Now that the researcher has established a background for the current dissertation, it is necessary to still provide additional information on what has been documented about the design optimisation cum performance analyses of the 12/10 and/or 12/14 RFM structured FSMs. By so doing, a clearer and narrower direction on the proposed research can be articulated.
Hence, over the years, the design, analyses and performance characteristics of the proposed 12/10 and 12/14 machines have been demonstrated in many studies. A track of some of these studies are summarised as follows:
Amara et al (2005) [54] presented a design procedure of the 12/10 machine using both ferrite and rare–earth PMs, based on geometry parameterisation (no optimisation) and FEA. The machines were designed at 2 kW for HS airborne applications, and compared in terms of mass, cost, and temperature sensitivity. The comparison reveals, among other things that, alt- hough the rare–earth machine uses fewer magnets, it is much more expensive than the ferrite design.
Based on a 2 kW, 1500 r/min, 12/10 machine, Hua et al (2006) [61] proposed a general de-
sign procedure for PM–FSMs by replacing the traditional sizing equation with .
Thus, equipped with only the power requirements and stator/rotor topology, among others, they confirmed by FEA and experimental results that the volume of the machine and other dimensional parameters can be so determined.
Pang et al (2007) [47] compared both analytically and by FEA the electromagnetic perfor- mance of the 12/10 PM–FSM to an 18/12 IPM machine for traction drives. By considering different split ratios based on parametric analyses, they found that the former has slightly higher torque and flux weakening capability.
Also, using parametric analyses coupled with FEA, Zhu et al (2008) [62] investigated the in- fluence of design parameters on the output torque of the 12/10 PM–FSM for motor applica- tions. They showed among other things that, if the machine’s stator tooth width, stator magnet thickness and slot opening are kept equal, maximum output torque is produced.
Chen et al (2009) [82] proposed the 12/14 machine for the first time by comparing it to the 12/10 machine. Again, based on FEA parametric evaluations, they were able to show the su- perior torque and torque ripple performance of the 12/14 machine.
Chen and Zhu (2010) [65] developed analytically, the general conditions for balanced sym- metrical back–EMF waveforms in PM–FSMs. They found that the best stator to rotor pole number combinations must be very close and that with larger rotor pole number, a relatively
higher torque is obtained. Then concentrating on the 12/10 and 12/14 machines, they validat- ed their proposal both by FEA and experiment at a rated speed of 400 r/min.
Xu et al (2011) [50] proposed four rotor–based cogging torque reduction schemes (rotor– pole pairing, rotor pole–notching, rotor–pole chamfering, and rotor–pole skewing) to improve the adaptability of the 12/14 machine for HS plug–in hybrid electric vehicles (PHEV). Even- tually, six important performance indexes, including the cogging torque, were normalized with respect to the original rotor scheme and compared in FEA. The results showed that the best effects of the four is the rotor–pole pairing scheme.
Tang et al (2012) [67] proposed, for the first time, the wound–field version of the 12/14 ma- chine for enhanced field weakening capabilities. Their design, which preserves the flux focus- ing effect and compares shoulder–to–shoulder with its PM counterpart, was fashioned for an electric truck and analysed using FEA.
Somesan and Viorel (2013) [68] embarked on design optimisation based on deterministic al- gorithms and performance analyses of a 3000 r/min, 30 kW 12/10 machine using analytic ex- pressions concocted from the design–sizing theory. Later, FEA was adopted to validate the electromagnetic performance of the optimally designed machine, as well as establish the posi- tive influence of rotor–pole shaping on cogging torque reduction.
McFarland, Jahns and El–Rafaie (2014) [55] provided insights on the static demagnetisation characteristics in PM–FSMs using the 12/10 machine. They found that, due to the arrange- ment of the PMs and the stator coils, their MMFs (PM and current) seem to form common partnership, thereby ensuring minimal demagnetisation risks in the PMs during normal opera- tion, “regardless of the current’s axis orientation or polarity”. According to them, this peculiar behavior underscores the prospects of using less expensive rare–earth–free materials.
Based on the 12/10 and 12/14 machines, Raminosoa et al (2015) [71] assessed the potentials of three different designs, which either reduce or remove rare–earth materials, for HEV trac- tion applications. They exploited the special magnetic configuration of FSMs already broad- casted by McFarland, Jahns and El–Rafaie (2014) [55] to justify two of the designs which used PMs, with the key design requirements being 55 kW peak power at 2800 r/min base speed. The third one was designed using only wound–fields, whose topology is different from that proposed in Tang et al (2012) [67]; hence, it could not satisfy the efficiency requirement among the three designs. Among other things, they found as usual that, the 12/14 machine has a higher torque density than a 12/10 machine, with higher efficiency in the latter due to re- duced losses.
12/10 and 12/14 machines, it is commonly observed that a well thought out design optimisation that accommodates multiple design objectives, sequel to some constraint functions, is fundamentally ab- sent. A good number of the published works have been so dedicated to parametric resolution for the optimal design (Ojeda et al (2012) [37] for example), and most times they confuse such “sensitivity analyses” for “design optimisation”. Where this is not the case, deterministic algorithms are invoked to optimise these machines based on single objective problems or their hybrids, such that they fail to promote the absolute optimum of such design ventures.
