source_calculation/source_calculation.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Introduction\n",
    "\n",
    "This notebook investigates the effect of putting a very large short circuit power (`sk`) in the source in power flow calculation, including:\n",
    "\n",
    "* How it can influence the numerical stability of the whole power flow?\n",
    "* Does the node voltage converge to the source `u_ref` so that the source becomes an ideal source?\n",
    "* How it can influence the numerical stability of source injection calculation. And how to improve it?\n",
    "\n",
    "# Background\n",
    "\n",
    "The source in `power-grid-model` is a Thévenin's equivalent circuit with an ideal voltage source and an internal impedance.\n",
    "The impedance is represented by the short circuit power `sk` of the source.\n",
    "Some other power flow packages treat source as ideal source without impedance.\n",
    "To replicate that behavior, we can put a large `sk` in the `pgm` input. \n",
    "However, this could cause numerical instability.\n",
    "We want to test that and see possible solutions.\n",
    "\n",
    "# Approach\n",
    "\n",
    "We conduct two experiments:\n",
    "\n",
    "* A series of PGM power flow using different level of `sk`. We check the resulted voltage, line flow, and source flow.\n",
    "* A hand-made calculation of linear and Newton-Raphson power flow. We try to understand how extremely high `sk` can influence the numerical stability."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from power_grid_model import PowerGridModel, CalculationMethod\n",
    "from power_grid_model.utils import json_deserialize_from_file\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.linalg import solve_triangular"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# PGM Source Comparison\n",
    "\n",
    "We read the input data from [`grid.json`](./grid.json).\n",
    "Run a series of power flows using different `sk` value.\n",
    "We then record the following results:\n",
    "\n",
    "* `u_pu` of the `node` which contains the `source`.\n",
    "* `p_from` of the `line` which connects to the `node` which contains the `source`\n",
    "* `p` of the `source`.\n",
    "\n",
    "According to Kirchhof's Law we should have `p_from == p`, which should be approximately the total loads in the grid plus some losses.\n",
    "We plot the figures including the difference between `p_from` and `p`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def calculate_all_source_sk(start_sk_log, end_sk_log, method: CalculationMethod = CalculationMethod.newton_raphson):\n",
    "    n_steps = end_sk_log - start_sk_log\n",
    "    source_p = np.zeros(n_steps, dtype=np.float64)\n",
    "    node_voltage_pu = np.zeros(n_steps, dtype=np.float64)\n",
    "    line_p = np.zeros(n_steps, dtype=np.float64)\n",
    "\n",
    "    input_data = json_deserialize_from_file(\"grid.json\")\n",
    "\n",
    "    for i, sk_log in enumerate(range(start_sk_log, end_sk_log)):\n",
    "        sk = float(10 ** sk_log)\n",
    "        input_data[\"source\"][\"sk\"] = sk\n",
    "        model = PowerGridModel(input_data)\n",
    "        result = model.calculate_power_flow(calculation_method=method)\n",
    "        source_p[i] = result[\"source\"][\"p\"][0]\n",
    "        node_voltage_pu[i] = result[\"node\"][\"u_pu\"][0]\n",
    "        line_p[i] = result[\"line\"][\"p_from\"][0]\n",
    "    \n",
    "    return {\n",
    "        \"source_p\": source_p, \n",
    "        \"node_voltage_pu\": node_voltage_pu, \n",
    "        \"line_p\": line_p, \n",
