- Email: [email protected]
Performance enhancement of cascaded qZS-HB based renewable energy system using Model Predictive Control
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 7 ) 1 e1 1
Available online at www.sciencedirect.com
ScienceDirect journal homepage: www.elsevier.com/locate/he
Performance enhancement of cascaded qZS-HB based renewable energy system using Model Predictive Control Mohamed Trabelsi a,*, Sertac Bayhan a,b, Haitham Abu-Rub a, Lazhar Ben-Brahim c a
Texas A&M University at Qatar, Department of Electrical and Computer Engineering, Qatar Foundation, Doha, Qatar b Department of Electronics and Automation, Gazi University, Ankara, Turkey c Qatar University, Department of Electrical Engineering, Doha, Qatar
article info
abstract
Article history:
This paper presents a multi-objective Model Predictive Control (MPC) for a grid connected
Received 15 November 2016
2-cell 5-level quasi Z-Source (qZS) Cascaded H-Bridge (CHB) inverter. The main contribu-
Received in revised form
tion of the proposed control approach is the design of a multi-constraint cost function to
18 April 2017
achieve multi-objective MPC strategy dealing with the complex nature of the presented
Accepted 19 April 2017
qZS-CHB topology. The designed cost function takes into account three control objectives,
Available online xxx
which are the minimization of the grid current, input current, and capacitors' voltages tracking errors. The best performance scenario is realized through the fine tuning of the
Keywords:
constraints' weighting factors based on the grid current's error minimization and the
Quasi-Z-source network
reduction of the double-line frequency ripples on the input current. As a result, the pro-
Grid integration
posed scheme achieves high-quality tracking of the encompassed state variables with the
Model predictive control
elimination of the double-line frequency power flow through the qZS inductors leading to
Multilevel inverter
the reduction of the hysteresis losses and the increase of the overall system efficiency. The
Renewable energy sources
performance of the proposed MPC strategy has been investigated and compared to the state of art PI controller. Theoretical analysis and implementation results are given to show that the proposed scheme is suitable for all system configurations and has good performances even during disturbances. © 2017 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
Introduction Research and development of the next-generation Renewable Energy (RE) inverters are driven by system requirements to use cost effective techniques [1], highly reliable and efficient system architecture and components [2e5], new inverter
topologies [6e10], new control methodologies for maximum power extraction [11] and grid code compliance [12]. In particular, the structures of utility RE inverters are moving toward multilevel topologies, which could provide better harmonic spectra, reduce the weight of the filtering components, provide modularity and increase efficiency.
* Corresponding author. E-mail address: [email protected] (M. Trabelsi). http://dx.doi.org/10.1016/j.ijhydene.2017.04.200 0360-3199/© 2017 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved. Please cite this article in press as: Trabelsi M, et al., Performance enhancement of cascaded qZS-HB based renewable energy system using Model Predictive Control, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.04.200
2
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 7 ) 1 e1 1
Nomenclature Vin C VCi.1,2 L iLi1,2 ig Vout Vgrid f Vpni P Lf rf D B Ts g lig lVc liL
input voltage capacitance of the qZS network capacitors capacitor voltages of the qZS network capacitors of cell i inductance of the qZS network inductors inductor currents of the qZS network inductors of cell i injected grid current output voltage grid voltage fundamental frequency DC-link voltage of cell i output power filtering inductor internal resistance of the filtering inductor shoot-through duty cycle boosting factor sampling time cost function weighting factor of the grid current constraint weighting factor of the capacitor voltage constraint weighting factor of the inductor current constraint
A number of papers have recently appeared in the scientific literature dealing with Multilevel Inverters (MLI) for small and large-scale RE plants. Among the most used MLI topologies are Modular Multilevel Converters (MMC), Diode Clamped multilevel Converters (DCC), T-type multilevel converter (TC), Packed U Cells (PUC) Multilevel Inverters, Flying Capacitors Inverters (FCI), and qZS multilevel converters. However, CHB multilevel converters are the most studied multilevel structures for RE systems [13e25]. In [13], authors propose a fault tolerant strategy to maintain balanced grid currents during faults with unequal power generation in healthy bridges, while [14] suggests a fully fuzzy logic controller/ modulator, mostly implemented in FPGA, for a single-phase configuration. A modulation for common mode voltage reduction is proposed in [15], while [16] suggests a strategy to overcome output voltage over modulation due to varied and non-uniform solar energy on segmented PV arrays. A fault tolerance strategy is implemented by several distributed algorithms to identify system operation in [17], while [18] provides modeling and analysis towards an improved grid power quality. [19] suggests a novel modulation for power balancing and [20,21] propose zero sequence injection method to counteract different power levels in the phases with providing reduced switching losses and high conversion efficiency. [22] compares delta and star grid connection of cascaded multilevel converters, [23] describe one of the most important feature a multilevel converter for PV applications needs to have such as an independent control of each dc-link voltages, enabling MPPT for each PV string, while [24] presents a transformer less connection to the grid. In [25], authors suggest a harmonic elimination modulation strategy optimized
with artificial neural networks for high performance PV connection. Moreover, [8,12,26e29] propose the use of quasiZ-Source (qZS)-CHB multilevel inverters for Grid connection of PV systems showing balanced dc voltage and voltage boost capabilities saving 30% of power modules compared to other structures. The qZS inverter (variant of the Z-sourced inverter) can provide voltage buck/boost and dc/ac conversion functionalities using an additional basic impedance (LC) network. This topology takes advantage of the shoot-through states to boost the input voltage and regulate the DC link voltage of the inverter. Moreover, when connected to H-Bridge inverters and cells are connected in series, the cascaded topology becomes very competitive and suitable for RE applications. In [8], authors propose a 1 MW grid-tied PV system consisting of a 3-phase 48-cell CHB inverter where each module is fed by a qZS network. [12] suggests a control strategy achieving grid-tie current injection, dc-link voltage balancing, and anti-islanding protection for the qZS structure. In [26], each PV connects to a qZS network designed to minimize the harmonic voltage and current ripple, while in [27] a modulation strategy is proposed for the same structure in order to minimize component losses. For the same topology, [28] proposes the inclusion of an energy storage system for each PV array to balance stochastic fluctuation of PV power, while [29] provides a comprehensive modeling and control design. In one hand, as any power electronics converter, the performance of the qZS-CHB inverter highly depends on the control properties. Good dynamics of the response must be followed by high accuracy of the reference tracking. With satisfying these requirements, the finite control set MPC technique is considered as an alternative method to classical linear controllers, having the capability to include constraints with different natures, dealing with nonlinearities, and easy to implement (no modulation stage) [30e32]. In the other hand, similar to the traditional single-phase inverter, the double-line frequency (2f) power flows through dc-link of the qZS-CHB inverter. This leads to 2f ripples on the dc-link and capacitor voltages and 2f inductors current ripples. Most particularly, high 2f inductor current ripples results in high hysteresis losses, which reduces the overall system efficiency. One way to minimize these current ripples is to use large qZS inductance that considerably increase the inverter size, weight, and cost. For that reason, using such system requires advanced control techniques to reduce or eliminate the 2f ripples. This paper proposes a multi-objective MPC for a grid connected 2-cell 5-level qZS-CHB inverter. The main contribution of the proposed control approach is the design of a multiconstraint cost function to achieve a multi-objective control strategy dealing with the complex nature of the presented qZS-CHB topology. The designed cost function takes into account three control objectives, which are the grid current, input current, and capacitors' voltages tracking errors. The multi-constraint errors minimization leads to the elimination of the double-line frequency 2*f power flow through the qZS inductors and in turn the reduction of the hysteresis losses and the increase of the overall system efficiency. The performance of the proposed MPC strategy is investigated and
Please cite this article in press as: Trabelsi M, et al., Performance enhancement of cascaded qZS-HB based renewable energy system using Model Predictive Control, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.04.200
3
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 7 ) 1 e1 1
Fig. 1 e Proposed 2-cell 5-level qZS-CHB inverter.
compared to the state of art PI controller. Theoretical analysis and implementation results are given to show that the proposed scheme is suitable for all system configurations and has good performances even during disturbances. The presented approach could be extended for qZS-CHB inverters with a large number of cells.
