CN109638812B - Self-adaptive distribution line ultra-short term load prediction method and system - Google Patents
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
- H02J3/04—Circuit arrangements for ac mains or ac distribution networks for connecting networks of the same frequency but supplied from different sources
- H02J3/06—Controlling transfer of power between connected networks; Controlling sharing of load between connected networks
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
- H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
- H02J3/46—Controlling of the sharing of output between the generators, converters, or transformers
- H02J3/48—Controlling the sharing of the in-phase component
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
- H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
- H02J3/003—Load forecast, e.g. methods or systems for forecasting future load demand
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Abstract
The invention relates to a self-adaptive distribution line ultra-short term load prediction method and a self-adaptive distribution line ultra-short term load prediction system, which are used for realizing the following steps: acquiring load data of a distribution transformer of a power utilization information acquisition system and distribution data of a distribution automation system at the same time; sequentially preprocessing historical load data of the distribution transformer, and extrapolating a load prediction value of the distribution transformer by using a linear trend extrapolation ultra-short term load prediction algorithm based on similar days, wherein the preprocessing comprises the step of performing normalization processing on a reasonable range, missing data and redundant data of the load data of the distribution transformer; predicting the loss of the distribution line based on the acquired data to obtain a prediction result; and correcting the prediction result to obtain a corrected prediction result. The invention has the beneficial effects that: the method can automatically adapt to the change of the operation mode of the power distribution network, synchronously realizes the load prediction of the distribution transformer, completes the prediction of line loss, meets the application requirements of various distribution automation, and has good popularization value.
Description
Technical Field
The invention relates to a self-adaptive distribution line ultra-short term load prediction method and a self-adaptive distribution line ultra-short term load prediction system, and belongs to the field of computers and electric power.
Background
Ultra-short term load prediction plays an important role in controlling the energy balance of the power grid. The ultra-short-term prediction of the line load in the distribution automation system is widely applied to multiple aspects of overload early warning, operation mode optimization, line switching, fault processing, state estimation and the like.
However, the medium-voltage distribution network has the disadvantages of variable operation modes, large fluctuation range of power load and the like, so that the traditional load prediction method is difficult to be directly popularized and applied in the distribution network: traditional distribution line load prediction mainly implements prediction based on power data collected at a line outlet, and when a line operation mode changes, a predicted value cannot quickly track the change of an actual load.
Disclosure of Invention
Summary several example aspects of the disclosure are as follows. This summary is provided for the convenience of the reader to provide a basic understanding of these embodiments and does not fully define the scope of the invention. This summary is not an extensive overview of all contemplated embodiments, and is intended to neither identify key or critical elements of all aspects nor delineate the scope of any or all aspects. Its sole purpose is to present some concepts of one or more embodiments in a simplified form as a prelude to the more detailed description that is presented later. For convenience, the term "some embodiments" may be used herein to refer to a single embodiment or to multiple embodiments of the disclosure.
Aiming at the problems, the invention provides a self-adaptive distribution line ultra-short term load prediction method and a self-adaptive distribution line ultra-short term load prediction system.
The technical scheme of the invention comprises a self-adaptive distribution line ultra-short term load prediction method, which is characterized by comprising the following steps: s1, acquiring the load data of the distribution transformer of the electricity consumption information acquisition system and the distribution data of the distribution automation system at the same time; s2, sequentially preprocessing historical load data of the distribution transformer, and extrapolating the load prediction value of the distribution transformer by using a linear trend extrapolation ultra-short term load prediction algorithm based on similar days, wherein the preprocessing comprises the step of normalizing the reasonable range, the missing data and the redundant data of the load data of the distribution transformer; s3, predicting the loss of the distribution line based on the data acquired in the step S2 to obtain a prediction result; and S4, correcting the prediction result to obtain a corrected prediction result.
