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An accurate prediction of medium-voltage induction motor (IM) power factor in rated conditions is important in the design stage to verify the machine compliance with specifications according to international testing standards. Laboratory and industrial experiences suggest that significant errors in full-load power factor calculation can result for two-pole IMs in particular, due to the eddy currents induced in the solid-steel shaft at rated slip. Such eddy currents are responsible for rejecting the main flux into rotor laminated yokes causing an increase in their saturation and, hence, in the required magnetizing current with respect to no-load conditions. This article proposes a method to study the phenomenon through a combination of analytical and simplified Finite Element (FE) calculations as a computationally-efficient alternative to conventional FE simulations. The results of the proposed approach are experimentally assessed by comparison with measurements on a set of built and tested medium-voltage two-pole IMs of different sizes, showing very good accuracy and computational performance.

This paper presents a droop-based dis- tributed control strategy for multi-three-phase machines that provides augmented controllability during power shar- ing transients. The proposed strategy is able to mitigate the mutual interactions among different sets of windings without controlling any sub-space variable, also offering a modular and redundant design. On the contrary, in a centralised configuration sub-spaces would be controlled using the Vector Space Decomposition, but fault tolerance and reliability levels required by the stricter regulations and policies expected in future transportation systems would not be satisfied. The proposed method is analytically com- pared against the state-of-the-art power sharing technique and equivalent models and control design procedures have been derived and considered in the comparison. Uncon- trolled power sharing transients and their effects on mu- tual couplings among isolated sets of windings have been compared against the proposed regulated ones. Experi- mental results on a 22kW nine-phase multi-three-phase synchronous machine rig validate the design procedures showing good agreement with the expected performances.

Solid rotor synchronous motors are widely used in the Oil&Gas industry, because of their mechanical robustness and self-starting capability. The starting performance calculation for these machines is a challenging task. In this paper the specific case of a solid salient pole motor rated 17.5 MW at 1500 rpm is addressed. A simplified but accurate method is proposed and validated experimentally to predict the motor current and torque during direct-on-line (DOL) starting. The proposed methodology combines Finite Element Analysis (FEA) with a lumped-parameter machine model to obtain the best compromise between accuracy and computational efficiency.

Load-commutated inverters (LCIs) are reliable and efficient drives to supply synchronous motors in high power industrial applications. However, inadequate attention is dedicated to this type of drive especially for higher phase numbers and in the case of faults. It is a proven fact that the fault tolerance of the voltage-source inverter (VSI)-fed multiphase machines is enhanced as the number of phases increases. However, the same principle is not necessarily applicable to the LCI-fed multiphase synchronous machine drives. As it will be shown in this paper, a thyristor failure may cause the drive instability and the situation can be more critical for higher phase numbers. In this paper, open-circuit faults and their consequences are investigated and compared for symmetrical and asymmetrical multiphase LCI-fed drives. Also, a new control strategy is proposed to restore the drive stability in the case of open-circuit faults in LCI-fed drives. Simulation results for a five-phase drive show that the control system can efficiently keep the machine synchronism in the event of phase open-circuit faults.

This paper deals with the optimal fault-tolerant operation of a 5-phase permanent magnet (PM) brushless DC (BLDC) drive. In particular, this paper (Part I) proposes the modelization used to optimize the motor current supply to obtain the maximum power in healthy conditions and its analytical solution is presented. In the companion paper (Part II) the drive is considered both in healthy and faulty conditions and the optimization problem is solved numerically. In all cases the solution is compared with the one obtained with a “Maximum Torque Per Ampere” objective.

This paper deals with the optimal fault-tolerant operation of a 5-phase permanent magnet (PM) brushless DC (BLDC) drive. In particular, the companion paper (Part I) proposes the optimization of the current supply to obtain the maximum power in healthy conditions and its analytical solution. In the present paper (Part II), by constraining the proposed model with healthy and fault specific conditions, the magnitude schedule of the currents in the surviving phases is determined in order to obtain the maximum average power and the optimization problem is solved through a numerical approach. In all cases the solution is compared with the one obtained with a “Maximum Torque Per Ampere” criterion.

