Novel Control of a Modular Multilevel Converter for

103 http://www.transeem.org

Novel Control of a Modular Multilevel Converter forPhotovoltaic Applications

1. INTRODUCTION

Recently, photovoltaic (PV) systems as an important aspect of distributed generation (DG) have played a vital role in the power generation industry. Studies demonstrate that the PV will be an essential component of future power plants. In this respect, the development of new structures with low cost, high reliability, and efficient control processes need to be considered. As a result, new transformerless converters, named modular multilevel converters (MMCs), have been introduced in contrast to traditional transformer isolated converters in grid tied mode. In the structure of MMCs, several modules are connected in series in each leg and an appropriate output ac signal can be generated by switching the modules. The control of voltage across each module and output ac

current is the main challenge outlined in the literature [1,2].A major challenge in the MMC structure used in compensation

and conversion applications is balancing of the upper and lower arms. Many studies have addressed this problem. Accordingly, several control methods have been proposed. In [3], a multilevel cascaded H-bridge converter is used to directly integrate the PV arrays into the grid. The proposed controller is based on MPPT algorithms for each H-bridge. In this way, a two stage controller was implemented, where the first stage is based on a control loop in order to regulate the sum of the power cell dc voltages to its desired value and in the second stage, the desired dc voltage of each PV array was determined to obtain the maximum power from the sun irradiation.

A sinusoidal based pulse width modulation (PWM) strategy in [4] was introduced to control a multilevel transformerless single-phase topology, based on the H-bridge with an active clamping. Also, several studies have focused on new circuit topologies of MMCs in photovoltaic grid applications [5-7]. A switching loss and THD analysis of PV systems based MMC was carried out in [8], where a DC-DC converter with maximum power point tracking (MPPT) and MMC with filter were used in a PV system. The gate pulse of single

TRANSACTIONS ON ELECTRICAL AND ELECTRONIC MATERIALS

Vol. 18, No. 2, pp. 103-110, April 25, 2017

pISSN: 1229-7607 eISSN: 2092-7592

Milad Samady ShadluDepartment of Electrical Engineering, Young Researchers and Elite Club, Bojnourd Branch, Islamic Azad University,Bojnourd, Iran

Received August 5, 2016; Revised September 9, 2016; Accepted September 12, 2016

The number of applications of solar photovoltaic (PV) systems in power generation grids has increased in the last decade because of their ability to generate efficient and reliable power in a variety of low installation in domestic applications. Various PV converter topologies have therefore emerged, among which the modular multilevel converter (MMC) is very attractive due to its modularity and transformerless features. The modeling and control of the MMC has become an interesting issue due to the extremely large expansion of PV power plants at the residential scale and due to the power quality requirement of this application. This paper proposes a novel control method of MMC which is used to directly integrate the photovoltaic arrays with the power grid. Traditionally, a closed loop control has been used, although circulating current control and capacitors voltage balancing in each individual leg have remained unsolved problem. In this paper, the integration of model predictive control (MPC) and traditional closed loop control is proposed to control the MMC structure in a PV grid tied mode. Simulation results demonstrate the efficiency and effectiveness of the proposed control model.

Keywords: Solar photovoltaic, Modular multilevel converter, Closed loop control, Model predictive control

DOI: http://dx.doi.org/10.4313/TEEM.2017.18.2.103

OAK Central: http://central.oak.go.kr

Author to whom all correspondence should be addressed:E-mail: [email protected]

Copyright ©2017 KIEEME. All rights reserved.This is an open-access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted noncommercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

104 Trans. Electr. Electron. Mater. 18(2) 103 (2017): M. S. Shadlu

phase MMC is generated based on PWM.An integrated control system was applied in [9] to control the

combined system of static Var generator (SVG) and PV power generation based on MMC. Its controller mainly includes three parts: a control algorithm for reactive power compensation, the capacitor voltage balancing control of the PV-MMC, and control scheme of carrier phase shifted sinusoidal pulse width modulation (CPS-SPWM). In [10] an MMC structure is used to interface a solar PV array and a power grid, of which the controller is composed of two control loops. An inner current control loop is designed to control grid currents. In its outer control loop, the reference DC link voltage is generated by the MPPT algorithm and its difference with real DC link voltage is eliminated using a Proportional-Integral (PI) controller. A two-level control scheme was proposed in [11], in which the first level is designed to control the input, output, and circulating current components and the second level controls the individual capacitor voltage in each arm.

A lead controller followed by an integrator was used in [12] in order to manage the DC-link voltage in a single-stage gridconnected

PV power plant based MMC. Also, the incremental conductance (IC) algorithm, which adjusts the command voltage to track the maximum power, is proposed. Finally, a current controller is developed in the D-Q reference frame which consists of PI controllers and feed-forward terms. In [13], a new topology based on MMC composed of a full-bridge converter (FBC) connected to multiple high frequency link (HFL) modules via high frequency transformers was proposed. In the presented configuration, the module voltage can be controlled by changing the FBC duty cycle, while each individual arm and positive and negative arms were modulated based on phase shifted PWM and level shifted PWM, respectively.

On the other hand, in many studies, another topology based on cascaded multilevel inverters (CMI) has been widely used in PV systems. Some of these have focused on analyzing the CMI structure in terms of harmonic contents and voltage stress across the switches [14-16], and others have introduced new advanced controllers to compensate reactive power for grid tied PV systems [17-20], to compensate the unequal voltages of separate PV modules [21,22], for the voltage control of the floating dc capacitors [23,24] and to track the maximum power point (MPP) in PV based CMI systems [25-27].

The remainder of the paper is organized as follows. In Section II we describe a PV based MMC structure and its mathematical representation in order to provide a comprehensive control model based on model predictive control (MPC). Output currents and the circulating currents control algorithm are presented in Section III. The proposed algorithm is verified based on simulation in Section IV and a conclusion is finally presented in Section V.

2. DESCRIPTION OF PV SYSTEM BASED ONMMC STRUCTURE

Figure 1 illustrates a simple PV system connected to a 3 phase load. The system consists of several PV arrays, of which the output DC voltage passes through a DC-DC converter and is applied to an DC-AC converter based on the MMC structure. Clearly, by using this structure, unlike the proposed power converter structure in [28], a transformer is not required to connect the converter to the load or main grid. This advantage enables simplification of the entire topology of the PV system and some risks can be avoided such as the saturation and nonlinear operation of the transformer.

It is clear that in each individual leg of MMC, two current components flow across each submodule connected in series in each arm: the AC current and the circulating current. The circulating current component is induced by the inaccuracy switching of the

upper and lower modules and accordingly must be removed to provide a moderately sinusoidal AC current component in the output. Also, by eliminating this, the capacitors voltage balancing in the upper and lower arms is performed automatically. Traditionally, only a closed loop control has been designed, of which the principle was based on removing the energy difference between the upper and lower stack modules. In this study, a closed loop control model based on model predictive control (MPC) is proposed. In the following section, a mathematical model of MMC is presented.

2.1 Single phase MMC structure

In this section, a simple single phase MMC structure is considered, as shown in Fig. 2. In this structure, a half-bridge rectifier paralleled with a capacitor forms a basic module which consists of two terminals. In modular multilevel converters, no external connection is required to transfer the energy to the module, while in order to control the voltage of each module, only a specified switching pattern is needed. Figure 2(a) shows the basic structure of a half-bridge module and Fig. 2(b) shows a singlephase circuit model of an MMC.

We can now extract the MMC mathematical model using this structure.

Trans. Electr. Electron. Mater. 17(6) 1 (2016): M. S. Shadlu3

a PV system. The gate pulse of single phase MMC is generated based on PWM.

An integrated control system was applied in [9] to control the combined system of static Var generator (SVG) and PV power generation based on MMC. Its controller mainly includes three parts: a control algorithm for reactive power compensation, the capacitor voltage balancing control of the PV-MMC, and control scheme of carrier phase shifted sinusoidal pulse width modula-tion (CPS-SPWM). In [10] an MMC structure is used to interface a solar PV array and a power grid, of which the controller is composed of two control loops. An inner current control loop is designed to control grid currents. In its outer control loop, the reference DC link voltage is generated by the MPPT algorithm and its difference with real DC link voltage is eliminated using a Proportional-Integral (PI) controller. A two-level control scheme was proposed in [11], in which the first level is designed to con-trol the input, output, and circulating current components and the second level controls the individual capacitor voltage in each arm.

A lead controller followed by an integrator was used in [12] in order to manage the DC-link voltage in a single-stage grid-connected PV power plant based MMC. Also, the incremental conductance (IC) algorithm, which adjusts the command volt-age to track the maximum power, is proposed. Finally, a cur-rent controller is developed in the D-Q reference frame which consists of PI controllers and feed-forward terms. In [13], a new topology based on MMC composed of a full-bridge converter (FBC) connected to multiple high frequency link (HFL) modules via high frequency transformers was proposed. In the presented configuration, the module voltage can be controlled by changing the FBC duty cycle, while each individual arm and positive and negative arms were modulated based on phase shifted PWM and level shifted PWM, respectively.

On the other hand, in many studies, another topology based on cascaded multilevel inverters (CMI) has been widely used in PV systems. Some of these have focused on analyzing the CMI structure in terms of harmonic contents and voltage stress across the switches [14-16], and others have introduced new advanced controllers to compensate reactive power for grid tied PV sys-tems [17-20], to compensate the unequal voltages of separate PV modules [21,22], for the voltage control of the floating dc capaci-tors [23,24] and to track the maximum power point (MPP) in PV based CMI systems [25-27].

The remainder of the paper is organized as follows. In Section II we describe a PV based MMC structure and its mathemati-cal representation in order to provide a comprehensive control model based on model predictive control (MPC). Output cur-rents and the circulating currents control algorithm are pre-sented in Section III. The proposed algorithm is verified based on simulation in Section IV and a conclusion is finally presented in Section V.

2. DESCRIPTION OF PV SYSTEM BASED ON MMC STRUCTURE Figure 1 illustrates a simple PV system connected to a 3 phase

load. The system consists of several PV arrays, of which the out-put DC voltage passes through a DC-DC converter and is applied to an DC-AC converter based on the MMC structure. Clearly, by using this structure, unlike the proposed power converter structure in [28], a transformer is not required to connect the converter to the load or main grid. This advantage enables sim-plification of the entire topology of the PV system and some risks can be avoided such as the saturation and nonlinear operation of the transformer.

It is clear that in each individual leg of MMC, two current com-ponents flow across each submodule connected in series in each arm: the AC current and the circulating current. The circulating current component is induced by the inaccuracy switching of the upper and lower modules and accordingly must be removed to provide a moderately sinusoidal AC current component in the output. Also, by eliminating this, the capacitors voltage balanc-ing in the upper and lower arms is performed automatically. Tra-ditionally, only a closed loop control has been designed, of which the principle was based on removing the energy difference be-tween the upper and lower stack modules. In this study, a closed loop control model based on model predictive control (MPC) is proposed. In the following section, a mathematical model of MMC is presented.


