Variable Sampling Time Finite Control-Set Model Predictive Current Control for Voltage Source Inverters

Transcription

1 Variable Sampling Time Finite Control-Set Model Predictive Current Control for Voltage Source Inverters Nils Hoffmann*, Markus Andresen*, Friedrich W. Fuchs*, Lucian Asiminoaei** and Paul B. Thøgersen*** *Institute for Power Electronics and Electrical Drives Christian-Albrechts-University of Kiel D Kiel, Germany Abstract This work introduces the control concept of variable sampling time finite control-set model predictive control (FCS- MPC). The new control concept is introduced in theory based on a review of the conventional FCS-MPC concepts performed with a constant sampling time. Based on the partitioning of the sampling instant in multiple smaller sampling instants it is possible to optimize, besides the switching states, the switching states turn-on times. Therefore, the proposed variable sampling time FCS-MPC sets both: the switching state and the related turn-on times. To utilize the available calculation power for longer sampling instants an adaptation of the control- and prediction horizon to the sampling time is proposed. The theoretical control concepts are applied to the control of a grid connected two-level voltage-source converter where a simple L- type line filter is used to demonstrate the control performance of the variable sampling time FCS-MPC algorithms in the laboratory environment. NOMENCALTURE Control horizon Prediction horizon Sampling time Variable at sampling instant t = (k-1)t s Variable at sampling instant t = kt s Variable at sampling instant t = (k+1)t s I. INTRODUCTION In the last decades model predictive control (MPC) emerged tremendously in the field of power electronic engineering. The enormous success of MPC for power electronic applications is traced back to the distinguished features provided by this control approach. Compared to conventional approaches MPC offers to include complex constrained optimization problems, model nonlinearities and discrete event-based problem formulations in the controller design process. Furthermore, the achievable control performance of MPC algorithms appears to be excellent and very convincing in terms of reference- and disturbance rejection as well as robustness in relation to model- and parameter uncertainties [1,2]. One of the major concerns about using MPC in industrial relevant power electronic applications is the high computation burden that is inherent to the complex control formulation. **Danfoss Solar Inverters A/S DK Sønderborg, Denmark las@danfoss.com ***KK-Electronic A/S DK-9220 Aalborg, Denmark patho@kk-electronic.com Nevertheless, academic and industrial researchers spent high efforts to overcome this aforementioned issue making the MPC approaches more practicable, more reliable and thus more cost efficient to a wide range of power electronic applications [3,4]. MPC approaches are classified into continuous control-set (CCS) MPC approaches and into finite control-set (FCS) MPC approaches. In this context continuous control-set refers to a theoretically infinite choice of possible control actuating variables whereas finite control-set refers to a limited (finite) choice of possible control actuating variables. In power electronic applications CCS-MPC approaches are often used in connection with modulators (e.g. pulse-width modulation) to transform the reference output waveforms to the representative switching states and duty cycles of the semiconductor devices [5,6]. In contrast to that, FCS-MPC approaches are influencing the switching states of power electronic converters directly. The set of possible switching states, and thus of possible set of output values for the control law formulation depends on the used converter topology [7,8]. Another approach to classify MPC algorithms uses the way how the control performance is optimized. The control performance can be either optimized prior (offline) or during (online) the real-time control calculations. MPC algorithms that are using offline optimized control performances are referred to as explicit MPC algorithms whereas MPC algorithms that are using online optimization are referred to as linear MPC algorithms. A study of recently published articles about MPC reveals that explicit (CCS-) MPC algorithms are mostly applied when more than one system state variable is controlled which is especially interesting when systems with resonances are studied [6,9]. Linear (FCS-) MPC is more likely applied when complex converter topologies with a limited number of system states are controlled [10-12]. This work focuses on linear FCS-MPC used for the current control of voltage-source inverters (VSIs). In [7] the underlying principle of FCS-MPC applied to the current control for VSIs is explained. The performance of FCS-MPC based current control is compared with hysteresis- and PWMbased current control and it is concluded to be comparable very well to these classical control methods. A detailed guideline for the implementation of FCS-MPC to a state-of-the art DSP is presented. The work presented in [13] basically continues this work presenting a graph algorithm included to the FCS-MPC /12/$ IEEE 2215