The method for predicting the ultra-short term load of the self-adaptive distribution line is characterized by further comprising the following steps: obtaining total power of predicted circuit, using itIdentifying the total power of the line at each time, where PfdrFor line head power, PkMeasured power, P, for the kth distribution transformerlossIs the total power loss of the line.
According to the adaptive distribution line ultra-short term load prediction method, step S2 specifically includes: preprocessing distribution transformer historical load data, performing normalization processing on the distribution transformer load data, and specifically performing reasonable value range verification, missing data completion and redundant data deletion processing on the distribution transformer load data in a distribution change period in sequence; selecting similar days, and sequentially taking out historical load data of a plurality of recent similar days of the same type according to the type of the predicted target date; and generating a load prediction value of the distribution transformer, and generating the load value of the distribution transformer by using a linear trend extrapolation ultra-short term load prediction algorithm.
According to the adaptive distribution line ultra-short term load prediction method, the generation of the distribution transformer load prediction value specifically comprises the following steps: extracting corresponding distribution transformer load data from the same time point of a plurality of similar days to form a single sequence, fitting a polynomial by using a least square fitting method and extrapolating to obtain the load of the corresponding time point of the predicted day, wherein the calculation formula isAnd a and b are 0, simplifying to obtain XN+1A + b (N +1), where xtAnd XtThe real load value and the fitting value of the distribution transformer at a certain time point on the t day, N is the total number of days, a and b are unknown variables, and the formula is used for expressing the real load value and the fitting value of the distribution transformer at each predicted dayAnd (4) performing one-time trend extrapolation calculation on the time points, and forming a sequence by the obtained prediction points to further obtain a prediction result.
According to the adaptive distribution line ultra-short term load prediction method, step S3 specifically includes: based onCalculating the line loss power P of each time point of similar daysloss_t(ii) a The line loss is predicted by using a linear trend extrapolation algorithm, and the calculation mode isWherein a 'and b' are linear extrapolation parameters, wherein Ploss_N+1And the target predicted value of the line loss is obtained.
According to the adaptive distribution line ultra-short term load prediction method, step S4 specifically includes: calculating the load predicted value of each distribution transformer as Pk_forecast(ii) a Predicting the line loss at the corresponding time as Ploss_forecast(ii) a Calculating a predicted line load valueCorrecting the predicted value of the line load according to the predicted deviation value at the current moment, specifically, the predicted value is that P is equal to Pfdr_forecast(0)-Pfdr_forecast(0)Where Δ P is the predicted deviation value at the current time, Pfdr_forecast(0)For the actual load measurement value at the present moment, Pfdr_forecast(0)Predicting a load value for the current moment; the corrected load predicted value is P'fdr_forecast=Pfdr_forecast+ΔP。
The technical solution of the present invention further includes an adaptive distribution line ultra-short term load prediction system for implementing any of the above methods, wherein the system includes: the data acquisition module is used for acquiring the load data of a distribution transformer of the electricity utilization information acquisition system and the distribution data of the distribution automation system at the same time; the data normalization module is used for sequentially preprocessing historical load data of the distribution transformer and extrapolating a load prediction value of the distribution transformer by using a linear trend extrapolation ultra-short term load prediction algorithm based on similar days, wherein the preprocessing comprises the step of normalizing a reasonable range, missing data and redundant data of the load data of the distribution transformer; the data prediction module predicts the loss of the distribution line based on the data acquired by the data normalization module to obtain a prediction result; and the data correction module is used for correcting the prediction result to obtain a corrected prediction result.
The invention has the beneficial effects that: the method can automatically adapt to the change of the operation mode of the power distribution network. In the calculation process, the load prediction of the distribution transformer is synchronously realized, and the prediction of the line loss is completed, so that the application requirements of various distribution automation can be met, and the method has good popularization value.
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FIG. 1 shows a general flow diagram of a method according to the invention;
FIG. 2 is a block diagram of a system according to an embodiment of the present invention.
