smib_milano_ex8p1_4ord_dashb.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# SMIB system as in Milano's book example 8.1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib widget"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.optimize as sopt\n",
    "import ipywidgets\n",
    "import pydae.ssa as ssa\n",
    "import pandas as pd\n",
    "plt.style.use('presentation.mplstyle')\n",
    "colors = plt.rcParams['axes.prop_cycle'].by_key()['color']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from core.smib_milano_ex8p1_4ord import smib_milano_ex8p1_4ord_class,daesolver"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "syst = smib_milano_ex8p1_4ord_class()\n",
    "syst.t_end = 15.0\n",
    "syst.Dt = 0.05\n",
    "syst.decimation =1\n",
    "syst.update()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def test(syst,p_m,v_f,use_numba=True):\n",
    "    # simulation parameters\n",
    "    syst.struct[0].imax = 50    # maximum number of iterations\n",
    "    syst.struct[0].itol = 1e-6  # relative tolerance to stop iteration\n",
    "    syst.struct[0].solvern = 5  # 5 = DAE trapezoidal solver (fixed step)\n",
    "    syst.struct[0].it = 0       # set time step to zero\n",
    "    syst.struct[0].it_store = 0 # set storage to zero\n",
    "    syst.struct[0].t = 0.0      # set time to zero\n",
    "    \n",
    "    syst.struct[0].D = 5   \n",
    "    syst.struct[0].p_m = 0\n",
    "    \n",
    "    syst.struct[0].T1d0 = 8\n",
    "\n",
    "    syst.struct.P_t = 0\n",
    "    syst.struct.Q_t = 0    \n",
    "    \n",
    "    # compute initial conditions using x and y_ini \n",
    "    xy0 = np.ones(syst.N_x+syst.N_y)\n",
    "    xy = sopt.fsolve(syst.ini_problem,xy0 )\n",
    "\n",
    "    # from ini system to run system\n",
    "    syst.struct[0].p_m = xy[syst.xy_ini_list.index('p_m')]\n",
    "    syst.struct[0].v_f = xy[syst.xy_ini_list.index('v_f')]\n",
    "\n",
    "    syst.struct[0].x[:,0] = xy[0:syst.N_x]\n",
    "    syst.struct[0].y[:,0] = xy[syst.N_x:]\n",
    "\n",
    "    syst.struct[0].y[syst.y_list.index('P_t'),0] = syst.struct.P_t\n",
    "    syst.struct[0].y[syst.y_list.index('Q_t'),0] = syst.struct.Q_t\n",
    "    \n",
    "    # solve system\n",
    "    syst.struct.t_end = 1.0  \n",
    "    daesolver(syst.struct)    # run until 1 s\n",
    "    syst.struct[0].p_m = p_m  # apply step in mechanical power p_m\n",
    "    syst.struct[0].v_f = v_f  # apply step in mechanical power p_m\n",
    "    syst.struct.t_end = 20.0  \n",
    "    daesolver(syst.struct)    # run until 10 s\n",
    "        \n",
    "    T = syst.struct[0]['T'][:syst.struct[0].it_store]\n",
    "    X = syst.struct[0]['X'][:syst.struct[0].it_store,:]\n",
    "    Y = syst.struct[0]['Y'][:syst.struct[0].it_store,:]\n",
    "\n",
    "    return T,X,Y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "T,X,Y =test(syst,0.0,1.0,use_numba=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
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       "          </g>\n",
       "        </g>\n",
       "      </g>\n",
       "    </g>\n",
       "  </g>\n",
       "</svg>"
      ],
      "text/plain": [
       "<IPython.core.display.SVG object>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import SVG\n",
    "SVG('./figures/dash_smib.svg')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.ioff()\n",
    "plt.clf()\n",
    "\n",
    "\n",
    "fig, axes = plt.subplots(nrows=2, ncols=2, figsize=(9, 4), frameon=False)\n",
    "fig.canvas.toolbar_visible = False\n",
    "\n",
    "T,X,Y =test(syst,0.0,1.0,use_numba=True)\n",
    "line_delta = axes[0,0].plot(T, X[:,syst.x_list.index('delta')], label='$\\sf \\delta$', color=colors[4])\n",
    "line_omega = axes[1,0].plot(T, X[:,syst.x_list.index('omega')], label='$\\sf \\omega$', color=colors[1])\n",
