1

A COMPARISON OF INVERTER CURRENT CONTROL AND RECTIFIER

CURRENT CONTROL FOR HVDC SYSTEMS

Dragan Jovcic,

Lecturer, Electrical and Mechanical Engineering, University of Ulster,

Newtownabbey, BT37 0QB, UK, d.jovcic@ulster.ac.uk

Abstract--This paper presents a comparison between traditional rectifier current control and a

proposed inverter current control for HVDC systems, considering both dynamic and functional

steady-state aspects. The analytical system model, implemented in MATLAB, is used for the

eigenvalue analysis and studies based on the time domain performance index. It is shown that

inverter current control has noticeable dynamic benefits particularly for long cable DC systems and

for weak inverter AC system configurations. Conventional rectifier current control is superior only

with systems having very weak rectifier AC system. Mode transition analysis fully confirms

functionality of the inverter current control method but it also reveals particular new phenomena. A

PSCAD simulation study with CIGRE benchmark model supplements salient results in the paper.

Index Terms—HVDC Transmission, HVDC Transmission control, eigenvalues and

eigenstructures.

2

1 Introduction

In order to evaluate the inverter located main current control, two types of studies are required: the

investigation of dynamics around a nominal operating point, complemented by functional mode transition

analysis. Complete analysis should also be weighed against similar studies with traditional rectifier side

controls. In the literature however, such studies cannot be found. A recent paper [2], uses inverter current

control as an option for long cable HVDC systems, nevertheless in dynamic aspects the study is based only

on time domain simulation runs. This research aims to offer generic comparison of current control (CC) at

the inverter side against traditional rectifier CC from both dynamic and functional points of view.

The motivation for this research stems from the possible benefits this controller may return:

reactive power consumption at a minimum and to enable fast rectifier responses following DC side faults.

However, considering other possible benefits with improved HVDC controls, like better dynamic stability

or improved robustness and commutation failure resilience, the above arguments should be carefully

weighed.

r

In the existing HVDC schemes, rectifier converter has been selected as the main current controlling

terminal, and normally inverter current controller is auxiliary, trying to maintain DC current at a reference

reduced by the current margin [1]. Evidently, the inverter based current controller can perform the basic

duty of regulating DC current but it is not used as the primary (steady-state) controller in conventional

HVDC. The main reasons for adopting the rectifier based current controller are: maintaining inverte

• Improvement in performance, reliability or robustness of HVDC systems,

• Expanding possible application areas for HVDC transmission,

• The uses of conventional HVDC for applications where less economically viable new HVDC

technologies have to be considered.

To investigate the above possible benefits, the main objectives of the study are:

• To confirm functionally (steady-state) and dynamically inverter current control for HVDC,

3

• To compare this control method with a typical HVDC rectifier CC, particularly for difficult operating

conditions like long DC cables or weak AC systems,

• To highlight any possible difficulties with this scheme that might occur in some applications.

It is envisaged that the results will be of particular use for future system designers but planners and

system operators should also benefit from the findings.

2 System model and approach in studies

2.1 Simulation and modeling approach

The analytical system model, as presented in [3], is employed together with MATLAB control systems

tools to perform eigenvalue analysis, frequency domain analysis and comparison by performance index, as

shown in section 3.

PSCAD/EMTDC simulation software [4] is used for the final controller testing and verification of

results. This software uses only time domain studies, which means it is not best suited for generic system

analysis or controller structure modifications. The time domain based trial and error simulation studies

involving modifying circuit parameters or varying controller structure/gains are tedious in reaching broad

conclusions.

2.2 Main circuit model structure

The CIGRE HVDC benchmark system [5] which has SCR=2.5 on both sides is used as the starting test

system. In this study, both AC systems are made equivalent to eliminate influence of AC system topology

on the results. The CIGRE rectifier AC system is employed since it is known to be difficult for control

having more pronounced second harmonic resonance [5]. Identical AC systems enable symmetry in the

total power system and therefore objective comparison of converter controls.

