CN110889554A - Power load fluctuation analysis and risk early warning method based on recurrence time interval analysis method - Google Patents

Abstract

The invention discloses a power load fluctuation analysis and risk early warning method based on a recurrence time interval analysis method. The method comprises the following steps: preprocessing data, fitting a power load fluctuation recurrence time interval data sequence, and constructing a recurrence time interval sequence probability distribution model; constructing a conditional probability density function model, and verifying the short-term correlation of the recurring time interval of the power load; predicting the extreme fluctuation risk loss probability in the power load fluctuation re-time interval sequence by combining the risk function and the loss probability distribution function; judging the long-term correlation of the power load recurrence time interval; and extracting data points which have no influence on the whole fluctuation of the original load data sequence as critical points of normal fluctuation of the load data sequence, namely a load risk early warning threshold. The method provides an objective reference threshold value for risk early warning, avoids blindness of subjective experience determination, analyzes typical industrial load fluctuation, and provides a reference basis for scientific power grid planning and safe and stable operation.

Description

Power load fluctuation analysis and risk early warning method based on recurrence time interval analysis method

Technical Field

The invention belongs to the technical field of power system planning, and particularly relates to a power load fluctuation analysis and risk early warning method.

Background

As a key link in power system planning and daily operation, the result of load prediction directly influences the construction and development planning of a power grid, and accurate prediction of power load becomes a key problem which is increasingly concerned by power supply companies and power utilization enterprises. For a long time, scholars have made a lot of research on load prediction and established a lot of prediction models. However, these load prediction models are mainly based on load data of the entire region, and there is no study on load prediction of a specific power utility industry. And most of the areas with stable load or strong regularity are subjected to less research on the power utilization industry with large load fluctuation. Under the environment of electric power marketization, higher requirements are put forward on the utilization efficiency of electric energy, so that the current situation of power utilization of each electric industry in China is changed newly, and a new load fluctuation characteristic is presented. Therefore, load prediction research needs to be carried out for typical industries in China, particularly for the electricity utilization industry with certain impact load. To develop load forecasting studies for a typical power utility industry, studies on the load fluctuation characteristics of a specific power utility industry cannot be ignored. Extreme load fluctuations may cause a regional grid to be paralyzed and even have a great risk of causing serious accidents, which requires that power supply companies have load management strategies for different industries, in particular risk early warning for extreme fluctuations of power load. Therefore, the development of the risk early warning research of extreme fluctuation is of great significance.

Time series analysis is one of quantitative prediction methods, and is to establish a mathematical model capable of accurately reflecting dynamic relations contained in a sequence according to observation data with limited length so as to realize future prediction. Time series analysis methods are widely used in load prediction, and examples of the widely used models include an autoregressive model, a moving average model, an autoregressive-moving average model, and the like. The time series method is mainly applied to short-term load prediction. In addition, the scholars also provide a fuzzy time series prediction model aiming at the problem that the random factor of the time series method is greatly changed.

In recent years, risk early warning for power loads is mainly to determine the risk level or state through risk identification, risk system construction and evaluation, the methods have subjective experience, an algorithm is generally required to weaken subjective factors, the method belongs to static evaluation, and the method is not suitable for real-time risk early warning with high requirement on reaction speed. Because the occurrence of the load fluctuation risk, especially the extreme fluctuation risk, is often accompanied with the occurrence of the electric power safety accident, in the past load risk early warning research, the load is generally alarmed when the load is about to reach the system peak value, or the load is compared and monitored according to a historical load prediction curve and an actual load, the adoption of the mode has no unified standard for the threshold value of the load risk early warning, and the load risk early warning is often limited according to statistical experience or man-made, lacks of theoretical basis, and brings uncertain influence to the electric power load risk management.

Disclosure of Invention

In order to solve the technical problems mentioned in the background art, the invention provides a power load fluctuation analysis and risk early warning method based on a recurrence time interval analysis method.

In order to achieve the technical purpose, the technical scheme of the invention is as follows:

a power load fluctuation analysis and risk early warning method based on a recurrence time interval analysis method comprises the following steps:

(1) preprocessing the data, fitting the power load fluctuation recurrence time interval data sequence based on a least square method, and constructing a power load fluctuation recurrence time interval sequence probability distribution model;

(2) establishing a conditional probability density function model, and verifying whether short-term correlation exists at the time interval of power load reproduction so as to determine whether risk prediction can be carried out through the short-term correlation;

(3) predicting the extreme fluctuation risk loss probability in the power load fluctuation re-time interval sequence by combining the risk function and the loss probability distribution function;

(4) judging whether the power load recurrence time interval has long-term correlation or not by adopting multi-fractal detrending fluctuation analysis;

(5) and extracting data points which have no influence on the overall fluctuation of the original load data sequence on the basis of verifying the existence of long-term correlation, taking the data points as critical points of normal fluctuation of the load data sequence, and further determining a load risk early warning threshold value according to the numerical values of the critical points.

