Modelling of the High Speed Multi-Pole Synchronous Generator for Application in More Electric Aircraft Power Systems

03/02/2015
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Modelling of the High Speed Multi-Pole Synchronous Generator  for Application in More Electric Aircraft Power Systems

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application/pdf Modelling of the High Speed Multi-Pole Synchronous Generator for Application in More Electric Aircraft Power Systems Michał Michna, Filip Kutt, Mieczysław Ronkowski
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Modelling of the High Speed Multi-Pole Synchronous Generator  for Application in More Electric Aircraft Power Systems

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Modelling of the High Speed Multi-Pole Synchronous Generator for Application in More Electric Aircraft Power Systems Michał Michna (1), Filip Kutt (2), Mieczysław Ronkowski (3) Faculty of Electrical and Control Engineering, Gdansk University of Technology, Poland 1 : michal.michna@pg.gda.pl, 2 : filip.kutt@pg.gda.pl 3 : mieczyslaw.ronkowski@pg.gda.pl Abstract In this paper different models of the synchronous generator are presented. The simulation results compared with the measurements are shown. Certain physical phenomena are included in described models for the porpoise of adequate analysis of the more electric aircraft power system. For different modelling levels, such as functional level or behavioural level, different physical phenomena have been included. Simulation results for simple functional level model and behavioural level model have been presented. The behavioural level model incorporates such physical phenomena as: magnetic saturation effect and the poliharmonic distribution of the air gap field. The models have been implemented into the Synopys/Saber software using the modelling language MAST. The carried out simulation and measured results have proved that the proposed approach can be recommended for analysis of MEA power systems. Introduction Synchronous generator (SG) is one of the most important components of the MEA onboard autonomous electrical power system (AEPS) (fig. 1). The prime mover in this instance is the aircraft jet engine. Fig. 1: General structure of AEPS Generally brushless, two or three stage, SG is used as the main generator in modern aircraft AEPS. This machine is composed of two synchronous machines and a rectifier on the same shaft [1]–[3]. Most important part of this generator in terms of modelling the system is the main synchronous generator. The rms value of generated voltage is controlled by the generator control unit (GCU). The main advantage of multiple stage generator is the very low excitation current of the exciter comparison to nominal current of the main generator. This means that the GCU can be much smaller and more reliable. In aircraft AEPS the SG has high influence on the system electric power parameters such as voltage and frequency but also the harmonic content of voltage and current. For the evaluation of AEPS performance in steady and transient states a novel and adequate modelling and simulation tools have been developed [4]–[9]. A key technique in achieving this is the use of an advanced network solver such as Synopsys/Saber based on a mixed-signal hardware description language called MAST [8], [10]. While using the modelling language MAST one is not only able to develop the various mathematical-based models needed, but is also able to develop mixed-signal and multi-physical (mixed-technology) models. Moreover, MAST models can be made at any level of abstraction – from simple transfer function descriptions, to detailed physics-based descriptions. And they can be mixed throughout multiple levels of hierarchy. The importance of SG in electrical power systems has been well recognized. They are highly nonlinear, complex electromechanical devices, whose dynamic behaviour directly impacts the performance and reliability of the power system network [1]–[3], [9], [11], [12]. To analyze the dynamic behaviour of the SG, an effective and accurate simulation model is desired. Models of different accuracy are used for different simulations of MEA AEPS. Generally, considering the four modelling levels of MEA power system, the four types of models can be characterized, as shown in Fig.1. At the architectural level the models represents the steady-state power consumptions (no dynamic response). The models are usually used for power budget studding. Fig. 2: Schematic of MEA power system modelling levels Modelling levels Architectural Functional Behavioral Component Complexity At the functional level the models represents the steady-state power consumptions and transient behaviour (inrush current, energy consumption dynamics with regards to input voltage transients, etc.). Such models do not include switching. The band frequency to be modelled is between 0 to 133Hz for periodic phenomena. The models are usually used for network logic and network stability studying. At the functional level the models represents the steady-state power consumptions and transient behaviour (inrush current, energy consumption dynamics with regards to input voltage transients, etc.). Such