Modeling and optimizing transmission lines with GIS and Multi-Criteria Decision Analysis

Abstract In planning transmission lines with the use of Geographic Information Systems, the use of the Least Cost Path (LCP) algorithm has been established while relevant criteria are modeled using Multi-Criteria Decision Analysis (MCDA). Despite their established use, this combination (MCDA/LCP) often leads to results that do not correspond to realistic conditions. Therefore, the MCDA/LCP computation must usually be optimized on an algorithmic level as well as on the decision model and the underlying data relevant for the MCDA. The current paper presents the state-of-the-art of an ongoing research project that aims to solve these issues. First results are promising since a stable algorithm has been developed that computes a cost surface, a Least Cost Corridor (LCC), a LCP, and the transmission towers' positions by simple additive weighting based on user's weights. Optimizations on the MCDA models have already been implemented and tested. The findings are integrated into a 3D Decision Support System which aims at facilitating the work of TL planners by realistic modeling and by reducing the approval process for new TL.


Introduction
Nowadays, Europe's power grid operators are confronted with big challenges concerning the planning of future transmission lines (TL).The reasons for these challenges are manifold: Europe's population has been growing for decades, and per capita consumption of energy is still rising; thus, more energy must be transmitted.Therefore, ex-isting 230 kV grids are going to be replaced by 400 kV TL to transmit more power than in the past.However, TL planners are confronted with stricter legal regulations than in the past [1] and a growing residents' opposition because the planning of TL has usually not been a democratic issue [2].Moreover, renewable power plants are normally planned in remote areas which must be connected to the existing grid.All these issues require planning solutions that consider high transmission efficiency beside legal, economic, ecological, and social impact factors.
Geographic Information Science [3] supports the TL planning process by using well-established algorithms to compute an ideal Least Cost Path (LCP) or by acting as a Decision Support System (DSS) to assist stakeholders in finding a decision for a given problem.Such a DSS interactively computes a result and visualizes it in 3D, which is more accessible than drawing plans and modeling paths by hand.Because transmission line planning has typically not been participatory, a DSS could foster transparency by visualizing the impact of transmission towers on a landscape and giving affected residents the chance to discuss their concerns within a group of different stakeholders.Thus, Geographic Information Science may offer solutions to develop a DSS aiming at supporting the planning process by integrating computation, visualization and communication in one system.
To date, a combination of two methods to compute ideal TL has been widely used in Geographic Information Science: Multi-Criteria Decision Analysis (MCDA) and Least Cost Path (LCP).MCDA mathematically determines the most appropriate decision for a problem based on the analysis and weighting of multiple criteria [4].The weighting and decision rules of an MCDA can further be applied within Geographic Information Systems (GIS) on differently weighted, spatially explicit factors in order to compute a cost surface-a surface describing how expensive (in terms of costs or friction) it is to pass every cell [5].With these known costs to pass the cells, the LCP algorithm determines the LCP between two given points, which means that every path deviating from the LCP causes higher costs.However, the LCP should not be seen as the one and only, incontrovertible solution because the optimal path in TL planning arises from the comparison of different alternatives-ideally in accordance among different stake-holders [6].Thus, different alternative paths with similar costs are commonly expected to be found in nearby areas of the LCP.By defining an amount of additional cost that can be taken into consideration for deviating from the LCP, GIS are able to determine the Least Cost Corridor (LCC).This LCC describes a corridor in which different paths have comparable costs that are defined within a given cost range.Therefore, TL planners use the LCC as a basis for discussion in order to find a consistent solution within a set of alternatives.
The combination of MCDA and LCP for finding the optimal TL has been established also because of the compatibility with raster-based data, which are commonly used in GIS.One of the reasons for this establishment is simple additive weighting [7]-a method developed to calculate the weighted sum of different criteria and easily implemented in GIS with map algebra [8].In contrast, vector-based approaches [9], [10] could not assist in the planning of TL because they mainly aim at avoiding obstacles and finding the shortest Euclidean path while neglecting different costs per area.Furthermore, the raster-based approach and the LCP algorithm have been established despite some disadvantages described in the literature [11][12][13].One of the most important ones is that the result of the LCP analysis must be optimized in almost every case in order to fit practical requirements.Thus, post hoc optimization is an indispensable part of applying the combined MCDA/LCP approach for the planning of TL.From this problem, the question arises: how should a DSS including the MCDA/LCP chain as well as post-hoc optimization be built in order to compute a practicable result for TL planners?The answer to this question complies with the scope of the presented research project "Application of 3D Geographic Information Systems for transparent and sustainable planning of electric power systems", conducted at ETH Zurich, Switzerland, in collaboration with three grid operators.It began in October 2014 with a term of three years.

