diff --git a/Power Grid Model Benchmark.ipynb b/Power Grid Model Benchmark.ipynb
index 040997d..53a0d9f 100644
--- a/Power Grid Model Benchmark.ipynb	
+++ b/Power Grid Model Benchmark.ipynb	
@@ -36,8 +36,8 @@
     "\n",
     "The notebook runs a power flow calculation with the same input data in `power-grid-model` and `pandapower`. It runs the following calculations:\n",
     "\n",
-    "* Single calculation with solver initialization.\n",
-    "* Single calculation without solver initialization (using pre-cached internal matrices).\n",
+    "* Single calculation.\n",
+    "* Pre-initialized single calculation (using pre-cached internal matrices).\n",
     "* Time-series calculation\n",
     "* N-1 calculation\n",
     "\n",
@@ -112,10 +112,10 @@
     "    np.zeros(shape=(8, 5), dtype=np.float64),\n",
     "    columns=['PGM Linear Impedance', 'PGM Linear Current' ,'PGM Newton-Raphson', 'PGM Iterative Current', 'PandaPower Newton-Raphson'],\n",
     "    index=[\n",
-    "        'Symmetric calculation with solver initialization',\n",
-    "        'Symmetric calculation without solver initialization',\n",
-    "        'Asymmetric calculation with solver initialization',\n",
-    "        'Asymmetric calculation without solver initialization',\n",
+    "        'Symmetric calculation',\n",
+    "        'Pre-initialized Symmetric calculation',\n",
+    "        'Asymmetric calculation',\n",
+    "        'Pre-initialized Asymmetric calculation',\n",
     "        'Time series symmetric calculation',\n",
     "        'Time series asymmetric calculation',\n",
     "        'N-1 symmetric calculation',\n",
@@ -310,8 +310,8 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "benchmark_pgm_power_flow(symmetric=True, calculation_type='Symmetric calculation with solver initialization', with_intialization=True)\n",
-    "pgm_result = benchmark_pgm_power_flow(symmetric=True, calculation_type='Symmetric calculation without solver initialization', with_intialization=False)\n"
+    "benchmark_pgm_power_flow(symmetric=True, calculation_type='Symmetric calculation', with_intialization=True)\n",
+    "pgm_result = benchmark_pgm_power_flow(symmetric=True, calculation_type='Pre-initialized Symmetric calculation', with_intialization=False)\n"
    ]
   },
   {
@@ -333,13 +333,13 @@
     "start = time.time()\n",
     "pp.runpp(pp_net, algorithm='nr', calculate_voltage_angles=True, distributed_slack=True, lightsim2grid=use_lightsim2grid)\n",
     "end = time.time()\n",
-    "summary_df.loc['Symmetric calculation with solver initialization', 'PandaPower Newton-Raphson'] = end - start\n",
+    "summary_df.loc['Symmetric calculation', 'PandaPower Newton-Raphson'] = end - start\n",
     "\n",
-    "# second calculation with existing solver\n",
+    "# second calculation with pre-initialized solver\n",
     "start = time.time()\n",
     "pp.runpp(pp_net, algorithm='nr', calculate_voltage_angles=True, distributed_slack=True, lightsim2grid=use_lightsim2grid)\n",
     "end = time.time()\n",
-    "summary_df.loc['Symmetric calculation without solver initialization', 'PandaPower Newton-Raphson'] = end - start"
+    "summary_df.loc['Pre-initialized Symmetric calculation', 'PandaPower Newton-Raphson'] = end - start"
    ]
   },
   {
@@ -386,8 +386,8 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "benchmark_pgm_power_flow(symmetric=False, calculation_type='Asymmetric calculation with solver initialization', with_intialization=True)\n",
-    "pgm_result = benchmark_pgm_power_flow(symmetric=False, calculation_type='Asymmetric calculation without solver initialization', with_intialization=False)"
+    "benchmark_pgm_power_flow(symmetric=False, calculation_type='Asymmetric calculation', with_intialization=True)\n",
+    "pgm_result = benchmark_pgm_power_flow(symmetric=False, calculation_type='Pre-initialized Asymmetric calculation', with_intialization=False)"
    ]
   },
   {
@@ -409,13 +409,13 @@
     "start = time.time()\n",
     "pp.runpp_3ph(pp_net, algorithm='nr', calculate_voltage_angles=True, distributed_slack=True, lightsim2grid=use_lightsim2grid)\n",
     "end = time.time()\n",
-    "summary_df.loc['Asymmetric calculation with solver initialization', 'PandaPower Newton-Raphson'] = end - start\n",
+    "summary_df.loc['Asymmetric calculation', 'PandaPower Newton-Raphson'] = end - start\n",
     "\n",
-    "# second calculation with existing solver\n",
+    "# second calculation with pre-initialized solver\n",
     "start = time.time()\n",
     "pp.runpp_3ph(pp_net, algorithm='nr', calculate_voltage_angles=True, distributed_slack=True, lightsim2grid=use_lightsim2grid)\n",
     "end = time.time()\n",
-    "summary_df.loc['Asymmetric calculation without solver initialization', 'PandaPower Newton-Raphson'] = end - start\n"
+    "summary_df.loc['Pre-initialized Asymmetric calculation', 'PandaPower Newton-Raphson'] = end - start\n"
    ]
   },
   {
@@ -1047,7 +1047,7 @@
