IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 42, NO. 3, MAY/JUNE 2006
681
Computation of the No-Load Voltage Waveform of Laminated Salient-Pole Synchronous Generators Stefan Keller, Student Member, IEEE, Mai Tu Xuan, and Jean-Jacques Simond, Member, IEEE
Abstract—This paper presents a combined analytical and finite-element (FE) method for computation of the no-load voltage waveform of laminated salient-pole synchronous generators. The described method takes into account saturation effects as well as the damper bar currents due to the slot pulsation field. The method calculates first the damper bar currents and then includes them in the calculation of the no-load voltage. The combination of magnetostatic two-dimensional (2-D) FE simulations for calculating the magnetic coupling between the machine windings and of an analytical resolution results in a very precise prediction of the no-load voltage. At the same time, simulation time is drastically reduced compared with transient magnetic 2-D FE simulations. The method was verified on several examples, comparing the obtained results (damper bar currents and no-load voltage) with results obtained from transient magnetic FE simulations and, in one case, with the measured no-load voltage. Index Terms—Damper currents, damper winding, modeling, no-load voltage waveform, synchronous machines.
I. I NTRODUCTION
I
T IS VERY important for the designer of salient-pole synchronous generators to be able to predict the no-load voltage waveform in a fast and reliable way. This is above all true in the case of a design where a low number of stator slots per pole and per phase have been chosen to reduce costs. Knowing in advance the harmonics content of the no-load voltage is important for satisfying standards requirements (telephone harmonic factor, etc.). Also, the computation of the losses due to currents in the damper bars, induced by the slot pulsation field, is important for the design. Furthermore, systematic industrial application calls for a fast method to be applied in a user-friendly way. Also, the analysis of the influence of the damper bar currents as well as of different stator winding schemes on unbalanced electromagnetic pull in the case of various rotor eccentricity conditions calls for a fast and, at the same time, precise calculation method. These problems have been addressed by several authors, applying different analytical, numerical, and combined methods.
Paper IPCSD-06-016, presented at the 2005 Industry Applications Society Annual Meeting, Hong Kong, October 2–6, and approved for publication in the IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS by the Electrical Machines Committee of the IEEE Industry Applications Society. Manuscript submitted for review November 19, 2005 and released for publication February 27, 2006. The authors are with the Laboratory for Electrical Machines, Swiss Federal Institute of Technology, CH-1015 Lausanne, Switzerland (e-mail: stefan.
[email protected];
[email protected];
[email protected]). Digital Object Identifier 10.1109/TIA.2006.873663
Traxler-Samek et al. [1] apply a fast analytical methods, whose output can be used as a criteria for the selection of the number of stator slots. On the other extreme, transient finite-element (FE) simulations allow very precise computation, not only of the noload voltage waveform but also of the damper bar currents or of the magnetization of the machine. In [2], transient FE analysis is used for computation of the no-load voltage shape, and in [3], this same method is used for the design of the damper winding of a single-phase generator. As this method is very time-consuming, especially in the case of a fractional slot stator winding, it is not very suitable for comparing several different machine geometries. Also, a certain number of combined methods were presented. In [4], a combined analytical and FE modeling method is used for calculation of the currents induced in the damper winding and for calculation of the force-density harmonics including the effects of these currents. In [5] and [6], the modified winding function approach and the magnetic circuits approach have been used for modeling the synchronous machine performance under dynamic air-gap eccentricity. In [7], a combined analytical and FE approach, similar to the one presented in this paper, is proposed. A comparison of the method presented in this paper and the one proposed in [7] is made in Section V. Finally, in [8], the harmonic balance FE method is used to calculate the synchronous machine no-load voltage. In this paper, the authors will present a combined analytical and FE method for computation of the damper bar currents and the voltage waveform in no-load conditions. This method takes into account saturation effects as well as all geometrical data of the machine (except effects of the end regions). Skin effect (arising especially in the damper bars) is not taken into account, but a way of taking of taking it into account is mentioned in Section VII. The method allows the aforementioned computations in steady-state conditions: The goal was to develop a very fast method allowing systematic industrial application. The results obtained were compared with the results obtained from transient FE simulations and, in one case, to the measured no-load voltage. These comparisons were done on several synchronous generators, in the range from 10 to 30 MVA, including integer and fractional slot stator windings, and damper windings centered or shifted on the pole shoes. The described method was implemented in a tool that is currently used by one of our major industrial partners. A generalization of the method for analyzing various rotor eccentricity and stator deformation conditions in synchronous machines is in development. Summarized, the method consists in calculating, using magnetostatic two-dimensional (2-D) FE simulations, the magnetic coupling of the machine electrical conductors (damper bars,
0093-9994/$20.00 © 2006 IEEE
682
IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 42, NO. 3, MAY/JUNE 2006
field, and stator windings) for a certain number of positions of the rotor, considering the machine rotational periodicity. In a second step, the damper bar currents and the no-load voltage can be calculated by solving the differential equation system formed of the inductances calculated in the first step. The hypotheses assumed are the following: • constant field current; • no eddy currents; • neglect effects of end regions.
