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2016 China International Conference on Electricity Distribution (CICED 2016) Xi’an, 10-13 Aug, 2016 Grid-connected PV system modeling and control based on the variable step size of MPPT algorithm Li Cuiping1, Zhuo Junwu1, Li Junhui1, Yao Zhizhong2 (1. School of Electrical Engineering, Northeast Dianli University, Jilin 132012, Jilin Province, China;2. Jilin Electric Power Co.,Ltd.,Changchun 130021, China;) observation (P&O), and incremental conductance(INC) Abstract—Based on two kinds of maximum power point tracking (MPPT), this paper proposed an improved variable step size incremental conductance algorithm which combined with constant voltage tracking. The operating point of PV array is located near the maximum power point (MPP) rapidly by using the fixed voltage method, and the PV array is controlled to run at the MPP quickly and accurately adopting different disturbance step. Grid-connected inverter adopts the double closed-loop control strategy of based on feed-forward decoupling to realize the decoupling control of active and reactive power. In PSCAD/EMTDC, the model of grid-connected photovoltaic system (GCPS) has been implemented and verified the effectiveness of the improved MPPT algorithm. Index Terms—Constant voltage tracking, Variable step incremental conductance method, Modeling gridconnected photovoltaic system, feed-forward decoupling, double closed-loop control I. I NTRODUCTION method. Due to these three methods have some shortcomings, the improved MPPT control method are often constructed at present. In [5], Xiong Yuansheng combined CVT and P&O to solve the disadvantages of CVT that ignores temperature change, and reduced the oscillation near the MPP. In [6], Jiao Yang combined CVT with INC of duty ratio perturbation MPPT algorithm which improved the power tracking speed and precision, and lowered power disturbance at the same time. In [7], Chen Yaai proposed a gradient variable step size perturbation and observation method which based on gradient optimizing ideology. In the optimizing process, the step size can be changed automatically with the slope of P-U characteristic curve, therefore by increasing optimizing efficiency. The photovoltaic system simulation model is established Solar energy is one of the most dominant renewable in the PSCAD/EMTDC software. Based on the traditional energy. By the end of 2015, total installed capacity of INC, this paper proposed the method of combining the Chinese photovoltaic generation is 43.18GW, of which open circuit voltage with variable step INC, and verify the distributed photovoltaic account for about 14%. During effectiveness of the proposed method. Several dynamic the 13th Five Year Plan, the installed targets of PV is performance of photovoltaic power generation systems is 150GW, and distributed photovoltaic generation will evaluated from the aspects of power control, current break through 46% of the total. With the rapid harmonic. development of photovoltaic power generation, II. MODELING AND CHARACTERISTIC distributed photovoltaic power generation has a broad RESEARCH OF PHOTOVOLTAIC PANELS application prospect[1]. Due to the high cost of PV modules, we need to improve A. The mathematical model of PV pane the efficiency of the photovoltaic array as much as Consider diode characteristics of PV panels, Fig. 1 can be possible. The output voltage, current, power of PV array used as equivalent circuit to describe. A series resistor Rs which are influenced by the external environment show and parallel resistor Rsh are used as being equivalent to the nonlinear characteristics. So we need to adjust the load loss of panels. characteristics of the PV array to work at MPP in real time, and the MPPT technology is the key to improve the efficiency of photovoltaic power generation[2-3]. Conventional MPPT control methods mainly include: constant voltage tracking(CVT)[4], perturbation and CICED2016 Session 3 Paper No 1 Page /6 2016 China International Conference on Electricity Distribution (CICED 2016) expressed Rs series modules (N S) and parallel modules(NP) . IL Rsh Id Isc by Xi’an, 10-13 Aug, 2016 V I L N P I SC 1 C1 exp( ) 1 N s C2VOC V (4) When external irradiance and temperature changes, we can calculate Isc、Voc、Im、Vm under the common condition Fig.1 photovoltaic battery equivalent circuit As shown in Fig.1, the I-V equation of photovoltaic panels according to Isc,ref、Voc,ref、Im,ref、Vm,ref under the standard may be written as Eq.