In this section, a simple single phase MMC structure is consid-ered, as shown in Fig. 2. In this structure, a half-bridge rectifier paralleled with a capacitor forms a basic module which consists of two terminals. In modular multilevel converters, no external connection is required to transfer the energy to the module, while in order to control the voltage of each module, only a specified switching pattern is needed. Fig. 2(a) shows the basic structure of a half-bridge module and Fig. 2(b) shows a single-phase circuit model of an MMC.


Fig. 1. PV system based on MMC structure.

Fig. 2. (a) Basic structure of a half-bridge module (b) single-phase cir-cuit model of an MMC.

110V Photovoltaic Arrays


R

L

Loa

d

Loa

d

Loa

d

PM PM PM

PM PM PM

R

L

R

L

R

L

R

L

R

L

iLoad (3Phases)

AC Current

Circulating Current

V P

V N

=

=

+

+

-

-

DC-DC

MMC

C

ip3

in3in2

ip2

in1

ip1

icir 2 icir 3

icir 1

Vpcc1Vpcc2 Vpcc3

UP1

UN1

+

-

+

-

UP2+

-

UN2+

-UN3

+

-

UP3

+

-

−+

−+

2UD

ui

li

Load+−

LΙ

ΙΙ

ΣCuU

−

+

N

1

−

+

N ′

1′

1S

2S −+

CVC

cu−

+i

Ci

)(a )(b

2UD

R

R

L

ΣClU

Loadu

Vi

idiff

(a)

−+

−+

2UD

ui

li

Load+−

LΙ

ΙΙ

ΣCuU

−

+

N

1

−

+

N ′

1′

1S

2S −+

CVC

cu−

+i

Ci

)(a )(b

2UD

R

R

L

ΣClU

Loadu

Vi

idiff

(b)

















R

L

Loa

d

Loa

d

Loa

d

PM PM PM

PM PM PM

R

L

R

L

R

L

R

L

R

L

iLoad (3Phases)

AC Current

Circulating Current

V P

V N

=

=

+

+

-

-

DC-DC

MMC

C

ip3

in3in2

ip2

in1

ip1

icir 2 icir 3

icir 1

Vpcc1Vpcc2 Vpcc3

UP1

UN1

+

-

+

-

UP2+

-

UN2+

-UN3

+

-

UP3

+

-

−+

−+

2UD

ui

li

Load+−

LΙ

ΙΙ

ΣCuU

−

+

N

1

−

+

N ′

1′

1S

2S −+

CVC

cu−

+i

Ci

)(a )(b

2UD

R

R

L

ΣClU

Loadu

Vi

idiff

(a)

−+

−+

2UD

ui

li

Load+−

LΙ

ΙΙ

ΣCuU

−

+

N

1

−

+

N ′

1′

1S

2S −+

CVC

cu−

+i

Ci

)(a )(b

2UD

R

R

L

ΣClU

Loadu

Vi

idiff

(b)

















R

L

Loa

d

Loa

d

Loa

d

PM PM PM

PM PM PM

R

L

R

L

R

L

R

L

R

L

iLoad (3Phases)

AC Current

Circulating Current

V P

V N

=

=

+

+

-

-

DC-DC

MMC

C

ip3

in3in2

ip2

in1

ip1

icir 2 icir 3

icir 1

Vpcc1Vpcc2 Vpcc3

UP1

UN1

+

-

+

-

UP2+

-

UN2+

-UN3

+

-

UP3

+

-

−+

−+

2UD

ui

li

Load+−

LΙ

ΙΙ

ΣCuU

−

+

N

1

−

+

N ′

1′

1S

2S −+

CVC

cu−

+i

Ci

)(a )(b

2UD

R

R

L

ΣClU

Loadu

Vi

idiff

(a)

−+

−+

2UD

ui

li

Load+−

LΙ

ΙΙ

ΣCuU

−

+

N

1

−

+

N ′

1′

1S

2S −+

CVC

cu−

+i

Ci

)(a )(b

2UD

R

R

L

ΣClU

Loadu

Vi

idiff

(b)

















R

L

Loa

d

Loa

d

Loa

d

PM PM PM

PM PM PM

R

L

R

L

R

L

R

L

R

L

iLoad (3Phases)

AC Current

Circulating Current

V P

V N

=

=

+

+

-

-

DC-DC

MMC

C

ip3

in3in2

ip2

in1

ip1

icir 2 icir 3

icir 1

Vpcc1Vpcc2 Vpcc3

UP1

UN1

+

-

+

-

UP2+

-

UN2+

-UN3

+

-

UP3

+

-

−+

−+

2UD

ui

li

Load+−

LΙ

ΙΙ

ΣCuU

−

+

N

1

−

+

N ′

1′

1S

2S −+

CVC

cu−

+i

Ci

)(a )(b

2UD

R

R

L

ΣClU

Loadu

Vi

idiff

(a)

−+

−+

2UD

ui

li

Load+−

LΙ

ΙΙ

ΣCuU

−

+

N

1

−

+

N ′

1′

1S

2S −+

CVC

cu−

+i

Ci

)(a )(b

2UD

R

R

L

ΣClU

Loadu

Vi

idiff

(b)

105Trans. Electr. Electron. Mater. 18(2) 103 (2017): M. S. Shadlu

2.2 Mathematical model based on energy equations

The total energy stored in the capacitors of the upper and lower arms of each phase is represented by WCu

Σ and WClΣ, respectively.

According to these two definitions and Fig. 2(b), a static relationship occurs between the total energy and the capacitors voltage of all modules in each arm. For example, if we assume that the energy is equally divided between the modules, then the voltages of the upper and lower arms, UCu

Σ and UClΣ, respectively, is

calculated as follows [29]:


2.2 Mathematical model based on energy equa-tions


∑ and WCl∑, respectively.

According to these two definitions and Fig. 2(b), a static re-lationship occurs between the total energy and the capacitors voltage of all modules in each arm. For example, if we assume that the energy is equally divided between the modules, then the voltages of the upper and lower arms, UCu

∑ and UCl∑, respectively,

is calculated as follows [29]:

(1)

where C is the capacitor in each individual module and N rep-resents the number of modules in each arm. Also, we have:

(2)

If we define the voltage of the affected capacitors in each arm as uCu and uCl, and define the total voltage of all capacitors as UCu

∑ and UCl∑, respectively, in this case the modulation index for

the upper and lower arms will be as follows:

(3)

For further investigation, we divide the current of each arm into two parts. One part is the ac current which is naturally divid-ed into two equal parts and flows through the upper and lower arms. The difference between these two currents is considered as a differential current, idiff that flows through the DC source and series arms which is called a circulating current. This current is defined as follows:

(4)

where iV is the output current. The following equations can be given according to Fig. 2(b) and equation (4):

(5)

(6)

According to equations (4), (5), and (6) and simplification, we have:

(7)

Also, by inserting (7) into (5) we obtain:

(8)

According to the above equations, we can conclude that:

* The load ac voltage (uLoad) only depends on ac current and the difference between the upper and lower affected capaci-tors voltages (UCu

∑ - UCl∑).

* The difference in voltage between the two arms acts as an internal ac voltage in the converter, while inductor L and re-sistor R form an internal passive impedance in the ac current path generated by the ac power supply.

* Differential current idiff only depends on the DC link voltage and the sum of the affected voltages, UCu

∑ + UCl∑.

* Differential current idiff can be calculated independent of the parameters of the ac side. In other words, it is only the result of a differential voltage component which is created because of the difference between the upper and lower affected ca-pacitors voltages. This differential voltage is called udiff and the affected voltage in each arm is equal to:

(9)

In this equation, eV is the optimal internal voltage in the ac side and udiff is the voltage that produces idiff. Therefore, we have:

(10)

3. PROPOSED CONTROL ALGORITHM In this paper, the output currents control of the PV system

based on MMC is performed using a novel control model based on the average model and model predictive control. The average model is used to derive the mathematical model based on circuit equations. In addition, model predictive control is used to design the controller based on the mathematical model.

3.1 Average model In this model, the switching signals for MMC modules are

considered as control parameters, and the voltage and current of each module will be written as a function of these switching signals [30]. The equivalent circuit of a half-bridge module based on the average model is shown in Fig. 3.

22

22

2 2

2 2

2

2

CuCu Cu

ClCl Cl

Cu Cu

Cl Cl

UC CW N UN N

UC CW N UN N

NU WCNU W

C

ΣΣ Σ

ΣΣ Σ

Σ Σ

Σ Σ

= = = =

=

=

.

.

Cuu Cu

Cll Cl

dW i udt

dW i udt

Σ

Σ

=

= −

Cuu

Cu

Cll

Cl

unUunU

Σ

Σ

=

=

2

2

2

Vu diff

Vl diff

u ldiff

ii i

ii i

i ii

= +

= −

−=

( )( ) : 02

diffuDu diff Cu Load

didiUkvl I R i i L U udt dt

Σ − + + + + + + =

( )( ) : 02

difflDl diff Cl Load

didiUkvl II R i i L U udt dt

Σ + − + − − + =

2 2 2Cu Cl V

Load VU U diR Lu i

dt

Σ Σ−= − −

2 2diff Cu ClD

diff

di U UUL Ridt

Σ Σ++ = −

2

2

DCu V diff

DCl V diff

UU e u

UU e u

Σ

Σ

= − −

= + −

2 2V

Load V V

diffdiff diff

diR Lu e idt

diL Ri u

dt

= − −

+ =

(1)

where C is the capacitor in each individual module and N represents the number of modules in each arm. Also, we have:








(1)


(2)




(3)


(4)


(5)

(6)


(7)


(8)



∑ - UCl∑).



∑ + UCl∑.


(9)


(10)





22

22

2 2

2 2

2

2

CuCu Cu

ClCl Cl

Cu Cu

Cl Cl

UC CW N UN N

UC CW N UN N

NU WCNU W

C

ΣΣ Σ

ΣΣ Σ

Σ Σ

Σ Σ

= = = =

=

=

.

.

Cuu Cu

Cll Cl

dW i udt

dW i udt

Σ

Σ

=

= −

Cuu

Cu

Cll

Cl

unUunU

Σ

Σ

=

=

2

2

2

Vu diff

Vl diff

u ldiff

ii i

ii i

i ii

= +

= −

−=

( )( ) : 02



Σ − + + + + + + =

( )( ) : 02



Σ + − + − − + =

2 2 2Cu Cl V

Load VU U diR Lu i

dt

Σ Σ−= − −

2 2diff Cu ClD

diff

di U UUL Ridt

Σ Σ++ = −

2

2

DCu V diff

DCl V diff

UU e u

UU e u

Σ

Σ

= − −

= + −

2 2V

Load V V

diffdiff diff

diR Lu e idt

diL Ri u

dt

= − −

+ =

(2)


Σ and UCl

Σ, respectively, in this case the modulation index for the upper and lower arms will be as follows:








(1)


(2)




(3)


(4)


(5)

(6)


(7)


(8)



∑ - UCl∑).



