Long Prediction Horizon FCS-MPC for Power Converters and Drives

Received 13 March 2023; revised 17 April 2023; accepted 25 April 2023. Date of publication 4 May 2023; date of current version 15 May 2023. The review of this article was arranged by Associate Editor Y. Liu. Digital Object Identifier 10.1109/OJIES.2023.3272897 Long Prediction Horizon FCS-MPC for Power Converters and Drives EDUARDO ZAFRA 1(Graduate Student Member, IEEE), SERGIO VAZQUEZ 2(Fellow, IEEE), TOBIAS GEYER 3(Fellow, IEEE), RICARDO P. AGUILERA 4(Member, IEEE), AND LEOPOLDO G. FRANQUELO 2(Life Fellow, IEEE) 1Electronics Department, Universidad de Sevilla, 41092 Sevilla, Spain 2Laboratory of Engineering for Energy and Environmental Sustainability, Universidad de Sevilla, 41092 Sevilla, Spain 3ABB System Drives, 5300 Turgi, Switzerland 4School of Electrical and Data Engineering, University of Technology Sydney, Broadway, NSW 2007, Australia CORRESPONDING AUTHOR: EDUARDO ZAFRA (e-mail: [email protected]) The work of Eduardo Zafra, Sergio Vazquez, and Leopoldo G. Franquelo was supported in part by the Project PID2020-115561RB-C31 funded by MCIN/AEI/10.13039/501100011033 and in part by the project TED2021-130613B-I00 funded by MCIN/AEI/10.13039/501100011033 and by the “European Union NextGenerationEU/PRTR.” The work of Eduardo Zafra was supported by the Spanish Ministry of Universities under Grant FPU18/02704. The work of Ricardo P. Aguilera was supported by the Australian Government through the Australian Research Council through Discovery Project DP210101382. ABSTRACT Finite control set model predictive control (FCS-MPC) is a salient control method for power conversion systems that has recently enjoyed remarkable popularity. Several studies highlight the performance benefits that long prediction horizons achieve in terms of closed-loop stability, harmonic distortions, and switching losses. However, the practical implementation is not straightforward due to its inherently high computational burden. To overcome this obstacle, the control problem can be formulated as an integer least-squares optimization problem, which is equivalent to the closest point search or closest vector problem in lattices. Different techniques have been proposed in the literature to solve it, with the sphere decoding algorithm (SDA) standing out as the most popular choice to address the long prediction horizon FCS-MPC. However, the state of the art in this field offers solutions beyond the conventional SDA that will be described in this article alongside future trends and challenges in the topic. INDEX TERMS Optimization methods, parallel algorithms, power converters, predictive control. I. INTRODUCTION The control of power conversion systems is an important research field, which is partly driven by the growth of renewable energy sources and the need to integrate them into the grid [1], [2],[3]. Power electronics and the control of power converters are a crucial aspect to achieve the transition to carbon-free power generation. Advances in control theory translate to performance and efficiency improvements that are key to further propel the growth of these technologies [4]. Within this paradigm, model predictive control (MPC) strategies are becoming a prominent research topic in the field of power electronics [5],[6]. There are several elements that explain this increase in popularity over more traditional control techniques. First, MPC has a straightforward formulation that provides an intuitive method of approaching the control of complex systems. Through MPC techniques, it is possible to consider multiple control objectives, system nonlinearities, and constraints simultaneously and intuitively. For these reasons, research works propose different MPC techniques for the control of power electronic systems, including a wide range of power converter topologies and applications [7],[8]. Among the different families of MPC methods, direct MPC or finite control set MPC (FCS-MPC) enjoys greater popularity as a result of its more natural formulation compared with other alternatives. In FCS-MPC, the discrete nature of the power converter is considered to formulate an integer optimization problem where both control and modulation are addressed in the same computational stage [9]. To this end, the control inputs are restricted to the admissible switching states of the power converter. This set of admissible inputs is the so-called finite control set (FCS). In contrast to continuous control set methods, the optimization problem of one-step This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ VOLUME 4, 2023 159 ZAFRA ET AL.: LONG PREDICTION HORIZON FCS-MPC FOR POWER CONVERTERS AND DRIVES FIGURE 1. Harmonic performance of FCS-MPC with horizon Npfor medium-voltage drive with NPC inverter as a function of the average switching frequency ¯ fsw (Hz). FCS-MPC can easily be solved, e.g., through exhaustive enumeration. This method, also known as the exhaustive search algorithm (ESA), is the most common optimization algorithm in FCS-MPC applications. The ESA enumerates every possible candidate in the FCS, predicts the future states for each control input, and evaluates a cost function to select the optimal switch position in terms of the selected control criteria [5]. The shortcomings of this strategy are revealed in the long prediction horizon (LPH) problem due to its computational costs. The prediction horizon (Np) is the number of time steps considered in the predictions. Enlarging Npexponentially increases the amount of existing combinations of switching states. Thus, an exhaustive enumeration becomes intractable. However, larger Npvalues imply a longer prediction window that feeds the controller with additional information. This feature is particularly relevant in more complex systems, such as secondor third-order systems with one or more resonant frequencies [6]. Performancewise, a longer Npreduces the harmonic distortion and/or the switching frequency, thus achieving a more efficient operation of the power converter. An extract of [10] is shown in Fig. 1to illustrate the performance benefits of extending Npin a medium-voltage drive. In this figure, FCS-MPC with several Npis compared with space vector modulation (SVM) and optimized pulse pattern (OPP), computed according to advanced methods as described in [10]. The total demand distortion (TDD) is used as a measure of the harmonic quality. The current TDD ITDD (%) is computed as follows: ITDD(%) =1 √2Inom  n=1 (ˆ in)2(1) where Inom is the nominal rms value of the current and ˆ inis the amplitude of harmonic components at frequency ntimes the fundamental. Furthermore, since OPP can be considered to present optimal steady-state behavior, the TDD of different methods in Fig. 1are shown in relative terms to the OPP results, computing Irel TDD(%) as Irel TDD(%) =ITDD −ITDD,OPP ITDD,OPP .