{
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  {
   "cell_type": "code",
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   "source": [
    "import numpy as np\n",
    "import control\n",
    "from bokeh.plotting import figure\n",
    "from bokeh.io import show, output_notebook"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Plot tooltips\n",
    "TOOLTIPS = [\n",
    "    (\"index\", \"$index\"),\n",
    "    (\"(t, val)\", \"($x, $y)\"),\n",
    "    ]"
   ]
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   "source": [
    "# Step 1: DC-DC single leg with current control\n",
    "![dcdc_single_leg_current_control](fig/dc_single_leg_current_control.png)"
   ]
  },
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   "execution_count": 3,
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   "source": [
    "# Electrical parameters\n",
    "L = 6e-3\n",
    "Rload = 30\n",
    "E = 600\n",
    "fsw = 16e3"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
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   "source": [
    "The controller is designed here with a compensation of the output voltage.\n",
    "\n",
    "![current_control_with_voltage_compensation](fig/current_control_with_voltage_compensation.png)\n",
    "\n",
    "Closed loop transfer function : $$ TF_{CL}(s) = \\dfrac{1 + \\frac{K_p}{K_i} s}{1 + \\frac{K_p}{K_i} s + \\frac{L}{E ~ K_i} s^2 } $$\n",
    "\n",
    "Which leads to:\n",
    "$$ K_i = \\dfrac{L \\omega_n^2}{E}  ~~~~ \\text{et} ~~~~  K_p = \\dfrac{2 \\xi K_i}{\\omega_n} $$\n",
    "\n",
    "\n",
    "\n"
   ]
  },
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   "attachments": {},
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   "source": [
    "### Step 1.a) compute $K_p$ and $K_i$ coefficients with $\\xi = 0.707$ \n",
    "Parameter $\\omega_n$ is chosen to get the same dynamic in closed loop as in open-loop with a nominal load (as this dynamic is high enough for this application) and the damping factor is limited to 0.707."
   ]
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   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0707\n",
      "250.0\n"
     ]
    }
   ],
   "source": [
    "wn = Rload / L   # same dynamic as in open-loop\n",
    "xi = 0.707\n",
    "Ki = wn ** 2 * L / E\n",
    "Kp = 2 * xi * Ki / wn\n",
    "print(Kp)\n",
    "print(Ki)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Le's check the closed loop transfer function with these coefficients:"
   ]
  },
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   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
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     "source_hidden": true
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response\"},\"id\":\"1003\",\"type\":\"Title\"},{\"attributes\":{},\"id\":\"1052\",\"type\":\"Selection\"},{\"attributes\":{\"coordinates\":null,\"data_source\":{\"id\":\"1037\"},\"glyph\":{\"id\":\"1038\"},\"group\":null,\"hover_glyph\":null,\"muted_glyph\":{\"id\":\"1040\"},\"nonselection_glyph\":{\"id\":\"1039\"},\"view\":{\"id\":\"1042\"}},\"id\":\"1041\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"active_drag\":{\"id\":\"1023\"},\"tools\":[{\"id\":\"1021\"},{\"id\":\"1022\"},{\"id\":\"1023\"},{\"id\":\"1024\"},{\"id\":\"1025\"},{\"id\":\"1026\"},{\"id\":\"1028\"}]},\"id\":\"1029\",\"type\":\"Toolbar\"},{\"attributes\":{},\"id\":\"1005\",\"type\":\"DataRange1d\"},{\"attributes\":{},\"id\":\"1007\",\"type\":\"DataRange1d\"},{\"attributes\":{},\"id\":\"1014\",\"type\":\"BasicTicker\"},{\"attributes\":{\"axis_label\":\"time (s)\",\"coordinates\":null,\"formatter\":{\"id\":\"1049\"},\"group\":null,\"major_label_policy\":{\"id\":\"1050\"},\"ticker\":{\"id\":\"1014\"}},\"id\":\"1013\",\"type\":\"LinearAxis\"},{\"attributes\":{},\"id\":\"1011\",\"type\":\"LinearScale\"}],\"root_ids\":[\"1002\"]},\"title\":\"Bokeh Application\",\"version\":\"2.4.2\"}};\n  const render_items = [{\"docid\":\"33e1689c-c35a-431b-a234-1eee03fd358d\",\"root_ids\":[\"1002\"],\"roots\":{\"1002\":\"29e74a6f-bad4-494b-9c5c-9d7d4131b9ab\"}}];\n  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n\n  }\n  if (root.Bokeh !