AU2021298025A1

AU2021298025A1 - Method for power prediction of an energy system

Info

Publication number: AU2021298025A1
Application number: AU2021298025A
Authority: AU
Inventors: Oliver DÖLLE; Houssame Houmy; Sebastian Schreck; Sebastian THIEM
Original assignee: Siemens AG
Current assignee: Siemens AG
Priority date: 2020-06-22
Filing date: 2021-05-03
Publication date: 2023-02-02
Anticipated expiration: 2041-05-03
Also published as: DE102020207706A1; AU2021298025B2; WO2021259540A1; EP4143938A1

Abstract

The invention relates to a method for determining an aggregation of power profiles P

Description

Method for power prediction of an energy system

The invention relates to a method according to the preamble of patent claim 1 and to a method according to the preamble of patent claim 11.

A power system, for example a borough, a separate network, a campus or an industrial complex, typically comprises multiple power subsystems, for example residential buildings, commercial buildings, industrial plants and/or distributed power plants. In particular, power subsystems increasingly comprise power engineering installations that generate renewable energies, for example photovoltaic installations and/or wind power installations.

In order to operate such a power system as efficiently as possible, a forecast of load or generation powers with a sufficiently high level of accuracy is required in principle(or: short-term load forecast; STFL for short). The forecast typically extends up to a few minutes in advance.

In particular with regard to a local energy market, a sufficiently accurate forecast is advantageous for efficient operation. This is the case because a local energy market allows the participating power systems to exchange and trade locally generated energy, in particular electrical energy (electricity). Due to its distributed technical configuration, the local energy market allows the locally generated energy to be efficiently coordinated with local energy consumption. Thus, a local energy market is particularly advantageous with regard to renewable energies, which are typically generated locally. A forecast that is as accurate as possible is therefore required for efficient coordination of this kind.

A local energy market is known, by way of example, from the document EP 3518369 Al.

Owing to the high volatility of the generation and/or consumption in the individual power subsystems, a forecast at power subsystem level is not expedient. Inaccurate and unsatisfactory generation forecasts or load forecasts would result for the power subsystems.

Aggregation of the generation profiles and/or load profiles (power profiles) of the power subsystems is used to attempt to increase forecast accuracy. The aim of the aggregation is to reduce, balance out and/or average the individual fluctuations in the power subsystems.

The disadvantage of aggregation is that details (information) relating to the respective power subsystem are lost as a result.

The object of the present invention is to improve a forecast based on aggregated power profiles through improved aggregation.

The object is achieved by way of a method having the features of independent patent claim 1 and by way of a method having the features of independent patent claim 11. Advantageous embodiments and developments of the invention are specified in the dependent patent claims.

The method according to the invention for determining an aggregation of power profiles P1 ,...,P of n power subsystems of a power system into m<n aggregated power profiles 1 in particular for a power forecast, for which purpose the power subsystems are classified, and each of the m classes of one of the classifications is assigned one of the aggregated power profiles 51,..,m, is characterized by at least the following steps: - creating multiple initial classifications, each classification having disjoint classes of the n power profiles P1 ,...,Pn; - providing an evolutionary algorithm containing search operators, the following steps being repeated until a termination condition is satisifed: - calculating a forecastability value f2 for each class of each classification by means of a sum of the power profiles associated with the respective class; - calculating a fitness value of the classification by means of a sum of the forecastability values f2 of the classification for each classification; - selecting k classifications having the k highest fitness values; and - creating new classifications by means of the search operators on the set of selected k classifications; - stipulating the aggregated power profiles 51,..,m using the classification having the highest fitness value.

The method according to the invention and/or one or more functions, features and/or steps of the method according to the invention and/or its embodiments may be computer-aided.

Power systems and/or power subsystems typically comprise multiple components relating to the production (generation), conversion, supply and/or use of energy, in particular electrical energy (electricity) and/or thermal energy (heat). A power system or power subsystem is, by way of example, a city, a district, a municipality, a residential building, an office building and/or another commercial building, an industrial plant, a power plant and/or a campus. In particular, power systems or power subsystems comprise multiple power-engineering installations, for example energy conversion installations, consumption installations and/or storage installations. For example, the power system is a borough or a municipality that comprises multiple residential buildings and/or office buildings and/or commercially used buildings and/or distributed power plants, in particular photovoltaic installations, combined heat and power plants and/or waste incineration plants, as power subsystems. The power system may also be a building having multiple units as power subsystems.

A power profile of a power subsystem characterizes the time dependency or a time characteristic of the power subsystem's power provided, in particular generated, and/or consumed by the power subsystem. Load (consumption) and generation may exist together within the time range (residual power). In other words, a power profile may be a load profile and/or a generation profile. Furthermore, a power profile may exist as a time signal, for example as a function, and/or as a discrete-time time signal (time series). The power profile may also be referred to as a signal.

