An Exact Linearization Method for DC-Side Controllers of Z-Source Inverters in Grid-Tied PV System Applications

Nội dung text: An Exact Linearization Method for DC-Side Controllers of Z-Source Inverters in Grid-Tied PV System Applications

1. JST: Smart Systems and Devices Volume 31, Issue 1, May 2021, 132-139 An Exact Linearization Method for DC-Side Controllers of Z-Source Inverters in Grid-Tied PV System Applications Vu Hoang Phuong, Nguyen Manh Linh* Hanoi University of Science and Technology, Hanoi, Vietnam *Email: linh.nguyenmanh@hust.edu.vn Abstract This paper presents a new control strategy for grid-connected Z-source inverter which is a part of the residential photovoltaics (PV) system. The control system consists of a DC control loop, which is designed based on the exact linearization method to guarantee that the DC input voltage of the ZSI quickly tracks the reference value which is given by the maximum power point tracking (MPPT) algorithm. By using the proposed control strategy, the maximum power is delivered to the grid despite the variety of environmental temperature and solar irradiation. The effectiveness of the proposed control strategy is verified by simulation using Matlab/Simpower systems under various operating conditions of the PV. Keywords: Z-source inverters (ZSI), grid-tied PV system, an exact linearization method 1. Introduction energy. To achieve a high voltage and power for a grid-tied application, multiple PV modules are A*practical photovoltaics (PV) system includes connected in series and parallel. In [1], the I-V multiple arrays connected in parallel and series to characteristic of a PV system is given as follows: achieve sufficient output voltage and power. For an inverter-based PV system that injects power into the Nss vpv + Ris pv grid, the power electronics control is responsible for N keeping the DC-link voltage at the input of the inverter i= Ni−− Niexppp 1 pv pp ph pp 0 N va at a constant and suitable value so that the injected ss t power to the grid is maximum under different PV  operating conditions. This paper presents a control (1) N strategy for a grid-tied Z-source inverter (ZSI) for PV v+ ss Ri pv N s pv system applications. A ZSI has a unified structure with − pp both buck-boost capabilities, and its advantages N ss R compared to other inverter configurations are discussed p N pp in [3,5] The model of a PV system is also based on (1). The control scheme at the DC-side of the ZSI is designed based on an exact linearization approach. The model of the ZSI is shown in Fig. 1. It is This proposed method guarantees that the input voltage assumed that the Z-source impedance network is of the ZSI closely tracks the output reference value symmetrical, i.e., iL = iL1 = iL2; uC = uC1 = uC2. The provided by the maximum-power-point-tracking average models of the Z-source in dTs and (1-d) Ts (MPPT) algorithm of the PV. Therefore, the power periods are shown in Fig. 1b and Fig. 1c. By injected into the grid is always at its maximum value combining these average models, the average model under varying conditions of temperature and solar of the ZSI in one cycle Ts is shown in (7). irradiance. The exact linearization effectively handles The average model of the system in Fig. 1b is the nonlinear characteristics in the model of the ZSI- given as follows: based PV system, which improves the control quality of the entire system compared to the existing works in dtx( ) [4-6]. K= Ax11(tt) + Bu( ) dt 2. The Modelling of ZSI and PV L 00 iiLL010    00 A PV module consists of multiple PV cells, d    ipv 0Cu 0 CC=−+100  u 00 which are semiconductor components that have p-n dt   i    inv junction, which converts solar energy to electrical 00Cpv uupv 000  pv  10 (2) ISSN: 2734-9373 Received: September 17, 2020; accepted: January 15, 2021 132
