CN111598475A - Power grid risk prediction method based on improved gray Markov model - Google Patents

Power grid risk prediction method based on improved gray Markov model Download PDF

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CN111598475A
CN111598475A CN202010443021.6A CN202010443021A CN111598475A CN 111598475 A CN111598475 A CN 111598475A CN 202010443021 A CN202010443021 A CN 202010443021A CN 111598475 A CN111598475 A CN 111598475A
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邹淇超
郑河荣
潘翔
邱雷
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Abstract

The invention relates to a power grid risk prediction method based on an improved gray Markov model, which predicts a risk index by adopting a method of combining a gray system theory and the Markov model and optimizes the selection of a background value of a traditional gray system model; the invention effectively combines the two prediction models after optimization, proves the feasibility of the combined model through data, and can predict according to the risk early warning index of past months, thereby providing specific suggestions for the subsequent power grid policy formulation and having great application market.

Description

Power grid risk prediction method based on improved gray Markov model
Technical Field
The invention relates to the technical field of power grid early warning analysis, in particular to a power grid risk prediction method based on an improved gray Markov model.
Background
After twenty-first century, society is continuously advanced, economy is gradually developed, and the development of the power industry is also different day by day. Reasonable and scientific power grid risk early warning research is one of important contents of power industry development research. Accurate risk early warning can effectively improve the safety level of the power industry and is beneficial to making strategic plan and policy of power industry development.
At present, many researches and researches on prediction methods are carried out, and a set of relatively complete quantitative prediction theory system is formed, mainly comprising a regression analysis method, a grey prediction method, a genetic algorithm, a neural network model, a trend analysis method and the like. Although different prediction models have certain accuracy under different conditions, the power grid risk early warning is often restricted by multiple factors, and no prediction model has universality in the power grid risk early warning. Compared with a single prediction model, the method has certain defects and limitations, so that different prediction models need to be combined, the advantages of the different prediction models are fully utilized, effective information is extracted as much as possible, the limitation of the single model is made up, and the purpose of improving the prediction accuracy of the model is achieved by making up for the deficiencies of the effective information. Currently, combinatorial models have become a new development trend in the field of prediction. At present, the grey system theory has no small limitation: the more discrete and irregular the data, the lower the prediction accuracy.
Disclosure of Invention
The invention aims to overcome the defects and provides a power grid risk prediction method based on an improved gray Markov model, and the method adopts a method of combining a gray system theory and the Markov model to predict a risk index and optimizes the selection of a background value of a traditional gray system model; the invention effectively combines the two prediction models after optimization, proves the feasibility of the combined model through data, and can predict according to the risk early warning index of past months, thereby providing specific suggestions for the subsequent power grid policy formulation and having great application market.
The invention achieves the aim through the following technical scheme: a power grid risk prediction method based on an improved gray Markov model is characterized by comprising the following steps:
(1) reading risk early warning month data of a safety risk management and control system of an electric power company work project, establishing an improved gray model by utilizing the early warning data, optimizing a background value, and obtaining a preliminary fitting predicted value based on the improved gray model;
(2) dividing state intervals according to relative errors between the real values and the fitting predicted values, and calculating a Markov one-step state transition matrix according to the conversion between states;