Motivation
Despite the wide acceptance, the combined MCDA/LCP approach must be treated with caution in TL planning.A thorough literature review revealed that both methods come with some limitations that can negatively affect the outcome of the TL siting.From these limitations, we identified two research gaps that will be explained in the following paragraphs in detail.
First, LCP provides solutions that often do not correspond to the best application in reality.For example, a resulting LCP usually includes too many bends and thus must be straightened.Furthermore, the proposed nodes-which correspond to the positions of transmission towers-do not consider legal and technical requirements regarding the topography.They must be spotted so that the transmission towers withstand the cables' weight and that the sag complies with legal regulations.Thus, the optimal application in reality is to plan the TL as straight as possible by identifying and circumventing avoidance areas where required and by taking the topography into account when setting the nodes.This can be done with two methods: On the one hand, rules could be defined that reduce the number of feasible alternatives while building the network graph.These rules could, for example, punish an angular deviation or allow nodes to be set only within a given distance range [14] and in accordance to the local topography between two nodes.On the other hand, post-hoc optimization methods could be applied to obtain the best solution in reality.Even if many optimization approaches have been presented in recent years [11][12][13]15], they mainly focused on solving isolated problems by the use of low-complexity, non-realistic models.Thus, studies are lacking in evaluating LCP optimization approaches based on realistic models.Therefore, there is still potential to develop new approaches that model a TL corridor more realistically than existing approaches do.
The second gap is that existing approaches do not explicitly focus on improving the MCDA model.Since MCDA is not an explicit technique, but a collection of techniques to weight and process different factors according to an evaluation system, it is unclear which method model costs best for determining a TL.For example, a cost surface built by using simple additive weighting might vary from another that is built by extracting the factors' maximum friction values.By applying both models to a bird protection area that is partly located within a marshland, the former model results in higher friction values because overlapping is considered, whereas the latter model chooses the maximum friction without considering overlapping.However, the high friction resulting from spatially overlapping factors might be overvalued compared to the effective degree of protection.As a solution, multiple assessments can be considered-as suggested e.g., by Eisenführ et al. [6]-but by reducing their effect the more factors overlap.Another example integrates spatial autocorrelation [16]-a theory describing that spatial phenomena are often not sharp-edged, but continuous-into the MCDA model.In this way, the extents of protected areas are enlarged across their borders depending of their degree of protection.Since the theory of spatial autocorrelation assumes that the friction decreases with increasing dis-tance to the core of the protection area, different gradients (whether the friction decreases linearly, logarithmically, or exponentially), might produce different cost surfaces.Since the notions presented can widely be combined with each other, various MCDA models can be built which might compute different cost surfaces, thus different corridor and path patterns while using the same weight.How far the resulting corridor and path patterns correlate to each other and which MCDA models contribute the most to a realistic solution, is thus open to further investigation.

Research questions
The answering of two main questions will allow the development of an integrated GIS-based data procedure workflow to compute results that can be used in practice: 1.How can a data processing chain including path optimization be built to compute a result that TL planners can use in their daily work? 2. Which decision rules should an MCDA model follow to compute a result that TL planners can use in their daily work?

