energies Article Tien Hai Nguyen and Kyeong-Hwa Kim *

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1 energies Article Finite Control Set Model Predictive Control with Modulation to Mitigate Harmonic Component in Output Current for a Grid-Connected Inverter under Distorted Grid Conditions Tien Hai Nguyen and Kyeong-Hwa Kim * Department of Electrical and Information Engineering, Seoul National University of Science and Technology, 232 Gongneung-ro, Nowon-gu, Seoul 01811, Korea; nguyentienhai@hotmail.com.vn * Correspondence: k2h1@seoultech.ac.kr; Tel.: ; Fax: Received: 14 June 2017; Accepted: 29 June 2017; Published: 2 July 2017 Abstract: This paper presents an improved current control strategy for a three-phase grid-connected inverter under distorted grid conditions. In terms of performance, it is important for a grid-connected inverter to maintain harmonic contents of inverter output currents below specified limit even when grid is subject to harmonic distortion. To address this problem, this paper proposes a modulated finite control set model predictive control (FCS-MPC) scheme, which effectively mitigates harmonic components in output current of a grid-connected inverter. In proposed scheme, system behavior in future is predicted from system model in discrete-time domain. Then, cost function is selected based on control objective of system. This cost function is minimized during optimization process to determine control signals that minimize cost function. In addition, since proposed scheme requires pure sinusoidal reference currents in stationary frame to work successfully, moving average filter (MAF) is employed to enhance performance of traditional phase lock loop (PLL). Due to control performance of FCS-MPC scheme as well as harmonic disturbance rejection capability of MAF-PLL, proposed scheme is able to suppress harmonic distortion even in presence of distorted grid condition, while retaining fast transient response. Comparative simulation results of different controllers verify effectiveness of proposed control scheme in compensating harmonic disturbance. To validate practical feasibility of proposed scheme, whole control algorithm is implemented on a 32-bit floating-point digital signal processor (DSP) TMS320F28335 to control a 2 kw three-phase grid-connected inverter. As a result, proposed scheme is a promising approach toward improving current quality of a grid-connected inverter under distorted grid conditions. Keywords: current control; distorted grid conditions; DSP TMS320F28335; grid-connected inverter; harmonic mitigation; model predictive control; power quality 1. Introduction Due to transition from fossil fuels to renewable energy in many countries, development of distributed generation (DG) systems has attracted attention from academia. DG systems are connected in parallel with each or to form a microgrid. Generally, a microgrid is able to function eir in grid-connected mode or in islanded mode [1,2]. Furrmore, it is essential to effectively manage exchange of active and reactive powers between microgrid and utility grid [3,4]. To fulfill all functionalities, control strategy for a microgrid operation system consists of three levels of hierarchical structure [5]. To follow development trend of microgrids, a DG system should provide stable and continuous operation. In addition, a DG system should be able to improve power quality Energies 2017, 10, 907; doi: /en

2 Energies 2017, 10, of 25 transferred to main grid even during adverse grid conditions. In order to be allowed to connect to main grid, DG systems have to meet interface standards, as stated in [6,7]. According to se standards, harmonic contents of current injected to main grid must satisfy a certain current distortion level in order to guarantee power quality. Traditionally, a linear controller such as proportional-integral (PI) control on synchronous reference frame has been employed to control grid-connected inverters (GCI) due to its simplicity and stability [8]. This method takes advantage of using a pulse width modulator (PWM) to keep switching frequency at a constant value during operation, which reduces unwanted harmonic distortion caused by varying switching frequency. The PI controller is simple to design and implement. In addition, its low demand in computational resources is very appealing to industrial applications. Despite se advantages, however, PI controller generally has limited capability for rejecting harmonic distortion, which makes it unusable for applications in grid-connected inverter in presence of distorted grid voltages. To overcome this disadvantage of PI controller, a proportional-resonant (PR) controller has been presented with main purpose of eliminating harmonic distortion in output currents [9]. This control scheme is implemented eir in stationary or in rotating reference frame. The PR control scheme is categorized as a selective harmonic compensation method because separate resonant terms are selectively employed in order to suppress each harmonic component [10]. Due to this feature, this method is only applicable when harmonic compensation for only a few harmful harmonics in low order is important. As number of harmonic components increases, required number of resonant terms will complicate control system and even makes it impractical. Furrmore, PR controller is easily affected by variation of grid frequency [11]. To deal with harmonic mitigation in a grid-connected inverter, anor approach based on system model decomposition and sliding mode control has been studied [12]. In this technique, system model is divided into fundamental model and harmonic model. Using se decomposed models, two types of controllers are separately designed. The fundamental component is regulated by using PI decoupling controller while harmonic component is controlled by sliding mode controller. However, this work used fourth-order band pass filters (BPFs) for system model decomposition by extracting current and voltage harmonic components. As will be stated below in this paper, control system exhibits a slow transient response mainly due to slow dynamic characteristic of BPF, even though harmonic suppression capability in output current is satisfactory. Furrmore, slow transient response increases possibility of instability during transient duration. As anor approach to mitigate harmonics in inverter current, nonlinear controllers such as predictive control [13,14] or repetitive control [15] have been investigated. As opposed to PR controller, se schemes are classified as non-selective harmonic compensator since se controllers work in wide range of frequency. In spite of improved control performance, se methods have ir own problems such as slow dynamics in repetitive control and parameter sensitivity in predictive control. Finite control set model predictive control (FCS-MPC) has been presented as a new approach to control grid-connected inverter [16 18]. Contrary to PI or PR controllers, this control scheme directly drives inverter switches without requiring PWM technique. This method is proven to provide a very fast transient response. Moreover, it is possible to include more control objectives or than current tracking due to flexible nature of cost function. However, this control scheme has a crucial disadvantage of variable switching frequency, which generates a wide spectrum of harmonic distortion even at low frequencies, leading to high total harmonic distortion (THD) value. In [19], a modulated MPC for a three-phase rectifier has been proposed to reduce harmonic distortion in currents caused by variable switching frequency. However, distorted grid voltages have not been considered in this study. Moreover, this scheme is not effective to mitigate harmonic currents in a grid-connected inverter in presence of distorted grid condition. Or methods considering multiple active voltage vectors during sampling time have been proposed