Further, in the step (1), the data preprocessing comprises a logarithmic processing and a standardization processing; the logarithm processing is as follows:

r(t)＝lnl(t)-lnl(t-Δt) (1)

in the above formula, r (t) is a power load fluctuation sequence, l (t) is a power load at time t, and Δ t is a sample data sampling frequency; the normalization process is as follows:

in the above formula, R (t) is a normalized value of r (t), E represents a mathematical expectation of the variable, [ Er (t)²-E²r(t)]^1/2Is the standard deviation of r (t).

Further, in step (1), for each threshold q, a power load fluctuation recurrence time interval sequence is defined as a time interval τ (t) between sequences r (t) exceeding the threshold q:

τ(t)＝min{t-t′:R(t)＞q,t＞t′,q＞0} (3)

in the above formula, t' refers to a previous time point when the load fluctuation exceeds a certain threshold q.

Further, in the step (1), the power load fluctuation recurrence time interval sequence probability distribution model is constructed as follows:

(101) based on a least square fitting method, a tensile index function is selected as a fitting function of a reproduction time interval sequence, and the standard form is as follows:

in the above formula, a, β and gamma are function parameters, e is a natural constant,

is the mean value of the time intervals of recurrence of the fluctuations of the power load determined by a threshold q, the probability distribution function of the time intervals of recurrence of the fluctuations of the power load τ being P for a given threshold q_q(τ)；

(102) And estimating function parameters of the tensile index by adopting a least square method, and performing single-sample K-S test to reproduce the coincidence degree of time interval distribution and tensile index function distribution.

Further, in step (102), the method of the single-sample K-S test is as follows:

first, assume that: the empirical distribution is the same as the best fit tensile index distribution;

secondly, calculating K-S statistic D between the fitting sample and the simulation sample_ma：

D_max＝max(|F_q-F_SE|) (5)

In the above formula, F_qFor empirical cumulative distribution under corresponding threshold, F_SEIs a cumulative distribution integrated by a fitted tensile index;

then, given the significance level α and the number of sample data, the threshold value D of the single-sample K-S suggestion is determined_αGenerating M synthetic samples from the best fit distribution, and then reconstructing a cumulative distribution F of the simulated samples from the integrals of the fitted stretch indices_simAnd its cumulative distribution function F_sim,SETo determine K-S statistics D between the fitted and simulated samples_α：

D_α＝max(|F_sim-F_sim,SE|) (6)

If D is_max<D_αThen the assumption is true, otherwise the assumption is false.

Further, in step (2), the method for verifying the short-term correlation of the power load recurring time interval is as follows:

(201) introducing a conditional probability density function P_q(τ|τ₀)，P_q(τ|τ₀) Defined as the extreme fluctuation having occurred twice in succession at the same threshold q, with a time interval τ₀Then the probability of extreme fluctuations occurring again within the time interval of τ from this moment;

(202) setting the fluctuations above a threshold q to extreme fluctuations, for a given threshold q, obtaining a number N_qThe sequence Q is arranged in ascending order and is equally distributed among four different subsequences Q₁、Q₂、Q₃、Q₄Inner, i.e. Q ═ Q₁∪Q₂∪Q₃∪Q₄Wherein

i is not equal to j; then calculating the same threshold q at the reproduction time interval tau₀Lower, conditional probability density function P_q(τ|Q_i)＝P_q(τ|τ₀，τ₀∈Q_i) And performing short-term correlation judgment: if the recurring sequence of time intervals does not have short-term correlation, then there is P_q(τ|Q_i)＝P_q(τ|Q_j)，i≠j。

Further, in step (3), the method for predicting the probability of the extreme fluctuation risk loss in the power load fluctuation re-time interval sequence is as follows:

(301) introducing a risk function W_q(Δt|t)，W_q(Δ t | t) is defined as the probability that a certain extreme fluctuation exceeding the threshold q has occurred at least once before t unit time, and then at least once again in the future Δ t |:

(302) and (3) analyzing the rule that the extreme fluctuation recurrence risk probability changes along with the threshold value by adopting a risk value method and utilizing a loss probability distribution function:

probability of loss of risk P at threshold q^*The calculation formula of (2):

in the above formula, P (R) is a probability distribution function of the normalized sequence R (t);

calculating a reproduction time interval average

In the above formula, τ_q,iAn ith re-time interval in the sequence of load fluctuation re-time intervals that exceeds the threshold q; n is a radical of_qFor the number of reproduction time intervals below the threshold q,

approximately equal to the total number of reproduction time sequences;

predicting risk loss probability:

in the above formula, number of R (t) ≧ q indicates the number of sequences R (t) which is equal to or greater than the threshold value q; total number R (t) represents the total number of sequences R (t).

