CN112801415A - Ultra-short-term load prediction method and system based on Markov chain distribution model - Google Patents
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Abstract
The utility model provides an ultra-short term load forecasting method and system based on a Markov chain distribution model, which is used for acquiring power consumption data of a preset time period before a moment to be forecasted; inputting the power consumption data of the moment before the moment to be predicted into a preset Markov chain distribution model to obtain the power consumption data of the moment to be predicted; the method comprises the following steps of obtaining a training data set according to power consumption data of a preset time period, carrying out box separation on the training data set, calculating a transition matrix between boxes, and carrying out training on a Markov chain distribution model by combining the transition matrix; the method and the device solve the problem that neither standard of a reference model nor performance index is lacked in the probability load prediction, provide a potential reference for the probability load prediction and the correct use of the performance index, and improve the accuracy of the load prediction.
Description
Technical Field
The disclosure relates to the technical field of load prediction, in particular to an ultra-short-term load prediction method and system based on a Markov chain distribution model.
Background
The statements in this section merely provide background information related to the present disclosure and may not necessarily constitute prior art.
Prediction of power consumption has been a fundamental business problem for over a century. The business relates to energy system topics such as operations, energy trading, and power system planning. As a special case, short-term power usage forecasting is important for demand-side management and for policy making to reduce building energy consumption. Most power usage studies have focused on point forecasting, and over the past few decades, the number of studies focused on probabilistic load forecasting has increased.
Generally, probabilistic load prediction aims to provide probabilistic predictions of future states, which may be more valuable to the public than single point prediction. Typically, probabilistic predictions contain information about the uncertainty of random variables, not just expected values. This allows the decision maker to perform a worst case optimization (with a very high quantile) or a random optimization (with samples from the distribution), which can increase revenue. The probabilistic model may produce a median or mean of the prediction distribution, which may be interpreted as a point prediction. The large difference between point prediction and probability prediction is also that predictions are quantified using metrics, e.g., Root Mean Square Estimation (RMSE) is commonly used for point prediction, while Continuous Ranking Probability Scores (CRPS) can be used in probability prediction. However, researchers have suggested that probabilistic load prediction lacks a sophisticated evaluation index to a higher degree than point load prediction.
The inventors have found that probabilistic ultra-short term load prediction (i.e., prediction within one day), some of the early examples use a hybrid kalman filter to predict loads with a time resolution of 5 minutes, some use fractal regression (QR) to predict power consumption with a half-hour resolution in conjunction with gradient boosting, some use gaussian processes with ARIMA reference models to predict residential loads with a half-hour resolution, some use log-normal processes to predict residential loads with a half-hour resolution and compare them with gaussian processes, and some use random forests to predict hours with a power consumption resolution and compare them with regression trees and support vector regression as references. It can be concluded that the lack of both the benchmark model standards and performance metrics in probabilistic load prediction is a relatively immature impact in the PLF domain compared to deterministic load prediction and remains to be solved.
Disclosure of Invention
In order to overcome the defects of the prior art, the ultra-short-term load prediction method and system based on the Markov chain distribution model solve the problem that neither standard of a reference model nor performance index is lacked in probability load prediction, provide a potential reference for probability load prediction and correct use of the performance index, and improve the accuracy of load prediction.
In order to achieve the purpose, the following technical scheme is adopted in the disclosure:
the disclosure provides an ultra-short term load prediction method based on a Markov chain distribution model.
An ultra-short-term load prediction method based on a Markov chain distribution model comprises the following steps:
acquiring power consumption data of a preset time period before a time to be predicted;
inputting the power consumption data of the moment before the moment to be predicted into a preset Markov chain distribution model to obtain the power consumption data of the moment to be predicted;
the method comprises the steps of obtaining a training data set according to power consumption data of a preset time period, carrying out box separation on the training data set, calculating a transition matrix between boxes, and carrying out training on a Markov chain distribution model by combining the transition matrix.
A second aspect of the disclosure provides an ultra-short term load prediction system based on a markov chain distribution model.
