An Analog Technique for Distributed MPPTPV Applications

R.sathiyapriya and R.Rajalakshmi, EEE, SSMIET,Dindigul .

Abstract—TEODI is the acronym of a maximum power point tracking (MPPT) technique which has been recently presented in the literature. Such a technique is particularly suitable in distrib-uted MPPT photovoltaic (PV) applications, and it is based on the equalization of the output operating points, of the dc/dc converters dedicated to each subsection of the PV array, in correspondence of the forced displacement of their input operating points. The main advantages of TEODI, its performances in terms of MPPT efficiency and speed of tracking, and the intrinsic capability to attenuate the effect, on the voltages of the PV modules, of the 100/120 Hz disturbances coming from the grid are shown by means of simulation results and experimental findings obtained by using a laboratory prototype developed by means of analog circuitry only.

Index Terms—Maximum power point tracking (MPPT), photo-voltaic (PV) systems.

I. INTRODUCTIONIN PHOTOVOLTAIC (PV) applications, the so-called “mis-match” conditions take place in case of different orientations of the PV modules belonging to the same PV field, shadowing effects determined by clouds and bodies surrounding the plant, manufacturing tolerances, nonuniformity of ambient tempera-ture in proximity of each module due to uneven sun irradiation and air circulation, dust and spot dirtiness such as leaves or bird droppings, PV cell and/or PV glass protection damages, etc. In mismatch conditions, the power versus voltage (P-V) characteristic of the PV field may have more than one peak, and maximum power point tracking (MPPT) algorithms can fail causing a drastic drop in the overall system efficiency, unless the entire P-V characteristic is periodically swept. In any case, the absolute maximum power of a mismatched PV field is lower than the sum of the available maximum powers that the mismatched modules are able to provide. Distributed MPPT (DMPPT) [1]–[4] allows to overcome these problems, since it is based on the use of a module dedicated dc/dc converter for the MPPT of each PV module (Fig. 1).

Fig. 1. Grid-connected PV system with DMPPT.

In [5], [6] a novel MPPT technique which is suitable for DMPPT applications has been introduced. Such a Technique is based on the Equalization of the Output operating points in correspondence of the forced Displacement of the Input operat-ing points of two identical PV systems and has been indicated with the acronym TEODI. Indeed, the idea of comparing the operating points of two identical PV systems was proposed for the first time in [7]. Nevertheless, the approach proposed in [7] is characterized by many significant differences with respect to TEODI. In fact, the technique presented in [7] needs the sensing of both PV currents and voltages, it requires three different control loops for each dc/dc converter, and it does not exploit the fact that the output ports of the two dc/dc converters are connected in parallel or in series. On the contrary, TEODI needs the sensing of the only output currents (if the output ports of the two dc/dc converters are connected

in parallel) or output voltages (if the output ports of the two dc/dc converters are connected in series) and requires only one control loop for the whole system. The design of the control loop required by TEODI is quite simple [6], while, in the case of the technique discussed in [7], the design of the control loops must be carried out by taking into account that, in order to avoid instability, the dynamics of the MPPT inner control loop must be slower than that one of the outer voltage loop leading to a reduced MPPT speed of the system. In the following, without loss of generality, we will refer to the case shown in Fig. 2 where the output ports of the two dc/dc converters are connected in parallel.

The main advantages offered by TEODI have been discussed in detail in [5]; they can be summarized as it follows.

1) The hardware implementation of TEODI requires few components, and it can be done in fully analog form,

Fig. 2. Schematic representation of the operating principle of TEODI.because it does not need any memory operation. To this regard, it is worth

noting that the two classical approaches, the perturb and observe (P&O) and the incre-mental conductance (IC) methods require a comparison of voltage/current/power values in two different operating points of the PV system, so that the adoption of a memory capability and therefore of a more or less cheap digital controller is mandatory.

TEODI does not require any measurement of the PV power, that is, it does not require multiplication of cur-rents and voltages.

