# Impact of Natural Gas Distribution Network Structure and Operator Strategies on Grid Economy in Face of Decreasing Demand

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## Abstract

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## 1. Introduction

- What is the trend of customer development?
- What are the grid-specific factors that influence the profitability of a natural gas grid?
- What are the options for grid operators, regulators and what are the impacts on grid users?

- Within a structural grid analysis, we estimate a functional relationship between required grid length and the amount of customers with a power law approach (Section 3.2.1) for different exit patterns in all grids (Section 4.2). Within a correlation analysis, we identify possible structural parameters for the prediction of the exponent k of the power law, a parameter which determines the disproportionality between grid length and number of customers when they leave the grid (Section 4.3).
- To calculate the total costs of grid operation within an economic analysis, we apply a mixed integer linear optimization model based on a yearly cash flow calculation and transform it into a simplified calculation model considering the functional relationship found in the previous section (Section 3.3.2 and Section 3.3.3). After a validation of the simplified model (Section 4.4.1 and Section 4.4.2), we compare the total costs of operation and resulting grid charges for several exit patterns and DNO investment strategies in Section 4.4.3.

## 2. Literature Review

#### 2.1. Scenarios for Gas Demand from an International and German Perspective

_{2}emissions are set to −55% in 2030 and −80% to −95% in 2050 compared to the values of 1990 [30,31]. The government emphasizes that the achievement of this goal should be “technology-neutral” and “open to innovation” [18,31]. Like other European studies, the German ones span the two extreme scenarios described above (Figure 1).

#### 2.2. Investment Decisions in Building Sector and Their Influence on Grid Economics

_{2}- and cost-optimized modernization measures for building envelope and heating between natural gas-based systems and electrical ones. They predict that gas-based solutions are more sensitive to fluctuations in energy procurement costs than electrical solutions based on heat pumps. From the perspective of the DNO, with a declining demand for natural gas, the profitability of the gas grid tends to decrease. Dependent on grid age, topology and load density as well as the DNO strategy, this might lead to rising grid charges [18], which can in turn influence building owner decisions against gas powered heating systems—a self-reinforcing effect.

#### 2.3. Effects of Grid Structure and Asset Composition on Defection Scenarios

#### 2.4. Economic Factors of Operating a Natural Gas Infrastructure

- “stable revenue cap”, an approach in which the DNO tries to keep the absolute revenue cap constant,
- “stable grid value”, an approach in which the revenue cap is constraint by a stable grid age, and
- “stable grid charges”, an approach in which the DNO tries to keep grid charges at a constant level.

#### 2.5. Different Strategies for Grid Operation

## 3. Data and Methods

#### 3.1. Gas Grid Data and Software Tools

#### 3.2. Structural Network Analysis

#### 3.2.1. Analysis of the Functional Relation between Grid Length and User Number

#### 3.2.2. Correlation Analysis

#### 3.3. Cash Flow Analysis

#### 3.3.1. Economic Parameters and Principles

#### 3.3.2. Optimization Model

- Only one renewal per line allowed within the planning horizon.
- Lines have to stay in operation as long as customers are connected [57].
- Lines have to be closed if no customer is connected anymore.