Moreover, an existing framework which is established on the widely utilised design–sizing method as proposed in Hua et al (2006) [61], used in Somesan and Viorel (2013) [68], and empha- sised in Zhang et al (2009) [45] to trigger this process, is still not fully exploited. When this technique is fully deployed, an initial design that can be conceptualised to activate the optimisation process is produced. Thereafter, it becomes easy to collectively evaluate a part or all of the aforementioned de- sign requirements such as power factor, torque ripple and torque density among others, bearing in mind, the optimum performance of the associated drivetrain components.
Granted, the study by Somesan and Viorel (2013) [68] does not address a single objective prob- lem per se since the objective function considered is to maximise the torque density, nevertheless the approach falls short because it was a non–constrained deterministic (i.e., gradient–based) search method, with only five design parameters considered. This point is stressed because in the optimal design of electrical machines, a good number, both of the design parameters and the design require- ments, which hustle for relevance, must be taken into account initially, Duan and Ionel: 2013 [87] and Stipetic, Miebach and Zarko: 2015 [88]. Thus, if the competition is not properly arbitrated by the designer, the resulting optimal solution is merely a local optimum. For this not to happen, the pre- ferred optimisation methods should be multi–objective stochastic (non–gradient) based algorithms. As quipped in Vanderplaats (2007) [99], it does go without saying that the researcher understands fully, that no given optimisation problem, especially with so–called non–convex problems, can guar- antee a finite optimum solution without a quid pro quo. But when the case for realising a design, as close as possible to the global optimum is admitted, the satisfaction of the imposed design criteria comes without doubt.
Short of reference to any application area, it still must be said that other studies have optimised and/or compared the 12/10 and 12/14 machines. For instance in terms of rare–earth–free designs, studies by Zhou and Zhu (2014) [70] and Sulaiman, Kosaka and Matsui (2012) [95] only dealt on deterministic optimisation methods in their studies; whereas Raminosoa et al (2015) [71] and Tang et al (2012) [67] processed some design and comparison aspects, but without any form of optimisation
mentioned. Thus, to the best of the researcher’s knowledge, it appears that for the relevant design re- quirements, they are yet to be collectively optimised for best results of the 12/10 and 12/14 machines, especially in line with the proposed geared MS wind generator operation.
An example of a multi–objective and multi–constraint optimisation problem is reported for IPM synchronous motor for HEV/EV applications in Zhang, Ionel and Demerdash (2016) [89], wherein “three concurrent objective functions are minimized: material cost, losses, in order to ensure high efficiency, and the difference between the rated and the characteristic current, aiming to achieve very high constant–power flux–weakening range” [sic.], having a minimum of ten design variables and three constraints for a prescribed problem. As expected, their study highlighted the use of stochastic algorithms e.g., differential evolution, which can produce a population of non–dominant optimal solution as a Pareto optimal set. Remarkably, a search by the researcher reveals that the Pare- to effect has never been attempted for any combination of performance parameters in the design op- timisation of the proposed 12/10 and 12/14 machines.
In the meantime, it has to be said that stochastic algorithms do not come without their concerns in the design optimisation of electrical machines. The main challenge posed is that they are computa- tionally expensive and time consuming to implement. Furthermore, the use of FEA–based numerical optimisation, in tandem, is considered an additional burden to the computation time, viz., costs. But, FEA is, without doubt, both robust and highly efficient for electrical machine design and analyses. To do otherwise, would suggest that increased accuracy is being sacrificed on the altar of enhanced speed in the process chain. To the researcher, the former situation is preferred to the latter for the pre- sent inquiry. Notwithstanding, the fear of aggregating both the computer memory and design cycle may not be deep seated, as the researcher intends to adopt a “powerful and efficient” two– dimensional (2–D) static FEA optimisation program (SEMFEM) developed by Gerber (2011) [91], with script–based interface and a propensity for parallel processing which speeds up the process in any case.
However, SEMFEM which is based on 2–D FEA modelling is limited by the fact that com- pared to 3–D FEA solutions, the end–winding effects can result in huge disparities for the proposed FSMs. Even more, seeing that the case being made for rare–earth–free designs includes the presence and arrangement of the phase coils over the field coils in the WF–FSM topology, usually with a very large split ratio in comparison to the aspect ratio, it becomes indispensable to devise an approximate calculation which accounts for the end–winding effects in 2–D FEA. Besides, to devise such end– winding approximation is also for the sake of the design optimisation procedure converging to the true optimal design.
Hence, the method of considering only the end–winding resistance and ignoring the end– winding inductance as done in Zhou and Zhu (2014) [70] is limited for design optimisation, same as for prescribing a fixed margin to account for end effects as done in Raminosoa et al (2015) [71]. To this end, the incorporation of an approximate formula which captures, in real–time, the end–winding effect in the 2–D FEA is meant to enhance the accuracy of the design optimisation process.
Based on the foregoing, the researcher, at this juncture, formally proposes the use of FEA solu- tions interfaced with a robust multi–objective stochastic algorithm in the design optimisation and per- formance evaluation of the 12/10 and 12/14 FSMs benchmarked for geared MS wind generator drivetrains. In pursuit of the underlying research objectives, additional emphasis is to be placed on the generators’ design characteristics for both small–scale and utility–scale systems.