== undefined) {\n    embed_document(root);\n  } else {\n    let attempts = 0;\n    const timer = setInterval(function(root) {\n      if (root.Bokeh !== undefined) {\n        clearInterval(timer);\n        embed_document(root);\n      } else {\n        attempts++;\n        if (attempts > 100) {\n          clearInterval(timer);\n          console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n        }\n      }\n    }, 10, root)\n  }\n})(window);",
      "application/vnd.bokehjs_exec.v0+json": ""
     },
     "metadata": {
      "application/vnd.bokehjs_exec.v0+json": {
       "id": "1002"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Simulation of the transfer function with a step response\n",
    "tf = control.tf(np.array([Kp / Ki, 1]), np.array([1 / wn**2, 2 * xi / wn, 1]))\n",
    "simutime = np.linspace(0, 10 / wn, 1000)\n",
    "(simutime, output) = control.step_response(tf, simutime, X0=0)\n",
    "# Plot step response\n",
    "step_response = figure(width = 800, height = 300, \n",
    "                       title = 'Step response',\n",
    "                       x_axis_label = 'time (s)', y_axis_label = 'Output (p.u.)',\n",
    "                       tools='pan,wheel_zoom,box_zoom,reset,save',\n",
    "                       active_drag='box_zoom',\n",
    "                       tooltips = TOOLTIPS)\n",
    "step_response.line(simutime, output, color=(0, 50, 0))\n",
    "output_notebook()\n",
    "show(step_response)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The overshoot of the step response can not be acceptable as it is around 20%. This is due to zero of the numerator of the transfer function which is probably too close to the real part of a denominator pole. Let's check this with the *pzmap* function of the control toolbox:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([-3535.+3536.06773125j, -3535.-3536.06773125j]), array([-3536.0678925]))"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "control.pzmap(tf, plot=True, grid=False, title='Pole Zero Map')"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It confirms that thes $K_p$ and $K_i$ values lead to a zero in the transfer function which is too close to the poles. Different solutions can be considered to solve this issue. For example:\n",
    "* increase the value of $\\xi$.\n",
    "* compensate the zero,\n",
    "\n",
    "Let's try the first solution and perform a sweep of the damping coefficient $\\xi$ to evaluate its influence on the overshoot and on the pole / zero map."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 1.b) Sweep of the damping coefficient $\\xi$\n",
    "\n",
    "#### With the *step_response* function of the control package."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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VKC2Dc3vxP4g1ym3Ud/E/tR12rDh08T/MDt1KoHDxP16ga1QLbfE/LWxP1Hlp8T+opXfV62XxP++wlWJhYvE/Urkdhtpe8T86R0dKV1vxP5DVDbnXV/E/m2Yx3FtU8T9DGDe941DxP9S3aWVvTfE/H1Xa3f5J8T8T1WAvkkbxP7qDnGIpQ/E/oqX0f8Q/8T+tCJmPYzzxP0WUgpkGOfE/+Nhzpa018T9vn/m6WDLxP9J2a+EHL/E/gELsH7sr8T8wx2p9cijxP2U3ogAuJfE/Rb8asO0h8T/MDyqSsR7xP07p86x5G/E/X6VqBkYY8T8FwE+kFhXxP0lgNIzrEfE/GeB5w8QO8T98U1JPogvxPx8PwTSECPE/KS6beGoF8T9qF4gfVQLxP9UBAi5E//A/R3hWqDf88D+f3KaSL/nwPyLq6PAr9vA/KTfnxizz8D8ftkEYMvDwP8U1bug77fA/wuC4Okrq8D98vEQSXefwPzUnDHJ05PA/fVXhXJDh8D/Xzm7VsN7wP7bpN97V2/A/u0aZef/Y8D8vS8mpLdbwP9Ka2HBg0/A/35Cy0JfQ8D9guB3L083wP75DvGEUy/A/loMMllnI8D/VXGlpo8XwPwm+Ct3xwvA/CBQG8kTA8D/IvU6pnL3wP31/tgP5uvA/+/TtAVq48D9ZA4Wkv7XwP85J6+sps/A/1JFw2Jiw8D+KPkVqDK7wP1i7eqGEq/A/zekDfgGp8D+/jrX/gqbwP7O+RiYJpPA/c0lR8ZOh8D/2JFJgI5/wP3zXqXK3nPA/6+CcJ1Ca8D9tI1R+7ZfwP1NL3XWPlfA/JzYrDTaT8D8RWRZD4ZDwP28mXRaRjvA/r3KkhUWM8D9t2HeP/onwP8sbSjK8h/A/D411bH6F8D95ajw8RYPwP2NByZ8QgfA/m04vleB+8D8A3moatXzwP12pYS2OevA/jTbjy2t48D/WNKnzTXbwP47ZV6I0dPA//zt+1R9y8D+LsJaKD3DwPxkjB78DbvA/vHAhcPxr8D+nwCOb+WnwP1zcOD37Z/A/J4d4UwFm8D/X1OfaC2TwP75/edAaYvA/+j0OMS5g8D/8FXX5RV7wP12yayZiXPA/9LSetIJa8D81Caqgp1jwP9s1GefQVvA/0q1nhP5U8D9yIAF1MFPwP/rIQbVmUfA/Y712QaFP8D9qPN4V4E3wP/T6py4jTPA/tnD1h2pK8D8qJNodtkjwP9P1W+wFR/A/yWpz71lF8D+V9gsjskPwP11EBIMOQvA/W38uC29A8D+mmlC30z7wP02YJIM8PfA/uM9Yaqk78D9pM5BoGjrwPwiWYnmPOPA/u+5cmAg38D/dnAHBhTXwPwOryO4GNPA/VhEgHYwy8D8+92tHFTHwP2/0BmmiL/A/P1FCfTMu8D9dRmZ/yCzwP9s7smphK/A/lAddOv4p8D/nKpXpnijwP9UPgXNDJ/A/b0U/0+sl8D+ou+YDmCTwP4P+hgBII/A/mnAoxPsh8D8FhcxJsyDwP6P4bYxuH/A/wQoBhy0e8D8atXM08BzwP0vjrY+2G/A/kamRk4Aa8D/+evs6ThnwPwZfwoAfGPA/eSa4X/QW8D/Xn6nSzBXwPxbLXtSoFPA/xgybX4gT8D+lYB1vaxLwP5WLoP1REfA/+0zbBTwQ8D+Qj4CCKQ/wP5OZP24aDvA/czzEww4N8D/WA7d9BgzwPx1kvZYBC/A/T+h5CQAK8D9zX4zQAQnwP14JkuYGCPA/7MIlRg8H8D+zMeDpGgbwPyPvV8wpBfA/G7Mh6DsE8D/yfdA3UQPwP/nB9bVpAvA/b4whXYUB8D/treInpADwP5rEjSGM/+8/C/C1JNb97z8F7lVOJvzvP++NhJN8+u8/WapX6dj47z+Uc+REO/fvPz65P5uj9e8/0DJ+4RH07z8jx7QMhvLvP//S+BEA8e8/p25g5n/v7z9hsgJ/Be7vPxD699CQ7O8/zSda0SHr7z+O5UR1uOnvP8zl1bFU6O8/SCMtfPbm7z/MH23JneXvPwkiu45K5O8/f3I/wfzi7z94lyVWtOHvPx2QnEJx4O8/ow7XezPf7z+IsQv3+t3vP/Q7danH3O8/Ls1SiJnb7z80F+iIcNrvP3aUfaBM2e8/pbxgxC3Y7z+4OOTpE9fvPwcWYAb/1e8/kfgxD+/U7z9xTL3549PvP252a7vd0u8/yQOsSdzR7z8w2fSZ39DvP9lgwqHnz+8/3beXVvTO7z+72v6tBc7vPxLRiJ0bze8/l9jNGjbM7z86j20bVcvvP4ocD5V4yu8/U1phfaDJ7z98/BrKzMjvPx64+nD9x+8/32nHZzLH7z+TO1Cka8bvPxnJbBypxe8/gUT9xerE7z99meqWMMTvPxWQJoV6w+8/pe6rhsjC7z81m36RGsLvPwa8q5twwe8/h9dJm8rA7z+N83iGKMDvP+GzYlOKv+8/J3g6+O++7z8PeT1rWb7vP/DksqLGve8/qPvrlDe97z/qKUQ4rLzvP9ojIYMkvO8/Df/ya6C77z/pSzTpH7vvP2YuavGiuu8/MHYkeym67z8ytv18s7nvP35bm+1Aue8/qMOtw9G47z+CUvD1ZbjvP0WHKXv9t+8/JhErSpi37z9Z49FZNrfvP4VIBqHXtu8/pPW7Fny27z9cHPKxI7bvP8V8s2nOte8/p3YWNXy17z8xGj0LLbXvPyg4VePgtO8/h3GYtJe07z+qRkx2UbTvP+glwh8OtO8/r3lXqM2z7z8ntnUHkLPvP0dmkjRVs+8/ezgvJx2z7z/ICtrW57LvP3H2LDu1su8/LFvOS4Wy7z/V6XAAWLLvP7Su01Atsu8/SBvCNAWy7z+eDxSk37HvPzfjrZa8se8/hG2ABJyx7z/hDYnlfbHvPzWz0TFise8/GeNw4Uix7z+XwInsMbHvP34STEsdse8/T0n09Qqx7z+/hMvk+rDvP9iYJxDtsO8/rRJrcOGw7z+0PAX+17DvP68icrHQsO8/R5U6g8uw7z87LfRryLDvPyxOQWTHsO8/GCnRZMiw7z9vvl9my7DvP9TftWHQsO8/fTGpT9ew7z9CKxwp4LDvP00Z/ubqsO8/exxLgvew7z9hKgz0BbHvPwYNVzUWse8/QGJOPyix7z/LmiELPLHvPwD5DJJRse8/Uo9ZzWix7z9pPl22gbHvP/yyekacse8/WmMhd7ix7z+tjM1B1rHvP+0vCKD1se8/kg5nixay7z/4poz9OLLvP4AwKPBcsu8/bZf1XIKy7z97eL09qbLvPzEcVYzRsu8/93GeQvuy7z/lCohaJrPvP1YUDc5Ss+8/OFI1l4Cz7z8kGRWwr7PvPzRIzRLgs+8/n0KLuRG07z8c6YieRLTvPweTDLx4tO8/TwdpDK607z8zdf2J5LTvP7dsNS8cte8/+NaI9lS17z877nvajrXvP8o1n9XJte8/rnGP4gW27z8ZnvX7QrbvP8HmhhyBtu8/6p0EP8C27z9ZMzxeALfvPw8rB3VBt+8/0RNLfoO37z+Lffl0xrfvP4zvD1QKuO8/gN6XFk+47z9eoqa3lLjvPxZsXTLbuO8/HTvpgSK57z/Y0oKharnvP9ivboyzue8/7fz8Pf257z8jiImxR7rvP4a3e+KSuu8/131GzN667z8KT2hqK7vvP7EUa7h4u+8/QSLksca77z8zKXRSFbzvPwgtx5VkvO8/LXeUd7S87z/Hip7zBL3vP1EYswVWve8/MfGqqae97z8l+2nb+b3vP5Qj35ZMvu8/y1IE2J++7z8XX96a877vP9P/fNtHv+8/TcD6lZy/7z+f8nzG8b/vP2miM2lHwO8/f4dZep3A7z91+DP288DvPxfdEtlKwe8/2aBQH6LB7z8gJVLF+cHvP4qzhsdRwu8/EfBnIqrC7z8uy3nSAsPvP9tzStRbw+8/jElyJLXD7z8ZzpO/DsTvP5CXW6JoxO8/AkKAycLE7z83YcIxHcXvP1ty7Nd3xe8/nM3SuNLF7z+8l1PRLcbvP5CzVh6Jxu8/frPNnOTG7z/iyrNJQMfvP3a/DSKcx+8/p9rpIvjH7z/k2l9JVMjvP9/kkJKwyO8/y3Sn+wzJ7z+QT9eBacnvP/VzXSLGye8/wAuA2iLK7z/bXI6nf8rvP2S64Ibcyu8/wXXYdTnL7z+tz99xlsvvPzrpaXjzy+8/1rTyhlDM7z9I5/6arczvP6zoG7IKze8/ZMXfyWfN7z8UH+nfxM3vP48d3/Ehzu8/xl9x/X7O7z+87FcA3M7vP2wkU/g4z+8/u7Ar45XP7z9hdrK+8s/vP9aFwIhP0O8/QAw3P6zQ7z9cRP/fCNHvP3RnCmll