#### 3.3.3. Simplified Cash Flow Calculation

**Stable grid charges**: The grid charges ${\mathrm{c}}_{\U0001d4c9}^{\mathrm{GCG}}$ are set to their initial value and ${\mathrm{MRBVF}}_{\mathrm{t}}^{\mathrm{Grid}}$ is calculated, until its value reaches 0. After that, grid charges are a function of the yearly OPEX and supplied energy.$${\mathrm{c}}_{\U0001d4c9}^{\mathrm{GCG}}=\text{}\{\begin{array}{c}{\mathrm{c}}_{\U0001d4c9}^{\mathrm{GCG}}={\text{}\mathrm{c}}_{\U0001d4c9=0}^{\mathrm{GCG}};{\text{}\mathrm{for}\text{}\mathrm{MRBVF}}_{\mathrm{t}}^{\mathrm{Grid}}0\\ {\mathrm{c}}_{\U0001d4c9}^{\mathrm{GCG}}=\mathrm{f}\left({\mathrm{L}}_{\U0001d4c9}^{\mathrm{Grid}},{\text{}\mathrm{E}}_{\U0001d4c9}^{\mathrm{Gas}}\right);{\text{}\mathrm{for}\text{}\mathrm{MRBVF}}_{\mathrm{t}}^{\mathrm{Grid}}=0\end{array}$$**Stable grid value**: The mean rest book value factor is set to its initial value and the revenue cap is calculated.$${\mathrm{MRBVF}}_{\mathrm{t}}^{\mathrm{Grid}}={\text{}\mathrm{MRBVF}}_{\mathrm{t}=0}^{\mathrm{Grid}}\text{}$$**Stable revenue cap**: The revenue cap is set to its initial value and the mean rest book value factor is calculated until its value reaches 1. After that, the revenue cap is a function of the yearly costs.$${\mathrm{RC}}_{\U0001d4c9}^{\mathrm{G}}=\text{}\{\begin{array}{c}{\mathrm{RC}}_{\U0001d4c9}^{\mathrm{G}}={\text{}\mathrm{RC}}_{\U0001d4c9=0}^{\mathrm{G}};{\text{}\mathrm{for}\text{}\mathrm{MRBVF}}_{\mathrm{t}}^{\mathrm{Grid}}1\\ {\mathrm{RC}}_{\U0001d4c9}^{\mathrm{G}}=\mathrm{f}\left({\mathrm{L}}_{\U0001d4c9}^{\mathrm{Grid}},{\text{}\mathrm{E}}_{\U0001d4c9}^{\mathrm{Gas}}\right);{\text{}\mathrm{for}\text{}\mathrm{MRBVF}}_{\mathrm{t}}^{\mathrm{Grid}}=1\end{array}$$

## 4. Results

#### 4.1. Verification of Pressure Losses in the Distribution Grids

#### 4.2. Structural Analysis

- k < 1: The decrease of grid length $\frac{{\mathrm{L}}_{\U0001d4c9}^{\mathrm{Grid}}}{{\mathrm{L}}_{\U0001d4c9=0}^{\mathrm{Grid}}}$ is slower than the decrease of customer number $\frac{{\mathrm{n}}_{\U0001d4c9}^{\mathrm{Cust}}}{{\mathrm{n}}_{\U0001d4c9=0}^{\mathrm{Cust}}}$.
- k > 1: The decrease of grid length $\frac{{\mathrm{L}}_{\U0001d4c9}^{\mathrm{Grid}}}{{\mathrm{L}}_{\U0001d4c9=0}^{\mathrm{Grid}}}$ is faster than the decrease of customer number $\frac{{\mathrm{n}}_{\U0001d4c9}^{\mathrm{Cust}}}{{\mathrm{n}}_{\U0001d4c9=0}^{\mathrm{Cust}}}$.

^{2}values > 0.9, see Figure 6b) and generally rises with the amount of customers, with single outliers for small grid areas with less than 50 customers.

#### 4.3. Correlation Analysis

#### 4.4. Cost Analysis

#### 4.4.1. DNO Costs of Operating a Natural Gas Infrastructure

#### 4.4.2. Comparison of Optimization-Based and Simplified Cash Flow Calculations

#### 4.4.3. Cash Flow Analysis for All 57 Grid Areas

## 5. Discussion and Conclusions

#### 5.1. Options, Risks and Conclusions for Distribution Network Operators

- Reducing the investment rate, and with that the CAPEX, leads to an increase of the grid age, thus its reliability drops, which in turn increases the operational costs.
- Shortening the depreciation period of lines has the same effects like a changed capitalization strategy in the long term.

#### 5.2. Options, Risks and Conclusions for Grid Users

#### 5.3. Macro-Economic Perspective and Regulatory Options

#### 5.4. Further Research

#### 5.4.1. Limits and Transferability of the Approach

#### 5.4.2. Decisions of Single Actors

_{2}optimized renewal measures [35,36,38]. However, a validation of the German Energy Saving Ordinance shows that, especially in the residential sector, investment decisions are made on the basis of a wider spread of socio-economic factors [86,87]. To be able to quantify the risk of a customer’s exit from the gas network, models are needed that determine realistic refurbishment options for individual buildings respectively their owners. Based on these options, the risk in terms of future gas demand for individual network areas can be quantified and taken into account when planning renewal measures in the gas grid. For this purpose, existing investment valuation models, such as portfolio analysis as a one-period model or real options analysis as a multi-period model, which are already used in the energy economy, have to be adapted [88]. Moreover, the role of different regulatory regimes within such transformation paths should also be examined.