To further test controller robustness, a test system with lower SCR is used. The controller is designed for

the above nominal system (SCR=2.5) and it is tested with lower SCR that would correspond to a fault or

disturbance scenario. The AC system SCR is modified in a similar manner as in [6].

4

The additional test configuration reflects issues with large cable capacitance, considering approximately

500km DC cable and the method of analysis follows the one described in [7].

The test system and controller data are given in the Appendix, with the variable/parameter notation being

consistent with [1] and [6].

2.3 Controller structure

The system with the main current control at the inverter side (inverter CC) has an inverter controller as

shown in Figure 1, where all variables use common HVDC notation as given in [1]. There are two possible

modes: current control and gamma (minimum) control mode. Current control mode uses PI controller

acting on the angle beta (βcc) to regulate DC current at reference Iord. The reference extinction angle

(gamma min) is usually set at 15deg and it is regulated using PI control acting on beta angle (βmin). These

two controllers are compared using the “max” element in order to enable sufficiently high beta values to

prevent commutation failure. Because of the maximum comparison, the main inverter current controller

cannot indefinitely reduce beta. As a consequence, the inverter current controller saturates for high DC

currents. To extend the current control range with this strategy, the controller at the rectifier side has it’s

own current controller that is normally inactive and rests at the minimum limit (amin=5deg). The rectifier

controller uses higher current reference (increased by margin Im, Irm=Iord+Im) and it takes over current

control only during faults, at higher DC currents (during the inverter controller saturation).

The performance of the above control scheme is compared with a classical HVDC control structure

(rectifier CC) assuming rectifier based main current controller with gamma controller at the inverter side.

5

Ir - reference current, Iinv - measured currentmin - (min.) reference gamma, γ γ

β - measured gamma

c - constant beta

ikps

kii

skiγ

γkp

Figure 1. Inverter controller structure.

2.4 Method of studies

The dynamic system responses are analysed using the performance index J that penalizes both rectifier

and inverter direct current deviation over the time horizon T:

( ) ( )∫∫ −+−=T

rinv

T

rrec IIT

IIT

J0

2

0

2 11

(1)

where Irec is rectifier current and Iinv is inverter current. This index gives larger values for controller gains

with poor tracking of the reference. In addition, the eigenvalue location and frequency domain tools are

used in reaching the conclusions. The nominal controller gains are normally adjusted such that the system

has 5.0>ς , corresponding to an overshoot below 20%.

3 Dynamic analysis

3.1 CIGRE Model

This section compares small the signal dynamic performance of the inverter CC versus a traditional

rectifier CC.

Table 1 shows the location of four of the most influential system eigenvalues (system model is of 45th

order) for the case of inverter and rectifier current control. Observing the eigenvalue location it is seen that

both control methods enable stable system operation with similar dynamic characteristics. Further

6

inspection of the performance index in first row of Table 2 also confirms that inverter CC gives only

slightly better responses. Analyzing only the dynamic operation at the nominal operating point, it is

concluded that there are no strong preferences for either control method.

The same system configuration is further studied with respect to robustness. A number of system

parameters are varied, including AC voltage level, controller gains, PLL controller gains and the current

reference. The responses confirm a minor advantage from using inverter CC.

TABLE 1. DOMINANT EIGENVALUES FOR CIGRE MODEL

Inverter CC Rectifier CC 1. -68.2 -55±59j 2. -66±180j -62±459j 3. -68±473j -81±192j 4. -81±1012j -89±396j

3.2 Weak AC System

This section studies robustness properties, i.e. the dynamic behavior under reduction in AC systems

strength. Each AC system is individually modified to have SCR reduced to SCR=1.4 and then to SCR=1.0

with the power angle unaffected.

Figure 2 shows movement of the four eigenvalues for inverter AC system weakening. Each locus branch

starts with eigenvalue (pair) from Table 1 (1r,2r, …1i,2i,..), and consists of three positions corresponding

to SCR=2.5, SCR=1.4 and SCR=1.0. A significant difference is observed in favor of CC at the inverter

side by considering final location of eigenvalues, and particularly at lower frequencies. The branch

corresponding to 1r, representing rectifier CC, allows rapid approaching towards imaginary axis, and rapid

stability deterioration, whereas inverter eigenvalues move left along branch 1i.

