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Modular Differential Power Processing in Solar System A Thesis Presented by Chang Liu to The Department of Electrical and Computer Engineering in partial fulfillment of the requirements for the degree of Master of Science in Electrical and Computer Engineering Northeastern University Boston, Massachusetts October 2019

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  • Modular Differential Power Processing in Solar System

    A Thesis Presented

    by

    Chang Liu

    to

    The Department of Electrical and Computer Engineering

    in partial fulfillment of the requirements

    for the degree of

    Master of Science

    in

    Electrical and Computer Engineering

    Northeastern University

    Boston, Massachusetts

    October 2019

  • i

    To my dream.

  • ii

    Contents

    List of Figures iii

    List of Tables iv

    List of Acronyms v

    Acknowledgments vi

    Abstract of the Thesis vii

    1 Introduction 1

    2 Introduction on Modular Differential Power Processing 7

    2.1 Differential Power Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

    2.2 PV Panel to Virtual PV Panel (P2VP) Transfer . . . .. . . . . . . . . . . . . . . . . . 8

    2.3 PV Panel to PV Panel (P2P) Transfer . . . . . . . . . . . . . . . . . . . . . . . . . 10

    3 Challenge and Control Strategy for PV Panel to PV Panel Transfer 13

    3.1 Mathematical Model and Control Challenge . . . . . . . . . . . . . . . . . . . . . . 13

    3.2 Dual Loop Controller Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .15

    3.3 Power Outer and Voltage Inner Loop . . . . . . . . . . . . . . . . . . . . . . . . .16

    3.4 PI Controller Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .21

    4 Simulation Results 23

    4.1 Steady State Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23

    4.2 Simulation Result of PI Controller . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

    4.3 MonteCarlo Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

    4.4 Efficiency Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .28

    5 Experiment Results 30

    5.1 mDPP Hardware Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

    5.2 Indoor Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .33

    5.3 Outdoor Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

    5.4 Plug and Play Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

    6 Conclusion 37

    Bibliography 39

  • iii

    List of Figures

    1. Modular Solar Panel Concept with Plug-and-Play . . . . . . . . . . . . . . . . . . . . 1 2. DPP with different connection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3. DPP in series connection with central converter . . . . . . . . . . . . . . . . . . . . . 4 4. Modular Differential Power Processing Diagram . . . . . . . . . . . . . . . . . . . . 5 5. Panel to Virtual Panel (P2VP) Method for mDPP . . . . . . . . . . . . . . . . . . . . 9 6. Panel to Panel (P2P) Method for mDPP . . . . . . . . . . . . . . . . . . . . . . . . . 11 7. Control Diagram of Power Outer Loop and Current Inner Loop . . . . . . . . . . . . .15 8. Modular Differential Power Processing Diagram . . . . . . . . . . . . . . . . . . . . 17 9. Simulation schematic for mDPP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 10. Simulation Schematic of a Solar System in PSIM . . . . . . . . . . . . . . . . . . . .25 11. Startup Waveform of Power of Each PV Panel . . . . . . . . . . . . . . . . . . . . . 26 12. Comparison of Fraction of PV Power Processed of P2P and P2VP . . . . . . . . . . . 27 13. mDPP Hardware Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 14. Indoor Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 15. Outdoor Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 16. Waveform of Outdoor Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 17. Simplified Schematic of plug-and-play experiment . . . . . . . . . . . . . . . . . . . 35 18. Waveform of plug-and-play experiment . . . . . . . . . . . . . . . . . . . . . . . . . 36

  • iv

    List of Tables

    1 Simulation Result Of Steady State (Watts) . . . . . . . . . . . . . . . . . . . . . . . .24

    2 System Efficiency Study Of Different Dpp Structures . . . . . . . . . . . . . . . . . . 28

    3 Key Component for Hardware Prototype . . . . . . . . . . . . . . . . . . . . . . . . 32

    4 Comparison Experiment for dMPPT and mDPP Method . . . . . . . . . . . . . . . . 33

  • v

    List of Acronyms

    mDPP Modular Differential Power Processing method. Define the major contribution of this

    work containing both hardware and software for this architecture.

    DPP Differential Power Processing method. A concept that has usually lower system loss than

    the traditional method.

    FPP Full Power Processing method. A concept that is contrast to the DPP. Full power processing

    method usually convert all the power from the source.

    MPPT Maximum power point tracking. An algorithm used to tract peak power output of the PV

    panel. May have different detail implement method.

    P2P One of two mDPP implement methods: PV Panel to PV Panel transfer method

    P2VP One of two mDPP implement methods: PV Panel to Virtual PV Panel transfer method

    dMPPT Distributed maximum power point tracking. Compared with cMPPT, a MPPT method

    that each PV panel has its own distributed MPPT converter.

    cMPPT Centralized maximum power point tracking. Compared with dMPPT, a MPPT method

    that all PV panels share one centralized MPPT converter.

    pDPP Parallel Differential Power Processing method. A DPP method works only at parallel

    connected PV panel system.

    sDPP series Differential Power Processing method. A DPP method works only at series

    connected PV panel system.

  • vi

    Acknowledgments

    Here I wish to thank my parents to support my study in Northeastern University. Also

    thanks to Prof. Brad Lehman for his guidance and support on my research as my advisor.

    Finally, thanks to so many people who have paved my way to this work and not blocked

    me from somewhere amazing.

  • vii

    Abstract of the Thesis

    Modular Differential Power Processing in Solar System

    by

    Chang Liu

    Master of Science in Electrical and Computer Engineering

    Northeastern University, Oct 2019

    Advisor: Dr. Brad Lehman

    This thesis proposes a realization of the photovoltaic (PV) panel to PV panel (P2P) method

    for the modular differential power processing (mDPP). The approach is modular and permits panels to

    be added to or removed from either series strings or paralleled connections. A voltage inner loop and

    power outer loop control strategy tracks the individual maximum power point of the PV panel, while

    the power converters only process the differential power. The proposed method decouples the

    control loop performance of each PV module, making design simple. Simulation and experimental

    results validate the Plug-and-Play function for scalable PV system and MPPT accuracy. Hardware

    prototype is also built, and both indoor and outdoor experiments are provided to exhibit the

    advantage of this P2P method.

  • 1

    Chapter 1

    Introduction

    Solar energy is a type of sustainable energy sources that can be used to create electricity,

    remote heating, battery charging, as well as provide energy for many other applications. When the

    photovoltaic (PV) panels are used, the sun’s radiated power is directly converted to electricity.

    When this occurs, it is common to add maximum power point tracking (MPPT) electronics to the

    PV system to guide operation of PV array at the optimal voltage that produces highest power.

    Common maximum power point tracking (MPPT) algorithms are used to maximize the power

    output of the PV system, such as perturb & observe (P&O) [1], the incremental conductance (INC)

    [2], the hill climbing method [3], fuzzy logic topology algorithm [4] and neural network method

    [5]. In large photovoltaic (PV) systems, MPPT is often performed with a centralized power

    Fig. 1 Modular Solar Panel Concept with Plug-and-Play

    1 PV blanket contains 12 removable PV units

    One DC-DC submodule

    One PV unit

    One PV subpanel

  • 2

    converter [6, 7]. In this approach, PV panels are connected in series as a string, and then multiple

    series strings are connected in parallel through the combiner box. The output of the series-

    parallel connection becomes the input of the centralized MPPT converter, which is often an

    inverter for the AC output [8-10]. The approach is low cost and has high reliability.

    In recent years, with the drastic price reduction of the solar panels, a new trend has

    emerged: solar panels and strings are beginning to be added to increase the capacity of older PV

    installations. Sometimes, there is not even an update on the capacity of the inverter, so it is just

    the DC capacity that is increased. However, this practice results in a new loss of energy because

    the old PV panels might not have similar performance characteristics as the new, more efficient

    panels. This mismatch can become even more apparent when the older PV panels have

    manufacturing variation, aging degradation, silicon impurities, dust accumulation or even might

    have partial shading [11]. All these factors will influence adjacent PV panel performance and may

    even by limit the total energy generation.

