CN112446545A - Load prediction method based on overlapped Markov chain - Google Patents
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Abstract
The invention discloses a load prediction method based on a superposed Markov chain. Firstly, grouping acquired load historical data at the same time according to different dates and converting the load historical data into state variables; then, calculating corresponding state transition matrixes according to different step lengths, weather, seasons and date types; then calculating the analog value of the next time point according to the initial state and the transfer matrix in sequence; and finally, adding error compensation to obtain a final load predicted value. The load prediction method is different from a general Markov chain method, overcomes the defect that the state intervals are uniformly divided by the traditional method, classifies the state transition matrix, adopts the superposed Markov chain for prediction, improves the defect of low precision of the traditional method, and ensures that the load prediction result is more accurate.
Description
Technical Field
The invention belongs to the technical field of load prediction, and particularly relates to a load prediction method based on a superposed Markov chain. The method overcomes the defect that the conventional Markov chain is low in prediction precision.
Background
Electrical loads are important components of electrical power systems. In the operation planning of the power system, load prediction is one of the most critical links, and has direct influence on planning quality, operation regulation and control and economic factors, so that the establishment of a method capable of accurately predicting the load of the power system is very important.
In the existing load prediction method, typical daily load is selected in research, and load data is regarded as a function of year, month and time to predict, but the method is essentially repeated moment of the typical daily load and is difficult to realize actual distribution of the load data; another common method is to use a similar daily load curve to predict the short-term load, but this method cannot reflect the randomness and volatility of the load; the calculation process is opaque and cannot be deduced by using more machine learning methods such as neural networks and the like; when the general Markov chain method is used for predicting the load, factors which can influence the load fluctuation such as weather and seasons are not considered, and the obtained result has a certain difference from the actual result.
Disclosure of Invention
Aiming at the defects of the prior art, the technical problem to be solved by the invention is to provide a load prediction method based on a superposed Markov chain. According to the method, historical data are classified according to weather, seasons and the like, transfer matrixes with different step lengths are respectively calculated, and a superposition Markov chain is adopted for prediction, so that the result is more accurate.
The invention adopts the following technical scheme:
a load prediction method based on an overlapped Markov chain comprises the following steps:
step 1, acquiring historical load data of the same type in the same region, and selecting n data points from the historical load data of each day; the historical load data is the span of m days, and the time of the n data points selected each day is the same; constructing a load data matrix L by using the selected data sequence of n data points each day for m days, wherein the formula (1) is as follows:
in the above formula, LijRepresenting the historical load value at the j time of the ith day;
and 2, taking out each column of the load data matrix L independently, wherein the formula (2) is as follows:
Lj＝[L1j,L2j,...Lij,...Lmj]T (2)
Lja data sequence consisting of historical load values of the jth time point of each day in m days; obtaining n data sequences according to the load data matrix L, wherein each sequence comprises m data points;
sequence of statistical data LjThe historical load value in Matlab is utilized to carry out kernel density estimation by using ksDensity function in Matlab, and then the probability density function f is fitted according to the resultLj(x) Then integrated to obtain a cumulative distribution function FLj(x) Through the above operation, the data sequence L is obtainedjThe historical load values in (1) are distributed on a longitudinal axis by 0-1; the cumulative distribution function FLj(x) The longitudinal axis of the system is uniformly divided into k intervals, namely equal-probability division intervals, the length of each interval is 1/k, and all the intervals are marked as 1,2.. k from small to large; substituting the values of the upper and lower bounds of each longitudinal axis interval into an inverse function of the cumulative distribution function to obtain an actual load value interval corresponding to each longitudinal axis interval, wherein the marks of the actual load value interval are the same as those of the longitudinal axis interval; as shown in formula (3), GLj(y) is FLj(x) The inverse function of (c);