The inductances are obtained using magnetostatic 2-D FE simulations. For the determination of Ldiff k,j , the results of two FE simulations are necessary: one with the field windings supplied with the current corresponding to the chosen main flux and one with the field windings supplied with the same current and with damper bar k supplied with a test current. Ldiff k,j is then calculated as follows:
II. M AGNETIC C OUPLING OF THE M ACHINE C ONDUCTORS
where ϕexc,k,j
Due to magnetic coupling, a voltage is induced in each conductor of the machine. The voltage induced in conductor j is given by the derivative of the flux seen by conductor j, i.e., vj =
dϕj . dt
(1)
The flux linked to a conductor is the integration in space of the flux density from the location of the conductor to infinity, which is, in our case, the outer boundary of the machine where the flux density is supposed to be zero (boundary condition in the FE model). It is therefore equal to the flux linked to a (hypothetical) coil formed of the conductor in question and closed outside the machine (where zero flux density is assumed). This flux linkage value can be obtained easily by multiplying the vector potential value (the result of an FE calculation) at the location of the conductor with the length of the machine. This approach has the advantage of calculating the flux linked to each conductor separately (and not the flux linked with a coil); the conductors can therefore form any type of circuit, and the same calculated flux linkages can be used (especially interesting for the stator conductors; see also end of Sections III and IV). The flux linked to a conductor j (damper bar or conductor on the stator) can be expressed as the sum of the flux linkage contributions of the currents in the field windings and in the N damper bars. As the magnetomotive force (MMF) caused by the damper bar currents is significantly lower than the MMF caused by the current in the field windings, the flux created by the damper bar currents is assumed to not influence the level of saturation of the generator (more of these assumption in Section VII). Therefore, the contribution of the damper bar k can be expressed as the multiplication of the current in the damper bar k with a mutual differential inductance, describing the change in flux linkage with conductor j when the current in the damper bar k changes, i.e., ϕj = ϕexc,j +
N k=1
ϕk,j = ϕexc,j +
N
Ldiff k,j ik .
(2)
k=1
These differential inductances depend on the rotor position and on the saturation of the machine. Thus, they have to be determined for a given main flux (given field current) and for different rotor positions. As the stator has, as seen from the rotor, a rotational periodicity of one stator slot pitch, the inductances have to be determined only for some positions of the rotor within one stator slot pitch.
Ldiff k,j =
ϕexc,k,j − ϕexc,j ik
(3)
flux linked with conductor j, created by the field windings and the current in conductor k; flux linked with conductor j, created only by the ϕexc,j field windings. As each simulation can be used for the calculation of several inductances, the necessary number of magnetostatic FE simulations is (N + 1)W , where N is the number of damper bars and W is the number of rotor positions considered within one stator slot pitch. The simulations with only the field windings supplied provide also the values of flux linkage caused by the current in the field windings [as used in (2)]. As in the case of transient FE simulations, only a part of the machine has to be considered; therefore, a typical number of magnetostatic FE simulations could be (20 + 1)20 = 420 (one pole pair, ten damper bars per pole, 20 positions of the rotor). In the examples presented in this paper, the magnetostatic FE calculations were carried out using Cedrat Flux2d.1 The actual nonlinear characteristics of the magnetic materials were considered; the current distribution in the field windings was assumed uniform. An equivalent length of the machines was calculated taking into account the ventilation ducts. It could be imagined, for each position of the rotor, to carry out the FE calculation with only field windings supplied using the actual nonlinear characteristics of the magnetic materials and to fix the permeability of each element in the geometry to the value obtained through this calculation for the following calculations with additionally each time one damper bar supplied. This would mean, for the aforementioned example, to carry out 20 nonlinear magnetostatic FE calculations and 400 linear magnetostatic FE calculations. The calculation time could, therefore, be further reduced. Using magnetostatic FE simulations to determine the magnetic coupling of the machine electrical conductors allows to take into account precisely saturation effects as well as all geometrical data of the machine (pole shoe shape, rotor and stator slotting, damper bar distribution, etc.) except end-region effects. All these influencing factors are contained in the values of flux linkages and in the differential inductances, which can be calculated using a standardized scheme of magnetostatic FE calculations for any type of salient-pole synchronous generator (integer and fractional slot stator windings, various damper bar distributions, various pole shoe shapes, etc.). These FE calculations can be carried out with FE calculation programs readily available on the market; no special software is needed.