Further, a risk function W_q(Δ t | t) is calculated according to the following formula:

in the above formula, τ_qRefers to a load fluctuation re-interval exceeding a threshold q; count (t)<τ_qT + Δ t) represents the number of times the temporal interval lies within the interval (t, t + Δ t) when reproduced at the same threshold, count (τ)_q>t) represents the number of reproduction time intervals exceeding t.

Further, in step (4), a long-term correlation index of the power load fluctuation re-interval sequence is calculated, and if the long-term correlation index is within the [0.5,1] interval, it indicates that there is a long-term correlation, otherwise there is no long-term correlation.

Further, in step (5), the load risk early warning threshold is determined by the following method:

(501) let the original power load data sequence be L ═ L_iI 1,2, … …, N being the sequence length, determining the minimum value L in the sequence L_minMaximum value l_maxAnd a demarcation reference value

Is the average of the raw power load data;

(502) the dispersion of the original payload data sequence and the sequence D are then calculated:

(503) with l_maxThe interval d is obtained from [1/100,1/20 ] of the power load data sequence L]Randomizing the mth interval L_m＝{l_j,l_j≤l_maxD x m, the remaining data sequences being kept unchanged, so as to obtain in turn a new load data sequence, a dispersion of the new data sequence and a sequence D_J：

Wherein m is int (1,2, …, (l)_max-RV)/d), int represents the value calculation, J ═ l_max-d×m；

(504) With l_minRandomizing the mth interval L with RV as the end point_m＝{l_j,l_j≥l_minThe data sequence of + dXm } and the rest data sequences are not changed, so as to obtain new load sequence, obtain dispersion of new data sequence and sequence D_J：

Wherein, the interval d is the same as the step (503), m is int (1,2, …, (l)_max-RV)/d)，J＝l_min+d×m；

(505) Respectively calculating the dispersion of the load data sequences obtained in the steps (503) and (504) and the sequence D_JOf the Hurst index h_q ^JDrawing h_q ^JHurst index h of curve and power load fluctuation re-time interval sequence_qBy contrast, when only extreme data is replaced, h_q ^JTrend of change and h_qClose, when the number of substitute data is as high as h_q ^JAbrupt change occurs and the change trend deviates from h_qThe time abrupt change point is a critical value point of an extreme data point of the power load data sequence, namely a load risk early warning threshold.

Adopt the beneficial effect that above-mentioned technical scheme brought:

the method can provide reference basis for scientific power grid planning and operation, predict the risk probability of extreme load fluctuation, ensure the safe and stable operation of the power grid, and provide reference for power utilization enterprises to formulate economic power utilization strategies. The invention can also objectively determine the risk early warning threshold value, and avoids the subjectivity and the risk of the conventional risk threshold value determination method.

Drawings

FIG. 1 is a flow chart of a method of the present invention;

FIG. 2 is a graphical illustration of the logarithmic return of a sequence of power load fluctuations;

FIG. 3 is a graph showing a comparison of empirical and theoretical probability distributions for recurring time intervals at different thresholds;

FIG. 4 is a graph showing a comparison of scaled probability densities using ratios of the mean values of the recurring time intervals at different thresholds;

in FIG. 5 is₀∈Q₁And τ₀∈Q₄Comparing the conditional probability density function of (1) with a schematic diagram;

fig. 6 shows the risk function W when the threshold q is 1.0, 1.2, 1.4, 1.6, 1.8_qA diagram of empirical (scatter) and theoretical (curve) values for (Δ t 15| t);

FIG. 7 is a graph illustrating a loss probability function at a threshold q;

FIG. 8 is a schematic diagram of a p-order Hurst index result of a multi-fractal detrending fluctuation analysis;

fig. 9 is a schematic diagram of determining the power load risk early warning threshold.

Detailed Description

The technical scheme of the invention is explained in detail in the following with the accompanying drawings.

The invention designs a power load fluctuation analysis and risk early warning method based on a recurrence time interval analysis method, as shown in figure 1, the steps are as follows:

s1: preprocessing data, fitting a power load fluctuation recurrence time interval data sequence based on a least square method, and constructing and establishing a load fluctuation recurrence time interval sequence probability distribution model;

s2: constructing a conditional probability density function model, and verifying whether short-term correlation exists at the time interval of power load reproduction so as to determine whether risk prediction can be carried out through the short-term correlation;

s3: predicting the extreme fluctuation risk loss probability in the power load fluctuation re-time interval sequence by combining the risk function and the loss probability distribution function;

s4: judging whether the power load recurrence time interval has long-term correlation by adopting traditional multi-fractal detrended fluctuation analysis (MF-DFA);

s5: and extracting data points which have no influence on the overall fluctuation of the original load data sequence on the basis of verifying the existence of long-term correlation, taking the data points as critical points of normal fluctuation of the load data sequence, and further determining a load risk early warning threshold value according to the numerical values of the critical points.