∑ + UCl∑.


(9)


(10)





22

22

2 2

2 2

2

2

CuCu Cu

ClCl Cl

Cu Cu

Cl Cl

UC CW N UN N

UC CW N UN N

NU WCNU W

C

ΣΣ Σ

ΣΣ Σ

Σ Σ

Σ Σ

= = = =

=

=

.

.

Cuu Cu

Cll Cl

dW i udt

dW i udt

Σ

Σ

=

= −

Cuu

Cu

Cll

Cl

unUunU

Σ

Σ

=

=

2

2

2

Vu diff

Vl diff

u ldiff

ii i

ii i

i ii

= +

= −

−=

( )( ) : 02



Σ − + + + + + + =

( )( ) : 02



Σ + − + − − + =

2 2 2Cu Cl V

Load VU U diR Lu i

dt

Σ Σ−= − −

2 2diff Cu ClD

diff

di U UUL Ridt

Σ Σ++ = −

2

2

DCu V diff

DCl V diff

UU e u

UU e u

Σ

Σ

= − −

= + −

2 2V

Load V V

diffdiff diff

diR Lu e idt

diL Ri u

dt

= − −

+ =

(3)

For further investigation, we divide the current of each arm into two parts. One part is the ac current which is naturally divided into two equal parts and flows through the upper and lower arms. The difference between these two currents is considered as a differential current, idiff that flows through the DC source and series arms which is called a circulating current. This current is defined as follows:








(1)


(2)




(3)


(4)


(5)

(6)


(7)


(8)



∑ - UCl∑).



∑ + UCl∑.


(9)


(10)





22

22

2 2

2 2

2

2

CuCu Cu

ClCl Cl

Cu Cu

Cl Cl

UC CW N UN N

UC CW N UN N

NU WCNU W

C

ΣΣ Σ

ΣΣ Σ

Σ Σ

Σ Σ

= = = =

=

=

.

.

Cuu Cu

Cll Cl

dW i udt

dW i udt

Σ

Σ

=

= −

Cuu

Cu

Cll

Cl

unUunU

Σ

Σ

=

=

2

2

2

Vu diff

Vl diff

u ldiff

ii i

ii i

i ii

= +

= −

−=

( )( ) : 02



Σ − + + + + + + =

( )( ) : 02



Σ + − + − − + =

2 2 2Cu Cl V

Load VU U diR Lu i

dt

Σ Σ−= − −

2 2diff Cu ClD

diff

di U UUL Ridt

Σ Σ++ = −

2

2

DCu V diff

DCl V diff

UU e u

UU e u

Σ

Σ

= − −

= + −

2 2V

Load V V

diffdiff diff

diR Lu e idt

diL Ri u

dt

= − −

+ =

(4)









(1)


(2)




(3)


(4)


(5)

(6)


(7)


(8)



∑ - UCl∑).



∑ + UCl∑.


(9)


(10)





22

22

2 2

2 2

2

2

CuCu Cu

ClCl Cl

Cu Cu

Cl Cl

UC CW N UN N

UC CW N UN N

NU WCNU W

C

ΣΣ Σ

ΣΣ Σ

Σ Σ

Σ Σ

= = = =

=

=

.

.

Cuu Cu

Cll Cl

dW i udt

dW i udt

Σ

Σ

=

= −

Cuu

Cu

Cll

Cl

unUunU

Σ

Σ

=

=

2

2

2

Vu diff

Vl diff

u ldiff

ii i

ii i

i ii

= +

= −

−=

( )( ) : 02



Σ − + + + + + + =

( )( ) : 02



Σ + − + − − + =

2 2 2Cu Cl V

Load VU U diR Lu i

dt

Σ Σ−= − −

2 2diff Cu ClD

diff

di U UUL Ridt

Σ Σ++ = −

2

2

DCu V diff

DCl V diff

UU e u

UU e u

Σ

Σ

= − −

= + −

2 2V

Load V V

diffdiff diff

diR Lu e idt

diL Ri u

dt

= − −

+ =

(5)4Trans. Electr. Electron. Mater. 17(6) 1 (2016): M. S. Shadlu







(1)


(2)




(3)


(4)


(5)

(6)


(7)


(8)



∑ - UCl∑).



∑ + UCl∑.


(9)


(10)





22

22

2 2

2 2

2

2

CuCu Cu

ClCl Cl

Cu Cu

Cl Cl

UC CW N UN N

UC CW N UN N

NU WCNU W

C

ΣΣ Σ

ΣΣ Σ

Σ Σ

Σ Σ

= = = =

=

=

.

.

Cuu Cu

Cll Cl

dW i udt

dW i udt

Σ

Σ

=

= −

Cuu

Cu

Cll

Cl

unUunU

Σ

Σ

=

=

2

2

2

Vu diff

Vl diff

u ldiff

ii i

ii i

i ii

= +

= −

−=

( )( ) : 02



Σ − + + + + + + =

( )( ) : 02



Σ + − + − − + =

2 2 2Cu Cl V

Load VU U diR Lu i

dt

Σ Σ−= − −

2 2diff Cu ClD

diff

di U UUL Ridt

Σ Σ++ = −

2

2

DCu V diff

DCl V diff

UU e u

UU e u

Σ

Σ

= − −

= + −

2 2V

Load V V

diffdiff diff

diR Lu e idt

diL Ri u

dt

= − −

+ =

(6)









(1)


(2)




(3)


(4)


(5)

(6)


(7)


(8)



∑ - UCl∑).



∑ + UCl∑.


(9)


(10)





22

22

2 2

2 2

2

2

CuCu Cu

ClCl Cl

Cu Cu

Cl Cl

UC CW N UN N

UC CW N UN N

NU WCNU W

C

ΣΣ Σ

ΣΣ Σ

Σ Σ

Σ Σ

= = = =

=

=

.

.

Cuu Cu

Cll Cl

dW i udt

dW i udt

Σ

Σ

=

= −

Cuu

Cu

Cll

Cl

unUunU

Σ

Σ

=

=

2

2

2

Vu diff

Vl diff

u ldiff

ii i

ii i

i ii

= +

= −

−=

( )( ) : 02



Σ − + + + + + + =

( )( ) : 02



Σ + − + − − + =

2 2 2Cu Cl V

Load VU U diR Lu i

dt

Σ Σ−= − −

2 2diff Cu ClD

diff

di U UUL Ridt

Σ Σ++ = −

2

2

DCu V diff

DCl V diff

UU e u

UU e u

Σ

Σ

= − −

= + −

2 2V

Load V V

diffdiff diff

diR Lu e idt

diL Ri u

dt

= − −

+ =

(7)









(1)


(2)




(3)


(4)


(5)

(6)


(7)


(8)



∑ - UCl∑).



∑ + UCl∑.


(9)


(10)





22

22

2 2

2 2

2

2

CuCu Cu

ClCl Cl

Cu Cu

Cl Cl

UC CW N UN N

UC CW N UN N

NU WCNU W

C

ΣΣ Σ

ΣΣ Σ

Σ Σ

Σ Σ

= = = =

=

=

.

.

Cuu Cu

Cll Cl

dW i udt

dW i udt

Σ

Σ

=

= −

Cuu

Cu

Cll

Cl

unUunU

Σ

Σ

=

=

2

2

2

Vu diff

Vl diff

u ldiff

ii i

ii i

i ii

= +

= −

−=

( )( ) : 02



Σ − + + + + + + =

( )( ) : 02



Σ + − + − − + =

2 2 2Cu Cl V

Load VU U diR Lu i

dt

Σ Σ−= − −

2 2diff Cu ClD

diff

di U UUL Ridt

Σ Σ++ = −

2

2

DCu V diff

DCl V diff

UU e u

UU e u

Σ

Σ

= − −

= + −

2 2V

Load V V

diffdiff diff

diR Lu e idt

diL Ri u

dt

= − −

+ =

(8)

According to the above equations, we can conclude that:* The load ac voltage (uLoad) only depends on ac current and the

difference between the upper and lower affected capacitors voltages (UCu

Σ - UClΣ).

* The difference in voltage between the two arms acts as an internal ac voltage in the converter, while inductor L and resistor R form an internal passive impedance in the ac current path generated by the ac power supply.


Σ + UClΣΣ.

* Differential current idiff can be calculated independent of the parameters of the ac side. In other words, it is only the result of a differential voltage component which is created because of the difference between the upper and lower affected capacitors voltages. This differential voltage is called udiff and the affected voltage in each arm is equal to:








(1)


(2)




(3)


(4)


(5)

(6)


(7)


(8)



∑ - UCl∑).



∑ + UCl∑.


(9)


(10)





22

22

2 2

2 2

2

2

CuCu Cu

ClCl Cl

Cu Cu

Cl Cl

UC CW N UN N

UC CW N UN N

NU WCNU W

C

ΣΣ Σ

ΣΣ Σ

Σ Σ

Σ Σ

= = = =

=

=

.

.

Cuu Cu

Cll Cl

dW i udt

dW i udt

Σ

Σ

=

= −

Cuu

Cu

Cll

Cl

unUunU

Σ

Σ

=

=

2

2

2

Vu diff

Vl diff

u ldiff

ii i

ii i

i ii

= +

= −

−=

( )( ) : 02



Σ − + + + + + + =

( )( ) : 02



Σ + − + − − + =

2 2 2Cu Cl V

Load VU U diR Lu i

dt

Σ Σ−= − −

2 2diff Cu ClD

diff

di U UUL Ridt

Σ Σ++ = −

2

2

DCu V diff

DCl V diff

UU e u

UU e u

Σ

Σ

= − −

= + −

2 2V

Load V V

diffdiff diff

diR Lu e idt

diL Ri u

dt

= − −

+ =

(9)









(1)


(2)




(3)


(4)


(5)

(6)


(7)


(8)



∑ - UCl∑).



∑ + UCl∑.


(9)


(10)





22

22

2 2

2 2

2

2

CuCu Cu

ClCl Cl

Cu Cu

Cl Cl

UC CW N UN N

UC CW N UN N

NU WCNU W

C

ΣΣ Σ

ΣΣ Σ

Σ Σ

Σ Σ

= = = =

=

=

.

.

Cuu Cu

Cll Cl

dW i udt

dW i udt

Σ

Σ

=

= −

Cuu

Cu

Cll

Cl

unUunU

Σ

Σ

=

=

2

2

2

Vu diff

Vl diff

u ldiff

ii i

ii i

i ii

= +

= −

−=

( )( ) : 02



Σ − + + + + + + =

( )( ) : 02



Σ + − + − − + =

2 2 2Cu Cl V

Load VU U diR Lu i

dt

Σ Σ−= − −

2 2diff Cu ClD

diff

di U UUL Ridt

Σ Σ++ = −

2

2

DCu V diff

DCl V diff

UU e u

UU e u

Σ

Σ

= − −

= + −

2 2V

Load V V

diffdiff diff

diR Lu e idt

diL Ri u

dt

= − −

+ =

(10)

3. PROPOSED CONTROL ALGORITHM

In this paper, the output currents control of the PV system based on MMC is performed using a novel control model based on the average model and model predictive control. The average model is used to derive the mathematical model based on circuit equations. In addition, model predictive control is used to design the controller based on the mathematical model.


