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Improvised multi‐objective model predictive control of matrix converter using fuzzy logic and space vectors for switching decisions

2019; Institution of Engineering and Technology; Volume: 13; Issue: 4 Linguagem: Inglês

10.1049/iet-pel.2018.5873

1755-4543

Tabish Nazir Mir, Bhim Singh, Abdul Hamid Bhat,

Advanced Battery Technologies Research

IET Power ElectronicsVolume 13, Issue 4 p. 758-764 Research ArticleFree Access Improvised multi-objective model predictive control of matrix converter using fuzzy logic and space vectors for switching decisions Tabish Nazir Mir, Corresponding Author Tabish Nazir Mir mir.tabish.az@gmail.com orcid.org/0000-0003-1152-112X Department of Electrical Engineering, Indian Institute of Technology Delhi, Hauz Khas, New Delhi, 110016 India Department of Electrical Engineering, National Institute of Technology Srinagar, Hazratbal, Srinagar, 190006 IndiaSearch for more papers by this authorBhim Singh, Bhim Singh Department of Electrical Engineering, Indian Institute of Technology Delhi, Hauz Khas, New Delhi, 110016 IndiaSearch for more papers by this authorAbdul Hamid Bhat, Abdul Hamid Bhat Department of Electrical Engineering, National Institute of Technology Srinagar, Hazratbal, Srinagar, 190006 IndiaSearch for more papers by this author Tabish Nazir Mir, Corresponding Author Tabish Nazir Mir mir.tabish.az@gmail.com orcid.org/0000-0003-1152-112X Department of Electrical Engineering, Indian Institute of Technology Delhi, Hauz Khas, New Delhi, 110016 India Department of Electrical Engineering, National Institute of Technology Srinagar, Hazratbal, Srinagar, 190006 IndiaSearch for more papers by this authorBhim Singh, Bhim Singh Department of Electrical Engineering, Indian Institute of Technology Delhi, Hauz Khas, New Delhi, 110016 IndiaSearch for more papers by this authorAbdul Hamid Bhat, Abdul Hamid Bhat Department of Electrical Engineering, National Institute of Technology Srinagar, Hazratbal, Srinagar, 190006 IndiaSearch for more papers by this author First published: 01 March 2020 https://doi.org/10.1049/iet-pel.2018.5873Citations: 1AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract Finite control set model predictive control (FCS-MPC) has lately received noteworthy attention in the control of power converters. Such converters have a finite number of switching states, which ensure a small sample space of predictions and minimum computational burden. Although unanimously popular in most converters, multi-objective FCS-MPC (Mo-FCS-MPC) is a particularly attractive choice in the control of matrix converters (MCs), as it enables attainment of multiple objectives with relative ease. Conventionally, a weighing factor-based approach is undertaken in the implementation of Mo-FCS-MPC wherein a cost-function is framed such that each of its constituent objectives, is assigned a relative weight according to its significance. However, the tuning of weights is empirical in nature and hence tedious. This study proposes an improvised technique for implementing Mo-FCS-MPC in MCs while simultaneously meeting a number of objectives such as load current, source current, and input power factor control. Sector information from space vectors of reference output voltages and reference input currents, coupled with a fuzzy decision-making criterion is used to make the final switching decision, hence eliminating the conventional weighing factor-based approach. The inclusion of space vector modulation into predictive control enhances the quality of both loads as well as source current waveforms. 1 Introduction Matrix converters (MCs), owing to dedicated research from the scientific community, have been successfully able to carve their niche in the sphere of three-phase to three-phase converters (3ϕ–3ϕ) AC–AC power conversion. Some distinctly interesting features of MCs include sinusoidal load and source currents, complete control over the input power factor, intrinsic bi-directionality and direct conversion of AC power without a transitional DC link. In spite of their advantages, limitations in their output voltage ratio and difficult commutation have hindered industry acceptability of MCs [1]. However, progressive research continuously aims at bridging these gaps. A step forward in making MCs more industry acceptable is the use of predictive control techniques [2, 3] in their control and modulation. Since the control of MCs is often associated with simultaneous attainment of numerous objectives, multi-objective finite control set model predictive control (Mo-FCS-MPC) is naturally a popular choice. Conventionally, Mo-FCS-MPC involves the prediction of the variables to be controlled for each switching state of the converter, using the discretised model of system equations. Subsequently, the