2968 ieee transactions on power electronics, vol. 28, …€¦ · 2970 ieee transactions on power...

2968 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 28, NO. 6, JUNE 2013

Differential Power Processing for Increased EnergyProduction and Reliability of Photovoltaic Systems

Pradeep S. Shenoy, Member, IEEE, Katherine A. Kim, Student Member, IEEE,Brian B. Johnson, Student Member, IEEE, and Philip T. Krein, Fellow, IEEE

Abstract—Conventional energy conversion architectures in pho-tovoltaic (PV) systems are often forced to tradeoff conversion ef-ficiency and power production. This paper introduces an energyconversion approach that enables each PV element to operate at itsmaximum power point (MPP) while processing only a small frac-tion of the total power produced. This is accomplished by providingonly the mismatch in the MPP current of a set of series-connectedPV elements. Differential power processing increases overall con-version efficiency and overcomes the challenges associated withunmatched MPPs (due to partial shading, damage, manufacturingtolerances, etc.). Several differential power processing architec-tures are analyzed and compared with Monte Carlo simulations.Local control of the differential converters enables distributed pro-tection and monitoring. Reliability analysis shows significantly in-creased overall system reliability. Simulation and experimental re-sults are included to demonstrate the benefits of this approach atboth the panel and subpanel level.

Index Terms—Differential power processing, local control, max-imum power point tracking (MPPT), photovoltaic power, renew-able energy.

I. INTRODUCTION

I F SOLAR photovoltaic (PV) systems are to reach grid par-ity, they need to reliably produce as much energy as possible

over the life of the system [1]. This conclusion is reached whencomparing the levelized cost of energy (LCOE) of PV systemsto other resources [2]. The viability of PV is strengthened by rel-atively long panel lifetimes, with warranties typically 25 yearsor more [3]. In past practice, the power electronics used to con-vert and control energy from a PV installation tended to have amuch lower mean time to failure (MTTF) than PV panels, whichincreases the balance of system costs [4]. While reliability hasbeen improved through developments in inverters [5], [6], itremains important that the power processing architecture and

Manuscript received May 17, 2012; revised July 12, 2012; accepted July 13,2012. Date of current version December 7, 2012. This work was supported inpart by the Grainger Center for Electric Machinery and Electromechanics atthe University of Illinois at Urbana-Champaign. The information, data, or workpresented herein was funded in part by the Advanced Research Projects Agency-Energy, U.S. Department of Energy, under Award DE-AR0000217. This workwas also supported in part by the National Science Foundation GraduateResearch Fellowships Program. Recommended for publication by AssociateEditor T. Suntio.

P. S. Shenoy is with Kilby Labs, Texas Instruments, Dallas, TX 75243 USA(e-mail: [email protected]).

K. A. Kim, B. B. Johnson, and P. T. Krein are with the Department of Elec-trical and Computer Engineering, University of Illinois at Urbana-Champaign,Urbana, IL 61801 USA (e-mail: [email protected]; [email protected];[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.2012.2211082

Fig. 1. Existing PV power processing architectures include (a) series PV withcentral inverter, (b) modular cascaded dc–dc converters with a central inverter,and (c) module-integrated inverters (microinverters).

components result in high efficiency, reliability, safety, and per-formance of the overall PV system. The differential power pro-cessing approach introduced in this paper can effectively meetthese objectives.

Existing architectures for PV power processing are illustratedin Fig. 1. The conventional bulk conversion approach, shown inFig. 1(a), is a series string of PV panels connected to a cen-tral inverter. This approach is efficient and effective only whenmaximum power point (MPP) current levels are well matched.It has substantially reduced power output when even one seg-ment is degraded (due to shading, damage, manufacturing tol-erances, degradation, etc.) [7]. Modular panel-by-panel archi-tectures, shown in Fig. 1(b) and (c), have been introduced toovercome reduced output [8], [9]. These approaches allow eachpanel to operate at its local MPP through distributed controlsand enable relatively simple installation and maintenance [10].However, overall conversion efficiency may decrease. Noticethat in Fig. 1(b) all power must be converted twice, and eachdc–dc converter must have power and reliability ratings to matcha full PV panel. Although the approach shown in Fig. 1(c) mayappear to remove a conversion stage, many module integratedinverters actually consist of two cascaded stages: one dc–dcstage and one dc–ac stage. Significant cost, reliability, and com-plexity challenges arise when attempting to scale down theseapproaches to the subpanel level. Even so, reliable system-leveldesigns based on Fig. 1(c) have been presented [6], [11]. Asis well known, inverter designs often seek to avoid electrolyticcapacitors to enhance reliability [12]. In this paper, we discuss afundamentally different approach that increases energy capturewithout suffering from increased energy conversion losses.

