IC1b until I realized it is a Howland VCCS circuit. Jung recommends a 100pf cap from pin 6 to 7 to quench oscillations.
I enjoy the quantity and content of your submissions and learn quite a lot from them.
Your mug shot is a little too Truman Capote but who cares?
John Linstrom - 2009-11-2 14:16:00 PST -
Dear Mr. Woodward,
I have some questions on the article "Solar-array controller needs no
multiplier to maximize power". I am a student in Oregon Institute of
Technology's Renewable Energy Engineering program. I am designing
the maximum power point electronics for a small (100 watt) vertical
axis wind turbine and I would like to adapt this design for my
application. I know that you published a similar design in 1998
"Maximum-Power-Point- Tracking Solar Battery Charger" using an
LTC1149 regulator.
In that design you suggested some minor changes that would make
the design suitable for a wind turbine-changing the dither rate from
50 hz to 0.5-5hz. I was wondering if I could do the same with the
newer design based on the LTM4607? Also, above ~40 watts or so the
wind turbine generator will have enough voltage so that the regulator
will be operating in buck mode. I should be able (with minor changes)
to use the same regulator to output 14V @ 8A per the LT specs on the
regulator. Is this correct?
Thanks for any feedback you can provide. I like both designs. Both are
elegant and simple.
Sincerely,
David Parker
Portland, OR
David Parker - 2009-4-2 17:48:00 PST
