11
IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 28, NO. 6, JUNE 2013 2957 Submodule Integrated Distributed Maximum Power Point Tracking for Solar Photovoltaic Applications Robert C. N. Pilawa-Podgurski, Member, IEEE, and David J. Perreault, Senior Member, IEEE Abstract—This paper explores the benefits of distributed power electronics in solar photovoltaic applications through the use of submodule integrated maximum power point trackers (MPPT). We propose a system architecture that provides a substantial in- crease in captured energy during partial shading conditions, while at the same time enabling significant overall cost reductions. This is achieved through direct integration of miniature MPPT power converters into existing junction boxes. We describe the design and implementation of a high-efficiency (>98%) synchronous buck MPPT converter, along with digital control techniques that en- sure both local and global maximum power extraction. Through detailed experimental measurements under real-world conditions, we verify the increase in energy capture and quantify the benefits of the architecture. Index Terms—DC-DC power converters, energy harvesting, photovoltaic cells, power integrated circuits, solar energy. I. INTRODUCTION W ITH rising world-wide energy demands and soaring prices of fossil fuels, interest in renewable energy sources has increased. Among these, solar photovoltaic (PV) energy has seen a rapid growth in the last few years, resulting in decreased prices of PV panels as production capacity increases at a fast pace. As the PV panel prices decrease, the cost of the power electronics required to extract the maximum power of the PV panels and to interface the PV system to the grid is becoming a larger part of the overall system cost [1]. Much at- tention has, therefore, been given to the development of power electronics that enable a cost reduction of the overall system. In addition, much research is focused on increasing the efficiency of the power processing stage, as well as on improving the power yield of the overall system [2], [3]. Many PV installations suffer from current mismatch between different panels, due to nonuniform shading of the array, dirt accumulation, or manufacturing variability. Ensuring uniform illumination is particularly challenging in residential PV appli- cations, where large current mismatch can be present due to external objects that cause shading. Shown in Fig. 1(a) is the Manuscript received May 15, 2012; revised July 12, 2012; accepted September 7, 2012. Date of current version December 7, 2012. This work was supported by the National Science Foundation under Grant 0925147. Recommended for publication by Associate Editor T. Suntio. R. C. N. Pilawa-Podgurski is with the University of Illinois at Urbana- Champaign, Urbana, IL 61801 USA (e-mail: [email protected]). D. J. Perreault is with the Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139 USA (e-mail: djperrea@ mit.edu). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TPEL.2012.2220861 most common solar PV architecture, which connects all panels in series. In this architecture, any partial shading or other source of cell current mismatch will cause the overall system output power to be reduced, since the current in the string is limited by the weakest panel. While panels used today typically employ bypass diodes that help protect the panels and limit the negative effect of partial shading, it is still the case that partial shading has a significant negative effect on any solar installation. The microinverter (also known as panel-level inverter or ac- module) concept shown in Fig. 1(b) has been exploited to ad- dress this problem by operating each panel at its unique maxi- mum power point (MPP), and providing separate dc-to-ac con- version for each panel. Using this architecture, any shading of a single panel only affects its output power, without limiting the performance of the other panels in the installation. While the microinverter architecture can increase overall energy capture in a system, microinverters typically suffer from lower overall efficiency than high-voltage string-level inverters, owing to the large voltage transformation required to interface the panel volt- age (e.g., 20–40 V DC ) to the grid (e.g., 120–240 V AC rms), and often suffer from relatively high cost. Recently, the concept of cascaded dc-dc converters (dc–dc optimizers) has become popular [4]–[6], where each PV panel employs a dc–dc converter that performs maximum power point tracking (MPPT), and the outputs of the converters are con- nected in series. This architecture is shown in Fig. 1(c). Through dc–dc optimizers, localized control of panel voltage and current can be achieved, and each panel can operate at its independent MPP, thus improving the energy extraction of the overall sys- tem. The series connection of the outputs provides an inherent voltage stacking that enables each dc–dc converter to operate at a relatively low-voltage conversion ratio (enabling high con- version efficiency), while still achieving high overall output voltage, which is desirable as it enables the use of a central, high-voltage, high-efficiency inverter. To date, however, the promise of dc–dc optimizers has not been fully realized, primarily due to the difficulty of simultane- ously achieving high conversion efficiency and low cost of the power electronics. Low dc–dc conversion efficiency can easily negate any increase in energy capture that is offered by more localized (panel-level) control and must therefore be addressed. It should be mentioned that it is not merely the efficiency of the power electronics that must be addressed, but also how much of the available power that is extracted. It is possible to employ circuit architectures that achieve very high power conversion efficiency, such as switched-capacitor converters [7], but which does not achieve maximum power extraction, due to an inability to operate over a wide voltage range. A goal is thus to achieve 0885-8993/$31.00 © 2012 IEEE

Submodule Integrated Distributed Maximum Power Point Tracking for Solar Photovoltaic Applications

  • Upload
    david-j

  • View
    227

  • Download
    2

Embed Size (px)

Citation preview

Page 1: Submodule Integrated Distributed Maximum Power Point Tracking for Solar Photovoltaic Applications

IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 28, NO. 6, JUNE 2013 2957

Submodule Integrated Distributed Maximum PowerPoint Tracking for Solar Photovoltaic Applications

Robert C. N. Pilawa-Podgurski, Member, IEEE, and David J. Perreault, Senior Member, IEEE

Abstract—This paper explores the benefits of distributed powerelectronics in solar photovoltaic applications through the use ofsubmodule integrated maximum power point trackers (MPPT).We propose a system architecture that provides a substantial in-crease in captured energy during partial shading conditions, whileat the same time enabling significant overall cost reductions. Thisis achieved through direct integration of miniature MPPT powerconverters into existing junction boxes. We describe the design andimplementation of a high-efficiency (>98%) synchronous buckMPPT converter, along with digital control techniques that en-sure both local and global maximum power extraction. Throughdetailed experimental measurements under real-world conditions,we verify the increase in energy capture and quantify the benefitsof the architecture.

Index Terms—DC-DC power converters, energy harvesting,photovoltaic cells, power integrated circuits, solar energy.

I. INTRODUCTION

W ITH rising world-wide energy demands and soaringprices of fossil fuels, interest in renewable energy

sources has increased. Among these, solar photovoltaic (PV)energy has seen a rapid growth in the last few years, resulting indecreased prices of PV panels as production capacity increasesat a fast pace. As the PV panel prices decrease, the cost of thepower electronics required to extract the maximum power ofthe PV panels and to interface the PV system to the grid isbecoming a larger part of the overall system cost [1]. Much at-tention has, therefore, been given to the development of powerelectronics that enable a cost reduction of the overall system. Inaddition, much research is focused on increasing the efficiencyof the power processing stage, as well as on improving the poweryield of the overall system [2], [3].

