Photovoltaic High-Frequency Pulse Charger for Lead-Acid Battery under Maximum Power Point Tracking

Abstract

A photovoltaic pulse charger (PV-PC) using high-frequency pulse train for charging lead-acid battery (LAB) is proposed not only to explore the charging behavior with maximum power point tracking (MPPT) but also to delay sulfating crystallization on the electrode pores of the LAB to prolong the battery life, which is achieved due to a brief pulse break between adjacent pulses that refreshes the discharging of LAB. Maximum energy transfer between the PV module and a boost current converter (BCC) is modeled to maximize the charging energy for LAB under different solar insolation. A duty control, guided by a power-increment-aided incremental-conductance MPPT (PI-INC MPPT), is implemented to the BCC that operates at maximum power point (MPP) against the random insolation. A 250 W PV-PC system for charging a four-in-series LAB (48 V_dc) is examined. The charging behavior of the PV-PC system in comparison with that of CC-CV charger is studied. Four scenarios of charging statuses of PV-BC system under different solar insolation changes are investigated and compared with that using INC MPPT.

1. Introduction

Renewable energy sources have become indispensable and applicable in our life in consideration to the lack of fossil fuel, especially for the photovoltaic and wind energies. As for energy storage, lead-acid battery (LAB) is always the interesting device due to low cost; even its lifecycle time is low. Fortunately, the experiment reported that, after charging the battery in 5–10 hours with a short-period large current, the sulfating crystallization covered on the plates of positive electrode area will be reduced, and the battery is without overheat and thereby increases the discharge efficiency to extend battery life [1–3]. Thus, the pulse charge method has become one of the available charging strategies in battery management. The LAB is basically composed of two electrodes, the negative electrode made of metallic lead (Pb) and the positive one lead-oxide (PbO₂), immersed in a sulphuric acid solution (H₂SO₄), which produces chemical reaction during charging and discharging processes. During discharge state, both the electrodes in battery will build up lead sulfate PbSO₄ and the electrolyte is then converted to H₂O, but the opposite process will occur in charging state. When the battery approaches 85–95% of the state of charge (SOC), the majority of the PbSO₄ will be converted to Pb and PbO₂, in which the battery voltage might be greater than the gassing voltage. The overcharge reaction possibly results in the gas evolution of hydrogen appearing at negative electrode and of oxygen at positive electrode. This undesired phenomenon may lead to heat, increasing charging time, and shorten the battery life, even exists explosive potential if the gas is not vented. Above all, if some PbSO₄ is crystallized on the pores of positive electrode, the discharging current will be limited due to the reduction of effective surface area on the positive electrode. In order to prolong the battery life, a high-frequency photovoltaic pulse charger (PV-PC) system for LAB is presented, which contributes the pulsate effect for delaying the mentioned sulfating crystallization during the adjacent tiny pulse break times. In this work, a boost current converter (BCC) associated with the PV module is modeled to maximize the energy charging to LAB under maximum power transfer [4]. In order to maximize the energy pumped from PV module, a duty cycle control guided by a power-increment-aided incremental-conductance maximum power point tracking (PI-INC MPPT), derived from the incremental-conductance maximum power point tracking (INC MPPT), is adopted to sustain the PV-BCC pumping energy from PV module that is fast and accurate against the random solar insolation [4–8]. The weakness of the INC-MPPT is its ambiguous incremental conductance occurring in the left side of the MPP, which may delay the tracking behavior of MPPT. To clearly describe the dynamic tracking behavior in charging, four scenarios of solar insolation change under the guidance of PI-INC MPPT and INC-MPPT are, respectively, investigated and compared to each other in this work. An experimental study for verifying the charging behavior of the PV-PC system with a four-in-series 45-AH (ampere hour) LABs (48 V_dc) is examined. The charging characteristics of the PV-PC system in comparison with that of conventional constant-current constant-voltage (CC-CV) charger are studied. Experimental result validates that high-frequency pulse train can actually delay the sulfating crystallization on the plates of electrodes of the LAB, which prolongs the battery life.

2. Analysis of PV-PC System

Figure 1(a) shows the circuit diagram of the PV-PC system, which is formed by a BCC guided by a MPPT controller. Dynamic states of the BCC at boundary condition are shown in Figure 1(b), in which the output current 𝑖_𝑜 is certainly a form of pulse train that is used as a charging source. The PV BCC driven by a duty period 𝑑_𝐵𝑇_𝑠 from PI-INC MPPT can operate between discontinuous-conduction mode (DCM) and boundary-conduction mode (BCM) for pulse charging to the LAB.

