SCIENTIA SINICA Informationis, Volume 49, Issue 8: 1066-1082(2019) https://doi.org/10.1360/N112018-00207

Optimized configuration of controllers of microgrids based on controllability

More info
  • ReceivedAug 2, 2018
  • AcceptedDec 17, 2018
  • PublishedAug 7, 2019


A method for studying the controllability of microgrids beyond structural controllability, which is applicable to actual microgrids, is proposed. Also, the cutoff frequency of the low-pass filter of a microgrid is proven to be a major factor affecting the minimum number of controllers required. In addition, according to the elementary transformation of the feature matrix of a microgrid, the nodes that require independent and non-independent control are identified and a general system control matrix construction method to fully control the state of the microgrid is proposed. Furthermore, according to the error curve of the node state, the constructed control matrix is proven to guarantee the controllability of the microgrid. An example of a microgrid with seven distributed generations was used to verify the effectiveness of the proposed method.

Funded by





[1] Chen J, Chen X, Feng Z Y, et al. A control strategy of seamless transfer between grid-connected and islanding operation for microgrid. Proc CSEE, 2014, 34: 3089--3097. Google Scholar

[2] Sun Q Y, Zhou J G, Guerrero J M. Hybrid Three-Phase/Single-Phase Microgrid Architecture With Power Management Capabilities. IEEE Trans Power Electron, 2015, 30: 5964-5977 CrossRef ADS Google Scholar

[3] Sun Q Y, Huang B N, Li D S. Optimal Placement of Energy Storage Devices in Microgrids via Structure Preserving Energy Function. IEEE Trans Ind Inf, 2016, 12: 1166-1179 CrossRef Google Scholar

[4] Luo Q, Deng F Q, Mao X R, et al. Theory and application of stability for stochastic reaction diffusion system. Sci Sin Inform, 2007, 37: 1272--1284. Google Scholar

[5] Zhang J Y, Ju P, Yu Y P, et al. Responses and stability of power system under small Gauss type random excitation. Sci China Tech Sci, 2012, 42: 851--857. Google Scholar

[6] Kalman R E. Mathematical description of linear dynamical systems. SIAM J Control, 1963, 1: 152--192. Google Scholar

[7] Song J L, Xiao H M, Li Z Q. Partial variable controllability of Boolean control network. IEEE Trans Autom Control, 2016, 46: 338--349. Google Scholar

[8] Newman M E J, Watts D J. Renormalization group analysis of the small-world network model. Phys Lett A, 1999, 263: 341-346 CrossRef ADS Google Scholar

[9] Liu Y Y, Slotine J J, Barabási A L. Controllability of complex networks. Nature, 2011, 473: 167-173 CrossRef PubMed ADS Google Scholar

[10] Lin C T. Structural controllability. IEEE Trans Automat Contr, 1974, 19: 201-208 CrossRef Google Scholar

[11] Wang W X, Ni X, Lai Y C. Optimizing controllability of complex networks by minimum structural perturbations. Phys Rev E, 2012, 85: 026115 CrossRef PubMed ADS Google Scholar

[12] Yan G, Ren J, Lai Y C. Controlling Complex Networks: How Much Energy Is Needed?. Phys Rev Lett, 2012, 108: 218703 CrossRef PubMed ADS Google Scholar

[13] Wang B, Gao L, Gao Y. Maintain the structural controllability under malicious attacks on directed networks. EPL, 2013, 101: 58003 CrossRef ADS Google Scholar

[14] Sun J, Motter A E. Controllability Transition and Nonlocality in Network Control. Phys Rev Lett, 2013, 110: 208701 CrossRef PubMed ADS arXiv Google Scholar

[15] Liu Y Y, Slotine J J, Barabasi A L. From the Cover: Observability of complex systems. Proc Natl Acad Sci USA, 2013, 110: 2460-2465 CrossRef PubMed ADS Google Scholar

[16] Chen G R. Problems and Challenges in Control Theory under Complex Dynamical Network Environments. Acta Automatica Sin, 2013, 39: 312-321 CrossRef Google Scholar

[17] Xi Y G. Large-scale Systems Control and Complex Networks--Exploration and Thinking. Acta Automatica Sin, 2013, 39: 1758-1768 CrossRef Google Scholar

[18] Li L Z, Zhao S Q, Pan Y J. Research on controllability and observability Of LF oscillation modes in multi-unit power system. North China Electric Power, 2001, 1: 4--6. Google Scholar

[19] Li X F. Research on the fundamental theory of controllability of complex networks. Dissertation for Ph.D. Degree. Zhejiang: Zhejiang University, 2017. Google Scholar

