Power consumption prediction method and system based on grey Markov model
By combining the gray model and the Markov model, an electricity consumption prediction system was established, which solved the problems of poor adaptability and incomplete information of traditional electricity consumption prediction algorithms, and achieved higher prediction accuracy and reliability.
Patent Information
- Application Number
- CN202411694544.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-11-25
- Publication Date
- 2025-04-11
AI Technical Summary
Traditional power consumption prediction algorithms rely on a large amount of historical data, are poor in adaptability, and are difficult to effectively apply in scenarios with data scarcity, and fail to make full use of data from other influencing factors, resulting in incomplete information and low prediction accuracy.
Using the electricity prediction method based on the gray Markov model, a prediction system combining the gray model and the Markov model is established, and the model parameters are estimated using two-multiple method, the prediction error of the gray model is corrected, and the accuracy and reliability of the prediction are improved.
It improves the accuracy and reliability of electricity usage prediction, can more comprehensively reflect the complex factors affecting power demand, adapt to new situations, and be suitable for data scarcity scenarios.
Smart Images
Figure CN119809012A_ABST
Abstract
Description
Technical Field
[0001] The invention relates to the field of electric power technology, and in particular to a method and system for predicting electricity consumption based on a grey Markov model. Background Art
[0002] Electricity consumption is affected by many factors, such as economic development, industrial structure, income level and national policies. The randomness and correlation of these factors vary greatly, making accurate prediction very difficult. The traditional gray model is suitable for situations where electricity consumption grows slowly, but actual electricity consumption is difficult to change exponentially, which leads to a long-term forecast growth rate that is too fast and low prediction accuracy. In addition, the structure of the gray model is relatively fixed, which may not be flexible enough for complex and changeable data sequences. When there are obvious trend changes in the data, the prediction accuracy may be affected.
[0003] Traditional electricity consumption prediction algorithms rely on a large amount of historical data for training, have poor adaptability to new situations, and are difficult to apply to data-scarce scenarios. Most existing models are based on historical loads and fail to make full use of data from other influencing factors, resulting in incomplete information. Some high-precision prediction models are black boxes, and their internal prediction mechanisms cannot be analyzed, reducing the credibility of the models. Summary of the invention
[0004] In view of the problems existing in the existing multi-source power grid information fusion and system based on the Internet of Things, the present invention is proposed.
[0005] Therefore, the purpose of the present invention is to provide a method and system for predicting electricity consumption based on a grey Markov model. Traditional electricity consumption prediction algorithms rely on a large amount of historical data for training and have poor adaptability to new situations. The present invention solves this problem by using a method and system for predicting electricity consumption based on a grey Markov model.
[0006] In order to solve the above technical problems, the present invention provides the following technical solutions:
[0007] In the first aspect, an embodiment of the present invention provides an electricity consumption prediction method based on a grey Markov model, which includes establishing a grey model, accumulating and generating variables, estimating model parameters using the square multiplication method, and solving differential equations to obtain a prediction model; establishing a Markov model, determining a state transition probability matrix, and after calculating the equilibrium state probability, using the Markov model to correct the prediction error of the grey model; using the prediction error result of the corrected grey model, establishing a grey model process, and completing the electricity consumption prediction of the grey Markov model.
[0008] As a preferred solution of the method for predicting electricity consumption based on the grey Markov model of the present invention, wherein: the establishment of the grey model includes a grey model established from a first-order differential equation to n variables, which is used to predict the relationship between energy and multiple variables;
[0009] For a given n variables x1, x2, ..., x n , a sequence consisting of n historical data, namely:
[0010]
[0011] Among them, for The cumulative generation of 1-AGO is:
[0012]
[0013] In this case, similar to the model GM(1,n), a first-order linear differential equation is constructed.
[0014] As a preferred solution of the power consumption forecasting method based on the grey Markov model of the present invention, the specific formula for constructing the first-order linear differential equation is:
[0015]
[0016] Among them, there is a first-order differential equation model with n variables, written as GM(1,n), where n represents the parameter, N means calculation according to the square method;
[0017] The formula for the square multiplication calculation is:
[0018]
[0019] Among them, find the unique solution of the column parameters and transform the parameter matrix Generate back the differential equation and obtain the system state equation established by n variables.
[0020] As a preferred solution of the power consumption prediction method based on the grey Markov model of the present invention, the formula of the system state equation is:
[0021]
[0022] Among them, the prediction model represents the prediction model, Indicates prediction.
