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Sept.3-5, 2013, China AORC-A-6-0002 CIGRE-AORC 2013 Simulation and Mathematical Modelling for Grid-connected Photovoltaic Power System Based on ADPSS Xiaowei Wang 1, Xiaobo Duan 1, Xinkui Xi 2, Zhengang Shi 1,Wenping Hu 1 1 Hebei Electric Power Research Institute 2 Hebei Electric Power Corpration China SUMMARY The three-phase grid-connected photovoltaic power system includes MPPT and currentcontrolled voltage source inverter. The photovoltaic arrays maximum power point tracking is realized applying the former boost circuit. A mathematical model for photovoltaic power system based on the three-phase grid-connected photovoltaic power system is developed. The mathematical model for photovoltaic power system is developed applying Matlab which includes photovoltaic array, Maximum Power Point Tracking (MPPT), DC/DC and the inverter system applying voltage and current loop control. The simulation results show that the mathematical model can reflect characteristics and functions of the actual photovoltaic power system precisely. And it can be used in the simulation on grid-connected photovoltaic power system. After the precise mathematical model is established, the UD (user defined) model of grid-connected photovoltaic power system is established based on PSASP. A effective tool is given for studying the interrelationship between PV system and power grid . And it can also confirm the capacity of grid-connected PV power system. The ability of photovoltaic power sytem connected with grid is improved. And the ability to run stably is improved also after the photovoltaic power sytem is connected with grid. It adapt to the requirement of vigorous development solar energy. It plays an active role to speed up the construction of smart grid. KEYWORDS - 60 - Grid-connected Photovoltaic Power System; MPPT; Inverter System; Mathematical Modeling; Matlab; Simulation I INTRODUCTION The output of photovoltaic power is intermittent, periodic and random. A series of problems will be brought to power system planning, operation control and management along with the large scale photovoltaic power and large-scale building-integrated photovoltaic power are connected to power grid. The study on the basic principle of photovoltaic power generation and the establishment of the mathematical model of photovoltaic power are significant. They are important for the study of the effect on the power system with penetration of photovoltaic power system. It also adapts to the trend of vigorous development the new energy in China. The necessary technical support is supplied for secure and stable operation while large capacity new resource connecting into power grid. There isn’t photovoltaic power system model in common power system analysis software package in the domestic now. Therefore, it is very important to establish model of PV and realize its control law in the software. It will provide important theoretical support and calculation tool for the research and planning of PV. A simulation module of photovoltaic system is added in PSASP in this project. And it can be called easily in the program. It has laid the foundation for digital simulation of photovoltaic power generation in the future. II ESTABLISHMENT OF THREE-PHASE GRID-CONNECTED PV SYSTEM MODEL IN MATLAB First, the basic characteristics, actual operation characteristics and control methods are researched for each main component in PV system, and then realistic mathematical model is established according to system’s basic structure and principle. Three-phase gridconnected PV system model is established in MATLAB and validated with simulation. The grid-connected PV system is generally composed of four parts, which are PV array module, inverter, AC circuit and controller. The inverter reverses the power generated by PV cell into sinusoidal current which is connected into grid. The controller is to control the PV cell maximum power point tracking, the grid-connected power from inverter and the current waveform, so then it makes the power transferred to grid balance with the maximum electrical power from PV array module. In terms of the structure of energy conversion, the present grid-connected PV system can be divided into single-stage energy conversion and - 61 - dual-stage energy conversion according to the number of stages. The main research in this paper is dual-stage grid-connected system, and the structure diagram for dual-stage energy conversion is shown in Fig.1. Dual-stage grid-connected PV system is mainly composed of PV cell array, DC/DC converter, DC/AC PV grid-connected inverter and controller and so on. Its working principle is to transform the DC generated by PV cell array into that in another voltage level through DC/DC converter, which is generally a conversion with voltage boosted. And then the DC is transformed into AC further through DC/AC PV grid- connected inverter, and the AC is input into power grid. Fig. 1. The structure diagram of dual-stage grid-connected PV system The first-stage conversion needs to realize maximum power tracking function for PV cell array at the same time. The second-stage PV grid-connected inverter is to reverse the DC in DC bus into AC, which is provided for local load. It feeds the excess energy into grid and realizes the voltage stabilization function for middle DC bus. 1 PV Array Simulation Model PV array model is composed of a large number of PV modules, and the mathematical expression for PV array is as follows. Where, - 62 - PV array model is established in matlab/simulink through the derivation of formulas. 