The power profile may exist as a time series or measurement series, in particular in the form of data, and/or analytically, for example as a fitted function. Typically, the power profile or power profiles is/are measurement-based.

The concept of power relates to energy consumed and/or provided, in particular generated, within a time range. Thus, in the present invention, the terms power and energy are equivalent and interchangeable.

Furthermore, the power profile is in particular an electrical power profile, that is to say a time dependency of an electrical power, or a thermal power profile, for example with regard to a heat output and/or cold output. A mixed power profile may also exist.

The forecastability value is a value of a forecastability function. In particular, the forecastability function has values in the range from 0 to 1. The forecastability function may be regarded as a measure of forecastability. A forecastability value close to the value 1 means that the associated aggregated power profile has a high level of forecastability. It is therefore easy to predict, for example by virtue of its regular behavior. A forecastability value close to the value 0 indicates little to no forecastability. With this in mind, the associated aggregated power profile exhibits a high level of randomness and little to no regular behavior. Forecastability is therefore a measure of the predictability of the associated aggregated power profile. In principle, multiple measures, that is to say multiple functional dependencies, are conceivable for quantifying forecastability. A minimum requirement imposed on the measure may preferably be that it has a higher value the more regular the time characteristic of the associated signal is. The more erratic the signal is, for example owing to noise and/or high volatility, the lower the forecastability value should be. Normalization to the value range from 0 to 1 is expedient, although there may be provision for other normalizations.

The fitness value is a value of a fitness function. Typically, the evolutionary algorithm has such a fitness function, which is a measure of the fitness of each classification symbolically with regard to the search operators of the evolutionary algorithm. In the present case, the fitness value is formed by the sum of the forecastability values assigned to a classification, and so the fitness value forms an overall or cumulative forecastability value for the respective classification.

A classification may also be referred to as a grouping, and so the classes form the groups of the grouping.

Assigning a power subsystem to a class is equivalent to assigning the power profile associated with or provided by the power subsystem.

According to the evolutionary algorithm, the classification is formed by the individuals in the population. The population is formed by all the classifications or by the sum total or set of the classifications, that is to say the sum total of the individuals.

According to the present invention, the n power profiles, in particular load profiles, of the power subsystems of the power system are divided into m classes, with each class of one of the classifications being assigned an aggregated power profile. There may also be provision for the empty class, for example if there is no provision for a fixed number of classes. Furthermore, multiple such classifications having typically at least partly different aggregated power profiles and thus at least partly different classes are provided, in particular created. In other words, the n power profiles are grouped into m aggregated power profiles. An aggregated power profile thus corresponds to a totalled subset/group of the power profiles.

Each of the aggregated power profiles may be calculated using a sum and/or weighted sum of the power profiles associated with or assigned to the respective class.

In other words, {P1 ,...,P }={Pi}i for I={1,...,n} will be the set of power profiles, that is to say each power subsystem provides one of the power profiles Pi, Pi being assigned to the power subsystem i. The power profiles are time-dependent, that is to say Pi = Pi(t) or Pi = Pit for t E T, where T denotes the time range for which the power profiles were provided and over which they extend.

The set of power profiles is divided into m disjoint classes KEk for each of the classifications k. In other words, Y=

UKEgK, the classes K of any classification being disjoint, that is to say KnL=0 for K#L and K,LER. Disjoint partitioning of the set of power profiles or of the power profiles is thus carried out for each classification k. Each class KER is assigned an aggregated power profile, for example using P=

EP:PEKP, that is to say using the sum of the power profiles P in the respective class K (PEK). There may be provision for a weighted sum. D(K):= D(P)=2(ZP:PEKP) is then used to assign each class K of the classification k a forecastability value D2(K), where f2 denotes the forecastability function. Furthermore, according to the invention, each of the classifications k is assigned a fitness value, which is formed from the sum of all the forecastability values of the respective classification R, by means of F(k):= 2K:KEk2.(K).

According to the present invention, the evolutionary algorithm is used to determine a classification that has a highest fitness value. This determined classification corresponds to an aggregation of the power profiles into aggregated power profiles having the highest possible predictability. In other words, a synergetic compromise is made between aggregation, which always involves a loss of details about the power subsystems, and the highest possible predictability. According to the present invention, as little as possible is thus lost during the aggregation. This significantly improves a forecast that is based on the aggregated power profiles. The best aggregation in this context is determined according to the invention by means of the evolutionary algorithm.