Theoretical study qZS-CHB topology and modelling Fig. 1 shows the proposed qZS-CHB inverter topology. In order to achieve the boost capability, the 5-level qZS-CHB inverter
Table 1 e All Possible Switching Patterns of the studied 2-cell qZS-CHB inverter. Switching state Non-shoot-through states
Shoot-through states
Vout 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
0
Vin
Vin
2Vin 2Vin Vin Vin 0
S11
S12
S13
S14
S21
S22
S23
S24
0 0 0 1 1 1 0 0 0 1 0 1 1 1 0 1 1 1 1
1 1 1 0 0 0 1 1 1 0 1 0 0 0 1 0 1 0 1
0 0 1 0 1 1 0 1 1 1 0 0 0 1 1 0 0 0 0
1 1 0 1 0 0 1 0 0 0 1 1 1 0 0 1 1 1 1
0 1 1 0 0 1 0 0 1 0 1 0 1 1 0 1 1 1 1
1 0 0 1 1 0 1 1 0 1 0 1 0 0 1 0 0 1 1
0 1 0 1 0 1 1 0 1 1 0 0 1 0 1 0 0 0 0
1 0 1 0 1 0 0 1 0 0 1 1 0 1 0 1 1 1 1
Please cite this article in press as: Trabelsi M, et al., Performance enhancement of cascaded qZS-HB based renewable energy system using Model Predictive Control, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.04.200
4
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 7 ) 1 e1 1
Fig. 2 e The equivalent circuit of the qZS network; (a) non-shoot-through state, (b) shoot-through state.
makes use of one more switching state (shoot-through state, where both switches in the same leg must be turned on at the same time) compared to the traditional 2-cell CHB inverter. The resulted switching states are illustrated in Table 1 (19 switching states are illustrated, 16 are common for any 2-cell CHB inverter, 1 for the shoot-through of the first cell, another one for the shoot-through of the second cell, and one more when the 2 cells are short-circuited). In the non-shoot-through state, the studied system can be illustrated by a constant current source (Fig. 2(a)). The derivations of the state variables iLi1, and Vci1 for each cell (i is the cell number) are obtained by (1) and (2). dVCi1 ¼ iLi1 ðtÞ ig ðtÞ ¼ iCi1 ðtÞ dt
(1)
diLi1 ¼ Vin VCi1 ðtÞ ¼ VLi1 ðtÞ L dt
(2)
C
In the other case (shoot-through state), the inverter is illustrated by a short-circuit of the dc-link voltage (Fig. 2(b)). The system equations for this state are given by (3) and (4).
C
dVCi1 ðtÞ ¼ iLi2 ðtÞ ¼ iCi1 ðtÞ dt
(3)
L
diLi1 ðtÞ ¼ VCi2 ðtÞ þ Vin ðtÞ ¼ VLi1 ðtÞ dt
(4)
In addition, according to Fig. 1, the output voltage Vout in terms of its current and filter parameters is given by: Vout ðtÞ ¼ Lf
dig ðtÞ þ rf ig ðtÞ þ Vgrid ðtÞ dt
(5)
The steady state capacitors and dc-link voltages can be obtained by (6) where B is the boosting factor and D is the shoot-through duty cycle. 8 > > > > > > > < > > > > > > > b pn :V
1D Vin 1 2D D Vin VCi2 ¼ 1 2D 1 Vin ¼ BVin ¼ VCi1 þ VCi2 ¼ 1 2D VCi1 ¼
(6)
Please cite this article in press as: Trabelsi M, et al., Performance enhancement of cascaded qZS-HB based renewable energy system using Model Predictive Control, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.04.200
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 7 ) 1 e1 1
5
minimizing the cost function g, for a predefined horizon in time N ¼ 1, subject to the model and the restrictions of the system. The result is a sequence of N optimal actuations. The objectives of the proposed controller are the regulation of the injected grid current, the maintain of the inductor currents in continuous mode with low ripples to reduce the input stress, and the regulation of the capacitors' voltages around the desired values, which in turn balances the dc-link voltage. The proposed MPC strategy predicts the tracking error of the next sampling for the sixteen possible switching patterns by calculating the cost functions. The proposed intuitive predictive approach consists of the below three main steps illustrated in Fig. 3 and the overall control scheme is shown in Fig. 4.
References generation In PV applications, the voltage references are usually generated through maximum power point tracking algorithm. However, the objective of this paper is the control performance of the qZS-CHB inverter using MPC. Thus, the reference dc-link voltage is defined according to the grid voltage magnitude (240 Vrms). On the other hand, the reference input (inductor) current is calculated according to the inverter power rating as i*L ¼ P/2Vin, where Vin and P are the input voltage and output power of the studied qZS-CHB inverter respectively.
Model prediction
Fig. 3 e Detailed description of the proposed MPC algorithm steps.
