# Multistage Expansion Co-Planning of Integrated Natural Gas and Electricity Distribution Systems

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## Abstract

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## 1. Introduction

- Developing a MILP model for co-expansion planning of EHs, natural gas and electricity distribution grids
- Modelling the impacts of autonomous DG units on natural gas and electricity distribution networks using the EH concept
- Deriving a novel mixed-integer linear formulation for natural gas distribution system expansion planning
- Taking into account the effect of recovered heat from gas-fired DG units on heat demand reduction.

## 2. Methodology

#### 2.1. General Structure of the Proposed Framework

#### 2.2. Problem Formulation

#### 2.2.1. Expansion Planning of Energy Hubs

_{h}and N

_{L}are number of EHs and load levels, respectively.

#### 2.2.2. Electricity Distribution Network Expansion Planning

_{lp,t}to be one when node lp is in-service and set it to zero otherwise. It is worth mentioning that a bus is considered in-service as long as it is connected to at least one in-service feeder.

#### 2.2.3. Natural Gas Distribution Network Expansion Planning

#### 2.2.4. Co-Expansion Formulation

## 3. Linearization of the Proposed Optimization Model

#### 3.1. Linearization of EHs Planning Model

#### 3.2. Linearization of Electricity Distribution Planning Model

#### 3.3. Linearization of Natural Gas Distribution Network Expansion Planning

_{pln}is the number of blocks of piecewise linear pipeline flow function. Now, we have reached a linear model for co-planning study of a multicarrier energy system which can be efficiently solved using available commercial optimization software packages.

## 4. Case Study

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

Sets | |

T | Set of time stages of planning horizon. |

${\Gamma}_{b}^{Fe}$ | Candidate alternatives for reinforcement of the existing feeder in the path of branch b. |

${\Gamma}_{b}^{Pi}$ | Candidate alternatives for reinforcement of the existing pipeline in the path of branch b. |

${\Gamma}_{c}^{Cig}$ | Candidate alternatives for reinforcement of city gate c. |

${\Gamma}_{s}^{Sub}$ | Candidate alternatives for reinforcement of substation s. |

$\Lambda $ | Set of gas network branches. $\Lambda =\{{\Lambda}^{c},{\Lambda}^{f},{\Lambda}^{r}\}$ where ${\Lambda}^{c},{\Lambda}^{f},{\Lambda}^{r}$ are sets of candidate branches for construction of new pipelines, branches with fixed pipelines and candidate branches for reinforcement of existing pipelines, respectively. |

$O$ | Set of city gates. $O=\{{O}^{c},{O}^{f},{O}^{r}\}$ where ${O}^{c},{O}^{f},{O}^{r}$ are sets of candidate new city gates which can be constructed, fixed city gates and existing ones which can be reinforced, respectively. |

$\Pi $ | Set of electricity network branches. $\Pi =\{{\Pi}^{c},{\Pi}^{f},{\Pi}^{r}\}$ where ${\Pi}^{c},{\Pi}^{f},{\Pi}^{r}$ are sets of candidate branches for construction of new feeders, branches with fixed feeders and candidate branches for reinforcement of existing feeders, respectively. |

$\Theta $ | Set of substations. $\Theta =\{{\Theta}^{c},{\Theta}^{f},{\Theta}^{r}\}$ where ${\Theta}^{c},{\Theta}^{f},{\Theta}^{r}$ are sets of candidate new substations which can be constructed, fixed substations and existing ones which can be reinforced, respectively. |

${\mathsf{\Upsilon}}_{b}^{Fe}$ | Candidate alternatives for construction of a new feeder in the path of branch b. |

${\mathsf{\Upsilon}}_{b}^{Pi}$ | Candidate alternatives for construction of a new pipeline in the path of branch b. |

${\mathsf{\Upsilon}}_{c}^{Cig}$ | Candidate alternatives for construction of city gate c. |

${\mathsf{\Upsilon}}_{s}^{Sub}$ | Candidate alternatives for construction of substation s. |

$\Xi $ | Set of gas network nodes. $\Xi =\{{\Xi}^{D},{\Xi}^{C}\}$ where ${\Xi}^{D},{\Xi}^{C}$ are sets of demand and city gate nodes. |

$\Omega $ | Set of electricity network nodes. $\Omega =\{{\Omega}^{D},{\Omega}^{S}\}$ where ${\Omega}^{D},{\Omega}^{S}$ are sets of demand and substation nodes. |