1 Finite Element Simulation Software, Flux2D, Version 8.1D, Cedrat, Meylan, France.
KELLER et al.: COMPUTATION OF NO-LOAD VOLTAGE WAVEFORM OF SALIENT-POLE SYNCHRONOUS GENERATORS
683
Therefore, and expressing ϕi,j also using the differential inductances ∂Ldiff i,j dϕi,j dii = Ldiff i,j + ii Ω. dt dt ∂α
(7)
The following equation is obtained for each loop of Fig. 1: Fig. 1.
Electrical circuit associated with the damper cage.
III. E LECTRICAL C IRCUIT OF THE D AMPER C AGE AND C ALCULATION OF THE D AMPER B AR C URRENTS The machine conductors form the following three galvanically separated circuits: • field windings; • damper cage; • stator windings. As the current in the field windings is considered constant and the machine is considered in no-load conditions, the field windings and the stator windings do not have to be modeled. The electrical circuit of Fig. 1 is associated with the damper cage. In Fig. 1, only a part of the damper circuit is shown, the whole circuit consists of one branch for each damper bar present in the part of the machine considered for calculation of the inductances, as described in Section II. As can be seen in Fig. 1, each damper bar is modeled as one branch composed of a resistance and a voltage source. The resistance models obviously the resistance of the damper bar, whereas the voltage source models the voltage induced, which is the derivative of the flux linked with the damper bar [as in (1)]. The resistance of the short-circuit rings is neglected but could also be considered, changing slightly the equations described below. Additionally, the skin effect in the damper bars can be taken into account, knowing the frequency of the damper bar currents (frequency of the slot pulsation field), by adjusting the resistance of the damper bars as well as the slot linkage inductance part of the inductance values obtained according to Section II (e.g., as described in [9]). For each loop in the electrical circuit, the following equation can be written as: Rbarj ibarj − Rbarj+1 ibarj+1 +
dϕj+1 dϕj − = 0. dt dt
(4)
The flux linked to each one of the two bars, ϕj and ϕj+1 , can be replaced with (2), and the derivative in time of the flux terms in (2) can be replaced with its partial derivatives as follows: ∂ϕi,j dii ∂ϕi,j dϕi,j = + Ω dt ∂ii dt ∂α
(5)
where α is the position of the rotor and its derivative in time, the rotating speed Ω. The derivation of the flux linkage with respect to the current can be replaced with a differential inductance as described in Section II, i.e., ∂ϕi,j = Ldiff i,j . ∂ii
(6)
Rbarj ibarj −Rbarj+1 ibarj+1 N dik ∂Ldiff k,j dϕexc,j + + ik Ω + Ldiff k,j dt dt ∂α k=1 N dϕexc,j+1 dik ∂Ldiff k,j+1 − + + ik Ω = 0. Ldiff k,j+1 dt dt ∂α k=1
(8) Finally, the current in the last bar can be expressed as the negative sum of the currents in all other damper bars (Kirchhoff’s law) Rbarj ibarj −Rbarj+1 ibarj+1 +
N −1 k=1
dik (Ldiffk,j −LdiffN,j −Ldiffk,j+1 +LdiffN,j+1) dt
N −1
+Ω
k=1
ik
∂Ldiffk,j ∂LdiffN,j ∂Ldiffk,j+1 ∂LdiffN,j+1 − − + ∂α ∂α ∂α ∂α
dϕexc,j dϕexc,j+1 − = 0. + dt dt
(9)
As all Ldiff k,j and ϕexc,j have been determined as described in Section II and the only remaining unknowns being the damper bar currents, the system of differential equations formed of N − 1 equations (where N is the number of damper bars, the current in the last bar being calculated as mentioned above) of the type of (9) can be expressed in matrix form as follows: ∂L −→ dφ d −→ −→ i(t) + =0 Ri(t) + L i(t) + Ω dt ∂α dt
(10)
where R, L, and φ are the matrices containing the resistance, inductance, and flux linkage values according to (9). The matrix form was not used throughout the presentation of the method (4)–(9) for easier understanding of the equations and for easier implementation of the method. Also, the matrix form given in (10) does not correspond to the matrix form of similar equations given in literature, but it allows the direct implementation of the method using the flux linkage and inductance values as described in Section II. The equation system given in (10) can be solved using a numerical method. In the case of this paper, the second-order Runge–Kutta method (also called Heuns method) was applied for solving the system of differential equations. The described method could also be used in the case of several galvanically separated damper cages (e.g., one on each pole shoe) or in the case of parallel circuits on the stator including the effects of currents circulating in the parallel circuits in no-load conditions (especially in the case of an eccentric
684
IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 42, NO. 3, MAY/JUNE 2006
Fig. 2. Reassignment of stator conductors. Fig. 3.