    In contrast of the central converter method, distributed maximum power point tracker

    (dMPPT) method has been proposed to mitigate any power mismatch problems [12, 13]. Each PV

    panel has its own converter and distributed controller to perform MPPT and deliver the power to

    the voltage bus [13]. Degradation of each PV panel will only influence its own MPP, and the

    partial shading effect will only lower the power output of those shaded PV panel. Other than this

    advantage, the dMPPT method also has modularity. PV panels can be added to an existing

    installation, or as in the papers [12, 13], an individual panel can be composed of modular sub-

    panels, each with its own maximum power point tracker as in Fig. 1. Then the sub-panels can be

    slid in and out of a “blanket” to increase or decrease the PV power of the panel, without

    influencing each other sub-modules’ performance, while using Plug-and-Play function in Fig.1.

    In both these above methods, the converters are designed based on full power

    processing (FPP) of the PV panel or sub-panel that it is connected to. That is, the converter

    processes all the power generated by the source and delivers this entire power to the load. Given

    the assumption that the power loss is proportional to the power processed by the converter, the

    system efficiency is limited by the converter efficiency. Meanwhile, the DC-DC converter in Fig.

    1 is introduced to boost up the subpanel’s voltage to the bus voltage which leads to a high voltage

    gain but may also add certain extra power loss [14-16]. As an alternative, differential power

    processing (DPP) can be applied to a PV system [17]. In order to improve the efficiency, DPP

    brings a new idea for the power delivery [18, 19]. In this approach only the mismatched power

  • 3

    from the PV sources is processed through the converter. Most of the power is instead processed

    directly through the wire connections between the PV panels. By converting only a small part of

    the power, the total power loss is constrained to a lower level, which means a higher overall

    efficiency. A simple example could be explained as powering a 3.3V load with a typical 5V input.

    The usual solution will take full 5V voltage input and use a buck converter to transform the power

    to 3.3V. As a matter of fact, with the switching converter bucking down the voltage, the output

    current is higher than the input current. Differential power processing method, on the other hand,

    can be connected between the voltage source and load. The converter takes the voltage difference

    between the input and output (which is 1.7V in this case) and only process the extra current that

    the input does not directly supply. As the second method is processing less power and with low

    power/voltage rating, DPP usually has higher system efficiency compared with traditional full

    power converter. An experiment in this thesis demonstrated in [20] shows the DPP system has ~7%

    efficiency boost with nearly same converter than the traditional dMPPT system.

    There are generally two approaches to DPP, classified as series DPP in Fig. 2(a) and

    parallel DPP in Fig. 2(b). More specifically, Fig. 2(a) shows the series DPP (sDPP) method with

    panel to virtual bus transfer [21-24] as an example, while neighbor to neighbor transfer method is

    presented in [25-29] and panel to bus method in [27, 30-32] have also been proposed. In Fig. 2(a),

    differential power is processed from each PV panel to the virtual bus or in the opposite direction.

    Because only small amounts of power are processed, DPP is feasible to be embedded in power

    management integrated circuit (PMIC) design for the cell level DPP function [33]. Under certain

    power converter rating limitation, a power-limited DPP converter [34] becomes more feasible for

    mismatched PV system.

    n

    #1

    #2

    #3

    #n

    DPP2

    DPPn

    Voltage Bus

    DPP3

    DPP1

    #1

    DPP1 DPPm

    #m

    Voltage Bus

    (a) DPP in series connection (b) DPP in parallel connection

    Fig. 2 DPP with different connection

  • 4

    n

    #1

    #2

    #3

    #n

    DPP2

    DPPn

    Voltage Bus

    DPP3

    DPP1

    Central Converter

    (a) PV to the series string

    (a) PV to PV

    Fig. 3 DPP in series connection with central converter

    #11

    #12

    #13

    #1n

    DPP1,2

    DPP1,n-1

    n

    CentralConverter

    #m,1

    #m,2

    #m,3

    #m,n

    DPPm,2

    DPPm,n-1

    m

    CentralConverter

    DPP1,1 DPPm,1

    Voltage Bus

    Besides the higher efficiency, the DPP solution mentioned above also enjoys many

    other advantages such as low-power rating, smaller DPP converter size and reliability

    enhancement. Unfortunately, these approaches have difficulties with scalability. Typically, a

    string of series DPP (sDPP) as in Fig. 2(a), cannot easily be connected in parallel to another group

    of sDPP. The voltage of each sDPP is the sum of each PV sub panel voltage at its MPP, which is

    different from other strings. Paralleling operation will clamp other strings, and force strings to

    work away from MPP and produce less power. Similarly, parallel DPP (pDPP), such as in Fig.

    2(b), cannot effectively have PV panels connected in series. Fig. 3 illustrates two recently

    proposed series DPP structure with central converters (sDPPcc) and improved modularity [25, 35-

    37]. Since the central converter is indispensable for the MPPT function, the PV power is

    processed via dual stages. Processing full power of the PV system, central converter usually pays

    for the penalty of extra power loss and system cost. Further, communication is required to

  • 5

    Voltage Bus

    PVm,1

    PVm,2

    PVm,n-1

    DC/DC

    DC/DC

    DC/DC

    DC/DC

    Controllable current source

    PV1,1

    PV1,2

    PV1,n-1

    DC/DC

    DC/DC

    DC/DC

    DC/DC

    Iout is current difference between PV panels

    Virtual PV panel

    Vcap is voltage difference between the string and the bus

    PVVmpp=?VImpp=0A

    PV1,n PVm,n

    Fig. 4 Modular Differential Power Processing Diagram

    improve the system dynamic performance, and this adds difficulty when scaling PV system or

    adding new PV panel to existed PV system.

    This research proposes a modular differential power processing (mDPP) concept to

    solve the modularity and scalability problem. A modular solar PV system is defined as PV system

    where PV modules can be removed, replaced or added to the existed installation in either series or

    parallel configuration. To meet this design criteria, mDPP system architecture is proposed to have

    MPPT function in each DPP block and avoid the requirement of central converter. This concept

    yields the high levels of system efficiency and plug-and-play function [20, 38] in Fig. 4. To solve

    the complexity of previous hardware and firmware design, the distributed controller enables the

    plug and play function and simplified the wire connection by avoiding communication between

    converters. Each mDPP converter module has the same hardware configuration and software

    implementation, which could be installed for every PV panel in the PV array without any

    modification as the previous dMPPT method [12, 13]. Benefits of the proposed approach also

    include:

    1. A central converter is no longer needed for MPPT, which is typical of other DPP

    methods [35, 36]. This eliminates the power losses associated with a full power processing

    converter.

    2. Communication and data sharing between PV modules is eliminated. Instead a

    distributed controller is proposed. This enables the modular Plug & Play capability and

    simplified wire connections (57% reduction from previous method [35, 36]).

    The remainder of this thesis is organized as follows: Architecture and topology of the

    modular differential power processing method is introduced in Chapter 2. The challenge and

    proposed control strategy are presented in Chapter 3. The detailed mathematic model and steady

  • 6

    state analysis of the inner control loop is discussed in Chapter 3. Simulation is provided in

    Chapter 4. Hardware implementation and experimental verification is performed in Chapter 5.

    Finally, Chapter 6 concludes the thesis.

  • 7

    Chapter 2

    Introduction on Modular Differential

    Power Processing

    Most converters in the power electronics field processes full power from the source and

    delivers it to the load. Differential power processing (DPP) method however processes only part

    of the total power while the rest of the required power is delivered to the load directly from the

    source. DPP usually has higher efficiency. This thesis proposes a modular differential power

    processing (mDPP) method to add modularity to the previous DPP methods for the first time,

    which brings simplicity and plug-and-play function. By redesigning the system architecture, the

    proposed mDPP eliminates the centralized converter, which usually has most of the system loss in

    the traditional DPP method. Therefore, higher system efficiency is achieved. To implement this

    mDPP method, two different kinds of system architectures are proposed: 1) the PV panel to PV

    panel(P2P) method and 2) the PV panel to virtual PV panel (P2VP). Both methods have their

    advantages and disadvantages and are introduced in the following sections.