The digital implementation of the proposed control algorithm requires the use of a discrete-time model of the studied system. Since the proposed controller handles three control objectives, the predictive model makes use of three discrete-time equations. This paper employs the first-order approximation given in (7) for the prediction of the state variables at the (k þ 1) sample in terms of the measurements at the previous (k) sample as expressed by (8e10). It is worth noting that the expressions of iCi1(t) and VLi1(t) are calculated by (1e4) depending on the qZS network state (shoot-through in cell-1, cell-2, both cells, or non-shootthrough state) df ðtÞ f ðk þ 1Þ f ðkÞ ¼ dt Ts
Model Predictive Control In the current work, a Finite Control Set MPC (FCS-MPC) is implemented to control the power flow of the grid connected qZS-CHB topology. The FCS strategy is used instead of the Continuous Control Set one considering the finite number of output states of the converter. The proposed FCS-MPC considers the controlled plant as a finite set of linear models, each representing a physical switching state. The advantage of FCS-MPC is that concept is very simple and intuitive. Implementation is also simple especially in this study where the prediction horizon is selected to N ¼ 1 (low complexity). The proposed MPC is an optimization problem that consist of
Vci1 ðk þ 1Þ ¼ Vci1 ðkÞ þ
iLi1 ðk þ 1Þ ¼ iLi1 ðkÞ þ ig ðk þ 1Þ ¼
1
(7) Ts iCi1 ðtÞ C
Ts VLi1 ðtÞ L
rf Ts Ts ig ðkÞ þ Vout ðkÞ Vgrid ðkÞ Lf Lf
(8)
(9)
(10)
Cost function minimization In order to satisfy the control objectives, three terms are defined within the cost function given by (11). The first term in the cost function is responsible to minimize the error between
Please cite this article in press as: Trabelsi M, et al., Performance enhancement of cascaded qZS-HB based renewable energy system using Model Predictive Control, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.04.200
6
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 7 ) 1 e1 1
Fig. 4 e Control diagram for the control of the 2-cell qZS-CHB inverter. the reference and predicted grid current. The second term
Table 2 e System parameters. Parameters
Value
Total output power (Ptotal) AC grid RMS voltage (Vgrid) qZS inductances (L1, L2) qZS capacitances (C1, C2) Filtering inductance (L) Input voltage for qZS-HBI module (Vin) DC-link voltage reference V*pn Grid frequency (f)
1.2 kW 240 V 2.5 mH 4.7 mF 1 mH 150 V 240 V 50 Hz
handles the reference tracking of the capacitor voltage, while the third one minimizes the error between the reference and predicted inductor current values. 2 X * lVc Vc1 * Vci1 ðk þ 1Þ g ¼lig ig ig ðk þ 1Þ þ i¼1
þ
2 X
* liL iL1 iLi1 ðk þ 1Þ
(11)
i¼1
where the weighting factors lig, lVc, and liL are tuned to ensure the best performance scenario. As the priority targets are the smooth power injection to the grid (reduction of the grid current ripples) and the elimination of the double line frequency oscillations on the input current (reduction of high
Fig. 5 e Grid and inductor currents against their respective references using PI controllers. Please cite this article in press as: Trabelsi M, et al., Performance enhancement of cascaded qZS-HB based renewable energy system using Model Predictive Control, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.04.200
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 7 ) 1 e1 1
7
Fig. 6 e Grid and inductor currents against their respective references using tuned MPC controller.
Fig. 7 e Grid and inductor currents against their respective references using untuned MPC controller: effect of weighting factor (liL ¼ 0.5) on the performance of the inductor current tracking.
hysteresis losses), the weighting factors are tuned accordingly in order to satisfy the aforementioned goals.
Implementation results The proposed control algorithm has been implemented using a dSPACE dS1103 controller board. The parameters used in the implementation tests are given in Table 2. In order to show the
effectiveness of the proposed MPC controller in achieving the control goals, the transient and steady state performances were compared with those achieved using PI controllers (using a dual loop strategy). The upper part of Fig. 5 depicts the grid current tracking suitably its reference using PI controller. The lower parts shows that the inductor current is maintained in continuous mode with noticeable ripples. Similar to traditional single-phase inverter, the double-line frequency 2*f power flows through dc-link of the qZS-CHB inverter. This
Please cite this article in press as: Trabelsi M, et al., Performance enhancement of cascaded qZS-HB based renewable energy system using Model Predictive Control, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.04.200
8
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 7 ) 1 e1 1
Fig. 8 e Grid and inductor currents against their respective references using untuned MPC controller: effect of weighting factor (lig ¼ 0.25) on the performance of the grid current tracking.
Fig. 9 e PI controllers performances during a 100% step change of the reference current: grid and inductor currents are depicted.
leads mainly to a 2*f dc-link and capacitors voltages ripples and inductors currents ripple. The latter results mainly in high hysteresis losses, which reduces the overall system efficiency. One way to minimize these current ripples is to use large qZS source inductors that considerably increase the inverter size, weight, and cost. To overcome this problem, this work proposes a multi-objective MPC strategy where both inductors'
currents and capacitors' voltages are included as constraints in the cost function. The weighting factors lig, lVc, and liL are tuned to ensure the best performance scenario. Consequently, the lower part of Fig. 6 shows that the inductor current is maintained in the continuous mode and tracking its reference with very low current ripples allowing reducing the input stress. As the weighting factors used in the cost function have
Please cite this article in press as: Trabelsi M, et al., Performance enhancement of cascaded qZS-HB based renewable energy system using Model Predictive Control, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.04.200
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 7 ) 1 e1 1
9
Fig. 10 e MPC performance during a 100% step change of the reference Power: inductor current, grid current, and total power are depicted.
Fig. 11 e Grid synchronization results: PF, grid current, and grid voltage are depicted.
significant effect on the quality of the tracking processes, it is worth to illustrate this effect by varying the values if these weighting factors. Fig. 7 and Fig. 8 show the implementation results with different values of lig and liL. Notice that the grid and inductor currents tracking are degraded when less priority is given to lig and liL respectively. Fig. 9 and Fig. 10 show the transient state performances of both controllers during a step change of the power reference
from 50% to 100% of the rated value. As expected, MPC show very high dynamic performances in re-tracking the references (Fig. 10). The synchronization of the grid current with the grid voltage at the coupling point (unity power factor) is shown in Fig. 11. Finally, the upper part of Fig. 12 shows the 5-level output voltage with the grid voltage while the lower part shows the regulated DC-link voltage (240 V) and capacitor voltages.
Please cite this article in press as: Trabelsi M, et al., Performance enhancement of cascaded qZS-HB based renewable energy system using Model Predictive Control, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.04.200
10
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 7 ) 1 e1 1
Fig. 12 e qZS network and output voltages, Upper: 5-level output voltage waveform with the grid voltage, Lower: Regulated DC-link and capacitors voltages.
Conclusions A multi-objective MPC for grid-tied 2-cell 5-level qZS-CHB inverter was proposed in this paper. The main contribution of the proposed approach is the design of a multi-constraint cost function achieving a multi-optimization control dealing with the complex nature of the presented qZS-CHB topology. The designed cost function takes into account three control objectives, which are the minimizations of the grid current, input current, and capacitors' voltages tracking errors. In order to ensure the best control performances, the weighting factors were finely tuned within the cost function to minimize the grid current ripples as well as the double-line frequency ripples on the measured inductor current. Implementation results confirmed the significant effect of the optimal tuning on the controller performance. The transient and steady state performance of the proposed MPC strategy has been investigated and compared to the PI controller's one. Implementation results were given to show that the proposed scheme is ensuring smooth power injection to the grid under different operating conditions (high dynamic performances during disturbances) with reduction of the hysteresis losses (the inductor current is maintained in the continuous mode with very low current ripples) and the increase of the overall system efficiency.
Acknowledgement This work was made possible by NPRP-EP Grant no. X-033-2007 from the Qatar National Research Fund (a member of Qatar Foundation). The statements made herein are solely the responsibility of the authors.
