CN104463371A - Markov chain modeling and predicating method based on wind power variable quantity - Google Patents

Abstract

The invention discloses a Markov chain modeling and predicating method based on wind power variable quantity. The method comprises the steps that firstly, linear transformation is carried out on existing original power data to obtain a wind power variable quantity data sample, then, according to the variable quantity data size and a statistical result of probability distribution, state space of a Markov chain model is divided as fine as possible, after the state is determined, a transition probability matrix of the variable quantity is obtained through statistical calculation, and Markov chain model construction is completed. The Markov chain model can be used for constructing a short-period and ultra-short period wind power predication method, and the theoretical basis is laid for real-time economic dispatch comprising a wind power system, optimized decision and model prediction control based on a Markov chain.

Description

Markov chain modeling and predicting method based on wind power variation

Technical Field

The invention relates to a Markov chain modeling and predicting method based on wind power variation.

Background

With the increasingly prominent energy and environmental problems, wind power generation has been rapidly developed with its advantages of being clean, renewable, large in reserves, etc. According to the latest statistics of the wind energy society of China, in 2013, the newly added installed capacity of 16088.7MW in China (excluding Taiwan areas) is increased by 24.1% on a same scale; the cumulative installed capacity is 91412.89MW, which is increased by 21.4% on the same scale. The two data of the newly added installation and the accumulated installation are all the first in the world. Although wind power generation technology is mature continuously, randomness, fluctuation and uncontrollable property of wind power output still bring much trouble to large-scale wind power grid connection. Therefore, accurate modeling of wind power fluctuation characteristics is of great significance to flexible scheduling and optimal control of the power grid.

The Markov chain model has the advantages of simple method, high calculation speed, high precision and the like, and is widely applied to modeling, reliability evaluation and active power prediction of a wind power time sequence. Document [1] applies an MCMC method to generate a wind power time series, and describes a fluctuation process of the wind power time series by using a transition probability matrix of a discrete Markov process. The literature [2] extracts the change characteristics and the stability characteristics of the wind power by using a transition probability matrix of a Markov chain model. The document [3] uses a Markov chain model for ultra-short-term wind power single-step prediction with a forward-looking time of 10min, and obtains a better prediction effect compared with a traditional continuous method. In order to study the influence factors of model accuracy, improve the model structure, and reduce the prediction error, a great deal of research and study has been conducted in the literature. Document [4] constructs a Markov chain model with different state space dimensions for the same wind speed data, and the comparison result shows that the statistical characteristics and the probability characteristics of the actual wind speed are more accurately reflected by increasing the state space dimensions of the model. The document [5] verifies the Markov property of the wind power random process, and indicates that more modeling data and detailed space division can obtain a high-precision prediction result. Document [6] compares a wind power probability prediction method based on a first-order and a second-order Markov chain model with a traditional continuous method, and considers that when a state space is constant, the effect of the second-order Markov chain model on reducing prediction errors is optimal. Document [7] proposes a wind power probability prediction method based on a first-order and second-order Markov chain hybrid model, and the method obtains a better prediction effect compared with a single first-order model.

Although the above documents achieve obvious improvement effects, no matter the state division fineness is increased, the model order is increased, or a hybrid model is established, a large amount of modeling data is needed to ensure that the constructed transition probability matrix can accurately reflect the fluctuation and the transition characteristics of the wind power, and the number of samples often becomes a limiting condition of analysis. And increasing the model order increases the complexity of the model, reduces the calculation speed, and causes difficulty in the application of real-time model predictive control. Furthermore, during multi-step transitions using the Markov chain model, if the state space partitioning is not fine enough, the state shift of any step during the multi-step transition may be rapidly amplified in subsequent transitions.

In order to solve the problems, the invention takes the wind power variation as modeling sample data and constructs the Markov chain model based on the wind power variation. The wind power variation is a variation value of wind power at two adjacent moments. It is noted that the probability of a minute-scale rate of change (or variation) of wind field force between 0 and 1.5% is about 99%, and the probability of greater than 1.5% is only about 1%. Document [8] analyzes the fluctuation characteristics of the wind power at different time intervals by using the wind power change rate, and counts the probability distribution of the change rate, and the result shows that the shorter the time interval is, the smaller the wind power change rate is. Document [9] fits a probability density function of wind power variation data by using t location-scale distribution at different time intervals. On the basis of the fitting result, upper and lower limit per unit values of 95% confidence intervals of the average power variation of the wind power plants are given, and the average power variation of adjacent min is mostly within 1% of the installed capacity. The above documents only perform statistical studies on the distribution characteristics of the variation, and do not utilize the variation data for further modeling applications.

According to the existing documents, the wind power variation (change rate) of short time scale has the characteristics of symmetrical distribution, centralized value taking, relatively small fluctuation and the like. Compared with the existing wind power original power data modeling method, the Markov chain model based on the variable quantity has the advantages that: firstly, the variation value range of a short time scale (such as 15min) is small, and the characteristic determines that under the condition of the same sample number, the variation state space division is necessarily finer relative to the original power. Secondly, because the variation distribution of the short time scale is concentrated, if a Markov chain model is established by using variation data, a fine state space can be constructed for a large amount of data in a small range to solve the problem of insufficient data. Finally, the data characteristics of the variable Markov chain model and the fineness degree of the state space can greatly reduce the probability of error accumulation caused by state deviation in the multi-step transfer process and slow down the speed of error accumulation.

The documents mentioned are respectively:

[1]Papaefthymiou G,Klockl B.MCMC for wind power simulation[J].IEEE Transactions onEnergy Conversion,2008,23(1):234-240.

[2]Lopes V V,Scholz T,Estanqueiro A,et al.On the use of Markov chain models for theanalysis of wind power time-series[C]//Proceedings of IEEE 11th International Conference onEnvironment and Electrical Engineering(EEEIC),May 18-25,2012,Venice:770-750.

[3]Pierre Pinson and Henrik Madsen.Probabilistic Forecasting of Wind Power at theMinute Time-Scale with Markov-Switching Autoregressive Models[C]//Proceedings of IEEEthe 10th International Conference on Probabilistic Methods Applied to Power Systems(PMAPS),May 25-29,2008,Rincon,Puerto rico:98-105.

[4]Hocaoglu F O,Gerek O N,Kurban M.The effect of Markov Chain State Size for syntheticWind Speed Generation[C]//Proceedings of IEEE the 10th International Conference onProbabilistic Methods Applied to Power Systems(PMAPS),May 25-29,2008,Rincon,PuertoRico:113-116.

[5] weekel, King Li Si, Wang Propen, et al. wind power prediction performance analysis based on high-order Markov chain model [ J ] Power System protection and control, 2012,40(6):6-10.

ZHOU Feng,JIN Lisi,WANG Bingquan,et al.Analysis of the wind power forecastingperformance based on high-order Markov chain models[J].Power System Protection andControl,2012,40(6):6-10.

[6]Carpinone A,Langella R,Testa A,et al.Very short-term probabilistic wind powerforecasting based on Markov chain models[C]//Proceedings of IEEE the 11th InternationalConference on Probabilistic Methods Applied to Power Systems(PMAPS),June 14-17,2010,Singapore:107-112.

[7] Perimeter seal, jin lis, liu jian, etc. wind power probability prediction based on multi-state space hybrid Markov chain [ J ] power system automation, 2012,36(6):29-33.

ZHOU Feng,JIN Lisi,LIU Jian,et al.Probabilistic wind power forecasting based onmuti-state space and hybrid Markov chain models[J].Automation of Electric Power Systems,2012,36(6):29-33.

[8] Youhua, great school, the army, and the like, active power fluctuation characteristic analysis of large-scale wind power grid access and power generation plan simulation [ J ] power grid technology, 2010, 34(5):60-66.

HOU Youhua,FANG Dazhong,QI Jun,et al.Analysis on Active Power FluctuationCharacteristics of Large-Scale Grid-Connected Wind Farm and Generation SchedulingSimulation Under Different Capacity Power Injected From Wind Farms Into Power Grid[J].Power System Technology,2010,34(5):60-66.

[9] Forest satellite, Wenqui, Everest, and the like, probability distribution research on wind power fluctuation characteristics [ J ]. China Motor engineering report, 2012,32(1):38-46.

LIN Weixing,WEN Jinyu,AI Xiaomeng,et al.Probability Density Function of Wind PowerVariations[J].Proceeding of the CSEE,2012,32(1):38-46.

Disclosure of Invention

The invention provides a Markov chain modeling and predicting method based on wind power variation, aiming at solving the problems. And then dividing the state space of the Markov chain model as finely as possible according to the variable quantity data quantity and the statistical result of the probability distribution. After the state is determined, a transition probability matrix of the variation is obtained through statistical calculation, and the construction of a Markov chain model is completed, wherein the model can be used for constructing short-term and ultra-short-term wind power prediction.

In order to achieve the purpose, the invention adopts the following technical scheme:

a Markov chain modeling and predicting method based on wind power variation comprises the following steps:

(1) establishing a Markov chain model with discrete time and state;

(2) dividing a continuous time shaft into discrete moments, and constructing a sample space of a Markov chain model by converting an original power sample space into a wind power variable quantity sample space;

(3) fitting a probability density function of variable probability distribution according to a sample space of wind power variable quantity and a distribution statistical result of wind power variable quantity sample data, setting a confidence interval, and constructing a corresponding state space;

(4) according to the Markov property in the random process, counting and calculating a transition probability matrix of a Markov chain model, obtaining the conditional transition probability of the wind power variable quantity among all states, and describing the change characteristic and the fluctuation rule of the wind power;

(5) and performing single-step prediction and multi-step prediction based on the Markov chain model of the wind power variation, and analyzing the accumulated condition of multi-step prediction errors.

In the step (1), both time and state are discrete random processes { X }_nX (n), n is 0,1,2₁,S_2,…, assuming state S as long as the process is at the current time_iThere is a fixed probability that the process will be in state S at the next time_jThat is, assume for all states and all n ≧ 0, have

P{X_n＝S_j|X₁＝S₁,X₂＝S₂,…X_n-1＝S_i}

＝P{X_n＝S_j|X_n-1＝S_i},S_·∈I (1)

In the formula, ". in s. denotes an arbitrary footer.

Such a stochastic process is called Markov chain;

for a Markov chain, given a past state S₀，S₁，…，S_n-1And the present state S_nTime, future state X_n+1Is independent of the past state and only depends on the present state S_nBy means of one-step transition probability pi of pi memory_ijMatrix of (d), n_ijIndicating that the process is in state S_iThe next time to transition to state S_jThe conditional probability transition matrix of (1), whose elements satisfy:

<math> <mrow> <msub> <mi>&pi;</mi> <mi>ij</mi> </msub> <mo>&GreaterEqual;</mo> <mn>0</mn> <mo>,</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mo>&infin;</mo> </munderover> <msub> <mi>&pi;</mi> <mi>ij</mi> </msub> <mo>=</mo> <mn>1</mn> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> <mo>.</mo> </mrow> </math>

in the step (2), the specific method is as follows: dividing the continuous time axis into discrete times with a time interval Δ t, then for any two adjacent times t-1 and t there are:

t＝t-1+Δt (3)

converting an original power sample space into a wind power variable sample space through one-step linear transformation, wherein the variable of the wind power at a time interval [ t-1, t ] can be expressed as:

V_t＝P_t-P_t-1 (4)

wherein P is_t-1And P_tWind power values V at t-1 moment and t moment respectively_tFor wind power at time interval [ t-1, t]The variable quantity of the method is obtained by calculating the wind power variable quantity of any two adjacent moments in the random process at corresponding time intervals, and a historical sample sequence of the wind power variable quantity can be obtained by adopting one-step differential linear transformation according to the historical time sequence of the wind power, and the historical sample sequence is used as a sample space for constructing a Markov chain model.

In the step (3), for establishing a Markov chain model, a corresponding state space is firstly constructed for a sample space of the wind power variation, and the specific method includes:

(3-1) fitting a probability density function of the variation probability distribution based on the distribution statistical result of the wind power variation sample data;

(3-2) setting a confidence level alpha, solving a corresponding variable quantity confidence interval D, and constructing a state space of the Markov chain model by taking two end points of the confidence interval D as upper and lower limits of variable quantity state division;

and (3-3) selecting the number of the power intervals to represent all the states.

The specific method of the step (3-3) is as follows:

after the upper limit and the lower limit of the state division are determined, the state space of the Markov chain model can be constructed, and for the samples falling in the confidence interval, the number of the power intervals is selected as follows:

(1) except for the intervals at the two ends, the number of samples falling into each interval is not less than 5;

(2) the grouping number is calculated according to a Moore formula:

K-2≈C×N^2/5 (5)

k is the total number of interval division, including two power intervals outside the confidence interval, an integer value is taken, and K-2 is the number of equally divided power intervals; n is the number of samples; c is a formula coefficient, and the defined interval length is as follows:

$l=\frac{V_{\max }-V_{\min }}{K-2}---\left(6\right)$

V_maxand V_minFor the upper and lower limits of the confidence interval of the variation, K power intervals correspond to the state space of the Markov chain model of the variationK states.