The analysis of eigenvalue movement for the case of weakening rectifier AC system gives the opposite

conclusions as shown in Figure 3. The rectifier CC behaves better than the inverter CC, as demonstrated by

the low frequency eigenvalues (branches 1r and 1i). However, in this case the difference is less

pronounced since 3r also moves towards the imaginary axis and at higher frequencies the rectifier CC

7

further destabilizes the system. These conclusions are clearly confirmed using the performance index J as

shown in Table 2.

From figures 2 and 3, it is summarized that each control configuration can handle well a local

disturbance, i.e. weakening of the nearby AC system. The disturbance on the opposite line end will cause

fast stability degradation. This confirms that the inverter CC is superior for a weak inverter AC and the

rectifier CC is better if rectifier AC system is weak. Overall however, inverter CC behaves better since

better joint responses are observed for disturbance at the opposite line end.

F

re

in

-100 -80 -60 -40 -20 0-500

-400

-300

-200

-100

0

100

200

300

400

500

1i1r

1r

2i

2i

3i

3i

2r

2r

3r

3r

4r

4r

Figure 2. Movement of dominant eigenvalues with inverter SCR

reduction (SCR=2.5, SCR=1.4, SCR=1.0). “x” – Current control

at inverter side, “o” – Current control at rectifier side

TABLE 2. VALUE OF PERFORMANCE INDEX J IN

Configuration RecC

CIGRE system 7Rec. SCR=1.0 9Inv. SCR=1.0 1Long DC cable 1

-100 -80 -60 -40 -20 0-500

-400

-300

-200

-100

0

100

200

300

400

500

1r

1r

2i

2i

3i

3i

2r

2r

3r

3r

4r

4r

igure 3. Movement of dominant eigenvalues with rectifier SCR

duction (SCR=2.5, SCR=1.4, SCR=1.0). “x” – Current control at

verter side, “o” – Current control at rectifier side

VARIOUS CONFIGURATIONS.

tifier C

Inverter CC

60 682 36 1092 668 819 139 1140

8

3.3 Long DC cable System

This section investigates dynamics of HVDC system with approximately 500km DC cable. The

eigenvalue location in Table 3 and the performance index from Table 2, demonstrate similar global

performance for the two controllers. Observing further the time domain responses in Figure 4, the principal

conclusion is that each controller tightly controls local variables. The variables at the opposite end of the

system are far slower because of the large cable capacitance and effective decoupling between the rectifier

and the inverter. Furthermore, all states at the inverter side, including AC and DC variables, are well

bounded, should the inverter be selected as the main current controller. This result has significant

implications for HVDC controls since the inverter side is prone to commutation failure and it is more

important to keep the inverter variables well constrained. For commutation failure reasons therefore, the

inverter CC has great advantages over rectifier CC in the case of long DC cables even though global

stability is similar with the two control strategies.

Time (s)

0

0

20

20

40

40

60

60

80

80

100

100

120

120

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

Cur. control at inverter

Cur. control at inverter

Inverter current response

Rectifier current response

Cur. control at rectifier

Cur. control at rectifier

Iinv

(kA)

Irec

(kA)

Figure 4. System with 500km long DC cable. System responses

following a 100A reference current step change (MATLAB

Model).

TABLE 3. DOMINANT EIGENVALUES FOR 500KM DC CABLE.

Dominant Eigenvalues

Rectifier CC Inverter CC

1 -12.1 -9.1 2 -67±93j -51±399j 3 -72±414j -79±123j 4 -91

9

4 Steady-state studies

With a conventional HVDC, mode transition is well understood and it is often analyzed using static V-I

curves. The presented control scheme has the inverter based main current controller competing with the

extinction angle controller, which can lead to a current controller saturation. The mode transitions are

therefore more complex calling for more detailed studies. A new methodology that offers better insight

into HVDC mode transition is developed, and it can also be used with conventional HVDC. The study

assumes the steady state conditions neglecting dynamic transients.