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
-       "      <th>Symmetric calculation with solver initialization</th>\n",
+       "      <th>Symmetric calculation</th>\n",
        "      <td>0.000674</td>\n",
        "      <td>0.000581</td>\n",
        "      <td>0.001120</td>\n",
@@ -1055,7 +1055,7 @@
        "      <td>0.018997</td>\n",
        "    </tr>\n",
        "    <tr>\n",
-       "      <th>Symmetric calculation without solver initialization</th>\n",
+       "      <th>Pre-initialized Symmetric calculation</th>\n",
        "      <td>0.000271</td>\n",
        "      <td>0.000272</td>\n",
        "      <td>0.000758</td>\n",
@@ -1063,7 +1063,7 @@
        "      <td>0.015893</td>\n",
        "    </tr>\n",
        "    <tr>\n",
-       "      <th>Asymmetric calculation with solver initialization</th>\n",
+       "      <th>Asymmetric calculation</th>\n",
        "      <td>0.001913</td>\n",
        "      <td>0.001567</td>\n",
        "      <td>0.003933</td>\n",
@@ -1071,7 +1071,7 @@
        "      <td>0.888648</td>\n",
        "    </tr>\n",
        "    <tr>\n",
-       "      <th>Asymmetric calculation without solver initialization</th>\n",
+       "      <th>Pre-initialized Asymmetric calculation</th>\n",
        "      <td>0.000906</td>\n",
        "      <td>0.000655</td>\n",
        "      <td>0.003089</td>\n",
@@ -1116,50 +1116,50 @@
       ],
       "text/plain": [
        "                                                    PGM Linear Impedance  \\\n",
-       "Symmetric calculation with solver initialization                0.000674   \n",
-       "Symmetric calculation without solver initializa...              0.000271   \n",
-       "Asymmetric calculation with solver initialization               0.001913   \n",
-       "Asymmetric calculation without solver initializ...              0.000906   \n",
+       "Symmetric calculation                                           0.000674   \n",
+       "Pre-initialized Symmetric calculation                          0.000271   \n",
+       "Asymmetric calculation                                          0.001913   \n",
+       "Pre-initialized Asymmetric calculation                         0.000906   \n",
        "Time series symmetric calculation                               0.263931   \n",
        "Time series asymmetric calculation                              0.947188   \n",
        "N-1 symmetric calculation                                       0.481238   \n",
        "N-1 asymmetric calculation                                      1.363434   \n",
        "\n",
        "                                                    PGM Linear Current  \\\n",
-       "Symmetric calculation with solver initialization              0.000581   \n",
-       "Symmetric calculation without solver initializa...            0.000272   \n",
-       "Asymmetric calculation with solver initialization             0.001567   \n",
-       "Asymmetric calculation without solver initializ...            0.000655   \n",
+       "Symmetric calculation                                         0.000581   \n",
+       "Pre-initialized Symmetric calculation                        0.000272   \n",
+       "Asymmetric calculation                                        0.001567   \n",
+       "Pre-initialized Asymmetric calculation                       0.000655   \n",
        "Time series symmetric calculation                             0.267153   \n",
        "Time series asymmetric calculation                            0.472705   \n",
        "N-1 symmetric calculation                                     0.511463   \n",
        "N-1 asymmetric calculation                                    1.264282   \n",
        "\n",
        "                                                    PGM Newton-Raphson  \\\n",
-       "Symmetric calculation with solver initialization              0.001120   \n",
-       "Symmetric calculation without solver initializa...            0.000758   \n",
-       "Asymmetric calculation with solver initialization             0.003933   \n",
-       "Asymmetric calculation without solver initializ...            0.003089   \n",
+       "Symmetric calculation                                         0.001120   \n",
+       "Pre-initialized Symmetric calculation                        0.000758   \n",
+       "Asymmetric calculation                                        0.003933   \n",
+       "Pre-initialized Asymmetric calculation                       0.003089   \n",
        "Time series symmetric calculation                             0.709902   \n",
        "Time series asymmetric calculation                            3.288390   \n",
        "N-1 symmetric calculation                                     1.022064   \n",
        "N-1 asymmetric calculation                                    3.805486   \n",
        "\n",
        "                                                    PGM Iterative Current  \\\n",