The step (3-3) is to divide the variation data outside the confidence interval into separate states, if P is_NFor rated installed capacity, the delta data will be at [ -P_N,P_N]An internal value, thus, the variation is taken to be [ -P ]_N,V_min]And [ V ]_max,P_N]Is divided into a first state and a K-th state,

all states constitute a state space I_VIt can be expressed as:

<math> <mrow> <msub> <mi>I</mi> <mi>V</mi> </msub> <mo>=</mo> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <msub> <mi>S</mi> <mn>1</mn> </msub> <mo>,</mo> <mi>V</mi> <mo>&Element;</mo> <mo>[</mo> <mo>-</mo> <msub> <mi>P</mi> <mi>N</mi> </msub> <mo>,</mo> <msub> <mi>V</mi> <mi>min</mi> </msub> <mo>]</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>S</mi> <mi>k</mi> </msub> <mo>,</mo> <mi>V</mi> <mo>&Element;</mo> <mo>(</mo> <msub> <mi>V</mi> <mi>min</mi> </msub> <mo>+</mo> <mi>l</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>-</mo> <mn>2</mn> <mo>)</mo> </mrow> <mo>,</mo> <msub> <mi>V</mi> <mi>min</mi> </msub> <mo>+</mo> <mi>l</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>]</mo> <mo>,</mo> <mi>k</mi> <mo>=</mo> <mn>2,3</mn> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <mi>K</mi> <mo>-</mo> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <msub> <mi>S</mi> <mi>K</mi> </msub> <mo>,</mo> <mi>V</mi> <mo>&Element;</mo> <mo>[</mo> <msub> <mi>V</mi> <mi>max</mi> </msub> <mo>,</mo> <msub> <mi>P</mi> <mi>N</mi> </msub> <mo>]</mo> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> <mo>.</mo> </mrow> </math>

in the step (4), after the sample space transformation and the state space division are completed, the transition probability matrix of the Markov chain model is counted and calculated, and S is recorded_tFor the variation at time intervals t-1, t]According to the Markov property of the stochastic process, [ t, t + 1]]Wind power variable quantity state S_t+1By S only_tThe decision, can be expressed as

P{X_t+1＝S_t+1|X₁＝S₁,X₂＝S₂,…X_t＝S_t}

＝P{X_t+1＝S_t+1|X_t＝S_t},S_·∈I (8)

For calculating the transition probability matrix, defining a transition frequency matrix N as the transition frequency of the adjacent wind power variable quantity between each state, wherein the element N is_ijStatistically obtained by the following formula:

wherein N is_ijThe variable quantity of the wind power is [ t-1, t ]]S of the time period_iState transition to [ t, t + 1]]S of the time period_jNumber of states, T is total number of samples, N_ijSatisfies the following formula:

<math> <mrow> <msub> <mi>N</mi> <mi>ij</mi> </msub> <mo>&le;</mo> <mi>T</mi> <mo>,</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>K</mi> </munderover> <munderover> <mi>&Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>K</mi> </munderover> <msub> <mi>N</mi> <mi>ij</mi> </msub> <mo>=</mo> <mi>T</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>10</mn> <mo>)</mo> </mrow> </mrow> </math>

the element pi in the probability matrix pi is transferred_ijThe calculation method of (2) is as follows:

<math> <mrow> <msub> <mi>&pi;</mi> <mi>ij</mi> </msub> <mo>=</mo> <mi>P</mi> <mo>{</mo> <msub> <mi>S</mi> <mi>j</mi> </msub> <mo>|</mo> <msub> <mi>S</mi> <mi>i</mi> </msub> <mo>}</mo> <mo>=</mo> <mfrac> <msub> <mi>N</mi> <mi>ij</mi> </msub> <mrow> <munderover> <mi>&Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>K</mi> </munderover> <msub> <mi>N</mi> <mi>ij</mi> </msub> </mrow> </mfrac> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>=</mo> <mn>1,2</mn> <mo>,</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <mi>K</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>11</mn> <mo>)</mo> </mrow> </mrow> </math>

and satisfies the following conditions:

<math> <mrow> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <msub> <mi>&pi;</mi> <mi>ij</mi> </msub> <mo>&GreaterEqual;</mo> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <munderover> <mi>&Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>K</mi> </munderover> <msub> <mi>&pi;</mi> <mi>ij</mi> </msub> <mo>=</mo> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>=</mo> <mn>1,2</mn> <mo>,</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <mo>,</mo> <mi>K</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>12</mn> <mo>)</mo> </mrow> <mo>.</mo> </mrow> </math>

in the step (5), the single-step prediction method based on the Markov chain model of the wind power variation includes: predicting the value of the variable quantity from the current moment to the next moment and the probability distribution thereof by utilizing the established model, and then constructing the value interval of the wind power to obtain the prediction result of the wind power, wherein the prediction result specifically comprises the following steps:

for sample data of a given wind power time sequence, firstly dividing a continuous time axis into discrete moments according to a time scale delta t, and calculating wind power variation at any two adjacent moments according to a formula (4) so as to obtain data samples of the variation; then, according to the method in the step (3), determining a state space division scheme, finely dividing the variable quantity state space into K states, then counting a frequency transfer matrix N and calculating a transfer probability matrix pi, and completing construction of a variable quantity Markov chain model;

for convenience of description, the previous time is denoted as t-1, the current time is denoted as t, and the next time is denoted as t +1, which are called the current time and the previous time (time period [ t-1, t)]) The wind power variation is the current variation V_tThe current time and the next time (time period [ t, t + 1]]) The wind power variation is the next variation V_t+1If the current variation V is_tIf the actual value of (c) is known, the next variation V can be obtained by using the transition probability matrix of the variation Markov chain model_t+1A probability distribution of (a);

defining state selection unit row vectors_t，_tCurrent change V in_tThe element corresponding to the belonged state is 1, the other elements are 0, and the next variation V_t+1Is only limited by the current variance V_tIs determined by the state of

<math> <mrow> <msubsup> <mover> <mi>&pi;</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>V</mi> </msubsup> <mo>=</mo> <msub> <mi>&Gamma;</mi> <mi>t</mi> </msub> <mi>&Pi;</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>13</mn> <mo>)</mo> </mrow> </mrow> </math>

II, obtaining a transition probability matrix from a current variable quantity state to a next variable quantity state;is the next variable V_t+1Taking the probability vector of each state;

predicting the expectation of the probability distribution by using the variation as a deterministic prediction value of the variation; except for the intervals at two ends, multiplying the probability of the variation falling into each interval by the median value of each interval and then summing; because the two-end interval is positioned outside the confidence interval, the probability that the variation falls in the two-end interval is very small, the expected calculation result is hardly influenced, the two-end interval is not considered when the deterministic prediction value is calculated, and the following expression is expressed by an expression (14):

<math> <mrow> <msub> <mover> <mi>V</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>2</mn> </mrow> <mrow> <mi>K</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msubsup> <mover> <mi>&pi;</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>V</mi> </msubsup> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> <mo>&times;</mo> <msub> <mi>V</mi> <mi>mid</mi> </msub> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>14</mn> <mo>)</mo> </mrow> </mrow> </math>

wherein, V_mid(i) The median of each variation power interval is shown.

In order to convert the variable probability distribution prediction result into the prediction probability distribution of the wind power, firstly, a value power interval and a false value power interval of the wind power are constructedSetting a set formed by possible value intervals of predicted wind power as I_P，I_P(i) For the ith interval therein, it is required to satisfyEach interval corresponds to a wind power state, and the known wind power actual value P at the current moment is used_tAccumulating the variable quantity and the upper limit and the lower limit of each prediction interval one by one to obtain a prediction wind power interval, and defining the following constraint conditions:

<math> <mrow> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <mn>0</mn> <mo>&le;</mo> <msub> <mi>P</mi> <mi>t</mi> </msub> <mo>+</mo> <msub> <mi>V</mi> <mi>min</mi> </msub> <mo>&le;</mo> <msub> <mi>P</mi> <mi>N</mi> </msub> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> <mo>&le;</mo> <msub> <mi>P</mi> <mi>t</mi> </msub> <mo>+</mo> <msub> <mi>V</mi> <mi>max</mi> </msub> <mo>&le;</mo> <msub> <mi>P</mi> <mi>N</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>V</mi> <mi>min</mi> </msub> <mo>&lt;</mo> <msub> <mi>V</mi> <mi>max</mi> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>15</mn> <mo>)</mo> </mrow> </mrow> </math>

(1) if P_tSatisfy the formula(15) And predicting the power interval of the wind power as follows:

<math> <mrow> <msub> <mi>I</mi> <mi>P</mi> </msub> <mo>=</mo> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <msub> <mi>S</mi> <mi>l</mi> </msub> <mo>,</mo> <msub> <mover> <mi>P</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>&Element;</mo> <mo>[</mo> <mn>0</mn> <mo>,</mo> <msub> <mi>P</mi> <mi>t</mi> </msub> <mo>+</mo> <msub> <mi>V</mi> <mi>min</mi> </msub> <mo>]</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>S</mi> <mi>k</mi> </msub> <mo>,</mo> <msub> <mover> <mi>P</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>&Element;</mo> <mo>(</mo> <msub> <mi>P</mi> <mi>t</mi> </msub> <mo>+</mo> <msub> <mi>V</mi> <mi>min</mi> </msub> <mo>+</mo> <mi>l</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>-</mo> <mn>2</mn> <mo>)</mo> </mrow> <mo>,</mo> <msub> <mi>P</mi> <mi>t</mi> </msub> <mo>+</mo> <msub> <mi>V</mi> <mi>min</mi> </msub> <mo>+</mo> <mi>l</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>]</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>S</mi> <mi>K</mi> </msub> <mo>,</mo> <msub> <mover> <mi>P</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>&Element;</mo> <mo>[</mo> <msub> <mi>P</mi> <mi>t</mi> </msub> <mo>+</mo> <msub> <mi>V</mi> <mi>max</mi> </msub> <mo>,</mo> <msub> <mi>P</mi> <mi>N</mi> </msub> <mo>]</mo> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>16</mn> <mo>)</mo> </mrow> </mrow> </math>

wherein, K is 2,3, … K-1, l is each equal section length corresponding to the variation state; at this time, the number of power intervals for predicting the wind power is the same as the number of power intervals for predicting the variation, and the wind power P is predicted_t+1And the predicted variation V_t+1The probability of falling in the corresponding interval is also equal, i.e.

<math> <mrow> <msubsup> <mover> <mi>&pi;</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>P</mi> </msubsup> <mo>=</mo> <msubsup> <mover> <mi>&pi;</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>V</mi> </msubsup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>17</mn> <mo>)</mo> </mrow> </mrow> </math>

Wherein,the probability of the wind power value at the moment of t +1 falling in each power interval is the probability prediction result;

(2) if Pt does not satisfy formula (15) and Pt + V_min<0, introducing an integer parameter K₁So that:

P_t+V_min+l·K₁≥0 (18)

K₁taking the smallest integer satisfying the above formula, namely:

$K_1=\mathrm{int}\left(\frac{-V_{\min }-P_t}{l}\right)+1---\left(19\right)$

wherein int () is a rounding function;

at this time, the number of power intervals for predicting the wind power is less than K, and is set to K', and the power interval set can be expressed as

<math> <mrow> <msub> <mi>I</mi> <mi>P</mi> </msub> <mo>=</mo> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <msub> <mi>S</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mover> <mi>P</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>&Element;</mo> <mo>[</mo> <mn>0</mn> <mo>,</mo> <msub> <mi>P</mi> <mi>t</mi> </msub> <mo>+</mo> <msub> <mi>V</mi> <mi>min</mi> </msub> <mo>+</mo> <mi>l</mi> <mo>&CenterDot;</mo> <msub> <mi>K</mi> <mn>1</mn> </msub> <mo>]</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>S</mi> <mrow> <msub> <mi>k</mi> <mn>1</mn> </msub> <mo>-</mo> <msub> <mi>K</mi> <mn>1</mn> </msub> </mrow> </msub> <mo>,</mo> <msub> <mover> <mi>P</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>&Element;</mo> <mo>(</mo> <msub> <mi>P</mi> <mi>t</mi> </msub> <mo>+</mo> <msub> <mi>V</mi> <mi>min</mi> </msub> <mo>+</mo> <mi>l</mi> <mo>&CenterDot;</mo> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <mo>-</mo> <mn>2</mn> <mo>)</mo> </mrow> <mo>,</mo> <msub> <mi>P</mi> <mi>t</mi> </msub> <mo>+</mo> <msub> <mi>V</mi> <mi>min</mi> </msub> <mo>+</mo> <mi>l</mi> <mo>&CenterDot;</mo> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <mo>-</mo> <mn>1</mn> <mo>)</mo> <mo>]</mo> <mo>-</mo> </mrow> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>20</mn> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <msub> <mi>S</mi> <mrow> <mi>K</mi> <mo>&prime;</mo> </mrow> </msub> <mo>,</mo> <msub> <mover> <mi>P</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>&Element;</mo> <mo>[</mo> <msub> <mi>P</mi> <mi>t</mi> </msub> <mo>+</mo> <msub> <mi>V</mi> <mi>max</mi> </msub> <mo>,</mo> <msub> <mi>P</mi> <mi>N</mi> </msub> <mo>]</mo> </mtd> </mtr> </mtable> </mfenced> </mrow> </math>

Wherein k is₁＝K₁+2,K₁+3,…,K-1；K'＝K-K₁(ii) a In order to meet the property of probability distribution, according to the basic principle of scene reduction, the probability of the removed scene is combined into the scene probability with the shortest distance from the probability, and the probability of the wind power falling in the first power interval is taken as the variable number from 1 to K₁The prediction probability of each state and the probability of falling into other power intervals are the prediction probabilities corresponding to the variation intervals, and the probability of the wind power falling into each power interval at the moment of t +1 can be represented as:

<math> <mrow> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <msubsup> <mover> <mi>&pi;</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>P</mi> </msubsup> <mrow> <mo>(</mo> <mi>l</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>K</mi> <mn>1</mn> </msub> </munderover> <msubsup> <mover> <mi>&pi;</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>V</mi> </msubsup> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <msubsup> <mover> <mi>&pi;</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>P</mi> </msubsup> <mrow> <mo>(</mo> <mi>j</mi> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mover> <mi>&pi;</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>V</mi> </msubsup> <mrow> <mo>(</mo> <msub> <mi>K</mi> <mn>1</mn> </msub> <mo>+</mo> <mi>j</mi> <mo>)</mo> </mrow> <mo>,</mo> <mi>j</mi> <mo>=</mo> <mn>2,3</mn> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <mi>K</mi> <mo>&prime;</mo> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>21</mn> <mo>)</mo> </mrow> <mo>;</mo> </mrow> </math>

(3) if Pt does not satisfy formula (15) and Pt + V_max>P_NIntroduction of an integer parameter K₂So that

P_t+V_min+l·K₂≤P_N (22)

K2 is the largest integer satisfying the above formula, i.e.

