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

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

Bibliography

[1] A. K. Abdelsalam, A. M. Massoud, S. Ahmed, and P. N. Enjeti, “High-Performance

Adaptive Perturb and Observe MPPT Technique for Photovoltaic-Based Microgrids,” IEEE

Transactions on Power Electronics, vol. 26, no. 4, pp. 1010-1021, 2011.

[2] F. Liu, S. Duan, F. Liu, B. Liu, and Y. Kang, “A Variable Step Size INC MPPT Method for

PV Systems,” IEEE Transactions on Industrial Electronics, vol. 55, no. 7, pp. 2622-2628,

2008.

[3] X. Weidong and W. G. Dunford, "A modified adaptive hill climbing MPPT method for

photovoltaic power systems," in 2004 IEEE 35th Annual Power Electronics Specialists

Conference (IEEE Cat. No.04CH37551), 2004, vol. 3, pp. 1957-1963 Vol.3.

[4] J. L. Agorreta, L. Reinaldos, R. Gonzalez, M. Borrega, J. Balda, and L. Marroyo, “Fuzzy

Switching Technique Applied to PWM Boost Converter Operating in Mixed Conduction

Mode for PV Systems,” IEEE Transactions on Industrial Electronics, vol. 56, no. 11, pp.

4363-4373, 2009.

[5] A. Varnham, A. M. Al-Ibrahim, G. S. Virk, and D. Azzi, “Soft-Computing Model-Based

Controllers for Increased Photovoltaic Plant Efficiencies,” IEEE Transactions on Energy

Conversion, vol. 22, no. 4, pp. 873-880, 2007.

[6] L. Chen, A. Amirahmadi, Q. Zhang, N. Kutkut, and I. Batarseh, “Design and Implementation

of Three-Phase Two-Stage Grid-Connected Module Integrated Converter,” IEEE

Transactions on Power Electronics, vol. 29, no. 8, pp. 3881-3892, 2014.

[7] Q. Zhang et al., “A Center Point Iteration MPPT Method With Application on the

Frequency-Modulated LLC Microinverter,” IEEE Transactions on Power Electronics, vol.

29, no. 3, pp. 1262-1274, 2014.

[8] B. J. Pierquet and D. J. Perreault, “A Single-Phase Photovoltaic Inverter Topology With a

Series-Connected Energy Buffer,” IEEE Transactions on Power Electronics, vol. 28, no. 10,

pp. 4603-4611, 2013.

[9] W. Cha, Y. Cho, J. Kwon, and B. Kwon, “Highly Efficient Microinverter With Soft-

Switching Step-Up Converter and Single-Switch-Modulation Inverter,” IEEE Transactions

on Industrial Electronics, vol. 62, no. 6, pp. 3516-3523, 2015.

40

[10] X. Zhang, M. Amirabadi, and B. Lehman, "A Long-Lifespan Single-Phase Single-Stage

Multi-Module Inverter for PV Application," in IECON 2018 - 44th Annual Conference of the

IEEE Industrial Electronics Society, 2018, pp. 6103-6109.

[11] L. F. L. Villa, T. Ho, J. Crebier, and B. Raison, “A Power Electronics Equalizer Application

for Partially Shaded Photovoltaic Modules,” IEEE Transactions on Industrial Electronics,

vol. 60, no. 3, pp. 1179-1190, 2013.

[12] Y. Li, Y. Zheng, S. Sheng, B. Scandrett, and B. Lehman, "Modular subpanel photovoltaic

converter system: Analysis and control," in 2016 IEEE Applied Power Electronics

Conference and Exposition (APEC), 2016, pp. 417-423.

[13] Y. Zheng, Y. Li, S. Sheng, B. Scandrett, and B. Lehman, "Distributed control for modular

plug-and-play subpanel photovoltaic converter system," in 2017 IEEE Applied Power

Electronics Conference and Exposition (APEC), 2017, pp. 1267-1271.

[14] M. Das and V. Agarwal, “Design and Analysis of a High-Efficiency DC–DC Converter With

Soft Switching Capability for Renewable Energy Applications Requiring High Voltage Gain,”

IEEE Transactions on Industrial Electronics, vol. 63, no. 5, pp. 2936-2944, 2016.

[15] G. Zhang, B. Zhang, Z. Li, D. Qiu, L. Yang, and W. A. Halang, “A 3-Z-Network Boost

Converter,” IEEE Transactions on Industrial Electronics, vol. 62, no. 1, pp. 278-288, 2015.