2. JST: Smart Systems and Devices Volume 31, Issue 1, May 2021, 132-139 ipv idc iL idc idc_2 s L1 D iC C1 C2 u inverter pv Cpv S iinv PV t ic i CS_2 L2 a) ipv iL ipv Idc_s2 iL t L1 L1 i iC_S1 iC_S2 CS_1 C2 C1 C1 C2 iL i upv C upv C L pv PV pv iinv PV L2 L2 dTs (1-d)Ts t Ts b) c) d) Fig. 1. Model at the dc side of the ZSI a) Equivalent dc-side circuit of the ZSI connected to PV, b) shoot-through state c) non-shoot-through state, d) currents flowing in ZSI components. The average model of the system in Fig. 1c is By combining (2) and (6), the average model of given as follows: the model in Fig. 1a is given as follows:  di dtx( ) L = − L uupv C K=d A12 +−(1 dt) Ax( )  dt dt  du C +dB12 +−(1 dt) Bu( ) C= iiL − inv (3)  dt  du L 00 iL Cpv = ii − d   pv pv dc_2 s =  dt 00CuC dt The average current flowing in the capacitors  00Cpv u pv is zero in each cycle. In Fig. 1d, the average value of (7) 0 2dd−− 11 the current idc-s2 is shown as follows: ( ) ( ) iL 00 ipv − +− (12d) 0 0 udC  0( 1)  idc_2 s= ii L + C_ S 2  iinv  (4) −1 0 0u  10 =−+− = pv  iCL di(10 d) iCS_2 The model in (7) is the foundation to design the or: control for the DC side of the ZSI and is a bilinear  i = L characteristic. The bilinearity of the (7) is idc_2 s  1− d characterized by the multiplication between control  (5) di signal d and state variable x, hence the system requires i = L  CS_2 1− d a nonlinear control solution. In this paper, we present an approach of using an exact linearization method to From (3) and (5), the average model of the ZSI design the control for the voltage control loop at the is derived as follows: DC side of the ZSI. dtx( ) K= Ax(tt) + Bu( ) 3. Controller Design dt 22 The control structure of a grid-tied ZSI-based PV  system is shown in Fig. 2. L 0 0 ii0− 11 0 0 LL i d  pv The control loops at the AC side have the 0Cu 0 CC=0 00u+− 0 1 dt i inv setpoints equal to the reference voltage uc_ref and 00Cpv uupv 1 pv 1 0 − 00 power factor by regulating the current components isq. 1− d On the other hand, the control loop at the DC side has (6) the reference value equal to the output of the MPPT 133
3. JST: Smart Systems and Devices Volume 31, Issue 1, May 2021, 132-139 algorithm. The control variable is the duty cycle d to The structure of the current control loop identifies the achieve the MPP in the I-V characteristic of the PV. reference voltage vector us, which is given as follows: 3.1. AC-Side Controller  Ls T usd ( k+=1)  ykd ( ) + eknd ( + 1) The control loop at the AC side is responsible for TLs  keeping the DC-link capacitor voltage constant as well  (9)  L T as regulating the power factor of the PV system. The +=s + + usq ( k1)  ykq ( ) eknq ( 1) output of the current loop is the reference signal for  TLs the modified space-vector modulation index (MSVM). where the output y is given as follows: To reduce the size of the output filters, the MSVM is calculated with the shoot-through state divided into 6  TR yk=  ikik -  - 1-s ik -1 - ik -1  equal sectors for 6 different switching combinations.  d ( ) sd( ) sd ( ) sd ( ) sd ( )   Ls In addition, to guarantee that the output current is in  ω Tikik* + yk-2 phase with the grid current, isq is set to zero. To s sq( ) sq ( ) d ( )  regulate the power factor of the system, the power TR   s  factor control loop is designed based on the following ykq ( ) = ikiksq( ) - sq ( ) - 1- iksq ( -1) - iksq ( -1)   L  equation:  s ++ω *  sTikik sd( ) - sd ( ) ykq ( -2) iisq sq sinϕ = = (8) (10) i 22 s iisd+ sq The outer dc-voltage loop is responsible for To improve the dynamic performance of the regulating the capacitor voltage uC across capacitors system, this paper uses current loops that are of dead- C1 and C2 in the impedance network. The dc-voltage beat type [7]. The synchronization with the grid controller is designed as a conventional PI controller voltage is achieved by the phase-lock-loop (PLL) [9]. in the s domain. Fig. 2. The control of a Z-source inverter in grid-tied PV system applications 134
