Transformer Core Parameter Identiﬁcation Using

IEEE TRANSACTIONS ON MAGNETICS, VOL. 46, NO. 1, JANUARY 2010 141

Transformer Core Parameter Identification UsingFrequency Response AnalysisA. Shintemirov, W. H. Tang, and Q. H. Wu

Department of Electrical Engineering and Electronics, The University of Liverpool, Liverpool L69 3GJ, U.K.

We present a novel model-based approach for parameter identification of a laminated core, such as magnetic permeability and elec-trical conductivity, of power transformers on the basis of frequency response analysis (FRA) measurements. The method establishes atransformer core model using the duality principle between magnetic and electrical circuits for parameter identification with genetic al-gorithms. We use reference input impedance frequency responses, calculated by a well-known lumped parameter model of a three-phasetransformer and finite-element computations, to analyze identification accuracy of the method. The results verify the ability of theapproach to accurately identify the core lamination parameters with respect to the reference values. The approach can be used for pa-rameter identification of a demagnetized core with known geometrical parameters when the core lamination samples are unavailable forexperimental tests. The approach can also be employed for transformer core modeling and FRA result interpretation at low frequencies.

Index Terms—Frequency response analysis, genetic algorithm, magnetic-electric duality principle, parameter identification, trans-former core.

I. INTRODUCTION

D URING recent years, frequency response analysis (FRA)has been recognized as the most reliable condition moni-

toring technique for transformer winding displacement and de-formation assessment. It is established upon the fact that theshape of a winding frequency response at high frequencies is as-sociated with winding geometry. The appearance of clear shiftsin resonance frequencies or new resonant points on a responsemay characterize faulty conditions of windings [1].

A range of research activities have been undertaken to utilizeFRA in the development of suitable lumped parameter mathe-matical models of transformer windings [2]–[6]. In [2]–[4] ana-lytical expressions were used to estimate parameters of windingmodels based on the geometry of windings. The finite-elementmethod (FEM) was applied in [5] and [6] for accurate param-eter estimation. It was shown that the geometry of the laminatedmagnetic core and its frequency-dependent characteristics, i.e.,permeability and eddy-current losses, have to be taken into ac-count during the calculation of inductive and resistive param-eters, which clearly affect the frequency responses of a trans-former at low frequencies [4], [5], [7].

One of the techniques to model low-frequency responses as-sociated with a transformer core is to apply the duality principlebetween magnetic and electrical circuits [8], [9]. This approachhas been widely used for time domain transient studies of powertransformers [10]–[12] and subsequently was applied for trans-former low-frequency response analysis [7], [13], [14]. In theabove core simulation studies the parameters of a core lamina-tion were assumed to be constant and known. However, it is nec-essary to take into account frequency dependent behaviors of thelamination in order to accurately model frequency responses ofa transformer core.

Manuscript received November 07, 2008; revised April 14, 2009. Currentversion published December 23, 2009. Corresponding author: Q. H. Wu (e-mail:[email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TMAG.2009.2026423

In practice, magnetic core parameters are determined usingadditional experimental tests on lamination samples. For in-stance, a lamination sample taken out from a transformer wasused for precise measurements of complex permeability with asingle sheet tester in [15], [16]. However, in industry conditionsit is not always possible to obtain a core lamination sample froma stacked core of a transformer to perform additional tests.

For the case when the magnetic core geometry is known,an indirect method of estimation of small signal permeabilitywas proposed in [15]. However, this method utilizes inductancemeasurements of a transformer winding section at low frequen-cies and a 3-D FEM model of a power transformer presented in[17]–[19], that introduces complex computations and, thereby,reduces the method practicability.

Recently, evolutionary algorithms such as genetic algorithms(GAs) [20], particle swarm optimizer (PSO) [21], etc., wereutilized to identify parameters of transformer winding modelsusing FRA measurements. During a learning process, an evo-lutionary algorithm optimizes model parameters in order to re-duce the difference between real FRA measurements and corre-sponding simulations of winding models [22], [23]. One of theadvantages of this model-based approach is that evolutionary al-gorithms require only approximate range of possible values foreach parameter as initial estimates for learning. This disregardsadditional tests on transformer insulation samples, which are notalways possible to obtain.

This paper presents a novel approach for parameter identifi-cation of a laminated core of power transformers based on ref-erence FRA measurements with GA. The magnetic-electric du-ality principle is applied to establish the equivalent electricalcircuit and mathematical model of a core, which is used formodel-based parameter identification. Reference frequency re-sponses, being calculated with a well-known lumped parametermodel of a three-phase transformer and FEM computations, areutilized to explore the potential of the proposed identificationapproach.