2 based current controller to reduce the inverters switching losses in steady state converter operation. The focus of [13] is set to high power applications. The graph algorithm introduced to the FCS-MPC based current control leads to a switching behavior where only one inverter-leg is switched in each control period. This work aims to contribute to the FCS-MPC based current control of VSIs. In contrast to the FCS-MPC algorithms presented in literature so far, where a fixed sampling time and thus constant pulse-width resolution is used, the proposed FCS-MPC varies the sampling time based on the predicted system behavior and the applied cost functions leading to variable pulse-widths applied by the FCS-MPC based current controller. Therefore, compared to the conventional FCS-MPC algorithms that are operated with a constant sampling time the proposed FCS-MPC control that is operated with a variable sampling time optimizes both, the switching states and the related turn-on times. This new FCS- MPC approach is referred to as variable sampling time FCS- MPC. Further, this work presents a possibility to improve the FCS-MPC control performance by including additional sampling time adaptive control functions to utilize the available computation power. The proposed variable sampling time FCS-MPC approach is applied to the current control of a grid connected two-level VSI with a simple L filter to demonstrate the achievable control performance of variable sampling time FCS-MPC. This converter topology is chosen because of its industrial relevance and widespread applications. However, the studies presented here are theoretically not limited to this two-level inverter topology. The proposed control principle can be applied to every voltage-source inverter topology where an average output voltage level is achieved by variation of the duty cycle ratios of switched semiconductor devices such as switched-mode power supplies, DC-DC converters or multi-level converters. This work is structured as follows: In the second chapter a system description is presented. The third chapter reviews the conventional constant sampling time FCS-MPC approach and the proposed variable sampling-time FCS-MPC approach is introduced in the fourth chapter. A measurement study is presented in the fifth chapter. The paper is closed by a detailed conclusion presented in the last chapter. Fig. 1: Block-diagram of three-phase three-wire grid connected voltagesource converter with L filter type line-filter II. SYSTEM DESCRIPTION AND CONTROL BLOCK DIAGRAM In Fig. 1 the block diagram of a three-phase three-wire grid connected voltage source inverter with an L filter is presented. An active load is indicated emphasizing that the grid connected converter operates under non constant, time dependent load conditions. The inverter is composed of three inverter phase legs whereas each phase leg consists of two insulated gate bipolar transistors (IGBTs) with anti parallel diodes. To avoid fault conditions due to a short circuit in the inverters phase leg it is not allowed switching the complementary IGBTs of each phase-leg at the same time. Taking this into account, eight possible switching states of the two-level VSI can be identified. These eight possible switching states lead to seven different output voltage states which are summarized in Table I. Based on the corresponding output voltage level the presented space vectors (SV) are separated into active state (SV1 SV6) and zero state (SV0, SV7) space vectors. TABLE I SWITCHING STATE DEFINITIONS AND CONVERTER OUTPUT VOLTAGES Switching vector Switch states Converter output voltage U αβ Conv S 1S 4 S 3S 6 S 5S 2 U Conv,α U Conv,β SV SV /3 U DC 0 SV /3 U DC 1/ 3 U DC SV /3 U DC 1/ 3 U DC SV /3 U DC 0 SV /3 U DC -1/ 3 U DC SV /3 U DC -1/ 3 U DC SV Notation: 0 Switch S x open, 1 Switch S x closed To demonstrate the principles of the proposed variable pulse-width FCS-MPC approach the control scheme of the voltage-oriented control (VOC) is used [14]. The VOC scheme is composed of cascaded control-loops with an inner current control loop and an outer DC link voltage control loop. By aligning the controlled converter currents to the phase angle of the fundamental grid voltage the active and the reactive power drawn or fed-in to the mains can be controlled independently. The phase angle of the grid voltage phasor is achieved by means of phase locked loop (PLL) technique. III. CONSTANT SAMPLING TIME FCS-MPC Several approaches have been published introducing the general idea of FCS-MPC [2,7,13,15-17] and specifically for three-phase VSI applications [7,8,13,18-20]. To provide a deeper understanding of the underlying principles of FCS- MPC the application of a constant sampling time FCS-MPC based current controller for a grid connected VSI is reviewed in the next sections. A. System equations of converter model A three-phase three-wire grid connected VSI as it has already been illustrated in Fig. 1 is considered. Applying Kirchhoff s law to the L filter type line-filter and using the Clarke (αβ) transformation the line side filter dynamics are expressed as presented in (1). (X denotes a space vector) 2216