An ultra-short term load prediction system based on a Markov chain distribution model, comprising:
a data acquisition module configured to: acquiring power consumption data of a preset time period before a time to be predicted;
a load prediction module configured to: inputting the power consumption data of the moment before the moment to be predicted into a preset Markov chain distribution model to obtain the power consumption data of the moment to be predicted;
the method comprises the steps of obtaining a training data set according to power consumption data of a preset time period, carrying out box separation on the training data set, calculating a transition matrix between boxes, and carrying out training on a Markov chain distribution model by combining the transition matrix.
A third aspect of the present disclosure provides a computer-readable storage medium, on which a program is stored, which when executed by a processor, implements the steps in the markov chain distribution model-based ultra-short term load prediction method according to the first aspect of the present disclosure.
A fourth aspect of the present disclosure provides an electronic device, including a memory, a processor, and a program stored on the memory and executable on the processor, where the processor implements the steps in the markov chain distribution model-based ultra-short term load prediction method according to the first aspect of the present disclosure when executing the program.
Compared with the prior art, the beneficial effect of this disclosure is:
the method, the system, the medium or the electronic equipment disclosed by the disclosure realize the load probability prediction of the future state, solve the problem that the probability load prediction lacks both the standard of a reference model and the performance index, and provide a potential reference for the probability load prediction and the correct use of the performance index.
Advantages of additional aspects of the disclosure will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the disclosure.
Drawings
The accompanying drawings, which are included to provide a further understanding of the disclosure, illustrate embodiments of the disclosure and together with the description serve to explain the disclosure and are not to limit the disclosure.
Fig. 1 is a conceptual illustration of an MCM model prediction process for ultra-short term load prediction based on a markov chain distribution model according to embodiment 1 of the present disclosure.
Fig. 2 is example power consumption data of ultra-short term load prediction based on a markov chain distribution model according to embodiment 1 of the present disclosure.
Fig. 3 is a reliability diagram associated with MCM, QR, and PeEn simulations of ultra-short term load prediction based on a markov chain distribution model according to embodiment 1 of the present disclosure.
Fig. 4 is an rMAE diagram of ultra-short term load prediction based on a markov chain distribution model according to embodiment 1 of the present disclosure.
Fig. 5 is a PINAW diagram for MCM, QR, and PeEn simulation based on ultra-short term load prediction of a markov chain distribution model according to embodiment 1 of the present disclosure.
Fig. 6 is nCRPS results of MCM, QR and PeEn for ultra-short term load prediction based on a markov chain distribution model according to embodiment 1 of the present disclosure.
Fig. 7 is a sensitivity analysis of ultra-short term load prediction based on a markov chain distribution model according to embodiment 1 of the present disclosure.
Detailed Description
The present disclosure is further described with reference to the following drawings and examples.
It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the disclosure. 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 to which this disclosure belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments according to the present disclosure. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, and it should be understood that when the terms "comprises" and/or "comprising" are used in this specification, they specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof, unless the context clearly indicates otherwise.
The embodiments and features of the embodiments in the present disclosure may be combined with each other without conflict.
Example 1:
as shown in fig. 1 to 7, embodiment 1 of the present disclosure provides a method for ultra-short term load prediction based on a markov chain distribution model, including the following steps:
step 1: the method is used for training a data set of power consumption of a user and completing the prediction of the power consumption of the user by using an MCM model half an hour in advance, and comprises the following steps: binning a training data set, calculating a transition matrix M for transitions between bins, training the data set, and estimating a nonparametric probability distribution for a next time step using an input test data value.
Step 2: for verifying reliability and correctness of MCM models, comprising: comparing the prediction result with a persistent integration (PeEn) serving as a simple reference model, comparing the result with a Quantile Regression (QR) serving as a high-level reference model, comparing the reliability, the average absolute error (rMAE), the normalized average width of the Prediction Interval (PINAW), the normalized continuous ranking probability score (nCRPS) and sensitivity analysis under the three models.
Step 1.1: performing box separation on the training data set;
defining a training and testing resident electricity time series [ a, b ] within a limit, selecting N boxes for use in the model, classifying the training time series into the N boxes and evenly distributing [ a, b ] over the range.
