tutorials/shortcircuit.ipynb

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    "# Short-Circuit Calculation according to IEC 60909\n",
    "\n",
    "pandapower supports short-circuit calculations with the method of equivalent voltage source at the fault location according to IEC 60909. The pandapower short-circuit calculation supports the following elements:\n",
    "\n",
    "- sgen (as motor or as full converter generator)\n",
    "- gen (as synchronous generator)\n",
    "- ext_grid\n",
    "- line\n",
    "- trafo\n",
    "- trafo3w\n",
    "- impedance\n",
    "\n",
    "with the correction factors as defined in IEC 60909. Loads and shunts are neglected as per standard. The pandapower switch model is fully integrated into the short-circuit calculation. \n",
    "\n",
    "The following short-circuit currents can be calculated:\n",
    "- ikss (Initial symmetrical short-circuit current)\n",
    "- ip (short-circuit current peak)\n",
    "- ith (equivalent thermal short-circuit current)\n",
    "\n",
    "either as\n",
    "\n",
    " - symmetrical three-phase or\n",
    " - asymmetrical two-phase\n",
    " \n",
    "short circuit current. Calculations are available for meshed as well as for radial networks. ip and ith are only implemented for short circuits far from synchronous generators.\n",
    "\n",
    "The results for all elements and different short-circuit currents are tested against commercial software to ensure that correction factors are correctly applied. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example Network\n",
    "\n",
    "Here is a little example on how to use the short-circuit calculation. First, we create a simple open ring network with 4 buses, that are connected by one transformer and two lines with one open sectioning point. The network is fed by an external grid connection at bus 1:\n",
    "\n",
    "<img src=\"shortcircuit/example_network_sc.png\">"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
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   "outputs": [],
   "source": [
    "import pandapower as pp\n",
    "import pandapower.shortcircuit as sc\n",
    "\n",
    "def ring_network():\n",
    "    net = pp.create_empty_network()\n",
    "    b1 = pp.create_bus(net, 220)\n",
    "    b2 = pp.create_bus(net, 110)\n",
    "    b3 = pp.create_bus(net, 110)\n",
    "    b4 = pp.create_bus(net, 110)\n",
    "    pp.create_ext_grid(net, b1, s_sc_max_mva=100., s_sc_min_mva=80., rx_min=0.20, rx_max=0.35)\n",
    "    pp.create_transformer(net, b1, b2, \"100 MVA 220/110 kV\")\n",
    "    pp.create_line(net, b2, b3, std_type=\"N2XS(FL)2Y 1x120 RM/35 64/110 kV\" , length_km=15.)\n",
    "    l2 = pp.create_line(net, b3, b4, std_type=\"N2XS(FL)2Y 1x120 RM/35 64/110 kV\" , length_km=12.)\n",
    "    pp.create_line(net, b4, b2, std_type=\"N2XS(FL)2Y 1x120 RM/35 64/110 kV\" , length_km=10.)\n",
    "    pp.create_switch(net, b4, l2, closed=False, et=\"l\")\n",
    "    return net"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Symmetric Short-Circuit Calculation\n",
    "\n",
    "### Maximum Short Circuit Currents\n",
    "Now, we load the network and calculate the maximum short-circuit currents with the calc_sc function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
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     "name": "stderr",
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     "text": [
      "hp.pandapower.shortcircuit.calc_sc - WARNING: Branch results are in beta mode and might not always be reliable, especially for transformers\n",
      "C:\\Users\\mmilovic\\Documents\\Python Scripts\\pandapower\\pandapower\\shortcircuit\\currents.py:123: RuntimeWarning: invalid value encountered in log\n",
      "  m = (np.exp(4 * f * tk_s * np.log(kappa - 1)) - 1) / (2 * f * tk_s * np.log(kappa - 1))\n",
      "C:\\Users\\mmilovic\\Documents\\Python Scripts\\pandapower\\pandapower\\shortcircuit\\currents.py:265: RuntimeWarning: All-NaN slice encountered\n",
      "  ppci[\"branch\"][:, IKSS_F] = np.nan_to_num(minmax(ikss_all_f, axis=1) / baseI[fb])\n",
      "C:\\Users\\mmilovic\\Documents\\Python Scripts\\pandapower\\pandapower\\shortcircuit\\currents.py:266: RuntimeWarning: All-NaN slice encountered\n",
      "  ppci[\"branch\"][:, IKSS_T] = np.nan_to_num(minmax(ikss_all_t, axis=1) / baseI[tb])\n",
      "C:\\Users\\mmilovic\\Documents\\Python Scripts\\pandapower\\pandapower\\shortcircuit\\currents.py:283: RuntimeWarning: All-NaN slice encountered\n",
