modular multilevel converter using single dc capacitor

7/28/2019 Modular Multilevel Converter using Single DC Capacitor

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A Modular Multilevel Inverter Using Single

DC Voltage Source for Static Var CompensatorsFirman Sasongko

1and Pekik Argo Dahono

2

School of Electrical Engineering and Informatics, Institute of Technology Bandung

Jl. Ganesha 10, Bandung 40132, [email protected]@konversi.ee.itb.ac.id

Abstract — Multilevel inverter has emerged as a new solution of

power converter for high power applications. Many efforts have

been done to obtain the best performance of multilevel inverter

to provide the need of power converter for high-power medium-

voltage applications. Multilevel inverter using modular-cascaded

topology with single dc voltage source is presented in this

manuscript. Inverter topology, features and control method will

be discussed. Simulation and experimental results for static var

compensator application are included to verify the effectiveness

of the proposed method.

Keywords — Modular multilevel inverter, control system, static

var compensator.

I. I NTRODUCTION

Reactive power compensation has become an indispensable

requirement to provide a better power system performance [1],

[2]. Var compensator system has three major roles: improvingthe transient stability, damping the power oscillation, and

supporting the grid voltage to prevent voltage instability. In

recent years, static var compensators are preferable to their

traditional counterpart of using rotating synchronous

condenser and mechanically switched capacitors or inductors

[3] – [6]. Static var compensator provides faster time responseto absorb or generate the reactive power. The advances of

power electronic devices, analytical tools, and micro-

computer technologies has create the more sophisticated

power converter to be used for static var compensator and

other high-power applications.

Multilevel system is especially important in high-power

applications such as Flexible AC Transmission System

(FACTS). At present, most of FACTS controllers that have

been installed worldwide are using conventional two-level

inverter modules that are interconnected by using a special

design multipulse transformer [7] – [9]. In order to reduce theswitching losses, the inverter switching devices are switched

at the fundamental frequency. The transformer is configured

in such a way so that certain low-frequency harmonics are

eliminated. The output voltage is controlled by adjusting the

dc voltage of the inverter with the consequence of slow

control response. Thus, a multilevel inverter may become an

alternative solution to achieve a simple structure converter

with a fast control response for high-power applications.

The concept of multilevel converters has been introduced

since 1975. Since then, various multilevel converter

topologies were proposed [10] – [13]. These converters aresuitable for high-power medium-voltage applications. The

main advantage of multilevel converter is that high output

voltage can be obtained without series connection of

switching devices. Moreover, better output waveforms can be

obtained without the need of high switching frequency

operation with the associated high switching losses.

Several inverter topologies are available today for

multilevel output voltage operation [10] – [12]. Diode-clamped

multilevel inverter, especially the three-level inverter, also

known as neutral-point clamped (NPC) inverter, has found

wide application in high-power medium-voltage (MV) drives.

This inverter topology has some drawbacks such as additional

clamping diodes, complicated PWM switching pattern design,and possible deviation of neutral point voltage. Another

apparent multilevel topology is the multilevel flying-capacitor

inverter which evolved from the two-level inverter by adding

dc capacitors to the cascaded switches. However, this inverter

topology has some limitations including the need of a largenumber of dc capacitors with separate pre-charge circuits and

complex capacitor voltage balancing control problem.

Cascaded H-bridge (CHB) multilevel inverter is one of the

popular converter topologies used in high-power medium-

voltage applications. It is composed of a multiple units of

single-phase H-bridge power cells. The H-bridge cells are

normally connected in cascade on their ac side to obtain

medium-voltage operation and low harmonic distortion. In practice, the number of power cells in a CHB inverter is

mainly determined by its operating voltage and manufacturing

cost. The use of identical power cells leads to a modular

structure, which is an effective means for cost reduction. In

this inverter topology, however, a number of isolated dc

sources for each H-bridge cell are needed. Thus, a complex

control method is required to ensure voltage balance in each

dc capacitor [13].

In this paper, a new modular multilevel inverter topology based on cascaded H-bridge cells is proposed. Neither



complicated transformer nor separate dc sources are required.

