Convergence problems on large net models in PandaPower state estimation module

alex_l · 24 June 2021 16:02

Hi all,

I’m testing state estimation capabilities of PandaPower lib. To emulate measurements i pass power flow results as feedback. For small test grids from pandapower.networks submodule (case9, case30, case39) all works fine, estimation is precise and bad data detection function robust to distortions in voltage, injection and flow meases. But when I try to apply this method to a little more larger networks (case89pegase for example) both basic WLS and advanced robust estimation algorithms don’t converge to correct point, or even diverges at all:

from pandapower.estimation import estimate
from pandapower.networks import *
from math import fabs
import pandapower as pp

def get_net():
    return case89pegase()

def print_net_est_res(net):

    print("\n########################################################################################################")

    print(">>> est_res_bus:")
    print(net.res_bus_est[['vm_pu', 'p_mw', 'q_mvar']])
    print(">>> est_res_trafo:")
    print(net.res_trafo_est[['p_hv_mw', 'q_hv_mvar', 'p_lv_mw', 'q_lv_mvar', 'i_hv_ka', 'i_lv_ka']])
    print(">>> est_res_trafo3w:")
    print(net.res_trafo3w_est[['p_hv_mw', 'q_hv_mvar', 'p_mv_mw', 'q_mv_mvar', 'p_lv_mw', 'q_lv_mvar', 'i_hv_ka', 'i_mv_ka', 'i_lv_ka']])
    print(">>> est_res_line:")
    print(net.res_line_est[['p_from_mw', 'q_from_mvar', 'p_to_mw', 'q_to_mvar', 'i_from_ka', 'i_to_ka']])

def print_est_comparison(net, net2, alarm_thr, noise_lim):
    pd.set_option('display.max_rows', None)
    pd.set_option('display.max_columns', None)
    pd.set_option('display.width', None)

    def diff_stat(ref_val, val, alarm_thr, noise_lim):
        try:
            abs_diff = ref_val - val
        except Exception as ex:
            print(ex)

        if fabs(ref_val) < noise_lim or fabs(val) < noise_lim:
            return '+'
        else:
            rel_diff = fabs(100 * abs_diff / ref_val)
            if rel_diff > alarm_thr:
                return '{:.3e}({:.2f}%)'.format(abs_diff, rel_diff)
            else:
                return '+'

    # bus`s
    for busIndex in net.bus.index:
        net2.res_bus_est.vm_pu[busIndex] = diff_stat(net.res_bus.vm_pu[busIndex], net2.res_bus_est.vm_pu[busIndex], alarm_thr, noise_lim)
        net2.res_bus_est.p_mw[busIndex] = diff_stat(net.res_bus.p_mw[busIndex], net2.res_bus_est.p_mw[busIndex], alarm_thr, noise_lim)
        net2.res_bus_est.q_mvar[busIndex] = diff_stat(net.res_bus.q_mvar[busIndex], net2.res_bus_est.q_mvar[busIndex], alarm_thr, noise_lim)

    # line`s
    for lineIndex in net.line.index:
        net2.res_line_est.p_from_mw[lineIndex] = diff_stat(net.res_line.p_from_mw[lineIndex], net2.res_line_est.p_from_mw[lineIndex], alarm_thr, noise_lim)
        net2.res_line_est.p_to_mw[lineIndex] = diff_stat(net.res_line.p_to_mw[lineIndex], net2.res_line_est.p_to_mw[lineIndex], alarm_thr, noise_lim)

        net2.res_line_est.q_from_mvar[lineIndex] = diff_stat(net.res_line.q_from_mvar[lineIndex], net2.res_line_est.q_from_mvar[lineIndex], alarm_thr, noise_lim)
        net2.res_line_est.q_to_mvar[lineIndex] = diff_stat(net.res_line.q_to_mvar[lineIndex], net2.res_line_est.q_to_mvar[lineIndex], alarm_thr, noise_lim)

        net2.res_line_est.i_from_ka[lineIndex] = diff_stat(net.res_line.i_from_ka[lineIndex], net2.res_line_est.i_from_ka[lineIndex], alarm_thr, noise_lim)
        net2.res_line_est.i_to_ka[lineIndex] = diff_stat(net.res_line.i_to_ka[lineIndex], net2.res_line_est.i_to_ka[lineIndex], alarm_thr, noise_lim)

    # trafo`s
    for trafoIndex in net.trafo.index:
        net2.res_trafo_est.p_hv_mw[trafoIndex] = diff_stat(net.res_trafo.p_hv_mw[trafoIndex], net2.res_trafo_est.p_hv_mw[trafoIndex], alarm_thr, noise_lim)
        net2.res_trafo_est.p_lv_mw[trafoIndex] = diff_stat(net.res_trafo.p_lv_mw[trafoIndex], net2.res_trafo_est.p_lv_mw[trafoIndex], alarm_thr, noise_lim)

        net2.res_trafo_est.q_hv_mvar[trafoIndex] = diff_stat(net.res_trafo.q_hv_mvar[trafoIndex], net2.res_trafo_est.q_hv_mvar[trafoIndex], alarm_thr, noise_lim)
        net2.res_trafo_est.q_lv_mvar[trafoIndex] = diff_stat(net.res_trafo.q_lv_mvar[trafoIndex], net2.res_trafo_est.q_lv_mvar[trafoIndex], alarm_thr, noise_lim)

        net2.res_trafo_est.i_hv_ka[trafoIndex] = diff_stat(net.res_trafo.i_hv_ka[trafoIndex], net2.res_trafo_est.i_hv_ka[trafoIndex], alarm_thr, noise_lim)
        net2.res_trafo_est.i_lv_ka[trafoIndex] = diff_stat(net.res_trafo.i_lv_ka[trafoIndex], net2.res_trafo_est.i_lv_ka[trafoIndex], alarm_thr, noise_lim)

    # trafo3w`s
    for trafoIndex in net.trafo3w.index:
        net2.res_trafo3w_est.p_hv_mw[trafoIndex] = diff_stat(net.res_trafo3w.p_hv_mw[trafoIndex], net2.res_trafo3w_est.p_hv_mw[trafoIndex], alarm_thr, noise_lim)
        net2.res_trafo3w_est.p_lv_mw[trafoIndex] = diff_stat(net.res_trafo3w.p_lv_mw[trafoIndex], net2.res_trafo3w_est.p_lv_mw[trafoIndex], alarm_thr, noise_lim)
        net2.res_trafo3w_est.p_mv_mw[trafoIndex] = diff_stat(net.res_trafo3w.p_mv_mw[trafoIndex], net2.res_trafo3w_est.p_mv_mw[trafoIndex], alarm_thr, noise_lim)

        net2.res_trafo3w_est.q_hv_mvar[trafoIndex] = diff_stat(net.res_trafo3w.q_hv_mvar[trafoIndex], net2.res_trafo3w_est.q_hv_mvar[trafoIndex], alarm_thr, noise_lim)
        net2.res_trafo3w_est.q_lv_mvar[trafoIndex] = diff_stat(net.res_trafo3w.q_lv_mvar[trafoIndex], net2.res_trafo3w_est.q_lv_mvar[trafoIndex], alarm_thr, noise_lim)
        net2.res_trafo3w_est.q_mv_mvar[trafoIndex] = diff_stat(net.res_trafo3w.q_mv_mvar[trafoIndex], net2.res_trafo3w_est.q_mv_mvar[trafoIndex], alarm_thr, noise_lim)

