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UNIVERSITY OF STRATHCLYDE

Voltage Source Converter Modeling in DC Grid and Power System

Studies: appropriateness and limitations This work is part of twenties project-work package 5 and supported by European Union Under

Seventh Framework Program (FP7)

G.P. Adam, S.J. Finney and B.W. Williams

8/28/2012

This presentation tries to identify the attributes and limitations of the existing voltage source converter modeling approaches when used to analyzed hybrid

power systems that contain ac and dc networks. The importance of such work is that it may assist power systems engineers to conduct their studies with

appropriate converter models, knowing the scopes and limitations of each modeling approach. Therefore, brief discussions on converter modeling will be

presented that include detail switch model, switching function approach, and time average mode; and limitation of each approach will be highlighted. This

work will be substantiated by comparing the steady-state and transient responses of the four and six-terminals DC grids obtained from detail switch and

average models.

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Fig. 1: Detail switch model

1. Could reproduce transients associated with fundamental

and harmonic voltages and currents, including interaction

between ac and dc sides.

2. Its switches mimic conduction of physical IGBT;

therefore, suitable for dc fault studies.

3. Suitable for wide range of studies where the detail

converter behavior is of great importance.

4. Prohibitively slow for large power system simulation.

5. AC harmonic filters must be included.

6. Not applicable for small signal stability.

Fig. 2: Ideal switch model (equivalent to switching function approach)

1. Its ideal switch representation does not permit reverse

current flow into dc side of when converter dc link is

suppressed; therefore, not suitable for dc fault studies of

traditional converters.

2. Could reproduce transients associated with fundamental

and harmonic voltages and currents. Could be used for

dynamic interactions between ac and dc sides during ac

network faults only.

3. AC harmonic filters must be included.

4. Prohibitively slow for large power system simulation.

5. Not applicable for small signal stability.

Vabc1

½Vdc

-½Vdc

0 t

Vgabc

Iabc

Va0

Zero power factor

line

Unity power factor

lineUnder excitation

Over excitation

Vc1

Vc1Vc1

Vc1

Vg

Vabc1

½Vdc

-½Vdc

0 t

Vgabc

Iabc

Va1

Zero power factor

line

Unity power factor

lineUnder excitation

Over excitation

Vc1

Vc1Vc1

Vc1

Vg

3

Fig. 3: Average model (controlled voltage source behind phase impedance)

1. This approach ignores any harmonics while

considers slow dynamics associated with power

frequency components only.

2. Could be used to analyze dynamic interactions

between ac and dc sides during ac network

faults only.

3. Not suitable for fast transients, including dc

network faults.

4. Relatively fast and suitable for transient

stability studies of medium-scale power

systems.

5. AC harmonic filters can be added to the model

to represent their effect at power frequencies.

6. Not applicable for small signal stability.

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Fig. 4: Differential equations approach

DC side dynamics, including dc voltage controller:

1

*

*

1,

* 2 2

*

2 2

1

( )

( )

1( )

mdcj

dcjk

kj

dc

idc dcj dcj

m

dcjj pdc dcj dcj dc dcjk

k k j

dcj dcjj

dj q q dj qj

dj base

qj j j dj

qj

dj qj

dVI

dt C

dk V V

dt

I k V V I

V II V I R I I

V S

V P Q VI

V V

ξ

ξ

=

= ≠

=

= −

= − + −

= − − +

−=

+

∑

∑ (1)

AC side dyamics, including current controller:

*

*

( )

( )

( )

dqj

ii dqj dq

cdqj pi dqj dq j dqj dqj

dq cdqj dqj j dqj j dq

j

dk I I

dt

V k I I i L I

dI V V R I i L I

dt L

ψ

ω ψ

ω

= −

= − + +

− − −=

(2)

1. This approach considers only power frequency

dynamics. The converter model can be

expressed in abc or d-q synchronous reference

frame. However, modelling in d-q frame is

preferred.

2. When all controllers are incorporated, it can be

used to analyze transient and small signal

stability of large power powers. Also it can be

used to analyze dynamic interactions between

converters controls in dc grid and synchronous

machines in ac sides.

3. Small signal and transient analysis can be

conducted without the need for conventional or

sequential load flow, and manual linearization

of power system equations.

4. The DC current at the converter node is set by

the local dc voltage control loop and the current

from the DC link which is a function of the

local DC voltage and the voltages at all other

DC nodes, in the steady state the local control

will force the net current into the node to zero.

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Fig. 5: Modular multilevel converter (M2C) detailed model

1. Reproduces all the transients

associated with power and

harmonic frequencies and detail

dynamic interactions between ac

and dc sides.

2. Takes into account all the

dynamics associated with

capacitor voltage balancing, phase

circulating and dc offset arm

currents.

3. Its switches mimic operation of

physical IGBTs, therefore suitable

for detail studies.

4. Prohibitively slow, therefore this

approach is not suitable for large

dc grids.

5. Not applicable to small signal

stability analysis.

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Fig. 6: Modular multilevel converter (M2C) detailed model

1. Capable of reproducing power

frequency transients and ac/dc

dynamic interactions initiated by

disturbances in the ac side.

2. It is suitable for demonstration of

M2C active and reactive power

control, and voltage support

capability. Therefore, it may be

suitable for transient stability

studies of relatively large ac/dc

power systems.

3. This approach is unable to

reproduce the transients when the

M2C dc link is suppressed.

Therefore. Not suitable for dc

network fault studies.

4. Not applicable for small signal

stability; however, it can be twig

for small signal stability.

5. Dynamics of distributed M2C cell

capacitors can be modelled by

means of ‘virtual single lumped

capacitor and reflected current

source’. This models net energy

transfer between the M2C cells

and the AC and DC networks but

neglects sharing effects.

