# Multi-Objective Optimisation Based Planning of Power-Line Grid Expansions

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## Abstract

**:**

## 1. Introduction

- development and implementation of a client-server based Pareto-optimisation system for power-line routing,
- design and implementation of an interactive visualisation system for intuitive navigation of Pareto-optimal solutions and support of decision-making.

## 2. Background

#### 2.1. Common Planning Workflow

#### 2.2. State of the Art in Multi-Criteria Spatial Analysis

#### 2.3. State of the Art in Multi-Objective Shortest Path Methods

## 3. Methods

#### 3.1. Overview

#### 3.2. Modelling of Optimisation Criteria

#### 3.3. Building the Grid Graph

#### 3.4. Multi-Objective Optimisation

#### 3.5. Designing an Interactive Visualisation System

## 4. Data

#### 4.1. Study Area

#### 4.2. Criteria

**economic efficiency**(see Figure 5a),

**settlement structures and important land use types**(see Figure 5d) as well as

**nature and environmental protection**, biodiversity and recreation areas (see Figure 5c) and priority areas of

**regional planning regulations**(see Figure 5b).

## 5. Results

#### 5.1. Automated Identification of Power-Line Routes

#### 5.2. Interactive Identification of Power-Line Routes

#### 5.2.1. Scenario 1 “Settlement”

#### 5.2.2. Scenario 2 “Environment”

#### 5.2.3. Scenario 3 “Bundling”

## 6. Discussion and Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Overview of the presented workflow: After a set of suitable criteria for a planned grid expansion is identified by start and end point, the modelling of the study area and optimisation criteria is performed by the implemented ArcMap add-in (client). Processed data is transferred to the optimisation server by means of a RESTful web service. A discrete structure (grid graph) is derived from preprocessed spatial data and the optimisation process is started. After an approximation of the Pareto-front (a set of suitable paths) is calculated, results are transferred back to the client for analysis.

**Figure 2.**Criteria generation with the developed ArcMap Add-In: ⓐ definition of start and end point and study area; ⓑ feature layers from the ArcMap data frame added to the list of criteria; ⓒ classified in an arbitrary amount of criteria categories (groups); ⓓ by defining an priority value for each layer, an inter-group weighting of the criterion is achieved; ⓔ criteria with positive impact are flagged as bundling criteria; ⓕ definition of the length of graph edges in metres; ⓖ visualisation of the criteria layers in the ArcMap map view. Data copyright by GeoBasis-DE/BKG 2017.

**Figure 3.**Creation of the grid graph: (

**a**) spatial data is preprocessed using GIS; (

**b**) objective function is modelled (visualisation of three exemplary weight layers) and (

**c**) view of the resulting graph structure. Colour mapping from high values (red) to low values (green) is used.

**Figure 4.**Interactive Visualisation System: (

**a**,

**c**): spider-plot as a graphical control element to support navigation through the set of Pareto-optimal solutions. Criteria are classified into groups (visualised by different colours of sliders and labels). The blue polygon outlines the current slider positions and thus restrictions in the accompanying solution space dimension. The magenta coloured inner polygon shows the minimum possible values for each criterion induced by the current constraints. In the centred circular area of the widget, the current length restriction of the highlighted criterion is shown (in map units, here metre). (

**b**,

**d**): resulting paths for different solution space restrictions are visualised in GIS.

**Figure 5.**Criteria used to model the impact of power-line routings in the study area. Criteria are categorised into four categories of protective goods. Data copyright by GeoBasis-DE/BKG 2017. (

**a**) 200 $\mathrm{m}$ buffers of linear infrastructures (positive impact); (

**b**) Regional Planning Regulations (negative impact); (

**c**) Nature and Environmental Protection areas (negative impact); (

**d**) Settlement Structures and Urban Land Use (negative impact).

**Figure 6.**(

**a**) overview of the resulting 4667 Pareto-optimal paths; (

**b**) statistically identified paths of interest. Visualisation of the paths minimising each of the five criteria. The path with minimal length is also the path with minimal crossing of priority areas (regional planning regulations). The Nearest-To-Ideal classified path is the one with minimum Euclidean distance to the approximation of the ideal point (see Section 3.4). Data copyright by GeoBasis-DE/BKG 2017.