        net2.res_trafo3w_est.i_hv_ka[trafoIndex] = diff_stat(net.res_trafo3w.i_hv_ka[trafoIndex], net2.res_trafo3w_est.i_hv_ka[trafoIndex], alarm_thr, noise_lim)
        net2.res_trafo3w_est.i_lv_ka[trafoIndex] = diff_stat(net.res_trafo3w.i_lv_ka[trafoIndex], net2.res_trafo3w_est.i_lv_ka[trafoIndex], alarm_thr, noise_lim)
        net2.res_trafo3w_est.i_mv_ka[trafoIndex] = diff_stat(net.res_trafo3w.i_mv_ka[trafoIndex], net2.res_trafo3w_est.i_mv_ka[trafoIndex], alarm_thr, noise_lim)

    print_net_est_res(net2)

def pass_meases_feedback(net, net2, v_stddev, pq_stddev, i_stddev):
    # bus`s
    for busIndex in net.bus.index:
        vn_pu = net.res_bus.vm_pu[busIndex]
        pp.create_measurement(net2, "v", "bus", vn_pu, v_stddev, element=busIndex)

        p_mw = net.res_bus.p_mw[busIndex]
        if p_mw != 0:
            pp.create_measurement(net2, "p", "bus", p_mw, pq_stddev, element=busIndex)
        q_mvar = net.res_bus.q_mvar[busIndex]
        if q_mvar != 0:
            pp.create_measurement(net2, "q", "bus", q_mvar, pq_stddev, element=busIndex)

    # line`s
    for lineIndex in net.line.index:
        p_from_mw = net.res_line.p_from_mw[lineIndex]
        pp.create_measurement(net2, "p", "line", p_from_mw, pq_stddev, element=lineIndex, side="from")
        p_to_mw = net.res_line.p_to_mw[lineIndex]
        pp.create_measurement(net2, "p", "line", p_to_mw, pq_stddev, element=lineIndex, side="to")

        q_from_mvar = net.res_line.q_from_mvar[lineIndex]
        pp.create_measurement(net2, "q", "line", q_from_mvar, pq_stddev, element=lineIndex, side="from")
        q_to_mvar = net.res_line.q_to_mvar[lineIndex]
        pp.create_measurement(net2, "q", "line", q_to_mvar, pq_stddev, element=lineIndex, side="to")

        # i_from_ka = net.res_line.i_from_ka[lineIndex]
        # pp.create_measurement(net2, "i", "line", i_from_ka, i_stddev, element=lineIndex, side="from")
        # i_to_ka = net.res_line.i_to_ka[lineIndex]
        # pp.create_measurement(net2, "i", "line", i_to_ka, i_stddev, element=lineIndex, side="to")

    # trafo`s
    for trafoIndex in net.trafo.index:
        p_hv_mw = net.res_trafo.p_hv_mw[trafoIndex]
        pp.create_measurement(net2, "p", "trafo", p_hv_mw, pq_stddev, element=trafoIndex, side="hv")
        p_lv_mw = net.res_trafo.p_lv_mw[trafoIndex]
        pp.create_measurement(net2, "p", "trafo", p_lv_mw, pq_stddev, element=trafoIndex, side="lv")

        q_hv_mvar = net.res_trafo.q_hv_mvar[trafoIndex]
        pp.create_measurement(net2, "q", "trafo", q_hv_mvar, pq_stddev, element=trafoIndex, side="hv")
        q_lv_mvar = net.res_trafo.q_lv_mvar[trafoIndex]
        pp.create_measurement(net2, "q", "trafo", q_lv_mvar, pq_stddev, element=trafoIndex, side="lv")

        # i_hv_ka = net.res_trafo.i_hv_ka[trafoIndex]
        # pp.create_measurement(net2, "i", "trafo", i_hv_ka, i_stddev, element=trafoIndex, side="hv")
        # i_lv_ka = net.res_trafo.i_lv_ka[trafoIndex]
        # pp.create_measurement(net2, "i", "trafo", i_lv_ka, i_stddev, element=trafoIndex, side="lv")

    # trafo3w`s
    for trafoIndex in net.trafo3w.index:

        p_hv_mw = net.res_trafo3w.p_hv_mw[trafoIndex]
        pp.create_measurement(net2, "p", "trafo3w", p_hv_mw, pq_stddev, element=trafoIndex, side="hv")
        p_lv_mw = net.res_trafo3w.p_lv_mw[trafoIndex]
        pp.create_measurement(net2, "p", "trafo3w", p_lv_mw, pq_stddev, element=trafoIndex, side="lv")
        p_mv_mw = net.res_trafo3w.p_mv_mw[trafoIndex]
        pp.create_measurement(net2, "p", "trafo3w", p_mv_mw, pq_stddev, element=trafoIndex, side="mv")

        q_hv_mvar = net.res_trafo3w.q_hv_mvar[trafoIndex]
        pp.create_measurement(net2, "q", "trafo3w", q_hv_mvar, pq_stddev, element=trafoIndex, side="hv")
        q_lv_mvar = net.res_trafo3w.q_lv_mvar[trafoIndex]
        pp.create_measurement(net2, "q", "trafo3w", q_lv_mvar, pq_stddev, element=trafoIndex, side="lv")
        q_mv_mvar = net.res_trafo3w.q_mv_mvar[trafoIndex]
        pp.create_measurement(net2, "q", "trafo3w", q_mv_mvar, pq_stddev, element=trafoIndex, side="mv")

        # i_hv_ka = net.res_trafo3w.i_hv_ka[trafoIndex]
        # pp.create_measurement(net2, "i", "trafo3w", i_hv_ka, i_stddev, element=trafoIndex, side="hv")
        # i_lv_ka = net.res_trafo3w.i_lv_ka[trafoIndex]
        # pp.create_measurement(net2, "i", "trafo3w", i_lv_ka, i_stddev, element=trafoIndex, side="lv")
        # i_mv_ka = net.res_trafo3w.i_mv_ka[trafoIndex]
        # pp.create_measurement(net2, "i", "trafo3w", i_mv_ka, i_stddev, element=trafoIndex, side="mv")

#################################################################################################################################

net = get_net()
pp.runpp(net, calculate_voltage_angles=True, enforce_q_lims=False)

net2 = get_net()

v_stddev = 0.01 # pu
pq_stddev = 0.01 # MW/Mvar
i_stddev= 0.002 # kA

pass_meases_feedback(net, net2, v_stddev, pq_stddev, i_stddev)

#chi2_test = chi2_analysis(net)
#success_rn_max = remove_bad_data(net2)

success = estimate(net2, calculate_voltage_angles=True, zero_injection='auto', init='flat')
if success:
    print_est_comparison(net, net2, 1, 0.001)

Above code output absolute and relative differences between meas and its estimation if it >1% and ‘+’ for other measurements. PF result on input is not distorbed in this test:

>>> est_res_bus:
               vm_pu                p_mw                q_mvar
0   4.476e-02(4.48%)    1.189e-02(5.99%)    -4.371e+00(96.75%)
1   4.997e-02(4.75%)    3.510e-01(1.50%)      6.642e-01(1.16%)
10  4.262e-02(4.10%)                   +    -1.352e+01(55.40%)
11  4.382e-02(4.28%)  2.145e-01(116.59%)    2.699e+00(170.75%)
12  4.699e-02(4.54%)                   +                     +
13  4.958e-02(4.87%)                   +                     +
14  4.429e-02(4.40%)                   +    -1.005e+01(59.93%)
15  5.071e-02(4.85%)                   +                     +
16  4.433e-02(4.41%)                   +    -9.396e+00(64.33%)
17  4.419e-02(4.38%)  -4.605e-02(26.34%)     5.664e-01(38.00%)
18  4.555e-02(4.31%)                   +    -5.919e+00(61.02%)
19  5.279e-02(5.16%)                   +     -1.446e+00(1.06%)
2   5.056e-02(4.86%)                   +     -1.338e+00(4.99%)
20  4.309e-02(4.15%)                   +                     +
21  4.328e-02(4.17%)                   +     4.698e+00(12.02%)
22  5.330e-02(5.24%)   -1.280e-01(1.49%)    -1.396e+00(94.35%)
23  4.306e-02(4.15%)                   +      2.455e+00(1.22%)
24  4.468e-02(4.50%)  3.853e-01(213.38%)    -1.321e+01(59.09%)
25  5.087e-02(4.88%)                   +                     +
26  4.481e-02(4.52%)   2.602e-02(10.92%)    -6.196e-01(55.17%)
27  4.752e-02(4.37%)                   +      3.800e+00(3.68%)
28  4.477e-02(4.48%)  -1.658e-02(28.89%)    -2.528e+00(66.43%)
29  4.165e-02(3.96%)                   +  -7.791e+00(1133.28%)
3   4.199e-02(3.99%)   2.464e-02(48.45%)    4.671e+00(231.58%)
30  5.141e-02(5.03%)                   +     -2.514e+00(4.16%)
31  4.231e-02(4.03%)                   +   -1.161e+01(174.19%)
32  5.009e-02(4.75%)                   +      2.491e+00(3.03%)
33  4.702e-02(4.55%)                   +                     +
34  5.052e-02(4.85%)                   +      7.217e-01(1.18%)
35  5.188e-02(5.17%)                   +   -1.321e+00(219.03%)
36  4.258e-02(4.05%)                   +                     +
37  5.011e-02(4.85%)                   +                     +
38  5.087e-02(4.88%)                   +   -6.204e-01(173.32%)
39  5.110e-02(4.93%)                   +     -8.452e-01(1.09%)
4   4.198e-02(3.99%)  7.738e-01(401.33%)    -1.671e+01(20.44%)
40  5.079e-02(4.89%)                   +                     +
41  5.042e-02(4.81%)                   +                     +
42  5.065e-02(4.88%)                   +                     +
43  4.162e-02(3.95%)    6.423e-01(1.73%)    -2.210e+01(46.29%)
44  5.009e-02(4.75%)    4.562e-01(2.16%)     1.319e+00(41.98%)
45  5.163e-02(5.01%)                   +                     +
46  4.730e-02(4.58%)                   +      4.013e+00(5.40%)
47  4.297e-02(4.14%)                   +    -7.332e+00(27.06%)
48  4.479e-02(4.49%)  4.891e-01(156.22%)    -7.681e+00(44.54%)
49  5.051e-02(4.85%)                   +   -2.039e+00(570.29%)
5   4.703e-02(4.55%)                   +      1.437e+00(3.43%)
50  4.294e-02(4.12%)                   +    -8.431e-01(34.80%)
51  4.991e-02(4.65%)                   +      1.225e+00(1.52%)
52  4.430e-02(4.39%)   1.656e-01(56.06%)   -2.385e+00(557.30%)
53  4.297e-02(4.12%)  -7.878e-02(44.17%)     1.925e+00(44.04%)
54  4.536e-02(4.64%)                   +     -1.238e+01(7.47%)
55  4.196e-02(3.99%)                   +                     +
56  4.443e-02(4.47%)                   +    -1.446e+01(43.47%)
57  4.460e-02(4.17%)                   +     -6.392e+00(4.32%)
58  4.456e-02(4.44%)   1.043e-01(49.08%)   -1.012e+00(149.35%)
59  4.192e-02(3.98%)                   +     -5.364e+00(1.96%)
6   4.332e-02(4.20%)                   +                     +
60  4.976e-02(4.62%)                   +      1.152e+00(1.40%)
61  4.592e-02(4.74%)   1.783e-01(77.20%)   -6.170e+00(135.91%)
62  4.393e-02(4.33%)                   +    -1.126e+01(51.67%)
63  4.597e-02(4.73%)   1.822e-01(82.51%)    -2.861e+00(71.90%)
64  5.011e-02(4.85%)                   +     8.730e-01(16.23%)
65  4.411e-02(4.34%)                   +     -6.864e-01(1.09%)
66  5.028e-02(4.83%)                   +     1.411e+00(11.02%)
67  4.364e-02(4.21%)  1.623e+00(521.83%)     6.094e+00(91.92%)
68  4.406e-02(4.36%)  5.770e-01(185.64%)    -1.020e+01(20.60%)
69  5.035e-02(4.75%)                   +      7.018e-01(2.34%)
7   5.189e-02(5.18%)                   +      2.465e+00(1.61%)
70  4.197e-02(3.99%)                   +     -5.533e+00(3.59%)
71  4.364e-02(4.34%)                   +     -5.209e-01(4.87%)
72  4.455e-02(4.45%)  4.370e-01(224.30%)    -9.612e+00(50.10%)
73  4.455e-02(4.44%)  3.376e-01(159.45%)    -6.259e+00(94.13%)
74  4.991e-02(4.65%)                   +                     +
75  4.248e-02(4.07%)  3.579e-01(219.17%)   -2.878e+00(128.69%)
76  4.959e-02(4.87%)                   +                     +
77  5.070e-02(4.84%)                   +                     +
78  4.444e-02(4.43%)   1.265e-01(28.05%)    -8.414e+00(39.80%)
79  4.368e-02(4.20%)                   +      9.454e+00(6.71%)
8   4.165e-02(3.96%)                   +  -7.743e+00(1269.69%)
80  4.379e-02(4.28%)                   +     -2.407e+00(1.24%)
81  4.410e-02(4.36%)  -4.189e-02(22.62%)   -1.641e+00(181.74%)
82  4.433e-02(4.40%)                   +    -7.410e+00(44.67%)
83  5.331e-02(5.25%)                   +                     +
84  4.187e-02(3.96%)  4.631e-01(293.48%)    -1.729e+01(61.20%)
85  4.455e-02(4.43%)  3.150e-01(151.52%)    -2.111e+00(67.97%)
86  4.434e-02(4.41%)                   +    -1.014e+01(65.77%)
87  5.268e-02(5.14%)   -2.261e-01(1.26%)    -3.603e+00(15.46%)
88  4.197e-02(3.99%)                   +     -5.532e+00(3.59%)
9   4.415e-02(4.37%)                   +    -9.518e+00(58.20%)
>>> est_res_trafo:
   p_hv_mw            q_hv_mvar p_lv_mw           q_lv_mvar            i_hv_ka            i_lv_ka
0        +   -4.616e+00(66.46%)       +   3.769e+00(23.75%)  -8.166e-03(4.64%)  -1.403e-02(4.64%)
1        +   -5.392e+00(36.87%)       +   4.543e+00(18.86%)  -8.133e-03(4.39%)  -1.403e-02(4.39%)
10       +    -7.653e+00(8.21%)       +    4.152e+00(6.46%)  -2.307e-02(5.88%)  -5.566e-02(5.88%)
11       +    -3.811e+00(4.68%)       +                   +  -2.227e-02(4.86%)  -5.212e-02(4.86%)