Related work
The combined use of MCDA and LCP is well-established in the TL planning process even though the number of studies conducted is limited.Two important studies are EPRI-GTC [17] and OPTIPOL [18].On the one hand, the EPRI-GTC project was conducted in Georgia, USA and aimed at developing a hands-on approach to compute the most optimal path and corridor of a TL.The authors used a funnel approach to determine consecutively a macro corridor, alternative corridors, alternative routes and last, the optimal path.The authors applied a two-step approach using MCDA to derive a resulting cost surface.First, they built four cost surfaces by using different weightings on three factors in the MCDA: built environment, natural environment, and engineering environment.Next, they added them to get a resulting cost surface.Additionally, the authors conducted sensitivity analyses to investigate the effects of different weights.The knowledge gained through EPRI-GTC was important for the conduction of further studies [19].On the other hand, the OPTIPOL project was conducted in Norway and aimed at determining an optimal design and routing of TL concerning ecological, social, technical, and economical perspectives.The authors recognized that the choice of the MCDA weightings should be reflective, transparent, and participatory.They devel-oped a method that preferred bundling with existing linear infrastructure.Furthermore, they investigated the modeling of the visibility of a TL by taking into consideration the height of a mountain ridge.In contrast to this approach, Grassi et al. [20] discretized the exponential proximity function to calculate weights for the visual impact on buildings.
The weighting of the influencing factors is a crucial part of the model building.For land suitability analysis, this is typically done by using MCDA [21,22].Whereas some researchers determined the weightings through a Delphi process combined with the Analytical Hierarchical Process conducted with experts [17,18], other researchers took weightings given by experts [20,[23][24][25].The factors mostly considered in the MCDA are the TL's visibility, including proximity to buildings [20,26], additional landscape and natural protection [25,27], engineering limitations, and economical costs [17,18].
Sensitivity analysis is an important method to investigate the effect and the robustness of an MCDA model.Bagli et al. [25] investigated the effect of varying one specific parameter in a sensitivity analysis.They found significant differences in the path obtained by slightly varying the start and end point.Thus, the cost surface changed, leading to different paths.The sensitivity analysis for twenty different category weightings did not lead to significant differences in the paths and thus substantiated the model's robustness.Robustness while using MCDA and GIS has been a significant research topic during the last years.In general, a robust MCDA model provides valuable results based on different weights [28].To evaluate the impact of these weights, uncertainty and sensitivity techniques are combined to determine which criteria contributed significantly to the result.Feizizadeh and Blaschke [29] investigated the landslide susceptibility by first conducting a sensitivity analysis to simulate the error propagation based on a Monte-Carlo simulation.Then, they produced land susceptibility maps by using the resulting weight probability density functions and three different MCDA methods.In contrast, Ligmann-Zielinska and Jankowski [22] first created a suitability and an uncertainty map with all possible weight combinations to determine the optimal habitat for a plant to grow, since this area was most robust against all possible criteria weights.Then, they conducted a sensitivity analysis to determine the criteria that contributed significantly to the result.
Another study that aimed at similar research questions as the current project is SYNOPTRA [14].The author developed a 3D visualization tool that computed the optimal path for an overhead TL by considering the visibility, the costs, and the chance to be approved by authorities.
Therefore, he compared an evolutionary algorithm, Simulated Annealing, and Dijkstra's algorithm with each other while optimizing the functions to a number of considered factors.The author suggested to use a distance range for placing the transmission towers and to punish angular deviations from a target azimuth.As a result, the evolutionary algorithm was fastest in computing practical solutions, even if the results were computed probabilistically compared to the other deterministic algorithms.
Other research focused on the investigation of the LCP algorithm's characteristics [11,13] by offering solutions to optimize a cost surface and its resulting LCP.Expanding the lattice in order to find cheaper connections between remote pixels while causing a higher computational effort has also been a discussion point [10][11][12]15], from which only Collischonn and Pilar [15] implemented a hands-on solution.
Some research projects aimed at lowering the computational effort by using a vector-based solution to solve the shortest path problem instead of raster-based LCP algorithms [9,10].Medrano and Church [9] compared different pathfinding algorithms that were used to build not one, but k-shortest cost paths.In contrast, Hong [10] improved the convexpath algorithm by reducing the number of vertices that come into question while solving the shortest path problem.He compared the computing times of his vector-based convexpath algorithm with those of an approximated raster-based LCP version and noticed that the computing time is much lower using vector-based solutions.
Last, an approach for the calculation of monetary costs for a TL has been presented in the EPRI-GTC project [17] and in SYNOPTRA [14] whereas Yildirim and Nisanci [24] implemented the estimation of the land affected by the construction of the TL.Furthermore, Seifi and Sepasian [30] explained how the costs for a power grid are calculated in detail.Yu et al. [31] indicated to pay attention when calculating monetary costs by means of LCP because of the complexity and nonlinearity of influencing factors.