3 Energies 2017, 10, of 25 in [20,21]. However, none of se methods have dealt with presence of harmonic distortion in grid voltages. The main objective of this paper is to develop a current control scheme of improving output currents in three-phase grid-connected inverter even when grid voltages are severely distorted. The proposed scheme is based on principle of model predictive control, which determines control signals by minimizing cost function. Similar to scheme in [19], proposed scheme introduces weighting factors that are duty ratios of each individual active vector. Since each space vector is active for a certain duty interval during sampling period, se duty ratios are chosen as weighting factors for corresponding vectors. This modification results in better THD performance in inverter output currents. While existing scheme tries to reduce harmonic distortion caused by variable switching frequency in rectifier applications, proposed scheme aims to mitigate current harmonics of grid-connected inverter under harmonic-distorted grid voltages. Furrmore, since proposed scheme requires harmonic-free reference currents in stationary reference frame to work successfully, moving average filter (MAF) is used to enhance performance of phase lock loop (PLL) [22,23].As a result, proposed control scheme can effectively control a grid-connected inverter with a good harmonic suppression capability during steady-state as well as transient periods even under adverse grid conditions. The feasibility and effectiveness of proposed scheme are verified through comparative simulations and experiments using a prototype grid-connected inverter system based on digital signal processor (DSP) TMS320F28335 controller [24]. This paper is organized as follows: Section 2 presents a mamatical model of system. Section 3 describes proposed control scheme composed of modulated FCS-MPC and MAF-PLL. Simulation results are presented in Section 4. Afterwards, experimental results are given in Section 5. Finally, conclusions are given in Section Modeling of a Grid-Connected Inverter 2.1. Modeling of a Grid-Connected Inverter with L-Filter Since MPC is a model-based controller as implied by name, a precise system model and discretization are key factors o design controller successfully. To obtain system model on stationary reference frame, all three-phase variables are transformed into variables on stationary reference frame using transformation matrix P as follows: [ eα e β ] T = P[ea e b e c ] T (1) [ vα v β ] T = P[va v b v c ] T (2) [ iα i β ] T = P[ia i b i c ] T, (3) where subscript αβ denotes variables on stationary reference frame, subscript abc denotes variables in three-phase coordinate, e a, e b, and e c denote three-phase grid voltages, respectively, v a, v b, and v c are three-phase inverter output voltages, respectively, i a, i b, and i c represent three-phase inverter output currents, respectively, e α and e β are grid voltages in stationary reference frame, respectively, v α and v β represent inverter output voltages in stationary reference frame, respectively, i α and i β are inverter output currents in stationary reference frame, and P is transformation matrix expressed as: P = 2 3 [ ].

4 Energies 2017, 10, of 25 A three-phase grid-connected inverter is shown in Figure 1 in which V dc denotes DC-link Energies 2017, 10, 7 4 of 25 voltage. Considering filter inductance L s and resistance R s, voltage equations of a grid-connected inverter in stationary reference frame are presented as follows: = + di a v a = R s i a + L + (4) s dt + e a (4) = + di v b = R s i b + L + b (5) s + e dt b (5) di c = v c = R+ s i c + L + s. dt + e c. (6) (6) Figure 1. Block diagram of a three-phase grid-connected inverter. Figure 1. Block diagram of three-phase grid-connected inverter. Through transformation, voltage voltage equations equations can becan transformed be transformed into into stationary stationary reference frame reference as follows: frame as follows: di α v α = R s i α + L s = + + dt + e α (7) (7) di β v β = R s i β + L s dt + e β. (8) From Equations (7) and (8), a state-space = + model + is derived. as follows: (8) From Equations (7) and (8), a state-space dx model is derived as follows: = Ax + Bu, (9) dt = +, (9) where x = [ i T e T] T [ ] T [ ] T = iα i β e α e β is state vector, u = vα v β is control vector, and system matrices where =[ A ] and B are expressed = as: is state vector, = is control vector, and system matrices A and B are expressed R s as: L s L s 0 0 R s A = L0 0 s 0 1 L s 0 1 L s ω,b = 0 Ls 0 0. = 0 0, = ω The system states are controlled 0 by0 control 0vector u, which 0 0 consists of inverter output voltages in stationary reference frame. The system states are controlled by control vector u, which consists of inverter output 2.2. voltages Discretization in stationary reference frame. The discrete-time model of grid-connected inverter system at time instant k can be 2.2. Discretization expressed as: x[k + 1] = A The discrete-time model of grid-connected d x[k] + B inverter d u[k], (10) system at time instant k can be expressed as: [ +1] = [ ] + [ ], (10) where Ad and Bd are system and control matrices of discrete-time state-space model and can be calculated as:

5 Energies 2017, 10, of 25 where A d and B d are system and control matrices of discrete-time state-space model and can be calculated as: a 11 a 12 a 13 a 14 A d = e AT s = I + AT s + A2 Ts 2 a + = 21 a 22 a 23 a 24 (11) 1! 2! a 31 a 32 a 33 a 34 a 41 a 42 a 43 a Output Voltage Vectors B d = A 1 (A d I)B = b 11 b 12 b 21 b 22 b 31 b 32 b 41 b 42. (12) With 2 3 switching states, switching vector s of a three-phase inverter is defined as follows: s = S a S b S c, s S a, b,c = {1, 1} 3, (13) where S a, S b, and S c denote switching states for each phase. For switching state S a,b,c = 1, corresponding upper switch is turned on and output terminal voltage becomes + V dc 2. On or hand, for switching state S a, b,c = 1, corresponding lower switch is turned on and output voltage of V dc 2 is applied. The inverter output voltages in stationary reference frame (αβ coordinate) can be obtained using switching vector and transformation matrix as follows: [ vα v β ] T = P s V dc 2. (14) The switching states and corresponding output voltages in αβ coordinate are listed in Table 1. Table 1. Switching states and corresponding output voltages in αβ coordinate. Vector S a S b S c v ff v fi V dc V dc 3 3 V dc V dc 3 3 V dc 3 3 V dc V dc V 3 dc 3 V dc V dc Proposed Control Scheme A FCS-MPC scheme generally consists of system model, cost function, and cost function optimization process. The system model is used to predict system behavior in future. The cost function is obtained based on control objectives of system, which are usually error between predicted current and reference value. This cost function is minimized during optimization process. Once cost function is minimized, control signals that minimize cost function are fed into inverter. In traditional FCS-MPC method, determined switching states of inverter are applied during whole sampling period, which increases current harmonics in wide spectrum. Since se harmonics are very difficult to filter out, it causes decrease in quality of output current.

6 Energies 2017, 10, of 25 Energies 2017, 10, 7 6 of 25 Figure 2 shows block block diagram of of proposed proposed FCS-MPC FCS-MPC scheme scheme for a grid-connected for a grid-connected inverter, inverter, whichin which inverter inverter is connected is connected to grid to through grid through L filter. L In filter. In proposed proposed method, method, duty duty intervals intervals d 1 and1 dand 2 ford2 each for each active active voltage voltage vector vector are calculated are calculated based based on on reference reference voltages. voltages. These These duty intervals, duty intervals, predicted predicted currents, currents, and and harmonic-free reference reference currents currents generated generated by by MAF-PLL MAF-PLL are used are used to obtain to obtain cost function. cost function. The cost The function cost function is optimized is optimized to produce to produce switching switching signals forsignals grid-connected for grid-connected inverter. inverter. Figure2. Block diagramof proposed FCS-MPC Predictionof ofoutput Currents Assuming that system variables are are constant constant during during each each sampling sampling interval, interval, prediction prediction of of currents currents can can be be obtained obtained from from discrete-time discrete-time model model in Equation in Equation (10) (10) as as follows: follows: [ +1] i α [k + = 1] = a [ ] + [ ] + [ ] + [ ] (15) 11 i α [k] + a 13 e α [k] + a 14 e β [k] + b 11 v α [k] (15) i [ +1] β [k + 1] = a 22 i β [k] + a 23 e α [k] + a = [ ]+ [ ] 24 e + [ ] β [k] + b 22 v β [k]. (16) + [ ]. (16) In a digital implementation of control algorithm, control signals cannot be applied instantly to inverter. In a digital Instead, implementation control signals of determined control algorithm, at present control step aresignals only applicable cannot be at applied next instantly samplingto period, inverter. which Instead, results incontrol a timesignals delay. determined In order to consider at present and compensate step are only this applicable time delay, at two-step-ahead next sampling prediction period, which of currents results is introduced a time delay. in In control order algorithm to consider as follows: and compensate this time delay, two-step-ahead prediction of currents is introduced in control algorithm as follows: i α [k + 2] = ( a 11 i α [k + 1] + a 13 e α [k + 1] + a 14 e β [k + 1] ) + b 11 v α [k + 1] (17) [ +2] = [ +1] + [ +1] + [ +1] + [ +1] (17) i β [k + 2] = (a 22 i β [k + 1] + a 23 e α [k + 1] + a 24 e β [k + 1]) + b 22 v β [k + 1]. (18) When [ +2] =( zero vector [ +1] 0 or 7 in + Table 1 is [ +1] applied, + predicted [ +1])+ currents at [ +1]. sampling instant (18) (k+2) can be obtained as follows: When zero vector 0 or 7 in Table 1 is applied, predicted currents at sampling instant (k+2) can be obtained i 0 α[k as follows: + 2] = a 11 i α [k + 1] + a 13 e α [k + 1] + a 14 e β [k + 1] (19) [ +2] = [ +1] + [ +1] + [ + 1] (19)