$K_2=\mathrm{int}\left(\frac{P_N-P_t-V_{\min }}{l}\right)---\left(23\right)$

The number of power intervals for predicting the wind power is less than K, the power intervals are set to be K', and the power interval set can be expressed as

<math> <mrow> <msub> <mi>I</mi> <mi>P</mi> </msub> <mo>=</mo> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <msub> <mi>S</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mover> <mi>P</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>&Element;</mo> <mo>[</mo> <mn>0</mn> <mo>,</mo> <msub> <mi>P</mi> <mi>t</mi> </msub> <mo>+</mo> <msub> <mi>V</mi> <mi>min</mi> </msub> <mo>]</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>S</mi> <msub> <mi>k</mi> <mn>2</mn> </msub> </msub> <mo>,</mo> <msub> <mover> <mi>P</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>&Element;</mo> <mo>(</mo> <msub> <mi>P</mi> <mi>t</mi> </msub> <mo>+</mo> <msub> <mi>V</mi> <mi>min</mi> </msub> <mo>+</mo> <mi>l</mi> <mo>&CenterDot;</mo> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <mo>-</mo> <mn>2</mn> <mo>)</mo> </mrow> <mo>,</mo> <msub> <mi>P</mi> <mi>t</mi> </msub> <mo>+</mo> <msub> <mi>V</mi> <mi>min</mi> </msub> <mo>+</mo> <mi>l</mi> <mo>&CenterDot;</mo> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <mo>-</mo> <mn>1</mn> <mo>)</mo> <mo>]</mo> <mo>-</mo> </mrow> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>24</mn> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <msub> <mi>S</mi> <mrow> <mi>K</mi> <mo>&prime;</mo> <mo>&prime;</mo> </mrow> </msub> <mo>,</mo> <msub> <mover> <mi>P</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>&Element;</mo> <mo>[</mo> <msub> <mi>P</mi> <mi>t</mi> </msub> <mo>+</mo> <msub> <mi>V</mi> <mi>min</mi> </msub> <mo>+</mo> <mi>l</mi> <mo>&CenterDot;</mo> <msub> <mi>K</mi> <mn>2</mn> </msub> <mo>,</mo> <msub> <mi>P</mi> <mi>N</mi> </msub> <mo>]</mo> </mtd> </mtr> </mtable> </mfenced> </mrow> </math>

Wherein k is₂＝2,3,…K₂+1；K″＝K₂+2. The probability that the wind power predicted value falls in the Kth power interval is used for taking the variation Kth₂The probability sum of K states, the probability of falling into other power intervals is the prediction probability corresponding to the variation interval, and the probability of the wind power falling into each power interval at the moment of t +1 can be represented as:

<math> <mrow> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <msubsup> <mover> <mi>&pi;</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>P</mi> </msubsup> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mover> <mi>&pi;</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>V</mi> </msubsup> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> <mo>,</mo> <mi>i</mi> <mo>=</mo> <mn>1,2</mn> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <msub> <mi>K</mi> <mn>2</mn> </msub> <mo>+</mo> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <msubsup> <mover> <mi>&pi;</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>P</mi> </msubsup> <mrow> <mo>(</mo> <mi>K</mi> <mo>&prime;</mo> <mo>&prime;</mo> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mrow> <munderover> <mi>&Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <msub> <mi>K</mi> <mn>2</mn> </msub> </mrow> <mi>K</mi> </munderover> <mover> <mi>&pi;</mi> <mo>^</mo> </mover> </mrow> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>V</mi> </msubsup> <mrow> <mo>(</mo> <mi>j</mi> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>25</mn> <mo>)</mo> </mrow> <mo>;</mo> </mrow> </math>

the power interval of the predicted wind power is formed on the basis of the actual value Pt at the current moment, so that the prediction is updated in a rolling mode every time.

In the step (5), the multi-step prediction method based on the Markov chain model of the wind power variation comprises the following steps: dividing the time span from the current time to the prediction time by delta t, decomposing the prediction of a relatively long time scale into a plurality of single-step prediction processes, taking the actual value as the known input in the first step, taking the output result of the previous step prediction in each intermediate step as the known input of the next step prediction, assuming that the time span from the prediction time to the current time is L, and obtaining the wind power of the prediction time from the known condition of the current time requires M steps of calculation, wherein the number of the prediction steps M is as follows:

<math> <mrow> <mi>M</mi> <mo>=</mo> <mfrac> <mi>L</mi> <mi>&Delta;t</mi> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>27</mn> <mo>)</mo> </mrow> </mrow> </math>

assume that the variation prediction probability distribution of any one of the steps (not assumed to be the mth step) in the multi-step prediction isThe predicted value of the variation isCorresponds to the state ofThe predicted variation probability distribution of the (m + 1) th step is as follows:

<math> <mrow> <msubsup> <mover> <mi>&pi;</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mi>m</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>V</mi> </msubsup> <mo>=</mo> <msub> <mover> <mi>&Gamma;</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mi>m</mi> </mrow> </msub> <mi>&Pi;</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>28</mn> <mo>)</mo> </mrow> </mrow> </math>

wherein,predicting state for variation at time t + mSelecting a unit row vector according to the corresponding state, wherein pi is a transition probability matrix, and the predicted value of the variation in the (m + 1) th step is as follows:

<math> <mrow> <msub> <mover> <mi>V</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mi>m</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>2</mn> </mrow> <mrow> <mi>K</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msubsup> <mover> <mi>&pi;</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mi>m</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>V</mi> </msubsup> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> <mo>&times;</mo> <msub> <mi>V</mi> <mi>mid</mi> </msub> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>29</mn> <mo>)</mo> </mrow> <mo>,</mo> </mrow> </math>

determining wind power output at t + m +1 th momentPredicting power intervals, the probability distribution of each power interval isNamely:

<math> <mrow> <msub> <mover> <mi>P</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mi>m</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>G</mi> </munderover> <msubsup> <mover> <mi>&pi;</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mi>m</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>P</mi> </msubsup> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> <mo>&times;</mo> <msubsup> <mi>P</mi> <mrow> <mi>mid</mi> <mo>,</mo> <mi>t</mi> <mo>+</mo> <mi>m</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>G</mi> </msubsup> <mo>,</mo> </mrow> </math> g ═ K, K', or K "(30).

In the step (5), the method for analyzing the multi-step prediction error accumulation condition comprises the following steps: and (4) the state of the Markov chain is represented by X, in the original power model, X represents the wind power state, and in the variable quantity model, X represents the variable quantity state. Assuming that any one step in the multi-step prediction process from the time t to the time t + M is set as the mth step, the prediction state isThe actual state of the wind power output (or wind power variation) at the moment is Xt + m, and the state deviation of the predicted state relative to the actual state is recorded as delta_m，

<math> <mrow> <msub> <mi>&Delta;</mi> <mi>m</mi> </msub> <mo>=</mo> <msub> <mover> <mi>X</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mi>m</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>X</mi> <mrow> <mi>t</mi> <mo>+</mo> <mi>m</mi> </mrow> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>31</mn> <mo>)</mo> </mrow> </mrow> </math>

According to the multi-step prediction method, the predicted value of the mth step is used as the input of the (m + 1) th step due to the existence of the state deviation delta_mSet to a predicted stateWhen the wind power (or the wind power variable quantity) is input in the (m + 1) th step, the probability distribution of the wind power (or the wind power variable quantity) at the t + m +1 moment obtained by predicting the (m + 1) th step is

<math> <mrow> <msubsup> <mover> <mi>&pi;</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mi>m</mi> <mo>+</mo> <mn>1</mn> </mrow> <mo>*</mo> </msubsup> <mo>=</mo> <mi>&Gamma;</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>X</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mi>m</mi> </mrow> </msub> <mo>)</mo> </mrow> <mi>&Pi;</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>32</mn> <mo>)</mo> </mrow> </mrow> </math>

Corresponding to the step prediction value ofWhileWill be used as the input of the m +2 step, and so on, the state offset delta produced by the m step_mIt is possible that subsequent M-M step predictions have an impact such that errors are accumulated in subsequent M-M predictions.

In the step (5), when the wind power variation Markov chain model is used for multi-step prediction, the characteristic that variation data has small value reduces the probability of state deviation generated in the prediction process, and the fine state space division effectively slows down the speed of error accumulation; defining an offset ratio lambda_mTo indicate the deviation degree of the predicted value of the mth step from the actual value

<math> <mrow> <msub> <mi>&lambda;</mi> <mi>m</mi> </msub> <mo>=</mo> <mfrac> <mrow> <mi>l</mi> <mo>&times;</mo> <msub> <mi>&Delta;</mi> <mi>m</mi> </msub> </mrow> <msub> <mi>P</mi> <mi>N</mi> </msub> </mfrac> <mo>,</mo> <mi>m</mi> <mo>=</mo> <mn>1,2</mn> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <mi>M</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>33</mn> <mo>)</mo> </mrow> </mrow> </math>

When delta_m＝0，λ_mWhen the number is equal to 0, the number of the predicted states is the same as the number of the actual states, and the prediction state is simply referred to as no offset; when delta_m>At 0, λ_m>0, indicating that the number of predicted states is greater than the number of actual states, referred to as positive offset for short; when delta_m<At 0, λ_m<0, indicating that the number of predicted states is less than the number of actual states, called negative offset for short; lambda_mThe larger | is, the farther the predicted state deviates from the actual state is; by calculation ofλ1～λ_MThe deviation situation of each step prediction in the whole multi-step prediction process is quantitatively described.

The invention has the beneficial effects that:

(1) compared with the existing wind power Markov chain model, the state space of the model is finer under the same modeling data quantity, the model precision can be effectively improved, and the error accumulation in the multi-step transfer process can be reduced;

(2) the wind power prediction method based on the variable Markov chain model can not only provide the predicted value of the wind power at the prediction moment, but also provide the probability distribution condition of the predicted value, and the prediction precision, particularly the multi-step prediction precision is obviously improved compared with the original power method;

(3) besides being used for wind power prediction, the Markov chain model based on the wind power variation can also lay a theoretical foundation for real-time economic dispatching of a wind power system, optimization decision based on the Markov chain and model prediction control.

Drawings

FIG. 1 is a diagram illustrating the division of the variation states into upper and lower limits;

FIG. 2 is a schematic diagram of a multi-step error accumulation process;

FIG. 3 is a schematic diagram of a wind power variation probability density;

FIG. 4 is a diagram illustrating a single step rolling prediction result;

FIG. 5 is a graph showing the result of a probability distribution for a single step prediction;

FIG. 6 is a diagram illustrating a multi-time scale prediction error index;

FIG. 7 is a comparison graph of absolute error of prediction for each step.

The specific implementation mode is as follows:

the invention is further described with reference to the following figures and examples.

1 Markov chain model based on wind power variation

1.1 discrete Markov chain model

Random process { X ] with discrete time and state_nX (n), n is 0,1,2₁,S₂… }. Suppose that the process is in state S at the present time_iThere is a fixed probability that the process will be in state S at the next time_jThat is, assume for all states and all n ≧ 0, have

P{X_n＝S_j|X₁＝S₁,X₂＝S₂,…X_n-1＝S_i}

＝P{X_n＝S_j|X_n-1＝S_i},S_·∈I (1)

Such a stochastic process is called Markov chain. For a Markov chain, given a past state S₀，S₁，…，S_n-1And the present state S_nTime, future state X_n+1Is independent of the past state and only depends on the present state S_n. Probability pi of one-step transition in II memory_ijMatrix of (d), n_ijIndicating that the process is in state S_iThe next time to transition to state S_jThe conditional probability transition matrix of (1), whose elements satisfy:

<math> <mrow> <msub> <mi>&pi;</mi> <mi>ij</mi> </msub> <mo>&GreaterEqual;</mo> <mn>0</mn> <mo>,</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mo>&infin;</mo> </munderover> <msub> <mi>&pi;</mi> <mi>ij</mi> </msub> <mo>=</mo> <mn>1</mn> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow> </math>

1.2 Markov chain model construction based on wind power variation

The wind power variation is a variation value of wind power at two adjacent moments. The wind power variation can quantitatively measure the variation trend of the wind power. The analysis of the distribution characteristics and the transfer rule of the variable quantity has important significance for researching the fluctuation characteristics and the probability distribution characteristics of the wind power and predicting the active power. The chi-square test method is adopted to prove that the random sequence of the wind power meets Markov property and can be used as a Markov chain for treatment. The time sequence of the wind power variation is obtained by linear operation of wind power original data, so that the time sequence still has Markov property. The construction process of the model, including the processes of sample data acquisition, state space division, transition probability matrix definition, statistical calculation and the like, is elaborated in detail in this section.

1.2.1 variable sample space construction

By dividing the continuous time axis into discrete times at intervals Δ t, there are any two adjacent times t-1 and t

t＝t-1+Δt (3)

Converting an original power sample space into a wind power variable sample space through one-step linear transformation, wherein the variable of the wind power at a time interval [ t-1, t ] can be expressed as

V_t＝P_t-P_t-1 (4)

Wherein P is_t-1And P_tWind power values V at t-1 moment and t moment respectively_tFor wind power at time interval [ t-1, t]The amount of change in (c). By analogy, the wind power variation of any two adjacent moments in the random process at the corresponding time intervals can be calculated by adopting the method. Therefore, according to the historical time sequence of the wind power, a historical sample sequence of the wind power variation can be obtained by adopting one-step difference linear transformation, and the historical sample sequence is used as a sample space for constructing a Markov chain model.

1.2.2 variable Markov chain model State space partitioning

Aiming at the sample space of the wind power variation, in order to establish a Markov chain model, a corresponding state space is firstly constructed.

Assuming that the rated output of wind power is P_NThen the wind power original power is [0, P ]_N]The values are taken internally and the distribution is more dispersed. When a Markov chain model is constructed based on wind power original power data, the value range [0, P ] of the wind power is always divided by the rated power percentage_N]And (4) carrying out equal division, wherein each power interval corresponds to one state of the Markov chain model to form a state space. The length of the equal power division interval determines the precision of the state space, so that the division is reasonable as much as possible, each state has enough sample quantity, and the fineness degree of the state space is improved as much as possible. If the model precision is improved by reducing the length of the power interval and increasing the number of the states, the number of the samples in some states cannot meet the requirement due to the limitation of the number of the samples.

Wind power variable data in interval (-P)_N,P_N]The method has internal value and has the following two data characteristics: on one hand, the wind power variation value is small and the fluctuation is not obvious, and the data characteristic essentially requires that the division of the state space is much finer than the original power; on the other hand, the characteristics of symmetrical distribution and concentrated values of the variation should be fully considered. If the conventional method is adopted, the interval [ -P ] is subjected to_N,P_N]The halving and corresponding state space will give rise to a number of situations where the number of state samples is insufficient or even 0. Therefore, when the Markov chain model is constructed based on the wind power variation data, before the state space is divided, firstlyThe probability distribution condition of the wind power variation is firstly counted, and a probability density function is fitted. Then setting a confidence level, solving a corresponding variable value confidence interval, and carrying out conventional equal division on the interior of the confidence interval according to the rated power percentage, wherein each equal division interval corresponds to one state; meanwhile, in order to keep the integrity of the state space, the state space of the Markov chain model based on the wind power variation is guaranteed to cover all possible variation value states, and the states are divided independently for data outside the confidence interval. The method can effectively narrow the range of the divided states, so that the length of the variable quantity model power interval is much smaller than that of the original power model power interval under the same state number, namely the state space is much finer. The specific method comprises the following steps:

firstly, fitting a probability density function of variable probability distribution based on a distribution statistical result of wind power variable sample data. And setting a confidence level alpha, solving a corresponding variable quantity confidence interval D, and taking two end points of the confidence interval D as upper and lower limits of the variable quantity state division. The confidence interval D is not set to [ V ]_min,V_max]As shown in FIG. 1, the upper and lower limits of the variation state division are V_maxAnd V_min。

And after the upper limit and the lower limit of the state division are determined, the state space of the Markov chain model can be constructed. For most samples falling within the confidence interval, the invention selects the number of power intervals according to the following rule:

(1) except for the intervals at the two ends, the number of samples falling into each interval is not less than 5;

(2) the number of groups was calculated according to the Moore formula (equation (5)).