0e8/Rp5R2MHR7z//8dUrHtLvPyk9oGF60u8/oxzBd9bS7z+g4FBsMtPvP5t9bz2O0+8/YH1E6enT7z8Q8P5tRdTvPyNd1cmg1O8/fbQF+/vU7z+AP9X/VtXvPyGSkNax1e8/B3yLfQzW7z+u+SDzZtbvP5IlszXB1u8/XSmrQxvX7z8eL3kbddfvP4hSlLvO1+8/OJJ6IijY7z/9wLBOgdjvPzJ3wj7a2O8/FwRC8TLZ7z82X8hki9nvP9IZ9Zfj2e8/X1BuiTva7z/9m+A3k9rvPwUE/6Hq2u8/mO+CxkHb7z89FyykmNvvP4x2wDnv2+8/1T0MhkXc7z/kw+GHm9zvP8J3GT7x3O8/hdKRp0bd7z81SS/Dm93vP6c+3I/w3e8/ePWIDEXe7z8Hgis4md7vP4a8vxHt3u8/CzNHmEDf7z+zG8nKk9/vP9VGUqjm3+8/QBH1Lzng7z96Vslgi+DvPyRj7Dnd4O8/UOeAui7h7z//6K7hf+HvP5O2o67Q4e8/YtmRICHi7z9QCLE2ceLvP3EaPvDA4u8/xPl6TBDj7z/4la5KX+PvPzbXJOqt4+8/EZEuKvzj7z9jdSEKSuTvP1wHWImX5O8/hI4xp+Tk7z/gCRJjMeXvPxYjYrx95e8/rSGPssnl7z9X3gpFFeb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Cu8D9GijLFZ63wPwB6LgCwrPA/RRYz8fir8D+0xtmXQqvwP6wwuvOMqvA/Z0ZqBNip8D+kVX7JI6nwPwsWiUJwqPA/Jrcbb72n8D8B7sVOC6fwP34CFuFZpvA/RtyYJaml8D91D9ob+aTwP+voY8NJpPA/Unq/G5uj8D/XpXQk7aLwP5UpCt0/ovA/vKoFRZOh8D9swOtb56DwP0n+PyE8oPA/z/6ElJGf8D9fbTy1557wPw8Q54I+nvA/NtEE/ZWd8D++yBQj7pzwPzlFlfRGnPA/s9QDcaCb8D9YTd2X+prwP9nVnWhVmvA/l+3A4rCZ8D+jdMEFDZnwP36zGdFpmPA/rWJDRMeX8D8dsrdeJZfwP01Q7x+ElvA/UHFih+OV8D+e1YiUQ5XwP73Q2UaklPA/sk/MnQWU8D9Q39aYZ5PwP16ybzfKkvA/jacMeS2S8D9JTyNdkZHwP2bxKOP1kPA/pZKSCluQ8D8L+tTSwI/wPyW2ZDsnj/A/GCK2Q46O8D+Yaj3r9Y3wP7eSbjFejfA/mni9FceM8D8H2p2XMIzwP9dYg7aai/A/S3/hcQWL8D87xCvJcIrwPzGP1bvcifA/ZTxSSUmJ8D+XIBVxtojwP9qMkTIkiPA/NdI6jZKH8D85RYSAAYfwP3FB4QtxhvA/xCzFLuGF8D+5eqPoUYXwP6Sv7zjDhPA/vGMdHzWE8D8dRqCap4PwP7Qf7Koag/A/D9Z0T46C8D8jbq6HAoLwP/gODVN3gfA/PQQFseyA8D/TwAqhYoDwPzjhkiLZf/A/8i0SNVB/8D/Qnf3Xx37wPzRYygpAfvA/M7ftzLh98D+4Sd0dMn3wP4rVDv2rfPA/R1n4aSZ88D9WDhBkoXvwP7lqzOoce/A/4yKk/Zh68D91Kw6cFXrwP+u6gcWSefA/SEt2eRB58D+lm2O3jnjwP72xwX4NePA/a9sIz4x38D8ZsLGnDHfwPyYSNQiNdvA/OzAM8A128D+bhrBej3XwP2bgm1MRdfA/zlhIzpN08D9DXDDOFnTwP5epzlKac/A/FVOeWx5z8D+PvxroonLwP2Wrv/cncvA/eykJiq1x8D8upHOeM3HwP0HeezS6cPA/t/OeS0Fw8D+tWlrjyG/wPy3kK/tQb/A/8LyRktlu8D8mbgqpYm7wPyXeFD7sbfA/IFEwUXZt8D/OadzhAG3wPw4qme+LbPA/gPPmeRds8D8eiEaAo2vwP8YKOQIwa/A/xf8//7xq8D9VTd12SmrwPx88k2jYafA/qXfk02Zp8D/MDlS49WjwPxp0ZRWFaPA/SH6c6hRo8D+HaH03pWfwP+TSjPs1Z/A/msJPNsdm8D9mokvnWGbwP85CBg7rZfA/atoFqn1l8D8pBtG6EGXwP4vJ7j+kZPA/3I7mODhk8D9qJ0ClzGPwP7jLg4RhY/A/pxs61vZi8D+kHuyZjGLwP8xDI88iYvA/DWJpdblh8D9HuEiMUGHwP2XtSxPoYPA/dRD+CYBg8D++mOpvGGDwP9BlnUSxX/A/kr+ih0pf8D9NVoc45F7wP7VC2FZ+XvA/7QUj4hhe8D+KifXZs13wP5Uf3j1PXfA/hIJrDetc8D821SxIh1zwP+6ise0jXPA/Q9+J/cBb8D8b5kV3XlvwP5R7dlr8WvA/+Muspppa8D+oa3pbOVrwPwZXcXjYWfA/X/Ij/XdZ8D/QCSXpF1nwPyvRBzy4WPA/2eNf9VhY8D++RMEU+lfwPxZewJmbV/A/UQHygz1X8D/vZuvS31bwP18uQoaCVvA/0V2MnSVW8D8SYmAYyVXwP18OVfZsVfA/O5wBNxFV8D8/q/3ZtVTwP/BA4d5aVPA/i8hERQBU8D/VEsEMplPwP+xV7zRMU/A/Dy1pvfJS8D9smMilmVLwP+n8p+1AUvA/7yOilOhR8D8yO1KakFHwP3fUU/44UfA/WuVCwOFQ8D8Vx7vfilDwP0U2W1w0UPA/qVK+Nd5P8D/snoJriE/wP2AARv0yT/A/xb6m6t1O8D8DhEMziU7wP/Jbu9Y0TvA/D7St1OBN8D9FW7osjU3wP6GBgd45TfA/Fbij6eZM8D808MFNlEzwP+t7fQpCTPA/Pg14H/BL8D8EtlOMnkvwP57nslBNS/A/tXI4bPxK8D/xhofeq0rwP6+yQ6dbSvA/wOIQxgtK8D8cYpM6vEnwP5rZbwRtSfA/q09LIx5J8D8MKMuWz0jwP34jlV6BSPA/gV9PejNI8D8BVqDp5UfwPxTdLqyYR/A/rCaiwUtH8D9JwKEp/0bwP7SS1eOyRvA/ruHl72ZG8D+qS3tNG0bwP3zJPvzPRfA/D67Z+4RF8D8ZpvVLOkXwP9G3POzvRPA/nUJZ3KVE8D/K/vUbXETwPz/9vaoSRPA/LKdciMlD8D/CvX20gEPwP+JZzS44Q/A/1Ov39u9C8D/3OqoMqELwP3JlkW9gQvA/6t9aHxlC8D8zdbQb0kHwPwRGTGSLQfA/p8jQ+ERB8D+syPDY/kDwP55mWwS5QPA/sxfAenNA8D9+pc47LkDwP6UtN0fpP/A/kCGqnKQ/8D8cRtg7YD/wP06zciQcP/A/BtQqVtg+8D+yZbLQlD7wP/93u5NRPvA/j2z4ng4+8D+m9hvyyz3wP+Ma2YyJPfA/7y7jbkc98D8z2e2XBT3wP4cQrQfEPPA/6hvVvYI88D8wkhq6QTzwP7xZMvwAPPA/LqjRg8A78D8YAq5QgDvwP7E6fWJAO/A/jXP1uAA78D9MHM1TwTrwP1DyujKCOvA/cQB2VUM68D+znrW7BDrwP/dxMWXGOfA/s2uhUYg58D+lyb2ASjnwP4oVP/IMOfA/ziTepc848D9IGFSbkjjwP+pbWtJVOPA/e6aqShk48D9I+f4D3TfwP92fEf6gN/A/uy+dOGU38D8NiFyzKTfwP17RCm7uNvA/VH1jaLM28D9fRiKieDbwP3gvAxs+NvA/0YPC0gM28D+S1hzJyTXwP48Cz/2PNfA//CmWcFY18D8qti8hHTXwPz1XWQ/kNPA/5APROqs08D8R+VSjcjTwP7K5o