A basic operating challenge with series strings of PV ele-ments, as in Fig. 1(a), is mismatch in MPP current. In a se-ries string, the voltage of each element is independent, but thecurrent of each element must be equal. The differential power

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SHENOY et al.: DIFFERENTIAL POWER PROCESSING FOR INCREASED ENERGY PRODUCTION AND RELIABILITY 2969

Fig. 2. Conceptual diagram of differential power processing. Differential con-verters enable each PV element to operate at its local MPP without processingthe total PV power.

processing approach overcomes the challenge of mismatchedMPP current in PV series strings [13]–[15], while facilitatingefficient power delivery and system scaling. Local MPP track-ing of each PV element is achieved with small converters thatprovide the difference in MPP current between two adjacent PVelements, as shown in Fig. 2. Earlier research that has employeda similar approach includes a generation control circuit [16]and bypass converters [17]. The technique introduced in [16]maintains the series PV configuration while adding external dc–dc converters. The approach does not lead directly to small,local differential converters, as in this paper, relies on a cen-tral controller, and requires more complex (e.g., isolated) gatedriving circuits. As the number of PV elements increases, theswitch current and voltage ratings increase and MPP trackingslows down. The approach in [16] may not scale well, but theunderlying concept is introduced. In [17], dual half-bridge cir-cuits are explored at the panel level but it is not clear howMPP operation is achieved. Returned energy current convert-ers, introduced in [18], utilize a synchronous flyback topologyfor energy conversion but rely on a central controller whichprovides the same PWM signal to all converters. Current di-verters utilizing a half-bridge topology have been suggested forenabling cascaded dc–dc optimizers to operate at the MPP, butthis adds an unnecessary energy conversion step [19]. Morerecently, delta converters [20] and other voltage equalizationtechniques [21]–[23] have been proposed using half-bridge, fly-back, and switched capacitor circuits. Although this approachhas its merits, it does not guarantee MPP operation for each PVelement as the MPP voltages may not be equal. The contributionin this study is to optimize and more fully develop the differen-tial power processing method, seeking to minimize conversionloss and cost. This paper quantitatively analyzes and comparesseveral differential power processing architectures for efficientand effective extraction of the maximum available power fromPV systems. An important practical advantage is substantial re-duction in PV system cost as the approach facilitates large-scalePV systems. This method can be applied at various scales in-cluding multiple panel strings, single panels, and also at thesubpanel level as is highlighted in this study. The differentialpower processing architectures here can track the true MPP of

Fig. 3. Differential power converters act as controllable current sources toallow series PV elements to operate at independent current levels.

each series PV element while processing only a small fractionof the total energy produced. The series connection of the PVelements is maintained and bulk power is processed only once.The proposed method enables distributed control and improvesoverall system reliability.

Several differential power processing architectures are pre-sented and compared in Section II. Section III examines con-trol objectives including distributed MPP tracking, protection,and monitoring. A comparative reliability analysis of three PVsystem architectures is presented in Section IV. Experimentalresults demonstrating improved energy capture with differen-tial converters operating at the subpanel level are shown inSection V. Conclusions are discussed in Section VI.

II. DIFFERENTIAL POWER PROCESSING

One key to improving PV energy conversion efficiency is tooperate converters only when necessary and only with as muchpower as necessary. Differential power processing offers a wayto overcome past tradeoffs by enabling each PV element in a se-ries string to operate at its MPP by providing only the generallysmall difference in the MPP current between two adjacent PVelements, shown conceptually in Fig. 3. If there is no mismatch,no power exchange is needed. More generally, given limitedMPP mismatch, every local MPP can be reached while process-ing only a small fraction of the total power being produced. Theseries string is not broken, and bulk power flows in a direct path.A differential converter acts as a controllable current source withlimited ratings.

When the MPPs of series PV elements match, the energy pro-duced can be sent directly to an output, such as a grid-connectedinverter, without additional processing. Power is processed justonce by the inverter thereby avoiding local conversion loss. Dif-ferential converters take advantage of this by only processingpower if there is mismatch in the MPP current of the series PVelements. If MPP currents are matched, differential convertersneed not operate (i.e., have no output current). This is in contrastto cascaded dc–dc converters, as in Fig. 1(b), that must processthe entire PV power over all operating conditions [8], [9].

Differential power processing can be implemented using avariety of architectures and converter topologies. Differentialconverters can be designed to interact with other PV elements,the main bus, an independent energy storage element (e.g., avirtual bus), or even a battery. Isolated or nonisolated converterscan be used for energy conversion, depending on configuration


Fig. 4. Differential power converters using a buck–boost topology connected to (a) neighboring nodes and (b) the main bus. Flyback differential convertersinterface with the main bus in (c).

details and requirements. Differential power processing appliesat any level: panel by panel, string by string, or even cell bycell. Two differential architectures are described in more detailbelow.

A. PV-to-PV Architecture

Differential converters that transfer energy between neighbor-ing PV elements utilize a PV-to-PV architecture. Bidirectional,buck–boost converters, as shown in Fig. 4(a), are a possible im-plementation. This approach [24] and others [25] follow frombattery equalization strategies and have similar objectives. Re-search on series-connected digital circuits has also informedthis differential power processing architecture [26]. In Fig. 4(a),the drain of switch q1 and the source of switch q2 are shownconnected to the neighboring PV voltage nodes. The illustratedconfiguration enables a low voltage rating for the switches (twicethe PV element maximum voltage) and simplifies local control.Each PV element is likely to have a parallel capacitor for filter-ing, not shown for clarity. The duty ratios of the switches arecontrolled such that the inductor provides the necessary currentfor MPP operation of the respective PV element. If the config-uration in Fig. 4(a) is used for the entire series PV stack, theaverage inductor current of the ith differential converter is