Step 1.2: calculating a transition matrix M for conversion between boxes;
by counting the number of transitions from one state to another in the training data. That is, the transition matrix MijState transition i → j for i, j ∈ [1, N)]Can be estimated from the following training data:
wherein n isijIs the number of transitions from state i to j, from one time step to the next (including transitions from state to itself) in the entire training time sequence.
Equation (1) estimates the number of transitions from state i to j, which are normalized using the sum of the transitions from state in order to keep the total probability of transitions constant, the transition matrix being resolution dependent, in this embodiment half an hour resolution is used, and if the resolution is changed, the model needs to be retrained.
Step 1.3: training the data set;
observing x (t) to which test data t corresponds and determining which bin i e [1, … …, N ] it belongs, row i of the transition matrix M corresponds to a piecewise-evenly-distributed prediction for x (t +1), changing time step t → t +1 in order to predict power usage at the next time step, and then starting a iteration using the new observation x (t +1) and determining which bin it belongs to, which makes the prediction method recursive.
The predicted probability distribution of x (t) is equal to the uniform distribution of the segments corresponding to the ith row of the transition matrix. Formally, the probability density function f for a prediction x (t +1) can be expressed as:
n is the nth box of observed data points, each fi(x)＝μ(xi,xi+1) Is defined as
A uniform probability density distribution.
Step 2.1: acquiring a data set;
the data used in this example includes residential power usage in the Sydney district of Australia. The data set is publicly available, containing 300 anonymous residential customers, whose electricity consumption was measured every half hour from 7/1/2010 to 6/30/2013. Through a careful data cleansing process, data was predicted by randomly selecting 69 th, 74 th, 157 th, 211 th and 274 th customers from 54 customers in the next three years, for a total of 17536 data points per year for each customer.
Step 2.2: setting in a simulation mode;
the simulation is divided into multiple scenarios, in each of which the electricity usage for a customer one year is predicted half an hour ahead. This is based on the training data for the remaining two years of power usage for the same customer. Thus, the model can be used to generate predictions for each house (69, 74, 157, 211, and 273) per year (1, 2, 3), for a total of 15 simulation scenarios. The training data sets each contained 35072 data points and the test data sets each contained 17536 data points. For the protocol, to enable 10-step adjustment of QR and PeEn, the first data point predicted in each test dataset is data point 11 in 17536. Specifically, the results are shown in Table 1.
Table 1: average value (KW)/standard deviation (KW) of each quantity of electricity in the data set used
Step 2.3: comparing the prediction results with a persistent ensemble (PeEn) as a simple reference model and a Quantile Regression (QR) as an advanced reference model;
as a simple reference model, continuous integration (PeEn), a common probabilistic predictive reference model, is used in this embodiment, where x (t +1) defines the prediction of power usage as the previous power usage data point x (t), x (t-1), …, x (t- (h-1)) one step ahead. Here h is chosen to be 10, which is an arbitrary choice. However, in order to correct such ambiguity, sensitivity analysis is performed, which is different in this case. The intuitive explanation for persistent integration is that it generalizes the persistent prediction horizon for deterministic predictions to probabilistic prediction settings.
As an alternative to continuous integration, a high-level form of Quantile Regression (QR) is used as a benchmark in the present embodiment to generate probabilistic predictions of power usage. The QR model adapted to power usage is implemented using the quantreg software package in R, and the following is a brief introduction to the general QR model, including particular applications in predicting power usage.
QR is similar to linear regression-a linear relationship between an explanatory variable x and an output y is proposed:
y＝xβ+∈ (3)
β is the vector of parameters and e is the random error.
To learn parameters
The following minimization problems must be solved:
τ represents the quantile probability (0)<τ<1)，ρτIs a marble loss function, which is a typical loss used in QR predictionThe loss function, defined as:
according to (6), each quantile is estimated independently, so there is a risk that the model may violate monotonicity:
In this embodiment, y (τ) is the quantile τ e [1, …, Q of the power consumption amount x (t +1) of the prediction time step t +1]The predicted value of (2). This is done by the time step before x (t) and the previous training
The parameters are calculated. In this embodiment, the quantile Q is typically set to 19, evenly distributed over [0.05, …, 0.95 ]]。
Step 2.4: comparing the reliability and the mean absolute error (rMAE) under the three models;
as a method of comparing the reliability of the model, it is estimated as reliability mae (rmae) from the average absolute deviation of the diagonal and the number of average bits q (τ).
