{
  "scope": "Synthetic three-bus verification example; not an industrial benchmark.",
  "environment": {
    "python": "3.13.5",
    "numpy": "2.3.5",
    "scipy": "1.17.0"
  },
  "base_mva": 100.0,
  "base_case": {
    "newton_steps": 4,
    "residual_history_pu": [
      0.8166666666666665,
      0.04185735204027197,
      0.00031060632123824927,
      1.858632547868666e-08,
      1.887379141862766e-15
    ],
    "voltage_magnitudes_pu": [
      1.04,
      1.02,
      0.956912891031405
    ],
    "voltage_angles_degrees": [
      0.0,
      -3.572405502168944,
      -6.763479175367291
    ],
    "net_bus_injections_pu_P_Q": [
      [
        0.4379121078996288,
        0.2076352874998309
      ],
      [
        0.4999999999999981,
        0.18037418256925267
      ],
      [
        -0.8999999999999996,
        -0.3499999999999985
      ]
    ],
    "branch_from_powers_pu_P_Q": [
      [
        -0.11827508000257361,
        0.017649611619485483
      ],
      [
        0.5561871879022029,
        0.1899856758803431
      ],
      [
        0.3814345365771917,
        0.22835264623484347
      ]
    ],
    "branch_to_powers_pu_P_Q": [
      [
        0.11856546342280673,
        -0.047978463665593545
      ],
      [
        -0.5302434935159547,
        -0.1371206212343751
      ],
      [
        -0.36975650648404496,
        -0.21287937876562338
      ]
    ],
    "total_branch_absorption_pu_P_Q": [
      0.03791210789962805,
      0.03800947006908002
    ]
  },
  "q_limited_case": {
    "bus_2_qmax_pu": 0.1,
    "newton_steps_after_mode_change": 3,
    "residual_history_pu": [
      0.08037418256925266,
      0.0003449896721627044,
      6.626782345087179e-09,
      1.4432899320127035e-15
    ],
    "voltage_magnitudes_pu": [
      1.04,
      1.0158318005392462,
      0.9543319714030899
    ],
    "voltage_angles_degrees": [
      0.0,
      -3.4918300032168963,
      -6.737878246902398
    ],
    "net_bus_injections_pu_P_Q": [
      [
        0.4382781224155356,
        0.289430644753183
      ],
      [
        0.49999999999999917,
        0.09999999999999856
      ],
      [
        -0.9000000000000001,
        -0.3500000000000014
      ]
    ]
  },
  "verification": {
    "complex_power_balance_abs_pu": 5.150024430634711e-15,
    "terminal_law_vs_ybus_max_abs_pu": 6.302471701247068e-15,
    "uniform_angle_rotation_max_abs_pu": 3.560078619640797e-15,
    "angle_derivative_null_vector_max_abs": 8.881784197001252e-16,
    "alternative_nonlinear_solve_max_voltage_error_pu": 2.0014830212433607e-16,
    "directional_jacobian_relative_errors": {
      "1e-02": 1.694408894440631e-05,
      "1e-03": 1.694412545788353e-07,
      "1e-04": 1.6944079050457152e-09,
      "1e-05": 1.6367089561312757e-11,
      "1e-06": 3.6755323761817355e-11,
      "1e-07": 2.7871175470276053e-09
    },
    "zip_directional_jacobian_relative_errors": {
      "1e-02": 1.602166197519284e-05,
      "1e-03": 1.6021696669652157e-07,
      "1e-04": 1.6021178169676523e-09,
      "1e-05": 1.539343882300987e-11,
      "1e-06": 3.4754383964630255e-11,
      "1e-07": 2.670253737869508e-09
    },
    "zip_final_residual_pu": 1.3322676295501878e-15,
    "shunt_parallel_branch_scalar_error_pu": 5.893143399678001e-15,
    "shunt_parallel_branch_power_balance_pu": 5.332751740125942e-16,
    "bus_permutation_max_voltage_error_pu": 4.163336342344337e-17,
    "unreferenced_island_rejected": true
  },
  "external_validation": "MATPOWER case supplied separately; MATLAB/Octave comparison not executed here."
}