IL,i = IPV ,i+1 − IPV ,i + Di−1IL,i−1 + (1 − Di+1)IL,i+1(1)

where IL is the inductor current, IPV is the PV element current,and D is the steady-state duty ratio of switch q1 . Equation (1) is

slightly altered for the first and last intermediate nodes; the firstnode will omit the IL,i−1 term, and the last node will omit theIL,i+1 term. The duty ratio D of each converter depends on PVelement voltage and is ideally

Di =VPV ,i

VPV ,i+1 + VPV ,i(2)

where VPV ,i is the voltage across the ith PV element. In a PVsystem with limited mismatch, the duty ratio is close to 50%.Kirchhoff’s Current Law (KCL) can be applied to the top (orbottom) node in the series stack to determine the main outputcurrent, which is

Imain = IPV ,n − Dn−1IL,n−1 = IPV ,1 + (1 − D1)IL,1 . (3)

The KCL equations for the PV-to-PV architecture can be writtenin tridiagonal matrix form as shown in (4) at the bottom of thepage.

The resulting system of linear equations is of the form Ax =b, and a unique solution exists. There are n – 1 PV-to-PV dif-ferential converters in a system with n PV elements. The nth

control actuator is the central converter. Given that each PVelement operates at its local MPP, (3) yields a unique value ofthe main current. The central converter voltage is required tobe the sum of MPP voltages of the elements, and the desiredoperating point of central converter is unique. Hence, there aren desired operating conditions (i.e., IPV ,i = IMPP ,i , ∀i) and ncontrol actuators. The system is fully determined, and there isone set of duty ratios that will allow each PV element to operate

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎣

1 −(1 − D2) 0 · · · 0 0

−D1 1 −(1 − D3). . .

......

0 −D2. . .

. . . 0...

.... . .

. . . 1 −(1 − Dn−1)...

0 · · · 0 −Dn−2 1 00 · · · · · · 0 Dn−1 1

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎦

⎡⎢⎢⎢⎢⎢⎢⎣

IL,1IL,2

...IL,n−2IL,n−1Imain

⎤⎥⎥⎥⎥⎥⎥⎦

=

⎡⎢⎢⎢⎢⎢⎢⎣

IPV ,2 − IPV ,1IPV ,3 − IPV ,2

...IPV ,n−1 − IPV ,n−2IPV ,n − IPV ,n−1

IPV ,n

⎤⎥⎥⎥⎥⎥⎥⎦

(4)


at its MPP. It is also important to note that the average inductorcurrent of each converter in this architecture is influenced by theinductor current in the other converters, as can be seen in (1).

The amount of power processed by differential convertersdepends on how much variation exists in the MPP current ofthe series PV elements. The expression in (4) can be invertedto determine the inductor currents as a function of MPP currentmismatch. The total power processed by PV-to-PV differentialconverters is

PDPP =n−1∑i=1

VPV ,i |IL,i | (5)

under ideal conditions. If the inductor current is positive, theproduct VPV ,i |IL,i | represents the differential converter outputpower; if the inductor current is negative, the product VPV ,i |IL,i |represents the input power. As the difference in PV MPP currentsincreases, the necessary differential converter inductor currenttends to increase, resulting in more power being processed. Still,it is generally a small fraction of the total generated power. Thefraction of total power processed by differential converters β isdefined as

β =PDPP

PPV(6)

where PPV is the total power produced by the PV elements.An efficiency term η could be included to describe differentialconverter losses.

B. PV-to-Bus Architecture

Differential converters transfer energy between PV elementsand a collective bus (e.g., the main bus) in a PV-to-bus architec-ture. Numerous converter topologies and control strategies canbe implemented with this architecture. A benefit of the buck–boost converters shown in Fig. 4(b) is that the steady-state in-ductor currents are independent of each other. The inductorsprovide only the difference in PV MPP current, which is

IL,i = IPV ,i+1 − IPV ,i . (7)

The KCL equations for the system can be written in matrixform as

⎡⎢⎢⎢⎢⎢⎢⎢⎣

1 0 · · · · · · · · · 0

0 1. . .

......

. . .. . .

. . ....

.... . .

. . .. . .

...0 · · · · · · 0 1 0

D1 · · · · · · · · · Dn−1 1

⎤⎥⎥⎥⎥⎥⎥⎥⎦

⎡⎢⎢⎢⎢⎢⎢⎣

IL,1IL,2

...IL,n−2IL,n−1Imain

⎤⎥⎥⎥⎥⎥⎥⎦

=

⎡⎢⎢⎢⎢⎢⎢⎣


...IPV ,n−1 − IPV ,n−2IPV ,n − IPV ,n−1

IPV ,n

⎤⎥⎥⎥⎥⎥⎥⎦

. (8)

As before, there are n control objectives and n control ac-tuators (i.e., a fully determined system) resulting in one set of

duty ratios that enable each PV element to operate at its MPP.Downsides of this approach are that the converter switches mustbe rated for the entire bus voltage and, compared to other dif-ferential approaches, more power is processed under certainconditions. Even though the inductor current may be moderate,the differential converter output voltage is the sum of the PVelement voltages up to that node. Hence, the power processedby buck–boost, PV-to-bus converters is

PDPP =n−1∑i=1

(|IL,i |

i∑k=1

VPV ,k

). (9)

The PV-to-bus architecture can also be implemented with nisolated converters, as shown in Fig. 4(c). This arrangementtends to reduce the total power processed by the differentialconverters. The overall goal is to minimize power loss due toenergy conversion. The intermediate node KCL equation is

IDC ,i = IPV ,i+1 − IPV ,i + IDC ,i+1 (10)

where IDC ,i is the average output current of the ith isolateddifferential converter. The KCL equation of the top node is

IDC ,n = Istring − IPV ,i (11)

where Istring is the current going out of the top node into thecentral converter. The system can be written in matrix form as

⎡⎢⎢⎢⎢⎢⎢⎣

1 −1 0 · · · 0

0 1 −1. . .