It is estimated from the average absolute deviation of the diagonal and the average number of bits q (τ) as reliability mae (rmae), and expressed as:
q is the quantile, which is also called the difference or reliability index.
The similarity between MCM and QR is predicted by analyzing the data set and the model median and prediction interval for power usage data, MCM, QR, and PeEn, but qualitatively different, with one specific example being the difference in prediction intervals for different models associated with a large peak at hour 13. Here, both MCM and QR have short high peaks in the prediction interval width, PeEn has lower but wider peaks because PeEn contains higher peaks in several steps after its occurrence.
All models were approximately aligned to the diagonal by analyzing the reliability map, but each data set had some variability, except for PeEn, which typically underestimates the variation of the data.
By calculating rMAE to vary from house to house and year to year, we conclude that PeEn has the highest rMAE in all cases, which means MCM and QR are more reliable.
Step 2.5: comparing the normalized average widths (PINAWs) of the prediction intervals under the three models;
the clarity of the prediction interval is measured by a PINAW score, which is defined as:
t is the number of data points in the time series, η is the nominal coverage, qt,τIs the quantile of τ to the observation number t, and R is a normalization constant, generally defined as the difference between the maximum and minimum of the test data set. Here, the normalization constant is defined as R ═ b-a |, [ a, b |, and]is the scope of the test data set.
By calculating PINAW, the quantile in the graph is less since the PeEn prediction contains only 10 data points. Overall, all models are of comparable clarity, with some variation between customers and years. Overall, MCM and QR are very similar, with QR usually being slightly superior in clarity.
Step 2.6: comparing normalized continuous ranking probability scores (nCRPS) under the three models;
clarity and reliability are quantified by nCRPS score for observation t is defined as:
Ftis a cumulative distribution function of the predicted distribution, ytIs the observed value and R is the range of the experimental data set. nCRPS is the predicted average per year.
The average nCRPS of both MCM and QR is better than PeEn by calculating nCRPS, in detail, QR is lowest in average nCRPS of 11 scenes, and MCM is lowest in average nCRPS of 4 scenes. On average, the similarity is high, with an average nCRPS of 2.5 for MCM, 2.45 for QR, and only 2% lower for QR.
Step 2.7: comparing the sensitivity analysis under the three models;
sensitivity by analysis MCM was constant in these simulations since it only depends on a time step lag. With nCRPS, MCM and QR converge to reduce latency, while PeEn has more variable patterns and is less effective than MCM and QR for all latencies. With regard to rMAE, MCM and QR converge to lower hysteresis in a similar manner as nCRPS, but in this case PeEn drops and approaches zero as the number of hysteresis increases. This is because the distribution of the PeEn converges to the distribution of the test data set as the lag increases. For less than about 24 lags, MMA and QR perform excellently in rMAE.
Example 2:
the embodiment 2 of the present disclosure provides an ultra-short term load prediction system based on a markov chain distribution model, including:
a data acquisition module configured to: acquiring power consumption data of a preset time period before a time to be predicted;
a load prediction module configured to: inputting the power consumption data of the moment before the moment to be predicted into a preset Markov chain distribution model to obtain the power consumption data of the moment to be predicted;
the method comprises the steps of obtaining a training data set according to power consumption data of a preset time period, carrying out box separation on the training data set, calculating a transition matrix between boxes, and carrying out training on a Markov chain distribution model by combining the transition matrix.
The working method of the system is the same as the ultra-short-term load prediction method based on the markov chain distribution model provided in embodiment 1, and details are not repeated here.
Example 3:
the embodiment 3 of the present disclosure provides a computer-readable storage medium, on which a program is stored, which when executed by a processor, implements the steps in the ultra-short term load prediction method based on the markov chain distribution model according to the embodiment 1 of the present disclosure.