7 Energies 2017, 10, of 25 i 0 β [k + 2] = a 22 i β [k + 1] + a 23 e α [k + 1] + a 24 e β [k + 1], (20) where i 0 α and i 0 β denote predicted output currents in αβ coordinate when zero vector is applied. Substituting Equations (19) and (20) into Equations (17) and (18) results in: i α [k + 2] = i 0 α[k + 2] + b 11 v α [k + 1] (21) i β [k + 2] = i 0 β [k + 2] + b 22 v β [k + 1]. (22) According to Table 1, a three-phase inverter has eight possible output voltage vectors. Unlike conventional FCS-MPC scheme that applies switching states during whole sampling period, proposed control strategy mimics behavior of PWM by applying three vectors during each sampling period. Two active voltage vectors are applied for duty intervals of d 1 and d 2 while zero vector is applied for remaining time of sampling period. In this case, average voltages produced by inverter can be calculated as: V α [k + 1] = V β [k + 1] = [ ] d 1 v i α + d 2 vα j (23) [ ] d 1 v i β + d 2v j β, (24) where v i α and v i β denote output voltages in αβ coordinate according to voltage vector i, and (i, j) represents a pair of adjacent active vectors among six possible pairs as follows: (i, j) = (1, 2), (2, 3), (3, 4), (4, 5), (5, 6), (6, 1). (25) The prediction of output currents can be calculated from Equations (21) and (22) for each pair of active vectors (i, j) as follows: i i α[k + 2] = i 0 α[k + 2] + b 11 v i α[k + 1] (26) i i β [k + 2] = i0 β [k + 2] + b 22 v i β [k + 1] (27) i j α[k + 2] = i 0 α[k + 2] + b 11 v j α[k + 1] (28) i j β [k + 2] = i0 β [k + 2] + b 22 v j β [k + 1], (29) where iα i and i i β denote inverter output currents in αβ coordinate corresponding to voltage vector i Generation of Reference Voltages The current errors between reference and predicted values are defined as follows: i α (k + 2) = i α[k + 2] i α [k + 2] (30) i β (k + 2) = i β [k + 2] i β[k + 2], (31) where symbol * denotes reference quantity. In order to achieve control objective that reduces tracking error to zero, it is reasonable to assume: i α[k + 2] = i α [k + 2] (32) i β [k + 2] = i β[k + 2]. (33)

8 Energies 2017, 10, of 25 Substituting Equations (32) and (33) into Equations (21) and (22) results in: i α[k + 2] = i 0 α[k + 2] + b 11 v α [k + 1] (34) i β [k + 2] = i0 β [k + 2] + b 22 v β [k + 1]. (35) From Equations (34) and (35), desired expressions for output voltage references that achieve zero tracking error can be obtained as: 3.3. Calculation of Duty Intervals v α[k + 1] = i α [k + 2] i 0 α[k + 2] b 11 (36) v β [k + 1] = i β [k + 2] i0 β [k + 2]. (37) b 22 Using Equations (23) and (24), output voltage references can be expressed in terms of output voltage vectors and duty intervals as: v α[k + 1] = [ ] d 1 v i α + d 2 vα j v β [k + 1] = [d 1 v i β + d 2v j β (38) ]. (39) From Equations (38) and (39), duty intervals of each active voltage vector are obtained as follows: d 1 = v β [k + 1]vj α v α[k + 1]v j β v j αv i β vi αv j β (40) d 2 = v β [k + 1]vi α v α[k + 1]v i β v i αv j β vj αv i β. (41) The zero vector is applied for remaining time of sampling period as: d o = 1 d 1 d 2, (42) where d o denotes duty interval of zero vector. These duty intervals are calculated for each pair of active voltage vectors (i, j) in Equation (25) similar to prediction algorithm of output currents Cost Function Minimization Both prediction of output currents and calculation of duty intervals are processed simultaneously for each pair of active voltage vectors defined in Equation (25). Based on se values, cost functions for each pair of active voltage vectors are calculated as follows: G i = (i α[k + 2] i i α[k + 2] ) 2 + (i β [k + 2] ii β [k + 2] ) 2 (43) ( ) G j = iα[k + 2] iα j 2 ( ) 2 [k + 2] + i β [k + 2] ij β [k + 2] (44) G = d 1 G i + d 2 G j. (45)

9 Energies 2017, 10, of 25 Since each vector is applied for duty intervals d 1 and d 2, respectively, se duty intervals are used as weighting factors to evaluate effect of each vector in final cost function in Equation (45). In every sampling period, cost functions G are calculated for six possible pairs of voltage vectors in Equation (25). These values of cost function calculated for six possible pairs are compared with each or to determine minimum value of cost function. Then, pair of active vectors that produces minimum value of cost function G is chosen to apply se active vectors to inverter in next sampling period Harmonic Mitigation and MAF-PLL The purpose of proposed scheme is to minimize error between reference currents and predicted ones by using cost functions in Equations (43) (45). Since proposed scheme is designed in stationary reference frame, stationary reference currents without harmonic distortion are required for proposed scheme to work successfully with high quality of inverter output currents. The PLL scheme is generally employed in a grid-connected inverter in order to achieve synchronization of DG system with main grid. For this purpose, traditional synchronous reference frame phase lock loop (SRF-PLL) has been usually employed in applications of grid-connected inverter to determine angular displacement of grid voltage. However, due to limitation of PI controller, performance of this scheme deteriorates significantly when it operates under distorted grid condition. In this condition, resulting grid angular displacement often contains harmonic contents caused by distorted grid voltages. If reference currents in αβ coordinate are generated by using this angular displacement contaminated by harmonic distortion, reference currents are also distorted with harmonic contents, resulting in performance degradation of proposed control scheme. To obtain pure sinusoidal reference currents in αβ coordinate, MAF-PLL is used to replace traditional SRF-PLL in proposed scheme. The MAF-PLL scheme employs MAF as an ideal low pass filter to obtain DC-quantity of d-axis voltage [13].The transfer function of MAF can be described as: 1 H MAF (s) T w2 s + 1, (46) where T w is window length of MAF. The transfer function of MAF-PLL can be obtained from Equation (46) and conventional SRF-PLL as follows: H MAF PLL (s) = H MAF (s) k ps + k i s s 2, (47) where k p and k i denote PI gains of SRF-PLL, respectively. The MAF-PLL method is capable of detecting grid phase angle accurately even when grid voltages are highly distorted. From this phase angle information, stationary sinusoidal reference currents can also be generated without harmonic contamination. Sinusoidal reference currents can be also obtained from BPF-based harmonic extraction, as in [12]. However, use of BPF results in much slower transient response in comparison to that of MAF-PLL due to sluggish dynamics of BPF. The simulation results are given to demonstrate effect of MAF-PLL on current control performance.