errors corresponding to each objective are calculated and a cost function is framed for each switching state, with relative importance of each objective designated in the cost function by means of its relative weight. The switching state that corresponds to the least (or most minimised) cost function, hence results in the least error and is switched in real-time. However, the choice of weighing factors generally requires assessing the system performance for a wide set of data points. Moreover, for a constant weighing factor, the system performance is often unsatisfactory at dynamic conditions [4, 5]. The available literature [6, 7] proposes a wide variety of optimal tuning techniques for weighing factors used in framing the cost function while implementing Mo-FCS-MPC. However, in [8], the use of fuzzy logic is demonstrated as an effective means of making switching decisions without using weighing factors explicitly. In this study, the control scheme is further improvised upon by introducing sector information of reference output voltages and currents besides using fuzzy membership functions in making the final choice of the switching state to be realised. Using the improvised strategy, substantial improvement in the quality of source current and some improvement in the quality of load current is also observed. Moreover, incorporation of space vector modulation (SVM) helps to curb the variations in switching frequency that is otherwise encountered with traditional predictive control. 2 Multi-objective model predictive current control of a 3ϕ–3ϕ MC Mo-FCS-MPC of MCs has been explored in many applications [9-11]. It is especially becoming increasingly popular because of the relative ease with which different constraints can be included within a common cost function, hence making it one of the most dynamic means of controlling a power converter. Moreover, predictive control enables the unification of modulation and control. Since MCs allow concurrent control of input power factor, source current, and load current, Mo-FCS-MPC becomes more relevant in this case. A 3-ϕ (ABC)–3-ϕ (abc) MC enables power conversion through nine bi-directional switches as can be seen in Fig. 1. With 27 valid operational states, generally only 21 states are used, three of which correspond to zero vectors. Fig. 1Open in figure viewerPowerPoint 3ϕ–3ϕ MC feeding an inductive load Mo-FCS-MPC involves the prediction of load current [12] for each of these 21 switching states using the forward Euler approximation of the discretised model of the load as given (1)where correspond to the switching states of MC, is the output phase voltage corresponding to the jth switching state that can be determined from Table 1 and is the previous load current. Once the load current predictions are made, the error or deviation () from the reference output current () is calculated for each switching state. This is mathematically expressed as (2)Furthermore, the source current reference is generated by using power balance across the input and output of the MC while ensuring a unity input power factor operation, assuming that the converter losses are negligible. The reference source currents () are, therefore, given as (3)where are the input phase voltages of the MC. Table 1. Switching states and resultant output voltages and input currents in a 3ϕ–3ϕ MC State +1 0 −1 0 +2 0 −2 0 +3 0 −3 0 +4 0 −4 0 +5 0 −5 0 +6 0 −6 0 +7 0 −7 0 +8 0 −8 0 +9 0 −9 0 0 0 0 0 0 0 0 0 0 Thereafter, using the switching details of MC as given in Table 1, the source current is determined for each switching state as a function of the predicted load currents (4)Using these source current predictions, the error () from reference source currents () is calculated for each switching state as given (5)It must be noted that the discretised model of input filter [13] may be used for more accurate source current predictions, although the unfiltered source current can also be used in the calculation of error (). After the calculation of output current error () and input current error (), the final choice or switching decision can be made in a number of ways. Conventionally, a cost function (F) is formulated as a weighted sum of errors associated with each objective, as follows: (6)where and are weights associated with the error in load currents () and error in source currents (), respectively. In the classical Mo-FCS-MPC, the cost function (F) is evaluated for each sample time and the switching state that minimises it is selected. However, as already mentioned, the tuning of weights in the cost function is generally empirical in nature. The choice of weights is based on the analysis of a wide set of data points, making it cumbersome. Moreover, the system dynamic response is sensitive to this choice. In [8], the use of a fuzzy logic decision-making criterion has been advocated to make the switching decisions without explicitly formulating a cost function, hence avoiding weight selection altogether. Both objectives, viz. load current control and source current control, have been considered equally significant, and fuzzy logic has been essentially used to normalise the errors with respect to each objective. This study proposes the use of sector information for making switching decisions from fuzzy logic processed errors, in order to enhance the load current and source current profile, especially at high-sampling time, while considering both objectives as equally significant. 