The proposed approach is applied only for a demagnetizedcore due to the strong effect of remanent core magnetizationon FRA measurements at low frequencies, associated with the

0018-9464/$26.00 © 2009 British Crown Copyright

142 IEEE TRANSACTIONS ON MAGNETICS, VOL. 46, NO. 1, JANUARY 2010

Fig. 1. Cross section of a three-limb transformer.

magnetic core of power transformers. In fact, the amount of re-manent magnetization determines the small signal permeabilityof the core and, hence, changes of both the magnitudes and fre-quencies of the first resonances, which affects identification re-sults of core parameters [24].

II. MATHEMATICAL MODEL OF A TRANSFORMER CORE

A. Equivalent Magnetic Circuit

Consider a cross section of a typical three-limb wound coretransformer as shown in Fig. 1, where the phase A winding isexcited for frequency response measurements. Assume that allthe magnetic fluxes are confined to the magnetic material of thecore and the leakage fluxes in the air paths around the windingsare considered to be negligible. Thus, the magnetic core of thetransformer can be divided into three sections with respect touniform fluxes and of each transformer phase [9].

To establish the equivalent magnetic circuit of the core, eachsection of the magnetic core is represented by its reluctance ,which provides a relation between the corresponding flux andthe magnetomotive force required to establish that flux alongthe length of the section. The reluctance of a section is deter-mined by the magnetic parameters of lamination and the coregeometry [8], [9]:

(1)

where is the length of the magnetic flux path along each sec-tion, is the cross-sectional area of the core, denotes thecomplex effective relative permeability of the core laminationin the rolling direction, and is the free space permeability.

The complex effective relative permeability is definedusing the following expression [5], [17]:

(2)

where denotes the skin depth, represents thestacking factor, i.e., the fraction of steel in the laminated core,

and are the thicknesses of a single lamination sheet of thecore with and without insulation layer included respectively, and

denotes the local magnetic permeability.

Fig. 2. Equivalent magnetic circuit of a transformer core.

The skin depth depends on the angular frequency of themagnetic field and is defined as follows:

(3)

where is the electrical conductivity of the core lamination.The equivalent magnetic circuit of the core is presented in

Fig. 2, where and represent the reluctances of thethree paths in the magnetic core carrying magnetic fluxes

and respectively. The magnetomotive force is definedby the number of turns and the current of the excitedwinding on phase A as below [9]:

(4)

In general, the magnetic paths for the lateral phase A andphase C sections can be assumed to be equal, i.e., ,which are different from the path of central phase B. There-fore, the relations between the reluctances are expressed as fol-lows [13]:

(5)

where is the symmetry coefficient of the transformer and.

B. Equivalent Electrical Circuit

According to the topological principle of duality, the equiv-alent electrical circuit of a transformer core is derived directlyfrom its magnetic circuit. Consider the equivalent magneticcircuit of the core in Fig. 2. The circuit contains two internalmeshes (loops) in which two nodes 1 and 2 are pointed, anda reference node 0 is marked outside the circuit. These nodesare then joined by branches, one of which passes through eachelement of the magnetic circuit (dotted lines in Fig. 2) [9]. Thecorresponding equivalent electrical circuit of the core is shownin Fig. 3, where the corresponding nodes are marked.

Since the complex reluctance of each core section isnot only nonlinear and frequency dependent but also takesinto account eddy currents effect due to complex magneticpermeability (1), [17], it is represented by a corresponding

SHINTEMIROV et al.: TRANSFORMER CORE PARAMETER IDENTIFICATION USING FREQUENCY RESPONSE ANALYSIS 143

Fig. 3. Equivalent electrical circuit of a transformer core.

impedance in the equivalent electrical circuit in the formof an inductance to include a nonlinear relationship and aresistance to reflect eddy-current losses in the core. Theimpedance is given as follows [15], [16]:

(6)

where permeance is the reciprocal of reluctance.Taking into account that , the corresponding in-ductance and resistance of each section of the equivalent circuitare [16]:

(7)

In addition to inductive and resistive elements, the parallel ca-pacitances are added into the equivalent electrical circuit torepresent the total stray capacitances of windings on each limbof the transformer core [13], [14], [25]. These capacitances de-pend on the geometry of windings, and are generally the combi-nations of series intersection or interturn capacitances of wind-ings and shunt capacitances between windings and between awinding and a core [26], [27]. The dielectric losses of windingsare not considered due to their negligible contribution at low fre-quencies comparing to the eddy-current losses of the core.