      "  ppci[\"branch\"][:, IP_F] = np.nan_to_num(minmax(abs(ip_all_f), axis=1) / baseI[fb])\n",
      "C:\\Users\\mmilovic\\Documents\\Python Scripts\\pandapower\\pandapower\\shortcircuit\\currents.py:284: RuntimeWarning: All-NaN slice encountered\n",
      "  ppci[\"branch\"][:, IP_T] = np.nan_to_num(minmax(abs(ip_all_t), axis=1) / baseI[tb])\n",
      "C:\\Users\\mmilovic\\Documents\\Python Scripts\\pandapower\\pandapower\\shortcircuit\\currents.py:296: RuntimeWarning: All-NaN slice encountered\n",
      "  ppci[\"branch\"][:, ITH_F] = np.nan_to_num(minmax(ith_all_f, axis=1) / baseI[fb])\n",
      "C:\\Users\\mmilovic\\Documents\\Python Scripts\\pandapower\\pandapower\\shortcircuit\\currents.py:297: RuntimeWarning: All-NaN slice encountered\n",
      "  ppci[\"branch\"][:, ITH_T] = np.nan_to_num(minmax(ith_all_t, axis=1) / baseI[fb])\n"
     ]
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       "      <th></th>\n",
       "      <th>ikss_ka</th>\n",
       "      <th>skss_mw</th>\n",
       "      <th>ip_ka</th>\n",
       "      <th>ith_ka</th>\n",
       "      <th>rk_ohm</th>\n",
       "      <th>xk_ohm</th>\n",
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       "      <th>0</th>\n",
       "      <td>0.262432</td>\n",
       "      <td>100.000000</td>\n",
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       "      <td>0.263723</td>\n",
       "      <td>175.878566</td>\n",
       "      <td>502.510189</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.476454</td>\n",
       "      <td>90.776637</td>\n",
       "      <td>0.942589</td>\n",
       "      <td>0.479039</td>\n",
       "      <td>44.276323</td>\n",
       "      <td>139.778739</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.466671</td>\n",
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       "      <td>0.915418</td>\n",
       "      <td>0.469123</td>\n",
       "      <td>46.571323</td>\n",
       "      <td>142.268739</td>\n",
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      "text/plain": [
       "    ikss_ka     skss_mw     ip_ka    ith_ka      rk_ohm      xk_ohm\n",
       "0  0.262432  100.000000  0.505834  0.263723  175.878566  502.510189\n",
       "1  0.476454   90.776637  0.942589  0.479039   44.276323  139.778739\n",
       "2  0.466671   88.912758  0.915418  0.469123   46.571323  142.268739\n",
       "3  0.469892   89.526397  0.924301  0.472386   45.806323  141.438739"
      ]
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     "execution_count": 2,
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   "source": [
    "net = ring_network()\n",
    "sc.calc_sc(net, case=\"max\", ip=True, ith=True, branch_results=True)\n",
    "net.res_bus_sc"
   ]
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   "source": [
    "where ikss is the initial short-circuit current, ip is the peak short-circuit current and ith is the thermal equivalent current.\n",
    "\n",
    "For branches, the results are defined as the maximum current flows through that occurs for a fault at any bus in the network. The results are available seperately for lines:"
   ]
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  {
   "cell_type": "code",
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       "      <th></th>\n",
       "      <th>ikss_ka</th>\n",
       "      <th>ip_ka</th>\n",
       "      <th>ith_ka</th>\n",
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      "text/plain": [
       "    ikss_ka     ip_ka    ith_ka\n",
       "0  0.466671  0.915418  0.469123\n",
       "1  0.000000  0.000000  0.000000\n",
       "2  0.469892  0.924301  0.472386"
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     "execution_count": 3,
     "metadata": {},
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   ],
   "source": [
    "net.res_line_sc"
   ]
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and transformers:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
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       "      <th></th>\n",
       "      <th>ikss_hv_ka</th>\n",
       "      <th>ikss_lv_ka</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
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      "text/plain": [
       "   ikss_hv_ka  ikss_lv_ka\n",
       "0    0.238227    0.476454"
      ]
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     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
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   "source": [
    "net.res_trafo_sc"