**Figure 7.**Crossing length for the identified alternatives (cf. Figure 9). Criteria with zero crossings were omitted. (

**a**) scenario 1 “Settlement” with Alternatives A, B, C; (

**b**) scenario 2 “Environment” with Alternatives D, E, F; (c) scenario 3 “Bundling” with Alternatives G, H, I.

**Figure 8.**Using the interactive visualisation tool to set constraints on the approximation of the Pareto-front: (

**a**) Minimum Settlement Impact Constraints: Maximum crossing length for mining sites, waste deposition sites, cemeteries and sensitive structures are set to zero. Maximum crossing length of urban settlement buffers is restricted to 1.8 km; (

**b**) Minimum Nature and Environmental Impact Constraints: Crossing of habitats directive areas, water bodies greater than 10 ha, protected biotopes and wildlife areas are constrained to zero. The impact on forests is limited to crossing length below 500 m and crossing length with land conservation areas is limited to 8 km.

**Figure 9.**Visualisation of exemplary results from interaction with the approximated Pareto-front. Data copyright by GeoBasis-DE/BKG 2017.

**Table 1.**Evaluated criteria for finding optimised transmission line routes and their impact classes.

Category | ID | Description | Impact Class |
---|---|---|---|

bundling with linear infrastructure (+ 200 $\mathrm{m}$ buffer) | ${o}_{1}$ ${o}_{2}$ ${o}_{3}$ | concentration along existing power-lines concentration along motorways concentration along main roads | high moderate low |

regional planning regulations | ${o}_{4}$ ${o}_{5}$ ${o}_{6}$ ${o}_{7}$ ${o}_{8}$ | priority areas for urban development priority areas for farming priority areas for forestry priority areas for industrial development priority areas for surface water bodies | lowest lowest lowest lowest lowest |

nature and environmental protection | ${o}_{9}$ ${o}_{10}$ ${o}_{11}$ ${o}_{12}$ ${o}_{13}$ ${o}_{14}$ ${o}_{15}$ ${o}_{16}$ ${o}_{17}$ | habitats directive areas nature conservation areas protected wildlife areas protected biotopes forests water bodies > 10 $\mathrm{h}\mathrm{a}$ landscape conservation areas natural parks biotope networks | high moderate moderate low low low lowest lowest lowest |

settlement structures and urban land use | ${o}_{18}$ ${o}_{19}$ ${o}_{20}$ ${o}_{21}$ ${o}_{22}$ ${o}_{23}$ ${o}_{24}$ | urban settlement areas + 400 $\mathrm{m}$ buffer rural settlement areas + 200 $\mathrm{m}$ buffer sensitive structures (e.g., hospitals) cemeteries industrial sites waste deposition sites mining sites | high high moderate moderate moderate moderate moderate |

length | ${o}_{25}$ | length | high |

**Table 2.**Overview of the resulting cost values for the 4667 Pareto-optimal solutions. Groups ${g}_{1},\cdots ,{g}_{4}$ are weighted sums of the criteria depicted in Table 1. ${g}_{5}$ represents the lengths of the paths and thus equals ${o}_{25}$ (see Table 3). Note: ${g}_{1}$ is a bundling criterion and thus represents the accumulated lengths along which no linear infrastructure corridors are crossed.

