Model Predictive Control of H5 Inverter for Transformerless PV Systems with Maximum Power Point Tracking and Leakage Current Reduction

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1 THIS WORK HAS BEE ACCEPTED B THE 44TH AUAL COFERECE OF THE IEEE IDUSTRIAL ELECTROICS SOCIET (IECO 218). THIS IS A PREPRIT. 1 Model Predictive ntrol of H Inverter for Transformerless Systems with Maximum Power Point Trackin and Leakae Current Reduction Abdulrahman J. Babqi, Zhehan i, Di Shi, Xiaoyin Zhao Department of Electrical Enineerin, Taif University, Taif, Saudi Arabia GEIRI orth America, San Jose, CA s: ajbabqi@tu.edu.sa, {zhehan.yi, di.shi, xiaoyin.zhao}@eirina.net arxiv: v1 [math.oc] 26 Jul 218 Abstract Transformerless rid-connected solar photovoltaic () systems have iven rise to more research and commercial interests due to their multiple merits, e.., low leakae current and small size. In this paper, a model-predictive-control ()- based stratey for controllin transformerless H inverter for sinle-phase distributed eneration system is proposed. The method further reduces the leakae current in a cost-effective and safe manner and it shows a satisfactory fault-ride-throuh capability. Moreover, for the first of its kind, maximum power point trackin is implemented in the sinle-stae H inverter usin -based controllers. Various case studies are carried out, which provide the result comparisons between the proposed and conventional control methods and verify the promisin performance of the proposed method. Index Terms Solar System, H Inverter, distributed eneration, renewable interation, model predictive control, leakae current, maximum power point trackin, fault ride throuh. I. ITRODUCTIO Renewable distributed enery resources (DERs), such as solar photovoltaic () and wind power systems, have been ettin more attentions recently to be used as alternatives of fossil fuels [1] [3]. power systems are considered as one of the most attractive renewable DER technoloies thanks to the abundance of solar enery and the declinin capital and operational expenses [4], []. Generally, systems can be interfaced with the utility rid throuh transformer-isolation or transformerless confiurations. Since line frequency transformers are heavy, inefficient, and cost-ineffective for systems, transformerless confiurations are attractin more and more interests from both research and commercial points of view. However, the lack of alvanic isolation in the transformerless confiurations will lead to a common-mode (CM) leakae current between the panels and the round throuh parasitic capacitors, which reduces the overall efficiency and rid current quality and may cause serious electromanetic interference and insecurity issues [6]. The parasitic capacitance is approximately 6 nf to 11 nf every kilowatt of the array [7]. Therefore, various inverter topoloies with specific modulation strateies have been introduced to suppress the leakae current, in which only a few topoloies have been This work is supported by the SGCC Science and Technoloy Proram Distributed Hih-Speed Frequency ntrol under UHVDC Bipolar Blockin Fault Scenario. + V - i Cp i i Leak + V out V i L + - V GD Fi. 1. A typical confiuration of the H transformerless inverter in a system. developed into industrial products, e.., H, H6, and HERIC inverters. The H structure is adopted by the SMA Solar Technoloy due to its simple topoloy with the least number of switches [8]. Fi. 1 illustrates a typical rid-connected transformerless system usin a H inverter, where i Leak stands for the CM leakae current, C P is the parasitic capacitor mentioned previously. In order to extract the maximum power of a array under different ambient conditions (irradiance and temperature), maximum power point trackin (MPPT) alorithms, such as Perturb & Observe (P&O) and Incremental nductance (In- nd), are employed to control the power-electronics stae. Althouh there are numerous existin methods to implement MPPT for rid-tied systems, most of them use twostae cascaded DC/DC-DC/AC convertin systems [9] [11] or sinle-stae DC/AC inverters [12] [1] with -based controllers or their variants. These methods may suffer from one or multiple of the followin major drawbacks: -based controllers require iterative tunin efforts when system parameters chane; It is relatively difficult to find optimal ain and time constants for the controllers; Extra pulse width modulation (PWM) modules are required; Some of the methods require multiple staes of costly converters, which reduces the convertin efficiency; and CM leakae current is not considered in most methods. Furthermore, very few research has tried to control the MPPT usin a transformerless sinle-stae H inverter. V