2 The simulation model of MPPT function model Based on the PV cell simulation model above, the S-function is written with the tool of simulink, and then the simulation model of MPPT is established. The input of S-function is the voltage and current which is from PV cell array and the output could be the reference voltage or current for grid-connected control method. The strategy of MPPT detects the output power of PV array in real time, which uses certain control algorithm to predict the maximum possible output power under the present operating mode. And then it could meet the requirement of maximum power output by changing the present impedance. In this paper, MPPT is realized with the disturbance observation method and the DC/DC circuit is used for maximum power tracking. PV array is influenced by the change of sunlight intensity and ambient temperature, so the output voltage and current is constantly changing and the equivalent resistance is constantly changing too. DC/DC converter is added between PV array and load. The duty cycle of power switching device in DC/DC converter circuit is adjusted to regulate the external load, which makes the external load equal to the equivalent resistance of PV array and the external load obtains maximum power, so the purpose of PV array maximum power point tracking is achieved. 3 Inverter system model The whole idea of PV inverter system is illustrated as follows. The post-circuit controls the grid-connected current to track the command current and it also controls the voltage stability of capacitor C2. The Pre-Boost circuit adjusts the output voltage of PV array by regulating the duty cycle of full-controlled device S to realize MPPT. The method of three-phase gridconnected control system in this paper has inner-loop and outer-loop control. The outer-loop control is voltage control loop, which controls DC/DC output voltage to track the specified voltage U*dc by a PI regulator. The inner-loop control is current control loop, which uses current-controlled voltage source inverter to decoupling control the grid-connected current of d-q axis by two PI regulators in the synchronous rotation coordinate system. The d-axis current adjusts the active power output of PV inverter, which makes the PV array work at the maximum power operating point. While the q-axis current adjusts the reactive power output of PV inverter and controls the gird-connected power factor. The diagram of control part in grid-connected PV system is shown in Fig.2. - 63 - 4 Simulation analysis Based on the analysis for various models and control part in the PV system above, the dynamic model for grid-connected PV system is established with matlab/simulink, which is shown in Fig.3. The system takes PV array as input source and supplies power for three-phase inverter system through Boost circuit. The grid voltage is 380V. The improved conductivity method for MPPT controller is written by S-Function. The voltage at maximum power point is 348V and - 64 - the maximum power is 4780W. The parameters in Boost circuit are as follows: C1=1000μF, L=2.5mH, C2=2600μF, AC filtering inductance L=10H, equivalent resistance R=0.1Ω. The parameters of controller Cdi(s) are that KPd=0.03, KId=0.8. The parameters of controller Cdv(s) are that KP=0.02, KI=8. a) Steady-state simulation After a few cycles, the inverter system makes the gird-connected current and the system voltage have same frequency and phase through the phase lock link. When the light intensity is 1kW/m2, the grid A-phase voltage from 0.2s to 0.4s is shown in Fig.4-(b) and the gridconnected current whose phase is identical with the voltage is shown in Fig.4-(a). It is known from above simulation that the pre-inverter system realizes the dynamic tracking for PV array maximum power point voltage well through maximum power point tracking control. The post-inverter system uses voltage and current double closed loop control algorithm, which guarantees the grid-connected current in sync with the system voltage. b) Transient simulation In Fig.5, it shows that the transient changing process of PV system voltage and current when the AC system has 0.01-second three-phase short circuit fault. The AC parameters between PV system and three-phase short circuit point are that R1=0.1273Ω,X1=9.337mH. It is known from the waveform that when the PV system has three-phase short circuit fault, its voltage and current would return to steady state based on the regulation effect itself after 0.04-second transient process. Fig.4 The simulation waveforms of grid-connected current - 65 - Fig.5 The simulation waveform of grid-connected current and grid voltage when the threephase short circuit fault has occurred Based on the transient simulation analysis, it is gotten that the grid-connected PV system should be able to return to steady state quickly after the change of light intensity. Furthermore, when the system has short-term short circuit fault, the short-circuit current should not have significant influence on PV system or power grid and it should return to synchronous operation state quickly. III ESTABLISHMENT OF THE UD MODEL OF PV SYSTEM IN PSASP In the paper above, a complete three-phase grid-connected PV system model is established by the tools of Matlab/Simulink and Sympowersystem. It validates the grid-connected PV system maximum power tracking and the inversion output, and takes optimization design for system parameters through a large number of simulations. The UD model of PV system is established in PSASP, which makes it have some PV generation simulation ability. The transfer function of each main part in PV system is constructed first, and the model of PV system is added in PSASP program based on designed model framework and transfer function. The model is taken for simulation test according to the principle of PV generation, and then the model’s correctness is validated. Moreover, the model parameters are adjusted