references
[1] Nojavan S, Majidi M, Zare K. Risk-based optimal performance of a PV/fuel cell/battery/grid hybrid energy system using information gap decision theory in the presence of demand response program. Int J Hydrogen Energy 2017;42:11857e67. [2] Molina MG, Espejo EJ. Modeling and simulation of gridconnected photovoltaic energy conversion systems. Int J Hydrogen Energy 2014;39:8702e7. [3] Pacas JM, Molina MG, dos Santos Jr EC. Design of a robust and efficient power electronic interface for the grid integration of solar photovoltaic generation systems. Int J Hydrogen Energy 2012;37:10076e82. ndez LM, Jurado F. [4] Garcı´a CA, Llorens F, Garcı´a P, Ferna Improving voltage harmonic compensation of a single phase inverted-based PEM fuel cell for stand-alone applications. Int J Hydrogen Energy 2014;39:4483e92. [5] Seyezhai R, Mathur BL. Modeling and control of a PEM fuel cell based hybrid multilevel inverter. Int J Hydrogen Energy 2011;36:15029e43. [6] Ozdemir S. Z-source T-type inverter for renewable energy systems with proportional resonant controller. Int J Hydrogen Energy 2016;41:12591e602. [7] Trabelsi M, Bayhan S, Metry M, Abu-Rub H, Ben-Brahim L, Balog R. An effective Model Predictive Control for grid connected Packed U Cells multilevel inverter. In: IEEE Power and Energy Conference at Illinois (PECI), Urbana, IL; 2016, pp. 1e6. [8] Trabelsi M, Abu-Rub H, Ge B. 1-MW quasi-Z-source based multilevel PV energy conversion system. In: IEEE International Conference on Industrial Technology (ICIT), Taipei; 2016, pp. 224e229. [9] Bayhan S, Trabelsi M, Abu-Rub H. Model Predictive Control of Z-Source four-leg inverter for standalone Photovoltaic system with unbalanced load. In: IEEE Applied Power Electronics Conference and Exposition (APEC), Long Beach, CA; 2016, pp. 3663e3668.
Please cite this article in press as: Trabelsi M, et al., Performance enhancement of cascaded qZS-HB based renewable energy system using Model Predictive Control, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.04.200
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 7 ) 1 e1 1
[10] Trabelsi M, Bayhan S, Ghazi KA, Abu-Rub H, Ben-Brahim L. Finite-control-set model predictive control for gridconnected packed-U-cells multilevel inverter. IEEE Trans Ind Electron Nov. 2016;63(11):7286e95. [11] Ramos-Hernanz J, Lopez-Guede JM, Barambones O, Zulueta E, Fernandez-Gamiz U. Novel control algorithm for MPPT with Boost converters in photovoltaic systems. Int J Hydrogen Energy 2017. http://dx.doi.org/10.1016/ j.ijhydene.2017.02.028. [12] Trabelsi M, Abu-Rub H. A unique active anti-islanding protection for a quasi-Z-Source based Power Conditioning System. In: 2015 IEEE applied power electronics conference and exposition (APEC), Charlotte, NC; 2015. p. 2237e43. [13] Yu Y, Konstantinou G, Hredzak B, Agelidis VG. Operation of cascaded H-Bridge multilevel converters for large-scale photovoltaic power plants under bridge failures. IEEE Trans Ind Electron 2015;62(11):7228e36. [14] Cecati C, Ciancetta F, Siano P. A multilevel inverter for photovoltaic systems with fuzzy logic control. IEEE Trans Ind Electron 2010;57(12):4115e25. [15] Selvamuthukumaran R, Garg A, Gupta R. Hybrid multicarrier modulation to reduce leakage current in a transformerless cascaded multilevel inverter for photovoltaic systems. IEEE Trans Power Electron 2015;30(4):1779e83. [16] Liu Liming, Li Hui, Xue Yaosuo, Liu Wenxin. Decoupled active and reactive power control for large-scale gridconnected photovoltaic systems using cascaded modular multilevel converters. IEEE Trans Power Electron 2014;30(1):176e87. [17] Nguyen Luan Viet, Tran Hoang Dung, Johnson TT. Virtual prototyping for distributed control of A fault-Tolerant modular multilevel inverter for photovoltaics. IEEE Trans Energy Convers 2014;29(4):841e50. [18] Alexander A, Thathan M. Modelling and analysis of modular multilevel converter for solar photovoltaic applications to improve power quality. Renew Power Gener IET 2014;9(1):78e88. [19] Yifan Yu, Konstantinou G, Hredzak B, Agelidis VG. Power balance of cascaded H-Bridge multilevel converters for largescale photovoltaic integration. IEEE Trans Power Electron 2016;31(1):292e303. [20] Islam MR, Youguang Guo, Jianguo Zhu. A multilevel medium-voltage inverter for step-up-transformer-less grid connection of photovoltaic power plants. IEEE J Photovoltaics 2014;4(3):881e9. [21] Yu Y, Konstantinou G, Hredzak B, Agelidis VG. Power balance optimization of cascaded H-Bridge multilevel converters for
[22]
[23]
[24]
[25]
[26]
[27]
[28]
[29]
[30]
[31]
[32]
11
large-scale photovoltaic integration. IEEE Trans Power Electron 2016;31(2):1108e20. Sochor P, Akagi H. Theoretical comparison in energybalancing capability between star- and delta-configured modular multilevel cascade inverters for utility-scale photovoltaic systems. IEEE Trans Power Electron 2015. Volume: PP, Issue: 99, Pages: 1 1, [IEEE Early Access Articles]. Xiao Bailu, Hang Lijun, Mei Jun, Riley Cameron, Tolbert Leon M, Ozpineci Burak. Modular cascaded H-Bridge multilevel PV inverter with distributed MPPT for grid-connected applications. IEEE Trans Ind Appl March/April 2015;51(2). Zhou Yan, Li Hui. Analysis and suppression of leakage current in cascaded-multilevel-inverter-based PV systems. IEEE Trans Power Electron October 2014;29(10). Filho Faete, Tolbert Leon M, Cao Yue, Ozpineci Burak. Realtime selective harmonic minimization for multilevel inverters connected to solar panels using artificial neural network angle generation. IEEE Trans Ind Appl September/October 2011;47(5). Sun Dongsen, Ge Baoming, Yan Xingyu, Bi Daqiang, Zhang Hao, Liu Yushan, Abu-Rub H, Ben-Brahim L, Peng Fang Zheng. Modeling, impedance design, and efficiency analysis of quasi-Z-source module in cascaded multilevel photovoltaic power system. IEEE Trans Ind Electron 2014;61(11):6108e17. Liu Yushan, Ge Baoming, Abu-Rub H, Peng Fang Zheng. Phase-shifted pulse-width-amplitude modulation for quasiZ-source cascade multilevel inverter-based photovoltaic power system. Power Electron IET 2014;7(6):1444e56. Sun Dongsen, Ge Baoming, Liang Weihua, Abu-Rub H, Peng Fang Zheng. An energy stored quasi-Z-source cascade multilevel inverter-based photovoltaic power generation system. IEEE Trans Ind Electron 2015;62(9):5458e67. Liu Yushan, Ge Baoming, AbuRub H, Peng Fang Zheng. An effective control method for three-phase quasi-Z-source cascaded multilevel inverter based grid-tie photovoltaic power system. IEEE Trans Ind Electron 2014;61(12):6794e802. Rodriguez J, Kazmierkowski MP, Espinoza JR, Zanchetta P, Abu-Rub H, Young HA, et al. State of the art of finite control set model predictive control in power electronics. IEEE Trans Ind Inf 2013;9:1003e16. Trabelsi M, Ben-Brahim L, Ghazi KA. An improved Real-Time Digital Feedback Control for grid-tie multilevel inverter. In: The 39th Annual Conference of the IEEE Industrial Electronics Society (IECON), Vienna; 2013, pp. 5776e5781 Trabelsi M, Ghazi KA, Al-Emadi N, Ben-Brahim L. An original controller design for a grid connected PV system. In: The 38th Annual Conference on IEEE Industrial Electronics Society (IECON), Montreal, QC; 2012, pp. 924e929.