K-2≈C×N^2/5 (5)

K is the total number of interval division, including two power intervals outside the confidence interval, an integer value is taken, and K-2 is the number of equally divided power intervals; n is the number of samples; c is a formula coefficient which is generally 1-3. Defining the interval length as

$l=\frac{V_{\max }-V_{\min }}{K-2}---\left(6\right)$

V_maxAnd V_minFor the upper and lower limits of the variable confidence interval, the K power intervals correspond to K states in the variable Markov chain model state space.

For delta data outside a few confidence intervals, separate states are partitioned. If PN is rated installed capacity, the variation data will be in [ -P [ ]_N,P_N]An internal value. Therefore, the variation is set to [ -P ]_N,V_min]And [ V ]_max,P_N]Is divided into a first state and a kth state, respectively.

All states constitute a state space I_VCan be represented as

<math> <mrow> <msub> <mi>I</mi> <mi>V</mi> </msub> <mo>=</mo> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <msub> <mi>S</mi> <mn>1</mn> </msub> <mo>,</mo> <mi>V</mi> <mo>&Element;</mo> <mo>[</mo> <mo>-</mo> <msub> <mi>P</mi> <mi>N</mi> </msub> <mo>,</mo> <msub> <mi>V</mi> <mi>min</mi> </msub> <mo>]</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>S</mi> <mi>k</mi> </msub> <mo>,</mo> <mi>V</mi> <mo>&Element;</mo> <mo>(</mo> <msub> <mi>V</mi> <mi>min</mi> </msub> <mo>+</mo> <mi>l</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>-</mo> <mn>2</mn> <mo>)</mo> </mrow> <mo>,</mo> <msub> <mi>V</mi> <mi>min</mi> </msub> <mo>+</mo> <mi>l</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>]</mo> <mo>,</mo> <mi>k</mi> <mo>=</mo> <mn>2,3</mn> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <mi>K</mi> <mo>-</mo> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <msub> <mi>S</mi> <mi>K</mi> </msub> <mo>,</mo> <mi>V</mi> <mo>&Element;</mo> <mo>[</mo> <msub> <mi>V</mi> <mi>max</mi> </msub> <mo>,</mo> <msub> <mi>P</mi> <mi>N</mi> </msub> <mo>]</mo> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow> </math>

1.2.3 transition probability matrix statistics and calculation

And after the sample space conversion and the state space division are completed, counting and calculating a transition probability matrix of the Markov chain model. Note S_tFor the variation at time intervals t-1, t]According to the Markov property of the stochastic process, [ t, t + 1]]Wind power variable quantity state S_t+1By S only_tThe decision, can be expressed as

P{X_t+1＝S_t+1|X₁＝S₁,X₂＝S₂,…X_t＝S_t}

＝P{X_t+1＝S_t+1|X_t＝S_t},S_·∈I (8)

For calculating the transition probability matrix, defining a transition frequency matrix N as the transition frequency of the adjacent wind power variable quantity between each state, wherein the element N is_ijObtained by statistics of the formula

Wherein N is_ijThe variable quantity of the wind power is [ t-1, t ]]S of the time period_iState transition to [ t, t + 1]]S of the time period_jNumber of states, T is total number of samples, N_ijSatisfies the following formula

<math> <mrow> <msub> <mi>N</mi> <mi>ij</mi> </msub> <mo>&le;</mo> <mi>T</mi> <mo>,</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>K</mi> </munderover> <munderover> <mi>&Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>K</mi> </munderover> <msub> <mi>N</mi> <mi>ij</mi> </msub> <mo>=</mo> <mi>T</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>10</mn> <mo>)</mo> </mrow> </mrow> </math>

The element pi in the probability matrix pi is transferred_ijIs calculated as follows

<math> <mrow> <msub> <mi>&pi;</mi> <mi>ij</mi> </msub> <mo>=</mo> <mi>P</mi> <mo>{</mo> <msub> <mi>S</mi> <mi>j</mi> </msub> <mo>|</mo> <msub> <mi>S</mi> <mi>i</mi> </msub> <mo>}</mo> <mo>=</mo> <mfrac> <msub> <mi>N</mi> <mi>ij</mi> </msub> <mrow> <munderover> <mi>&Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>K</mi> </munderover> <msub> <mi>N</mi> <mi>ij</mi> </msub> </mrow> </mfrac> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>=</mo> <mn>1,2</mn> <mo>,</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <mi>K</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>11</mn> <mo>)</mo> </mrow> </mrow> </math>

And satisfy

<math> <mrow> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <msub> <mi>&pi;</mi> <mi>ij</mi> </msub> <mo>&GreaterEqual;</mo> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <munderover> <mi>&Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>K</mi> </munderover> <msub> <mi>&pi;</mi> <mi>ij</mi> </msub> <mo>=</mo> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>=</mo> <mn>1,2</mn> <mo>,</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <mo>,</mo> <mi>K</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>12</mn> <mo>)</mo> </mrow> <mo>.</mo> </mrow> </math>

The transition probability matrix is the most important component of the Markov chain model, reflects the conditional probability of the variable quantity to be transferred from the current state to the next state, and is the basis of the application of the model.

A wind power variable quantity Markov chain model constructed based on a wind power variable quantity sample space realizes the fine division of a model state space by using the data characteristics of variable quantities, and the state space is expressed as shown in a formula (7). The conditional transition probability of the wind power variation among the states is obtained by calculating a transition probability matrix pi, and the change characteristic and the fluctuation rule of the wind power are described as shown in a formula (11).

2 wind power variable Markov chain model prediction application

The Markov chain model based on the wind power variation takes actual operation data as a modeling basis, and presents the variation rule of the wind power variation by using a transition probability matrix. The model can be used in the fields of wind power prediction, real-time economic dispatching of a wind power system, Markov chain-based optimization decision, model prediction control and the like. In order to embody the superiority of the variable Markov chain model, a wind power prediction method based on the variable Markov chain model is provided by taking a wind power prediction application scene as an example.

At present, wind power prediction methods are mainly divided into a deterministic prediction method and a probabilistic prediction method. The traditional deterministic prediction method takes the wind power value at the moment of prediction as a prediction result, and the prediction information is single. Compared with a deterministic prediction method, the probability prediction of the wind power takes the probability distribution of the wind power output at the future moment as a prediction result, and can provide more sufficient decision information for risk analysis and dynamic economic scheduling of the power system. The wind power probability prediction and certainty prediction method based on the Markov chain model has the advantages of being simple in modeling method, high in calculation speed, high in accuracy and the like. However, in the existing method, wind power original power is used as a Markov chain modeling sample, the fineness of model state space division is limited by the modeling data volume, the rough state division is easy to influence the prediction precision in prediction, and particularly the problem of error accumulation in the multi-step prediction process is prominent.

The invention provides a wind power prediction method based on a variable Markov chain model, which is used for predicting the probability distribution and the predicted value of the variable in the future time period and indirectly obtaining the prediction result of the wind power. Compared with a prediction method using a wind power original power Markov chain model, the method can obtain higher prediction precision due to more detailed state space division and smaller error accumulation in the multi-step transfer process.

2.1 Single-step prediction method based on wind power variation Markov chain model

The premise of prediction is that sample data is trained to construct a relatively accurate Markov chain model. For sample data of a given wind power time sequence, firstly, a continuous time axis is divided into discrete moments according to a time scale delta t, and wind power variation can be calculated according to an equation (4) at any two adjacent moments, so that data samples of the variation are obtained. Then, according to the method in section 1.2.2, a state space division scheme is determined, and the variable state space is divided into K states in detail. And then, counting the frequency transfer matrix N and calculating a transfer probability matrix pi to complete the construction of the variable Markov chain model.

For convenience of description, the previous time is denoted as t-1, the current time is denoted as t, and the next time is denoted as t +1, which are called the current time and the previous time (time period [ t-1, t)]) The wind power variation is the current variation V_tThe current time and the next time (time period [ t, t + 1]]) The wind power variation is the next variation V_t+1. If the current variation V is_tIf the actual value of (c) is known, the next variation V can be obtained by using the transition probability matrix of the variation Markov chain model_t+1Probability distribution of (2).

Defining state selection unit row vectors_t，_tCurrent change V in_tThe element corresponding to the state of the device is 1, and the other elements are 0. Next variable V_t+1Is only limited by the current variance V_tIs determined by the state of

<math> <mrow> <msubsup> <mover> <mi>&pi;</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>V</mi> </msubsup> <mo>=</mo> <msub> <mi>&Gamma;</mi> <mi>t</mi> </msub> <mi>&Pi;</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>13</mn> <mo>)</mo> </mrow> </mrow> </math>

II, obtaining a transition probability matrix from a current variable quantity state to a next variable quantity state;is the next variable V_t+1And taking the probability vector of each state.

The expectation of the probability distribution is predicted with the variance as a deterministic predictor of variance. Except for the intervals at two ends, multiplying the probability of the variation falling into each interval by the median value of each interval and then summing; because the two-end interval is positioned outside the confidence interval, the probability that the variation falls in the two-end interval is very small, the expected calculation result is hardly influenced, the two-end interval is not considered when the deterministic prediction value is calculated, and the following expression is expressed by an expression (14):

<math> <mrow> <msub> <mover> <mi>V</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>2</mn> </mrow> <mrow> <mi>K</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msubsup> <mover> <mi>&pi;</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>V</mi> </msubsup> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> <mo>&times;</mo> <msub> <mi>V</mi> <mi>mid</mi> </msub> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>14</mn> <mo>)</mo> </mrow> </mrow> </math>

wherein, V_mid(i) The median of each variation power interval is shown.

In order to convert the variable probability distribution prediction result into the prediction probability distribution of the wind power, a value power interval of the wind power is constructed. Assuming that a set formed by possible value intervals for predicting wind power is I_P，I_P(i) For the ith interval therein, it is required to satisfyEach interval corresponds to a wind power state. The known wind power actual value P at the current moment is used as the power value_tAccumulating the variable quantity with the upper limit and the lower limit of each prediction interval one by one to obtain a prediction wind power interval, and defining the following constraint conditions

<math> <mrow> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <mn>0</mn> <mo>&le;</mo> <msub> <mi>P</mi> <mi>t</mi> </msub> <mo>+</mo> <msub> <mi>V</mi> <mi>min</mi> </msub> <mo>&le;</mo> <msub> <mi>P</mi> <mi>N</mi> </msub> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> <mo>&le;</mo> <msub> <mi>P</mi> <mi>t</mi> </msub> <mo>+</mo> <msub> <mi>V</mi> <mi>max</mi> </msub> <mo>&le;</mo> <msub> <mi>P</mi> <mi>N</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>V</mi> <mi>min</mi> </msub> <mo>&lt;</mo> <msub> <mi>V</mi> <mi>max</mi> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>15</mn> <mo>)</mo> </mrow> </mrow> </math>

(1) If P_tIf the formula (15) is satisfied, the power interval of the wind power is predicted to be

<math> <mrow> <msub> <mi>I</mi> <mi>P</mi> </msub> <mo>=</mo> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <msub> <mi>S</mi> <mi>l</mi> </msub> <mo>,</mo> <msub> <mover> <mi>P</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>&Element;</mo> <mo>[</mo> <mn>0</mn> <mo>,</mo> <msub> <mi>P</mi> <mi>t</mi> </msub> <mo>+</mo> <msub> <mi>V</mi> <mi>min</mi> </msub> <mo>]</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>S</mi> <mi>k</mi> </msub> <mo>,</mo> <msub> <mover> <mi>P</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>&Element;</mo> <mo>(</mo> <msub> <mi>P</mi> <mi>t</mi> </msub> <mo>+</mo> <msub> <mi>V</mi> <mi>min</mi> </msub> <mo>+</mo> <mi>l</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>-</mo> <mn>2</mn> <mo>)</mo> </mrow> <mo>,</mo> <msub> <mi>P</mi> <mi>t</mi> </msub> <mo>+</mo> <msub> <mi>V</mi> <mi>min</mi> </msub> <mo>+</mo> <mi>l</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>]</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>S</mi> <mi>K</mi> </msub> <mo>,</mo> <msub> <mover> <mi>P</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>&Element;</mo> <mo>[</mo> <msub> <mi>P</mi> <mi>t</mi> </msub> <mo>+</mo> <msub> <mi>V</mi> <mi>max</mi> </msub> <mo>,</mo> <msub> <mi>P</mi> <mi>N</mi> </msub> <mo>]</mo> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>16</mn> <mo>)</mo> </mrow> </mrow> </math>

Where K is 2,3, … K-1, and l is the length of each equal section corresponding to the variation state. At this time, the number of power intervals for predicting the wind power is the same as the number of power intervals for predicting the variation, and the wind power P is predicted_t+1And the predicted variation V_t+1The probability of falling in the corresponding interval is also equal, i.e.

<math> <mrow> <msubsup> <mover> <mi>&pi;</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>P</mi> </msubsup> <mo>=</mo> <msubsup> <mover> <mi>&pi;</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>V</mi> </msubsup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>17</mn> <mo>)</mo> </mrow> </mrow> </math>

Wherein,and the probability of the wind power value at the moment of t +1 falling in each power interval is the probability prediction result.

(2) If P_tDoes not satisfy formula (15) and P_t+V_min<0, introducing an integer parameter K₁So that

P_t+V_min+l·K₁≥0 (18)

K₁Taking the smallest integer satisfying the above formula, i.e.

$K_1=\mathrm{int}\left(\frac{-V_{\min }-P_t}{l}\right)+1---\left(19\right)$

Where int () is a rounding function.