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   "source": [
    "### Minimum Short Circuit Currents"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Minimum short-circuits can be calculated in the same way. However, we need to specify the end temperature of the lines after a fault as per standard first:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "hp.pandapower.shortcircuit.calc_sc - WARNING: Branch results are in beta mode and might not always be reliable, especially for transformers\n",
      "C:\\Users\\mmilovic\\Documents\\Python Scripts\\pandapower\\pandapower\\shortcircuit\\currents.py:123: RuntimeWarning: invalid value encountered in log\n",
      "  m = (np.exp(4 * f * tk_s * np.log(kappa - 1)) - 1) / (2 * f * tk_s * np.log(kappa - 1))\n",
      "C:\\Users\\mmilovic\\Documents\\Python Scripts\\pandapower\\pandapower\\shortcircuit\\currents.py:265: RuntimeWarning: All-NaN slice encountered\n",
      "  ppci[\"branch\"][:, IKSS_F] = np.nan_to_num(minmax(ikss_all_f, axis=1) / baseI[fb])\n",
      "C:\\Users\\mmilovic\\Documents\\Python Scripts\\pandapower\\pandapower\\shortcircuit\\currents.py:266: RuntimeWarning: All-NaN slice encountered\n",
      "  ppci[\"branch\"][:, IKSS_T] = np.nan_to_num(minmax(ikss_all_t, axis=1) / baseI[tb])\n",
      "C:\\Users\\mmilovic\\Documents\\Python Scripts\\pandapower\\pandapower\\shortcircuit\\currents.py:283: RuntimeWarning: All-NaN slice encountered\n",
      "  ppci[\"branch\"][:, IP_F] = np.nan_to_num(minmax(abs(ip_all_f), axis=1) / baseI[fb])\n",
      "C:\\Users\\mmilovic\\Documents\\Python Scripts\\pandapower\\pandapower\\shortcircuit\\currents.py:284: RuntimeWarning: All-NaN slice encountered\n",
      "  ppci[\"branch\"][:, IP_T] = np.nan_to_num(minmax(abs(ip_all_t), axis=1) / baseI[tb])\n",
      "C:\\Users\\mmilovic\\Documents\\Python Scripts\\pandapower\\pandapower\\shortcircuit\\currents.py:296: RuntimeWarning: All-NaN slice encountered\n",
      "  ppci[\"branch\"][:, ITH_F] = np.nan_to_num(minmax(ith_all_f, axis=1) / baseI[fb])\n",
      "C:\\Users\\mmilovic\\Documents\\Python Scripts\\pandapower\\pandapower\\shortcircuit\\currents.py:297: RuntimeWarning: All-NaN slice encountered\n",
      "  ppci[\"branch\"][:, ITH_T] = np.nan_to_num(minmax(ith_all_t, axis=1) / baseI[fb])\n"
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       "      <td>73.242307</td>\n",
       "      <td>0.860874</td>\n",
       "      <td>0.387974</td>\n",
       "      <td>29.969247</td>\n",
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      "text/plain": [
       "    ikss_ka    skss_mw     ip_ka    ith_ka      rk_ohm      xk_ohm\n",
       "0  0.209946  80.000000  0.462534  0.211736  118.650262  593.251309\n",
       "1  0.384422  73.242307  0.860874  0.387974   29.969247  162.464019\n",
       "2  0.377608  71.943998  0.832832  0.380846   32.815047  164.954019\n",
       "3  0.379861  72.373180  0.841982  0.383197   31.866447  164.124019"
      ]
     },
     "execution_count": 5,
     "metadata": {},
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   "source": [
    "net = ring_network()\n",
    "net.line[\"endtemp_degree\"] = 80\n",
    "sc.calc_sc(net, case=\"min\", ith=True, ip=True, branch_results=True)\n",
    "net.res_bus_sc"
   ]
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The branch results are now the minimum current flows through each branch:"
   ]
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       "      <th></th>\n",
       "      <th>ikss_ka</th>\n",
       "      <th>ip_ka</th>\n",
       "      <th>ith_ka</th>\n",
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       "    ikss_ka     ip_ka    ith_ka\n",
       "0  0.377608  0.832832  0.380846\n",
       "1  0.000000  0.000000  0.000000\n",
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>ikss_hv_ka</th>\n",
       "      <th>ikss_lv_ka</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.188804</td>\n",
       "      <td>0.377608</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   ikss_hv_ka  ikss_lv_ka\n",
       "0    0.188804    0.377608"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "net.res_trafo_sc"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Asynchronous Motors\n",
    "\n",
    "Asynchronous motors can be specified by creating a static generator of type \"motor\". For the short circuit impedance, an R/X ratio \"rx\" as well as the ratio between nominal current and short circuit current \"k\" has to be specified:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "This pandapower network includes the following parameter tables:\n",