(2) As can be seen, FCS-MPC harmonic performance is improved as a longer horizon is achieved, completely superseding SVM results for Np=10 and getting closer to the benchmark OPP. To overcome the combinatorial explosion of FCS-MPC with large Np, the optimization problem can be reformulated as an integer least-squares (ILS) problem [9]. Mathematically, this formulation is equivalent to finding the closest point vector in a given lattice. Several techniques have been proposed to solve this problem. Among LPH FCS-MPC, a modified version of the sphere decoding algorithm (SDA) enjoys great popularity in the literature. After this initial research, subsequent studies propose modifications or improvements of the original works [11],[12],[13]. This article presents an overview of the existing state-of-the-art techniques to achieve long Np.1 The rest of this article is organized as follows. The LPHFCS-MPC problem is illustrated in Section II. The basic search algorithms to solve the optimization problem are introduced in Section III. Implementation techniques are presented in Section IV, highlighting some of the main practical challenges that have been studied and solved in the literature. In Section V, the main remaining challenges and future trends are described. Finally, Section VI concludes this article. II. FCS-MPC PROBLEM AND ILS TRANSFORMATION FOR LPH FCS-MPC relies on a receding horizon policy [14]; the control algorithm is executed at discrete time steps at a rate equal to the sampling frequency fs. At each time step, the optimal control action calculated in the previous sampling interval is applied to the power converter. This process is repeated at every time step with new measurements from the system. This characteristic is not altered by extending Np. More time steps are considered in the predictions, but only the first control input within the optimal sequence is applied to the power converter. To define an FCS-MPC strategy, one needs three basic elements: a prediction model, a cost function, and an optimization algorithm. The prediction model computes the evolution of the system state variables at future time steps for given an initial state and a possible sequence of control inputs that can be applied through the prediction horizon. The cost function evaluates the suitability of each possible trajectory and control inputs according to the control objectives. The optimization algorithm minimizes the objective function and selects the optimal sequence of control inputs. This section focuses on the formulation and definition of the FCS-MPC elements. This includes the necessary analysis to transform and solve the LPH-FCS-MPC problem. 1Example MATLAB codes to solve LPH FCS-MPC can be found in https: //github.com/ezafra1/LongHorizon-FCSMPC. 160 VOLUME 4, 2023 A. PREDICTION MODEL The prediction model is a mathematical model of the physical system whose behavior is desired to be controlled to meet specific requirements. For the generic case study of a power converter, the system is an electric circuit that can be analyzed in terms of a finite number of variables through fundamental electrical theory. It is a common practice to write the model in state-space representation with a vector of state variables. The state variables are physical system variables whose future values depend on their present and past values and on the system input values. Specifically, a state-space representation with the minimum number of state variables is desirable. Thus, state variables should be linearly independent. Also, due to the use of digital controllers, a discrete-time state-space representation is required xk+1=Axk+Buk(3a) yk=Cxk(3b) In (3), subindex kindicates the time step of each variable. In general, vector x∈Rncontains the system state variables, whereas y∈Rnyis the system output and u∈Rnuthe system input. Generally, the output contains the variables to be controlled in the application. For power converter systems, the input is usually described by a vector of nuinteger variables representing the switching states of the power converter. As an example, for the case of a three-phase power converter, the input vector is given by u=[uaubuc]. In this particular case, nu=3, as there is a control input or switch position for each phase. The possible integer values for each element depend on the power inverter topology. For the case of a two-level inverter, ua,ub,uc∈{0,1}; for the three-level case, one has ua,ub,uc∈{−1,0,1}. For the general case, ubelongs to the FCS. This can be expressed as u∈Vnu, where V⊂Zis the set of integer switch positions in a given phase. Matrices A∈Rnxn ,B∈Rnxn u, and C∈Rnyxn are the system, input, and output matrices, respectively. For simplicity they are considered to be time-invariant matrices. However, it is possible under this formulation to consider also time-variant matrices. When considering LPH it is opportune to define the input and output sequences. These sequences are vectors that contain the corresponding input and output values for a prediction horizon of length Np. For the input, the switching sequence Uk∈RnuNpis defined as Uk=(uk)T(uk+1)T... (uk+Np−1)TT .(4) Similarly, the output vector and output reference vector sequences, Yk,Y k∈RnyNp, can be defined as Yk=(yk+1)T(yk+2)T...(yk+Np)TT (5) Y∗ k=(y k+1)T(y k+2)T...(y k+Np)TT (6) where y kis the discrete-time system output reference at time step k. Finally, it is convenient to obtain the state vector expression at a future sampling instant +1. This can be achieved by successively applying the state-space model equation (3), resulting in the following equation: x+1=A−k+1xk+[A−kB...A0B]Uk.(7) B. COST FUNCTION The cost function maps the control objectives into a single number. The lower the number, the better the control objectives are achieved. As stated in Section I, one of the main advantages of FCSMPC is its simplicity with which different control objectives can be addressed at once. To achieve this, different terms can be added to the cost function. Each of these terms can address the minimization of a tracking error, the penalization of certain events, or many other considerations. In the literature, the usage of quadratic Euclidean norms is recommended to penalize the tracking error between the system output and the output reference [15]. Another commonly used term in MPC is the penalization of the control effort. This term reduces the average switching frequency ¯ fsw of the power converter and, thus, the switching power losses. To define the relative importance of each term, weighting factors are introduced. To illustrate a standard FCS-MPC problem, a cost function with two quadratic terms will be considered. One of them evaluates the tracking error between the predicted system output and the reference. The other term evaluates the control effort. Weighting factor λ≥0 is added to adjust the tradeoff between both terms. Higher values of λemphasize the minimization of the switching effort over the tracking accuracy. Thus, a standard cost function for the LPH-FCS-MPC can be defined as gk= k+Np−1  =ky+1−y +12 2+λu−u−12 2(8) where kis the current time step. Thus, gkrepresents the cost function values from time step kuntil the end of the prediction horizon at time step k+Np. Note that the outputs y+1are predicted based on (3b) and (7). C. OPTIMIZATION ALGORITHM The optimization algorithm determines the switching sequence Ukthat provides the minimum value of gk.The optimization problem can be defined as Uopt k=arg min Uk gk(9a) s.t. Uk∈U(9b) u∞≤1 (9c) where (9b) are the input constraints. They impose that members of Ukbelong to the FCS U. In Section II-A,it was stated that u∈Vnu. This is the constraint for the nudimensional control input vector at one time step. For the VOLUME 4, 2023 161 ZAFRA ET AL.: LONG PREDICTION HORIZON FCS-MPC FOR POWER CONVERTERS AND DRIVES FIGURE 2. FCS-MPC for power conversion system. LPH problem, constraints are imposed in the entire switching sequence through the considered Nptime steps. This is represented in the optimization problem as Uk∈U, where U=VnuNp.