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Power System Flicker Analysis and Numeric Flicker Meter Emulation X. Yang, Member, IEEE, and M. Kratz

Abstract— This paper presents a methodology for flicker propagation analysis, numeric IEC flickermeter emulation and flicker source modeling. The main results of this study are: • To create a distribution load model by which the flicker propagation from HV to MV can be studied, • To build numeric IEC flickermeter with improved algorithm (demodulator and nonlinear classification), • To build simplified actual disturbance source models (electric arc furnace, welding machine, motor starter, etc), which can be used in frequency domain and load-flow flicker assessment. The complexity of nonlinear models for simulating the dynamic behavior of arc furnaces and welding machines is well known. For this reason, previous works are generally based on time domain solutions. In this paper, a simplified approach has been studied by using RMS value-based modeling. The models have been validated against experimental results and site measurements. After integration of these models and a numeric flickermeter in a frequency domain software, it is possible to simulate almost all low frequency electrical disturbances with very short computing time and to survey interactions among them, for example, between voltage dip and flicker. Index Terms— Frequency domain modeling, flicker source models, IEC flickermeter, flicker transfer ratio, welding machine, electric arc furnace (EAF).

T

I. INTRODUCTION

HE main purpose of this paper is to simplify flicker phenomenon modeling and propagation analysis in distribution and transmission systems. Flicker phenomenon can be performed by a time domain approach [10][11][12] [13][14], but our study is focused on RMS value-based analysis by frequency domain software or load-flow software in order to reduce computation time. It is composed of distribution load model for flicker propagation analysis, simplified flicker source modeling and numeric flickermeter emulation. The developed numeric flickermeters and load models have been validated by measurements effectuated on different industrial sites. Two case studies have been detailed at the end of this paper.

Manuscript received November 27, 2006. IEEE PES Conference Power Tech 2007, 1-5 July 2007, Lausanne, Switzerland X. Yang is with R&D, Electricité de France, 92141 Clamart, France. ([email protected]). M. Kratz is with R&D, Electricité de France, 92141 Clamart, France. ([email protected]).

II. FLICKER PROPAGATION ANALYSIS FROM TRANSMISSION SYSTEM TO DISTRIBUTION NETWORK

In electric power system, voltage fluctuations can propagate from transmission to distribution systems with some level of attenuation. Field measurements and experimental researches have revealed that a number of base loads assisted in attenuating flicker as it propagates from its source to lower voltage levels that supply such base loads. ). Authors [3] give some empirical flicker transfer ratios from EHV to HV to MV to LV and another CIGRE Task Force C4.108 will continue working on this topic. Arc furnace

Pst = 1 Grid

Distribution loads

Substation transformer

225kV

Pst = 0.81

20 kV

PQ

Fig.1: Flicker propagation from HV to MV network

For a given substation (Fig. 1), when power supply voltage fluctuates, a distribution load can behave very differently according to its own nature: the variations of its active power P and reactive power Q are more important than the grid voltage’s ones. In other words, when voltage goes down, the overall distribution load impedance increases and the relative voltage dip crossing substation transformer decreases consequently. This is the observed flicker attenuation phenomenon. Flicker is mainly caused by variation of Q because the network impedance is generally inductive, an important dQ/dV makes considerable flicker attenuation effect. The studies [4] show that a great number of loads have high dQ/dV, i.e., a small voltage fluctuation can cause an important variation of reactive power (important current variation), which brings about flicker attenuation effect: TABLE I: DISTRIBUTION POWER VARIATION VERSUS VOLTAGE FLUCTUATION

Load class characteristics Industrial sector Commercial sector Residential sector

dP/dV 0.18 1.3 1.5

dQ/dV 6.0 3.1 3.2

The results from the recent research [6] indicate that the induction motor helps attenuate modulating frequency components that are present in the supply voltage subsequently leading to an attenuation of the overall flicker. While there is no dedicated load model to simulate flicker propagation, our research has been focused on creating a

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simplified distribution load model based on dP/dV, dQ/dV and a first order high-pass filter. At each step of simulation, voltage variation dV is calculated by instantaneous voltage V and mean value voltage Vm. Afterwards, power variations dP and dQ are defined from dV by initial coefficient Kv (see table I) and they are sent through a high-pass filter G(s) in order to take into account of the duration of voltage variation effect (load response time). The obtained power variations dQu and dPu will be used to modify the load equivalent impedance model during the simulation. s ⋅ Tf (1) dQu = dQ ⋅ G (s) = K v ⋅ dV ⋅ G (s) = K v ⋅ dV ⋅ 1 + Tf s Voltage measuring