Please cite this article in press as: Trabelsi M, et al., Performance enhancement of cascaded qZS-HB based renewable energy system using Model Predictive Control, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.04.200
Available online at www.sciencedirect.com
ScienceDirect journal homepage: www.elsevier.com/locate/he
Performance enhancement of cascaded qZS-HB based renewable energy system using Model Predictive Control Mohamed Trabelsi a,*, Sertac Bayhan a,b, Haitham Abu-Rub a, Lazhar Ben-Brahim c a
Texas A&M University at Qatar, Department of Electrical and Computer Engineering, Qatar Foundation, Doha, Qatar b Department of Electronics and Automation, Gazi University, Ankara, Turkey c Qatar University, Department of Electrical Engineering, Doha, Qatar
article info
abstract
Article history:
This paper presents a multi-objective Model Predictive Control (MPC) for a grid connected
Received 15 November 2016
2-cell 5-level quasi Z-Source (qZS) Cascaded H-Bridge (CHB) inverter. The main contribu-
Received in revised form
tion of the proposed control approach is the design of a multi-constraint cost function to
18 April 2017
achieve multi-objective MPC strategy dealing with the complex nature of the presented
Accepted 19 April 2017
qZS-CHB topology. The designed cost function takes into account three control objectives,
Available online xxx
which are the minimization of the grid current, input current, and capacitors' voltages tracking errors. The best performance scenario is realized through the fine tuning of the
Keywords:
constraints' weighting factors based on the grid current's error minimization and the
Quasi-Z-source network
reduction of the double-line frequency ripples on the input current. As a result, the pro-
Grid integration
posed scheme achieves high-quality tracking of the encompassed state variables with the
Model predictive control
elimination of the double-line frequency power flow through the qZS inductors leading to
Multilevel inverter
the reduction of the hysteresis losses and the increase of the overall system efficiency. The
Renewable energy sources
performance of the proposed MPC strategy has been investigated and compared to the state of art PI controller. Theoretical analysis and implementation results are given to show that the proposed scheme is suitable for all system configurations and has good performances even during disturbances. © 2017 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
Introduction Research and development of the next-generation Renewable Energy (RE) inverters are driven by system requirements to use cost effective techniques [1], highly reliable and efficient system architecture and components [2e5], new inverter
topologies [6e10], new control methodologies for maximum power extraction [11] and grid code compliance [12]. In particular, the structures of utility RE inverters are moving toward multilevel topologies, which could provide better harmonic spectra, reduce the weight of the filtering components, provide modularity and increase efficiency.
* Corresponding author. E-mail address: [email protected] (M. Trabelsi). http://dx.doi.org/10.1016/j.ijhydene.2017.04.200 0360-3199/© 2017 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved. Please cite this article in press as: Trabelsi M, et al., Performance enhancement of cascaded qZS-HB based renewable energy system using Model Predictive Control, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.04.200
2
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 7 ) 1 e1 1
Nomenclature Vin C VCi.1,2 L iLi1,2 ig Vout Vgrid f Vpni P Lf rf D B Ts g lig lVc liL
input voltage capacitance of the qZS network capacitors capacitor voltages of the qZS network capacitors of cell i inductance of the qZS network inductors inductor currents of the qZS network inductors of cell i injected grid current output voltage grid voltage fundamental frequency DC-link voltage of cell i output power filtering inductor internal resistance of the filtering inductor shoot-through duty cycle boosting factor sampling time cost function weighting factor of the grid current constraint weighting factor of the capacitor voltage constraint weighting factor of the inductor current constraint
A number of papers have recently appeared in the scientific literature dealing with Multilevel Inverters (MLI) for small and large-scale RE plants. Among the most used MLI topologies are Modular Multilevel Converters (MMC), Diode Clamped multilevel Converters (DCC), T-type multilevel converter (TC), Packed U Cells (PUC) Multilevel Inverters, Flying Capacitors Inverters (FCI), and qZS multilevel converters. However, CHB multilevel converters are the most studied multilevel structures for RE systems [13e25]. In [13], authors propose a fault tolerant strategy to maintain balanced grid currents during faults with unequal power generation in healthy bridges, while [14] suggests a fully fuzzy logic controller/ modulator, mostly implemented in FPGA, for a single-phase configuration. A modulation for common mode voltage reduction is proposed in [15], while [16] suggests a strategy to overcome output voltage over modulation due to varied and non-uniform solar energy on segmented PV arrays. A fault tolerance strategy is implemented by several distributed algorithms to identify system operation in [17], while [18] provides modeling and analysis towards an improved grid power quality. [19] suggests a novel modulation for power balancing and [20,21] propose zero sequence injection method to counteract different power levels in the phases with providing reduced switching losses and high conversion efficiency. [22] compares delta and star grid connection of cascaded multilevel converters, [23] describe one of the most important feature a multilevel converter for PV applications needs to have such as an independent control of each dc-link voltages, enabling MPPT for each PV string, while [24] presents a transformer less connection to the grid. In [25], authors suggest a harmonic elimination modulation strategy optimized
with artificial neural networks for high performance PV connection. Moreover, [8,12,26e29] propose the use of quasiZ-Source (qZS)-CHB multilevel inverters for Grid connection of PV systems showing balanced dc voltage and voltage boost capabilities saving 30% of power modules compared to other structures. The qZS inverter (variant of the Z-sourced inverter) can provide voltage buck/boost and dc/ac conversion functionalities using an additional basic impedance (LC) network. This topology takes advantage of the shoot-through states to boost the input voltage and regulate the DC link voltage of the inverter. Moreover, when connected to H-Bridge inverters and cells are connected in series, the cascaded topology becomes very competitive and suitable for RE applications. In [8], authors propose a 1 MW grid-tied PV system consisting of a 3-phase 48-cell CHB inverter where each module is fed by a qZS network. [12] suggests a control strategy achieving grid-tie current injection, dc-link voltage balancing, and anti-islanding protection for the qZS structure. In [26], each PV connects to a qZS network designed to minimize the harmonic voltage and current ripple, while in [27] a modulation strategy is proposed for the same structure in order to minimize component losses. For the same topology, [28] proposes the inclusion of an energy storage system for each PV array to balance stochastic fluctuation of PV power, while [29] provides a comprehensive modeling and control design. In one hand, as any power electronics converter, the performance of the qZS-CHB inverter highly depends on the control properties. Good dynamics of the response must be followed by high accuracy of the reference tracking. With satisfying these requirements, the finite control set MPC technique is considered as an alternative method to classical linear controllers, having the capability to include constraints with different natures, dealing with nonlinearities, and easy to implement (no modulation stage) [30e32]. In the other hand, similar to the traditional single-phase inverter, the double-line frequency (2f) power flows through dc-link of the qZS-CHB inverter. This leads to 2f ripples on the dc-link and capacitor voltages and 2f inductors current ripples. Most particularly, high 2f inductor current ripples results in high hysteresis losses, which reduces the overall system efficiency. One way to minimize these current ripples is to use large qZS inductance that considerably increase the inverter size, weight, and cost. For that reason, using such system requires advanced control techniques to reduce or eliminate the 2f ripples. This paper proposes a multi-objective MPC for a grid connected 2-cell 5-level qZS-CHB inverter. The main contribution of the proposed control approach is the design of a multiconstraint cost function to achieve a multi-objective control strategy dealing with the complex nature of the presented qZS-CHB topology. The designed cost function takes into account three control objectives, which are the grid current, input current, and capacitors' voltages tracking errors. The multi-constraint errors minimization leads to the elimination of the double-line frequency 2*f power flow through the qZS inductors and in turn the reduction of the hysteresis losses and the increase of the overall system efficiency. The performance of the proposed MPC strategy is investigated and
Please cite this article in press as: Trabelsi M, et al., Performance enhancement of cascaded qZS-HB based renewable energy system using Model Predictive Control, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.04.200
3
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 7 ) 1 e1 1
Fig. 1 e Proposed 2-cell 5-level qZS-CHB inverter.
compared to the state of art PI controller. Theoretical analysis and implementation results are given to show that the proposed scheme is suitable for all system configurations and has good performances even during disturbances. The presented approach could be extended for qZS-CHB inverters with a large number of cells.