......

. . .. . .

. . . 0...

. . . 1 −10 · · · · · · 0 1

⎤⎥⎥⎥⎥⎥⎥⎦

⎡⎢⎢⎢⎢⎣

IDC ,1IDC ,2

...IDC ,n−1IDC ,n

⎤⎥⎥⎥⎥⎦

=

⎡⎢⎢⎢⎢⎣


...IPV ,n − IPV ,n−1Istring − IPV ,n

⎤⎥⎥⎥⎥⎦

. (12)

This system is underdetermined because there are n controlobjectives (PV MPP operation) and n + 1 control actuators(IDC ,i , for i = 1. . .n and Istring ). The extra degree of freedomcan be used to minimize power loss.

One way power loss minimization could be implemented isto adjust Istring using the central converter such that powerprocessed by differential converters is minimized. A sweep ofIstring is shown in Fig. 5 for a test case with MPP variability in asystem with eight series PV elements. The flexibility inherent inthis approach allows each PV element to operate at its local MPPover the entire sweep of Istring . The minimum power processedby differential converters occurs at a string current of 4.63 A inthis example.

C. Comparison

Ten thousand simulations were run using a Monte Carlo ap-proach to compare the power processed by the three differentialapproaches introduced above. The aim was to gain insight into


Fig. 5. Main string current can be adjusted to minimize the power processed byisolated, PV-to-bus differential converters while simultaneously tracking localMPPs.

Fig. 6. Comparison of fraction of total PV power processed by several differ-ential power processing architectures for 10,000 Monte Carlo runs, given panelswith a coefficient of variation of 0.1.

how each architecture responds to a random set of MPP condi-tions. The simulations use a normal distribution of MPP currentsacross a series set of eight PV elements with a coefficient ofvariation equal to 0.1. A histogram tallying the fraction of totalpower processed is shown in Fig. 6. The resulting distributionsof fraction of PV power processed indicate that buck–boost,PV-to-bus converters tend to process the most power whereasisolated PV-to-bus converters tend to process the least power.The power processed by isolated PV-to-bus converters was min-imized in each run as demonstrated in Fig. 5. Fig. 6 implies thatthe relative power ratings needed in the isolated PV-to-bus ar-chitecture are on the same order as the coefficient of variation.This analysis is helpful because instead of examining specificcases that favor one architecture or another, a broad range ofconditions is examined to discern overall performance.

III. LOCAL CONTROL

Differential power processing is well suited for local control.Differential converters can maximize the power output of theirrespective PV element with only local information. Protectionand monitoring activities can add value to the converters.

Fig. 7. Maximum power point tracking with local information.

A. Maximum Power Point Tracking

A variety of maximum power point tracking (MPPT) algo-rithms can be implemented using local information [27]. SomeMPPT algorithms may be less suitable in the context of differ-ential converters. For example, a fractional open-circuit voltageapproach may not be desirable since it must open the maincircuit path. Simple, low power overhead techniques may beappropriate when power conversion is managed at the submod-ule level [28].

The aim of the local controller is to maximize the powerout of its respective PV element as shown in Fig. 7. In thiswork, a basic perturb-and-observe (P&O) algorithm is imple-mented. Periodic voltage and current measurements are madelocally at each PV element. These measurements inform thelocal controller whether power has increased or decreased fromthe previous step. The algorithm can generate a reference for acompensator or simply update a duty ratio value. The duty ratioof the switches controls the average voltage of the PV elementto operate at the local MPP. If the PV element is operating atits MPP voltage, it must be generating its MPP current sincethe I–V curve is a one-to-one mapping function. The differentialconverter current follows from the need of the system to balancethe flow of charge. A differential converter can be disabled tosave energy if its average current is close to zero.

In a system with n PV elements and n – 1 differential con-verters, the central converter acts as the nth control actuator. Ingeneral, the differential converters would be able to track theirlocal MPPs more quickly than the global MPP tracking capa-bility of the central converter. This time-scale separation aidseffective MPP tracking and should limit unwanted interaction.With differential power processing, the true MPP of each PVelement can be reached with little conversion loss.

B. Protection and Monitoring

The need for local protection and monitoring is a major issuein PV systems, especially in large-scale installations. In the dif-ferential power approach, each local converter can be enhancedwith protection and monitoring functions, and even active diag-nostics. For instance, if an arc fault occurs, local converters cansafely act to prevent fire or other hazards. Differential convert-ers could use local information to determine if shunting aroundthe PV element or opening the circuit is necessary. Local con-verters can report outlying behavior, such as cases in which any


Fig. 8. Tracking the MPP of three series PV panels with local differential converters. In (a), differential converters inject current to enable each PV panel tooperate at its (b) MPP voltage and (c) MPP current.

individual converter is processing more than a target power level.The enhanced safety performance and ability to identify localtrouble is likely to reduce system operation and maintenancecosts.