V

High-pass filter

Load model P

dV

Q

block 2 in order to complete the existing squaring demodulator defined in IEC61000-4-15. In fact, the use of a squaring demodulator [1][2] is to reproduce the fluctuations of RMS values. If RMS voltage values are directly used as input of flickermeter, the squaring demodulator is redundant because in RMS value calculations, flicker frequencies have already been integrated and demodulated. A full wave rectifier demodulator needs just an absolute value calculation, so that computation time is shortened a little here and particularly there is no second harmonic side band component as in a squaring demodulation process. Flowchart of Fig. 4 shows that the demodulation type is chosen by the nature of input signals in developed numeric flickermeters. Squaring demodulator

Wave form

V = Ut x Ut

dPu, dQu

dP, dQ

Full wave demodulator

Fig. 2 : Principle of flicker behavior modeling of distribution load

This model has been built and implanted in a load-flow simulation software and validated thanks to a large number of theoretical simulations and on the field measurement (see case study B). III. EMULATION OF IEC FLICKER IN TIME AND FREQUENCY DOMAINS

Based on the analogical IEC flickermeter (Fig.3), there are more and more digital flickermeter integrated in power quality measuring devices[7][8][9]. Although there is no international standard giving detailed technical description for the numeric flickermeter, the digitalized analogical IEC flickermeter has well been accepted by utilities and customers in power quality studies and monitoring. Block

RMS value

B. Over sampling in Z_transfer of Butterworth filter Numeric flickermeter is generally built from analogical IEC flickermeter by means of Z-transfer [5]. Following formulas shows the frequency domain transfer function of the first band-pass filter (Butterworth type) in block 3: 3

H(s) =

ω c2

∏

(2)  π (2k − 1)  2 s 2 + 2. cos  . ω ⋅ s + ω c  c  2n  The transfer function (2) can be converted into its numeric form with sampling period Te : k =1

3

k =1

with: u = In time domain flickermeter emulation, i.e., the input is waveform signal; there is no particular problem. If sampling frequency is high enough compared to the analyzed signal, the IEC61000-4-15 compliance test will be accomplished successfully on an emulated numeric flickermeter. After performing a time domain numeric flickermeter emulator in C++ language, our study has also been focused on flicker calculation by means of RMS voltage evolution. Using RMS values is an easier way to simulate and estimate flicker level with short computation time. In order to optimize calculation, several modifications have been done in original IEC flickermeter blocks. A. Demodulation based on full wave rectifier One of the accomplished improvements is to add a fullwave rectifier demodulator (as used in AM radio receiver) in

V = Ut

Fig. 4 : Two demodulators

H ( Z ) = ∏ a 0k .

Fig. 3 : Function blocks 2 to 5 of IEC61000-4-15 flickermeter

Flickermeter algorithm: blocks 3, 4, 5

(1 + Z −1 ) 2 1 + b1k . Z −1 + b2k . Z −2

(3)

1 1 , ak = , α = 2.cos  π ( 2k − 1)  , 0 k  2 n  1 + u.α k + u2 tan(π . f c .Te )

b1k = 2. a 0k .(1 − u2 ) , b2k = a 0k .(1 − u.α k + u 2 ) , ωc = 2πfc If RMS voltage values are used for flicker calculation, modification of sampling frequency is necessary in performing the formula (3). In fact, RMS values are often calculated during each period of fundamental frequency (or half period in certain power quality meters). In consequence, the sampling frequency of the input signal the flickermeter is equal to one or two times of fundamental frequency. An over sampling process in this case has to be done in Z-transfer function of the Butterworth filter in block 3 of a numeric flickermeter. In fact, because of the the cut frequency of this filter fc = 35Hz, it is crucial to increase the sampling frequency > 2*35Hz in order to ensure the stability of Ztransfer function. In our application, we have fixed Te of block 3 equal or smaller than a quarter of fundamental period which is equivalent to an over sampling frequency > 200Hz,