A single dc source is used for the whole single-phase H-bridgecells. High output voltage is accomplished by the use of

identical single-phase transformer connected in series at the ac

side. Each cell output voltage can be controlled using phase

difference between each leg. The output voltage harmonics

are minimized by controlling the phase differences of H-

bridge cells. By using fundamental switching frequency, all

H-bridge cells have identical device rating and utilizationfactor. The proposed inverter topology and also control

scheme for static var compensator are presented. Simulated

results show the effectiveness of the proposed multilevel

inverter for static var compensator application.

II. PROPOSED TOPOLOGY

Multilevel inverter can be considered as a series connection

of several ac voltage sources as shown in Fig. 1. In most

applications, the resultant of the voltage must be adjustable in

magnitude and low in harmonic contents. In high-power applications, PWM switching operation is avoided because of

switching losses problem. Thus, the inverter switching devices

must be operated at fundamental frequency. To comply with

these constraints, the following methods can be chosen:

i) Controlling the dc voltage and using a special

connection transformer to reduce the harmonics.ii) Controlling the devices gating signals to produce a

staircase waveform which control the output voltage

and reduce harmonic contents.

The first method is simple but the response is slow because

of large time constant of dc circuit. Moreover, a special

transformer connection is necessary. The second method ismore promising because of faster control response by using

controlled switching of inverter legs. Separate dc sources are

necessary if no galvanic isolation provided in the ac side.

Using many large dc electrolytic capacitors is prone to failure.

Therefore, using single dc capacitors with galvanic isolatedsystem is preferable here.

Several choices are available to use transformer as a

galvanic means. A special connected transformer can be used

to reduce the harmonics, which however, different

transformers have to be used if the number of levels is

changed. Thus, modularity of the system cannot be achieved.

V 1

V 2

V 3

V 4

V 5

V out V out

V 1

V 2

V 3

V 4

V 5

V 1

V 5

V 2

V 3

V 4

Fig. 1. Series connection and phasor diagram of several voltage sources.

The preferred system is the one without custom-made

transformer. An ordinary transformer can be used to reducethe harmonic contents by controlling the gating signals of the

inverters. Reference [13] proposes the gating pattern as the

one shown in Fig. 2 which produced a staircase waveform.

However, utilization factor of each level is different and so

does the losses of each level and cooling system requirements.

A. Circuit Arrangement Fig. 3 shows the topology of the proposed modular

multilevel inverter discussed in this paper. All single-phase H-

bridge inverter and transformer are identical, therefore, can be

considered as one module for each level. A single large dc

capacitor is connected in parallel on dc side. IGCTs or IGBTs

can be used as the switching devices. In practice, a small LCL

filter is usually connected on the ac side to reduce high-order

harmonics. As the output voltage levels increase, the filter

may be omitted.

The proposed method produces a staircase waveform by

controlling the phase angle differences among inverter levels.

In general, for N H-bridge cells, the optimum phase angle

difference is 60o/ N which associated with the order of harmonic contents of (1)

For example, in three-, four-, and five-cell system, the

required phase angle difference is 20o, 15

o, and 12

o

respectively. By using N = 5, the minimum harmonic order is

29 which can be eliminated easily by a very small filter.

5V dc

-5V dc

va1

va2

va3

va4

va5

θ5 π-θ5

π-θ4θ4

θ3

θ2

θ1

π-θ3

π-θ2

π-θ1

van

π 2π0

Fig. 2. Output voltage of cascaded multilevel inverter.



v N2

v N3

v N4

v N5

V dc v N1

a

n

v N1

v N2

v N3

v N4

v N5

v an

5V dc

-5V dc

12o

Fig. 3. Modular cascaded multilevel inverter and its waveform.

