Multilevel modular converters for off-shore wind farm HVDC

transmission system

Valentin Plyusnin

Under supervision of Prof. Dr. F. Silva

Dep. of Electrical and Computer Engineering, IST, Lisbon, Portugal

April 2014

Abstract - The aim of this work is to design a

decentralized DC capacitor voltage balancing

controller for high voltage multilevel modular

converters in direct current cable transmission

systems within and from off-shore wind farms to

inland. The high voltage direct current (HVDC)

system has been designed to transfer electric

power from off-shore generators to inland

substations. Carried out simulations of 81-level

converter system included the stress testing of

developed decentralized algorithms in order to

confirm their performance. Additional closed loop

power control system has been developed and

implemented. It was demonstrated that the

developed decentralized converter system is able

to balance the capacitor divider voltages and can

operate on a reduced subset of levels to provide

redundancy. Functionality of the whole HVDC

system has been tested by simulation of the

dynamics of its parameters within the specified

values.

Introduction

The high voltage direct current (HVDC) systems

are becoming more widely used in networks for

electric power transmission and distribution from

off-shore wind farms to inland due to their

advantages in comparison to other solutions.

These systems are characterized by lower losses

and the absence of reactive power problems. This

means that there is no need to use an additional

equipment for correction of power factor or

compensation of reactive power. However, the

necessity of additional equipment for conversion

of electric power generated in AC mode makes

expensive the use of HVDC system on short

distances. When the distance increases larger than

80 km this solution becomes economically

advantageous [1].

The concept of Modular Multilevel Converter

(M2C) [5] is increasingly used in the HVDC

transmission systems since this new design offers

better characteristics and increased efficiency.

Limited working space available on off-shore

stations imposes restrictions on the size of

converters and requires certain design features for

further minimization. Unfortunately, most of the

investigated multilevel converters topologies

(diode-clamped type (NPC), capacitor-clamped

type (flying capacitors)) does not meet these

requirements [2, 5]. Unlike other systems, M2C

satisfies to these requirements due to its modular

structure. Besides this point, a lot of other

important aspects have to be taken into account.

Main requirements are: the fast and independent

control of active and reactive power flow, the

operation without bulky passive filters, the black

start capability and the option of extending the DC-

network to more than two stations. At severe fault

conditions and disturbances, including short

circuits, the DC-side must be managed fast and

safely [2, 3, 4].

This paper includes 5 sections. A description of

M2C is given in the first part. Second part provides

a description of the proposed voltage control

techniques and introduces a new decentralized cell

selection algorithm to balance capacitor voltages.

In the third section power injection control is

developed. Simulation results are presented in a

fourth section and finally, conclusions are drawn in

the last part.

1. Multilevel Modular Converter (M2C)

1.1. Principle of M2C topology

The modular multilevel converter (M2C) is a

new type of voltage source converter (VSC) for

medium or high-voltage DC power transmission

[4]. Figure 1 presents the M2C circuit topology

which is formed by 2-level cells (SM). These cells

are externally driven in order to obtain the

required multilevel output voltage waveforms.

Each converter half-arm creates discrete voltage

levels between zero and power supply value U. The

sum of both half-arm voltages gives the output

voltage in range of [U, -U].

The N-level converter output voltage is given

by (1), where is a discrete variable (2) and single

cell capacitor voltage uci can be calculated from (3).

uo = U (1)

{ 1 , N 3

N 1 , , 0 , ,

N 3

N 1 , 1 } (2)

uci = UdcN 1

(3)

Figure 1b schematically presents an equivalent

circuit for converter arm modelling.

1.2. Calculation of M2C single arm parameters

Since a three-phase M2C converter can be

considered a three-phase balanced system, the

single phase equivalent model is here used to

derive transmission power. Furthermore, the

converter output voltages have nearly sinusoidal

waveforms, so it can be approximated by an AC

voltage source (V1), as it is shown on Figure 2, in

which the equivalent circuit of M2C arm connected

to the grid is illustrated.

It is important to note that protection chokes

arm inductors, which are inserted in each half-arm

to limit the AC-current whenever the DC-Bus is

short circuited (fault-condition), are not

considered [4], since the circulating current is

usually small enough.

Figure 1a Three-phase schematic of M2C Figure 1b equivalent circuit of M2C single arm

Figure 2 Equivalent circuit of M2C single arm connected to the grid

Current I is given by:

I =V1 V2jXL

(4)

The AC power flow between the two sources is

given by the following equations [1]:

P12 = V1rms V2rms sin

XL (5)

Q12 = V1rms2 V1rms V2rms cos

XL (6)

The phase difference angle expression (7) can be

obtained from (5) and (6).