Figure 5 shows a matrix of six plots describing controller mode transitions. Two of the most often

encountered disturbances are the independent variables, as shown in abscissa axes: the inverter AC bus

voltage in Figure 5 a) and the rectifier AC bus voltage in Figure 5 b). The first column therefore depicts the

system variables following variations in the inverter AC voltage, and the second column follows the

rectifier AC disturbance. Contrary to the V-I curves where voltages are analysed, in this Figure the

ordinates show the controller outputs (firing angles), since these variables determine mode transitions. The

third row is given for completeness, showing the actual steady-state value of the controlled variable (DC

current). The curves are derived using the common steady state converter equations as given in [1].

The nominal operating point would be the position A in all plots. It is located on the αmin curve at the

rectifier side and on the βCC inverter curve since inverter is the main current controller. If the inverter AC

voltage rises (Figure 5 a), the inverter controller maintains constant DC current by increasing the beta

firing angle, and the operating point moves along βCC and αmin towards E. In this scenario, the controller

can handle large disturbances, since beta increases beyond E without restriction.

If the inverter AC voltage reduces, starting from position A, the operating point moves along βCC and

αmin towards the point B. It would not be possible to indefinitely reduce beta since βCC mode is

competing with βmin mode whose purpose is to guard from a commutation failure. Because of the “max”

elements, the actual angle value is the largest of the values in the corresponding intersection curves. The

10

point B is the inverter mode transition point signifying that the controller changes to βmin mode, and the

inverter loses current control. At the point B and immediately to the left, rectifier cannot take over current

control (it remains in αmin mode) since the actual current is still below the rectifier reference (Iord+Im),

implying that rectifier is further moving the angle alpha into saturation (below αmin). To the left of the

point B, the DC current freely increases up to the value of the rectifier reference, corresponding to the point

C. The rectifier undertakes current control at the point C, which is the rectifier mode changing point.

Consequently, inside the interval B-C the current control is lost (current is not at the reference), and the

actual current value will be between Iord and Irm, determined solely by the inverter AC system voltage.

Moving further to the left, beyond C and towards D, the rectifier controls current at Irm along the αCC

curve, whereas the inverter angle moves along βmin(Irm) curve, which is the same βmin mode but the

actual current is at the higher value (Irm). Recovering back from AC voltage depression, the system will

move along the path D-C-B-A. Considering a similar scenario with a DC line fault (resembling operation to

the left of D), it is also readily concluded that this control configuration enables that the rectifier always

takes over current control, preventing a high current, and DC faults will not be more critical than with a

traditional rectifier CC.

In Figure 5 a), the nominal rectifier voltage can be considered as a parameter. A different Er will have

the same mode transition but the curves slide sidewise along the βmin(Irm) curve, as shown by the dotted

lines in the Figure.

Redirecting the analysis to the rectifier side AC voltage reduction (Figure 5 b), the system would move

from the point A towards N and the mode transition would not occur. If the rectifier AC voltage increases,

however, the inverter reduces angle beta to the point K where the inverter mode changes to the βmin mode.

A further voltage increase would similarly lead to “lost current control” in region K-L and then to rectifier

current control (αCC) to the right of the mode changing point L. The phenomenon of lost control (B-C and

K-L) is not in itself dangerous from the stability point of view but an asymptotic stability does not exist.

Since in this region the current is bounded on both sides, by the inverter CC on the lower side and by the

11

rectifier control on the higher current side, a real instability cannot occur. The current value can simply

“float” in the zone between Iord and Irm, depending only on the actual inverter/rectifier AC voltage.

330340350360370380390048121620330340350360370380390353637383940414243

330 340 350 360 370 380 39035

36

37

38

39

40

41

42

43

in

v (d

eg

)β in

v (d

eg

)β

βn A

B

CD

E

βmin (Iord)

βmin (Irm)

βcc

αre

c (d

eg

)330 340 350 360 370 380 390

0

4

8

12

16

20

αnαre

c (d

eg

)

AB

C

D

E

αcc

αmin

330 340 350 360 370 380 3901.9

2

2.1

2.2

2.3

Irec,

Iinv

(kA)

Irec,

Iinv

(kA)

Ei (kV) Er (kV)