B. Output Voltage Control

Inverter cell output voltage of the proposed multilevel

inverter is determined by phase difference of each leg. Each

single-phase H-bridge inverter is operated under quasi square-

wave mode as shown in Fig. 4, ensuring the same utilization

factors of each level. The effective output voltage is controlled

by adjusting the β angle. The effective fundamental voltage of

each cell can be defined as √ ⁄ (2)

For N H-bridge cells, the general expression of phase

output voltage can be obtained as

∑ ∑

(3)

where h is odd harmonic number only. For N = 5, using

transformer ratio of 1 : r , the phase-to-phase effectivefundamental output voltage is

⁄ (4)

v1

v2

v N1 = v1 - v2

0

0

0

V dc

V dc

V dc

-V dc

β

Fig. 4. Signal waveform of each inverter leg in each cell.

It can be seen from (2) and (4) that the output voltage varieslinearly to cosines of β ⁄ 2. This feature has the advantage to

generate a simple switching control scheme.

C. Comparative Evaluation

In order to clarify the performance of the proposed modular

multilevel inverter system, a conceptual design of static var

compensator with 10 MVAR rating is used. It is assumed that

the static var compensator is designed to operate on medium-

voltage of distribution system (20 kV). The proposed

multilevel inverter design is then compared to the ones using

quad-series [9] and cascaded [13] inverter systems. Using the

most advanced power switching devices with rating up to

6kV/6kA, the dc source voltage can be as high as 3.1 kV.

Table I shows performance comparison among the three types

of static var compensator.

TABLE I

COMPARISON SUMMARY

AspectsInverter Topology

Quad-series Cascade ProposedVoltage level 11 21 21

Capacitor 1 15 1

DC voltage ±3100 V ±3100 V ±3100 V

Transformer

Complexconfiguration

-

15single phase

ΔS – ΔP = 1:2

ΔS – YP = √ :21:1

Converter

construction

Identical but not

modular

Identical

and modular

Identical

and modular

Utilization

factor equal unequal equal

Power switch 24 60 60

Control

strategies α angle

α angle and

MI

α and β

angleDC

unbalance

problem

No Yes No

Response

timeMedium Fast Fast

THD 8.7% 6.6 – 7.2% 3.6 – 7.6%



III. CONTROL METHOD

A static var compensator can be considered as voltage

source converter which connected in parallel to the power grid

through series inductance as shown in Fig. 5. The line

resistance is usually very small and can be neglected. The

objective of multilevel inverter control system is to ensure dc

voltage and reactive power flow at a desired command. When

the inverter voltage vi

is higher than grid voltage vg, inverter

current will lead the voltage by 90o

(reactive power injection).

On the contrary if the inverter voltage vi is smaller than grid

voltage vg, then inverter current will lag the voltage by 90o

(reactive power absorption). Thus, controlling the inverter

voltage magnitude means controlling the reactive power flow.Although theoretically var compensator does not exchange

active power to the grid, the inverter internal losses will cause

the capacitor voltage to deviate from its nominal value. By

adjusting the phase angle α between inverter and grid voltages,

the active current will flow in/out to keep the dc voltage

constant.

V g

V i jω LC I i

I iV g

V i

jω LC I i I i

V g

V i I i

V L

Leading Reactive Power

Lagging Reactive Power

Charging

Discharging

Power Grid

v i i i v g

Static Var

Compensator

V dc

LC

V iV L

V g

I i

α

α

Fig. 5. Static var compensator model and its operation modes.

The circuit equation for three-phase system as in Fig. 5 can

be written as

(5)

In d – q synchronous reference frame, this equation can be

written as follows:

[] [ ] (6)

where ω is system frequency; the subscript ‗d‘ and ‗q‘ are d-

axis and q-axis voltage/current component respectively.

Because the grid voltage vector is always aligned with d -

axis voltage component vgd, the q-axis component of grid

voltage vgq is always zero. The instantaneous active and

reactive power in d – q synchronous reference frame can be

expressed as [14]

(7)

From (7), the active and reactive power control can directly be determined by active and reactive current provided a

constant grid voltage. Therefore, controlling the reactive

current iiq alone is sufficient to control reactive power to the

grid. Moreover, to keep a constant dc voltage by controllingactive power flow, only the active current iid need to becontrolled. Thus, a fast current controller is desirable in this

method to achieve the system with fast dynamic time response.