In a first step of the method or the evolutionary algorithm (initialization), multiple initial classifications are created, each classification having disjoint classes of the n power profiles. In regard to the evolutionary algorithm, this represents the initial population.

In a second step, the evolutionary algorithm containing search operators and a fitness function is initially provided. Subsequently, a loop that is performed until the termination criterion is satisfied is used to create new classifications.

In a first substep of the loop, a fitness value is assigned to each classification. In other words, each individual in the population is assigned a fitness value. The assignment or determination/calculation of the fitness values is carried out on the basis of the forecastability values of the classes associated with each classification. To this end, the forecastability value for each class of each classification is calculated by means of a sum of the power profiles associated with the respective class. The fitness value is then calculated by means of a sum of the forecastability values of each classification (as described above). Thus, each individual (classification) in the population (sum total of the classifications) has a fitness value that is greater the greater its forecastability and thus the higher the predictability of the aggregation associated with the individual (classification).

In a second substep, the selection is made. In other words, the k-fittest individuals (classifications) in terms of their fitness values are determined, ascertained or selected.

In a third substep, new individuals, that is to say new classifications, are performed on the set of k-fittest individuals by means of the search operators, for example mutation of an individual or recombination of two individuals. Each newly created classification is in turn assigned a fitness value (evaluation).

If the thereby newly created population does not satisfy the termination criterion, the loop is performed again. If the termination criterion is satisfied, a selection is made again. In other words, the classification having the highest fitness value, in this context the fittest individual, is ascertained. The best aggregation in terms of predictability is stipulated and thus determined by the classification having the highest fitness value.

According to the present invention, the aggregation is thus carried out not at random or according to fixed criteria, for example by way of combination according to the type of power subsystems, but rather dynamically with regard to as high a predictability/forecast content as possible. The invention's forming of the fitness function, or of the fitness values, on which the evolutionary algorithm is based by means of the forecastability values that are dependent on the respective information content drives the classifications/aggregations, or the population, to a higher level of forecastability. Thus, a synergetic compromise between an aggregation and the associated loss of information is determined. In particular, this improves the accuracy of a power forecast that is based on the aggregation. Furthermore, the termination criterion may even predefine a forecast accuracy, and so a, in this context, minimal aggregation that complies with the required forecastability may be determined by means of the present invention. In other words, symbolically, only as much aggregation as is required for a stipulated forecast accuracy or forecastability is carried out.

In particular with regard to a local energy market in which the power system or at least some of its power subsystems is/are involved, the present invention allows improved forecasting and thus more efficient integration of the power system or its participating power subsystems.

With regard to electrical systems, the present invention allows the network to be operated safely and efficiently. Furthermore, unnecessary overload management, such as redispatch, may be avoided.

Furthermore, the present invention is advantageous for a power system design. If, for example, a load on the power system or the power subsystem is difficult to predict, that is to say that it has a comparatively low forecastability value, then it could be advantageous to provide for additional storage capacities.

According to an advantageous embodiment of the invention, the initial classifications are created by randomly assigning the power profiles P1 ,...,P to the classes.

In other words, the initial classifications, that is to say the initial population of the evolutionary algorithm, are each formed by randomly drawing from the set of power profiles without replacing them. This advantageously avoids initial biased assignment. Alternatively or additionally, there may be provision for an advantageous selection for the initial population or at least part of the initial population.

In an advantageous development of the present invention, the forecastability value f2 is determined by means of 2 = 1-Ha, where Ha denotes the value of the normalized Shannon entropy to the base a of the aggregated power profile assigned to the class.

The information content of the aggregated power profile is advantageously ascertained using the Shannon entropy. In other words, the Shannon entropy of the aggregated power profile is a measure of the information content of the aggregated power profile. The higher the information content, the more random the aggregated power profile and the less predictable it is.

The normalized Shannon entropy is formed from the ratio of the Shannon entropy and the maximum value of the Shannon entropy. The normalized Shannon entropy thus has values in the range from to 1. Furthermore, the normalized Shannon entropy is referred to as efficiency . The maximum value of the Shannon entropy occurs for a uniform distribution, that is to say that the associated power profile is white noise. Thus, if the aggregated power profile is white noise or comparable to such, the normalized Shannon entropy has a value close to 1. Although the information content of white noise is 1, it is unpredictable, and so its forecastability value is 0. In other words, f2=0 for white noise, that is to say that the associated aggregated power profile is unpredictable. If power profiles are thus aggregated into almost white noise, the aggregated power profile has little to no forecastability. In other words, a signal having a high information content has low forecastability and thus low predictability. It is thus advantageous to determine the forecastability value using fD = -Ha. A classification that has multiple such classes having low forecastability has low fitness, that is to say a low fitness value.