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Z-transfer function of this filter works correctly and has been tested for all flicker’s frequencies generated by a digital signal generator. C. Nonlinear classification In block 5 of IEC flickermeter, a non-linear classification unit has been developed in order to shorten computation time and reduce substantially memory occupation. These modifications make it possible to calculate one Pst value during only one data scan without iteration and remove scale changer from original IEC flickermeter. In block 5, A 4000 double floating data table is used to build the Cumulative Probability Function (CPF). The main interest of this numeric flickermeter emulator is to calculate flicker level Pst without important data storage. This is very important when using several flickermeters in different points of a simulated grid. D. Frequency domain flickermeter Our research interest is also put on studying off-line frequency domain IEC flickermeter that works on the Fast Fourier Transform (FFT). FFT windows’ width has to be set according to the input signals. For a repetitive flicker phenomenon, FFT windows has to cover the lowest flicker frequency, but for un-known or isolated event such as voltage dip, FFT window width should be extended in order to reduce error (Fig. 5). Our tests have been done from 60 to 300 seconds.

Fig. 5 : Function blocks of frequency domain IEC flickermeter

One of the main advantages of a frequency domain flickermeter is to adapt easily other arbitrary shaped weighting filter responses. It will be very easy to adjust and modify the transfer function if there is a future evolution in international flicker standard amendment or in new lighting bulb flicker assessment. Therefore, the main disadvantage of FFT-based flickermeter is huge memory occupation. Two numeric IEC flickermeter emulators have successfully been accomplished (one in time domain and another one in frequency domain). Laboratory simulations and computations from site recordings show these two flickermeters are compliant with IEC61000-4-15 requirements and can work with either waveform or RMS value as input. However, if RMS voltage values are used as input signal, it is only possible to calculate flicker effect aroused by voltage fluctuations < 25 Hz. In numeric flicker level simulation, it is enough as the main frequency range of most industrial loads

3 such as arc furnace and welding machine is lower than 25Hz. For the particular case where the flicker frequencies are > 25Hz, waveform signal will be used as flickermeter’s input. TABLE II gives a short summary of these two numeric flickermeters. TABLE II: SUMMARY OF TWO TYPES OF NUMERIC FLICKERMETERS

Time domain Advantage

Power quality study with IEC standard Disadvantage Difficult in changing type of filters Purpose of Built-in module in our research power quality software

Frequency domain Easy to adapt other weighting filters in block 3 Huge memory occupation if FFT width is big The future IEC standard evolution

IV. FLICKER SOURCE MODELLING Our work has been focused on simplified flicker source modeling versus RMS values. The purpose is to simulate flicker sources and flicker propagation by a load flow software in order to reduce substantially simulating time: sampling just one value per network voltage period instead of 32 to 256 values generally used in time domain simulation. In distribution system operator (DSO) side, the prediction and limitation planning of power system flicker is of increasing importance. In the low voltage networks of industrial installations especially, resistance spot welding machines necessitate the prediction and planning of the voltage quality. It has been found that classical time domain load flow simulations are time consuming. A new fast simulation method based on RMS value has been developed, enabling the simulation of power systems with a high number of rapidly fluctuating loads. With the integration of IEC61000-4-15 flickermeter module and simplified flicker source models in a frequency domain software, it is possible to calculate flicker level at any point of a network. The system has been successfully tested and applied for a number of industrial power system flicker assessment (welding machines, electric arc furnace, etc). A. Simple flicker source model The simplest way to simulate flicker source is to use a timed switch controlling a load model which is defined by constant active power P and reactive power Q. If the actual P and Q are relatively stable, this method gives enough flicker assessment accuracy. In this case, controls of the switch will be defined by ON duration and OFF duration of the load. However, this method is not suitable for irregular load profile. B. Advanced flicker source models As the power of most of flicker source loads are variable such as welding machine, motor starting, electric arc furnace, etc, the simple model mentioned above can just roughly estimate flicker level, it can’t reveal flicker effect owing to a nonlinear load profile. By means of nonlinear and chaotic function, several dedicated flicker source models have been studied in order to simulate flicker resulted from nonlinear loads.

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1) Welding machine An industrial welding machine can be modeled by a constant reactance and a variable resistance (Fig. 6). At the given power supply voltage U, the load powers P and Q can be calculated by: P=

U2 R2 + X2 Power supply

⋅ R and Q =

U

U2 R2 + X2

⋅X

Welding machine model

(4) X R

modified by motor sliding during the motor’s starting period and the whole starting duration is also defined by square of network voltage.

