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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.

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.

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.

The study of electric machines subject to rotor eccentricity is usually performed using a winding and permeance function approach. In this paper, an alternative method is investigated based on conformal mapping. The geometry of a an eccentric round-rotor machine is mapped into a uniform air-gap topology by means of Moebius conformal map. The mathematical details of the method are provided along with explicit formulas to compute the air-gap field and inductances of the eccentric machine. It shown how, unlike conventional winding-function theory, the proposed method yields closed-form formulas which do not involve series expansions nor require numerical integrations and are thus particularly fit for implementation into fast simulation programs. Such expressions are assessed by comparison with Finite Element Analysis (FEA).

The study of electric machines subject to rotor eccentricity is usually performed using a winding and permeance function approach. In a companion paper, an alternative method is investigated based on conformal mapping. The geometry of a an eccentric round-rotor machine has been mapped into a uniform air-gap topology by means of Moebius conformal map. In this paper, the approach is used to derive explicit formulas to compute the unbalanced magnetic pull of the eccentric machine. It shown how, unlike conventional winding-function theory, the proposed method yields closed-form formulas which do not involve series expansions nor require numerical integrations and are thus particularly fit for implementation into fast simulation programs. Such expressions are assessed by comparison with Finite Element Analysis (FEA).

The complex relative permeance function is a useful mathematical tool to study the magnetic field of electric machines with slotted air gap. In the literature, the complex permeance function is usually identified by means of numerical techniques based on conformal mapping. In this paper an alternative analytical approach is proposed. The method is based on solving the magnetostatic differential field equation over a portion of the slotted air gap by imposing suitable boundary conditions in the slot opening region. Such boundary conditions exploit the mathematical law which governs the divergence of the magnetic field in the neighborhood of corner-shaped ferromagnetic regions. Furthermore, the results of Carter theory on slot fringing effects on the air gap field are used. A simple easy-to-compute formula is obtained for the complex permeance function. Its accuracy is assessed by comparison with Finite Element Analysis (FEA).

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.

Fractional slot windings based on concentrated tooth coils are frequently used in today's electric machines. A drawback of these windings is the occurrence of large space harmonics in the air gap, which can cause torque ripple issues and rotor additional losses. Various provisions have been proposed in the literature to improve the air-gap harmonic content due to concentrated-winding armature reaction. This paper proposes an enhancement based on a multiple-layer design characterized by tooth coils with different number of turns. The improvement is proposed for 12-slot 10-pole permanent magnet machines but can be generalized to other possible topologies. It is shown that the proposed approach leads to the same air-gap field harmonic content as for a dual-three-phase dual-layer winding with all space harmonics reduced by the same coefficient (equal to 0.928). Pros and contras of the proposed design with respect to other existing improved solutions are highlighted in the paper. Comparisons and assessments are provided based on Finite Element Analysis (FEA).

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

Round conductive bars embedded in semi-closed slots are frequently used in the construction of electric machinery, for instance in the squirrel cage of induction motors. Frequently, such as in the study of induction motor steady-state performance at rated slip, it is useful to estimate the slot leakage inductance of these conductors under the hypothesis of no eddy currents and no magnetic saturation. This is usually done through simple approximated analytical formulas available in the literature. In this paper, an improved explicit ready-to-use leakage inductance expression for circular bars embedded in semi-closed slots is derived by solving Poisson's equation in the slot domain. The precision of the proposed formulation is assessed against Finite Element Analysis (FEA) for various slot geometries and is shown to always give very accurate results, with errors below 2%. Conversely, approximated simplified formulas available from the literature are demonstrated to possibly give large errors, which exceed 20% for some explored slot geometries.

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.

Slot leakage field accounts for an important quota of the total leakage flux in electric machines. The computation of unsaturated slot leakage inductances can rely on analytical formulas for simple open slot shapes, while the case of semiclosed slots is more critical and typically requires finite element analysis (FEA) or analytically solving the field over the whole machine domain. This paper sets forth an analytical procedure for computing the leakage field in semiclosed slots of unsaturated electric machines. The method is based on solving Maxwell's equations in the slot domain alone, which is made possible by appropriately defining boundary conditions in the slot opening region. The method proposed is assessed by comparison with FEA. Validations indicate that a good accuracy is achieved by the presented approach in predicting unsaturated leakage inductances, while FEA is required when magnetic saturation effects need to be taken into account.

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.

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.

Various analytical techniques have been proposed in the literature for cogging torque computation in Surface Permanent Magnet (SPM) machines. Among the various available methods, the ones found to be satisfactorily accurate are based on the Maxwell's stress tensor, which involves both normal and tangential air-gap field and lead to quite involved calculation formulas. In this paper, a relatively simple alternative is proposed where permanent magnets are modeled as equivalent field circuits to which a well defined winding function can be associated. The approach leads to a plain cogging torque formulation where only the normal no-load air-gap flux density appears. The accuracy of the method is assessed by Finite Element (FE) analysis on some sample SPM machine geometries. The results are shown to match FE simulations with a satisfactory accuracy compared to Maxwell-stress-tensor-based analytical techniques available from the literature.

Many shipboard loads requiring high torques at very low speeds, like capstans, bow thrusters, rudders, stabilizing fins, etc., are presently driven by hydrostatic actuators. This paper presents an innovative inverter-fed electric linear motor prototype conceived to replace hydrostatic drives with large expected benefits in compactness, maintenance, efficiency and reliability. The linear motor prototype has been designed through special optimization algorithms based on finite element analysis to maximize the force density. The electromagnetic and mechanical structure has been also selected to achieve superior reliability by means of structural simplicity, robustness and redundancy. Along with design criteria, the paper outlines the prototype technology and the construction issues and provides some testing results collected during the experimental performance assessment.

It is known from the literature that in electric machines with open stator slots, the air-gap flux partly enters the slot openings and induces eddy currents in the conductors placed closest to the air gap, possibly causing local overheating issues. For the study of such phenomenon, time-stepping finite-element analysis (TSFEA) is employed by many authors. This paper presents an alternative approach based on a set of time-harmonic finite-element analysis (THFEA) simulations. The proposed method can be applied to surface permanent-magnet machines and offers the advantage of a shorter computation time with respect to THFEA. It is also more suitable for being integrated into automatic design optimization programs. The accuracy of the approach is assessed by comparing stator eddy-current losses independently computed by THFEA and TSFEA for different machine geometries and operating conditions. Results obtained in the two ways are shown to be in good accordance.

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.

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.

In this paper two possible design alternatives are investigated for a high-power synchronous motor propulsion drive employing two voltage-source inverters for motor supply. The two arrangements are compared based on their steady-state behavior in both normal and faulty conditions (i.e. with one out-of-service inverter), predicted by time-stepping finite-element simulations. Simulation results found consistent with the results expected theoretically and based on previous studies. Pros and contras of the two design alternatives are highlighted together with the possible design strategies that could help mitigate their drawbacks.