(10) For high-power multilevel converters, switching constraints are also usually considered in the optimization problem as in (9c). This is a voltage level transition constraint that avoids solutions that lead to a high dv/dt or risk damaging the converter [in the case of a neutral-point (NP) clamped converter]. At the end of the optimization process, only the first element of Uopt kis applied to the converter, i.e., uopt k, according to the receding horizon policy. As summary, a diagram of a conventional FCS-MPC algorithm is shown in Fig. 2. In practice, a nonnegligible computational delay exists such that uopt kcannot be applied exactly at time step k.The mainstream solution to address this delay involves one extra prediction step from time step kto time step k+1 assuming that the control input ukis maintained during the sampling interval [16]. Then, the LPH-FCS-MPC is formulated starting from time step k+1. The additional prediction step is not a part of the horizon Np. For notation simplicity, the idealized formulation of the algorithm disregarding computational delays will be used in the rest of this article. In order to solve the optimization problem, different algorithms can be considered. For short horizons, such as Np={1,2}, it is feasible to apply an ESA. Nonetheless, this method is impracticable for longer horizons. Therefore, the optimization problem needs to be reformulated. D. FCS-MPC REFORMULATION FOR THE LPH PROBLEM The optimization problem in (9) can be rewritten as an equivalent ILS-problem. This step is necessary to enable the use of branch-and-bound techniques, such as SDA, to solve the problem efficiently. First, the predicted states (7) along with the output equation (3b) are inserted in the cost function expression. This allows one to write the cost function as a quadratic function of Uk[9],[17] gk=(Uk)TWUk+2(Fk)TUk+k(11) where W=(ϒ)Tϒ+λSTS(12a) Fk=(ϒ)T(xk−Y∗ k)−λSTEuk−1.(12b) Expressions of matrices ϒ,,S, and Ecan be found in [9]. The term kis time varying and a function of the state xkand the initial input uk−1. However, it is independent of Uk. Therefore, it is merely an offset to the cost function, which does not influence the solution of the optimization problem. It can, thus, be disregarded. By completing the squares, expression (11) can be further simplified into gk=Uk−Uunc kTWUk−Uunc k(13) where Uunc kis the unconstrained solution to the optimization problem in (9), or equivalently Uunc k=arg min Uk gk=−W−1Fk(14) where the integer constraints in (9b) are not considered. By definition, the matrix Wis symmetric and positive definite for λ>0. Thus, Cholesky factorization can be applied in order to obtain a nonsingular, lower triangular matrix H such that W=HTH[18]. In practical terms, matrix Hcan be computed noting that its inverse H−1is also lower triangular and can be obtained by the Cholesky decomposition of W−1:W−1=H−1H−T. The cost function in (13) can then be expressed in terms of the matrix H. Therefore, the original problem (9) takes the form Uopt k=arg min Uk gk=arg min UkHUk−¯ Uunc k2 2(15a) subj. to Uk∈U(15b) u∞≤1 (15c) where ¯ Uunc k=HUunc k. Through the definition of the matrix Hand its triangular property, the problem is computationally easy to solve. Geometrically, His a lattice generator matrix that forms a discrete space wherein the solution lies. Thus, the optimization problem is now equivalent to finding the optimal switching sequence Ukwith the shortest distance to ¯ Uunc kin the transformed space. This problem is known as the closest vector problem (CVP) or the closest point search [19]. E. CLOSEST VECTOR PROBLEM (CVP) The CVP or closest point search was formally introduced in [19] as the postoffice problem, and has since been studied in depth in the fields of mathematics and computer science, where it is also known as the box-constrained integer least squares (BILS) problem. BILS is also a target of study in communication theory for modulation and decoding applications [20],[21],[22]. In the BILS problem, one seeks to efficiently enumerate candidates that fulfill the box-constrained condition in order to find the solution. Within the LPH-FCS-MPC framework, this is equivalent to finding the optimal switching sequence Uopt kthat fulfills the switching constraints in (15b). Suppose an initial candidate solution Uini kof a switching sequence is available. This initial candidate solution must fulfill (15b). By definition, the candidate solution defines a 162 VOLUME 4, 2023 hypersphere Sini of radius ρini around the unconstrained solution in the space created by the generator matrix H[23] Sini =Uini k:ρini k2 =HUini k−k2 2(16) where k=¯ Uunc kis the hypersphere center. The optimal solution Uopt kis, by definition, contained in the hypersphere, thus it must fulfill HUopt k−¯ Uunc k2 2≤HUini k−¯ Uunc k2 2.(17) The selection procedure of the initial solution will be discussed in Section IV-B. The main mathematical property that is fundamental to solving the BILS problem is that only candidate integer solutions within the hypersphere (centered at the unconstrained solution ¯ Uunc k) need to be considered. The integer solution with the smallest (squared) distance to the unconstrained solution is the optimal solution. Solutions outside of the sphere are, by definition, suboptimal and do not need to be further considered. This property is crucial because it can be exploited to address the computational complexity of the BILS problem, which is NP-hard2[24],[25]. The squared distance can be evaluated separately in each dimension. Each component of Ukadds a partial cost that is sequentially calculated and added in order to compute the cost of a complete switching sequence Uk. Thus, for each 1-D component, the partial squared distance is calculated as ρ2(i)=H(i,1:i)Uk(1 : i)−¯ Uunc k(i)2 2+ρ2(i−1) (18) where H(i,1:i) is the partial vector formed by the first i elements of the ith row of matrix H. In this case, iis the considered component of the switching sequence Uk.During the search strategy, it is desired to reach the last component so that ρ2(i) yields the complete cost of the evaluated candidate Uk. Then, the decision to update the incumbent solution can be made, guaranteeing convergence to the optimal solution during the process. Conveniently, it is possible to stop exploring a candidate in an intermediate component iif the partial cost exceeds that of the incumbent. In this case, it can also be guaranteed that the subsequent components will only increase the squared distance and, thus, it can be pruned from the search space. In practical terms, this allows one to remove possible candidates and progressively reduce the FCS in a process that is known as bounding. III. BASIC SEARCH ALGORITHMS The search strategy is a crucial aspect to solve the optimization problem. This section is dedicated to introduce the main search methods that were proposed in the literature to solve the BILS problem. The search starts with the first element 2In NP problems, an algorithm that finds the solution in polynomial time is not known, but tentative solutions can be verified in polynomial time. NP hard problems are at least as difficult to solve as the most difficult NP problems. FIGURE 3. Search tree. The root