rotor). In these cases, the equations described above have to be modified. IV. C ALCULATION OF THE N O -L OAD V OLTAGE Having calculated the currents in all damper bars, the noload voltage in each phase can be obtained by summing the derivatives of the flux link to each conductor of the phase. The flux link to each conductor can again be expressed as the sum of the contributions of the field windings and the N damper bars [as in (2)]. In the case of the conductors on the stator, the differential inductances and the values of flux linkage caused by the field windings, calculated for some rotor positions within one stator slot pitch, have to be reassigned to the conductors on the stator after a rotation of the rotor of one stator slot pitch (the conductors have to be shifted to the next slot); then, the values calculated for the same rotor positions can be reused. Fig. 2 shows the way the conductors should be shifted for a given rotating direction. The simple technique takes fully into account the rotational periodicity of the machine and allows to use the magnetic coupling, calculated only for some rotor positions within one stator slot pitch, for any position of the rotor. As the flux linkages and mutual inductances were calculated separately for each conductor and not for coils, any kind of winding scheme can be analyzed with the same flux linkage values and inductances. The following formula was used for the numerical derivation of the flux linkage: ϕj (tk ) − ϕj (tk−1 ) d ϕj (tk ) ∼ . = dt tk − tk−1
(11)
V. I MPLEMENTATION As described in Sections II and III, the computation of the no-load voltage and damper bar currents is carried out in two steps. The computation of the flux linkage values and mutual inductances using the 2-D magnetostatic FE method is done first and is completely independent of the resolution of the differential equation system formed of these values. This is one
Comparison of the no-load voltage waveform.
major difference to the method presented in [7], where the FE calculations are linked to the resolution of the circuit equations. In the method presented in this paper, the knowledge of the basic geometrical machine data allows to calculate a very limited set of flux linkage values and inductances and to solve the circuit equations afterward, taking into account the layout of the machine electrical circuits. The same flux linkage values and inductances can be used for different stator winding schemes (parallel circuits, etc.). Therefore, the FE calculations can be performed with an FE program readily available on the market. On the other hand, the described method does only allow the simulation in steady-state conditions (given main flux), whereas the method presented in [7] allows also simulations in transient conditions. The implementation of the resolution of the circuit equations is done as follows. • Load results of FE calculations (vector potential values for all nodes for each calculated case and rotor position). • Compute flux linkage values and mutual inductances. • Solve system of differential equations formed of these values using Runge–Kutta and compute at the same time the no-load voltage. • Save results. VI. C OMPARISON OF THE R ESULTS The damper bar currents and the no-load voltage obtained using the described method were compared with the currents and the voltage obtained from 2-D transient FE simulations and, in one case, also to the measured no-load voltage. The transient magnetic FE calculations were carried out using the nonlinear characteristics of the magnetic materials and taking into account the skin effect in the damper bars. Again, the current distribution in the field windings was assumed uniform, and an equivalent length of the machine was calculated taking into account the ventilation ducts. Figs. 3 and 4 compare the no-load voltage waveform of an existing generator (6.3 kV, 11 MVA, 750 r/min, 50 Hz, Fig. 5) obtained using the described method with the no-load voltage
KELLER et al.: COMPUTATION OF NO-LOAD VOLTAGE WAVEFORM OF SALIENT-POLE SYNCHRONOUS GENERATORS
Fig. 4.
