I. INTRODUCTION

The increasing use of HVDC transmission systems has made ita competitive alternative to AC transmission systems. AlthoughHVDC transmission systems have many advantages over AC trans-mission systems, such systems are used primarily in specializedcircumstances due to their cost and inherent difficulties to operatewith weak AC systems [1].

Traditionally, HVDC transmission systems use PI controllerswith fixed PI gains. Such controllers work well for perturbationswithin a small operating range. However, when AC systems areweak, the HVDC systems are prone to repetitive commutation fail-ures under disturbances, which may lead to the instability and col-lapse of the DC link.

To overcome above-mentioned problems, some advanced con-trollers have been proposed. However, it has been shown that dueto the absence of insight into system performance under large dis-turbances, modern control methods (i.e. adaptive control, slidingmode control) may actually be ineffective and even degrade theperformance because these controllers need an accurate plantmodel and the algorithms used are complicated [2].

Incremental Fuzzy PI Control of a HVDC Plant

Recently, extensive research in the area of intelligent systems,due to their ability to mimic human beings, has drawn more atten-tion for applications in power systems. Among the intelligent sys-tems, Neural Networks (NNs) have been applied due to their abilityto acquire information and to learn through training [3]. FL hasbeen used to handle uncertainties for large non-linear systems [4].The insensitivity of intelligent controllers to the mathematicalmodel of the systems enables us to improve dynamic performanceof HVDC transmission systems especially when connected withweak AC systems. The NN-based controllers developed in [5, 6]used simple feed forward NN architecture to control the current ofrectifier of an HVDC transmission system under typical systemperturbations and faults. FL based approaches for the on-linescheduling of the control parameters are presented in [7, 2, and 8]to cope with non-linearity and uncertainty. Both NN and FL controlresults show their advantages over the conventional control.

While interesting techniques and results have been presented inthe above-mentioned publications, there is room for improved per-formance. Using the different rule bases for tuning PI gains, it ishoped that FL controllers will improve the control performance.

The objective of this research is to utilize FL techniques forHVDC systems under various disturbances. Specifically, the goal isto improve transient response performance to stabilize the system.In order to achieve this objective, an IFGSPIC is studied. In sectionII, a HVDC model is briefly presented. In section III, analysis of aFL controller is provided and new fuzzy control rules are proposedwith respect to scheduling PI gains. In section IV, a comparativestudy is conducted on the performance of a FL controller and aconventional PI controller via simulations under the EMTP RVsimulation environment. In section V, conclusions are presented.

II. HVDC SYSTEM MODEL

The model used in the research is a 6-pulse bipolar system, i.e.it consists of positive and negative poles in the converter station. A6-pulse system is used for faster computation purposes only. TheHVDC system model (Fig. 1) consists of three sub-systems:

1. Sub-system 1: This part is the rectifier AC system. Itincludes a constant voltage, constant frequency source and equiva-lent impedances. Harmonics filters tuned at 11th, 13th, and highpass frequencies are used in the AC side. A Short Circuit Ratio(SCR) of either 3.8 or 2.3 is used by selecting system parameters torepresent either a strong or a weak system respectively. The ACbus bar voltage rating is 230 kV.

2. Sub-system 2: Two 0.35 H smoothing reactors are usedbetween rectifier and inverter. The nominal DC line voltage Vd atpoint G is 440 kV. The DC current Id of the link is 1600 A. Thenominal value of DC power Pd is 704 MW.

3. Sub-system 3: This part is the inverter DC system. It is sim-plified as a battery (440 kV) with a diode as focus is on rectifier.

J. Qi, nonmember, V.K. Sood*, Senior member, IEEE, V. Ramachandran, Fellow, IEEE

Concordia University, Montreal, QC (Canada)

* Email:vijay@ece.concordia.ca

Abstract - This paper investigates a Fuzzy Logic (FL) basedcurrent controller for a High Voltage Direct Current (HVDC)plant connected to a weak AC system under the EMTP RV sim-ulation environment. A typical HVDC system is modeled with adetailed representation of the converter, converter controls andAC system. An Incremental Fuzzy Gain Scheduling Propor-tional and Integral Controller (IFGSPIC) is used for the recti-fier current control. The current error and its derivative aretaken as two parameters necessary to adapt the proportional(P) and integral (I) gains of the controller based on fuzzy rea-soning. Two different fuzzy rule bases are designed to tune thePI gains independently. The fuzzy control rules and analysis ofIFGSPIC are presented. To improve performance, the IFG-SPIC is designed like a hybrid controller that combines theadvantages of a FL and conventional PI controllers. Duringtransient states, the PI gains are adapted by the IFGSPIC todamp out undesirable oscillations around the set point andreduce settling time. During the steady state, the controller isautomatically switched to the conventional PI controller tomaintain the control stability and accuracy. Performance eval-uation under AC fault and set-point step change is studied. Aperformance comparison between the conventional PI control-ler and hybrid IFGSPIC is made. Results from the various testsshow that the proposed controller outperforms its conventionalcounterpart in each case.

