光伏

Abstract —Photovoltaic power generation is growing at a rapid rate. Most new PV installations are grid-connected small-scale system. The impact of these installations on the grid operation need to be carefully studied to investigated. This paper presentsthe development of simulation tools required for suchinterconnection studies. The simulation tools were developed in the popular electromagnetic transient simulation program PSCAD/EMTDC and include a PV array model, maximum power point tracking controller model, and a grid connected inverter. An example of an interconnection study using the developed simulation tools is presented.Index Terms —Photovoltaic generation, PV systemssimulation, PV model, PV system grid interconnection, Distributed generation, PV grid interconnection studies, Electromagnetic transient simulation, Maximum power point tracking, PV inverter. I. I NTRODUCTION ROWING attention to distributed generation (DG) and green energy alternatives to conventional fossil fuel-based electricity generation has revived interest in grid-connected photovoltaic (PV) systems. The global PV systemmarket has been expanding steadily during the last few years.As the cost of PV coming down due to economy of scale effects and development of new technologies, applicationssuch as building integrated PV systems are becoming increasingly popular and cost effective [1]. When larger PV installations are designed, studies need to be performed at the power system level to examine the impacts of these grid-connected PV systems. For small scale distributed generators connected to medium or low voltage networks, interconnection standards such as IEEE 1547 2003 [2] andlocal utility interconnection regulations define the grid interface response to system disturbances. The protection isbased on the philosophy that in case of grid disturbances, e.g. voltage drops or frequency deviation, distributed generatorswill be disconnected from the network immediately. Thus the protection system at the grid interface and DG control need to be designed to meet applicable requirements.Time domain simulation using Electromagnetic Transient(EMT) programs is a powerful method that can be used forstudies involving controller tuning, protection setting, powerquality investigations and system validations. These computerA. D. Rajapakse is with the University of Manitoba, Winnipeg, MB,Canada (e-mail: Athula@ee.umanitoba.ca).D. Muthumuni is with the Manitoba HVDC Research Centre, Winnipeg, MB, Canada (e-mail: dharshana@hvdc.ca).programs offer the advantage of ability to model powerelectronic systems and associated control systems in detail [3]. Several approaches to incorporate PV array models in online simulation have been investigated. In [4] a fuzzy regression model is proposed to simplify calculations and minimize datarequirements. An incremental model of solar cell based on the truncated Taylor series expansion of PV cell voltage has been used in [5] to avoid numerical iterations during the simulations. It is not uncommon to find that the PV array models used in simulation studies are oversimplified. While these approximations may be sufficient for some studies, theoutput of a PV array is highly non-linear, and to simplify thearray to a constant voltage source or a current controlled voltage source is often not appropriate. Specially, when the PV system is equipped with MPP tracking controls, use of very simple models could lead to inaccuracies. In order toovercome this deficiency, this paper develops a customcomponent of a PV array for the well-known EMT programPSCAD/EMTDC. The developed PV array model is used in a PV grid integration simulation study. II. PV A RRAY S IMULATION A. PV Array ModelA solar cell can be modeled using an electrical equivalent circuit that contains a current source anti-parallel with a diode, a shunt resistance and a series resistance as shown in Fig. 1. IFig. 1 PV cell equivalent circuitThe DC current, I g , generated when the cell is exposed tolight, varies linearly with solar irradiance. The current I dthrough the anti-parallel diode is largely responsible forproducing the nonlinear I-V characteristics of the PV cellshown in Fig. 2. The PV cell model can be further refined byincluding a second diode [2] as shown connected by the dashed lines. The second diode provides an even more accurate I-V curve that accounts for the difference in current Simulation Tools for Photovoltaic System GridIntegration StudiesAthula D. Rajapakse, Senior Member, IEEE , and Dharshana MuthumuniG2009 IEEE Electrical Power & Energy Conference 978-1-4244-4509-7/09/$25.00 ©2009 IEEEflow at low current values due to charge recombination in the semiconductor's depletion region. However, for most studies a PV model with a single diode is sufficient and with two diodes model, determination of model parameters becomes slightly complicated.II sco cFig. 2 Typical I-V characteristics of a PV cellThe basic equation that characterizes the solar cell I-V relationship can be derived considering the equivalent circuit shown in Fig. 1. The Kirchoff’s current law gives.