Methodology
The numbering of the applied methodology refers to the research questions listed in Section 2. The following two subsections explain the applied methodology in detail.

Research Question 1: creating an MCDA-based DSS practicable for TL planning
Since the combined use of MCDA and LCP has been established, both concepts are first investigated by literature research and then compared to other studies of related research fields.In accordance with TL planning experts, different TL computation models are then conceptualized and implemented by a customized GIS-based function to calculate a cost surface, the LCC, the LCP, and the transmission tower positions (see Figure 1).The DSS is configured in order to allow a user to apply simple additive weighting.Therefore, at least an influencing factor's cell friction and its weight must be modifiable.Then, the effects of the different TL computation models are investigated through uncertainty and sensitivity analysis.

Research Question 2: finding the most effective MCDA model for TL planning
First, the needed geodata are defined according to official guidelines [32], which comprise social, economic, environmental, and technical aspects.These geodata are then acquired and assessed with regard to their quality and to thematic overlapping.Since it must be expected that some datasets are redundant, a strategy to handle redundancy must be defined.Then, different MCDA models are built according to the notions listed in the motivation section (see above).Since it is expected that some of them yield similar cost surfaces, correlation and cluster analysis is conducted to determine 3 to 4 principally different approaches.These MCDA models including relevant attributes, and threshold values are then defined and implemented in the DSS in cooperation with the collaborating grid operators.TL planning experts then evaluate different MCDA models with regard to practical usability concerning the data categorization and weighting constraints.Their answers are statistically evaluated in order to improve the MCDA model.After having developed the DSS according to the requirements of research question 1, another function computes different alternative paths by varying the weights in order to determine the LCC, the LCP, and other threshold values probabilistically.Sensitivity analyses are then conducted to optimize the MCDA model regarding robustness and significance.

Validation
Last, TL planning experts test the efficiency of the developed approaches in three case studies conducted in cooperation with the collaborating grid operators.They are asked to complete a questionnaire and to provide quan-titative and qualitative feedback regarding the practical usability of the developed approach.Their answers will be statistically evaluated in order to validate and improve the developed approaches.The results will be compared with a statistical cross-validation between the developed TL computation models.

First results
Although the developed approach has not been validated so far, first results are promising.Procedures relevant for future studies could be conceptualized and implemented.The following subsections refer to the results obtained by answering the research Questions 1 and 2.

Research Question 1: Cost surface computation by MCDA
The current MCDA/LCP data procedure workflow reliably computes a cost surface according to the user's weightings and the geodata used.The computation of 28 307 pixels (see Figure 1; approximately 17 × 18 km of extension with a cell size of 100 m) times 19 influencing factors took 14 seconds (on an Intel i7 CPU with 8 cores @ 2.80 GHz and 16 GB RAM).The reason for this comparably low computational time lies in the data model since time-consuming pre-processing functions have been applied and stored in advance.