       "   - bus (4 elements)\n",
       "   - sgen (1 element)\n",
       "   - switch (1 element)\n",
       "   - ext_grid (1 element)\n",
       "   - line (3 elements)\n",
       "   - trafo (1 element)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "net = ring_network()\n",
    "pp.create_sgen(net, 2, p_mw=0, sn_mva=0.5, k=1.2, rx=7., type=\"motor\")\n",
    "net"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we run the short-circuit calculation again, we can see that the currents increased due to the contribution of the inverteres to the short-circuit currents."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\mmilovic\\Documents\\Python Scripts\\pandapower\\pandapower\\shortcircuit\\currents.py:123: RuntimeWarning: invalid value encountered in log\n",
      "  m = (np.exp(4 * f * tk_s * np.log(kappa - 1)) - 1) / (2 * f * tk_s * np.log(kappa - 1))\n"
     ]
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       "      <th></th>\n",
       "      <th>ikss_ka</th>\n",
       "      <th>skss_mw</th>\n",
       "      <th>ip_ka</th>\n",
       "      <th>ith_ka</th>\n",
       "      <th>rk_ohm</th>\n",
       "      <th>xk_ohm</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.264007</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>0.508061</td>\n",
       "      <td>0.265306</td>\n",
       "      <td>175.878566</td>\n",
       "      <td>502.510189</td>\n",
       "    </tr>\n",
       "    <tr>\n",
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       "      <td>0.479603</td>\n",
       "      <td>90.776637</td>\n",
       "      <td>0.947043</td>\n",
       "      <td>0.482205</td>\n",
       "      <td>44.276323</td>\n",
       "      <td>139.778739</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.469820</td>\n",
       "      <td>89.512758</td>\n",
       "      <td>0.919871</td>\n",
       "      <td>0.472289</td>\n",
       "      <td>46.571323</td>\n",
       "      <td>142.268739</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.472998</td>\n",
       "      <td>89.526397</td>\n",
       "      <td>0.928693</td>\n",
       "      <td>0.475509</td>\n",
       "      <td>45.806323</td>\n",
       "      <td>141.438739</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    ikss_ka     skss_mw     ip_ka    ith_ka      rk_ohm      xk_ohm\n",
       "0  0.264007  100.000000  0.508061  0.265306  175.878566  502.510189\n",
       "1  0.479603   90.776637  0.947043  0.482205   44.276323  139.778739\n",
       "2  0.469820   89.512758  0.919871  0.472289   46.571323  142.268739\n",
       "3  0.472998   89.526397  0.928693  0.475509   45.806323  141.438739"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sc.calc_sc(net, case=\"max\", ith=True, ip=True)\n",
    "net.res_bus_sc"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Synchronous Generators\n",
    "\n",
    "Synchronous generators can also be considered in the short-circuit calculation with the gen element. According to the standard, the rated power factor (cos$\\varphi$) \"cos_phi\", rated voltage \"vn_kv\", rated apparent power \"sn_kva\" and subtransient resistance \"rdss\" and reactance \"xdss\" are necessary to calculate the short circuit impedance:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "This pandapower network includes the following parameter tables:\n",
       "   - bus (4 elements)\n",
       "   - gen (1 element)\n",
       "   - switch (1 element)\n",
       "   - ext_grid (1 element)\n",
       "   - line (3 elements)\n",
       "   - trafo (1 element)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "net = ring_network()\n",
    "pp.create_gen(net, 2, p_mw=0, vm_pu=1.0, cos_phi=0.8, vn_kv=22, sn_mva=5, xdss_pu=0.2, rdss_ohm=0.005)\n",
    "net"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and run the short-circuit calculation again:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "hp.pandapower.shortcircuit.calc_sc - WARNING: aperiodic, thermal short-circuit currents are only implemented for faults far from generators!\n",
      "C:\\Users\\mmilovic\\Documents\\Python Scripts\\pandapower\\pandapower\\shortcircuit\\currents.py:123: RuntimeWarning: invalid value encountered in log\n",
      "  m = (np.exp(4 * f * tk_s * np.log(kappa - 1)) - 1) / (2 * f * tk_s * np.log(kappa - 1))\n"
     ]
    },
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       "      <th></th>\n",
       "      <th>ikss_ka</th>\n",