Having obtained the equivalent electrical circuit of the core,it is possible to derive the expression for the input impedance ofthe core measured from the terminals of the phase A winding ofthe transformer:

(8)

where the equivalent admittances of each phase section of thecircuit are defined as below:

(9)

Fig. 4. Typical input impedance frequency response of a core model (a lateralphase winding is excited).

A similar procedure is used to derive the expressions for theinput impedance of the core taken from phases B and C of thetransformer, assuming the same number of turns of the corre-sponding excited windings, i.e., :

(10)

(11)

III. ESTIMATION OF THE EQUIVALENT CIRCUIT PARAMETERS

FROM FRA MEASUREMENTS

It is known that the very low-frequency region of the opencircuit FRA measurements of a transformer is mainly associ-ated with the properties of a magnetic core [1], [3]. Consider atypical input impedance frequency response of the core modelwhen the lateral phase A is excited. The response is calculatedusing (8) and is divided into the three frequency ranges as shownin Fig. 4. In fact, different combinations of the core model pa-rameters are mostly responsible for certain frequency ranges inFig. 4, [13], [14]. With regard to the equivalent electrical cir-cuit of a core (Fig. 3), the FRA responses in frequency range 1are mostly determined by the combination of the section imped-ances , whereas the responses in range 3 are mainly defined bythe combinations of the section capacitances . These featurescan be used for the estimation of the equivalent electrical circuitparameters from FRA measurements as discussed below.

A. Impedance Estimation

The frequency response below the first resonance frequency(range 1 in Fig. 4) is mostly determined by the combination ofthe phase section impedances since they are much lowerthan the parallel capacitor impedances of each phase


Fig. 5. Equivalent electrical circuits for impedance and capacitance estimation.

section [14]. In this case, the capacitor impedances can be ne-glected due to its sufficiently higher values. The equivalent elec-trical circuit is then simplified as shown in Fig. 5(a).

Taking into account (5) and (6), the relations between thephase section impedances are given as below [13]:

(12)

Thus, with aid of (12) the expression for the input impedancetaken from the phase A winding at low frequencies (range 1 inFig. 4) can be obtained as follows:

(13)

Hence, knowing from FRA measurements the fol-lowing parameters can be estimated:

(14)

and using (12):

(15)

B. Capacitance Estimation

A similar procedure is applied for capacitance estimation. Infrequency range 3 beyond the main resonance peaks as shownin Fig. 4, the parallel capacitor impedance of each phasesection is much lower than the corresponding section impedance

[14]. As a result, the phase section impedances can beneglected and the equivalent electrical circuit is simplified asshown in Fig. 5(b), [13].

In practice, transformer windings on different core limbshave the same design. Therefore, it is reasonable to assume thatthe parallel capacitances related to different phase windings areequal [13]:

(16)

Thus, the expression for the input impedance taken from thephase A winding in frequency range 3 (Fig. 4) is derived asfollows:

(17)

Thus, having obtained from FRA measurements the ca-pacitances can be estimated as follows:

(18)

IV. MODEL-BASED IDENTIFICATION OF TRANSFORMER

CORE PARAMETERS

In practice, the parameters of core lamination, such as localmagnetic permeability and the conductivity of the core lam-ination , are usually determined by a number of experimentaltests using a lamination sample [15], [16]. However, as men-tioned in Section I, in many occasions such tests can not be con-ducted due to the unavailability of the core lamination samples.In this study, GA is employed for the identification of the corelamination parameters utilizing reference FRA measurementsof transformer windings.

A. Foundation of GAs

GA is a powerful evolutionary optimization technique, whichis established based upon the principles of genetics and nat-ural selections [20]. The fundamental differences between GAsand traditional optimization techniques, such as the least squareoptimization, etc., is that the GAs can perform highly parallelsearch of the solution space and do not demand accurate initialestimates [28].

GAs preserve the biological terminology and operate with aset (population) of optimized parameters (analogous to genes)being coded as a finite-length strings (analogous to chromo-somes), representing potential solutions of an optimizationproblem. The population of the individuals (chromosomes)is undergone by the procedure of fitness evaluation, whichrepresents the survivability of individuals during a selectionprocedure. Then the fittest individuals are chosen as parentsfor performing crossover and/or mutation, thereby producingoffsprings, which constitute a new generation of a population.The process continues until a given termination criterion ismet or simply a certain number of generations is reached. Thefinally survived individual is treated as a variant of a desiredsolution [29].