(3) and judging a future state according to the state transition matrix, calculating and correcting prediction data by using a Markov coefficient, and calculating to obtain a prediction result.
Preferably, in the step (1), the method for establishing the improved gray model comprises:
(i) let the original data sequence be X(0)＝(x(0)(1)，x(0)(2)，…，x(0)(n)), the new sequence generated by first-order accumulation of the original data is X(1)＝(x(1)(1)，x(1)(2)，…，x(1)(n))；
(ii) Establishing a gray differential equation for the sequence of numbers formed by the accumulation:
Figure BDA0002504651670000021
(iii) calculating the values of a and b parameters by least square method, and making Z(1)(k)＝0.5x(1)(k)+0.5x(1)(k-1) is X(1)The basic form of the GM (1,1) gray model is then: x is the number of(0)(k)+aZ(1)(k)＝b
Is provided with
Figure BDA0002504651670000031
Is a parameter sequence of
Figure BDA0002504651670000032
Gray differential equation x(0)(k)+aZ(1)(k) B is obtained by solving with the least square method:
Figure BDA0002504651670000033
(iv) substituting the values of the parameters a and b into a gray differential equation, and solving to obtain a GM (1,1) gray model as follows:
Figure BDA0002504651670000034
preferably, the method for optimizing the GM (1,1) gray model by using the background value optimization method is as follows:
is provided with an original data sequence X(0)After summation of first order, a new sequence X is generated(1)If the first order differential equation has a solution, the background value is:
Figure BDA0002504651670000035
wherein L (k) is ln x(0)(k)-ln x(0)(k-1)，k＝2，3，…，n。
Preferably, the step (2) is specifically: firstly, dividing state intervals according to relative errors, and then calculating a Markov one-step state transition matrix according to conversion between states, wherein the Markov one-step state transition matrix is as follows:
Figure BDA0002504651670000036
in the formula, PijIndicating that the data is in slave state QiTo state QjProbability after one-step transition, nijIndicating that after a one-step transition, the slave state QiTo state QjNumber of times, NiRepresents a state QiA total number of co-occurrences; from this, the one-step state transition matrix is:
Figure BDA0002504651670000041
preferably, when the corrected prediction data is calculated using the markov coefficient in step (3), the following two cases are separately processed:
1) if only one maximum transition probability Z appears in the one-step state transition matrixikThe prediction result being determined by the median of the relative error ranges of the respective states, i.e.
Figure BDA0002504651670000042
Wherein V (t) is a desired predicted value,
Figure BDA0002504651670000043
prediction of the grey prediction model for the relevant month, (A)i+Bi) The relative error range of the state of the month;
2) if multiple identical Zs occur in the one-step state transition matrixikThe prediction result is determined by the median of the relative error ranges of the states and the corresponding probability of their occurrence, i.e.
Figure BDA0002504651670000044
In the formula, ZikRepresenting the maximum probability in the one-step state transition matrix, V (t) being the predicted value,
Figure BDA0002504651670000045
prediction of the grey prediction model for the relevant month, (A)i+Bi) Is the relative error range of the state of the month.
The invention has the beneficial effects that: (1) the method can predict according to the risk early warning indexes of the past months, so that specific suggestions can be provided for the later power grid policy making, and the method has a great application market; (2) the method can make up the defect that the grey system theory has low prediction precision on the data sequence with large random fluctuation, and can make up the defect of the Markov model, and has low cost and little profit; meanwhile, the early deployment of the electric power department according to the early warning index can be effectively assisted, and the loss caused by dangerous operation is greatly reduced, so that the early deployment method has great economic benefit.
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FIG. 1 is a schematic flow diagram of the process of the present invention;
FIG. 2 is a diagram illustrating background value selection errors of a conventional GM (1,1) model according to the present invention;
FIG. 3 is a graph showing the comparison of the model prediction results of the present invention with those of other gray methods.
Detailed Description