12       +    -4.257e+00(6.31%)       +    1.152e+00(3.13%)  -1.943e-02(4.95%)  -4.603e-02(4.95%)
13       +    -5.509e-01(2.27%)       +                   +  -1.182e-02(4.96%)  -1.734e-02(4.96%)
14       +   -9.139e+00(10.56%)       +   3.740e+00(11.14%)  -2.526e-02(4.97%)  -6.316e-02(4.97%)
15       +     7.832e-02(1.42%)       +   -3.207e-01(3.92%)  -6.333e-03(4.41%)  -9.288e-03(4.41%)
16       +   -2.485e-01(16.41%)       +   -1.344e-01(2.41%)  -1.108e-02(4.61%)  -1.625e-02(4.61%)
17       +    -5.771e+00(6.14%)       +    2.197e+00(3.43%)  -2.510e-02(5.78%)  -5.875e-02(5.78%)
18       +                    +       +   -3.570e+00(2.99%)  -2.469e-02(5.02%)  -5.635e-02(5.02%)
19       +    -4.707e+00(2.02%)       +   -4.335e+00(3.17%)  -3.349e-02(4.60%)  -7.834e-02(4.60%)
2        +   -7.084e+00(12.40%)       +   5.033e+00(12.37%)  -1.849e-02(6.06%)  -4.369e-02(6.06%)
20       +    -2.698e+00(2.34%)       +                   +  -2.081e-02(5.13%)  -4.871e-02(5.13%)
21       +    -4.543e+00(4.97%)       +   -6.506e-01(1.57%)  -2.574e-02(5.07%)  -6.098e-02(5.07%)
22       +    -7.410e+00(4.58%)       +   -2.777e+00(5.81%)  -3.703e-02(4.37%)  -6.185e-02(4.37%)
23       +   -4.520e-01(28.15%)       +                   +  -2.256e-03(4.46%)  -3.308e-03(4.46%)
24       +   -1.342e+00(20.26%)       +   -1.004e-01(1.10%)  -9.075e-03(4.48%)  -1.331e-02(4.48%)
25       +    -4.464e-01(5.27%)       +    3.253e-01(3.13%)  -1.309e-03(3.07%)  -1.920e-03(3.07%)
26       +    -1.440e-01(9.01%)       +    5.355e-02(2.05%)  -6.037e-04(4.35%)  -8.854e-04(4.35%)
27       +   -1.216e-01(16.70%)       +    5.048e-02(3.29%)  -4.820e-04(4.31%)  -7.070e-04(4.31%)
28       +    -4.213e+00(3.91%)       +   -1.090e+00(1.91%)  -2.820e-02(5.09%)  -6.679e-02(5.09%)
29       +   -2.371e-01(22.34%)       +    3.515e-02(1.09%)  -1.154e-03(4.54%)  -1.692e-03(4.54%)
3        +    -2.573e+00(2.14%)       +                   +  -2.035e-02(5.42%)  -4.703e-02(5.42%)
30       +    -4.379e+00(6.59%)       +    1.941e+00(4.33%)  -1.896e-02(5.48%)  -4.592e-02(5.48%)
31       +   -6.178e+00(19.11%)       +   4.140e+00(28.92%)  -1.624e-02(5.50%)  -3.983e-02(5.50%)
32       +   -6.682e-01(19.75%)       +                   +  -4.315e-03(4.57%)  -6.329e-03(4.57%)
33       +    -3.240e+00(1.76%)       +   -1.905e+00(1.43%)  -2.750e-02(4.98%)  -6.403e-02(4.98%)
34       +   -7.605e+00(11.30%)       +   4.523e+00(11.32%)  -2.101e-02(5.49%)  -5.051e-02(5.49%)
35       +    -1.264e-01(1.96%)       +                   +  -2.404e-03(4.93%)  -3.525e-03(4.93%)
36       +    -2.927e+00(3.17%)       +                   +  -1.516e-02(4.89%)  -2.532e-02(4.89%)
37       +    -2.990e+00(3.17%)       +                   +  -1.549e-02(4.89%)  -2.587e-02(4.89%)
38       +    -2.662e-01(5.42%)       +    2.051e-01(3.47%)  -6.928e-04(2.99%)  -1.016e-03(2.99%)
39       +   -7.472e-02(11.06%)       +    2.938e-02(2.50%)  -3.054e-04(4.43%)  -4.479e-04(4.43%)
4        +    -2.448e-02(3.64%)       +   -6.199e-03(1.59%)  -3.262e-04(5.28%)  -4.784e-04(5.28%)
40       +    -4.454e+00(4.85%)       +    1.868e+00(2.69%)  -1.929e-02(5.64%)  -4.567e-02(5.64%)
41       +    -1.611e+00(1.82%)       +   -1.623e+00(2.97%)  -2.024e-02(4.65%)  -4.682e-02(4.65%)
42       +    -5.889e-01(5.94%)       +    5.209e-01(4.87%)  -2.600e-03(4.27%)  -6.667e-03(4.27%)
43       +    -6.626e+00(4.72%)       +  -3.381e+00(10.79%)  -3.454e-02(4.48%)  -8.165e-02(4.48%)
44       +   -1.212e+01(11.65%)       +   -9.454e+00(6.71%)  -8.237e-02(4.31%)  -8.237e-02(4.31%)
45       +    -9.952e-01(1.67%)       +    6.864e-01(1.09%)  -1.270e-02(4.46%)  -1.270e-02(4.46%)
46       +    -2.283e+00(2.06%)       +   -1.060e+00(1.36%)  -2.191e-02(4.97%)  -5.129e-02(4.97%)
47       +    -4.306e+00(4.76%)       +                   +  -2.381e-02(5.14%)  -5.628e-02(5.14%)
48       +    -5.160e+00(2.10%)       +   -3.605e+00(2.35%)  -3.531e-02(4.65%)  -8.260e-02(4.65%)
49       +     8.462e-01(2.16%)       +   -1.892e+00(3.71%)  -2.269e-02(4.32%)  -2.269e-02(4.32%)
5        +    -2.884e+00(1.88%)       +   -2.335e+00(2.29%)  -2.919e-02(4.90%)  -6.799e-02(4.90%)
6        +   -7.899e+00(14.84%)       +   4.423e+00(21.16%)  -2.242e-02(5.24%)  -5.385e-02(5.24%)
7        +  -6.924e+00(497.86%)       +   5.760e+00(53.81%)  -1.004e-02(4.70%)  -1.729e-02(4.70%)
8        +    -6.843e-03(3.42%)       +    2.725e-03(1.70%)  -9.466e-05(5.03%)  -1.388e-04(5.03%)
9        +    -2.687e+00(2.63%)       +   -1.550e+00(2.57%)  -2.373e-02(4.93%)  -5.552e-02(4.93%)
>>> est_res_trafo3w:
Empty DataFrame
Columns: [p_hv_mw, q_hv_mvar, p_mv_mw, q_mv_mvar, p_lv_mw, q_lv_mvar, i_hv_ka, i_mv_ka, i_lv_ka]
Index: []
>>> est_res_line:
              p_from_mw           q_from_mvar            p_to_mw            q_to_mvar           i_from_ka             i_to_ka
0                     +     2.103e+00(31.54%)                  +   -3.027e+00(73.58%)   -2.202e-02(4.20%)   -2.202e-02(4.20%)
1                     +      1.239e+00(2.49%)                  +    -2.485e+00(6.82%)   -1.668e-02(4.55%)   -1.668e-02(4.55%)
10     4.639e-01(7.90%)      2.035e+00(9.36%)  -4.557e-01(7.89%)    -1.998e+00(9.38%)    3.665e-03(4.33%)    3.665e-03(4.33%)
100                   +                     +                  +    -2.224e-03(1.05%)   -9.955e-05(5.71%)   -9.955e-05(5.71%)
101                   +      1.027e+00(4.97%)                  +   -1.712e+00(12.57%)   -1.797e-02(4.75%)   -1.797e-02(4.75%)
102    2.748e-03(3.16%)     -3.686e-03(1.95%)  -2.752e-03(3.17%)     3.414e-03(1.78%)                   +                   +
103   -2.021e-02(6.71%)     -3.439e-02(2.20%)   1.993e-02(6.58%)     3.251e-02(2.09%)   -4.059e-04(6.97%)   -4.059e-04(6.97%)
104   -4.480e-01(7.68%)     -7.410e-01(2.20%)   4.416e-01(7.52%)     7.011e-01(2.10%)   -8.738e-03(7.01%)   -8.738e-03(7.01%)
105                   +      1.632e+00(8.80%)                  +   -1.769e+00(10.34%)   -1.503e-02(4.65%)   -1.503e-02(4.65%)
106                   +                     +                  +    -2.323e+00(1.68%)   -3.386e-02(4.74%)   -3.386e-02(4.74%)
107                   +      3.817e+00(4.32%)                  +    -4.392e+00(4.68%)   -2.513e-02(4.96%)   -2.513e-02(4.96%)
108                   +     -8.277e-02(6.26%)                  +     6.485e-02(5.70%)   -8.903e-04(4.72%)   -8.903e-04(4.72%)