Detailed Description
The technical scheme of the invention comprises a self-adaptive distribution line ultra-short term load prediction method and a self-adaptive distribution line ultra-short term load prediction system, which are suitable for the following clear and complete description of the concept, the specific structure and the generated technical effect of the invention by combining the embodiment and the attached drawings so as to fully understand the aim, the scheme and the effect of the invention.
It should be noted that, unless otherwise specified, when a feature is referred to as being "fixed" or "connected" to another feature, it may be directly fixed or connected to the other feature or indirectly fixed or connected to the other feature. Furthermore, the descriptions of upper, lower, left, right, etc. used in the present disclosure are only relative to the mutual positional relationship of the constituent parts of the present disclosure in the drawings. As used in this disclosure, the singular forms "a", "an", and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. Furthermore, unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art. The terminology used in the description herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. As used herein, the term "and/or" includes any combination of one or more of the associated listed items.
It will be understood that, although the terms first, second, third, etc. may be used herein to describe various elements, these elements should not be limited by these terms. These terms are only used to distinguish one element of the same type from another. For example, a first element could be termed a second element, and, similarly, a second element could be termed a first element, without departing from the scope of the present disclosure. The use of any and all examples, or exemplary language ("e.g.," such as "or the like") provided herein, is intended merely to better illuminate embodiments of the invention and does not pose a limitation on the scope of the invention unless otherwise claimed.
Because of reasons such as line transformation, fault, overhaul or optimization operation, the operation mode of the distribution line often changes, which makes it difficult to perform line load prediction simply according to line outlet power: it is difficult to handle the unconventional operation modes such as line load transfer and partial section power failure.
Although the line operation mode is changed, the electricity utilization rule of the related user group is not changed. That is to say: regardless of the change of the operation mode, the power consumption power (load power) of the user can be supplied according to the current operation mode, and the power supply power at the line outlet (line head end) can be reversely deduced. For medium voltage distribution networks, the power measurement of the distribution transformer can be taken as the terminal load power.
Fig. 1 shows a general flow chart of the method according to the invention. The method specifically comprises the following steps: s1, acquiring the load data of the distribution transformer of the electricity consumption information acquisition system and the distribution data of the distribution automation system at the same time; s2, sequentially preprocessing historical load data of the distribution transformer, and extrapolating the load prediction value of the distribution transformer by using a linear trend extrapolation ultra-short term load prediction algorithm based on similar days, wherein the preprocessing comprises the step of normalizing the reasonable range, the missing data and the redundant data of the load data of the distribution transformer; s3, predicting the loss of the distribution line based on the data acquired in the step S2 to obtain a prediction result; and S4, correcting the prediction result to obtain a corrected prediction result.
Specifically, the method comprises the following steps:
assuming a distribution line in a certain operation mode, the electric topology search is used to obtain that the line supplies power to m distribution transformers, and according to the power balance principle (note: the power P described herein represents active power), the following steps are provided:
wherein, PfdrFor head-end power of the line, PkMeasured power, P, for the kth distribution transformerlossThe total power loss of the line.
Obviously, it is only necessary to predict the distribution load power P at each momentkAnd total line loss PlossThe total line power at each time can be found according to equation (1).
(1) The load prediction of the distribution transformer is carried out,
the existing distribution automation system is provided with few distribution transformer acquisition devices, and distribution transformers lack real-time measurement. The algorithm compensates the measurement deficiency in the distribution automation system by accessing the distribution and transformation load data of the power utilization information acquisition system (called the 'utilization and acquisition system' for short). The power measurement of the system is the basis of the electricity charge measurement, and relatively, the system has higher accuracy and stable data quality.
The problem that distribution transformer load is unknown can be effectively solved by accessing distribution transformer metering data of the utilization and acquisition system on the basis of own data of the distribution automation system. Generally, there is a time lag in obtaining the distribution transformation measurement data from the utilization system, and the transmission to the distribution automation system generally has a time delay of 2 hours to 1 day. Considering that the distribution transformer load prediction uses historical load data and has low requirement on the real-time performance of the data, the influence caused by the delayed transmission can be completely avoided.