Keywords: FL Controller; Gain scheduling; EMTP RV

Proceedings of the2005 IEEE Conference on Control ApplicationsToronto, Canada, August 28-31, 2005

WA5.1

0-7803-9354-6/05/$20.00 ©2005 IEEE 1305

III. FUZZY LOGIC CONTROLLER

A. Fuzzy Rule-based Systems

A fuzzy rule-based system is composed of the following fourcomponents: fuzzifier, inference engine, defuzzifier and fuzzy rulebase.

Fuzzy singletons are used as fuzzifiers.

where x' is a crisp input value from a process.

The Larsen inference engine is used because it has a simpleand efficient computation.

where x and y are inputs, and z is output, A, B, C are fuzzy sub-sets, and µ presents a membership function (MF).

A center average defuzzifier is used for defuzzification.Finally, a closed form representation of the fuzzy system can beachieved as follows:

When unbiased MFs, i.e. symmetrical triangles and trapezoidswith equal base and 50% overlap with neighboring MFs, are used(Fig.2), the following condition can be achieved

otherwise

xxifxA 0

'1)(' (1)

)()()(),,( zyxzyxiiii CBAR

(2)

n

iBA

BA

n

ii

yx

yxzyxf

ii

ii

1

1

'

)()(

)()(),( (3)

n

i BA yxzyxfii1

' )()(),( (4)

This simplifies the computation for EMTP RV modeling and isthe primary reason that the Larsen inference engine and centeraverage defuzzifier are chosen here.

A set of fuzzy if-then rules constructs the fuzzy rule base.

Fig. 2: Membership functions of e, e and u

B. Incremental Fuzzy Gain Scheduling PI Controller

A conventional PI controller, in conjunction with a set of fuzzyrules and a fuzzy reasoning mechanism to tune the PI gains online,is used in this paper. Comparing with other FL controllers, such asPI-like fuzzy controllers, this kind of controller has obvious advan-tages [9]. By virtue of fuzzy reasoning, these types of fuzzy PI con-trollers can adapt themselves to varying environments. Based onthis principle, an IFGSPIC is proposed.

IFGSPIC is similar to the conventional gain scheduling (GS)controller in changing the gains for varied operating conditions orprocess dynamics. IFGSPIC provides a FL supervised PI controlscheme in which parameters of a PI controller are updated online asa function of the operational conditions of the controlled plant, thusimproving the behavior of fixed gain conventional PI controller. Itcombines the advantages of both FL and conventional PI control-lers. The closed-loop system of IFGSPIC is shown in Fig. 3.

Fig. 3: Closed-loop system of IFGSPIC

(x)

x

NB NM NS ZE PS PM PB

-1 -0.5 0 0.5 1

PlantPI

Fuzzyreasoning

Fuzzyreasoning

r ye, e

Kp

Ki

RectifierDCfilter

To Bipolar DC system

AC Filters

Invert er

Subsystem1 Subsystem2 Subsystem3+

AC1

1 2YY

1 2YgD

3-p hase +

-gates

6-pulse bridge+

L 1

3-p hase +

-gates

6-pulse bridge

+

L3

+

R3

DC1

DC2

+RL1

D1

+

R1

D2

RLC

+

RLC1

RLC

+

RLC2

RLC

+

RL C4

+

L5

+C5

+

R5RLC

+

RL C3

+

L 4

+L2

+

R2

+

R4

re c_ star_ bus

rec_d elta_ bus

rec_bus

G ND

rec_bu s2re c_ sta r_f i ri ng

re c_ del ta _fi rin g

Fig. 1: HVDC system model

G

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The IFGSPIC controller has the following form:

where Kp0 and Ki0 represent initial PI gains, which can beobtained by a Ziegler-Nichols tuning method, Genetic Algorithms,etc., and proportional and integral fuzzy-control matrices areexpressed by CVp and CVi whose elements are fuzzy gains as func-tions of error and change of error. The fuzzy coefficients kp and kiare scaling factors.

In eq. (7), there are two terms: one is of conventional PI control,uc(t), and the other is of incremental output coming from fuzzy rea-soning, u(t). Combining the fuzzy reasoning with the conventionalPI control within the framework, the IFGSPIC can properly sched-ule PI gains to improve the conventional PI controller's perfor-mance.

