Weighting Factor Design Research Articles

A review on model predictive control strategies for AC motor drives

AbstractIn the past decade, model predictive control (MPC) has been widely used in AC motor drives. Although a series of improved MPC strategies have been proposed, researchers are still seeking more effective solutions for different application backgrounds and application requirements to achieve the goals such as algorithm simplification, weighting factor design, parameter robustness enhancement, current/torque ripple suppression, and so on. In this paper, aiming at the above problems, the MPC strategy and its optimisation technology for AC motor drive system are comprehensively reviewed. Firstly, this paper introduces the classical MPC technology with the permanent magnet synchronous motor drive system fed by two‐level voltage source inverter as the control object. Secondly, this paper introduces and discusses the existing MPC optimisation methods from the aspects of current/torque ripple suppression, algorithm simplification, weight factor design and parameter robustness enhancement. Finally, based on the current industrial development requirements for AC motor drive systems and the research status of MPC optimisation methods in the existing literature, the current challenges and future trends of MPC technology are discussed.

Optimal Weighting Factor Design of Finite Control Set Model Predictive Control Based on Multiobjective Ant Colony Optimization

Optimal Weighting Factor Design of Finite Control Set Model Predictive Control Based on Multiobjective Ant Colony Optimization

Optimal weighting factor design based on entropy technique in finite control set model predictive torque control for electric drive applications

In the conventional finite control set model predictive torque control, the cost function consists of different control objectives with varying units of measurements. Due to presence of diverse variables in cost function, weighting factors are used to set the relative importance of these objectives. However, selection of these weighting factors in predictive control of electric drives and power converters still remains an open research challenge. Improper selection of weighting factors can lead to deterioration of the controller performance. This work proposes a novel weighting factor tuning method based on the Multi-Criteria-Decision-Making (MCDM) technique called the Entropy method. This technique has several advantages for multi-objective problem optimization. It provides a quantitive approach and incorporates uncertainties and adaptability to assess the relative importance of different criteria or objectives. This technique performs the online tuning of the weighting factor by forming a data set of the control objectives, i.e., electromagnetic torque and stator flux magnitude. After obtaining the error set of control variables, the objective matrix is normalized, and the entropy technique is applied to design the corresponding weights. An experimental setup based on the dSpace dS1104 controller is used to validate the effectiveness of the proposed method for a two-level, three-phase voltage source inverter (2L-3P) fed induction motor drive. The dynamic response of the proposed technique is compared with the previously proposed MCDM-based weighting factor tuning technique and conventional MPTC. The results reveal that the proposed method provides an improved dynamic response of the drive under changing operating conditions with a reduction of 28% in computational burden and 38% in total harmonic distortion, respectively.

Weighting Factor Design Techniques for Predictive Control of Power Electronics and Motor Drives

The rapid growth of energy demand requires progressive energy generation. This, together with the demand for higher efficiency and flexibility, has promoted the application of power electronics in energy systems. During the past decade, model predictive control (MPC) of power electronics has witnessed significant advancements in both dynamic performance and optimal control of the multi-objective terms. Several of these terms can have equal control priorities, resulting in a symmetrical cost function; however, most objectives have different priorities and require weighting factors to resolve the asymmetry in the cost function. Currently, researchers continue to encounter challenges in the optimal design of weighting factors. Moreover, the relative performance of different techniques that either utilize or avoid the weighting factor are uncertain. Therefore, this study focuses on weighting factor design techniques in the literature as applied to wind/solar energy conversion, microgrids, grid-connected converters, and other high-performance converter-based systems. These are grouped under the heuristic, offline tuning, sequential, and online optimization methods. This study demonstrates that optimal online tuning of weighting factors and sequential MPC methods can both offer improved robustness against parameter uncertainties. In addition, the advantages and limitations of different techniques are highlighted.

