A Novel Stability Simulation Algorithm of Microgrids Based on Projective Integration Method
Li Peng1, Yuan Kai1, Wang Chengshan1, Huang Xiaoyun2, Huang Hongyuan2
1. Key Laboratory of Smart Grid of Ministry of Education Tianjin University Tianjin 300072 China; 2. Guangdong Power Grid Corporation Foshan 528000 China
Abstract：The increasing penetration of variety kinds of distributed generation (DG) results in the multiple time scale of the connected microgrid, which leads to a higher requirement on the numerical stability and calculation efficiency of the integration algorithms for microgrid stability simulation. This paper proposes an enhanced projective integration method for the stability simulation of microgrids. Each compound step of the method is combined with several small size steps (inner integrator) and a large one (outer integrator), the step sizes of which are selected based on the time constants of the fast and slow dynamic behaviors. The proposed method is consistent of order 2 and greatly improves the numerical stability of traditional numerical integration algorithms. Finally, some case studies are performed based on a low voltage microgrid and the accuracy and effectiveness of the proposed projective method is shown through comparing with the commercial software for the stability simulation of power systems.
李鹏, 原凯, 王成山, 黄小耘, 黄红远. 一种基于投影积分算法的微电网稳定性仿真方法[J]. 电工技术学报, 2014, 29(2): 93-101.
Li Peng, Yuan Kai, Wang Chengshan, Huang Xiaoyun, Huang Hongyuan. A Novel Stability Simulation Algorithm of Microgrids Based on Projective Integration Method. Transactions of China Electrotechnical Society, 2014, 29(2): 93-101.
[1] 王成山,李鹏. 分布式发电,微网与智能配电网的发展与挑战[J]. 电力系统自动化,2010, 34(2): 10-14. Wang Chengshan, Li Peng. Development and challenges of distributed generation , the microgrid and smart distribution system[J]. Automation of Electric Power Systems, 2010, 34(2): 10-14. [2] 吴卫民,何远彬,耿攀,等. 直流微网研究中的关键技术[J]. 电工技术学报,2012, 27(1): 98-106. Wu Weimin, He Yuanbin, Geng Pan, et al. Key technologies for DC micro-grids[J]. Transactions of China Electrotechnical Society, 2012, 27(1): 98-106. [3] Kundur P. Power system stability and control[M]. New York: McGraw-Hill, 1994. [4] Ascher U M, Petzold L R. Computer methods for ordinary differential equations and differential-algebraic equations[M]. Philadelphia: SIAM, 1998. [5] Soultanis N L, Papathanasiou S A, Hatziargyriou N D. A stability algorithm for the dynamic analysis of inverter dominated unbalanced LV microgrids[J]. IEEE Transactions on Power Systems, 2007, 22(1): 294-304. [6] Hofer E. A partially implicit method for large stiff systems of ODEs with only few equations introducing small time-constants[J]. SIAM Journal on Numerical Analysis, 1976, 13(5): 645-663. [7] Gear C W, Saad Y. Iterative solution of linear equations in ODE codes[J]. SIAM Journal on Scientific and Statistical Computing, 1982, 4(4): 583-601. [8] Yang D, Ajjarapu V. A decoupled time-domain simulation method via invariant subspace partition for power system analysis[J]. IEEE Transactions on Power Systems, 2006, 21(1): 11-18. [9] Gear C W, Kevrekidis I G. Projective methods for stiff differential equations: problems with gaps in their eigenvalue spectrum[J]. SIAM Journal on Scientific Computing, 2006, 24(4): 1091-1106. [10] Gear C W, Kevrekidis I G. Telescopic projective methods for parabolic differential equations[J]. Journal of Computational Physics, 2003, 187(1): 95-109. [11] Molina M G, Mercado P E. Modeling and control of grid-connected photovoltaic energy conversion system used as a dispersed generator[C]. Transmission and Distribution Conference and Exposition: Latin America, 2008． [12] 王成山. 微电网分析与仿真理论[M]. 北京: 科学出版社, 2013. [13] Esram T, Chapman P L. Comparison of photovoltaic array maximum power point tracking techniques[J]. IEEE Transaction on Energy Conversion, 2007, 22(2): 439-499. [14] Li Y H, Choi S S, Rajakaruna S. An analysis of the control and operation of a solid oxide fuel-cell power plant in an isolated system[J]. IEEE Transactions on Energy Conversion, 2005, 20(2): 381-387. [15] Tremblay O, Dessaint L A, Dekkiche A I. A generic battery model for the dynamic simulation of hybrid electric vehicles[C]. Vehicle Power and Propulsion Conference, 2007. [16] Wanner G, Hairer E. Solving ordinary differential equations II[M], Berlin: Springer-Verlag, 1991. [17] 彭克, 王成山, 李琰, 等. 典型中低压微电网算例系统设计[J]. 电力系统自动化, 2011, 35(18): 31-35. Peng Ke, Wang Chengshan, Li Yan, et al. Design of a typical medium-low voltage microgrid network[J]. Automation of Electric Power Systems, 2011, 35(18): 31-35. [18] DIgSILENT GmbH. DIgSILENT PowerFactory V15.0 BETA-User Manual[M]. DIgSILENT GmbH, 2012.
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