(1) Substitution of relevant expressions for the diode current Id and the shunt branch current Ish yields. (2)In (2) I sc is the photo current and it is a function of the solar radiation on the plane of the solar cell G and the cell temperature T c :(3)whereI scR is the short circuit current at the reference solarradiation G R and the reference cell temperature T cR . The parameter αT is the temperature coefficient of photo current. The current I o in (2) is called the dark current, a function of cell temperature only, and given by (4) where I oR is the dark current at the reference temperature.The other parameters appearing in (2)-(4) are the electroncharge q , the Boltzmann constant k , the band-gap energy ofthe solar cell material e g , and the diode ideality factor n whichis between 1-2 (1.3 is typical for silicon solar cells). All of theconstants in the above equations can be determined byexamining the manufacturer’s specifications of the PVmodules and the published or measured I-V curves of the array. Since a PV module is composed primarily of series-connected cells, and a PV array is composed of series- andparallel-connected modules, the single cell circuit can bescaled up to represent any series/parallel combination. B. Simulation of PV Array The above PV cell model was implemented as a customcomponent in PSCAD (see Fig. 3). The PV array wasinterfaced as a nonlinear current source. Implementation ofequation (2) which is highly nonlinear in a fixed time-step simulation program is challenging. In fact accurate implementation on the above equation requires iterative solution of (2) simultaneously with the network equations. However, considering the small time steps used in typical emt simulations, voltage calculated from the last time step can be used to determine the new current injections. In order to ensure the simulation stability under rapidly changing output voltages, feedback of the voltage at previous time step was provided through a first order filter. Although this numerical technique improves the simulation stability around the knee point, it introduces a slight inaccuracy near the knee point when simulation is run at larger time-steps.III. M AXIMUM P OWER P OINT T RACKINGThe amount of power that can be drawn by a solar cell depends on the operating point on the I-V curve and the maximum power output occurs around the knee point of the curve. A maximum power point tracker (MPPT) is a power electronic DC-DC converter inserted between the PV array and its load to achieve optimum matching. By using an intelligent algorithm, it ensures the PV module always operates at its maximum power point as the temperature, solar radiation and the load vary. A number of tracking algorithms have been proven and used and a number of DC-DC converter topologies are possible [7-9]. A commonly used simple technique is the Perturb and Observe (P&O) algorithm but it has many limitations. Another popular but slightly advanced MPPT algorithm [7, 9] is the Incremental Conductance method shown in Fig. 4. This algorithm was implemented in PSCAD (see Fig. 3).IV. T EMPERATURE E FFECTS The open circuit voltage and the maximum power point voltage are sensitive to the cell temperature. At higher temperatures the efficiency of solar cells drops. These temperature dependencies are included in the PV cell modeland it requires cell temperature as an input. Calculation of Tcrequires a thermal model which takes various inputs such assolar radiation, wind velocity, ambient temperature, etc. andparameters such as tilt angle of the array, surface emissivity,etc (see Fig. 3). Since the thermal time constants are muchlarger than electrical time constants, in most emt simulationsuse of constant cell temperature should be sufficient.Tsky Gt Tamb Wvel Tpv Tgnd Ppv TiltFig. 3 PV system simulation components library developed for PSCADV. G RID C ONNECTED PV I NVERTER S YSTEM A simple example of using these components for a system study is shown in Fig. 5. For the simplicity of presentation, thethe system impedance. The inverter is connected to the 11 kV grid through a step-up transformer. Except for the transformer winding inductance and the smoothing inductor, no additional harmonic filtering is provided. The output voltage of the 200 kWp PV array is controlled at the maximum power point (around 1500 V) by the MPPT system. The controller used for Fig. 6 Dc-dc converter control with MPP trackingVI. S IMULATION R ESULTSA. I-V Characteristics MPPT PerformanceThe I-V curve of the simulated PV array at a constant The thick green line superimposed on the I-V characteristics curve shows the variation of the operating point of the PV array, when the maximum power point tracking is enabled. Even at constant radiation level, the operating point oscillates due to tracking action.Maximum power point tracking performance under variable solar radiation and temperature conditions is shown in Fig. 8. The solar radiation and the cell temperature were varied during the simulation resulting in a series of I-V curves. The