    2.1 Differential Power Processing

    It is sometimes required to increase PV system size from both series and parallel

    connection. Traditional sDPP can compensate the differential current as a controllable current

    source to expand the system in series connection. On the other hand the pDPP can provide the

    differential voltage between the strings or between the string and the bus to extend paralleled

  • 8

    branch for the system. Meanwhile modularity requires the uniformity of every sub module for the

    system. A modular differential power processing (mDPP) structure is proposed in this research to

    obtain the scalability of the system and modularity as seen in Fig. 4. This approach combines the

    sDPP and pDPP and can be implemented by various topologies, two of which are described

    below.

    For mDPP, each PV series string has an additional series capacitor that compensates

    the mismatch of voltages when connected in parallel with another or a voltage bus. It allows each

    PV panel to work at its own MPP when the sum of PV panels’ voltage differs from the bus

    voltage. Hence, it is possible to scale the mDPP system by paralleling strings without clamping

    each other and losing energy. In the steady state, the voltage of each string will be fixed; therefore,

    the voltage difference between the bus and total PV panels is fixed. The capacitor voltage keeps

    constant in steady state so that the average capacitor current is zero.

    From the steady state point of view, the capacitor works as an absent PV panel in the

    string. Similar with other PV panels in the series, this capacitor acts as a ‘Virtual PV Panel’ and

    holds differential voltage between the voltage bus and the series PV panel voltage in the string. In

    the previous serious DPP method, the central converter is required to compensate the voltage

    difference between the PV string and the voltage bus [36], [35]. This The central converter

    usually reduces the system power loss and requires high system power rating since the central

    converters are is usually designed for full power.

    The string current will flow in the direction illustrated in Fig. 4. Meanwhile the mDPP

    structure will force the differential power to go through the DPP blocks in Fig. 4. With the help of

    mDPP, the PV modules can be connected in series to build up the voltage, yet maintain the

    maximum power output of the individual PV solar cell strings. Since PV panels in series will

    share the same string current, mDPP converter works as a controllable current source for each

    intermediate node between panels, including the virtual panel. By providing separate paths for the

    differential current and the string current, the differential power is transferred either to the

    adjacent PV panel or to the virtual panel. This research presents two architectures to achieve

    mDPP, which will be discussed in the following sections.

    2.2 PV Panel to Virtual PV Panel (P2VP) Transfer (Fig. 5)

  • 9

    #1

    #2

    #3

    #n

    DPP2

    DPPn

    Voltage Bus

    n

    IS

    Vn

    DPP3

    DPP1

    In

    Pdpp1

    Q3

    Q4

    Q1

    Q2

    Q7

    Q8

    Q5

    Q6

    H1 H2

    vh1 vh2

    Ll

    Vc

    Ic

    Fig. 5 Panel to Virtual Panel (P2VP) Method for mDPP

    Differential power can be transferred directly to the series capacitor, which we term

    the virtual PV panel. The bidirectional converter will be used for DPP function since differential

    power can flow either from the PV panel to the capacitor or in the other direction. No common

    ground is shared by the PV panels. Therefore, isolation is further required for this application.

    The P2VP approach is shown in Fig. 5 with a dual active bridge for the mDPP

    structure. When ith PV panel works at its maximum power point (MPP), the voltage and current

    are denoted as Vi,mpp and Ii,mpp, with power Pi,mpp. This means

    ,

    ,

    ( 1,2,3,..., )

    i i mpp

    i i mpp

    I I

    V V

    i n

    =

    =

    . (1)

    The differential power is transferred from each PV panel to the series capacitor

    directly which serves as an energy buffer as well as a voltage balancer. Similar to PV-to-Bus

    method in [39], the power through P2VP transfer can be expressed as (2) by the assumption of no

    current limitation. Vi×(Ii,mpp-Is) is defined as the differential power to be extracted from the

    individual PV panel to make each PV panel work at its own MPP because this amount of power

    can adjust the current through the PV panel from string current, Is, to its MPP current, Ii,mpp. Note

    here the power through the converter, Pdppi, is the same as the differential power.

    ,( )dppi i i mpp sP V I I= − . (2)

    In steady state the voltage across the capacitor keeps constant and the average

    current through the capacitor is zero. Applying KCL and KVL equations to the negative terminal

    of the capacitor, then (3) could be derived steady state as

  • 10

    1

    0cn

    c bus i

    i

    I

    V V V=

    =

    = − . (3)

    The capacitor has zero average power flow through it as

    1

    ,

    1 1 1

    0

    ( ) ( )

    n

    cap dppi c s

    i

    n n n

    i i mpp i s bus i s

    i i i

    P P V I

    V I V I V V I

    =

    = = =

    = − =

    = − − −

    . (4)

    Simplifying (4), (5) can be derived as

    ,

    1

    n

    bus s i mpp

    i

    V I P=

    = . (5)

    From (5), the string power is the sum of each PV panel’s maximum power. Further,

    the PV string voltage can be different from the bus voltage or other voltage strings. Therefore, the

    proposed mDPP structure now allows different PV strings to be placed in parallel, since the

    strings no longer clamp the voltage of each other. This explains the scalability of the system. The

    capacitor compensates for the voltage difference in the steady state.

    2.3 PV Panel to PV Panel (P2P) Transfer (Fig. 6)

    Differential power can also be transferred between adjacent PV modules using the

    bidirectional buck-boost converter instead of transferring the power from PV panel to the series

    capacitor in the P2VP method described above. This PV Panel to PV Panel (P2P) transfer

    approach extends the architecture presented in [36] to consist of n converters instead of (n-1),

    where n is the number of PV modules per string. The schematic for the P2P transfer structure is

    shown in Fig. 6.

    The duty ratio for DPPi converter, Di, and its complimentary duty ratio, Di’=1-Di, is

    generated for the synchronized buck-boost converter by a distributed controller. The duty ratio is

    adjusted to regulate the power of each PV panel to its maximum power. The bidirectional buck-

    boost converter has the ideal relationship for Fig. 6 as

    1

    ' 1

    i i i

    i i i

    V D D

    V D D

    + = =−

    . (6)

    Every P2P transfer structure will deliver the certain power from one PV panel to the

  • 11

    next series PV panel.

    As the result, the power of each mDPP model, Pdppi,in, is related to its previous one,

    Pdppi-1,out, which introduces coupling effect and adds complexity to the distributed controller

    design.

    Assuming 100% efficiency with Pdppi,in=Pdppi-1,out, the DPPi in Fig. 6 will be

    processing power flow from and to DPPi-1 and DPPi+1. The power through the converter, Pdppi,

    contains 2 parts in (7), the differential power for ith PV panel and the power from its previous

    DPP module.

    ,in , 1,( )dppi i i mpp s dppi outP V I I P −= − + (7)

    Applying (7) to calculate power through the nth mDPP module leads to

    , , 1,

    ,

    1 1

    ,

    1 1

    ( )

    ( )

    dppn in n n mpp s dppn out

    n n

    i i mppt s i

    i i

    n n

    i mppt s i

    i i

    P V I I P

    V I I V

    P I V

    = =

    = =

    = − +

    = −

    = −

     

       . (8)

    For the nth DPP module, an additional equation is described as

    ,ddpn out C onP V I=

    . (9)

    In steady state, the capacitor voltage is fixed as the voltage difference between the bus

    and total PV panels and has zero average current through it as in (3). The steady state DC output

    current of nth DPP module is the string current as below

    Fig. 6 Panel to Panel (P2P) Method for mDPP

  • 12

    on sI I=

    . (10)

    Considering (8), (9) and (10), the output power of the string can be calculated as

    ,

    1

    n

    bus s i mppt

    i

    V I P=

    =. (11)

    Therefore, (11) has the same form as (5), although different system connection is used.

