## Abbreviations
\begin{tabular}{l l} \(\mathbf{T_{\rm C}}\) & Node-extraction incidence matrix \\ \(R_{\rm C}^{0}\) & Specified squared boost ratio \\ \(D_{\rm C}^{0}\) & Specified squared boost difference \\ \(\Pi_{0}^{\rm I}\) & Specified squared inlet pressure \\ \(\Pi_{\rm O}^{\rm II}\) & Specified squared outlet pressure \\ \(f_{\rm C}^{0}\) & Specified compressor flow rate \\ \(w_{\rm N,k_{\rm J}}/w_{\rm N,k_{\rm J}}\) & Control parameter of slack source node pressure/compressor inlet node pressure \\ \(w_{\rm N,k_{\rm J}}/w_{\rm E,k}/d_{k}\) & Control parameter of compressor outlet node pressure/equipment flow/compressor \\ \(\Pi_{\rm s}/\Pi_{\rm i}/\Pi_{\rm o}\) & Squared pressure of slack source node/compressor inlet node/compressor outlet node \\ \(f_{\rm E,k}\) & Gas flow of the equipment \\ \(G^{\rm equ}\) & Equipment set of DGN \\ \(\mathbf{W_{\rm N}}/\mathbf{W_{\rm E}}/\mathbf{d}\) & Control parameter matrix \\ \(G_{\rm c}^{\rm trap,j}/G^{\rm type}\) & Set of compressors extracting from node \(i\)/gas source types \\ \(G_{\rm c}^{\rm trap,j}/G_{\rm c}^{\rm out,j}\) & Set of compressors entering/leaving node \(i\) \\ \(G_{\rm c}^{\rm trap,j}/G_{\rm P}^{\rm out,j}\) & Set of pipelines entering/leaving node \(i\) \\ \(G^{\rm node}\) & Set of DGN nodes \\ \(f_{\rm C}^{\rm in}/f_{\rm C}^{\rm out}\) & Compressor flow entering/leaving node \(i\) \\ \(f_{\rm P}^{\rm in}/f_{\rm P}^{\rm out}\) & Pipeline flow entering/leaving node \(i\) \\ \(\rho^{\rm in}/\rho^{\rm out}\) & Specific gravity of gas entering/leaving node \(i\) \\ \(q^{\rm in}/q^{\rm out}\) & GCV of gas entering/leaving node \(i\) \\ \(\rho_{\rm S}/q_{\rm S}\) & Specific gravity/GCV of injected gas \\ \(\rho^{\rm c}/q^{\rm c}\) & Gas specific gravity/GCV of type \(\ell\) \\ \(f_{\rm S}\) & Known pressure source flow \\ \(f_{\rm I}^{\rm f}\) & Known injection source flow of type \(\ell\) \\ \(\rho_{\rm S}/q_{\rm S}\) & Specific gravity/GCV vector of injected gas at \(\pi\) nodes \\ \(\mathbf{B}_{\rm g}^{\rm f}\) & Node-non-slack source type incidence matrix of DGN \\ \(f_{\rm I}^{\rm f}\) & Non-slack source flow vector of type \(\ell\) \\ \(\epsilon^{\rm c}\) & Nodal molar fraction vector of gas type \(\ell\) \\ \(\epsilon^{\rm c}_{\rm S}\) & Molar fraction vector of gas type \(\ell\) at known-pressure sources \\ \(\mathbf{\pi}\) & Average pressure vector of gas pipelines \\ \(\mathbf{T_{\rm cr}}/\mathbf{P_{\rm cr}}\) & Critical temperature/pressure vector of the mixture \\ \(\mathbf{v}\) & Specific property vector of the mixture \\ \(v^{\ell}\) & Specific property of gas type \(\ell\) \\ \(\mathbf{\omega_{\rm cp}}/\mathbf{\omega_{\rm cv}}\) & Specific heat capacity vector at constant pressure/volume \\ \(f_{\rm I}/f_{\rm C}/f_{\rm P}/f_{\rm D}\) & Known injection source/compressor/gas pipeline/gas load flow \\ \(\Delta f_{\rm L}\) & Nodal deviation flow \\ \(S_{\rm g}^{\rm C}/S_{\rm g}^{\rm S}/S_{\rm g}^{\rm T}\) & Directional factor vector of compressor/known pressure source/consumption flow \\ \(\Delta\ f_{\rm L}^{\rm in}/f_{\rm D}^{\rm in}\) & Deviation/load flow entering node \(i\) \\ \(f_{\rm S}^{\rm in}/\tau_{\rm C}^{\rm out}\) & Known pressure source/compressor consumption flow entering node \(i\) \\ \(\Delta\ f_{\rm L}^{\rm out}/f_{\rm D}^{\rm out}\) & Deviation/load flow leaving node \(i\) \\ \(f_{\rm S}^{\rm out}/\tau_{\rm C}^{\rm out}\) & Known pressure source/compressor consumption flow leaving node \(i\) \\ \(\rho_{\rm sp}/q_{\rm sp}\) & Specified specific gravity/GCV of gas flow entering node \(i\) \\ \(\epsilon_{\rm sp}^{\rm c}\) & Specified molar fraction vector of gas type \(\ell\) for gas flow entering the node \\ \(z_{\rm CHPI}/z_{\rm CHPI}\) & Control parameter of CHPI/CHPI \\ \(\Phi_{x}/P_{x}/f_{x}/\eta_{x}\) & Heat power/electrical power/gas consumption/conversion efficiency of device \(x\) \\ \(q_{\rm gas}/q_{\rm SNG}\) & GCV of the consumed gas/SNG \\ \(f_{\rm P2C}/P_{\rm P2G}\) & Injected flow rate of SNG/consumed power of P2G \\ \(P_{\rm C}/P_{\rm CP}\) & Driving power of MC/CP \\ \(m_{\rm cp}\) & Mass flow through CP \\ \(g\) & Gravitational acceleration \\ \(h_{\rm cp}\) & Pump head \\ \(\mathbf{x_{\rm e}}/\mathbf{x_{\rm h}}/\mathbf{x_{\rm g}}\) & State variable vector of DEN/DHN/DGN \\ \(\mathbf{F_{\rm e}}/\mathbf{F_{\rm h}}/\mathbf{F_{\rm g}}\) & Mismatch vector of DEN/DHN/DGN \\ \end{tabular}