10 Energies 2017, 10, 7 10 of 25 of MAF-PLL due to sluggish dynamics of BPF. The simulation results are given to demonstrate effect of MAF-PLL on current control performance. Energies 2017, 10, of Simulation Results In order to prove to prove feasibility feasibility of proposed of proposed FCS-MPC with FCS-MPC modulation with for modulation a grid-connected for a inverter grid-connected as depicted inverter Figure as depicted 2, in simulations Figure 2, have simulations been done. have The been systemdone. parameters The system are summarized parameters are in Table summarized 2. in Table 2. Table System parameters of of a grid-connected inverter. Parameters Symbol SymbolValue ValueUnits Units Rated Ratedpower PR P R 2 2 kw kw Grid voltage E E V V Grid frequency F F Hz Hz DC-link voltage V dc 420 V Vdc 420 V Filter inductance L s 7 mh Filter inductance Ls 7 mh Filter resistance R s 0.5 Ω Switching Filter resistance frequency f s Rs khz Ω Switching frequency fs 10 khz The harmonic compensation capability of proposed control scheme is evaluated using PSIM software under a distorted grid condition. For an adverse grid condition, 5th and 7th harmonics with 10% of fundamental component and 11th 11th and and 13th 13th harmonics with with 1% 1% of of fundamental component are are injected to to ideal grid voltages. The resultant waveform of distorted grid voltages is demonstrated in Figure 3. Figure 3. Distorted three-phase grid voltages. Figure Figure 4 4 shows shows performance performance of of conventional conventional PI decoupling PI decoupling controller controller under under ideal ideal grid condition grid condition for comparison for comparison purpose. purpose. It can be It clearly can be seen clearly that seen PI that decoupling PI decoupling controller controller performs well performs under well such under a condition such a condition and does and not does give a not severe give harmonic a severe harmonic distortion distortion in three-phase in three-phase output output currents. As is shown in Figure 4b, q-axis and d-axis currents iq and id currents. As is shown in Figure 4b, q-axis and d-axis currents i are well controlled q and i d are well controlled to track to track reference reference currents currents without steady-state without steady-state errors or errors fluctuation. or fluctuation.

11 Energies 2017, 10, of 25 Energies 2017, 10, 7 11 of 25 Figure Figure 4.Inverter 4. Inverter currents currents of of conventional conventional PI decoupling PI decoupling controller controller under under ideal grid ideal voltages. grid voltages. Phase currents; Phase currents; q-axis and q-axis d-axis and currents. d-axis currents. Figure 5 shows performance of same PI controller under distorted grid voltages as Figure 5 shows performance of same PI controller under distorted grid voltages as shown shown in Figure 3. As is obviously shown in Figure 5a, performance of this controller is not in Figure 3. As is obviously shown in Figure 5a, performance of this controller is not satisfactory satisfactory any longer, developing considerable harmonic contents in three-phase current any longer, developing considerable harmonic contents in three-phase current waveforms due to waveforms due to distorted grid voltages. In addition, q-axis and d-axis currents iq and id distorted grid voltages. In addition, q-axis and d-axis currents i show large fluctuation caused by harmonic components. This performance q and i d show large fluctuation deterioration comes caused by harmonic components. This performance deterioration comes from traditional from traditional SRF-PLL and existence of grid disturbance due to harmonic distortion. SRF-PLL and existence of grid disturbance due to harmonic distortion. The SRF-PLL scheme The SRF-PLL scheme cannot completely filter out effect of harmonic contents in grid voltages in cannot completely filter out effect of harmonic contents in grid voltages in obtaining angular obtaining angular displacement and angular frequency. Moreover, PI controller naturally has displacement and angular frequency. Moreover, PI controller naturally has a poor disturbance a poor disturbance rejection capability. The FFT result of phase current in Figure 5c shows that re rejection capability. The FFT result of phase current in Figure 5c shows that re exist 5th, 7th, exist 5th, 7th, 11th, and 13th harmonics in output currents, which leads to a relatively high 11th, and 13th harmonics in output currents, which leads to a relatively high THD value of 3.57%. THD value of 3.57%.

12 Energies 2017, 10, of 25 Energies 2017, 10, 7 12 of 25 (c) Figure Figure Inverter Inverter currents currents of of conventional conventional PI decoupling PI decoupling controller controller under distorted under distorted grid voltages. grid voltages. Phase currents; Phase currents; q-axis andq-axis d-axisand currents; d-axis currents; (c) FFT result (c) FFT of a-phase result of current. a-phase current. The PR controller is anor classical control method that is usually employed in a The PR controller is anor classical control method that is usually employed in a grid-connected grid-connected inverter application with purpose of reducing harmonics in inverter output inverter application with purpose of reducing harmonics in inverter output currents. In Figure 6, currents. In Figure 6, performance of PR controller is presented under same distorted grid performance of PR controller is presented under same distorted grid voltages shown in voltages shown in Figure 3. Despite of giving more sinusoidal phase currents as compared with Figure 3. Despite of giving more sinusoidal phase currents as compared with case of PI case of PI controller, a slight distortion in phase current is still observed. This distortion can be seen more clearly in FFT result of a-phase current in Figure 6b, which shows small 5th, 7th, 11th,

