A grid-connected PV system with LLC resonant DC-DC converter

A Grid-Connected PV System with LLC Resonant DC-DC Converter Concettina Buccella, Carlo Cecati, Hamed Latafat, Kaveh Razi Department of Industrial and Information Engineering and Economics, University of L’Aquila, and DigiPower s.r.l. Via G. Gronchi, 18 - 67100 L’Aquila, Italy emails: [given_name.family_name]@univaq.it Abstract—This paper presents a grid-connected photovoltaic (PV) system with a three level voltage source converter (VSC) using double closed loop control strategy. The outer DC voltage control loop is to regulate the DC bus voltage, and the inner current control loop is to synchronize the output current with the grid voltage, thus ensuring unity power factor. A LLC resonant DC-DC converter is used in the proposed system to step-up the voltage of the PV array and to extract maximum power. It is intrinsically isolated by a high frequency transformer, then the parasitic capacitance of the PV panels to ground could not be of concern; furthermore, because of soft switching technique, it operates at high frequency with low switching losses. Size and cost of the magnetic components and DC-link capacitor are decreased compared with traditional boost converters. An incremental conductance method integrated within PI controller was used to extract maximum power by PV. Simulation results based on MATLAB/Simulink verify the validity and dynamic performance of the proposed system during fast solar irradiation changes and ensure DC bus voltage stability. Index Terms—Photovoltaic (PV) systems, Maximum power point tracking (MPPT), Grid-connected, LLC resonant converter, Grid synchronization. I. I NTRODUCTION Photovoltaic (PV) generation is one of the leading technology in the new energy market. The PV source could be used to supply stand-alone as well as grid-connected systems in a wide power range from few Watt up to several MW. First case requires a storage system to save the captured energy but the latter may not require any storage and has widely used in highpower applications. It is expected that the energy injected into the grid by the PV arrays at the point of common coupling (PCC), should have low current and voltage harmonics [1]. The efficiency of the generation system depends on the capability of the inverter to extract the maximum available power from the PV arrays in real time. A large number of maximum power point tracking (MPPT) techniques have been proposed in the literature such as perturb and observe (P&O) method [2] and [3], incremental conductance method [4], ripple correlation control (RCC) Technique [5], One-Cycle Control (OCC) Technique [6] and [7], Intelligence MPPT Techniques [8], distributed MPPT Technique [9], currentbased technique [10], etc. These algorithms could be easily designed and implemented using a digital signal processor (DSP) or an FPGA [11]. 978-1-4673-4430-2/13/$31.00 ©2013 IEEE 
  

     


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   $#  #      Figure 1. Configuration of typical three Phase Grid-Connected PV System. A dual stage grid-connected PV system shown in Fig. 1 has been widely used due to the simple control and independent operation. These systems compose of PV arrays, a DC-DC converter, a voltage source converter (VSC), and a line filter. Isolation between the input and output powers could be achieved through a DC–DC converter or by using an isolation transformer after the VSC [12]. The control system consists of a MPPT controller of DC-DC converter and the inverter controller which includes an outer DC voltage loop and an inner current loop. The outer loop is to ensure a tight regulation of the DC-link voltage to generate the amplitude of the reference current. The inner current loop uses the reference current in order to synchronize the output current of the inverter with the grid voltage thus ensuring unity Power Factor (PF) [13], [14], [15], [16]. Conventionally, the boost DC-DC converter is used for boosting the PV voltage to the higher level and also for tracking the maximum point of the PV output power in real time. Considering the fact that switching of semiconductor devices occurs at high currents, efficiency of these converters are low at high