Spatial electric load forecasting

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The information used in this work is readily available in most of the electric utilities around the world, allowing fast implementation. To allocate the future loads inside the service area, it is necessary to consider several factors; for example, a pollutant industry cannot be allocated near residential zones; residential consumers like to live near other residential zones, but not too far away from commercial zones and not too distant from their workplaces and so on.

These preferences are sensitive to location and culture; hence, they are specific for each city. If static rules were adopted, it will be necessary to change them for each study. Some of these new consumers will be allocated in already populated zones having further growth opportunities, while others will be allocated in new zones that will be populated in the midterm with new infrastructure.

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The local authorities have made a series of studies related with the city growth; unfortunately, this information is not reliable because of its political dependence. Hence, future growth studies should use this information only as an indicator, not as a rule. One of the tools used to decide which new zones will be populated in the mid- and long-term in the service area was the classification rules, discussed first in Chow et alii , , and broadly used in different algorithms since then.

In Miranda, Monteiro, , classification rules were introduced to this problem to determine a land use score; these rules can be expressed as:. Here, Object refers to a set of elements of interest to be considered in the process, like structures schools, roads, highways, activity center , nearby zones, or other elements of interest. Attribute refers to the measure of the relations between the different zones and the elements. If one element is distance to a road , the rules are expressed by near, close, away, faraway.

For an element of residential electrical density , the rules are expressed in low, normal , and high. Each Attribute corresponds to a finite and exclusive set in the domain of the corresponding object. For example: All the distances from 0 km to 1km inclusive to a school is considered near; All the distances between 1. The range of values for each attribute are selected based on an statistical analyses of all the data for each object. For each object , customers have different preferences, and that is why a different set of attributes exist for each one, for example, the attribute near does not have the same meaning for a school or for the activity center of the city.

To extract and use the knowledge from the spatial database, it is necessary to set up an acceptable coding to efficiently store the information gathered during the process. The classification rules Input and Output are coded as a vector, where each position represents an element of interest, and the value stored represents a linguistic expression suiting to the specific object.

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All the elements are related with the AND operator. Thus, a vector containing linguistic expressions for a set of objects represents a rule. This rule can be represented as L, N, The input and output objects are not fixed and can comprise any combination of objects, so long as a linguistic definition set for them exists. To characterize the service territory, it is necessary to find out the classification rules that will allow us to settle the future land use preferences. These rules and the defining sets could be determined manually by the planner using rules supported by common sense and practice, however, these rules could work well for one specific city based on the expertise and the knowledge of the planner.

The differences between cities around the world demonstrate the need to settle a different set of rules for each one. The method in this paper presents a systematic way to extract a set of rules automatically for each city.

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Using the information available from the spatial database, it is possible to create a database of known rules that can be later used to settle the preferences for future areas, considering that the growth of the city is a stationary stochastic process. The procedure for creating such database is as follows:. Being R 1 the set of rules for the populated areas with known output,.

In the spatial database, identify all the elements of interest Input , like activity centers, schools, major highways and roads, parks, among others;. Establish the linguistic expression for each element of interest;. Calculate the linguistic expressions for each element of interest, considering the relation of the subarea with the elements of interest and their surroundings, form the linguistic rule and store it in R1.

With this algorithm all the knowledge present in the populated area is extracted and processed. In some knowledge-extracting algorithms, the known rules will be mixed using different evolutionary operators to create new rules Yi-Chung et alii , This approach is not used because most of the rules created will be useless; instead, each unpopulated area is analyzed to find out its output, by optimizing resources and minimizing computational time.

To compare how similar two rules are, the Hamming distance is used. The Similarity SM 1 is defined as the Hamming distance between two rules, that is, the number of positions where the corresponding values of the rule A are different than the ones in rule B Hamming, One way to deal with the rules for the unpopulated area will be to build the input part of the linguistic classification rules and settle the output according to the same part of the rule with the highest SM value among all the rules in R 1.

Calculate the SM value between the rule in analysis and all the elements in R 1;. Assign to the output part of the classification rule in analysis, the output of the rule in R 1 with the highest SM. In this manner, however, the randomness of the behavior for this particular problem is lost. Besides, owing to the nature of the distribution of the unpopulated areas generally outside the service area , the SM value could be low and not significant enough to assign a logical output.

Another problem arises when several rules with the same input part have different outputs; hence, it is not possible to choose one instead of another only with this information. To overcome these problems, an evolutionary approach is proposed by selecting the output part of the classification rule with more than one source of similar rules. The output part of the classification rule is determined by selecting out a set of similar rules RSM , sorting it using the SM value for each one as the fitness function, and applying a uniform crossover between two candidates selected by a tournament.

In this way, the output parts of the rules are chosen using the characteristic of this genetic operator as controlled randomness and statistical survival of the fittest. In a tournament selection, two or more solutions are picked at random and a tournament strategy is used to select one after a number of rounds are played. In each round, a number of solutions come together to compete, and only the fittest solution will win and be selected Chambers, For this particular application, two rounds are played, each one with two solutions randomly picked using the SM value as the fitness function.

The crossover operator is one of the most important operators in genetic algorithm. This operator is the one in charge of propagating the genetic information of two elements of the current population to the next, by combining their genetic code to generate a descendant. The complete process is detailed in the following algorithm:.