[0023] As a preferred solution of the method for predicting electricity consumption based on the grey Markov model of the present invention, wherein: the establishment of the Markov model includes obtaining state variables from the Chapman-Kolmogorov equation;
[0024] If the probability vector of the system's initial state is: , where the initial state probability of each element in state i is j after k steps of transmission;
[0025] The formula for obtaining the state variable from the Chapman-Kolmogorov equation is:
[0026]
[0027] in, is the probability of uniform taste after k transfers;
[0028] The established Markov prediction model is expressed in vector form as:
[0029] S (k+1) =S k ·P
[0030] From the recursive relation we get:
[0031] in, is the probability after k transmissions; P ij is the probability of going from state i to state j after the first transmission.
[0032] As a preferred solution of the power consumption forecasting method based on the grey Markov model of the present invention, wherein: the grey model establishment process includes optimal estimation of the 0th order state transition probability matrix based on Markov chain identification, and when the Markov optimal forecasting model is applied to forecast the power consumption structure, a one-step transition probability matrix is determined;
[0033] Adopting the optimal thinking, the optimization model is established based on the minimum sum of square errors between the actual state probability vector and the theoretically calculated state probability vector;
[0034] When α(t)=(p t (1),p t (2),…p t When (n)) is the probability vector of the system in n states, time t, t = 1, 2, ..., m, the state transition probability matrix for each step is P = (p ij ) n×n ;
[0035] When the objective environment changes objectively, the transfer probability matrix of each step in adjacent time intervals is different. Therefore, there is an error between α(t+1) and α(t)P, t=0,1,2,…m-1. Taking the minimum sum of squared errors as the criterion, the following optimization model is established:
[0036]
[0037] Among them, the constraints come from the definition of the one-step transition probability matrix, and the optimization model represents a quadratic programming problem.
[0038] As a preferred solution of the method for predicting electricity consumption based on the grey Markov model of the present invention, wherein: the electricity consumption prediction based on the grey Markov model includes:
[0039] Under the condition that the transition probability matrix remains unchanged, as time goes by, the system reaches an equilibrium state, and the probability of each state in the system remains unchanged. (k+1) =S k When , the calculation in matrix form is completed:
[0040]
[0041] Among them, the equilibrium state of the system will be obtained, and the probability of each state of the system in the stable state will be determined.
[0042] In the second aspect, an embodiment of the present invention provides an electricity consumption prediction system based on a grey Markov model, which includes: an establishment module, which establishes a grey model, accumulates and generates variables, estimates model parameters using the square multiplication method, and solves differential equations to obtain a prediction model; a prediction module, which establishes a Markov model, determines a state transition probability matrix, calculates the equilibrium state probability, and then uses the Markov model to correct the prediction error of the grey model; a correction module, which uses the prediction error result of the corrected grey model to establish a grey model process and complete the electricity consumption prediction of the grey Markov model.
[0043] In a third aspect, an embodiment of the present invention provides a computer device, including a memory and a processor, wherein the memory stores a computer program, wherein: when the processor executes the computer program, any step of the above-mentioned power consumption prediction method based on the grey Markov model is implemented.
[0044] In a fourth aspect, an embodiment of the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein: when the computer program is executed by a processor, any step of the above-mentioned method for predicting electricity consumption based on a grey Markov model is implemented.
[0045] The beneficial effects of the present invention are as follows: the present invention improves the accuracy and reliability of prediction. The traditional grey model has certain limitations when processing power demand prediction. The present invention combines the grey model with the Markov chain and uses the Markov model to adjust the prediction error of the grey model, thereby improving the accuracy and reliability of prediction and more comprehensively reflecting the complex factors affecting power demand. Using the grey model to predict power demand can more comprehensively reflect the complex factors affecting power consumption. BRIEF DESCRIPTION OF THE DRAWINGS
[0046] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for describing the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work. Among them:
[0047] Figure 1 A specific flow chart of a method and system for predicting electricity consumption based on a grey Markov model is provided for one embodiment of the present invention.
[0048] Figure 2 A schematic diagram of a prediction method and system for power consumption prediction based on a grey Markov model is provided in accordance with an embodiment of the present invention. DETAILED DESCRIPTION
[0049] In order to make the above-mentioned purposes, features and advantages of the present invention more obvious and easy to understand, the specific implementation methods of the present invention are described in detail below in conjunction with the drawings of the specification. Obviously, the described embodiments are part of the embodiments of the present invention, but not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary persons in the art without creative work should fall within the scope of protection of the present invention.