node (white) is in layer i=0. in the switching sequence at time step kand then proceeds forward in time until time step k+Np. To illustrate the search process, a search tree with nuNplevels, as shown in Fig. 3, is usually constructed with the different candidates. Each level contains a fixed number of nodes that represent possible individual switching sequences from the top level of the tree to the bottom level i. These nodes are partial candidates Uk(1 : i)=Uk(1) Uk(2) ... Uk(i)T . Efficient search of the different branches in the tree is paramount to conclude the search process as fast as possible. To this end, several search algorithms have been proposed in the general BILS literature. A. BACKGROUND OF SEARCH ALGORITHMS FOR BILS An overview of the main conventional search algorithms for the CVP can be found in [26]. In total, two techniques can be especially highlighted for their importance: The Pohst [27], [28] and Kannan [29],[30] strategies. Their most fundamental difference is that Pohst’s proposal examined lattice points lying inside a hypersphere while Kannan used polytopes. The vastly popular Schnorr–Euchner method provided a refinement of Pohst’s ideas with a more efficient enumeration of points [31]. Methods based on the usage of hyperspheres are collectively known as sphere decoders. One of the most relevant topics for researchers is to seek further refinements of these strategies to improve the efficiency of the sphere decoder and solve increasingly complex problems [26] [32]. For LPH-FCS-MPC, seminal work [9] introduced the usage of the SDA to solve the problem. A modified sphere decoder based on the Pohst method was proposed and adapted to the power converter control problem. Since then, and analogously to the CVP research, great attention has been paid to the optimization algorithm design, as efficient search was revealed to be a crucial aspect to unlock the full performance potential of LPH-FCS-MPC. For instance, computational variability is a relevant aspect of SDA as the position of the unconstrained (or target) solution in relation to the lattice points can greatly impact the required time to obtain the optimal solution. Conveniently, many of the concepts developed within the CVP theoretical framework can be applied to the LPH-FCS-MPC problem. For example, computational variability is also an undesirable feature in this field. As a means to solve this VOLUME 4, 2023 163 ZAFRA ET AL.: LONG PREDICTION HORIZON FCS-MPC FOR POWER CONVERTERS AND DRIVES TAB LE 1. Basic LPH-FCS-MPC Search Strategies FIGURE 4. Three-layer search tree for Np=1andnu=3. (a) Conventional SDA. (b) K-best SDA. issue, K-best SDA techniques have been proposed in the literature [33],[34]. The K-best SDA also searches within a hypersphere; however, it presents a different search strategy that fixes the amount of explored lattice points, as will be discussed in Section III-C. In the vast CVP literature, it is also possible to find other algorithms differing further from sphere decoders. As examples, consider the iterative slicer [39] or the Micciancio– Voulgaris [40] algorithm, which use the concept of Voronoi cells to explore the lattice points in a different manner. These methods reduce the variability in the computational complexity but tend to incur a higher computational burden when used for LPH [41]. For this reason, the discussion in this article will focus on the most relevant search strategies used for LPH-FCS-MPC, namely the Conventional SDA and the K-best SDA. A comparative summary of both algorithms is provided in Table 1. Their search strategies are also depicted in Fig. 4with a search tree for an FCS such that Uk∈{0,1}3. B. CONVENTIONAL SDA The conventional SDA adopts a depth-first search strategy by progressing as quickly as possible to the bottom layer i=nuNp. For this, vertical advance from a parent to a children node is prioritized (blue arrows). The partial cost of each node is compared with the total cost of the current incumbent candidate (yellow square). If this quantity exceeds the incumbent’s total cost, it is guaranteed that the subsequent nodes in this branch will not yield an optimal solution. Thus, these children nodes do not need to be explored and can be discarded. This is done by performing a sidetracking movement (yellow arrows), for which a different switching position Uk(i) is assessed at the current tree layer i. If all the individual switch positions originating from a parent node have been explored and none of them yielded a better candidate than the incumbent, the branch can be pruned (branches in grey), effectively removing all the subsequent children of red triangle nodes from the search space. This is done by performing a backtracking movement (red arrows), by moving one layer up, which corresponds to the parent node (i−1). Several backtracking movements may be performed until an appropriate parent node is found with children nodes remaining to be explored. The SDA provides a certificate of optimality. This happens when the optimal termination criterion is achieved during the search stage. This criterion consists in backtracking to the root node of the tree. At this point, the search process can be stopped and the incumbent solution is guaranteed to be optimal (green node) even if several branches have been pruned. Therefore, the SDA typically achieves a significant reduction in the computational burden compared with exhaustive enumeration while nevertheless obtaining the optimal solution to the problem. This feature has been a key factor to enable the practical application of LPH-FCS-MPC. Despite this progress, there is still an important drawback to the conventional SDA method, namely, its inherently high computational variability. This feature is particularly critical in LPH-FCS-MPC applications because power converter controllers operate with a hard timing constraint. For this reason, it is necessary to introduce computational upper bounds that limit the amount of explored nodes so that a solution is made 164 VOLUME 4, 2023 available within the given time, even if it is suboptimal [42]. If the number of explored nodes reaches the limit, the early termination criterion is triggered and the SDA search ends prematurely. As a consequence, the certificate of optimality is lost and a certain degree of suboptimality is introduced [35]. This can degrade the performance of LPH-FCS-MPC. Nevertheless, feasibility of the solution is ensured, i.e., the solution meets the FCS integer constraint. C. K-BEST SDA The K-best SDA proposes a breadth-first strategy. In each tree layer, a maximum number of 2Kbnodes are explored. Following the breadth-first principle, horizontal assessment of nodes is prioritized. Thus, in layer i,ni=min{nav i,2Kb} nodes are evaluated. Here, nav iis the number of existing nodes in the current layer. Generally, ni=2Kbdue to the exponential growth of nav i. Once the nipartial costs have been computed, nopt i=min{ni,Kb}nodes are selected as surviving nodes. These nodes are further extended to the next layer i+1. Thus, the algorithm only advances in depth once the search in one horizontal layer has been completed. When the horizontal search of the last tree layer is finished, the best solution at that point is selected. As can be inferred, there is no optimality certificate in this algorithm, as several branches can be discarded prematurely. Nonetheless, the