3 1 (1) Using the Park (dq) transformation to calculate the line filter dynamics in the rotating dq reference frame (with the angular line-frequency ω Line ) the equation (2) holds place whereas a coupling term between the d- and q-current components occurs. 1 (2) For the sake of simplicity it is assumed that the converter currents I Conv, and the line voltages U Line are measured. Thus, every systems state of (2) is known except the converter output voltages U Conv. However, utilizing the principle of a finite control-set with respect to the possible switching states of the two-level VSI (see Table I) the converter s output voltage can be expressed dependent on the inverters switching state and the DC link voltage U DC (3) where the switching states S 1, S 3 and S 5 address the calculated switching states of the former calculation instant (here: t = kt s ). (Notation of switching states: see Table I) 2, 3, (3) B. Prediction of system states The system equations of the grid connected VSI (1)-(3) are now used to achieve a prediction equation of the controlled system states. A convenient state space model formulation of the d- and q-current line filter dynamics is used for illustration purposes (4). 1 (4) 1 Using explicit Euler approximation to derive the derivative converter current dynamics between two sampling instants the discrete prediction equation is calculated (5) (5) The current evolution for each possible switching state of the two-level VSI can be predicted combining (3) and (5). The prediction principle is used in an iterative manner leading to current predictions for multiple sampling instants to the future. C. Cost function and switching optimization The presented prediction equations are used to optimize the control performance. Different optimization goals can be included in the switching state optimization of FCS-MPC based current controllers [17]. The optimization goals are dependent on the specific control performance requirements set by the converter application. The optimization goal of this work is set to switching loss reduction with an acceptable range of harmonic current distortion and reference current tracking in the same time. To achieve this optimization goal a quadratic cost function is introduced to the switching state optimization (6). The future (predicted) current control deviations are used to evaluate the costs of each possible switching state:,, (6) D. Switching frequency reduction due to switching state restrictions The former paragraphs present the principles of FCS-MPC operating with constant sampling time. Basically, an appropriate choice of the cost-function is used to optimize the control performance. The converters topology, i.e. the possible and allowed switching state combinations, is considered in the prediction law formulation. In [13] another possibility to influence the switching performance of the chosen two-level VSI converter topology is presented. A switching state flow graph is included to the current prediction algorithms to further manipulate the inverters switching behavior. The related switching state flowgraph is depicted in Fig. 2. The flow graph is designed to allow only one switching transition at maximum in all of the three inverter legs in each sampling period (i.e. sampling time). Fig. 2 Switching state flow-graph to allow at maximum one switching transition in sampling instant based on [13] As aforementioned the control performance goal is set to switching loss reduction with an acceptable range of harmonic current distortion and reference current tracking in the same time. To achieve this goal a quadratic cost function is used. To further reduce the inverters switching losses with an acceptable amount of harmonic current distortion the discussed flow graph is used for the converter output current prediction. E. Calculation burden The presented principles of FCS-MPC reveal a significant amount of calculations involved. To reduce the basic calculation burden of these FCS-MPC algorithms different approaches have been presented in literature [4,19]. An appropriate choice of the reference frame (here the rotating dq reference frame is chosen) for the FCS-MPC control problem 2217

4 formulation [19] as well as an adaptation of mathematical programming techniques [4] reduces the basic calculation burden. Here a two-level VSI is used with a switching state flow graph that allows one switching transition at maximum in all of the three inverter legs for each sampling period. Thus four possible switching states have to be considered in each sampling time instant for the current prediction and cost function evaluation. This leads to the basic calculation burden presented in (7)., 4 4 (7) IV. VARIABLE SAMPLING TIME FCS-MPC The principles of constant sampling time FCS-MPC based current control are reviewed in the former paragraphs. Except the FCS-MPC based concept of model predictive direct torque control proposed by Geyer et. al. [15,16] (here the switching performance is optimized based on state extrapolation with given switching boundaries) these reviewed methods have in common that the system is sampled and the switching states are updated with a fixed sampling time. Thus, giving a maximum control horizon N R and prediction horizon N P, the voltage pulse width set by the FCS-MPC controller is restricted by the applied sampling time resolution. When the control algorithms are executed with a fixed sampling time, the switching states are optimized in each sampling instant leading to: First, a high computational burden even when no switching transitions occur between multiple sampling periods and second, unnecessary (non-optimal) switching transitions that occur because of model- and parameters uncertainties when the receding horizon concept is utilized. To overcome these drawbacks of a constant sampling time FCS-MPC a variable sampling time FCS-MPC