    "line_v_1 = axes[0,1].plot(T, Y[:,syst.y_list.index('v_1')], label='$\\sf v_1$', color=colors[5])\n",
    "#line_theta_1 = axes[0,1].plot(T, Y[:,syst.y_list.index('theta_1')], label='$\\sf \\\\theta_1$')\n",
    "line_p_t = axes[1,1].plot(T, Y[:,syst.y_list.index('P_t')], label='$\\sf P_t$', color=colors[2])\n",
    "line_q_t = axes[1,1].plot(T, Y[:,syst.y_list.index('Q_t')], label='$\\sf Q_t$', color=colors[0])\n",
    "\n",
    "x_0 = X[0,:]\n",
    "y_0 = Y[0,:]\n",
    "\n",
    "y_labels = ['$\\delta$','$\\omega$','$P_t$']\n",
    "\n",
    "axes[0,0].set_ylim((-1,2))\n",
    "axes[1,0].set_ylim((0.95,1.05))\n",
    "axes[0,1].set_ylim((0.8,1.2))\n",
    "axes[1,1].set_ylim((-0.5,1.5))\n",
    "\n",
    "axes[0,0].grid(True)\n",
    "axes[1,0].grid(True)\n",
    "axes[0,1].grid(True)\n",
    "axes[1,1].grid(True)\n",
    "axes[0,0].legend(loc='best')\n",
    "axes[1,0].legend(loc='best')\n",
    "axes[0,1].legend(loc='best')\n",
    "axes[1,1].legend(loc='best')\n",
    "\n",
    "axes[1,0].set_xlabel('Time (s)')  \n",
    "axes[1,1].set_xlabel('Time (s)') \n",
    "\n",
    "fig.tight_layout()\n",
    "#axes[0].set_title('Par en función de la velocidad')\n",
    "#axes[1].set_title('Corriente en función de la velocidad')\n",
    "\n",
    "\n",
    "sld_p_m = ipywidgets.FloatSlider(orientation='horizontal',description = \"$\\sf p_m$\", \n",
    "                                value=0.0, min=0.0,max= 1.2, \n",
    "                                step=.1)\n",
    "\n",
    "\n",
    "sld_v_f = ipywidgets.FloatSlider(orientation='horizontal',description = \"$\\sf v_f$\", \n",
    "                                value=syst.struct.v_f, min=0.5,max= 3, \n",
    "                                step=.01)\n",
    "\n",
    "prog_c = ipywidgets.IntProgress(\n",
    "    value=100,\n",
    "    min=0,\n",
    "    max=120,\n",
    "    step=1,\n",
    "    description='SM Load:',\n",
    "    bar_style='', # 'success', 'info', 'warning', 'danger' or ''\n",
    "    orientation='horizontal' \n",
    ")\n",
    "\n",
    "prog_damp = ipywidgets.IntProgress(\n",
    "    value=10,\n",
    "    min=0,\n",
    "    max=20,\n",
    "    step=1,\n",
    "    description='ζ = 1.0',\n",
    "    bar_style='', # 'success', 'info', 'warning', 'danger' or ''\n",
    "    orientation='horizontal' \n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
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       "model_id": "14f5d87da5d04cc7b4d445bd4687b09c",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "VBox(children=(HBox(children=(Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def update(change):\n",
    "    \n",
    "    p_m = sld_p_m.value\n",
    "    v_f = sld_v_f.value\n",
    "   \n",
    " \n",
    "    T,X,Y = test(syst,p_m,v_f,use_numba=True)\n",
    "\n",
    "    line_delta[0].set_data(T, X[:,syst.x_list.index('delta')])\n",
    "    line_omega[0].set_data(T, X[:,syst.x_list.index('omega')])\n",
    "    line_v_1[0].set_data(T, Y[:,syst.y_list.index('v_1')])\n",
    "    #line_theta_1[0].set_data(T, Y[:,syst.y_list.index('theta_1')])\n",
    "    line_p_t[0].set_data(T, Y[:,syst.y_list.index('P_t')])\n",
    "    line_q_t[0].set_data(T, Y[:,syst.y_list.index('Q_t')])\n",
    "\n",
    "    c = np.abs(Y[-1,syst.y_list.index('i_d')]+1j*Y[-1,syst.y_list.index('i_q')])\n",
    "\n",
    "    prog_c.bar_style = 'success'\n",
    "    if c>0.9:\n",
    "        prog_c.bar_style = 'warning'\n",
    "    if c>1.0:\n",
    "        prog_c.bar_style = 'danger'\n",
    "    prog_c.value = 100*c\n",
    "\n",
    "    fig.canvas.draw_idle()\n",
    "     \n",
    "   \n",
    "    \n",
    "sld_p_m.observe(update, names='value')\n",
    "sld_v_f.observe(update, names='value')\n",
    "\n",
    "layout_row1 = ipywidgets.HBox([fig.canvas])\n",
    "layout_row2 = ipywidgets.HBox([sld_p_m,sld_v_f,prog_c])\n",
    "\n",