3) Electric Arc furnace (EAF) As the power curves of an electric arc furnace are very irregular, it is impossible to simulate an EAF by a simple defined function. Authors [11][13] have studied time domain EAF modeling for transient analysis. Our proposed method concerns a simplified EAF model by setting a chaotic variation on equivalent arc resistance R. The principle of this method is based on electric equivalent model of EAF (Fig. 9). P

Fig. 6 : Welding machine model

As flicker is caused by fast voltage variation, it is very important to simulate the arising time and dropping time of the powers P and Q. The key step of the modeling is to represent correctly the arising and dropping slope. In order to simplify computing time, some assumptions have been applied in load arising period simulation: • In resistance spot welding process, X is almost constant and R varies from infinite to value 1 in pu (per unit). • In electric arc welding process: X is almost constant and R varies from 0 to 1 at the beginning of welding. The variation of R can be set either by a linear function or by a nonlinear function. Fig.7 gives evolutions of powers P and Q (rated values: 250kW and 200kVAr) by 5 time zones and 3 power-segments settings (R varies linearly during the arising and dropping periods). P and Q of one phase

Fig. 7 : Industrial automatic welding machine model

2) Motor starting In RMS value simulation, it is simple to simulate flicker owing to a motor starting. Fig. 8 shows a general equivalent induction motor model and starting curve.

X

EAF model

R

EAF: function of powers P and Q

Beginning of melting

Distribution R measured during 20s

Resistance value in Ohm

Resistance value in Ohm

Fig. 9: Power recording from a 60MW EAF and equivalent R classification

The classification of equivalent resistance R from site recording (Fig. 9) shows that R variation can nearly be simplified by a normal distribution. The first step is to calculate rated impedance represented by series Xn and Rn. At each sampling step, R will be modified by two coefficients: magnitude multiplier Cr and time delay constant Te which represent irregular variation of EAF. Two independent chaotic functions are used to create Cr and Te. At each moment when the time constant Te is reached, impedance multiplier Cr (Normal distribution with mean value µ and standard derivation σ) and time delay Te (chaotic) are refreshed (Fig. 10). At each computation sampling j, R is defined by: j Rj = Rn ⋅ [Cr[k ] + (Cr[ k + 1] − Cr[ k ])]⋅ (5) N N is the total calculation number during time constant Te and j is instantaneous calculation number from k to k+1. The term j/N represents a linear extrapolation from k to k+1. σ

Normal Distribution Te[k]

Cr Is: starting current In: Rated current Cs: Starting torque Cn: Rated torque Cos(phi): Motor’s cosine (phi)

Fig. 8 : Induction motor starting model and curve

In this classical motor starting model, the resistance R2 is

End of melting

Distribution R measured during 20s

Chaotic x (-1, 1)

R1: Stator series resistance X1: Stator series reactance Rm: magnetization resistance Xm: magnetization reactance R2: Rotator series resistance X2: Rotator series reactance

Q

µ

Te[k+1]

Conversion

Cr

Te[k+2]

Cr[k+1] Cr[k+2] Cr[k] k

j

k+1

k+2

t

Fig. 10 : Application of chaotic values on Cr and Te

Following values of Te and Cr have been used to simulate a 60 MW EAF (µ and σ are represented in pu):

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• Time constant Te varies from 0.02 to 0.2 second • Begin melting: Cr generated with µ = 1.1, σ = 0.5 • End melting: Cr generated with µ = 1.4, σ = 0.9 In order to validate the model, a simulation circuit has been created, it simulates power supply system of 60MW EAF of a melting plant (Fig.11). Two numeric flickermeters indicate the Pst of each side of the 100 MVA transformer. The flicker level Pst at PCC (Point of Common Coupling) is about 1.75 at the beginning of melting, and 0.45 in the end melting. These simulation results are very near to site measurements. PCC

R.arc distribution during 20s

P(MW)

Q(MVAr)

(Ω) Fig. 11 : EAF modeling by two chaotic functions per phase

C. Model defined by site recordings For particular case or for more precise analysis, it is suggested to use directly site recordings to perform flicker study (Fig.12).

• Deduce load equivalent impedance X and R • Built the load model by variable impedances X and R This method can be applied to any time-variation load (welding machine, motor starting, EAF, etc). V.