0g6NPA/bA58KgI08D9SBZ1IyjPwP53xxaKSM/A/aWu2OFsz8D9rTy4KJDPwP6++7RbtMvA/Th61XrYy8D8sF0XhfzLwP6+VXp5JMvA/fMnClRMy8D8xJTPH3THwPyFecTKoMfA/EGw/13Ix8D/siF+1PTHwP4swlMwIMfA/aCCgHNQw8D9bV0alnzDwP1oVSmZrMPA/NdtuXzcw8D9OaniQAzDwP1zEKvnPL/A/KStKmZwv8D9KIJtwaS/wP99k4n42L/A/U/nkwwMv8D8aHWg/0S7wP2xOMfGeLvA/CEoG2Wwu8D/xCq32Oi7wPy3K60kJLvA/g/6I0tct8D8+XEuQpi3wP+vU+YJ1LfA/GJdbqkQt8D8VDjgGFC3wP7fhVpbjLPA/EvZ/WrMs8D9Da3tSgyzwPyydEX5TLPA/MiML3SMs8D8I0DBv9CvwP2axSzTFK/A/1A8lLJYr8D9oboZWZyvwP4qKObM4K/A/s1sIQgor8D83E70C3CrwPwAcIvWtKvA/WBoCGYAq8D+r6yduUirwP0imXvQkKvA/KJlxq/cp8D+xSyyTyinwP3t9WqudKfA/FCbI83Ap8D/HdEFsRCnwP2DQkhQYKfA/79aI7Oso8D+SXfDzvyjwPzdwliqUKPA/ZlFIkGgo8D8DetMkPSjwPxeZBegRKPA/l5Os2eYn8D8qhJb5uyfwP/C6kUeRJ/A/Sr1sw2Yn8D+hRfZsPCfwPzBD/UMSJ/A/ydlQSOgm8D+fYcB5vibwPwxnG9iUJvA/XqoxY2sm8D+dH9MaQibwP1Tuz/4YJvA/XXH4DvAl8D+mNh1LxyXwPwD/DrOeJfA/5L2eRnYl8D9AmZ0FTiXwP0Hp3O8lJfA/HzguBf4k8D/lQWNF1iTwPz30TbCuJPA/O27ARYck8D8rAI0FYCTwP1orhu84JPA/4aF+AxIk8D90RklB6yPwPy0suajEI/A/V5ahOZ4j8D8++NXzdyPwP/f0KddRI/A/Ml9x4ysj8D8FOYAYBiPwP7mzKnbgIvA/mi9F/Loi8D/BO6SqlSLwP+aVHIFwIvA/LSqDf0si8D/0Eq2lJiLwP6CYb/MBIvA/cDGgaN0h8D9JgRQFuSHwP4dZosiUIfA/ybgfs3Ah8D/IymLETCHwPx7oQfwoIfA/HJaTWgUh8D+Zhi7f4SDwP8GX6Ym+IPA/59ObWpsg8D9VcRxReCDwPx/SQm1VIPA/8oPmrjIg8D/lP98VECDwP03qBKLtH/A/j5IvU8sf8D/scjcpqR/wP17w9COHH/A/XZpAQ2Uf8D+/KvOGQx/wP4CF5e4hH/A/nLjwegAf8D/e++0q3x7wP7Owtv69HvA/A2Ik9pwe8D/+wxARfB7wP/OzVU9bHvA/IzjNsDoe8D+Xf1E1Gh7wP/LhvNz5HfA/SN/pptkd8D/vH7OTuR3wP1l086KZHfA/5NSF1Hkd8D+0YUUoWh3wP4JiDZ46HfA/e0a5NRsd8D8NpCTv+xzwP784K8rcHPA/DOmoxr0c8D80wHnknhzwPxXweSOAHPA//9CFg2Ec8D+P4XkEQxzwP4LGMqYkHPA/j0qNaAYc8D88XmZL6BvwP7gXm07KG/A/sLIIcqwb8D8okIy1jhvwP1Q2BBlxG/A/b1BNnFMb8D+UrkU/NhvwP5VFywEZG/A/1C684/sa8D8fqPbk3hrwP4UTWQXCGvA/MPfBRKUa8D8//Q+jiBrwP6DzISBsGvA/6svWu08a8D8zmw12MxrwP+6ZpU4XGvA/xSN+RfsZ8D9vt3Za3xnwP5D2bo3DGfA/kKVG3qcZ8D92q91MjBnwP8URFNlwGfA/VATKglUZ8D8q0d9JOhnwP17oNS4fGfA/6tusLwQZ8D+MXyVO6RjwP6VIgInOGPA/C46e4bMY8D/vR2FWmRjwP7Kvqed+GPA/yB9ZlWQY8D+OE1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\",\"dtype\":\"float64\",\"order\":\"little\",\"shape\":[1000]}},\"selected\":{\"id\":\"1173\"},\"selection_policy\":{\"id\":\"1172\"}},\"id\":\"1157\",\"type\":\"ColumnDataSource\"},{\"attributes\":{},\"id\":\"1147\",\"type\":\"BasicTickFormatter\"},{\"attributes\":{},\"id\":\"1116\",\"type\":\"BasicTicker\"},{\"attributes\":{\"axis\":{\"id\":\"1115\"},\"coordinates\":null,\"group\":null,\"ticker\":null},\"id\":\"1118\",\"type\":\"Grid\"},{\"attributes\":{\"source\":{\"id\":\"1157\"}},\"id\":\"1162\",\"type\":\"CDSView\"},{\"attributes\":{\"active_drag\":{\"id\":\"1125\"},\"tools\":[{\"id\":\"1123\"},{\"id\":\"1124\"},{\"id\":\"1125\"},{\"id\":\"1126\"},{\"id\":\"1127\"},{\"id\":\"1128\"},{\"id\":\"1130\"}]},\"id\":\"1131\",\"type\":\"Toolbar\"},{\"attributes\":{},\"id\":\"1111\",\"type\":\"LinearScale\"},{\"attributes\":{\"line_alpha\":0.1,\"line_color\":\"rgb(0, 100, 0)\",\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1159\",\"type\":\"Line\"},{\"attributes\":{\"label\":{\"value\":\"xi = 1.1\"},\"renderers\":[{\"id\":\"1180\"}]},\"id\":\"1196\",\"type\":\"LegendItem\"},{\"attributes\":{},\"id\":\"1124\",\"type\":\"WheelZoomTool\"},{\"attributes\":{},\"id\":\"1217\",\"type\":\"Selection\"},{\"attributes\":{\"coordinates\":null,\"data_source\":{\"id\":\"1197\"},\"glyph\":{\"id\":\"1198\"},\"group\":null,\"hover_glyph\":null,\"muted_glyph\":{\"id\":\"1200\"},\"nonselection_glyph\":{\"id\":\"1199\"},\"view\":{\"id\":\"1202\"}},\"id\":\"1201\",\"type\":\"GlyphRenderer\"},{\"attributes\":{},\"id\":\"1194\",\"type\":\"Selection\"},{\"attributes\":{\"axis_label\":\"Output (p.u.)