Load commutated inverters (LCIs) are still widely used for their robustness and reliability in high-power synchronous motor drives, in either single or multiple three-phase configurations. A restriction to their use in high-speed applications is due to the criticalities of thyristor operation at high switching frequencies. The upper frequency limits of LCIs are usually addressed in the existing literature as something independent of the drive architecture. On the contrary, this paper highlights how the maximum frequency that can be safely attained closely relates to the number of LCIs that are used to supply the synchronous motor. In fact, moving from a single to multiple three-phase arrangements is proved to introduce more stringent frequency constraints due to the mutual interaction between stator windings during commutations. Frequency limits for safe operation of single- and multiple-LCI drives are derived in quantitative terms and experimentally assessed on a 2-MW synchronous motor fed by a couple of LCIs. Practical implications of such limits in the design of high-power high-speed drives are finally discussed.

An electric machine equipped with n stator phases is characterized by a set of n × n phase inductances as concerns the stator section. In the case of nonuniform air gap, these inductances vary as the rotor moves. For their numerical determination as functions of the rotor position an accurate computation algorithm is proposed in this paper based on winding function theory. For permeance function identification, a numerically efficient method is employed based on the magnetostatic finite-element analysis of only three appropriately simplified machine models. In the presence of a field circuit, computation of mutual inductances among it and stator phases is also covered with the same approach. An extension of the method to permanent-magnet machines is also presented. Results are assessed on a six-phase synchronous generator prototype equipped with either a salient-pole wound-field rotor or with an interior permanent-magnet rotor.

Slotless permanent magnet machines are attractive in some modern drive and power generation fields, where the cogging torque and additional losses need to be minimized or removed. The stator slotless design can be combined with different surface permanent magnet (SPM) rotor topologies. In this paper, explicit analytical expressions are derived to analytically compute the slotless machine torque and no-load back Electro-Motive Force in the case of segmented SPM rotor with parallel, radial, or Halbach-array magnetization patterns. The expressions are found by solving the magnetic field due to the slotless stator winding and to the permanent magnet blocks; the latter modeled through equivalent surface current densities. The accuracy of the method is successfully assessed by comparison with the finite-element analys is (FEA). The proposed formulas are an effective alternative to the FEA to quickly compare different design solutions as well as to optimize them. Application examples are provided in which the presented method is adopted to define the machine cross section that maximizes the torque density.

This paper investigates the hydraulic system drive used onboard ships to actuate stabilizing fins. The hydraulic drives are often characterized by low efficiencies, heavy maintenance, frequent oil leaks and large weight and size. To overcome these draw-backs, in this paper a concept design of a full-scale permanent magnet linear synchronous motor directly coupled to the shipboard fin stabilizer, is presented, used as a servo-motor. The innovative electric drive is based on prototype of high thrust linear motor built in a previous research. A complete Simulink model, where electric, mechanical and hydraulic domains can be connected, has been realized. Simulations has been performed to evaluate the hydraulic drive efficiency and in order to assess the servo-assistance capabilities. The results show the feasibility of the proposed solution for a future practical application. This research has been carried out in the framework of the Italian Defence Research National Program for the development of ‘dual use’ technologies.

Cogging torque is a known disadvantage of surface permanent magnet (SPM) machines, especially if equipped with open stator slots. A possible strategy to reduce the cogging torque is to use suitably designed non-isotropic magnetic wedges. The design of such wedges for cogging torque minimization requires a genetic optimization approach. This has been done in previous works using Finite Element Analysis (FEA) simulations to predict the cogging torque for each machine design being explored, leading to a very time consuming optimization process. In this paper, the same optimization is performed using an analytical method to compute the cogging torque. It is shown that the optimization process, based on the analytical formula for cogging torque prediction, leads to the same result as the FEA-based procedure, but with a significant reduction in the computational burden.

Salient-pole synchronous machines are conventional electric machines which have been widely used and studied over decades. Some aspects of their modeling and analysis, however, still constitute a challenge for designers and require state-of-the-art methodologies to be applied. As an example, this paper addresses a 14-MVA salient-pole shipboard alternator, of which full-scale prototypes are built and tested with different damper cage designs. A time-stepping finite-element (FE) analysis is assessed against test results as a method to predict generator performance for the various damper cage design alternatives. FE simulations are shown to give accurate results even without model tuning if continuous end rings are used to short circuit damper bars. For the design solution with partial end arcs, model tuning is required, instead. For this purpose, a calibration method is proposed and successfully validated, which only requires a set of impedance measurements to be taken on the machine at standstill