related literature highlights that the likelihood of optimality rapidly increases as the value of Kbis increased with noticeable practical success [43].Themain advantage of the K-best strategy lies in its inherently fixed computational costs. Also, it eliminates the need for the selection of an initial candidate or the need for backtracking to previous levels. Other works in the literature also cite a better suitability for parallel hardware implementation in comparison with the conventional SDA. However, it relies on costly sorting operations [43]. Within the LPH-FCS-MPC paradigm, K-best SDA has been first used in [38]. However, only simulation results and short prediction horizons (Np={1,2})were provided and implementation concerns were not addressed. Latter, it was experimentally validated for LPH in [36]. IV. LPH IMPLEMENTATION CHALLENGES AND SOLUTIONS FCS-MPC reformulation to a BILS problem, alongside the definition of sphere decoding optimization methods, was the first step to enable the study of LPH-FCS-MPC. However, first, LPH-FCS-MPC works were only simulation based [44], [45],[46]. This is because the problem is still inherently challenging in terms of implementation design and computational burden. Consequently, beyond having an accurate prediction model and properly selecting and tuning the cost function [47], the optimization algorithm is also crucial in determining the overall controller performance. Thus, one must carefully design and implement the search strategy. This section provides an analysis of the main solutions proposed in the literature to overcome several of the challenges that researchers face to implement an LPH-FCS-MPC technique. These proposals can be classified in two main groups that are studied in their respective subsections: implementation techniques and preconditioning techniques. The former focus on the improvements of the search stage for efficient implementation while the latter attempt to introduce modifications in the problem definition or in the search prerequisites so that less nodes are explored. A. IMPLEMENTATION TECHNIQUES Regarding implementation of digital controllers for power converters, microprocessors and digital signal processors (DSP) are still the main protagonists in both industry and academia. One can find inexpensive models that offer very specialized computational capabilities and suitable peripherals for each application. Also, software design methods for these platforms are usually preferred by practitioners in this field. However, these platforms are computationally limited and their usage is generally discouraged to achieve highperformance LPH-FCS-MPC. To solve this, the concept of field programmable system on chip (FPSoC) has emerged with noticeable momentum. In essence, an FPSoC is an embedded control platform that provides several microprocessor cores and an field programmable gate array (FPGA) fabric on a single chip. This allows designers to combine existing high-level software solutions with the powerful parallel computing possibilities of FPGAs on a single chip with internal and fast communication between the different computational elements [48],[49]. There exists a wide range of product families that are offered by various manufacturers at different prices. Thus, it is possible to find very cost-competitive solutions that nevertheless offer a performance that exceeds that of a traditional DSP. Following this trend, different works delve into FPSoC platforms to implement LPH-FCS-MPC. By doing this, researchers have broadened the amount of computational resources at their disposal and have accordingly developed several advanced techniques that will be described in the rest of this section. A comparative summary of these techniques is given in Table 2. 1) RAPID CONTROL PROTOTYPING (RCP) First, experimental validations of LPH-FCS-MPC were made possible, thanks to RCP platforms. In works, such as [11] and [17], a DSPACE system is used to implement the controller, generally reaching Np=4 and sampling frequencies of 8 or 10 kHz. The employed search strategy was the conventional SDA. RCP platforms offer powerful hardware similar to FPSoC platforms alongside high-level software programming support. Most notably, these platforms can be programmed from typical simulation software, such as MATLAB Simulink. Also, manufacturers provide built-in and intuitive monitorization tools that simplify many of the typically required tasks to safely operate a power converter. Thus, translation from simulation to experimental prototypes is very straightforward. VOLUME 4, 2023 165 ZAFRA ET AL.: LONG PREDICTION HORIZON FCS-MPC FOR POWER CONVERTERS AND DRIVES TAB LE 2. LPH-FCS-MPC SDA Implementation Techniques The main drawback of these solutions is their high cost, which renders RCP platforms generally unsuitable for industrial and commercial application. Another concern is that by using high-level programming, the potential to achieve computationally efficient designs can be limited. 2) NONRECURSIVE SDA The nonrecursive SDA provided a reformulation of the conventional SDA of [9] that avoids recursion by introducing pointers. This allows the implementation of the SDA on the FPGA of an FPSoC [13] using the standard SDA search strategy as in [9]. In the proposed implementation, several of the matrix operations required in the algorithm’s preliminary stages could be parallelized to increase performance. The design achieved Np=5 with sampling frequency of up to 40 kHz in a direct current control problem for a three-level NPC converter. However, in this method, the search stage is still performed sequentially. The design was implemented in a low-cost Intel Altera platform and followed a hardware description language (HDL)-based design workflow. 3) HLS-BASED SDA Some interesting proposals involve the usage of high-level synthesis (HLS) techniques. HLS is a family of automatic hardware code generation tools that seek to facilitate the transition of software designers to hardware platforms. Fundamentally, HLS attempts to automatically transform software code into firmware for the FPGA, avoiding the usage of HDL. Discussion about automatic generation tools is still ongoing. Manufacturers are investing in developing and improving HLS to make FPGA devices more accessible to designers [53]. Ideally, it would desirable to reduce the application development time and effort close to RCP platforms levels with costs that are reasonable for production and commercialization. While HLS has vastly improved in recent years, some drawbacks still persist. Design effort reduction is palpable, but there is still progress to be made. Also, HLS cannot generally match the efficiency of native hardware designs in terms of timing and area consumption [54],[55]. This might translate into higher requirements for the targeted FPSoC platform, i.e., a low-cost device might not suffice. An HLS-designed SDA is proposed in [50]. In this article, the nonrecursive SDA formulation is coded in software, then transformed to FPGA code by means of Xilinx’s HLS tools. Guidelines to accomplish this process are provided in this article alongside hardware-in-the-loop (HIL) verification. The results indicate the validity of the proposal in terms of execution time, reaching Np=4 with sampling frequency of up to 40 kHz. However, FPGA resource consumption is high, leading to increased hardware requirements. In particular, a Zynq Ultra-Scale+ platform is used in this work, which belongs to the high-cost family of Xilinx products. 