The rule base design of IFGSPIC is based on the desired tran-sient and steady state step responses. The expected incremental out-put values, which are the fuzzy-matrix elements, are deducedaccording to the tendencies of error and error sum as shown inTables I and II. In designing the integral fuzzy matrix CVi, for

example, the error sum term is almost always positive

for a step up change. Therefore, the element of integral fuzzymatrix CVi should be negative to suppress an overshoot and positiveto overcome an undershoot.

C. Implementing FL controller Using EMTP RV

To implement FL controller using EMTP RV, several buildingblocks in the control library of EMTP RV are used. Fig. 4 gives anexample of the detailed scheme of the FL controller with four rules.

),(0

eeCVkKK pppp (5)

),(0 eeCVkKK iiii(6)

)()(

)(),()(),(

])()([)()()(

0

000

0

tutu

deeeCVkteeeCVk

deKteKdeKteKtu

c

t

iipp

t

ip

t

ip

(7)

de )(

As indicated previously, FL controller has four parts: fuzzification,fuzzy rule base, fuzzy inference engine, and defuzzification.

IV. SIMULATION RESULTS ANALYSIS

A. Test Plant

To examine the transient as well as the steady state behaviors ofcontrollers, a fourth-order test plant with the following transferfunction was used:

To compare the controllers' performance, the following perfor-mance measures were used: rising time (tr), percent maximum over-shoot (%OS), 5% settling time (ts), integral of the squared error(ISE) and integral of the absolute error (IAE) [10].

The initial parameters of the conventional PI controller weredetermined by Ziegler-Nichols method: Kp=0.45×Kr=2.304,Ti=0.85×Tr=2.321, and Ki=Kp/Ti=0.992. The parameters Kr=5.12and Tr=2.73 were obtained experimentally.

The initial value of PI gains of IFGSPIC were selected to beKp=1 and Ki=0.992. Comparing to the PI controller, the Kp of theIFGSPIC was reduced to 1 from 2.304 in order to reduce the over-shoot and settling time. The initial value of integral gain, obtainedfrom the Ziegler-Nichols method, was kept unchanged. When thesystem enters steady state, the output of IFGSPIC was zero, so theinitial value of integral gain would keep the system at high accuracyand have fewer tendencies for system oscillation. Thus, the IFG-

Table I: Fuzzy Rules for Computation of CVp

e(k)/ e(k) NB NM NM ZE PS PM PBNB PB PB PB ZE NM NS ZENM PB PB PB ZE NS ZE PSNS PB PB PM ZE ZE PS PMZE PB PM PS ZE PS PM PBPS PM PS ZE ZE PM PB PBPM PS ZE NS ZE PB PB PBPB ZE NS NM ZE PB PB PB

Table II: Fuzzy Rules for Computation of CVi

e(k)/ e(k) NB NM NM ZE PS PM PBNB NB NB NB NB NM NS ZENM NB NB NB NM NS ZE PSNS NB NB NM NS ZE PS PMZE NB NM NS ZE PS PM PBPS NM NS ZE PS PM PB PBPM NS ZE PS PM PB PB PBPB ZE PS PM PB PB PB PB

3)3)(1(27)(

sssG (8)

Tab1

Tab2

Tab3

Tab4

PROD12

Product1

PROD12

Product2

PROD12

Product3

PROD12

Product4

Gain1

1

Gain2

-1

Gain3

1

Gain4

-1

SUM

1234

SUM

e

de

CEN

EP

CEP

EN

r1

r4

r3

r2

u

Fig. 4: Scheme of FL controller using EMTP RV

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SPIC is also a hybrid controller i.e. at transient state, it is a FL con-troller to get a faster response and in the steady state, it is aconventional PI controller to obtain high accuracy [9].

From Table III and Fig. 5, it can be seen that the IFGSPIC hasthe better performance, i.e. a faster response and a smaller over-shoot when a step input is applied.

B. HVDC Plant

In order to test the effectiveness of the proposed controller onthe HVDC plant, both the FL and conventional methods were sim-ulated and the results were compared with different Short CircuitRatio (SCR) AC systems. The behavior of the controllers in con-trolling the desired current for a current order step change and athree-phase rectifier fault was studied.