Thus, according to Fig. 3(b) we have:

(11)

(12)

In addition, for each individual leg of the MMC structure shown in Fig. 1 and according to (11), the voltage of modules in the upper and lower arms in each leg is as follows:

(13)

(14)

where UCu(j)∑ and UCl(j)

∑ are the total capacitors voltage in the upper and lower arms of phase j, respectively. Also, the switching function

( )jS t

is our control parameter to the AC current control in phase j.

3.2 Extracting circuit equations

According to Fig. 1 for each leg, we have:

(15)

(16)

In Fig. 1, the individual arms in each leg are the same, so |ipj|=|inj|. By summing equations (15) and (16) and by simplifying, we can calculate d/dt(icirj) for each leg as follows:

(17)

With respect to the above equation and according to (13) and (14), we have:

(18)

It is worth noting that the circulating currents of the individual arms of the legs have the same direction, thus the switching sig-nals Spj(t) and SNj(t) in equation (18) are equal and are generally

represented by ( )jS t

. Also, by considering Fig. 2(b) we have:

(19)

So we can rewrite (18) as follows:

(20)

3.3 Model predictive control

Based on the model predictive control (MPC) in [30] and [31], equation (20) can be rewritten as follows:

(21)

where TS is the switching period (TS=1/fS).According to equation (21), the instantaneous switching signal

for each phase can be calculated as follows:

(22)

In (22), icirj is the circulating current in each phase which is equal to:

(23)

Also, icirjref is the reference value of the circulating current

which can be considered equal to 0. This is because the goal of the proposed controller is to eliminate the circulating cur-rent in order to achieve a pure sinusoidal current in MMC output.

3.4 Proposed controller

Our proposed controller is shown in Fig. 4. The proposed current controller consists of two parts, one of

which is based on a closed loop controller which has been imple-mented according to the energy equations and the other is based on MPC. The output of the closed loop controller is modulation index (n) that calculates according to (3). The output of the con-

Fig. 3. (a) Half-Bridge module and (b) equivalent circuit of a half-bridge module based on average model.

1S

2S −+

CVC

cu−

+i

Ci

−+

CVCcu

−

+i

−+C(t).VS

(t).iS

)(a )(b

Ci

1S

2S −+

CVC

cu−

+i

Ci

−+

CVCcu

−

+i

−+C(t).VS

(t).iS

)(a )(b

Ci

( ).c Cu S t V=

( ).i S t iC =

( ) ( ). 1, 2,3Pj Pj Cu jU S t U jΣ= =

( ) ( ). 1, 2,3Nj Nj Cl jU S t U jΣ= =

( ) ( )1,2,3

P PCCj Pj pj cirj pj cirjdV V U R i i L i idt

j

− = + + + +

=

( ) ( )1,2,3

PCCj N Nj nj cirj nj cirjdV V U R i i L i idt

j

− = + − + + − +

=

( )2 2 2

1,2,3

Pj Nj P Ncirj cirj

U U V VRi iL L L L

j

−−= − − +

=

( ) ( ) ( )( ) ( ). .2 2 2

1, 2,3

Pj Cu j Nj Cl j P Ncirj cirj

S t U S t U V VRi iL L L L

j

Σ Σ −−= − − +

=

,2 2

D DP N

U UV V −= =

( ) ( ) ( ).2 2 2

1,2,3

Cu j Cl j Dcirj cirj j

U U URi i S tL L L L

j

Σ Σ −= − + +

=

( ) ( ) ( ).2 2 2

1,2,3

refcirj cirj Cu j Cl j D

cirj jS

i i U U UR i S tT L L L L

j

Σ Σ − −= − + +

=

( ) ( ) ( ) ( )2 2

: ( ) 1, 2,3

upper j lower j pj cirj nj cirjcirj

pj nj

i i i i i ii

with i i j

+ + + − += =

= =

( )( ) ( )

2

2 21, 2,3

refcirj cirjD

cirjS

jCu j Cl j

i iUR iL L T

S tU U

L Lj

Σ Σ

−− + −

=+

=



(11)

(12)


(13)

(14)



( )jS t




(15)

(16)


(17)


(18)




(19)


(20)



(21)



(22)


(23)







1S

2S −+

CVC

cu−

+i

Ci

−+

CVCcu

−

+i

−+C(t).VS

(t).iS

)(a )(b

Ci

1S

2S −+

CVC

cu−

+i

Ci

−+

CVCcu

−

+i

−+C(t).VS

(t).iS

)(a )(b

Ci

( ).c Cu S t V=

( ).i S t iC =

( ) ( ). 1, 2,3Pj Pj Cu jU S t U jΣ= =

( ) ( ). 1, 2,3Nj Nj Cl jU S t U jΣ= =

( ) ( )1,2,3


j

− = + + + +

=

( ) ( )1,2,3


j

− = + − + + − +

=

( )2 2 2

1,2,3

Pj Nj P Ncirj cirj

U U V VRi iL L L L

j

−−= − − +

=

( ) ( ) ( )( ) ( ). .2 2 2

1,2,3



j

Σ Σ −−= − − +

=

,2 2

D DP N

U UV V −= =

( ) ( ) ( ).2 2 2

1,2,3



j

Σ Σ −= − + +

=

( ) ( ) ( ).2 2 2

1,2,3


cirj jS


j

Σ Σ − −= − + +

=

( ) ( ) ( ) ( )2 2

: ( ) 1,2,3


pj nj

i i i i i ii

with i i j

+ + + − += =

= =

( )( ) ( )

2

2 21,2,3

refcirj cirjD

cirjS

jCu j Cl j

i iUR iL L T

S tU U

L Lj

Σ Σ

−− + −

=+

=

(a)

(b)


3.1 Average model

In this model, the switching signals for MMC modules are considered as control parameters, and the voltage and current of each module will be written as a function of these switching signals [30]. The equivalent circuit of a half-bridge module based on the average model is shown in Fig. 3.




(11)

(12)


(13)

(14)



( )jS t




(15)

(16)


(17)


(18)




(19)


(20)



(21)



(22)


(23)







1S

2S −+

CVC

cu−

+i

Ci

−+

CVCcu

−

+i

−+C(t).VS

(t).iS

)(a )(b

Ci

1S

2S −+

CVC

cu−

+i

Ci

−+

CVCcu

−

+i

−+C(t).VS

(t).iS

)(a )(b

Ci

( ).c Cu S t V=

( ).i S t iC =

( ) ( ). 1, 2,3Pj Pj Cu jU S t U jΣ= =

( ) ( ). 1, 2,3Nj Nj Cl jU S t U jΣ= =

( ) ( )1, 2,3


j

− = + + + +

=

( ) ( )1, 2,3


j

− = + − + + − +

=

( )2 2 2

1,2,3

Pj Nj P Ncirj cirj

U U V VRi iL L L L

j

−−= − − +

=

( ) ( ) ( )( ) ( ). .2 2 2

1,2,3



j

Σ Σ −−= − − +

=

,2 2

D DP N

U UV V −= =

( ) ( ) ( ).2 2 2

1,2,3



j

Σ Σ −= − + +

=

( ) ( ) ( ).2 2 2

1,2,3


cirj jS


j

Σ Σ − −= − + +

=

( ) ( ) ( ) ( )2 2

: ( ) 1, 2,3


pj nj

i i i i i ii

with i i j

+ + + − += =

= =

( )( ) ( )

2

2 21,2,3

refcirj cirjD

cirjS

jCu j Cl j

i iUR iL L T

S tU U

L Lj

Σ Σ

−− + −

=+

=

(11)



(11)

(12)


(13)

(14)



( )jS t




(15)

(16)


(17)


(18)




(19)


(20)



(21)



(22)


(23)







1S

2S −+

CVC

cu−

+i

Ci

−+

CVCcu

−

+i

−+C(t).VS

(t).iS

)(a )(b

Ci

1S

2S −+

CVC

cu−

+i

Ci

−+

CVCcu

−

+i

−+C(t).VS

(t).iS

)(a )(b

Ci

( ).c Cu S t V=

( ).i S t iC =

( ) ( ). 1, 2,3Pj Pj Cu jU S t U jΣ= =

( ) ( ). 1, 2,3Nj Nj Cl jU S t U jΣ= =

( ) ( )1, 2,3


j

− = + + + +

=

( ) ( )1, 2,3


j

− = + − + + − +

=

( )2 2 2

1,2,3

Pj Nj P Ncirj cirj

U U V VRi iL L L L

j

−−= − − +

=

( ) ( ) ( )( ) ( ). .2 2 2

1,2,3



j

Σ Σ −−= − − +

=

,2 2

D DP N

U UV V −= =

( ) ( ) ( ).2 2 2

1,2,3



j

Σ Σ −= − + +

=

( ) ( ) ( ).2 2 2

1,2,3


cirj jS


j

Σ Σ − −= − + +

=

( ) ( ) ( ) ( )2 2

: ( ) 1, 2,3


pj nj

i i i i i ii

with i i j

+ + + − += =

= =

( )( ) ( )

2

2 21, 2,3

refcirj cirjD

cirjS

jCu j Cl j

i iUR iL L T

S tU U

L Lj

Σ Σ

−− + −

=+

=

(12)




(11)

(12)


(13)

(14)



( )jS t




(15)

(16)


(17)


(18)




(19)


(20)



(21)



(22)


(23)







1S

2S −+

CVC

cu−

+i

Ci

−+

CVCcu

−

+i

−+C(t).VS

(t).iS

)(a )(b

Ci

1S

2S −+

CVC

cu−

+i

Ci

−+

CVCcu

−

+i

−+C(t).VS

(t).iS

)(a )(b

Ci

( ).c Cu S t V=

( ).i S t iC =

( ) ( ). 1, 2,3Pj Pj Cu jU S t U jΣ= =

( ) ( ). 1, 2,3Nj Nj Cl jU S t U jΣ= =

( ) ( )1, 2,3


j

− = + + + +

=

( ) ( )1, 2,3


j

− = + − + + − +

=

( )2 2 2

1,2,3

Pj Nj P Ncirj cirj

U U V VRi iL L L L

j

−−= − − +

=

( ) ( ) ( )( ) ( ). .2 2 2

1,2,3



j

Σ Σ −−= − − +

=

,2 2

D DP N

U UV V −= =

( ) ( ) ( ).2 2 2

1,2,3



j

Σ Σ −= − + +

=

( ) ( ) ( ).2 2 2

1,2,3


cirj jS


j

Σ Σ − −= − + +

=

( ) ( ) ( ) ( )2 2

: ( ) 1, 2,3


pj nj

i i i i i ii

with i i j

+ + + − += =

= =

( )( ) ( )