A Graphic Weighting Factor Design Method for Finite Control Set Model Predictive Control of Power Converters

Finite control set model predictive control (FCS-MPC) has been widely used in the control of power converters. However, for converters with multiple optimization objectives, the design of the weighting factors in the cost function is a tricky problem. To solve the weighting factor design problem in multiobjective FCS-MPC, a graphic weighing factor design method is proposed in this article. First, the discrete control variables are taken into the prediction model to determine the state boundaries of each control objective under all the system states. Then, the priorities and weighting factors of the control objectives are determined and designed by adjusting the intersection area of these state boundaries, so as to optimize the system performance. Finally, the operating condition feedback is introduced to realize an adaptive adjusting of the weighting factors so that the relationship of the state boundaries between different control objectives will not be affected by the change of system operating condition, and the controller robustness can be guaranteed. Analysis and experiment are carried out based on the parallel three-level dc–dc system. The results show that the proposed method can effectively solve the weighting factor design problem of multiobjective FCS-MPC. It is simple, efficient, and robust.

A Simplified Model Predictive Control for Asymmetrical Six-Phase Induction Motors That Eliminates the Weighting Factor

The conventional model predictive control (MPC) is an attractive control scheme for the regulation of multiphase electric drives, since it easily exploits their inherent advantages. However, as the number of phases increases, the MPC’s complexity increases exponentially, posing a high computational burden. Additionally, the MPC still presents other issues related to the weighting factor design in the cost function. Accordingly, this paper proposes a low-complexity hysteresis model predictive current control (HMPCC) that can significantly reduce the computational burden, improve the motor’s performance, and completely avoid the weighting factor design. The proposed method is a hybrid control method, consisting of two distinct controls that complement one another. The hysteresis control is used to reduce the number of iterations per sampling period, thereby reducing the computational effort required to choose the voltage vector that actively produces torque/flux, and nullifying the weighting factor requirement. Finally, the MPC is used to improve the torque and current quality. The effectiveness of the proposed method is verified through experimental data, and the results emphasize the improvement of the proposed HMPCC scheme.

Robust Predictive Speed Control of SPMSM Drives With Algebraically Designed Weighting Factors

Predictive speed control (PSC) is a promising control strategy for high dynamic performance electrical drives. However, its implementation faces two challenges: the selection of weighting factors and the elimination of steady-state errors (SSEs). The weighting factors are commonly selected through trial-and-error, which is time consuming. Additionally, SSEs are frequently observed due to model uncertainties and parameter mismatches. Focusing on the aforementioned issues, this article proposes a PSC strategy for surface-mounted permanent-magnet synchronous motor drives, where the weighting factors are designed algebraically and SSEs are eliminated. The weighting factor design process is illustrated through rearranging the equivalent speed tracking error. The SSEs are eliminated by incorporating integral terms into the cost function. The performance of the proposed strategy is validated through comparative experiments with field-oriented control and adaptive integral sliding-mode predictive control. The results demonstrate the effectiveness of the designed weighting factors and the robustness of the system.

Model Predictive Direct Speed Control With Novel Cost Function for SMPMSM Drives

The model predictive direct speed control (MPDSC) can improve the speed dynamic performance effectively. However, due to the large difference between the mechanical and electrical time constants, short prediction could result in large current ripples at steady state, which becomes a critical problem. Besides, the conventional MPDSC methods have not deeply investigated the online-adjustable weighting factor design and the problem of <i>i_d</i> transient oscillation. In this article, a model predictive direct speed control with novel cost function is proposed. In the proposed method, two different <i>q</i>-axis current references are generated, one to improve the speed dynamics, and the other to ensure the low current ripples. The two current tracking are assigned with different weighting factors unified in one cost function. In order to determine which current tracking to play a major role under different operations, the speed error is designed as weighting factor. With the proposed cost function and designed weighting factor, the high speed dynamics and low steady current ripples can be achieved simultaneously. Finally, the effectiveness of proposed method is verified by experiments.