2) It only requires the sensing of the currents at the output of the dc/dc converters dedicated to each subsection of the PV string. In its dual implementation, TEODI only needs the sensing of the converters’ output voltages. It is worth noting that, in general, the tracking based on a minimum number of electrical variables is preferable from a reliability point of view. Moreover, a reduction in the overall costs of the control circuitry is also achieved.

3)4) TEODI approach can be applied to any topology of dc/dc power

converter dedicated to a single module. 5)6) The MPPT efficiency that TEODI is able to guarantee is higher than

that one obtainable by means of perturbative approaches like P&O and IC techniques. In fact, it is well known that perturbative approaches reach a steady-state condition characterized by a periodic oscillation of the PV voltage around the MPP, so that a kind of parametric optimization is needed [8]. On the contrary, TEODI is not a perturbation-based technique, so that, at steady state, there are no fluctuations of the PV operating point.

7)8) In this paper, the principle of operation of TEODI is only briefly

recalled since the complete description is provided in [5]. The novelty of this paper is represented by the experimental validation of the theoretical results shown in [5] by means of some experimental measurements performed on a laboratory prototype which has been entirely developed by using analog

Fig. 3. Power versus voltage characteristic of each subsection.

circuitry. Moreover, an additional new feature of this paper is represented by the analysis of the rejection of the 100 Hz/ 120 Hz disturbances, which, in single-phase ac applications, propagate from the dc/ac power stage toward the PV module. Such an analysis is carried out in detail by using simulation and experimental results in order to corroborate the theoretical findings.

II. WORKING PRINCIPLE OF TEODI

9) In Fig. 2, the PV subsections A and B represent two iden-tical subsections of a given PV generator operating under the same levels of irradiance and ambient temperature. Each PV subsection with its own associated dc/dc converter will be referred to as switched-mode PV source (SMPVS). Due to the parallel connection of the output ports of the two SMPVSs, it is vA2 = vB2 = Vout. Therefore, if it occurs that iA2 = iB2, then the powers delivered from the two SMPVSs assume the same value. In such a case, by assuming that the efficiencies of the power stages of the two dc/dc converters are equal,

the power extracted by the two PV subsections must assume the same

value Pin. Apart from the trivial case vA1 = vB1, the equality of such powers can occur only in the case in which the operating voltages of the two PV subsections are properly located at the opposite sides with respect to the MPP voltage v MPP as shown in Fig. 3. In the system of Fig. 2, the high-frequency switching content of the quantity k (iA2 −∗ iB2), where k is a constant gain equal to −1, is filtered out by means of a low-pass filter whose output is k (_iA2_ − _iB2 _), where variables∗ within brackets represent the low-frequency content of the corresponding variables. The proportional-integral controller ensures that.In the system of Fig. 2, the duty cycles dA(t) and dB(t) driving the main switches of the two dc/dc converters differ since dA(t) = dB(t) − d where d = dV/Vs (0 < d < 1), Vs is the peak amplitude of the saw-tooth carrier waveforms of the two pulse width modulation (PWM) modulators, and dV is a constant voltage offset. Without loss of generality, by assuming that Vout > vA1 and Vout > vB1, the operation of TEODI can be explained by assuming that the boost topology is adopted for the two dc/dc converters. As shown in [5], by assuming continuous conduction mode operation for each boost converter, it is always vA1 > vB1, so that three possible cases may occur.

Whenever vA1 and vB1 are both on the left side or both on the right side with respect to vMPP, the powers drawn by the two PV subsections are different and, as a consequence, iA2 is different from iB2. In this case, the signal at the input of the PI controller is not null, and therefore its output signal vc(t) is a decreasing or an increasing function of time. The same conclusion holds for dB(t), dA(t), and the voltage conversion ratios of the two dc/dc converters. As a consequence, with the output voltage Vout fixed, both voltages vA1(t) and vB1(t) are increasing or decreasing functions of time as required to move the operating points of both the PV subsections toward the MPP. The only possible equilibrium condition, in which the input of the PI controller is nearly equal to zero and quan-tities dB(t), dA(t),

