PV-Wind Hybrid Systems for Swedish Locations

PV-Wind-Hybrid systems for stand-alone applications have the potential to be more cost efficient compared to PV-alone systems. The two energy sources can, to some extent, compensate each others minima. The combination of solar and wind should be especially favorable for locations at high latitudes such as Sweden with a very uneven distribution of solar radiation during the year. In this article PV-Wind-Hybrid systems have been studied for 11 locations in Sweden. These systems supply the household electricity for single family houses. The aim was to evaluate the system costs, the cost of energy generated by the PV-Wind-Hybrid systems, the effect of the load size and to what extent the combination of these two energy sources can reduce the costs compared to a PV-alone system. The study has been performed with the simulation tool HOMER developed by the National Renewable Energy Laboratory (NREL) for techno-economical feasibility studies of hybrid systems. The results from HOMER show that the net present costs (NPC) for a hybrid system designed for an annual load of 6000 kWh with a capacity shortage of 10% will vary between $48,000 and $87,000. Sizing the system for a load of 1800 kWh/year will give a NPC of $17,000 for the best and $33,000 for the worst location. PV-Wind-Hybrid systems are for all locations more cost effective compared to PV-alone systems. Using a Hybrid system is reducing the NPC for Borlänge by 36% and for Lund by 64%. The cost per kWh electricity varies between $1.4 for the worst location and $0.9 for the best location if a PV-Wind-Hybrid system is used.

How do different densities in a network affect the optimal location of service centers?

The p-median problem is often used to locate p service centers by minimizing their distances to a geographically distributed demand (n). The optimal locations are sensitive to geographical context such as road network and demand points especially when they are asymmetrically distributed in the plane. Most studies focus on evaluating performances of the p-median model when p and n vary. To our knowledge this is not a very well-studied problem when the road network is alternated especially when it is applied in a real world context. The aim in this study is to analyze how the optimal location solutions vary, using the p-median model, when the density in the road network is alternated. The investigation is conducted by the means of a case study in a region in Sweden with an asymmetrically distributed population (15,000 weighted demand points), Dalecarlia. To locate 5 to 50 service centers we use the national transport administrations official road network (NVDB). The road network consists of 1.5 million nodes. To find the optimal location we start with 500 candidate nodes in the network and increase the number of candidate nodes in steps up to 67,000. To find the optimal solution we use a simulated annealing algorithm with adaptive tuning of the temperature. The results show that there is a limited improvement in the optimal solutions when nodes in the road network increase and p is low. When p is high the improvements are larger. The results also show that choice of the best network depends on p. The larger p the larger density of the network is needed. 

How does data quality in a network affect heuristic solutions?

To have good data quality with high complexity is often seen to be important. Intuition says that the higher accuracy and complexity the data have the better the analytic solutions becomes if it is possible to handle the increasing computing time. However, for most of the practical computational problems, high complexity data means that computational times become too long or that heuristics used to solve the problem have difficulties to reach good solutions. This is even further stressed when the size of the combinatorial problem increases. Consequently, we often need a simplified data to deal with complex combinatorial problems. In this study we stress the question of how the complexity and accuracy in a network affect the quality of the heuristic solutions for different sizes of the combinatorial problem. We evaluate this question by applying the commonly used p-median model, which is used to find optimal locations in a network of p supply points that serve n demand points. To evaluate this, we vary both the accuracy (the number of nodes) of the network and the size of the combinatorial problem (p). The investigation is conducted by the means of a case study in a region in Sweden with an asymmetrically distributed population (15,000 weighted demand points), Dalecarlia. To locate 5 to 50 supply points we use the national transport administrations official road network (NVDB). The road network consists of 1.5 million nodes. To find the optimal location we start with 500 candidate nodes in the network and increase the number of candidate nodes in steps up to 67,000 (which is aggregated from the 1.5 million nodes). To find the optimal solution we use a simulated annealing algorithm with adaptive tuning of the temperature. The results show that there is a limited improvement in the optimal solutions when the accuracy in the road network increase and the combinatorial problem (low p) is simple. When the combinatorial problem is complex (large p) the improvements of increasing the accuracy in the road network are much larger. The results also show that choice of the best accuracy of the network depends on the complexity of the combinatorial (varying p) problem.