In other words, information about the individual power subsystems should be lost during aggregation, and so the aggregated power profile created as a result has less information content according to the Shannon entropy, but improved predictability. As a result, an advantageous compromise may be achieved between loss of information and predictability/forecastability, which compromise may be controlled/adjusted according to the present invention.

According to an advantageous embodiment of the invention, the Shannon entropy is determined by means of the spectral density (or: power spectral density; PSD for short) of the respective aggregated power profile P1,...,AM.

Any aggregated power profile Pk has an associated spectral density Spk(o) for k=1,...,m as a time signal/time series. If

fk() = Spk ()/Var(Pk) is the spectral density (probability density function) normalized to the variance of the aggregated time signal, the Shannon entropy is preferably formed, or calculated, or determined by means of

Ha(Pko)ffk()) loga f (a) d . Here, a denotes the angular frequency and loga denotes the logarithm to the base a, and so the Shannon entropy is also formed to the base a. The Shannon entropy is thus formed using the differential entropy, there likewise being provision for discrete formations. The specific form, whether discrete or continuous, depends on the form of the time signal (continuous or discrete). For example, a uniform distribution (white noise) over an interval [-o, wo] results in the normalized spectral density f(w) = 1/(2a 0 ) and thus the maximum Shannon entropy of Ha = loga(2O).

In an advantageous embodiment of the invention, the spectral density is determined by means of the autocorrelation of the respective aggregated power profile P1,...,"m.

The autocorrelation of one of the aggregated power profiles is ascertained using Ypk(T) = E[(Pk;t - pk)( Pk;t_ - Ip)], where E denotes the expected value and ppk denotes the time average of the aggregated power profile Pk. For a discrete-time power profile,

YPk(r) = E[(Pk;t - kP)Pk;t-r - 1Pp)], with r E Z. This is advantageous because the autocorrelation is a measure of correlations within the respective power profile and thus of its regularity. Furthermore, the spectral density may be calculated efficiently using the Wiener-Khinchin theorem by means of the autocorrelation.

According to an advantageous development of the invention, the search operators used for the evolutionary algorithm are mutation and/or recombination.

This advantageously allows preferred new classifications to be formed from the previous classifications. The search operators of the evolutionary algorithm operate on the set of the k-fittest classifications.

In the event of a mutation or a mutation event, the assignment or association of a power profile to/with a class of the classification is changed at random. In other words, at least one power profile of the classification is reassigned to a class of the classification with a stipulated probability. In other words, the class assignment of a power profile is changed at random within the same classification. This forms a new random classification. There may be provision for one or more mutations.

A recombination (or: cross over) creates a new classification, that is to say a descendant (or: offspring), on the basis of two classifications (parents). This involves mixing two classifications, there being a 0.5 (50 percent) probability of using one class from the two classifications as the class of the new classification (offspring). In other words, the new classification comprises, on average, 50 percent of each parent's classes. There may be provision for multiple recombinations. Mutations and recombinations are preferably mixed.

In an advantageous development of the invention, the classes of the classifications, in particular the classifications freshly created within the evolutionary algorithm, are organized.

This advantageously allows a bijective mapping (or: one-to-one mapping) between the classification and its organization of the classes. In other words, reorganization/rearrangement/set organization (or: reordering) of the class arrangements within a classification is carried out. In this case, the classes are preferably reorganized or renumbered whenever new classifications are freshly created, that is to say after the initialization (first creation of the classifications) and/or after application of a search operator, in particular after a mutation and/or recombination. A preferred reorganization is achieved by reorganizing or renumbering the classes according to the order in which they appear in the classification, for example from right to left.

According to an advantageous embodiment of the invention, the termination condition is formed by means of the fitness values.

In other words, the fitness values collectively determine when a sufficiently advantageous population (set of classifications) is achieved. This ensures that a classification having the highest possible fitness value for the aggregation may be determined. The termination condition is particularly preferably formed by the average of the fitness values. If the average of the fitness values does not change over multiple previous generations, the loop is preferably stopped and the aggregation is determined by the classification having the highest fitness value of the present generation. Alternatively or additionally, a threshold value for the fitness values and/or for the average of the fitness values may be stipulated. In other words, the termination condition is formed by the threshold value. If the average of the fitness values is above the mentioned threshold value, for example, then the termination condition is satisfied and the loop of the evolutionary algorithm stops. This advantageously allows a classification having the highest possible fitness value to be determined in an appropriate computing time. There may alternatively or additionally be provision for further termination conditions. The termination condition is basically a kind of measure of the overall fitness of the population.

In an advantageous development of the invention, the power profile used is a load profile and/or a generation profile of the respective power subsystem.