13 Energies 2017, 10, of 25 Energies 2017, 10, 7 13 of 25 controller, a slight distortion in phase current is still observed. This distortion can be seen more clearly and in 13th FFTharmonic result of a-phase components. current The inresultant Figure 6b, THD which value shows is 2.22%, small 5th, which 7th, is 11th, lower and than 13th harmonic case of components. PI controller. The resultant THD value is 2.22%, which is lower than case of PI controller. Figure 6. Inverter currents of PR controller under distorted grid voltages. Phase currents; Figure 6. Inverter currents of PR controller under distorted grid voltages. Phase currents; FFT result of a-phase current. FFT result of a-phase current. In comparison with conventional PI and PR controllers, performance of proposed FCS-MPC In comparison scheme with with modulation conventional under PI and same PR distorted controllers, grid condition performance is shown of in Figure proposed 7, in which FCS-MPC BPF scheme is employed with modulation in SRF-PLL under to same obtain distorted grid grid angular condition displacement is shown without in Figure 7, influence in which of BPF harmonic-distorted is employed in grid SRF-PLL voltages, to obtain and thus, grid to generate angular pure displacement sinusoidal without reference currents influence in of αβ coordinate harmonic-distorted without grid harmonic voltages, and contamination. thus, to generate Due to pure an sinusoidal effective harmonic reference suppression, currents in αβ coordinate phase current without waveforms harmonic remain contamination. quite sinusoidal Due in spite to an of effective an abnormal harmonic grid condition suppression, as shown phase in Figure current 7a in waveforms contrast with remain those quite in Figures sinusoidal 5 and in 6. spite In addition, of an abnormal FFT result grid of condition phase current as shown in Figure in Figure 7b shows 7a in contrast only a negligible with those amount in Figures of harmonic 5 and 6. In contents. addition, The THD FFT value result is of 1.67%, phase which current is in smaller Figure than 7b shows both only PI a controller negligible and amount PR of controller, harmonic contents. being comparable The THD to value THD is 1.67%, value which of is PI smaller controller than under both PI ideal controller grid condition. and PR Although controller, being harmonic comparable mitigation to in inverter THD value currents of can PI controller be achieved under at steady ideal state grid even condition. under Although distorted grid harmonic voltages mitigation by using in proposed inverter currents FCS-MPC can scheme be achieved with at modulation steady state and even under BPF, transient distorted response grid voltages becomes by using slower than proposed that of FCS-MPC conventional scheme with control modulation schemes, and which BPF, is not acceptable transient response for DG applications becomes slower since than current that of dynamics conventional are supposed control schemes, to be faster which than is not those acceptable of outer-loop for DG system. applications Such a since slow transient current results dynamics from are supposed adoption to of be faster BPF than in those SRF-PLL of outer-loop to obtain system. harmonic-free Such a slow reference transient results currents from in stationary frame. The BPF normally takes a considerable time for filter output to reach steady state.

14 Energies 2017, 10, of 25 adoption of BPF in SRF-PLL to obtain harmonic-free reference currents in stationary Energies frame. 2017, The10, BPF 7 normally takes a considerable time for filter output to reach steady state. 14 of 25 Figure7. 7. Inverter Invertercurrents of of FCS-MPC FCS-MPC scheme scheme with with BPF BPF under under distorted distorted grid grid voltages. voltages. Phase Phase currents; currents; FFT FFT result result of a-phase of a-phase current. current. In order to improve transient response while retaining good harmonic mitigation In order to improve transient response while retaining a good harmonic mitigation performance, PLL scheme based on MAF is introduced instead of BPF. The MAF is able performance, PLL scheme based on MAF is introduced instead of BPF. The MAF is to filter out harmonic contents in grid voltages faster than BPF. Thus, purpose of able to filter out harmonic contents in grid voltages faster than BPF. Thus, purpose of MAF-PLL is to obtain angular displacement and angular frequency rapidly without harmonic MAF-PLL is to obtain angular displacement and angular frequency rapidly without harmonic distortion. In view of computational burden as well as dynamic response, MAF has been distortion. In view of computational burden as well as dynamic response, MAF has regarded as a more effective way as compared with BPF [13]. Through MAF-PLL, been regarded as a more effective way as compared with BPF [13]. Through MAF-PLL, harmonic-free sinusoidal reference currents on stationary reference frame can be generated more harmonic-free sinusoidal reference currents on stationary reference frame can be generated more simply and rapidly than BPF case. These sinusoidal reference currents play an important role in simply and rapidly than BPF case. These sinusoidal reference currents play an important role in improving quality of inverter output currents. improving quality of inverter output currents. Figure 8 shows proposed control scheme consisting of modulated FCS-MPC and Figure 8 shows proposed control scheme consisting of modulated FCS-MPC and MAF-PLL MAF-PLL under same distorted grid condition. The phase current waveforms in Figure 8a are under same distorted grid condition. The phase current waveforms in Figure 8a are similarly similarly sinusoidal at steady state as in Figure 7a. Also, FFT result of a-phase current shown in sinusoidal at steady state as in Figure 7a. Also, FFT result of a-phase current shown in Figure 8b is Figure 8b is consistent with case in Figure 7b, showing only negligible harmonics with THD consistent with case in Figure 7b, showing only negligible harmonics with THD value of 1.67%. value of 1.67%. This FFT result satisfies harmonic current regulation limit stated in IEEE std. This FFT result satisfies harmonic current regulation limit stated in IEEE std In addition to In addition to an improved harmonic suppression at steady state, proposed scheme shows much faster transient response than Figure 7. In Figure 8a, transient lasts only half a cycle before reaching steady state.

15 Energies 2017, 10, of 25 an improved harmonic suppression at steady state, proposed scheme shows much faster transient response Energies than 2017, Figure 10, 7 7. In Figure 8a, transient lasts only half a cycle before reaching steady 15 of 25 state. Energies 2017, 10, 7 15 of 25 Figure 8. Inverter currents of proposed control scheme consisting of FCS-MPC with MAF. Figure 8. Inverter currents of proposed control scheme consisting of FCS-MPC with MAF. Phase currents; FFT result of a-phase current. Phase Figure currents; 8. Inverter currents FFT result of ofproposed a-phase current. control scheme consisting of FCS-MPC with MAF. Phase currents; FFT result of a-phase current. Figure 9 shows comparison of generation of reference currents in αβ coordinate between Figure 9 shows BPF and comparison MAF. While both of schemes generation generate of pure reference sinusoidal currents reference incurrents αβ coordinate Figure 9 shows comparison of generation of reference currents in αβ coordinate between steady state, BPF andtransient MAF. While response both of schemes MAF is generate much smaller pure than sinusoidal that of reference BPF. between BPF and MAF. While both schemes generate pure sinusoidal reference currents currents at at steady state, steady transient state, response transient of response MAF of is much MAF is smaller much smaller than that than of that of BPF. BPF. Figure 9. Comparison of reference current generation in αβ coordinate between BPF and MAF. Figure Figure 9. Comparison 9. Comparison of of reference reference current current generation generation in αβ in αβ coordinate coordinate between between BPF BPF and and MAF. MAF.