Differential converters can also interact with the central in-verter or other central unit to provide distributed monitoring.This information could be relayed to a central hub or commu-nicated to other converters using a variety of techniques suchas power line communication or wireless transmission. The dif-ferential converter provides a natural framework for local diag-nostics, since the circuit can sense local voltage and current andhas information about local mismatch based on the amount ofpower it must handle. This added value with both energy pro-duction advantages and diagnostics represents a fundamentalinnovation.

C. Simulated Example

To further explore differential power processing, a systemwith three series-connected PV panels and two buck–boost, PV-to-PV differential converters is modeled and simulated. Thestructure of the system is similar to that in Fig. 4(a). Simulatinga system with three PV elements can demonstrate the key as-pects of differential converter operation without being unwieldy.BP7185N panels, with nominal open-circuit voltage of 44.2 V,are modeled using standard techniques. The first PV panel has90% insolation and short-circuit current of 4.58 A, while theother two panels have 100% insolation and short-circuit currentof 5.09 A. The MPP of each PV panel is reached with a P&Oalgorithm using local information. Every three milliseconds thelocal P&O algorithm updates the duty cycle of its converter.The differential converters switch at 250 kHz and have filtercomponent values of L = 50 μH and C = 50 μF.

MPP operation is achieved while only a fraction of the totalpower is processed in this example with a local 10% mismatch.Differential converters provide a low average current [less than1 A, shown in Fig. 8(a)] in keeping with theoretical analysis.Note that the differential converters in this configuration do notsimply provide the difference between PV elements’ MPP cur-rent because there is coupling, as shown in (1). This means thatthe differential converters process 25 W or less compared to

a total system output power of almost 550 W. Each PV panelreaches its local MPP, as shown in Fig. 8(b) and (c). The poweroutput from this system increases by about 16 W (a 3% increase)under the given conditions, compared to a direct series connec-tion without the differential converters. A resistor in series withthe inductor was included in the differential converter model torepresent losses.

IV. RELIABILITY ANALYSIS

Differential power processing actually improves system re-liability relative to conventional approaches. A local failure inthe basic differential architecture will not compromise conven-tional bulk power delivery, since a local, nonfunctional converteris simply a reversion to a conventional series connection. Underextreme circumstances, the power devices in the local convertercan perform other functions. For example, if heavy shading orlocal damage occurs within a panel, the associated substring canbe shunted and taken out of the energy production process. Thisaugments and potentially even replaces the function of protec-tion bypass diodes now employed in PV panels to prevent localthermal runaway. As the approach is implemented, we antici-pate that bypass diodes can be replaced, and hotspots can beavoided [29].

For quantitative analysis of reliability impact, a simple modelfor three PV systems is formulated, and a corresponding, closed-form reliability function is derived. The reliability functions arethen compared to obtain an MTTF for the system. This analysistakes an axiomatic interpretation of reliability and employs con-ventional modeling assumptions. For clarity, not all the potentialfailure modes or causes of a component failure are examined;component faults are modeled as leading directly to open orshort circuits. Components in the system are assumed to failrandomly and independently. While there may be a determin-istic cause for each failure, a probabilistic framework supportstractable analysis. With this approach in mind, let T be a ran-dom variable representing the time to failure of a component.The reliability R of that component at time t is the probabilitythat T is greater than t and can be expressed as

R(t) = Pr{T > t}. (13)


Fig. 9. Reliability model for series PV elements.

Failures are assumed to be exponentially distributed. Thismeans that the failure rate λ is constant (i.e., in the bottom partof the “bathtub curve”) during the operating life [30]. With thismodel, the reliability of a given component is

R(t) = e−∫

λdt = e−λt . (14)

The resulting MTTF of a component is

MTTF =∫ ∞

0R(t)dt =

1λ

. (15)

Failure rates of the same component type are assumed tobe the same. Thus, the failure rate of each of the PV elementsmatches (i.e., λp,1 = λp,2 = · · ·= λp,n = λp ), and the failure rateof each of the dc–dc converters (either cascaded or differential)is the same (i.e., λd,1 = λd,2 = · · · = λd,n = λd ).

A. Series PV String

Developing a reliability model for a series PV system, as inFig. 1(a), is fairly straightforward, following from [30]. Sincethis analysis examines the dc portion of the system, the centralinverter is viewed as external and is not included. Wheneverthere is a fault in one of the PV panels, the series string isconsidered to be open-circuited and the system fails. This systemcan be modeled from a reliability perspective as n PV elements inseries. The corresponding component-based reliability diagramis shown in Fig. 9. The failure rate λp of each PV element isassumed to be constant during the useful life of the system. Thereliability of the overall system is

R(t) = Pr{T > t}= Pr{T1 > t, T2 > t, . . . , Tn > t}= Pr{T1 > t} · Pr{T2 > t} · · ·Pr{Tn > t}

= e−λp , 1 t · e−λp , 2 t · · · e−λp , n t

=n∏

i=1

e−λp , i t . (16)

This product can be further simplified since the failure rateof each PV panel is the same. Hence, the system reliabilitybecomes

R(t) = e−nλp t . (17)

B. Cascaded DC–DC Power Optimizers

The reliability model for a PV system that employs cascadeddc–dc converters, as in Fig. 1(b), is based on the premise thatif one of the dc–dc converters in the series string fails, thenthe system fails as it can no longer deliver any power. Thedc–dc converter failure can be thought of as an open circuitin the string. On the other hand, when a PV panel fails, thesystem can still operate, presumably at a lower power level. Thesystem is no longer operational when all of the PV panels fail

Fig. 10. Reliability model for a PV system with cascaded dc power optimizers.

since there would be no output power from the system. This isrepresented in the component-based reliability model, shown inFig. 10, with the dc–dc converters in series and the PV panelsin parallel. Keep in mind that this is a reliability model and nota diagram depicting electrical connections. The model shows nPV elements and n cascaded dc–dc converters with failure ratesλp and λd , respectively.