Weighting factor design based on SVR–MOPSO for finite set MPC operated power electronic converters

Weighting factor design based on SVR–MOPSO for finite set MPC operated power electronic converters

Modulated Model Predictive Control for Multilevel Cascaded H-Bridge Converter-Based Static Synchronous Compensator

The model predictive control (MPC) methods have been widely applied due to the fast dynamic performance and multiple control targets. However, they show certain limits when applied to the multilevel converters, such as unfixed switching frequency, large computation burden, and complex weighting factors selection. This article proposes a novel modulated MPC (M <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> PC) method for cascaded H-bridge (CHB) converter-based static synchronous compensator (STATCOM). Instead of multitarget integration and weighting factor design, the proposed method disintegrates the voltage balancing control process from the cost function. The evaluated control sets for output current control is decided by the search step and the search range in each period. By proper design and selection of the adaptive search step for the output voltage references under <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">α–β</i> coordinate, the search range can be reduced, which greatly reduces the number of evaluated control sets in each control period. Therefore, the dynamic of output characteristics and the low computation burden of the MPC method are guaranteed simultaneously. In addition, with the simple and independent integration of the capacitor voltage balancing control, the proposed method can be easily applied in the CHB converter-based STATCOM application. Furthermore, this article provides a delay compensation for the prediction process, and it provides a fixed switching frequency for each H-bridge cell. Simulation and experimental results verify the effectiveness of the proposed M <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> PC method.

Pareto Optimal Weighting Factor Design of Predictive Current Controller of a Six-Phase Induction Machine Based on Particle Swarm Optimization Algorithm

Finite-set model predictive control (FS-MPC) as predictive current control (PCC) is considered an exciting option for the stator current control of multiphase machines due to their control flexibility and easy inclusion of constraints. The weighting factors (WFs) of PCC must be tuned for the variables of interest, such as the machine losses <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$x-y$ </tex-math></inline-formula> currents, typically performed by trial-and-error procedure. Tuning methods based on artificial neural network (ANN) or the coefficient of variation were proposed for three-phase inverter and motor drive applications. However, the extension of this concept to the multiphase machine application is not straightforward, and only empirical procedures have been reported. In this context, this article proposes an optimal method to tune the WF of the PCC based on the multiobjective particle swarm optimization (MOPSO) algorithm. A Pareto dominance concept is used for the MOPSO to find the optimal WF values for the PCC, comparing parameters of root-mean-square error of the stator tracking currents. The proposed method offers a systematic approach to the WF selection, with an algorithm of easy implementation with direct control over the size of the search space and the speed of convergence. Simulation and experimental results in steady-state and transient conditions are provided to validate the proposed offline tuning procedure of the PCC of a six-phase induction machine. The improvements of RMSE can be more than 500% for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$x-y$ </tex-math></inline-formula> subspace, with minor effect in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha -\beta $ </tex-math></inline-formula> subspace. Finally, the proposed method is extended to a more complex cost function, and the results are compared with an ANN approach.

Predictive current control of asymmetrical six-phase induction motor without weighting factors

Control of multi-phase machine in both healthy and post-fault operations has recently gained considerable interest. Finite control set model predictive control (FCS-MPC), in particular, has been proposed to drive multi-phase machines to avoid sophisticated pulse width modulation (PWM) methods. Nevertheless, FCS-MPC generally experiences some technical limitations. One of the widely reported challenges related to FCS-MPC is the weighting factor (WF) design, which is empirically designed and found to be an operating point dependent factor. Thus, assuming a constant WF can result in poor performance. In this paper, the prediction stage of FCS-MPC for asymmetrical six-phase (A6P) induction motor (IM) has been reformulated based on double dq (2dq) modeling approach. Unlike the reported vector space decomposing (VSD)-based FCS-MPC algorithms, the proposed approach results in four control variables (the stator sequence currents isα1,isβ1,isα2, and isβ2) which have the same priority. Thus, equal weighting factors could be used in the cost function, which will inherently minimize the effect of the circulating x-y current components. Performance comparison of the proposed method against VSD-based FCS-MPC is investigated. The theoretical findings are experimentally validated using a 1 kW prototype six-phase IM.