#### 5.4.3. Interdependencies between the Decisions of Different Actors

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A. Nomenclature and Parametrization

Name | Acronym | Name | Acronym |
---|---|---|---|

Building owner | BO | Grid charges | GC |

Capital expenditure | CAPEX | Operational expenditure | OPEX |

Distribution network operator | DNO | Revenue cap | RC |

Domestic hot water | DHW | Space heating | SH |

Parameter | Description [unit] | Value |
---|---|---|

Variables | ||

${\mathrm{b}}_{\U0001d4c7,\ell}^{\mathcal{O}\mathcal{R}}$ | Renewal of line ℓ in year 𝓇 (Binary decision variable of optimization model) | |

${\mathrm{b}}_{\U0001d4b8,\ell}^{\mathcal{C}}$ | Closure of line ℓ in year 𝒸 (Binary decision variable of optimization model) | |

${\mathrm{c}}_{\U0001d4c9}^{\mathrm{GCG}}$ | Grid charges gas in year 𝓉 [€/kWh] | |

${\mathrm{RBVF}}_{\ell ,\U0001d4c9}$ | Rest book value factor of line ℓ in year 𝓉 as a function of the binary decision variables | |

${\mathrm{MRBVF}}_{\mathrm{t}}^{\mathrm{Grid}}$ | Mean rest book value factor of the whole grid in year 𝓉 | |

${\mathrm{A}}_{\U0001d4c9,\ell}$ | Age of line ℓ in year 𝓉 as a function of the binary decision variables [a] | |

${\mathrm{b}}_{\ell}^{\mathrm{LT}}$ | Binary variable representing if a line is within its technical lifetime (function of the binary decision variables) | |

Power law function | ||

${\mathrm{n}}_{\U0001d4c9}^{\mathrm{Cust}}$ | Customer number of the grid | |

${\mathrm{L}}_{\U0001d4c9}^{\mathrm{Grid}}$ | Cumulated line length of the grid [m] | |

k | Exponent of the power law function | |

MSE | Mean squared error of power law fit | |

R^{2} | Correlation coefficient of power law fit | |

Cost components of the revenue cap | ||

${\mathsf{\alpha}}_{\U0001d4c9}^{\mathrm{CAPEX}}$ | Capital expenditures [€] | |

${\mathsf{\alpha}}_{\U0001d4c9}^{\mathrm{OPEX}}$ | Operational expenditures [€] | |

${\mathsf{\alpha}}_{\U0001d4c9}^{\mathrm{EC}}$ | Calculated return on equity [€] | |

${\mathsf{\alpha}}_{\U0001d4c9}^{\mathrm{BC}}$ | Interest on borrowed capital [€] | |

${\mathsf{\alpha}}^{\mathrm{Tax}}$ | Calculated trade tax [€] | |

${\mathsf{\alpha}}_{\U0001d4c9}^{\mathrm{Depr}}$ | Calculated interest on borrowed capital [€] | |

${\mathsf{\alpha}}_{\U0001d4c9}^{\mathrm{OC}}$ | Operational costs [€] | |

${\mathsf{\alpha}}_{\U0001d4c9}^{\mathrm{LC}}$ | Loss costs [€] | |

${\mathsf{\alpha}}_{\U0001d4c9}^{\mathrm{UpGCG}}$ | Upstream grid charges [€] | |

${\mathsf{\alpha}}_{\U0001d4c9}^{\mathrm{Conc}}$ | Concession fees [€] | |

Parameters used in Section 2 (methods and materials) | ||

${\mathrm{E}}_{\U0001d4c9}^{\mathrm{Gas}}$ | Supplied energy in year 𝓉 [kWh/a] | Scenario specific |

${\mathrm{C}}_{\ell}^{\text{}\mathrm{I}}$ | Historical acquisition expenditures for line ℓ [€/m] | 214 * |

${\mathrm{L}}_{\ell}$ | Line length of line ℓ [m] | Line specific |

${\mathrm{R}}_{\ell}^{\text{}\mathrm{EC}}$ | Interest rate equity capital of line ℓ | 0.0691 * |

${\mathrm{Q}}_{\ell}^{\text{}\mathrm{EC}}$ | Amount of equity capital of line ℓ | 0.4 * |

${\mathrm{R}}_{\ell}^{\text{}\mathrm{BC}}$ | Interest rate borrowed capital of line ℓ | 0.035 * |

${\mathrm{Q}}_{\ell}^{\text{}\mathrm{BC}}$ | Amount of borrowed capital of line ℓ | 0.6 * |