CASE-STUDIES:

APPLICATION AND VALIDATION

A. Flicker mitigation of a welding machine Based on the measurements of a resistance spot welding machine of an industrial site, a study has been performed by means of RMS flicker level simulation. In fact, a dynamic VAR compensator has been installed in this site so as to reduce the flicker disturbance caused by the welder. However, the flicker level at PCC is still higher compared to the power quality contracted value with DSO, the site owner wanted to know if the rated compensator power is enough, if not, how much compensation power has to be added in order to fulfill the power quality commitment with DSO. The study has been effectuated by using ExpertEC (a frequency domain software) embedded with the developed numeric flickermeter and the flicker source model. Flicker source is modeled directly by site measurements recorded every 20 ms: power Pm and Qm of the welder and reactive power Qc of the dynamic compensator. The flicker levels in HV and LV sides are calculated by two numeric flickermeters named by FLM1 and FLM2 (Fig. 13). Site recordings

Zoom Qm(kVAr)

P

Pm(kW) Qc(kW)

Q Site recordings

Fig. 12 : Modeling by site recordings

The key step is to create an interface between the recordings and the software. In time domain simulation, this interface has to read the sampling waveform data, and in frequency domain or RMS value simulation, this interface reads a series of RMS values (voltage, current or powers). Flicker source modeling can be effectuated either by measured powers P and Q or by measured impedance X and R. It is very easy to use directly measured powers P and Q values because a simple load model is enough. But in EAF case, it is recommended to use an improved model formed by X and R. This method allows to identify a specific EAF’s impedance which can be reused when the furnace is connected to other networks. Here is the procedure to build an EAF model by means of site recordings: • Extract from site recordings the powers P and Q evolution of each phase, • Recalculate equivalent impedances Xm and Rm • Subtract transformer’s impedance from Xm and Rm (transformer between the measuring point and EAF),

Pm, Qm PCC

Qc

Fig.13: Flicker study based on site recordings

Firstly, based on site-recorded values Pm, Qm and Qc, Pst values have been calculated (case 1 in the TABLE III). The two Pst values are verified by site measurements with error < 7%. Then, three situations have been studied by simulation: without compensator, +10% and –10% of the reactive power compensation. The table II shows the main results. TABLE III: SIMULATED FLICKER LEVEL AT PCC

Case 1: Present situation Case 2: Without VAR compensator Case 3: +10% of VAR compensation Case 4: -10% of VAR compensation

HV Pst 1.20 1.96 1.19 1.30

LV Pst 4.98 8.20 4.88 5.44

Simulation results show that the VAR compensator can follow nearly reactive power variation of the welder and the

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increase of rated power of welder can’t reduce flicker level. In fact, the welding duration is too short compared to the response time of the compensator. If rated power of the compensator is increased by 10%, the improvement is not observable: Pst comes down from 1.2 to 1.19 at PCC. It is thus recommended to do the following improvements in order to reduce significantly flicker level: • Set smaller VAR regulation step, • Reduce the measuring duration: try to measure RMS value during a half period of fundamental frequency, • Synchronize compensator with the welding control and preset a dedicated quantity of VAR compensation according to the welding process. This case study shows that with proposed methodology of flicker assessment, it is possible to extrapolate and reproduce future situations which help to take flicker mitigation decision.

B. Flicker propagation from HV to MV networks Based on the measurements issued from an industrial site (Fig. 14), a study has been performed with RMS flicker level simulation. High power flicker sources (60MW EAF) are modeled directly by site recordings P and Q. The distribution load in a neighbor substation is simulated by a studied dynamic model with high-pass filter correction (with Kv=5, Tf=0.5s). The flicker levels in different points of this network are simulated by proposed methodology. Flicker attenuation coefficient from HV to MV is about 0.80. Site measurements show this coefficient is between 0.80 and 0.82.

frequency domain software gives a single platform to analyze flicker and other disturbances with very short computing time. VII. REFERENCES [1] [2] [3] [4] [5]

[6] [7] [8]

[9] [10]

[11] [12]

HV

[13] [14]

MV

[15]