    From a system point of view, this P2P connection inherits two benefits: 1) the output power of the

    string is the sum of the maximum power of each PV panel; 2) PV string voltage can be different

    from the voltage bus or other PV string, which enables the paralleling of more PV strings.

    Furthermore, the converter used in P2P method does not require isolation which will bring great

    benefit to the efficiency, material cost and reliability considerations.

  • 13

    Chapter 3

    Challenge and Control Strategy for PV

    Panel to PV Panel Transfer

    This chapter demonstrates the output of a PV panel in a string will depend on the duty

    ratio of its own differential power processing converter, as well as the duty ratio of the other PV

    panels’ differential power processing converters. This coupling effect means that each differential

    power converters will influence the performance of each other. This effect will influence the

    dynamic performance as well as steady state behavior seen by series connected DPP method. As

    for the solar application, steady state error degrades the output power of the PV panel

    significantly. This chapter describe a method to mitigate these effects for the P2P architecture of

    the mDPP method.

    3.1 Mathematical Model and Control Challenge

    A bidirectional buck-boost converter between 2 PV panels is used for mDPP

    converter in Fig. 6. The differential current between the PV panel, IPVi, and the string current, Is,

    leads to differential power. This differential power is processed from one PV panel to its former

    PV panel sequentially. The top converter, DPP1 in Fig. 6, processes the differential power to the

    virtual PV panel, the series capacitor. During the steady state operation, the differential power

    flows to the voltage bus instead of charging the series capacitor. The virtual PV panel

    compensates the voltage difference between the PV strings and the voltage bus. The detailed

    power flow of each PV panel and mDPP converter is illustrated in our preliminary conference

  • 14

    [38].

    The low side switch of the bidirectional buck-boost converter has a duty ratio of di

    while the high side switch is controlled by the complementary duty ratio of (1-di). The voltage

    between the 2 terminals of the converter is defined in the Fig. 6 as vPVi-1 and vPVi respectively. A

    total number of n PV panels are connected in series in each string. di(t) is slowly adjusted

    discretely by the microcontroller. On this slow time scale with the assumption of a fast inner-loop

    controller, the mathematical model for the buck-boost converter can be approximated as

    1

    ( ) 1 ( )( 1,2,3... )

    ( ) ( )

    PVi i

    PVi i

    v t d ti N

    v t d t−

    −=

    . (12)

    Voltage across the virtual PV panel is defined as vc. As there is a P2P converter

    between every 2 panels, including the virtual PV panel, the voltage across the ith PV panel can be

    calculated as

    1

    1 ( )( ) ( )

    ( )

    ij

    PVi c

    j j

    d tv t v t

    d t=

    −=

    .

    (13)

    The voltage bus is regulated by external circuit, i.e. battery backup system or grid tie

    inverter, which can be considered to have a relatively constant voltage of Vbus. The sum of each

    PV panel including the virtual PV panel equals to the bus voltage in

    1 1

    ( ) ( )

    1 ( )( ) (1 )

    ( )

    bus c PVi

    iNj

    c

    i j j

    V v t v t

    d tv t

    d t= =

    = +

    −= +

    . (14)

    Combining (13) and (14), the voltage across ith PV panel vPVi can be modified in

    1

    1 1

    1 ( )

    ( )( )

    1 ( )(1 )

    ( )

    ij

    j j

    PVi bus iNj

    i j j

    d t

    d tv t V

    d t

    d t

    =

    = =

    = −

    +

    . (15)

    Equation (4) shows that vPVi is a function of every duty ratio of the P2P converter in

    the same string. This is called the coupling effect, because the control action of each mDPP

    module (vPVi) is related not only with its control signal (di) but also control signals (dj, j≠i) of all

    other models.

    Applying the traditional MPPT algorithm to this PV system is difficult because of this

  • 15

    Fig. 7 Control Diagram of Power Outer Loop and Current Inner Loop

    coupling effect [20]. The variation of the PV panel voltage is usually a simple function of the

    perturbance of a small converter duty ratio for traditional MPPT. However, in this DPP structure,

    the duty ratio of each PV panel occurs in all the other PV panels in the same string. Advanced

    control algorithms [35, 36] have been proposed for series DPP structures that face the similar

    coupling effect. For example, it is possible to use a Lagrangian equations to decouple the control

    parameter. This approach relies on both local voltage sensing and communication between all the

    differential power converters in the same string. In particular, the communication requirement

    increases the system cost as well as may influence reliability [40-42]. Further the advanced

    controller may require an additional global MPPT converter that handle full power from the PV

    system. This may take away the advantage brought by DPP. The goal of this research is to

    introduce control approach that helps mitigate this coupling effect and is simple to implement a

    plug & play function.

    3.2 Dual Loop Controller Design

    To mitigate the coupling problems of previous section, a distributed MPPT control

    algorithm based on the P2P transfer structure is proposed. The proposed dual loop controller is

    designed to mitigate this coupling effect and track the individual maximum power point with only

    local information.

    Power outer loop and voltage inner loop for ith PV module are shown in the Fig. 7.

    The inner loop regulates the ith PV panel voltage, while the outer loop deals with its maximum

    power point tracking function. The MPPT block represents the controller of the outer loop. PI

    block is the controller for the inner loop and generates the duty ratio for its related P2P converter.

    The DPP block is the bidirectional buck-boost converter in the mDPP system and the PV block is

    each PV panel. As no communication is required, this control algorithm depends on only local

    voltage and current information, which enables the Plug & Play function.

    The inner loop controller senses the local PV panel voltage vPVi and generates duty

  • 16

    ratio di from the PI controller. Power Outer loop is implemented by a voltage based maximum

    power point tracking (MPPT) controller. Perturb and observe (P&O) algorithm is used to seek for

    a reference voltage for ith PV panel, which is defined as vPVi*. And this voltage signal serves as

    the voltage reference of the voltage inner loop.

    Differential power processing method usually processes a small proportion of power.

    Thus, high frequency (hundreds of kilohertz) DC-DC converter with smaller volume is preferred.

    The speed of proposed voltage inner loop is around 1/10 or lower of switching frequency. Power

    outer loop is run much slower than the inner voltage loop so that the outer loop will adjust the

    voltage reference after the inner loop reaches its steady state and compensate the steady state

    error. It is common for MPPT to have less than 1/100 of the inner voltage loop bandwidth.

    Since modularity is required for the differential power processing method, each

    controller includes plug and play function.

    3.3 Power Outer and Voltage Inner Loop

    The coupling effect can be further discussed through a mathematical model for a PV

    string consist of N PV panels. Equation (12)-(15) are nonlinear in duty ratio, so linearization is

    applied. Assumed duty ratio di(t) consists of 2 parts: upper-case time-invariant DC term of Di and

    a small signal variation term of ˆ ( )id t . Similar decomposition can be applied to the other

    variables:

    * * *

    ˆ( ) ( )

    ˆ( ) ( )

    ˆ( ) ( )

    i i i

    PVi PVi PVi

    PVi PVi PVi

    d t D d t

    v t V v t

    v t V v t

    = +

    = +

    = +. (16)

    And the duty ratio can also be formed in a vector as

    11 1

    2 2 2

    ˆ ( )( )

    ˆ( ) ( )ˆ( ) ( )

    ( ) ˆ ( )N N N

    d td t D

    d t D d tt t

    d t D d t

    = = + = +

    d D d

    . (17)

    For the ith PV panel, the voltage vPVi(t) is defined as

  • 17

    1 2

    1

    1 1

    ˆ( ) ( ) ( ( ), ( ),..., ( ))

    1 ( )

    ( )( ( ))

    1 ( )(1 )

    ( )

    PVi PVi PVi i N

    ij

    j j

    i bus iNj

    i j j

    v t V v t f d t d t d t

    d t

    d tf t V

    d t

    d t

    =

    = =

    = + =

    = = −

    +

    d

    . (18)

    Expanding the function fi in a Taylor series and assuming the differential term is small

    enough, we can ignore higher order terms to obtain

    1

    ˆˆ( ( )) ( ) ( ( ))( )

    Ni

    i j

    j j

    ff t f d t

    d t=

    + = +

    D

    D d D

    , (19)

    where the term ( )

    i

    j

    f

    d t

    D means the partial derivative of function fi with respect to

    dj(t) and is evaluated at its steady state value D.