Many PV installations suffer from current mismatch betweendifferent panels, due to nonuniform shading of the array, dirtaccumulation, or manufacturing variability. Ensuring uniformillumination is particularly challenging in residential PV appli-cations, where large current mismatch can be present due toexternal objects that cause shading. Shown in Fig. 1(a) is the

Manuscript received May 15, 2012; revised July 12, 2012; acceptedSeptember 7, 2012. Date of current version December 7, 2012. This workwas supported by the National Science Foundation under Grant 0925147.Recommended for publication by Associate Editor T. Suntio.

R. C. N. Pilawa-Podgurski is with the University of Illinois at Urbana-Champaign, Urbana, IL 61801 USA (e-mail: [email protected]).

D. J. Perreault is with the Research Laboratory of Electronics, MassachusettsInstitute of Technology, Cambridge, MA 02139 USA (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TPEL.2012.2220861

most common solar PV architecture, which connects all panelsin series. In this architecture, any partial shading or other sourceof cell current mismatch will cause the overall system outputpower to be reduced, since the current in the string is limited bythe weakest panel. While panels used today typically employbypass diodes that help protect the panels and limit the negativeeffect of partial shading, it is still the case that partial shadinghas a significant negative effect on any solar installation.

The microinverter (also known as panel-level inverter or ac-module) concept shown in Fig. 1(b) has been exploited to ad-dress this problem by operating each panel at its unique maxi-mum power point (MPP), and providing separate dc-to-ac con-version for each panel. Using this architecture, any shading of asingle panel only affects its output power, without limiting theperformance of the other panels in the installation. While themicroinverter architecture can increase overall energy capturein a system, microinverters typically suffer from lower overallefficiency than high-voltage string-level inverters, owing to thelarge voltage transformation required to interface the panel volt-age (e.g., 20–40 VDC ) to the grid (e.g., 120–240 VAC rms), andoften suffer from relatively high cost.

Recently, the concept of cascaded dc-dc converters (dc–dcoptimizers) has become popular [4]–[6], where each PV panelemploys a dc–dc converter that performs maximum power pointtracking (MPPT), and the outputs of the converters are con-nected in series. This architecture is shown in Fig. 1(c). Throughdc–dc optimizers, localized control of panel voltage and currentcan be achieved, and each panel can operate at its independentMPP, thus improving the energy extraction of the overall sys-tem. The series connection of the outputs provides an inherentvoltage stacking that enables each dc–dc converter to operateat a relatively low-voltage conversion ratio (enabling high con-version efficiency), while still achieving high overall outputvoltage, which is desirable as it enables the use of a central,high-voltage, high-efficiency inverter.

To date, however, the promise of dc–dc optimizers has notbeen fully realized, primarily due to the difficulty of simultane-ously achieving high conversion efficiency and low cost of thepower electronics. Low dc–dc conversion efficiency can easilynegate any increase in energy capture that is offered by morelocalized (panel-level) control and must therefore be addressed.It should be mentioned that it is not merely the efficiency of thepower electronics that must be addressed, but also how muchof the available power that is extracted. It is possible to employcircuit architectures that achieve very high power conversionefficiency, such as switched-capacitor converters [7], but whichdoes not achieve maximum power extraction, due to an inabilityto operate over a wide voltage range. A goal is thus to achieve

0885-8993/$31.00 © 2012 IEEE

Page 2: Submodule Integrated Distributed Maximum Power Point Tracking for Solar Photovoltaic Applications

2958 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 28, NO. 6, JUNE 2013

DC

AC

DC

AC

DC

AC

DC

AC

(b) (c)(a)

DC

DC

DC

DC

DC

DC

DC

AC

Fig. 1. Schematic drawings of three kinds of distributed MPPT architectures for solar PV. (a) Series string architecture. (b) Microinverter architecture.(c) Cascaded dc–dc (dc–dc optimizer) architecture.

very high conversion efficiency in the power electronics, as wellas high tracking efficiency (a measure of how close to the trueMPP the panel is operated).

Furthermore, a solution that increases total energy capture bya few percent, but which also increases the overall cost by morethan the monetary value of the increased power (as compared tothe installed system cost), will likely fail in the marketplace. Inthis paper, we present a dc–dc optimizer system that achievesboth low cost and high conversion efficiency, while at the sametime capturing substantially more energy than dc–dc optimizerarchitectures presented to date. In addition, detailed field experi-ments are presented that illustrate the benefits of our architectureunder real-world partial shading conditions.

This paper is organized as follows. Our proposed system ispresented in Section II, and Section III provides implementa-tion details of the power converter designed for our architecture.The control implementation is discussed in Section IV, and ex-perimental results and analysis are provided in Section V. Aquantitative comparison to previous work is presented in Sec-tion VI, where we also introduce a figure of merit (FOM) thatincorporates cost, efficiency, and increase in energy capture.Finally, Section VII concludes this paper.

II. PROPOSED ARCHITECTURE

DC–DC optimizer systems can be implemented with severaldifferent circuit topologies. Previous work at the panel level hasemployed boost converters [5], [8] and noninverting buck–boostconverters [6]. While boost converters are an attractive optionbecause of their ability to increase the output voltage (requiringfewer panels for a given desired output voltage), their chief dis-advantage is their limited operating range. As discussed in [5]and [9], since the output current of a boost converter can neverbe higher than its input current, the range over which currentmismatch can be addressed is severely limited. The noninvert-ing buck–boost converter is employed in [6] and can providean output current that is both higher and lower than the inputcurrent, thus providing both a voltage increase and the abilityto handle shaded panels (although within a limited range, sinceeach converter only operates in buck or boost mode at a giventime). The chief disadvantages of the noninverting buck–boost

topology are the increased number of transistors, and the achiev-able conversion efficiency, which is typically lower than buckor boost converters for the same switch rating. A more detailedperformance analysis of a number of potential power convertertopologies for dc–dc optimizers can be found in [10].

In this paper, we chose to implement the dc–dc optimizer sys-tem using synchronous buck converters. While the synchronousbuck topology enables both high switching frequency (impor-tant for small size, low cost) and high efficiency, it does notcontribute any voltage gain (which would reduce the number ofpanels that must be series connected). In most residential andutility-based installations, however, there are a sufficient num-ber of PV panels to provide for the inherent stacking of volt-ages without requiring the additional step-up from the powerconverter. When not tasked with providing additional voltagestep-up, the power stage can be optimized for size, cost, and ef-ficiency. As our experimental results indicate, the synchronousbuck converter topology offers size, cost, and efficiency benefits,and the system can be operated in a manner where the control im-plementation is relatively simple. Meanwhile, the string currentcan be kept sufficiently low so that the added wiring conductionlosses are kept to a minimum. In addition, as will be discussedin the experimental section, cascaded buck converter systemscan often-times produce an output voltage that is higher than aconventional system under partial shading condition.