The invention will be further described with reference to specific examples, but the scope of the invention is not limited thereto:
example (b): the power grid risk prediction method based on the improved gray Markov model can make up for the defect that the prediction precision of a gray system theory on a data sequence with large random fluctuation is low and can make up for the defect of the Markov model. The improved gray Markov model goes through several main processes of establishing a gray system model, optimizing a background value, calculating a prediction function, dividing a state interval, establishing a state transition matrix, carrying out Markov correction and obtaining a predicted value, so that a series of prediction results with higher precision are obtained. As shown in fig. 1, a power grid risk prediction method based on an improved gray markov model includes the following steps:
(1) reading risk early warning month data of a safety risk control system of a job project of a Zhejiang power-saving company, wherein the risk early warning month data is shown as risk early warning indexes of 2018 years 1-10 years in Hangzhou city in the following table 1; and establishing an improved grey model by utilizing the early warning data, optimizing the background value, and obtaining a preliminary fitting predicted value based on the improved grey model.
Figure BDA0002504651670000051
Figure BDA0002504651670000061
TABLE 1
Let the original data sequence be：X(0)＝(x(0)(1)，x(0)(2)，…，x(0)(n))
Performing first-order accumulation on the original data, and generating a new sequence after the first-order accumulation: x(1)＝(x(1)(1)，x(1)(2)，…，x(1)(n))
The whitening equation of the gray differential equation is established for the sequence of numbers formed by the accumulation:
Figure BDA0002504651670000062
calculating the values of a and b parameters by least square method, and making Z(1)(k)＝0.5x(1)(k)+0.5x(1)(k-1) is x(1)The basic form of the GM (1,1) model is then: x is the number of(0)(k)+aZ(1)(k)＝b
Is provided with
Figure BDA0002504651670000063
Is a parameter sequence of
Figure BDA0002504651670000064
Gray differential equation x(0)(k)+aZ(1)(k) B is obtained by solving with the least square method:
Figure BDA0002504651670000065
substituting the values of the parameters a and b into a gray differential equation, and solving to obtain a GM (1,1) prediction model as follows
Figure BDA0002504651670000066
The above formula is reduced to obtain the predicted value of the original sequence
Figure BDA0002504651670000067
As can be seen from fig. 2, the cause of the error of the conventional GM (1,1) model is analyzed as follows:
the theoretical value of construction of the background value of the GM (1,1) model should be
Figure BDA0002504651670000068
Background value z(1)(k) Should be a fitted curve x(1)(t) in the interval [ k-1, k ]]The integral value of (1), i.e. the true background value, should be x(1)(t) in the interval [ k-1, k ]]The area enclosed by t is removed, and the traditional GM (1,1) model uses an approximate substitution method to directly replace the t
Figure BDA0002504651670000071
The background value was identified. From the above analysis, it can be seen that the conventional model error is derived from the use
Figure BDA0002504651670000072
Instead of the former
Figure BDA0002504651670000073
Due to the fact that
Figure BDA0002504651670000074
As background value z(1)(k) The method is more reasonable; so, here, background value optimization is performed, note:
Figure BDA0002504651670000075
is provided with an original data sequence X(0)After summation of first order, a new sequence X is generated(1)If the first order differential equation has a solution, the background value is:
Figure BDA0002504651670000076
wherein L (k) is ln x(0)(k)-ln x(0)(k-1)，k＝2，3，…，n。
Obtaining a calculation predicted value based on an improved grey model:
Figure BDA0002504651670000077
substituting into a specific month to obtain a primary predicted value, an absolute error value and a relative error value, wherein the table 2 shows a risk early warning index and predicted value comparison table in 2018 of Hangzhou city in 1-10 months; thereby facilitating the next state division.
Figure BDA0002504651670000078
Figure BDA0002504651670000081
TABLE 2
(2) Dividing state intervals according to relative errors between the real values and the fitting predicted values, and calculating a Markov one-step state transition matrix according to the conversion between states;