Preprocessing distribution transformer historical load data:
the method is characterized in that historical data are normalized to become reasonable load data suitable for a prediction algorithm, and the method mainly comprises the following steps: verification of reasonable value ranges, completion of missing data, deletion of redundant data (such as data repeatedly sampled at the same time), and the like.
Selecting similar days:
similar days have similar load curves. In general, they can be divided into 3 categories according to date characteristics: working days, weekend rest days, special festivals and holidays. And sequentially taking out historical load data of a plurality of recent similar days of the same type according to the type of the predicted target date. In consideration of the data processing time performance and the stability of the algorithm, about 10 pieces of similar daily data are preferably adopted.
Generating a predicted value of the distribution transformer load:
the number of distribution changes needing to be processed is large, and a stable and efficient linear trend extrapolation ultra-short-term load prediction algorithm is adopted. The algorithm principle is simple, loads are extracted from the same time point of a plurality of similar days to form a single sequence, a polynomial is fitted by using a least square fitting method and extrapolated, and the loads of corresponding time points of a predicted day can be obtained, wherein the method mainly comprises the following steps:
setting the distribution transformation real load value of a certain time point at the t day as xtThe fitting value is XtLet us assume that fitting is performed using a straight-line model, and the expression with respect to time t is XtA + b × t, in addition, an error formula between the true value and the fitted value can be found,
namely rt=Xt-xt=a+b×t-xt (2)
Now a and b are also two unknown variables, to be drawnThe best result is obtained by obtaining the square of the errorIs calculated by taking the partial derivatives of the variables a and b in the formula to 0,
After being unfolded, have
And (5) solving the linear equation system (8) to obtain the values a and b. Finally, the load for the target prediction day (i.e., day N +1) can be simply expressed by the following equation:
XN+1=a+b(N+1) (6)
for each time point of the prediction day, one trend extrapolation calculation is used, and the obtained prediction points form a sequence, which is the final prediction result of the whole day.
(2) Prediction of line loss:
the method for calculating the real loss of the line can be obtained by transforming the formula (1):
wherein, PfdrMeasuring power, P, for the head end of the linekMeasured power, P, for the kth distribution transformerlossThe power loss of the line is calculated.
The line loss power at each time point on the similar day can be calculated by using the formula (7) and is marked as Ploss_t. And then, continuously applying a linear trend extrapolation algorithm to predict the line loss, and directly applying the formulas (5) and (6):
equation (8) is a system of equations of the ternary equation in which a 'and b' are linear extrapolation parameters, where Ploss_N+1And the target predicted value of the line loss is obtained.
(3) And (3) correcting a prediction result:
the predicted load value of each distribution transformer can be calculated according to the formulas (5) and (6) and is marked as Pk_forecast。
According to equation (8), the line loss at the corresponding time can be predicted and is denoted as Ploss_forecast。
Then, according to equation (1), a predicted line load value P can be calculatedfdr_forecast:
Generally, ultra-short-term load prediction predicts a load curve from the current time to several hours in the future, and the prediction result can be corrected to a certain extent by using the prediction deviation value of the current time:
ΔP=Pfdr_forecast(0)-Pfdr_forecast(0) (10)
wherein, the delta P is the prediction deviation value of the current time, Pfdr_forecast(0)For the current time real Pfdr_forecast(0)Value of measurement of the load, Pfdr_forecast(0)A load value is predicted for the current time.
The corrected load predicted value is as follows:
P'fdr_forecast=Pfdr_forecast+ΔP (11)
through the correction processing of the formula (11), not only the prediction error at the current moment is reduced to 0, but also the prediction result in the future is appropriately corrected, which is beneficial to reducing the whole prediction error.