In order to increase the overall system energy capture, ourdesign employs submodule distributed MPPTs, as shown inFig. 2.1 Using this architecture, mismatch between different sub-modules within the same panel can be mitigated, which yieldsan increase in energy capture compared to panel-level MPPTs.Furthermore, each MPPT in Fig. 2 only sees a third of the panelvoltage and can thus be designed using components with lowervoltage rating than panel-level MPPTs. The use of low-voltagepower MOSFETs with their small parasitics in turn enables anincrease in achievable switching frequency, which enables re-duced passive component size and cost. As will be shown inSection III, it is even possible to miniaturize the MPPTs to the

1We will refer to all cells in a PV panel that are connected to the same bypassdiode as a submodule. The most common type of PV panels comprise threesubmodules.

Page 3: Submodule Integrated Distributed Maximum Power Point Tracking for Solar Photovoltaic Applications

PILAWA-PODGURSKI AND PERREAULT: SUBMODULE INTEGRATED DISTRIBUTED MAXIMUM POWER POINT TRACKING 2959

Fig. 2. Schematic drawing of the submodule integrated MPPT system. Acomponent listing is provided in Table I.

point where they can fit in the existing standard junction box atthe back of the PV panel. This leads to further cost reductions, asa large custom outdoor-rated enclosure contributes significantcost to a dc–dc optimizer system.

III. SUBMODULE DISTRIBUTED MPPT CONVERTER

The inset of Fig. 2 shows a schematic drawing of the sub-module MPPT architecture designed as part of this study. Thesystem comprises a synchronous buck converter power stagecontrolled by a microcontroller to achieve local MPP opera-tion. The microcontroller can sense voltage and also employslossless current sensing [11] for control algorithms that also re-quire current information. The input voltage is sensed (node VP )through the attenuating low-pass filter comprising RP T ,RP B ,and CP . Likewise, the output voltage is sensed (node VL )through the attenuating low-pass filter comprising RLT ,RLB ,and CL . With the addition of the attenuating low-pass filtercomprising RH T ,RH B , and CH , the average voltage acrossthe inductor (VH − VL ) can be measured, which gives a sig-nal that is proportional to the inductor current. Note that theinductor current was not needed in the control algorithms thatwe employed in this study, but was recorded in this manner fordiagnostic purposes.

Each converter employs an isolated I2C communication in-terface, enabling bidirectional information transfer to a masternode, which can be a dedicated microcontroller or a computer. Itshould be noted that each MPPT can operate without any com-munication interface, but the I2C interface is used here to gatherdiagnostic data from each converter, and to provide a simplemeans for controlling the global output power. Table I providesa listing of the components used in the design. A completebill-of-material and cost analysis can be found in [10].

Shown in Fig. 3(a) is a photograph of the complete converterprototype, together with a pencil for scale; the overall converter“box volume” is 4 cm3 . Shown in Fig. 3(b) is one of the MPPTsplaced in a typical solar panel junction box. In a full installa-tion, three converters are used per PV panel, one in parallelwith each bypass diode. It is evident from the photograph that

TABLE ICOMPONENT LISTING

Fig. 3. Photographs of submodule MPPT hardware. (a) Photograph of thesubmodule MPPT converter, with a pencil shown for scale. The power inductoris on the bottom side of the PCB. (b) Photograph showing the submodule MPPTtogether with a solar panel junction box. The three bypass diodes are also visible;an MPPT converter is placed in parallel with each diode.

TABLE IICONVERTER SPECIFICATIONS

three converters fit in the junction box, with plenty of space forconnectors and sufficient air flow for passive cooling. A goal ofthe power stage design was to achieve a small enough converterfootprint to fit into the junction box on the back of off-the-shelfPV panels. By utilizing the existing weather-resistant junctionbox as an enclosure, significant cost savings can be realized.The integrated power stage is a combined gate drive and powerMOSFET chip (FDMF6704A), which also incorporates a 5-Vlinear regulator, enabling the converter to be completely pow-ered from the submodule.

In order for the submodule distributed MPPT architecture ofFig. 2 to be effective, it is important that the additional powercaptured is not wasted by low conversion efficiency of the powerelectronics. Much care was thus taken in this study to achievehigh-efficiency operation, both through the choice of topologyand passive components, as well as the implementation of sens-ing and control. A detailed description of these efforts can befound in [10]. Shown in Table II is an overview of the specifi-cations of the converter, along with a performance summary.

A detailed efficiency and power characterization of the MPPTconverter has been carried out to measure performance across

Page 4: Submodule Integrated Distributed Maximum Power Point Tracking for Solar Photovoltaic Applications

2960 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 28, NO. 6, JUNE 2013

Fig. 4. Measured efficiency versus output voltage, parameterized by outputcurrent. A lower output voltage corresponds to a shaded submodule, while alower output current signifies a string with less insolation.

a wide load and output voltage range. Fig. 4 shows a plot ofefficiency versus output voltage, parameterized by output cur-rent, for a fixed input voltage of 12 V. No attempts were madein this design to provide increased light-load efficiency, but wenote that in general, this can be accomplished with suitablelight-load control scheme, such as pulse-frequency modulation,if desired. The converter will operate at lower output voltages ifit suffers from more shading relative to the other converters inthe string. A low output current would signify that the insolationof the entire string of MPPTs is relatively low.

Given these characteristics of the system, it is important toachieve high efficiency at high power levels (for maximum to-tal energy capture), as well as at operating points where theconverter is expected to spend significant time in real-worldscenarios. In Fig. 4, this would correspond to high output volt-age (no or little shading) and high current (>5 A, correspondingto high insolation). We see from the plot that we achieve an ef-ficiency above 97% under these conditions. The peak efficiencyof 98.2% is realized at an input voltage of 16 V and an outputcurrent of 5 A. It should be noted that all efficiency measure-ments include all sensing, gate drive, and control losses, as theconverter itself is powered from its input terminals. A more de-tailed performance characterization of the power stage across avariety of operating conditions can be found in [10]; excellentefficiency is maintained across an input range from 8 to 16 V,and the converter functions over a still much wider range.

IV. CONTROL IMPLEMENTATION

In conventional solar PV installations, the inverter must con-trol the voltage (or current) of the string of PV modules toensure that the system is operating at the MPP. An additionalchallenge in situations with partial shading is the fact that whenthe bypass diodes conduct around weak modules, the resultingI–V characteristics of the overall system can contain severalmaxima, of which typically only one is a true global maximum.

Most inverters periodically sweep the output voltage of the PVarray to detect such situations and to ensure that the systemoperates at the true global MPP. Distributed MPPT (DMPPT)systems present additional challenges, and complicated modelshave been used to simulate their behavior [12]. In this study,we seek to implement a control method that extracts maximumenergy from the DMPPT system, while keeping the overall com-plexity to a minimum.

