Measuring the Spatial Error in Load Forecasting for Electrical Distribution Planning as a Problem of Transporting the Surplus to the In-Deficit Locations

While there are many functions defined in the literature to measure the error magnitude (how much), the problem of dinning the spatial error (where) is not so well defined. For instance, in a given region it is expected a global growth in the electrical demand of 10MW. For the electrical system planning not only the amount but also the location must be considered. Predicting a growth of 10MW (how much) in the south (where) of a city would lead to complete different polices in terms of resources allocation (for instance a new substation) than predicting the same amount of 10MW in the north. Trying to cope with this difficulty, this paper proposes the concept of spatial error as the cost of transporting the surplus of one region to compensate another region deceit. This conceptual problem was written as an optimization transportation problem. This paper describes conceptually the difference between magnitude and spatial error measures and shows an algorithm to deal efficiently with the defined framework.