is proposed. The variation of the sampling time is included in the FCS-MPC prediction law formulation leading to a new degree of freedom for control performance optimization during online control processing. A. Concept In Fig. 3 the functional principle of the proposed variable sampling time FCS-MPC is highlighted. The functional concept of this control is explained in five steps: Step 1: At an arbitrary sampling instant k the system states are sampled and the system s switching state S (k-1) is updated due to the FCS-MPC calculations of the former sampling instant k-1. Then, for a given minimum sampling time T s,min and maximum sampling time T s,max, the next sampling instant k+1 is divided in multiple partitions. In the exemplary illustration the sampling instant k+1 is divided into five equidistant partitions (L = 5). Step 2: For a given control horizon N R k and prediction horizon N P k (which was set in the former sampling instant k-1) the converter currents are predicted using the same principles that have already been introduced for constant sampling time FCS-MPC but in this case for the different possible switching instant partitions L. The fragmentation of the maximal possible sampling time into multiple smaller partitions is used to optimize the turn-on times in addition to the switching state optimization. The related costs for each of these predicted currents are then evaluated for every possible partition and switching state. To reduce the calculation burden only the switching patterns with a minimum cost for each considered partition are compared with the minimum costs of every other considered partition. Step 3: In the next step the system switching state and the related turn-on time is updated based on the calculated optimal switching pattern and the related turn-on times. Only the first switching state is applied. Since the related turn-on time is optimized and thus known in advance also the counter value for the hardware interrupt to set the next (optimized) sampling instant is set by the FCS-MPC based current controller. Step 4: The calculation steps of the FCS-MPC with variable sampling time presented so far reveal that besides the optimal switching pattern also the turn-on times for each switching state are optimized. Thus, due to the predictive nature of the FCS-MPC algorithm, the switching state and the turn-on time for the next (future) sampling instant is known in advance. This knowledge is used to utilize the available calculation power for the varying sampling times. For increasing sampling times also the available calculation time increases. Thus, more calculations can be performed for these increased sampling times. Here, the prediction and the control horizon are varied based on the available calculation time. Fig. 3: Functional principle of FCS-MPC with variable sampling time 2218

5 Step 5: To realize a control state feedback the receding horizon concept is utilized: In the next sampling instant only the first optimized switching state and the related turn-on time is applied to the system. Then the steps 1 to 4 are performed again based on the sampled system states for this next sampling instant. B. Partitioning of sampling instants The presented idea of the partitioning of a given maximum sampling time T s,max into multiple smaller sampling instants provides the possibility to optimize the switching states and the related turn-on times for each switching state. By predicting the current waveforms for each possible switching state and each possible turn-on time the control performance can be optimized by evaluating the related costs for each of these switching states and turn-on times. From the whole set of possible switching states and turn-on times that switching sequence is chosen that minimizes the related cost function which thus leads to an optimal control performance. In the chosen example the partitioning of the maximum allowed sampling time is chosen to be equidistant. However, the partitioning is not limited to be equidistant. Different nonequidistant partitioning patterns are possible and the appropriate choice is dependent on the specific requirements set by the application of the power converter. Further, the selection of the minimum and maximum sampling times and the number of partitions is only restricted by the available online calculation power. Compared to a FCS-MPC performed with a constant sampling time this variable sampling time offers an additional degree of freedom for control performance optimization. C. Sampling time adaptive control functions Due to the variable sampling time and the predictive nature of the proposed FCS-MPC the sampling time of the next (future) sampling periods is known in advance. Assuming a fixed calculation power, an increased sampling time leads to an increased calculation time and thus to a higher number of calculations that have to be performed in one sampling period. This knowledge is used to utilize the available calculation power by including sampling time adaptive control functions. One intuitive choice is to adapt the control horizon to the variation of the sampling time (i.e. to the number of partitions L). For longer sampling periods a higher control horizon is applied to improve the quality of the predictions. For shorter sampling periods a lower control horizon has to be applied for the FCS-MPC calculations. The sampling time adaptive adjustment of