685
Comparison of the no-load voltage, detail. Fig. 7. Comparison of the currents in two adjacent damper bars.
Fig. 5.
Geometry of the first machine.
Fig. 8. Comparison of the no-load voltage harmonics.
Fig. 6.
Comparison of the no-load voltage harmonics.
obtained from transient FE simulations. Fig. 6 compares the no-load voltage harmonics (in percentage of the fundamental) of the same generator, this time also to the harmonics of the measured no-load voltage.
A very good agreement of the results can be observed, not only comparing the described method to transient FE analysis but also comparing to the measured values. Fig. 7 shows a comparison of the currents in two adjacent damper bars, obtained using the described method, with the current obtained from transient FE simulations. Also, in this case, the agreement is very good; therefore, the no-load losses due to currents in the damper bars can be predicted very precisely. Fig. 8 shows a comparison of the no-load voltage harmonics of another existing generator (10.6 kV, 31.5 MVA, 750 r/min, 50 Hz, Fig. 9) for two cases: 1) the real generator with damper cage shifted by ±(τs /4) on the pole shoes (τs being the stator slot pitch) and 2) a hypothetical case with damper cage centered on the pole shoes. As the described method calculates also the damper bar currents, the evolution of the MMF due to these currents can
686
IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 42, NO. 3, MAY/JUNE 2006
Fig. 9. Geometry of the second machine.
be calculated, allowing better understanding of the influence of the damper cage position on the no-load voltage harmonics. Figs. 10 and 11 show the spatial distribution as well as the evolution in time of the MMF due to the damper bar currents in both cases. One can clearly see that the MMF pulsates in time in both cases with the frequency of the slot pulsation field, but the frequency of the spatial distribution is two times higher in the case with shifted damper bars (two periods over one pole pair) compared with the case with centered damper bars (one period over one pole pair). Therefore, the damper bar currents induce the same voltage in each half coil of each phase in the case with shifted damper bars; the effect is therefore cancelled out. This explains the very low amplitude of the harmonics at the corresponding frequency compared with the case with centered damper bars. All calculations were performed on a desktop PC with Pentium 4 CPU (2.6 GHz, HyperTransport) and 1 GB of random access memory (RAM), running Windows XP Professional. The calculations applying the described method (including the magnetostatic FE calculations) were about 20 times faster than the transient FE simulations performed for comparison.
Fig. 10.
Damper bar MMF, centered damper bars.
Fig. 11.
Damper bar MMF, shifted damper bars.
VII. C ONCLUSION AND F URTHER R ESEARCH The modeling method presented in this paper allows the computation of the damper bar currents and of the no-load voltage of laminated salient-pole synchronous generators with almost the same precision as transient FE simulations. At the same time, simulation time was reduced by a factor of about 20. The aim of the method is to compute and analyze rapidly the following values: • no-load voltage waveform; • losses due to currents in the damper bars; • eccentricity and stator deformation conditions, unbalanced magnetic pull (after modification). The method takes into account saturation effects; comparisons carried out with damper bar currents and no-load voltage calculated from flux linkage values and inductances obtained through linear magnetostatic FE calculations with the results presented in this paper showed the nonnegligible effect of saturation in the main magnetic circuit and verified at the same time the assumption allowing the use of the differential inductances (mentioned in Section II). Skin effect can be taken into account, knowing the frequency of the damper bar currents (frequency
of the slot pulsation field), by adjusting the resistance of the damper bars as well as the inductance values (e.g., according to [9]). The waveform of damper bar currents would probably not change much (as can be seen in Fig. 7, the current waveform computation is already very precise without taking into account the skin effect), but no-load losses due to these currents would be affected because of the change in resistance. Skew could also be taken into account by dividing the machine in submachines in axial direction. The flux linkage and inductance values calculated for different rotor positions could be used without changes by distributing (shifting) them properly for each submachine. However, in our opinion, no major generator manufacturer uses this technique for generators in the range of power considered in this paper. The magnetostatic FE simulations, necessary for the determination of the magnetic coupling of the machine conductors, can be automatized and carried out using FE calculation programs readily available on the market. The calculation of the damper bar currents and the no-load voltage, based on the results of the FE simulations, has been implemented in a user-friendly graphical tool, allowing comfortable application of the method.