    "        \"sk\": np.array([float(10 ** sk_log) for sk_log in range(start_sk_log, end_sk_log)])\n",
    "    }\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "pgm_calculation = calculate_all_source_sk(8, 36, CalculationMethod.newton_raphson)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Compare active power\n",
    "\n",
    "The following two figures shows the difference betwee `p_from` of the `line` and `p` of the `source`.\n",
    "\n",
    "* The deviation becomes larger when `sk` increases. \n",
    "* The `p_from` of the `line` has the correct value.\n",
    "* The `p` of the `source` suffers from numerical instability."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(pgm_calculation[\"sk\"], pgm_calculation[\"source_p\"])\n",
    "plt.plot(pgm_calculation[\"sk\"], pgm_calculation[\"line_p\"])\n",
    "plt.xscale(\"log\")\n",
    "_ = plt.xlabel('Short Circuit Power of Source (VA)')\n",
    "_ = plt.ylabel('Calculated Active Power (W)')\n",
    "_ = plt.legend([\"Source Active Power\", \"Line Active Power\"])\n",
    "plt.title(\"Active Power Comparison\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p_error = np.abs(pgm_calculation[\"source_p\"] - pgm_calculation[\"line_p\"])\n",
    "plt.plot(pgm_calculation[\"sk\"], p_error)\n",
    "plt.xscale(\"log\")\n",
    "plt.yscale(\"log\")\n",
    "_ = plt.xlabel('Short Circuit Power of Source (VA)')\n",
    "_ = plt.ylabel('Error (W)')\n",
    "plt.title(\"Active Power Error\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Source node voltage\n",
    "\n",
    "The figure below shows the node voltage in `u_pu`.\n",
    "\n",
    "* The node voltage converges to `1 pu` which is the `u_ref` of the `source`.\n",
    "* This is expected behavior and there is no numerical instability."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(pgm_calculation[\"sk\"], pgm_calculation[\"node_voltage_pu\"])\n",
    "plt.xscale(\"log\")\n",
    "_ = plt.xlabel('Short Circuit Power of Source (VA)')\n",
    "_ = plt.ylabel('Calculated Voltage (pu)')\n",
    "_ = plt.legend([\"Source Node Voltage\"])\n",
    "plt.title(\"Node Voltage\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Hand calculation\n",
    "\n",
    "Now we want to understand why there is no numerical instability in the general power flow results, but only in source injection calculation.\n",
    "\n",
    "We use the following test network in real domain (like DC network). The source has an extremely high admittance.\n",
    "\n",
    "\n",
    "```\n",
    "bus_0 ---branch_0(y=100 pu)--- bus_1 ---branch_1(y=200 pu)-- bus_2 ---source(yk=1e50 pu, u= 1.05 pu)\n",
    " |                              |\n",
    " |                              |\n",
    "load_gen_0(-2 pu)             load_gen_1(1 pu)\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## LU factorization function\n",
    "\n",
    "We define our own custom LU factorization function and solver using forwards/backwards substitution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def lu_factorization(matrix: np.ndarray):\n",
    "    n = matrix.shape[0]\n",
    "    assert matrix.shape[1] == n\n",
    "    u = matrix.copy()                                               \n",
    "    l = np.eye(n)\n",
    "    for j in range(n-1):\n",
    "        lam = np.eye(n)\n",
    "        gamma = u[j+1:, j] / u[j, j]\n",
    "        lam[j+1:, j] = -gamma\n",
    "        u = lam @ u\n",
    "        \n",
    "        lam[j+1:, j] = gamma\n",
    "        l = l @ lam\n",
    "    return l, u, l - np.eye(n) + u\n",
    "\n",
    "def forwards_backwards(lu, b):\n",
    "    y = solve_triangular(lu, b, lower=True, unit_diagonal=True)\n",