       "      <th>skss_mw</th>\n",
       "      <th>ip_ka</th>\n",
       "      <th>ith_ka</th>\n",
       "      <th>rk_ohm</th>\n",
       "      <th>xk_ohm</th>\n",
       "    </tr>\n",
       "  </thead>\n",
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       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.568039</td>\n",
       "      <td>216.451899</td>\n",
       "      <td>1.285305</td>\n",
       "      <td>0.573572</td>\n",
       "      <td>40.720778</td>\n",
       "      <td>242.572728</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.180874</td>\n",
       "      <td>224.986699</td>\n",
       "      <td>2.710856</td>\n",
       "      <td>1.193297</td>\n",
       "      <td>8.060258</td>\n",
       "      <td>58.607387</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.187256</td>\n",
       "      <td>226.202637</td>\n",
       "      <td>2.777175</td>\n",
       "      <td>1.201155</td>\n",
       "      <td>7.204747</td>\n",
       "      <td>58.398291</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.144754</td>\n",
       "      <td>218.104981</td>\n",
       "      <td>2.570526</td>\n",
       "      <td>1.155476</td>\n",
       "      <td>9.590258</td>\n",
       "      <td>60.267387</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    ikss_ka     skss_mw     ip_ka    ith_ka     rk_ohm      xk_ohm\n",
       "0  0.568039  216.451899  1.285305  0.573572  40.720778  242.572728\n",
       "1  1.180874  224.986699  2.710856  1.193297   8.060258   58.607387\n",
       "2  1.187256  226.202637  2.777175  1.201155   7.204747   58.398291\n",
       "3  1.144754  218.104981  2.570526  1.155476   9.590258   60.267387"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sc.calc_sc(net, case=\"max\", ith=True, ip=True)\n",
    "net.res_bus_sc"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Once again, the short-circuit current increases due to the contribution of the generator. As can be seen in the warning, the values for peak and thermal equivalent short-circuit current will only be accurate for faults far from generators."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Meshed Networks\n",
    "\n",
    "The correction factors for aperiodic and thermal currents differ between meshed and radial networks. pandapower includes a meshing detection that automatically detects the meshing for each short-circuit location. Alternatively, the topology can be set to \"radial\" or \"meshed\" to circumvent the check and save calculation time.\n",
    "\n",
    "We load the radial network and close the open sectioning point to get a closed ring network:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th></th>\n",
       "      <th>ikss_ka</th>\n",
       "      <th>skss_mw</th>\n",
       "      <th>ip_ka</th>\n",
       "      <th>ith_ka</th>\n",
       "      <th>rk_ohm</th>\n",
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       "      <td>0.263723</td>\n",
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       "      <td>502.510189</td>\n",
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       "      <td>90.776637</td>\n",
       "      <td>0.942589</td>\n",
       "      <td>0.479039</td>\n",
       "      <td>44.276323</td>\n",
       "      <td>139.778739</td>\n",
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       "      <th>2</th>\n",
       "      <td>0.470593</td>\n",
       "      <td>89.660073</td>\n",
       "      <td>0.926244</td>\n",
       "      <td>0.473098</td>\n",
       "      <td>45.640917</td>\n",
       "      <td>141.259279</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.471649</td>\n",
       "      <td>89.861256</td>\n",
       "      <td>0.929174</td>\n",
       "      <td>0.474168</td>\n",
       "      <td>45.392809</td>\n",
       "      <td>140.990090</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    ikss_ka     skss_mw     ip_ka    ith_ka      rk_ohm      xk_ohm\n",
       "0  0.262432  100.000000  0.505834  0.263723  175.878566  502.510189\n",
       "1  0.476454   90.776637  0.942589  0.479039   44.276323  139.778739\n",
       "2  0.470593   89.660073  0.926244  0.473098   45.640917  141.259279\n",
       "3  0.471649   89.861256  0.929174  0.474168   45.392809  140.990090"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "net = ring_network()\n",
    "net.switch.closed = True\n",
    "sc.calc_sc(net, topology=\"auto\", ip=True, ith=True)\n",