A GA process can be briefly expressed in the form of a se-quence of operations:

1) Random generation of the initial population.2) Evaluation of individuals in the population and its fitness

values calculation.3) Performing selection procedure.4) Performing genetic operations on selected individuals.5) Replacing the previous generation by the offspring popu-

lation after the genetic operations are performed.


6) Repeating steps 2–5 until a termination criterion is met.7) Presentation of the best individual in the final population

as the GA output.

B. Parameter Identification With GA

The model-based parameter identification with GA is basedon searching for the optimal model parameters by minimizingthe difference, i.e., fitness, between reference and simulatedmodel frequency responses. Therefore, for each individual of apopulation in GA, its total fitness value is given as follows:

(19)

where and are themagnitude and phase frequency responses respectively of thereference and the simulated with the GA identified parametersinput impedances at frequency , whereis the number of frequency points involved in a GA learningprocess.

The following steps are performed for the core parameteridentification in this study.

• Experimental FRA data or simulation data derived from atransformer winding model with predefined parameters areused as reference frequency responses.

• Reference response points in a frequency range of interestare selected to create a reference dataset, being employedas training targets for GA learning.

• The initial search space for the identified parameters is es-tablished based on approximate estimations.

• GA learning is performed, in each step of which the prede-fined training dataset is compared with the correspondingvalues of the simulated frequency responses at the samefrequency points. The simulated frequency responses aregenerated using the established transformer core modelwith the parameters obtained during the GA learningprocess.

V. SIMULATION RESULTS AND COMPARISON

A. Reference Response Simulation

In order to analyze the identification accuracy of the proposedapproach, the lumped parameter model, presented in [4], [5], ofa three-phase experimental transformer (400 kVA, 15/0.4 kV)having a -Y winding configuration is employed to calculatereference input impedance frequency responses due to its highdegree of simulation accuracy in comparison with experimentalmeasurements. The geometrical dimensions of the transformerare presented in [18] and used for FEM computation of induc-tive and resistive parameters of the lumped parameter model[17]–[19]. Capacitance and conductances of the model are es-timated using the analytical expressions and measurements ofdielectric material properties presented in [6].

Fig. 6. Effective complex permeability �� in the rolling direction of a lami-nated core (real and imaginary parts).

The magnetic core effect is represented in the lumped param-eter model by the complex effective permeability of corelamination, calculated according to (2) and (3) using the fol-lowing reference parameters: mm,S/m, and [17]. As a result, the real andimaginary parts of the effective permeability in the rollingdirection of the lamination are presented in Fig. 6 as a functionof frequency according to (2).

B. Identification of Local Magnetic Permeability

The identification of the local magnetic permeability is im-plemented using the procedure for impedance estimation dis-cused in Section III-A.

The dataset for GA learning is created using the refer-ence input impedance responses in the frequency rangeof 100–300 Hz with aid of (14). Thus, GA learning is conductedusing a set of randomly generated values of to create an ini-tial population of GA individuals as explained in Section IV.The fitness evaluation of each individual in the population is per-formed by comparing , being analytically calculated using avalue of associated with the individual, with using (19).

In this study, the limits for parameter identification are estab-lished using a reasonable initial estimate of for the widelyused core lamination material. In order to show the potentialof GA learning the limits of the search space are assumed to bewithin % from the value , which is 60% more thanthe value , being used to obtain the reference responses inSection V-A. A reasonable estimate of electrical conductivity

S/m is initially selected to calculate the skin depthusing (3), which is a typical value for grain-oriented silicon

steels used for transformer core laminations [30], [31]. In fact,this parameter does not greatly affect the identification resultsas illustrated below.

The GA learning parameters are selected on the basis of nu-merous trials with various parameter combinations. The param-eters are listed in Table I. Fig. 7 illustrates the comparisons of thereference and the identified with GA magnitude frequency re-sponses of the transformer input impedance. The identified local


Fig. 7. Comparison of the input impedance magnitude frequency responses:reference and identified with GA.

TABLE IGA PARAMETERS

TABLE IICOMPARISON OF THE REFERENCE AND GA IDENTIFIED VALUES OF LOCAL

MAGNETIC PERMEABILITY (100–300 HZ FREQUENCY RANGE)

magnetic permeability , which is 1.53% more thanthe reference value .