2 THIS WORK HAS BEE ACCEPTED B THE 44TH AUAL COFERECE OF THE IEEE IDUSTRIAL ELECTROICS SOCIET (IECO 218). THIS IS A PREPRIT. 2 (a) (b) (c) (d) Fi. 2. The four operation modes of H inverter for rid-connected systems. Model predictive control () is an optimal control approach which uses the system model and measurements to predict the future behavior of the controlled states based on minimizin a cost function [16] [18]. It is a fast, robust, and accurate controller that requires little tunin efforts. Recently, has been seen in the literature for controllin power systems [19] [22]. However, these works only desin to control DC/DC converters. There is no existin work aimin at desinin for H inverters. To fill this ap and as an attempt to address the aforementioned issues, this paper proposes a -based stratey for controllin the sinlestae transformerless H inverter for distributed eneration systems. The control stratey further reduces the leakae current comparin with conventional control methods. Moreover, fast and accurate MPPT is implemented for the sinlestae H transformerless inverter usin. Additionally, the proposed method improves the robustness and the fault-ridethrouh capability of transformerless systems. The rest of the paper is oranized as follows: Section II presents the desin of H inverter and its operation modes; the proposed for H inverters is descried in Section III; case studies are carried out in Section IV to verify the control scheme; Section IV concludes the paper. II. H IVERTER OPERATIO MODES The topoloy of a H inverter is similar to the sinle-phase full-bride inverter by addin an extra DC-bypass switch that disconnects the array from the utility rid durin the current-freewheelin periods. Fi. 1 shows the topoloy of H inverter with the leakae current (i Leak ) between the array and round. In eneral, there are four operation modes for H inverters, which are depicted Fi. 2. The first operation mode (Fi. 2(a)) is the active mode which occurs durin the positive-half cycle, where the switches,, and are conductin and the current flows throuh and and then TABLE I H IVERTER SWITCHIG STATES Mode V out V P V V P V 4 1 Fi. 3. H inverter space vector modulation (SVM). returns to the cathode of the array throuh. The second mode of operation shown in Fi. 2(b) is also referred to as the current-freewheelin mode with the zero voltae vector. In this mode, is triered on, while and are turned-off. The current is conductin throuh the freewheelin diode of. Fi. 2(c) illustrates the third mode of operation of H inverter, which is the active mode that occurs durin the neativehalf cycle. Durin mode 3, switches,, and conduct and the current flows throuh the inductors and in the opposite direction of that in mode 1. The fourth mode is the freewheelin mode durin the zero voltae vector where and are turned-off and is on. Similar to in mode 2 (Fi. 2(b)), works as a freewheelin diode in mode 4. Table I and Fi. 3 show the operation modes and space vector modulation (SVM) of the H inverter. III. THE PROPOSED MODEL PREDICTIVE COTROL FOR TRASFORMERLESS H IVERTERS EABLIG MPPT A. State Predictions of H inverter As is mentioned above, in the first mode of operation,,, and are conductin. The system model can be derived

3 THIS WORK HAS BEE ACCEPTED B THE 44TH AUAL COFERECE OF THE IEEE IDUSTRIAL ELECTROICS SOCIET (IECO 218). THIS IS A PREPRIT. 3 by KCL and KVL, respectively: i P V = i + i L (1) V P V = V + V + V (2) Start Get V ( k ), i ( k ), il ( k) where i P V and V P V are the array output current and voltae, respectively. i and i L are the currents throuh capacitor and the inductor, respectively. V and V are the voltaes across inductor and and V is the utility rid voltae. In the second mode of operation where only is turned-on, the system model is: i P V = i, (3) di ( k) i ( k)? dv ( k) V ( k) dv ( k) V ( k) V ( k 1) di ( k) i ( k) i ( k 1) dv ( k)? di ( k)? V P V = V. (4) where V is the capacitor voltae. In the third mode,,, and are closed and the system model can be written as: di ( k) i ( k)? dv ( k) V ( k) di ( k)? i P V = i + i L, () V P V = V + V + V. (6) Durin the fourth mode, the only closed switch is and the system model can be iven as: i P V = i, (7) V P V = V. (8) Additionally, the capacitor current and inductor voltaes can be expressed as: i = dv P V, V = di dt dt, V = di dt. (9) For a system, the MPPT is realized by forcin the operatin pointin to be around maximum power point, namely, to control V P V to track the MPPT reference voltae V ref. Therefore, we have to predict the future values of array voltae, V P V (k + 1) per horizon step. To this end, (1), (3), (), and (7) must be discretized. Usin the forward finite difference formula for the derivative dx x(k + 1) x(k), (1) dt T s where T s is the samplin period, the future values of the output voltae for the aforementioned four operation modes are predicted as: V P V 1 (k + 1) = V P V (k) + T s [i P V (k) i L (k)] (11) V P