109    2.316e-01(2.27%)      1.300e+00(7.94%)  -2.307e-01(2.27%)    -1.296e+00(7.98%)    1.117e-03(1.57%)    1.117e-03(1.57%)
11                    +      2.069e-02(5.31%)                  +    -3.029e-02(6.59%)   -3.095e-04(6.64%)   -3.095e-04(6.64%)
110                   +      2.921e-01(6.41%)                  +    -2.980e-01(6.83%)   -3.260e-04(1.47%)   -3.260e-04(1.47%)
111                   +     -7.803e-02(7.81%)                  +     6.402e-02(7.44%)   -6.563e-04(4.93%)   -6.563e-04(4.93%)
112                   +     -4.054e-02(7.45%)                  +     2.802e-03(1.87%)   -1.181e-03(4.68%)   -1.181e-03(4.68%)
113                   +    -2.910e-02(11.61%)                  +    -1.391e-02(9.77%)   -6.077e-04(5.33%)   -6.077e-04(5.33%)
114                   +      3.261e-01(3.14%)                  +    -4.388e-01(3.80%)   -7.821e-03(4.75%)   -7.821e-03(4.75%)
115                   +      1.271e-02(1.64%)                  +    -1.990e-02(2.35%)   -3.682e-04(4.79%)   -3.682e-04(4.79%)
116                   +     -8.726e-01(7.31%)                  +     4.112e-01(5.63%)   -1.268e-02(4.86%)   -1.268e-02(4.86%)
117                   +     3.775e-02(28.85%)                  +   -4.327e-02(22.63%)   -2.621e-04(4.47%)   -2.621e-04(4.47%)
118    1.374e-02(5.25%)     3.454e-02(16.20%)  -1.351e-02(5.21%)   -3.394e-02(16.41%)    5.976e-05(4.77%)    5.976e-05(4.77%)
119  -1.884e-01(49.25%)     -4.295e-01(3.37%)  1.866e-01(47.59%)     4.163e-01(3.29%)   -4.113e-03(8.69%)   -4.113e-03(8.69%)
12                    +                     +                  +    -5.934e-01(1.40%)   -1.874e-02(5.63%)   -1.874e-02(5.63%)
120                   +     8.958e-01(32.07%)                  +   -1.009e+00(59.79%)   -9.746e-03(5.00%)   -9.746e-03(5.00%)
121                   +     -2.135e-02(7.74%)                  +     4.242e-03(3.21%)   -3.244e-04(5.78%)   -3.244e-04(5.78%)
122   -1.415e-02(1.76%)     -2.509e-02(6.54%)   1.392e-02(1.72%)     2.419e-02(6.46%)   -1.635e-04(4.94%)   -1.635e-04(4.94%)
123   -2.365e-01(8.87%)    -4.684e-01(14.18%)   2.359e-01(8.85%)    4.656e-01(14.12%)  -2.813e-03(17.88%)  -2.813e-03(17.88%)
124                   +     -2.874e-03(3.10%)                  +                    +   -1.248e-04(5.21%)   -1.248e-04(5.21%)
125    7.730e-01(2.77%)      1.172e+00(8.16%)  -7.752e-01(2.78%)    -1.186e+00(8.17%)   -3.504e-03(4.40%)   -3.504e-03(4.40%)
126                   +    -1.813e+00(13.12%)                  +    1.449e+00(14.31%)   -1.688e-02(4.82%)   -1.688e-02(4.82%)
127                   +                     +                  +    -9.783e-01(1.01%)   -2.678e-02(4.68%)   -2.678e-02(4.68%)
128                   +                     +                  +                    +                   +                   +
129                   +     -4.231e+00(6.54%)                  +     4.027e+00(5.91%)   -1.188e-02(2.91%)   -1.188e-02(2.91%)
13                    +   -1.734e+00(112.31%)                  +     6.116e-01(5.32%)   -6.113e-02(5.49%)   -6.113e-02(5.49%)
130                   +     3.199e-02(20.53%)  -1.096e-02(1.00%)   -3.627e-02(18.16%)   -1.963e-04(4.75%)   -1.963e-04(4.75%)
131                   +     1.933e-02(27.05%)                  +   -3.333e-02(43.74%)   -4.238e-04(4.63%)   -4.238e-04(4.63%)
132                   +     -1.308e-01(3.47%)                  +   -1.571e-01(14.60%)   -3.882e-03(5.22%)   -3.882e-03(5.22%)
133    1.750e-02(1.37%)      2.641e-02(7.12%)  -1.904e-02(1.52%)    -2.951e-02(7.28%)   -2.166e-04(4.41%)   -2.166e-04(4.41%)
134                   +      1.631e-02(9.02%)  -9.434e-03(1.03%)    -1.966e-02(9.09%)   -1.613e-04(4.60%)   -1.613e-04(4.60%)
135                   +     5.742e-01(18.85%)                  +  -8.851e-01(479.93%)   -8.106e-03(4.70%)   -8.106e-03(4.70%)
136                   +      1.058e+00(1.48%)                  +    -1.406e+00(1.88%)   -1.495e-02(5.10%)   -1.495e-02(5.10%)
137                   +     4.051e+00(28.46%)                  +   -4.060e+00(28.36%)   -3.980e-02(5.50%)   -3.980e-02(5.50%)
138    8.846e-03(4.86%)     3.182e-02(25.86%)  -8.747e-03(4.83%)   -3.139e-02(26.27%)                   +                   +
139                   +                     +                  +    -1.306e+00(4.11%)   -1.434e-02(4.66%)   -1.434e-02(4.66%)
14                    +     -1.142e-02(1.07%)                  +    -2.574e-02(1.84%)   -8.733e-04(5.54%)   -8.733e-04(5.54%)
140    6.322e-02(8.35%)      3.017e-01(9.92%)  -6.178e-02(8.32%)    -2.957e-01(9.92%)    6.048e-04(5.21%)    6.048e-04(5.21%)
141    4.384e-02(2.55%)     2.372e-01(11.93%)  -4.316e-02(2.53%)   -2.338e-01(12.11%)    2.978e-04(3.06%)    2.978e-04(3.06%)
142                   +                     +                  +    -3.156e+00(1.65%)   -2.740e-02(4.40%)   -2.740e-02(4.40%)
143                   +      9.558e-01(8.83%)                  +    -1.059e+00(9.09%)   -8.544e-03(6.11%)   -8.544e-03(6.11%)
144   -6.937e-02(1.18%)      1.128e+00(6.93%)   7.036e-02(1.19%)    -1.124e+00(6.97%)    8.415e-04(1.30%)    8.415e-04(1.30%)
145   -6.380e-03(1.53%)     -2.023e-02(6.62%)   6.357e-03(1.52%)     1.929e-02(6.46%)   -1.262e-04(6.58%)   -1.262e-04(6.58%)
146  -7.160e-03(30.19%)     -1.945e-02(5.58%)  7.108e-03(30.25%)     1.886e-02(5.45%)  -1.443e-04(11.14%)  -1.443e-04(11.14%)
147                   +                     +                  +    -2.490e-01(1.42%)   -9.992e-03(5.58%)   -9.992e-03(5.58%)
148                   +                     +                  +                    +   -8.395e-03(5.53%)   -8.395e-03(5.53%)
149                   +      3.974e-04(2.59%)                  +   -2.573e-03(33.91%)   -1.256e-04(4.64%)   -1.256e-04(4.64%)
15     9.653e-02(4.96%)      3.217e-01(9.16%)  -9.503e-02(4.94%)    -3.164e-01(9.23%)    4.787e-04(3.17%)    4.787e-04(3.17%)
150                   +      4.942e-03(4.51%)                  +    -6.007e-03(6.12%)   -9.685e-05(4.54%)   -9.685e-05(4.54%)
151                   +     -6.894e-01(8.38%)                  +     6.759e-01(8.03%)   -2.175e-03(3.58%)   -2.175e-03(3.58%)
152                   +     -3.873e+00(6.68%)                  +     3.771e+00(6.36%)   -1.120e-02(3.94%)   -1.120e-02(3.94%)