    "net.res_bus_sc"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "the network is automatically detected to be meshed and application factors are applied. This can be validated by setting the topology to radial and comparing the results:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th></th>\n",
       "      <th>ikss_ka</th>\n",
       "      <th>skss_mw</th>\n",
       "      <th>ip_ka</th>\n",
       "      <th>ith_ka</th>\n",
       "      <th>rk_ohm</th>\n",
       "      <th>xk_ohm</th>\n",
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       "      <th>0</th>\n",
       "      <td>0.262432</td>\n",
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       "      <td>0.263723</td>\n",
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       "      <td>0.476454</td>\n",
       "      <td>90.776637</td>\n",
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       "      <th>2</th>\n",
       "      <td>0.470593</td>\n",
       "      <td>89.660073</td>\n",
       "      <td>0.926244</td>\n",
       "      <td>0.473098</td>\n",
       "      <td>45.640917</td>\n",
       "      <td>141.259279</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.471649</td>\n",
       "      <td>89.861256</td>\n",
       "      <td>0.929174</td>\n",
       "      <td>0.474168</td>\n",
       "      <td>45.392809</td>\n",
       "      <td>140.990090</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    ikss_ka     skss_mw     ip_ka    ith_ka      rk_ohm      xk_ohm\n",
       "0  0.262432  100.000000  0.505834  0.263723  175.878566  502.510189\n",
       "1  0.476454   90.776637  0.942589  0.479039   44.276323  139.778739\n",
       "2  0.470593   89.660073  0.926244  0.473098   45.640917  141.259279\n",
       "3  0.471649   89.861256  0.929174  0.474168   45.392809  140.990090"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sc.calc_sc(net, topology=\"radial\", ip=True, ith=True)\n",
    "net.res_bus_sc"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we look at the line results, we can see that the line currents are significantly smaller than the bus currents:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "hp.pandapower.shortcircuit.calc_sc - WARNING: Branch results are in beta mode and might not always be reliable, especially for transformers\n"
     ]
    },
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       "      <th>0</th>\n",
       "      <td>0.279812</td>\n",
       "      <td>0.550740</td>\n",
       "      <td>0.281301</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.190781</td>\n",
       "      <td>0.375504</td>\n",
       "      <td>0.191796</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.344176</td>\n",
       "      <td>0.678046</td>\n",
       "      <td>0.346014</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    ikss_ka     ip_ka    ith_ka\n",
       "0  0.279812  0.550740  0.281301\n",
       "1  0.190781  0.375504  0.191796\n",
       "2  0.344176  0.678046  0.346014"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sc.calc_sc(net, topology=\"auto\", ip=True, ith=True, branch_results=True)\n",
    "net.res_line_sc"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "this is because the short-circuit current is split up on both paths of the ring, which is correctly considered by pandapower."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fault Impedance\n",
    "\n",
    "It is also possible to specify a fault impedance in the short-circuit calculation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\mmilovic\\Documents\\Python Scripts\\pandapower\\pandapower\\shortcircuit\\kappa.py:25: RuntimeWarning: invalid value encountered in true_divide\n",
      "  kappa = _kappa(ppc[\"bus\"][:, R_EQUIV] / ppc[\"bus\"][:, X_EQUIV])\n",
      "C:\\Users\\mmilovic\\Documents\\Python Scripts\\pandapower\\pandapower\\shortcircuit\\currents.py:123: RuntimeWarning: invalid value encountered in log\n",
      "  m = (np.exp(4 * f * tk_s * np.log(kappa - 1)) - 1) / (2 * f * tk_s * np.log(kappa - 1))\n"
     ]
    }
   ],
   "source": [
    "net = ring_network()\n",
    "sc.calc_sc(net, topology=\"radial\", ip=True, ith=True, r_fault_ohm=1., x_fault_ohm=2.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "which of course decreases the short-circuit currents:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>ikss_ka</th>\n",
       "      <th>skss_mw</th>\n",
       "      <th>ip_ka</th>\n",
       "      <th>ith_ka</th>\n",
       "      <th>rk_ohm</th>\n",
       "      <th>xk_ohm</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.261343</td>\n",