V 2 (k + 1) = V P V (k) + T s i P V (k) (12) V P V 3 (k + 1) = V P V (k) + T s [i P V (k) i L (k)] (13) V P V 4 (k + 1) = V P V (k) + T s i P V (k) (14) It is noteworthy that for the array voltae, the predictions of mode 1 and 3 are identical, so are mode 2 and 4. This will reduce the mode switchin frequency and thus the CM leakae current, which will be seen in the verification in the case studies (Section IV). V V dv ( k) V V dv ( k) ref ref V ( k 1) V ( k) i ( k 1) i ( k) Predict voltae in 4 modes: ref ref V 1( k 1) V ( k) [ i ( k) il ( k)] V 2 ( k 1) V ( k) i ( k) V 3 ( k 1) V ( k) [ i ( k) il ( k)] V 4 ( k 1) V ( k) i ( k) min J [ V V ( k 1)] ref i H Inverter Space Vector Modulation Fi. 4. The proposed -based MPPT control for transformerless H inverters. End B. Maximum Point Point ntrol of H Inverter Usin The proposed method is modified from one of the most popular MPPT alorithms, the Incremental nductance method [23], for extractin the maximum power output of the transformerless array with H inverter under varyin irradiance and temperature. Fi. 4 depicts the process of the proposed alorithm in detail. At every samplin period Ts, the controller samples the values of V P V, i P V, and i L from the transformerless system and follows the procedures of the flowchart to determine the optimal control inputs. After predictin the future value of the output voltae, a quadratic cost function: J = [V ref V P V (K + 1)] 2 (1) 2

4 THIS WORK HAS BEE ACCEPTED B THE 44TH AUAL COFERECE OF THE IEEE IDUSTRIAL ELECTROICS SOCIET (IECO 218). THIS IS A PREPRIT. 4 is desined to quantify the difference between the MPPT reference voltae V ref and the future array voltae V P V (k+1). The control process is then transferred into a optimization problem, which minimizes the quadratic function (1), i.e., the error between the reference and predicted value, and select the optimal control inputs with the least cost. This is achieved by evaluatin each possible scenario (i.e., the four modes of operation) and selectin the best operation mode at every samplin step. Once the optimal operation mode is determined, appropriate atin sinals are sent to the H inverter switches. Via optimization, the controller will automatically select the switch sinals that lead to a minimum error between the controllin states and references, which eliminates the tunin efforts that required by conventional controllers. Moreover, the switchin sinals will be directly applied to the H inverter without the needs for an extra PWM module, which lowers the cost and complexity of the control system. TABLE II CASE STUD SSTEM PARAMETERS Parameter Symbol Value Standard Testin Irradiance G 1 W/m 2 Standard Testin Temperature T 2 C Array Maximum Power (STC) P max 133 kw Array Maximum Point Point Voltae (STC) V ref 19 V DC Capacitor uf Output Filter Inductor 1 1 mh Output Filter Inductor 2 1 mh Output Filter Capacitor uf Grid Side Voltae V 1 V Samplin Period T s 1 us Parasitic Capacitance C P 133 nf 19 IV. CASE STUDIES V (V) 18 To examine the performance of the proposed control stratey for H inverters, multiple case studies are carried out in this section. The transformerless system with the same confiuration in Fi. 1 is modeled in the PSCAD/EMTDC platform, while the proposed alorithm is implemented usin Fortran. The numerical values of the tested system parameters are provided in Table II. The parameters of the array are measured under standard testin condition (STC, irradiance=1 W/m 2, temperature=2 C) It is noteworthy that, althouh the proposed method is verified in a testbed with certain parameters, it is scalable to work for different transformerless systems. For systems with other confiurations, similar approach can be used to desin the controller. The tested cases are elaborated below. I (A) V ref V P V I P V Fi.. output voltae and current usin the proposed control method. Fi. 1. Case Study 1 This case verifies the MPPT capability of the proposed control method, which aims at extractin the maximum power of the array under varyin irradiance situations. Fi. shows the array instantaneous output voltae (V P V ) and current (I P V ) as well as the MPPT voltae reference (V ref ). At the beinnin, the irradiance is set to 1 W/m 2 and the temperature is 2 C. At t = 2 s, the irradiance drops from 1 W/m 2 to 8 W/m 2. It can be seen from Fi. that the output current of the array decreases as the irradiance chanes without any undershootin. Moreover, the output voltae is trackin its reference V ref closely. A further decline of the irradiance occurred at t = 3 s. The irradiance reduces from 8 W/m 2 to 6 W/m 2. It is demonstrated that both voltae and current chane their values correspondinly because of the new irradiance level. Aain, it is clear that the output voltae follows its reference value. Therefore, the proposed control