Based on the reliability model, the reliability of the systemis found by aggregating the parallel PV components into onecomponent that is in series with the dc–dc converters. The re-liability RPV of the set of parallel PV components is found byutilizing the unreliability QPV and is

RPV(t) = 1 − QPV(t)

= 1 − (1 − Pr{T1 > t}) · · · (1 − Pr{Tn > t})

= 1 −n∏

i=1

(1 − Rp,i(t))

= 1 −n∏

i=1

(1 − e−λp , i t). (18)

This result can be used to find the system reliability which isgiven by

R(t) = RPV(t)Rdc,1(t) · · ·Rdc,n (t)

=

(1 −

n∏i=1

(1 − e−λp , i t)

)n∏

i=1

e−λd , i t . (19)

Since the failure rates of like components are the same, thereliability equation can be simplified to

R(t) = (1 − (1 − e−λp t)n )e−nλd t . (20)

C. Differential Power Processing

From a reliability modeling perspective, a differential con-verter is in parallel with its adjacent PV element. Since a differ-ential converter failure does not compromise the system relativeto a more basic series string, the model should show that theconverters improve overall system reliability. Just as in the se-ries PV system case, the PV elements are modeled in series. Oneor two differential converters are modeled in parallel with eachPV element, depending on the location in the system and thesystem architecture. In the model, if a differential converter failsopen, the system does not fail; furthermore, if a PV element failsopen, differential converters are used to bypass current aroundthe failed element. The first and last PV elements can only bebypassed by one circuit in the event of a failure. The rest of thePV elements can be bypassed by either of two differential con-verters in the PV-to-PV, buck–boost architecture. Hence, from


Fig. 11. Reliability model for a PV system with local, differential converters.

a reliability modeling perspective, the PV elements and differ-ential converters are modeled in parallel, as shown in Fig. 11.The model shows n PV elements and n – 1 differential powerconverters with failure rates λp and λd , respectively.

The system reliability function is found by analyzing the com-ponent model of the system. The component model is formed bya series string of parallel components. Each parallel segment canbe aggregated into one component that is analyzed in series withthe rest. If R1(t),. . .,Rn (t) represents the reliability function foreach parallel aggregate, then the system reliability function is

R(t) = R1(t)R2(t) · · ·Rn (t). (21)

As in the two previous systems, the failure rates for like com-ponents are equal. The reliability for the first and last segmentis therefore

R1(t) = Rn (t) = 1 − (1 − e−λp t)(1 − e−λd t)

= e−λp t + e−λd t − e−(λp +λd )t . (22)

The reliability of all of the intermediate segments is

R2(t) = · · · = Rn−1(t) = 1 − (1 − e−λp t)(1 − e−λd t)2 .(23)

Equations (22) and (23) can be substituted into (21) to obtainthe system reliability function which is

R(t) = [R1(t)]2 [1 − (1 − e−λp t)(1 − e−λd t)2 ]n−2 . (24)

D. Reliability Comparison

The reliability of each system can be compared using thereliability functions obtained. The reliability metric of MTTFis used for comparison. For example, it is assumed that theMTTF of each PV panel is 50 years, and the MTTF of eachdc–dc converter is 30 years. If more accurate failure rate data isavailable to the reader, the system reliabilities can be updated.The MTTF of a system is found by integrating the reliabilityfunction, as described in (15).

The final step is to examine a couple of sample systems.Systems with four PV panels and 20 PV panels are examined.This gives a sense of how reliability is affected as n, the numberof PV elements, changes. Using (17), (20), and (24), reliabilityfunctions are plotted in Fig. 12(a) and (b). It can be seen fromthe graphs that the reliability for the system with differentialconverters is the highest, followed by the basic series PV system,and trailed by the system with cascaded dc–dc converters in bothcases. When the number of PV panels increases, the benefit ofthe differential power processing architecture is more apparent;system reliability is considerably higher than for the other twosystem architectures [shown in Fig. 12(c)]. In PV systems with

four PV elements, the MTTF of the system with differentialconverters is 15 years longer that of a conventional series PVsystem and twenty years longer than the system with cascadeddc–dc converters. The benefits increase with system size. ForPV systems with 20 PV elements, the MTTF of the systemwith differential converters is over five times longer than of theseries PV system and almost ten times longer than the systemwith cascaded dc–dc converters.

V. EXPERIMENTAL RESULTS

Hardware prototypes were developed to operate at the sub-panel level to verify experimentally the potential of differentialpower processing. A diagram of a differential converter for onePV element in a series string is shown in Fig. 13(a). The pro-totypes, shown in Fig. 13(b), were designed around a single,analog IC that includes the switches, gate drivers, and most ofthe control. TI’s LM20343 chip was selected as it met the volt-age and current ratings needed, had synchronous switching forbidirectional current flow, and had the ability to adjust the out-put voltage via an analog reference voltage. This could be usedby an outer MPPT loop to update the output reference voltage.The prototypes had a 56-μH inductor with 14.1 μF of outputcapacitance and switched at 250 kHz. Only ceramic capacitorswere used.