In principle, the power profile may be a load profile, a generation profile or a residual profile mixed from load and generation. In the present case, generation is also understood to mean provision. In other words, the power profile of an energy store, in particular an electricity store and/or thermal energy store, may be used.

According to an advantageous embodiment of the invention, the determined aggregation of the power profiles of the power subsystems is used for forecasting the power, in particular for forecasting the load and/or forecasting the generation, of the power system.

The aggregated power profiles are particularly preferred for a power forecast for the power system, for example for some its power subsystems. This is the case because the power profiles of the power subsystems are aggregated not at random or according to stipulated criteria, but rather according to their fitness, that is to say according to their forecastability. As a result, it is possible to determine the most advantageous possible compromise between aggregation and predictability.

Further advantages, features and details of the invention will emerge from the exemplary embodiments described below and with reference to the drawings, in which, schematically:

Figure 1 shows an aggregation according to an embodiment of the present invention;

Figure 2 shows a flowchart of an evolutionary algorithm according to an embodiment of the present invention; and

Figure 3 shows an organization for a classification.

Identical, equivalent or functionally identical elements may be provided with the same reference signs in one of the figures or throughout the figures.

Figure 1 shows an aggregation, or a schematic sequence of an aggregation, according to an embodiment of the present invention.

A power system 1, for example a municipality, a borough, a building complex, an industrial plant and/or a campus, has multiple, in the present case n, power subsystems 11. For example, a borough has multiple residential buildings or a building complex has multiple apartments. The power subsystems are each denoted by the reference numeral 11.

In the present case, a measurement 6 relating to the respective power/energy is carried out on each of the power subsystems 11 at least within a time range, for example within a day, with an hourly resolution or a 15-minute resolution. As a result, n power profiles are provided, three being shown in the present case as an example. The power profiles, or the provision thereof, are denoted by the reference numeral 2. The measurements may be taken using a smartmeter and/or using a respective energy management system.

The power subsystems 11 are able to feed out (load) and/or feed in (provision or generation) a power via a grid 8, in particular an electricity grid. The power fed out and/or fed in is measured continuously or in fixed time steps, for example every 15 minutes or every hour, as a result of which the power profiles 2 are provided. By way of example, the power profiles extend over a day with a resolution of 15 minutes or an hour. Like the power, the respective generated/provided and/or consumed energy may be measured or recorded within a time interval, for example within minutes or one hour. The associated power is then obtained from the recorded energy per time interval.

In Figure 1, the measured or recorded power profiles 2 are each plotted as curves within a P-t graph (P power, t time). Differences in their regularity are discernible therein. These differences correspond to different predictabilities of the power profiles 2. By way of example, an approximately periodic power profile is easy to predict. A power profile having multiple erratic fluctuations is more difficult to predict. Typically, the fluctuations for the power subsystems 11 are too high for a sufficiently accurate forecast, and so an aggregation 4 is carried out. This allows fluctuations to be reduced and thus predictability to be increased.

The aggregation 4 classifies, or groups, the power subsystems 11. In other words, each of the power subsystems is assigned to exactly one class 42, or group, within the aggregation 4. The sum total of the classes forms a classification 40. In the exemplary embodiment shown, the classification 40 of the power subsystems 11 according to their power profiles 2, or the classification 40 of the power profiles 2, comprises only two classes 42, each class 42 being assigned two of the four power subsystems 11 shown.

The power profiles assigned to or associated with a class 42 are summed for the aggregation 4, as a result of which averaged, or aggregated, power profiles are formed. There may be provision for a weighted sum. Each class 42 is thus assigned an, or has an associated, aggregated power profile. A technical purpose of the aggregation 4 is to reduce fluctuations in the individual power subsystems 11. In other words, the aggregated power profiles should have lesser fluctuations, which improves their predictability. A forecast based on the aggregated power profiles may thus be more reliable, or more accurate.

In Figure 1, the aggregation 4 is carried out according to the present invention, that is to say it is carried out on the basis of a measure of forecastability, or a forecastability function, and by means of an evolutionary algorithm. This allows an aggregation 4 that is as optimum as possible in terms of its predictability to be determined. With this in mind, a classification 40 having the maximum possible predictability is determined. This aggregation that is as optimum as possible, which corresponds to the classification 40 in the figure, is the result of the aggregation 4. The evolutionary algorithm in this case is advantageous because the classification 40, or grouping, exhibits a strong nonlinear response with regard to the measure of forecastability.

Figure 2 illustrates a flowchart of an aggregation, in particular of the evolutionary algorithm used here.

In a starting step S of the aggregation, the power profiles of the power subsystems, which were recorded by means of a respective measurement, for example, are provided.