${\mathit{g}}_{1}$ | ${\mathit{g}}_{2}$ | ${\mathit{g}}_{3}$ | ${\mathit{g}}_{4}$ | ${\mathit{g}}_{5}$ | |
---|---|---|---|---|---|

mean | 262,215.54 | 135,263.14 | 94,531.76 | 94,083.08 | 27,052.36 |

std | 40,486.08 | 8393.63 | 27,074.91 | 38,241.67 | 1678.49 |

min | 176,490.00 | 118,364.00 | 34,113.70 | 25,723.70 | 23,672.79 |

25% | 232,537.00 | 129,646.00 | 74,141.05 | 64,968.20 | 25,929.22 |

50% | 265,687.00 | 133,836.00 | 94,012.90 | 87,675.10 | 26,767.26 |

75% | 289,193.50 | 139,407.00 | 112,216.50 | 115,919.00 | 27,881.48 |

max | 367,991.00 | 180,637.00 | 192,218.00 | 247,791.00 | 36,127.42 |

**Table 3.**Overview of the resulting crossing lengths for the 4667 Pareto-optimal solutions (corresponding to 12 of the 25 criteria). All values are in metres. Note: ${o}_{1}$ is a bundling criterion and thus represents the length along which no linear infrastructure corridors (existing power-lines) are crossed.

${\mathit{o}}_{1}$ | ${\mathit{o}}_{9}$ | ${\mathit{o}}_{10}$ | ${\mathit{o}}_{12}$ | ${\mathit{o}}_{13}$ | ${\mathit{o}}_{15}$ | ${\mathit{o}}_{17}$ | ${\mathit{o}}_{18}$ | ${\mathit{o}}_{19}$ | ${\mathit{o}}_{20}$ | ${\mathit{o}}_{22}$ | ${\mathit{o}}_{25}$ | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

mean | 16,400.10 | 650.24 | 814.71 | 259.98 | 2861.54 | 19,135.67 | 7663.80 | 6760.39 | 11,519.39 | 35.15 | 670.53 | 27,052.36 |

std | 6928.15 | 934.87 | 867.86 | 230.42 | 2288.32 | 3369.19 | 3384.64 | 5043.95 | 3071.71 | 58.76 | 471.50 | 1678.49 |

min | 77.25 | 0.00 | 0.00 | 0.00 | 91.75 | 5920.21 | 1068.14 | 736.38 | 4180.24 | 0.00 | 67.17 | 23,672.79 |

25% | 11,851.90 | 0.00 | 243.48 | 75.00 | 1011.57 | 17,226.39 | 4858.99 | 3311.09 | 9263.85 | 0.00 | 244.71 | 25,929.22 |

50% | 17,725.41 | 250.00 | 565.56 | 187.07 | 2348.32 | 19,533.72 | 7667.46 | 5398.64 | 11,302.53 | 14.14 | 723.30 | 26,767.26 |

75% | 21,447.03 | 730.42 | 1058.01 | 396.75 | 3932.75 | 21,431.00 | 10,167.91 | 8057.41 | 13,985.11 | 28.28 | 883.42 | 27,881.48 |

max | 30,281.46 | 5652.94 | 6022.24 | 1279.33 | 11,141.00 | 27,013.01 | 16,518.35 | 28,585.28 | 19,947.25 | 316.92 | 4283.53 | 36,127.42 |

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## Share and Cite

**MDPI and ACS Style**

Bachmann, D.; Bökler, F.; Kopec, J.; Popp, K.; Schwarze, B.; Weichert, F.
Multi-Objective Optimisation Based Planning of Power-Line Grid Expansions. *ISPRS Int. J. Geo-Inf.* **2018**, *7*, 258.
https://doi.org/10.3390/ijgi7070258

**AMA Style**

Bachmann D, Bökler F, Kopec J, Popp K, Schwarze B, Weichert F.
Multi-Objective Optimisation Based Planning of Power-Line Grid Expansions. *ISPRS International Journal of Geo-Information*. 2018; 7(7):258.
https://doi.org/10.3390/ijgi7070258

**Chicago/Turabian Style**

Bachmann, Daniel, Fritz Bökler, Jakob Kopec, Kira Popp, Björn Schwarze, and Frank Weichert.
2018. "Multi-Objective Optimisation Based Planning of Power-Line Grid Expansions" *ISPRS International Journal of Geo-Information* 7, no. 7: 258.
https://doi.org/10.3390/ijgi7070258