(a)

(b)

Figure 1 

(a) Proposed PV-PC system and (b) predicted energy-pumped waveforms of PV-BCC at boundary mode.

For convenience in analysis, the steady state of PV-BCC in BCM is described. If a battery 𝑉_𝐵 greater than maximum 𝑉_𝑝𝑣 is adopted and all components are presumed to be ideal, the peak inductor current 𝑖_{𝐿,𝑝𝑘} of the PV-BCC in BCM from Figure 1(b) can be represented by 𝑖_{𝐿,𝑝𝑘}=𝑉_𝑝𝑣𝐿⋅𝑑_𝐵𝑇_𝑠, (1) where 𝐿 is the boost inductor, 𝑑_𝐵 the duty ratio, and 𝑇_𝑠 the switching period. We then have average PV current 𝐼_𝑝𝑣: 𝐼_𝑝𝑣=𝑉_𝐵𝑉_𝑝𝑣𝑉_𝐵−𝑉_𝑝𝑣⋅𝑑²_𝐵2𝐿𝑓_𝑠, (2) where switching frequency 𝑓_𝑠=1/𝑇_𝑠. If power efficiency 𝜂 is considered, the average output current 𝐼_𝑜(=𝐼_𝐵) to LAB from (2) will be 𝐼_𝑜=𝜂𝑉²_𝑝𝑣𝑑²_𝐵2𝐿𝑉_𝐵−𝑉_𝑝𝑣𝑓_𝑠. (3) Equation (3) represents the control-to-output transfer function, in which the output current 𝐼_𝑜 is proportional to square of duty ratio 𝑑_𝐵 and inversely proportional to switching frequency 𝑓_𝑠. The model and simulation of control-to-output transfer function are presented in Figures 2(a) and 2(b), respectively. The duty ratio 𝑑_𝐵 of PV-BCC is designed associated with the PV characteristic as shown in Figure 3. The output power of PV-BCC can be obtained by 𝑃_𝑜=𝜂𝑉_𝐵𝑉²_𝑝𝑣𝑑²_𝐵2𝐿𝑉_𝐵−𝑉_𝑝𝑣𝑓_𝑠. (4)

(a)

(b)

Figure 2 

(a) The model of the proposed PV-PC and (b) simulated and experimented output-to-control responses.

Figure 3 

𝐼𝑝𝑣-𝑉𝑝𝑣 and 𝑃𝑝𝑣-𝑉𝑝𝑣 characteristic curves for a two-in-series PV module, where a tracking threshold zone (TTZ) is indicated for distinguishing PI-coarse tracking zone and INC-fine tracking zone [6].

If an interleaved configuration is considered in the PV-BCC, the average output current 𝐼_𝑜 and power 𝑃_𝑜 can be easily obtained from (3) and (4) by multiplying two.