FIG. 2 is a block diagram of a system according to an embodiment of the present invention. The method specifically comprises the following steps: the data acquisition module is used for acquiring the load data of a distribution transformer of the electricity utilization information acquisition system and the distribution data of the distribution automation system at the same time; the data normalization module is used for sequentially preprocessing historical load data of the distribution transformer and extrapolating a load prediction value of the distribution transformer by using a linear trend extrapolation ultra-short term load prediction algorithm based on similar days, wherein the preprocessing comprises normalizing a reasonable range, missing data and redundant data of the load data of the distribution transformer; the data prediction module predicts the loss of the distribution line based on the data acquired by the data normalization module to obtain a prediction result; and the data correction module is used for correcting the prediction result to obtain a corrected prediction result.
It should be recognized that embodiments of the present invention can be realized and implemented by computer hardware, a combination of hardware and software, or by computer instructions stored in a non-transitory computer readable memory. The methods may be implemented in a computer program using standard programming techniques, including a non-transitory computer-readable storage medium configured with the computer program, where the storage medium so configured causes a computer to operate in a specific and predefined manner, according to the methods and figures described in the detailed description. Each program may be implemented in a high level procedural or object oriented programming language to communicate with a computer system. However, the program(s) can be implemented in assembly or machine language, if desired. In any case, the language may be a compiled or interpreted language. Furthermore, the program can be run on a programmed application specific integrated circuit for this purpose.
Further, the operations of processes described herein can be performed in any suitable order unless otherwise indicated herein or otherwise clearly contradicted by context. The processes described herein (or variations and/or combinations thereof) may be performed under the control of one or more computer systems configured with executable instructions, and may be implemented as code (e.g., executable instructions, one or more computer programs, or one or more applications) collectively executed on one or more processors, by hardware, or combinations thereof. The computer program includes a plurality of instructions executable by one or more processors.
Further, the methods may be implemented in any type of computing platform operatively connected to a suitable connection, including but not limited to a personal computer, mini computer, mainframe, workstation, networked or distributed computing environment, separate or integrated computer platform, or in communication with a charged particle tool or other imaging device, and the like. Aspects of the invention may be embodied in machine-readable code stored on a non-transitory storage medium or device, whether removable or integrated into a computing platform, such as a hard disk, optically read and/or write storage medium, RAM, ROM, or the like, such that it may be read by a programmable computer, which when read by the storage medium or device, is operative to configure and operate the computer to perform the procedures described herein. Further, the machine-readable code, or portions thereof, may be transmitted over a wired or wireless network. The invention herein includes these and other different types of non-transitory computer-readable storage media when such media include instructions or programs that implement the above steps in conjunction with a microprocessor or other data processor. The invention also includes the computer itself when programmed according to the methods and techniques of the present invention.
A computer program can be applied to input data to perform the functions herein to transform the input data to generate output data that is stored to non-volatile memory. The output information may also be applied to one or more output devices, such as a display. In a preferred embodiment of the invention, the transformed data represents physical and tangible objects, including particular visual depictions of physical and tangible objects produced on a display.
The present invention is not limited to the above embodiments, and any modifications, equivalent substitutions, improvements, etc. within the spirit and principle of the present invention should be included in the protection scope of the present invention as long as the technical effects of the present invention are achieved by the same means. The invention is capable of other modifications and variations in its technical solution and/or its implementation, within the scope of protection of the invention.