${\mathrm{R}}^{\mathrm{Tax}}$ | Trade tax rate | 0.1365 * |

${\mathrm{T}}^{\mathrm{TL}}$ | Technical lifetime of a line [a] | 40 |

${\mathrm{T}}^{\mathrm{Planning}}$ | Planning horizon [a] | 33 |

${\mathrm{C}}_{\U0001d4c9}^{\mathrm{UpGCG}}$ | Specific costs of upstream grid charges [€/kWh] | 0.01 |

${\mathrm{C}}_{\U0001d4c9}^{\mathrm{Conc}}$ | Specific costs for concession fees [€/kWh] | 0.002 |

${\mathrm{C}}^{\mathrm{LC}}$ | Specific lost costs [€/kWh] | 0.008 |

${\mathrm{F}}^{\mathrm{Loss}}$ | Loss factor | 0 |

${\mathrm{C}}^{\mathrm{LRC}}$ | Specific operational costs [€/m] | 10.71 |

${\mathrm{T}}_{\ell}^{\text{}\mathrm{Init}}$ | Line age at the begin of planning horizon [a] | Line specific |

${A}^{MeanInit}$ | Length-weighted average age of the grid [a] | Grid specific |

Additional Parameters used in optimization model | ||

${\mathrm{LStat}}_{\U0001d4c7,\U0001d4c9}^{\mathcal{R}}$ | Status matrix for renewal measure 𝓇 in year 𝓉 | See Appendix C.1 |

${\mathrm{LStat}}_{\U0001d4c9,\ell}^{\mathcal{O}}$ | Status matrix for operation of line ℓ in year 𝓉 | See Appendix C.1 |

${\mathrm{LStat}}_{\U0001d4b8,\U0001d4c9}^{\mathcal{C}}$ | Status matrix for closure measure 𝒸 in year 𝓉 | See Appendix C.1 |

${\mathrm{E}}_{\mathrm{j},\U0001d4c9}^{\mathrm{BE}}$ | Energy demand of building 𝒿 in year 𝓉 [kWh] | Building and scenario specific |

${\mathrm{B}}_{\ell ,\U0001d4c9}^{\mathrm{BL}}$ | Status matrix of line ℓ in year 𝓉 | Line and scenario specific |

Indices and sets | ||

$\U0001d4bf\u03f5\mathcal{J}$ | A building 𝒿 of all buildings $\mathcal{J}$ connected to the grid | |

$\ell \u03f5\text{}\mathcal{L}$ | A line ℓ of all lines $\mathcal{L}$ in the grid | |

$\U0001d4c9\u03f5\text{}\mathcal{T}$ | A year 𝓉 within the planning horizon $\mathcal{T}$ | |

$\U0001d4c7\text{}\u03f5\text{}\mathcal{R}$ | Year of renewal measure 𝓇 of all possible years $\mathcal{R}$ within the planning horizon $\mathcal{T}$ | |

$\U0001d4b8\text{}\u03f5\text{}\mathcal{C}$ | Year of closure measure 𝒸 of all possible years $\mathcal{C}$ within the planning horizon $\mathcal{T}$ |

## Appendix B. Correlation Analysis

#### Appendix B.1. Parameters of Correlation Analysis

Parameter | Unit | Description, Literature source |
---|---|---|

${\mathrm{k}}^{\mathrm{Highest}\text{}\mathrm{impact}\text{}\mathrm{first}}$ | 1 | k value for “highest impact first” selection type of one grid. |

${\mathrm{k}}^{\mathrm{Longest}\text{}\mathrm{path}\text{}\mathrm{first}}$ | 1 | k value for “longest path first” selection type of one grid. |

$\mathrm{Mean}({\mathrm{k}}^{\mathrm{Radial}})$ | 1 | Mean value of k for 100 seeds “radial random selection” of one grid. |

$\mathrm{Mean}({\mathrm{k}}^{\mathrm{Weighted}\text{}})$ | 1 | Mean value of k for 100 seeds “weighted random selection” of one grid. |

$\mathrm{Mean}({\mathrm{k}}^{\mathrm{Random}})$ | 1 | Mean value of k for 100 seeds “random selection” of one grid. |

${\mathrm{k}}^{\mathrm{Shortest}\text{}\mathrm{path}\text{}\mathrm{first}}$ | 1 | k value for “Shortest path first” selection type of one grid. |