Example 4:
an embodiment 4 of the present disclosure provides an electronic device, which includes a memory, a processor, and a program stored in the memory and executable on the processor, where the processor executes the program to implement the steps in the method for predicting an ultra-short term load based on a markov chain distribution model according to embodiment 1 of the present disclosure.
As will be appreciated by one skilled in the art, embodiments of the present disclosure may be provided as a method, system, or computer program product. Accordingly, the present disclosure may take the form of a hardware embodiment, a software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present disclosure may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, optical storage, and the like) having computer-usable program code embodied therein.
The present disclosure is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the disclosure. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
It will be understood by those skilled in the art that all or part of the processes of the methods of the embodiments described above can be implemented by a computer program, which can be stored in a computer-readable storage medium, and when executed, can include the processes of the embodiments of the methods described above. The storage medium may be a magnetic disk, an optical disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), or the like.
The above description is only a preferred embodiment of the present disclosure and is not intended to limit the present disclosure, and various modifications and changes may be made to the present disclosure by those skilled in the art. Any modification, equivalent replacement, improvement and the like made within the spirit and principle of the present disclosure should be included in the protection scope of the present disclosure.
Claims (10)
1. An ultra-short-term load prediction method based on a Markov chain distribution model is characterized in that: the method comprises the following steps:
acquiring power consumption data of a preset time period before a time to be predicted;
inputting the power consumption data of the moment before the moment to be predicted into a preset Markov chain distribution model to obtain the power consumption data of the moment to be predicted;
the method comprises the steps of obtaining a training data set according to power consumption data of a preset time period, carrying out box separation on the training data set, calculating a transition matrix between boxes, and carrying out training on a Markov chain distribution model by combining the transition matrix.
2. The ultra-short term load prediction method based on a markov chain distribution model of claim 1, wherein:
acquiring a resident electricity consumption time sequence in the electricity consumption data, selecting a plurality of boxes used in the model, classifying the training time sequence into each box, and performing average distribution on the resident electricity consumption time sequence data.
3. The ultra-short term load prediction method based on a markov chain distribution model of claim 1, wherein:
the transition matrix is estimated from the transitions that occur between bins in the training data time series.
4. The ultra-short term load prediction method based on the markov chain distribution model of claim 3, wherein:
the transition matrix is derived from counting the number of transitions from one state to another in the training data.
5. The ultra-short term load prediction method based on the markov chain distribution model of claim 4, wherein:
and normalizing the transition matrix by using the sum of the state transition times.
6. The ultra-short term load prediction method based on a markov chain distribution model of claim 1, wherein:
and the electricity consumption data at the moment before the moment to be predicted belongs to the ith box, and the prediction probability density distribution at the moment to be predicted is equal to the subsection uniform distribution corresponding to the ith row of the transition matrix.
7. The ultra-short term load prediction method based on the markov chain distribution model of claim 6, wherein:
according to the prediction probability distribution of the moment before the moment to be predicted, combining the transition matrix to obtain the probability density distribution result of the moment to be predicted
8. An ultra-short term load prediction system based on a Markov chain distribution model is characterized in that: the method comprises the following steps:
a data acquisition module configured to: acquiring power consumption data of a preset time period before a time to be predicted;
a load prediction module configured to: inputting the power consumption data of the moment before the moment to be predicted into a preset Markov chain distribution model to obtain the power consumption data of the moment to be predicted;
the method comprises the steps of obtaining a training data set according to power consumption data of a preset time period, carrying out box separation on the training data set, calculating a transition matrix between boxes, and carrying out training on a Markov chain distribution model by combining the transition matrix.
9. A computer-readable storage medium, on which a program is stored, which program, when being executed by a processor, carries out the steps of the markov chain distribution model-based ultra-short term load prediction method according to any one of claims 1 to 7.
10. An electronic device comprising a memory, a processor and a program stored on the memory and executable on the processor, wherein the processor implements the steps of the markov chain distribution model based ultra short term load prediction method of any one of claims 1 to 7 when executing the program.
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