4. JST: Smart Systems and Devices Volume 31, Issue 1, May 2021, 132-139 3.2. DC-Side Controller Because x2 ≠ 2uC so that LLghf (x) ≠ 0 . The The voltage control loop at the DC side is modeling of DC-side of ZSI thus has relative order responsible for assuring the output voltage of the PV r = 2 in the state space. Therefore, it is exactly module to follow the reference value identified by the linearized using feedback state-space control as MPPT algorithm. The voltage controller is designed follows: using the exact linearization method discussed in [10]. = + With this approach, (11) become linear in the state up(xx) q( ) w (14) space, as shown below: where 2 dx Lgf (x) xU2 − C  =fx() + hx ()u p(x) =−=; (11)  dt LLghf (x) x2 − 2 UC  = (15) yg()x 1 L q(x) = = The voltage uC is kept constant by the voltage LLghf (x) x2 − 2 UC control loop shwn in Section 3.1. Equation (7) is rewritten under the form of (11) with functions f(x), With the feedback state-space control (4), h(x), u, and g(x) specified in (12). The variable vector system (11) becomes linear as follows: T T T x = [x1 x2] = [iL upv] dz 01   0 =+=Az Bww z + −     xU2 C  dt 00   1 (16)  2Ux− L C 2  = = =  yz1 fx( ) − ;;hx( ) L ixpv 1  (12)  0 C where the relation between the new state vector z and pv old state vector x is given as follows: g(x) = x2 ; ud = x2 z g (x)  1 − The Lie derivation is studied to check relative z = = = ixpv 1 (17) z2 Lg(x) f C order of model (11). pv −2Ux From (11), the control for the input variable ω in ∂g C 2 (16) is given as follows: Lg = = 01= 0  h (x) hx( ) [ ] L ∂x  2  0 ω=−2 ξωnny − ω ( yy −=)  (18) xU−  2 C −−kz22 k 1( z 1 − Upv _ ref )   ∂g L ixp − 1 Lg(x) = fx( ) = [01]= f ix− where ωn is the natural frequency and ξ is the  ∂x p 1 Cpv   damping ratio of the second-order system Cpv  From (14) and (18), the shoot-through control  ∂Lg(x) LLg(x) = f hx( ) variable is determined as follows:  hf ∂x  xU− 2Ux− =2 C −  C 2 (13) u xU2 − 2 C xU− 2  =[−=10] 2 C L (19)  L −  0 L ixpv 1 kx12( −+ Upv _ ref ) k 2  xU− 2 C 2 ∂Lgf (x) 2 C pv Lg(x) = fx( )  f ∂x  3. Simulation results xU2 − C    L − To demonstrate the effectiveness of the UxC 2  =[−=10] proposed controller, ZSI in a grid-tied PV system is ixpv − 1 L   simulated under different operating conditions using  Cpv Simpower Systems Toolbox in Matlab/Simulink. The simulation parameters of the grid-tied ZSI-based PV system are given in Table 1. The PV module used in this simulation is SQ160/Shell [12]. 135
5. JST: Smart Systems and Devices Volume 31, Issue 1, May 2021, 132-139 Table 1. ZSI parameters voltage and current at the MPP are identified from the characteristic curve of the Sell – SQ160 PV module ZSI output voltage 380 V/50 Hz specifications under different operating conditions shown in Table 2. DC-link reference 570 V Temperature T = 25 0C when t 0.3 s and solar irradiance G = 1000 W/m2. The simulation results in this case Switching frequency 5 kHz are shown in Fig. 4. 2 Z-source impedance L=1.4 mH; C=235 àF The solar irradiance G = 1000W/m within 2 network t 0.3s and the temperature T = 25 0C. The simulation results in this case are shown in Fig. 5. Cpv 470 àF The simulation results in Fig. 4 and Fig. 5 show Grid-side inductor 2mH the input DC voltage of the ZSI always maintains at the value corresponding to the MPP under different Parameters of the ωn = 10rad/s, ξ = 0.71 operating conditions in Table 2. The voltage across second order system the capacitors C1 and C2 are kept at 570 V and the total harmonic distortion (THD) of the grid-side Table 2. The values of Vmp and Imp under different current ig is 3.09%. operating conditions. 5. Conclusion Operating conditions Vmp Imp Pmp The paper presents a detailed DC-side model (W) and a control strategy for grid-tied ZSI-based PV 0 systems, which is the foundation to develop other T = 25 C, 280V 45.8A 12824 control strategies for the PV system under different G = 1000W/m2 operating conditions. The simulation results in Matlab verify the efficacy of the proposed exact T = 50 0C, 248V 45A 11160 linearization method, which guarantees that the ZSI input DC voltage closely tracks the reference value 2 G = 1000W/m from the MPPT algorithm. T = 25 0C, 278V 23A 6394 Acknowledgement G = 500W/m2 This research is funded by the Hanoi University of Science and Technology (HUST) under project Assume that the PV system includes 8 identical number T2020-SAHEP-004. PV modules in series and 10 identical PV modules in parallel, which have similar operating conditions. The z = Az + Bω  y = Cz T  y 0 ω [kk12] d dx x y up=(xx) + q( )ω =fx( ) + hx( )d g (x) dt g (x) z  Lgf (x) Fig. 3. The DC side controller a Z-source inverter in grid-tied PV system applications 136