frequencies because of the hard switching. In the other hand, at low frequencies the size and cost of the magnetic components and capacitor would be high. Furthermore, the parasitic capacitance of the PV panels to ground could cause leakage currents due to lack of isolation. To overcome these problems, a DC-DC full bridge LLC resonant converter is used in this paper [17], [18]. By using LLC converter, soft-switching operation can be achieved as well as electrical isolation and the size of magnetic and filter components could be reduced greatly. Furthermore, the DClink capacitor used to store power and act as a fixed DC bus for the inverter could be selected smaller in comparison with typical DC-DC boost converter. Simulation studies are presented using MATLAB/Simulink 777 to validate the response of the system to sudden changes of solar irradiation. 2 1 kW/m 350 II. PV A RRAY AND MPPT A LGORITHM 300 Although the power provided by the PV cells are low, it is possible to obtain the desired power by connecting more cells in series and in parallel. PV module modeled and simulated as a current source controlled by voltage, sensible to temperature and solar irradiation power. The mathematical equation for the model is given in Eq. 1. 250 Current (A) 0.75 kW/m2 200 0.5 kW/m2 150 0.25 kW/m2 100 50 0 0  q(V + Rs I) V + Rs I exp( )−1 − Ns KT a Rsh 50 100 150 200 Voltage (V) 250 300 350 4 (1) 10 x 10 P = 83937 V = 273.5 9 Where Ipv and I0 are the PV and the diode saturation currents, respectively. Ns is the number of series-connected cells, k is the Boltzmann constant (1.3806503 × 10 − 23 J/K), T (Kelvin) is the temperature of the p-n junction of the diode, and q (1.60217646 × 10 − 19◦ C) is the electron charge. Rs and Rsh are the equivalent series and shunt resistances of the module, and a is the diode constant factor (1 ≤ a ≤ 1.5). Fig. 2 shows characteristic curves of the simulated PV array, made of 55 parallel strings and 5 PV modules in each string, for different irradiance levels with constant ambient temperature of 25◦ C. The voltage and current at maximum power point (MPP) are also shown in the same figure. Since the extracted maximum power from PV array is continuously changing due to ambient temperature and the solar irradiance variations, a MPPT algorithm is necessary to track the MPP. Among the various MPPT algorithms, performance of the incremental conductance (InC) method under rapid solar variations is quite satisfactory [19]. Hence in the simulation model of the grid connected PV system, the InC technique has been used. To minimize the error, a PI controller has also been used as depicted in Fig. 3. The incremental conductance algorithm is based on the fact that at the MPP, the derivative of the output power with respect to output voltage of the PV array is zero. This derivative is positive on the left side of the MPP and negative on the right side of the MPP. So for deriving the output power P = V I, regarding the output voltage: dP d(V I) dI = =I +V dV dV dV (2) dI I dP = 0 =⇒ =− . dV dV V (3) The PI controller minimizes the error (dI/dV + I/V ) and its output passes through the Voltage Controlled Oscillator (VCO), since in LLC resonant converter the controller changes the frequency rather than the duty cycle. By considering the DC-link voltage to be fixed by VSC, it is possible to to get desired power from PV array by changing the voltage gain of the LLC resonant converter. This could be done by varying the equivalent input resistance of the converter. 1 kW/m2 8 7 Power (W) I = Ipv − I0  V = 273.5 I = 306.9 0.75 kW/m2 6 5 0.5 kW/m2 4 3 0.25 kW/m2 2 1 0 0 50 100 150 200 Voltage (V) 250 300 350 Figure 2. V-I and P-V characteristics of simulated PV array.  ✁  