UIE WG Disturbances, “Flicker measurement and evaluation,” Tech. Rep., 1992 CENELEC EN 61000-4-15. Electromagnetic compatibility (EMC): Testing and measurement techniques - Flickermeter - Functional and design specifications. 1998. Report of the joining CIGRE-CIRED WG C4.07 (36.07) “Power Quality Indices and Objectives”, 2005 P. Kundur, “Power System Stability and Control,” ISBN 0-07-035958X, McGraw-Hill, copyright 1994 Xavier Yang, “Methodology and Simulation Tool for Flicker Propagation Analysis,” Joint Conference: Power Quality and Applications, Advanced Distribution Automation, EPRI, July 24 - 26, 2006, Atlanta, USA S. Tennakoon, S. Perera, D. Robinson and S. Elphick. “Attenuation of Flicker by Induction Motor Loads: A Laboratory Investigation,” The 12th ICHQP, Cascais, Portugal, October 1 – 5, 2006 Salvatore Caldara, Salvatore Nuccio, and Ciro Spataro, “A Virtual Instrument for Measurement of Flicker,” IEEE Transactions on instrumentation and measurement, Vol. 47, No. 5, October 1998 Araceli Hernández, Julio G. Mayordomo, Rafael Asensi, and Luis F. Beites, “A New Frequency Domain Approach for Flicker Evaluation of Arc Furnaces,” IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 18, NO. 2, APRIL 2003 T. Keppler, N. R. Watson, S. Chen and J. Arrillaga. “Digital flickermeter realisation in the time and frequency domains”. University of Canterbury, New Zealand. O'Neill-Carrillo, E. Heydt, G.T. Kostelich, E.J. Venkata, S. S. Sundaram, “A. Nonlinear deterministic modeling of highly varying loads,” IEEE Transactions on Power Delivery, April 1999, Vol. 14 , Issue: 2, Pages: 537 – 542 G. Jang, W. Wang, G.T. Heydt, S.S. Venkata, B. Lee, “Development of enhanced electric arc furnace models for transient analysis”, Electric Power Components and Systems, Vol. 29, No. 11, 2001 M. Kratz, “Effect of adding reactance in AC arc furnace”. 5th European Electric Steel Congress, 1995, Paris, France M. Kratz, “Comparative study of disturbance generated by AC and DC arc furnaces”. Technical report 95NR00064, EDF, 1994, France Dhandapani, S. Bridges, M. Kannatey-Asibu, E., Jr. “Nonlinear electrical modeling for the resistance spot welding process”. American Control Conference, 1999. Proceedings of the 1999, p182-186 vol. 1 X. Yang, L. Berthet, « Methodology for Frequency Domain Disturbance Source Modelling for Multi Source Harmonic and Inter-harmonic Studies,” The 12th ICHQP, Cascais, Portugal, October 1 – 5, 2006

VIII. BIOGRAPHIES Fig. 14: HV to MV Flicker propagation analysis

VI. CONCLUSION The paper presents the development of flicker source models, numeric flickermeters and distribution load model for flicker propagation study. Distribution load behavior to flicker disturbance can be modeled by dQ/dV and Dp/dV. This will help to study flicker propagation in different voltage levels. However, further study is necessary to correct the high-pass filter coefficients according to the type of distribution load: individualize load reaction time to flicker disturbance coming from upstream. RMS value-based flicker calculation by numeric IEC flickermeter algorithm is a fast and easy way to perform flicker assessment. The integration of numeric flickermeter and flicker source models into a load-flow software or a

Dr. Xavier X. Yang (M'07) received his Electrical Engineering Diploma B.S. and M.S. degrees in Liaoning Technology University (China), and received the Ph.D. from National Polytechnic Institute of Toulouse (France). From 1994 through 2001, Dr. Yang was employed in French Electricity and Energy Consulting Companies in which he was in charge of site measurement and power quality mitigation. He is doing now research works in Electricite de France (EDF) R&D. His research interests are in the areas of electric power system modeling, power system harmonics, computer algorithms, fault detection and voltage sag mitigation. He is a member of IEC SC77A Working Group 1 and CIGRE Joint Working Group C4.105. Maurice Kratz graduated from École Nationale Supérieure d'Electricité et de Mécanique (ENSEM) in France in 1987. From 1989 to 1991 he worked at Electricité de France on controls related to the quality of the electric equipment in nuclear power station. In 2001 he joined the research center of EDF where his interests are in the field of HV power system supplies analysis, modeling and computer simulation.