153                   +     -4.851e+00(5.96%)                  +     4.666e+00(5.86%)   -2.409e-02(4.93%)   -2.409e-02(4.93%)
154                   +                     +                  +                    +                   +                   +
155                   +      3.814e+00(2.68%)                  +    -3.864e+00(2.70%)   -3.348e-02(4.34%)   -3.348e-02(4.34%)
156                   +                     +                  +    -8.357e-01(3.77%)   -1.389e-02(5.53%)   -1.389e-02(5.53%)
157                   +     -1.061e+00(3.39%)                  +                    +   -1.597e-02(5.64%)   -1.597e-02(5.64%)
158                   +     -3.530e-01(3.58%)                  +     3.139e-01(3.31%)   -6.620e-03(4.91%)   -6.620e-03(4.91%)
159                   +     -3.570e+00(2.34%)                  +     3.525e+00(2.30%)   -8.277e-02(4.66%)   -8.277e-02(4.66%)
16                    +                     +                  +    -7.856e-02(1.21%)   -2.735e-03(5.60%)   -2.735e-03(5.60%)
17                    +    -3.847e-01(12.66%)                  +     1.457e-01(2.83%)   -1.178e-02(5.49%)   -1.178e-02(5.49%)
18                    +      6.592e-01(1.13%)                  +    -6.921e-01(1.18%)   -6.979e-03(5.08%)   -6.979e-03(5.08%)
19                    +     -7.207e-01(4.21%)                  +    -7.186e-01(2.21%)   -2.556e-02(4.58%)   -2.556e-02(4.58%)
2                     +      4.840e-01(1.26%)                  +    -8.316e-01(1.98%)   -9.626e-03(4.67%)   -9.626e-03(4.67%)
20                    +      1.156e+00(2.15%)                  +    -1.187e+00(2.19%)   -7.556e-03(5.30%)   -7.556e-03(5.30%)
21                    +     -1.206e+00(2.13%)                  +     6.344e-01(1.01%)   -2.971e-02(4.64%)   -2.971e-02(4.64%)
22                    +    -2.530e-01(25.74%)                  +    2.432e-01(22.38%)   -1.426e-03(4.58%)   -1.426e-03(4.58%)
23                    +      3.368e-01(1.19%)                  +    -3.372e-01(1.20%)   -8.252e-03(5.69%)   -8.252e-03(5.69%)
24                    +      5.713e-03(1.11%)                  +    -1.249e-02(2.82%)   -1.772e-04(4.56%)   -1.772e-04(4.56%)
25                    +     -5.647e-02(7.84%)                  +     4.653e-02(7.56%)   -5.562e-04(4.62%)   -5.562e-04(4.62%)
26     2.288e-02(2.13%)                     +  -2.337e-02(2.19%)                    +   -5.199e-04(4.55%)   -5.199e-04(4.55%)
27    -2.141e-02(6.15%)    -4.420e-02(12.15%)   2.188e-02(6.19%)    4.516e-02(12.06%)    8.726e-05(4.58%)    8.726e-05(4.58%)
28     1.199e-02(3.22%)      1.797e-02(1.74%)  -1.210e-02(3.25%)    -1.960e-02(1.88%)   -2.669e-04(6.51%)   -2.669e-04(6.51%)
29                    +     -5.152e-01(5.36%)                  +     4.487e-01(4.34%)   -5.027e-03(4.54%)   -5.027e-03(4.54%)
3     -5.870e-01(1.78%)     -1.088e+00(1.65%)   4.501e-01(1.32%)     7.118e-01(1.13%)   -9.718e-03(5.36%)   -9.718e-03(5.36%)
30    -2.385e-02(1.01%)    -3.027e-02(19.96%)                  +     5.321e-03(8.81%)   -4.782e-04(5.72%)   -4.782e-04(5.72%)
31    -3.855e-01(1.49%)    -1.128e+00(32.13%)   3.831e-01(1.48%)    1.117e+00(30.23%)   -2.966e-03(3.07%)   -2.966e-03(3.07%)
32                    +     -8.693e-02(6.47%)                  +     8.629e-02(6.37%)   -2.321e-04(2.97%)   -2.321e-04(2.97%)
33                    +      1.387e+00(2.22%)                  +    -1.400e+00(2.23%)   -4.815e-02(5.29%)   -4.815e-02(5.29%)
34                    +      7.565e-02(3.35%)                  +    -7.805e-02(3.51%)   -4.169e-04(3.35%)   -4.169e-04(3.35%)
35                    +     -6.367e-02(3.38%)                  +   -1.032e-01(45.78%)   -7.682e-03(4.92%)   -7.682e-03(4.92%)
36                    +      1.020e-01(2.56%)                  +    -1.377e-01(3.87%)   -1.101e-03(4.05%)   -1.101e-03(4.05%)
37                    +     -1.467e-02(2.20%)                  +                    +   -4.459e-04(4.69%)   -4.459e-04(4.69%)
38     8.252e-02(1.32%)    2.145e-01(878.55%)  -8.559e-02(1.37%)  -2.221e-01(715.54%)   -1.534e-03(6.62%)   -1.534e-03(6.62%)
39    -1.805e-02(3.39%)    -3.309e-02(17.37%)   1.805e-02(3.34%)    3.309e-02(16.14%)                   +                   +
4                     +     -2.801e+00(1.79%)                  +     2.270e+00(1.50%)   -2.622e-02(5.36%)   -2.622e-02(5.36%)
40     2.198e-01(1.75%)      6.576e-01(7.37%)  -2.284e-01(1.82%)    -6.927e-01(7.61%)   -5.250e-03(9.14%)   -5.250e-03(9.14%)
41                    +     -1.901e-03(1.58%)                  +                    +   -1.279e-04(4.60%)   -1.279e-04(4.60%)
42                    +      2.884e-02(3.41%)                  +    -4.108e-02(5.85%)   -3.530e-04(4.20%)   -3.530e-04(4.20%)
43                    +     -1.977e-02(5.60%)                  +                    +   -3.930e-04(5.67%)   -3.930e-04(5.67%)
44                    +      5.807e-03(1.10%)                  +    -1.005e-02(2.07%)   -4.200e-04(4.69%)   -4.200e-04(4.69%)
45                    +    5.566e-01(173.51%)                  +  -5.807e-01(103.53%)   -5.361e-03(4.89%)   -5.361e-03(4.89%)
46                    +     -1.308e+00(3.16%)                  +     1.265e+00(3.01%)   -7.282e-03(3.45%)   -7.282e-03(3.45%)
47                    +      6.337e-01(2.28%)                  +    -6.713e-01(2.39%)   -9.239e-03(6.41%)   -9.239e-03(6.41%)
48                    +  -7.157e+00(1041.06%)                  +  7.157e+00(1041.03%)                   +                   +
49                    +     -2.861e+00(7.90%)                  +     2.476e+00(7.71%)   -1.354e-02(4.58%)   -1.354e-02(4.58%)
5                     +                     +                  +                    +   -1.430e-02(4.74%)   -1.430e-02(4.74%)
50                    +  -7.181e+00(1177.48%)                  +  7.181e+00(1177.44%)                   +                   +
51                    +     -3.368e+00(7.04%)                  +     2.917e+00(6.78%)   -1.589e-02(4.58%)   -1.589e-02(4.58%)
52    -8.665e-03(3.43%)     -2.257e-02(2.38%)   8.001e-03(3.22%)     1.926e-02(2.08%)   -1.718e-04(7.06%)   -1.718e-04(7.06%)
53                    +     -2.955e-01(1.77%)                  +     2.416e-01(1.48%)   -2.931e-03(6.13%)   -2.931e-03(6.13%)
54                    +                     +                  +                    +   -1.832e-02(4.66%)   -1.832e-02(4.66%)