Table II summarizes the reference and the parameters identi-fied with GA using different values of in order to analyze theeffect of its variation on identification results. The analysis ofthe table shows that the value of does not significantly affectthe identification results in a wide range of 20%–200% from thereference value , where deviations of do not exceed 2%from .

The deterioration of identification accuracy with the in-creased values of can be explained by the eddy current effectstrengthening with the increase of frequencies. This can be

TABLE IIICOMPARISON OF THE REFERENCE AND GA IDENTIFIED VALUES OF LOCAL

MAGNETIC PERMEABILITY (100–200 HZ FREQUENCY RANGE)

observed in Fig. 7, where the deviations between the impedanceresponses become larger at frequencies above 200 Hz.

To reduce the effect of on the identification accuracy, itis suggested to narrow the frequency range being used for GAlearning to lower frequencies. The results of identification ofusing impedance responses in the 100–200 Hz frequency rangefor GA learning are listed in Table III. As seen from the table,the identification accuracy of rapidly improves having onlyabout 0.01%–0.3% deviations from at different values of

, while the estimation range of is limited by 10%–200% fromthe reference value .

C. Identification of Conductivity and Capacitance

The identification of conductivity is carried out in frequencyrange 2 containing main resonance frequencies as shown inFig. 4. The reason is that the damping of the resonance peaksmostly depends on eddy-current losses characterized by theskin depth (3) and, hence, by the conductivity of the corelamination.

Similar to the previous case, GA learning is conducted using aset of randomly generated values of and for the calculationof with aid of (8). The fitness evaluation is performedby comparing with the reference dataset in thefrequency range of 800–1600 Hz (19).

As previously mentioned, the search space limits for param-eter identification are established using the reasonable initial es-timate of for the known lamination material. In order to showthe potential of GA learning the limits of the search space areassumed to be within % from the value S/m,which is 60% more than the value , being used to obtain thereference responses in Section V-A.

The initial estimate of the section capacitancesF is derived using the reference dataset in the fre-

quency range of 2300–2500 Hz (range 3 in Fig. 4) with aid of(18) as discussed in Section III-B. The value of , whichis within the range of the values identified in Section V-B, is uti-lized for calculation of during GA learning process.

The results of the GA parameter identification at differentvalues of are listed in Table IV. As clear from the table, theGA identified values of are very close to the referencewith less than 5% deviations across the range of % from

. At the same time, the identification error is only 0.2% inthe case of the reference value , being used in calculations.


TABLE IVCOMPARISON OF THE REFERENCE AND GA IDENTIFIED VALUES OF

CONDUCTIVITY AND CAPACITANCE

TABLE VINITIAL SEARCH SPACE LIMITS AND GA IDENTIFIED VALUES OF THE CORE

MODEL PARAMETERS

However, there is no reference value for , which repre-sents the total stray capacitances of windings of each phase sec-tion in the transformer core model. On the contrary, the refer-ence lumped parameter model divides windings into a groupof winding sections, i.e., discs and turns, which are representedby a number of lumped electrical elements such as disc induc-tance and resistance, capacitance between discs of a winding,capacitance between a disc and a core, etc. Thus, the referencemodel does not consider total winding capacitances as opposedto the established transformer core model used for the param-eter identification.

D. Frequency Response Simulation of Transformer Core

On the basis of the estimates of and being individ-ually identified in Sections V-B and V-C using FRA referencesin different frequency ranges, more narrow search space limitscan be established for final identification of the core parameterswith GA. These search space limits are listed in Table V. In thiscase GA learning is conducted using a set of randomly gener-ated values of and for the calculation of with aidof (8) in the frequency range of 100–2500 Hz.

As seen from Table V the final GA identified values of andare very close to the corresponding reference values having

negligible deviations in a practical sense. The identified param-eters are then used to simulate the input impedance magnitudefrequency response of phase A and B in Figs. 8 and 9 with theestablished transformer core model, where the correspondingreference responses of the three-phase lumped parameter modelare also given.

The responses in Fig. 8 show the first two resonance peaks,appearing on the frequency responses taken from the lateralphase A winding of the transformer. This can be explained bythe different flux paths through the central and the lateral limbs

Fig. 8. Comparison of the input impedance magnitude frequency responses ofphase A (LV winding) of a three-phase transformer using the core model andthe lumped parameter model.

Fig. 9. Comparison of the input impedance magnitude frequency responses ofphase B (LV winding) of a three-phase transformer using the core model andthe lumped parameter model.

of the transformer core as shown in Fig. 1. This results to thetwo different reluctances of the core equivalent magnetic cir-cuit as expressed by (5). On the other hand, only one resonancepeak appears at low frequencies on the impedance responses ofthe central phase B winding in Fig. 9 due to same flux pathsthrough the lateral limbs of the core [4].