-       "Symmetric calculation with solver initialization                 0.000714   \n",
-       "Symmetric calculation without solver initializa...               0.000432   \n",
-       "Asymmetric calculation with solver initialization                0.001666   \n",
-       "Asymmetric calculation without solver initializ...               0.000886   \n",
+       "Symmetric calculation                                            0.000714   \n",
+       "Pre-initialized Symmetric calculation                           0.000432   \n",
+       "Asymmetric calculation                                           0.001666   \n",
+       "Pre-initialized Asymmetric calculation                          0.000886   \n",
        "Time series symmetric calculation                                0.401892   \n",
        "Time series asymmetric calculation                               0.929971   \n",
        "N-1 symmetric calculation                                        0.603250   \n",
        "N-1 asymmetric calculation                                       1.701366   \n",
        "\n",
        "                                                    PandaPower Newton-Raphson  \n",
-       "Symmetric calculation with solver initialization                     0.018997  \n",
-       "Symmetric calculation without solver initializa...                   0.015893  \n",
-       "Asymmetric calculation with solver initialization                    0.888648  \n",
-       "Asymmetric calculation without solver initializ...                   0.180443  \n",
+       "Symmetric calculation                                                0.018997  \n",
+       "Pre-initialized Symmetric calculation                               0.015893  \n",
+       "Asymmetric calculation                                               0.888648  \n",
+       "Pre-initialized Asymmetric calculation                              0.180443  \n",
        "Time series symmetric calculation                                   18.355417  \n",
        "Time series asymmetric calculation                                 229.896856  \n",
        "N-1 symmetric calculation                                           15.211173  \n",
@@ -1198,7 +1198,7 @@
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
-       "      <th id=\"T_12be5_level0_row0\" class=\"row_heading level0 row0\" >Symmetric calculation with solver initialization</th>\n",
+       "      <th id=\"T_12be5_level0_row0\" class=\"row_heading level0 row0\" >Symmetric calculation</th>\n",
        "      <td id=\"T_12be5_row0_col0\" class=\"data row0 col0\" >28.17x</td>\n",
        "      <td id=\"T_12be5_row0_col1\" class=\"data row0 col1\" >32.70x</td>\n",
        "      <td id=\"T_12be5_row0_col2\" class=\"data row0 col2\" >16.97x</td>\n",
@@ -1206,7 +1206,7 @@
        "      <td id=\"T_12be5_row0_col4\" class=\"data row0 col4\" >1.00x</td>\n",
        "    </tr>\n",
        "    <tr>\n",
-       "      <th id=\"T_12be5_level0_row1\" class=\"row_heading level0 row1\" >Symmetric calculation without solver initialization</th>\n",
+       "      <th id=\"T_12be5_level0_row1\" class=\"row_heading level0 row1\" >Pre-initialized Symmetric calculation</th>\n",
        "      <td id=\"T_12be5_row1_col0\" class=\"data row1 col0\" >58.73x</td>\n",
        "      <td id=\"T_12be5_row1_col1\" class=\"data row1 col1\" >58.47x</td>\n",
        "      <td id=\"T_12be5_row1_col2\" class=\"data row1 col2\" >20.97x</td>\n",
@@ -1214,7 +1214,7 @@
        "      <td id=\"T_12be5_row1_col4\" class=\"data row1 col4\" >1.00x</td>\n",
        "    </tr>\n",
        "    <tr>\n",
-       "      <th id=\"T_12be5_level0_row2\" class=\"row_heading level0 row2\" >Asymmetric calculation with solver initialization</th>\n",
+       "      <th id=\"T_12be5_level0_row2\" class=\"row_heading level0 row2\" >Asymmetric calculation</th>\n",
        "      <td id=\"T_12be5_row2_col0\" class=\"data row2 col0\" >464.63x</td>\n",
        "      <td id=\"T_12be5_row2_col1\" class=\"data row2 col1\" >567.06x</td>\n",
        "      <td id=\"T_12be5_row2_col2\" class=\"data row2 col2\" >225.96x</td>\n",
@@ -1222,7 +1222,7 @@
        "      <td id=\"T_12be5_row2_col4\" class=\"data row2 col4\" >1.00x</td>\n",
        "    </tr>\n",
        "    <tr>\n",
-       "      <th id=\"T_12be5_level0_row3\" class=\"row_heading level0 row3\" >Asymmetric calculation without solver initialization</th>\n",
+       "      <th id=\"T_12be5_level0_row3\" class=\"row_heading level0 row3\" >Pre-initialized Asymmetric calculation</th>\n",
        "      <td id=\"T_12be5_row3_col0\" class=\"data row3 col0\" >199.11x</td>\n",
        "      <td id=\"T_12be5_row3_col1\" class=\"data row3 col1\" >275.61x</td>\n",
        "      <td id=\"T_12be5_row3_col2\" class=\"data row3 col2\" >58.42x</td>\n",
@@ -1305,4 +1305,4 @@
  },
  "nbformat": 4,
  "nbformat_minor": 5
-}
+}
\ No newline at end of file