vA1(t), and vB1(t) are nearly constant, is obtained when the operating voltages vA1 and vB1 are located at the opposite sides with respect to vMPP, such that PA = PB (Fig. 3). That is, the MPPs of the two PV subsections are not exactly reached, and there will be an error in the tracking. Of course, the value of d strongly affects the steady-state performances of TEODI. In fact it is: vA1 − vB1 = Vout d.∗ Therefore, in equilibrium conditions, the smaller the value of d, the smaller the displacement of the operating point of each PV subsection from the MPP and therefore the higher the MPPT efficiency. However, it is intuitive to understand that, in practical applications, because of the effect of tolerances of the physical components of the two SMPVS and of small but nonetheless unavoidable effects (due to temperature, humidity, and so on) that make the two SMPVS not perfectly equal, too small values of d could lead to the failure of the technique. In any case, the value of d also influences the speed of the whole tracking process in dynamic conditions: the higher the value of

d, the higher such a speed [5]. Therefore, the choice of d must be made on the basis of a reasonable compromise between accuracy of MPPT under stationary atmospheric conditions and speed of MPPT under time varying atmospheric conditions.

Fig. 4. Equivalent block diagram of the system of Fig. 2

Similar considerations also apply as concerns the choice of the amplitude of the perturbation of the controlled variable to be adopted when using the P&O technique [8], [9].

As shown in [5], by using the small signal representation of the power stage of the boost converter [10], it is possible to obtain the transfer functions which appear in the schematic block diagram of Fig. 4 and which are indispensable in order to investigate the dynamic performances of TEODI. In particular, the transfer functions referring to subsystem A are shown in the equations at the bottom of page) Of course, the transfer functions referring to subsystem B can be easily obtained by means of a formal substitution of the letter A with the letter B in the preceding expressions where symbols with hats represent small-signal variations around the quiescent values of the corresponding quantities. RA and RB are the differential resistances of modules A and B [9]. L is the inductance of the boost inductors, Cin is the capacitance of the input capacitors, and DA and DB are the dc values of the duty cycle of the two boost converters. The design of the compensator transfer function leading to a stable closed-loop system, with adequate phase margin and a sufficiently high crossover frequency.

out by applying the phase margin test to the compensated loop gain

Tc(s) = Gc(s) · Tu(s) (3)

here, Gc(s) is the proportional-integral controller transfer func-tion, and Tu(s) is the uncompensated loop gain

III. REJECTION OF LOW FREQUENCY DISTURBANCES

In [5], the performances which can be obtained by adopting TEODI have been compared with those ones which can be obtained by adopting the P&O technique. In particular, it has been shown that TEODI is characterized by a higher tracking speed with respect to the P&O technique, and this aspect represents a further advantage offered by TEODI, in addition to those ones already listed in the introduction.