${\mathrm{k}}^{\mathrm{Least}\text{}\mathrm{impact}\text{}\mathrm{first}}$ | 1 | k value for “Least impact first” selection type of one grid. |

${\mathrm{k}}^{\mathrm{Highest}\text{}\mathrm{impact}\text{}\mathrm{first}}-{\text{}\mathrm{k}}^{\mathrm{Least}\text{}\mathrm{impact}\text{}\mathrm{first}}$ | 1 | Difference of k values “highest impact first” and “least impact first” of one grid. |

$\mathrm{STD}\left({\mathrm{k}}^{\mathrm{Random}}\right)$ | 1 | Standard deviation of k for 100 seeds “random selection” of one grid. |

$\mathrm{max}\left({\mathrm{P}}_{\U0001d4bf}\right)$ | m | Longest path of a grid. |

$\mathrm{min}\left({\mathrm{P}}_{\U0001d4bf}\right)$ | m | Shortest path of a grid. |

$\mathrm{Mean}\left(\mathrm{Detourf}\right)$ | 1 | Average value of the detour factor of a grid (detour factor: path length normalized with linear distance). |

$\mathrm{STD}\left(\mathrm{Detourf}\right)$ | 1 | Standard deviation of the detour factor of a grid. |

${\mathrm{L}}^{\mathrm{Grid}}$ | m | Grid length of a grid. |

$\mathrm{Mean}\left({\mathrm{P}}_{\U0001d4bf}\right)$ | m | Average value of all paths lengths of a grid. |

$\mathrm{STD}\left({\mathrm{P}}_{\U0001d4bf}\right)$ | m | Standard deviation of all paths lengths of a grid. |

${\mathrm{E}}^{\mathrm{Grid}}$ | kWh/a | Cumulated yearly energy demand of a grid. |

$\mathrm{Mean}\left({\mathrm{E}}_{\U0001d4bf}\right)$ | kWh/a | Average energy demand of customers of a grid. |

$\mathrm{STD}\left({\mathrm{E}}_{\U0001d4bf}\right)$ | kWh/a | Standard deviation of the customer’s energy demands in a grid. |

$\mathrm{Max}\left({\mathrm{E}}_{\U0001d4bf}\right)$ | kWh/a | Maximal energy demand of a customer in a grid. |

${\mathrm{E}}^{\mathrm{Grid}}/{\mathrm{L}}^{\mathrm{Grid}}$ | kWh/(a * m) | Cumulated energy of grid area normalized to grid length. |

${\mathrm{N}}^{\mathrm{Cust}}/{\text{}\mathrm{L}}^{\mathrm{Grid}}$ | 1/(a * m) | Number of customers in grid area in relation to grid length. |

${\mathrm{N}}^{\mathrm{Cust}}$ | 1 | Number of customers in a grid area. |

${\mathrm{A}}^{\mathrm{Grid}}$ | m^{2} | Area size. |

${\mathrm{P}}^{\mathrm{Grid}}/{\text{}\mathrm{L}}^{\mathrm{Grid}}$ | 1 | Sum of all paths from user to regulator station normalized to grid length in a grid. |

$\mathrm{STD}\left({\mathrm{P}}_{\U0001d4bf}\right)/{\text{}\mathrm{P}}^{\mathrm{Grid}}$ | 1 | Standard deviation of path lengths normalized to sum of path lengths in a grid. |

$\mathrm{min}\left({\mathrm{P}}_{\U0001d4bf}\right)/{\text{}\mathrm{P}}^{\mathrm{Grid}}$ | 1 | Shortest path normalized to sum of path lengths in a grid. |

$\mathrm{max}\left({\mathrm{P}}_{\U0001d4bf}\right)/{\text{}\mathrm{P}}^{\mathrm{Grid}}$ | 1 | Longest path normalized to sum of path lengths in a grid. |

$\mathrm{VarC}\left({\mathrm{P}}_{\U0001d4bf}\right)$ | 1 | Variation coefficient of path lengths in a grid. |

$\mathrm{VarC}\left({\mathrm{L}}_{\ell}\right)$ | 1 | Variation coefficient of line lengths in a grid (of simplified graph, see chapt. 2). |

$\mathrm{Mean}\left({\mathrm{L}}_{\ell}\right)$ | m | Average line length (of simplified graph, see chapt. 2). |