[20] Li J, Due?as-Osorio L, Chen C. Characterizing the topological and controllability features of U.S. power transmission networks. Physica A-Statistical Mech its Appl, 2016, 453: 84-98 CrossRef ADS Google Scholar

[21] Pogaku N, Prodanovic M, Green T C. Modeling, Analysis and Testing of Autonomous Operation of an Inverter-Based Microgrid. IEEE Trans Power Electron, 2007, 22: 613-625 CrossRef ADS Google Scholar

[22] Kahrobaeian A, Mohamed Y A R I. Analysis and Mitigation of Low-Frequency Instabilities in Autonomous Medium-Voltage Converter-Based Microgrids With Dynamic Loads. IEEE Trans Ind Electron, 2014, 61: 1643-1658 CrossRef Google Scholar

[23] Lombardi A, H?rnquist M. Controllability analysis of networks. Phys Rev E, 2007, 75: 056110 CrossRef PubMed ADS Google Scholar

[24] Hautus M L J. Controllability and observability conditions of linear autonomous systems. Nederl Akad Wet Proc Ser A, 1969, 72: 443--448. Google Scholar

[25] Yuan Z, Zhao C, Di Z. Exact controllability of complex networks. Nat Commun, 2013, 4: 2447 CrossRef PubMed ADS arXiv Google Scholar

[26] Rugh W J. Linear System Theory. Englewood Cliffs: Prentice-Hall, Inc, 1996. Google Scholar