2.1 Fuzzy decision making (FDM) for switching implementation in Mo-FCS-MPC FDM has been extensively used in solving optimisation problems with multiple objectives [14]. In [8], FDM has been applied in the selection of switching states in MCs. Using a linear fuzzy membership function such as the one shown in (6), both errors and for all states are normalised in a range from 0 to 1, in order to bring them on a comparable scale. The new normalised errors are given as (7)where and are the maximum errors in output and input, respectively, and and are the minimum output and input errors, respectively, for all . The final switching decision is performed by assessment of an intersection membership function () for each state, which is mathematically equal to the minimum of errors corresponding to all objectives (8)Finally, the switching state with the maximum IMF is switched in real time. FDM-based state selection can be further improved upon by incorporating SVM alongside FDM in making the switching decisions. This provides the added advantage of a better steady-state response both in terms of source and load currents and also limits the switching frequency from rising to undesirably high values. 2.2 Improvised switching implementation by incorporating SVM in FDM It is required that all switching states should be assessed in each sample time, whether traditional weighing factors are used or FDM-based approach is adopted. Further in every next sample that switching decision is implemented, which results in the least cost function or the highest IMF. A better approach to state selection is the use of space vector information along with FDM. This involves sector identification of output reference voltages and input reference currents and identifying the most optimum switching states corresponding to the sector information. The assessment and mathematical predictions then follow for only the requisite states, thereby reducing the computational complexity. Moreover, embedding information of the reference vectors into the switching decisions gives a more refined steady-state performance. The dwell time of each state is chosen in proportion to its IMF. The first step involves generation of reference output voltages () from reference output currents () using the information of the load model (9)From the space vector diagram of reference output voltage () and reference input current () shown in Fig. 2, the most viable switching states are finalised and their dwell times are calculated using fuzzy data. It is known that in conventional FDM, the state with maximum IMF is switched. Quite naturally, the dwell time of each finalised state should be in direct proportion to its IMF, raised to some higher power 'n' (10)where j now corresponds to a reduced set of states finalised as per Table 2, and k is given as (11)The choice of 'n' is based on a trade-off between switching frequency and optimal performance. It is observed that '' corresponds to a constant switching frequency operation, albeit at a deteriorated steady-state performance. As the power 'n' increases, the system response is seen to improve. This, however, happens at the expense of rapidly varying dwell times hence resulting in higher switching frequency variations. The complete block diagram of the improvised algorithm is shown in Fig. 3. Table 2. Example of switching table generation from sector information Vectors to be switched 'ON' duration Switching state Fig. 2Open in figure viewerPowerPoint Reference output voltage () and reference input current () space vector diagrams in a 3ϕ–3ϕ MC Fig. 3Open in figure viewerPowerPoint Complete block diagram for the implementation of improvised Mo-FCS-MPC using fuzzy logic and sector information from space vectors 3 Results and discussion In order to test and compare the performance of proposed improvised Mo-FCS-MPC using FDM and SVM with respect to only FDM-based Mo-FCS-MPC, the two schemes have been simulated in Matlab/Simulink environment and then evaluated experimentally, with both simulations as well as experimental results corroborating and hence establishing the superiority of the proposed improvised algorithm. To effectively present a comparative