2

2 21,2,3

refcirj cirjD

cirjS

jCu j Cl j

i iUR iL L T

S tU U

L Lj

Σ Σ

−− + −

=+

=

(13)



(11)

(12)


(13)

(14)



( )jS t




(15)

(16)


(17)


(18)




(19)


(20)



(21)



(22)


(23)







1S

2S −+

CVC

cu−

+i

Ci

−+

CVCcu

−

+i

−+C(t).VS

(t).iS

)(a )(b

Ci

1S

2S −+

CVC

cu−

+i

Ci

−+

CVCcu

−

+i

−+C(t).VS

(t).iS

)(a )(b

Ci

( ).c Cu S t V=

( ).i S t iC =

( ) ( ). 1, 2,3Pj Pj Cu jU S t U jΣ= =

( ) ( ). 1, 2,3Nj Nj Cl jU S t U jΣ= =

( ) ( )1, 2,3


j

− = + + + +

=

( ) ( )1, 2,3


j

− = + − + + − +

=

( )2 2 2

1,2,3

Pj Nj P Ncirj cirj

U U V VRi iL L L L

j

−−= − − +

=

( ) ( ) ( )( ) ( ). .2 2 2

1,2,3



j

Σ Σ −−= − − +

=

,2 2

D DP N

U UV V −= =

( ) ( ) ( ).2 2 2

1,2,3



j

Σ Σ −= − + +

=

( ) ( ) ( ).2 2 2

1,2,3


cirj jS


j

Σ Σ − −= − + +

=

( ) ( ) ( ) ( )2 2

: ( ) 1, 2,3


pj nj

i i i i i ii

with i i j

+ + + − += =

= =

( )( ) ( )

2

2 21,2,3

refcirj cirjD

cirjS

jCu j Cl j

i iUR iL L T

S tU U

L Lj

Σ Σ

−− + −

=+

=

(14)

where UCu(j)Σ and UCl(j)

Σ are the total capacitors voltage in the upper and lower arms of phase j, respectively. Also, the switching function



(11)

(12)


(13)

(14)



( )jS t




(15)

(16)


(17)


(18)




(19)


(20)



(21)



(22)


(23)







1S

2S −+

CVC

cu−

+i

Ci

−+

CVCcu

−

+i

−+C(t).VS

(t).iS

)(a )(b

Ci

1S

2S −+

CVC

cu−

+i

Ci

−+

CVCcu

−

+i

−+C(t).VS

(t).iS

)(a )(b

Ci

( ).c Cu S t V=

( ).i S t iC =

( ) ( ). 1, 2,3Pj Pj Cu jU S t U jΣ= =

( ) ( ). 1, 2,3Nj Nj Cl jU S t U jΣ= =

( ) ( )1, 2,3


j

− = + + + +

=

( ) ( )1, 2,3


j

− = + − + + − +

=

( )2 2 2

1,2,3

Pj Nj P Ncirj cirj

U U V VRi iL L L L

j

−−= − − +

=

( ) ( ) ( )( ) ( ). .2 2 2

1,2,3



j

Σ Σ −−= − − +

=

,2 2

D DP N

U UV V −= =

( ) ( ) ( ).2 2 2

1,2,3



j

Σ Σ −= − + +

=

( ) ( ) ( ).2 2 2

1,2,3


cirj jS


j

Σ Σ − −= − + +

=

( ) ( ) ( ) ( )2 2

: ( ) 1, 2,3


pj nj

i i i i i ii

with i i j

+ + + − += =

= =

( )( ) ( )

2

2 21,2,3

refcirj cirjD

cirjS

jCu j Cl j

i iUR iL L T

S tU U

L Lj

Σ Σ

−− + −

=+

= is our control parameter to the AC current control in phase j.





(11)

(12)


(13)

(14)



( )jS t




(15)

(16)


(17)


(18)




(19)


(20)



(21)



(22)


(23)







1S

2S −+

CVC

cu−

+i

Ci

−+

CVCcu

−

+i

−+C(t).VS

(t).iS

)(a )(b

Ci

1S

2S −+

CVC

cu−

+i

Ci

−+

CVCcu

−

+i

−+C(t).VS

(t).iS

)(a )(b

Ci

( ).c Cu S t V=

( ).i S t iC =

( ) ( ). 1, 2,3Pj Pj Cu jU S t U jΣ= =

( ) ( ). 1, 2,3Nj Nj Cl jU S t U jΣ= =

( ) ( )1, 2,3


j

− = + + + +

=

( ) ( )1, 2,3


j

− = + − + + − +

=

( )2 2 2

1,2,3

Pj Nj P Ncirj cirj

U U V VRi iL L L L

j

−−= − − +

=

( ) ( ) ( )( ) ( ). .2 2 2

1,2,3



j

Σ Σ −−= − − +

=

,2 2

D DP N

U UV V −= =

( ) ( ) ( ).2 2 2

1,2,3



j

Σ Σ −= − + +

=

( ) ( ) ( ).2 2 2

1,2,3


cirj jS


j

Σ Σ − −= − + +

=

( ) ( ) ( ) ( )2 2

: ( ) 1, 2,3


pj nj

i i i i i ii

with i i j

+ + + − += =

= =

( )( ) ( )

2

2 21, 2,3

refcirj cirjD

cirjS

jCu j Cl j

i iUR iL L T

S tU U

L Lj

Σ Σ

−− + −

=+

=

(15)



(11)

(12)


(13)

(14)



( )jS t




(15)

(16)


(17)


(18)




(19)


(20)



(21)



(22)


(23)







1S

2S −+

CVC

cu−

+i

Ci

−+

CVCcu

−

+i

−+C(t).VS

(t).iS

)(a )(b

Ci

1S

2S −+

CVC

cu−

+i

Ci

−+

CVCcu

−

+i

−+C(t).VS

(t).iS

)(a )(b

Ci

( ).c Cu S t V=

( ).i S t iC =

( ) ( ). 1, 2,3Pj Pj Cu jU S t U jΣ= =

( ) ( ). 1, 2,3Nj Nj Cl jU S t U jΣ= =

( ) ( )1, 2,3


j

− = + + + +

=

( ) ( )1, 2,3


j

− = + − + + − +

=

( )2 2 2

1,2,3

Pj Nj P Ncirj cirj

U U V VRi iL L L L

j

−−= − − +

=

( ) ( ) ( )( ) ( ). .2 2 2

1,2,3



j

Σ Σ −−= − − +

=

,2 2

D DP N

U UV V −= =

( ) ( ) ( ).2 2 2

1,2,3



j

Σ Σ −= − + +

=

( ) ( ) ( ).2 2 2

1,2,3


cirj jS


j

Σ Σ − −= − + +

=

( ) ( ) ( ) ( )2 2

: ( ) 1, 2,3


pj nj

i i i i i ii

with i i j

+ + + − += =

= =

( )( ) ( )

2

2 21, 2,3

refcirj cirjD

cirjS

jCu j Cl j

i iUR iL L T

S tU U

L Lj

Σ Σ

−− + −

=+

=

(16)




(11)

(12)


(13)

(14)



( )jS t




(15)

(16)


(17)


(18)




(19)


(20)



(21)



(22)


(23)







1S

2S −+

CVC

cu−

+i

Ci

−+

CVCcu

−

+i

−+C(t).VS

(t).iS

)(a )(b

Ci

1S

2S −+

CVC

cu−

+i

Ci

−+

CVCcu

−

+i

−+C(t).VS

(t).iS

)(a )(b

Ci

( ).c Cu S t V=

( ).i S t iC =

( ) ( ). 1, 2,3Pj Pj Cu jU S t U jΣ= =

( ) ( ). 1, 2,3Nj Nj Cl jU S t U jΣ= =

( ) ( )1, 2,3


j

− = + + + +

=

( ) ( )1, 2,3


j

− = + − + + − +

=

( )2 2 2

1,2,3

Pj Nj P Ncirj cirj

U U V VRi iL L L L

j

−−= − − +

=

( ) ( ) ( )( ) ( ). .2 2 2

1,2,3



j

Σ Σ −−= − − +

=

,2 2

D DP N

U UV V −= =

( ) ( ) ( ).2 2 2

1,2,3



j

Σ Σ −= − + +

=

( ) ( ) ( ).2 2 2

1,2,3


cirj jS


j

Σ Σ − −= − + +

=

( ) ( ) ( ) ( )2 2

: ( ) 1, 2,3


pj nj

i i i i i ii

with i i j

+ + + − += =

= =

( )( ) ( )

2

2 21, 2,3

refcirj cirjD

cirjS

jCu j Cl j

i iUR iL L T

S tU U

L Lj

Σ Σ

−− + −

=+

=

(17)




(11)

(12)


(13)

(14)



( )jS t




(15)

(16)


(17)


(18)




(19)


(20)



(21)



(22)


(23)







1S

2S −+

CVC

cu−

+i

Ci

−+

CVCcu

−

+i

−+C(t).VS

(t).iS

)(a )(b

Ci

1S

2S −+

CVC

cu−

+i

Ci

−+

CVCcu

−

+i

−+C(t).VS

(t).iS

)(a )(b

Ci

( ).c Cu S t V=

( ).i S t iC =

( ) ( ). 1, 2,3Pj Pj Cu jU S t U jΣ= =

( ) ( ). 1, 2,3Nj Nj Cl jU S t U jΣ= =

( ) ( )1, 2,3


j

− = + + + +

=

( ) ( )1, 2,3


j

− = + − + + − +

=

( )2 2 2

1,2,3

Pj Nj P Ncirj cirj

U U V VRi iL L L L

j

−−= − − +

=

( ) ( ) ( )( ) ( ). .2 2 2

1,2,3



j

Σ Σ −−= − − +

=

,2 2

D DP N

U UV V −= =

( ) ( ) ( ).2 2 2

1,2,3



j

Σ Σ −= − + +

=

( ) ( ) ( ).2 2 2

1,2,3


cirj jS


j

Σ Σ − −= − + +

=

( ) ( ) ( ) ( )2 2

: ( ) 1, 2,3


pj nj

i i i i i ii

with i i j

+ + + − += =

= =

( )( ) ( )

2

2 21, 2,3

refcirj cirjD

cirjS

jCu j Cl j

i iUR iL L T

S tU U

L Lj

Σ Σ

−− + −

=+

=

(18)

It is worth noting that the circulating currents of the individual arms of the legs have the same direction, thus the switching signals Spj(t) and SNj(t) in equation (18) are equal and are generally represented by



(11)

(12)


(13)

(14)



( )jS t




(15)

(16)


(17)


(18)




(19)


(20)



(21)



(22)


(23)