  • Table 1   Parameters of the controller
    Parameter Value Parameter Value Parameter Value
    ${\omega_{f1}}$ 30.02 (rad/s) ${\omega~_{f2}}$ 30.34 (rad/s) ${\omega~_{f3}}$ 30.62 (rad/s)
    ${\omega~_{f4}}$ 30.95 (rad/s) ${\omega~_{f5}}$ 31.40 (rad/s) ${\omega~_{f6}}$ 30.58 (rad/s)
    ${\omega~_{f7}}$ 30.48 (rad/s) ${n_{q1}}$ 1.20E$-$6 (V/VAr) ${n_{q2}}$ 5.40E$-$6 (V/VAr)
    ${n_{q3}}$ 3.20E$-$6 (V/VAr) ${n_{q4}}$ 4.40E$-$6 (V/VAr) ${n_{q5}}$ 2.30E$-$6 (V/VAr)
    ${n_{q6}}$ 2.45E$-$6 (V/VAr) ${n_{q7}}$ 1.80E$-$6 (V/VAr) ${m_{p1}}$ 1.26E$-$7 (rad/s/W)
    ${m_{p2}}$ 3.14E$-$7 (rad/s/W) ${m_{p3}}$ 2.29E$-$7 (rad/s/W) ${m_{p4}}$ 3.64E$-$7 (rad/s/W)
    ${m_{p5}}$ 1.36E$-$7 (rad/s/W) ${m_{p6}}$ 3.19E$-$7 (rad/s/W) ${m_{p7}}$ 2.26E$-$7 (rad/s/W)
  • Table 2   Parameters of the line
    Parameter Value $(\Omega)$ Parameter Value $(\Omega)$ Parameter Value $(\Omega)$
    ${R_1}~+~{\rm~j}{X_1}$ $68.8~+~{\rm~j}108.6$ ${R_2}~+~{\rm~j}{X_2}$ $47.3~+~{\rm~j}89.3$ ${R_3}~+~{\rm~j}{X_3}$ $79.2~+~{\rm~j}118.8$
    ${R_4}~+~{\rm~j}{X_4}$ $107.4~+~{\rm~j}68.5$ ${R_5}~+~{\rm~j}{X_5}$ $104.2~+~{\rm~j}53.4$ ${R_6}~+~{\rm~j}{X_6}$ $54.6~+~{\rm~j}98.7$
    ${R_7}~+~{\rm~j}{X_7}$ $32.8~+~{\rm~j}104.9$ ${R}_{1~-~2}~+~{\rm~j}{X_{1~-~2}}$ $0.2~+~{\rm~j}0.26$ ${R}_{2~-~3}~+~{\rm~j}{X_{2~-~3}}$ $0.37~+~{\rm~j}0.58$
    ${R}_{3~-~4}~+~{\rm~j}{X_{3~-~4}}$ $0.29~+~{\rm~j}0.46$ ${R}_{4~-~5}~+~{\rm~j}{X_{4~-~5}}$ $0.27~+~{\rm~j}0.38$ ${R}_{5~-~6}~+~{\rm~j}{X_{5~-~6}}$ $0.42~+~{\rm~j}0.63$
    ${R}_{6~-~7}~+~{\rm~j}{X_{6~-~7}}$ $0.54~+~{\rm~j}0.98$
  • Table 3   Parameters of the steady state operation
    Parameter Value Parameter Value Parameter Value Parameter Value
    ${i_{q10}}$ ${\rm{~-~1}}{\rm{.06{E}~+~3}}~({\rm~A})$ ${i_{d10}}$ ${\rm{~-~1}}{\rm{.04E~+~3}}~({\rm~A})$ ${i_{q20}}$ ${\rm{~-~5}}{\rm{.83E~+~3}}~({\rm~A})$ ${i_{d20}}$ ${\rm{6}}{\rm{.70E~+~3}}~({\rm~A})$
    ${i_{q30}}$ ${\rm{4}}{\rm{.89E~+~3}}~({\rm~A})$ ${i_{d30}}$ ${\rm{~-~4}}{\rm{.83E~+~3}}~({\rm~A})$ ${i_{q40}}$ ${\rm{5}}{\rm{.39E~+~3}}~({\rm~A})$ ${i_{d40}}$ ${\rm{~-~3}}{\rm{.18E~+~3}}~({\rm~A})$
    ${i_{q50}}$ ${\rm{~-~7}}{\rm{.54E~+~3}}~({\rm~A})$ ${i_{d50}}$ ${\rm{~3}}{\rm{.89E~+~3}}~({\rm~A})$ ${i_{q60}}$ ${\rm{~8}}{\rm{.31E~+~3}}~({\rm~A})$ ${i_{d60}}$ ${\rm{~-~2}}{\rm{.68E~+~3}}~({\rm~A})$
    ${i_{q70}}$ ${\rm{~-~4}}{\rm{.39E~+~3}}~({\rm~A})$ ${i_{d70}}$ ${\rm{~-~1}}{\rm{.53E~+~3}}~({\rm~A})$ ${U_{q10}}$ ${\rm{~-~0}}{\rm{.22E~+~3}}~({\rm~V})$ ${U_{d10}}$ ${\rm{~10}}{\rm{.60E~+~3}}~({\rm~V})$
    ${U_{q20}}$ ${\rm{~0}}{\rm{.26E~+~3}}~({\rm~V})$ ${U_{d20}}$ ${\rm{~10}}{\rm{.56E~+~3}}~({\rm~V})$ ${U_{q30}}$ ${\rm{~-~0}}{\rm{.48E~+~3}}~({\rm~V})$ ${U_{d30}}$ ${\rm{~4}}{\rm{.60E~+~3}}~({\rm~V})$
    ${U_{q40}}$ ${\rm{~-~0}}{\rm{.29E~+~3}}~({\rm~V})$ ${U_{d40}}$ ${\rm{~3}}{\rm{.56E~+~3}}~({\rm~V})$ ${U_{q50}}$ ${\rm{~-~0}}{\rm{.32E~+~3}}~({\rm~V})$ ${U_{d50}}$ ${\rm{~5}}{\rm{.60E~+~3}}~({\rm~V})$
    ${U_{q60}}$ ${\rm{~0}}{\rm{.46E~+~3}}~({\rm~V})$ ${U_{d60}}$ ${\rm{~2}}{\rm{.56E~+~3}}~({\rm~V})$ ${U_{q70}}$ ${\rm{~-~0}}{\rm{.62E~+~3}}~({\rm~V})$ ${U_{d70}}$ ${\rm{~7}}{\rm{.60E~+~3}}~({\rm~V})$
  • Table 4   The control energy of ${u_1}~\sim~{u_7}$
    Input$~({\rm~V})$ Energy $~({\rm~J}~)$ Input$~({\rm~V})$ Energy $~(~{\rm~J}~)$ Input$~({\rm~V})$ Energy $~(~{\rm~J}~)$ Input$~({\rm~V})$ Energy $~(~{\rm~J}~)$
    ${u_1}$ $0.8~\times~{10^{~-~2}}$ ${u_2}$ ${\rm{0}}{\rm{.13}}$ ${u_3}$ ${\rm{0}}{\rm{.39}}$ ${u_4}$ ${\rm{0}}{\rm{.80}}$
    ${u_5}$ ${\rm{1}}{\rm{.97}}$ ${u_6}$ ${\rm{2}}{\rm{.54}}$ ${u_7}$ ${\rm{4}}{\rm{.19}}$ ${u_{\rm~MG}}$ ${\rm{10}}{\rm{.03}}$

Copyright 2020 Science China Press Co., Ltd. 《中国科学》杂志社有限责任公司 版权所有

京ICP备18024590号-1       京公网安备11010102003388号