16 Energies 2017, 10, of 25 Energies 2017, 10, 7 16 of 25 To demonstrate grid disturbance rejection capability of of proposed control control scheme, scheme, Figure Figure 10 shows 10 shows transient transient response of of proposed scheme when re is is aa sudden change in in grid condition. The ideal grid voltages are suddenly distorted to condition as in Figure 3 at 0.3 s. Even in this test condition, proposed scheme yields a stable control performance except for a slight change in in THD THD value value from from 1.61% 1.61% under under ideal ideal grid grid to 1.67% to 1.67% under under distorted distorted grid, which grid, proves which proves disturbance disturbance rejection rejection capability capability of proposed of scheme. proposed Through scheme. Through comparative comparative simulation results simulation between results between proposed scheme proposed and scheme traditional and ones, traditional is validated ones, that it is validated proposedthat scheme yields proposed better scheme current yields quality, better while current retaining quality, a fast while transient retaining response. a fast transient response. Figure Figure Transient Transient response response of of proposed proposed FCS-MPC FCS-MPC scheme scheme under sudden under change sudden inchange grid condition. in grid condition. Three-phase Three-phase grid voltages; grid voltages; three-phase three-phase inverter currents. inverter currents. Figure 11 shows transient response of proposed FCS-MPC scheme when ideal grid Figure 11 shows transient response of proposed FCS-MPC scheme when ideal grid voltages are suddenly unbalanced at 0.3 s where c-phase grid voltage is reduced to 80% of voltages are suddenly unbalanced at 0.3 s where c-phase grid voltage is reduced to 80% of nominal nominal grid voltages. As can be seen in se figures, transient behavior of current between two grid voltages. As can be seen in se figures, transient behavior of current between two grid grid conditions is stable and seamless except for a slight change in THD value, which proves that conditions is stable and seamless except for a slight change in THD value, which proves that proposed scheme works effectively even under sudden unbalanced grid condition. proposed scheme works effectively even under sudden unbalanced grid condition.

17 Energies 2017, 10, of 25 Energies 2017, 10, 7 17 of 25 Figure Figure Transient Transient response of of proposed proposed FCS-MPC FCS-MPC scheme in scheme presence in of apresence sudden unbalanced of a sudden unbalanced grid condition. grid condition. Three-phase Three-phase grid voltages; grid voltages; three-phase inverter three-phase currents. inverter currents. Figure Figure shows shows improvement of of transient transient response response through athrough modification a modification of proposed of proposed FCS-MPC FCS-MPC scheme. scheme. Because Because slow transient slow istransient mainly due is tomainly adoption due to of adoption MAF, modified of MAF, modified method works method with works FCS-MPC with scheme FCS-MPC and conventional scheme SRF-PLL and conventional at start-up instant. SRF-PLL Even though at start-up instant. this Even structure though does not this give structure better performance does not give thanbetter proposed performance schemethan in view of proposed THD scheme value, in view of transient THD response value, is significantly transient improved response as is shown significantly in Figure improved 12. As soon as as shown output in Figure currents 12. As soon reach as output steady state, currents control reach structure steady is changed state, to use control MAF-based structure PLL, is changed resultingto in use MAF-based same THD PLL, value resulting of proposed in scheme. same THD When value transient of response proposed of current scheme. is a When crucial concern, transient this modified control structure can be a good candidate to improve transient response. response of current is a crucial concern, this modified control structure can be a good candidate to improve transient response.

18 Energies 2017, 10, of 25 Energies 2017, 10, 7 18 of 25 Figure Improvement Improvement of of transient transient response response through through a modification a modification of proposed of FCS-MPC proposed FCS-MPC scheme. scheme Experimental Experimental Results Results 5.1. Experimental Setup In order to evaluate feasibility of proposed control method, control algorithm is implemented on 32-bit floating-point DSP TMS320F28335 to control 2 kw prototype grid-connected inverter [24]. The configuration of of entire system is is illustrated in in Figure Figure 13a. 13a. The The sampling period period is chosen is chosen as as 100µs, 100μs, which which results results in in switching switching frequency frequency of 10 of khz. 10 khz. The The inverter inverter phase phase currents currents are detected are detected using using Hall Hall effect effect sensors sensors and converted and converted through through 12-bit A/D 12-bit converter. A/D converter. An intelligent An intelligent power module power module is employed is employed for three-phase for three-phase grid-connected grid-connected inverter. Ainverter. three-phase A three-phase programmable programmable AC power source AC power is used source to emulate is used to emulate ideal grid as ideal wellgrid as distorted as well as grid distorted conditions. grid conditions. Figure 13b depicts Figure 13b photograph depicts photograph of experimental of experimental test setup. test setup. The whole control algorithm is implemented in C language program with software environment of of Code Code Composer Composer Studio. Studio. The main The main control control algorithm algorithm consists of consists current of prediction, current prediction, calculation calculation of cost function, of cost function, cost function cost minimization, function minimization, and MAF-PLL. and MAF-PLL. In addition, In addition, algorithm algorithm to operateto operate PWM andpwm A/Dand converter A/D converter is implemented. is implemented. To execute To execute main control main algorithm, control algorithm, about 40% about of 40% sampling of sampling period isperiod required. is required. During During this duration, this duration, main control main algorithm control algorithm determines determines duty intervals duty intervals of two active of two voltage active vectors voltage which vectors are which applied are to applied inverter to inverter next in sampling next period. sampling These period. duty intervals These duty of two intervals active voltage of two vectors active are voltage implemented vectors are by using implemented internal by using enhanced PWM internal (epwm) enhanced module PWM of (epwm) DSP. Inmodule addition, of to prevent DSP. In shoot-through addition, to in prevent DC-link shoot-through caused by in DC-link simultaneous caused conduction by simultaneous of both switches, conduction dead-time of both switches, should be considered. dead-time should This dead-time be considered. is implemented This dead-time by using is implemented built-in dead by band using generator built-in module dead within band generator epwm module. within epwm module Experimental Results Figure 14 shows distorted three-phase grid voltages used in experiments. Similar to simulations, se grid voltages contain 5th and 7th harmonics with 10% of fundamental component and 11th and 13th harmonics with 1% of fundamental component, respectively.

19 control algorithm determines duty intervals of two active voltage vectors which are applied to inverter in next sampling period. These duty intervals of two active voltage vectors are implemented by using internal enhanced PWM (epwm) module of DSP. In addition, to prevent shoot-through in DC-link caused by simultaneous conduction of both switches, dead-time band Energies 2017,should 10, 907 be considered. This dead-time is implemented by using built-in dead 19 of 25 generator module within epwm module. Energies 2017, 10, 7 19 of 25 Energies 2017, 10, 7 19 of 25 Figure 13. Experimental system. Configuration of overall system; photograph of experimental setup Experimental Results Figure 14 shows distorted three-phase grid voltages used in experiments. Similar to Figure 13. Experimental system. of overall photograph of Figure 13. Experimental system. Configuration Configuration harmonics overall system; system; photograph of simulations, se grid voltages contain 5th and of7th with 10% of fundamental experimental setup. experimental setup. component and 11th and 13th harmonics with 1% of fundamental component, respectively Experimental Results Figure 14 shows distorted three-phase grid voltages used in experiments. Similar to simulations, se grid voltages contain 5th and 7th harmonics with 10% of fundamental component and 11th and 13th harmonics with 1% of fundamental component, respectively. Figure 14. Distorted three-phase grid voltages used in experiments. Figure 15 shows inverter output current waveforms of proposed control scheme under ideal grid condition. It is shown that proposed scheme operates well and produces comparable result with conventional control schemes. Figure 14. Distorted three-phase grid voltages used in experiments. Figure 15 shows inverter output current waveforms of proposed control scheme under