½Vdc

-½Vdc

0 wt

Va1

VgabcVabc0

Vdc Iabc

Vce2

Vce1

iabc1

iabc2

1 1abc abcm i

2 2abc abcm i

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Fig. 7: Hybrid cascaded multilevel converter detail model

1. Models transient associated with

power and harmonic frequencies,

dynamic interactions between ac

and dc sides that could be initiated

in ac or dc sides. Also it models

cell capacitor dynamics

accurately, including dc fault

reverse blocking capability.

2. Suitable for detail studies;

however, it is prohibitively slow.

Therefore, it is not suitable for

large power systems.

0xv

0av

tω

0( )a tv

π 2π

tωπ 2π

0( )xv t

π 2π

( )HBv t

tω

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Fig. 8: Hybrid cascaded multilevel converter average model

1. Assumes ideal series active power

filter that is capable of attenuating

all the harmonics from the two-

level output voltage.

2. Suitable for ac side fault studies

of medium-scale dc grids, and

other applications that involve

manipulation of active and

reactive power exchange with ac

networks.

3. Relatively fast, therefore could be

used to model number of HVDC

links embedded in relatively large

power systems.

Va1

½Vd

c

-½Vdc

0

Va1Vc

Vdc

Vg

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Simulations illustrate appropriateness and limitation of two-level converter models

a) Active and reactive power at B1 and B2

b) Active and reactive power at B3 and B4

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Fig. 8: Waveforms illustrate responses of the detailed and average models of the two-level converter based dc grid to solid pole-to-pole dc fault at D5, with 200ms fault duration

a) Active and reactive power at B3 and B4 b) Active and reactive power at B3 and B4

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Converter 3 dc link current Converter 3 dc link voltage

Voltage magnitude at B3

Fig. 9: Waveforms illustrate steady-state and responses of the detailed and averaged models of the two-level converter to three-phase fault at G3

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Model validation of differential equations approach

(a) Six-terminal DC Grid illustrative model

(b) Active power VSC1, VSC2 and VSC3 inject into DC grid (c) Active power dc voltage regulator (VSC4, VSC5 and VSC6) inject in to AC grids 4,5 and 6

Idc1

Idc2

Idc3

Idc4

Idc5

Idc6

Ic1

Ic2

Ic3

Ic4

Ic5

Ic6

I14

I12

I23

I36

I45

I56

Vdc1

Vdc2

Vdc6 Vdc6

Vdc5

Vdc4V1

V2

V3

VSC1

VSC2

VSC3

VSC4

VSC5

VSC6

V4

V5

V6

I6

I5

I4I1

I2

I3

B1

B2

B3 B6

B5

B4

Vc2

Vc1

Vc3 Vc6

Vc5

Vc4

750MVA

400kV/300kV

Zt1=0.005+j0.2

750MVA

400kV/300kV

Zt2=0.005+j0.2

750MVA

400kV/300kV

Zt3=0.005+j0.2

750MVA

400kV/300kV

Zt4=0.005+j0.2

750MVA

400kV/300kV

Zt5=0.005+j0.2

750MVA

400kV/300kV

Zt6=0.005+j0.2

P14

P12

P45

P56P23

I25

P25

P36

P1

P2

P3 P6

P5

P4

Rc1 Rc4

Rc2 Rc5

Rc3 Rc6

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(d) Voltage magnitude at the dc nodes (Vdc1, Vdc2, Vdc3, Vdc4, Vdc5 and Vdc6)

(e) Power flow in the DC lines (P14, P25 and P36)

(f) Power flow in the DC lines (P12, P23, P45 and P56)

Fig. 9: Key results illustrate validation of the presented DC grid mathematical model against detailed model that represents each converter station by its three-phase switch model (do lines represent detail model)

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Table II: Eigenvalues demonstrate the stability of the DC grid in Fig, 1 under assumed operating condition

modes eigenvalues Damping time (s) Damping ratio

λ1,2 -359.0±j1960.1 0.00279 0.18

λ3,4 -359.2±j1208.8 0.00279 0.285

λ5,6 -359.1±j520.30 0.00279 0.568

λ7,8,9,10 -714.3 0.00140

λ11 -29.4 0.034

λ12,13 -29.3 0.034

λ14,15,16,17,18,19 -18.8±j46.3 0.053 0.376

λ20,21,22,23,24,25 -18.3±j46.5 0.053 0.366

λ26,27,28 -8.6 0.11627

λ29,33,38 -16.7 0.05988

λ30,31,32 -3983.3 0.0000251

λ34,35,40 -28.9 0.0346

λ36,37,39 -8.7 0.11494

Sample results illustrate response of M2C detail and average models to ac network faults

Active and reactive power converter exchanges with ac network

Current waveforms converter injects into ac network

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Phase voltage at converter terminal relative to supply mid-point Voltages across the M2C cell capacitors

Sample waveforms illustrate M2C detail and average models responses during ac faults

Conclusions

• There is no single voltage source converter model that could be used in all power system studies.

• Model selection must be based on the scale and type of studies need to be conducted, taking into account the model

limitations.

• Detailed converter models could be used in conjunction with simplified converter models where is appropriate to represent

part of the network needs to be investigated in detail.

• Average voltage source converter model seems to be appropriate for power systems studies of relatively large hybrid ac/dc

power systems, where the focus on the dynamics due to ac network disturbances.

• Differential equations approach appears to be suitable and efficient for transient and small signal stability studies of very large

power systems. However, this has to be confirmed. The efficiency of this approach in very large power system could be

further improved using more advanced routines from IMSL and NAG libraries.