AB

CD

E

Ein

Iord

Irm

310 320 330 340 350 360 37035

36

37

38

39

40

41

42

43

310 320 330 340 350 360 3700

4

8

12

16

20

310 320 330 340 350 360 3701.9

2

2.1

2.2

2.3

A

A

A

N

N

N

K

K

K

L

L

L

M

M

M

Ern

Iord

Irm

βmin (Irm)

βmin (Iord)

βccαmin

αcc

βn

αn

nominal ErIncreased Er

Inverter current control

Inverter current control

Rectifier curr. control

Rectifier curr. contr.

a) Inverter side disturbance b) Rectifier side disturbanceIordIrm Irm=Iord+Im

- Current reference at inverter - Current reference at rectifier

αcc Alpha in current control mode Beta in Gamma control with

Gamma control with

α

β

min

min(Irm)

Alpha minimum

Beta in min(Iord) Iord

Irmβ

Figure 5. Steady -state mode transition with inverter current controlled HVDC systems.

12

The exact AC voltage interval B-C (or K-L) is very small, less than 1% of Ein (or Ern), because of the

high steepness of B-C (or K-L) curves. This phenomenon occurs also with a conventional HVDC although

rarely since the rectifier AC voltage is normally more stable.

The next important observation with this control strategy is that the system recovery after large inverter

AC voltage depressions will always pass through αCC mode (D-C-B-A path). This mode controls the DC

current at Irm and as a result, during transients, current will be controlled at higher values and at final

recovery stages it will be attracted downward to the reference value Iord. As a consequence, a steeper post-

fault current recovery is expected leading to additional transient over shooting, when compared with

conventional rectifier CC HVDC.

5 Simulation studies

This section complements the above study of inverter CC using PSCAD/EMTDC simulation. Figure 6

shows the system step responses with a 500km long DC cable. As predicted theoretically, variables at

inverter side (inverter DC current in the Figure) are tightly controlled whereas the responses at the rectifier

side are much slower.

In Figure 7, the inverter CC is specially designed for extremely weak inverter AC systems (SCR=1.0)

and digital simulation confirms excellent responses. As predicted in Figure 2, stability is not jeopardized

and responses are very fast. The foremost conclusion in the analysis is that with very weak inverter AC

systems, the inverter CC is far superior.

Figure 6. System with 500km DC cable (Rec SCR=2.5, Inv SCR=2.5). Simulation response following a

-100A (2000A->1900A) reference current step change.

13

Figure 8 is a large disturbance system response, which confirms good recovery. In this case, it is seen that

the system transiently passes through αCC mode (between 0.1 and 0.4s) as predicted earlier, and the

current is transiently controlled at Irm, as confirmed by the slight overshoot in the top graph (just below

0.4s). The shape of the recovery curves is therefore different from present HVDC schemes and different

interactions with other power systems may be expected

6 Nominal operating parameters

Figure 7 may be used to determine a nominal operating point, i.e. to select nominal beta and operating

AC voltage.

The distance A-B is a design parameter and it should be sufficiently large to allow room for the control

variable beta to respond to usual disturbances. On the other hand, increasing the A-B distance increases

reactive power consumption. In the particular case a margin of 3 degrees is chosen that would correspond

to the 4.5% nominal Ei reduction (horizontal distance A-B). The dynamic simulation (taking into account

beta overshooting) also confirms that 3 degrees is sufficient and that mode transition does not occur with

over 3.5% Ei variation. It should be noted that with a typical HVDC system the difference between 15deg

(αn) and minimum limit of 5deg corresponds to only 3% AC voltage compensation. The reactive power

consumption is also compared with a typical HVDC system. It is calculated by overall summing of

rectifier and inverter requirements. The results show that if the rectifier is operated with αmin, the increase

at the inverter side is compensated and a very similar overall demand exists as for a typical HVDC scheme.

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2Time (s)

Irec,

Iinv

(kA)

Figure 7. System with Rec SCR=2.5, Inv SCR=1.0 (original cable). System response following a -100A

reference current step change.

