# Development of a Simulation Framework for Analyzing Security of Supply in Integrated Gas and Electric Power Systems

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## Abstract

**:**

## 1. Introduction

## 2. State of the Art

## 3. Security of Supply in Integrated Gas and Power Systems

## 4. Methodology

#### 4.1. Power System Model

#### 4.2. Gas System Model

#### 4.3. Interconnection between Gas and Power Systems

- Power supply to electric drivers installed in gas compressor stations:The electric power consumed by the compressor station can be described by the following expression (derived from the first and second law of thermodynamics for an isentropic compression process) describing the required driver power ${P}_{D,i}^{CS}$ for compressing the gas flow Q from inlet pressure ${p}_{1}$ to outlet pressure ${p}_{2}$ [56,57]:$$\begin{array}{c}\hfill {P}_{D,i}^{CS}=f{\displaystyle \frac{\kappa}{\kappa -1}}{\displaystyle \frac{{Z}_{1}{T}_{1}R{\rho}_{n}Q}{{\eta}_{ad}{\eta}_{m}}}\left(\right)open="["\; close="]">{{\displaystyle \frac{{p}_{2}}{{p}_{1}}}}^{{\displaystyle \frac{\kappa -1}{\kappa}}}-1,\phantom{\rule{3.33333pt}{0ex}}i=1\cdots {N}_{CS}\end{array}$$The power supply of the gas network is added to the active power demand in the electric model.
- Electric power supply to LNG terminals and UGS facilities:We capture this interaction by assuming a generic linear function in terms of the regasification or withdrawal rate ${L}_{rw}$, respectively:$${P}_{D,i}^{rw}={k}_{i,0}+{k}_{i,1}\xb7{L}_{rw,i}$$
- Fuel gas offtake from gas pipelines for power generation in GFPPs:The required fuel gas ${L}_{GFPP,i}$ for active power generation ${P}_{G,i}$ at plant i can be expressed in terms of the thermal efficiency ${\eta}_{T}$ of the GFPP and the gross calorific value $GCV$ of the fuel gas, as follows:$${L}_{GFPP,i}={\displaystyle \frac{{P}_{G,i}}{{\eta}_{T}\xb7GCV}},\phantom{\rule{1.em}{0ex}}i=1\cdots {N}_{GFPP}$$

#### 4.4. Integrated Simulation Framework for Security of Supply Analysis

- (i)
- a simulator (MATPOWER) for solving an AC-OPF for the power system,
- (ii)
- a transient hydraulic gas simulator (SAInt) for the gas system which includes sub-models of all relevant pipe and non-pipe facilities
- (iii)
- and an interface (SAInt) which handles the communication and data exchange between the two isolated simulators.

## 5. Model Application

^{3}/d) (Million standard cubic meter per day, where the reference pressure is 1.0135 (bar) and the reference temperature is 0 (°C)). The impact of this observation can be seen in Figure 8, Figure 9, Figure 10, Figure 11 and Figure 12. Figure 11 shows that the disruptions introduced in scenario 1 have the highest impact on the gas network, since the flow balance, which is the sum of inflow minus sum of outflow, is always negative; the system is not able to supply enough gas to balance the demand. In fact, the flow balance is quite negative throughout the time, peaking down to equivalent daily flows of $-32$ (Msm

^{3}/d). As a result, the quantity of gas stored in the pipeline (i.e., the line pack) reduces significantly as time passes. The flow balance can be viewed as the time derivative of the line pack, thus, if the flow balance is negative the line pack decreases and if positive the line pack increases. A zero flow balance corresponds to no change in line pack. Latter is the assumption made in steady state gas models, which cannot capture the changes in line pack, and therefore, the real behavior of the gas system appropriately. Moreover, Figure 11 shows a decrease in line pack from ca. 85 to 67 (Msm

^{3}/d) for scenario 1 (approx. 18 (Msm

^{3}/d) lost along the day in the pipelines). In contrast, in scenario 0 only approx. 1.5 (Msm

^{3}/d) of line pack is extracted.

^{3}/d) ) at CBE_1 station due to the pressure restriction.