6. JST: Smart Systems and Devices Volume 31, Issue 1, May 2021, 132-139 350 800 700 300 600 500 Uc (V) Upv(V) 400 250 300 200 200 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.2 0.25 0.3 0.35 0.4 0.45 0.5 t(s) t(s) b. Voltage across C1 & C2 a. Output PV voltage 50 80 45 70 40 60 35 50 30 40 Ipv (A) iL(A) 25 30 20 20 15 10 10 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0 t(s) 0.2 0.25 0.3 0.35 0.4 0.45 0.5 t(s) c. Output PV current d. Current in L1 & L2 40 30 20 10 0 iS (A) iS -10 -20 -30 -40 0.2 0.25 0.3 0.35 0.4 0.45 0.5 t(s) e. Output current of ZSI f. Harmonic spectrum of the grid-side current ig 0.5 1 0.9 0.45 0.8 0.4 0.7 0.6 0.35 dsh 0.5 0.4 0.3 0.3 0.25 0.2 0.1 0.2 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0 t(s) 0.2 0.202 0.204 0.206 0.208 0.21 0.212 0.214 0.216 0.218 0.22 g. Shoot-through duty ratio t(s) h. Waveforms of space vector modulation Fig. 4. Simulation results of the system when T changes from 25 to 50°C at t = 0.3 s, G = 1000 W/m2 137
7. JST: Smart Systems and Devices Volume 31, Issue 1, May 2021, 132-139 350 800 700 300 600 500 Upv (V) Uc (V) 250 400 300 200 200 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.2 0.25 0.3 0.35 0.4 0.45 0.5 t(s) t(s) a. Output PV voltage b. Voltage across C1 & C2 60 80 55 70 50 60 45 50 40 35 40 iL (A) Ipv (A) 30 30 25 20 20 10 15 10 0 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.2 0.25 0.3 0.35 0.4 0.45 0.5 t(s) t(s) c. Output PV current d. Current in L1 & L2 40 400 Ua Ia (x3) 30 300 20 200 10 100 0 0 iS (A) iS Ua (V), Ia (A) -10 -100 -20 -200 -30 -300 -40 -400 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.2 0.25 0.3 0.35 0.4 0.45 0.5 t(s) t(s) e. Output current of ZSI f. Phase A grid voltage and current 0.5 1 0.9 0.45 0.8 0.7 0.4 0.6 0.35 0.5 dsh 0.4 0.3 0.3 0.2 0.25 0.1 0.2 0 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.2 0.202 0.204 0.206 0.208 0.21 0.212 0.214 0.216 0.218 0.22 t(s) t(s) g. Shoot-through duty ratio h. Waveforms of space vector modulation Fig. 5. Simulation results of the system when G changes from 1000 W/m2 to 500 W/m2 at t = 0.3 s, T= 250C 138
8. JST: Smart Systems and Devices Volume 31, Issue 1, May 2021, 132-139 References [6] Antoneta Iuliana Bratcu, Iulian Munteanu, Seddik Bacha, Bertrand Raison, Maximum Power Point [1] M. G. Villalva, J. R. Gazoli, E. Ruppert F., Modeling Tracking of Grid-connected Photovoltaic Arrays by and circuit - based simulation of photovoltaic arrays, Using Extremum Seeking Control, Journal of Control COBEP'09 Power Electronics Conference, 2009, Engineering and Applied Informatics (CEAI) Vol.10 Brazilian. No. 4 pp. 3-12 2008. [7] Phung, Q.N., Jorg-Andreas, D., Vector control of [2] Trishan Esram, Patrick L. Chapman, Comparison of three-phase AC machines, Springer, Berlin– Photovoltaic Array Maximum Power Point Tracking Heidelberg, 2008 Techniques, IEEE Transaction of energy conversion, vol 22, no.2, June 2007. [8] Tran Trong Minh, Vu Hoang Phuong, Analysis of switching patterns in space vector modulation method for Z source inverter, pp 1-6, No. 91, Journal of [3] Fang Zheng Peng, Z-source inverter, IEEE Science & Technology Technical Universities, 2013. transactions on industry applications, vol.39, no.2, March/April, 2003. [9] N. Hoffmann, R. Lohde, M. Fischer and F. W. Fuchs, L. Asiminoaei, P.B. Thứgersen, A Review on Fundamental Grid-Voltage Detection Methods under [4] Po XU, Xing ZHANG, Chong-wei ZHANG, Ren- Highly Distorted Conditions in Distributed Power- xian,CAO and Liuchen CHANG, Study of Z-Source Generation Networks, Energy Conversion Congress Inverter for Grid-Connected PV Systems, PESC'06 and Exposition (ECCE), 2011 IEEE. th Power Electronics Specialists Conference, 2006, 37 IEEE. [10] Khalil, Nonlinear Systems, 3rd Edition, Prentice Hall, [5] Xiaogao Chen, QingFu, David Infield, Shijie YU, Upper Saddle River, 2002. Modeling and Control of Z-Source Grid-connected PV System with APF Function, Universities Power [11] Hebertt Sira-Ramớrez and Ramún Silva-Ortigoza, Engineering Conference (UPEC) 2009, Proceedings Control Design Techniques in Power Electronics of the 44th International. Devices, Springer-Verlag London Limited 2006. [12] Product Information Sheet, Sell - SQ160, 139