In this embodiment, the step S1 can be implemented by the following preferred scheme:

the data preprocessing process is divided into two parts:

(1) first, in order to smooth data and improve the collinearity and heteroscedasticity of data, the data is subjected to a logarithmic process, and therefore, the power load fluctuation is a logarithmic difference between two adjacent load values, which is expressed as follows:

r(t)＝lnl(t)-lnl(t-Δt) (1)

where l (t) denotes the power load at time t, and Δ t is the sample data sampling frequency.

(2) Then, the power load fluctuation data sequence is standardized:

wherein E represents the mathematical expectation of the variable, [ Er (t)²-E²r(t)]^1/2Is the standard deviation of r (t), for each threshold q, a set of data of the load fluctuation reproduction time interval τ is obtained, the sequence of load fluctuation reproduction time intervals is defined as the time interval between successive load time sequences r (t) exceeding a certain threshold q, and the mathematical expression of the sequence of reproduction time intervals τ (t) is as follows:

τ(t)＝min{t-t′:R(t)＞q,t＞t′,q＞0} (3)

the method for constructing the power load fluctuation recurrence time interval sequence probability distribution model comprises the following steps:

firstly, based on a least square fitting method, a tensile index function is selected as a fitting function of a reproduction time interval sequence, and the standard form is as follows:

where a, β and gamma are function parameters,

is a mean value of the recurring time intervals of the fluctuations determined by a threshold q, the probability distribution function of the recurring time intervals τ being, for a given threshold q, ofP_q(τ)。

And estimating function parameters by adopting a least square method, and performing single-sample K-S detection to reproduce the coincidence degree of time interval distribution and tensile index function distribution.

The K-S test method comprises the following steps:

first, an assumption is made: assuming the empirical distribution is the same as the best fit tensile index distribution proposed by the present invention, then a single sample K-S test is performed.

Then calculating K-S statistic D between the fitting sample and the simulation sample_maxThe calculation formula is as follows:

D_max＝max(|F_q-F_SE|) (5)

wherein, F_qFor empirical cumulative distribution under corresponding threshold, F_SEIs the cumulative distribution integrated by the fitted stretch index.

Then, given the significance level α and the number of sample data, the threshold value D of the single-sample K-S suggestion is determined_αSignificance level α was taken to be 0.05, 1000 synthetic samples were generated from the best fit distribution, and the cumulative distribution F of the simulated samples was then reconstructed from the integration of the fitted stretch indices_simAnd its cumulative distribution function F_sim,SETo determine K-S statistics D between the fitted and simulated samples_α：

D_α＝max(|F_sim-F_sim,SE|) (6)

If D is_max<D_αThen the assumption is true, otherwise the assumption is false.

In this embodiment, the step S2 can be implemented by the following preferred scheme:

the short-term correlation of the recurring time interval of load fluctuations is mainly divided into two parts:

1. introducing a conditional probability density function P_q(τ|τ₀)

P_q(τ|τ₀) Defined as the extreme fluctuation having occurred twice in succession at the same threshold q (at the same fluctuation level), with a time interval τ₀Then the probability of extreme fluctuations occurring again within the time interval of τ from this moment。

2. Verifying short-term correlations

Setting the fluctuation exceeding a certain threshold q as an extreme fluctuation, we can judge whether the probability of the extreme fluctuation reoccurring within a time interval and the reproduction time interval tau between the two extreme fluctuations₀There is a short-term correlation. If different threshold values q are corresponded, the load fluctuation reappears the time interval conditional probability density function P_q(τ|τ₀) Independent of τ₀The value of (A) is that the time series of the study object has no memory. In order to obtain accurate results, the invention does not adopt a fixed reproduction time interval, but changes the reproduction time interval within a fixed interval, and for a given threshold value, the probability distribution of four subsequences is distributively analyzed by dividing a reproduction time interval sequence into four disjoint subsets according to ascending order, so as to carry out memorability verification.