performing state division according to the relative error value obtained after prediction to enable Qi(i is 1, 2, …, n) is a divided state. According to the GM (1,1) prediction result of the risk early warning index of 2018 in Hangzhou city in 1-10 months, the relative error range is known to be between-3.12 and 3.04, so the relative error range is divided into 4 states as follows:
Q1：-3.2～1.6；Q2-1.6～0；Q3：0～1.6；Q4；1.6～3.2。
building a one-step matrix of Markov state transitions:
Figure BDA0002504651670000082
in the formula, PijIndicating that the data is in slave state QiTo state QjProbability after one-step transition, nijIndicating that after a one-step transition, the slave state QiTo state QjNumber of times, NiRepresents a state QiA total number of occurrences. From this, the one-step state transition matrix is:
Figure BDA0002504651670000083
obtaining a one-step state transition matrix:
Figure BDA0002504651670000084
(3) and judging a future state according to the state transition matrix, calculating and correcting prediction data by using a Markov coefficient, and calculating to obtain a prediction result.
And (3) state prediction: according to the one-step state transition matrix, if max (Z)ij)＝ZikThen, it can be determined: at QiAfter the state, the next time period, the system is most likely to turn to QkStatus. That is, Q will appear next in the systemkStatus.
Calculating a predicted value:
the first condition is as follows: if in a one-step transition matrix, only one Z appearsikThe prediction result being determined by the median of the relative error ranges of the respective states, i.e.
Figure BDA0002504651670000091
Wherein V (t) is a desired predicted value,
Figure BDA0002504651670000092
prediction of the grey prediction model for the relevant month, (A)i+Bi) Is the relative error range of the state of the month.
Case two: if multiple identical Zs are present in a one-step transition matrixikThe prediction result is determined by the median of the relative error ranges of the states and the corresponding probability of occurrence.
Figure BDA0002504651670000093
In the formula, ZikRepresenting the maximum probability in the one-step transition matrix, V (t) being the predicted value,
Figure BDA0002504651670000094
of grey prediction models for the relevant monthsPredicted value, (A)i+Bi) Is the relative error range of the state of the month.
In this example, Q is the occurrence status in 11 months in 20182. Since the 10-month state is Q3And the maximum probability value is based on the one-step transition matrix
Figure BDA0002504651670000095
So the next time the system is most likely to be composed of Q3State goes to Q2This case belongs to the above-described case one. Similarly, the occurrence status in 11 months is Q2And the occurrence probability of 12 months is Q1And Q3The same probability applies to the case two described above. The results of the correction of the original GM (1,1) are shown in Table 3.
Figure BDA0002504651670000096
Figure BDA0002504651670000101
TABLE 3
The risk early warning indexes of the hangzhou city in 2018 from 1 to 12 months are respectively fitted by 3 methods of traditional GM (1,1), traditional grey Markov and optimized grey Markov, and the comparison results of the prediction results of the 3 methods are shown in Table 4 and FIG. 3. M in Table 40Is the conventional GM (1,1) model, M1Is a conventional gray Markov model, M2Is a gray markov model after background value optimization.
Figure BDA0002504651670000102
TABLE 4
Comprehensive analysis, namely obtaining a fitting result of the risk early warning indexes of 1 to 10 months in 2018 and analyzing and calculating a prediction result of 11 and 12 months, and obtaining a model M0Has an average relative error of 1.2211%, model M1Has an average relative error of 0.5187%, andimproved grey Markov prediction model M after optimization of line background value2The average relative error of (2) was 0.4813%. Therefore, we can see that the gray markov prediction model with background value optimization has higher prediction accuracy than the other 2 methods. Meanwhile, fig. 3 shows that the improved gray markov model has better fitting effect and can clearly reflect the fluctuation of the relevant data of risk prediction. Therefore, the risk early warning indexes with more influence factors, more complex data and irregular distribution are predicted, the gray Markov model after background value optimization is more reasonable than the traditional gray GM (1,1) model, and the prediction precision is higher.
While the invention has been described in connection with specific embodiments thereof, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.