Ψ^{lp}, Z^{lp} | Set of branches connected to load point lp of electricity and gas distribution networks, respectively. |

Parameters | |

$C{C}_{(.),(.)}^{(.)}$ | Construction cost. |

${D}_{n,t,ll}^{(.)}$ | Electricity and heat demand of the nth EH at load level ll of stage t. |

Du_{t,ll} | Duration of load level ll of stage t (Hours). |

$E{G}_{s}^{\mathrm{max}},E{G}_{s,k}^{\mathrm{max}}$ | Maximum capacity of substations. |

${f}_{b}^{\mathrm{max}},{f}_{b,k}^{\mathrm{max}}$ | Maximum flow capacity of pipelines. |

$G{G}_{s}^{\mathrm{max}},G{G}_{s,k}^{\mathrm{max}}$ | Maximum capacity of city gates. |

${I}_{b}^{\mathrm{max}},{I}_{b,k}^{\mathrm{max}}$ | Maximum current capacity of feeders. |

IC(.) | Investment cost coefficient of CHP units, furnaces and transformers ($/kW). |

M | A big number. |

$MC{a}_{t}^{CHP}$ | Maximum allowable total capacity of CHP units within electricity distribution network. |

OC(.) | Operating cost coefficient of CHP units, furnaces and transformers ($/kWh). |

$O{C}_{(.)}^{(.)},O{C}_{(.),(.)}^{(.)}$ | Operating cost. |

pf_{n,t,ll} | Power factor. |

$P{r}_{t,ll}^{Elec},P{r}_{t,ll}^{Gas}$ | Grid electricity and natural gas prices ($/kWh) |

$R{C}_{(.),(.)}^{(.)}$ | Reinforcement cost. |

V_{min}, V_{max} | Lower and upper bounds of nodal voltages. |

V_{r} | Rated voltage of distribution network. |

Z_{b}, Z_{b,k} | Absolute value of branch impedance. |

${\overline{Z}}_{b}$,${\overline{Z}}_{b,k}$ | Branch impedance. |

α | Power-to-natural gas flow conversion factor. |

β_{b}, β_{b,k} | Weymouth constant of gas pipelines. |

${\chi}_{lp,b}^{Elec}$,${\chi}_{lp,b}^{Gas}$ | Element of node-branch incidence matrix for electricity and gas networks which is −1 or +1 if branch b is connected to load point lp and the predetermined current or flow direction is toward or away from node lp, respectively and is 0 otherwise. |

${\delta}_{t,Inv}$,${\delta}_{t,Op}$ | Present value factors for investment and operating costs. |

${\gamma}_{i}$,$\Delta {\pi}^{i,max}$ | Slope and width of block i of piecewise linear pipeline flow function. |

${\eta}_{ge}^{CHP}$,${\eta}_{gh}^{CHP}$ | Gas to electricity and gas to heat efficiency of CHP units. |

${\eta}^{Fur}$,${\eta}^{Tra}$ | Efficiency of furnaces and transformers. |

λ_{min}, λ_{max} | Lower and upper bounds of nodal gas pressures. |

${\xi}_{lp,s}^{Elec}$,${\xi}_{lp,c}^{Gas}$ | A binary parameter, which is 1 if substation s or city gate c is at load point lp and is 0 otherwise. |

Variables | |

$C{a}_{n,t}^{(.)}$ | Capacity of CHP, furnace and transformer of nth EH at stage t. |

CF^{(.)} | Cost functions. |

GD_{lp,t,ll}, GG_{c,t,ll} | Gas demand at load point lp and injected gas power from city gate c. |

f_{b,t,ll} | Natural gas flow. |

${\widehat{f}}_{b,t,ll}$, ${{\widehat{f}}^{\prime}}_{b,t,ll}$ | Positive variables associated with natural gas flow of branch b in predetermined direction and the opposite direction. |

$E{D}_{lp,t,ll}$, $E{G}_{s,t,ll}$ | Electricity demand at load point lp and injected electricity power from substation s. |

$E{G}_{s,t}^{Fict}$ | Fictitious power injection of substation s. |

${I}_{b,t,ll}$, ${V}_{lp,t,ll}$ | Magnitudes of branch currents and nodal voltages. |