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       !" !# !$" !$#  Figure 3. Block diagram of the MPPT controller using InC method. Hence, when the solar irradiation changes, the MPPT controller increases or decreases the converter gain regardingly, in order to reach the new MPP. The inputs for the MPPT controller are the voltage and current of the PV array, and the outputs are the gate signals of the DC-DC converter switches as shown in Fig. 3. III. DC-DC C ONVERTER Resonant full bridge LLC converter circuit configuration is shown in Fig.4 [20]. The converter has three main parts: First part consists of power switches to generate squarewave voltage, which are usually MOSFETs to be able to work at high frequencies. Second part is the resonant tank which consists of the series resonant capacitor (Cr ), the series resonant inductance (Lr ), and the magnetizing inductance of the transformer (Lm ). Transformer provides electrical isolation and boosts the voltage level to the desired value of the DC bus. Third part consists of a full-wave rectifier to convert AC voltage from the transformer’s secondary to DC voltage. 778 



           Figure 4. Full bridge DC-DC LLC resonant converter with MPPT controller. This circuit presents two different resonance frequencies as depicted in equations (4) and (5). fr1 = fr2 = 1 √ 2π Lr Cr 1  2π (Lr + Lm ) Cr (4) Figure 5. DC voltage gain versus switching frequency of the LLC resonant converter. (5)    where Lr , C r and Lm are series resonant inductance, series resonant capacitance, and magnetizing inductance, respectively. For LLC circuit design, the fundamental harmonic approximation (FHA) method has been used [21]. This method produces satisfactory results while operating close to the resonance frequency fr1 . In this method, only fundamental components of voltage and current are considered. Equation (6) could be obtained easily from energy considerations: 8 Ro (6) π2 where Req is the rectifiers AC port equivalent resistance and Ro is the actual DC side load resistance. Quality factor (Q) of the circuit could be defined as: Req = Q= Zo . Req (7) In equation 7, Zo is the characteristic impedance and could be calculated as:  Lr Zo = (8) Cr The relationship between DC voltage gain of the LLC resonant converter with normalized switching frequency could be expressed as: 1 M= (9) λ 2 (1 + λ + f 2 ) + Q2 − (fn − f1n )2 n where inductance ratio λ, and normalized switching frequency fn are defined in (7)-(11). Lr λ= Lm fswitch fn = . fr1 (10) (11)   ✁
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   ☎ ✄ "! "" "# "$ #! #" ## #$ Figure 6. Block diagram of the control strategy applied to the VSC. At frequencies higher than fr1 , ZVS operation of the primary switches and ZCS operation of the rectifier diodes are ensured. The equation (9) is plotted in Fig. 5 for different Q values with respect to switching frequency. The MPPT algorithm used for this converter is incremental conductance (InC) to ensure the maximum power point tracking that has shown in Fig. 3 and has discussed in Section II. IV. VOLTAGE S OURCE C ONVERTER The grid side inverter used in this work is a three level natural point clamped voltage source converter (VSC) that is made of Insulated Gate Bipolar Transistor switches. The rated apparent power capacity of the VSC is 100 kVA which converts the 500 Vdc to 260 Vac . The switching frequency of the VSC is 1980 Hz. The control strategy applied to the VSC consists of two cascaded loops: internal current loop for grid synchronization and external voltage loop to regulate the DC bus voltage [19]. A. DC-link Voltage Controller The controller regulates the DC bus voltage at 500 V. Fig. 6 shows the block diagram of the controller. The DC-link voltage is controlled regarding the desired active power. As it can be seen in Fig. 6, the output of the controller used as the reference for the active current controller. 779 B. Internal current loop Synchronous reference frame control or d − q control, uses abc → dq transformation of the grid voltage and current into a reference frame rotating synchronously with the grid voltage. A block diagram of the aforementioned dq control is depicted in Fig. 6. By using the synchronous reference frame, variables to be controlled become DC values, thus it is easier to design and implement controller and filter. The phase angle used by the abc → dq transformation has to be extracted from the grid voltages, in order to synchronize the controlled current with the grid voltage. The phase-locked loop (PLL) technique is used for extracting the phase angle of the grid voltage. In synchronous reference frame structure, the reference for the reactive current Iq is set to zero in order to maintain unity power factor and the reference