KELLER et al.: COMPUTATION OF NO-LOAD VOLTAGE WAVEFORM OF SALIENT-POLE SYNCHRONOUS GENERATORS
In a next stage, the method will be modified for analysis of the effects of various types of rotor eccentricity conditions and stator deformations in salient-pole synchronous generators. R EFERENCES [1] G. Traxler-Samek, A. Schwery, and E. Schmidt, “Analytic calculation of the voltage shape of salient pole synchronous generators including damper winding and saturation effects,” Int. J. Comput. Math. Elect. Electron. Eng. (COMPEL), vol. 22, no. 4, pp. 1126–1141, 2003. [2] A. Schwery, G. Traxler-Samek, and E. Schmidt, “Application of a transient finite element analysis with coupled circuits to calculate the voltage shape of a synchronous generator,” in Proc. CEFC, 2002, pp. 92–95. [3] K. Weeber, “Design of amortisseur windings of single-phase synchronous generators using time-stepping finite element simulations,” in Proc. ICEM, 1998, vol. 2, pp. 1042–1047. [4] A. M. Knight, H. Karmaker, and K. Weeber, “Use of a permeance model to predict force harmonic components and damper winding effects in salient-pole synchronous machines,” IEEE Trans. Energy Convers., vol. 17, no. 4, pp. 478–484, Dec. 2002. [5] H. A. Toliyat and N. A. Al-Nuaim, “Simulation and detection of dynamic air-gap eccentricity in salient-pole synchronous machines,” IEEE Trans. Ind. Appl., vol. 35, no. 1, pp. 86–91, Jan./Feb. 1999. [6] I. Tabatabaei, J. Faiz, H. Lesani, and M. T. Nabavi-Razavi, “Modeling and simulation of a salient-pole synchronous generator with dynamic eccentricity using modified winding function theory,” IEEE Trans. Magn., vol. 40, no. 3, pp. 1550–1555, May 2004. [7] S. Williamson and A. F. Volschenk, “Time-stepping finite element analysis for a synchronous generator feeding a rectifier load,” Proc. Inst. Electr. Eng.—Electr. Power Appl., vol. 142, no. 1, pp. 50–56, Jan. 1995. [8] J. Gyselinck, L. Vandevelde, J. Melkebeek, and W. Legros, “Steadystate finite element analysis of salient-pole synchronous machine in the frequency domain,” in Proc. 7th Int. Conf. Model. Simul. Elect. Mach. Convert. Syst., 2002, CD-ROM. [9] R. Tuschak, “Stromverdrangung von in kreisformigen nuten gebetteten massiven leitern,” Period. Polytech. Electr. Eng., vol. 1, pp. 27–51, 1957.
687
Stefan Keller (S’05) received the Master’s degree in 2003 from the Swiss Federal Institute of Technology (EPFL), Lausanne, Switzerland, where he is currently working toward the Ph.D. degree in the Laboratory for Electrical Machines. His main fields of activities are synchronous machine modeling and study of the effects of various rotor eccentricity and stator deformation conditions. His work concentrates on the analysis of the effects of rotor eccentricity and stator deformation conditions in synchronous hydro-generators.
Mai Tu Xuan received the Master’s and Ph.D. degrees in synchronous machine modeling from the Swiss Federal Institute of Technology (EPFL), Lausanne, Switzerland, in 1970 and 1977, respectively. He has been a Senior Researcher and Lecturer in the Laboratory for Electrical Machines, EPFL, for many years. His main fields of activities concern machine modeling, optimization and testing, parameter identification, measurement techniques, and field calculations.
Jean-Jacques Simond (M’03) received the Master’s and Ph.D. degrees in synchronous machine modeling from the Swiss Federal Institute of Technology (EPFL), Lausanne, Switzerland, in 1967 and 1976, respectively. Until 1990, he was with BBC/ABB, working in the field of large electrical machines, first as an R&D Engineer and later as Head of the Technical Department for Hydro and Diesel Generators. Since 1990, he has been a Full Professor at the EPFL and Director of the Laboratory for Electrical Machines. He is also a Consultant for different international electrical machine manufacturers and utilities.