\",\"coordinates\":null,\"formatter\":{\"id\":\"1147\"},\"group\":null,\"major_label_policy\":{\"id\":\"1148\"},\"ticker\":{\"id\":\"1120\"}},\"id\":\"1119\",\"type\":\"LinearAxis\"},{\"attributes\":{\"label\":{\"value\":\"xi = 0.9\"},\"renderers\":[{\"id\":\"1161\"}]},\"id\":\"1175\",\"type\":\"LegendItem\"},{\"attributes\":{\"axis\":{\"id\":\"1119\"},\"coordinates\":null,\"dimension\":1,\"group\":null,\"ticker\":null},\"id\":\"1122\",\"type\":\"Grid\"},{\"attributes\":{},\"id\":\"1120\",\"type\":\"BasicTicker\"},{\"attributes\":{\"callback\":null,\"tooltips\":[[\"index\",\"$index\"],[\"(t, val)\",\"($x, $y)\"]]},\"id\":\"1130\",\"type\":\"HoverTool\"},{\"attributes\":{},\"id\":\"1123\",\"type\":\"PanTool\"},{\"attributes\":{\"line_color\":\"rgb(0, 25, 0)\",\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1140\",\"type\":\"Line\"}],\"root_ids\":[\"1104\"]},\"title\":\"Bokeh Application\",\"version\":\"2.4.2\"}};\n  const render_items = [{\"docid\":\"49e9713f-3e6b-411f-aa7d-a0788ed5ceae\",\"root_ids\":[\"1104\"],\"roots\":{\"1104\":\"8c47fd4d-1611-4bb0-826c-49a604651c5d\"}}];\n  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n\n  }\n  if (root.Bokeh !== undefined) {\n    embed_document(root);\n  } else {\n    let attempts = 0;\n    const timer = setInterval(function(root) {\n      if (root.Bokeh !== undefined) {\n        clearInterval(timer);\n        embed_document(root);\n      } else {\n        attempts++;\n        if (attempts > 100) {\n          clearInterval(timer);\n          console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n        }\n      }\n    }, 10, root)\n  }\n})(window);",
      "application/vnd.bokehjs_exec.v0+json": ""
     },
     "metadata": {
      "application/vnd.bokehjs_exec.v0+json": {
       "id": "1104"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Create figure\n",
    "step_response_sweep = figure(width = 800, height = 300, \n",
    "                             title = 'Step response',\n",
    "                             x_axis_label = 'time (s)', y_axis_label = 'Output (p.u.)',\n",
    "                             tools='pan,wheel_zoom,box_zoom,reset,save',\n",
    "                             active_drag='box_zoom',\n",
    "                             tooltips = TOOLTIPS)\n",
    "green_color = 25\n",
    "\n",
    "# Step responses with xi parameter sweep\n",
    "for xi in [0.7, 0.9, 1.1, 1.4]:\n",
    "    Ki = wn ** 2 * L / E\n",
    "    Kp = 2 * xi * Ki / wn\n",
    "    tf = control.tf(np.array([Kp / Ki, 1]), np.array([1 / wn**2, 2 * xi / wn, 1]))\n",
    "    (simutime, output) = control.step_response(tf, simutime, X0=0)\n",
    "    step_response_sweep.line(simutime, output, color=(0, green_color, 0), legend_label='xi = ' + str(xi))\n",
    "    green_color += 75\n",
    "show(step_response_sweep)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([-11898.97948557,  -2101.02051443]), array([-1785.71428571]))"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot pzmap for xi = 1.4\n",
    "control.pzmap(tf, plot=True, grid=False, title='Pole Zero Map xi = ' + str(xi))"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The $K_p$ and $K_i$ values obtained for a damping coefficient $\\xi = 1.4$ seem to provide a good compromise between overshoot and speed.\n",
    "Let's check this with some simba simulations for the different values of $\\xi$.\n",
    "\n",
    "#### With *Simba* simulations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "  <div class=\"bk-root\" id=\"da551ab2-5934-4a13-b490-a02c3a5c1dbc\" data-root-id=\"1326\"></div>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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   "source": [
    "import os\n",
    "from aesim.simba import DesignExamples, ProjectRepository\n",
    "\n",
    "# Get project design and PI bloc\n",
    "file_path = os.path.join(os.getcwd(), \"direct_current_power_flow_control.jsimba\")\n",