55                    +     -3.829e+00(4.20%)                  +     3.362e+00(3.88%)   -2.332e-02(5.05%)   -2.332e-02(5.05%)
56                    +                     +                  +                    +   -1.682e-02(4.59%)   -1.682e-02(4.59%)
57                    +     -2.924e+00(2.66%)                  +     2.532e+00(2.38%)   -2.215e-02(5.05%)   -2.215e-02(5.05%)
58                    +                     +                  +    -3.088e+00(2.43%)   -4.788e-02(4.35%)   -4.788e-02(4.35%)
59                    +     -6.688e+00(5.96%)                  +     3.362e+00(4.36%)   -4.120e-02(4.62%)   -4.120e-02(4.62%)
6                     +     -5.518e+00(5.85%)                  +     5.021e+00(5.57%)   -2.450e-02(5.67%)   -2.450e-02(5.67%)
60                    +     -2.595e+00(3.11%)                  +     2.560e+00(3.09%)   -2.173e-02(4.74%)   -2.173e-02(4.74%)
61                    +                     +                  +    -5.049e+00(3.36%)   -4.964e-02(4.47%)   -4.964e-02(4.47%)
62                    +     -5.084e+00(7.34%)                  +     5.054e+00(7.33%)   -2.017e-02(5.12%)   -2.017e-02(5.12%)
63                    +                     +                  +    -1.485e+00(1.53%)   -4.330e-02(4.58%)   -4.330e-02(4.58%)
64                    +                     +                  +    -4.053e+00(1.27%)   -4.407e-02(4.29%)   -4.407e-02(4.29%)
65                    +                     +                  +    -9.079e+00(2.41%)   -8.468e-02(4.34%)   -8.468e-02(4.34%)
66                    +     -1.831e+00(1.22%)                  +                    +   -3.545e-02(4.28%)   -3.545e-02(4.28%)
67                    +                     +                  +    -6.694e+00(3.07%)   -3.857e-02(4.20%)   -3.857e-02(4.20%)
68                    +                     +                  +    -4.255e+00(1.30%)   -4.626e-02(4.29%)   -4.626e-02(4.29%)
69                    +      3.080e+00(3.03%)                  +    -3.335e+00(3.20%)   -2.406e-02(5.00%)   -2.406e-02(5.00%)
7                     +                     +                  +    -1.730e+00(1.10%)   -2.705e-02(4.95%)   -2.705e-02(4.95%)
70                    +     -1.588e+00(7.98%)                  +     4.956e-01(1.62%)   -4.254e-02(4.97%)   -4.254e-02(4.97%)
71                    +      7.248e+00(7.87%)                  +    -7.481e+00(7.96%)   -2.304e-02(5.88%)   -2.304e-02(5.88%)
72                    +      1.900e+00(1.74%)                  +    -1.922e+00(1.75%)   -6.446e-02(5.83%)   -6.446e-02(5.83%)
73    -3.492e-01(1.16%)    -2.050e+00(11.06%)   3.343e-01(1.12%)     1.967e+00(9.94%)   -4.460e-03(3.29%)   -4.460e-03(3.29%)
74                    +     -1.451e+00(3.24%)                  +     1.382e+00(3.01%)   -6.199e-03(3.05%)   -6.199e-03(3.05%)
75                    +     -1.018e-01(4.16%)                  +     9.996e-02(3.98%)   -1.371e-04(1.37%)   -1.371e-04(1.37%)
76                    +     -3.170e-02(5.54%)                  +     3.078e-02(5.17%)   -6.547e-05(2.03%)   -6.547e-05(2.03%)
77                    +    -9.279e-02(26.05%)                  +    -1.611e-01(8.88%)   -4.884e-03(5.68%)   -4.884e-03(5.68%)
78                    +                     +                  +    -3.765e-01(1.03%)   -1.350e-02(5.10%)   -1.350e-02(5.10%)
79                    +     -7.258e+00(3.83%)                  +     6.736e+00(3.65%)   -3.082e-02(4.93%)   -3.082e-02(4.93%)
8                     +      1.279e+00(5.82%)                  +    -1.337e+00(5.95%)   -2.588e-02(5.53%)   -2.588e-02(5.53%)
80                    +     -7.679e+00(2.87%)                  +    -2.349e+00(1.50%)   -6.326e-02(4.44%)   -6.326e-02(4.44%)
81                    +     -5.622e+00(3.68%)                  +     5.532e+00(3.59%)   -2.435e-02(3.78%)   -2.435e-02(3.78%)
82                    +     -5.620e+00(3.67%)                  +     5.533e+00(3.59%)   -2.435e-02(3.78%)   -2.435e-02(3.78%)
83                    +     -6.911e+00(3.06%)                  +     6.848e+00(3.02%)   -2.074e-02(3.35%)   -2.074e-02(3.35%)
84                    +     -9.744e+00(3.47%)                  +                    +   -7.228e-02(4.48%)   -7.228e-02(4.48%)
85                    +     -5.934e+00(2.22%)                  +     5.364e+00(1.96%)   -5.729e-02(4.02%)   -5.729e-02(4.02%)
86                    +     3.657e+00(10.97%)                  +   -3.681e+00(10.96%)   -6.311e-02(4.97%)   -6.311e-02(4.97%)
87                    +      2.699e-02(2.88%)                  +   -6.560e-02(12.68%)   -4.084e-04(4.50%)   -4.084e-04(4.50%)
88                    +      3.123e-01(2.13%)                  +   -9.224e-01(11.27%)   -6.477e-03(4.58%)   -6.477e-03(4.58%)
89                    +      5.335e-01(4.05%)                  +   -2.385e+00(37.93%)   -2.246e-02(4.65%)   -2.246e-02(4.65%)
9      1.249e-02(4.07%)      2.679e-02(7.50%)  -1.286e-02(4.17%)    -2.913e-02(7.94%)  -2.096e-04(11.83%)  -2.096e-04(11.83%)
90                    +      8.060e-01(4.38%)                  +    -8.540e-01(5.09%)   -1.196e-03(1.47%)   -1.196e-03(1.47%)
91                    +      1.215e-01(4.29%)                  +   -2.141e-01(11.82%)   -1.165e-03(4.44%)   -1.165e-03(4.44%)
92                    +      1.250e-01(6.28%)                  +   -2.003e-01(17.42%)   -1.000e-03(4.39%)   -1.000e-03(4.39%)
93                    +    -5.010e+00(13.06%)                  +    4.955e+00(12.66%)   -1.010e-02(3.49%)   -1.010e-02(3.49%)
94                    +     -1.231e+01(5.20%)                  +                    +   -8.278e-02(4.34%)   -8.278e-02(4.34%)
95                    +      7.838e-01(1.20%)                  +    -8.005e-01(1.22%)   -5.527e-02(5.61%)   -5.527e-02(5.61%)
96                    +                     +                  +                    +   -4.789e-02(4.18%)   -4.789e-02(4.18%)
97                    +    -1.384e+00(57.13%)                  +    1.384e+00(57.13%)  -2.256e-03(63.89%)  -2.256e-03(63.89%)
98                    +      5.777e-01(1.89%)                  +    -5.779e-01(1.89%)   -5.775e-03(3.89%)   -5.775e-03(3.89%)
99                    +    -7.609e-01(21.02%)                  +    2.726e-01(23.14%)   -1.370e-02(4.96%)   -1.370e-02(4.96%)