1) Step change in rectifier current order, Iref

HVDC systems are well known for their fast controllability totransmit the desired DC power, or to modulate the DC power toimprove the stability of an attached AC system. One measure offast controllability is usually verified by considering the current

Table III: Comparison of Performance of the Controllers

Type tr(s) %OS ts(s) ISE IAEPI 1.54 35.9 8.35 1.063 2.129

IFGSPIC 1.92 2.10 1.72 0.816 1.073

Fig. 6: PI control for 30% step change in Iref (SCR=3.8) Fig. 7: FL control for 30% step change in Iref (SCR=3.8)

Fig. 8: PI control for 30% step change in Iref (SCR=2.3) Fig. 9: FL control for 30% step change in Iref (SCR=2.3)

Fig. 5: Comparison of step responses of the controllers

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reference tracking performance. Therefore, the DC link powerincrease or decrease can be treated as a normal disturbance. Theobjective of the control is to keep the system in operation with fewtransients in DC link power under such a disturbance.

The response of the current controllers to a relatively large stepchange of 30% to the current order, Iref, are shown in Figs. 6, 7, 8and 9. The reference is step decreased at 0.3s from 1 to 0.7 pu andthen step increased at 0.45s back to 1.0 pu.

a) Strong System (SCR=3.8)

From Figs. 6 and 7, it can be seen that both PI and FL control-lers offered satisfactory performance as the rectifier side AC sys-tem was strong. However, the FL controller had a better transientperformance than the PI controller.

b) Weak System (SCR=2.3)

When the rectifier AC system was weak, the system collapsedfor the conventional PI controller (Fig. 8) since multiple commuta-

tion failures took place. However, the FL controller (Fig. 9) wasable to make a quick recovery after one commutation failure fol-lowed by application of the Voltage Dependent Current Limit(VDCL) protection. The application of the VDCL causes the cur-rent order Iref to be reduced to 0.3 pu. On recovery of the DC volt-age, the current order Iref is ramped up to 1.0 pu. This shows theadaptability of the controller to a change of operating conditions.Therefore, it has an acceptable transient and tracking performance.

2) Three Phase Fault at Rectifier End

When a 3-phase AC voltage fault takes place at the rectifierside, it causes the loss of the DC voltage. At this time, the VDCLprotection circuit is triggered. A 3-phase fault at the rectifier ACbus results in commutation failure of converter valves. During thefault the DC current drops to zero due to the lack of commutationvoltage. The zero current and zero power condition leads to a com-plete collapse of the DC link power. After the fault is cleared, thecurrent controller takes action, which influences the DC link opera-tion. Figs. 10, 11, 12 and 13 show (a) super-imposed 3-phase AC

Fig. 13: FL control for three-phase fault (SCR=2.3)Fig. 12: PI control for three-phase fault (SCR=2.3)

Fig. 10: PI control for three-phase fault (SCR=3.8) Fig. 11: FL control for three-phase fault (SCR=3.8)

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signals Va, Vb, and Vc, (b) super-imposed current order Iref andDC current Id, and (c) DC voltage Vd for PI and FL controllers.

a) Strong System (SCR=3.8)

The responses of the current controllers to a three phase ACfault at the rectifier bus were shown in Figs. 10 and 11 for a strongAC system. The PI controller (Fig. 10) was able to follow theVDCL ramp but Id had large spikes and overshoots. With the FLcontroller (Fig. 11), the response of the FL control was superior tothat of the PI controller. Due to its adaptability, DC current Id couldtrack VDCL better and had small spikes or almost no overshoot.DC voltage Vd was smooth and had smaller amplitude oscillations.Since DC current Id had the large oscillations under the PI control,there was a possibility that commutation failures would take place.

b) Weak System (SCR=2.3)

When the rectifier AC system was weak, the system collapsedagain for the conventional controller (Fig. 12) even though it hadthe VDCL protection circuit. For the FL controller (Fig. 13) itshowed a much better recovery with excellent tracking ability andfaster response.

V. CONCLUSIONS AND FUTURE WORK

In this paper, a method combining FL with a conventional PIcontroller is proposed and applied to the current controller of aHVDC plant. A performance comparison between the two types ofcontrollers showed that the robustness and adaptation of the pro-posed FL controller is better. For a strong AC system at the HVDCconverter, both controllers have an acceptable performance. Butwhen the AC system is weak (an increasingly important require-ment for such plants), the HVDC system is prone to collapse withthe conventional controller while the FL controller has a satisfac-tory performance.

The FL controller will also be used in the inverter side of theHVDC plant for future work.

