Analysis
Design optimisation forms an integral part of modern electrical machine development. Traditional optimisation methods use an in-line cascade series approach whereby the de- sign parameters are adjusted (within the design domain) after each iteration until the requirements are met. As an LS PMSM has two operational states, a two-tier approach as in Fig. 1.12 is used whereby: (i) the steady-state performance is optimised first; (ii) when a candidate design that satisfies the optimisation objectives is found, it undergoes
Figure 1.11: Modern LS PMSM topologies [29]
a synchronisation test. If synchronisation is achieved the optimisation is ended, if syn- chronisation is not achieved the whole process is repeated within the design optimisation framework. The two-tier optimisation continues until the candidate design passes both the steady-state and synchronisation tests. This approach has been used in several past publications and can easily be adapted for various modelling methods, like analytical [19], finite element analysis (FEA) [34] or a combination of the two [35–37].
1.3.1
Steady-state Performance Analysis Overview
There is extensive published work on steady-state design and optimisation of LS PMSMs using both classical machine theory and FEA. Steady-state performance is inspected with either classical machine theory (analytical approach), static FEA or transient time-step FEA simulations.
A publication by Honsinger in 1980 represented an analytical approach to determine the performance of an LS PMSM. This method used either phasor diagrams or machine admittance by which core losses are included [38]. According to Google Scholar, this pa- per has been cited in 106 other publications. This approach is used by most commercial machine packages [25]. Mellor developed a static test, which together with a no-load test can be used to determine the d-q axis parameters without the use of the load angle [39]. The method was implemented on the machine presented by Chalmers in [26].
With the development of FEA software packages during the mid to late 90’s, the im- plementation of optimisation was easier and the results gained from these simulations were more accurate. This was proven in 2000 by Knight in [35]. A basic steady-state op- timisation was implemented on a machine originally designed with the analytical method and a 4% increase in efficiency was gained. Since this implementation and advances in software packages, FEA simulations have gained interest and the majority of machine optimisation is done in this environment. The method proposed by Honsinger is in many cases used in conjunction with this approach as it is computational less expensive. In 2012, Sardarbadi presented a method to determine the equivalent circuit parameters of a PMSM [40]. This FEA method also incorporated the influence of skin effects into the cal- culation. Four FEA simulations were required to determine the parameters as saturation of magnetic structures can cause large changes in the parameters of an LS PMSM [25]. By using the d-q axis method, the machine parameters are assumed to remain constant.
1.3.2
Transient Performance Analysis Overview
A key part during the design of an LS PMSM is validating the synchronisation perfor- mance of the machine. Both the maximum load inertia synchronisation capability or the time to reach synchronisation are key performance indicators of a machine design. Cur- rently, transient time-step FEA simulations are mostly used to validate machine synchro- nisation. However, this verification method is computationally expensive thus limiting the possibility for designers to incorporate it into an optimisation procedure. The use of an analytical synchronisation model has been proposed by researchers such as Hon- singer [18], Miller [29], Rahman [16,19,41] and Soulard [42].
The first mention of the asynchronous performance requirements was in 1978 by Binns [43]. It was not until 1980 that Honsinger fully investigated each torque com- ponent. In his publication, focus was only places on the asynchronous operation of an LS PMSM [18]. Fig. 1.13 (closely resembling that of Fig. 1.4) contains both Ta components
namely Tm and Tcin (a) and (b). It is shown how Ta is determined from the instantaneous
torque during the acceleration up to synchronisation. The findings published in this paper are regarded as one of the key contributions on LS PMSM.
(a) (b)
Figure 1.13: Honsinger’s torque component classification for (a) average torque (b) run-up torque. Reconstructed from [18]
Miller’s findings in [29] can also be linked to Honsinger’s work. He investigated the synchronisation process of the machine during transient operation as well as the load synchronisation capability of the machine. The effects of the load inertia and what effect applying the load only after synchronisation has on performance were also included. It was found that the machine used for the investigation had the ability to drive a higher steady-state load than it could obtain synchronisation with. This applies to almost all LS PMSMs. Miller also states that Tm is present over all speeds and that near synchronous
speed a high gradient asynchronous cage torque profile is critical to achieving synchronisa- tion. His biggest contribution was the formulation of the first synchronisation projection criteria that included the effects of the p.u. load inertia.
One drawback of Miller’s method is that he assumed the magnetic flux to be con- stant, this, however, was addressed in [44] when a new model was proposed that took into account both the armature reaction, saturation and the effects they have on the flux distribution during transient synchronisation. This resulted in a better calculation of the dq flux linkages in the machine.
During synchronisation, two torque dips occur that influence the synchronisation ca- pability of the machine. The first and larger dip is due to the braking torque and the second dip is due to the asymmetric dq-axis difference in the rotor. The second dip was not included in past work as it was thought to be neglectfully small. However, this is only true for a well-designed machine. In his study, Isizaki formulated a method by combining FEA field calculations with a harmonic permeance coefficient to predict the asynchronous performance more accurately [45]. Both the torque dips due to peak braking torque and the dq asymmetric differences were noted and included.
During transient synchronisation, saturation occurs in both the rotor and stator iron and varies until steady-state is reached. The effect this has was discarded in the past and was included for the first time by Rahman. The method he proposed included the effects of saturation as well as investigating demagnetisation on the two-axis dq-system in transition numerical simulations [46]. In Rahman’s 1991 publication [47], a new method was introduced linked to his previous work (that determined the saturation) considering
both the back-EMF and the interactions between the dq-axis fields. The investigation was done on a typical 4-pole radial flux topology.
Analytical synchronisation criteria methods are very efficient and have a high accu- racy in predicting synchronisation. By implementing Raman’s analytical, energy based, synchronisation criteria as part of an optimisation framework the use of costly transient time-step FEA simulations could be minimised. The synchronisation process can be gram- matically represented in both the S − δ plane and torque-speed domain as in Fig. 1.14 and 1.15 respectively. For both figures, case (a) represents a synchronised machine as it settles at a fixed point in Fig. 1.14 (a) and 1500 rpm in Fig. 1.15 (a). Case (b) represents a non-synchronised as a continuous oscillation occurs at a sub-synchronous speed.
Figure 1.14: Graphical representation of analytical synchronisation method in the S−δ domain of (a) synchronise machine (b) non-synchronised machine
Figure 1.15: Graphical representation of analytical synchronisation method in the torque-speed domain of (a) synchronise machine (b) non-synchronised machine
As stated above, for validating the synchronisation performance of LS PMSMs, the more favoured approach is the use of transient time-step FEA simulations. This is because the designer does not require an in-depth background or understanding of complicated partial differential theory. However, this verification method is computationally expensive
not experimentally verified this was the first use of this approach. Since software packages (that are used to do 2D time-step FEA simulations) can incorporate the effects of different occurrences such as demagnetisation, material saturation, temperature influences, etc. to a great extent (and with less complexity than classical analytical methods) has made the use of this method favoured among designers. Fig. 1.16 illustrates the two resulting cases obtained from FEA simulations namely synchronise (yellow) and non-synchronised (blue). The same two machines were used to generate the plots as for Figures 1.14 and 1.15 as FEA packages also provide the user with the option to obtain plots for the torque-speed domain. 0.0 0.5 1.0 1.5 2.0 2.5 time (s) 500 0 500 1000 1500 2000 Speed (rpm) Synch: 2D-FEM Not synch: 2D-FEM
Figure 1.16: Graphical representation of FEA synchronisation method in the speed-time do- main for both synchronised and non-synchronised case