In this section, an additional, interesting feature exhibited by TEODI

will be analyzed. It is represented by the inherent capability exhibited by TEODI in attenuating low-frequency disturbances propagating from the output ports of the dc/dc converters toward their input ports, that is at the terminals of the two PV module subsections. This aspect is particularly relevant in single-phase grid-connected applications. In fact, it is worth noting that the energy-storage bulk capacitor placed at the interface between the dc/dc and the dc/ac stage of any grid connected PV system is the source of oscillations of the PV voltage taking place at the second harmonic of the grid frequency fac. It is well known that the voltage of such a capacitor must be allowed to increase or decrease in order to store or release the required energy. This allows to balance the dc power extracted from the PV array, with the instantaneous power injected into the grid. The presence of low-frequency oscillations in the PV voltage causes a more or less significant sweep, with frequency equal to 2 fac, of the operating point of the PV modules around the MPP. This of course is undesirable since, not only the operating point of the PV array is forced to oscillate more or less far from the MPP, but the MPPT algorithm can be confused leading to an additional waste of available energy. In the literature, some solutions aimed at reducing the amplitude of such oscillations have been proposed. The first solution is represented by the direct filtering which can be obtained either by means of passive or of active filters. As concerns passive filters, the easiest solution is represented by the adoption of larger capacitances at the interface between the dc/dc stage and the dc/ac stage and/or of larger capacitances at the PV array terminals. Indeed, the reduction of capacitances is highly desirable since this might allow the use of metalized polypropylene capacitors in order to get higher reliability with respect to the case of adoption of electrolytic capacitors. Moreover, with specific reference to the capacitor placed across the PV array terminals, the lowest its capacitance, the highest the MPPT speed. Of course, also more complicated passive filters could be adopted and placed across the PV array terminals; unfortunately, the necessity to damp such filters involves additional losses in the filters themselves leading to a more or less consistent decrease of the efficiency of the system. As concerns active filters, they generally involve an increased complexity in terms of control and the use of additional active and passive components. In [11], [12], an approach, based on a feedforward control structure, has been proposed for both PV and fuel cell-based applications. The main drawback of such a technique is represented by the need of a perfect phase lock of the sinusoidal oscillation at 2fac; therefore, the use of an auxiliary phase locked loop circuit is necessary. Furthermore, as in any feedforward approach, the proposed technique suffers from disturbances and uncertainties related to unmodeled phenomena and tolerances. Another limi-tation is represented by the fact that the attenuation is obtained only at a frequency equal to 2fac; in practical cases, such an harmonic component is the prevailing one, but also additional harmonics are produced by the system nonlinearity which also need to be removed. A further approach which can be applied to eliminate periodic disturbances is represented by repetitive control implemented in both analog and digital way [13], [14]. Such a solution is not able to remove all those disturbances, appearing in practical systems, which are characterized by frequencies that are difficult to be foreseen during the design process. In principle, by using adaptive repetitive control [14], it is possible to overcome such a drawback but at the expense of an increased complexity of the control circuitry which must be implemented in digital form. In [9], the problem of optimizing the P&O MPPT performances has been faced; no attempt has been made to reduce the 2fac voltage oscillations. In order to avoid mistakes of the P&O controller, in [9], it is shown that it is necessary to adopt very large values of the amplitude of the duty cycle perturbation. Of course, this is not desirable from the point of view of the steady-state MPPT efficiency. In [15], [16], in order to reduce the 2fac PV voltage oscillations, the P&O controller does not directly act on the duty cycle of the dc/dc stage (as in [9]), but it provides a proper reference voltage which must be followed by the PV voltage. The error voltage is then processed by a compensation network.

In the following section, it will be shown that the 100-Hz disturbances coming from the output are not able to cause the failure of TEODI, and, moreover, that the proposed technique is intrinsically able to provide an attenuation of such disturbances on the PV voltage.

The presence of the loop (evident in Fig. 2 or in Fig. 4) characterized by the compensated loop gain Tc is the respon-sibility of the

attenuations of 100/120-Hz disturbances, which, in single-phase ac applications, propagate from the dc/ac power stage toward the PV module. If a boost topology is adopted, the total attenuation of 100-Hz disturbances from the output to the input is approximately given by (VMPP/Vout)/|1 + Tc(100 Hz)|, where (VMPP/Vout) is the intrinsic attenuation provided by the boost topology and 1/|1 + Tc(100 Hz)| is the attenuation effect provided by TEODI. TEODI could be implemented, in principle, also by using a power stage topol-ogy different from the boost topology adopted in this paper. Should a different power stage topology be adopted, since the loop characterized by the compensated loop gain Tc is always present, then the attenuation effect provided by TEODI would be always given by 1/|1 + Tc(100 Hz)|.