At this time, the number of power intervals for predicting the wind power is less than K, and is set to K', and the power interval set can be expressed as

<math> <mrow> <msub> <mi>I</mi> <mi>P</mi> </msub> <mo>=</mo> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <msub> <mi>S</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mover> <mi>P</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>&Element;</mo> <mo>[</mo> <mn>0</mn> <mo>,</mo> <msub> <mi>P</mi> <mi>t</mi> </msub> <mo>+</mo> <msub> <mi>V</mi> <mi>min</mi> </msub> <mo>+</mo> <mi>l</mi> <mo>&CenterDot;</mo> <msub> <mi>K</mi> <mn>1</mn> </msub> <mo>]</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>S</mi> <mrow> <msub> <mi>k</mi> <mn>1</mn> </msub> <mo>-</mo> <msub> <mi>K</mi> <mn>1</mn> </msub> </mrow> </msub> <mo>,</mo> <msub> <mover> <mi>P</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>&Element;</mo> <mo>(</mo> <msub> <mi>P</mi> <mi>t</mi> </msub> <mo>+</mo> <msub> <mi>V</mi> <mi>min</mi> </msub> <mo>+</mo> <mi>l</mi> <mo>&CenterDot;</mo> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <mo>-</mo> <mn>2</mn> <mo>)</mo> </mrow> <mo>,</mo> <msub> <mi>P</mi> <mi>t</mi> </msub> <mo>+</mo> <msub> <mi>V</mi> <mi>min</mi> </msub> <mo>+</mo> <mi>l</mi> <mo>&CenterDot;</mo> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <mo>-</mo> <mn>1</mn> <mo>)</mo> <mo>]</mo> <mo>-</mo> </mrow> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>20</mn> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <msub> <mi>S</mi> <mrow> <mi>K</mi> <mo>&prime;</mo> </mrow> </msub> <mo>,</mo> <msub> <mover> <mi>P</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>&Element;</mo> <mo>[</mo> <msub> <mi>P</mi> <mi>t</mi> </msub> <mo>+</mo> <msub> <mi>V</mi> <mi>max</mi> </msub> <mo>,</mo> <msub> <mi>P</mi> <mi>N</mi> </msub> <mo>]</mo> </mtd> </mtr> </mtable> </mfenced> </mrow> </math>

Wherein k is₁＝K₁+2,K₁+3,…,K-1；K'＝K-K₁. In order to satisfy the property of probability distribution, the probability of the rejected scene is merged into the probability of the scene closest to the probability according to the basic principle of scene reduction. The probability of the wind power falling in the first power interval is taken as the variable number from 1 to K₁The prediction probability of each state and the probability of falling in other power intervals are taken as the prediction probability corresponding to the variation interval. the probability that the wind power at the time t +1 falls in each power interval can be expressed as

<math> <mrow> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <msubsup> <mover> <mi>&pi;</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>P</mi> </msubsup> <mrow> <mo>(</mo> <mi>l</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>K</mi> <mn>1</mn> </msub> </munderover> <msubsup> <mover> <mi>&pi;</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>V</mi> </msubsup> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <msubsup> <mover> <mi>&pi;</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>P</mi> </msubsup> <mrow> <mo>(</mo> <mi>j</mi> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mover> <mi>&pi;</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>V</mi> </msubsup> <mrow> <mo>(</mo> <msub> <mi>K</mi> <mn>1</mn> </msub> <mo>+</mo> <mi>j</mi> <mo>)</mo> </mrow> <mo>,</mo> <mi>j</mi> <mo>=</mo> <mn>2,3</mn> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <mi>K</mi> <mo>&prime;</mo> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>21</mn> <mo>)</mo> </mrow> </mrow> </math>

(3) If Pt does not satisfy formula (15) and Pt + V_max>P_NIntroduction of an integer parameter K₂So that

P_t+V_min+l·K₂≤P_N (22)

K₂Taking the largest integer satisfying the above formula, i.e.

$K_2=\mathrm{int}\left(\frac{P_N-P_t-V_{\min }}{l}\right)---\left(23\right)$

The number of power intervals for predicting the wind power is less than K, the power intervals are set to be K', and the power interval set can be expressed as

<math> <mrow> <msub> <mi>I</mi> <mi>P</mi> </msub> <mo>=</mo> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <msub> <mi>S</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mover> <mi>P</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>&Element;</mo> <mo>[</mo> <mn>0</mn> <mo>,</mo> <msub> <mi>P</mi> <mi>t</mi> </msub> <mo>+</mo> <msub> <mi>V</mi> <mi>min</mi> </msub> <mo>]</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>S</mi> <msub> <mi>k</mi> <mn>2</mn> </msub> </msub> <mo>,</mo> <msub> <mover> <mi>P</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>&Element;</mo> <mo>(</mo> <msub> <mi>P</mi> <mi>t</mi> </msub> <mo>+</mo> <msub> <mi>V</mi> <mi>min</mi> </msub> <mo>+</mo> <mi>l</mi> <mo>&CenterDot;</mo> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <mo>-</mo> <mn>2</mn> <mo>)</mo> </mrow> <mo>,</mo> <msub> <mi>P</mi> <mi>t</mi> </msub> <mo>+</mo> <msub> <mi>V</mi> <mi>min</mi> </msub> <mo>+</mo> <mi>l</mi> <mo>&CenterDot;</mo> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <mo>-</mo> <mn>1</mn> <mo>)</mo> <mo>]</mo> <mo>-</mo> </mrow> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>24</mn> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <msub> <mi>S</mi> <mrow> <mi>K</mi> <mo>&prime;</mo> <mo>&prime;</mo> </mrow> </msub> <mo>,</mo> <msub> <mover> <mi>P</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>&Element;</mo> <mo>[</mo> <msub> <mi>P</mi> <mi>t</mi> </msub> <mo>+</mo> <msub> <mi>V</mi> <mi>min</mi> </msub> <mo>+</mo> <mi>l</mi> <mo>&CenterDot;</mo> <msub> <mi>K</mi> <mn>2</mn> </msub> <mo>,</mo> <msub> <mi>P</mi> <mi>N</mi> </msub> <mo>]</mo> </mtd> </mtr> </mtable> </mfenced> </mrow> </math>

Wherein k is₂＝2,3,…K₂+1；K″＝K₂+2. The probability that the wind power predicted value falls in the Kth power interval is used for taking the variation Kth₂Probability sum of K states, probability of falling in other power intervalsAnd taking the prediction probability corresponding to the variation interval. the probability that the wind power at the time t +1 falls in each power interval can be expressed as

<math> <mrow> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <msubsup> <mover> <mi>&pi;</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>P</mi> </msubsup> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mover> <mi>&pi;</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>V</mi> </msubsup> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> <mo>,</mo> <mi>i</mi> <mo>=</mo> <mn>1,2</mn> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <msub> <mi>K</mi> <mn>2</mn> </msub> <mo>+</mo> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <msubsup> <mover> <mi>&pi;</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>P</mi> </msubsup> <mrow> <mo>(</mo> <mi>K</mi> <mo>&prime;</mo> <mo>&prime;</mo> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mrow> <munderover> <mi>&Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <msub> <mi>K</mi> <mn>2</mn> </msub> </mrow> <mi>K</mi> </munderover> <mover> <mi>&pi;</mi> <mo>^</mo> </mover> </mrow> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>V</mi> </msubsup> <mrow> <mo>(</mo> <mi>j</mi> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>25</mn> <mo>)</mo> </mrow> </mrow> </math>

Predicting the power interval of the wind power to be the actual value P at the current moment_tIs constructed so that each prediction is updated in a rolling fashion.

In order to facilitate practical application and error analysis, a deterministic prediction result of wind power needs to be obtained. The expectation of the wind power prediction probability distribution is used as the deterministic prediction value of the wind power, and the formula (26) is as follows:

<math> <mrow> <msub> <mover> <mi>P</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>G</mi> </munderover> <msubsup> <mover> <mi>&pi;</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>P</mi> </msubsup> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> <mo>&times;</mo> <msub> <mi>P</mi> <mrow> <mi>mid</mi> <mo>,</mo> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </mrow> </math> g ═ K or K' (26)

Wherein,the deterministic prediction value of the wind power at the moment t +1 is obtained; g is the number of possible value intervals of the predicted wind power, namely the state number; p_midAnd the median value of the wind power interval is obtained.

2.2 Multi-step prediction based on Markov chain model of wind power variation

In a multi-step prediction process, the state shift at any step in the process may be amplified step by step, which may finally result in a large error. Such error propagation can be effectively limited due to the fact that the Markov chain model of the variation has a fine state space. This advantage of the model is illustrated below by taking the multi-step prediction of wind power as an example.

2.2.1 Multi-step prediction based on Markov chain model of wind power variation

The multi-step prediction is to divide the time span from the current time to the prediction time by delta t and decompose the prediction of a relatively long time scale into a plurality of single-step prediction processes in order to provide wind power prediction of a longer time scale. Except that the actual value of the first step is used as the known input, the predicted output result of the previous step is used as the known input of the next prediction in each intermediate step. Assuming that the time span from the prediction moment to the current moment is L, obtaining the wind power at the prediction moment from the known condition of the current moment requires M steps of calculation, and the prediction step number M is

<math> <mrow> <mi>M</mi> <mo>=</mo> <mfrac> <mi>L</mi> <mi>&Delta;t</mi> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>27</mn> <mo>)</mo> </mrow> </mrow> </math>

Assume that the variation prediction probability distribution of any one of the steps (not assumed to be the mth step) in the multi-step prediction isThe predicted value of the variation isCorresponds to the state ofThe predicted variation probability distribution of the m +1 step is

<math> <mrow> <msubsup> <mover> <mi>&pi;</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mi>m</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>V</mi> </msubsup> <mo>=</mo> <msub> <mover> <mi>&Gamma;</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mi>m</mi> </mrow> </msub> <mi>&Pi;</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>28</mn> <mo>)</mo> </mrow> </mrow> </math>

Wherein,predicting state for variation at time t + mCorresponding stateUnit row vectors are selected, pi is a transition probability matrix. The predicted value of the variation of the m +1 th step is

<math> <mrow> <msub> <mover> <mi>V</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mi>m</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>2</mn> </mrow> <mrow> <mi>K</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msubsup> <mover> <mi>&pi;</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mi>m</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>V</mi> </msubsup> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> <mo>&times;</mo> <msub> <mi>V</mi> <mi>mid</mi> </msub> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>29</mn> <mo>)</mo> </mrow> </mrow> </math>

The predicted power interval of the wind power output at the t + m +1 th moment is determined according to the formula (16), the formula (20) and the formula (24), and the probability distribution of each power interval isNamely, it is

<math> <mrow> <msub> <mover> <mi>P</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mi>m</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>G</mi> </munderover> <msubsup> <mover> <mi>&pi;</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mi>m</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>P</mi> </msubsup> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> <mo>&times;</mo> <msubsup> <mi>P</mi> <mrow> <mi>mid</mi> <mo>,</mo> <mi>t</mi> <mo>+</mo> <mi>m</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>G</mi> </msubsup> <mo>,</mo> </mrow> </math> G ═ K, K 'or K' (30)

2.2.2 Multi-step predictive error accumulation analysis

In the process of carrying out long-time multi-step prediction by applying a Markov chain model, the offset of a certain step of prediction state relative to the actual state can be amplified step by step, so that the final prediction result has larger deviation. The section analyzes the accumulated influence of the state deviation of a certain step on the subsequent transfer process through the quantitative calculation of accumulated errors in the multi-step prediction process.

And (4) the state of the Markov chain is represented by X, in the original power model, X represents the wind power state, and in the variable quantity model, X represents the variable quantity state. Assume that the prediction state of any one of the steps (not the mth step) in the multi-step prediction process from time t to time t + M isThe actual state of the wind power output (or the wind power variable quantity) at the moment is X_t+mThe state deviation of the predicted state from the actual state is recorded as Δ_m

<math> <mrow> <msub> <mi>&Delta;</mi> <mi>m</mi> </msub> <mo>=</mo> <msub> <mover> <mi>X</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mi>m</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>X</mi> <mrow> <mi>t</mi> <mo>+</mo> <mi>m</mi> </mrow> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>31</mn> <mo>)</mo> </mrow> </mrow> </math>

According to the multi-step prediction method, the predicted value of the mth step is used as the input of the (m + 1) th step. Due to the presence of a state shift Δ_mSet to a predicted stateWhen the wind power (or the wind power variable quantity) is input in the (m + 1) th step, the probability distribution of the wind power (or the wind power variable quantity) at the t + m +1 moment obtained by predicting the (m + 1) th step is

<math> <mrow> <msubsup> <mover> <mi>&pi;</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mi>m</mi> <mo>+</mo> <mn>1</mn> </mrow> <mo>*</mo> </msubsup> <mo>=</mo> <mi>&Gamma;</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>X</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mi>m</mi> </mrow> </msub> <mo>)</mo> </mrow> <mi>&Pi;</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>32</mn> <mo>)</mo> </mrow> </mrow> </math>

Corresponding to the step prediction value ofWhileWill do asThe state offset delta generated in the m step is input in the m +2 step and so on_mIt is possible that subsequent M-M step predictions have an impact such that errors are accumulated in subsequent M-M predictions. A multi-step error accumulation diagram is shown in fig. 2.

When the wind power variation Markov chain model is used for multi-step prediction, the characteristic that variation data have small values reduces the probability of state deviation in the prediction process, and the fine state space division effectively slows down the speed of error accumulation.

Defining an offset ratio lambda_mTo indicate the deviation degree of the predicted value of the mth step from the actual value

<math> <mrow> <msub> <mi>&lambda;</mi> <mi>m</mi> </msub> <mo>=</mo> <mfrac> <mrow> <mi>l</mi> <mo>&times;</mo> <msub> <mi>&Delta;</mi> <mi>m</mi> </msub> </mrow> <msub> <mi>P</mi> <mi>N</mi> </msub> </mfrac> <mo>,</mo> <mi>m</mi> <mo>=</mo> <mn>1,2</mn> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <mi>M</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>33</mn> <mo>)</mo> </mrow> </mrow> </math>

When delta_m＝0，λ_mWhen the number is equal to 0, the number of the predicted states is the same as the number of the actual states, and the prediction state is simply referred to as no offset; when delta_m>At 0, λ_m>0, indicating that the number of predicted states is greater than the number of actual states, referred to as positive offset for short; when delta_m<At 0, λ_m<0, indicating that the number of predicted states is less than the number of actual states, called negative offset for short; lambda_mThe larger | is, the farther the predicted state deviates from the actual state. Thus, λ can be calculated₁～λ_MThe deviation situation of each step prediction in the whole multi-step prediction process is quantitatively described.

3 example analysis

Practical operation data of a certain wind power plant in the grid in the north of the wing from 1 month and 1 day 00:00 in 2013 to 31 month and 31 day in 2013 and 31 day 59 in 12 months are selected for example analysis, the sample sampling interval is 1min, and the total effective data is 525600.

According to the technical specification of accessing wind power plants to a power grid in China, the wind power plants should automatically report a wind power plant generating power prediction curve of 15 min-4 h in the future to a power grid dispatching department in a rolling mode every 15min, and the time resolution of a predicted value is 15 min. The time resolution of the day-ahead wind power prediction of the wind farm is also 15 min. For convenience of reference to scheduling, the present invention defines a time scale Δ t of 15min, and the whole day time is divided into 96 time instants. And selecting data with the time interval of 15min from the sample data to form a sample space of the wind power original power.

For convenient calculation and analysis, the active power is standardized:

<math> <mrow> <mi>P</mi> <mo>=</mo> <mfrac> <msub> <mi>P</mi> <mi>M</mi> </msub> <msub> <mi>P</mi> <mi>N</mi> </msub> </mfrac> <mo>&times;</mo> <mn>100</mn> <mo>%</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>34</mn> <mo>)</mo> </mrow> </mrow> </math>

wherein P is the rated output percentage, P_MFor actual measured active power, P_NThe rated capacity of the wind power plant is 150MW in the present example.