Squirrel-cage induction motors are the most widely used type of electric machinery in industrial applications thanks to their rugged, cheap and robust construction. For the fast prediction of induction motor steady-state performance without the need for time-consuming finite-element analyses, the equivalent circuit parameters of the machine need to be calculated, including rotor slot leakage inductances. This paper, in particular, proposes a new improved analytical formula to determine the rotor slot leakage inductance in squirrel-cage induction motors with rectangular-shaped bars. The formula is obtained by solving Poisson's equation in the slot domain. Results are assessed by comparison against Finite Element Analysis (FEA). The precision of the presented methodology is also compared to that of approximated analytical models available from the literature. The comparison shows that the accurate formula proposed is in excellent agreement with FEA with errors below 2%, while the simplified model generally leads to errors above 10% which increase as the height-to-width bar ratio decreases.

Split-phase synchronous motors equipped with multiple-stator three-phase windings, each supplied by a load-commutated inverter, play an important role in today's very high power electrical-drive applications. A criticality of these systems is the possibility that commutations occur in different motor windings simultaneously. The resulting electromagnetic transient depends on the magnetic coupling of motor phases among them and with rotor circuits. In this paper, a model to describe this phenomenon is presented along with some dedicated tests, conducted on various split-phase configurations, to assess the model validity.

The stator winding of multi-phase machines can be designed according to different schemes, which differ by either the number or the spatial arrangement of phases. For control and analysis purposes, it is often useful that the stator inductance matrix is reduced to a diagonal form. This allows for the multiphase machine to be split into independently-controllable systems and directly leads to stator harmonic impedance determination. Simple and compact diagonalization algorithms are established in this paper covering all possible multi-phase schemes of practical importance with a unified approach, under the hypothesis of uniform air-gap and negligible magnetic saturation. In a companion paper, All the proposed equations are experimentally assessed though dedicated tests on several multiphase winding schemes.

This paper (Part II), together with a companion one (Part I), deals with the fault-tolerant operation of a 5-phase permanent magnet (PM) brushless DC (BLDC) drive. In particular, this paper takes advantage of the drive model formulated in Part I to determine automatically the motor current supply, namely scheduling and magnitude of the currents for the surviving phases, in the cases of a drive with two and three open phase faults. Maximum magnitude of the supply currents is also determined by equating the rms value of current in the most solicited phase to the nominal rms value Open faults of adjacent and non-adjacent phases are studied and for each fault location, besides determining the motor current supply, the torque developed by the motor is calculated. The results indicate that the reduction in the motor torque as well as the extent of the torque ripple is depending on the relative location of the faults.

Hydrostatic drives used on board ships are often characterized by low efficiencies, heavy maintenance, frequent oil leaks and large weight and size. To overcome these drawbacks, oil-free inverter-fed alternative drives can be proposed. This paper analyzes the ship rudder hydraulic drive performances, and a proposal for improvements is shown. A full-scale permanent magnet linear synchronous motor directly coupled to a twin rudder is presented, used as a servo-motor. Both servo-assistance features and performance and efficiency improvements are evaluated by using a complete physical model in Simulink environment.

This paper (Part I), together with a companion one (Part II), deals with the fault-tolerant operation of a 5-phase permanent magnet (PM) brushless DC (BLDC) drive. In particular, this paper proposes an algebraic approach to set up a model of the motor current supply in healthy conditions. Afterwards, a faulty drive is considered with one or more open phases and, by constraining the proposed model with fault-specific conditions, scheduling and magnitude of the currents in the surviving phases are determined automatically as well as the maximum magnitude of the currents and the maximum torque developed by the motor. At last, the paper applies the model to the case of a drive with one open phase fault. In the companion paper the model is applied to the cases of more-than-one open phase faults.

The accurate determination of stator leakage inductances is presently an open issue in the analysis and testing of multi- phase electric machines. Calculation methods are available, which involve complicated and often poorly precise three-dimensional (3-D) analyses. Experimental determination techniques, using measurements on the wound stator with the rotor removed, are also possible, but quite impractical, as they need to be performed during machine manufacturing or require rotor withdrawal. In this paper, a new approach is proposed to determine all the stator self- and mutual leakage inductances of a nine-phase synchronous machine based on a minimal set (a couple) of magnetostatic finite- element (FE) simulations, and on the measurements taken during no-load and short-circuit routine tests. The procedure is applied to a wound-field salient pole nine-phase synchronous generator for validation, showing good accordance with the results obtained from measurements on the machine with the rotor removed. A discussion is also proposed on the possibility to extend the presented procedure to other multiphase topologies