Theoretical study qZS-CHB topology and modelling Fig. 1 shows the proposed qZS-CHB inverter topology. In order to achieve the boost capability, the 5-level qZS-CHB inverter
Table 1 e All Possible Switching Patterns of the studied 2-cell qZS-CHB inverter. Switching state Non-shoot-through states
Shoot-through states
Vout 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
0
Vin
Vin
2Vin 2Vin Vin Vin 0
S11
S12
S13
S14
S21
S22
S23
S24
0 0 0 1 1 1 0 0 0 1 0 1 1 1 0 1 1 1 1
1 1 1 0 0 0 1 1 1 0 1 0 0 0 1 0 1 0 1
0 0 1 0 1 1 0 1 1 1 0 0 0 1 1 0 0 0 0
1 1 0 1 0 0 1 0 0 0 1 1 1 0 0 1 1 1 1
0 1 1 0 0 1 0 0 1 0 1 0 1 1 0 1 1 1 1
1 0 0 1 1 0 1 1 0 1 0 1 0 0 1 0 0 1 1
0 1 0 1 0 1 1 0 1 1 0 0 1 0 1 0 0 0 0
1 0 1 0 1 0 0 1 0 0 1 1 0 1 0 1 1 1 1
Please cite this article in press as: Trabelsi M, et al., Performance enhancement of cascaded qZS-HB based renewable energy system using Model Predictive Control, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.04.200
4
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 7 ) 1 e1 1
Fig. 2 e The equivalent circuit of the qZS network; (a) non-shoot-through state, (b) shoot-through state.
makes use of one more switching state (shoot-through state, where both switches in the same leg must be turned on at the same time) compared to the traditional 2-cell CHB inverter. The resulted switching states are illustrated in Table 1 (19 switching states are illustrated, 16 are common for any 2-cell CHB inverter, 1 for the shoot-through of the first cell, another one for the shoot-through of the second cell, and one more when the 2 cells are short-circuited). In the non-shoot-through state, the studied system can be illustrated by a constant current source (Fig. 2(a)). The derivations of the state variables iLi1, and Vci1 for each cell (i is the cell number) are obtained by (1) and (2). dVCi1 ¼ iLi1 ðtÞ ig ðtÞ ¼ iCi1 ðtÞ dt
(1)
diLi1 ¼ Vin VCi1 ðtÞ ¼ VLi1 ðtÞ L dt
(2)
C
In the other case (shoot-through state), the inverter is illustrated by a short-circuit of the dc-link voltage (Fig. 2(b)). The system equations for this state are given by (3) and (4).
C
dVCi1 ðtÞ ¼ iLi2 ðtÞ ¼ iCi1 ðtÞ dt
(3)
L
diLi1 ðtÞ ¼ VCi2 ðtÞ þ Vin ðtÞ ¼ VLi1 ðtÞ dt
(4)
In addition, according to Fig. 1, the output voltage Vout in terms of its current and filter parameters is given by: Vout ðtÞ ¼ Lf
dig ðtÞ þ rf ig ðtÞ þ Vgrid ðtÞ dt
(5)
The steady state capacitors and dc-link voltages can be obtained by (6) where B is the boosting factor and D is the shoot-through duty cycle. 8 > > > > > > > < > > > > > > > b pn :V
1D Vin 1 2D D Vin VCi2 ¼ 1 2D 1 Vin ¼ BVin ¼ VCi1 þ VCi2 ¼ 1 2D VCi1 ¼
(6)
Please cite this article in press as: Trabelsi M, et al., Performance enhancement of cascaded qZS-HB based renewable energy system using Model Predictive Control, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.04.200
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 7 ) 1 e1 1
5
minimizing the cost function g, for a predefined horizon in time N ¼ 1, subject to the model and the restrictions of the system. The result is a sequence of N optimal actuations. The objectives of the proposed controller are the regulation of the injected grid current, the maintain of the inductor currents in continuous mode with low ripples to reduce the input stress, and the regulation of the capacitors' voltages around the desired values, which in turn balances the dc-link voltage. The proposed MPC strategy predicts the tracking error of the next sampling for the sixteen possible switching patterns by calculating the cost functions. The proposed intuitive predictive approach consists of the below three main steps illustrated in Fig. 3 and the overall control scheme is shown in Fig. 4.
References generation In PV applications, the voltage references are usually generated through maximum power point tracking algorithm. However, the objective of this paper is the control performance of the qZS-CHB inverter using MPC. Thus, the reference dc-link voltage is defined according to the grid voltage magnitude (240 Vrms). On the other hand, the reference input (inductor) current is calculated according to the inverter power rating as i*L ¼ P/2Vin, where Vin and P are the input voltage and output power of the studied qZS-CHB inverter respectively.
Model prediction
Fig. 3 e Detailed description of the proposed MPC algorithm steps.
The digital implementation of the proposed control algorithm requires the use of a discrete-time model of the studied system. Since the proposed controller handles three control objectives, the predictive model makes use of three discrete-time equations. This paper employs the first-order approximation given in (7) for the prediction of the state variables at the (k þ 1) sample in terms of the measurements at the previous (k) sample as expressed by (8e10). It is worth noting that the expressions of iCi1(t) and VLi1(t) are calculated by (1e4) depending on the qZS network state (shoot-through in cell-1, cell-2, both cells, or non-shootthrough state) df ðtÞ f ðk þ 1Þ f ðkÞ ¼ dt Ts
Model Predictive Control In the current work, a Finite Control Set MPC (FCS-MPC) is implemented to control the power flow of the grid connected qZS-CHB topology. The FCS strategy is used instead of the Continuous Control Set one considering the finite number of output states of the converter. The proposed FCS-MPC considers the controlled plant as a finite set of linear models, each representing a physical switching state. The advantage of FCS-MPC is that concept is very simple and intuitive. Implementation is also simple especially in this study where the prediction horizon is selected to N ¼ 1 (low complexity). The proposed MPC is an optimization problem that consist of
Vci1 ðk þ 1Þ ¼ Vci1 ðkÞ þ
iLi1 ðk þ 1Þ ¼ iLi1 ðkÞ þ ig ðk þ 1Þ ¼
1
(7) Ts iCi1 ðtÞ C
Ts VLi1 ðtÞ L
rf Ts Ts ig ðkÞ þ Vout ðkÞ Vgrid ðkÞ Lf Lf
(8)
(9)
(10)
Cost function minimization In order to satisfy the control objectives, three terms are defined within the cost function given by (11). The first term in the cost function is responsible to minimize the error between
Please cite this article in press as: Trabelsi M, et al., Performance enhancement of cascaded qZS-HB based renewable energy system using Model Predictive Control, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.04.200
6
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 7 ) 1 e1 1
Fig. 4 e Control diagram for the control of the 2-cell qZS-CHB inverter. the reference and predicted grid current. The second term
Table 2 e System parameters. Parameters
Value
Total output power (Ptotal) AC grid RMS voltage (Vgrid) qZS inductances (L1, L2) qZS capacitances (C1, C2) Filtering inductance (L) Input voltage for qZS-HBI module (Vin) DC-link voltage reference V*pn Grid frequency (f)
1.2 kW 240 V 2.5 mH 4.7 mF 1 mH 150 V 240 V 50 Hz
handles the reference tracking of the capacitor voltage, while the third one minimizes the error between the reference and predicted inductor current values. 2 X * lVc Vc1 * Vci1 ðk þ 1Þ g ¼lig ig ig ðk þ 1Þ þ i¼1
þ
2 X
* liL iL1 iLi1 ðk þ 1Þ
(11)
i¼1
where the weighting factors lig, lVc, and liL are tuned to ensure the best performance scenario. As the priority targets are the smooth power injection to the grid (reduction of the grid current ripples) and the elimination of the double line frequency oscillations on the input current (reduction of high
Fig. 5 e Grid and inductor currents against their respective references using PI controllers. Please cite this article in press as: Trabelsi M, et al., Performance enhancement of cascaded qZS-HB based renewable energy system using Model Predictive Control, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.04.200
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 7 ) 1 e1 1
7
Fig. 6 e Grid and inductor currents against their respective references using tuned MPC controller.