${\overline{I}}_{b,t,ll}$, ${\overline{V}}_{lp,t,ll}$ | Branch current and nodal voltage phasors. |

${I}_{b,t}^{Fict}$ | Fictitious current of branch b at time stage t. |

$In{v}_{t}^{(.)}$ | Investment cost at stage t. |

LPM_{lp,t} | A binary variable associated with the load point mode, which is 1 when load point lp is in service at stage t and is 0 otherwise. |

$NC{a}_{n,t}^{(.)}$ | Newly installed capacity of CHP, furnace and transformer in nth EH at stage t. |

$O{p}_{t}^{(.)}$ | Operating cost at stage t. |

${P}_{n,t,ll}^{Elec}$, ${P}_{n,t,ll}^{Gas}$ | Electricity and natural gas power input of the nth EH at load level ll of stage t. |

Δπ_{b,t,ll} | Square pressure loss for branch b. |

$\Delta {\pi}_{b,t,ll}^{i}$ | Square pressure loss in block i of piecewise linear pipeline flow function. |

${\phi}_{(.),t}^{(.),(.)},{\phi}_{(.),k,t}^{(.),(.)}$ | Binary utilization variables. |

λ_{b,k,t} | Nodal gas pressures. |

${\sigma}_{(.),k,t}^{(.),Ne}$ | Binary investment variables for construction of new feeders, substations, pipelines and city gates. |

${\sigma}_{(.),k,t}^{(.),Re}$ | Binary investment variables for reinforcement of existing feeders, substations, pipelines and city gates. |

${\upsilon}_{n,t,ll}$ | Dispatch factor of the nth EH at load level ll of stage t. |

Abbreviations | |

CHP | Combined heat and power |

Cig | City gate |

EDN | Electricity distribution network |

EH | Energy hub |

Elec | Electricity |

Fe | Feeder |

Fi | Fixed |

GDN | Gas distribution network |

Ne | New |

Pi | Pipeline |

Re | Reinforcement |

Sub | Substation |

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Simulation Outcome | Case I | Case II | |
---|---|---|---|

$C{\mathrm{F}}^{EH}$ (M$) | Inv. | 0.686 | 0.689 |

Op. | 20.576 | 20.509 | |

$C{\mathrm{F}}^{EDN}$ (M$) | Inv. | 5.928 | 7.066 |

Op. | 0.002 | 0.002 | |

$C{\mathrm{F}}^{GDN}$ (M$) | Inv. | 8.339 | 8.737 |

Op. | 0.002 | 0.002 | |

Total Cost (M$) | 35,533 | 37,005 | |

Total Installed CHP Capacity (MW) | 1 | 1 | |

Total Electricity Served by CHPs (GWh) | 21.191 | 27.039 | |

Total Electricity Energy from the Grid (GWh) | 161.760 | 155.790 | |

Total Gas from the Grid (Mm^{3}) | 31.610 | 32.441 | |

Electricity Network Peak Demand (MW) | 8.036 | 8.036 | |

Natural Gas Network Peak Demand (m^{3}/h) | 1554.396 | 1554.396 | |

CHP Nodes | 6-7-10-11-15 | 1-4-5-6-8-13-16 | |

Simulation Time (s) | 477.64 | 74.69 |

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## Share and Cite

**MDPI and ACS Style**

Jooshaki, M.; Abbaspour, A.; Fotuhi-Firuzabad, M.; Moeini-Aghtaie, M.; Lehtonen, M.
Multistage Expansion Co-Planning of Integrated Natural Gas and Electricity Distribution Systems. *Energies* **2019**, *12*, 1020.
https://doi.org/10.3390/en12061020

**AMA Style**

Jooshaki M, Abbaspour A, Fotuhi-Firuzabad M, Moeini-Aghtaie M, Lehtonen M.
Multistage Expansion Co-Planning of Integrated Natural Gas and Electricity Distribution Systems. *Energies*. 2019; 12(6):1020.
https://doi.org/10.3390/en12061020

**Chicago/Turabian Style**

Jooshaki, Mohammad, Ali Abbaspour, Mahmud Fotuhi-Firuzabad, Moein Moeini-Aghtaie, and Matti Lehtonen.
2019. "Multistage Expansion Co-Planning of Integrated Natural Gas and Electricity Distribution Systems" *Energies* 12, no. 6: 1020.
https://doi.org/10.3390/en12061020