    "project = ProjectRepository(file_path)\n",
    "direct_current_continuous_controller = project.GetDesignByName('1-direct_current_continuous_controller')\n",
    "PI = direct_current_continuous_controller.Circuit.GetDeviceByName('PI')\n",
    "\n",
    "# Figure\n",
    "simba_sweep = figure(width = 800, height = 500, \n",
    "                             title = 'Simba simulation',\n",
    "                             x_axis_label = 'time (s)', y_axis_label = 'Current (A)',\n",
    "                             tools='pan,wheel_zoom,box_zoom,reset,save',\n",
    "                             active_drag='box_zoom',\n",
    "                             tooltips = TOOLTIPS)\n",
    "green_color = 25                            \n",
    "\n",
    "# Simba simulations and plot with xi parameter sweep\n",
    "for xi in [0.7, 0.9, 1.1, 1.4]:\n",
    "    Ki = wn ** 2 * L / E\n",
    "    Kp = 2 * xi * Ki / wn\n",
    "    PI.Kp = Kp\n",
    "    PI.Ki = Ki\n",
    "    sweep_job = direct_current_continuous_controller.TransientAnalysis.NewJob()\n",
    "    status = sweep_job.Run()\n",
    "    simba_time_continuous = sweep_job.TimePoints\n",
    "    iL_continuous = sweep_job.GetSignalByName('L1 - Instantaneous Current').DataPoints\n",
    "    simba_sweep.line(simba_time_continuous, iL_continuous, color=(0, green_color, 0), legend_label='xi = ' + str(xi))\n",
    "    green_color += 75\n",
    "show(simba_sweep)"
   ]
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    "### Step 1.c) Discrete Z-controller : continuous to discrete transformation using Tustin method\n",
    "The continuous to discrete transformation using Tustin method gives: $ s = \\dfrac{2}{T_s} \\dfrac{z-1}{z+1} $,\n",
    "\n",
    "which leads to $ C(z) = \\dfrac{1}{1-z^{-1}} \\left(K_p + \\frac{1}{2} K_i T_s + (- K_p + \\frac{1}{2} K_i T_s) ~ z^{-1}\\right) $\n",
    "\n",
    "and then to the recurrence equation:\n",
    "$$ \\alpha(k) = \\alpha(k-1) + \\left(K_p + \\frac{1}{2} K_i T_s \\right) \\epsilon(k) + \\left(-K_p + \\frac{1}{2} K_i T_s \\right) \\epsilon(k-1) $$\n",
    "\n",
    "And finally: $ a_0 = -K_p + \\frac{1}{2} K_i T_s $ and $ a_1 = K_p + \\frac{1}{2} K_i T_s $"
   ]
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     "text": [
      "a0 =  -0.1321875\n",
      "a1 =  0.1478125\n"
     ]
    }
   ],
   "source": [
    "Ts = 1 / fsw\n",
    "a0 = -Kp + Ts * Ki / 2\n",
    "a1 = Kp + Ts * Ki / 2\n",
    "print('a0 = ', a0)\n",
    "print('a1 = ', a1)"
   ]
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   "cell_type": "markdown",
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   "source": [
    "### Step 1.d) Simba Simulation: continuous and discrete controller"
   ]
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   "cell_type": "code",
   "execution_count": 11,
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    "\n",
    "# Load design with discrete controller\n",
    "direct_current_discrete_controller = project.GetDesignByName('2-direct_current_discrete_controller')\n",
    "a0_element = direct_current_discrete_controller.Circuit.GetDeviceByName('a0')\n",
    "a1_element = direct_current_discrete_controller.Circuit.GetDeviceByName('a1')\n",
    "a0_element.Value = a0\n",
    "a1_element.Value = a1\n",
    "discrete_job = direct_current_discrete_controller.TransientAnalysis.NewJob()\n",
    "status = discrete_job.Run()\n",
    "\n",
    "# Get results\n",
    "simba_time_continuous =  sweep_job.TimePoints\n",
    "iL_continuous =  sweep_job.GetSignalByName('L1 - Instantaneous Current').DataPoints\n",
    "duty_cycle_continuous =  sweep_job.GetSignalByName('duty_cycle - Out').DataPoints\n",
    "\n",
    "simba_time_discrete = discrete_job.TimePoints\n",
    "iL_discrete = discrete_job.GetSignalByName('L1 - Instantaneous Current').DataPoints\n",