In our architecture, owing to the subpanel integrated dc–dcconverters, there are no local maxima in the I–V characteristicsof the overall system, as each submodule provides whatevervoltage it can to the system, while all submodules share thesame output current. In order to extract maximum energy froma PV installation with submodule power tracking, each MPPTmust continuously operate its submodule at the correct currentand voltage, while also allowing all other MPPTs do the samefor their individual submodules. We must thus design a controlalgorithm that ensures that each submodule operates at its localMPP, while also ensuring that the overall system operates at theglobal MPP (i.e., the overall string voltage and current are suchthat all submodules are operating at their respective MPPs).

A. Local MPPT Algorithm

Since the outputs of the individual power trackers are con-nected in series (as seen in Fig. 2), all of them share the sameoutput current Istring . If the number of series-connected convert-ers is large (which is typically the case in a system installation,where a large output voltage is desired), the string current (fromthe perspective of a single MPPT) can be considered constant.With a constant output current, each converter can then maxi-mize its own output power by maximizing its output voltage. Itthus follows that a local MPPT algorithm can be implementedby driving the local output voltage to its maximum value. Wecan denote the output voltage of the ith converter Vout,i , andthe output voltage of the string of PV modules Vstring . The out-put current of the string of PV modules, Istring , is the sameas the output current of each local converter, since they areseries-connected. The local control objective thus becomes

arg maxDi ∈〈0,1〉

(Vout,i(Di) × Istring ) (1)

where each converter strives to find the duty cycle Di whichwill maximize the output power.

In our implementation, we employ a perturb and observe(P&O) algorithm that continuously tracks the MPP by makingsmall changes to the duty cycle in order to drive the converteroutput voltage to its maximum. Shown in Fig. 5 is a flowchartdiagram of the local MPPT algorithm.

In order to quickly locate the approximate location of theMPP, the converter starts by performing a coarse sweep of itsduty cycle and measuring the corresponding values of outputvoltage. The duty cycle corresponding to the maximum voltageobserved is recorded, and at the end of the startup sweep, theconverter is set to operate at this duty cycle. At this point,the steady-state tracking algorithm begins, which uses a P&Oalgorithm which aims to maximize the converter output voltageby making small changes (ΔD) to the duty cycle D. In this

Page 5: Submodule Integrated Distributed Maximum Power Point Tracking for Solar Photovoltaic Applications

PILAWA-PODGURSKI AND PERREAULT: SUBMODULE INTEGRATED DISTRIBUTED MAXIMUM POWER POINT TRACKING 2961

Fig. 5. Flowchart diagram illustrating the local MPPT algorithm. The ap-proximate MPP is first found via a coarse startup sweep, followed by a P&Oalgorithm that strives to maximize converter output voltage.

TABLE IIIMPPT TRACKING PARAMETERS

manner, the submodule MPPT will continuously track the MPPand oscillate around it to within the finite precision of its voltagesensing and duty cycle control.

The MPPT P&O rate used in our experiments was 10 Hz.It should be pointed out that this rate was limited by the I2Ccommunication bandwidth. The delay between each time stepwas caused by each converter communicating its input and out-put voltage, as well as duty cycle to the computer for dataanalysis. The microcontroller itself is capable or operating at anMPPT rate in excess of 25 kHz, which is significantly faster thanwhat is required for this application. Table III provides infor-mation about our sensing and pulsewidth modulation (PWM)resolution and step-size for the experimental prototype. Theminimum achievable duty cycle step-size with the hardware weimplemented was 0.4%, but the 0.8% step-size provided a goodtradeoff between conversion speed and steady-state accuracy.The minimum achievable duty cycle step-size is governed bythe ratio of our switching frequency (250 kHz) and the frequencyof the phase-locked loop that drives the PWM components ofour microcontroller (64 MHz).

B. Global MPPT Algorithm

The local MPPT algorithm that we have implemented hasthe attractive feature of not requiring any local current sensing,which would add both cost, complexity, and power loss to the

overall solution. In order to ensure that the overall system op-erates at the MPP, the central controller (typically an inverter)must adjust the string current Istring . Previous work on globalcontrol in DMPPT applications has relied on time synchroniza-tion between the inverter and the local converters [13], [14].In [13], a circuit topology (the “two-stage chopper”) is em-ployed where each converter operates for only a brief periodof time, and the switching of each converter is updated sequen-tially. In this approach, each local converter is directly controlledby the central converter, as it controls each switching transition.In addition to poor utilization of the power converters in thisapproach, the control method does not scale well to large num-bers of converters, as the control complexity grows quickly andthe tracking speed decreases linearly with the number of con-verters. The control method of [14] is similar to that of [13], buthere regular boost converters are employed as local converter.Each converter is sequentially perturbed in a P&O approach, andthe global output power is measured to guide the direction ofthe next perturbation. Similarly to [13], the achievable trackingspeed of the system decreases linearly with N , and the centralinverter must be able to communicate with each local converter.Both of these approaches rely on time synchronization betweenthe central inverter and the local converters.

The control method employed in this study does not requiretime synchronization, but rather relies on frequency separationto achieve improvements in achievable tracking speed and pos-sible reduction in communication hardware. By adjusting theduty ratio, the local MPPT can autonomously achieve MPP op-eration so long as the submodule current at its MPP is equal toor less than that of the string.2 To achieve global MPP opera-tion, each submodule controller adjusts its duty ratio for MPPoperation (e.g., in a “fast” loop) based on the string current,while the system level controller (typically implemented by thegrid-interface inverter) adjusts the string current (in a “slow”loop) such that there is just sufficient string current available forthe submodule with the highest MPP current. In this manner,the control problem can be separated into a local MPPT controlfor each submodule, along with a single global control loop thatonly requires limited information.

A key requirement for our control method to work is that thereis sufficient time between changes in the string current for the lo-cal converters to reach their new local MPP equilibrium, so thatthe change in power can be observed by the central controller.Practically, the local MPPT frequency in our implementationhas an upper bound of approximately 25 kHz (with a switch-ing frequency of 250 kHz). We estimate that the central MPPTfrequency in this scenario should be below 2.5 kHz (ten timesslower). In practice, much lower central MPPT frequencies aretypically employed, owing to the low switching frequency ofthe high-voltage, high-power electronics, and the relatively slowchanges in insolation that the system is experiencing. For a sys-tem with N local converters, the central converter thus must

2This constraint is due to the chosen power converter topology (buck con-verter), which can only provide an output current greater than or equal to theinput current.

Page 6: Submodule Integrated Distributed Maximum Power Point Tracking for Solar Photovoltaic Applications

2962 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 28, NO. 6, JUNE 2013

strive to maximize the total output power, given by

N∑

i=1

Vi(Istring ,Di) × Istring (2)

where we have denoted the local converter output voltage byVi(Istring ,Di) to make explicit its dependence on the stringcurrent (the global control variable) and Di (the local controlvariable).