A. Static Var Compensator with Proposed Multilevel Inverter

The complete control system and block diagram of the

proposed static var compensator is shown in Fig. 6. There are

two reference values in this system, which are the dc voltage

reference and q-axis current reference which

proportional to reactive power q. The control system will then

produce α* and β * commands, which will control the activeand reactive power respectively. The α*and β * angle can be

obtained from d - and q-axis voltage references as

(

) (8)

(9)

where K is a topology characteristic constant and r is the

transformer ratio. The K value will be unique for each cell

numbers as in (3) with h = 1. For N = 5, K is equal to 7.45,

while for N = 3, K is equal to 4.49.

The inverter output voltage must be synchronized to the

power grid voltage. For this purpose, a phase locked loop

(PLL) circuit is used to obtain the grid voltage angle θ . This

angle will be used for all d – q transformation process.

The dc voltage reference is compared to the actual dc

capacitor voltage which then will be processed by a PI

controller to generate the d -axis current reference . The

actual d - and q-axis currents, which obtained from inverter

currents using d – q transformation, are then compared to the

reference values and the PI current controllers will

compensate the errors. The output of the current controllers isthe desired d -axis and q-axis inverter output voltages. By

using a look up table, the required β and α angle can bedetermined.

B. Decoupled Current Control

The plant block diagram as shown in Fig. 6 implies that the

d - and q-axis currents cannot be controlled independently. To

solve the coupling problem, a feed-forward technique as

shown in current controller block diagram of Fig. 6 is used.

The actual output currents I id and I iq are multiplied by the line

reactance ωLC to produce additional signals to cancel out the

coupling effects. By using this method, the d -axis currents can



I id V id*Σ

I id*

Gcd

Current

Controller

Σ

V gd

Σ I iq

Gcq Σ

V gq I iq* = q*/V g

V iq*

ω LC

ω LC

GVdc

Σ

V dc*

V dc

I id sLC

1Σ

V gd

I iq

sLC

1Σ

V gq

Plant

V id

V iq

I n v e r t

e r M u l t i l e v e l

M

o d u l a r v i

i i

v g

LC

v g abc

i i abc

Control

System

M o d u l a r

M u l t i l e v e l

I n v e r t e r

V dc*

q*

S abc v dc

v dcSwitching

Modulator

α* β *

Proposed Static Var Compensator System

Power Grid

ω LC

ω LC

Fig. 6. Proposed static var compensator system and its control block diagram.

be controlled independently as shown in Fig. 7. The control

method for q-axis current has the same approach. The inverter is assumed to have a unity gain, so the inverter output voltage

V id is equal to the voltage reference V id*.

I id*

≈1+ K C K C sT C

Σ Σ1

sLC

V gd + ω LC I iq

Σ

V gd + ω LC I iq

I idV id* V id

Fig. 7. Decoupled current control block diagram.

From Fig. 7, the transfer function of d -axis current can be

determined as (10)

The damping ratio ζ C and undamped natural frequency ωnC

can be obtained as follows:

ζ ⁄ (11)

(12)

By using critically damped control response, the damping

ratio is ζ C = 1 and the current control gain K C and time

constant T C can be determined as

V/A with ms (13)

C. DC Capacitor Voltage Control

Single dc capacitor is used in the proposed system. Asimple control system is required to maintain dc voltage level.

By avoiding the resonance condition between dc capacitor andline reactor, reduction of the dc voltage fluctuation can be

achieved. A simple right-hand rule can be used to determine

the required capacitance for single capacitor circuit with

nominal reactive power of QVAR [13] as follows:

(14)

The dc capacitor voltage may deviate from its nominal

value because of overall losses in the inverter. The regulation

factor of dc voltage ε is defined as

(15)

This factor may range from 5-20% practically. Using the

regulation factor ε of 10% in the 10 MVAR of static var

compensator system connected to 20 kV of distributionsystem, the required capacitance C is 8.28 mF for 3.1 kV

nominal dc voltage.

If the total system losses can be expressed as D, then the

inverter active power flow can be defined as

(16)

The instantaneous dc capacitor voltage can be written as

(17)

∫ (18)



where V dc is the average dc voltage and Δvdc is the dc voltage

ripple. From Fig. 6, (16) and (18), the block diagram for dcvoltage control can be depicted as in Fig. 8 assuming an ideal

current control with unity gain.