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

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 |

${a}_{i,j}$ | 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 |

${I}_{f}$ | electric curent injection at from bus |

${I}_{t}$ | electric curent injection at to bus |

j | imaginary number |

${k}_{0},{k}_{1}$ | coefficients of coupling equation |

L | nodal load |

${L}_{GFPP}$ | 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 |

${N}_{CS}$ | number of compressor stations |

${N}_{g}$ | number of power generation units |

${N}_{GFPP}$ | number of GFPPs |

${N}_{iq}$ | number of inequality constraints |

${N}_{l}$ | number of transmission lines and transformers |

${P}_{D}$ | active power demand |

${P}_{D}^{CS}$ | power demand of compressor stations |

${P}_{D}^{rw}$ | power demand of LNG terminals and UGS facilities |

${P}_{G}$ | active power generation |

${\mathbf{P}}_{\mathbf{G}}$ | 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 |

${\mathbf{Q}}_{\mathbf{G}}$ | vector of reactive power generation |

R | gas constant, line resistance |

${S}_{k}^{f}$ | apparent power injection at from bus of branch k |

${S}_{k}^{max}$ | maximum transmission capacity of branch k |

${S}_{k}^{t}$ | apparent power injection at to bus of branch k |

$\mathbf{S}$ | 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 |

${\mathbf{V}}_{\mathbf{m}}$ | vector of complex bus voltage magnitudes |

$\left|V\right|$ | 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 |

${\mathbf{Y}}_{\mathbf{br}}$ | branch admittance matrix |

${\mathbf{Y}}_{\mathbf{bus}}$ | bus admittance matrix |

Z | compressibility factor, impedance |

Greek Symbols | |

α | inclination |

$\alpha ,\beta ,\gamma $ | coefficients of heat rate curve |

δ | voltage angle |

Δ | vector of bus voltage angles |

ϵ | residual tolerance |

${\eta}_{ad}$ | compressor adiabatic efficiency |

${\eta}_{m}$ | driver efficiency |

${\eta}_{T}$ | thermal efficiency |

κ | isentropic exponent |

λ | friction factor |

$\varphi $ | transformer phase shift angle |

ρ | gas density |

${\rho}_{n}$ | gas density at reference conditions |

Physical Units | |

(bar-g) | bar gauge (absolute pressure minus atmospheric pressure) |

(p.u.) | per unit |

(Msm^{3}) | millions of standard cubic meters (line pack, inventory) |

(Msm^{3}/d) | millions of standard cubic meters per day (gas flow rate) |

(sm^{3}) | standard cubic meters (line pack, inventory) |

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**Figure 1.**Generic branch model (π-circuit) for modeling transmission lines (${t}_{ft}=1$ & ${\varphi}_{ft}=0$), in-phase transformers (${\varphi}_{ft}=0$) and phase-shifting transformers (${\varphi}_{ft}\ne 0$). The transformer tap ratio is modeled only on the from-Bus side of the branch model.

**Figure 4.**Integrated gas and power network applied in the case study. Map shows a real network of an European region, which has been disguised due to confidentiality reasons. The network data and properties used for the case studies, however, are original input data for the actual network. The solid black lines (lines 1–3, 7–12, 14–18) represent interconnections between Gas Fired Power Plants (GFPPs) in the power grid (

**left**) and their fuel gas offtake points in the gas grid (

**right**), while the dashed black lines (4–6, 13) represent interconnections between electric buses in the power grid (

**left**) supplying electric power to connected facilities in the gas grid.

**Figure 6.**Timing of initial (

**black**) and cascading (

**orange**,

**red**) events for Scenario 1. Abbreviation PNS stands for power not supplied, while GNS stands for gas not supplied, value in brackets refers to the fraction of not supplied power/gas with respect to total power/gas loads.

**Figure 7.**Timing of initial (

**black**) and cascading (

**orange**,

**red**) events for Scenario 2. Abbreviation PNS stands for power not supplied, value in brackets refers to the fraction of not supplied power with respect to total loads.

**Figure 8.**Time evolution of gas supply and pressure at the cross border import (CBI) node for the computed scenarios.

**Figure 9.**Time evolution of gas supply and pressure at the production field for the computed scenarios.

**Figure 10.**Time evolution of regasification rate and pressure at the liquefied natural gas (LNG) terminal for the computed scenarios.

**Figure 11.**Time evolution of flow balance (sum of inflow minus sum of outflow) and line pack for the computed scenarios.