Research Question 1: Computation of LCP, LCC, and transmission towers' positions
Apart from the cost surface, the current MCDA/LCP implementation allows for the identification of the LCC, of a simplified LCP, and of the transmission towers' positions.These three results are explained in the following paragraphs more in detail.
The LCP of the current version is computed by the LCP algorithm using an 8 × 8 lattice.The resulting path must be smoothed because it usually is too curvy and thus does not represent a realistic TL path.Even if Berry [13] rejected cartographic smoothing on a LCP, it has nevertheless been applied because the typical shape characteristics are maintained.Furthermore, it produces straightened segments that are realistic to build in reality and it requires less computational time than altering the cost surface in order to straighten the path.However, the binding on the 8 × 8 lattice is constraining since cheaper solutions with remote pixels are neglected which might result in straighter paths.Thus, the approach to build a network graph within a distance range and to punish angular deviations from the ideal azimuth [14] is promising and will be taken into consideration in a future version.
The LCC is derived from the LCP by taking into consideration nearby pixels of the LCP and, thus, higher costs compared to the LCP.The higher the additional costs that a user wants to take into consideration, the larger the LCC becomes.A user is thus allowed to define the maximum costs to regulate the LCC's extension.He can do this by defining how many standard deviations of the current cost surface values should be taken into account.First investigations revealed that the number of pixels as well as the LCC's shape vary depending on the user's preferences.It is thus a matter of further research to investigate a robust method to determine the LCC based on a user's setting.
The transmission towers' positions correspond to the vertices of the smoothened LCP (see Figure 1).In the current version, missing intermediate points are interpolated according to a pre-defined maximum spanning distance between two transmission towers.However, topographic constraints are not yet considered.Thus, we plan to implement an approach that builds a network graph between feasible points by considering the topography as well as the sag.

Research Question 2: Expert assessment about MCDA models that comprise fuzzy buffers
For humans, the visual impact of transmission towers varies with distance: the closer a transmission tower is to an observer, the higher the degree of perceived disturbance [26].We thus wondered how this effect can be reversed and applied to protection areas.In our model, we assume that every area emits a friction against the construction of a TL.This friction is high in areas worth protecting, and low in areas suitable for TL siting.We further assume that areas with a high protective effect radiate a decreasing friction beyond their borders.The higher the protective effect is, the larger the radiance radius becomes.We call this the buffering effect.
Thus, we wondered, how TL planning experts would assess our model quantitatively and qualitatively.For this, 10 TL planning experts were asked to assess the factors relevant for the MCDA and to fill in a questionnaire.This was done in order to find out which influencing factors should be assessed with an additional buffer area around the given borders, how large it should be and whether the friction should decrease linearly, logarithmically, or exponentially with increasing distance to the borders.
First, the suggested MCDA method considering the buffering effect received positive feedback since perception is continuous and not bound on sharp-edged borders.The evaluation of the questionnaires indicated that assessing the sensitive areas is subjective, therefore results were heterogeneous.No tendency could be determined whether the decrease should be consequently modeled linearly, logarithmically, or exponentially.However, experts assessed the buffering distances-depending on the influencing factor-in a similar range.Large buffer radii (around 500-1500 m) have been chosen for factors regarding the protection of sensitive landscapes and of local recreation areas.Medium buffer radii (100-300 m) have been chosen for factors regarding environmental protection.Low buffer radii (0-20 m) have been chosen for factors regarding linear infrastructure, which endorses the aim of bundling TL with existing linear infrastructure.