(1) condition. I L I SC q(V I L Rs ) (V I L Rs ) (1) I 0 exp 1 AKT Rsh T T Tref IL is the load current; V is the load voltage of the battery; ISC is the excitation current S which depends on solar irradiance S and cell temperature t; I0 is the saturation current of the PV panels without light; T is the absolute temperature ; q is the electronic charge(1.6×10-19C); K I sc,ref I sc is the Boltzmann’s constant (1.38×10-23J/K); A is the constant factor (when positive bias voltage is high, A is equal to 1). 1 S (1 aT ) Sref (6) (7) (8) S I m I m (1 T ) Sref (9) Vm Vm (1 T ) ln(1 S ) (10) PV cells is very small and Rsh is big. Eq.(1) can be simplified as Eq.(2) : (2) S ref Voc Voc (1 T ) ln(1 S ) Generally, (V+IL·Rs)/Rsh can be ignored because the Rs of q(V I L Rs ) I L I SC I 0 exp 1 AKT S (5) The typical values of α、β、γ are α=0.0025/℃,β=0.5, Eq. (2) ignored the Rsh, its deviation with real PV cell is γ=0.00288/℃. very small, so it can express the role of the irradiance and Based on the Eq.(3)-(10), build the simulation model of [8] temperature in essence . photovoltaic panels, its output as shown in Fig.2. Overall, B. Engineering mathematics model of PV panels photovoltaic panels are affected by the changes of Above Eq.(1) and (2) belong to a transcendental equation irradiance more than affected by temperature changes. At and the solution of equation is very difficult. When we do the same time the P-V curve shows that in a given the actual engineering calculation, we make use of short irradiance and temperature conditions, photovoltaic circuit current Isc, open circuit voltage Voc, the current Im panels have an unique MPP. and the voltage Vm of MPP which are from photovoltaic cell manufacturer tests under standard condition(t=25 ℃ ,S=1000W/m ). So to simplify the 2 Eq.(2) : V I L I SC 1 C1 exp( ) 1 C V 2 OC (3) Im -Vm Im Im -1 Where C1=1- ·exp , C2= -1·ln(1- ) Isc Isc C2Voc Isc PV array is consists of a series parallel modules. Based on the Eq.(4) and Fig.1, the PV array output current IL can be CICED2016 Session 3 Paper No 2 Page /6 2016 China International Conference on Electricity Distribution (CICED 2016) 10 Variable step conductance increment method is on the 300 1000W/m2 800W/m2 600W/m2 250 8 Xi’an, 10-13 Aug, 2016 basis of Eq. (13), to calculate the tangent slope absolute 200 I(A) P(W) 6 4 1000W/m2 800W/m2 600W/m2 2 value (k = |A1*dP/dU|) of the working point, as a 150 100 coefficient of disturbance step. Far from the MPP, the 50 0 0 10 20 V(v) 30 0 0 40 (a) 300 8 250 30 40 disturbance step size are small also to enhance the tracking precision. Specific work process is shown in Fig.3. P(W) 150 15℃ 25℃ 35℃ 4 100 2 value of the |dP/dU| and perturbation step length are big to improve the tracking speed. Near the MPP, | dP/dU | and 200 t=15℃ t=25℃ t=35℃ I(A) 20 V(v) t=25℃ 10 6 10 Start 50 0 0 10 20 V(v) 30 40 0 0 10 20 V(v) 30 Sample T,V,I Vref=0.79*Voc 40 Caculate dT=T(k)-T(k-1) (b) S=1000W/m2 Voc'=Voc-Voc*K*dT Fig.2 The I-V and P-V curve of PV cells under different Y | T(k)-Tref |>ε environmental conditions N III. VARIABLE STEP INCREMENTAL Caculate dV=V(k)-V(k-1) dI=I(k)-I(k-1) CONDUCTANCE METHOD OF MPPT CONTROL k=|A1*dP/dU)| STRATEGY step=k*step The photovoltaic cell P-V curves show that under different environmental conditions, the VM of PV array is approximately proportional to change when the Voc of PV array change. Approximate linear relationship exists between Vm and Voc, namely VM≈k1×Voc, in this paper k1=0.78*Voc is affected by illumination change slightly and is influenced by the temperature change strongly. When the temperature change is big, Voc is updated by online calculation. By adopting online open circuit voltage correction method, Voc can be updated through testing environment changes, and then multiply the approximate proportionality factor, the VM can be calculated roughly. According to Eq.(8), select the proper temperature correction coefficient K. According to Eq.