**Figure 12.**Time evolution of withdrawal rate and pressure at underground gas storage (UGS) facility for the computed scenarios.

**Figure 15.**Time evolution of bus voltage before load shedding (

**left**) and after (

**right**) for scenario 1. All four buses where load shedding was applied are shown in this figure.

**Figure 16.**Time evolution of bus voltages before load shedding (

**left**) and after (

**right**) for scenario 2. Load shedding was applied at 15 buses. Among these buses are the 4 buses from scenario 1, which are shown in this figure.

Element Types | Description |
---|---|

Passive Elements | |

pipe | models a section of a pipeline, basic properties are length, diameter, roughness and pipe efficiency |

resistor | models passive devices that cause a local pressure drop (e.g., meters, inlet piping, coolers, heaters, scrubbers etc.) |

Active Elements | |

compressor | models a compressor station with generic constraints, allows the specification of a control mode of the station (e.g., outlet pressure control, inlet pressure control, flow rate control etc.) |

regulator | models a pressure reduction and metering station located at the interface of two neighboring networks with different maximum operating pressures, allows the specification of a control mode of the station (e.g., outlet pressure control, inlet pressure control, flow rate control etc.) |

valve | models a valve station, which is is either opened or closed |

Node Type | Description | Facilities |
---|---|---|

demand | point, where gas is extracted from the network, connected facilities are typically flow or pressure controlled | CGS, CBE, GFPP, IND |

supply | point, where gas is injected into the network; connected facilities are typically flow or pressure controlled; for LNG regasification terminals the working gas inventory is monitored and the flow rate is reduced in case of low inventory | PRO, CBI, LNG |

storage | point, where gas is injected or extracted from the network and where the maximum supply/loads depend on the working gas inventory, which is monitored along the transient simulation; connected facilities are typically flow or pressure controlled | UGS |

junction | point, where a topological change or a change in pipe properties occurs (e.g., diameter, inclination); no specific control | - |

**Table 3.**Compressor station control (PRSET—Pressure Ratio Set Point) and constraints (PRMAX— Maximum Pressure Ratio, PWMAX—Maximum Available Driver Power, POMAX—Maximum Discharge Pressure, PIMIN—Minimum Suction Pressure).

Compressor Station | PRSET (-) | PRMAX (-) | PWMAX (MW) | POMAX (barg-g) | PIMIN (barg-g) |
---|---|---|---|---|---|

CS_1 | 1.05 | 1.6 | 10 | 54 | 34 |

CS_2 | 1.02 | 1.45 | 44 | 54 | 25 |

CS_3 | 1.01 | 1.6 | 60 | 54 | 25 |

CS_4 | 1.2 | 1.45 | 25 | 54 | 25 |

CS_5 | 1.2 | 1.45 | 80 | 54 | 25 |

CS_6 | 1.2 | 1.3 | 35 | 54 | 25 |

CS_7 | 1.2 | 1.45 | 50 | 54 | 25 |

CS_8 | 1.2 | 1.7 | 20 | 54 | 25 |

CS_9 | 1.2 | 1.7 | 20 | 54 | 25 |

CS_10 | 1.05 | 2 | 10 | 65 | 25 |

Gas Supply | ${\mathbf{k}}_{0}$ (MW) | ${\mathbf{k}}_{1}$$\left(\right)open="("\; close=")">\frac{\mathbf{MW}}{{\mathbf{sm}}^{\mathbf{3}}\mathbf{/}\mathbf{s}}$ | $\mathbf{PSET}$ (Barg) |
---|---|---|---|

CBI | - | - | 50 |

PRO | - | - | 52.6 |

UGS | 3.5 | 0.01 | 56 |

LNG | 5 | 0.03 | 50 |

**Table 5.**Input data for GFPPs connected to the gas and electric power system. Numbering of GFPPs corresponds to the numbering of the solid interconnection lines in Figure 4.