assessment of two schemes, both the schemes have been simulated and experimentally evaluated at the same sampling rate. For simulation, both algorithms employ a sampling time of 5 μs, while for experimentation, a sampling period of 50 μs has been used. 3.1 Simulation results Different parameters used in the simulation study have been enlisted in Table 3. Both algorithms have been tested for a sinusoidal load current reference of at 50 Hz, where the reference source currents have been subsequently generated from (3). Table 3. System parameters used in simulation System parameter Specification source voltage per phase 230 V 50 Hz resistance per phase (R) inductance per phase (L) 30 mH simulation step time Fig. 4 assesses the relative performance of the two techniques in terms of load voltage and load currents. Quite obviously, load voltages are better defined in the improvised technique owing to ensured switching as per sector identification of reference voltage vector. Moreover, as seen from the harmonic spectra of load currents shown in Fig. 5, there is a marginal improvement in the quality of load current when FDM is undertaken along with SVM. Fig. 4Open in figure viewerPowerPoint Load voltage () and load currents () for (a) Conventional FDM, (b) Load voltage and load currents for improvised FDM with SVM Fig. 5Open in figure viewerPowerPoint Harmonic spectrum of load current (); (a) Conventional FDM, (b) Improvised FDM with SVM The improvised modulation technique is observed to be particularly instrumental in improving the response of source current. This is because sector identification of reference source current and reference load voltage vectors is done simultaneously and conventional FDM is incorporated as well. Fig. 6 shows the source voltage (), unfiltered source current (), and filtered source current () in both the conventional case and the improvised case. In both cases, the unity displacement factor is observed. However, due to a more well-defined sector-based switching in the improvised FDM–SVM algorithm, the response of filtered source current is naturally better. The harmonic spectra of filtered source currents are compared in Fig. 7, and the total harmonic distortion (THD) of source current improves from 10.70% in conventional FDM-based Mo-FCS-MPC to 5.00% in the improvised scheme based on FDM and SVM, which is well within the stipulated limits of the IEEE Std. 519. Fig. 6Open in figure viewerPowerPoint Source voltage (), unfiltered source current () and filtered source current () (a) Conventional FDM, (b) Improvised FDM with SVM Fig. 7Open in figure viewerPowerPoint Harmonic spectrum of filtered source current () (a) Conventional FDM, (b) Improvised FDM with SVM One of the major drawbacks of traditional predictive control techniques in power converters is operation at variable switching frequency which can reach detrimentally high values. By incorporation of SVM in traditional predictive control of MC, as proposed, the switching frequency variations can be largely curbed. As discussed in Section 2, the choice of 'n' is a trade-off between switching frequency variations and optimal steady-state response. Table 4 outlines a comparative system performance in terms of the THD of load current and source current as well as the average switching frequency () for different choices of 'n'. It is evident that the most optimum performance is achieved for ''. Table 4. Choice of control parameter 'n' Conventional FDM-based Mo-FCS-MPC Improvised Mo-FCS-MPC based on FDM and SVM THD of 1.73% 6.04% 1.71% 1.39% 1.38% THD of 10.70% 24% 12.6% 6.21% 5% 26 kHz 5 kHz 6 kHz 9 kHz 11 kHz 3.2 Experimental results In order to validate the performance of the proposed algorithm, experimental verification has been undertaken for both the FDM-based Mo-FCS-MPC and the improvised SVM-FDM-based Mo-FCS-MPC. Fig. 8 shows the various components of the experimental prototype. A four-layer printed circuited board design of MC is used and over voltage protection is provided through a clamp circuit. Both control algorithms discussed above, are implemented using a dSPACE 1202 controller. For addressing commutation issues [15] of MC, four-step commutation [16] is implemented using a SPARTAN6 field programmable gate array (Mimas Numato Lab). Current sensing for four-step commutation has been done using Hall effect-based current sensors (LEM LA-55P). For running the predictive models, input line voltages are sensed using voltage sensors (LEM LV-25P). Test results have been observed through a digital storage oscilloscope (Tektronix TDS2014C) and a power quality analyser (Fluke 43B). The various system parameters used in experimentation are enlisted in Table 5. Table 5. System parameters used in experimentation System parameter Specification source voltage per phase 230 V 50 Hz