A unified approach to main flux saturation modelling in D-Q axismodels of induction machines

Main flux saturation is most frequently modelled by selecting either stator and rotor d-q axis currents or stator and rotor d-q axis flux linkages as state-space variables. This paper attempts to unify main flux saturation modelling in d-q axis models of induction machines by presenting a general method of saturation modelling. Selection of state-space variables in the saturated machine model is arbitrary and appropriate models in terms of different state-space variables result by application of the method. A couple of models, obtainable with different selection of state-space variables, are presented. The cross-saturation effect is explicitly present in all the models, except for the one with stator and rotor flux linkage d-q axis components as state-space variables. The models are verified by simulation and experimental investigation of induction generator self-excitation     

Constraints on saturation modeling in AC machines

The author presents constraints which must be satisfied by saturation models of lossless fields. Nonlinear terms are added to linear models to represent the saturation phenomenon. The major point is to emphasize that these nonlinear terms cannot be arbitrarily specified when lossless fields are assumed. This is done by returning to the fundamental laws which make up a typical dynamic model and showing that the traditional assumptions impose well defined constraints on the nonlinear terms. The constraints are derived from energy balance principles and must be satisfied by the flux linkage/current relationships in order to ensure consistency with the assumptions of a lossless field. The constraints are used to design a consistent saturation model for a synchronous machine     

A generalized 3-D dynamic modelling for transverse flux homopolarlinear machines based on statistical saliency-effect superpositionmethod

This paper presents a prototype of a transverse flux homopolar linear machine system, along with a systematic and generalized 3-D approach which is capable of analyzing three kinds of these linear machines: the transverse flux linear induction machine; the homopolar linear synchronous machine; and the transverse flux linear reluctance machine; all in one compact mathematical model. A novel methodology which combines the state-space technique with the statistical saliency effect superposition method is proposed. With such a detailed and generalized modelling approach, the capability of analyzing the saliency effects induced by the distributed windings in practical linear machine systems is enhanced, and the representations of all the related linear machine system equations can be manipulated in compact matrix forms. Experimental verifications confirm that this comprehensive theoretical approach is a convenient and reliable mathematical basis for computer-aided analysis and design studies on linear machine systems     

Direct control of air-gap flux in permanent-magnet machines

A new field weakening and adjustment technology for PM machines by direct control of air-gap fluxes is introduced. This new technology requires no current decomposition by the inverter eliminating the need for a position sensor. Demagnetization, which normally occurs during field weakening, does not occur with this new method. The field-weakening ratio can reach 10:1 or higher. This technology is robust and particularly useful for, but not limited to, electric vehicle drives and PM generators     

Force density limits in low-speed permanent-magnet machines due to saturation

This work discusses the practical limits imposed by magnetic saturation for the force density in low-speed permanent-magnet electric machines. The force density dependence on current density and slot depth is investigated with the aid of finite-element modeling. For saturation reasons, shallow slots are more favorable for achieving high force densities. However, for thermal reasons, deeper slots become favorable. Therefore, an optimum slot depth that maximizes the force density for each current density level exists. The maximum allowable slot depth range for four low-speed applications has been identified for a given maximum motor diameter.     

Experimental study of the saturation and the cross-magnetizingphenomenon in saturated synchronous machines

The cross-magnetizing effect in both the d- and q-axis in a small salient-pole machine was measured. Two simple equations describing the cross-magnetizing effect in both axis directions are derived. An accurate saturation representation that includes the effect of both the machine-saturated reactances and the cross-magnetizing phenomena is also given. In addition to this, the modified phasor diagram and power/load angle relationship are obtained. The results of the machine output power obtained by this technique show a good agreement with those obtained from test. The saturation effect in changing the power/load angle curves is seen to be noticeably large and depends mainly upon the cross-magnetizing effect     