20 Energies 2017, 10, of 25 Figure 15 shows inverter output current waveforms of proposed control scheme under ideal grid condition. It is shown that proposed scheme operates well and produces comparable resultenergies with 2017, conventional 10, 7 control schemes. 20 of 25 Energies 2017, 10, 7 20 of 25 Figure Figure 15. Experimental 15. Experimental result result of of inverter inverter currents currents for for proposed proposed control control scheme under ideal ideal grid condition. grid condition. Figure 15. Experimental result of inverter currents for proposed control scheme under Figures ideal 16 grid and condition. 17 show experimental results for inverter output currents when PI Figures decoupling 16 controller and 17 show and PR experimental controller are results employed for under inverter output distorted currents grid voltages when as PI shown in Figures Figure 16 14, and respectively. 17 show experimental Except for results difference for inverter in output THD currents value when as a result PI decoupling controller PR controller are employed under distorted grid voltages as of shown decoupling controller and PR controller are employed under distorted grid voltages as in Figure implementation 14, in a real hardware system, all experimental results well match with shown respectively. in Figure 14, Except respectively. for Except difference for in difference THD value in as THD a result value of as implementation a result of in a real hardware simulation system, results. The all phase experimental current waveforms results well are quite match distorted with because simulation se types results. of current implementation in a real hardware system, all experimental results well match with The phase current controllers waveforms simulation cannot results. are effectively quite The phase distorted compensate current because waveforms harmonic se are quite types distortion distorted of current caused because controllers by se distorted types of cannot grid current voltages. effectively The FFT controllers results cannot indicate effectively that re compensate exists relatively harmonic large distortion quantity caused of unwanted by distorted harmonic grid voltages. contents in compensate harmonic distortion caused by distorted grid voltages. The FFT results indicate that inverter The output FFT results currents. indicate The that THD re exists values relatively of PI large control quantity and of unwanted PR control harmonic are contents 6.3% and in 4.3%, re exists relatively large quantity of unwanted harmonic contents in inverter output currents. The respectively. inverter output currents. The THD values of PI control and PR control are 6.3% and 4.3%, THD values respectively. of PI control and PR control are 6.3% and 4.3%, respectively. Figure 16. Cont.

21 Energies 2017, 10, of 25 Energies 2017, 10, 7 21 of 25 Energies 2017, 10, 7 21 of 25 Figure 16. Experimental results of inverter currents for conventional PI control scheme under 16. distorted Experimental results of inverter currents for conventional PI control scheme condition.results Phase current waveforms; FFTconventional result of a-phase current. Figure 16. grid Experimental of inverter currents for PI control scheme under Figure distorted distorted grid condition. Phase current FFT result of a-phase grid condition. Phase currentwaveforms; waveforms; FFT result of a-phase current.current. Energies 2017, 10, 7 under 22 of 25 Figure 17. Experimental results of inverter currents for PR control scheme under distorted Figure 17.grid Experimental results of inverter currents for PR control scheme under distorted grid condition. Phase current waveforms; FFT result of a-phase current. condition. Phase current waveforms; FFT result of a-phase current. Figure 18 shows experimental results for proposed control scheme under same grid condition as cases in PI decoupling controller and PR controller. Unlike conventional schemes, proposed scheme shows nearly sinusoidal current waveforms due to a good harmonic compensation capability as shown in Figure 18a. The FFT result shows that harmonics in output currents are significantly reduced. The THD value of proposed scheme is only 2.73%, which is considerably smaller than those of PI and PR controllers. Obviously, all harmonic components are within harmonic current regulation limit specified by IEEE std The experimental result of transient response for proposed control scheme is shown in

22 grid condition. Phase current waveforms; FFT result of a-phase current. Figure 18 shows experimental results for proposed control scheme under same grid condition as cases in PI decoupling controller and PR controller. Unlike conventional schemes, proposed scheme shows nearly sinusoidal current waveforms due to a good harmonic Energies 2017, 10, of 25 compensation capability as shown in Figure 18a. The FFT result shows that harmonics in output currents are significantly reduced. The THD value of proposed scheme is only 2.73%, which is considerably Figure 18smaller shows than experimental those of results PI and for proposed PR controllers. Obviously, scheme under all same harmonic grid components condition asare within cases in harmonic PI decoupling current controller regulation and limit specified PR controller. by IEEE Unlike std conventional schemes, The experimental proposedresult scheme of shows transient nearlyresponse sinusoidal for current proposed waveforms control duescheme to a good is shown harmonic in Figure compensation 19. To capability evaluate as shown transient in Figure behavior 18a. of The output FFT result current, shows that q-axis current harmonics reference in output is changed currents are by significantly step. As can reduced. be observed, The THD value inverter of output proposed currents scheme instantly is onlyreach 2.73%, a which new steady-state, is considerably which smaller demonstrates than those offast transient PI and response PR controllers. of proposed Obviously, scheme. all Such harmonic a fast transient components can are be achieved within by harmonic fast nature current of regulation MPC as limit well specified as adoption by IEEE of std MAF-PLL. Energies 2017, 10, 7 23 of 25 Figure Experimental results results of of inverter inverter currents currents for for proposed proposed control scheme control under scheme distorted under grid distorted condition. grid condition. Phase current Phase waveforms; current waveforms; FFT result FFT of a-phase result of current. a-phase current. The experimental result of transient response for proposed control scheme is shown in Figure 19. To evaluate transient behavior of output current, q-axis current reference is changed by step. As can be observed, inverter output currents instantly reach a new steady-state, which demonstrates fast transient response of proposed scheme. Such a fast transient can be achieved by fast nature of MPC as well as adoption of MAF-PLL.

23 Figure 18.Experimental results of inverter currents for proposed control scheme under Energies 2017, 10, of 25 distorted grid condition. Phase current waveforms; FFT result of a-phase current. Figure 19. Experimental result of transient response for proposed control scheme. Figure 19. Experimental result of transient response for proposed control scheme. 6. Conclusions In this paper, an improved current control strategy for a three-phase grid-connected inverter based on a modulated FCS-MPC and and MAF-PLL has has been been presented presented with with purpose purpose of mitigating of mitigating harmonic harmonic components components in inverter inverter output output currents currents when when grid is polluted grid is by polluted harmonic by distortion. harmonic distortion. In terms ofin terms performance, of performance, it is important it is important for a grid-connected for a grid-connected inverter toinverter maintainto maintain harmonic harmonic contents ofcontents inverter output of inverter currents output belowcurrents specified below limit even specified in limit presence even of harmonic-distorted in presence of harmonic-distorted grid. To consider grid. modulated To consider FCS-MPC modulated as an effective FCS-MPC wayas of an suppressing effective way harmonics of suppressing a grid-connected harmonics inverter a grid-connected under distorted inverter grid, under proposed distorted control grid, scheme proposed consists control of several scheme steps. consists First, of accurate several system steps. First, model inaccurate discrete-time system model domain in is developed discrete-time to predict domain is future developed behavior to predict of system. Based future on behavior predicted of system. output Based currents, on both predicted generation output currents, of reference both voltages generation and of reference calculationvoltages of dutyand intervals calculation are accomplished. of duty intervals By using are accomplished. informationby onusing duty information intervals as on weighting duty factors, intervals a cost as weighting function isfactors, determined a cost by function considering is determined control by objective. considering Then, control cost objective. function isthen, minimized cost through function is optimization minimized process through to determine optimization control process signals to determine for inverter. control In addition, signals for for inverter. purpose of improving transient response, MAF-PLL is employed to replace traditional SRF-PLL. By using MAF, harmonic components caused by distorted grid voltages can be removed effectively and rapidly. This can contribute to generate harmonic-free sinusoidal reference currents on stationary reference frame, which is vital part of mitigating harmonic distortion in inverter currents. The principle and mamatical description of proposed scheme have been analyzed to emphasize simplicity of control structure. The whole control algorithm has been implemented on a 32-bit floating-point DSP TMS320F28335 to control a 2 kw prototype grid-connected inverter. Comparative simulation and experimental results prove that proposed scheme is an effective way to improve performance of a grid-connected inverter under highly distorted grid voltages. Acknowledgments: This research was supported by Basic Science Research Program through National Research Foundation of Korea (NRF), funded by Ministry of Education (NRF-2016R1D1A1B ). This work was also supported by Human Resources Development of Korea Institute of Energy Technology Evaluation and Planning (KETEP) grant funded by Korean government s Ministry of Trade, Industry & Energy (No ). Author Contributions: Tien Hai Nguyen and Kyeong-Hwa Kim conceived main concept of control structure and developed entire system. Tien Hai Nguyen carried out research and analyzed numerical data with guidance from Kyeong-Hwa Kim. Tien Hai Nguyen and Kyeong-Hwa Kim collaborated to prepare manuscript. Conflicts of Interest: The authors declare no conflict of interest.