the control horizon for the system used in this work is summarized in (8) (8) In this work the focus of the control performance optimization is set to the minimization of the switching losses. However, different sampling time adaptive control functions can be implemented to the variable sampling time FCS-MPC to utilize the available calculation power. In [21] a FCS-MPC based selective harmonic elimination for multilevel converters is introduced. There, the proposed algorithm uses sliding discrete Fourier transformations to calculate the individual harmonic components that are optimized by the FCS-MPC controller in real time. For this control approach an adaptation of the harmonic components considered for the spectral analysis is another promising example for a sampling time adaptive control function. D. Calculation burden The presented principle of variable sampling time FCS- MPC uses a partitioning of the predicted system states between a minimal and maximal sampling time. A sampling frequency adaptive adaptation of the control horizon is proposed to utilize the available calculation power. The resulting calculation costs are summarized in (9).,, 4 4 (9) Compared with the calculation costs presented for the constant sampling time FCS-MPC the calculation costs for the variable sampling time FCS-MPC are increased by the number of partitions used. When a sampling time adaptive adjustment of the control horizon is implemented, the resulting calculation costs are dependent on the number of partitions and vary during the real-time control calculations. TABLE II MEASUREMENT SYSTEM PARAMETERS Symbol Quantity Value (per unit) U LL Line-to-Line Voltage (rms) 400 V (1.0) U DC DC-link voltage 650 V (1.63) ω Angular line frequency 2π 50 Hz (1.0) I L Rated converter current (rms) 31 A (1.0) L L Filter inductance 5 mh (0.21) R L Filter resistance 50 mω (0.01) C DC DC-link capacitance 2200 μf (5.0) T S Sampling time (variable) 40 μs 200 μs V. MEASUREMENT STUDY A measurement study is carried out to examine the variable sampling time FCS-MPC under laboratory conditions. To compare the achievable control performance of the proposed variable sampling time FSC-MPC with the conventional constant sampling time FCS-MPC additional measurements using identical system conditions are carried out. To study the effect of the proposed sampling time adaptive control functions the measurements for the variable sampling time FCS-MPC are presented with and without adaption of the control and prediction horizon to the variable sampling time. A. Test-setup description A 22 kva laboratory system is used to verify the proposed control concepts. The system is composed of a grid and a 2219

6 N R, N P I conv,abc [A] Fig. 4: Measurement results: steady-state analysis of FCS-MPC with constant sampling time: converter currents, switching pattern, sampling frequency and control horizon motor connected two-level VSI. An L filter is used to connect the grid side converter to the mains. The control algorithms are implemented on dspace DS1006 board where custom written (DWO, digital waveform output) codes are used to generate the pulse signals and the variable (hardware interrupt-based) sampling time for the control of the grid side converter. The general system parameters are summarized in Table II. All presented measurements are performed on the same experimental setup without changing the system parameters. The sampling time for the constant sampling time FCS-MPC is set equal to the minimum sampling time of the variable sampling time FCS-MPC (here: T s,min = 40μs). B. Steady-state control performance In Fig. 4 the measurement results for the steady-state performance of constant sampling time FCS-MPC are presented. The measured converter current waveforms and the related switching pattern of each inverter leg (S a,s b,s c ) are highlighted in Fig. 4 and. A total harmonic current distortion (THD I ) of 3.4 % and an effective switching frequency (average switching frequency over one fundamental period) of 2.93 khz are measured. In Fig. 5 the measurement results for the variable FCS- MPC without using sampling time adaptive control functions are presented. For these measurements a minimal sampling Fig. 5: Measurement results: steady-state analysis of FCS-MPC with variable sampling time: converter currents, switching pattern, sampling frequency and control horizon Fig. 6: Measurement results: steady-state analysis of FCS-MPC with variable sampling time and sampling time dependent control horizon adaptation: converter currents, switching pattern, sampling frequency and control horizon time T s,min of 40 μs and a maximum sampling time of T s,max of 200 μs with a partitioning L of 5 is chosen. The measured current waveforms and the switching patterns reveal a THD I of 3.75 % and an effective switching frequency of 2.87 khz, see Fig. 5,. In Fig. 5 the measured variation of the sampling time is presented. The maximum sampling time (L = Ts/T s,min = 5) is not reached in the presented experimental results. The sampling time is increased every time two current phases cross each other. In Fig. 6 the measurement results for the variable FCS- MPC with the proposed adaptation of the control and prediction horizon to the variable sampling time is presented. The measured current waveforms and the switching patterns reveal a THD I of 3.85% and an effective switching frequency of 2.85kHz, see Fig. 6,. In Fig. 5 the measured variation of the sampling time is presented. The maximum sampling time (L = Ts/T s,min = 5) is reached only once in the presented experimental results. The control- and prediction are varied based on the applied sampling time; see Fig. 6. The presented measurement results of the steady state performances of the constant and variable sampling time FCS- MPC based current control reveal that it is possible to reduce the effective switching frequency of the inverter by an and the related turn-on times. Further, the measurement results proof 2220