Fig. 7 e Grid and inductor currents against their respective references using untuned MPC controller: effect of weighting factor (liL ¼ 0.5) on the performance of the inductor current tracking.
hysteresis losses), the weighting factors are tuned accordingly in order to satisfy the aforementioned goals.
Implementation results The proposed control algorithm has been implemented using a dSPACE dS1103 controller board. The parameters used in the implementation tests are given in Table 2. In order to show the
effectiveness of the proposed MPC controller in achieving the control goals, the transient and steady state performances were compared with those achieved using PI controllers (using a dual loop strategy). The upper part of Fig. 5 depicts the grid current tracking suitably its reference using PI controller. The lower parts shows that the inductor current is maintained in continuous mode with noticeable ripples. Similar to traditional single-phase inverter, the double-line frequency 2*f power flows through dc-link of the qZS-CHB inverter. This
Please cite this article in press as: Trabelsi M, et al., Performance enhancement of cascaded qZS-HB based renewable energy system using Model Predictive Control, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.04.200
8
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 7 ) 1 e1 1
Fig. 8 e Grid and inductor currents against their respective references using untuned MPC controller: effect of weighting factor (lig ¼ 0.25) on the performance of the grid current tracking.
Fig. 9 e PI controllers performances during a 100% step change of the reference current: grid and inductor currents are depicted.
leads mainly to a 2*f dc-link and capacitors voltages ripples and inductors currents ripple. The latter results mainly in high hysteresis losses, which reduces the overall system efficiency. One way to minimize these current ripples is to use large qZS source inductors that considerably increase the inverter size, weight, and cost. To overcome this problem, this work proposes a multi-objective MPC strategy where both inductors'
currents and capacitors' voltages are included as constraints in the cost function. The weighting factors lig, lVc, and liL are tuned to ensure the best performance scenario. Consequently, the lower part of Fig. 6 shows that the inductor current is maintained in the continuous mode and tracking its reference with very low current ripples allowing reducing the input stress. As the weighting factors used in the cost function have
Please cite this article in press as: Trabelsi M, et al., Performance enhancement of cascaded qZS-HB based renewable energy system using Model Predictive Control, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.04.200
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 7 ) 1 e1 1
9
Fig. 10 e MPC performance during a 100% step change of the reference Power: inductor current, grid current, and total power are depicted.
Fig. 11 e Grid synchronization results: PF, grid current, and grid voltage are depicted.
significant effect on the quality of the tracking processes, it is worth to illustrate this effect by varying the values if these weighting factors. Fig. 7 and Fig. 8 show the implementation results with different values of lig and liL. Notice that the grid and inductor currents tracking are degraded when less priority is given to lig and liL respectively. Fig. 9 and Fig. 10 show the transient state performances of both controllers during a step change of the power reference
from 50% to 100% of the rated value. As expected, MPC show very high dynamic performances in re-tracking the references (Fig. 10). The synchronization of the grid current with the grid voltage at the coupling point (unity power factor) is shown in Fig. 11. Finally, the upper part of Fig. 12 shows the 5-level output voltage with the grid voltage while the lower part shows the regulated DC-link voltage (240 V) and capacitor voltages.
Please cite this article in press as: Trabelsi M, et al., Performance enhancement of cascaded qZS-HB based renewable energy system using Model Predictive Control, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.04.200
10
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 7 ) 1 e1 1
Fig. 12 e qZS network and output voltages, Upper: 5-level output voltage waveform with the grid voltage, Lower: Regulated DC-link and capacitors voltages.
Conclusions A multi-objective MPC for grid-tied 2-cell 5-level qZS-CHB inverter was proposed in this paper. The main contribution of the proposed approach is the design of a multi-constraint cost function achieving a multi-optimization control dealing with the complex nature of the presented qZS-CHB topology. The designed cost function takes into account three control objectives, which are the minimizations of the grid current, input current, and capacitors' voltages tracking errors. In order to ensure the best control performances, the weighting factors were finely tuned within the cost function to minimize the grid current ripples as well as the double-line frequency ripples on the measured inductor current. Implementation results confirmed the significant effect of the optimal tuning on the controller performance. The transient and steady state performance of the proposed MPC strategy has been investigated and compared to the PI controller's one. Implementation results were given to show that the proposed scheme is ensuring smooth power injection to the grid under different operating conditions (high dynamic performances during disturbances) with reduction of the hysteresis losses (the inductor current is maintained in the continuous mode with very low current ripples) and the increase of the overall system efficiency.
Acknowledgement This work was made possible by NPRP-EP Grant no. X-033-2007 from the Qatar National Research Fund (a member of Qatar Foundation). The statements made herein are solely the responsibility of the authors.
references
[1] Nojavan S, Majidi M, Zare K. Risk-based optimal performance of a PV/fuel cell/battery/grid hybrid energy system using information gap decision theory in the presence of demand response program. Int J Hydrogen Energy 2017;42:11857e67. [2] Molina MG, Espejo EJ. Modeling and simulation of gridconnected photovoltaic energy conversion systems. Int J Hydrogen Energy 2014;39:8702e7. [3] Pacas JM, Molina MG, dos Santos Jr EC. Design of a robust and efficient power electronic interface for the grid integration of solar photovoltaic generation systems. Int J Hydrogen Energy 2012;37:10076e82. ndez LM, Jurado F. [4] Garcı´a CA, Llorens F, Garcı´a P, Ferna Improving voltage harmonic compensation of a single phase inverted-based PEM fuel cell for stand-alone applications. Int J Hydrogen Energy 2014;39:4483e92. [5] Seyezhai R, Mathur BL. Modeling and control of a PEM fuel cell based hybrid multilevel inverter. Int J Hydrogen Energy 2011;36:15029e43. [6] Ozdemir S. Z-source T-type inverter for renewable energy systems with proportional resonant controller. Int J Hydrogen Energy 2016;41:12591e602. [7] Trabelsi M, Bayhan S, Metry M, Abu-Rub H, Ben-Brahim L, Balog R. An effective Model Predictive Control for grid connected Packed U Cells multilevel inverter. In: IEEE Power and Energy Conference at Illinois (PECI), Urbana, IL; 2016, pp. 1e6. [8] Trabelsi M, Abu-Rub H, Ge B. 1-MW quasi-Z-source based multilevel PV energy conversion system. In: IEEE International Conference on Industrial Technology (ICIT), Taipei; 2016, pp. 224e229. [9] Bayhan S, Trabelsi M, Abu-Rub H. Model Predictive Control of Z-Source four-leg inverter for standalone Photovoltaic system with unbalanced load. In: IEEE Applied Power Electronics Conference and Exposition (APEC), Long Beach, CA; 2016, pp. 3663e3668.