1) One-bit Feedback Global Algorithm: One method to en-sure that the overall system is operating at the global MPP isto signal to the global (“slow”) loop controller when one of thelocal MPPTs is operating at or near its maximum permitted dutycycle. At this point, the system loop controller may not decreasethe current Istring any further, as the strongest MPPT wouldthen not be operating at its MPP. This 1-bit feedback signal canbe implemented either using a very simple single-interconnector zero-interconnect communications link, or by encoding theinformation to communicate it directly via the series string in-terconnect. (We note that such methods are well known in othertypes of distributed power conversion systems [15], [16] andcan be implemented without significant expense in this applica-tion.) One disadvantage of this method is that it would requirethe global controller (the inverter in a typical installation) toimplement this functionality, such that separate dedicated hard-ware and firmware is required at the inverter level. This is similarto the limitations of [13] and [14], both of which also requirededicated communication hardware between the local convert-ers and the central inverter. A benefit of the approach presentedhere is that the control method scales well with the number oflocal converters N , since each local converter operates indepen-dently of the central inverter and only communicates with thecentral inverter when the string current is too low (and typicallyonly the strongest of the local converters communicates thisinformation).

2) Communicationless Global Algorithm: It is also conceiv-able that with the appropriate submodule level control, globalMPP operation can be ensured without any communicationbetween individual converters, or between converters and thestring-level inverter. All PV inverters used with conventionalsolar panels today already implement an MPPT functionality.It would be highly desirable to leverage this existing infrastruc-ture to achieve both global and local optimization with existinginverter hardware.

If the global MPPT controller draws too little current, thestrongest MPP will operate at its maximum duty cycle, and itssubmodule will deliver Istring , which will be less than its Impp .Since this submodule is no longer operating at its individualMPP, the overall output power of the string will decrease. Whenthe global controller detects this decrease in power, it will act toreverse this change, thus increasing the string current. The globalMPPT algorithm itself can thus ensure that the string current isnot operating at a current that is lower than the highest Impp ofthe submodules.

The buck topology can theoretically produce any output cur-rent that is higher than its input current (although there arecertainly practical limits such as device parasitics, duty cycle

Camera

Solar Panel

MPPTs

Electronic Load

Shading Object

Fig. 6. Annotated photograph of the field experiment setup.

resolution, and loss mechanisms that limit the maximum out-put current). In a real converter, the conduction losses in theMOSFETs, inductor, and wiring will increase as the output cur-rent is increased, leading to lower conversion efficiency at veryhigh currents. A lower conversion efficiency in the submoduleMPPTs will lead to lower string power, which can be detectedby the global MPPTs algorithm if the output current is increasedtoo much. It should be noted that this effect (decrease in out-put power by reduced conversion efficiency) is much less pro-nounced than the relatively sharp drop-off in power observedin a regular PV panel when it operates away from the MPP.The distributed MPPT thus have the effect of significantly “flat-tening” the power versus voltage (or current) characteristics ofthe system. The advantage of this is that the central invertercan operate at many different voltage and current levels (whiledrawing near maximum power from the system). There is, how-ever, a risk that the central inverter may not be able to detectthe small changes in power associated with the change in sub-module MPPT efficiency, and may continuously wander acrossa wide current and voltage range as it searches for the globalMPPT.

In the experimental measurements of Section V, we will seethe results of a control mechanism that makes use of the 1-bitfeedback global MPPT algorithm. The flattening effect of thedistributed MPPTs will also be observed and enables us to quan-tify the resolution required to implement the communication-less global MPPT algorithm in practice. It should be noted thatboth of these control methods still require both local and globalMPPT algorithms, but the level of communication between thecentral and local converters differs between the two approaches.

V. FIELD MEASUREMENT EXPERIMENTAL RESULTS

In order to fully evaluate the distributed MPPT system in a realsetting, we chose to perform outdoor field experiments under avariety of conditions. A PV panel (the STP175S-24/Ab01 72-cell monocrystalline Si panel from Suntech) was mounted in asouth-facing direction together with test equipment on a flat roofof a building on the MIT campus. The camera was used to pro-duce time-lapse photos of the shading pattern of the panel. Thephotos were synchronized with the output power measurement,providing a visual check to discern shading patterns related topanel I–V characteristics. Fig. 6 shows an annotated photograph

Page 7: Submodule Integrated Distributed Maximum Power Point Tracking for Solar Photovoltaic Applications

PILAWA-PODGURSKI AND PERREAULT: SUBMODULE INTEGRATED DISTRIBUTED MAXIMUM POWER POINT TRACKING 2963

Fig. 7. Schematic drawing of the MPPT bypass circuit which is poweredthrough the USB port and controlled by a general purpose pin on the I2C hostadapter.

of the field setup. The distributed MPPTs were connected acrosseach submodule (in parallel with the existing junction diodes, asshown in Fig. 2), and their output is connected to an electronicload (HP6060B). The electronic load was controlled throughthe GPIB interface by a small netbook computer that recordedall data.

To effectively characterize the performance benefit ofthe submodule distributed power electronics compared to aconventional solar panel, a low on-state resistance bypassMOSFET (PSMN8R5-60YS by NXP) was used, such thatthe system could be alternated between employing distributedMPPT (MPPTs on, bypass MOSFET OFF), and conventionaloperation (MPPTs OFF, bypass MOSFET ON). The bypassMOSFET was connected as shown in Fig. 7, where it can beturned ON or OFF by an isolated dc–dc converter, which is inturn controlled by an enable/disable PMOS driven by a generalpurpose I/O pin on the USB-connected I2C controller (theAardvark I2C Host Adapter from Total Phase).

The host adapter provides bidirectional translation of the com-mands from the USB port to the I2C bus. Custom control soft-ware was written in Python to communicate with each MPPT,execute the tracking algorithms, and store data with informa-tion about operating voltage, current, and duty cycle of eachconverter for tracking analysis.

Fig. 8 shows an annotated photograph of the circuit boardwhere the bypass circuit, I2C isolation components, and theMPPTs were mounted, together with connectors. Although eachcircuit board has room for four MPPTs, only three were em-ployed in our experiments, since our solar panel has three bypassdiodes.

A. Static Performance Evaluation

Our first experiment was to evaluate the relative perfor-mance improvement offered by the distributed MPPT duringa static submodule mismatch scenario. In this case, we per-formed measurements with and without distributed MPPT for apanel where a single cell experienced various degrees of shad-ing (as shown in Fig. 9). This scenario is representative of staticmismatch caused by, for example, dirt accumulation, bird drop-pings, a damaged cell, or a severe local degradation of the panelencapsulant.