24 Energies 2017, 10, of 25 References 1. De Matos, J.; Silva, F.; Ribeiro, L. Power control in AC isolated microgrids with renewable energy sources and energy storage systems. IEEE Trans. Ind. Electron. 2014, 62, [CrossRef] 2. Rocabert, J.; Luna, A.; Blaabjerg, F.; Rodríguez, P. Control of power converters in ac microgrids. IEEE Trans. Power Electron. 2012, 27, [CrossRef] 3. Han, H.; Hou, X.; Yang, J.; Wu, J.; Su, M.; Guerrero, J.M. Review of power sharing control strategies for islanding operation of ac microgrids. IEEE Trans. Smart Grid 2015, 7, [CrossRef] 4. Lasseter, R.; Akhil, A.; Marnay, C.; Stephens, J.; Dagle, J.; Guttromson, R.; Meliopoulous, A.S.; Yinger, R.; Eto, J. The CERTS Microgrid Concept, White Paper on Integration of Distributed Energy Resources; U.S. Department of Energy: Washington, DC, USA, Guerrero, J.M.; Vasquez, J.C.; de Vicuña, L.G.; Castilla, M. Hierarchical control of droop Controlled AC and DC microgrids A general approach toward standardization. IEEE Trans. Ind. Electron. 2011, 58, [CrossRef] 6. IEEE Standards Association IEEE Standard for Interconnecting Distributed Resources with Electric Power Systems; IEEEStd.: Piscataway Township, NJ, USA, (IEC)International Electrotechnical Commission. Photovoltaic (PV) Systems Characteristic of Utility Interface; Ed.2; IEC: London, UK, Bouzid, A.M.; Guerrero, J.M.; Cheriti, A.; Bouhamida, M.; Sicard, P.; Benghanem, M. A survey on control of electric power distributed generation systems for microgrid applications. Renew. Sustain. Energy Rev. 2015, 44, [CrossRef] 9. Blaabjerg, F.; Teodorescu, R.; Liserre, M.; Timbus, A.V. Overview of control and grid synchronization for distributed power generation systems. IEEE Trans. Ind. Electron. 2006, 53, [CrossRef] 10. Teodorescu, R.; Blaabjerg, F.; Liserre, M.; Loh, P.C. Proportional-resonant controllers and filters for grid-connected voltage-source converters. IEE Proc. Electr. Power Appl. 2006, 153, [CrossRef] 11. Judewicz, M.G.; Sergio, A.G.; Noelia, I.E.; Jonatan, R.F.; Daniel, O.C. Generalized predictive current control (GPCC) for grid-tie three-phase inverters. IEEE Trans. Ind. Electron. 2016, 63, [CrossRef] 12. Kang, S.W.; Kim, K.H. Sliding mode harmonic compensation strategy for power quality improvement of a grid-connected inverter under distorted grid condition. IET Power Electron. 2015, 8, [CrossRef] 13. Lai, N.B.; Kim, K.H. An improved current control strategy for a grid-connected inverter under distorted grid conditions. Energies 2016, 9, 190. [CrossRef] 14. Hu, J.; Shang, L.; He, Y.; Zhu, Z.Q. Direct active and reactive power regulation of grid-connected dc/ac converters using sliding mode control approach. IEEE Trans. Power Electron. 2011, 26, [CrossRef] 15. Chen, D.; Zhang, J.; Zhang, Z. An improved repetitive control scheme for grid-connected inverter with frequency-adaptive capability. IEEE Trans. Ind. Electron. 2013, 60, [CrossRef] 16. Narimani, M.; Bin, W.; Venkata, Y.; Cheng, Z.; Navid, R.Z. Finite control-set model predictive control (FCS-MPC) of nested neutral point-clamped (NNPC) converter. IEEE Trans. Power Electron. 2015, 12, [CrossRef] 17. Quevedo, D.E.; Ricardo, P.A.; Marcelo, A.P.P.C.; Ricardo, L. Model predictive control of an AFE rectifier with dynamic references. IEEE Trans. Power Electron. 2012, 27, [CrossRef] 18. Rodríguez, J.; Marian, P.K. State of art of finite control set model predictive control in power electronics. IEEE Trans. Ind. Inf. 2013, 9, [CrossRef] 19. Tarisciotti, L.; Pericle, Z.; Alan, W.; Jon, C.C.; Degano, M.; Bifaretti, S. Modulated model predictive control for a three-phase active rectifier. IEEE Trans. Ind. Appl. 2015, 2, [CrossRef] 20. Ramirez, O.R.; Espinoza, J.R.; Villarroel, F.; Maurelia, E.; Reyes, M.E. A novel hybrid finite control set model predictive control scheme with reduced switching. IEEE Trans. Ind. Electron. 2014, 61, [CrossRef] 21. Song, Z.F.; Tian, Y.J.; Chen, Z.; Hu, W.T. Enhanced predictive current control of three-phase grid-tied reversible converters with improved switching patterns. Energies 2016, 9, 41. [CrossRef] 22. Wang, L.; Jiang, Q.; Hong, L.; Zhang, C.; Wei, Y. A novel phase-locked loop based on frequency detector and initial phase angle detector. IEEE Trans. Power Electron. 2013, 28, [CrossRef]

25 Energies 2017, 10, of Golestan, S.; Malek, R.; Josep, M.G.; Francisco, D.F.; Mohammad, M. Moving average filter based phase-locked loops: Performance analysis and design guidelines. IEEE Trans. Power Electron. 2014, 29, [CrossRef] 24. Texas Instrument. TMS320F28335 Digital Signal Controller (DSC) Data Manual; Texas Instrument: Dallas, TX, USA, by authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under terms and conditions of Creative Commons Attribution (CC BY) license (