The method comprises the steps of selecting data of the first 51 weeks in a sample of the whole year as modeling data, and solving a transition probability matrix of a Markov chain model; data from week 52 was selected for prediction and error analysis.

3.1 construction of Markov chain model with wind power variation

The sample data is wind power original power data, and according to the method of 1.2.1, the wind power original power sample space is converted into a variable quantity sample space through linear transformation, and the variable quantity sample space is used for constructing a Markov chain model of wind power variable quantity. The variation sample space is formed by the variation of the wind power at adjacent moments, so that the modeling data amount N is 34367.

The probability distribution of wind power variation at the statistical adjacent moments is shown in fig. 3. Strictly speaking, a probability density function is fitted according to the probability distribution statistical result, then a confidence level is set, and a confidence interval is solved through integral calculation. In order to simplify the calculation, the confidence interval is simply determined by adopting a probability accumulation method. Setting the confidence level alpha to be 0.999, and simply accumulating the probability to obtain the confidence interval of the wind power variation corresponding to [ -0.20,0.20]. Therefore, the upper and lower limits of the variation state division are respectively V_max＝0.20，V_min＝-0.20。

The state space of the variation is divided into K states according to equation (5), corresponding to the power intervals of the K variations.

K-2＝C×34367^2/5≈65.2C,C＝1～3

The value ranges of the upper limit and the lower limit and K are divided by combining the variable quantity state, the appropriate variable quantity power interval length l is taken to simplify the calculation, C is 1.25, and K is 82, so that the calculation is simplified

$l=\frac{0.20-(-0.20)}{82-2}=0.005$

Therefore, the state space of the variation is divided into 82 states with 0.5% of the rated power as the interval length, and the state space IV can be expressed as

<math> <mrow> <msub> <mi>I</mi> <mi>V</mi> </msub> <mo>=</mo> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <msub> <mi>S</mi> <mn>1</mn> </msub> <mo>,</mo> <mi>V</mi> <mo>&Element;</mo> <mo>[</mo> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mo>-</mo> <mn>0.20</mn> <mo>]</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>S</mi> <mi>k</mi> </msub> <mo>,</mo> <mi>V</mi> <mo>&Element;</mo> <mo>(</mo> <mo>-</mo> <mn>0.20</mn> <mo>+</mo> <mn>0.005</mn> <mrow> <mo>(</mo> <mi>k</mi> <mo>-</mo> <mn>2</mn> <mo>)</mo> </mrow> <mo>,</mo> <mo>-</mo> <mn>0.20</mn> <mo>+</mo> <mn>0.005</mn> <mrow> <mo>(</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>]</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>S</mi> <mn>82</mn> </msub> <mo>,</mo> <mi>V</mi> <mo>&Element;</mo> <mo>[</mo> <mn>0.20,1</mn> <mo>]</mo> </mtd> </mtr> </mtable> </mfenced> </mrow> </math>

Where k is 2,3, … 81. After the state space is determined, the transition frequency matrix N can be counted according to the formulas (9) to (12), and the transition probability matrix pi can be calculated, wherein the N and pi are 82 multiplied by 82 square matrixes.

To pairCompared with the prediction precision of a prediction method based on a wind power variable Markov chain model and a prediction method based on an original power Markov chain model, the method constructs the Markov chain model by a similar method for a wind power original data sample space before linear transformation is carried out to obtain a variable sample space. The model is different from a variable Markov chain model in that the original power data take values randomly from 0 to rated output and are distributed in a dispersed manner, so that the state division range of the original power Markov chain model is [0, P ]_N]，P_NIs the rated installed capacity. When the state space is divided, the power interval corresponding to each state is wide, and the division of the state space is relatively rough. For comparison with a wind power prediction method based on variation, the number of the equal power intervals is 80, and each power interval corresponds to one state. Thus, the length of the power division is divided into equal parts

<math> <mrow> <mi>l</mi> <mo>&prime;</mo> <mo>=</mo> <mfrac> <mrow> <mn>1.00</mn> <mo>-</mo> <mn>0</mn> </mrow> <mn>80</mn> </mfrac> <mo>=</mo> <mn>0.0125</mn> </mrow> </math>

The case of 0 output is divided into one state individually, and a total of 81 states. The state space of the original power Markov chain model can be expressed as

<math> <mrow> <msub> <mi>I</mi> <mi>W</mi> </msub> <mo>=</mo> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <msub> <mi>S</mi> <mn>1</mn> </msub> <mo>,</mo> <mi>P</mi> <mo>=</mo> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <msub> <mi>S</mi> <mi>k</mi> </msub> <mo>,</mo> <mi>P</mi> <mo>=</mo> <mo>(</mo> <mn>0.0125</mn> <mrow> <mo>(</mo> <mi>k</mi> <mo>-</mo> <mn>2</mn> <mo>)</mo> </mrow> <mo>,</mo> <mn>0.0125</mn> <mrow> <mo>(</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>]</mo> <mo>,</mo> <mi>k</mi> <mo>=</mo> <mn>2</mn> <mo>,</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <mo>,</mo> <mn>81</mn> </mtd> </mtr> </mtable> </mfenced> </mrow> </math> Wherein IW is a state space of a wind power Markov chain model; and P is wind power data.

3.2 Single step scrolling prediction with a 15min look ahead

If the wind power variable quantity V from the previous moment t-1 to the current moment t is known_tThe wind power variable quantity from the current moment t to the next moment t +1 can be predicted according to the transition probability matrixAnd the wind power output value and the probability distribution at the moment of t + 1. When the actual value of the wind power comes temporarily at the next moment, the known condition can be refreshed, and the actual value V is changed according to the wind power_t+1Predicting wind power variation from t +1 moment to t +2 momentAnd the wind power output value and the probability distribution at the moment of t + 2. And rolling calculation in this way to obtain a single-step predicted wind power time sequence with a look-ahead of 15 min.

In order to evaluate the prediction accuracy of the method of the invention, the mean absolute error E is introduced_MAERoot mean square error E_RMSEAnd correlation coefficient I_ccThree error indexes are determinedThe effect of the prediction was evaluated.

<math> <mrow> <msub> <mi>E</mi> <mi>MAE</mi> </msub> <mo>=</mo> <mfrac> <mn>1</mn> <mi>n</mi> </mfrac> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <mo>|</mo> <msub> <mover> <mi>y</mi> <mo>^</mo> </mover> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>|</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>35</mn> <mo>)</mo> </mrow> </mrow> </math>

<math> <mrow> <msub> <mi>E</mi> <mi>RMSE</mi> </msub> <mo>=</mo> <msqrt> <mfrac> <mn>1</mn> <mi>n</mi> </mfrac> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msup> <mrow> <mo>(</mo> <msub> <mover> <mi>y</mi> <mo>^</mo> </mover> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </msqrt> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>36</mn> <mo>)</mo> </mrow> </mrow> </math>

$I_{\mathrm{cc}}=\frac{\mathrm{cov}(y_i,{\hat{y}}_i)}{\sqrt{D{y}_i}\sqrt{D{\hat{y}}_i}}---\left(37\right)$

The average absolute error E is expressed by the formula (35)_MAEWhereinTo predict value, y_iN is the number of predicted times, which is an actual measurement value. E_MAEThe method is used for evaluating the average amplitude of the prediction error and measuring whether the prediction result is unbiased, and the closer the value is to 0, the smaller the prediction error is, and the better the prediction effect is. Equation (36) is the root mean square error E_RMSEThe more the value is close to 0, the better the prediction effect is. The formula (37) is a correlation coefficient I_ccAnd evaluating indexes which can help to judge whether the main error source of the prediction system is a transverse error or a longitudinal error, so that different correction means are adopted in a targeted manner. The closer the value result is to 1, the more obvious the longitudinal error is, and the better the prediction effect is; conversely, the more significant the lateral error, the worse the prediction.

For convenience of description, hereinafter, the wind power prediction method based on the variable quantity Markov chain model is simply referred to as a variable quantity method, and the wind power prediction method using the original power Markov chain model is simply referred to as an original power method. Table 1 compares the prospective 15min rolling prediction error indexes of the wind power plant under different methods. Meanwhile, in order to reflect the influence of the state space fineness on the model precision, the prediction error index of the original power method is added in table 1 when the original power Markov chain model state number is respectively 51 and 21. The data in table 1 show that when a Markov chain model is constructed by using raw power, the prediction accuracy of the model can be effectively increased by increasing the number of states; by using variable data modeling, the state space can be divided more finely, and the prediction error is further reduced. In addition, for the wind power single-step prediction with the forward-looking 15min, when the original power model state division is fine to a certain degree, the advantage of the variation method compared with the original power method is not obvious.

TABLE 1 Single step Rolling prediction error index

Table 1The error indexes of one-step ahead rolling forecasting

Fig. 4 shows a comparison curve between the predicted value and the actual value by the variation method, and since there are many data, in order to clearly present the comparison effect, this graph plots 1 data point every 10 data points. It can be seen from the figure that the variation method can accurately reflect the actual size and fluctuation condition of the wind power at each moment.

The invention only selects one prediction to analyze the probability prediction result, which is limited by space. The actual value P of the wind power at the previous moment is known in the prediction_t-10.3622; the actual value of the wind power at the current moment is P_t0.3913; therefore, the wind power variation is V_t0.0291, belonging to the 47 th state in the variation state space, the wind power variation V between the next time and the current time according to the method described in section 2.1_t+1Has a probability distribution of

<math> <mrow> <msubsup> <mover> <mi>&pi;</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>V</mi> </msubsup> <mo>=</mo> <msub> <mi>&Gamma;</mi> <mi>t</mi> </msub> <mi>&Pi;</mi> </mrow> </math>

Wherein,_tis a unit row vector of 82 × 1, the 47 th element is 1, and the rest are 0. Because of P_tSatisfies inequality (15), and V_min＝-0.20，V_max0.20, the wind power probability distribution when the probability distribution of the variation is converted into the wind power probability distribution can be expressed as

<math> <mrow> <msub> <mi>I</mi> <mi>P</mi> </msub> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <msub> <mi>S</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mover> <mi>P</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>&Element;</mo> <mo>[</mo> <mn>0,0.1913</mn> <mo>]</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>S</mi> <mi>k</mi> </msub> <mo>,</mo> <msub> <mover> <mi>P</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>&Element;</mo> <mo>(</mo> <mn>0.1913</mn> <mo>+</mo> <mn>0.005</mn> <mrow> <mo>(</mo> <mi>k</mi> <mo>-</mo> <mn>2</mn> <mo>)</mo> </mrow> <mo>,</mo> <mn>0.1913</mn> <mo>+</mo> <mn>0.005</mn> <mrow> <mo>(</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>]</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>S</mi> <mn>82</mn> </msub> <mo>,</mo> <msub> <mover> <mi>P</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>&Element;</mo> <mo>[</mo> <mn>0.5913,1</mn> <mo>]</mo> </mtd> </mtr> </mtable> </mfenced> </mrow> </math> Where k is 2,3, … 81. The probability of each power interval is shown in fig. 5.

In the subsequent multi-step prediction process of the wind power, the probability prediction result shown in fig. 5 can be provided by each step of prediction at intervals of 15min, so as to provide auxiliary analysis information for the Markov chain-based model prediction control and optimization decision.

3.3 Multi-step predictive analysis

3.3.1 Multi-time Scale predictive analysis

The prediction time scale is gradually increased from 15min to 2h by Δ t, denoted as L, in steps of Δ t-15 min. Then L takes values of 15, 30, …, 120 in sequence, and the predicted step numbers are determined to be 1,2, …,8 according to equation (27). And (3) performing multiple predictions of the prospective L by using actual data of the last week in 2013 and respectively adopting an original power method and a variation method under a certain time scale L, and explaining the superiority of the variation method in the multi-step prediction application by comparing error indexes of the two methods under the same time scale.

Fig. 6 shows the variation and comparison of the prediction error of the variation method and the raw power method with the increase of the prediction time scale. It can be seen visually that with the increase of the prediction time scale, the average absolute error and the root mean square error of the two methods are increased, the indexes of the correlation coefficient are reduced, and the prediction precision is reduced; the longer the time scale is, the more obvious the advantages of the variable method are; the rate of error accumulation is slower for the variable method compared to the original power method.

3.3.2 Multi-step error accumulation analysis

In order to quantitatively describe the error accumulation process in the multi-step prediction process, taking the multi-step prediction with a certain look-ahead of 2h as an example, the offset rate lambda of each step is calculated according to the method described in 2.2.2₁,λ₂To lambda_M(M ═ 8), the accumulation of each step shift was observed, as shown in table 2.

TABLE 2 offset rate of some look-ahead 2h prediction

The calculation results in table 2 show that, when the original power method is used for the prediction, when the negative offset occurs in the first-step prediction state, the absolute value of the offset rate of each subsequent step gradually increases with the number of predicted steps, and the accumulation effect is obvious; when the prediction is carried out by using a variation method, the deviation rate of each subsequent step does not have an obvious increasing trend after the positive deviation appears in the first-step prediction state.

The fine state space division of the variable Markov chain model reduces the possibility that after a certain state offset occurs in the prediction process, the offset is gradually amplified along with the increase of the prediction step number; meanwhile, due to the small state offset, the probability that no offset (lambda is 0) occurs in a certain subsequent step after the state offset occurs is increased.

In order to further illustrate the limiting effect of the wind power Markov chain model on the multi-step prediction process error accumulation, the following multi-step prediction is carried out on the wind power output in the time period from 00:00 to 02:00 in 4 consecutive days, namely the 02:00 wind power active power is obtained from the 00:00 active power actual value through 8-step prediction. The change rule of the absolute error of the predicted value and the actual value of each step in the prediction every day along with the number of the predicted steps is respectively counted, and the accumulation condition of the error along with the prediction step length can be reflected, as shown in fig. 7.

As can be seen from fig. 7, for the original power method, once a large error occurs in a certain step in the multi-step prediction process, the probability that the error of each subsequent step continuously increases is high; for the variable quantity method, absolute errors of all steps are always in a lower level, the changes along with the steps are not obvious, and the prediction effect is obviously better than that of the original power method.

The invention provides a Markov chain model based on wind power variation and a wind power prediction method established by applying the model. Compared with the existing wind power Markov chain model, the state space of the model is finer under the same modeling data quantity, the model precision can be effectively improved, and the error accumulation in the multi-step transfer process is reduced. The wind power prediction method based on the variable Markov chain model can not only provide the predicted value of the wind power at the prediction time, but also provide the probability distribution condition of the predicted value, and the prediction precision, particularly the multi-step prediction precision is obviously improved compared with the original power method. Besides being used for wind power prediction, the Markov chain model based on the wind power variation can also lay a theoretical foundation for real-time economic dispatching of a wind power system, optimization decision based on the Markov chain and model prediction control.