Electric drives with a three-phase structure are commonly utilized in road vehicles for propulsion and in aeronautics as control-surface actuators. In recent times, some concerns have emerged on the use of three-phase drives in such applications in regard to power capability, efficiency and fault-tolerance. A way to effectively cope with these concerns is the adoption of multiphase drives. In this sense, a five-phase drive is a promising solution as it does not imply an excessively complicated structure. In this paper a five-phase PM BLDC drive is considered and its torque capabilities are investigated for square-wave current supply. Specifically, the torque developed by a five-phase drive is first compared to the three-phase counterpart; torque comparison is carried out by keeping motor size and loading unchanged and by considering two hypotheses: equal phase back-emf and equal phase rms current. Then the torque available from a five-phase drive is determined under various supply modes, characterized by the simultaneous conduction of a reduced number of phases; the torque available is determined by imposing an equal rms phase current in the supply modes.

The finite reluctance approach is very well suited for fast modeling and dynamic simulation of permanent magnet synchronous machines with inverter feeding. This paper shows validating simulations, in both steady-state and transient conditions, carried out for a permanent magnet linear motor designed for on board ship load actuation. The basics of the method are resumed. The simulations obtained by using the finite reluctance approach are compared with FEM simulations, showing good agreement. Keywords—Dynamic model, dynamic simulation, linear machine, magnetic network, reluctance.

The finite reluctance approach is based on a simple synergy between a basic magnetic domain decomposition rule and the voltage balance at the terminals of any winding acting in the domain. The finite reluctance approach is thought as a tool for fast dynamic simulations of any kind of machine, but it is particularly adapt for irregular flux geometries as in fractional-slot surface-mounted permanent magnet machines with large slots and high slot flux leakages, for which only the finite element method has found good usage. This approach is based on the definition of a complementary mesh interlaced with the reluctance mesh, on the concept of material cell, and on unique rules to carry out both reluctances and magneto-motive forces. At this scope, definitions of mesh nodes, co-nodes, and auxiliary nodes are shown. The iron saturation can be easily taken in account, as well as motion effects. The circuit flux linkages are elected as state variables for integration, and they are directly linked to the loop fluxes in the magnetic network. The finite reluctance approach has been applied in this paper for dynamic modeling of an inverter-fed permanent-magnet linear synchronous motor.

Induction motors are presently the most widespread kind of electric machinery used for industrial and general purpose applications. The parameters of their equivalent circuit model can be determined with a combination of magneto-static and time-harmonic Finite Element Analysis (FEA) simulations. This paper investigates how equivalent circuit parameters depend on current and frequency variations. Calculation results obtained from FEA combined with analytical formulas are experimentally assessed by measurements on a small sample motor used for household appliances.

Load-commutated inverters (LCIs) in conjunction with the wound-field synchronous motors (WFSMs) are one of the most applicable drive topologies, and in some cases the only choice, in high-power medium-voltage applications. In this paper, a novel strategy is presented for field oriented control (FOC) of these drives in stator flux coordinates. Considering rotor saliency, independent flux and speed control is carried out to achieve maximum torque to ampere ratio. Furthermore, the proposed strategy provides a simple way to design the PI controllers' parameters according to the phase-controlled DC machine and WFSM drive analogy. Simulation studies are presented to verify the performance of the total proposed control scheme. Comparisons show the superiority of the proposed method over the conventional drive technologies for LCI-fed WFSM drives.

A fault-tolerant machine used for safety-critical tasks must a) guarantee at least a reduced-performance operation in case of partial machine fault and b) guarantee avoidance of drive mechanical jam/stall in case of total machine fault, to allow for the intervention of the back-up systems. Classical hydrostatic transmissions used on board ships for critical tasks such as rudder and stabilizing fin steering gears fulfill both the requirements a), b) above, but recent proposals for substitution with full-electric drives (rotary motors coupled with multistage reduction gears) usually do not. Especially the requirement b) needs particular attention and increased complexity when dealing with geared drives. This paper proposes a linear permanent-magnet direct drive fulfilling both the requirements above, for (but not limited to) rudder/fin steering gears. The absence of gears grants the requirement b), whereas the full-modular structure satisfies a), with independently fed stator modules and multiple inverters. This paper addresses some fault scenarios including electrical failures, in the machine winding (short-circuited coils) and in the inverters (trip of one or more units). The performance degradation is studied and assessed for the cases considered by both simulations and measurements on a prototype.