Shown in Fig. 10 is a plot of measured panel output powerversus load current when a single cell in the panel is shadedby 50% (as per Fig. 10, under constant outdoor insolation (i.e.,a short measurement on a cloud-free day). The solid blue linerepresents the measurement when the panel was connected di-rectly to the electronic load, without distributed MPPTs. In thiscase, the electronic load was first connected to each individualsubmodule to generate a plot of power versus output current.It can be clearly seen that submodule 3 has a lower maxi-mum output current (and hence power) due to the single shadedcell.

Furthermore, from the plot showing the full panel power with-out distributed MPPT, two maximum power points can be seen.This is due to the bypass diode connected to submodule 3 con-ducting when the electronic load is drawing more current thanthe maximum current available from submodule 3. In this case,it can be seen that the global MPP is the case where the bypassdiode is not conducting, whereas the other point is a local MPP.Situations like this present problems for the MPPT algorithms inboth centralized inverters and microinverters, as they can easilyget stuck on the local MPP. Table III provides the MPPT trackingparameters used for this and all subsequent MPPT tests.

The green circles in Fig. 10 represent discrete data pointscollected with the distributed MPPT converters enabled, for avariety of output currents (stepped by the electronic load). In thismeasurement, the electronic load stepped the output current tothe indicated values with enough time (a few seconds) betweensteps to ensure that the distributed MPPTs reached their steady-state points after each step. For this shading scenario (a singlecell shaded by 50%), a 24% increase in achievable power out-put can be observed. The increase in power output is of coursedependent on the particular shading pattern (we have measuredinstances of more than 30% increase in output power for certainshading patterns). Furthermore, the panel with integrated sub-module MPPTs produces close to its maximum power acrossa broad range of output currents. In a complete system with acentral inverter, this characteristic would enable the inverter toextract maximum power over a wide voltage and current range,rather than the single point associated with a conventional PVsystem.

It should be noted that in the shading scenario shown inFig. 10, the distributed MPPT system actually produces an out-put voltage that is higher than what a conventional system wouldproduce, despite the use of synchronous buck converters. Ina conventional system, shaded sections are entirely bypassed,thereby reducing the output voltage of the system. In our pro-posed system, even the weak submodules are able to contributewhatever voltage they can to the output, thereby often-timeincreasing the output voltage compared to a conventional PVmodule. DMPPT systems employing buck converters are oftenerroneously believed to always produce a lower output voltage,but as shown in Fig. 10, this is not always the case. The systemmust certainly be designed with sufficient voltage headroom toensure operation across the expected operation range, but in thisregard, our system is no different than conventional PV installa-tions which must do the same to account for any bypass diodesconducting due to partial shading.

Page 8: Submodule Integrated Distributed Maximum Power Point Tracking for Solar Photovoltaic Applications

2964 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 28, NO. 6, JUNE 2013

I2C isolator

MPPT

BypassMOSFET

Isolated dc−dc

Fig. 8. Annotated photograph of the experimental prototype converters with isolated communication. The bypass MOSFET (powered by the isolated dc–dcconverter) enables the MPPT to be bypassed entirely (for evaluation purposes).

Fig. 9. Drawing of the solar panel illustrating the physical location of the threesubmodules that are accessible through the junction box (corresponding to theelectrical wiring schematic shown in Fig. 2). The bottom right cell in submodule3 is partially shaded in this experiment. The solar panel used in this experimentwas the STP175S-24/Ab01 72-cell monocrystalline Si panel from Suntech.

Fig. 10. Plot of power versus current with and without distributed MPPT, for50% shading of one cell in submodule 3. A power increase of 24% is observedby the use of the submodule MPPTs. These data were taken at MIT on October6, 2011, which was a very sunny day with no cloud coverage.

We have performed a number of measurements on differentstatic scenarios, details of which can be found in [10]. Table IVsummarizes these results, where the relative improvement ofthe distributed MPPT architecture can be clearly seen. For aperfectly matched panel with no shading throughout the day,

TABLE IVSTATIC SHADING PERFORMANCE

however, our proposed system would not be beneficial, as seenfrom the decrease in output power when employing the dis-tributed MPPT for 0% shading of a single cell. This shouldcome as no surprise, as any added power electronics incur someloss, and if there is no inherent mismatch in the panel, thereis nothing to be gained from employing additional MPPTs. Itshould be pointed out, however, that it is fairly trivial to im-plement a bypass mode in the MPPTs themselves, such thatduring times of no shading the MPPTs are bypassed altogetherand thus are not contributing any loss. This bypass mode can beimplemented in firmware only (turning the top MOSFET ONpermanently, with some additional conduction loss in the switchand inductor), or with one additional bypass MOSFET with lowon-state resistance (this approach will give the lowest loss inno-shading situations).

B. Dynamic Performance Evaluation

To evaluate the performance of the subpanel distributedMPPT architecture under dynamic partial shading conditions,we performed the following field experiment under practicalreal-world conditions.

The panel was placed near a metal chimney (visible in Fig. 6),so that only a small number of cells were shaded, as illustrated inFig. 11. As the sun moves throughout the day, the location of theshadow on the panel moves as well, covering different sectionsof the panel to varying degrees. This situation is very similar towhat would happen in residential installations, where chimneys,power lines, trees, antennas, and other structures block parts ofthe panel throughout the day.

The system was set up such that approximately every minuteit would switch between bypassing the distributed MPPTs andconnecting them to the panel. When the MPPTs are bypassed(i.e., the panel is configured just like a conventional panel), the

Page 9: Submodule Integrated Distributed Maximum Power Point Tracking for Solar Photovoltaic Applications

PILAWA-PODGURSKI AND PERREAULT: SUBMODULE INTEGRATED DISTRIBUTED MAXIMUM POWER POINT TRACKING 2965

Fig. 11. Photograph illustrating the shading (owing to a protruding pipe) thatmoves across the panel for the dynamic performance experiment.

Fig. 12. Instantaneous measured power versus time for a sunny day (October 6,2011) for a conventional panel, as well as with the distributed MPPT employed,for the test setup illustrated in Fig. 6. Up to a 30% increase in captured poweris observed.

electronic load performs a full I–V sweep of the panel, and thehighest power is recorded. When the MPPTs are connected, theelectronic load starts at a current (6 A) that is higher than thepanel short-circuit current (5.2 A), and waits for the MPPT out-puts to reach steady state (a few seconds). It then decreases thecurrent, at each time waiting for the MPPTs to settle again. Itcontinues to decrease the current until one of the MPPTs (theone connected to the strongest submodule) reaches its maximumallowed duty cycle (0.99). At this time, any further decreases inpanel output current will mean that at least one of the MPPTs isnot operating at the submodule MPP, so the sweep is stopped,and the highest output power is recorded. This effectively re-flects operation with the 1-bit feedback global MPPT algorithmdescribed in Section IV.

