Framework
In this section, the system layout and working procedure of the optimisation framework are presented. The Taguchi-based regression rate framework as defined by Weng in [154,155] forms the foundation of the proposed iterative optimisation method for LS PMSM design. By adapting Weng’s framework to incorporate p.u. parameter design equations, using any machine analysis platform and the capability to combine multiple operational domain objectives into a single OEC, a single-tier LS PMSM design framework is formulated.
3.4.1
The System Layout of the Proposed Optimisation
Framework
The flowchart of the proposed LS PMSM optimisation framework utilising Weng’s Taguchi- based regression rate framework functionality is presented in Fig. 3.6. The framework comprises of the following five sub-units. The functioning of each sub-unit can be adapted to suit the specific design optimisation.:
• Domain space initialisation (shown by green blocks) • Taguchi functionality (shown by yellow blocks) • Multi-response combiner (shown by red blocks)
• Parameter regression and placement (shown by blue blocks) • Termination criteria (shown by grey blocks)
The green phase is divided into two initialisation phases. First, the machine optimi- sation is initialised by setting the required rated machine conditions, selecting the desired topologies (rotor and stator slots, PM duct topology, winding configuration etc.) and identifying both design and noise parameters. The main dimensions and topology infor- mation are linked to the p.u. design equations that are used to compile the trial machines. Once the machine optimisation domain has been set the OA required for both the main and noise parameters is selected.
Once the rated and operating conditions of the machine has been selected the OEC optimisation objectives are selected. The OEC is linked to the termination criteria. Once the performance objectives has been specified the machine analysis platform is specified in accordance with the required objectives or the designer’s preference.
Depending on the parameter design range and the level difference as determined by the OA, the minimum acceptable level difference for each parameter has to be set along with the regression rate value and the minimum view-to-view convergence difference as this also influence the termination criteria
Figure 3.6: Proposed Taguchi based optimisation framework using a level difference regression rate
The next phase is the Taguchi functionality (yellow blocks). The purpose of this phase is to compile the trial machine as set out by the selected OA and analyse the OEC us- ing the ANOM and ANOVA to identify and verify the current view’s optimum machine. To compile the trial machines the p.u. parameter level values are converted into metric dimensions using the p.u. topology equations. If an outer noised design is included in the optimisation, secondary states for each main trial machine are compiled. The total number of trial machines are the product of the main machines and the noise states.
The current evaluation criteria (CEC) of the current view is analysed as with any single response Taguchi method. The ANOM is used to identify the optimum level values for each parameter and the ANOVA is used to analyse each parameter’s contribution towards performance variance. Once the optimum values have been identified, the view optimum machine is analysed (and exposed to the same noise OA conditions) to determine its OEC performance. Although Weng’s method did not include the ANOVA analysis, in the proposed framework it is used to track the view-to-view parameter variance and to adapt the regression rate during the newly proposed dynamic regression rate optimisation.
Once all the trial machines have been analysed and the desired performance objective values obtained, the results are combined by the multi-response combiner (red blocks in Fig. 3.6). Regardless whether the outer noise design was used, each performance objective must be normalised within the main OA reference frame. This ensures equal representa- tion of each objective when combining into one CEC value for each specific trial machine. Depending on the performance objectives, several methods are available to combine the normalised objective into one workable response such as the weighted function and fuzzy- logic methods [158]. Each method has its advantages and disadvantages which must be considered by the designer during the initial stages of the design. The CEC of each trial is then used by the CEC analysis as part of the Taguchi framework (yellow blocks).
The CEC should not be confused with the OEC. The CEC is normalised within the current view’s reference frame before being combined into one response and only has rel- evance within the current view. The OEC is normalised within a larger frame to track the overall performance. The main OA trials are used for the CEC whereas the optimum conformation trial is used for the OEC. It is possible to compare the trial averages against the optimum performance using the same OEC formulation.
If another iterative view is required the same procedure is followed as with Weng’s method in the blue blocks. The current optimum parameters are placed in the level-21slot
after which (3.3) is applied to the current level differences to determine the next view’s parameters. The new parameters are verified if they are still within the design range. If any of the parameters fall outside the range, the specific parameter needs to be adjusted before the next iteration can be conducted.
The termination criteria verifier (grey blocks) determines whether another view is required or not. There are two main benchmarks checked after each succession of the Taguchi framework. If either one of the benchmarks is met the process is stopped and the design is finalised. The first termination benchmark is (as with Weng’s method), the convergence of the OEC after (3.2) has been satisfied. If this benchmark has been achieved the optimisation is deemed a success. The second benchmark is once the maximum number of iterations has been reached even if (3.2) has not been satisfied. For this case, the OEC does not converge, and the final machine cannot be seen as the optimum design. However, as the view-to-view performance of the OEC is traced, the designer can investigate whether or not the final machine is acceptable.
3.4.2
Functionality Overview
This section aims to provide a summary regarding the working functionality of the pro- posed framework as presented in Fig. 3.6. The framework comprises of three main sec- tions, namely, initialisation, Taguchi-based machine analysis and parameter regression. The optimisation loop is formed by the Taguchi based machine analysis and parameter regression. The initialisation is only done once at the beginning of the optimisation, whereas the parameter regression is only carried out if the termination criteria are not met after each Taguchi based machine analysis.
The following is an overview of Fig. 3.6’s working functionality: Initialisation:
• Design initialisation: Parameter design, tolerance design or sensitivity design • Machine initialisation: Set machine’s rated conditions, applications, topology, de-
sign and noise parameters. Determine each parameter’s design range for conversion to p.u. values.
• Problem initialisation: Selects OAs and determine LD for each parameter. Set per- formances objectives, compile OEC and termination criteria. Set machine analysis platform(s). Set parameter regression rate.
Taguchi-based machine analysis:
• Step 1: Compile trial machines as per selected OA(s) using the p.u. design values and equations.
• Step 2: Analyse trial machines for both steady-state and transient in selected plat- forms.
• Step 3: For each main trial machine combine the multiple performance objectives into a singular CEC response.
• Step 4: Analyse the main OA trial results using ANOM and ANOVA. Identify relative optimum parameters.
• Step 5: Analyse the relative optimum and compile the current view’s OEC.
• Step 6: Check termination criteria. If the criteria are satisfied, the current view’s optimum is the final design. If the criteria are not satisfied, apply parameter regres- sion steps.
Parameter regression:
• Apply regression rate: Reduce the current LD using the set regression rate method (static or dynamic). Calculate the next view’s parameter level value with the new LD using the current optimum as a centre reference value.
• Check parameter range: Check if all the parameter levels are within the original design range. If all the levels are in range, each parameter level must be placed into the correct slot. If a parameter level is not in range, it has to be adjusted accordingly.
• Return to Step 1: The main OA is ready for the next Taguchi view with the reduced parameter range.