then to the data sequence LjThe historical load values in the process are processed, each historical load value is distributed into the actual load value interval to which the historical load value belongs according to the size of the historical load value, the average value of all the historical load values in each actual load value interval is obtained, and a state average value vector a at the moment j is formedjAs shown in formula (4); simultaneously transmitting the data sequence LjThe history load value in the range is converted into the label 1 to the actual load value rangek, data sequence LjConversion to a sequence of state variables CjAll elements in the state variable sequence are integers from 1 to k; by the method, state mean value vectors of n moments and corresponding state variable sequences are obtained;
aj＝[a1j,a2j,...akj] (4)
Cj＝[C1j,C2j,...,Cmj] (5)
step 3, according to the state variable sequence C of the data sequence of each column in the load data matrix L obtained in the step 2jConstructing a state variable matrix C as shown in formula (6), wherein Cij＝1,2,...k；
Each behavior in the state variable matrix C corresponds to state variable data of a corresponding day in m days;
taking the types of weather of sunny, cloudy, rainy/snowy, spring, summer, autumn and winter in seasons and the types of dates of working days or holidays as influence factors, and combining the three types of influence factors to obtain 24 different conditions of influence factors; extracting the m-day state variable data in the state variable matrix C to the state variable matrix D of the 24 corresponding influencing factors of different conditions according to the selected influencing factors of different conditions corresponding to each of the m days1,D2,...,Dq,...,D24Performing the following steps;
step 4, obtaining a state variable matrix D of the influencing factors of different conditions in the step 31,D2,...,Dq,...,D24Calculating state transition matrices of different step sizes using markov chain method
Wherein 1-r represent different step lengths;
step 5, taking the state interval label of the historical load value of the last time point of the mth day as the state interval label of the first time point of the mth +1 day, constructing the probability state vector of the first time point of the mth +1 day, determining the corresponding state transition matrix according to the weather, season, date type conditions and step length of the mth +1 day, and calculating the probability state vectors of the n time points point by point; multiplying the probability state vector of each time point with the state mean vector of the corresponding time obtained in the step 2, and averaging the results obtained in different step lengths to obtain the load simulation value of each time point;
step 6, calculating the data sequence L in the step 2jThe historical load value L inijCounting the difference values of the same actual load value interval at the same moment with the difference values of the mean values of all historical load values of the corresponding actual load value interval, carrying out kernel density estimation on the difference values by utilizing a ksDensity function in Matlab, and fitting a probability density function e according to the resultij(x) And then obtaining the cumulative distribution function E of the difference valuesij(x) (ii) a Cumulative distribution function E of differenceij(x) As an error function, a random value between 0 and 1 is substituted into a cumulative distribution function E of the difference valuesij(x) Is inverse function of
Obtaining an error compensation value at a corresponding moment; and (5) respectively adding the load analog value of each time point of the m +1 th day obtained in the step (5) with the error compensation value of the corresponding time, wherein the obtained result is the load predicted value of the n time points of the m +1 th day.
Compared with the prior art, the invention has the beneficial effects that:
(1) compared with a typical day or similar day load curve prediction method, the load prediction method simulates the randomness and the fluctuation of the load and accords with the change characteristic of the actual load on the time sequence.
(2) Compared with the general Markov chain method, the load prediction method of the invention takes the factors of season, weather, working day and the like into consideration and utilizes the method of overlapping the Markov chain to overcome the defect of low precision of the traditional method.
Drawings
FIG. 1 is a flowchart of a method of load prediction according to an embodiment of the present invention.
Fig. 2 is a graph comparing the historical load value at the last time point of each day of the load data of residents of the year 2018 data in tianjin wuqing area with the historical load value at the first time point of the following day.
Fig. 3 is a comparison graph of load prediction data of day 300 obtained by a conventional markov chain method and load actual data thereof, with load data of residents in the last 299 days of year-round data in 2018 of Tianjin Wuqing area as historical load data.
Fig. 4 is a comparison graph of load prediction data of 300 th day obtained by the load prediction method of the present invention and load actual data thereof, with load data of residents in the first 299 days of year 2018 year round in Tianjin Wuqing area as historical load data.
Detailed Description
Specific examples of the present invention are given below. The specific examples are only for illustrating the present invention in further detail and do not limit the scope of protection of the present application.