It is seen that for a part of the measurement the estimations differs significantly from the PF result. Another observation: for some networks estimations done without using current measuremets is better then with it. I also tried to use PF result as an initial point for SE algo (init=‘results’), however i got the same result. Could enyone explain what i’m doing wrong or give any advice? Is it correct way to use PF result for test SE? Or mayby i use inappropriate meas error weights (stddev) or estimate() function params?

test_panda_se.ipynb (12.0 KB)
result.txt (30.8 KB)

Thanks

robbie.morrison · 24 June 2021 16:38

Just to say that if you set your python code in triple back-ticks and note “python” after the first set, you should get syntax highlighting. More here:

Extended Syntax | Markdown Guide

alex_l · 24 June 2021 16:42

Thanks, Robbie. Next time I’ll do it

marvha · 24 June 2021 19:24

Hi,
I never did state estimation with pandapower, but in my state estimation implementation experience the following things can lead to convergence problems:

problem scaling: an instance of this could be very small variances, i.e., very large measurement weights,
large differences in the weights: if your voltage variances are, e.g., e-2 while your power variances are e-15 (or anyway, very different), gauss-newton algorithms tend to not like it
very large measurement errors: if you are accidentally adding very large random errors (much beyond the three sigma of the gaussian random uncertainty) to the power flow result before using it as input for state estimation

Do you add random errors to the power flow results before using them as input to the state estimation? I think a first useful step to debug is to add no errors at all and see if it converges to the right solution then.
Also, do you have a lot of virtual measurements (zero injection buses)? If so, it could be an idea to replace them with equality constraints

alex_l · 25 June 2021 11:08

Hi Marvha!

I guess the problem is really hidden somewhere here. The voltage measurement errors is easy to fit (in my tests it’s 0.01pu), but there are difficulties with how errors of flows and injections can be modeled. Power measurements in models that I use for tests vary in wide range, from tens of kW to hundreds of MW. I cannot fully understand whether it is possible in such conditions to use the same stddev for all power meases? Too large common power stddev leads to ignoring small values in power meases, too small stddev on the other hand leads to large weights for large values.

I’m passing not distorbed PF results to SE input. More over, i’m running SE algorithm with voltage vectors calculated in PF as initial point instead “flat start”. One would expect that under such conditions the algorithm should finish after the first iteration, but it carries out many iterations and takes the solution to the same wrong point as in the case of a flat start. However, this bad behavior is only observed for large networks. The algorithm works correctly on small networks.

Yes i’m using zero injection constraints. And I tried both ways of accounting for them in the SE algorithm:

The form of virtual measurements with small stddev;
The form of strict equality constraints in the Lagrangian.

marvha · 2 July 2021 12:19

Hello @alex_l,

indeed, if all the other things check out, I also suspect that there might be something wrong with the input data. You can narrow down the cause of the problem further by using the “lav” robust estimator, which I believe that PandaPower offers: the result of this is independent on the measurement weights, as it normally assigns unitary weights to all measurements (not sure how this is enforced in pandapower, but that’s at least the definition of a “lav” state estimator). If that does not converge either, then I would say that something is wrong with the network data themselves. Perhaps some branch with zero impedance that confuses the solver? or something along these lines.

Regarding the differences in the weights of power measurements, of course they depend on the accuracy of the different meters and they can be very diverse and there is little that you can do about it. But, for instance, if your “per unit” constant for power is 100MW, then standard deviations of 1W will be on the order of 1e-8, which is then squared in the WLS, which is very small. But if you change your “per unit” constant to 1kW, than these become more acceptable. Of course, if you change this divider, you also have to update your per unit impedance values, but it might be that it helps the solver a bit.

Maybe it is a silly remark and you did so already, but I have no idea how extensively the pandapower community is represented in this forum, so you might get more to-the-point help if you open an issue on their github repository perhaps?