$\mathrm{Max}\left(\mathrm{l}\right)/{\mathrm{L}}^{\mathrm{Grid}}$ | 1 | Maximal line length normalized to grid length (of simplified graph, see chapt. 2). |

$\mathrm{Mean}\left(\mathrm{PR}\right)$ | 1 | Mean value of page rank [76,77]. (weights = line lengths; dumping factor d = 0.85) |

$\mathrm{VarC}\left(\mathrm{PR}\right)$ | 1 | Variation coefficient of page rank. |

$\mathrm{Mean}\left(\mathrm{SP}\right)$ | m | Sum of shortest paths between every nodes of the graph normalized by squared customers number (weights = line lengths) [91]. |

${\mathrm{K}}^{\mathrm{W}}\left(1\right)$ | 1 | Weighted average nearest neighbor degree of nodes with degree d [75,77]. (d = 1) |

${\mathrm{K}}^{\mathrm{W}}\left(3\right)$ | 1 | Weighted average nearest neighbor degree of nodes with degree d. (d = 3) |

${\mathrm{D}}^{\mathrm{Grid}}$ | 1 | Diameter of the graph, which represents its maximum eccentricity. The eccentricity of a node v is the maximum distance from v to all other nodes in G [92]. |

${\mathrm{R}}^{\mathrm{Grid}}$ | 1 | Radius of the graph, which represents its minimum eccentricity [92]. |

#### Appendix B.2. Correlation Matrix of All Parameters

#### Appendix B.3. Structural Parameters of the 57 Grid Areas

Grid | Length/m | Number of Customers | Yearly Energy Demand/MWh | Length Weighted Average Initial Age/a |
---|---|---|---|---|