Although the embodiments of the present invention have been described with reference to the accompanying drawings, it is not intended to limit the scope of the present invention, and it should be understood by those skilled in the art that various modifications and variations can be made without inventive efforts by those skilled in the art based on the technical solution of the present invention.

Claims (10)

1. A Markov chain modeling and predicting method based on wind power variation is characterized by comprising the following steps: the method comprises the following steps:

(1) establishing a Markov chain model with discrete time and state;

(2) dividing a continuous time shaft into discrete moments, and constructing a sample space of a Markov chain model by converting an original power sample space into a wind power variable quantity sample space;

(3) fitting a probability density function of variable probability distribution according to a sample space of wind power variable quantity and a distribution statistical result of wind power variable quantity sample data, setting a confidence interval, and constructing a corresponding state space;

(4) according to the Markov property in the random process, counting and calculating a transition probability matrix of a Markov chain model, obtaining the conditional transition probability of the wind power variable quantity among all states, and describing the change characteristic and the fluctuation rule of the wind power;

(5) and performing single-step prediction and multi-step prediction based on the Markov chain model of the wind power variation, and analyzing the accumulated condition of multi-step prediction errors.

2. The Markov chain modeling and predicting method based on wind power variation as set forth in claim 1, wherein: in the step (1), both time and state are discrete random processes { X }_nX (n), n is 0,1,2₁,S₂…, assuming that the process is in state S as long as it is at the present time_iThere is a fixed probability that the process will be in state S at the next time_jThat is, assume for all states and all n ≧ 0, have

P{X_n＝S_j|X₁＝S₁,X₂＝S₂,…X_n-1＝S_i}

＝P{X_n＝S_j|X_n-1＝S_i},S_·∈I (1)

Such a stochastic process is called Markov chain;

for a Markov chain, given a past state S₀，S₁，…，S_n-1And the present state S_nTime, future state X_n+1Is independent of the past state and only depends on the present state S_nBy means of one-step transition probability pi of pi memory_ijMatrix of (d), n_ijIndicating that the process is in state S_iThe next time to transition to state S_jThe conditional probability transition matrix of (1), whose elements satisfy:

<math> <mrow> <msub> <mi>&pi;</mi> <mi>ij</mi> </msub> <mo>&GreaterEqual;</mo> <mn>0</mn> <mo>,</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mo>&infin;</mo> </munderover> <msub> <mi>&pi;</mi> <mi>ij</mi> </msub> <mo>=</mo> <mn>1</mn> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow> </math>

3. the Markov chain modeling and predicting method based on wind power variation as set forth in claim 1, wherein: in the step (2), the specific method is as follows: dividing the continuous time axis into discrete times with a time interval Δ t, then for any two adjacent times t-1 and t there are:

t＝t-1+Δt (3)

converting an original power sample space into a wind power variable sample space through one-step linear transformation, wherein the variable of the wind power at a time interval [ t-1, t ] can be expressed as:

V_t＝P_t-P_t-1 (4)

wherein P is_t-1And P_tWind power values V at t-1 moment and t moment respectively_tFor wind power at time interval [ t-1, t]The variable quantity of the method is obtained by calculating the wind power variable quantity of any two adjacent moments in the random process at corresponding time intervals, and a historical sample sequence of the wind power variable quantity can be obtained by adopting one-step differential linear transformation according to the historical time sequence of the wind power, and the historical sample sequence is used as a sample space for constructing a Markov chain model.

4. The Markov chain modeling and predicting method based on wind power variation as set forth in claim 1, wherein: in the step (3), for establishing a Markov chain model, a corresponding state space is firstly constructed for a sample space of the wind power variation, and the specific method includes:

(3-1) fitting a probability density function of the variation probability distribution based on the distribution statistical result of the wind power variation sample data;

(3-2) setting a confidence level alpha, solving a corresponding variable quantity confidence interval D, and constructing a state space of the Markov chain model by taking two end points of the confidence interval D as upper and lower limits of variable quantity state division;

and (3-3) selecting the number of the power intervals to represent all the states.

5. The Markov chain modeling and predicting method based on wind power variation as set forth in claim 4, wherein: the specific method of the step (3-3) is as follows:

after the upper limit and the lower limit of the state division are determined, the state space of the Markov chain model can be constructed, and for the samples falling in the confidence interval, the number of the power intervals is selected as follows:

(1) except for the intervals at the two ends, the number of samples falling into each interval is not less than 5;

(2) the grouping number is calculated according to a Moore formula:

K-2≈C×N^2/5 (5)

k is the total number of interval division, including two power intervals outside the confidence interval, an integer value is taken, and K-2 is the number of equally divided power intervals; n is the number of samples; c is a formula coefficient, and the defined interval length is as follows:

$l=\frac{V_{\max }-V_{\min }}{K-2}---\left(6\right)$

V_maxand V_minCorresponding to the variable Markov chain model for K power intervals as the upper and lower limits of the variable confidence intervalK states in a type state space;

for variable data outside the confidence interval, dividing the individual states, if P_NFor rated installed capacity, the delta data will be at [ -P_N,P_N]An internal value, thus, the variation is taken to be [ -P ]_N,V_min]And [ V ]_max,P_N]Is divided into a first state and a K-th state,

all states constitute a state space I_VIt can be expressed as:

<math> <mrow> <msub> <mi>I</mi> <mi>V</mi> </msub> <mo>=</mo> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <msub> <mi>S</mi> <mn>1</mn> </msub> <mo>,</mo> <mi>V</mi> <mo>&Element;</mo> <mo>[</mo> <mo>-</mo> <msub> <mi>P</mi> <mi>N</mi> </msub> <mo>,</mo> <msub> <mi>V</mi> <mi>min</mi> </msub> <mo>]</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>S</mi> <mi>k</mi> </msub> <mo>,</mo> <mi>V</mi> <mo>&Element;</mo> <mrow> <mo>(</mo> <msub> <mi>V</mi> <mi>min</mi> </msub> <mo>+</mo> <mi>l</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>-</mo> <mn>2</mn> <mo>)</mo> </mrow> <mo>,</mo> <msub> <mi>V</mi> <mi>min</mi> </msub> <mo>+</mo> <mi>l</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>]</mo> <mo>,</mo> <mi>k</mi> <mo>=</mo> <mn>2,3</mn> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <mi>K</mi> <mo>-</mo> <mn>1</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <msub> <mi>S</mi> <mi>K</mi> </msub> <mo>,</mo> <mi>V</mi> <mo>&Element;</mo> <mo>[</mo> <msub> <mi>V</mi> <mi>max</mi> </msub> <mo>,</mo> <msub> <mi>P</mi> <mi>N</mi> </msub> <mo>]</mo> </mtd> </mtr> </mtable> </mfenced> <mo>.</mo> </mrow> </math>

6. the Markov chain modeling and predicting method based on wind power variation as set forth in claim 1, wherein: in the step (4), after the sample space transformation and the state space division are completed, the transition probability matrix of the Markov chain model is counted and calculated, and S is recorded_tFor the variation at time intervals t-1, t]According to the Markov property of the stochastic process, [ t, t + 1]]Wind power variable quantity state S_t+1By S only_tThe decision, can be expressed as

P{X_t+1＝S_t+1|X₁＝S₁,X₂＝S₂,…X_t＝S_t}

＝P{X_t+1＝S_t+1|X_t＝S_t},S_·∈I (8)

For calculating the transition probability matrix, defining a transition frequency matrix N as the transition frequency of the adjacent wind power variable quantity between each state, wherein the element N is_ijStatistically obtained by the following formula:

wherein N is_ijThe variable quantity of the wind power is [ t-1, t ]]S of the time period_iState transition to [ t, t + 1]]S of the time period_jNumber of states, T is total number of samples, N_ijSatisfies the following formula:

<math> <mrow> <msub> <mi>N</mi> <mi>ij</mi> </msub> <mo>&le;</mo> <mi>T</mi> <mo>,</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>K</mi> </munderover> <munderover> <mi>&Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>K</mi> </munderover> <msub> <mi>N</mi> <mi>ij</mi> </msub> <mo>=</mo> <mi>T</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>10</mn> <mo>)</mo> </mrow> </mrow> </math>

the element pi in the probability matrix pi is transferred_ijThe calculation method of (2) is as follows:

<math> <mrow> <msub> <mi>&pi;</mi> <mi>ij</mi> </msub> <mo>=</mo> <mi>P</mi> <mo>{</mo> <msub> <mi>S</mi> <mi>j</mi> </msub> <mo>|</mo> <msub> <mi>S</mi> <mi>i</mi> </msub> <mo>}</mo> <mo>=</mo> <mfrac> <msub> <mi>N</mi> <mi>ij</mi> </msub> <mrow> <munderover> <mi>&Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>K</mi> </munderover> <msub> <mi>N</mi> <mi>ij</mi> </msub> </mrow> </mfrac> <mo>,</mo> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>=</mo> <mn>1,2</mn> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mi>K</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>11</mn> <mo>)</mo> </mrow> </mrow> </math>

and satisfies the following conditions:

<math> <mrow> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <msub> <mi>&pi;</mi> <mi>ij</mi> </msub> <mo>&GreaterEqual;</mo> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <munderover> <mi>&Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>K</mi> </munderover> <msub> <mi>&pi;</mi> <mi>ij</mi> </msub> <mo>=</mo> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>=</mo> <mn>1,2</mn> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <mi>K</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>12</mn> <mo>)</mo> </mrow> </mrow> </math>

7. the Markov chain modeling and predicting method based on wind power variation as set forth in claim 1, wherein: in the step (5), the single-step prediction method based on the Markov chain model of the wind power variation includes: predicting the value of the variable quantity from the current moment to the next moment and the probability distribution thereof by utilizing the established model, and then constructing the value interval of the wind power to obtain the prediction result of the wind power, wherein the prediction result specifically comprises the following steps:

for sample data of a given wind power time sequence, dividing a continuous time axis into discrete moments according to a time scale delta t, and calculating wind power variation at any two adjacent moments so as to obtain data samples of the variation; then, determining a state space division scheme, finely dividing the variable quantity state space into K states, then counting a frequency transfer matrix N and calculating a transfer probability matrix pi, and completing construction of a variable quantity Markov chain model;

for convenience of description, the previous time is recorded as t-1, the current time is t, the next time is t +1, and the current time and the previous time are called, i.e. the period [ t-1, t [ ]]The wind power variation is the current variation V_tCurrent time and next time, i.e. time segment [ t, t + 1]]The wind power variation is the next variation V_t+1If the current variation V is_tIf the actual value of (c) is known, the next variation V can be obtained by using the transition probability matrix of the variation Markov chain model_t+1A probability distribution of (a);

defining state selection unit row vectors_t，_tCurrent change V in_tThe element corresponding to the belonged state is 1, the other elements are 0, and the next variation V_t+1Is only limited by the current variance V_tIs determined by the state of

<math> <mrow> <msubsup> <mover> <mi>&pi;</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>V</mi> </msubsup> <mo>=</mo> <msub> <mi>&Gamma;</mi> <mi>t</mi> </msub> <mi>&Pi;</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>13</mn> <mo>)</mo> </mrow> </mrow> </math>

II, obtaining a transition probability matrix from a current variable quantity state to a next variable quantity state;is the next variable V_t+1Taking the probability vector of each state;

predicting the expectation of the probability distribution by using the variation as a deterministic prediction value of the variation; except for the intervals at two ends, multiplying the probability of the variation falling into each interval by the median value of each interval and then summing; when the deterministic prediction value is calculated, the interval between the two ends is not considered, and the formula (14) is expressed as follows:

<math> <mrow> <msub> <mover> <mi>V</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>2</mn> </mrow> <mrow> <mi>K</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msubsup> <mover> <mi>&pi;</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>V</mi> </msubsup> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> <mo>&times;</mo> <msub> <mi>V</mi> <mi>mid</mi> </msub> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>14</mn> <mo>)</mo> </mrow> </mrow> </math>

wherein, V_mid(i) Representing the median of each variable quantity power interval;

in order to convert the variable probability distribution prediction result into the prediction probability distribution of the wind power, firstly, a value power interval of the wind power is constructed, and a set formed by the possible value intervals of the predicted wind power is assumed as I_P，I_P(i) For the ith interval therein, it is required to satisfyEach interval corresponds to a wind power state, and the known wind power actual value P at the current moment is used_tAccumulating the variable quantity with the upper limit and the lower limit of each prediction interval one by one to obtain a prediction wind power intervalThe following constraints are defined:

<math> <mrow> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <mn>0</mn> <mo>&le;</mo> <msub> <mi>P</mi> <mi>t</mi> </msub> <mo>+</mo> <msub> <mi>V</mi> <mi>min</mi> </msub> <mo>&le;</mo> <msub> <mi>P</mi> <mi>N</mi> </msub> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> <mo>&le;</mo> <msub> <mi>P</mi> <mi>t</mi> </msub> <mo>+</mo> <msub> <mi>V</mi> <mi>max</mi> </msub> <mo>&le;</mo> <msub> <mi>P</mi> <mi>N</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>V</mi> <mi>min</mi> </msub> <mo>&lt;</mo> <msub> <mi>V</mi> <mi>max</mi> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>15</mn> <mo>)</mo> </mrow> </mrow> </math>

(1) if P_tIf equation (15) is satisfied, the power interval of the predicted wind power is as follows:

<math> <mrow> <msub> <mi>I</mi> <mi>P</mi> </msub> <mo>=</mo> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <msub> <mi>S</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mover> <mi>P</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>&Element;</mo> <mo>[</mo> <mn>0</mn> <mo>,</mo> <msub> <mi>P</mi> <mi>t</mi> </msub> <mo>+</mo> <msub> <mi>V</mi> <mi>min</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>S</mi> <mi>k</mi> </msub> <mo>,</mo> <msub> <mover> <mi>P</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>&Element;</mo> <mrow> <mo>(</mo> <msub> <mi>P</mi> <mi>t</mi> </msub> <mo>+</mo> <msub> <mi>V</mi> <mi>min</mi> </msub> <mo>+</mo> <mi>l</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>-</mo> <mn>2</mn> <mo>)</mo> </mrow> <mo>,</mo> <msub> <mi>P</mi> <mi>t</mi> </msub> <mo>+</mo> <msub> <mi>V</mi> <mi>min</mi> </msub> <mo>+</mo> <mi>l</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>]</mo> <mo></mo> </mrow> </mtd> </mtr> <mtr> <mtd> <msub> <mi>S</mi> <mi>K</mi> </msub> <mo>,</mo> <msub> <mover> <mi>P</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>&Element;</mo> <msub> <mi>P</mi> <mi>t</mi> </msub> <mo>+</mo> <msub> <mi>V</mi> <mi>max</mi> </msub> <mo>,</mo> <msub> <mi>P</mi> <mi>N</mi> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>16</mn> <mo>)</mo> </mrow> </mrow> </math>

wherein, K is 2,3, … K-1, l is each equal section length corresponding to the variation state; at this time, the number of power intervals for predicting the wind power is the same as the number of power intervals for predicting the variation, and the wind power P is predicted_t+1And the predicted variation V_t+1The probability of falling in the corresponding interval is also equal, i.e.