1S

2S −+

CVC

cu−

+i

Ci

−+

CVCcu

−

+i

−+C(t).VS

(t).iS

)(a )(b

Ci

1S

2S −+

CVC

cu−

+i

Ci

−+

CVCcu

−

+i

−+C(t).VS

(t).iS

)(a )(b

Ci

( ).c Cu S t V=

( ).i S t iC =

( ) ( ). 1, 2,3Pj Pj Cu jU S t U jΣ= =

( ) ( ). 1, 2,3Nj Nj Cl jU S t U jΣ= =

( ) ( )1,2,3


j

− = + + + +

=

( ) ( )1,2,3


j

− = + − + + − +

=

( )2 2 2

1,2,3

Pj Nj P Ncirj cirj

U U V VRi iL L L L

j

−−= − − +

=

( ) ( ) ( )( ) ( ). .2 2 2

1, 2,3



j

Σ Σ −−= − − +

=

,2 2

D DP N

U UV V −= =

( ) ( ) ( ).2 2 2

1,2,3



j

Σ Σ −= − + +

=

( ) ( ) ( ).2 2 2

1,2,3


cirj jS


j

Σ Σ − −= − + +

=

( ) ( ) ( ) ( )2 2

: ( ) 1, 2,3


pj nj

i i i i i ii

with i i j

+ + + − += =

= =

( )( ) ( )

2

2 21, 2,3

refcirj cirjD

cirjS

jCu j Cl j

i iUR iL L T

S tU U

L Lj

Σ Σ

−− + −

=+

=. Also, by considering Fig. 2(b) we have:



(11)

(12)


(13)

(14)



( )jS t




(15)

(16)


(17)


(18)




(19)


(20)



(21)



(22)


(23)







1S

2S −+

CVC

cu−

+i

Ci

−+

CVCcu

−

+i

−+C(t).VS

(t).iS

)(a )(b

Ci

1S

2S −+

CVC

cu−

+i

Ci

−+

CVCcu

−

+i

−+C(t).VS

(t).iS

)(a )(b

Ci

( ).c Cu S t V=

( ).i S t iC =

( ) ( ). 1, 2,3Pj Pj Cu jU S t U jΣ= =

( ) ( ). 1, 2,3Nj Nj Cl jU S t U jΣ= =

( ) ( )1, 2,3


j

− = + + + +

=

( ) ( )1, 2,3


j

− = + − + + − +

=

( )2 2 2

1,2,3

Pj Nj P Ncirj cirj

U U V VRi iL L L L

j

−−= − − +

=

( ) ( ) ( )( ) ( ). .2 2 2

1,2,3



j

Σ Σ −−= − − +

=

,2 2

D DP N

U UV V −= =

( ) ( ) ( ).2 2 2

1,2,3



j

Σ Σ −= − + +

=

( ) ( ) ( ).2 2 2

1,2,3


cirj jS


j

Σ Σ − −= − + +

=

( ) ( ) ( ) ( )2 2

: ( ) 1, 2,3


pj nj

i i i i i ii

with i i j

+ + + − += =

= =

( )( ) ( )

2

2 21, 2,3

refcirj cirjD

cirjS

jCu j Cl j

i iUR iL L T

S tU U

L Lj

Σ Σ

−− + −

=+

=

(19)




(11)

(12)


(13)

(14)



( )jS t




(15)

(16)


(17)


(18)




(19)


(20)



(21)



(22)


(23)







1S

2S −+

CVC

cu−

+i

Ci

−+

CVCcu

−

+i

−+C(t).VS

(t).iS

)(a )(b

Ci

1S

2S −+

CVC

cu−

+i

Ci

−+

CVCcu

−

+i

−+C(t).VS

(t).iS

)(a )(b

Ci

( ).c Cu S t V=

( ).i S t iC =

( ) ( ). 1, 2,3Pj Pj Cu jU S t U jΣ= =

( ) ( ). 1, 2,3Nj Nj Cl jU S t U jΣ= =

( ) ( )1, 2,3


j

− = + + + +

=

( ) ( )1, 2,3


j

− = + − + + − +

=

( )2 2 2

1,2,3

Pj Nj P Ncirj cirj

U U V VRi iL L L L

j

−−= − − +

=

( ) ( ) ( )( ) ( ). .2 2 2

1,2,3



j

Σ Σ −−= − − +

=

,2 2

D DP N

U UV V −= =

( ) ( ) ( ).2 2 2

1,2,3



j

Σ Σ −= − + +

=

( ) ( ) ( ).2 2 2

1,2,3


cirj jS


j

Σ Σ − −= − + +

=

( ) ( ) ( ) ( )2 2

: ( ) 1, 2,3


pj nj

i i i i i ii

with i i j

+ + + − += =

= =

( )( ) ( )

2

2 21, 2,3

refcirj cirjD

cirjS

jCu j Cl j

i iUR iL L T

S tU U

L Lj

Σ Σ

−− + −

=+

=

(20)





(11)

(12)


(13)

(14)



( )jS t




(15)

(16)


(17)


(18)




(19)


(20)



(21)



(22)


(23)







1S

2S −+

CVC

cu−

+i

Ci

−+

CVCcu

−

+i

−+C(t).VS

(t).iS

)(a )(b

Ci

1S

2S −+

CVC

cu−

+i

Ci

−+

CVCcu

−

+i

−+C(t).VS

(t).iS

)(a )(b

Ci

( ).c Cu S t V=

( ).i S t iC =

( ) ( ). 1, 2,3Pj Pj Cu jU S t U jΣ= =

( ) ( ). 1, 2,3Nj Nj Cl jU S t U jΣ= =

( ) ( )1, 2,3


j

− = + + + +

=

( ) ( )1, 2,3


j

− = + − + + − +

=

( )2 2 2

1,2,3

Pj Nj P Ncirj cirj

U U V VRi iL L L L

j

−−= − − +

=

( ) ( ) ( )( ) ( ). .2 2 2

1,2,3



j

Σ Σ −−= − − +

=

,2 2

D DP N

U UV V −= =

( ) ( ) ( ).2 2 2

1,2,3



j

Σ Σ −= − + +

=

( ) ( ) ( ).2 2 2

1,2,3


cirj jS


j

Σ Σ − −= − + +

=

( ) ( ) ( ) ( )2 2

: ( ) 1, 2,3


pj nj

i i i i i ii

with i i j

+ + + − += =

= =

( )( ) ( )

2

2 21, 2,3

refcirj cirjD

cirjS

jCu j Cl j

i iUR iL L T

S tU U

L Lj

Σ Σ

−− + −

=+

=

(21)





(11)

(12)


(13)

(14)



( )jS t




(15)

(16)


(17)


(18)




(19)


(20)



(21)



(22)


(23)







1S

2S −+

CVC

cu−

+i

Ci

−+

CVCcu

−

+i

−+C(t).VS

(t).iS

)(a )(b

Ci

1S

2S −+

CVC

cu−

+i

Ci

−+

CVCcu

−

+i

−+C(t).VS

(t).iS

)(a )(b

Ci

( ).c Cu S t V=

( ).i S t iC =

( ) ( ). 1, 2,3Pj Pj Cu jU S t U jΣ= =

( ) ( ). 1, 2,3Nj Nj Cl jU S t U jΣ= =

( ) ( )1, 2,3


j

− = + + + +

=

( ) ( )1, 2,3


j

− = + − + + − +

=

( )2 2 2

1,2,3

Pj Nj P Ncirj cirj

U U V VRi iL L L L

j

−−= − − +

=

( ) ( ) ( )( ) ( ). .2 2 2

1,2,3



j

Σ Σ −−= − − +

=

,2 2

D DP N

U UV V −= =

( ) ( ) ( ).2 2 2

1,2,3



j

Σ Σ −= − + +

=

( ) ( ) ( ).2 2 2

1,2,3


cirj jS


j

Σ Σ − −= − + +

=

( ) ( ) ( ) ( )2 2

: ( ) 1, 2,3


pj nj

i i i i i ii

with i i j

+ + + − += =

= =

( )( ) ( )

2

2 21, 2,3

refcirj cirjD

cirjS

jCu j Cl j

i iUR iL L T

S tU U

L Lj

Σ Σ

−− + −

=+

=

(22)




(11)

(12)


(13)

(14)



( )jS t




(15)

(16)


(17)


(18)




(19)


(20)



(21)



(22)


(23)







1S

2S −+

CVC

cu−

+i

Ci

−+

CVCcu

−

+i

−+C(t).VS

(t).iS

)(a )(b

Ci

1S

2S −+

CVC

cu−

+i

Ci

−+

CVCcu

−

+i

−+C(t).VS

(t).iS

)(a )(b

Ci

( ).c Cu S t V=

( ).i S t iC =

( ) ( ). 1, 2,3Pj Pj Cu jU S t U jΣ= =

( ) ( ). 1, 2,3Nj Nj Cl jU S t U jΣ= =

( ) ( )1, 2,3


j

− = + + + +

=

( ) ( )1, 2,3


j

− = + − + + − +

=

( )2 2 2

1,2,3

Pj Nj P Ncirj cirj

U U V VRi iL L L L

j

−−= − − +

=

( ) ( ) ( )( ) ( ). .2 2 2

1,2,3



j

Σ Σ −−= − − +

=

,2 2

D DP N

U UV V −= =

( ) ( ) ( ).2 2 2

1,2,3



j

Σ Σ −= − + +

=

( ) ( ) ( ).2 2 2

1,2,3


cirj jS


j

Σ Σ − −= − + +

=

( ) ( ) ( ) ( )2 2

: ( ) 1, 2,3


pj nj

i i i i i ii

with i i j

+ + + − += =

= =

( )( ) ( )

2

2 21,2,3

refcirj cirjD

cirjS

jCu j Cl j

i iUR iL L T

S tU U

L Lj

Σ Σ

−− + −

=+

=

(23)

Also, icirjref is the reference value of the circulating current which

can be considered equal to 0. This is because the goal of the proposed controller is to eliminate the circulating current in order to achieve a pure sinusoidal current in MMC output.


troller based on MPC is the instantaneous switching signal ( ( )jS t

) for each phase which obtains from (22). By summing these two parameters, a unique control parameter named M calculates for each individual leg. A phase-shifted PWM method was used to generate control pulses, as shown in Fig. 5 for a typical 4-level MMC.

As can be seen in Fig. 4, unlike the proposed controllers in [9], [20], and [32], none of the voltage or current components need to be transformed to the “dqo” frame and all of the computations can be performed in “abc” coordinates. This reduces the com-putational burden in the proposed controller and increases the speed of the computation.

It is worth noting that control pulses only need to be gener-ated for one arm in each phase and this is sufficient to invert the generated pulses for another arm in the same leg. In the other words, we can control the output and circulating current components by using a single controller in each leg, unlike the traditional closed loop controller in [33] and [34], where the modulation index was separately generated for each individual arm. Using a single procedure to generate the modulation index in each leg can simplify the experimental implementation of the MMC controller in practical applications.