    "    x = solve_triangular(lu, y, lower=False)\n",
    "    return y, x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Grid Input\n",
    "\n",
    "This is the input data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "from dataclasses import dataclass\n",
    "\n",
    "@dataclass\n",
    "class GridInput:\n",
    "    ybus: np.ndarray\n",
    "    load: np.ndarray\n",
    "    yk: float\n",
    "    u_ref: float\n",
    "    slack_bus: int\n",
    "\n",
    "def get_input():\n",
    "    return GridInput(\n",
    "        ybus = np.array([\n",
    "            [100.0, -100.0, 0.0],\n",
    "            [-100.0, 300.0, -200.0],\n",
    "            [0.0, -200.0, 200.0]\n",
    "        ], dtype=np.float64),\n",
    "        load = np.array([-2.0, 1.0, 0.0], dtype=np.float64),\n",
    "        yk = 1e50,\n",
    "        u_ref = 1.05,\n",
    "        slack_bus = 2\n",
    "    )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linear PF\n",
    "\n",
    "We first run the calculation using linear power flow. This is the observation:\n",
    "\n",
    "* The high source admittance results a huge value in the diagonal entry and righ-hand-side.\n",
    "* It does not produce high value in the off-diagonals of the matrix.\n",
    "* This leads to theoretically huge condition number. However, the linear equation is perfectly solvable without any numerical issues.\n",
    "* The huge number at both diagonal entry and righ-hand-side canceled each other in the backwards substitution. We get the enfornced voltage value from `u_ref`.\n",
    "* If we calculate source injection by using the voltage difference between node and `u_ref`, it procudes the wrong value because the floating point values of these two are the same.\n",
    "* Everything else calculated from branch parameter or node admittance matrix is fine, including calculating the source injection using node admittance matrix.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def linear_pf(grid_input: GridInput):\n",
    "    matrix = grid_input.ybus.copy()\n",
    "    np.fill_diagonal(matrix, matrix.diagonal() - grid_input.load)\n",
    "    rhs = np.zeros_like(grid_input.load)\n",
    "    rhs[grid_input.slack_bus] = grid_input.u_ref * grid_input.yk\n",
    "    matrix[grid_input.slack_bus, grid_input.slack_bus] += grid_input.yk\n",
    "    l, u, lu = lu_factorization(matrix)\n",
    "    u_temp, bus_u = forwards_backwards(lu, rhs)\n",
    "    source_p = (grid_input.u_ref - bus_u[grid_input.slack_bus]) * grid_input.yk * bus_u[grid_input.slack_bus]\n",
    "    print('----Linear Power FLow-----')\n",
    "    print('Matrix')\n",
    "    print(matrix)\n",
    "    print(f'RHS {rhs}')\n",
    "    print('LU Matrix')\n",
    "    print(lu)\n",
    "    print(f'Forwards Result {u_temp}')\n",
    "    print(f'Backwards Result: Bus Voltage {bus_u}')\n",
    "    print(f'Source Active Power: {source_p}')\n",
    "    print(f'Injection by Y Bus {(grid_input.ybus @ bus_u) * bus_u}')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "----Linear Power FLow-----\n",
      "Matrix\n",
      "[[ 1.02e+02 -1.00e+02  0.00e+00]\n",
      " [-1.00e+02  2.99e+02 -2.00e+02]\n",
      " [ 0.00e+00 -2.00e+02  1.00e+50]]\n",
      "RHS [0.00e+00 0.00e+00 1.05e+50]\n",
      "LU Matrix\n",
      "[[ 1.02000000e+02 -1.00000000e+02  0.00000000e+00]\n",
      " [-9.80392157e-01  2.00960784e+02 -2.00000000e+02]\n",
      " [ 0.00000000e+00 -9.95219046e-01  1.00000000e+50]]\n",
      "Forwards Result [0.00e+00 0.00e+00 1.05e+50]\n",
      "Backwards Result: Bus Voltage [1.02449019 1.04498    1.05      ]\n",
      "Source Active Power: 0.0\n",