The invention provides a load prediction method (a load prediction method for short, see figure 1) based on an overlapped Markov chain, which comprises the following steps:
step 1, acquiring historical load data of the same type in the same region, such as one of commercial load, industrial load, residential load and the like, wherein the historical load data needs to include load data of four seasons including spring, summer, autumn and winter without interruption. Selecting a data point at intervals of a certain time (generally 15min) by taking the historical load data of one day as a basic unit, and selecting n data points from the historical load data of one day; the historical load data is the span of m days, and the time of the n data points selected each day is the same. Constructing a load data matrix L by using the selected data sequence of n data points each day for m days, wherein the formula (1) is as follows:
in the above formula, LijRepresenting the historical load value of the ith day at the jth moment, wherein n is the number of the historical load data points selected per day, and m is the total days of the historical load data.
Step 2, each column of the load data matrix L is taken out independently, and each column is a one-dimensional data sequence formed by historical load values at the same time of m days, as shown in formula (2):
Lj＝[L1j,L2j,...Lij,...Lmj]T (2)
Ljand the data sequence is composed of historical load values of j time points of each day in m days. According to the load data matrix L, n data sequences can be obtained, and each sequence comprises m data points.
Sequence of statistical data LjThe historical load value in Matlab is utilized to carry out kernel density estimation by using ksDensity function in Matlab, and then the probability density function f is fitted according to the resultLj(x) Then integrated to obtain a cumulative distribution function FLj(x) Through the above operation, the data sequence L is obtainedjThe historical load values in (1) are distributed on a longitudinal axis by 0-1; the cumulative distribution function FLj(x) The longitudinal axis of the system is uniformly divided into k intervals, namely equal-probability division intervals, the length of each interval is 1/k, and all the intervals are marked as 1,2.. k from small to large; substituting the values of the upper and lower bounds of each longitudinal axis interval into an inverse function of the cumulative distribution function to obtain an actual load value interval corresponding to each longitudinal axis interval, wherein the marks of the actual load value interval are the same as those of the longitudinal axis interval; as shown in formula (3), GLj(y) is FLj(x) The inverse function of (c);
then to the data sequence LjThe historical load value in the step (1) is processed, each historical load value is distributed into the actual load value interval to which the historical load value belongs according to the size of the historical load value, and all historical load values in each actual load value interval are obtainedMean of the load values, forming a state mean vector a at time jjAs shown in formula (4); simultaneously transmitting the data sequence LjThe historical load value in (1) is converted into the labels 1-k (namely the state section labels) of the corresponding actual load value sections, and the data sequence L is converted into a data sequence LjConversion to a sequence of state variables CjAll elements in the state variable sequence are integers from 1 to k. By the method, the state mean vector and the corresponding state variable sequence at n moments are obtained.
aj＝[a1j,a2j,...akj] (4)
Cj＝[C1j,C2j,...,Cmj] (5)
Step 3, according to the state variable sequence C of the data sequence of each column in the load data matrix L obtained in the step 2jConstructing a state variable matrix C as shown in formula (6), wherein Cij＝1,2,...k。
Each behavior in the state variable matrix C corresponds to state variable data of a corresponding day in m days;
because different weather, different seasons and whether the day is a working day can influence the load curve, the influence factors of sunny, cloudy, rainy/snowy weather, spring, summer, autumn and winter in seasons and the influence factors of the type of the day being a working day or a holiday are used as the influence factors, and the influence factors of the three types are combined to obtain 24 (3, 4, 2 and 24) influence factors under different conditions; extracting the m-day state variable data in the state variable matrix C to the state variable matrix D of the 24 corresponding influencing factors of different conditions according to the selected influencing factors of different conditions corresponding to each of the m days1,D2,...,Dq,...,D24Performing the following steps;
for example, if Dq(24 is more than or equal to q is more than or equal to 1) represents the state variable matrix of the influencing factors of the conditions of summer, fine day and working day, the state variable data corresponding to V (m is more than or equal to V is more than or equal to 0) days of the influencing factors of the conditions of summer, fine day and working day in m days are extracted out to form the state variable matrix D of the influencing factors of the conditions of summer, fine day and working dayq。
Step 4, obtaining a state variable matrix D of the influencing factors of different conditions in the step 31,D2,...,Dq,...,D24Calculating state transition matrices of different step sizes using markov chain method
Wherein 1-r represent different step lengths (step length is the number of sequential delays between two data points selected during calculation, 1 is the first data point after sequential delay is selected, 2 is the second data point after sequential delay is selected, for example, r is 2, after the first data point is selected, 2 bits are sequentially delayed to reach the third data point, the third data point is selected, and so on). Due to the ineffectiveness of the Markov chain, the state transition matrix between every two time instants is independent.