in the validation process, which make the simulation results tend to accurate. The so-called user-defined modeling is that users design various models according to their demands of calculation and analysis and they don’t need to know the internal structure or programming. Their designs use the concepts that engineers are familiar with and the methods easy to grasp. These models could simulate any system component, automatic - 66 - device and control function. When users establish the UD model of PV system, they establish mathematical models of simulation components first, draw function block diagram, build connection relationship between function block and specify the system input-output relationship. And then they establish the user-defined model and balance initial values. Initial values balance is to deal with the model, so the output values from each block of model are reasonable. It makes the model’s initial output coincide with the initial state values of stability calculation, which ensure the validity of stability calculation. The UD model of PV system is integrated into PSASP program, which could be public resources for other power grid or calculation. It is realized to call the PV system model by filling out the model’s calling data. Calling data is that the model’s application location is specified and the concrete buses and branches which used for model are given, so that it is convenient to make calculation for the model. The grid-connected buses of PV station are set in the "Basic data" and "Bus data". The PV stations are set in the "Generator and regulator data" of "Basic data". The synchronous machine model uses PV station model and the parameters of PV station are entered and modified by clicking the button of edit parameters. After the entering and editing for calling data, users could make actual grid calculation. It is needed to refresh the power flow database first, introduce the PV station model into calculation and modify the power flow data properly, and then the power flow could be calculated. It is turned into transient stability calculation after power flow calculation. Users should refresh the power flow work which the transient stability work bases on, and then they could take various transient stability calculation and analysis, such as setting grid fault, setting node disturbance and calling other UD models and so on. When the calculation is finished, it is realized to output the model’s variables through view mode. IV CONCLUSION In this paper, the three-phase grid-connected PV control system is realized by using the Pre-Boost circuit, which combines the PV array maximum power point tracking with the current-controlled voltage source inverter. On the base of the analysis for three-phase gridconnected PV system, the PV system dynamic simulation models are developed in matlab/ simulink, which includes PV array model, PV array MPPT model, DC/DC boost circuit and inverter system with voltage-loop and current-loop control. The simulation results indicate that the developed models can reflect the features and functions of PV system accurately and they could be used for the simulation research of PV grid-connected generation. The UD model of grid-connected system is established in PSASP based on the correct mathematical - 67 - model. The UD model is user-defined and its correctness is validated through simulation. The PV system simulation models are developed in PSASP and they could be called in program conveniently. However, there is no PV system model in the domestic existing various power system analysis software package. So the completion of this project enriches the program's function, which is suit to the national smart grid development needs and lays the foundation for the future PV generation digital simulation research work. Based on the PV system model developed in this project, the security and stability of whole grid could be analyzed and researched when the PV system is connected into grid. Then it could provide predictable solutions for the stability problem caused by PV system grid-connected, which improves the ability to connect PV system into power grid and the stable operation ability after gridconnected. This project suits our development needs of exploiting solar energy resources for generation vigorously, so it has positive role to accelerate the development of smart grid. BIBLIOGRAPHY [1] Koutroulis E, Kalaitzkis K, Voulgaris N C. “Development of a Microcontroller-based Photovoltaic Maximum Power Point Tracking Control System,” IEEE Trans,on Power Electronics,2001,16(1): 46-45. [2] Kawamura,Harada K,Ishihara Y,et a1. “Analysis of MPPT characteristics in photovoltaic power system,” Solar Energy Materials and Solar Cells,1997,47:155-165. [3] Hussein K H,Muta I, Hoshino T, et al. “Maximum photovoltaic power tracking:an Algorithm for rapidly changing atmospheric conditions,” Generation,Transmission and Distribution, IEE Proceedings,199 5,142(1):59-64. [4] Tan Y T. Daniel S K, Nicholas J. “A model of PV generation suitable for stability analysis,” IEEE Trans on Energy Conversion,2004,l9(4): 748-755. [5] O.Wasynczuk. “Modeling and Dynamic Performance of a Line-commutated Photovoltaic Inverter System,” IEEE Transactions on Power Conversion,Vol.4,No.3,September 1989:337343. [6] Abouzahr I,Ramakumar R, “An approach to assess the performance of utility- interactive photovoltaic systems,” IEEE Transactions on EnergyConversion,Vol.8,No.2,June 1993,145~153. [7] Andres E Feijoo,Jose Cidras. “Modeling of wind farm in the load flow analysis,” IEEE transactions on power system,2000,15(1):110-115. - 68 - Short Bio-data of Main Author Xiaowei Wang (1970---), the engineer of Hebei Electric Power Research Institute, mainly engaged in power system simulation . - 69 -