Voltage magnitude constraints for 'bus' matrix output not met

[joelfo...@gmail.com]

I am a student working on developing an OPF model for a 15 bus power system with Pypower.

I discovered an issue whereby the converged voltage magnitudes do not keep within the voltage constraints, which is selected as V_max=1.05 > V_i > V_min=0.95. 

This occurs primarily for the PF study. For instance, when the load is increased for one of the buses, the PF study would still converge after several iterations, but several of the voltage magnitude values violated the maximum and minimum constraints.

I would like to inquire about the purpose of the 12th and 13th column inputs of the bus matrix below if the output for voltage magnitude is not kept within the constraints.

   ppc["bus"] = array([

        [1,     3,  1192.84,    1192.84,    0,  0,  1,  1,  0,  230,    1,  1.05,   0.95],

        [2,     1,        0,          0,    0,  0,  1,  1,  0,  400,    1,  1.05,   0.95],

        [3,     1,        0,          0,    0,  0,  1,  1,  0,  230,    1,  1.05,   0.95],

        [4,     1,   723.69,    723.690,    0,  0,  1,  1,  0,  230,    1,  1.05,   0.95],

        [5,     1,   117.40,     117.40,    0,  0,  1,  1,  0,  230,    1,  1.05,   0.95],

        [6,     1,        0,          0,    0,  0,  1,  1,  0,  400,    1,  1.05,   0.95],

        [7,     1,   313.48,     313.48,    0,  0,  1,  1,  0,  230,    1,  1.05,   0.95],

        [8,     1,        0,          0,    0,  0,  1,  1,  0,  400,    1,  1.05,   0.95],

        [9,     1,   217.265,    217.265,   0,  0,  1,  1,  0,  230,    1,  1.05,   0.95],

        [10,    1,   405.870,    405.870,   0,  0,  1,  1,  0,  230,    1,  1.05,   0.95],

        [11,    1,   374.315,    374.315,   0,  0,  1,  1,  0,  230,    1,  1.05,   0.95],

        [12,    1,        0,          0,    0,  0,  1,  1,  0,  400,    1,  1.05,   0.95],

        [13,    1,   561.735,    561.735,   0,  0,  1,  1,  0,  230,    1,  1.05,   0.95],

        [14,    1,   557.455,    557.455,   0,  0,  1,  1,  0,  230,    1,  1.05,   0.95],

        [15,    1,   535.950,    535.950,   0,  0,  1,  1,  0,  230,    1,  1.05,   0.95]

    ])

Output

Bus Voltage Generation Load Lambda($/MVA-hr) # Mag(pu) Ang(deg) P (MW) Q (MVAr) P (MW) Q (MVAr) P Q ----- ------- -------- -------- -------- -------- -------- ------- ------- 0 1.038 0.000* 1881.00 2799.97 0.00 1192.84 18.997 0.035 1 1.050 -0.369 718.20 1028.78 - - 19.017 - 2 1.050 -0.132 1224.26 1455.28 - - 19.000 - 3 1.012 -1.674 - - 723.69 723.69 19.067 0.086 4 1.028 -1.044 - - 117.40 117.40 19.039 0.050 5 1.030 -1.039 - - - - 19.046 0.047 6 1.010 -1.756 - - 313.48 313.48 19.071 0.091 7 1.031 -1.017 - - - - 19.045 0.045 8 1.016 -1.611 - - 217.26 217.26 19.064 0.075 9 1.008 -1.922 - - 405.87 405.87 19.080 0.095 10 1.023 -1.309 - - 374.31 374.31 19.056 0.063 11 1.025 -1.221 - - - - 19.053 0.058 12 0.990 -2.766 - - 561.74 561.74 19.118 0.138 13 0.982 -3.005 - - 557.46 557.46 19.130 0.161 14 1.006 -1.807 - - 535.95 535.95 19.074 0.104 -------- -------- -------- -------- Total: 3823.46 5284.03 3807.16 5000.00

[Richard Lincoln]

Power flow just works out the bus voltages and branch flows given a set of generator set-points. It can be made to observe Q limits, but this involves repeated solutions.  OPF will adjust the generator outputs to minimise cost while observing constraints.

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[joelfo...@gmail.com]

I see, thank you very much! 

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