    "layout = ipywidgets.VBox([layout_row1,layout_row2])\n",
    "layout"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "eb0028fecc194260b464da911d1f3e5e",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HTMLMath(value='$\\\\sf \\\\cdot$')"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ipywidgets.HTMLMath('$\\sf \\cdot$')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
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       "      <th>Real</th>\n",
       "      <th>Imag</th>\n",
       "      <th>Freq.</th>\n",
       "      <th>Damp</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Mode 1</th>\n",
       "      <td>-1.146328</td>\n",
       "      <td>7.895269</td>\n",
       "      <td>1.256571</td>\n",
       "      <td>0.143685</td>\n",
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       "      <td>1.000000</td>\n",
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       "      <th>Mode 4</th>\n",
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       "            Real      Imag     Freq.      Damp\n",
       "Mode 1 -1.146328  7.895269  1.256571  0.143685\n",
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      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ssa.eval_A(syst)\n",
    "ssa.damp_report(syst)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Mode 1</th>\n",
       "      <th>Mode 2</th>\n",
       "      <th>Mode 3</th>\n",
       "      <th>Mode 4</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>delta</th>\n",
       "      <td>0.51</td>\n",
       "      <td>0.51</td>\n",
       "      <td>0.01</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>omega</th>\n",
       "      <td>0.51</td>\n",
       "      <td>0.51</td>\n",
       "      <td>0.03</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>e1q</th>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>e1d</th>\n",
       "      <td>0.10</td>\n",
       "      <td>0.10</td>\n",
       "      <td>1.03</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       Mode 1  Mode 2  Mode 3  Mode 4\n",
       "delta    0.51    0.51    0.01     0.0\n",
       "omega    0.51    0.51    0.03     0.0\n",
       "e1q      0.00    0.00    0.00     1.0\n",
       "e1d      0.10    0.10    1.03     0.0"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ssa.participation(syst).abs().round(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>delta</th>\n",
       "      <th>omega</th>\n",
       "      <th>e1q</th>\n",
       "      <th>e1d</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Mode 1</th>\n",
       "      <td>0.45∠ -8.2</td>\n",
       "      <td>0.46∠-101.3</td>\n",
       "      <td>0.00∠ -3.4</td>\n",
       "      <td>0.10∠179.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Mode 2</th>\n",
       "      <td>0.45∠  8.2</td>\n",
       "      <td>0.46∠101.3</td>\n",
       "      <td>0.00∠  3.4</td>\n",
       "      <td>0.10∠-179.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Mode 3</th>\n",
       "      <td>0.01∠180.0</td>\n",
       "      <td>0.02∠ -0.0</td>\n",
       "      <td>0.00∠180.0</td>\n",
       "      <td>1.03∠ -0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Mode 4</th>\n",
       "      <td>0.00∠  0.0</td>\n",
       "      <td>0.00∠ -0.0</td>\n",
       "      <td>0.94∠ -0.0</td>\n",
       "      <td>0.00∠ -0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             delta        omega         e1q          e1d\n",
       "Mode 1  0.45∠ -8.2  0.46∠-101.3  0.00∠ -3.4   0.10∠179.0\n",
       "Mode 2  0.45∠  8.2   0.46∠101.3  0.00∠  3.4  0.10∠-179.0\n",
       "Mode 3  0.01∠180.0   0.02∠ -0.0  0.00∠180.0   1.03∠ -0.0\n",
       "Mode 4  0.00∠  0.0   0.00∠ -0.0  0.94∠ -0.0   0.00∠ -0.0"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ssa.shape2df(syst)"
   ]
  }
 ],
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