In an initialization step I, the power profiles provided are taken as a basis for carrying out an initial, or opening, classification of the power subsystems, or of the power profiles. In other words, the power subsystems, or their power profiles, are divided into, or assigned to, multiple classes, in the present case m classes. Each power subsystem is assigned exactly one power profile, and so a classification of the power subsystems and a classification of the power profiles is equivalent. Each class of the initial classification is thus assigned none, one or more of the power profiles. The initial classification is preferably performed by randomly assigning/dividing the power profiles, or the power subsystems, to/into the m classes.

This random division of the power subsystems into m disjoint classes creates a possible classification corresponding to a possible aggregation. In the initialization step I, multiple such possible classifications are furthermore created, in particular at random. This sum total of created initial classifications forms the initial population according to the evolutionary algorithm. The classifications are thus the individuals in the population. The initial population is thus created by means of randomly created individuals.

In an evaluation step Li, the initial population or the classifications are evaluated. This requires an assessment measure that quantifies how fit an individual, that is to say a classification, is with regard to the evolutionary algorithm. The fitter an individual, the more likely it is that its characteristics, or classes, will be found in future generations.

According to the present invention, in a first partial step Lla, each class of each classification is first assigned a forecastability value. Then, in a second substep Lib, a fitness value is assigned to a classification, or to an individual, by way of the sum of the forecastability values of its classes. In other words, an overall forecastability is assigned to each classification, or each individual. The classifications are thus rated according to their forecastability per the above. An individual, or a classification, is all the fitter the higher their overall forecastability, that is to say the higher their predictability. The assessment measure, or the selection criterion, of the evolutionary algorithm is thus formed by predictability. The decisive factor here is the assignment of the forecastability value to each class.

The forecastability value of a class is calculated by means of the aggregated power profile assigned to the class. The aggregated power profile in this case is the sum of the power subsystems' power profiles assigned to the class. There may be provision for a weighted sum in this case. If the sum is weighted evenly, the aggregated power profile corresponds to the average of the power profiles.

The temporal autocorrelation of the aggregated power profile is calculated for the calculation or determination of the forecastability value of a class by means of the aggregated power profile assigned to or associated with the class. The autocorrelation may be determined for a discrete-time aggregated Pk;t power profile (for k 1,...,m power subsystems at the time t) by way w f ypo(r) = E[[yoPf - 1pXp)k;t-r -- ip)], for rE Z (or: lag), where E denotes the expected value and p denotes the temporal average of the aggregated power profile Pk;t.

The calculated autocorrelation is used to calculate the spectral density Spk () of the aggregated power profile by way of,

SNkw IYPkre, w[w]

where i= 1 denotes the imaginary unit. The spectral density

fpk(a) =Spk ()/Var(Pk) normalized to the variance forms a probability density function, by means of which the forecastability value may be determined. In particular, it holds that 0 fk(a) 1 and fk(a) do = 1, as required for a probability density function. For example, the constant normalized spectral density, or probability density function, fyk(a)= 1/(27) is obtained for an aggregated power profile, which is in the form of white noise. For a sine or cosine signal, or aggregated power profile Pk;t = A - cos(2ft + 0), with 0 - U(-, 7) and fPp (j) independent of 0, that is to say with a random frequency according to the probability distribution Ppk(0), it holds that fyk(w)= ppk(w). The uncertainty of a forecast in this case results exclusively from the probability distribution Ppk(a).

The probability density function fPk(a) is taken as a basis for calculating the Shannon entropy of the aggregated power profile by means of

Ha(Pk) - fk F(a) 1oga fk k(a) do

. The Shannon entropy, or the logarithm, is formed to the base a. The Shannon entropy is a measure of the information content of the aggregated power profile. A high information content corresponds to a high randomness of the aggregated power profile, and so the predictability thereof is low. Information content and predictability are therefore symbolically opposed. It is therefore of particular advantage to define, or calculate, the forecastability of the aggregated power profile by way of f 2 (Pk)= 1- Ha(Pk)/max(Ha(Pk)). Here, max(Ha(Pk)) denotes the maximum of the Shannon entropy over all possible aggregated power profiles. The maximum of the Shannon entropy is ascertained using an aggregated power profile in the form of white noise, and so it holds that max(Ha(Pk))=1oga(2), since in the present case |[-,w]| = 2w.

The measure D2(k)= 1- Ha(Pk)/max(Ha(Pk)) = 1- H2 (pk) thus particularly advantageously quantifies the forecastability of the aggregated power profile. It holds that O J 9 (Pk) 1. The aggregated power profile is particularly predictable when its forecastability value D2(Pk) is approximately 1. The aggregated power profile is not very predictable, that is to say it has a 2 high level of randomness, if (P) is approximately 0.