0 | 480 | 4 | 233 | 15.1 |

1 | 2270 | 40 | 2235 | 33.1 |

2 | 2390 | 79 | 2224 | 28.3 |

3 | 1140 | 22 | 2496 | 36.1 |

4 | 2620 | 82 | 4529 | 31.4 |

5 | 4220 | 90 | 1581 | 22.4 |

6 | 7680 | 266 | 6787 | 35.8 |

7 | 4460 | 124 | 8828 | 20.7 |

8 | 8630 | 299 | 8032 | 34.6 |

9 | 5590 | 174 | 4877 | 25.7 |

10 | 650 | 17 | 2335 | 29.0 |

11 | 5200 | 191 | 5445 | 27.1 |

12 | 3660 | 69 | 3625 | 22.9 |

13 | 8080 | 229 | 6524 | 24.5 |

14 | 1830 | 44 | 1575 | 29.9 |

15 | 2430 | 75 | 7457 | 29.1 |

16 | 5510 | 166 | 2284 | 20.4 |

17 | 4590 | 189 | 3889 | 28.6 |

18 | 3210 | 148 | 1638 | 17.0 |

19 | 4270 | 167 | 5633 | 22.7 |

20 | 2870 | 126 | 3009 | 29.1 |

21 | 980 | 31 | 1444 | 28.7 |

22 | 5650 | 212 | 4550 | 25.1 |

23 | 3620 | 127 | 4540 | 30.7 |

24 | 1510 | 61 | 2708 | 26.1 |

25 | 2150 | 36 | 2185 | 16.9 |

26 | 6390 | 152 | 5660 | 21.6 |

27 | 9510 | 247 | 7060 | 26.4 |

28 | 5890 | 209 | 4286 | 26.2 |

29 | 2990 | 64 | 4046 | 22.0 |

30 | 4440 | 205 | 5229 | 33.6 |

31 | 2550 | 130 | 2690 | 35.9 |

32 | 5650 | 228 | 7193 | 25.5 |

33 | 5140 | 234 | 8473 | 30.9 |

34 | 7680 | 245 | 9616 | 23.4 |

35 | 4660 | 199 | 9029 | 29.2 |

36 | 7520 | 363 | 19,092 | 29.9 |

37 | 5070 | 180 | 13,916 | 30.8 |

38 | 500 | 8 | 136 | 14.3 |

39 | 3810 | 129 | 3322 | 21.3 |

40 | 8110 | 258 | 13,229 | 31.3 |

41 | 7300 | 227 | 6336 | 35.1 |

42 | 10,080 | 390 | 16,786 | 27.2 |

43 | 4200 | 131 | 4694 | 27.0 |

44 | 4960 | 181 | 4626 | 21.4 |

45 | 3030 | 100 | 2583 | 28.6 |

46 | 2390 | 76 | 2133 | 26.3 |

47 | 6940 | 281 | 14,294 | 28.9 |

48 | 1600 | 101 | 3822 | 33.0 |

49 | 3290 | 193 | 8625 | 32.1 |

50 | 470 | 23 | 1538 | 35.8 |

51 | 6300 | 276 | 17,462 | 28.7 |

52 | 5550 | 144 | 8993 | 29.5 |

53 | 2790 | 56 | 4012 | 19.5 |

54 | 10,760 | 481 | 20,192 | 31.5 |

55 | 11,960 | 507 | 21,045 | 33.3 |

56 | 1350 | 31 | 1024 | 21.5 |

## Appendix C. Cash Flow Analysis

#### Appendix C.1 Optimization Model

#### Appendix C.2. Simplified Cash Flow Model

#### Appendix C.3. Global Scenario of the Cost Analysis

**Figure A2.**Normalized scenario used as global scenario for the cash flow calculation compared to literature values for Germany (maximum and minimum of all sources).

#### Appendix C.4. Results of the Cost Analysis

**Figure A3.**Comparison of grid charges for optimization (full) and simplified (hashed) cash flow calculation during declining gas demand in a single gas grid. (Grid: #18, DNO strategy: constant grid value, selection type: random selection (mean k value), global scenario: linear decrease of gas demand 2018–2050).

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**Figure 1.**Measured and predicted values of gas consumption for Germany in selected studies (Numbers: [cited source].scenario; linearly interpolated between projected years).

**Figure 2.**(

**a**) Separated radial grid areas [66]; (

**b**) Pressure for all house connection points (n = 9118) in low-pressure stage for the original operated meshed topology and the radial topology (after demarcation of sub grid areas).

**Figure 4.**Pressure of all house connection points for the median of the 100 scenarios of “random selection” for all 57 grids dependent on the number of customers leaving the grid from 0 up to 75%.

**Figure 5.**Required grid length for declining customer numbers in a low-pressure gas grid. (

**a**) Network structure of grid area 18 on the top with all customers, (

**b**) with 50% of costumers (exemplary random selection, resulting grid length: 71%, background map in [66]). Blue dots: active customers, black lines: active lines, red: inactive lines, red dot: pressure regulator station. (

**c**) Distribution of grid length for 100 random exit patterns (“Actual grid length” corresponds to black lines in (

**b**), “Initial grid length” corresponds to all lines in B, Blue box: median and 25%/75% percentiles, whiskers: +/-1.5 IQD, red crosses: values for an example distribution, red dotted line: power law fit to example data).

**Figure 6.**(

**a**) Dots: $\mathrm{k}$ for ranked and $\mathrm{Mean}\left(\mathrm{k}\right)$ for stochastic selection types of Table 2 for each of 57 grids with different selection types of user exits. (

**b**) ${\mathrm{R}}^{2}$ for ranked and $\mathrm{Mean}\left({\mathrm{R}}^{2}\right)$ for stochastic selection types of Table 2 for each of 57 grids with different selection types of user exits. Boxes: Median and 25%/75% percentiles of the distribution. Whiskers: +/-1.5 IQD).

**Figure 8.**k values for different grid sizes. (

**a**) $\mathrm{Mean}\left(\mathrm{k}\right)$ of each grid for different grid lengths; (

**b**) Grid length and customer amount for individual grid areas.

**Figure 10.**k values for different structural parameters. (

**a**) Weighted average nearest neighbor degree of nodes with degree 3 against sum of path lengths normalized to grid length; (

**b**) Weighted average nearest neighbor degree of nodes with degree 3 against maximal line length normalized to grid length (Colors: $\mathrm{Mean}\left({\mathrm{k}}^{\mathrm{Random}}\right)$, Sizes: $\mathrm{STD}\left({\mathrm{k}}^{\mathrm{Random}}\right)$ ).

**Figure 11.**Comparison of revenue caps for optimization (full) and simplified (hashed) cash flow calculation during declining gas demand in a single gas grid. Loss costs are modeled as 0. (Grid: #18, DNO strategy: constant grid value, selection type: random selection (mean k value), global scenario: linear decrease of gas demand 2018–2050).

**Figure 12.**(

**a**) Grid charge development for individual grids at different DNO strategies with median k values. (

**b**) Grid charge development for individual grids at different k values for the DNO strategy “stable grid value” (percentiles of random selection k values, 100 seeds). Dots: individual grids, boxes: median and 25%/75% percentiles of the resulting distribution, whiskers: +/-1.5 IQD.