From Fig. 8, the transfer function can be obtained as

(19)

The damping ratio ζ dc and undamped natural frequency ωndc

are given by

ζ ⁄ (20)

(21)

By using critically damped control response, the dampingratio is ζ dc =1, leading to control system parameters as follows:

(22)

IV. SIMULATION R ESULTS

To verify the proposed multilevel inverter topology as

static var compensator, the simulation using 7-level inverter

was carried out. The system configuration and system parameters are shown in Fig. 6 and Table II. The system is

connected to low-voltage distribution system of 380 V and

controlling a 5 kvar of reactive power flow. The utility voltage

is assumed to be balanced three-phase system with constant

magnitude and frequency.

I id* I id≈1+ K dc

K dc

sT dcΣ

V dc* V dc

V gd

Σ

D

1

sCV dcΣ

V dc

x

~

Fig. 8. DC capacitor voltage control block diagram.

TABLE II

SIMULATION PARAMETERS

System Voltage V G 380 V 50 Hz

Var Rating QVAR ±5 kvar

DC Voltage V dc ±97.7V

Interface Inductance LC 12% (11 mH)

Source Impedance LS 2% (1.8 mH)

Cell Number N 3

DC Capacitor C 8.337 mF

Regulation Factor ε 5%

Transformer Turn Ratio r 1:1

q

via

iia

Fig. 9. Simulated results when the reactive power is step changed.

q

vdc

Fig. 10. Simulated result of DC capacitor voltage when the reactive power is

step changed.

The simulation results of the proposed static var

compensator can be seen from Figs. 9 – 10. The system has the

capability to inject/absorb 5 kvar of reactive power. Fig. 9

shows the phase voltage and current of the proposed

multilevel inverter when the reactive power is change from 2kvar leading to 5 kvar leading and finally to 5 kvar lagging.

The inverter voltage reacts instantaneously whenever the

reactive power reference is changed suddenly. Although the

reactive power reference changes from injecting to absorbing

mode, the inverter voltage can adapt the reactive power

demand with fast time response.

The dc voltage can be kept constant at approximately 97.7

V and only a small distortion occurs when the reactive power

is changed, as can be seen from Fig. 10. The selection of

regulation factor ε will affect the distortion in the capacitor

voltage.



V. EXPERIMENTAL SYSTEM

To further validate the proposed system and its control

strategy as a static var compensator, a prototype of seven-level

modular inverter has been built and carry out the experiment

based on Table II parameters. The control system will be

implemented in dSPACE (DS1104) platform which has

MPC8240 250 MHz core processor with DSP TMS320F240

as slave. The controller can provide a powerful system for

floating point numbers calculation.

For real time evaluation of the control system, a Graphical

User Interface (GUI) will be designed using MATLAB/

Simulink and dSPACE platform as can be seen in Fig. 11. The

previously explained control scheme will be automatically processed and run in DS1104 via PCI card slot. The GUI

platform will provide the input references such as reactive

power and capacitor voltage references, and also shows the

system parameters continuously, e.g. the system voltage,

inverter voltage and current, phase angle, injected reactive

power and dc capacitor voltage.

Fig. 11. Experimental control system.

VI. CONCLUSION

This paper has proposed a modular cascaded multilevelinverter. Inverter topology, switching pattern and control

system for static var compensator have been presented in

detail. The simulation results show that the proposed

multilevel inverter has a fast dynamic response to

inject/absorb reactive power to/from the system. With the proposed control system scheme, the control response can be

adjusted as desired. Moreover, the dc voltage can be

maintained at a constant level under dynamic condition.

In general, the proposed topology has the advantages of its

modularity, equal utilization factors among inverter blocksand simple control procedure. As a single dc capacitor is used,

neither unbalance problem nor complex controllers are existed.

Thus, the proposed modular multilevel inverter provides some

features with which very applicable to low-cost high-power

applications.

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modular multilevel converter using single dc capacitor

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