Please cite this article in press as: Trabelsi M, et al., Performance enhancement of cascaded qZS-HB based renewable energy system using Model Predictive Control, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.04.200
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 7 ) 1 e1 1
[10] Trabelsi M, Bayhan S, Ghazi KA, Abu-Rub H, Ben-Brahim L. Finite-control-set model predictive control for gridconnected packed-U-cells multilevel inverter. IEEE Trans Ind Electron Nov. 2016;63(11):7286e95. [11] Ramos-Hernanz J, Lopez-Guede JM, Barambones O, Zulueta E, Fernandez-Gamiz U. Novel control algorithm for MPPT with Boost converters in photovoltaic systems. Int J Hydrogen Energy 2017. http://dx.doi.org/10.1016/ j.ijhydene.2017.02.028. [12] Trabelsi M, Abu-Rub H. A unique active anti-islanding protection for a quasi-Z-Source based Power Conditioning System. In: 2015 IEEE applied power electronics conference and exposition (APEC), Charlotte, NC; 2015. p. 2237e43. [13] Yu Y, Konstantinou G, Hredzak B, Agelidis VG. Operation of cascaded H-Bridge multilevel converters for large-scale photovoltaic power plants under bridge failures. IEEE Trans Ind Electron 2015;62(11):7228e36. [14] Cecati C, Ciancetta F, Siano P. A multilevel inverter for photovoltaic systems with fuzzy logic control. IEEE Trans Ind Electron 2010;57(12):4115e25. [15] Selvamuthukumaran R, Garg A, Gupta R. Hybrid multicarrier modulation to reduce leakage current in a transformerless cascaded multilevel inverter for photovoltaic systems. IEEE Trans Power Electron 2015;30(4):1779e83. [16] Liu Liming, Li Hui, Xue Yaosuo, Liu Wenxin. Decoupled active and reactive power control for large-scale gridconnected photovoltaic systems using cascaded modular multilevel converters. IEEE Trans Power Electron 2014;30(1):176e87. [17] Nguyen Luan Viet, Tran Hoang Dung, Johnson TT. Virtual prototyping for distributed control of A fault-Tolerant modular multilevel inverter for photovoltaics. IEEE Trans Energy Convers 2014;29(4):841e50. [18] Alexander A, Thathan M. Modelling and analysis of modular multilevel converter for solar photovoltaic applications to improve power quality. Renew Power Gener IET 2014;9(1):78e88. [19] Yifan Yu, Konstantinou G, Hredzak B, Agelidis VG. Power balance of cascaded H-Bridge multilevel converters for largescale photovoltaic integration. IEEE Trans Power Electron 2016;31(1):292e303. [20] Islam MR, Youguang Guo, Jianguo Zhu. A multilevel medium-voltage inverter for step-up-transformer-less grid connection of photovoltaic power plants. IEEE J Photovoltaics 2014;4(3):881e9. [21] Yu Y, Konstantinou G, Hredzak B, Agelidis VG. Power balance optimization of cascaded H-Bridge multilevel converters for
[22]
[23]
[24]
[25]
[26]
[27]
[28]
[29]
[30]
[31]
[32]
11
large-scale photovoltaic integration. IEEE Trans Power Electron 2016;31(2):1108e20. Sochor P, Akagi H. Theoretical comparison in energybalancing capability between star- and delta-configured modular multilevel cascade inverters for utility-scale photovoltaic systems. IEEE Trans Power Electron 2015. Volume: PP, Issue: 99, Pages: 1 1, [IEEE Early Access Articles]. Xiao Bailu, Hang Lijun, Mei Jun, Riley Cameron, Tolbert Leon M, Ozpineci Burak. Modular cascaded H-Bridge multilevel PV inverter with distributed MPPT for grid-connected applications. IEEE Trans Ind Appl March/April 2015;51(2). Zhou Yan, Li Hui. Analysis and suppression of leakage current in cascaded-multilevel-inverter-based PV systems. IEEE Trans Power Electron October 2014;29(10). Filho Faete, Tolbert Leon M, Cao Yue, Ozpineci Burak. Realtime selective harmonic minimization for multilevel inverters connected to solar panels using artificial neural network angle generation. IEEE Trans Ind Appl September/October 2011;47(5). Sun Dongsen, Ge Baoming, Yan Xingyu, Bi Daqiang, Zhang Hao, Liu Yushan, Abu-Rub H, Ben-Brahim L, Peng Fang Zheng. Modeling, impedance design, and efficiency analysis of quasi-Z-source module in cascaded multilevel photovoltaic power system. IEEE Trans Ind Electron 2014;61(11):6108e17. Liu Yushan, Ge Baoming, Abu-Rub H, Peng Fang Zheng. Phase-shifted pulse-width-amplitude modulation for quasiZ-source cascade multilevel inverter-based photovoltaic power system. Power Electron IET 2014;7(6):1444e56. Sun Dongsen, Ge Baoming, Liang Weihua, Abu-Rub H, Peng Fang Zheng. An energy stored quasi-Z-source cascade multilevel inverter-based photovoltaic power generation system. IEEE Trans Ind Electron 2015;62(9):5458e67. Liu Yushan, Ge Baoming, AbuRub H, Peng Fang Zheng. An effective control method for three-phase quasi-Z-source cascaded multilevel inverter based grid-tie photovoltaic power system. IEEE Trans Ind Electron 2014;61(12):6794e802. Rodriguez J, Kazmierkowski MP, Espinoza JR, Zanchetta P, Abu-Rub H, Young HA, et al. State of the art of finite control set model predictive control in power electronics. IEEE Trans Ind Inf 2013;9:1003e16. Trabelsi M, Ben-Brahim L, Ghazi KA. An improved Real-Time Digital Feedback Control for grid-tie multilevel inverter. In: The 39th Annual Conference of the IEEE Industrial Electronics Society (IECON), Vienna; 2013, pp. 5776e5781 Trabelsi M, Ghazi KA, Al-Emadi N, Ben-Brahim L. An original controller design for a grid connected PV system. In: The 38th Annual Conference on IEEE Industrial Electronics Society (IECON), Montreal, QC; 2012, pp. 924e929.
Please cite this article in press as: Trabelsi M, et al., Performance enhancement of cascaded qZS-HB based renewable energy system using Model Predictive Control, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.04.200