**Figure 13.**(

**a**) Revenue cap development for individual grids at different DNO strategies with median k values. (

**b**) Revenue cap development for individual grids at different k values for the DNO strategy “stable grid value” (percentiles of random selection k values, 100 seeds). Dots: individual grids, boxes: median and 25%/75% percentiles of the resulting distribution, whiskers: +/-1.5 IQD.

**Figure 14.**CAPEX development for individual grids at different DNO strategies with median k values. (

**a**) Selected years until 2025; (

**b**) years until 2050. Dots: individual grids, boxes: median and 25%/75% percentiles of the resulting distribution, whiskers: +/-1.5 IQD.

**Table 1.**Regulation mechanisms in different European countries [61].

Country | Gas DNO | |
---|---|---|

Regulation Method | Incentive Regulation | |

Austria | Price-cap | Yes |

France | Revenue-cap | Yes |

Germany | Revenue-cap | Yes |

Ireland | Revenue-cap | Yes |

Norway | Revenue-cap | Yes |

Netherlands | Price-cap | Yes |

Cost Component | Grid Length | Grid Age | Energy | Overall Share in Case Study ** (%) | |
---|---|---|---|---|---|

CAPEX${\mathsf{\alpha}}^{\mathrm{CAPEX}}$ | Calc. return equity ${\mathsf{\alpha}}^{\mathrm{EC}}$ | + | − | 9.9 | |

Calc. trade tax ${\mathsf{\alpha}}^{\mathrm{Tax}}$ | + | − | 1.3 | ||

Interests on borrowed capital ${\mathsf{\alpha}}^{\mathrm{BC}}$ | + | − | 6.6 | ||

Calc. depreciations ${\mathsf{\alpha}}^{\mathrm{Depr}}$ | + | − | 15.0 | ||

OPEX ${\mathsf{\alpha}}^{\mathrm{OPEX}}$ | Operational costs ${\mathsf{\alpha}}^{\mathrm{OC}}$ | + | * | * | 33.6 |

Loss costs ${\mathsf{\alpha}}^{\mathrm{LC}}$ | + | 0.0 | |||

Upstream grid charges ${\mathsf{\alpha}}^{\mathrm{UpGGG}}$ | + | 19.0 | |||

Concession fees ${\mathsf{\alpha}}^{\mathrm{Conc}}$ | + | 14.7 |

**+**: linear positive dependence;

**−**: negative linear dependence; *: possible dependence, not modelled in paper, **: Derived from real data of Bamberg from 2017.

Name | Selection Type; Seeds | Determination of Customer Exits | Interpretation |
---|---|---|---|

Shortest path first | Ranked selection; 1 | Order and drop customers by their path length to the connection point. | Worst case |

Longest path first | Best case | ||

Least impact first | Drop costumers by their impact on grid length. Determine the impact after every exit. | Worst case | |

Highest impact first | Best case | ||

Random selection | Stochastic selection; 100 | Choose customers for exit randomly. | Stochastic selection |

Weighted random selection | Choose customer exits based on a conditional probability calculated by building ages and pseudo random numbers. | Stochastic selection based on building age | |

Radial selection | Choose a random starting point. Drop customers by radial distance to this point. Start with the lowest distance. | Extreme case of a weighted stochastic selection |

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**MDPI and ACS Style**

Then, D.; Spalthoff, C.; Bauer, J.; Kneiske, T.M.; Braun, M.
Impact of Natural Gas Distribution Network Structure and Operator Strategies on Grid Economy in Face of Decreasing Demand. *Energies* **2020**, *13*, 664.
https://doi.org/10.3390/en13030664

**AMA Style**

Then D, Spalthoff C, Bauer J, Kneiske TM, Braun M.
Impact of Natural Gas Distribution Network Structure and Operator Strategies on Grid Economy in Face of Decreasing Demand. *Energies*. 2020; 13(3):664.
https://doi.org/10.3390/en13030664

**Chicago/Turabian Style**

Then, Daniel, Christian Spalthoff, Johannes Bauer, Tanja M. Kneiske, and Martin Braun.
2020. "Impact of Natural Gas Distribution Network Structure and Operator Strategies on Grid Economy in Face of Decreasing Demand" *Energies* 13, no. 3: 664.
https://doi.org/10.3390/en13030664