Each class of a classification is assigned a forecastability value calculated as above. The classification is assigned its fitness value by means of the sum of its forecastability values. In other words, for the fitness value of one of the classifications, it holds that F = (Pk), P~kPkiq all the classes of the classification k being used for summation. The fitness value F is therefore a measure of the overall forecastability of the classification and thus of the aggregation. This is implemented in evaluation step Li for all the classifications. In other words, each classification has such a fitness value. The fitness value of 0 is assigned to an empty class.

A termination step T comprises checking whether a termination criterion is satisfied. The termination criterion is in particular formed by means of the sum total of the fitness values, for example by means of the average of the fitness values.

If the termination criterion is satisfied, the final aggregation is determined by the classification having the highest fitness value and thus having the comparatively best predictability. This ends or stops the evolutionary algorithm (end E).

If, on the other hand, the termination criterion is not satisifed, then the k fittest individuals, that is to say the classifications having the k highest fitness values, are determined. This selection is denoted by the reference sign L2.

Within the further step L3, the k selected individuals are used to create new classifications from the previous ones. In other words, a new population is created from the previous population in step L3. According to the evolutionary algorithm, this new population forms the descendants of the k fittest individuals. In other words, only the k fittest individuals may reproduce.

The descendants, or the new classifications, are created by means of search operators L3b and L3c from the k fittest classifications. For this purpose, the search operator to be implemented is selected in a step L3a. In the present case, a mutation L3b or a recombination L3c may be implemented.

In the case of a mutation L3b, the new classification is created from the previous one by randomly changing an association of a power profile with a class of the classification.

The mutation, or a mutation event, is meant to be illustrated for eight power subsystems 1,...,8 in three classes 1,...,3. Let (1,2,2,3,1,2,3,1) be a possible classification. This notation means that the power subsystem 1 is assigned to class 1, the power subsystem 2 is assigned to class 2, the power subsystem 3 is assigned to class 2, the power subsystem 4 is assigned to class 3, the power subsystem 5 is assigned to class 1, the power subsystem 6 is assigned to class 2, the power subsystem 7 is assigned to class 3 and the power subsystem 8 is assigned to class 1. In other words, K 1 ={1,5,8}, K 2 ={2,3,6} and K 3 ={4,7}, or in the equivalent notation for the power profiles Pi of the power subsystems K1 ={P1 ,Ps,P}, K 2 ={P 2 ,P 3 ,P} and K 3 ={P 4 ,P 7}, where Kk denotes the class k. Each class Kk is assigned an aggregated power profile Pk, for example by way of P-- =ZP:rPiKk Pi, by means of its power profiles. In the present case, the aggregated power profile P 1 =P1 +Ps+P 8 is assigned to the first class K1 , the aggregated power profileP 2 =P2 +P 3 +P 6 is assigned to the second class K 2 and the aggregated power profile P 3 =P4 +P 7 is assigned to the third class K 3 . The first class K1 has the forecastability fD(K 1)=D(P 1)=D(P 1 +Ps +P 8 ), the second class K2 has the forecastability D(K 2 ) =.(P2 ) =.(P2 +P 3 +P 6 ) and the third class K3 has the forecastability D(K3 )=D(P 3 )=D(P4+P 7 ).

A mutation, or a mutation event, now randomly changes the association of a power subsystem, or a power profile, with a class. For example, (1,2,2,3,1,2,3,1) - (1,2,1,3,1,2,3,1) is such a mutation event. Here, the power subsystem 3, which was originally assigned to class 2, was reassigned to class 1 by way of the mutation. This forms a new classification. In this case, a power subsystem may be chosen at random and randomly assigned to one of the classes again. There may be provision for multiple mutations L3b in succession and/or in parallel on the set of k fittest classifications.

In the case of a recombination L3c, a new classification is determined from two previous classifications (parents). In this case, 50% of the previous classifications have a 50% probability of being mixed. In other words, the new classification has a 50% probability of having the class of one or the other parent. If for example (1,2,2,3,1,2,3,1) and (1,1,1,2,3,1,2,2) are the previous classifications (parents), a recombination could create the new classification (1,2,2,3,1,1,3,2) as a descendant. There may be provision for multiple recombinations L3c in succession and/or in parallel on the set of k fittest classifications.

In summary, applying the search operators L3b and L3c, possibly together with previous classifications, creates a new population, which in turn is supplied to the evaluation step. This starts the loop of the evolutionary algorithm from the beginning. Said loop L is performed until the termination criterion is satisifed. If the termination criterion is satisfied, the final aggregation is determined by the classification having the highest fitness value and thus having the comparatively best predictability.