3. PI-INC MPPT for PV-PC System

The PV-BCC guided by PI-INC MPPT controller can draw energy from PV module fast and accurate according to the guidance specified on 𝐼_𝑝𝑣-𝑉_𝑝𝑣 and 𝑃_𝑝𝑣-𝑉_𝑝𝑣 characteristic curves in Figure 3, in which the tracking references for executing power-increment tracking (PI) and incremental-conductance (INC) tracking are clearly described in [6, 8]. The PI-INC MPPT can provide a PI-coarse tracking quick toward a specified threshold-tracking zone (TTZ) using 𝑃_𝑝𝑣-𝑉_𝑝𝑣 curve, to avoid delay tracking that stems from some ambiguous conductance detection in the right-hand side of maximum power point (MPP) in 𝐼_𝑝𝑣-𝑉_𝑝𝑣 curve by using INC MPPT method [4, 5, 9]. In Figure 3, two mutual equivalent TTZs are, respectively, defined in the 𝐼_𝑝𝑣-𝑉_𝑝𝑣 and 𝑃_𝑝𝑣-𝑉_𝑝𝑣 curves used to distinguish the roles of PI-INC MPPT tracking and conventional INC MPPT. A PI-coarse tracking along 𝑃_𝑝𝑣-𝑉_𝑝𝑣 curve executes quick toward TTZ when the PV-BCC operates outside the TTZ. Once the detected power increment Δ𝑃 is within TTZ, INC-fine tracking is provided toward the MPP using 𝐼_𝑝𝑣-𝑉_𝑝𝑣 curve. Thus, a fast and accurate tracking performance is applicable in PI-INC MPPT in comparison to that in the conventional INC-MPPT. The MPP for INC MPPT, reported by Wasynczuk [5], can then be given by 𝑑𝐼_𝑝𝑣𝑑𝑉_𝑝𝑣𝐼=−^𝑝𝑣𝑉_𝑝𝑣,Δ𝐼_𝑝𝑣Δ𝑉_𝑝𝑣≈𝑑𝐼_𝑝𝑣𝑑𝑉_𝑝𝑣𝐼=−^𝑝𝑣𝑉_𝑝𝑣. (5) It is clearly shown that in Figure 3 the measure Δ𝐶 is bounded by the two ratios 𝜌₁ and 𝜌₂ on the 𝐼_𝑝𝑣-𝑉_𝑝𝑣 curve, and correspondingly the measure Δ𝑃 is bounded between limits 𝑃_𝜌1 and 𝑃_𝜌2 on the 𝑃_𝑝𝑣-𝑉_𝑝𝑣 curve, in which 𝑃_𝜌1 and 𝑃_𝜌2 are derived from the two ratios 𝜌₁ and 𝜌₂. From the specified Δ𝐶 on the 𝐼_𝑝𝑣-𝑉_𝑝𝑣 curve, the tracking bound in TTZ will be −𝜌₁𝐼_𝑝𝑣𝑉_𝑝𝑣>Δ𝐶>−𝜌₂𝐼_𝑝𝑣𝑉_𝑝𝑣 (6) and outside the TTZ when Δ𝐶>−𝜌₁𝐼_𝑝𝑣𝑉_𝑝𝑣 (7) or Δ𝐶<−𝜌₂𝐼_𝑝𝑣𝑉_𝑝𝑣, (8) where Δ𝐶 is defined as Δ𝐶=Δ𝐼_𝑝𝑣Δ𝑉_𝑝𝑣. (9) The two ratios 𝜌₁ and 𝜌₂ are real numbers. Equation (9) is always negative because Δ𝐼_𝑝𝑣 and Δ𝑉_𝑝𝑣 have opposite signs. Accordingly, the corresponding relation to PI-INC MPPT derived from the specified bounds of INC MPPT will be, from (6)–(9), 𝑃_𝜌1>Δ𝑃>𝑃_𝜌2 (10) within TTZ, where Δ𝑃=𝑃_𝑛+1−𝑃_𝑛,Δ𝑉=𝑉_𝑛+1−𝑉_𝑛, and Δ𝐼=𝐼_𝑛+1−𝐼_𝑛, and Δ𝑃>𝑃_𝜌1 (11) or Δ𝑃<𝑃_𝜌2 (12) outside of TTZ. The two power threshold limits in (10) are defined by 𝑃_𝜌1≡1−𝜌₁Δ𝑉𝐼_𝑛+1,𝑃_𝜌2≡1−𝜌₂Δ𝑉𝐼_𝑛+1. (13)

The flow chart of PI-INC MPPT for duty control presented in Figure 4 will enable MPPT controller adaptively providing proper duty ratio 𝑑_𝐵 for PV-BCC to pump energy from PV module at MPP in which a simplified program with 𝑃_𝜌1=𝑃_𝜌2=0 is examined. In other words, the program is a special case of the PI-INC MPPT without TTZ.

(a)

(b)

Figure 4 

Programming of PI-INC MPPT: (a) main program and (b) subroutine program without THZ, as a simplified case of PI-INC MPPT.