4) PARALLEL SDA In [35], a parallel SDA is proposed to achieve concurrent search of the SDA tree. To this end, a parallelization method that effectively decouples the evaluation of different regions in the search space is described and implemented. Up to this point, the literature in this field considered the SDA as an iterative method where information from previous layers is always needed to evaluate the current node. Thus, true concurrent search was not considered [50]. Zafra et al.[35] proposed to divide the search space in equally sized regions that are explored by independent sphere decoders. Internally, these sphere decoders follow the same search pattern described in Section III. An important property of parallelizing the tree structure is that in each region different incumbent solutions will be found during the search stage. This information is shared by the parallel sphere decoders so that the global incumbent solution is used to decide if branches are pruned. This allows one to further tighten the incumbent hypersphere and accelerate the search process. This technique is implemented on a Zynq-7000 board, which belongs to the low-cost family of the Xilinx FPSoC portfolio. Application to a twolevel inverter with output LC filter and voltage regulation control problem is achieved up to Np=6. 5) K-BEST SDA Some of the concepts developed for the implementation in [35] are also applied in [36], where a parallel implementation of the K-best SDA is proposed. In this work, the inherent parallelization of K-best SDA is exploited by proposing a 166 VOLUME 4, 2023 design where the 2Kbexplored nodes in each layer are computed in parallel. The Ukpartial candidates, alongside their partial costs, are stored in a matrix. Sorting operations are performed in this matrix in order to select the Kbsurvivors that will be further developed to the next tree layer. To make efficient use of the FPGA platform, the usage of bitonic sorting networks was proposed. This is more advantageous for hardware implementation as calculation times can be greatly reduced with moderate FPGA area consumption. One of the main conclusions of this work is that for equal number of explored nodes, the K-best SDA can reduce the proportion of suboptimal solutions in comparison with the conventional SDA even for a low number of parallel blocks. B. PRECONDITIONING TECHNIQUES FOR SDA Regardless of the selected search strategy, proper problem conditioning is crucial to alleviate the computational burden. Preconditioning techniques include methods to select the initial candidate hypersphere and techniques that reformulate or transform the optimization problem before starting the search stage. 1) STANDARD SDA INITIALIZATION As mentioned in Section II-E, depth-first SDA techniques require to obtain an initial control input sequence candidate, Uini k. Geometrically, these two vectors Uini kand Uunc kform an initial sphere, Sini, as per (16). In order to reduce the computational time required to obtain Uopt k, the initial sphere Sini should be small enough containing as few candidate solutions as possible, but should not be empty. In [9], it is proposed to initialize the SDA by considering an educated-guess initial vector, Ueg k, which is obtained by shifting the previous optimal solution, Uopt k−1, by one time-step and repeating the last optimal input, i.e., Uini k=Ueg k= ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ 0I0··· 0 00 I··· . . . . . ........... . . 0··· 0··· I 0··· 0··· I ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ Uopt k−1.(19) This initialization method, i.e., ρini k=ρeg k, is particularly suitable for steady-state operations, since it exploits the MPC receding horizon policy, and Ueg kis feasible since satisfies the constraints in (9b). In [45] and [42], the Babai estimate method is introduced and assessed. The Babai estimate is obtained by rounding the unconstrained solution to the closest integer vector Uini k=Ubab k=Uunc k.(20) In more recent works, the initial hypersphere is selected as the minimum of both techniques [13] Uini k=min ρbab k,ρeg k.(21) FIGURE 5. Graphical representation of the direct MPC problem (an FCS U of nine control input vectors) for transient operation, where both the standard and the transient operation SDA initializations are represented. (a) Original space and (b) transformed space generated by H. These techniques are widespread in LPH-FCS-MPC works as they generally provide a good initial sphere candidate. However, several works in the literature have proposed alternative techniques to enhance the initial candidate selection. 2) SDA INITIALIZATION FOR TRANSIENT OPERATIONS An illustration of the optimization process during a transient operation is depicted in Fig. 5. This example is shown for an FCS Uof nine control input vectors (gray solid circles). Here, CHrepresents the convex hull of the FCS U[56], i.e., CH=Conv(U) (22) which as per definition, CHis the smallest convex set in which U⊂CH. Moreover, the ellipses centered in Uunc krepresent the level sets of the original optimization problem (15). The matrix Hin (15) introduces a linear transformation that generates a new transformed space in Fig. 5(b). In this space, the original ellipses are transformed into circles, S, (spheres for larger dimensions) centered in k=¯ Uunc k=HUunc k, as per (16). In fact, this is space where the SDA operates. During transients, the system output ykmight be far away from its reference y k. In this case, a large actuation is required to lead it back to its reference. This can place Uunc kfar away from CH; see Fig. 5(a). In this situation, no matter what initial candidate Uini kis chosen, a large initial radius ρini will be always obtained. To overcome this problem, a computationally efficient preconditioning approach for the SDA during transient was proposed in [12],[17], and [57]. This approach consists of obtaining a new center kfor SDA during transients by projecting Uunc konto the boundary of CH. This is achieved by solving the following box-constrained quadratic programming (QP) problem: Ubc k=arg min UkHUk−¯ Uunc k(23a) subj. to Uk∈CH.(23b) VOLUME 4, 2023 167 ZAFRA ET AL.: LONG PREDICTION HORIZON FCS-MPC FOR POWER CONVERTERS AND DRIVES [57] R. Baidya et al., “Enabling multistep model predictive control for transient operation of power converters,” IEEE Open J. Ind. Electron. Soc., vol. 1, pp. 284–297, 2020, doi: 10.1109/OJIES.2020.3029358. [58] A. K. Lenstra, H. W. Lenstra Jr., and L. Lovász, “Factoring polynomials with rational coefficients,” Mathematische Annalen, vol. 261, no. 4, pp. 515–534, Dec. 1982. [59] P. Karamanakos, T. Geyer, and R. Kennel, “A computationally efficient model predictive control strategy for linear systems with integer inputs,” IEEE Trans. Control Syst. Technol., vol. 24, no. 4, pp. 1464–1471, Jul. 2016. [60] H.-L. Chiang and S.-G. Chen, “An efficient hybrid sphere decoding algorithm for MIMO systems,” in Proc. IEEE 10th Int. Symp. Spread Spectr. Techn. Appl., 2008, pp. 339–343, doi: 10.1109/ISSSTA. 