In the formula (I), the compound is shown in the specification,
the probability of state a transitioning to state b (where state a, b refers to one of 1-k) for a step size r,
state variable matrix D of influencing factors of different conditions1,D2,...,Dq,...,D24The values of the inner data points are all numbers from 1 to k; let s be the frequency (number of times) of occurrence of the state a in the state variable matrix of the influencing factors of the different conditions to which it belongsab(r) state a transitions to state b (state a at the present time)If the state at the next time is b, the frequency of transition from state a to state b) is sa(r), then:
and 5, taking the state interval label of the historical load value of the last time point on the m +1 th day as the state interval label of the first time point on the m +1 th day, constructing the probability state vector of the first time point on the m +1 th day, determining the corresponding state transition matrix according to the weather, season, date type conditions and step length of the m +1 th day, and calculating the probability state vectors of the n time points point by point. Multiplying the probability state vector of each time point with the state mean vector of the corresponding time obtained in the step 2, and averaging the results obtained in different step lengths to obtain the load simulation value of each time point;
the specific process of the step 5 is as follows:
501. counting the correlation between the historical load value of the last time point of each day in m days and the historical load value of the first time point of the next day, and when the correlation coefficient is greater than 0.8, determining that the historical load value of the last time point of the previous day and the historical load value of the first time point of the next day have high correlation; and when the correlation coefficient is larger than 0.8, taking the label (one value from 1 to k) of the actual load value interval to which the historical load value of the last time point of the mth day belongs as the label of the actual load value interval to which the first time point of the m +1 day belongs. According to statistics, in the load data of residents in the 2018 year-round data of the Tianjin Wuqing area, the correlation coefficient of the historical load value of the last time point of each day and the historical load value of the first time point of the next day is 0.98.
502. Setting the mark number of the actual load value interval of the first time point of the m +1 th day as h (h belongs to 1-k), and constructing a row vector A containing k elements11，A11Is characterized in that: the h element is 1, and the other elements are 0, then called A11Probability state direction of the first time point of the m +1 th dayAn amount;
503. selecting the corresponding single-step and multi-step state transition matrix calculated in the step 4 according to the weather condition, season and whether the day of the m +1 day is a working day
504. A is to be11Multiplying the single-step long state transition matrix in step 503 to obtain a probability state vector A of a second time point21Next, A is11And A21Multiplying the three-step state transition matrix by the two-step and single-step state transition matrix respectively to obtain a probability state vector A of a third time point31、A32By analogy, the probability state vector of each time point, which is transferred to the time point from different time points through different lengths, is obtained; for example, if the step size between the first time point and the second time point is 1, A will be11Multiplying with the single step length state transition matrix to obtain a probability state vector A of a second time point21(ii) a The third time point can be reached from the first time point through the step length 2, and can also be reached from the second time point through the step length 1, so that the probability state vectors of the third time point are two, and the probability state vector calculation method of the later time point refers to the process until the probability state vectors of the n time points are obtained;
505. multiplying the probability state vector of each time point with the state mean vector of the corresponding time obtained in the step 2, and averaging the results obtained in different step lengths to obtain the load simulation value of each time point; for the x-th time point, the load simulation value is set as
Then there are:
respectively calculating load simulation values of n time points of the m +1 th day according to a formula (10);
step 6, calculating the data sequence L in the step 2jThe historical load value L inijRespectively counting the difference values of the same actual load value interval at the same moment with the difference values of the mean values of all historical load values of the corresponding actual load value interval, carrying out kernel density estimation on the difference values by utilizing a ksDensity function in Matlab, and fitting a probability density function e of the difference values according to the resultij(x) And then obtaining the cumulative distribution function E of the difference valuesij(x) In that respect Cumulative distribution function E of differenceij(x) As an error function, a random number between 0 and 1 is brought into the cumulative distribution function E of the differencesij(x) Is inverse function of
Obtaining an error compensation value at a corresponding moment; and (5) respectively adding the load analog value of each time point of the m +1 th day obtained in the step (5) with the error compensation value of the corresponding time, wherein the obtained result is the load predicted value of the n time points of the m +1 th day.