Two versions of the subpanel differential converter wereconstructed. One had the LM20343 chip and no outer MPPTloop; the second version had a TI MSP430 microcontroller pro-grammed with a P&O MPPT algorithm. In the first version, thevoltage reference of the converter was set with a potentiometer tothe PV’s rated MPP voltage. The second version used a digital-to-analog converter to provide the output voltage reference.

Efficiency measurements were taken with a lab power supplyand an electronic load over a range of input voltages. The ef-ficiency of both subpanel prototype versions with 10-V outputvoltage is shown in Fig. 14. The microcontroller code was notoptimized for low power consumption and was left in activemode the entire time the efficiency measurements were taken.This provides an estimate of the lower bound on its efficiency.As seen in Fig. 14, the efficiency curves are nearly the same witha peak efficiency around 95% for both versions. The efficiencyof the prototype with the microcontroller is lower at lower out-put current levels. This is expected because the control powerconsumption overhead remains the same as the power outputdecreases.

The subpanel differential converters were tested outside withPV modules to demonstrate their ability to harvest additionalenergy. The PV modules were rated for 20 W with the MPP at9.5 V and 2.3 A. Two strings of two modules each were con-nected to separate channels of an electronic load. One stringconsisted of series PV modules and the other string had a differ-ential converter. The electronic load tracked the global MPP ofeach string and was controlled by a computer that also recordedthe experimental data. The global MPPT step rate was approxi-mately one step per second.

The power and energy generated on a sunny day by the two PVsystems is shown in Fig. 15. A small section of a PV panel wasshaded (less than 5% of the panel surface area). The differential


Fig. 12. Reliability of a PV system using series panels, cascaded dc–dc converters, and local differential converters with (a) four PV panels and (b) 20 PV panels.In (c), the MTTF of each system is shown for various number of PV panels.

Fig. 13. Diagram of the components contained in one subpanel differential converter prototype is shown in (a). Local information is used to track the respectivePV element’s MPP. Hardware prototypes are shown in (b).

Fig. 14. Measured efficiency of subpanel differential converter prototypes (a)without a microcontroller and (b) with a microcontroller.

system generates about 50% more average power than the seriessystem during the 5-min time interval of the test. This resultsin approximately 50% more energy generated at the end of thetest period. The global MPP for each system is reached afterapproximately 25 s. This is seen during the initial increase inpower in Fig. 15. The dip in power seen around 120 s is probablydue to a cloud.

Fig. 15. Measured (a) power and (b) energy generated by two series PVstrings with and without differential power processing under 5% partial shadedconditions.

PV and differential converter states for two shading condi-tions are shown in Fig. 16. When the upper PV substring oftwo substrings is partially shaded, its MPP current decreases.The differential converter enables the lower substring to bypassits current around the shaded module. The resulting inductorcurrent is negative, as shown in Fig. 16(a). When the lower PVsubstring is partially shaded, the differential converter injects


Fig. 16. PV voltage, current, and differential converter inductor current for a shading condition that results in (a) negative inductor current and (b) positiveinductor current.

current into the intermediate node to enable MPP operation, asshown in Fig. 16(b).

These experimental results demonstrate the potential of dif-ferential power processing. Differential power processing en-ables a series PV system to track the true global MPP byreaching the MPP of each PV element. Only a small frac-tion of the total output power is processed when a mismatchin MPP current exists. Differential power processing has thepotential to substantially improve the LCOE of PV systems.Because the processed current is relatively small in most cir-cumstances, it may be possible to integrate differential con-verters in small packages or on chip for high-volume, low-costproduction.

VI. CONCLUSION

Differential converters enable a series PV system to truly op-timize power production by reaching the MPP of each seriesPV element. Only a small fraction of the total output power isprocessed when a mismatch among MPP currents exists. Dif-ferential converters offer several advantages that tend to keepcosts low: 1) differential converter requirements are simple androutine in a power conversion sense, with many possible scal-able, local conversion solutions, 2) voltage and current ratingsare modest (and a small fraction of system current), and 3) thereare no special dynamic performance requirements, as MPPTperformance on time scales of a few milliseconds is the state ofthe art.

Differential power processing has the potential to substan-tially improve the LCOE of PV systems. A comparative anal-ysis of system reliability concludes that the differential powerprocessing architecture results in a longer MTTF than other dcarchitectures. Protection and monitoring capabilities add valueto locally controlled differential converters. Global MPPT in acentral inverter is simplified because local maxima (the kinks inthe I–V curve) can be eliminated, and overall energy generationincreases. Because differential converters process little power,there is potential to integrate these systems in small packages oron chip for high-volume, low-cost production.

Several differential power processing architectures were pre-sented and compared. Results show that isolated PV-to-bus dif-

ferential converters tend to process the least amount of powerand have the ability to minimize the power processed by differ-ential converters. Simulation results demonstrate MPP trackingwith local information. Experimental results show differentialconverters generating up to 50% more energy under a 5% partialshading condition for two series PV subpanel modules.