      "Injection by Y Bus [-2.09916032  1.0919832   1.05420041]\n"
     ]
    }
   ],
   "source": [
    "linear_pf(get_input())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Newton-Raphson PF\n",
    "\n",
    "We then run the power flow using Newton-Raphson method. To make less bias, we put random numbers in the initial voltages. This is the observation:\n",
    "\n",
    "* The high source admittance results a huge value in the diagonal entry of Jacobian matrix and power mismatch in the right hand side.\n",
    "* It does not produce high value in the off-diagonals of the Jacobian matrix.\n",
    "* This leads to theoretically huge condition number. However, the linear equation is perfectly solvable without any numerical issues.\n",
    "* The huge number at both Jacobian diagonal entry and power mismatch cancelled each other in the backwards substitution. We get reasonable `delta_u` to iterate.\n",
    "* During the iteration the huge number forces that the voltage at source bus converges to `u_ref`.\n",
    "* If we calculate source injection by using the voltage difference between node and `u_ref`, it procudes the wrong value because the floating point values of these two are the same.\n",
    "* Everything else calculated from branch parameter or node admittance matrix is fine, including calculating the source injection using node admittance matrix.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def newton_raphson_pf(grid_input: GridInput, u_init: np.ndarray, n_iter: int = 5):\n",
    "    u = u_init.copy()\n",
    "    for i in range(n_iter):\n",
    "        print(f'----Newton Raphson Iteration {i}----')\n",
    "        print(f'Current Voltage {u}')\n",
    "        i_bus = grid_input.ybus @ u\n",
    "        p_bus = i_bus * u\n",
    "        jacobian = np.diag(i_bus) + np.diag(u) @ grid_input.ybus\n",
    "        delta_p = grid_input.load -  p_bus\n",
    "        delta_p[grid_input.slack_bus] += u[grid_input.slack_bus] * (grid_input.u_ref - u[grid_input.slack_bus]) * grid_input.yk\n",
    "        jacobian[grid_input.slack_bus, grid_input.slack_bus] -= (grid_input.u_ref - 2 * u[grid_input.slack_bus]) * grid_input.yk\n",
    "        _, _, lu = lu_factorization(jacobian)\n",
    "        delta_temp, delta_u = forwards_backwards(lu, delta_p)\n",
    "        u += delta_u\n",
    "        print(f'Jacobian')\n",
    "        print(jacobian)\n",
    "        print(f'Delta P {delta_p}')\n",
    "        print('LU Matrix')\n",
    "        print(lu)\n",
    "        print(f'Forwards Result {delta_temp}')\n",
    "        print(f'Backwards Result: delta U {delta_u}')\n",
    "        print(f'Updated Voltage {u}')\n",
    "        print('\\n')\n",
    "        \n",
    "    source_p = (grid_input.u_ref - u[grid_input.slack_bus]) * grid_input.yk * u[grid_input.slack_bus]\n",
    "    print('\\n----Newton Raphson result-----')\n",
    "    print(f'Final Voltage {u}')\n",
    "    print(f'Source Active Power: {source_p}')\n",
    "    print(f'Injection by Y Bus {(grid_input.ybus @ u) * u}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "----Newton Raphson Iteration 0----\n",
      "Current Voltage [1.06639452 1.0957071  1.03924347]\n",
      "Jacobian\n",
      "[[ 1.03708194e+02 -1.06639452e+02  0.00000000e+00]\n",
      " [-1.09570710e+02  3.42936114e+02 -2.19141420e+02]\n",
      " [ 0.00000000e+00 -2.07848694e+02  1.02848694e+50]]\n",
      "Delta P [ 1.12587761e+00 -1.45853207e+01  1.11786559e+48]\n",
      "LU Matrix\n",
      "[[ 1.03708194e+02 -1.06639452e+02  0.00000000e+00]\n",
      " [-1.05652896e+00  2.30268445e+02 -2.19141420e+02]\n",