Name | ${\mathbf{c}}_{0}$ | ${\mathbf{c}}_{1}$ | ${\mathbf{c}}_{2}$ | ${\mathit{\eta}}_{\mathit{T}}$ | ${\mathbf{P}}_{\mathbf{G}}^{\mathbf{max}}$ | ${\mathbf{P}}_{\mathbf{G}}^{\mathbf{min}}$ | ${\mathbf{Q}}_{\mathbf{G}}^{\mathbf{max}}$ | ${\mathbf{Q}}_{\mathbf{G}}^{\mathbf{min}}$ | ${\mathbf{p}}^{\mathbf{min}}$ |
---|---|---|---|---|---|---|---|---|---|

$\left(\right)open="("\; close=")">\mathbf{\u20ac}$ | $\left(\right)open="("\; close=")">\frac{\mathbf{\u20ac}}{\mathbf{MW}}$ | $\left(\right)open="("\; close=")">\frac{\mathbf{\u20ac}}{{\mathbf{MW}}^{2}}$ | (%) | (MW) | (MW) | (MVAr) | (MVAr) | (Barg) | |

GFPP_1 | 0 | 220.86 | 0 | 60 | 475 | 0 | 332.5 | −285 | 30 |

GFPP_2 | 0 | 220.86 | 0 | 41 | 130 | 0 | 91 | −78 | 30 |

GFPP_3 | 0 | 220.86 | 0 | 57 | 101 | 0 | 70.7 | −61 | 30 |

GFPP_7 | 0 | 220.86 | 0 | 45 | 180 | 0 | 126 | −108 | 30 |

GFPP_8 | 0 | 220.86 | 0 | 44.5 | 105 | 0 | 73.5 | −63 | 30 |

GFPP_9 | 0 | 220.86 | 0 | 51 | 420 | 0 | 294 | −252 | 30 |

GFPP_10 | 0 | 220.86 | 0 | 30 | 1127 | 0 | 788.9 | −676 | 30 |

GFPP_11 | 0 | 220.86 | 0 | 40 | 360 | 0 | 252 | −216 | 30 |

GFPP_12 | 0 | 220.86 | 0 | 48 | 420 | 0 | 294 | −252 | 30 |

GFPP_14 | 0 | 220.86 | 0 | 30 | 766.7 | 0 | 536.7 | −460 | 30 |

GFPP_15 | 0 | 220.86 | 0 | 45 | 147.8 | 0 | 103.5 | −89 | 30 |

GFPP_16 | 0 | 220.86 | 0 | 61 | 435 | 0 | 304.5 | −261 | 30 |

GFPP_17 | 0 | 220.86 | 0 | 67 | 390 | 0 | 273 | −234 | 30 |

GFPP_18 | 0 | 220.86 | 0 | 55 | 410 | 0 | 287 | −246 | 30 |

Parameter | Symbol | Value | Unit |
---|---|---|---|

time step | $\Delta t$ | 900 | (s) |

total simulation time | ${t}_{max}$ | 24 | (h) |

gas temperature | T | 288.15 | (K) |

dynamic viscosity | η | $1.1\times {10}^{-5}$ | (kg/m·s) |

pipe roughness | k | $0.012$ | (mm) |

reference pressure | ${p}_{{\scriptstyle n}}$ | 1.01325 | (bar) |

reference temperature | ${T}_{{\scriptstyle n}}$ | 273.15 | (K) |

relative density | d | 0.6 | (-) |

gross calorific value | $GCV$ | 41.215 | (MJ/sm^{3}) |

© 2017 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Pambour, K.A.; Cakir Erdener, B.; Bolado-Lavin, R.; Dijkema, G.P.J.
Development of a Simulation Framework for Analyzing Security of Supply in Integrated Gas and Electric Power Systems. *Appl. Sci.* **2017**, *7*, 47.
https://doi.org/10.3390/app7010047

**AMA Style**

Pambour KA, Cakir Erdener B, Bolado-Lavin R, Dijkema GPJ.
Development of a Simulation Framework for Analyzing Security of Supply in Integrated Gas and Electric Power Systems. *Applied Sciences*. 2017; 7(1):47.
https://doi.org/10.3390/app7010047

**Chicago/Turabian Style**

Pambour, Kwabena Addo, Burcin Cakir Erdener, Ricardo Bolado-Lavin, and Gerard P. J. Dijkema.
2017. "Development of a Simulation Framework for Analyzing Security of Supply in Integrated Gas and Electric Power Systems" *Applied Sciences* 7, no. 1: 47.
https://doi.org/10.3390/app7010047