Circuit:RTD Maximum Power Point Voltage Conditioning Amplifiers

Theory of Operation

Written:Brenton Salmi, Bryce Salmi

RTD Maximum Power Point Voltage ConditioningAmplifiers Overview

The Maximum Power Point Tracker (MPPT) achieves maximum power point tracking by predicting the solar panel Maximum Power Point Voltage (MPPV) and regulating the solar panel voltage to the predicted value. Accurate measurement and conditioning of the temperature is critical to obtain accurate tracking. Each MPPT has a RTD attached to the solar panel it operates with as temperature of each solar cell is assumed to be uniform across the entire solar panel. The voltage developed across the RTD is directly related to panel temperature, however, the voltage is small and changes in the opposite direction over temperature as compared to the MPPV over temperature. Therefore, the temperature signal must be amplified as well as conditioned to correspond with and predict the expected MPPV extremely accurately over the solar panel operating temperature range.

Figure 1 shows the schematic to be referenced during the analysis of the MPPV conditioning amplifier. Additionally, Table 1 tabulates the calculated values for the MPPV, scaled MPPV as applied to the UC2524 error amplifier non-inverting input, RTD resistance, and the voltage drop across the RTD with 1mA constant current drive. The following analysis will reference these items extensively.

RTD Differential Amplifier

A difference amplifier has been implemented as shown in Figure 1 with R1, R2, R3, R4, and U2. Since R1 is equal to R3 and R2 is equal to R4, the output voltage equation can be simplified as shown in Equation 1:

(1)

The output voltage of U2 is simply the ratio of R2 and R1 multiplied by the voltage difference between the non-inverting and inverting inputs of the op-amp. This constitutes the differential amplifier with a gain of 10 required. Assuming operation at 28°C, the voltage applied to R5, and the inverting input of U1, is calculated in Equation 2:

(2)

Simultaneous Equation Voltage Conditioning Amplifier

The amplifier differential voltage from U2 still changes in the opposite direction of the solar panel MPPV. As seen in Table 1, the MPPV is at its maximum when the RTD voltage (Vrtd) is at its minimum. The MPPV is also at its minimum when Vrtd is at its maximum voltage. Therefore, the slope of the RTD voltage must be flipped and scaled to match the predicted MPPV. Using SLOA076[1] from Texas Instruments as reference, simultaneous equations were used to force the RTD voltage to follow the line in Equation 3:

(3)

Which equates to the line in Equation 4:

(4)

The negative value of m in Equation 4 flips the slope of input voltage while the amplitude of m also provides a scaling function. The amplifier implemented with U1 also provides and offset voltage used to move the signal to force the RTD voltage applied to the inverting input of the UC2524 to exactly match the expected scaled solar panel MPPV. RTDVOUT in Figure 1 is expected to match the scaled MPPV in Table 1 and become 2.270V at 60°C, 2.491V at 28°C, and 3.091V at -60°C. To find the value of m, Equation 5 and Equation 6 are solved for b and set equal to each other. This removes the second variable and allows m to be solved for in Equation 7.

(5)

(6)

SolvingEquation 6for b provides Equation 7:

(7)

Substituting for b in Equation 5 results in Equation 8 from which the value of m can be determined:

(8)

(9)

Finally, plugging m back into Equation 6 provides the value of b in Equation 10:

(10)

The line that the solar panel scaled voltage follows, and the RTD voltage must follow to correctly predict the MPPV, is shown in Equation 11:

(11)

The value of m corresponds to gain U1, and the value of b corresponds to the offset voltage applied to the input signal. Using the derived values of m and b, the resistance values for R7 and R5 can be calculated with Equation 12:

(12)

Using the relationship in Equation 12, the offset voltage and voltage reference are used in Equation 13 to calculated the values of R7 and R6. The values of R5 and R8 were chosen to be 100kΩ by inspection. Tabulated resistance values for the simultaneous equation condition amplifier are shown in Table 2.

(13)

The graph shown in Figure 2 plots the amplified output of the differential amplifier, U2, in red on the bottom of the graph and the scaled voltage after the conditioning amplifier, U1, in blue on the top of the graph. Notice that the scaling and slope of the scaled RTD temperature measurement is inverted and slightly amplified from the differential amplifier output. The scaled temperature corresponds to the values predicted in Table 1. The left-side of the graph is the RTD operating at -60°C and the right-side of the graph is the RTD operating at 60°C. The output signal from the RTD amplification system successfully predicts the expected maximum power point voltage and enables the algorithm used to produce maximum power from the Fox-2 satellite solar panels..

[1]SLOA076 (PDF) Single-Supply Op Amp Design Techniques