[0050] In the following description, many specific details are set forth to facilitate a full understanding of the present invention, but the present invention may also be implemented in other ways different from those described herein, and those skilled in the art may make similar generalizations without violating the connotation of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.
[0051] Secondly, the term "one embodiment" or "embodiment" as used herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The term "in one embodiment" that appears in different places in this specification does not necessarily refer to the same embodiment, nor does it refer to a separate or selective embodiment that is mutually exclusive with other embodiments.
[0052] The present invention is described in detail with reference to schematic diagrams. When describing the embodiments of the present invention, for the sake of convenience, the cross-sectional diagrams showing the device structure will not be partially enlarged according to the general scale, and the schematic diagrams are only examples, which should not limit the scope of protection of the present invention. In addition, in actual production, the three-dimensional dimensions of length, width and depth should be included.
[0053] At the same time, in the description of the present invention, it should be noted that the directions or positional relationships indicated by the terms "upper, lower, inner and outer" are based on the directions or positional relationships shown in the drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific direction, be constructed and operated in a specific direction, and therefore cannot be understood as limiting the present invention. In addition, the terms "first, second or third" are only used for descriptive purposes and cannot be understood as indicating or implying relative importance.
[0054] In the present invention, unless otherwise clearly specified and limited, the terms "install, connect, connect" should be understood in a broad sense, for example: it can be a fixed connection, a detachable connection or an integral connection; it can also be a mechanical connection, an electrical connection or a direct connection, or it can be indirectly connected through an intermediate medium, or it can be the internal communication of two components. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.
[0055] Example 1
[0056] Reference Figure 1 and Figure 2 , which is the first embodiment of the present invention, and provides a method for predicting electricity consumption based on a grey Markov model, comprising:
[0057] S1: Establish a grey model, accumulate and generate variables, estimate model parameters using the square method, and solve differential equations to obtain a prediction model.
[0058] Among them, the establishment of grey model includes the grey model established from the first-order differential equation to n variables, which is used to predict the relationship between energy and multiple variables;
[0059] For a given n variables x1, x2, ..., x n , a sequence consisting of n historical data, namely:
[0060]
[0061] Among them, for The cumulative generation of 1-AGO is:
[0062]
[0063] In this case, similar to the model GM(1,n), a first-order linear differential equation is constructed.
[0064] S1.1: The specific formula for constructing a first-order linear differential equation is:
[0065]
[0066] Among them, there is a first-order differential equation model with n variables, written as GM(1,n), where n represents the parameter, N means calculation according to the square method;
[0067] The formula for the square multiplication method is:
[0068]
[0069] Among them, find the unique solution of the column parameters and transform the parameter matrix Generate back the differential equation and obtain the system state equation established by n variables.
[0070] S1.2: The formula of the system state equation is:
[0071]
[0072] Among them, the prediction model represents the prediction model, Indicates prediction.
[0073] S2: Establish a Markov model, determine the state transition probability matrix, calculate the equilibrium state probability, and use the Markov model to correct the prediction error of the grey model.
[0074] Among them, establishing the Markov model includes obtaining state variables from the Chapman-Kolmogorov equation;
[0075] If the probability vector of the system's initial state is: , where the initial state probability of each element in state i is j after k steps of transmission;
[0076] The formula for the state variable obtained from the Chapman-Kolmogorov equation is:
[0077]
[0078] in, is the probability of uniform taste after k transfers;
[0079] The established Markov prediction model is expressed in vector form as:
[0080] S (k+1) =Sk ·P
[0081] From the recursive relation we get:
[0082] in, is the probability after k transmissions; P ij is the probability of going from state i to state j after the first transmission.
[0083] S3: Based on the prediction error results of the corrected grey model, the grey model process is established to complete the electricity consumption prediction of the grey Markov model.