ACKNOWLEDGMENT

The authors would like to thank R. Pilawa, A. Domı́nguez-Garcı́a, and S. Dhople for insightful discussions related to solarPV and reliability. Special thanks go to R. Pilawa for providingsome of the hardware tools that enabled this work. The authorswould also like to thank Plexim for use of the PLECS toolboxused in simulations.

The information, data, or work presented herein was fundedin part by an agency of the United States Government. Neitherthe United States Government nor any agency thereof, nor anyof their employees, makes any warranty, express or implied,or assumes any legal liability or responsibility for the accuracy,completeness, or usefulness of any information, apparatus, prod-uct, or process disclosed, or represents that its use would notinfringe privately owned rights. Reference herein to any specificcommercial product, process, or service by trade name, trade-mark, manufacturer, or otherwise does not necessarily constituteor imply its endorsement, recommendation, or favoring by theUnited States Government or any agency thereof. The views andopinions of authors expressed herein do not necessarily state orreflect those of the United States Government or any agencythereof.

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Pradeep S. Shenoy (S’06–M’12) received the B.S.degree in electrical engineering from the Illinois In-stitute of Technology, Chicago, in 2007, and the M.S.and Ph.D. degrees in electrical engineering from theUniversity of Illinois, Urbana-Champaign, in 2010and 2012, respectively.

In 2008, he participated in the National ScienceFoundation’s East Asia and Pacific Summer Insti-tutes program doing research at Tsinghua University,Beijing, China. He interned with Caterpillar’s Elec-tric Power Division in 2005 and with Texas Instru-

ment’s Systems and Applications Lab in 2011. He is currently with Kilby Labs,Texas Instruments, Dallas.

Dr. Shenoy was awarded the Camras scholarship in 2003–2007 and a ForeignLanguage and Area Studies fellowship in 2009–2010. He received the IllinoisInternational Graduate Achievement Award in 2010 and was a finalist for theLemelson-MIT Illinois Student Prize for innovation in 2012. He was the ViceChair of the IEEE Power Engineering Society and Power Electronics SocietyJoint Student Chapter at the University of Illinois in 2009–2010 and the Co-Director of the 2011 IEEE Power and Energy Conference at Illinois. He servesas the Student Liaison for the IEEE Power Electronics Society.

Katherine A. Kim (S’05) received the B.S. de-gree in electrical and computer engineering from theFranklin W. Olin College of Engineering, Needham,MA, in 2007. She received the M.S. degree in elec-trical and computer engineering from the Universityof Illinois at Urbana-Champaign, Urbana, in 2011,where she is currently working toward the Ph.D.degree.

She received the National Science Foundation EastAsian and Pacific Studies Institute Fellowship in 2010and Graduate Research Fellowship in 2011. Her cur-

rent research interests are power electronics, modeling, and control for photo-voltaic systems.

Ms. Kim was the Chair of the IEEE Power Engineering Society and PowerElectronics Society Joint Student Chapter at the University of Illinois in 2010–2011 and the Co-Director of the 2012 IEEE Power and Energy Conference atIllinois.


Brian B. Johnson (S’08) received the B.S. degree inphysics from Texas State University, San Marcos, in2008, and the M.S. degree in electrical and computerengineering from the University of Illinois at Urbana-Champaign, Urbana, in 2010, where he is currentlyworking toward the Ph.D. degree in electrical andcomputer engineering.

His research interests are in control of powerelectronics with an emphasis in renewable energysystems.

Philip T. Krein (S’76–M’82–SM’93–F’00) receivedthe B.S. degree in electrical engineering and the A.B.degree in economics and business from LafayetteCollege, Easton, Pennsylvania, and the M.S. andPh.D. degrees in electrical engineering from the Uni-versity of Illinois, Urbana.

He was an Engineer with Tektronix, Beaverton,OR, then returned to the University of Illinois atUrbana-Champaign. Currently, he holds the GraingerEndowed Director’s Chair in Electric Machinery andElectromechanics as Professor and Director of the

Grainger Center for Electric Machinery and Electromechanics, Departmentof Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana. He published an undergraduate textbook Elements ofPower Electronics (Oxford, U.K.: Oxford Univ. Press, 1998). In 2001, he helpedinitiate the International Future Energy Challenge, a major student competitioninvolving fuel cell power conversion and energy efficiency. He holds twentyU.S. patents with additional patents pending. His research interests address allaspects of power electronics, machines, drives, and electrical energy, with em-phasis on nonlinear control and distributed systems.

Dr. Krein is a Registered Professional Engineer in the States of Illinois andOregon. He was a senior Fulbright Scholar at the University of Surrey, Surrey,U.K., in 1997–1998, and was recognized as a University Scholar in 1999, thehighest research award at the University of Illinois. In 2003, he received theIEEE William E. Newell Award in Power Electronics. He is an Ex-President ofthe IEEE Power Electronics Society, and served as a member of the IEEE Boardof Directors. In 2005–2007, he was a Distinguished Lecturer for the IEEE PowerElectronics Society. In 2008, he received the Distinguished Service Award fromthe IEEE Power Electronics Society. He serves as Academic Advisor for theDepartment of Electronic and Information Engineering at Hong Kong Polytech-nic University. He is the Chairman of the Board of SolarBridge Technologies, adeveloper of long-life integrated solar energy systems.

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