[16] G. Wu, X. Ruan, and Z. Ye, “Nonisolated High Step-Up DC–DC Converters Adopting

Switched-Capacitor Cell,” IEEE Transactions on Industrial Electronics, vol. 62, no. 1, pp.

383-393, 2015.

[17] T. Shimizu, M. Hirakata, T. Kamezawa, and H. Watanabe, “Generation control circuit for

photovoltaic modules,” IEEE Transactions on Power Electronics, vol. 16, no. 3, pp. 293-300,

2001.

[18] P. S. Shenoy and P. T. Krein, “Differential Power Processing for DC Systems,” IEEE

Transactions on Power Electronics, vol. 28, no. 4, pp. 1795-1806, 2013.

[19] P. S. Shenoy, K. A. Kim, B. B. Johnson, and P. T. Krein, “Differential Power Processing for

Increased Energy Production and Reliability of Photovoltaic Systems,” IEEE Transactions

on Power Electronics, vol. 28, no. 6, pp. 2968-2979, 2013.

[20] C. Liu, Y. Zheng, D. Li, and B. Lehman, "Distributed MPPT for Modular Differential Power

Processing in Scalable Photovoltaic System," in 2018 IEEE Applied Power Electronics

Conference and Exposition (APEC), 2018.

[21] E. Candan, D. Heeger, P. S. Shenoy, and R. C. N. Pilawa-Podgurski, "A series-stacked power

delivery architecture with hot-swapping for high-efficiency data centers," in 2015 IEEE

Energy Conversion Congress and Exposition (ECCE), 2015, pp. 571-578.

[22] E. Candan, D. Heeger, P. S. Shenoy, and R. C. N. Pilawa-Podgurski, “Hot-Swapping

Analysis and Implementation of Series-Stacked Server Power Delivery Architectures,” IEEE

Transactions on Power Electronics, vol. 32, no. 10, pp. 8071-8088, 2017.

41

[23] E. Candan, P. S. Shenoy, and R. C. N. Pilawa-Podgurski, “A Series-Stacked Power Delivery

Architecture With Isolated Differential Power Conversion for Data Centers,” IEEE

Transactions on Power Electronics, vol. 31, no. 5, pp. 3690-3703, 2016.

[24] Y. Levron, D. R. Clement, B. Choi, C. Olalla, and D. Maksimovic, “Control of Submodule

Integrated Converters in the Isolated-Port Differential Power-Processing Photovoltaic

Architecture,” IEEE Journal of Emerging and Selected Topics in Power Electronics, vol. 2,

no. 4, pp. 821-832, 2014.

[25] S. Qin, S. T. Cady, A. D. Domínguez-García, and R. C. N. Pilawa-Podgurski, "A distributed

approach to MPPT for PV sub-module differential power processing," in 2013 IEEE Energy

Conversion Congress and Exposition, 2013, pp. 2778-2785.

[26] S. Qin and R. C. N. Pilawa-Podgurski, "Sub-module differential power processing for

photovoltaic applications," in 2013 Twenty-Eighth Annual IEEE Applied Power Electronics

Conference and Exposition (APEC), 2013, pp. 101-108.

[27] K. Sun, Z. Qiu, H. Wu, and Y. Xing, “Evaluation on High-Efficiency Thermoelectric

Generation Systems Based on Differential Power Processing,” IEEE Transactions on

Industrial Electronics, vol. 65, no. 1, pp. 699-708, 2018.

[28] F. Wang, T. Zhu, F. Zhuo, and H. Yi, “An Improved Submodule Differential Power

Processing-Based PV System With Flexible Multi-MPPT Control,” IEEE Journal of

Emerging and Selected Topics in Power Electronics, vol. 6, no. 1, pp. 94-102, 2018.

[29] N. B. Kumar and M. K. N. Mounika, "Implementation of Differential Power Processing to

Optimize the Solar Power Generation," in 2018 International Conference on Current Trends

towards Converging Technologies (ICCTCT), 2018, pp. 1-7.

[30] Y. T. Jeon, H. Lee, K. A. Kim, and J. H. Park, “Least Power Point Tracking Method for

Photovoltaic Differential Power Processing Systems,” IEEE Transactions on Power

Electronics, vol. 32, no. 3, pp. 1941-1951, 2017.

[31] Y. Jeon and J. Park, “Unit-Minimum Least Power Point Tracking for the Optimization of

Photovoltaic Differential Power Processing Systems,” IEEE Transactions on Power

Electronics, vol. 34, no. 1, pp. 311-324, 2019.

