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


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