For a given threshold q, a number N is obtained_qThe sequence Q is arranged in ascending order and is equally distributed among four different subsequences Q₁、Q₂、Q₃、Q₄Inner, i.e. Q ═ Q₁∪Q₂∪Q₃∪Q₄Wherein

i≠j。

Then calculating the same threshold level q at the reproduction time interval tau₀Lower, conditional probability density function P_q(τ|Q_i)＝P_q(τ|τ₀，τ₀∈Q_i) And performing short-term correlation judgment: if the recurring sequence of time intervals does not have short-term correlation, then there is P_q(τ|Q_i)＝P_q(τ|Q_j)，i≠j。

In this embodiment, the step S3 can be implemented by the following preferred scheme:

the extreme fluctuation risk loss probability prediction step is as follows:

1. introducing a risk function W_q(Δt|t)：

W_q(Δ t | t) is defined as a certain threshold value exceededThe probability that the extreme fluctuation of q occurred last time before t unit time, and then at least once again in the future at times, which is related to the probability density function of the recurring time interval, is as follows:

except that the risk function W can be solved by integration_q(Δ t | t), which can also be solved from practical empirical values:

wherein, tau_qRefers to a load fluctuation re-interval exceeding a threshold q; count (t)<τ_qT + Δ t) represents the number of times the temporal interval lies within the interval (t, t + Δ t) when reproduced at the same threshold, count (τ)_q>t) represents the number of reproduction time intervals exceeding t.

2. And (3) analyzing the rule that the extreme fluctuation recurrence risk probability changes along with the threshold value by adopting a risk value method (VaR) and utilizing a loss probability distribution function:

calculating the risk probability under the threshold q, wherein the calculation formula is as follows:

where p (r) is a probability distribution function of the normalized sequence r (t), the average value of the recurring time intervals can be represented as:

wherein, tau_q,iRefers to the ith re-time interval in the load fluctuation re-time interval sequence exceeding the threshold value q; n is a radical of_qFor the number of reproduction time intervals below the threshold q,

approximately equal to reproduction time sequenceTotal number of columns.

Predicting a risk loss probability, which can be expressed as:

wherein number of R (t) ≧ q represents the number of normalized sequences R (t) greater than or equal to threshold q; totalnumberrof R (t) represents the total number of sequences R (t) after normalization.

In this embodiment, the step S4 can be implemented by the following preferred scheme:

calculating long-term correlation index h of power load fluctuation re-time interval sequence_qIf 0.5 < h_qIf the time interval sequence of the power load fluctuation is not more than 1, the long-term correlation does not exist, otherwise, the invention can not be applied.

In this embodiment, the step S5 can be implemented by the following preferred scheme:

(1) let the original power load data sequence be L ═ L_iI 1,2, … …, N being the sequence length, determining the minimum value L in the sequence L_minMaximum value l_maxAnd a demarcation reference value

Is the average of the raw power load data;

(2) the dispersion of the original payload data sequence and the sequence D are then calculated:

(3) with l_maxThe interval d is obtained from [1/100,1/20 ] of the power load data sequence L]Randomizing the mth interval L_m＝{l_j,l_j≤l_maxData order of-d × m }, restThe data sequence is kept unchanged, so that new load data sequences are obtained in sequence, the dispersion of the new data sequences and a sequence D are obtained_J：

Wherein m is int (1,2, …, (l)_max-RV)/d), int represents the value calculation, J ═ l_max-d×m；

(4) With l_minRandomizing the mth interval L with RV as the end point_m＝{l_j,l_j≥l_minThe data sequence of + dXm } and the rest data sequences are not changed, so as to obtain new load sequence, obtain dispersion of new data sequence and sequence D_J：

Wherein, the interval d is the same as the step (503), m is int (1,2, …, (l)_max-RV)/d)，J＝l_min+d×m；

(5) Respectively calculating the dispersion of the load data sequences obtained in the steps (3) and (4) and the sequence D_JOf the Hurst index h_q ^JDrawing h_q ^JHurst index h of curve and power load fluctuation re-time interval sequence_qBy contrast, when only extreme data is replaced, h_q ^JTrend of change and h_qClose, when the number of substitute data is as high as h_q ^JAbrupt change occurs and the change trend deviates from h_qThe time abrupt change point is a critical value point of an extreme data point of the power load data sequence, namely a load risk early warning threshold.

In the embodiment, a certain electronic enterprise in Nanjing, Jiangsu province is randomly selected as a research object, annual power load data of the electronic enterprise is collected and analyzed, the sample acquisition frequency is 15min, the sample period is from 1 month and 1 day in 2018 to 12 months and 31 days in 2018, firstly, in order to smooth the data and improve the co-linearity and heteroscedasticity of the data, the data is logarithmized without destroying the original characteristics, and further analysis is facilitated. The logarithmic return values of the power load fluctuation sequence are shown in fig. 2:

the corresponding statistical results of the power load fluctuation sequence are shown in table 1:

TABLE 1 statistical results of power load fluctuation sequences

As can be seen from fig. 2, the power load fluctuation sequence is not normally distributed, and a sharp peak with severe fluctuation appears, and it can be seen from table 1 that the fluctuation rate is asymmetric, negative values correspond to amplitudes higher than positive values, and the reproduction time interval is short and dense in the time period of large-amplitude fluctuation aggregation. On the contrary, in a stationary period in which the fluctuation range is small, the reproduction time interval is large and sparse.