= acos (V1rmsV2rms

P

P2 + Q2) + atan2(Q, P) (7)

In order to avoid problems in the series

connection of semiconductors in each cell,

according to the manufacturers available power

devices, 3 kV voltage cells were assumed. DC input

and AC output voltages (U and V1rms) for 81-level

converter (single phase) can be calculated using

(1)-(3).

Figures 3a, 3b present temporal evolutions at

steady state conditions of output current and

voltage.

Cell capacitors were designed accordingly to

(8), as in [6].

C = ict

Vc (8)

According to (8), the maximum displacement

current that flows through the capacitor

corresponds to the arm current, which can be

calculated from [7].

1.3. Lower losses and efficiency of M2C

The efficiency is an important parameter of the

M2C. All power losses have to be identified and

taking into account in simulations. The efficiency of

the M2C can be given by (9), where the input

power (denominator) is represented by the sum of

the output power (Po) and the power losses (Plosses)

[9].

=Po

Po + Plosses (9)

In this study the losses of the cell DC capacitors

and arm inductors can be included, if significant

[8], by considering the respective resistive terms

associated to the semiconductor on-state

resistances. Therefore, Plosses is a sum of the

semiconductor on-state and switching losses. The

on-state losses (PLon) are characterized by the

semiconductor on-state resistance (Ron) and the

root mean square value of the arm current Irms:

PLon = Ron Irms2 (10),

As it is shown in [8], the switching losses are

dominant. To evaluate these losses the dissipated

energy in each switching (11) is given as:

Wpcn = Vcemax ipcn tr+tf

2 (11),

where the semiconductor fall and rise times (tf and

tr) are provided by the manufacturer, Vcemax

corresponds to the maximum cell voltage value

and ipcn (red curve in Fig. 4) is the current that

flows through the cell in the switch instant.

Figure 3a M2C output current (81-level converter)

Figure 3b M2C line-to-neutral output voltage (81-level

converter)

Since half of the output current flows in each arm

[7], the switching power losses of the

semiconductors are given by:

PT2=

WpT2

T2

= Vcemax IcavT2

tr + tf2

(12)

The developed approach to calculate M2C

losses will be used in section 3 for the

determination of a 25-level M2C efficiency.

2. M2C Control Method Description

2.1. Sigma-Delta Modulator

To obtain the desired converter output voltage

level, a Sigma-Delta modulator based on PWM

modulation technique (Fig. 5) is used. In this PWM

modulator the areas of the modulating reference

voltage (vref) and of the scaled converter output

voltage (vout) must be equal during one period,

therefore the error between vref and vout signals is

integrated (13). When the result of (13) exceeds

specified limits, the voltage level is increased or

decreased, as it is shown in Figure 6.

1

TC vref vout

TC

o

dt = 0 (13)

The reference voltage is generated in external

control system designed in section 3.2.

2.2. Cell capacitor voltage balancing technique

A proper cell selection algorithm is necessary

to ensure the cell capacitor voltage tracks a

reference value, together with low switching

frequency for each cell [3].

Capacitors can be charged or discharged

respectively upon the sign of the current that flows

through. Since there are redundant levels (several

cell combinations are possible for the same level

realization), selection of different cells, can be

made based on cell capacitor voltage comparison.

Thus if the current sign is positive, cells should be

ordered increasingly (low to higher capacitor

voltages) and ordered in the opposite if the current

sign is negative. It is important to notice that each

M2C half-arm currents have different signs,

therefore the sorting should be made separately

for each half-arm. As it can be seen in Figure 7,

once the algorithm is implemented, cell capacitor

voltages are maintained within specified margins.

With this voltage balancing centralized

method, all cells voltage need to be compared in

order to obtain an accurate result.

Figure 5 Sigma-Delta control

Figure 6 Modulator output level (1) and error (2) signals

Figure 4 - M2C output current and single cell switching

instants

This implies the use of a very sophisticated central

control unit (CCU), capable of making a fast signal

processing.

2.3. Decentralized control of the M2C

The new proposed decentralized cell capacitor

voltage control methodology allows to each M2C

cell to define its own control. As a result, each cell

is capable to decide on its respective state based

on the comparison of cell voltage with another cell.

This means that the required input data could be

significally decreased (level, cell voltage, another

cell voltage) resulting in a simplification through

cooperation of the controller unit.

