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

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  • 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.

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  • 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 $~(~{\rm~J}~)$
    ${u_1}$ $0.8~\times~{10^{~-~2}}$ ${u_2}$ ${\rm{0}}{\rm{.13}}$ ${u_3}$ ${\rm{0}}{\rm{.39}}$ ${u_4}$ ${\rm{0}}{\rm{.80}}$
    ${u_5}$ ${\rm{1}}{\rm{.97}}$ ${u_6}$ ${\rm{2}}{\rm{.54}}$ ${u_7}$ ${\rm{4}}{\rm{.19}}$ ${u_{\rm~MG}}$ ${\rm{10}}{\rm{.03}}$

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