for active current Id comes from the DC-link voltage controller as discussed in the previous subsection. Considering the grid connected system shown in Fig. 7, the AC-side equations could be written as follow: uca = Rf ia + Lf dia dia + R T ia + LT + uga dt dt (12) ucb = Rf ib + Lf dib dib + R T i b + LT + ugb dt dt (13) ugd = ucd + ωLiq − L ucq = Rf iq +Lf (19) diq . (20) dt Voltage outputs of the current controller, are then converted to three modulating signals used by the three-level PWM pulse generator. The proportional integral (PI) controllers are used in this structure, since they are easy to implement and they have good performance for regulating DC variables [12]. ugq = ucq − ωLid − L V. S IMULATION R ESULTS The proposed three phase dual stage grid connected PV system is shown in Fig. 7. Passive elements, C1,C2 and L1, were used for smoothing the output voltage and current of the PV array. All of the control blocks were discussed in previous sections. The entire PV system model was implemented and simulated using Matlab/Simulink [22] software. Specifications of the PV modules and array under standard test condition, STC (irradiance = 1000 W/m2 , temperature = 25 ◦ C) are given in Table I. The grid parameters, filters, DClink voltage, and other system parameteres are represented in Table II. All of the proportional and integral constants of the PI controllers were obtained by trial and error effort. Table I PV A RRAY S PECIFICATIONS U NDER STC. dic dic (14) ucc = Rf ic + Lf + R T i c + LT + Igc dt dt where uca , ucb , and ucc , are VSC outputs of each phase, while uga , ugb , and ugc , are grid voltages of each phase, respectively. Rf and Lf are the parameters of the line filter as depicted in Fig. 7. RT and LT are total transformer resistance and leakage inductance, respectively. The following equations is obtained between converter output and utility grid in synchronous reference frame by applying Park’s transform to equations (16)-(18). ucd = Rf id +Lf did dt Parameter Module open-circuit voltage (Voc ) Module short-circuit current (Ioc ) Module voltage at maximum power point (Vmp ) Module current at maximum power point (Imp ) Number of series-connected modules per string Number of parallel strings PV Array maximum power at 1000 W/m2 (Pmp ) PV Array voltage at 1000 W/m2 PV Array maximum power at 250 W/m2 PV Array voltage at 250 W/m2 Value 64.2 V 5.96 A 54.7 V 5.58 A 5 55 83.9 kW 273.5 V 18.8 kW 252.4 V did did −ωLf iq +RT id +LT −ωLT iq +ugd (15) dt dt Table II G RID C ONNECTED PV P LANT S YSTEM PARAMETERS . diq diq +ωLf id +RT iq +LT +ωLT id +ugq . (16) dt dt Parameter C1, C2 [µF] L1 [µH] C3, C4 [µF] Rf [mΩ] / Lf [µH] DC-DC Converter resonance frequency [kHz] 3-level VSC switching frequency [kHz] DC link refrence voltage [V] Transformer resistance [p.u.]/leakage reactance [p.u.] Transformer primary [kV]/secondary voltage [V] Grid nominal line voltage [kV] / frequency [Hz] Base power [kVA] In these equations, ucd and ugd , ucq and ugq , are VSC and grid voltages respect to d and q axes of the synchronous d − q coordinates. By considering R = Rf + RT and L = Lf + LT , equations (15) and (16) can be expressed as follows: ucd = Rid + L did − ωLiq + ugd dt (17) diq + ωLid + ugq . (18) dt Choosing L ≫ R , equations (17) and (18) yields the following equations, in which L is the total inductance connected between VSC and grid bus bar and ω is the angular frequency of the grid voltage. ucq = Riq + L Value 1500 0.22 3000 2 / 500 100 4 500 0.001 / 0.03 25 / 260 25 / 60 100 To test the performances of the MPPT control algorithm applied to LLC resonant converter and demonstrate the grid synchronization and DC bus voltage regulation of the VSC, ramp and step changes in solar irradiation were considered and 780  !" #$ %& &'()( & '     * +   %/   +