IV. NUMERICAL RESULTS

The results shown in this section refer to the following set of values for the two boost converters: L = 47 µH; Vout = 12 V; fs = 100 kHz; Cin = 33 µF. Each subsection of the PV module considered for the numerical tests has the electrical characteristics reported in Table I.The crossover frequency of Tc(s) has been chosen equal toabout 1500 Hz; moreover, d = 0.05; Vs = 1; Gc(s) = (2.5 10−6s +∗ 0.059)/(5 10−5s), LP(s) = 1/(2.53 10−10s2 + 2.228 10−5s + 1).∗ ∗ ∗

In Figs. 5 and 6, the Bode plots of Tu, Tc, and 1/(1 + Tc) are shown. The magnitude of Tc at 100 Hz is equal to about 22 dB. Therefore, as an example, if superimposed on Vout, we consider a sinusoidal 100-Hz disturbance with a peak-to-peak value of 3 V, we expect a sinusoidal 100 Hz component, on the voltage of each PV subsection, with a peak-to-peak value approximately equal to the value obtainable in open loop (3 V M P P/V out) multiplied by |1/(1 + Tc(100 Hz))|.∗ That is, the expected peak-to-peak value of the 100-Hz dis-turbance on the PV voltage is approximately equal to (22/20) V = 0.175 V.

Results shown in Fig. 7 obtained in PSIM simulation en-vironment, by superimposing on Vout a sinusoidal 100-Hz disturbance with a peak-to-peak value equal to 3 V, confirm the validity of the above observations. In particular, in Fig. 7, the time-domain behavior of the voltages of the two subsections of the PV module and of the output voltage are shown by considering the following values of irradiance G and ambient temperature T: G = 1000 W/m2, T = 25 ◦C.

Fig. 6. (a) Bode plots of Tc. (b) Bode plots of 1/(1 + Tc).

Fig. 7. Time-domain behavior of the voltages of the two subsections of the

PV module (G = 1000 W/m2, T = 25 ◦C).

In Fig. 8, the powers of the two subsections of the PV module, during the turn on transient of the boost converters, are shown and compared with the maximum power. In Fig. 9 the duty cycles driving the two dc/dc converters are reported.

The significant attenuation effect provided by TEODI and evidenced in Fig. 7 can be explained just by analyzing the waveforms reported in Fig. 9.

The presence of 100-Hz oscil-lations in the duty cycle waveforms of the two boost converters just represents the correction action played by TEODI control circuitry. Should such oscillations of the control variables be absent, then there would be no possibility to attenuate the

Fig. 8. Time-domain behavior of the powers of the two subsections of the PV

module (G = 1000 W/m2, T = 25

◦C).

Fig. 9. Time-domain behavior of the duty cycles of the two subsections of the

PV module (G = 1000 W/m2, T = 25

◦C).

effect of 100-Hz disturbances propagating from the output ports toward the input ports of the dc/dc converters.

V. EXPERIMENTAL RESULTS

The experimental results shown in this section have been obtained by using a laboratory prototype which has been de-veloped by means of analog circuitry only. Two subsections of a commercial PV module have been used. The nominal electrical parameters of each PV subsection are reported in Table I. In order to minimize the path for the control loop, the two dc/dc converters have been integrated into a single board, as shown in Fig. 10(a). The values of the components of the dc/dc power stages and the converter operating conditions are the same reported in Section III. Some details on the implemen-tation of the analog control circuitry are reported in Fig. 10(b) and (c). In Fig. 11, some preliminary results are shown. The vertical lines, shown together with the P-V characteristics of the two subsections, put into evidence the operating voltages of the two subsections in the three possible cases discussed in Section II. Even if some discrepancy exists between the P-V characteristics of the two modules, due to manufacturing tolerances, the theoretical predictions regarding the sign of the difference of the output currents of the two SMPVSs are confirmed, as shown by the clock-shaped indicators reported on the right high side of each figure. In each one of the

Fig. 10. (a) Picture of the laboratory prototype developed by using analog circuitry only. (b) Schematic for generating two synchronized PWM modulator.(c) Schematic of the TEODI compensation network.

plots in Fig. 11, the color bars (on the right side) show the instantaneous duty cycle (Duty) of the PWM signal used to drive the MOSFET of the converter connected to the section A