    Therefore, the voltage of the PV panel can be approximated as

    1

    ˆˆ( ) ( ) ( ) ( ( ))( )

    Ni

    PVi PVi PVi j

    j j

    fv t V v t f d t

    d t=

    = + +

    D

    D , where ( )PViV f D in steady state.

    Therefore, we can obtain

    1

    ˆˆ ( ) ( )( )

    Ni

    PVi j

    j j

    fv t d t

    d t=

    =

    D .

    (20)

    Define the partial derivative of function fi to dj(t) as

    Fig. 8 Modular Differential Power Processing Diagram

  • 18

    ˆ ( )

    iij

    j

    fa

    d t

    =

    D . (21)

    which represents the influence of jth duty ratio on the ith PV panel. Let ˆ ( )sv

    represents the voltage

    of each PV panel in Laplace domain as

    1

    2

    111 12 1

    21 22 2 2

    1 2

    ˆ ( )

    ˆ ( )ˆˆ ( ) ( )

    ˆ ( )

    ˆ ( )

    ˆ ( )

    ˆ ( )

    PV

    PV

    PVN

    N

    N

    N N NNN

    v s

    v ss s

    v s

    d sa a a

    a a a d s

    a a a d s

    = =

    =

    v Ad

    . (22)

    For each ith PV panel, each j (j=1, 2, ..., N, j ≠ i) PV panel together with its mDPP

    converter has influence on ˆ ( )PViv s with the coupling effect term of aij. The transfer block

    diagram with voltage inner loop and coupling effect shows in Fig. 8. The upper loop represents

    the controller of ith PV panel while the lower loop of jth PV panel introduces the coupling effect to

    the ith PV panel. To simplify the diagram, only this coupling effect to the ith PV panel is shown

    here to represent N-1 of coupling loop in the real system. Fig. 8 is valid for all DPP converter

    connection used in Fig.6, regardless of the converter topology itself. Different converter topology,

    i.e. buck-boost or isolated converter, only alters the value of coupling effect term of aij.

    If a PI controller is assumed in the form of i

    p

    KK

    s+ . Then, the control to output

    transfer function shows as below

    *

    ( )ˆ ( )

    ( )ˆ ( )

    1 ( )PVi

    iii p

    PViii

    iii p

    Ka K

    v s sG sKv s

    a Ks

    +

    = =

    + +. (23)

    where ˆ ( )PViv s is the small signal variation term of the PV panel voltage and *ˆ ( )PVi

    v s is the small

    signal term of its related control referece.

    Applying (23) to the jth loop, we can get

  • 19

    *

    ( )ˆ ˆ( ) ( )

    1 ( )

    ip

    j PVji

    jj p

    KK

    sd s v sK

    a Ks

    +

    =

    + +. (24)

    Suppose we define the internal coupling voltage, the control effort of jth PV panel has

    influence on the ith PV panel is consider as the disturbance. Then the disturbance to output

    transfer function for ith PV panel is calculated as

    ˆ ( ) 1( )

    ˆ ( )1 ( )

    pvi

    inini

    ii p

    v sG s

    Kv sa K

    s

    = =

    + +. (25)

    So, the transfer function from jth PV panel reference to ith PV panel voltage can be

    expressed as

    * *

    ˆ ( )ˆ ˆ ˆ( ) ( ) ( )( )

    ˆˆ ˆ ˆ( ) ( ) ( )( )

    ( )1

    1 ( ) 1 ( )

    PVj

    jPVi PVi niij

    ni PVjj

    iij p

    i iii p jj p

    d sv s v s v sG s

    v s v s v sd s

    Ka K

    sK K

    a K a Ks s

    = =

    +

    =

    + + + +. (26)

    The response of each PV panel can be calculated as

    1

    2

    1

    2

    *

    11 12 1

    *

    21 22 2

    *1 2

    ˆ ( )

    ˆ ( )ˆ ˆ( ) ( )

    ˆ ( )

    ˆ ( )( ) ( ) ( )

    ˆ ( )( ) ( ) ( )

    ( ) ( ) ( ) ˆ ( )

    PV

    PV

    PVN

    PV

    PV

    PVN

    N

    N

    N N NN

    v s

    v ss s

    v s

    v sG s G s G s

    v sG s G s G s

    G s G s G s v s

    = =

    =

    *v Gv

    . (27)

    where G is the transfer function matrix of Gij(s). The diagonal term has the

    expression as (23) while otherwise Gij(s) can be calculated as (26), which also presents the

    coupling effect from a transfer function point of view.

    To keep the stability of the proposed system, the bounded-input bounded-output

    stability of each transfer function Gij(s) in G should be maintain. Considering (23) and (26), this

  • 20

    implies all poles of Gij(s) and Gii(s) should be located on the open left half plate. That is, the real

    part of the roots of following equation should always be less than zero.

    1 ( ) 0, [1,2.. ]iii pK

    a K i Ns

    + + = (28)

    By constraining the choice of PI controller gain, Kp and Ki, the stability of the all the

    proposed matrix can always be satisfied. It will be discussed in detail about the design boundary

    in the following section.

    As mentioned in previous section, the speed of the MPPT loop is usually at two

    orders of magnitude slower than the voltage inner loop, which is designed not to interact between

    these two loops by separating them from frequency point of view. In this case, the response of the

    adjustment from the MPPT loop can reach its steady state value before next adjustment. The

    reference of voltage inner loop is the output of the power outer loop, MPPT. Thus, it can be

    simplified as a step signal with a certain voltage amplitude as

    *

    ˆ ( )PVi

    PVi

    vv s

    s=

    . (29)

    For ith PV panel, the response can be divided into 2 parts. One comes from its own

    reference while the rest N-1 terms come from other PV panels as

    * *

    1,

    ˆ ˆ ˆ( ) ( ) ( ) ( ) ( )N

    PVi ii PVi ij PVj

    j j i

    v s G s v s G s v s=

    = + . (30)

    So, applying final value theorem (FVT) to (30), the time domain response can be

    obtained as

    0

    * *

    01,

    ˆ ˆlim ( ) lim ( )

    ˆ ˆlim ( ( ) ( ) )

    PVi PVit s

    NPVi PVi

    ii ijs

    j j i

    v t s v s

    v vs G s G s

    s s

    → →

    →=

    =

    = + . (31)

    Applied 2 limitation to (31) and get the asymptotic steady state value as,

  • 21

    0

    0

    ( )

    lim( ) 1

    1 ( )

    ( )1

    lim( ) 0

    1 ( ) 1 ( )

    iii p

    si

    ii p

    iij p

    si i

    ii p jj p

    Ka K

    sK

    a Ks

    Ka K

    sK K

    a K a Ks s

    +

    + + +

    + + + + . (32)

    we can yield

    * *

    1,

    ˆ ˆ ˆlim ( ) 1 0N

    PVi PVi PVjt

    j j i

    v t v v→

    =

    + . (33)

    And it can also be written in time domain matrix form as

    1

    2

    1

    2

    *

    *

    *

    ˆ ( )

    ˆ ( )ˆ ˆ( ) ( )

    ˆ ( )

    ˆ ( )1 0 0

    ˆ ( )0 1 0ˆ ˆ( ) ( )

    0 0 1 ˆ ( )

    PV

    PV

    PVN

    PV

    PV

    PVN

    v t

    v tt t

    v t

    v t

    v tt t

    v t

    = =

    = = =

    *

    * *

    v Gv

    Iv v

    . (34)

    PI controller only requires local voltage and current measurement and no information

    and prior knowledge of PV installation is required. From (34), the coupling effect does not show

    up after PI control loop reaches its steady state with zero steady state even. This analysis assumes

    the gains of the controller are selected so the real parts of the solution of (28) have Re(s)

  • 22

    actual operation condition are considered to be used and compensated by the mDPP

    converter. But the voltage difference is usually small compare with PV panel

    voltage

    2. The voltage difference between the PV string and voltage bus is smaller than one

    PV panel voltage. This research considers a certain margin, usually Vc≈0.25VPV is

    suggested, where Vpv is the voltage of one PV panel.