Figure 3 shows an organization for a classification 40 that is advantageously applied whenever the classification 40 has been newly created, for example by the search operators.

Application of the search operators typically results in an unorganized classification, the organization referring to the order, in the present case from right to left, of the numbering of the classes 42. The numbering/denotation of the classes 42 is basically irrelevant. In other words, it does not matter whether a class 42 is denoted as the first or, for example, the second class.

In principle, any organization may be selected. However, it is advantageous to organize, or number, the classes 42 according to their occurrence within the classification.

In the exemplary embodiment shown, the classification 40 (2,1,1,3,2,1,3,2) of the power subsystems 11 (1, ... , 8) of the power system 1 is therefore unorganized, since class 2 comes first. For an advantageous arrangement, class 1 should occur first, followed by class 2 and 3. Therefore, the classes 41 of the classification 40 are advantageously organized by way of (2,1,1,3,2,1,3,2) -> (1,2,2,3,1,2,3,1), that is to say by renaming class 2 as class 1 and class 1 as class 2 or by interchanging the first and second classes. Thus, (1,2,2,3,1,2,3,1) is the organized classification 40' of the unorganized classification 40.

Although the invention has been described and illustrated in more detail by way of the preferred exemplary embodiments, the invention is not restricted by the disclosed examples or other variations may be derived therefrom by a person skilled in the art without departing from the scope of protection of the invention.

List of reference signs

1 power system 2 power profiles 4 aggregation 6 measurement 8 power grid 11 power subsystems , 40' classification 42, 42' classes S start step I initialization step L loop Li evaluation step T termination step L2 selection step L3 creation step L3a search operator selection L3b mutation L3c recombination E end

Claims

1. A method for determining an aggregation (4) of power profiles P,...,J% (2) of n power subsystems (11) of a power system (1) into m<n aggregated power profiles 1 (2), in particular for a power forecast, for which purpose the power subsystems (11) are classified (40), and each of the m classes (42) of one of the classifications (40) is assigned one of the aggregated power profiles 5t,..,m (2), characterized by the following steps: - (I) creating multiple initial classifications (40), each classification (40) having disjoint classes (42) of the n power profiles P1 ,...,Pn (2); - (L) providing an evolutionary algorithm containing search operators, the following steps being repeated until a termination condition is satisifed: - (Lla) calculating a forecastability value () for each class (42) of each classification (40) by means of a sum of the power profiles (2) associated with the respective class (42); - (Lib) calculating a fitness value of the classification by means of a sum of the forecastability values () of the classification (40) for each classification (40); - (L2) selecting k classifications (40) having the k highest fitness values; and - (L3) creating new classifications (40) by means of the search operators on the set of selected k classifications (40); - (T) stipulating the aggregated power profiles l,..,m (2) using the classification (40) having the highest fitness value.

2. The method as claimed in claim 1, characterized in that the initial classifications (40) are created (I) by randomly assigning the power profiles P1 ,...,P to the classes (42).

3. The method as claimed in claim 1 or 2, characterized in that the forecastability value () is determined by means of (=1 -Ha, where Ha denotes the value of the normalized Shannon entropy to the base a of the aggregated power profile (2) assigned to the class (42).

4. The method as claimed in claim 3, characterized in that the Shannon entropy is determined by means of the spectral density of the respective aggregated power profile 51,..,m (2).

5. The method as claimed in claim 4, characterized in that the spectral density is determined by means of the autocorrelation of the respective aggregated power profile 51,..,m (2).

6. The method as claimed in one of the preceding claims, characterized in that the search operators used are mutation and/or recombination.

7. The method as claimed in one of the preceding claims, characterized in that the classes (42) of the classifications (40), in particular the classifications (40) freshly created within the evolutionary algorithm, are organized.

8. The method as claimed in one of the preceding claims, characterized in that the termination condition is formed by means of the fitness values.

9. The method as claimed in one of the preceding claims, characterized in that the power profile used is a load profile and/or a generation profile of the respective power subsystem.

10. The method as claimed in one of the preceding claims, characterized in that the determined aggregation (4) of the power profiles of the power subsystems (11) is used for forecasting the power, in particular for forecasting the load and/or forecasting the generation, of the power system (1).

11. A method for forecasting the power of a power system (1) having multiple power subsystems (11), each of the power subsystems (11) providing a power profile P1 ,...,P, and the power forecast being carried out on the basis of an aggregation (4) of the power profiles P1 ,...,Pa, characterized in that the aggregation (4) is carried out by means of a method as claimed in one of the preceding claims.

12. The method as claimed in claim 11, characterized in that the power forecast is carried out by means of an energy management system of the power system (1).