Research Question 2: How spatial autocorrelation is implemented into the MCDA model
According to the concept of spatial autocorrelation [16], borders of areas in which the construction of TL should be avoided are rather fuzzy than sharp.A friction is thus not limited to borders.Instead, it radiates beyond the borders but decreases in intensity with increasing distance.This approach can be used for areas as well as for lines or points.It prevents the LCP algorithm from computing paths which undesirably follow sharp borders, called proximity effect [11].In other words: The more sensitive an area is, the higher the distance to a TL is expected to be.Thus, buffers around sensitive areas suppress the possibly occurring proximity effect.
We decided to build, on the one hand, sharp-edged MCDA models and, on the other hand, MCDA models with buffers.Since for the application of a buffer also its radius and the shape for the decrease function have to be defined, we subdivided buffered models using a 3 × 3 matrix.
One dimension of the matrix consists of the three levels "low radius", "medium radius", and "large radius", which are derived from the lower, medium, and upper quartile of the expert assessment about MCDA models we conducted in advance.These values were rounded up to the next 100 meters since the cell size corresponds to 100 meters.
The second dimension of the matrix consists of the tree levels "linear decrease", "logarithmic decrease", and "exponential decrease" with increasing distance.Every level of each dimension can thus be combined with each other, resulting in 9 different combinations.
We further distinguished between three different decision models how values of different influencing factors should be processed to a cost surface.First, the easiest method is to use simple additive weighting, which builds the cost surface from the weighted sum of all factors.Second, the cost surface can be built by choosing per pixel the maximum value of all influencing factors.Third, simple additive weighting can be lowered by integrating a punishment for overlapping, thus redundant pixels.These three decision models can now be combined with the 9 combinations from the 3 × 3 matrix described above, leading to 27 MCDA models with and 3 MCDA models without buffering.
We conducted an experiment with 6 different MCDA models, but constant weightings.Then, we compared the resulting corridors by eye and noticed similarities between some MCDA models.For example, Figure 2 shows a LCC resulting from overlaying the LCPs' corresponding LCCs.Because the LCCs indeed looked very similar, we intend to investigate the effects of the different MCDA models in more detail.Thus, we plan to conduct correlation and cluster analysis in the near future while varying the weightings and the study area.
Another experiment in a different study area focused on the distinction between using a buffer or not.In this case, the buffer radius linearly increased with increasing friction.Furthermore, we built the cost surface by choosing the maximum value.The test revealed that applying buffering before conducting the combined MCDA/LCP approach leads to a different result than by conduct- ing MCDA/LCP without buffering.Figure 3 illustrates this statement since the paths computed by the unbuffered (left) and the buffered (right) cost surface differ substantially from each other.Furthermore, time can be saved by pre-calculating every possible buffering value with the given buffering distance in advance. .Right: Gradually decreasing buffers were applied on the cost surface with increasing radii the higher the cell friction was.Note that the LCP (green line) shifted westwards and passes through more lakes than on the original cost surface.

Research Question 2: Computing the LCC probabilistically
The LCP is usually derived from the LCC by using Houston and Johnson's funnel approach [17].However, the LCC could also be determined probabilistically by applying a probability function on known LCPs.By keeping the weightings and thus, the scenario constant, the LCPs can be generated by varying the MCDA model.
As Figure 4 shows, six different MCDA models have been used to compute six LCPs.Then, the LCC has been determined by applying a kernel density estimation.The current results show that determining the LCC in this way depends on the weightings of the underlying LCPs and on the number of trajectories that pass through a specific area.We assessed this method to be promising; thus, we will focus in the near future on how it can be combined with a k-least cost path algorithm in order to determine the LCC.

Conclusion and outlook
The current research project investigates methods regarding how the results occurring in the planning of TL can be optimized.Since many approaches have neither been implemented nor evaluated so far, there is still potential for investigating the effects of various optimization methods.First results are promising since a stable program has been developed that integrates multi criteria weighting while considering expert knowledge and decision rules used in urban planning.However, further research is needed to implement novel optimization approaches and more realistic cost estimation functions in order to get results that can be used in practice.Future work will mainly include the conduction and evaluation of sensitivity analyses and of (geo)statistical analyses in order to make the developed approach feasible for practical use in the planning of TL.

Figure 1 :
Figure 1: Four overlaying layers of an MCDA/LCP output.First, the cost surface was calculated (greyscale map; black = low costs) from which the LCC was derived (purple area).Then, the LCP (cyan line) was optimized.Last, the transmission towers' positions (orange points) were derived from the LCP and interpolated if needed.

Figure 3 :
Figure3: Left: Original cost surface plus its LCP (green line).Right: Gradually decreasing buffers were applied on the cost surface with increasing radii the higher the cell friction was.Note that the LCP (green line) shifted westwards and passes through more lakes than on the original cost surface.

Figure 4 :
Figure 4: Different MCDA models result in different LCPs, from which the corridor can be derived by a probabilistic function (Kernel Density Estimation).