    Solving (28) for the root of s as

    01

    ii i

    ii p

    a Ks

    a K= −

    + (35)

    Considering (36), the stability requirement for (37) will be further transformed as

    max

    10 , [1,2.. ]p

    ii

    K i Na

    (36)

    Therefore, (36) demonstrates that as sufficiently small Kp can always be selected that all

    the pole specified in (35) are in open left half plane no matter if aii is positive or negative.

    With this appropriate design of the PI controller, the system stability could be

    maintained. Therefore, the steady state error of the voltage across PV panels can be brought to

    zero, and the differential power controller can force operation at designed reference.

  • 23

    Chapter 4

    Simulation Result

    This chapter includes the simulation result for the proposed method. The first section is

    a general simulation to verify the feasibility of the proposed method and how much efficiency

    mDPP can improve from a central MPPT converter. The second section simulates how the

    controller maintains MPPT function when new PV panel is added. This part also validates the

    plug-and-play function. The third section uses Monte Carlo method to simulate the mDPP method

    performance when given a distribution on the power difference between PV panel. The last

    section compares the overall system efficiency between different DPP method in a general PV

    application.

    4.1 Steady State Simulation Results

    To verify the mDPP concept, a PV blanket simulation is implemented in PSIM. This

    section focuses primarily on system level topology; thus the controller will be implemented by a

    fixed duty ratio with open loop controller. Ideal converters are implemented to simplify steady

    state simulation. Eliminating the influence of the controller design, this simulation verifies the

    efficiency improvement of the proposed method.

    As shown in Fig. 9, the PV blanket containing 6 PV panels is connected to a 20V bus.

    Panel #13 has 5V, 2A MPP and Panel #22 has 5.9V, 1.04A MPP due to the fabrication factor and

    shading effect. 6 buck-boost converters and 2 capacitors are used for mDPP P2P transfer purposes.

    The MPP information (Vmpp, Impp) of each PV panel is shown in Fig. 9. To simplify the

    simulation, a resistive load paralleled with a 20V voltage source is applied to represent the grid-

  • 24

    Fig. 9. Simulation schematic for mDPP

    TABLE I. SIMULATION RESULT OF STEADY STATE (WATTS)

    PV#11 PV#12 PV#13 PV#21 PV#22 PV#23 Total

    Ideal MPP (W) 13.23 12.3 10 12.59 6.13 12.81 67.06

    Simulated Power with mDPP (W) 13.23 12.3 10 12.58 6.13 12.81 67.05

    Simulated Power with cMPPT (W) 12.53 11.71 9.51 8.87 4.69 8.67 55.98

    tied inverter or bidirectional backup battery charger.

    For baseline comparison, a traditional centralized MPPT (cMPPT) converter is applied

    to the same PV blanket as shown in Fig. 9. 3 PV panels are connected in series as a PV string

    while 2 PV strings are connected in parallel as the input of the centralized MPPT converter

    without mDPP structure.

    The simulation results and comparison are shown in Table I. All the PV panels with

    mDPP structure work in each own MPP status thus a scalable system is built. The system is

    robust because it continues to work when partial shading occurs on Panel #22. However, the

    traditional centralized MPPT converter produced less power at a global MPP, that is, most of the

    PV panels do not work at each own MPP. As Table I shows for this example, there is a ~20%

    increase in power when mDPP is used compared to cMPPT.

    4.2 Simulation Result of PI Controller

    In this section, simulation of a PV blanket includes mDPP converter of each PV panel

    and the influence of the proposed distributed controller. These simulation results validate the

    concept of Plug & Play function and validates the MPPT algorithm. Ideal switching is used in the

    simulation, so the power loss and parasitic effect are not concerned in this section and will be

  • 25

    (a) Simulation Schematic of PV Blanket

    (b) P2P Transfer Converter for PV1

    (c) Distributed Controller for PV1

    Fig. 10 Simulation Schematic of a Solar System in PSIM

    further discussed in the experimental part.

    Fig. 10(a) shows the PV blanket with smaller PV panel in series and parallel

    connection. At time t=0, PV1-PV6 is installed in the PV blanked with 8V/2A rating. As shown in

    box#1, 3 PV panels are connected in series and 2 PV string are connected in parallel. Considering

    the aging effect [43, 44], a 10% of degradation with random value is given to each PV panel on

    their performance at MPP (Vmpp, Impp).

    Then, different PV panels, PV7-PV11 with 11V/3A rating are added to the existed

    installation with both series connection and parallel connection. Noted in Box #2, PV7 and PV8

    are added in series with previous PV string at time 2s. At time 4s, PV9, PV10 and PV11 build the

  • 26

    Fig. 11 Startup Waveform of Power of Each PV Panel

    0

    50

    100

    150

    200

    250

    300Pm Pout

    0 1 2 3 4 5 6

    Time (s)

    0

    2

    4

    6

    8

    10

    12

    V11 V12 V13 V14 V21 V22 V23 V24 V31 V32 V33

    3rd string and are connected in parallel in Box #3. Fig. 10(a) only shows the final connection of

    PV blanket for clearer schematic.

    Fig. 10(b) shows one typical mDPP converter connected between adjacent PV panel.

    The proposed close loop control algorithm for one mDPP module is shown in Fig. 10(c). Note

    that each mDPP module measures only its local PV panel voltage and current and no information

    is shared between modules. Inner voltage loop consists of proportional-integral (PI) controller

    while outer MPPT loop is implemented in P&O method respectively. Using calculation method

    stated in Chapter 3, the limit of the proportional gain Kp is calculated to make Kp sufficiently

    small. In fact, an additional 20% margin of Kp is assumed from the value (38) to assume stability,

    when the PI controller is implemented.

    Fig. 11(a) shows the ideal maximum output power, Pm, and actual output power of

    the entire PV blanket, Pout. The ideal maximum output power is calculated as the sum of the

    maximum power of all the PV panels in the circuit. So, the ideal output power suddenly increases

    at the time when new PV panels are added. The actual output power is measured at the output of

    whole PV system. After some transient time after new PV panel is added, the actual output power

    reaches its ideal maximum power, which verifies the effectiveness of the MPPT function.

    Fig. 11 (b) shows the voltage across each PV panel. Note here the voltage shows 0V

    for the new PV panel before it is added to the system. At time 2s, the PV7 is connected in series

    with PV1, PV2 and PV3, which influences the voltage of the other PV panels due to the coupling

    effect. But after duty ratio adjustments of each mDPP converter, each voltage settles to its MPP

  • 27

    Fig. 12. Comparison of Fraction of PV Power Processed of P2P and

    P2VP Method in Monte Carlo Simulation

    voltage. At time 4s, new PV string is added to the system and does not impact other existed PV

    units. Later on, PV9, PV10 and PV 11 reaches its own MPP state.

    The simulations also demonstrate important behavior demonstrates:

    1. When new PV panels are added in the same PV system, it normally causes some PV

    panels to operate away from MPP and generate less power unless proper compensation is

    provided.