4. Design and Realization

A 250 W PV-PC system configured as in Figure 1(a) consisting of a two-in-series PV module (Kyocera KC130T), a BCC, and a four-in-series LAB (Kawasaki MF50B24, 12 V_dc, 45 AH, each) is designed and realized for assessing the charging behavior of LAB guided by PI-INC MPPT, and validating the feasibility in application. The PV-PC system operates at constant frequency of 40 kHz with duty varied from 0 to 0.36 under solar insolation from 0 to 1 kW/m², in which the duty at 𝑑_𝐵=0.36 is when solar insolation at 1 kW/m², where the peak charging current for LAB is 16 A. The program of PI-INC MPPT is executed by microchip dsPIC33FJ06GS202 according to the tracking guidance in Figure 4, in which a simplified case of PI-INC MPPT without THZ is presented for instance. The PI-coarse tracking along 𝑃_𝑝𝑣-𝑉_𝑝𝑣 curve can perform fast and accurate tracking toward MPP in comparison with the INC tracking along 𝐼_𝑝𝑣-𝑉_𝑝𝑣 curve. The waveforms of the PV-BCC working at solar insolation of 600 W/m² and 1000 W/m² are measured in Figures 5 and 6, respectively, in which the boost inductor current 𝑖_𝐿 is in DCM at 600 W/m² but in CCM at 1000 W/m². In spite of the state modes either DCM or CCM, the output currents 𝑖_𝑜 clearly shown in Figures 5(b) and 6(b) are always available pulse trains for charging the LABs. Figure 7 shows the comparison of the tracking behaviors of PI-INC MPPT and INC MPPT in the PV-PC system under four kinds of solar insolation scenarios. The voltage tracking in Figure 7(a) and power tracking in Figure 7(b) clearly display that the PI-INC MPPT is much more fast and accurate toward the MPP than the INC MPPT. The PI-INC MPPT can only pay few seconds to track at MPP when the solar jump step initially occurs in either side of the MPP. In other words, there is no ambiguous detection happened in PI-INC MPPT. As for the INC MPPT, it is ambiguous to detect the incremental conductance in the left-hand side of the MPP, which may lead much delay in MPPT, such behaviors as in scenarios 1 and 3; the tracking times toward MPP should be much more over 4–10 times of the PI-INC MPPT. The measured data of tracking response shown in Table 1 show that the PI-INC MPPT is more reliable than INC MPPT in tracking process during the four scenario changes; in particularly, there is no abrupt delay response occurring in PI-INC MPPT during the insolation change, in comparison to the response of INC MPPT. The state of charge (SOC) of the PV-PC system compared with that of CC-CV charger is shown in Figure 8, and the detail charging statuses are measured in Table 2. The measured result reveals faster response of 195 min for PV-PC system than that of 210 min for CC-CV charger over about 8%, compared at SOC about 95%.

Table 1 

Comparison of MPPT tracking scenarios under different insolation changes.

Table 2 

Comparison of charging statuses between CC-CV and pulse charge.

(a)

(b)

Figure 5 

Measured waveforms of PV-BCC at 600 W/m2, MPPT conditions: 𝑉𝑝𝑣=32.7 V, 𝐼𝑝𝑣=4.3025 A, 𝑓𝑠=40 kHz, and 𝑑𝐵=0.29, (a) Hor.: 10 𝜇/div. and (b) Hor.: 50 𝜇/div.

(a)

(b)

Figure 6 

Measured waveforms of PV-BCC at 1000 W/m2, MPPT conditions: 𝑉𝑝𝑣=34.3 V, 𝐼𝑝𝑣=47.193 A, 𝑓𝑠=40 kHz, and 𝑑𝐵=0.36, (a) Hor.: 10 𝜇/div. and (b) Hor.: 50 𝜇/div.

(a)

(b)

Figure 7 

Tracking comparison of PI-INC MPPT and INC MPPT for PV-PC system under four scenarios of solar insolation change (a) voltage tracking behavior and (b) power tracking behavior.

Figure 8 

Comparison of charging behaviors between CC-CV and PV-PC.

5. Conclusion

The PV pulse charge directly using PV energy without through a dc-to-dc converter as energy buffer enhances the utilization of renewable energy. The brief pulse break existing between adjacent high-frequency pulses can actually perform the discharge refreshing of LAB for delaying sulfate crystallization on electrodes. The charging behavior using pulse charge is faster than that using CC-CV charge, which reveals that the resulted sulfate crystallization on the positive electrode of the LAB is slow in pulse charging process, which is good for prolonging the battery life. Moreover, the PI-INC MPPT compared with INC MPPT advantages much better tracking behavior without abrupt tracking delay during solar insolation change.

Acknowledgments

The authors would like to thank the National Science Council with the project NSC 101-2221-E-415-010 and joint project of Lien-Chang Electronics Enterprise Ltd. Co. 991206 for their financial support.