In many applications, electric machines are designed for operation over a wide speed range and require important flux weakening capabilities at high speeds. This paper presents and innovative rotor mechanical design that endows an interior permanent magnet (IPM) machine with an intrinsic capability of reducing its own rotor flux at high speeds. Unlike most state-of-the-art flux-weakening techniques, the design does not involve any additional current source nor demagnetization currents to be injected into stator circuits. It relies on a purely mechanical device that establishes a partial magnetic short circuit between rotor permanent magnets. The device is able to self-activate by centrifugal force when the speed exceeds a given threshold that can be fixed by design. The paper presents criteria for dimensioning the new IPM rotor and a mathematical model to predict its performance. The proposed solution is implemented into a motor prototype whose manufacturing and testing are discussed for experimental validation.

An approach to machine modeling by using finite reluctances is proposed. The finite reluctance approach is well suited for fast modeling and dynamic simulation of electrical machines in general and of fractional-slot surface-mounted permanent magnet machines in particular. The latter usually have very large air gap and slots, with relevant leakage and large tangential components of flux density in air gap, slot, and magnets as well. Modeling tools as winding functions are not accurate enough in this case, and thus time-stepping finite elements are used, which are slow and with limited time-step resolution (i.e. low simulation frequency). The approach used in this paper uses magnetic networks built on the principle of the cell theory. Network reluctances and magnet MMFs are defined by using unique rules. This paper shows that, besides faster dynamic simulations, the finite reluctance approach allows the graphical representation of the magnetic vector and scalar fields inside the machine, in a way very similar to the more cumbersome finite element method, but with a much smaller computational effort. The results from both the methods are presented and compared for a case study of permanent magnet linear synchronous motor.

Synchronous reluctance (SynRel) motors with rotor flux barriers are gaining increasing attractiveness in automotive applications thanks to their cheap, rugged and magnet-free rotor construction. When equipped with a split-phase stator winding and supplied from multiple inverters, these machines can exhibit further merits as traction motors in regard to enhanced fault tolerance compared to conventional three-phase solutions. Since SynRel motors are usually designed through iterative optimization techniques, it is highly desirable to have accurate and fast methods to predict their performance without the need for time-consuming finite element analysis (FEA) simulations. An analytical procedure is set forth in this paper to analytically model and simulate a SynRel motor with a split-phase stator winding through a magnetic equivalent circuit (MEC) technique. MEC parameters are computed from analytical formulas describing the air-gap magneto-motive force distribution and the magnetic field inside flux barriers. As an output, the air-gap flux density of the SynRel motor can be computed through the presented technique at any operating point. Results are positively assessed by comparison with FEA simulation on a sample SynRel motor including magnetic saturation effects.

Synchronous reluctance motors with rotor flux barriers are a promising type of electric machines thanks to various benefits, among the others, the absence of permanent magnets and rotor excitation. A challenge in the study of these motors is the accurate prediction of their air-gap field analytically taking into proper account the effects of rotor flux barriers. This paper proposes a technique for this purpose based on reluctance network solution and winding functions. The reluctance associated to each flux barrier is computed by means of conformal mapping. Furthermore, the slotting effect is also considered through appropriate permeance function definition. Analytical results are compared to finite element analysis showing a good matching for various machine topologies characterized by a different number of flux barriers.

Permanent magnet synchronous machines, especially if designed with open stator slots, may suffer from important cogging torque issues. A special magnetic wedge design has been presented in a companion paper to cope with this problem. The design of such wedge is herein processed through a genetic algorithm in order to find the optimal configuration, which leads to cogging torque minimization. An optimal design configuration is found and compared to non-optimal ones to quantify the benefits that can be achieved by genetic optimization.

Inverter-fed Induction motor performance is known to be noticeably affected by the supply voltage waveform. Nevertheless, the prediction of how supply voltage harmonics impact on motor operation in terms of losses, noise and thermal behavior is still a problem that can be hardly approached through simulations and analysis, therefore experimental data constitute an important source for information. In this paper the test results of two high-power induction-motor drives are presented showing their performance under different voltage waveforms. Among the other things, it is shown how low-frequency distortions in the supply voltage may have considerably stronger impacts on motor behavior than PWM harmonics, although the overall THD under PWM supply is higher.