    2. During transient period, every PV panel voltage is changing because they are tightly

    coupled in the same PV string through converters. After transient time, the changes due to adding

    PV panel is compensated by changing the duty cycle through the control scheme.

    This simulation verifies the coupling effect can be eliminated after several control duty

    ratio steps by the individual distributed controllers.

    4.3 Monte Carlo Simulations

    Monte Carlo approach is implemented to compare the power processed by the two

    mDPP method introduced above: P2P and P2VP. Previous section focuses mainly on the

    mismatch brought by the series capacitor while neglecting the mismatch from manufactories,

    aging or shading. Assuming power loss is proportional to the power processed by the converter,

  • 28

    TABLE II. SYSTEM EFFICIENCY STUDY OF DIFFERENT DPP STRUCTURES

    cMPPT dMPPT sDPP sDPPcc P2P(ours)

    Output Power (Pout - Watts)

    53.56 62.36 42.60 61.07 65.86

    System Efficiency (ηsys - %)

    79.86% 92.99% 63.51% 91.05% 97.9%

    Monte Carlo simulation introduces an intuitive point of view from system loss and efficiency. A

    more detailed loss model is used for simulation in next sub-section.

    One PV string with 3 PV panels having nominal 6V,2A MPP, 2V series capacitor and

    20V voltage bus is used for Monte Carlo simulation in [19]. A Gaussian Distribution of MPP

    voltages and currents (Vmpp, Impp) is used for each PV panel with a coefficient of variation of 0.1

    from [45]. The simulation was run 10,000 times and the fraction of total power processed in (11),

    , is shown as x-axis while probability as y-axis in Fig. 12. The overall distribution in the

    histogram indicates P2VP tends to transfer more power (nearly twice) than P2P. A wide range of

    conditions are simulated to evaluate the overall performance and make a more trustworthy

    comparison.

    4.4 Efficiency Study

    The efficiency and output power is compared in Table II among traditional central

    MPPT (cMPPT), distributed MPPT converter (dMPPT) [13], series DPP (sDPP) [23], series DPP

    with central converter (sDPPcc) [36] and proposed P2P method (P2P).

    Simulation result in Table II are based on the same PV panel configuration in Fig. 9

    with a 20V voltage bus, which is a more typical operation condition. On-resistance for MOSFET,

    ESR of capacitor and inductor are added in the simulation to create more precise module for the

    converter. For the synchronized buck-boost converter in the simulations the converter efficiency

    varied from ~93% at full load (~5W) to ~81% at light load (~1.5W). The output power, Pout, in

    Table II is the power delivered to the voltage bus. The system efficiency, ηsys, is the output power

    divided by the ideal maximum power, Pideal, which is the sum of each PV panel maximum power.

    6

    ,

    1

    out outsys

    ideali mpp

    i

    P P

    PP

    =

    = =

    (39)

    The traditional central MPPT method has lowest output power, since all the PV panels

    are treated as one panel. When any mismatch between the panels occurs, the output power is

    dramatically reduced. The sDPP with central controller [35, 36] and dMPPT method have similar

    performance in output power and system efficiency. Since the sDPP method is not compatible for

    paralleling to voltage bus, it has the worst performance among these methods. Only the proposed

  • 29

    mDPP method generates the most output power and obtains the highest system efficiency. Note

    that a highly mismatched PV blanket model is used for this simulation the system. The system

    efficiency is much lower than its normal performance.

    The previous study mainly focuses on a general configuration of PV panels and

    demonstrates that modules can be connected in parallel. This is beneficial when low bus voltage

    is desired. In the same way, the mDPP PV modules can be connected in series to satisfy any high

    voltage bus requirement. High power efficiency output is still maintained.

    In summary, these simulations validate the following characteristic of mDPP method:

    1. mDPP method has higher system efficiency and maintains Plug & Play function.

    2. Two different mDPP architecture (P2P and P2VP) have different performance in

    real production. But both of them still have higher system efficiency compared with

    traditional full power converter.

    3. mDPP has best efficiency performance compared with other DPP method, due to

    the saving of centralized full power processing converter.

  • 30

    Chapter 5

    Experiment Results

    This section is divided into 4 parts. First, modular DPP structure is introduced to

    have simplified wire connection compared with existing methods. Then, indoor experiments

    verify the MPPT function of proposed method. Furthermore, outdoor experiments validate the

    performance of system under real world shading effect. At last, plug & play experiments show the

    benefit of easy installation.

    5.1 mDPP hardware design

    PV panels normally have a junction box on their back side where usually the bypass

    diodes are installed. Therefore, it is possible to merge the mDPP board into the junction box and

    replace the bypass diode. The proposed Panel to Panel (P2P) for mDPP method is shown in Fig.

    13.

    Each mDPP converter has current and voltage measurements for its specific PV

    panel to track the panel’s individual maximum power point. The mDPP converter could also be

    applied to each PV subpanel to replace the bypass diode individually to gain even better

    performance. Since the differential power processor usually has low power and voltage rating, it

    is easy to design a converter with small volume to fit into the junction box for subpanel or panel

    level solution. Fig. 13 (a) shows the block diagram for the simplified connection while Fig. 13 (b)

    is the photo of the hardware design integrated in the PV junction box.

    Each PV panel with its mDPP board in their junction box is called one PV module.

    In Fig. 13 (a), each module will only have 3 terminals: 2 main power terminals, ‘+’ for positive

    terminal and ‘–’ for negative terminal, and one differential power terminal (DP). The positive

  • 31

    (a) Modular Differential Power Processing Diagram

    (b) Photo of mDPP converter emerged in junction box

    Fig. 13 mDPP Hardware Design

    terminal of ith PV panel is connected to the negative terminal of (i-1) thPV panel while the

    negative terminal is connected to the positive terminal of (i+1) thPV panel, which connects each

    PV panel in series as usual. The third terminal, DP terminal, is connected to the positive terminal

    of (i-1) thPV panel. Under this connection the proposed mDPP method is applied for the PV array.

    One benefit of the proposed mDPP structure is that it requires only 3 terminals

    connections. Previous mDPP methods [26, 36], 3 DPP terminals are required for each submodule

    converter while 2 communication ports are used for i2c communicaiton between modules, which

  • 32

    (a) Annotated Experiment Setup Photo

    (b) mDPP Experiment Schematic

    (c) dMPPT Experiment Schematic

    Fig. 14 Indoor Experiment

    TABLE III Key Component for Hardware Prototype

    Component Description Quantity

    Microcontroller STM32F334K8 1

    Power Module CSD97394Q4M 1

    Inductor 4.7 μH 1

    Capacitor (per converter) 10 μF 4

    Current Sensor INA250A2 1

    Series capacitor (per string) 100μF 1

    is in total of 7 terminal per PV panel. The proposed method in this paper only requires 3 terminal

    which is 57% reduction in the total wire requirement and simplify the PV panel installation.

    The key components and design detail of the hardware prototype are shown in the

    Table. III. PWM is running at 230 kHz to eliminate the volume of filter design. The inner voltage

  • 33

    TABLE IV Comparison Experiment for dMPPT and mDPP Method

    dMPPT mDPP

    V (V) I(A) P(W) V(V) I(A) P(W)

    PV11 6.25 2.02 12.63 6.34 1.96 12.43

    PV12 6.30 1.81 11.4 6.32 1.77 11.18

    PV13 6.44 1.84 11.85 6.40 1.88 12.03

    Bus 20.04 1.63 32.67 20.05 1.75 35.12

    sys 91.1% 98.4%

    loop is running in 1 kHz while the MPPT algorithm is around 10 Hz, which is much faster than

    the real commercial product. The frequency can be further reduced to eliminate the system cost

    and energy consumption of the micro controller.