(11), the Voc' can be calculated approximately under the new environment. Voc Voc Voc K T (11) Power curve is single peak function in the whole voltage range. At the maximum power point voltage dP/dU = 0, on both sides of the Vm are opposite, and the farther the distance from MPP is, the greater the value of | dP/dU | becomes. At the MPP, dP/dV should be zero and the sign of dP/dV may be identified by Eq. (12). Y Y (12) N dI/dV=-I/V I(k)-I(k-1)=0 N dI/dV>-I/V N Y Vref=Vref+step Y N I(k)-I(k-1)>0 N Y Vref=Vref-step Vref=Vref+step Vref=Vref-step Return Fig.3 The flow chart of variable step conductance increment method Ⅳ. CONTROL STRATEGY OF INVERTER The PV inverter consists of a diode, a dc-link capacitor, a voltage source inverter (VSI) with a harmonic reduction filter and a step-up transformer, as shown in Fig.5. i2 ipv S1 S3 S5 ic + Linv udc ia ib ic Cdc S4 O dP dI I U 0 dU dU V(k)-V(k-1)=0 S6 iga igb igc S2 Cinv Fig.5 Circuit model of a grid connection inverter The design of the PV inverter control system uses double In practical application, dI/dU is replaced by △I/△U, and closed-loop control structure. The outer loop on the compare the conductance of the working point (I/U) and voltage of dc-link capacitor and reactive power control is instantaneous value of conductance increment (△I/△U). converted into the active current and reactive current CICED2016 Session 3 Paper No 3 Page /6 2016 China International Conference on Electricity Distribution (CICED 2016) Xi’an, 10-13 Aug, 2016 control. The inner loop current controller adopts the Vq Eq LT current feedback and voltage feed-forward decoupling control strategy to realize the current fast tracking and dI q dt LT I d (14) outer loop controller is used for determining the current In the synchronously rotating frame, ud and uq are the reference value. The measurement and calculation grid-side voltage, Vd and Vq are port voltage of the inverter modules sense the three phase inverter current(ia、ib、 voltage, and ω is system angular frequency. Consider error ic), the three phase grid-side voltage (ua、ub、uc)and is caused by the reactor and eliminated by PI controller Eq. current and voltage of the three-phase static coordinate (13) and (14) may be transformed into Eq. (15) and (16). system are converted into two phase synchronous d-q rotating frame. MPPT module monitors the PV array Vd Ed N1 LT I q ud N2 (15) Vq Eq N1 LT I d uq N2 (16) current (IPV) and the dc-link voltage (Vdc) to use for tracking the MPP of the PV array. The phase-locked-loop (PLL) blocks and measures the phase of grid-side voltage Esa to provide the reference phase angle used for d-q transformation. In the synchronous rotating frame, the dc- ud and uq can be expressed as Eq. (17) and (18) link voltage and reactive power of the VSI can be controlled separately by Iq and Id of the inverter. The input ud ( K p Ki * )( I d I d ) S (17) uq ( K p Ki * )( I q I q ) S (18) of current controller is the output of outer loop, the output of current controller are S1-S6 gate trigger signals which are obtained from making a comparison between the triangle wave and the reference of VSI output port voltage under synchronous d-q rotating frame, as shown in Fig.6. Ipv L1 + - C1 Cdc md PCC Detecting currunt and phase SPWM udc L2 id iq ud uq idref iqref Outer loop controler Eq N1/N2 Vt.max Detecting voltage and phase θ ia,b,c mq Inner loop controler The Kp and Ki are the proportional and integral gains of the PI controller. Based on above control equation, the current controller may be implemented as shown in Fig.7. iqref iq θ ua,b,c idref park + + - id - PI uq - ++ Vq ωLid PI ud - Vd ωLiq Vt Vt=sqrt(Vtq2+Vtd2) δ =tan-1(Vtq/Vtd) Vt.min δ mq* mq= Vt cosδ md = Vt sinδ md* Q Qref Fig.7 Current controller of GPCS. MPPT udc,ref udc Ipv Current controller compares the actual with reference values of d-q rotating frame,and generates the reference values Vd and Vq as the inverter voltage which are fed into Fig.6 Control block diagram of GPCS the terminal node. Through PWM the high frequency The step-up transformer is equivalent to a reactor with switching IGBT, m*d and m*q are transformed into actual inductance LT ,and transformation ratio is N1–N2 .The AC voltage Vd and Vq. side voltage equation can be written as Eq. (13) and (14) in the synchronously rotating frame[9]. dI Vd Ed LT d LT I q dt CICED2016 Session 3 Ⅴ. SIMULATION ANALYSIS A. MPPT algorithm validation PV array under standard conditions (25 ℃, 1000 W/m2) (13) parameters as: Voc,ref = 38.4 V, Isc = 8.37 A, Vm = 30.6 V, Im = 8.17 A, NP = 6, Ns = 6. Paper No 3 Page /6 2016 China International Conference on Electricity Distribution (CICED 2016) Table 1 Environment changing Environment Xi’an, 10-13 Aug, 2016 The output power of PV array and the change of gridconnected power as shown in Fig.9. When the S/W/m2 t/℃ 0~0.4s 800 25 conductance method tracks the MPP fast and realizes 0.4~0.8s 1000 25 transmission of active power from dc to ac smoothly. 