## Abbreviations  
The following abbreviations are used in this manuscript:  
_Abbreviations_  
AC  Alternating current  
API  Application Programming Interface  
EU  European Union  
ED  Economic dispatch  
CBE  Cross Border Export  
CBI  Cross Border Import  
CBP  Cross Border Point  
CEI  Critical Energy Infrastructures  
CGS  City Gate Station  
DC  Direct current  
DTA  Dynamic Time Step Adaptation  
GB  Great Britain  
GFPP  Gas Fired Power Plant  
GNS  Gas not supplied  
GUI  Graphical User Interface  
IND  Large Industrial Customer  
KCL  Kirchoff's Current Law  
LNG  Liquefied Natural Gas  
NGTS  National Gas Transport System  
P2G  Power to Gas  
PF  Power Flow  
PDE  Partial Differential  
PNS  Power not supplied  
PRO  Production Fields  
OPF  Optimal Power Flow  
SAInt  Scenario Analysis Interface  
SCUC  Security Constraint Unit commitment  
SNG  Synthetic Natural Gas  
TSO  Transmission System Operator  
UC  Unit commitment  
UGS  Underground Gas Storage  
_Mathematical Symbols_  
\(A\)  cross-sectional area  
\(a\)  transformer tap ratio  
\(a\)  elements of the node-branch incidence matrix  
\(b\)  line charging susceptance  
\(c\)0, \(c\)1, \(c\)2  coefficients of cost function  
\(c\)  speed of sound  
_CV_  control volume  
\(D\)  inner pipe diameter  
\(e\)  Euler's number  
\(E\)  set of branches  
\(f\)  electric driver factor  
\(g\)  gravitational acceleration  
\(G\)  directed graph  
_GCV_  gross calorific value  
\(I\)  electric current injection at from bus  
\(h\)  electric current injection at to bus  
\(j\)  imaginary number  
\(k\)0, \(k\)1  coefficients of coupling equation  
\(L\)  nodal load  
_LGFPP_  fuel gas offtake for power generation at GFPPs  
\(l\)  pipe length  
_LP_  line pack  
\(M\)  number of pipe section  
\(n\)  simulation time point  
_N_n_  number of gas nodes  
_N_b_  number of buses, number of branches  
_NCS_  number of compressor stations  
_Ng_  number of power generation units \begin{tabular}{l l} \(N_{GFP}\) & number of GFPPs \\ \(N_{iq}\) & number of inequality constraints \\ \(N_{l}\) & number of transmission lines and transformers \\ \(P_{D}\) & active power demand \\ \(P_{D^{\prime}}^{CS}\) & power demand of compressor stations \\ \(P_{D^{\prime}}^{tw}\) & power demand of LNG terminals and UGS facilities \\ \(P_{G}\) & active power generation \\ \(\mathbf{P_{G}}\) & vector of active power generation \\ \(p\) & gas pressure (vector) \\ \(p_{1}\) & inlet pressure \\ \(p_{2}\) & outlet pressure \\ \(p_{m}\) & mean pipe pressure \\ \(Q\) & gas flow rate, reactive power \\ \(\mathbf{Q_{G}}\) & vector of reactive power generation \\ \(R\) & gas constant, line resistance \\ \(S^{f}_{hax}\) & apparent power injection at from bus of branch \(k\) \\ \(S^{max}_{k}\) & maximum transmission capacity of branch \(k\) \\ \(S^{f}_{k}\) & apparent power injection at to bus of branch \(k\) \\ \(\mathbf{S^{\prime}}\) & vector of apparent power flow \\ \(t\) & time, complex transformer tap \\ \(t_{n}\) & time point \\ \(\Delta t\) & time step \\ \(T\) & temperature \\ \(T_{n}\) & reference temperature \\ \(v\) & gas velocity \\ \(V\) & complex bus voltage, set of nodes \\ \(\mathbf{V}\) & vector of complex bus voltage \\ \(\mathbf{V_{m}}\) & vector of complex bus voltage magnitudes \\ \(|V|\) & bus voltage magnitude \\ \(V_{i}\) & nodal volume \\ \(X\) & line reactance \\ \(x\) & pipeline coordinate \\ \(\mathbf{X}\) & vector of decision variables \\ \(\Delta x\) & pipe segment length \\ \(Y\) & line admittance \\ \(\mathbf{Y_{br}}\) & branch admittance matrix \\ \(\mathbf{Y_{bus}}\) & bus admittance matrix \\ \(Z\) & compressibility factor, impedance \\ \end{tabular}   
_Greek Symbols_