Calculate the SM value between the rule and all the elements in R 1;. Select two candidates to be crossed over using tournament selection;. Crossover the output part of the two candidates selected, and assign that value to the output part of the classification rule in analysis. The size of the RSM set was determined as 10 for a vector of 13 elements 10 inputs, 3 outputs by experimentation; with values higher than 10 the SM values are too low, and with lower values the diversification is low.

At the end of the process, all the unpopulated areas are classified into different preferences for consumer class and expected load density, creating a preference map where it is possible to identify different areas of interest to the planner. Considering the stochastic nature of this process, the algorithm is repeated several times to identify the interest areas more clearly.

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The classification rule for an unpopulated subarea under analysis is given by:. For this vector, the RSM set size is determined as 6 for experimentation. The vector is compared with all the elements in the set R1, and an RSM set is formed with 6 elements, as shown in Table 1. Using a tournament selection, vectors 1 and 3 from the RSM Set presented in Table 1 are selected to be crossed over.

With the results obtained until this point, it is enough to make an entry-level spatial electric load forecasting process that is able to identify all the new zones with possibility of growth. But to complement the results and lower the spatial error, it is necessary to consider some level of redevelopment inside the service area. The redevelopment process considered is the urban core growth. The rule database and the same principles of similarities between zones are used in this step; hence, there is no need for new data or different mechanisms than the ones already developed.

The process starts by identifying the activity center by searching for the subareas with the highest values of residential and commercial energy consumption. The location of this special subareas is easy to identify because in the spatial database a zone identified as the urban core in the "elements of interest" already exists. This value represents the relationships between the urban core and its immediate neighbors.

When presented graphically, the results of this exercise will show how the different subzones share similarities with the urban core, and especially, how the different factors in the city will take the urban core growth in a specific direction. An outline of the complete method is presented in Fig.

This process is done for each planning horizon. The results obtained in planning horizon n-1 are used as input elements for planning horizon n. Some information obtained about the service area, especially information on future land developments, were not included in the database. This would be used as a validation set for the results. With the information available, the next objects were chosen to form the classification rules for this particular system:.

Figure 3 presents the results obtained for the residential class.

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In this figure, the circles represent the zones of the service area where some load is already present. The area expected to be occupied according to the information obtained from the utility planning department validation set is identified by diamonds, and the area expected to be occupied is identified by squares. In Fig. This is because a large project is expected to be built in that part of the city, changing the classification of this area from industrial to commercial. Because of the industrial classification of the zone, the algorithm did not consider this area suitable for residential occupation.

In other tests, considering the change of the land use classification and the inclusion of a large simulated load in this zone, it was possible to match this expected behavior. Another interesting result is the number of areas identified by the algorithm that were not identified by the manual simulation of the utility planning department.

This is because the zones forecasted by the planning department were based in present and future development projects, and not likely the terrain characteristics. Therefore, the answer obtained from the algorithm is more complete because it is possible to identify all the zones of interest in the long term. The results for the industrial and commercial sector are presented in Figs. Finally, it is necessary to settle the temporal allocation of these areas. To do this, after calculating the expected growth because of new consumers in the service area using traditional methods, the areas are assigned considering neighboring characteristics, assigning first the ones with a bigger load density nearby, obtaining the results presented in Fig.

The methodologies used to calculate the load growth are not part of the scope of this work. This load growth was calculated using time series and population data, but any other method could be used to determine this value.

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The first areas to be occupied are located in the southeast part of the service area, an area with rapid and constant urban projects for mid- and high economic levels, and in the north of the city, where proximity to another small city and land intended to popularize housing are important factors. This information was not introduced into the algorithm. Figure 8 shows the redevelopment preference map based on the urban core growth.

Obviously, the areas with higher probability of redevelopment are the ones around the urban core, but it is important to note that the urban core is not growing axially around that point, but that it has a strong influence to grow in the southwest. This behavior is explained by the growth in commercial and residential density in that direction, especially for high-income housing. Meanwhile, to the north and east of the urban core, growth is not expected because of the low growth in electrical load density.

For the long term 20 years there were no results to compare to. These results are considered very good, specially because the manual simulation from Lee, could take easily one month of work for several employees. A simple and efficient algorithm to settle future land use and occupation in the spatial electric load forecasting process has been presented by considering the identification of new zones with potential growth and the redevelopment of the existing ones.

This application has been proved to be an important tool in assisting distribution network planning engineers to identify important zones with the possibility of growth inside the service area.

The algorithm uses simple procedures to extract the knowledge related to user preferences about land use from a multidimensional spatial database. This knowledge is stored in the form of linguistic classification rules. It is possible that several classification rules with the same input present different outputs.

This is because of the stochastic nature of the process, which makes the use of fixed classification rules a problem. To overcome this difficulty, the consumers' stochastic characteristic is considered using elements from evolutionary algorithms to create new classification rules for the vacant areas using the knowledge previously extracted. The results obtained prove the efficacy of the approach and encourage more work in that direction. One of the main advantages of this method is the reduced set of data needed to execute it, using only the distribution utility commercial database and a georeferenced data set of the network elements.

This approach could be helpful to utilities with limited resources and few available data. The multidimensional spatial database created for this application can be used as support information to solve other problems related to the planning and operation of the distribution network. Select the China site in Chinese or English for best site performance. Other MathWorks country sites are not optimized for visits from your location. Toggle Main Navigation. Search MathWorks. Load Forecasting. Trial software Contact sales. Develop and deploy algorithms for accurate electricity load forecasting Power companies rely on accurate electricity load forecasting to minimize financial risk and optimize operational efficiency and reliability.

Critical load forecasting tasks include:. admin