<math> <mrow> <msubsup> <mover> <mi>&pi;</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>P</mi> </msubsup> <mo>=</mo> <msubsup> <mover> <mi>&pi;</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>V</mi> </msubsup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>17</mn> <mo>)</mo> </mrow> </mrow> </math>

Wherein,the probability of the wind power value at the moment of t +1 falling in each power interval is the probability prediction result;

(2) if Pt does not satisfy formula (15) and Pt + V_min<0, introducing an integer parameter K₁So that:

P_t+V_min+l·K₁≥0(18)

K₁taking the smallest integer satisfying the above formula, namely:

$K_1=\mathrm{int}\left(\frac{-V_{\min }-P_t}{l}\right)+1---\left(19\right)$

wherein int () is a rounding function;

at this time, the number of power intervals for predicting the wind power is less than K, and is set to K', and the power interval set can be expressed as

<math> <mrow> <msub> <mi>I</mi> <mi>P</mi> </msub> <mo>=</mo> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <msub> <mi>S</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mover> <mi>P</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>&Element;</mo> <mo>[</mo> <mn>0</mn> <mo>,</mo> <msub> <mi>P</mi> <mi>t</mi> </msub> <mo>+</mo> <msub> <mi>V</mi> <mi>min</mi> </msub> <mo>+</mo> <mi>l</mi> <mo>&CenterDot;</mo> <msub> <mi>K</mi> <mn>1</mn> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>S</mi> <mrow> <msub> <mi>k</mi> <mn>1</mn> </msub> <mo>-</mo> <msub> <mi>K</mi> <mn>1</mn> </msub> <mo>,</mo> </mrow> </msub> <msub> <mover> <mi>P</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>&Element;</mo> <mrow> <mo>(</mo> <msub> <mi>P</mi> <mi>t</mi> </msub> <mo>+</mo> <msub> <mi>V</mi> <mi>min</mi> </msub> <mo>+</mo> <mi>l</mi> <mo>&CenterDot;</mo> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <mo>-</mo> <mn>2</mn> <mo>)</mo> </mrow> <mo>,</mo> <msub> <mi>P</mi> <mi>t</mi> </msub> <mo>+</mo> <msub> <mi>V</mi> <mi>min</mi> </msub> <mo>+</mo> <mi>l</mi> <mo>&CenterDot;</mo> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> <mo>]</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>S</mi> <msup> <mi>K</mi> <mo>&prime;</mo> </msup> </msub> <mo>,</mo> <msub> <mover> <mi>P</mi> <mo>^</mo> </mover> <mrow> <mi>T</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>&Element;</mo> <mo>[</mo> <msub> <mi>P</mi> <mi>t</mi> </msub> <mo>+</mo> <msub> <mi>V</mi> <mi>max</mi> </msub> <mo>,</mo> <msub> <mi>P</mi> <mi>N</mi> </msub> <mo>]</mo> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>20</mn> <mo>)</mo> </mrow> </mrow> </math>

Wherein k is₁＝K₁+2,K₁+3,…,K-1；K'＝K-K₁(ii) a In order to meet the property of probability distribution, according to the basic principle of scene reduction, the probability of the removed scene is combined into the scene probability with the shortest distance from the probability, and the probability of the wind power falling in the first power interval is taken as the variable number from 1 to K₁The prediction probability of each state and the probability of falling into other power intervals are the prediction probabilities corresponding to the variation intervals, and the probability of the wind power falling into each power interval at the moment of t +1 can be represented as:

<math> <mrow> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <msubsup> <mover> <mi>&pi;</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>P</mi> </msubsup> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>K</mi> <mn>1</mn> </msub> </munderover> <msubsup> <mover> <mi>&pi;</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>V</mi> </msubsup> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <msubsup> <mover> <mi>&pi;</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>P</mi> </msubsup> <mrow> <mo>(</mo> <mi>j</mi> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mover> <mi>&pi;</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>V</mi> </msubsup> <mrow> <mo>(</mo> <msub> <mi>K</mi> <mn>1</mn> </msub> <mo>+</mo> <mi>j</mi> <mo>)</mo> </mrow> <mo>,</mo> <mi>j</mi> <mo>=</mo> <mn>2,3</mn> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <msup> <mi>K</mi> <mo>&prime;</mo> </msup> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>21</mn> <mo>)</mo> </mrow> <mo>;</mo> </mrow> </math>

(3) if Pt does not satisfy formula (15) and Pt + V_max>P_NIntroduction of an integer parameter K₂So that

P_t+V_min+l·K₂≤P_N (22)

K2 is the largest integer satisfying the above formula, i.e.

$K_2=\mathrm{int}\left(\frac{P_N-P_t-V_{\min }}{l}\right)---\left(23\right)$

The number of power intervals for predicting the wind power is less than K, the power intervals are set to be K', and the power interval set can be expressed as

<math> <mrow> <msub> <mi>I</mi> <mi>P</mi> </msub> <mo>=</mo> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <msub> <mi>S</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mover> <mi>P</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>&Element;</mo> <mo>[</mo> <mn>0</mn> <mo>,</mo> <msub> <mi>P</mi> <mi>t</mi> </msub> <mo>+</mo> <msub> <mi>V</mi> <mi>min</mi> </msub> <mo>]</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>S</mi> <msub> <mi>k</mi> <mn>2</mn> </msub> </msub> <mo>,</mo> <msub> <mover> <mi>P</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>&Element;</mo> <mrow> <mo>(</mo> <msub> <mi>P</mi> <mi>t</mi> </msub> <mo>+</mo> <msub> <mi>V</mi> <mi>min</mi> </msub> <mo>+</mo> <mi>l</mi> <mo>&CenterDot;</mo> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <mo>-</mo> <mn>2</mn> <mo>)</mo> </mrow> <mo>,</mo> <msub> <mi>P</mi> <mi>t</mi> </msub> <mo>+</mo> <msub> <mi>V</mi> <mi>min</mi> </msub> <mo>+</mo> <mi>l</mi> <mo>&CenterDot;</mo> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>]</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <msub> <mi>S</mi> <msup> <mi>K</mi> <mo>&Prime;</mo> </msup> </msub> <mo>,</mo> <msub> <mover> <mi>P</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>&Element;</mo> <mrow> <mo>(</mo> <msub> <mi>P</mi> <mi>t</mi> </msub> <mo>+</mo> <msub> <mi>V</mi> <mi>min</mi> </msub> <mo>+</mo> <mi>l</mi> <mo>&CenterDot;</mo> <msub> <mi>K</mi> <mn>2</mn> </msub> <mo>,</mo> <msub> <mi>P</mi> <mi>N</mi> </msub> <mo>)</mo> </mrow> <mo>]</mo> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>24</mn> <mo>)</mo> </mrow> </mrow> </math>

Wherein k is₂＝2,3,…K₂+1；K″＝K₂+2, the K th change is taken according to the probability that the wind power predicted value falls in the K' th power interval₂The probability sum of K states, the probability of falling into other power intervals is the prediction probability corresponding to the variation interval, and the probability of the wind power falling into each power interval at the moment of t +1 can be represented as:

<math> <mrow> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <msubsup> <mover> <mi>&pi;</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>P</mi> </msubsup> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mover> <mi>&pi;</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>V</mi> </msubsup> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> <mo>,</mo> <mi>i</mi> <mo>=</mo> <mn>1,2</mn> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <msub> <mi>K</mi> <mn>2</mn> </msub> <mo>+</mo> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <msubsup> <mover> <mi>&pi;</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>P</mi> </msubsup> <mrow> <mo>(</mo> <msup> <mi>K</mi> <mrow> <mo>&prime;</mo> <mo>&prime;</mo> <mo></mo> </mrow> </msup> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <msub> <mi>K</mi> <mn>2</mn> </msub> </mrow> <mi>K</mi> </munderover> <msubsup> <mover> <mi>&pi;</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>V</mi> </msubsup> <mrow> <mo>(</mo> <mi>j</mi> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>25</mn> <mo>)</mo> </mrow> <mo>;</mo> </mrow> </math>

the power interval of the predicted wind power is formed on the basis of the actual value Pt at the current moment, so that the prediction is updated in a rolling mode every time.

8. The Markov chain modeling and predicting method based on wind power variation as set forth in claim 1, wherein: in the step (5), the multi-step prediction method based on the Markov chain model of the wind power variation comprises the following steps: dividing the time span from the current time to the prediction time by delta t, decomposing the prediction of a relatively long time scale into a plurality of single-step prediction processes, taking the actual value as the known input in the first step, taking the output result of the previous step prediction in each intermediate step as the known input of the next step prediction, assuming that the time span from the prediction time to the current time is L, and obtaining the wind power of the prediction time from the known condition of the current time requires M steps of calculation, wherein the number of the prediction steps M is as follows:

<math> <mrow> <mi>M</mi> <mo>=</mo> <mfrac> <mi>L</mi> <mi>&Delta;t</mi> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>27</mn> <mo>)</mo> </mrow> </mrow> </math>

assuming any one of the multi-step prediction, the variation prediction probability distribution of the mth step is set asThe predicted value of the variation isCorresponds to the state ofThe predicted variation probability distribution of the (m + 1) th step is as follows:

<math> <mrow> <msubsup> <mover> <mi>&pi;</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mi>m</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>V</mi> </msubsup> <mo>=</mo> <msub> <mover> <mi>&Gamma;</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mi>m</mi> </mrow> </msub> <mi>&Pi;</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>28</mn> <mo>)</mo> </mrow> </mrow> </math>

wherein,predicting state for variation at time t + mSelecting a unit row vector according to the corresponding state, wherein pi is a transition probability matrix, and the predicted value of the variation in the (m + 1) th step is as follows:

<math> <mrow> <msub> <mover> <mi>V</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mi>m</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>2</mn> </mrow> <mrow> <mi>K</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msubsup> <mover> <mi>&pi;</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mi>m</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>V</mi> </msubsup> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> <mo>&times;</mo> <msub> <mi>V</mi> <mi>mid</mi> </msub> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>29</mn> <mo>)</mo> </mrow> <mo>,</mo> </mrow> </math>

determining a wind power output prediction power interval at the t + m +1 th moment, wherein the probability distribution of each power interval isNamely:

<math> <mrow> <msub> <mover> <mi>P</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mi>m</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>G</mi> </munderover> <msubsup> <mover> <mi>&pi;</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mi>m</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>P</mi> </msubsup> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> <mo>&times;</mo> <msubsup> <mi>P</mi> <mrow> <mi>mid</mi> <mo>,</mo> <mi>t</mi> <mo>+</mo> <mi>m</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>G</mi> </msubsup> <mo>,</mo> </mrow> </math> g ═ K, K', or K "(30).

9. The Markov chain modeling and predicting method based on wind power variation as set forth in claim 1, wherein: in the step (5), the method for analyzing the multi-step prediction error accumulation condition comprises the following steps: setting the state of a Markov chain as X, in an original power model, X represents the wind power state, in a variable quantity model, X represents the variable quantity state, assuming any one step in a multi-step prediction process from time t to time t + M as the mth step, and the prediction state isThe actual state of the wind power output or wind power variation at the moment is Xt + m, and the state deviation of the predicted state relative to the actual state is recorded as delta_m，

<math> <mrow> <msub> <mi>&Delta;</mi> <mi>m</mi> </msub> <mo>=</mo> <msub> <mover> <mi>X</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mi>m</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>X</mi> <mrow> <mi>t</mi> <mo>+</mo> <mi>m</mi> </mrow> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>31</mn> <mo>)</mo> </mrow> </mrow> </math>

According to the multi-step prediction method, the predicted value of the mth step is used as the input of the (m + 1) th step due to the existence of the state deviation delta_mSet to a predicted stateWhen the wind power is input in the (m + 1) th step, the probability distribution of the wind power or the wind power variation at the t + m +1 moment obtained by predicting the (m + 1) th step is

<math> <mrow> <msubsup> <mover> <mi>&pi;</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mi>m</mi> <mo>+</mo> <mn>1</mn> </mrow> <mo>*</mo> </msubsup> <mo>=</mo> <mi>&Gamma;</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>X</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mi>m</mi> </mrow> </msub> <mo>)</mo> </mrow> <mi>&Pi;</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>32</mn> <mo>)</mo> </mrow> </mrow> </math>

Corresponding to the step prediction value ofWhileWill be used as the input of the m +2 step, and so on, the state offset delta produced by the m step_mIt is possible that subsequent M-M step predictions have an impact such that errors are accumulated in subsequent M-M predictions.

10The Markov chain modeling and prediction method based on wind power variation as set forth in claim 1, characterized in that: in the step (5), when the wind power variation Markov chain model is used for multi-step prediction, the characteristic that variation data has small value reduces the probability of state deviation generated in the prediction process, and the fine state space division effectively slows down the speed of error accumulation; defining an offset ratio lambda_mTo indicate the deviation degree of the predicted value of the mth step from the actual value

<math> <mrow> <msub> <mi>&lambda;</mi> <mi>m</mi> </msub> <mo>=</mo> <mfrac> <mrow> <mi>l</mi> <mo>&times;</mo> <msub> <mi>&Delta;</mi> <mi>m</mi> </msub> </mrow> <msub> <mi>P</mi> <mi>N</mi> </msub> </mfrac> <mo>,</mo> <mi>m</mi> <mo>=</mo> <mn>1,2</mn> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <mi>M</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>33</mn> <mo>)</mo> </mrow> </mrow> </math>

When delta_m＝0，λ_mWhen the number is equal to 0, the number of the predicted states is the same as the number of the actual states, and the prediction state is simply referred to as no offset; when delta_m>At 0, λ_m>0, indicating that the number of predicted states is greater than the number of actual states, referred to as positive offset for short; when delta_m<At 0, λ_m<0, indicating that the number of predicted states is less than the number of actual states; lambda_mThe larger | is, the farther the predicted state deviates from the actual state is; by calculating λ 1- λ_MThe deviation situation of each step prediction in the whole multi-step prediction process is quantitatively described.