[0084] Among them, the process of establishing the grey model includes the optimal estimation of the 0th order state transition probability matrix based on Markov chain identification, and when the Markov optimal prediction model is applied to predict the electricity consumption structure, the one-step transition probability matrix is determined;
[0085] Adopting the optimal thinking, the optimization model is established based on the minimum sum of square errors between the actual state probability vector and the theoretically calculated state probability vector;
[0086] When α(t)=(p t (1),p t (2),…p t When (n)) is the probability vector of the system in n states, time t, t = 1, 2, ..., m, the state transition probability matrix for each step is P = (p ij ) n×n ;
[0087] When the objective environment changes objectively, the transfer probability matrix of each step in adjacent time intervals is different. Therefore, there is an error between α(t+1) and α(t)P, t=0,1,2,…m-1. Taking the minimum sum of squared errors as the criterion, the following optimization model is established:
[0088]
[0089] Among them, the constraints come from the definition of the one-step transition probability matrix, and the optimization model represents a quadratic programming problem.
[0090] S3.1: Complete the electricity consumption forecast of the grey Markov model including
[0091] Under the condition that the transition probability matrix remains unchanged, as time goes by, the system reaches an equilibrium state, and the probability of each state in the system remains unchanged. (k+1) =S k When , the calculation in matrix form is completed:
[0092]
[0093] Among them, the equilibrium state of the system will be obtained, and the probability of each state of the system in the stable state will be determined.
[0094] In a preferred embodiment, a power consumption prediction system based on a grey Markov model includes an establishment module, which establishes a grey model, accumulates and generates variables, estimates model parameters using the square method, and solves differential equations to obtain a prediction model; a prediction module, which establishes a Markov model, determines a state transition probability matrix, calculates the equilibrium state probability, and then uses the Markov model to correct the prediction error of the grey model; and a correction module, which uses the prediction error result of the corrected grey model to establish a grey model process and complete the power consumption prediction of the grey Markov model.
[0095] The above-mentioned unit modules may be embedded in or independent of a processor in a computer device in the form of hardware, or may be stored in a memory in a computer device in the form of software, so that the processor can call and execute operations corresponding to the above-mentioned modules.
[0096] The computer device may be a terminal, and the computer device includes a processor, a memory, a communication interface, a display screen and an input device connected via a system bus. The processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system and a computer program. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The communication interface of the computer device is used to communicate with an external terminal in a wired or wireless manner, and the wireless manner can be achieved through WIFI, an operator network, NFC (near field communication) or other technologies. The display screen of the computer device may be a liquid crystal display screen or an electronic ink display screen, and the input device of the computer device may be a touch layer covering the display screen, or a key, trackball or touchpad provided on the housing of the computer device, or an external keyboard, touchpad or mouse, etc.
[0097] In summary, the present invention improves the accuracy and reliability of prediction. The traditional grey model has certain limitations when processing electricity demand prediction. The present invention combines the grey model with the Markov chain and uses the Markov model to adjust the prediction error of the grey model, thereby improving the accuracy and reliability of prediction and more comprehensively reflecting the complex factors affecting electricity demand. Using the grey model to predict electricity demand can more comprehensively reflect the complex factors affecting electricity consumption.
[0098] Example 2
[0099] Reference Figure 1 and Figure 2, which is the second embodiment of the present invention, and this embodiment provides a method for predicting electricity consumption based on a grey Markov model. In order to verify the beneficial effects of the present invention, a scientific demonstration is carried out through simulation experiments.
[0100] The present invention proposes a method and system for predicting electricity consumption based on a grey Markov model. The method aims to improve the accuracy of electricity consumption prediction by combining the grey model with the Markov model. The experiment selects the monthly electricity consumption data of a certain area from 2019 to 2022 as the sample set, with a total of 48 months of data, of which the data of the first 36 months are used for model training, and the data of the last 12 months are used to verify the prediction accuracy of the model. The electricity consumption is modeled using the grey model. In this experiment, n=3, which means that three influencing factors, temperature, humidity and holidays, are considered. By accumulating and generating a 1-AGO sequence, a first-order linear differential equation is constructed, and the model parameters are estimated by the square method. Finally, the system state equation is obtained. For the temperature variable, its cumulative generation sequence shows that from January 2020 to December 2022, the average monthly electricity consumption changes with temperature by about 0.03%. In order to correct the possible prediction deviation of the grey model, the Markov The model determines the state transition probability matrix by analyzing the changing trend of electricity consumption in the past three years. For example, when electricity consumption is at a low level, the probability of transferring to a medium level in the next month is 0.45, and the probability of maintaining a low level is 0.50. Based on the Chapman-Kolmogorov equation, the state probability after k-step transfer is calculated, and the model is further optimized. In order to ensure the robustness and accuracy of the model, the 0-order state transition probability matrix optimal estimation method based on Markov chain is also adopted to establish an optimization model. Specifically, the optimal one-step transfer probability matrix is determined by minimizing the square sum of the errors between the actual state probability vector and the theoretically calculated state probability vector. For example, in the forecast period from January 2022 to December 2022, the average forecast error rate obtained by the optimized model is 2.1%, which is significantly lower than the average forecast error rate of 3.5% of the unoptimized model. The experimental data of the present invention are shown in Table 1 below:
[0101] Table 1 Experimental data table of the present invention
[0102]
[0103] Table 1 clearly shows the main data points used in the experiment and their specific values, which helps to understand the effect of the power consumption prediction method based on the grey Markov model. The present invention is compared with the prior art as shown in Table 2 below:
[0104] Table 2 Comparison table between the present invention and the prior art
[0105]
[0106] It can be seen from Table 2 that the technical solution of the present invention is superior to the existing single model method in many aspects, especially in terms of prediction accuracy, adaptability and flexibility.