2008.68. [61] M. Dehghani Soltani, M. Alimadadi, and H. Amindavar, “A hybrid method to reduce the complexity of k-best sphere decoding algorithm,” in Proc. 22nd Iranian Conf. Elect. Eng., 2014, pp. 1765–1770, doi: 10.1109/IranianCEE.2014.6999824. [62] E. Zafra et al., “Computationally efficient sphere decoding algorithm based on artificial neural networks for long-horizon FCSMPC,” IEEE Trans. Ind. Electron., early access, Feb. 13, 2023, doi: 10.1109/TIE.2023.3243301. [63] B. Long, T. Cao, W. Fang, K. T. Chong, and J. M. Guerrero, “Model predictive control of a three-phase two-level four-leg grid-connected converter based on sphere decoding method,” IEEE Trans. Power Electron., vol. 36, no. 2, pp. 2283–2297, Feb. 2021, doi: 10.1109/TPEL.2020.3006432. [64] A. Andersson and T. Thiringer, “Assessment of an improved finite control set model predictive current controller for automotive propulsion applications,” IEEE Trans. Ind. Electron., vol. 67, no. 1, pp. 91–100, Jan. 2020, doi: 10.1109/TIE.2019.2898603. [65] F. Grimm, Z. Zhang, M. Abdelrahem, and R. Kennel, “Computationally efficient predictive control of three-level NPC converters with dc-link voltage balancing: A priori state selection approach,” in Proc. IEEE Int. Symp. Predictive Control Elect. Drives Power Electron., 2017, pp. 72–77, doi: 10.1109/PRECEDE.2017.8071271. [66] F. Grimm, Z. Zhang, F. Wang, and R. Kennel, “Multistep predictive control of three-level NPC converters using weak derivative linearization,” in Proc. Chin. Automat. Congr., 2017, pp. 4672–4677, doi: 10.1109/CAC.2017.8243604. [67] E. Liegmann, P. Karamanakos, T. Geyer, T. Mouton, and R. Kennel, “Long-horizon direct model predictive control with active balancing of the neutral point potential,” in Proc. IEEE Int. Symp. Predictive Control Elect. Drives Power Electron., 2017, pp. 89–94, doi: 10.1109/PRECEDE.2017.8071274. [68] L. Ortombina, P. Karamanakos, and M. Zigliotto, “Robustness analysis of long-horizon direct model predictive control: Induction motor drives,” in Proc. IEEE 21st Workshop Control Model. Power Electron., 2020, pp. 1–8. [69] A. Tregubov, P. Karamanakos, and L. Ortombina, “Long-horizon robust direct model predictive control for medium-voltage induction motor drives with reduced computational complexity,” IEEE Trans. Ind. Appl., vol. 59, no. 2, pp. 1775–1787, Mar./Apr. 2023, doi: 10.1109/TIA.2022.3219042. [70] L. Ortombina, P. Karamanakos, and M. Zigliotto, “Robustness analysis of long-horizon direct model predictive control: Permanent magnet synchronous motor drives,” in Proc. IEEE 21st Workshop Control Model. Power Electron., 2020, pp. 1–8. [71] X. Li, Q. Yang, W. Tian, P. Karamanakos, and R. Kennel, “A dual reference frame multistep direct model predictive current control with a disturbance observer for SPMSM drives,” IEEE Trans. Power Electron., vol. 37, no. 3, pp. 2857–2869, Mar. 2022, doi: 10.1109/TPEL.2021.3118572. [72] I. Hammoud, S. Hentzelt, T. Oehlschlaegel, and R. Kennel, “Longhorizon direct model predictive control based on neural networks for electrical drives,” in Proc. IECON 46th Annu. Conf. IEEE Ind. Electron. Soc., 2020, pp. 3057–3064, doi: 10.1109/IECON43393.2020. 9254388. [73] F. Grimm, P. Kolahian, Z. Zhang, and M. Baghdadi, “A sphere decoding algorithm for multistep sequential model-predictive control,” IEEE Trans. Ind. Appl., vol. 57, no. 3, pp. 2931–2940, May/Jun. 2021, doi: 10.1109/TIA.2021.3060694. [74] F. Grimm, Z. Zhang, and R. Kennel, “Sphere decoding based long-horizon predictive control of three-level NPC back-to-back PMSG wind turbine systems,” in Proc. Int. Power Electron. Conf. (IPEC-Niigata -ECCE Asia), 2018, pp. 2895–2900, doi: 10.23919/IPEC.2018.8507471. [75] P. Karamanakos, E. Liegmann, T. Geyer, and R. Kennel, “Model predictive control of power electronic systems: Methods, results, and challenges,” IEEE Open J. Ind. Appl., vol. 1, pp. 95–114, 2020, doi: 10.1109/OJIA.2020.3020184. [76] P. Cortes, J. Rodriguez, D. E. Quevedo, and C. Silva, “Predictive current control strategy with imposed load current spectrum,” IEEE Trans. Power Electron., vol. 23, no. 2, pp. 612–618, Mar. 2008, doi: 10.1109/TPEL.2007.915605. [77] M. Tomlinson, H. d. T. Mouton, R. Kennel, and P. Stolze, “A fixed switching frequency scheme for finite-control-set model predictive control–concept and algorithm,” IEEE Trans. Ind. Electron., vol. 63, no. 12, pp. 7662–7670, Dec. 2016, doi: 10.1109/TIE.2016.2593997. [78] M. Aguirre, S. Kouro, C. A. Rojas, J. Rodriguez, and J. I. Leon, “Switching frequency regulation for FCS-MPC based on a period control approach,” IEEE Trans. Ind. Electron., vol. 65, no. 7, pp. 5764–5773, Jul. 2018, doi: 10.1109/TIE.2017.2777385. [79] M. Aguirre, S. Kouro, C. A. Rojas, and S. Vazquez, “Enhanced switching frequency control in FCS-MPC for power converters,” IEEE Trans. Ind. Electron., vol. 68, no. 3, pp. 2470–2479, Mar. 2021, doi: 10.1109/TIE.2020.2973907. [80] B. Stickan, P. Rutquist, T. Geyer, and M. Diehl, “Spectrum shaping methods for predictive control approaches applied to a grid-connected power electronics converter,” in Proc. IEEE 58th Conf. Decis. Control, 2019, pp. 5223–5230, doi: 10.1109/CDC40024.2019.9030019. [81] N. Panten, N. Hoffmann, and F. W. Fuchs, “Finite control set model predictive current control for grid-connected voltage-source converters with LCL filters: A study based on different state feedbacks,” IEEE Trans. Power Electron., vol. 31, no. 7, pp. 5189–5200, Jul. 2016, doi: 10.1109/TPEL.2015.2478862. [82] M. Norambuena, J. Rodriguez, Z. Zhang, F. Wang, C. Garcia, and R. Kennel, “A very simple strategy for high-quality performance of ac machines using model predictive control,” IEEE Trans. Power Electron., vol. 34, no. 1, pp. 794–800, Jan. 2019, doi: 10.1109/TPEL.2018.2812833. [83] T. Geyer, “Algebraic tuning guidelines for model predictive torque and flux control,” IEEE Trans. Ind. Appl., vol. 54, no. 5, pp. 4464–4475, Sep./Oct. 2018. [84] B. Stellato, T. Geyer, and P. J. Goulart, “High-speed finite control set model predictive control for power electronics,” IEEE Trans. Power Electron., vol. 32, no. 5, pp. 4007–4020, May 2017, doi: 10.1109/TPEL.2016.2584678. [85] P. Karamanakos, T. Geyer, and R. Kennel, “Constrained longhorizon direct model predictive control for power electronics,” in Proc. IEEE Energy Convers. Congr. Expo., 2016, pp. 1–8, doi: 10.1109/ECCE.2016.7854957. [86] L. Ortombina, E. Liegmann, P. Karamanakos, F. Tinazzi, M. Zigliotto, and R. Kennel, “Constrained long-horizon direct model predictive control for synchronous reluctance motor drives,” in Proc. IEEE 19th Workshop Control Model. Power Electron., 2018, pp. 1–8, doi: 10.1109/COMPEL.2018.8460173. [87] H. A. Young, M. A. Perez, and J. Rodriguez, “Analysis of finite-controlset model predictive current control with model parameter mismatch in a three-phase inverter,” IEEE Trans. Ind. Electron., vol. 63, no. 5, pp. 3100–3107, May 2016, doi: 10.1109/TIE.2016.2515072. [88] Y.-j. Wu and G.-f. Li, “Adaptive disturbance compensation finite control set optimal control for PMSM systems based on sliding mode extended state observer,” Mech. Syst. Signal Process., vol. 98, pp. 402–414, 2018, doi : https://doi.org/10.1016/j.ymssp.2017.05.007 [89] O. Wallscheid and E. F. B. Ngoumtsa, “Investigation of disturbance observers for model predictive current control in electric drives,” IEEE Trans. Power Electron., vol. 35, no. 12, pp. 13563–13572, Dec. 2020, doi: 10.1109/TPEL.2020.2992784. [90] C.-K. Lin, J.-t. Yu, Y.-S. Lai, and H.-C. Yu, “Improved model-free predictive current control for synchronous reluctance motor drives,” IEEE Trans. Ind. Electron., vol. 63, no. 6, pp. 3942–3953, Jun. 2016, doi: 10.1109/TIE.2016.2527629. 