      " [ 0.00000000e+00 -9.02636457e-01  1.02848694e+50]]\n",
      "Forwards Result [ 1.12587761e+00 -1.33957984e+01  1.11786559e+48]\n",
      "Backwards Result: delta U [-0.03832659 -0.04783089  0.01086903]\n",
      "Updated Voltage [1.02806792 1.04787621 1.0501125 ]\n",
      "\n",
      "\n",
      "----Newton Raphson Iteration 1----\n",
      "Current Voltage [1.02806792 1.04787621 1.0501125 ]\n",
      "Jacobian\n",
      "[[ 1.00825963e+02 -1.02806792e+02  0.00000000e+00]\n",
      " [-1.04787621e+02  3.15896436e+02 -2.09575243e+02]\n",
      " [ 0.00000000e+00 -2.10022500e+02  1.05022500e+50]]\n",
      "Delta P [ 3.64267130e-02 -6.06993659e-01 -1.18135825e+46]\n",
      "LU Matrix\n",
      "[[ 1.00825963e+02 -1.02806792e+02  0.00000000e+00]\n",
      " [-1.03929204e+00  2.09050155e+02 -2.09575243e+02]\n",
      " [ 0.00000000e+00 -1.00465125e+00  1.05022500e+50]]\n",
      "Forwards Result [ 3.64267130e-02 -5.69135666e-01 -1.18135825e+46]\n",
      "Backwards Result: delta U [-0.00252967 -0.00283525 -0.00011249]\n",
      "Updated Voltage [1.02553825 1.04504096 1.05000001]\n",
      "\n",
      "\n",
      "----Newton Raphson Iteration 2----\n",
      "Current Voltage [1.02553825 1.04504096 1.05000001]\n",
      "Jacobian\n",
      "[[ 1.00603555e+02 -1.02553825e+02  0.00000000e+00]\n",
      " [-1.04504096e+02  3.14470749e+02 -2.09008192e+02]\n",
      " [ 0.00000000e+00 -2.10000002e+02  1.05000002e+50]]\n",
      "Delta P [ 7.73020978e-05 -1.63058618e-03 -1.26531465e+42]\n",
      "LU Matrix\n",
      "[[ 1.00603555e+02 -1.02553825e+02  0.00000000e+00]\n",
      " [-1.03877141e+00  2.07940767e+02 -2.09008192e+02]\n",
      " [ 0.00000000e+00 -1.00990299e+00  1.05000002e+50]]\n",
      "Forwards Result [ 7.73020978e-05 -1.55028697e-03 -1.26531465e+42]\n",
      "Backwards Result: delta U [-6.84391846e-06 -7.46753833e-06 -1.20506155e-08]\n",
      "Updated Voltage [1.02553141 1.04503349 1.05      ]\n",
      "\n",
      "\n",
      "----Newton Raphson Iteration 3----\n",
      "Current Voltage [1.02553141 1.04503349 1.05      ]\n",
      "Jacobian\n",
      "[[ 1.00602932e+02 -1.02553141e+02  0.00000000e+00]\n",
      " [-1.04503349e+02  3.14466955e+02 -2.09006699e+02]\n",
      " [ 0.00000000e+00 -2.10000000e+02  1.05000000e+50]]\n",
      "Delta P [ 4.26807922e-10 -1.16005632e-08 -2.33146835e+34]\n",
      "LU Matrix\n",
      "[[ 1.00602932e+02 -1.02553141e+02  0.00000000e+00]\n",
      " [-1.03877041e+00  2.07937787e+02 -2.09006699e+02]\n",
      " [ 0.00000000e+00 -1.00991745e+00  1.05000000e+50]]\n",
      "Forwards Result [ 4.26807922e-10 -1.11572077e-08 -2.33146835e+34]\n",
      "Backwards Result: delta U [-5.04543399e-11 -5.36566937e-11 -2.22044605e-16]\n",
      "Updated Voltage [1.02553141 1.04503349 1.05      ]\n",
      "\n",
      "\n",
      "----Newton Raphson Iteration 4----\n",
      "Current Voltage [1.02553141 1.04503349 1.05      ]\n",
      "Jacobian\n",
      "[[ 1.00602932e+02 -1.02553141e+02  0.00000000e+00]\n",
      " [-1.04503349e+02  3.14466955e+02 -2.09006699e+02]\n",
      " [ 0.00000000e+00 -2.10000000e+02  1.05000000e+50]]\n",
      "Delta P [ 3.10862447e-15  3.86357613e-14 -1.04296637e+00]\n",
      "LU Matrix\n",
      "[[ 1.00602932e+02 -1.02553141e+02  0.00000000e+00]\n",
      " [-1.03877041e+00  2.07937787e+02 -2.09006699e+02]\n",
      " [ 1.43517902e-14 -1.00991745e+00  1.05000000e+50]]\n",
      "Forwards Result [ 3.10862447e-15  4.18649084e-14 -1.04296637e+00]\n",
      "Backwards Result: delta U [ 2.36136653e-16  2.01333817e-16 -9.93301302e-51]\n",
      "Updated Voltage [1.02553141 1.04503349 1.05      ]\n",
      "\n",
      "\n",
      "\n",