stratey provides a fast response as well as ood dynamic performance under the varyin irradiance conditions. Case Study 2 The followin case aims at validatin the capability of the proposed control stratey for further reducin the CM leakae current in a transformerless system with a H inverter. Fi. 6 illustrates the instantaneous CM leakae currents of the transformerless system by the proposed and conventional controllers, as well as the leakae current of a system with a sinle-phase full-bride inverter by a controller. Fi. 7 presents their RMS values. To present a reasonable comparison, the MPPT alorithm for all these case are based on the Incremental nductance method. From these fiures, it is obvious that H inverter itself reduces the CM leakae current (RMS) from 3 A to 2. A approximately (black and red curves in Fi. 7). The results also presents that, for the same confiuration (transformerless H inverter), the proposed method further reduces the leakae current by almost % compared with conventional controller (blue curve in Fi. 7). This is because that, durin operation, the proposed method reduces the switchin modes of the H inverter as is analyzed in

5 THIS WORK HAS BEE ACCEPTED B THE 44TH AUAL COFERECE OF THE IEEE IDUSTRIAL ELECTROICS SOCIET (IECO 218). THIS IS A PREPRIT. Fi. 2. Fi. 1. Fi. 1. Fi. 2. -H -H -H -H -full bride -H Fi Leakae current comparison amon the -controlled H inverter, -controlled H inverter, and -controlled full-bride inverter. 4 Fi. 2. Vpv Vpv (V) (V) Ipv Ipv (A) (A) Time Time Time 6 (s) 6. 7 Fi mparison of the output voltae and current usin the proposed controller and a conventional controller. Fi Vpv Vpv (V) (V) Time , Time 1, Fi RMS values of the leakae current -full bride Fi. 3. Fi. 8 demonstrates the output voltae and current usin 2 -H -H -full bride Section III. 3.8 The lare 3.8leakae current 3.9 that occurs 3.9 with the 4 conventional controller will affect the reliability and efficiency of the system. More importantly, it may cause safety hazards to the system operator and maintenance personnel. both the proposed control stratey and conventional control for H inverter, which shows that the leakae current affects the performance of the system and makes it more oscillatory while proposed method ives a smoother and steadier performance. -full bride Ipv Ipv (A) (A) 1, 1, Fi Output voltae and current usin both proposed controller and Fi. conventional 1.. Case Study 3 This case demonstrates the fault-ride-throuh capability of the proposed control method. To this end, a round fault was applied to system at the output terminal of the array. Fi. 9 plots the output voltae and current of H inverter (usin both the proposed method and controller) before, durin, and after the fault. The round fault is applied at t = 1.4 s and it is cleared after 1 ms (Fi. 9). It can be seen that the system controlled by the controller is vulnerable. The voltae and current become unstable durin and even

6 THIS WORK HAS BEE ACCEPTED B THE 44TH AUAL COFERECE OF THE IEEE IDUSTRIAL ELECTROICS SOCIET (IECO 218). THIS IS A PREPRIT. 6 after the clearance of fault (red curves). The current increases immediately when the fault occurs, which may cause damae to the system if no further protection actions are applied. evertheless, the proposed control stratey shows a robust performance (blue curves) and a better fault-ridethrouh capability under faulted conditions. The voltae tracks its reference value V ref both durin and after the fault cleared, while the current is limited within a reasonable rane. V. COCLUSIOS This paper introduces an innovative control stratey for transformerless rid-connected systems with H inverters. A model-predictive-controlled method is desined to extract the maximum power under various operational conditions. The control stratey predicts the future behavior of the output voltae and enerates the optimal control sinals for the H inverter, which minimizes the error between the reference and the controlled variable. The case studies verifies that the proposed method provides a better dynamics response comparin with conventional methods. Moreover, the control stratey further reduces the CM leakae current in the H inverter by almost % compared with conventional controller. It also demonstrates the robustness and fault-ride-throuh capability of the proposed method. REFERECES [1] D. Shi, X. Chen, Z. Wan, X. Zhan, Z. u, X. Wan, and D. Bian, A distributed cooperative control framework for synchronized reconnection of a multi-bus microrid, IEEE Transaction on Smart Grid, vol. PP, no. 99, pp. 1 1, 217. [2]. Wan, Z. i, D. Shi, Z. u, B. Huan, and Z. Wan, Optimal distributed enery resources sizin for commercial buildin hybrid microrids, arxiv preprint arxiv:183.66, 218. [3] A. Aldhaheri and A. H. 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