14

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.900.5

11.5

22.5

33.5

44.5

Irec,

Iinv

(kA

)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.91020304050607080

Beta

(de

g)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90

20406080

100120

Alp

ha (d

eg

)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

050

100150200250300350400

Time (sec)

Ei (k

V)

Figure 8. System Rec SCR=2.5, Inv SCR=2.5 (original cable). Simulation responses following a three-

phase 5-cycle fault on inverter AC bus at 0.1s.

7 Conclusions

Comparing only the small-signal dynamic performance between inverter current control and rectifier

current control for a typical HVDC system, the study reveals some small advantage from using the inverter

current control method. However, dynamic analysis of a weak inverter AC system configuration, which is

not uncommon with HVDC systems and also corresponds to the conditions with AC faults, reveals

significant benefits of using current control at inverter side. Considering the inverter commutation failure

aspects, similar benefits of inverter CC are evident, and particularly for long DC cable HVDC systems.

Taking dynamic point of view, this study deduces that rectifier CC has advantages only in the case of very

weak rectifier AC systems.

Functional analysis of mode transition fully confirms the feasibility of using an inverter as the main

current controller. With inverter CC it is more often possible to “lose” current control for certain

disturbances in a very small voltage region, but this does not imply consequences for the system stability.

The paper concludes that inverter current control can be equally considered as the main current control

method in future HVDC projects.

15

8 Appendix, test system data

Rectifier CC: Ern=340kV, Ein=348kV, βn=βc=41deg, kpr=8.24e-4rad/kA. kir=68.68rad/kAs. kppll=1,

kipll=5. (αn≅15deg)

Inverter CC: Ern=340kV, Ein=360kV, αn=5deg, kpi=4.4e-4rad/kA. kii=36.6rad/kAs. kppll=1, kipll=5.

(βn≅41deg) (kpi=1.2rad/kA. kii=108.6rad/kAs in Figure 7).

Weak AC system: SCR=1.4, L1=0.26H; R2=2800Ω; Weak AC system: SCR=1.0, L1=0.35H;

R2=3600Ω;

Long DC cable (500km): Cdc=426e-6F. Rdcr=Rdci=7.5Ω. Rectifier CC: kpr=5.5e-3rad/kA.

kir=45.8rad/kAs. kppll=0.05, kipll=0.25, Inverter CC: kpi=0.132rad/kA. kir=32.97rad/kAs. kppll=0.5,

kipll=2.5

References

[1] Kundur,P Power System Stability and Control McGraw Hill, Inc 1994. Pp 500-514, pp 485-495,

[2] M.Meisingset, A.M.Gole, “Control of capacitor commutated converters in long cable HVDC-

Transmission” IEEE PES Winter meeting 2001.

[3] D.Jovcic N.Pahalawaththa, M.Zavahir, April 1999 “Analytical Modeling of HVDC-HVAC Systems”

IEEE Trans. on PD, Vol. 14, no 2, pp.506-511.

[4] Manitoba HVDC Research Centre, PSCAD/EMTDC Users Manual 1994, Tutorial Manual

[5] M. Szechman, T. Wess and C.V. Thio. "First Benchmark model for HVDC control studies", CIGRE

WG 14.02 Electra No. 135 April 1991 pages: 54-73.

[6] D.Jovcic N.Pahalawaththa, M.Zavahir, May 1999, “Inverter Controller for HVDC Systems Connected

to Weak AC Systems” IEE Proceedings - Generation, Transmission and Distribution, Vol. 146, no 3,

pp. 235-240.

[7] D.Jovcic, “Control of HVDC systems operating with long DC cables” IEE Conference on AC-DC

Transmission, Nov. 2000, pp113-8

16

Biography

Dragan Jovcic obtained B.Sc (Eng) degree from the University of Belgrade, Yugoslavia in 1993 and a

PhD degree from University of Auckland, New Zealand in 1999. He worked as a design Engineer in the

New Zealand power industry in 1999-2000. Since April 2000 he has been employed as a lecturer with

University of Ulster, UK. His research interests lie in the areas of control systems, HVDC systems and

FACTS. Dr Jovcic is IEEE PES and CSS member.