Simple two‐stage weighting factor design for finite control set model predictive control of modular multilevel converters

AbstractDue to discrete nature of power converters, finite control set model predictive control (FCS‐MPC) is considered as an attractive choice for these systems. Since this control technique provides advantages like improved dynamic performance and inclusion of several control objectives in a single cost function, it is especially appropriate for topologies like modular multilevel converters (MMCs), where multiple control goals, that is, output and circulating currents control, and cells' capacitor voltage balancing should be satisfied. Despite these advantages, huge computational burden and weighting factor selection are two serious obstacles. In this work, a simple two‐stage weighting factor selection scheme is suggested for FCS‐MPC applied to MMCs. At the first stage, some offline tests are conducted for different weighting factors; and a pre‐optimal value is selected, based on minimizing the total harmonic distortion (THD) of output current and root mean square (RMS) value of the circulating current. However, since optimal performance at different operating conditions is achieved by different weighting factors, the pre‐optimal value will be updated at the second stage by a simple online algorithm. Moreover, a technique is suggested for effectively decreasing the computational burden. Finally, by conducting several simulation and experimental tests, the satisfactory performance of proposed controller is validated, compared to fixed weighting factor FCS‐MPC.

Model Predictive Control Method Based on Deterministic Reference Voltage for Single-Phase Three-Level NPC Converters

When single-phase three-level neutral-point-clamped (NPC) converters operate, there are two main control objectives that need to be met for correct operation. First, the ac source current must be controlled to be sinusoidal. Second, the dc capacitor voltages must be balanced. In original model predictive control (MPC) methods for NPC converters, an optimization process involving an empirical weighting factor design is required to meet both of these objectives simultaneously. This study proposes an MPC approach developed for single-phase three-level NPC converters to meet these objectives using a single reference voltage consisting of a difference-mode term and a common-mode term in each phase. The difference-mode term and the common-mode term are responsible for sinusoidal ac source current synthesis and dc capacitor voltage balancing, respectively. Then, a single cost function compares the adjusted reference voltage with possible voltage candidates to select an optimal switching state, resulting in the smallest cost function value. Different from the conventional MPC method, the proposed approach avoids the selection of weighting factors and the attendance of various control objectives. Thanks to the deterministic approach, the proposed MPC method is straightforward to implement and maintain fast transient performance while guaranteeing the control objectives. Finally, the effectiveness and feasibility of the proposed approach for single-phase three-level NPC are verified through comprehensive experimental results.

Sequential Model Predictive Control of Three-Phase Direct Matrix Converter

The matrix converter (MC) is a promising converter that performs the direct AC-to-AC conversion. Model predictive control (MPC) is a simple and powerful tool for power electronic converters, including the MC. However, weighting factor design and heavy computational burden impose significant challenges for this control strategy. This paper investigates the generalized sequential MPC (SMPC) for a three-phase direct MC. In this control strategy, each control objective has an individual cost function and these cost functions are evaluated sequentially based on priority. The complex weighting factor design process is not required. Compared with the standard MPC, the computation burden is reduced because only the pre-selected switch states are evaluated in the second and subsequent sequential cost functions. In addition, the prediction model computation for the following cost functions is also reduced. Specifying the priority for control objectives can be achieved. A comparative study with traditional MPC is carried out both in simulation and an experiment. Comparable control performance to the traditional MPC is achieved. This controller is suitable for the MC because of the reduced computational burden. Simulation and experimental results verify the effectiveness of the proposed strategy.

Weighting Factor Design in Model Predictive Control of Power Electronic Converters: An Artificial Neural Network Approach

This paper proposes the use of an artificial neural network (ANN) for solving one of the ongoing research challenges in finite set-model predictive control (FS-MPC) of power electronics converters, i.e., the automated selection of weighting factors in cost function. The first step in this approach is to simulate a detailed converter circuit model or run experiments numerous times using different weighting factor combinations. The key performance metrics [e.g., average switching frequency ( $f_{{\rm sw}}$ ) of the converter, total harmonic distortion, etc.] are extracted from each simulation. This data is then used to train the ANN, which serves as a surrogate model of the converter that can provide fast and accurate estimates of the performance metrics for any weighting factor combination. Consequently, any arbitrary user-defined fitness function that combines the output metrics can be defined and the weighting factor combinations that optimize the given function can be explicitly found. The proposed methodology was verified on a practical weighting factor design problem in FS-MPC regulated voltage source converter for uninterruptible power supply system. Designed weighting factors for two exemplary fitness functions turned out to be robust to load variations and to yield close to expected performance when applied both to detailed simulation model (less than 3% error) and to experimental test bed (less than 10% error).