Reluctance distribution modelling of saturated salient polesynchronous machines

This model was developed in response to the demand for fast, simple, and reasonably accurate methods for modelling heavily saturated synchronous machines. This paper outlines the development and performance of a new air gap flux density model for saturated salient pole synchronous machines. The model has four main components and its performance is demonstrated by comparing its computed flux density distribution and rotor torque with measured results for static conditions. The model gives reasonable results considering its simplicity     

A two-factor saturation model for synchronous machines withmultiple rotor circuits

It is generally felt that no major accuracy breakthrough in predicting the steady-state and transient performance of synchronous machines could be achieved without taking proper account of the iron saturation effects as well as eddy-current losses. Although the two issues were often treated separately in the past, this paper attempts to unite them by developing a general model covering both the main-path magnetic saturation and frequency effects in the dynamic equations. Mathematical analysis in the d-q space pinpoints cross-saturation coupling which, a priori, does not seem to be symmetrical for salient-pole machines. Yet the model is theoretically sound, since it fulfils at least the physical constraints using energy balance principles. Some test points from a 555-MVA turbine-generator are used for an initial assessment the model's capability to predict the field current and internal angle for various loading conditions     

Measurement of the saturation characteristics in the quadrature axis of synchronous machines

For the accurate prediction of the performances of saturated synchronous machines, the saturation characteristics in both the direct and quadrature axes are needed. The d-axis saturation characteristic of a synchronous machine can be measured easily by the open-circuit test with the machine excited from its field winding. On the other hand, the q-axis saturation characteristic of a synchronous machine cannot be measured applying a similar easy, simple method and, as a result, these characteristics are usually not experimentally measured and are not available. In this paper, three possible experimental methods for determining the q-axis saturation characteristics of both cylindrical-rotor and salient-pole synchronous machines are presented. The merits and demerits of these experimental methods are discussed from the point of view of their complexity and their accuracy. Comparisons between the measured q-axis saturation characteristics obtained by these experimental methods are made for a cylindrical-rotor machine and two salient-pole machines. Moreover, the various sources of errors, which may affect the accuracy of determining the q-axis saturation characteristics by these methods, are investigated.     

Assessment of interbar currents in double-cage induction motorswith broken bars

Research has shown that it is possible for currents to flow in a broken rotor bar of a squirrel cage induction motor by means of interbar currents. Such research dealt only with single-cage motors. Further work was necessary when considering double-cage motors. This paper proves theoretically and experimentally that interbar currents also exist in double-cage motors. The influence of interbar currents on the current distribution around the broken bar is also shown     

Bond graph modelling and simulation of spice-pounding machines fed from a photovoltaic source

The dynamics of intermittent load systems fed from a PV source are explored, led by the expanding application of PV power in diverse areas. Most actual loads in small-scale village industry are intermittent and pulsating. For successful application of photovoltaics in these areas, the dynamical behaviour of such systems must be understood. This requires the formulation of dynamical models of PV-fed intermittent load systems. Bond graph methodology has recently emerged as a very convenient tool for dynamic modelling. This is the first application of this methodology in modelling photovoltaic systems. The spice-pounding operation is taken as a typical example of a pulsating load that can be fed from PV power. It is shown that the standard equivalent circuit of the PV cell gives rise to algebraic looping problems when expressed in the language of the bond graph. Means of overcoming the problem have been suggested. This is the first report of modelling the spice-pounding machine with the bond graph technique. The model has been simulated with COSMO–KGP software (developed at the I.I.T., Kharagpur, India) and the results reported. It is found that the dynamic behaviour of the PV-fed spice-pounding system differs significantly from that of a system fed from a constant voltage supply. Performance is compared for a shunt motor, a series motor and a separately excited motor, and three types of cam profiles, namely parabolic, cycloidal and half harmonic plus constant velocity. © 1997 by John Wiley & Sons, Ltd.     