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 %   ,'  8 ✁  9 :9 ,  9  :9  , Figure 7. Block diagram of the proposed large PV plant connected to MV grid. Irradiation (W/m2) 600 400 200 0.2 0.3 0.4 0.5 .06 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 450 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 time (s) 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 80 60 (kW) At first, the sun irradiance was set to 1000 W/m and the MPPT controller was disabled and the initial amount of power was transferred to the grid by DC-DC and VSC converters. At t = 0.2 s the MPPT controller was enabled and starts regulating the voltage gain by changing the switching frequency in order to extract maximum power. 800 pv 2 1000 40 P are shown in Fig. 8. In this regard irradiation was varied from 1000 W/m2 to 250 W/m2 and returns back to the primary value after some ramp and step changes. 20 0 PV system was arrived at steady state in about 17 milliseconds. At the steady state, Ppv = 83.94kW , Pout = 82.25kW , Vpv = 273.6 V were achieved as expected from PV array specifications and the efficiency of η = 98 % was obtained. At t = 0.3 s, the sun irradiance was decreased as a ramp to 250W/m2 in 0.5s. As shown in Fig. 8, PV mean power (Ppv ) and grid mean power (Pout ) follow the irradiation variation very close to the MPP. (kW) 80 40 P out 60 20 0 250 It should be noted that DC-link voltage was regulated by VSC controller during the all above disturbances, as shown in the lower graph of Fig. 8. The achieved results show the satisfactory performance of the MPPT which has been performed by LLC resonant DC-DC converter. Figure 9 shows voltage and current waveforms of grid phase A, while changing solar irradiance. The upper graph represents the ramp change and the lower graph shows the step changes. As it can be seen from this figure, voltage and current are in phase which confirms unity power factor provided by VSC controller. 200 550 dc (V) 150 V Power of the PV array, reaches its steady state with 30 ms delay and for the grid power, this delay was 40ms. PV voltage was then droped down to 246 V at t = 0.8 s. From t = 0.95 s to t = 1.4 s, irradiation was ramped up again from 250 W/m2 to 1000 W/m2 . It can be seen that MMPT controller have good performance tracking maximum power during solar irradiance changes. In order to test the performance of the MPPT controller with faster solar irradiance changes, from t = 1.5 s to 1.8 s step changes are applied and irradiance was changed about 750 W/m2 in 10 ms. PV and grid power were settled to their steady state values in about 60 ms and 70 ms for step-down part, and 28 ms for step-up part, respectively. V pv (V) 300 500 Figure 8. System parameters Ppv , Pout , Vpv and Vdc responses versus irradiation ramp and step changes. VI. C ONCLUSIONS This paper has presented an application of a full bridge LLC resonant converter in a three phase grid connected photovoltaic (PV) system. The LLC has the benefit of zero voltage switching, which results in a higher efficiency in comparison to conventional boost converters. Due to its operation at high frequencies, the use of smaller and cost effective magnetic components is possible. Furthermore, DC-link capacitor for the inverter could be chosen smaller thanks to the high switching frequency and fast dynamic response of the converter. The inverter controller consists of the outer loop to keep the 781 Voltage 20 5 12 3 4 1 0 0 í4 í1 12 í3 í5 20 0.24 0.26 0.28 0.3 0.32 0.34 time (s) 0.36 0.38 0.4 0.42 Voltage 20 5 3 12 4 1 0 0 í4 í1 12 í3 í5 20 1.48 1.5 1.52 1.54 1.56 1.58 time (s) 1.6 1.62 1.64 1.66 1.68 Figure 9. Grid phase A voltage and current, corresponding to ramp (upper graph) and step (Lower graph) change of irradiation. DC bus voltage constant, and the inner loop to synchronize the output voltage of the inverter with the grid voltage and also keep the output current in phase with voltage. The simulation results confirmed the effectiveness of the system to provide and ensure appropriate power and unity power factor to the grid, as well as DC-link voltage stability. The ability of the DC-DC converter to extract maximum power from the solar arrays under rapid changing irradiance, has also demonstrated. R EFERENCES [1] S. J. Chiang, K.T. Chang, C.Y. Yen, “Residential Photovoltaic Energy Storage System,” IEEE Trans. Ind. Electron., Vol. 45, No. 3, pp. 385 -394, Jun. 1998. [2] W.T. Chee , T.C. Green, A.C. Hernandez-Aramburo, “Analysis of perturb and observe maximum power point tracking algorithm for photovoltaic applications”, 2008 IEEE 2nd Int. Power and Energy Conf. (PECon 2008), 2008. 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