VI. APPENDIX

A. Rectifier end

Data for the AC filter at the rectifier end (230kV) is:

n 11th 13th high passR (ohms) 0.63 0.63 82.6L (H) 0.02783 0.01952 0.003846C (uF) 3.009 3.009 4.573

The equivalent impedances at rectifier end AC system:

SCR R (ohms) L (H)3.8 (88 deg) 0.25 0.062 2.3 (88.7 deg) 0.25 0.103

B. DC subsystemL = 0.35 H, R = 2.5 ohmsVd = 440kV, Id = 1600A, Pd = 704MWDC filter: R = 1 ohm, L = 0.2814 H, C = 1uF

C. TransformersY-Y: 230/205.45 kV and Y-D: 230/205.45 kV

VII. ACKNOWLEDGMENT

Authors acknowledge funding received from the CanadianNational Sciences and Engineering Research Council (NSERC).

VIII. REFERENCES1. V. K. Sood, “HVDC and FACTs Controllers,” Kluwer Academic Pub-

lishers, 2004, ISBN 1-4020-7890-0.[2]. P.K.Dash, A.C.Liew, and A. Routray, “High-performance controllers

for HVDC transmission links.” IEE, Proc.-Gener. Transm. Distrib.,Vol. 141, No. 5, September 1994.

[3]. S. Haykin, “Neural Networks: A Comprehensive Foundation.” 2nded. New York: Prentice-Hall, 1995.

[4]. Li-Xin Wang, “A Course in Fuzzy Systems and Control,” PrenticeHall PTR, 1997.

[5]. V.K. Sood, N. Kandil, R.V. Patel, and K. Khorasani, “Comparativeevaluation of neural-network-based and PI current controllers forHVDC transmission.”, IEEE Transactions on Power Electronics, Vol.9, No. 3, pp. 288-296, May 1994.

[6]. K.G. Narendra, V.K. Sood, K. Khorasani, and R.V. Patel, “Investiga-tion into an artificial neural network based on-line current controllerfor an HVDC transmission link.”, IEEE Transactions on Power Sys-tems, Vol. 12, No. 4, pp. 1425-1431, Nov. 1997.

[7]. P. K. Dash, A. Routray, and S. K. Panda, “Gain Scheduling AdaptiveControl Strategies for HVDC Systems Using Fuzzy Logic,” Proceed-ings of Int. Conf. on Power Electronics, Drivers and Energy Systemsfor Industrial Growth, 1995, Vol. 1, pp 134-139.

[8]. A. Daneshpooy, A. M. Gole, D. G. Chapman, and J. B. Davies, “FuzzyLogic Control for HVDC Transmission.” IEEE Transactions onPower Delivery, Vol. 12, No. 4, October 1997.

[9]. J. Qi, V.K. Sood, V. Ramachandran, “Modeling a Fuzzy Logic Con-troller for Power Converters in EMTP RV.” International Conferenceon Power Systems Transients (IPST'05) in Montreal, Canada on June19-23, 2005.

[10]. R. C. Dorf and R. H. Bishop, “Modern Control Systems.” AddisonWesley Longman Press, 8th ed., 1998.

IX. BIOGRAPHIES

Jian Qi was born in Tianjin, China, on Sept. 15, 1960. He received B.S. andM.S. degrees in 1983 and 1990 from Mechanical & Electrical Branch ofTianjin University, Tianjin, China and Harbin Institute of Technology, Har-bin, China, respectively. He has studied in Concordia University, Montreal,Canada since 2003. His research interests are intelligent Control Applica-tions, Power Electronics, and Embedded Systems Design.

Vijay Sood is an Adjunct Professor at Concordia University, Montreal. Heis a Member of the Ordre des ingènieurs du Québec, a Senior Member ofthe Institute of Electrical and Electronic Engineers (IEEE), a member ofIEE (UK) and a Fellow of the Engineering Institute of Canada. He is theManaging Editor of the IEEE Canadian Review (a quarterly journal forIEEE Canada). He is a Director and Treasurer of IEEE Montreal Confer-ences Inc. which provides funding for organizing conferences in Montrealregion. He is also a Director of the IEEE Canadian Foundation.

Venkatanarayana Ramachandran is a Professor in Concordia University,Montreal, Quebec, Canada. Previously, he worked in Indian Institute of Sci-ence, Bangalore, India and Technical University of Nova Scotia, Halifax,Canada. He is the author/coauthor of five well received text-books and aresearch monograph entitled “Some Aspects of the Relative Efficiencies ofIndian Languages: A Study from Information Theory Point of View”. Hehas published extensively in Signal Processing, and Circuits and Systems.He is the recipient of several awards for educational activities, including theOutstanding Engineering Educator Award of IEEE (Canada). He is a Fellowof IEEE, IEE (India), IETE, IEE (U.K.) and the Engineering Institute ofCanada.

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