The fitting function provided by the invention is subjected to single-sample K-S inspection, the degree of the reappearance time interval obeying the fitting function provided by the invention is inspected, and the table 2 shows the parameter change of the fitting function provided by the invention under different threshold values.

TABLE 2 variation of parameters of tensile index function

Threshold q	1.0	1.2	1.4	1.6	1.8
						a	2.228	0.720	0.207	0.120	0.025
β	89.399	23.148	5.756	4.660	0.338
						γ	0.2151	0.2269	0.2363	0.2260	0.2720
K-S test	0.1690	0.2526	0.3049	0.3261	0.4210

As can be seen from Table 2, all the K-S test values are greater than 0.1, which shows that the tensile index function provided by the invention can better fit the empirical probability distribution function, and the fitting degree is continuously increased along with the increase of the threshold q.

And then analyzing the probability distribution characteristics of the power load fluctuation recurrence time interval, wherein the figure 3 shows the empirical and theoretical probability distribution of the recurrence time interval under different threshold values. As can be seen from fig. 3, as the threshold q is increased, the probability of the corresponding reproduction time interval is increased, i.e., the occurrence probability of the large-amplitude fluctuation is high. It is clearly observed on the right side of fig. 3 that the probability of the empirical distribution slightly increases and then decreases, which means that the probability of occurrence of the corresponding load fluctuation slightly increases, i.e. when the factors affecting the load fluctuation occur, the load fluctuation is more frequent and severe afterwards if no processing is performed. By comparing table 2 with fig. 3, it is found that the fitting function curves corresponding to different thresholds in fig. 3 have similar shapes, and it is necessary to determine whether the probability distribution function has scaling behavior, i.e., whether the small-amplitude fluctuation rule is the same as the large-amplitude fluctuation rule.

FIG. 4 is a graph of the scaled probability density of the mean ratio of the recurring time intervals at different thresholds. As can be seen from fig. 4, corresponding to different threshold values q,

the method does not converge on any curve, and shows that no scale exists, namely, the general fluctuation rule of small-amplitude fluctuation is not suitable for extreme fluctuation or large-amplitude fluctuation.

Next, the short-term correlation of the recurring time interval is verified by first calculating and comparing a conditional probability density function P_q(τ|τ₀)，τ₀∈Q₁And τ₀∈Q₄Conditional probability density function P of_q(τ|τ₀) As shown in fig. 5. From FIG. 5, it can be seen that when τ is₀At the minimum and maximum subsets, P_q(τ|τ₀∈Q₁) Greater than P_q(τ|τ₀∈Q₄) I.e. P_q(τ|τ₀∈Q₁)≠P_q(τ|τ₀∈Q₄) The criterion is fulfilled and thus a short-term correlation exists.

Fig. 6 shows the risk function W when the threshold q is 1.0, 1.2, 1.4, 1.6, 1.8_qThe empirical values (scatter) and theoretical values (curve) (Δ t 15| t) indicate that the empirical values and the curve coincide well and the difference between the empirical values and the curve of theoretical values decreases with increasing t. Further, W_q(Δt＝15|t) decreases with increasing t, indicating that there is aggregation behavior and long-term correlation at repeated intervals, and that in a short time the theoretical value underestimates the risk. Thus for a given threshold q, the risk probability of extreme fluctuations can be calculated, enabling risk prediction.

The loss probability under the threshold q is calculated according to the formula (11), the graph of which is shown in fig. 7, and if the probability that the phase calculation risk value is 1%, only the loss probability is required to be calculated

And solving a corresponding threshold value q, and further calculating the risk probability.

Fig. 8 shows the analysis results of the multi-fractal detrending fluctuation under different thresholds q, respectively, and it can be found that the p-order Hurst index of each line is greater than 0.5, indicating that long-term correlation and multi-fractal characteristics exist in the recurrence time interval. On the basis of determining that long-term correlation exists, a risk pre-warning threshold is determined, as shown in FIG. 9, |_i' New payload data sequence after data replacement, when_iWhen' > is not less than RV, h_q ^JStarting with the original sequence h_qThere was little difference until J9756.66 changed, followed by h as J gradually decreased_q ^JGradual deviation h_qTherefore, the steepness change point J is 9756.66, which is a maximum threshold value. When l is_iWhen the diameter is not more than RV, h_q ^JH from the original sequence at the beginning_qThere was little difference until J was changed 7599.62, followed by h with increasing J_q ^JGradual deviation h_qTherefore, the steep point J of 7599.62 can be determined as the threshold of the minimum value. So 7599.62 is less than or equal to l_i' ≦ 9756.66 is the system safe operating range domain for the load sequence.