4. SIMULATION RESULTS

A PV system based on a three-phase 31-level MMC structure is implemented in a PLECS environment and our proposed controller was applied to control output currents. Simulation pa-rameters are presented in Table 1. The first part of the proposed controller shown in Fig. 4, the closed loop controller, applies as soon as the simulation begins and the second part of the pro-posed controller based on MPC activates at t=0.7 s. Simulation

results are obtained as follows. The single phase output voltage of MMC is illustrated in Fig.

6, showing the 31 levels of the output voltage of MMC. Also, the three-phase output voltages and currents of MMC are shown in Figs. 7 and 8, respectively. After applying the proposed current controller, three-phase circulating currents have been obtained as shown in Fig. 9 and the currents of the upper and lower arms in each phase are shown in Figs. 10, 11, and 12.

By eliminating the circulating current oscillations, we can control the upper and lower capacitors voltage balancing au-

Fig. 4. Our proposed controller.

WaveReference Detector

Amplitude

DetectorPhase

refaci

refA

refϕsin

)arg(Zarm

)(refCW Σ

ControllerPI

ControllerP

FilterPassLow

ΣCW

diffCW

)(refdiffCW

armC5.0

armC5.02u

2uΣ

)(upperCu

Σ)(lowerCu

diffurefCu

not

Pulses

IndexModulation

ΣCu

PWMShifted

2NP VV −

++

+

++

++ +

++

++

− −

−

−

++

×

ΣC

refC

uu

armR

armR

armL

armL

DC+

DC−

acn CalculatioSignalSwitching

gCirculatini Σ)(upperCu Σ

)(lowerCu

SignalSwitching M

Additional Controller Based on MPC

)tsin(A refref ϕω +

++

Traditional Controller Based on Closed Loop Control

Table 1. Simulation parameters.

Parameter Symbol ValueNumber of modules in each arm N 30

Phase inductance L 3 mH

Phase resistance R 0.1 Ω

Capacitor (in each module) C 500 µF

Switching frequency fs 5 kHz

Total PV arrays voltage UD/2 110 V

Load impedance R+jωL 0.5+jω0.1 Ω

Output current frequency f 50 Hz

Fig. 5. Phase-shifted PWM method to generate control pulses in a typical 4-level MMC structure.

Switching

keys

fT 1

=

1Pulse

2Pulse

3Pulse

Fig. 6. Single phase output voltage of MMC.













Amplitude

DetectorPhase

refaci

refA

refϕsin

)arg(Zarm

)(refCW Σ

ControllerPI

ControllerP

FilterPassLow

ΣCW

diffCW

)(refdiffCW

armC5.0

armC5.02u

2uΣ

)(upperCu

Σ)(lowerCu

diffurefCu

not

Pulses

IndexModulation

ΣCu

PWMShifted

2NP VV −

++

+

++

++ +

++

++

− −

−

−

++

×

ΣC

refC

uu

armR

armR

armL

armL

DC+

DC−



)(lowerCu

SignalSwitching M



++












Switching

keys

fT 1

=

1Pulse

2Pulse

3Pulse




Our proposed controller is shown in Fig. 4.The proposed current controller consists of two parts, one

of which is based on a closed loop controller which has been implemented according to the energy equations and the other is based on MPC. The output of the closed loop controller is modulation index (n) that calculates according to (3). The output of the controller based on MPC is the instantaneous switching signal (



(11)

(12)


(13)

(14)



( )jS t




(15)

(16)


(17)


(18)




(19)


(20)



(21)



(22)


(23)







1S

2S −+

CVC

cu−

+i

Ci

−+

CVCcu

−

+i

−+C(t).VS

(t).iS

)(a )(b

Ci

1S

2S −+

CVC

cu−

+i

Ci

−+

CVCcu

−

+i

−+C(t).VS

(t).iS

)(a )(b

Ci

( ).c Cu S t V=

( ).i S t iC =

( ) ( ). 1, 2,3Pj Pj Cu jU S t U jΣ= =

( ) ( ). 1, 2,3Nj Nj Cl jU S t U jΣ= =

( ) ( )1, 2,3


j

− = + + + +

=

( ) ( )1, 2,3


j

− = + − + + − +

=

( )2 2 2

1,2,3

Pj Nj P Ncirj cirj

U U V VRi iL L L L

j

−−= − − +

=

( ) ( ) ( )( ) ( ). .2 2 2

1,2,3



j

Σ Σ −−= − − +

=

,2 2

D DP N

U UV V −= =

( ) ( ) ( ).2 2 2

1,2,3



j

Σ Σ −= − + +

=

( ) ( ) ( ).2 2 2

1,2,3


cirj jS


j

Σ Σ − −= − + +

=

( ) ( ) ( ) ( )2 2

: ( ) 1, 2,3


pj nj

i i i i i ii

with i i j

+ + + − += =

= =

( )( ) ( )

2

2 21, 2,3

refcirj cirjD

cirjS

jCu j Cl j

i iUR iL L T

S tU U

L Lj

Σ Σ

−− + −

=+

=) for each phase which obtains from (22). By summing these two parameters, a unique control parameter named M calculates for each individual leg. A phase-shifted PWM method was used to generate control pulses, as shown in Fig. 5 for a typical 4-level MMC.

As can be seen in Fig. 4, unlike the proposed controllers in [9], [20], and [32], none of the voltage or current components need to be transformed to the “dqo” frame and all of the computations can be performed in “abc” coordinates. This reduces the computational burden in the proposed controller and increases the speed of the computation.

It is worth noting that control pulses only need to be generated for one arm in each phase and this is sufficient to invert the generated pulses for another arm in the same leg. In the other words, we can control the output and circulating current components by using a single controller in each leg, unlike the traditional closed loop controller in [33] and [34], where the modulation index was separately generated for each individual arm. Using a single procedure to generate the modulation index in each leg can simplify the experimental implementation of the MMC controller in practical applications.


A PV system based on a three-phase 31-level MMC structure is implemented in a PLECS environment and our proposed controller was applied to control output currents. Simulation parameters are presented in Table 1. The first part of the proposed controller shown in Fig. 4, the closed loop controller, applies as soon as the simulation begins and the second part of the proposed controller based on MPC activates at t=0.7s. Simulation results are obtained as follows.

The single phase output voltage of MMC is illustrated in Fig. 6, showing the 31 levels of the output voltage of MMC. Also, the three-phase output voltages and currents of MMC are shown in Figs. 7 and 8, respectively. After applying the proposed current controller,













Amplitude

DetectorPhase

refaci

refA

refϕsin

)arg(Zarm

)(refCW Σ

ControllerPI

ControllerP

FilterPassLow

ΣCW

diffCW

)(refdiffCW

armC5.0

armC5.02u

2uΣ

)(upperCu

Σ)(lowerCu

diffurefCu

not

Pulses

IndexModulation

ΣCu

PWMShifted

2NP VV −

++

+

++

++ +

++

++

− −

−

−

++

×

ΣC

refC

uu

armR

armR

armL

armL

DC+

DC−



)(lowerCu

SignalSwitching M



++












Switching

keys

fT 1

=

1Pulse

2Pulse

3Pulse














Amplitude

DetectorPhase

refaci

refA

refϕsin

)arg(Zarm

)(refCW Σ

ControllerPI

ControllerP

FilterPassLow

ΣCW

diffCW

)(refdiffCW

armC5.0

armC5.02u

2uΣ

)(upperCu

Σ)(lowerCu

diffurefCu

not

Pulses

IndexModulation

ΣCu

PWMShifted

2NP VV −

++

+

++

++ +

++

++

− −

−

−

++

×

ΣC

refC

uu

armR

armR

armL

armL

DC+

DC−



)(lowerCu

SignalSwitching M



++












Switching

keys

fT 1

=

1Pulse

2Pulse

3Pulse














Amplitude

DetectorPhase

refaci

refA

refϕsin

)arg(Zarm

)(refCW Σ

ControllerPI

ControllerP

FilterPassLow

ΣCW

diffCW

)(refdiffCW

armC5.0

armC5.02u

2uΣ

)(upperCu

Σ)(lowerCu

diffurefCu

not

Pulses

IndexModulation

ΣCu

PWMShifted

2NP VV −

++

+

++

++ +

++

++

− −

−

−

++

×

ΣC

refC

uu

armR

armR

armL

armL

DC+

DC−



)(lowerCu

SignalSwitching M



++












Switching

keys

fT 1

=

1Pulse

2Pulse

3Pulse

Fig. 6. Single phase output voltage of MMC. Trans. Electr. Electron. Mater. 17(6) 1 (2016): M. S. Shadlu7

tomatically. The upper and lower capacitors voltages in one phase are illustrated in Fig. 13. Also, the active and reactive

power consumptions in the MMC structure are depicted in Figs. 14 and 15, respectively. As can be seen in Figs. 14 and 15, active power oscillations are damped using the proposed cur-rent controller and the reactive power is eliminated consider-ably.

Fig. 7. Three-phase output voltages of MMC.

Fig. 8. Three-phase output currents of MMC.

Fig. 9. Three-phase circulating currents.

Fig. 10. Upper and lower currents of phase A.

Fig. 11. Upper and lower currents of phase B.

Fig. 12. Upper and lower currents of phase C.

Fig. 13. Upper and lower capacitors voltage in one phase.






















three-phase circulating currents have been obtained as shown in Fig. 9 and the currents of the upper and lower arms in each phase are shown in Figs. 10, 11, and 12.

By eliminating the circulating current oscillations, we can control the upper and lower capacitors voltage balancing automatically. The upper and lower capacitors voltages in one phase are illustrated in Fig. 13. Also, the active and reactive power consumptions in the

MMC structure are depicted in Figs. 14 and 15, respectively. As can be seen in Figs. 14 and 15, active power oscillations are damped using the proposed current controller and the reactive power is eliminated considerably.

As can be seen in Fig. 9, the three-phase circulating currents have smaller amplitude compared to the obtained results in [35] by using the proposed MPC controller. Accordingly, pure sinusoidal upper and lower currents are attained in each arm after activating MPC, as shown in Figs. 10~12. The fluctuation of the upper and lower capacitors voltage in Fig. 13 is less than 3 V, which is considerably less than that reported in [35]. This demonstrates the effectiveness and accuracy of the proposed MPC based




















Fig. 13. Upper and lower capacitors voltage in one phase. 8Trans. Electr. Electron. Mater. 17(6) 1 (2016): M. S. Shadlu

As can be seen in Fig. 9, the three-phase circulating currents have smaller amplitude compared to the obtained results in [35] by using the proposed MPC controller. Accordingly, pure sinusoidal upper and lower currents are attained in each arm after activating MPC, as shown in Figs. 10~12. The fluctuation of the upper and lower capacitors voltage in Fig. 13 is less than 3V, which is considerably less than that reported in [35]. This dem-onstrates the effectiveness and accuracy of the proposed MPC based controller.