Using the load data of the residents in the first 299 days in the year-round data of 2018 in Tianjin Wuqing area as historical load data, adopting the load prediction method to predict the load data of the 300 th day, and comparing the obtained load prediction data of the 300 th day with the load actual data thereof, as shown in FIG. 4; meanwhile, the load data of the 300 th day is predicted by adopting the traditional Markov chain method for the same historical load data, and the comparison graph of the obtained load predicted data of the 300 th day and the load actual data thereof is shown in FIG. 3. The load prediction data result shows that the load prediction method has higher accuracy compared with the traditional Markov chain method, the total error is basically controlled to be about 2 percent, and the load prediction method has practical application value.
Claims (4)
1. A load prediction method based on a superposed Markov chain is characterized by comprising the following steps:
step 1, acquiring historical load data of the same type in the same region, and selecting n data points from the historical load data of each day; the historical load data is the span of m days, and the time of the n data points selected each day is the same; constructing a load data matrix L by using the selected data sequence of n data points each day for m days, wherein the formula (1) is as follows:
in the above formula, LijRepresenting the historical load value at the j time of the ith day;
and 2, taking out each column of the load data matrix L independently, wherein the formula (2) is as follows:
Lj＝[L1j,L2j,...Lij,...Lmj] (2)
Lja data sequence consisting of historical load values of the jth time point of each day in m days; obtaining n data sequences according to the load data matrix L, wherein each sequence comprises m data points;
sequence of statistical data LjThe historical load value in Matlab is utilized to carry out kernel density estimation by using ksDensity function in Matlab, and then the probability density function f is fitted according to the resultLj(x) Then integrated to obtain a cumulative distribution function FLj(x) Through the above operation, the data sequence L is obtainedjThe historical load values in (1) are distributed on a longitudinal axis by 0-1; the cumulative distribution function FLj(x) The longitudinal axis of the system is uniformly divided into k intervals, namely equal-probability division intervals, the length of each interval is 1/k, and all the intervals are marked as 1,2.. k from small to large; substituting the values of the upper and lower bounds of each longitudinal axis interval into an inverse function of the cumulative distribution function to obtain an actual load value interval corresponding to each longitudinal axis interval, wherein the marks of the actual load value interval are the same as those of the longitudinal axis interval; as shown in formula (3), GLj(y) is FLj(x) The inverse function of (c);
then to the data sequence LjThe historical load values in the process are processed, each historical load value is distributed into the actual load value interval to which the historical load value belongs according to the size of the historical load value, the average value of all the historical load values in each actual load value interval is obtained, and a state average value vector a at the moment j is formedjAs shown in formula (4); simultaneously transmitting the data sequence LjThe historical load value in the data sequence L is converted into the labels 1-k of the corresponding actual load value intervals, and the data sequence L is processedjConversion to a sequence of state variables CjAll elements in the state variable sequence are integers from 1 to k; by the method, state mean value vectors of n moments and corresponding state variable sequences are obtained;
aj＝[a1j,a2j,...akj] (4)
Cj＝[C1j,C2j,...,Cmj] (5)
step 3, according to the state variable sequence C of the data sequence of each column in the load data matrix L obtained in the step 2jConstructing a state variable matrix C as shown in formula (6), wherein Cij＝1,2,...k；
Each behavior in the state variable matrix C corresponds to state variable data of a corresponding day in m days;
taking the types of weather of sunny, cloudy, rainy/snowy, spring, summer, autumn and winter in seasons and the types of dates of working days or holidays as influence factors, and combining the three types of influence factors to obtain 24 different conditions of influence factors; extracting the m-day state variable data in the state variable matrix C to the state variable matrix D of the 24 corresponding influencing factors of different conditions according to the selected influencing factors of different conditions corresponding to each of the m days1,D2,...,Dq,...,D24Performing the following steps;