The embodiments are only for illustrating the technical idea of the present invention, and the technical idea of the present invention is not limited thereto, and any modifications made on the basis of the technical scheme according to the technical idea of the present invention fall within the scope of the present invention.

Claims (10)

1. The power load fluctuation analysis and risk early warning method based on the recurrence time interval analysis method is characterized by comprising the following steps of:

(1) preprocessing the data, fitting the power load fluctuation recurrence time interval data sequence based on a least square method, and constructing a power load fluctuation recurrence time interval sequence probability distribution model;

(2) establishing a conditional probability density function model, and verifying whether short-term correlation exists at the time interval of power load reproduction so as to determine whether risk prediction can be carried out through the short-term correlation;

(3) predicting the extreme fluctuation risk loss probability in the power load fluctuation re-time interval sequence by combining the risk function and the loss probability distribution function;

(4) judging whether the power load recurrence time interval has long-term correlation or not by adopting multi-fractal detrending fluctuation analysis;

(5) and extracting data points which have no influence on the overall fluctuation of the original load data sequence on the basis of verifying the existence of long-term correlation, taking the data points as critical points of normal fluctuation of the load data sequence, and further determining a load risk early warning threshold value according to the numerical values of the critical points.

2. The reoccurring time interval analysis-based power load fluctuation analysis and risk early warning method according to claim 1, wherein in the step (1), the data preprocessing includes a logarithmic processing and a normalization processing; the logarithm processing is as follows:

r(t)＝ln l(t)-ln l(t-Δt) (1)

in the above formula, r (t) is a power load fluctuation sequence, l (t) is a power load at time t, and Δ t is a sample data sampling frequency; the normalization process is as follows:

in the above formula, R (t) is a normalized value of r (t), E represents a mathematical expectation of the variable, [ Er (t)²-E²r(t)]^1/2Is the standard deviation of r (t).

3. The reoccurring time interval analysis-based power load fluctuation analysis and risk early warning method according to claim 2, wherein in the step (1), for each threshold q, the power load fluctuation reoccurring time interval sequence is defined as a time interval τ (t) between a sequence r (t) exceeding the threshold q:

τ(t)＝min{t-t′:R(t)＞q,t＞t′,q＞0} (3)

in the above formula, t' refers to a previous time point when the load fluctuation exceeds a certain threshold q.

4. The method for analyzing power load fluctuation and early warning of danger based on the recurring time interval analysis method according to claim 3, wherein in the step (1), the power load fluctuation recurring time interval sequence probability distribution model is constructed by the following method:

(101) based on a least square fitting method, a tensile index function is selected as a fitting function of a reproduction time interval sequence, and the standard form is as follows:

in the above formula, a, β and gamma are function parameters, e is a natural constant,

is the mean value of the time intervals of recurrence of the fluctuations of the power load determined by a threshold q, the probability distribution function of the time intervals of recurrence of the fluctuations of the power load τ being P for a given threshold q_q(τ)；

(102) And estimating function parameters of the tensile index by adopting a least square method, and performing single-sample K-S test to reproduce the coincidence degree of time interval distribution and tensile index function distribution.

5. The method for power load fluctuation analysis and risk early warning based on the recurring time interval analysis method according to claim 4, wherein in the step (102), the method of the single-sample K-S test is as follows:

first, assume that: the empirical distribution is the same as the best fit tensile index distribution;

secondly, calculating K-S statistic D between the fitting sample and the simulation sample_ma：

D_max＝max(|F_q-F_SE|) (5)

In the above formula, F_qFor empirical cumulative distribution under corresponding threshold, F_SEIs a cumulative distribution integrated by a fitted tensile index;

then, given the significance level α and the number of sample data, the threshold value D of the single-sample K-S suggestion is determined_αGenerating M synthetic samples from the best fit distribution, and then reconstructing a cumulative distribution F of the simulated samples from the integrals of the fitted stretch indices_simAnd its cumulative distribution function F_sim,SETo determine K-S statistics D between the fitted and simulated samples_α：

D_α＝max(|F_sim-F_sim,SE|) (6)

If D is_max<D_αThen the assumption is true, otherwise the assumption is false.