I-V curves shown in Fig. 8 were obtained by simulating a second PV array model with the same parameters under the same solar radiation and cell temperature conditions as the PV array in the system. The thick green line indicates the variation of PV array operating point during the variations of the solar radiation and the cell temperature. It is evident that the MPPT controller tracks the knee point fairly accurately.Fig. 8 MPP tracking under variable solar radiation and temperature conditions.B. PV System Interconnection StudiesThe performance of the grid connected PV system under variable solar radiation conditions is shown in Figs. 9-11. The array voltage and current response to varying solar radiation level is shown in Fig. 9. The PV array voltage closely follows the reference voltage determined by the MPPT algorithm.The point of common coupling (PCC) rms voltage and the real and reactive power flow of the PV inverter during this period are shown in Fig. 10. The PCC rms voltage remains fairly constant while the output real power changes proportional to the changes in the solar radiation level. The inverter is set to operate at unity power factor, but during the transients, the reactive power output of the inverter changes. This is a result of the simple inverter controller used in this paper. Fluctuations in reactive power can be minimized by improving the inverter control, for example by using decoupled control based in d-q currents.Fig. 9 PV array output under variable radiation conditions. (note that the Dc-Dc converter very closely tracks the operating voltage commanded by MPPT)Fig. 10 Real and reactive power at the grid interfaceHarmonic injection by the grid connected PV inverters is a concern [10] and standards such the IEC s tandard 61727 ‘‘Photovoltaic (PV) y tem-----Characteris tics of the utility interface’’ and the IEEE s tandard 929-2000 ‘‘Recommendedpractice for utility interface of photovoltaic systems’’ provide guidelines on harmonic limits at the PCC. The three-phase current and voltage at the PCC are shown in Fig. 11. The voltage waveforms are not much distorted but the distortions in the current waveforms are quite visible. These waveforms can be processed to determine the THD and TDD values to check whether the system complies with the standards or the regulation set by the local utility.VII. C ONCLUSIONSA simulation model of a PV array was implemented in an electromagnetic transient simulation program. Numerical model interfacing issues due to nonlinear characteristics of the PV array was briefly discussed. A model to simulate the incremental conductance based maximum power point tracking algorithm was also implemented. Application of these simulation tools was demonstrated through an example of grid connected PV system simulation.VIII. R EFERENCES[1]P. Maycock and T. Bradford, “PV Technology, Performance, and Cost:2007 update”, Prometheus Institute for Sustainable Development and PV Energy Systems, Cambridge, MA, USA, 2007.[2]IEEE Standard for Interconnecting Distributed Resources with ElectricPower Systems, IEEE Standard 1547, 2003.[3] A. D. Rajapakse, D. Muthumuni, N. Perera, and K. Strunz,“Electromagnetic Transients Simulation for Renewable Energy Integration Studies”, in Proc. of IEEE PES Annual Meeting, Tampa, FL, USA, 24-28 June 2007.[4]V. Quaschning and R. Hanitsch, “Numerical simulation of photovoltaicgenerators with shaded cells”, in Proc. of the 30th Universities Power Engineering Conference, Greenwich, Sept. 5-7, 1995, pp. 583-586.[5]M.T. Elhagry, A.A.T. Elkousy, M.B. Saleh, T.F. Elshatter, and E.M.Abou-Elzahab, “Fuzzy modeling of photovoltaic panel equivalent circuit”, in Proc. of the 40th Midwest Symposium on Circuits and Systems, 3-6 Aug. 1997, pp. 60 - 63 Vol.1.[6] A. D. Theocharis, A. Menti, J. Milias-Argitis and Th. Zacharias,“Modeling and simulation of a single-phase residential photovoltaic system”, Proc. of IEEE Russia Power Tech, 27-30 June 2005, pp. 1-7. [7]Hussein K.H., Muta I., Hoshino T., Osakada, M.: “Maximumphotovoltaic power tracking: an algorithm for rapidly changing atmospheric conditions”, IEE Proc. Generation, Transmission and Distribution, Vol. 142 No. 1, Jan. 1995, pp. 59 – 64.[8]M. Veerachary, “Power tracking for nonlinear PV sources with coupledinductor SEPIC converter”, IEEE Trans. Aerospace and Electronic Systems, Vol. 41, No. 3, July 2005, pp. 1019-1029.[9]G. M. S. Azevedo, M. C. Cavalcanti, K. C. Oliveira, F. A. S. Neves andZ. D. Lins, “Evaluation of maximum power point tracking methods for grid connected photovoltaic systems”, in Proc. of IEEE Power Electronics Specialists Conference (PESC 2008), 15-19 June 2008, pp.1456 – 1462.[10]M. Aiello, A. Cataliotti, S. Favuzza, and G.Graditi, “Theoretical andexperimental comparison of total harmonic distortion factors for the evaluation of harmonic and interharmonic pollution of grid-connected photovoltaic systems”, IEEE Trans. Power Delivery, Vol. 21, No. 3, pp.1390-1397.IX. B IOGRAPHIES(M’99)received the B.Sc. (Eng.) degree from the obtained his B.Sc. (Eng) degree from the University。