[32] G. Chu and H. Wen, "Design and Optimization of PV-Isolated-Port Photovoltaic Differential

Power Porcessing System," in 2018 IEEE International Conference on Power Electronics,

Drives and Energy Systems (PEDES), 2018, pp. 1-6.

[33] M. S. Zaman et al., “A Cell-Level Differential Power Processing IC for Concentrating-PV

Systems With Bidirectional Hysteretic Current-Mode Control and Closed-Loop Frequency

Regulation,” IEEE Transactions on Power Electronics, vol. 30, no. 12, pp. 7230-7244, 2015.

[34] C. Olalla, C. Deline, D. Clement, Y. Levron, M. Rodriguez, and D. Maksimovic,

“Performance of Power-Limited Differential Power Processing Architectures in Mismatched

PV Systems,” IEEE Transactions on Power Electronics, vol. 30, no. 2, pp. 618-631, 2015.

[35] S. Qin, C. B. Barth, and R. C. N. Pilawa-Podgurski, “Enhancing Microinverter Energy

Capture With Submodule Differential Power Processing,” IEEE Transactions on Power

42

Electronics, vol. 31, no. 5, pp. 3575-3585, 2016.

[36] S. Qin, S. T. Cady, A. D. Domínguez-García, and R. C. N. Pilawa-Podgurski, “A Distributed

Approach to Maximum Power Point Tracking for Photovoltaic Submodule Differential

Power Processing,” IEEE Transactions on Power Electronics, vol. 30, no. 4, pp. 2024-2040,

2015.

[37] S. MallangadaBose, M. O. Badawy, and Y. Sozer, "A Novel Differential Power Processing

Architecture for a Partially Shaded PV String Using Distributed Control," in 2018 IEEE

Energy Conversion Congress and Exposition (ECCE), 2018, pp. 6220-6227.

[38] C. Liu, D. Li, Y. Zheng, and B. Lehman, "Modular differential power processing (mDPP),"

in 2017 IEEE 18th Workshop on Control and Modeling for Power Electronics (COMPEL),

2017, pp. 1-7.

[39] K. A. Kim, P. S. Shenoy, and P. T. Krein, “Converter Rating Analysis for Photovoltaic

Differential Power Processing Systems,” IEEE Transactions on Power Electronics, vol. 30,

no. 4, pp. 1987-1997, 2015.

[40] Y. Gu, X. Xiang, W. Li, and X. He, “Mode-Adaptive Decentralized Control for Renewable

DC Microgrid With Enhanced Reliability and Flexibility,” IEEE Transactions on Power

Electronics, vol. 29, no. 9, pp. 5072-5080, 2014.

[41] P. Prabhakaran, Y. Goyal, and V. Agarwal, “Novel Nonlinear Droop Control Techniques to

Overcome the Load Sharing and Voltage Regulation Issues in DC Microgrid,” IEEE

Transactions on Power Electronics, vol. PP, no. 99, pp. 1-1, 2017.

[42] S. Peyghami, P. Davari, H. Mokhtari, P. C. Loh, and F. Blaabjerg, “Synchronverter-Enabled

DC Power Sharing Approach for LVDC Microgrids,” IEEE Transactions on Power

Electronics, vol. 32, no. 10, pp. 8089-8099, 2017.

[43] L. Ciani, M. Catelani, E. A. Carnevale, L. Donati, and M. Bruzzi, “Evaluation of the Aging

Process of Dye-Sensitized Solar Cells Under Different Stress Conditions,” IEEE

Transactions on Instrumentation and Measurement, vol. 64, no. 5, pp. 1179-1187, 2015.

[44] Y. Hu, J. Zhang, J. Wu, W. Cao, G. Y. Tian, and J. L. Kirtley, “Efficiency Improvement of

Nonuniformly Aged PV Arrays,” IEEE Transactions on Power Electronics, vol. 32, no. 2,

pp. 1124-1137, 2017.

[45] K. A. Kim, P. S. Shenoy, and P. T. Krein, "Photovoltaic differential power converter trade-

offs as a consequence of panel variation," in 2012 IEEE 13th Workshop on Control and

Modeling for Power Electronics (COMPEL), 2012, pp. 1-7.

[46] S. Qin, K. A. Kim, and R. C. N. Pilawa-Podgurski, "Laboratory emulation of a photovoltaic

module for controllable insolation and realistic dynamic performance," in 2013 IEEE Power

and Energy Conference at Illinois (PECI), 2013, pp. 23-29.

Thesis_Chang_MDPP_in_SolarSystem V4Thesis_Chang_MDPP_in_SolarSystem V4.1