       "      <td>99.585098</td>\n",
       "      <td>0.503509</td>\n",
       "      <td>0.262627</td>\n",
       "      <td>176.878566</td>\n",
       "      <td>504.510189</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.469382</td>\n",
       "      <td>89.429305</td>\n",
       "      <td>0.926656</td>\n",
       "      <td>0.471909</td>\n",
       "      <td>45.276323</td>\n",
       "      <td>141.778739</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.459875</td>\n",
       "      <td>87.617950</td>\n",
       "      <td>0.900379</td>\n",
       "      <td>0.462274</td>\n",
       "      <td>47.571323</td>\n",
       "      <td>144.268739</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.463005</td>\n",
       "      <td>88.214388</td>\n",
       "      <td>0.908972</td>\n",
       "      <td>0.465446</td>\n",
       "      <td>46.806323</td>\n",
       "      <td>143.438739</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      "text/plain": [
       "    ikss_ka    skss_mw     ip_ka    ith_ka      rk_ohm      xk_ohm\n",
       "0  0.261343  99.585098  0.503509  0.262627  176.878566  504.510189\n",
       "1  0.469382  89.429305  0.926656  0.471909   45.276323  141.778739\n",
       "2  0.459875  87.617950  0.900379  0.462274   47.571323  144.268739\n",
       "3  0.463005  88.214388  0.908972  0.465446   46.806323  143.438739"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "net.res_bus_sc"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Asymetrical Two-Phase Short-Circuit Calculation\n",
    "\n",
    "All calculations above can be carried out for a two-phase short-circuit current in the same way by specifying \"2ph\" in the fault parameter:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\mmilovic\\Documents\\Python Scripts\\pandapower\\pandapower\\shortcircuit\\currents.py:123: RuntimeWarning: invalid value encountered in log\n",
      "  m = (np.exp(4 * f * tk_s * np.log(kappa - 1)) - 1) / (2 * f * tk_s * np.log(kappa - 1))\n"
     ]
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       "      <th></th>\n",
       "      <th>ikss_ka</th>\n",
       "      <th>skss_mw</th>\n",
       "      <th>ip_ka</th>\n",
       "      <th>ith_ka</th>\n",
       "      <th>rk_ohm</th>\n",
       "      <th>xk_ohm</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.227273</td>\n",
       "      <td>28.867513</td>\n",
       "      <td>0.438065</td>\n",
       "      <td>0.228391</td>\n",
       "      <td>175.878566</td>\n",
       "      <td>502.510189</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.412621</td>\n",
       "      <td>26.204958</td>\n",
       "      <td>0.816306</td>\n",
       "      <td>0.414860</td>\n",
       "      <td>44.276323</td>\n",
       "      <td>139.778739</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.404149</td>\n",
       "      <td>25.666902</td>\n",
       "      <td>0.792775</td>\n",
       "      <td>0.406272</td>\n",
       "      <td>46.571323</td>\n",
       "      <td>142.268739</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.406938</td>\n",
       "      <td>25.844045</td>\n",
       "      <td>0.800468</td>\n",
       "      <td>0.409099</td>\n",
       "      <td>45.806323</td>\n",
       "      <td>141.438739</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      ],
      "text/plain": [
       "    ikss_ka    skss_mw     ip_ka    ith_ka      rk_ohm      xk_ohm\n",
       "0  0.227273  28.867513  0.438065  0.228391  175.878566  502.510189\n",
       "1  0.412621  26.204958  0.816306  0.414860   44.276323  139.778739\n",
       "2  0.404149  25.666902  0.792775  0.406272   46.571323  142.268739\n",
       "3  0.406938  25.844045  0.800468  0.409099   45.806323  141.438739"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "net = ring_network()\n",
    "sc.calc_sc(net, fault=\"2ph\", ip=True, ith=True)\n",
    "net.res_bus_sc"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Two phase short-circuits are often used for minimum short-circuit calculations:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\mmilovic\\Documents\\Python Scripts\\pandapower\\pandapower\\shortcircuit\\currents.py:123: RuntimeWarning: invalid value encountered in log\n",
      "  m = (np.exp(4 * f * tk_s * np.log(kappa - 1)) - 1) / (2 * f * tk_s * np.log(kappa - 1))\n"
     ]
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       "      <th>0</th>\n",
       "      <td>0.181818</td>\n",
       "      <td>23.094011</td>\n",