The problem of accurately computing rotor eddy-current losses in synchronous machines subject to non-sinusoidal phase currents is usually approached with Time-Stepping Finite-Element Analysis (TSFEA), where rotor motion and armature current distortion effects are naturally included. The drawbacks of TSFEA are the long computation times and the need to wait for steady-state conditions to extract results. Such features make TSFEA unsuitable for integration into automatic design optimization programs. This paper illustrates how the problem can be alternatively solved by Time-Harmonic Finite-Element Analysis (THFEA) on a set of modified machine models conceived so that rotor motion and current distortion effects can be accounted for. As an illustrative example, the proposed method is applied to a Surface Permanent-Magnet (SPM) generator whose electromagnetic design is being processed through genetic optimization algorithms. Eddy-current losses are independently computed by both TSFEA and TFFEA in different generator operating conditions and design configurations showing that results are in good accordance. Furthermore, the proposed approach takes much smaller simulation times and can be easily incorporated into the overall optimization process.

For several reasons, relating to reliability, power segmentation and performance enhancement, it may be convenient for an induction motor to be supplied by two (if not more) three-phase inverters. The most common design solution for this purpose is the split-phase one, where the stator wining is split into two three-phase sections displaced by 30 electrical degrees apart, each fed by an inverter. An alternative possibility is explored in this paper where the two motor windings are not displaced and they are suitable for being fed by in-phase supply voltage systems. The solution has been implemented in a 13 MW induction motor drive. Its performance is reported in this paper based on measurements taken during system testing.

Salient-pole synchronous generators are conventional electric machines which have been widely studied over decades. Nevertheless, some aspects still constitute a challenge for designers and need to be approached with state-of-the-art modeling and computation techniques. An example is illustrated in this paper dealing with a 14 MVA synchronous generator. Different design solutions for its damper cage are studied and implemented on full-scale machine prototypes. Transient finite-element analyses are used to predict the influence of damper design on machine sub-transient reactances. Comparisons are presented between experimental results and finite element simulations and a physical interpretation is provided of the relationship found between damper structure and machine sub-transient reactances.

Electric motors equipped with multiple three-phase windings are often used for the advantages they offer in terms of reliability, performance, and inverter power segmentation. When the windings are fed by independent voltage-source inverters (VSIs), circulation harmonic currents can occur in stator phases. If the motor is an induction machine, circulation currents are known to originate form transient imbalances in the applied voltages due to inverter switching. This paper investigates the problem when a synchronous machine is used and shows how additional (and possibly major) sources for circulation currents can arise in this case (even with a round-rotor design) due to the nonsinusoidal air-gap flux distribution. The phenomenon is illustrated for a 45-MW quadruple three-phase synchronous motor supplied by four medium-voltage (MV) multilevel VSIs. Its circulation currents are predicted with two alternative methods, i.e., analytically and from time-stepping finite-element simulation. The results obtained in both ways are shown to well match measurement results collected on the actual motor during full-load system testing.

Multi-phase machines are of increasing importance in today’s electric drives and generation systems. While in three-phase machines stator leakage flux phenomena are usually described with a single parameter, a higher number of independent leakage inductances is required as the number of phases increases. The impact of leakage inductances on multi-phase machine performance, especially in PWM inverter-supplied motors, is proved by many studies. Hence the need originates for the electromagnetic designer to have easy-to-use but sufficiently accurate calculation formulas giving the complete set of mutual inductance in a multi-phase machine. This paper aims at providing such formulas making abstraction of the particular phase arrangement in the stator winding and under the hypothesis of equal phase belts. The computation algorithms provided are assessed against measurements on actual machines wherever possible; otherwise accurate Finite Element (FE) analyses are used for validation.

Phase-split synchronous motors supplied by multiple three-phase Load Commutated Inverters are of importance in high power applications. A criticality of such systems is the possibility that commutations within different stator windings may overlap. The analysis of the resulting transients is complicated by the magnetic interference of motor phases among them and with rotor circuits. In this paper the complete dynamic model of phase-split synchronous machines is manipulated to derive a simple analytical and circuital description of commutation transients, including the case of multiple simultaneous commutation events. Numeric simulation results are presented to cross-check the proposed model.