Shown in Fig. 12 is a plot of panel output power versus time,with and without the distributed MPPT electronics active, asdiscussed earlier. These measurements were taken on a verysunny day (October 6, 2011) at the times indicated in the plot.

Fig. 13. Accumulated energy versus time for a sunny day (October 6, 2011)for a conventional panel, as well as with the distributed MPPT employed. Thedistributed MPPT system collects more than 20% additional energy over aconventional panel.

It can be seen that at all times during the measurement period,the distributed MPPT system generated more power from thepanel than what a conventional panel would generate, thanks tothe mitigation of submodule current mismatch owing to partialshading.

Shown in Fig. 13 is the accumulated energy extracted fromthe panel during the measurement time, and it shows that thedistributed MPPT system collected over 20% more energy overthe course of this experiment than what a conventional panelwould achieve.

VI. PERFORMANCE COMPARISON

The previous section illustrates the improvements in overallpower and energy capture that can be realized with the use of thesubmodule MPPT architecture and the hardware implemented inthis study. In solar PV applications, which are very cost sensitive,it is illustrative to perform a cost analysis to quantify the cost-benefit tradeoff of this increase in power. A small increase inoutput power that comes at a large added system cost is clearlynot worthwhile, and in this section, we provide a quantitativeanalysis of this tradeoff, based on the empirical data captured inour experiment.

Shown in Table V is a comparative chart of our work, previousacademic work, as well as two selected commercial solutions.The topology, cost, power density, efficiency, and an FOM (dis-cussed below) are listed. For the academic work, we have at-tempted to estimate the complete converter cost from publishedresults3 (the commercial prices are estimates from reported retailprices) and adjusted the efficiencies so that they each include allcontrol and gate driver losses for a fair comparison. It should benoted that aside from the work presented here, none of the other

3Note that the cost presented in [6] does not include the cost of the microcon-troller, gate driver, auxiliary power supply, and many other components. Theyare added into the cost used here to provide a fair comparison.

Page 10: Submodule Integrated Distributed Maximum Power Point Tracking for Solar Photovoltaic Applications

2966 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 28, NO. 6, JUNE 2013

TABLE VDC–DC OPTIMIZER PERFORMANCE COMPARISON

solutions provide submodule tracking and thus only addressmismatch at the panel level. As was shown in the experimentalsection, submodule mismatch can contribute to significant en-ergy loss (up to 20%), which cannot be mitigated by the othersolutions. We find that both in terms of efficiency and cost, oursolution compares favorably to previously published work in thefield, while also offering a significant increase in overall energycapture during partial shading conditions.

A. FOM

The merits of distributed MPPT in any solar PV system areentirely dependent on the particular installation. Some installa-tions may benefit greatly from added power electronics, whereasothers may see no improvement in overall energy capture (e.g.,perfectly matched panels on a completely flat surface with noexternal objects that can cause shading). Due to the very site-specific circumstances, it is therefore difficult to quantify exactlyhow much a typical residential installation may benefit from ourapproach. It is, however, possible to quantify the relative meritsof the power electronic solution itself, compared to other similarsolutions. This is done in Table V, where we have introducedan FOM that aims to capture some of the cost/benefit tradeoffwith this approach. It should be pointed out that this FOM isa crude estimate of the relative performance between differentsolutions, and it should not be used as an absolute metric tojudge whether distributed MPPT will pay off or not.

The FOM attempts to capture the incremental cost for theadded average power to the PV system (given as $/Watt). Itcalculates the expected additional average power captured bythe system (accounting for the electrical conversion losses ofthe MPPTs in each case), for a given nominal power increasefactor α. This increase factor represents the fractional increase inaverage output power that can be expected with the distributedMPPT system and, as such, is highly installation dependent.For our analysis, an α of 0.1 is chosen for per-panel MPPTand 0.15 for submodule MPPT (this is a modest 5% increasefor submodule MPPT compared to per-panel MPPT, keepingin mind that we experimentally measured between a 10% and20% increase in captured energy for the submodule case versusregular panel-based MPPT in our field experiments). The FOMis given by

FOM =cost

〈Padded〉(3)

where Padded is the additional power captured owing to thepower electronics

〈Padded〉 = ηMPPTPrated(1 + α) − Prated (4)

and ηMPPT is the electrical conversion efficiency of the MPPTs,and Prated is the rated power of the MPPT. The FOM shouldbe compared to the typical installed cost of solar PV systems,which was estimated to be around $6/W in 2010 [18], but israpidly decreasing. In order for the distributed MPPT systemto be cost effective, the FOM must be below the installed costof the PV system, for a given installation. We see that for ourassumptions of a 10% and 15% total improvement in averagepower due to module and submodule tracking, respectively, thecost benefit of many of the solutions of Table V are marginal. Asthe installed cost of solar PV continues to decrease, even furtherprice pressure on the power electronics is expected. In light ofthis, our calculated FOM of 0.50 $/W makes our solution costcompetitive today, and for some time in the future.

It should be pointed out again that the FOM is highly depen-dent on the parameter α, which attempts to quantify the per-formance improvements offered by distributed MPPT. It is cer-tainly possible to better quantify this improvement with a moredetailed FOM that models the length of shading (in time), addi-tional panels, and weather data. Our attempt here was merely toelucidate some of the tradeoffs in terms of cost and performance,with rough estimates guided by our empirical data.

Finally, we should mention that the FOM described here onlycaptures the monetary value associated with increased energycapture. Distributed power electronics in solar PV installationscan provide additional benefits in terms of per-panel (or submod-ule) diagnostics and data capture, enabling the user to quicklyisolate and replace malfunctioning panels. Distributed powerelectronics also enables added protection with its ability to com-pletely turn off the panel output current, something which is notpossible with a simple series string architecture. It is expectedthat these additional services will receive more attention in thefuture and may become as important as the increased energycapture in choosing a system architecture.

VII. CONCLUSION

We have presented a submodule distributed MPPT architec-ture for solar PV applications, which enables more energy tobe extracted from the system. By employing low-voltage syn-chronous buck converters connected across each submodule ofthe panel, a high-frequency, very high-efficiency power stage

Page 11: Submodule Integrated Distributed Maximum Power Point Tracking for Solar Photovoltaic Applications

PILAWA-PODGURSKI AND PERREAULT: SUBMODULE INTEGRATED DISTRIBUTED MAXIMUM POWER POINT TRACKING 2967

can be used. The power electronics can then be miniaturized tothe point where they fit into the existing junction box, therebygreatly reducing cost. We have presented a hardware prototypefor use in submodule tracking of a PV panel, and discuss localand global control techniques to maximize the overall energycapture of the system. We measure up to a 20% improvement inoverall energy capture compared to per-panel MPPT implemen-tation, using field experiments with a partial shading obstacle,and perform static mismatch measurements that further validatethe performance of the system. Finally, we compare our im-plementation to other state-of-the-art commercial and academicsolutions, and find that the proposed solution offers attractivebenefits in terms of efficiency and cost, both of which are criticalin PV systems.