7 tst = 0.32ms iconv,q 10 0 iconv,d t [ms] Fig. 7: Measurement results: dynamic analysis of FCS-MPC with constant sampling time: converter currents in dq-frame, switching pattern, sampling frequency and control horizon Fig. 8: Measurement results: dynamic analysis of FCS-MPC with variable sampling time: converter currents in dq-frame, switching pattern, sampling frequency and control horizon Fig. 9: Measurement results: dynamic analysis of FCS-MPC with variable sampling time and sampling time dependent control horizon adaptation: converter currents in dq-frame, switching pattern, sampling frequency and control horizon the proposed concept of applying sampling time adaptive control functions (here the adaptation of the control and prediction horizon to the sampling time) to be a powerful tool to improve the control performance of variable sampling time FCS-MPC. The effect of the sampling time adaptive variation of the prediction horizon can be seen by comparing the measured effective switching frequencies and the THD I of the three concepts. While the effective switching frequency is decreased from the FCS-MPC with constant sampling time to the FCS-MPC with variable sampling time without and with adaptation of the control/prediction horizon the THD I values are increased respectively. Since the three control algorithms are performed with the same (minimum) sampling time, the effect of the switching state and turn-on time optimization can be seen from the decreased effective switching frequencies. The effect of the sampling time adaptive adjustment of the control/prediction horizon can be seen by an additional reduction of the effective switching frequencies. C. Dynamic control performance To study the dynamic performance of the three control concepts additional measurements are carried out. For each of these measurements reactive power reference steps were performed and the related q-current component step responses are evaluated concerning the measured settling times t st and number of switching transitions needed to adjust the reference values. The step response (reactive current step of 20 A) and the related switching pattern (S a,s b,s c ) of each inverter leg of the constant sampling time FCS-MPC are presented in Fig. 7 and. A settling time of 0.32 ms is measured where 6 switching transitions are needed to adjust the reference value. In Fig. 8 the dynamic performance of the FCS-MPC based current controller with variable sampling time and without an adaptation of the control/prediction horizon is presented. The measured step response, see Fig. 8, leads to a settling time of 0.32 ms where 2 switching transitions are needed to adjust the new reference value, see Fig. 8. From Fig. 8 it can be seen that the maximum sampling time and thus the maximum amount of partitions (here L= 5) is used by the FCS-MPC controller to optimize the dynamic control performance. Fig. 9 presents the dynamic measurement results of the proposed variable sampling time FCS-MPC with an 2221

8 adaptation of the control/prediction-horizon to the sampling time. The step response analysis reveals a sampling time of 0.24 ms, see Fig. 9 with 2 switching transitions needed to adjust the reference value; see Fig. 9. Further, the maximum sampling time is fully utilized during the reference step; see Fig. 9, which results from an increased controland prediction horizon adapted to utilize the available calculation power. The presented measurement results of the dynamic performance of the variable sampling time FCS-MPC with adaptation of the control /prediction horizon reveal an improved dynamic control performance in relation to the settling time and number of switching transitions needed to adjust the reference value in comparison to the constant sampling time FCS-MPC. VI. CONCLUSION The concept of variable sampling time FCS-MPC is introduced in this work. The new control concept is introduced in theory and compared to the conventional constant sampling time FCS-MPC based control algorithms. Based on a partitioning of the sampling instants into multiple smaller sampling instants it is possible to optimize, besides the switching states, the related switching turn-on times. To utilize the available calculation power when longer sampling instants are applied to the system an adaptation of the controland prediction horizon to the sampling time is proposed. The theoretical control concepts are applied to the control of a grid connected two-level voltage source converter where a simple L filter is used to demonstrate the control performance of the variable sampling time FCS-MPC algorithms. The presented measurements, performed on a 22 kva laboratory system, reveal the excellent control performance of the proposed control concept, especially during dynamic control conditions. 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