The comparison of the responses in the two figures showsa good resemblance both in resonance frequencies and magni-tudes between the responses at low frequencies associated withthe transformer core. This shows the accurate identification oflamination parameters of transformer core using FRA measure-ments. As a result, an accurate model of transformer core is de-veloped, which can be applied to FRA result interpretation atlow frequencies.


VI. CONCLUSION

In this paper a novel model-based identification approachhas been developed to determine parameters of a demagnetizedtransformer core on the basis of FRA measurements, withoutrequirements to carry out additional experimental tests onlamination samples. Based upon the duality principle betweenmagnetic and electrical circuits, a transformer core model isestablished and employed for model-based parameter identifi-cation with GA.

For numerical study, reference input impedance frequencyresponses are obtained using a well-known lumped parametermodel of a three-phase transformer including core effect. Theinitial search space for GA learning is defined based on the esti-mated values and the properties of widely used lamination ma-terial. The simulation results show that the presented identifi-cation approach allows to determine accurate parameter valueswith respect to the reference ones, where deviations between theidentified core parameters and the reference ones are negligiblein a practical sense. The core model is further applied to sim-ulate frequency responses of different phase windings, whichshow the potential for accurate transformer core modeling.

Comparing with the previously developed methods for mag-netic parameters estimation [15], [16], the proposed approachestablishes and utilizes the frequency-dependent core model,which has a simple form and a clear physical meaning. As aresult, it possesses great practicability for FRA result interpre-tation at low frequencies.

It should be mentioned that in the current study only thelinear case without hysteresis is considered. Therefore, furtherresearch should be directed to employ a more complex modelof frequency dependent behavior of magnetic materials takinginto account the hysteresis effect [33], [34]. Furthermore, sinceonly simulation studies are conducted in this study, a further in-vestigation should needs to be undertaken to verify the proposedidentification approach with experimental measurements.

ACKNOWLEDGMENT

The first author would like to thank the Center for Interna-tional Programs for awarding Kazakhstan Presidential BolashakScholarship and JSC “Science Fund” for a financial grant withinthe frame of the “Sharyktau” competition to support his Ph.D.research in the University of Liverpool, U.K.

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Almas Shintemirov was born in 1979. He studied electrical engineering atPavlodar State University named after S. Toraygirov, Kazakhstan, and receivedthe M.Eng. and Cand. Tech. Sci. (Ph.D.) degrees in 2001 and 2004, respectively.He received the Ph.D. degree in electrical engineering and electronics from theUniversity of Liverpool, Liverpool, U.K., in 2009.

His research interests include power transformer winding modeling and con-dition assessment, power system modeling, and evolutionary computation.

Wenhu Tang (M’05) received the B.Eng. and M.Eng. degrees in electrical engi-neering from Huazhong University of Science and Technology, Wuhan, China,in 1996 and 2000, respectively, and the Ph.D. degree in electrical engineeringfrom The University of Liverpool, Liverpool, U.K., in 2004.

He was a Postdoctoral Research Assistant at The University of Liverpoolfrom 2004 to 2006. Since 2006, he has held a Lectureship in Power Engineeringin the Department of Electrical Engineering and Electronics, The University ofLiverpool, U.K. His research interests are transformer condition monitoring,power system operation, evolutionary computation, multiple criteria decisionanalysis, and intelligent decision support systems.

Henry Wu (M’91, SM’97) received the M.Sc.(Eng.) degree in electrical engi-neering from Huazhong University of Science and Technology (HUST), China,in 1981 and the Ph.D. degree from The Queen’s University of Belfast (QUB),U.K., in 1987.

From 1981 to 1984, he was appointed Lecturer in Electrical Engineering atHUST. He worked as a Research Fellow and Senior Research Fellow at QUBfrom 1987 to 1991 and Lecturer and Senior Lecturer in the Department of Math-ematical Sciences, Loughborough University, U.K., from 1991 to 1995. Since1995, he has held the Chair of Electrical Engineering in the Department of Elec-trical Engineering and Electronics, The University of Liverpool, U.K., acting asHead of the Intelligence Engineering and Automation group. His research in-terests include adaptive control, mathematical morphology, evolutionary com-putation, condition monitoring and assessment, and power system control andoperation.

Prof. Wu is a Chartered Engineer. He is a Fellow of IEE.

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