Behavior of the developed algorithm for

decentralized controller can be divided for 2 parts.

In the first part input variables are evaluated.

Current sign is detected and cell voltage

comparison is made. The result obtained in this

part refers to the cell selection, made in pairs of

cells. This decision will be updated in the second

part of the algorithm, which refers to guarantee

the desired converter voltage output level. Second

part decision is based on the evaluation of internal

variables - cell number and counter A. According to

the level desired it is possible to know how many

cells should be in DC voltage mode. Counter A

variable, which is transmitted from cell to cell,

permits to conclude how many cells behind the

evaluated cell are already in this mode. Once

known the cell number, the output level and the

counter A value, the number of cells that should

have already been turned on can be calculated.

With this information, final decision about the cell

state is taken. Figure 8 shows the flowchart of the

decentralized algorithm.

With this new strategy, modular controllers

process a small amount of data each. It is

important to notice that cell voltage comparison

isnt made between random cells, but there is a

specific configuration that guarantees the correct

performance of these controllers. With this

configuration, nearly equal switching frequencies

of each cell were observed.

From [10], it is known that each cell needs

duplex optical-fiber (OF) cables to transmit the

data to the CCU. With this new autonomous cell

concept, only one OF cable is needed to transmit

the information about the desired voltage level.

Tests on single phase converters up to 81 level

were performed. Figure 9 shows that this new

control methodology permits to maintain the cell

capacitor voltages satisfactory balanced even in

unfavorable performance conditions, such as

redundant operation with low switching

frequency.

Figure 7 Cell capacitor voltages of 9 level converter

3. HVDC system

3.1. Calculation of the HVDC system

parameters

HVDC system consists of a wind farm and grid

circuits (RLe), two M2C converters operating in AC-

DC and DC-AC modes, two transmission power

cables and DC-Bus capacitors. All these

components are schematically shown in Figure 10.

Some extra power components (i.e. smoothing

coils) are added. In this small example, it is

assumed that 29 turbine wind farm (2 MW each)

Figure 8 - Flowchart of the decentralized algorithm

Figure 9 Low frequency redundant operation of 81 level

M2C with 21 levels

generates 56 MW of electric power, which is

transmitted by submarine power cables to the in-

land substation. The calculated system parameters

are presented in Table 2.

Additional active and reactive power controls (PQ system) have been developed in order to minimize the deviations in power values.

Table 2 HVDC system parameters

WIND FARM

Pfarm 56 MW

V 35.5 kV

IRMS 743.6 A

Imax 1051.6 A

L 7.4 mH

R 0.2

GRID

Pgrid 54 MW

V 35.5 kV

IRMS 717 A

Imax 1014 A

L 7.2 mH

R 0.21

M2C 1

N (number of levels) 25

Vcell 3047.5 V

Ccell 11.5 mF

99.5%

M2C 2

N (number of levels) 25

Vcell 3000 V

Ccell 11.3 mF

99.6%

DC cable

l (line length) 120 km

RL 0.7372

LL 0.084 H

UDC 72 kV

Ceq (DC-Bus eq. cap.) 0.84 F

3.2. Power injection control

To provide effective HVDC operation the PQ

system must monitor and control the output

currents (i1, i2 and i3) and DC-side voltage (Udc) (Fig.

9). Following the approach described in [1, 6] the

output currents in dq reference frame are obtained

solving the system (14), which describes the

processes of Figure 11.

{

diddt

= R

L id +

1

L (L iq + d Udc ed)

diq

dt=

R

L iq +

1

L ( L id + q Udc eq)

(14)

In (14), d and q are modulation indexes which,

after the transformation to 3-phase reference

frame, will be sent as input signals to the Sigma-

Delta controller. Active power injected into the grid

depends on the direct current component (id) (15).

The quadrature current component (iq) is related to

the reactive power which should be kept around

zero (15).

{p = ed id + eq iqq = ed iq + eq id

{p = ed idq = ed iq

(15)

The equivalent M2C model in dq coordinates is

shown in Figure 12. For the DC-side the following

equation is obtained:

C dUdcdt

= d id + q iq UdcReq

(16)

Figure 10 The schematic HVDC system

Figure 11 HVDC grid-side schematic

Figure 12 Equivalent M2C model in dq reference frame

Once decoupled applying

{Hd = (L iq + d Udc ed)

Hq = ( L id + q Udc eq) (17),

multiple input multiple output (MIMO) system in

(14), similarly to [6], single input single output

system (SISO) (18) is obtained.