A comparison of power density for axial flux machines based ongeneral purpose sizing equations

Based on the concept of the converter fed machine (CFM), an optimal machine design can be considered as the best match of the machine topology, the power electronic converter and the performance specification. To compare power production potential of axial flux machines with various topologies, different waveforms of back EMF and current, general purpose sizing and power density equations for such machines are needed. In this paper, a general approach is presented to develop and to interpret these equations. Sample applications of the sizing and power density equations are the axial flux toroidal permanent magnet utilized to compare the axial flux toroidal permanent magnet (AFTPM) machine and the axial flux two-stator permanent magnet (AF2SPM) machine     

Methods for determining the q-axis saturation characteristics of salient-pole synchronous machines from the measured d-axis characteristics

For the accurate analysis of salient-pole synchronous machines using the two-axis frame models, the direct- (d-) and quadrature-axis (q-axis) saturation characteristics are needed. Usually, the d-axis saturation characteristics can be obtained easily by the conventional open-circuit test with the machines excited from their field winding. On the other hand, the q-axis saturation characteristics of synchronous machines cannot be measured applying simple, conventional methods, and thus, they are usually not available. In this paper, four different methods for calculating the q-axis saturation characteristics of salient-pole synchronous machines from the measured d-axis saturation characteristics are explored. In these methods, the q-axis saturation characteristics can be calculated from the readily available test data, namely the d-axis saturation characteristics and the d- and q-axis unsaturated magnetizing reactances. Finally, a comparison between these methods is made.     

Solar thermal modelling of a non-airconditioned building: Evaluation of overall heat flux

This paper presents an investigation of the thermal behaviour of a non-airconditioned building with walls/roof being exposed to periodic solar radiation and atmospheric air while the inside air temperature is controlled by an isothermal mass, window and door in the walls of the room. The effects of air ventilation and infiltration, the heat capacities of the isothermal storage mass inside air and walls/roof, heat loss into the ground, and the presence/absence of the window/door have been incorporated in the realistic time dependent periodic heat transfer analysis to evaluate the overall heat flux coming into the room and the inside air temperature. A numerical computer model using typical weather data for Delhi has been made to appreciate the analytical results quantitatively. It is found that the heat fluxes through different walls have different magnitudes and phase lags w.r.t. the corresponding solair temperatures. The overall heat flux coming into the room as well as the room air temperature are sensitive functions of the number of air changes per hour, closing/opening of the window and the door ventilation. The effects of the heat capacity of the isothermal mass and the basement ground are found to reduce the inside air temperature swing and the presence of a window is found to increase the inside air temperature even when the window area is much smaller than the wall/roof area. The model presented would be an aid to a building architect for good thermal design of non-airconditioned buildings.     

Extension of the compensated distortion method to the critical heat flux modelling in rectangular inclined channel

Parameters of critical heat flux modelling in inclined rectangular channels for high-pressure convective two-phase flows have been derived using the compensated distortion method of Ahmad [Int. J. Heat Mass Transfer 16 (1973) 641]. Fréon R12 was used as the modelling fluid. A specific expression for the modelling parameter has been obtained by introducing a new dimensionless parameter that accounts for the effect of inclination on critical heat flux. This parameter is built by balancing the inertial force acting on a particle against the viscous effect corrected by a transverse term of gravity. In the same time, a dimensionless correlation of critical heat flux is proposed, which describes available data with an r.m.s. error of 13.1%.     

Experimental validation of CFD modelling for heat transfer coefficient predictions in axial flux permanent magnet generators

This paper describes the experimental validation of CFD modelling for heat transfer coefficients in an axial flux permanent magnet (AFPM) generator. A large scale low speed test rig was designed and constructed. The geometric parameters and the rotational speed of the test rig were determined by dimensional analysis, to ensure the flow characteristic remains unchanged as compared with commercial AFPM generators. The heat transfer coefficients in the test rig were measured at rotational Reynolds number, Re_ω from 0 to 2 × 10⁶, non-dimensional flow rate, C_w up to 11,000 and gap ratio, G = 0.016, by using the combination of heat flux sensors and thermocouples. Due to the large size of the scaled-up rig, natural convection played a significant part in the heat transfer and this had to be compensated for in the forced convection heat transfer coefficient calculations. Extra experiments were designed and conducted to identify the effect of natural convection on the machine’s cooling. The experimentally determined results were compared to heat transfer coefficients predicted by CFD models and good agreement was obtained.     