resistance per phase (R) inductance per phase (L) 50 mH sample time Fig. 8Open in figure viewerPowerPoint Experimental prototype of a 3ϕ–3ϕ MC Both algorithms have been evaluated for a sinusoidal load current reference of at 50 Hz. Fig. 9 shows the relative performance of the two techniques with regard to load voltage and load currents. Test results are seen to corroborate with simulated results of Fig. 4. Furthermore, the harmonic performance of load current () for both strategies has been shown in Fig. 10. Quite evidently, the load current THD of 3.4% (Fig. 10b) for the improvised algorithm is marginally better than the THD (4%) observed in the previously reported FDM-based Mo-FCS-MPC (Fig. 10a). Although the improvised algorithm shows some improvement in terms of load current quality, its major contribution is observed in terms of the quality of source current, especially when working with a high-sampling period. This is because, at higher sampling interval, conventional MPC often exhibits a degraded performance. The remarkable improvement in the quality of source current can be attributed to the incorporation of input current space vector information into FDM, as discussed earlier. The execution time of each algorithm is largely determined by the processor strength. For the controller used in this work, i.e. dSPACE real-time interface (RTI) 1202, the turnaround time for conventional fuzzy logic based Mo-FCS-MPC is , while that of the proposed improvised scheme is . The execution time for fuzzy-based Mo-FCS-MPC is for the digital signal processor controller used in [8]. This has improved to in this work, due to a more powerful processor, i.e. RTI 1202. Although the proposed algorithm builds at a higher sampling time due to sector identification and hence enhanced computations, the performance is significantly improved at higher sample time when compared to its conventional fuzzy-based counterpart. Fig. 9Open in figure viewerPowerPoint Experimental waveforms of load voltage () and load currents () for (a) Conventional FDM, (b) Load voltage and load currents for improvised FDM with SVM Fig. 10Open in figure viewerPowerPoint Harmonic spectrum of load current () in (a) Conventional FDM, (b) Improvised FDM with SVM Fig. 11 shows the various experimental waveforms on the source side, i.e. source voltage (), unfiltered source current (), and filtered source current () in both the conventional case and the improvised case. Typical to MC control, unity power factor operation is evident in both the cases. However, the filtered source current is markedly better in the improvised case (Fig. 11b) than the conventional FDM-based predictive control (Fig. 11a). As seen from the comparison of harmonic spectra of source current in Fig. 12, a significant improvement of source current THD from 31% in the conventional case to 5.4% in the improvised case is observed. This improvement in test results becomes more significant at a relatively higher sample time. Fig. 11Open in figure viewerPowerPoint Experimental waveforms of source voltage (), unfiltered source current () and filtered source current () for (a) Conventional FDM, (b) Improvised FDM with SVM Fig. 12Open in figure viewerPowerPoint Harmonic spectrum of the filtered source () in (a) Conventional FDM, (b) Improvised FDM with SVM 4 Conclusion It is concluded that while modulating MC, incorporation of space vector information of output reference voltages and input reference currents into traditional predictive control, results in significant improvement in source and load current quality. This is especially true when the sample periods are supposed to be large owing to the constraints of the controller. The load and source currents are suitably predicted from the mathematical model of the load and MC. For optimising and prioritising the switching process, FDM is used. Furthermore, SVM is incorporated for a more sector-restricted switching, wherein the dwell times of each state are calculated in proportion to their associated fuzzy decision variable. This not only aids in improving the steady-state response on the source and load side but also helps in limiting the switching frequency variations. Results have been tested through simulation followed by experimental validation on a laboratory prototype, hence establishing an improvised scheme for undertaking model predictive control of MC, using FDM and SVM. 5 References 1Rodriguez J., Rivera M., and Kolar J.W. et al.: 'A review of control and modulation methods for matrix converters', IEEE Trans. Ind. Electron., 2012, 59, (1), pp. 58– 70 2Rivera M., Wheeler P., and Olloqui A. et al.: ' A review of predictive control techniques for matrix converters, part I'. 2016 7th Power Electronics and Drive Systems Technologies Conf. 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