{

diddt

= R

L id +

1

L Hd

diq

dt=

R

L iq +

1

L Hq

(18)

Applying Laplace transform to (14) and (16) results

in transfer functions (19) and (20) which are

represented by block diagrams in Figures 13 and

14.

id,q(s) = Hd,q

sL + R (19)

Udc(s) =Req

s Req Ceq + 1 (d id + q iq) (20)

C(s) block in Figures 13 and 14 represent the

corresponding current and voltage PI controllers

which are described in [6], so that the respective

gains (Kpi,v, Kii,v) are given by (21) and (22) [6].

{Kii = n

2 L

Kpi = 2 n L R (21)

{

Td =

1

2 n

Kiv =n2 Td

d Req Kpv = Kiv Req Ceq

(22)

The Idref signal in Figure 14 serve as input

reference signal for the current control system (Fig.

13). The output signals of the whole control system

are 2 modulation indexes in dq reference frame

(23).

{

d =

Hd + L iq

Udc

q = Hq + eq + L id

Udc

(23)

Using Park and Concordia transforms on (23) one

can obtain Sigma-Delta input sinusoidal

modulation indexes for each phase.

4. Simulation Results

This section presents HVDC system with PQ

control and 25 level M2C converters modelled in

Simulink environment. The results are presented in

2 separate parts. The first part characterizes the

inland grid-side, while another one refers to the

offshore wind farm-side.

4.1. Grid-side

The simulation results for the output voltage

and current are shown in Figures 15a and 15b. 25-

level sinusoidal output waveform is obtained by

each arm of the converter. Voltage and current

total harmonic distortion (THD) were of 3.69% and

1.43% respectively. These THD values are

acceptable according to the high voltage

standards, needing almost no filtering.

Cell capacitor voltages (Figure 15c) are

stabilized around the reference value after a short

transient. This confirms the reliability of the

developed decentralized controllers.

Figure 13 Closed loop current control system

Figure 14 Closed loop voltage control system on DC-side

Figure 15a Grid-side 25 level M2C converter output

voltages (1-1.08s)

Figure 15b Grid-side 25 level M2C converter output currents

(1-1.08s)

Figures 15d-15g demonstrate the operation of

PQ control system. After a short transient the

output currents become balanced, and the

converter input voltage (UDC) is stabilized on the

specified reference value. Active power injected

into the grid is regulated to 54 MW. The reactive

power is kept around zero.

4.2. Wind farm-side

Figures 16a-16f demonstrate the wind farm-

side operation. THD values for the converter

output voltages and currents were of 4.01% and

1.43% respectively.

Similarly to section 4.1, cell capacitor voltages

(Fig. 16c) are balanced after a short transient.

Figure 15c Grid-side 25 level M2C cell voltages (0-3s)

Figure 15d Grid-side 25 level M2C converter output currents

(0-1s)

Figure 15g Reactive power injected into the grid (0-3s)

Figure 15f Active power injected into the grid (0-3s)

Figure 15e Underground DC power cable voltage (0-3s) Figure 16b - Wind farm-side 25 level M2C converter

output currents (1-1.08s)

Figure 16c Wind farm-side 25 level M2C cell voltages (0-3s)

Figure 16a Wind farm-side 25 level M2C converter output

voltages (1-1.08s)

Use of PQ control system provides fast

stabilization of the wind farm-side M2C output

currents at the wind farm active power kept equal

to 56 MW and the reactive power around zero (Fig.

16d-16f).

5. Conclusions

In this work an innovative algorithm for

decentralized balancing and control of M2C cell

capacitor voltages is presented. Tests

demonstrated suitable performance of converters

with up to 81 levels and revealed that this new

technique can assure M2C redundant operation

even with low switching frequency. Developed

methodology for decentralized control makes it

possible to provide the cell autonomy using

decentralized controller units decreasing the

required number of fibre-optical cables.

HVDC system based on two 3-phase 25-level

converters operating in both DC-AC (wind farm-

cable) and AC-DC (cable-grid) modes has been

designed. Additional PQ control also has been

developed to minimize the deviations of system

input/output powers (0.1%). Achieved

efficiencies of the converters were of 99.5% and

99.6%. The obtained current THD were 1.43% for

both converters, while voltage THD achieved of

4.01% for wind farm-side and 3.69% for grid-side.

The usefulness of the designed system has been

proved.

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Figure 16d Wind farm-side 25 level M2C converter output

currents (0-1s)

Figure 16e Active power injected into the DC power cable

(0-3s)

Figure 16f Reactive power injected into the DC power cable (0-3s)