REFERENCES

[1] “Trends in photovoltaic applications. Survey report of selected IEA coun-tries between 1992 and 2006,” Int. Energy Agency Photovoltaic PowerSyst., Paris, France, Tech. Rep. IEA-PVPS T1-16:2007, 2007 [Online].Available at www.iea-pvps.org

[2] S. Kjaer, J. Pedersen, and F. Blaabjerg, “A review of single-phase grid-connected inverters for photovoltaic modules,” IEEE Trans. Ind. Appl.,vol. 41, no. 5, pp. 1292–1306, 2005.

[3] J. Myrzik and M. Calais, “String and module integrated inverters forsingle-phase grid connected photovoltaic systems: A review,” in Proc.IEEE Bologna Power Tech., Jun. 2003, p. 8.

[4] T. Shimizu, M. Hirakata, T. Kamezawa, and H. Watanabe, “Generationcontrol circuit for photovoltaic modules,” IEEE Trans. Power Electron.,vol. 16, no. 3, pp. 293–300, May 2001.

[5] G. R. Walker and P. C. Sernia, “Cascaded dc–dc converter connectionof photovoltaic modules,” IEEE Trans. Power Electron., vol. 19, no. 4,pp. 1130–1139, 2004.

[6] L. Linares, R. W. Erickson, S. MacAlpine, and M. Brandemuehl, “Im-proved energy capture in series string photovoltaics via smart distributedpower electronics,” in Proc. 24th Annu. IEEE Appl. Power Electron. Conf.Expo., Feb. 2009, pp. 904–910.

[7] J. Stauth, M. Seeman, and K. Kesarwani, “A high-voltage CMOS IC andembedded system for distributed photovoltaic energy optimization withover 99% effective conversion efficiency and insertion loss below 0.1%,”in Proc. IEEE Int. Solid-State Circuits Conf., Feb. 2012, pp. 100–102.

[8] G. Adinolfi, N. Femia, G. Petrone, G. Spagnuolo, and M. Vitelli, “Designof dc/dc converters for DMPPT PV applications based on the conceptof energetic efficiency,” J. Solar Energy Eng., vol. 132, pp. 021005-1–021005-10, 2010.

[9] R. Alonso, E. Roman, A. Sanz, V. E. M. Santos, and P. Ibanez, “Analysis ofinverter-voltage influence on distributed MPPT architecture performance,”vol. 59, no. 10, pp. 3900–3907, 2012.

[10] R. C. N. Pilawa-Podgurski, “Architectures and circuits for low-voltage en-ergy conversion and applications in renewable energy and power manage-ment” Ph.D. dissertation, Dept. Electr. Eng. Comput. Sci. MassachusettsInst. Technol., Cambridge, 2012.

[11] R. C. N. Pilawa-Podgurski, N. A. Pallo, W. R. Chan, D. J. Perreault, andI. L. Celanovic, “Low-power maximum power point tracker with digitalcontrol for thermophotovoltaic generators,” in Proc. 25th Annu. IEEEAppl. Power Electron. Conf. Expo., Feb. 2010, pp. 961–967.

[12] N. Femia, G. Lisi, G. Petrone, G. Spagnuolo, and M. Vitelli, “Distributedmaximum power point tracking of photovoltaic arrays: Novel approachand system analysis,” IEEE Trans. Ind. Electron., vol. 55, no. 7, pp. 2610–2621, 2008.

[13] T. Shimizu, O. Hashimoto, and G. Kimura, “A novel high-performanceutility-interactive photovoltaic inverter system,” IEEE Trans. Power Elec-tron., vol. 18, no. 2, pp. 704–711, 2003.

[14] G. Petrone, C. A. Ramos-Paja, G. Spagnuolo, and M. Vitelli, “Granularcontrol of photovoltaic arrays by means of a multi-output maximum powerpoint tracking algorithm,” Progr. Photovoltaics: Res. Appl., 2012. doi:10.1002/pip.2179.

[15] D. Perreault, R. L. Selders, Jr., and J. Kassakian, “Frequency-basedcurrent-sharing techniques for paralleled power converters,” IEEE Trans.Power. Electron., vol. 13, no. 4, pp. 626–634, 1998.

[16] D. Perreault, K. Sato, R. L. Selders, Jr., and J. Kassakian, “Switching-ripple-based current sharing for paralleled power converters,” IEEETrans. Circuits Syst.—Part I: Fundamental Theory Appl., vol. 46, no. 10,pp. 1264–1274, 1999.

[17] E. Roman, R. Alonso, P. Ibanez, S. Elorduizapatarietxe, and D. Goitia,“Intelligent PV module for grid-connected PV systems,” IEEE Trans. Ind.Electron., vol. 53, no. 4, pp. 1066–1073, Jun. 2006.

[18] G. Barbose, N. Darghouth, R. Wiser, and J. Seel, “Tracking the sun IV:A historical summary of the installed cost of photovoltaics in the UnitedStates from 1998 to 2010,” Lawrence Berkeley Nat. Lab., Berkeley, CA,Rep. LBNL-5047E, 2011

Robert C. N. Pilawa-Podgurski (S’06–M’11) wasborn in Hedemora, Sweden. He received dual B.S. de-grees in physics, electrical engineering, and computerscience in 2005, the M.Eng. degree in electrical engi-neering and computer science in 2007, and the Ph.D.degree in electrical engineering in 2012, all from theMassachusetts Institute of Technology, Cambridge.

He is currently an Assistant Professor in the De-partment of Electrical and Computer Engineering,University of Illinois, Urbana-Champaign, Urbana,and is affiliated with the Power and Energy Systems

group. He performs research in the area of power electronics. His research in-terests include renewable energy applications, energy harvesting, CMOS powermanagement, and advanced control of power converters.

David J. Perreault (S’91–M’97–SM’06) receivedthe B.S. degree from Boston University, Boston,MA, and the S.M. and Ph.D. degrees from theMassachusetts Institute of Technology (MIT), Cam-bridge.

In 1997, he joined the MIT Laboratory for Elec-tromagnetic and Electronic Systems as a PostdoctoralAssociate, and became a Research Scientist in the lab-oratory in 1999. In 2001, he joined the Department ofElectrical Engineering and Computer Science, MIT,where he is currently a Professor of Electrical En-

gineering. His research interests include design, manufacturing, and controltechniques for power electronic systems and components, and in their use in awide range of applications.

Dr. Perreault received the Richard M. Bass Outstanding Young Power Elec-tronics Engineer Award from the IEEE Power Electronics Society, an ONRYoung Investigator Award, and the SAE Ralph R. Teetor Educational Award.He is a co-author of four IEEE prize papers.