step 4, obtaining a state variable matrix D of the influencing factors of different conditions in the step 31,D2,...,Dq,...,D24Calculating states of different step sizes using Markov chain methodTransfer matrix
Wherein 1-r represent different step lengths;
step 5, taking the state interval label of the historical load value of the last time point of the mth day as the state interval label of the first time point of the mth +1 day, constructing the probability state vector of the first time point of the mth +1 day, determining the corresponding state transition matrix according to the weather, season, date type conditions and step length of the mth +1 day, and calculating the probability state vectors of the n time points point by point; multiplying the probability state vector of each time point with the state mean vector of the corresponding time obtained in the step 2, and averaging the results obtained in different step lengths to obtain the load simulation value of each time point;
step 6, calculating the data sequence L in the step 2jThe historical load value L inijCounting the difference values of the same actual load value interval at the same moment with the difference values of the mean values of all historical load values of the corresponding actual load value interval, carrying out kernel density estimation on the difference values by utilizing a ksDensity function in Matlab, and fitting a probability density function e according to the resultij(x) And then obtaining the cumulative distribution function E of the difference valuesij(x) (ii) a Cumulative distribution function E of differenceij(x) As an error function, a random value between 0 and 1 is substituted into a cumulative distribution function E of the difference valuesij(x) Is inverse function of
Obtaining an error compensation value at a corresponding moment; and (5) respectively adding the load analog value of each time point of the m +1 th day obtained in the step (5) with the error compensation value of the corresponding time, wherein the obtained result is the load predicted value of the n time points of the m +1 th day.
2. The method for load prediction based on a superimposed Markov chain as claimed in claim 1, wherein the type of the historical load data in step 1 is one of commercial load, industrial load and residential load.
3. The method for load prediction based on the overlapped markov chain of claim 1, wherein the interval between the time points of the n data points selected each day in step 1 is 15 min.
4. The method for load prediction based on the superimposed markov chain according to claim 1, wherein the specific process of the step 5 is as follows:
501. counting the correlation between the historical load value of the last time point of each day in m days and the historical load value of the first time point of the next day, and when the correlation coefficient is greater than 0.8, determining that the historical load value of the last time point of the previous day and the historical load value of the first time point of the next day have high correlation; when the correlation coefficient is larger than 0.8, taking the label of the actual load value interval to which the historical load value of the last time point of the mth day belongs as the label of the actual load value interval to which the first time point of the m +1 day belongs;
502. setting the reference number h of the actual load value interval of the first time point of the m +1 th day, constructing a line vector A containing k elements11，A11Is characterized in that: the h element is 1, and the other elements are 0, then called A11Probability state vector of the first time point of the m +1 th day;
503. selecting the corresponding single-step and multi-step state transition matrix calculated in the step 4 according to the weather condition, season and whether the day of the m +1 day is a working day
504. A is to be11Multiplying the single-step long state transition matrix in step 503 to obtain a probability state vector A of a second time point21Next, A is11And A21Multiplying the three-step state transition matrix by the two-step and single-step state transition matrix respectively to obtain a probability state vector A of a third time point31、A32By the analogy, the method can be used,obtaining the probability state vector of each time point, which is transferred to the time point from different time points through different step lengths;
505. multiplying the probability state vector of each time point with the state mean vector of the corresponding time obtained in the step 2, and averaging the results obtained in different step lengths to obtain the load simulation value of each time point; for the x-th time point, the load simulation value is set as
Then there are:
according to the formula (10), the load simulation values at n time points of the m +1 th day are calculated respectively.
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