Claims (3)
1. An adaptive distribution line ultra-short term load forecasting method is characterized by comprising the following steps:
s1, acquiring the load data of the distribution transformer of the electricity consumption information acquisition system and the distribution data of the distribution automation system at the same time; the method further comprises the following steps: obtaining total power of predicted circuit, using itIdentifying the total power of the line at each time instant, where PfdrFor line head power, PkMeasured power, P, for the kth distribution transformerlossIs the total power loss of the line;
s2, sequentially preprocessing historical load data of the distribution transformer, and extrapolating the load prediction value of the distribution transformer by using a linear trend extrapolation ultra-short term load prediction algorithm based on similar days, wherein the preprocessing comprises the step of normalizing the reasonable range, the missing data and the redundant data of the load data of the distribution transformer; the step S2 specifically includes: preprocessing distribution transformer historical load data, performing normalization processing on the distribution transformer load data, and specifically performing reasonable numerical range verification, missing data completion and redundant data deletion processing on the distribution transformer load data in a distribution change period in sequence; selecting similar days, and sequentially taking out historical load data of a plurality of recent similar days of the same type according to the type of the predicted target date; generating a load prediction value of the distribution transformer, and generating the load value of the distribution transformer by using a linear trend extrapolation ultra-short term load prediction algorithm;
the generation of the predicted value of the load of the distribution transformer specifically comprises the following steps:
extracting corresponding distribution transformer load data from the same time point of a plurality of similar days to form a single sequence, fitting a polynomial by using a least square fitting method and extrapolating to obtain the load of the corresponding time point of the predicted day, wherein the calculation formula isAnd a and b are 0, simplifying to obtain XN+1=a+b(N+1),
Wherein xtAnd XtRespectively the real load value of distribution transformer at a certain time point of the t dayThe fitting value, N is the total number of days, a and b are unknown variables, the formula is used for indicating that for each time point of the prediction day, trend extrapolation calculation is used once, each obtained prediction point forms a sequence, and the prediction result is further obtained;
s3, predicting the loss of the distribution line based on the data obtained in the step S2 to obtain a prediction result; the step S3 specifically includes:
The line loss is predicted by using a linear trend extrapolation algorithm, and the calculation mode is
Wherein a 'and b' are linear extrapolation parameters, wherein Ploss_N+1A target predicted value of the line loss is obtained;
and S4, correcting the prediction result to obtain a corrected prediction result.
2. The adaptive distribution line ultra-short term load forecasting method according to claim 1, wherein the step S4 specifically includes:
calculating the load predicted value of each distribution transformer as Pk_forecast;
Predicting the line loss at the corresponding time as Ploss_forecast;
Correcting the predicted value of the line load according to the predicted deviation value at the current moment, specifically to correct the predicted value of the line load according to the predicted deviation value at the current moment
ΔP=Pfdr_forecast(0)-Pfdr_forecast(0)Which isMiddle delta P is the predicted deviation value of the current time, Pfdr_forecast(0)For the actual load measurement value at the present moment, Pfdr_forecast(0)Predicting a load value for the current moment;
the corrected load predicted value is P'fdr_forecast=Pfdr_forecast+ΔP。
3. An adaptive distribution line ultra-short term load forecasting system for implementing the method of any of claims 1-2, the system comprising:
the data acquisition module is used for acquiring the load data of a distribution transformer of the electricity utilization information acquisition system and the distribution data of the distribution automation system at the same time;
the data normalization module is used for sequentially preprocessing historical load data of the distribution transformer and extrapolating a load prediction value of the distribution transformer by using a linear trend extrapolation ultra-short term load prediction algorithm based on similar days, wherein the preprocessing comprises the step of normalizing a reasonable range, missing data and redundant data of the load data of the distribution transformer;
the data prediction module predicts the loss of the distribution line based on the data acquired by the data normalization module to obtain a prediction result;
and the data correction module is used for correcting the prediction result to obtain a corrected prediction result.
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CN105552902A (en) * | 2016-01-25 | 2016-05-04 | 中国电力科学研究院 | Super-short-term forecasting method for load of terminal of power distribution network based on real-time measurement of feeder end |
CN107666149A (en) * | 2017-10-23 | 2018-02-06 | 珠海许继芝电网自动化有限公司 | A kind of medium voltage distribution network line loss calculation method |
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