models do not include switching. The band frequency to be modelled is between 0 to 133Hz for periodic phenomena. The models are usually used for network logic and network stability studying. At the behavioural level the models are detailed functional models. They represent the actual dynamic waveforms, i.e., same representativeness as the functional models ones, and full representativeness of the waveforms (switching, HF rejection, etc.). Nevertheless, the phenomena above 250 kHz shall not be included. The models are usually used for network power quality studding. At the component level the models include a representative model of each single component of the MEA system or sub-system. The models are usually used for verification of local operation, and deep analysis of each component behaviour. Highest level of accuracy is achieved with FEM models. Unfortunately due to high complexity of the model it is impractical to use this model in AEPS analysis. For the behavioural and component level models a combination of FEM and lumped parameters models can be used. This combination takes form of lumped parameter model using the simulation results or data from previous simulations for definition of its parameters as functions of rotor position. However even though this approach is simpler the FEM model it still require high computing power to simulate. SG model A SG can be defined as a multiport electromechanical converter with electrical and mechanical ports. According to its degree of freedom the SG has two electrical and one mechanical ports. The main quantities of its model are voltages (vabc– stator, vqdr – rotor), currents (iabcs – stator, iqdr – rotor), rotor angular velocity (ωrm) and external torque (Tm). Fig. 3 shows the general structure of SG model. transformer couplings electromechanical couplings energy accumulators energu dissipators is ifd vs vfd Electrical stator ports Electrical rotor ports ωrm Tm Mechanical rotor port Fig. 3: General structure of SG model For developing the SG model in terms of its ports/terminals variables, i.e., especially for MEA power system analysis and design, the general equations of motion of SM are recalled. Fig. 4: Physical description of two-pole salient-pole synchronous generator with hybrid reference frames: axes as, bs and cs fixed in stator; axes q and d fixed in rotor Circuit theory is utilized to establish the general voltage and torque equations, expressed in terms of machine variables, for a SG shown in Fig.3 and Fig 4. The voltage, and torque equations in machine variables may be expressed as [13]: vabcs=-rsiabcs+ dλabcs dt (1) vqdr=rriqdr+ dλqdr dt (2) Te-Tm=J dωrm dt + Bmωrm (3) where: vabcs and i are respectively the stator 3- phase voltage and current, v and i are respectively rotor voltage and current in orthogonal direct and quadrature axis, r and r are the diagonal matrices of the stator and rotor winding resistances, is the electromagnetic torque is the inertia, friction coefficient, mechanical angular speed of the rotor The stator windings denoted by as, bs and cs are symmetrical and placed at the magnetic axes as, bs and cs displaced by 120 degrees (electrical), respectively. The rotor is equipped with a field winding denoted by fd, and two damper windings denoted by kq and kd placed at magnetic axes d and q are at right angle, respectively. The flux linkage vectors λ and λ in the equations (1) and (2) are following: = − (4) where the matrices denote: θ is the stator windings self and mutual inductance: = (5) is the rotor windings (field and damper cages) self and mutual inductance = ! ! 0 0 0 # # # ! 0 ! # ! ! (6) is the mutual inductance between stator and rotor windings = ! # ! ! # ! ! # ! (7) where the electrical angular displacement of the rotor, the subscripts $, %, & and ' denote stator, rotor, field and cage windings, respectively. The electromagnetic torque in terms of the energy stored in the coupling field: = ( ) 2 + ,- , , , , , (8) Where: - , , , , is coenergy function defined at [4]. The inductance’s functions in equations (4) – (8) can be calculated from FEM simulations or using simplified winding function approach [14]. The result are the functions described as Fourier series [8]. Equations (1) – (3) can be efficiently represented by an functional and behavioural model for MEA power systems analysis. Depending on the simulation objective the model of the synchronous generator can taking into account phenomena as: poliharmonic distribution of the air gap field and saturation effect [7], [8], [14]. Functional model of the SG Functional model is generally used in order to estimate the RMS values of voltages and currents in different parts of the AEPS. For this propose a simple dq0 model and the DC analysis is used. The Clark- Park transformation from three phase stator description (1)-(3) into orthogonal qd0 axes fixed to rotor [13] has been applied to describe machine model in reference frame variables. This transformation was based on the signal constant amplitude assumption. At the functional model terminals (three phase) the RMS values of voltages and currents is given. The transformation between the SG model dq values (fd, fq) and the terminal RMS values (fa, fb, fc) are given as: fa