Assessing transient response of DFIG based wind turbines during voltage dips regarding main flux saturation and rotor deep-bar effect

With increasing wind power penetration, transient responses of doubly-fed-induction-generator (DFIG) based wind turbines gain attentive focus. Accurate prediction of transient performance of DFIG under grid faults is required with increasing wind power penetration. Taking into account the main flux saturation and deep-bar effect, this paper concentrates on transient responses and stability of the DFIG system under symmetrical grid faults. Their roles played in the enhancement of system transient stability are clarified. The analyses proposed contribute greatly to proper selection, design and coordination of protection devices and control strategies as well as stability studies.     

Availability of luminous flux below a bended light-pipe: Design modelling under optimal daylight conditions

To quantify an averaged directionality of light beams transmitted by hollow light guides the asymmetry parameter has been introduced which is computed from the luminous intensity solid or curve. In many situations, the light guides with upper part elbowed toward the Southern sky are able to collect more light than a corresponding straight pipe. However, under different sunlight and skylight conditions the internal reflections are more complex, resulting in a large variety of light-pipe efficiency. A more realistic prediction of the luminous intensity solid under manifold exterior daylight conditions is significant for the optimal design and installation of passive illumination systems using bended light guides. Here, the orientation of the elbow is crucial for an efficient utilization of daylight, especially during a clear day. This study documents that the maximum efficiency of the bended light-pipe is reached when its upper part is pointed nearby the sun position but directly towards the sun.     

Aggregate modelling of wind farms containing full-converter wind turbine generators with permanent magnet synchronous machines: transient stability studies

When the transient interaction between a large wind farm and a power system is to be studied, there are two possible approaches to wind farm modelling. It can be modelled as one or more equivalent wind turbine generators (aggregate modelling) or each wind turbine generator (WTG) can be modelled separately (detailed modelling). When a power system with many wind farms is to be simulated, the aggregate approach becomes especially attractive. A successful aggregate model will reduce the simulation time without significantly compromising the accuracy of the results in comparison to the detailed model. Here, the aggregate modelling options for a wind farm with 5 MW full-converter WTGs (FCWTGs) using permanent magnet synchronous machines are presented. A braking resistor in the DC circuit of the FCWTG?s converter system is employed as a means of satisfying the latest grid code requirements. It will be shown that with a braking resistor implemented in the FCWTG there is scope for significant model simplifications, which is particularly relevant for transient stability studies of large-scale systems.     

Efficiency trends in electric machines and drives

Almost all electricity in the UK is generated by rotating electrical generators, and approximately half of it is used to drive electrical motors. This means that efficiency improvements to electrical machines can have a very large impact on energy consumption. The key challenges to increased efficiency in systems driven by electrical machines lie in three areas: to extend the application of variable-speed electric drives into new areas through reduction of power electronic and control costs; to integrate the drive and the driven load to maximise system efficiency; and to increase the efficiency of the electrical drive itself. In the short to medium term, efficiency gains within electrical machines will result from the development of new materials and construction techniques. Approximately a quarter of new electrical machines are driven by variable-speed drives. These are a less mature product than electrical machines and should see larger efficiency gains over the next 50 years. Advances will occur, with new types of power electronic devices that reduce switching and conduction loss. With variable-speed drives, there is complete freedom to vary the speed of the driven load. Replacing fixed-speed machines with variable-speed drives for a high proportion of industrial loads could mean a 15–30% energy saving. This could save the UK 15 billion kWh of electricity per year which, when combined with motor and drive efficiency gains, would amount to a total annual saving of 24 billion kWh.