      "----Newton Raphson result-----\n",
      "Final Voltage [1.02553141 1.04503349 1.05      ]\n",
      "Source Active Power: 0.0\n",
      "Injection by Y Bus [-2.          1.          1.04296637]\n"
     ]
    }
   ],
   "source": [
    "newton_raphson_pf(get_input(), u_init=np.random.rand(3) * 0.1 + 1.0, n_iter=5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Conclusion\n",
    "\n",
    "* A high short circuit power `sk` in sources will force the node voltage to approach to the source `u_ref`. The calculation itself will not have numerical stability issue.\n",
    "* The current way of calculating source injection power does suffer from numerical instability. The votlage difference between source node and source `u_ref` is too close.\n",
    "* We need to use the node admittance matrix to help with calculation of source injection.\n",
    "\n",
    "## Calculation using node admittance matrix\n",
    "\n",
    "* After the power flow, use the `YBus` to calculate the total current injection of a bus. \n",
    "* Subtract that injection with all the `load_gen` injection of that bus.\n",
    "* The remaining is the total source current injection of that bus. \n",
    "  * If there is only one (connected) source at that bus, assign the value to that source.\n",
    "  * If there are more than one (connected) sources at that bus, we need more refinement as the next section.\n",
    "* Use the bus voltage and source current injection to calculate source power injection.\n",
    "\n",
    "## More than one connected sources at one bus\n",
    "\n",
    "Here we work out the mathematics to divide the total source current injection. Given the following notation:\n",
    "\n",
    "* $i = 0 \\sim N - 1$ is the Source $i$ of in total $N$ connected sources in the bus.\n",
    "* $\\underline{U}_{ref,i}$ is the reference voltage of Source $i$.\n",
    "* $\\underline{Y}_{ref,i}$ is the admittance of Source $i$.\n",
    "* $\\underline{I}_{ref,i} = \\underline{U}_{ref,i} * \\underline{Y}_{ref,i}$ is the Norton equivalent current of Source $i$.\n",
    "* $\\underline{I}_{inj,t}$ is the total source current injection calculated from `YBus` and `load_gen`.\n",
    "* $\\underline{I}_{ref,t} = \\sum_{i=0}^{i<N} \\underline{I}_{ref,i}$ is the total Norton equivalent current of sources.\n",
    "* $\\underline{Y}_{ref,t} = \\sum_{i=0}^{i<N} \\underline{Y}_{ref,i}$ is the total admittance of sources.\n",
    "* $\\underline{Z}_{ref,t} = \\underline{Y}_{ref,t}^{-1}$ is the total impedance of the sources. For asymmetric calculation, this is a matrix inverse. The matrix only has two distinct values: diagonal and off-diagonal. So use the [fast inverse](https://github.com/PowerGridModel/power-grid-model/blob/b1903af981f2fad4897793f8000f3c9a56fbb2d8/power_grid_model_c/power_grid_model/include/power_grid_model/common/three_phase_tensor.hpp#L281-L285) method in the tensor module.\n",
    "* $\\underline{I}_{inj,i}$ is the current injection of Source $i$ to the bus, which needs to be calculated.\n",
    "\n",
    "We use the following to calculate $\\underline{I}_{inj,i}$. Note the parentheses of the first item. You should calculate that substraction first to avoid truncation error. Also note the order of impedance and admittance tensor in asymmetrical calculations.\n",
    "\n",
    "$$\n",
    "\\underline{I}_{inj,i} = \n",
    "\\Big ( \\underline{I}_{ref,i} - \\underline{Y}_{ref,i} \\underline{Z}_{ref,t} \\underline{I}_{ref,t} \\Big ) \n",
    "+ \\underline{Y}_{ref,i} \\underline{Z}_{ref,t} \\underline{I}_{inj,t}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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