6. The method for power load fluctuation analysis and risk early warning based on the recurrence time interval analysis method as claimed in claim 4, wherein in the step (2), the method for verifying the short-term correlation of the recurrence time interval of the power load is as follows:

(201) introducing a conditional probability density function P_q(τ|τ₀)，P_q(τ|τ₀) Defined as the extreme fluctuation having occurred twice in succession at the same threshold q, with a time interval τ₀Then the probability of extreme fluctuations occurring again within the time interval of τ from this moment;

(202) setting the fluctuations above a threshold q to extreme fluctuations, for a given threshold q, obtaining a number N_qThe sequence Q is arranged in ascending order and is equally distributed among four different subsequences Q₁、Q₂、Q₃、Q₄Inner, i.e. Q ═ Q₁∪Q₂∪Q₃∪Q₄Wherein

i is not equal to j; then calculating the same threshold q at the reproduction time interval tau₀Lower, conditional probability density function P_q(τ|Q_i)＝P_q(τ|τ₀，τ₀∈Q_i) And performing short-term correlation judgment: if the recurring sequence of time intervals does not have short-term correlation, then there is P_q(τ|Q_i)＝P_q(τ|Q_j)，i≠j。

7. The method for power load fluctuation analysis and risk early warning based on the recurring time interval analysis method according to claim 4, wherein in the step (3), the method for predicting the probability of the extreme fluctuation risk loss in the power load fluctuation recurring time interval sequence comprises the following steps:

(301) introducing a risk function W_q(Δt|t)，W_q(Δ t | t) is defined as the probability that a certain extreme fluctuation exceeding the threshold q has occurred at least once before t unit time, and then at least once again in the future Δ t |:

(302) and (3) analyzing the rule that the extreme fluctuation recurrence risk probability changes along with the threshold value by adopting a risk value method and utilizing a loss probability distribution function:

probability of loss of risk P at threshold q^*The calculation formula of (2):

in the above formula, P (R) is a probability distribution function of the normalized sequence R (t);

calculating a reproduction time interval average

In the above formula, τ_q,iAn ith re-time interval in the sequence of load fluctuation re-time intervals that exceeds the threshold q; n is a radical of_qFor the number of reproduction time intervals below the threshold q,

approximately equal to the total number of reproduction time sequences;

predicting risk loss probability:

in the above formula, number of R (t) ≧ q indicates the number of sequences R (t) which is equal to or greater than the threshold value q; total number of R (t) represents the total number of sequences R (t).

8. The method for analyzing fluctuation of power load and early warning of risk based on recurring time interval analysis according to claim 7, wherein the risk function W is a function of the risk_q(Δ t | t) is calculated according to the following formula:

in the above formula, τ_qRefers to a load fluctuation re-interval exceeding a threshold q; count (t)<τ_qT + Δ t) represents the number of times the temporal interval lies within the interval (t, t + Δ t) when reproduced at the same threshold, count (τ)_q>t) represents the number of reproduction time intervals exceeding t.

9. The method for power load fluctuation analysis and risk early warning based on the recurrence time interval analysis method as claimed in claim 1, wherein in step (4), a long-term correlation index of the power load fluctuation recurrence time interval sequence is calculated, and if the long-term correlation index is within the [0.5,1] interval, it indicates that there is a long-term correlation, otherwise there is no long-term correlation.

10. The method for power load fluctuation analysis and risk early warning based on the recurrence time interval analysis method as claimed in claim 1, wherein in step (5), the load risk early warning threshold is determined by the following method:

(501) let the original power load data sequence be L ═ L_iI 1,2, … …, N being the sequence length, determining the minimum value L in the sequence L_minMaximum value l_maxAnd a demarcation reference value

Is the average of the raw power load data;

(502) the dispersion of the original payload data sequence and the sequence D are then calculated:

(503) with l_maxThe interval d is obtained from [1/100,1/20 ] of the power load data sequence L]Randomizing the mth interval L_m＝{l_j,l_j≤l_maxD x m, the remaining data sequences being kept unchanged, so as to obtain in turn a new load data sequence, a dispersion of the new data sequence and a sequence D_J：

Wherein m is int (1,2, …, (l)_max-RV)/d), int represents the value calculation, J ═ l_max-d×m；

(504) With l_minRandomizing the mth interval L with RV as the end point_m＝{l_j,l_j≥l_minThe data sequence of + dXm } and the rest data sequences are not changed, so as to obtain new load sequence, obtain dispersion of new data sequence and sequence D_J：

Wherein, the interval d is the same as the step (503), m is int (1,2, …, (l)_max-RV)/d)，J＝l_min+d×m；

(505) Respectively calculating the dispersion of the load data sequences obtained in the steps (503) and (504) and the sequence D_JOf the Hurst index h_q ^JDrawing h_q ^JHurst index h of curve and power load fluctuation re-time interval sequence_qBy contrast, when only extreme data is replaced, h_q ^JTrend of change and h_qClose, when the number of substitute data is as high as h_q ^JAbrupt change occurs and the change trend deviates from h_qThe time abrupt change point is a critical value point of an extreme data point of the power load data sequence, namely a load risk early warning threshold.

Images