       "      <td>0.400566</td>\n",
       "      <td>0.183369</td>\n",
       "      <td>118.650262</td>\n",
       "      <td>593.251309</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.332920</td>\n",
       "      <td>21.143233</td>\n",
       "      <td>0.745538</td>\n",
       "      <td>0.335995</td>\n",
       "      <td>29.969247</td>\n",
       "      <td>162.464019</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.326772</td>\n",
       "      <td>20.752827</td>\n",
       "      <td>0.717815</td>\n",
       "      <td>0.329521</td>\n",
       "      <td>33.457647</td>\n",
       "      <td>164.954019</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.328807</td>\n",
       "      <td>20.882073</td>\n",
       "      <td>0.726834</td>\n",
       "      <td>0.331657</td>\n",
       "      <td>32.294847</td>\n",
       "      <td>164.124019</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    ikss_ka    skss_mw     ip_ka    ith_ka      rk_ohm      xk_ohm\n",
       "0  0.181818  23.094011  0.400566  0.183369  118.650262  593.251309\n",
       "1  0.332920  21.143233  0.745538  0.335995   29.969247  162.464019\n",
       "2  0.326772  20.752827  0.717815  0.329521   33.457647  164.954019\n",
       "3  0.328807  20.882073  0.726834  0.331657   32.294847  164.124019"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "net = ring_network()\n",
    "net.line[\"endtemp_degree\"] = 150\n",
    "sc.calc_sc(net, fault=\"2ph\", case=\"min\", ip=True, ith=True)\n",
    "net.res_bus_sc"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Single Phase Short-Circuit Calculation\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "pandapower can also calculate single phase short-circuits. The ground fault however depends on the zero-sequence parameters of the network, which have to be added in order to calculate a single line to ground fault:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "net = ring_network()\n",
    "\n",
    "#r/x ratio in zero sequence parameters\n",
    "net.ext_grid[\"r0x0_max\"] = 0.4\n",
    "net.ext_grid[\"x0x_max\"] = 1.0\n",
    "\n",
    "#zero sequence line parameters\n",
    "net.line[\"r0_ohm_per_km\"] = 0.244\n",
    "net.line[\"x0_ohm_per_km\"] = 0.336\n",
    "net.line[\"c0_nf_per_km\"] = 2000\n",
    "\n",
    "#transformer vector group, zero sequence short circuit voltage\n",
    "#and zero sequence magnetizing impedance\n",
    "net.trafo[\"vector_group\"] = \"Dyn\"\n",
    "net.trafo[\"vk0_percent\"] = 5.\n",
    "net.trafo[\"vkr0_percent\"] = 0.4\n",
    "net.trafo[\"mag0_percent\"] = 10\n",
    "net.trafo[\"mag0_rx\"] = 0.4\n",
    "net.trafo[\"si0_hv_partial\"] = 0.9"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "sc.calc_sc(net, fault=\"1ph\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
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       "      <th></th>\n",
       "      <th>ikss_ka</th>\n",
       "      <th>rk0_ohm</th>\n",
       "      <th>xk0_ohm</th>\n",
       "      <th>rk_ohm</th>\n",
       "      <th>xk_ohm</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.261047</td>\n",
       "      <td>201.004076</td>\n",
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       "      <td>175.878566</td>\n",
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       "      <th>1</th>\n",
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       "      <td>6.835257</td>\n",
       "      <td>44.276323</td>\n",
       "      <td>139.778739</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.668867</td>\n",
       "      <td>5.656564</td>\n",
       "      <td>12.811454</td>\n",
       "      <td>46.571323</td>\n",
       "      <td>142.268739</td>\n",
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       "      <th>3</th>\n",
       "      <td>0.680010</td>\n",
       "      <td>3.287676</td>\n",
       "      <td>10.346508</td>\n",
       "      <td>45.806323</td>\n",
       "      <td>141.438739</td>\n",
       "    </tr>\n",
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       "    ikss_ka     rk0_ohm     xk0_ohm      rk_ohm      xk_ohm\n",
       "0  0.261047  201.004076  502.510189  175.878566  502.510189\n",
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       "3  0.680010    3.287676   10.346508   45.806323  141.438739"
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     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "net.res_bus_sc"
   ]
  }
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