    "duty_cycle_discrete = discrete_job.GetSignalByName('duty_cycle - Out').DataPoints\n",
    "\n",
    "# plot\n",
    "TOOLTIPS = [\n",
    "    (\"index\", \"$index\"),\n",
    "    (\"(t, val)\", \"($x, $y)\"),\n",
    "    ]\n",
    "\n",
    "# figure\n",
    "current_control_fig = figure(width = 800, height = 300, \n",
    "                             title = 'Inductor current',\n",
    "                             x_axis_label = 'time (s)', y_axis_label = 'Current (A)',\n",
    "                             tools='pan,wheel_zoom,box_zoom,reset,save',\n",
    "                             active_drag='box_zoom',\n",
    "                             tooltips = TOOLTIPS)\n",
    "current_control_fig.line(simba_time_continuous, iL_continuous, color='limegreen', legend_label='continuous')\n",
    "current_control_fig.line(simba_time_discrete, iL_discrete, color='darkred', legend_label='discrete')\n",
    "\n",
    "output_notebook()\n",
    "show(current_control_fig)"
   ]
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   "cell_type": "markdown",
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   "source": [
    "# Step 2: Direct Current Power Flow Control\n",
    "![direct_current_power_flow_control](fig/dc_power_flow_control.png)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
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Application\",\"version\":\"2.4.2\"}};\n  const render_items = [{\"docid\":\"909ee02a-b638-4b26-aa74-14dc7ec21d1a\",\"root_ids\":[\"1949\"],\"roots\":{\"1949\":\"8c67e75f-17e2-477b-849e-290a45bebd0b\"}}];\n  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n\n  }\n  if (root.Bokeh !== undefined) {\n    embed_document(root);\n  } else {\n    let attempts = 0;\n    const timer = setInterval(function(root) {\n      if (root.Bokeh !== undefined) {\n        clearInterval(timer);\n        embed_document(root);\n      } else {\n        attempts++;\n        if (attempts > 100) {\n          clearInterval(timer);\n          console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n        }\n      }\n    }, 10, root)\n  }\n})(window);",
      "application/vnd.bokehjs_exec.v0+json": ""
     },
     "metadata": {
      "application/vnd.bokehjs_exec.v0+json": {
       "id": "1949"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Simulate\n",
    "direct_current_power_flow_control = project.GetDesignByName('3-direct_current_power_flow_control')\n",
    "a0_element = direct_current_power_flow_control.Circuit.GetDeviceByName('a0')\n",
    "a1_element = direct_current_power_flow_control.Circuit.GetDeviceByName('a1')\n",
    "a0_element.Value = a0\n",
    "a1_element.Value = a1\n",
    "power_flow_control_job = direct_current_power_flow_control.TransientAnalysis.NewJob()\n",
    "status = power_flow_control_job.Run()\n",
    "\n",
    "# Results\n",
    "simba_time_power_flow_control = power_flow_control_job.TimePoints\n",
    "power_ref = power_flow_control_job.GetSignalByName('PowerRef - Out').DataPoints\n",
    "power_average = power_flow_control_job.GetSignalByName('PowerEstimated - Out').DataPoints\n",
    "\n",
    "# figure\n",
    "p3 = figure(width = 800, height = 300, \n",
    "           title = 'Power',\n",
    "           x_axis_label = 'time (s)', y_axis_label = 'Power (W)',\n",
    "           tools='pan,wheel_zoom,box_zoom,reset,save',\n",
    "           active_drag='box_zoom',\n",
    "           tooltips = TOOLTIPS)\n",
    "p3.line(simba_time_power_flow_control, power_ref, color='limegreen', legend_label='reference')\n",
    "p3.line(simba_time_power_flow_control, power_average, color='darkred', legend_label='estimated')\n",
    "show(p3)"
   ]
  }
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