Claims (5)

1. A power grid risk prediction method based on an improved gray Markov model is characterized by comprising the following steps:
(1) reading risk early warning month data of a safety risk management and control system of an electric power company work project, establishing an improved gray model by utilizing the early warning data, optimizing a background value, and obtaining a preliminary fitting predicted value based on the improved gray model;
(2) dividing state intervals according to relative errors between the real values and the fitting predicted values, and calculating a Markov one-step state transition matrix according to the conversion between states;
(3) and judging a future state according to the state transition matrix, calculating and correcting prediction data by using a Markov coefficient, and calculating to obtain a prediction result.
2. The power grid risk prediction method based on the improved gray Markov model as claimed in claim 1, wherein: in the step (1), the method for establishing the improved gray model comprises the following steps:
(i) setting original data sequenceIs X(0)＝(x(0)(1)，x(0)(2)，…，x(0)(n)), the new sequence generated by first-order accumulation of the original data is X(1)＝(x(1)(1)，x(1)(2)，…，x(1)(n))；
(ii) Establishing a gray differential equation for the sequence of numbers formed by the accumulation:
Figure FDA0002504651660000011
(iii) calculating the values of a and b parameters by least square method, and making Z(1)(k)＝0.5x(1)(k)+0.5x(1)(k-1) is X(1)The basic form of the GM (1,1) gray model is then: x is the number of(0)(k)+aZ(1)(k)＝b
Is provided with
Figure FDA0002504651660000012
Is a parameter sequence of
Figure FDA0002504651660000013
Gray differential equation x(0)(k)+aZ(1)(k) B is obtained by solving with the least square method:
Figure FDA0002504651660000021
(iv) substituting the values of the parameters a and b into a gray differential equation, and solving to obtain a GM (1,1) gray model as follows:
Figure FDA0002504651660000022
3. the power grid risk prediction method based on the improved gray Markov model as claimed in claim 2, wherein: the method for optimizing the GM (1,1) gray model by adopting the background value optimization method comprises the following steps:
is provided with original dataSequence X(0)After summation of first order, a new sequence X is generated(1)If the first order differential equation has a solution, the background value is:
Figure FDA0002504651660000023
wherein L (k) is Inx(0)(k)-ln x(0)(k-1)，k＝2，3，…，n。
4. The power grid risk prediction method based on the improved gray Markov model as claimed in claim 1, wherein: the step (2) is specifically as follows: firstly, dividing state intervals according to relative errors, and then calculating a Markov one-step state transition matrix according to conversion between states, wherein the Markov one-step state transition matrix is as follows:
Figure FDA0002504651660000024
in the formula, PijIndicating that the data is in slave state QiTo state QjProbability after one-step transition, nijIndicating that after a one-step transition, the slave state QiTo state QjNumber of times, NiRepresents a state QiA total number of co-occurrences; from this, the one-step state transition matrix is:
Figure FDA0002504651660000025
5. the power grid risk prediction method based on the improved gray Markov model as claimed in claim 1, wherein: in the step (3), when the corrected prediction data is calculated using the markov coefficient, the following two cases are separately processed:
1) if only one maximum transition probability Z appears in the one-step state transition matrixikThe prediction result is located in the middle of the residual range of each stateIs determined by the value, i.e.
Figure FDA0002504651660000031
Wherein V (t) is a desired predicted value,
Figure FDA0002504651660000032
prediction of the grey prediction model for the relevant month, (A)i+Bi) The residual error range of the state of the month;
2) if multiple identical Zs occur in the one-step state transition matrixikThe prediction result is determined by the median of the residual range of each state and the probability of its corresponding occurrence, i.e.
Figure FDA0002504651660000033
In the formula, ZikRepresenting the maximum probability in the one-step state transition matrix, V (t) being the predicted value,
Figure FDA0002504651660000034
prediction of the grey prediction model for the relevant month, (A)i+Bi) Is the residual range of the state of the month.
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CN111080481A (en) * 2019-12-14 2020-04-28 广西电网有限责任公司电力科学研究院 Electric energy substitution potential gray analysis method based on Markov chain correction

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CN112769859A (en) * 2021-01-24 2021-05-07 中国电子科技集团公司第十五研究所 Network attack stage statistical and prediction method based on Markov chain
CN112769859B (en) * 2021-01-24 2021-08-27 中国电子科技集团公司第十五研究所 Network attack stage statistical and prediction method based on Markov chain
CN113570278A (en) * 2021-08-09 2021-10-29 国网上海市电力公司 Power distribution network risk early warning method based on Markov process

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