0.8~1.2s 1000 35 Time environment changes , the variable step incremental Set the changing environmental conditions according to pin :pv output power P: pv grid power Table 1. As shown in Fig. 8, fixed step incremental conductance method is adopted to track MPP. When step=0.5V the dynamic response time is short, but the oscillation of steady output voltage reference Vref is large. When step=0.1V the oscillation of steady output voltage reference Vref is small, but the dynamic response time is pin :pv output power P: pv grid power long. Fixed step conductance incremental conductance can’t meet the dynamic and static balance. The dynamic response of variable step incremental conductance method is faster than fixed step incremental conductance method and oscillation of steady state voltage is smaller than before and oscillation of steady state voltage is smaller than before. The dynamic and steady state performance is improved well. Fig.9 The waveform of tracking power change When double closed-loop control strategy is used, assign in reference of reactive power Qref = 0, grid-side of A phase voltage and current as shown in Fig.10, which has realized the same phase angle of the phase current and voltage, and the power factor approximates to 1. Voltage △t=0.013s △t=0.021s Current (a) step=0.5V Fig.10 Grid-connected current and voltage △t=0.025s When the irradiance changes from 800 W/m2 to 1000 W/m2, current amplitude changes from 46 A to 51 A and output power increases. When S=1000W/m2, t=25℃, we make the fast Fourier transform to A phase current of which the harmonic content is 63 and fundamental RMS is about 36.5A. As shown in Fig.11, current harmonic distortion (THD) is 2.8%, meet the requirements of grid-generation [10]. △t=0.05s (b) △t=0.003s (c) step=0.1V △t=0.002s Variable step Fig.8 Voltage of MPP under different step B. Power control performance of the GCPS CICED2016 Session 3 Paper No 5 Page /6 2016 China International Conference on Electricity Distribution (CICED 2016) Fig.11 Grid-connected three phase current [3] Xi’an, 10-13 Aug, 2016 CHEN Wei, AI Xin,WU Tao, et al. Influence of grid-connected photovoltaic system on power network[J]. Electric Power Automation Equipment, 2013, 33(2):26-32, 39. [4] ZHOU Lin, Wu Jian, Li Qiuhua, et al. Survey of Maximum Power Point Tracking Techniques for Photovoltaic Array[J]. High Voltage Engineering, 2008, 34(6): 1145-1154. [5] Xiong Yuansheng, Yu Li, Xu Jianming. MPPT control of photovoltaic generation system combining constant voltage method with perturb-observe method[J]. Electric Power Automation Equipment), 2009, 29(6):85-88. [6] Jiao Yang,Song Qiang,Liu Wenhua. Control strategy of gridconnected photovoltaic generation system based on modified MPPT method[J].Electric Power Automation Equipment, 2010, 30(12):92—96. [7] Chen Yaai, Zhou Jinghua, Li Jin, et al.Application of gradient variable step size MPPT algorithm in photovoltaic system[J].Proceedings of the CSEE,2014, 34(19):3156-3161. [8] Fig.12 Harmonic spectra of GCPS curren for S=1000W/m2 Rahman S A, Varma R K, Vanderheide T. Generalised model of a photovoltaic panel [J]. Iet Renewable Power Generation, 2014, Ⅵ.CONCLUSIONS 8(8):217-229. On the basis of traditional incremental conductance method, this paper proposed the method that combined CVT with variable step length incremental conductance method to make up for drawbacks of dynamic and steady-state response of the traditional INC, and reduced the power loss. The model and control method of grid photovoltaic power generation system are analyzed. Several dynamic performance of PV system [9] was evaluated including power control, grid current and major in the motor operation control and new energy grid. Zeng Q, Chang L, Song P. SVPWM-based current controller with grid harmonic compensation for three-phase grid-connected VSI[C]. IEEE PESC’04, 2004: 2494-2499. [10] Technical requirements for connecting photovoltaic power station to power system[S]. LI Cuiping(1982-): associate professor of Northeast Dianli University, voltage, current harmonic. The simulation results show that based on constant voltage tracking combined with variable step length incremental conductance method of photovoltaic power generation system can transmit the power from dc to ac stably and to achieve operation with unity power factor. REFERENCES [1] ZHAO Zhengming,LEI Yi,HE Fanbo,et al. Overview of largescale grid-connected photovoltaic power plants[J]. Automation of Electric Power Systems,2011,35(12) :101-107. [2] DING Ming,WANG Weisheng,WANG Xiuli,et al. A review on the effect of large-scale PV generation on power systems [J]. Proceedings of the CSEE,2014,34(1):1-8. CICED2016 Session 3 Paper No 6 Page /6