In order to demonstrate the fast response of the proposed controller, a step change in the solar irradiance from 385 W/m2 to 585 W/m2 is accomplished at t=0.6 s. The single phase output voltage and current are illustrated in Fig. 16. Also, the upper and lower capacitors voltage is depicted in Fig. 17. As shown in Figs. 16 and 17, the transient response of the proposed MMC control-ler is only about 0.1 second, which is shorter than that obtained in [5].

5. CONCLUSIONS In this paper, a novel control method is proposed to control

the output currents of a PV system based on an MMC structure. In order to eliminate the circulating currents and to ensure capacitors voltage balancing control in the structure, a model predictive control (MPC) is presented. The output of closed loop controller, i.e. modulation index (n) and the output of second

controller based on MPC, i.e. the switching signals ( ( )jS t

), are summed together and a unique parameter (M) is obtained to generate the switching pulses in each individual leg. The main advantages of the proposed controller are:

* High accuracy in eliminating circulating current oscillations and output current control

* Faster response compared with the other controllers in the literature

* Capability of real-time control of PV system * Only four sensors are needed to measure the upper and lower arms voltage and current

* The simple scheme of the proposed controller reduces the computational burden.

We intend to develop a complete implementation of the pro-posed controller based on MPC on a four-leg MMC structure as a compensator in the unbalanced and distorted load conditions with a focus on electrified railways in the future work.

REFERENCES

[1] M. Latran and A. Teke, Renewable and Sustainable Energy Reviews, 42, 361 (2015). [DOI: http://dx.doi.org/10.1016/j.rser.2014.10.030]

[2] M. Gonzalez, V. Cardenas, H. Miranda, and R. Salas, Solar Energy, 125, 381 (2016). [DOI: http://dx.doi.org/10.1016/j.solener.2015.12.033]

[3] A. Marquez, J. Leon, S. Vazquez, and L. Franquelo, 40th Annual Conference of the IEEE Industrial Electronics Society (IECON) (Dallas, USA, 2014) p. 4548.

[4] G. V´azquez, P. Rodriguez, J. Sosa, G. Escobar, and M. Juarez, 40th Annual Conference of the IEEE Industrial Electronics Soci-ety (IECON) (Dallas, USA, 2014) p. 1868.

[5] H. Nademi, L. Norum, and A. Das, 42nd Photovoltaic Specialist Conference (PVSC) (New Orleans, USA, 2015) p. 1.

[6] H. Nademi, A. Das, R. Burgos, and L. Norum, IEEE J. Emerging and Selected Topics in Power Electronics, 4, 393 (2016). [DOI: http://dx.doi.org/10.1109/JESTPE.2015.2509599]

[7] A. Alexander and M. Thathan, IET Renewable Power Generation, 9, 78 (2015). [DOI: http://dx.doi.org/10.1049/iet-rpg.2013.0365]

[8] G. Ramya and R. Ramaprabha, 11th International Conference on Power Electronics and Drive Systems (Sydney, Australia, 2015) p. 336.

[9] B. Tai, C. Gao, X. Liu, and J. Lv, 41st Annual Conference of the IEEE Industrial Electronics Society (IECON) (Yokohama, Japan, 2015) p. 2932.

[10] S. Rajasekar and R. Gupta, Students Conference on Engineering and Systems (SCES) (Allahabad, India, 2012) p. 1.

[11] M. Perez, D. Arancibia, S. Kouro, J. Rodriguez, 39th Annual Conference of the IEEE Industrial Electronics Society (IECON) (Vienna, Austria, 2013) p. 6993.

[12] M. Alsadah, F. David, North American Power Symposium (NAPS) (Pullman, Washington, 2014) p. 1.

[13] R. Leon, N. Mohan, 24th International Symposium on Indus-trial Electronics (ISIE) (Rio de Janeiro, Brazil, 2015) p. 294.

[14] M. Chithra, S. Dasan, International Conference on Emerg-

Fig. 14. Active power consumption in MMC structure.

Fig. 15. Reactive power consumption in MMC structure.

Fig. 16. Output voltage and current after a step change in solar irradi-ance at t=0.6s.

Fig. 17. Upper and lower capacitors voltage after a step change in so-lar irradiance at t=0.6s.













REFERENCES































REFERENCES








































controller.In order to demonstrate the fast response of the proposed

controller, a step change in the solar irradiance from 385 W/m2 to 585 W/m2 is accomplished at t=0.6s. The single phase output voltage and current are illustrated in Fig. 16. Also, the upper and lower capacitors voltage is depicted in Fig. 17. As shown in Figs. 16 and 17, the transient response of the proposed MMC controller is only about 0.1 second, which is shorter than that obtained in [5].

5. CONCLUSIONS

In this paper, a novel control method is proposed to control the output currents of a PV system based on an MMC structure. In order to eliminate the circulating currents and to ensure capacitors voltage balancing control in the structure, a model predictive control (MPC) is presented. The output of closed loop controller, i.e. modulation index (n) and the output of second controller based on MPC, i.e. the switching signals (



(11)

(12)


(13)

(14)



( )jS t




(15)

(16)


(17)


(18)




(19)


(20)



(21)



(22)


(23)







1S

2S −+

CVC

cu−

+i

Ci

−+

CVCcu

−

+i

−+C(t).VS

(t).iS

)(a )(b

Ci

1S

2S −+

CVC

cu−

+i

Ci

−+

CVCcu

−

+i

−+C(t).VS

(t).iS

)(a )(b

Ci

( ).c Cu S t V=

( ).i S t iC =

( ) ( ). 1, 2,3Pj Pj Cu jU S t U jΣ= =

( ) ( ). 1, 2,3Nj Nj Cl jU S t U jΣ= =

( ) ( )1,2,3


j

− = + + + +

=

( ) ( )1,2,3


j

− = + − + + − +

=

( )2 2 2

1,2,3

Pj Nj P Ncirj cirj

U U V VRi iL L L L

j

−−= − − +

=

( ) ( ) ( )( ) ( ). .2 2 2

1,2,3



j

Σ Σ −−= − − +

=

,2 2

D DP N

U UV V −= =

( ) ( ) ( ).2 2 2

1,2,3



j

Σ Σ −= − + +

=

( ) ( ) ( ).2 2 2

1,2,3


cirj jS


j

Σ Σ − −= − + +

=

( ) ( ) ( ) ( )2 2

: ( ) 1, 2,3


pj nj

i i i i i ii

with i i j

+ + + − += =

= =

( )( ) ( )

2

2 21,2,3

refcirj cirjD

cirjS

jCu j Cl j

i iUR iL L T

S tU U

L Lj

Σ Σ

−− + −

=+

=), are summed together and a unique parameter (M) is obtained to generate the switching pulses in each individual leg. The main advantages of the proposed controller are:



* Capability of real-time control of PV system* Only four sensors are needed to measure the upper and lower

arms voltage and current* The simple scheme of the proposed controller reduces the

computational burden.

We intend to develop a complete implementation of the proposed controller based on MPC on a four-leg MMC structure as a compensator in the unbalanced and distorted load conditions with a focus on electrified railways in the future work.

REFERENCES




[4] G. V´azquez, P. Rodriguez, J. Sosa, G. Escobar, and M. Juarez, 40th Annual Conference of the IEEE Industrial Electronics Society (IECON) (Dallas, USA, 2014) p. 1868.







[11] M. Perez, D. Arancibia, S. Kouro, and J. Rodriguez, 39th Annual Conference of the IEEE Industrial Electronics Society (IECON) (Vienna, Austria, 2013) p. 6993.

[12] M. Alsadah and F. David, North American Power Symposium (NAPS) (Pullman, Washington, 2014) p. 1.

[13] R. Leon and N. Mohan, 24th International Symposium on Industrial Electronics (ISIE) (Rio de Janeiro, Brazil, 2015) p. 294.

[14] M. Chithra and S. Dasan, International Conference on Emerging Trends in Electrical and Computer Technology (ICETECT) (Nagercoil, India, 2011) p. 442.

[15] L. Nathan, S. Karthik, and S. Krishna, 5th India International Conference on Power Electronics (IICPE) (Delhi, India, 2012) p. 1.

[16] M. Ranjana, P. Wankhade, and N. Gondhalekar, International Conference on Green Computing Communication and Electrical Engineering (ICGCCEE) (Coimbatore, India, 2014) p. 1.

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[19] S. Rajasekar and R. Gupta, International Conference on Power and Energy Systems (ICPS) (Chennai, India, 2011) p. 1.

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[22] Y. Liu, B. Ge, H. Rub, and F. Peng, Twenty-Eighth Annual IEEE Applied Power Electronics Conference and Exposition (APEC) (Long Beach, USA, 2013) p. 714.

[23] P. Sochor and H. Akagi, IEEE Energy Conversion Congress and Exposition (ECCE) (Montreal, Canada, 2015) p. 4706.

[24] B. Luna, C. Jacobina, A. Oliveira, and I. Silva, IEEE Energy Conversion Congress and Exposition (ECCE) (Montreal, Canada, 2015) p. 6877.

[25] B. Xiao, L. Hang, C. Riley, L. Tolbert, and B. Ozpineci, Twenty-Eighth Annual IEEE Applied Power Electronics Conference and Exposition (APEC) (Long Beach, USA, 2013) p. 468.

[26] B. Xiao, L. Hang, J. Mei, C. Riley, L. Tolbert, and B. Ozpineci, IEEE Transactions on Industry Applications, 51, 1722 (2015). [DOI: http://dx.doi.org/10.1109/TIA.2014.2354396]

[27] B. Xiao and L. Tolbert, IEEE Energy Conversion Congress and Exposition (ECCE) (Pittsburgh, USA, 2014) p. 4661.

[28] V. Pires, J. Martins, and C. Hao, International Conference on Power Engineering, Energy and Electrical Drives (POWERENG) (Malaga, Spain, 2011) p. 1.

[29] A. Antonopoulos, L. Angquist, and H. Nee, 13th European Conference on Power Electronics and Applications (Barcelona, Spain, 2009) p. 1-7.

[30] M. Shadlu, International Journal of Advanced Biotechnology and Research (IJBR), 7, 1273 (2016).

[31] M. Perez, J. Rodriguez, E. Fuentes, and F. Kammerer, IEEE Trans.













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[32] P. Münch, D. Görges, M. Izák, and S. Liu, 36th Annual Conference on IEEE Industrial Electronics Society IECON (Glendale, USA, 2010) p. 150.

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[34] L. Ängquist, A. Antonopoulos, D. Siemaszko, K. Ilves, M. Vasiladiotis, and H. Nee, International Power Electronics Conference (IPEC) (Sapporo, Japan, 2010) p. 1-2.

[35] S. Ma, Y. Wang, J. Lv, and G. Yu, 17th International Conference on Electrical Machines and Systems (ICEMS) (Hangzhou, China, 2014) p. 2460-2464. [DOI: http://dx.doi.org/10.1109/ICEMS.2014.7013904]

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