Solar-array controller needs no multiplier to maximize power

W Stephen Woodward, Chapel Hill, North Carolina

Solar-photovoltaic arrays are among the most efficient, costeffective, 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.

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-trackingcontrol 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-pointtracking- 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. This Design Idea relies on the well-known logarithmic behavior of transistor junctions, which translate into V_BE=(kT/q)log(I_C/I_S)=(kT/q) [log(I_C)-log(I_S)], where V_BE 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. IC_1A forces I_Q1 to equal IXx₁, where I is the solararray current and x₁ is a gain constant. IC_1B forces I_Q2 to equal V/499 kΩ, where V is the solar-array voltage. Thus, V_Q1=(kT₁/q)1[log(I)-log(I_S1) log(x₁)], and V_Q2=(kT₂/q)[log(V) -log(I_S2)-log(499 kΩ)]. V_Q1 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; I_S1 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; I_S2 is the saturation current of Q₂; K is degrees Kelvin; V_PF is the power-feedback signal; and V_IP is the calculated power-input signal. Because k, q, I_S1, I_S2, x₁, and 499 kΩ are all constants and T₁=T₂=T, for the purposes of the perturb-and-observe algorithm, which is interested only in observing the variation of current and voltage with perturbation, effectively, V_Q1=(kT/q)log(I), and V_Q2= (kT/q)log(V).

The series connection of Q₁ and Q₂ yields V_PF=V_Q1+V_Q2=(kT/q) [log(I)+log(V)]=(kT/q)log(VI), and, because of IC_1B’s noninverting gain of three, V_IP=3(kT/q)log(VI) 765 µV/% of change in watts. The V_IP log (power) signal couples through C₁ to synchronous demodulator S₁, and error integrator and control op amp IC_1C integrates the rectified S₁ output on C₃. The IC_1C 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-powerpoint- 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-pointtracking circuit and the regulator to only three connection nodes—I, V, and F—means that you can easily adapt the universal maximum-power-pointtracking circuit to most switching regulators and controllers. Therefore, this Design Idea offers the efficiency advantages of a maximum-power-pointtracking circuit to small solar-powered systems in which more complex, costly, and power-hungry implementations would be difficult to justify.

EDN Europe