    5.2 Indoor experiment

    In the indoor experiment, a programmable PV panel model is used as in [46]. By

    applying the same PV panel and program value, the MPPT function and accuracy of proposed

    control strategy can be validated by comparing the PV voltage and current in the dMPPT and

    mDPP experiment. Micro-grid system usually interfaces a regulated voltage bus and variable

    loads, which is modeled as DC electronic load in constant voltage mode. Fig. 14 (a) shows the

    annotated photography of the mDPP experiment setup. Three fully shaded PV panel together with

    3 controllable current sources emulates 3 different PV panels in [46]. The PV strings is connected

    to a 20V voltage bus. Fig. 14 (b) shows the schematic of the mDPP method. 3 distributed mDPP

    board is applied to each PV panel. As comparison, Fig. 14 (c) indicates the connection of

    traditional dMPPT method.

    In the steady state experiment, the voltage and the current of each PV panel is

    measured independently together with the string current, Is1, and the bus voltage, Vbus. mDPP

    method and distributed maximum power point tracker (dMPPT) method are applied to the same

    PV panel under the same condition alternatively, taking turns. The test result shows in Table. III.

    PV panel voltage and current of each PV panel is nearly the same in both methods.

    Small difference existed due to the tracking accuracy of the MPP. But the output power from the

    PV panel is within certain tracking accuracy. This verifies that both dMPPT and the proposed

    modular control strategy can track the MPP when it reaches its own steady state.

    The system efficiency is defined to represent the ability of the system to harvest

    much power as well as convert power with less loss. As the MPPT function have been verified,

  • 34

    (a) Annotated Experiment Setup Photo (b) Outdoor Experiment Schematic (NEED UPDATE)

    Fig. 15 Outdoor Experiment

    Fig. 16 Waveform of Outdoor Experiment

    the system efficiency can have a simplified representation as

    ,

    1

    PVi MPP

    out outsys

    PVi ideal MPP PVi P P

    s s

    N

    PVi PVi

    i

    P P

    P P

    V I

    V I

    =

    =

    = =

    =

    . (25)

    From the Table. IV, dMPPT method shows a 91.1% efficiency compared with

    proposed method running at 98.4% efficiency. This shows the advantage of the modular

    differential power processing method. DPP method only processes small amount of power

    through the converter.

    5.3 Outdoor experiment

    Shading is one of the common challenges faced by the PV system. Outdoor

    experiment was used to verify the proposed method under real irradiation. The photo of the

    experiment is shown in Fig. 15. 3 PV panels are connected in series according to the schematic in

  • 35

    Fig. 15 (b). Oscilloscope measures the voltage across each PV panel and the output current of the

    string. With a fixed bus voltage, the string current represents the output power of the whole system.

    The red notebook in the photo creates a partially shading on the PV2 as shown in the Fig. 15.

    The waveform of the field experiment is shown in Fig. 16. The shading object is

    inserted at time t2 and then removed at time t3. The system runs in standby mode before time t1

    and enters soft-start and MPPT function at time t1. After some adjustment and tracking, 3 PV

    panels reach certain steady state value before time t2, which can be verified as MPP in previous

    section. At time t2, a slight drop on the voltage of PV3 and a larger one on the string current can

    be observed due to the partial shading of PV2. Also, it reaches certain steady state value before

    time t3. At time t3, the shading object is removed. Each PV panel voltage and the string current

    start to recover and finally reach the same level before the time t2. As discussed in the previous

    section, the mDPP method can always operate the PV panel in certain steady state which is

    exactly the MPP of the PV panel. Since the shadow effect only happens for a short period of time,

    the irradiance and MPP of the PV panels could be considered as constant. This is also verified as

    all the waveforms keep the same before t2 and after t3.

    5.4 Plug-and-Play Experiment

    Following experiment explains the advantage of the plug and play function brought by

    the proposed control scheme. All 6 PV panels used in this experiment have similar MPP and are

    plugged-in at different time with different connection. Fig. 17 shows the connection of PV system

    when new PV panels in dash line box is plugged in. Note that only the connection of the PV panel

    connection is shown for simplification while there are corresponding mDPP converter for each

    panel connected in the manner described previously. Fig. 17 (a) shows the original connection,

    Fig. 17. Simplified Schematic of plug-and-play experiment

  • 36

    PV1 and PV2 are connected in series with a 20V voltage bus. At time t1, PV3 is plugged into the

    PV string in series with PV1 and PV2 as Fig. 17 (b). Furthermore, a new PV string with PV4,

    PV5 and PV6 is added in parallel with previous PV string at time t3 as in Fig. 17 (c).

    Fig.18 shows the waveform of experiment result. Noted in the Fig.17, Vcap1 and Vcap2

    represent the series capacitor voltage. Vpv3 is the voltage of the PV3, which is added at time t1.

    Is is the total current from the source, which indicates the total output power since a constant

    voltage load is applied to the system.

    Time t0 to t1: Only PV1 and PV2 is added in the system. Vcap1 is the voltage

    difference between 2 PV panel and the voltage bus, which is roughly 8V.

    Time t1 to t3: PV3 is added into the system and series capacitor voltage drops to ~1V at

    time t1. Vcap1 and Vpv3 keep moving to its steady state when the mDPP converter is looking for

    the MPP of PV3. At the same time, the Is is increasing, which also verifies the direction of

    moving towards the MPP. At time t2, the system reaches its steady state, three PV panels operate

    at its own MPP.

    Time after t3: PV string 2 is added into the system. Its corresponding mDPP converters

    start to operate PV panels towards its MPP. The Vcap2 reaches its steady state at time t4 while

    the output current reaches its maximum value.

    In this experiment, PV system with modular differential power processing has

    successfully demonstrated the features of operating at MPP when new panels are added.

    Modularity has been achieved without any modification on the existed system. This represents the

    first time that Plug & Play has been achieved with MPPT without a centralized converter. As

    demonstrated in the thesis, this leads to increased system power efficiency.

    Fig. 18. Waveform of plug-and-play experiment

  • 37

    Chapter 6

    Conclusion

    This research proposes a modular differential power processing (mDPP) concept to

    solve the modularity and scalability problem. A modular solar PV system is defined as PV system

    where PV modules can be removed, replaced or added to the existed installation in either series or

    parallel configuration. To meet this design criteria, mDPP system architecture is proposed to have

    MPPT function in each DPP block and avoid the requirement of central converter. Each DPP

    works as the controllable current source to compensate the current mismatch between the panels.

    The series capacitor which is used as a “virtual PV panel” can absorb any voltage difference

    between the PV string and the voltage bus. To implement this mDPP method, two different kinds

    of system architectures are proposed: 1) the PV panel to PV panel(P2P) method and 2) the PV

    panel to virtual PV panel (P2VP). Panel to Panel (P2P) transfer with non-isolated converter is a

    suitable solution to achieve the modular differential power processing when combined with a

    series capacitor in solar application.

    This concept yields the high levels of system efficiency and plug-and-play function. To

    solve the complexity of previous hardware and firmware design, the distributed controller enables

    the plug and play function and simplified the wire connection by avoiding communication

    between converters. Each mDPP converter module has the same hardware configuration and

    software implementation, which could be installed for every PV panel in the PV array without

    any modification as the previous dMPPT method. Benefits of the proposed approach also include:

    1. A central converter is no longer needed for MPPT, which is typical of other DPP

    methods. This eliminates the power losses associated with a full power processing converter.

    2. Communication and data sharing between PV modules is eliminated. Instead a

    distributed controller is proposed. This enables the modular plug & play capability and simplified

  • 38

    wire connections (57% reduction from previous method).

    The contribution of this theses is organized as follows: Architecture and topology of the

    modular differential power processing method is introduced in Chapter 2. The challenge and

    proposed control strategy are presented in Chapter 2. The detailed mathematic model and steady

    state analysis of the inner control loop is discussed in Chapter 2. Simulation is provided in

    Chapter 3. Hardware implementation and experimental verification is performed in Chapter 4

  • 39

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