174 VOLUME 4, 2023 [91] Y. Zhang, J. Jin, and L. Huang, “Model-free predictive current control of PMSM drives based on extended state observer using ultralocal model,” IEEE Trans. Ind. Electron., vol. 68, no. 2, pp. 993–1003, Feb. 2021, doi: 10.1109/TIE.2020.2970660. [92] I. Goodfellow, Y. Bengio, and A. Courville, Deep Learning. Cambridge, MA, USA: MIT Press, 2016, http://www.deeplearningbook.org [93] T. Dragiˇ cevi´ c and M. Novak, “Weighting factor design in model predictive control of power electronic converters: An artificial neural network approach,” IEEE Trans. Ind. Electron., vol. 66, no. 11, pp. 8870–8880, Nov. 2019, doi: 10.1109/TIE.2018.2875660. [94] M. Novak, H. Xie, T. Dragiˇ cevi´ c, F. Wang, J. Rodriguez, and F. Blaabjerg, “Optimal cost function parameter design in predictive torque control (PTC) using artificial neural networks (ANN),” IEEE Trans. Ind. Electron., vol. 68, no. 8, pp. 7309–7319, Aug. 2021, doi: 10.1109/TIE.2020.3009607. [95] S. Vazquez et al., “An artificial intelligence approach for real-time tuning of weighting factors in FCS-MPC for power converters,” IEEE Trans. Ind. Electron., vol. 69, no. 12, pp. 11987–11998, Dec. 2022, doi: 10.1109/TIE.2021.3127046. [96] I. S. Mohamed, S. Rovetta, T. D. Do, T. Dragicevi´ c, and A. A. Z. Diab, “A neural-network-based model predictive control of threephase inverter with an output LC filter,” IEEE Access,vol.7, pp. 124737–124749, 2019, doi: 10.1109/ACCESS.2019.2938220. [97] M. Novak and T. Dragicevic, “Supervised imitation learning of finiteset model predictive control systems for power electronics,” IEEE Trans. Ind. Electron., vol. 68, no. 2, pp. 1717–1723, Feb. 2021, doi: 10.1109/TIE.2020.2969116. [98] X. Liu, L. Qiu, Y. Fang, K. Wang, Y. Li, and J. Rodríguez, “A fuzzy approximation for FCS-MPC in power converters,” IEEE Trans. Power Electron., vol. 37, no. 8, pp. 9153–9163, Aug. 2022, doi: 10.1109/TPEL.2022.3157847. EDUARDO ZAFRA (Graduate Student Member, IEEE) was born in Seville, Spain, in 1994. He received the B.S. and M.S. degrees in industrial engineering, in 2016 and 2019, respectively, from the University of Seville, Seville, Spain, where he is currently working toward the Ph.D. degree in automatics, electronics, and telecommunications. His research interests include control and modulation of power converters and drives, model predictive control, and design for digital embedded systems. SERGIO VAZQUEZ (Fellow, IEEE) was born in Seville, Spain, in 1974. He received the M.S. and Ph.D. degrees in industrial engineering from the University of Seville (US), Seville, in 2006, and 2010, respectively. Since 2002, he has been with the Power Electronics Group working in R&D projects. He is an Associate Professor with the Department of Electronic Engineering, US. His research interests include power electronics systems, modeling, modulation, and control of power electronics converters applied to renewable energy technologies. Dr. Vazquez was the recipient as Coauthor of the 2012 Best Paper Award of the IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS and 2015 and 2022 Best Paper Award of the IEEE Industrial Electronics Magazine.Heis involved in the Energy Storage Technical Committee of the IEEE Industrial Electronics Society and is currently an Associate Editor for the IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS. TOBIAS GEYER (Fellow, IEEE) received the Dipl.-Ing. degree in electrical engineering, the Ph.D. degree in control engineering, and the Habilitation degree in power electronics from ETH Zürich, Zürich, Switzerland, in 2000, 2005, and 2017, respectively. After the Ph.D., he spent three years with GE Global Research, Munich, Germany, three years with the University of Auckland, Auckland, New Zealand, and eight years with ABB’s Corporate Research Centre, Baden-Dättwil, Switzerland. In 2020, he joined ABB’s Medium-Voltage Drive Division as R&D Platform Manager of the ACS6080. In 2022, he became a Corporate Executive Engineer. Working at the intersection of industry and academia, he is also an extraordinary Professor with Stellenbosch University, Stellenbosch, South Africa, from the year 2017 until 2023. He is the author of more than 35 patent families, 150 publications, and one book. He teaches a regular course on model predictive control at ETH Zürich. His research interests include medium-voltage and low-voltage drives, utility-scale power converters, optimized pulse patterns, and model predictive control. Dr. Geyer was the recipient of the PELS Modeling and Control Technical Achievement Award in 2022, Semikron Innovation Award in 2021, Nagamori Award in 2021, and two Prize Paper Awards of IEEE transactions and two Prize Paper Awards at IEEE conferences. He is a former Associate Editor for the Transactions on Industry Applications (from 2011 to 2014) and the Transactions on Power Electronics (from 2013 to 2019). He is a Distinguished Lecturer of the Power Electronics Society from 2020 until 2023. RICARDO P. AGUILERA (Member, IEEE) received the B.Sc. degree in electrical engineering from the Universidad de Antofagasta, Antofagasta, Chile, in 2003, the M.Sc. degree in electronics engineering from the Universidad Tecnica Federico Santa Maria, Valparaíso, Chile, in 2007, and the Ph.D. degree in electrical engineering from The University of Newcastle (UoN), Newcastle, NSW, Australia, in 2012. From 2012 to 2013, he was a Research Academic with UoN, where he was a part of the Centre for Complex Dynamic Systems and Control. From 2014 to 2016, he was a Senior Research Associate with The University of New South Wales, Kensington, NSW, Australia, where he was a part of the Australian Energy Research Institute. Since September 2016, he has been with the School of Electrical and Data Engineering, University of Technology Sydney, Ultimo, NSW, Australia, where he is currently an Associate Professor. His research interests include theoretical and practical aspects on model predictive control with application to power electronics, renewable energy integration, and microgrids. LEOPOLDO G. FRANQUELO (Life Fellow, IEEE) was born in Malaga, Spain. He received the Ph.D. degree in industrial engineering from the University of Seville, Seville, Spain, in 1980. Since 1986, he has been a Professor with the Department of Electronic Engineering, University of Seville. His current research interests include modulation techniques for multilevel inverters and their application to renewable energy systems. He has participated in more than 100 R&D projects and has authored or coauthored more than 350 papers, 120 of them in high impact journals. Dr. Franquelo has been the IES Vice President/President for conferences and is currently a Distinguished Lecturer at the Industrial Electronics Society (IES) since 2006. Committed to the work in IEEE, he was the Editor-in-Chief (2016–2019) of the IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS and is currently the Editor-in-Chief of the IEEE OPEN JOURNAL of the Industrial Electronics Society. He was the recipient of the prestigious Andalusian Research Award and the FAMA Award in recognition of the excellence of his research career in 2009 and 2013, and Eugene Mittelmann Outstanding Research Achievement Award and Anthony J. Hornfeck Service Award from IEEE-IES in 2012 and 2015, respectively. VOLUME 4, 2023 175