[0107] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention may be modified or replaced by equivalents without departing from the spirit and scope of the technical solutions of the present invention, which should all be included in the scope of the claims of the present invention.
Claims
1. A method for predicting electricity consumption based on a grey Markov model, characterized in that: include, Establish a grey model, accumulate and generate variables, use the square method to estimate model parameters, and solve differential equations to obtain a prediction model; Establish a Markov model, determine the state transition probability matrix, calculate the equilibrium state probability, and use the Markov model to correct the prediction error of the grey model; Based on the prediction error results of the corrected grey model, the grey model process is established to complete the electricity consumption prediction of the grey Markov model.
2. The method for predicting electricity consumption based on the grey Markov model according to claim 1, characterized in that: The grey model establishment includes a grey model established from a first-order differential equation to n variables, which is used to predict the relationship between energy and multiple variables; For a given n variables x1, x2, ..., x n , a sequence consisting of n historical data, namely: Among them, for The cumulative generation of 1-AGO is: In this case, similar to the model GM(1,n), a first-order linear differential equation is constructed.
3. The method for predicting electricity consumption based on the grey Markov model according to claim 2, characterized in that: The specific formula for constructing the first-order linear differential equation is: Among them, there is a first-order differential equation model with n variables, written as GM(1,n), where n represents the parameter, N means calculation according to the square method; The formula for the square multiplication calculation is: Among them, find the unique solution of the column parameters and transform the parameter matrix Generate back the differential equation and obtain the system state equation established by n variables.
4. The method for predicting electricity consumption based on the grey Markov model according to claim 3, characterized in that: The formula of the system state equation is: Among them, the prediction model represents the prediction model, Indicates prediction.
5. The method for predicting electricity consumption based on the grey Markov model according to claim 4, characterized in that: The establishment of the Markov model includes obtaining state variables from the Chapman-Kolmogorov equation; If the probability vector of the system's initial state is: , where the initial state probability of each element in state i is j after k steps of transmission; The formula for obtaining the state variable from the Chapman-Kolmogorov equation is: in, is the probability of uniform taste after k transfers; The established Markov prediction model is expressed in vector form as: S (k+1) =S k ·P From the recursive relation we get: in, is the probability after k transmissions; P ij is the probability of going from state i to state j after the first transmission.
6. The method for predicting electricity consumption based on the grey Markov model according to claim 5, characterized in that: The grey model establishment process includes optimal estimation of the 0th order state transition probability matrix based on Markov chain identification, and determining a one-step transition probability matrix when applying the Markov optimal prediction model to predict the electricity consumption structure; Adopting the optimal thinking, the optimization model is established based on the minimum sum of square errors between the actual state probability vector and the theoretically calculated state probability vector; When α(t)=(p t (1), p t (2), …p t When (n)) is the probability vector of the system in n states, at time t, t = 1, 2, ..., m, the state transition probability matrix for each step is P = (p ij ) n×n ; When the objective environment changes objectively, the transfer probability matrix of each step in adjacent time intervals is different. Therefore, there is an error between α(t+1) and α(t)P, t=0, 1, 2, ... m-1. Taking the minimum sum of squared errors as the criterion, the following optimization model is established: Among them, the constraints come from the definition of the one-step transition probability matrix, and the optimization model represents a quadratic programming problem.
7. The method for predicting electricity consumption based on the grey Markov model according to claim 6, characterized in that: The power consumption prediction of the grey Markov model includes Under the condition that the transition probability matrix remains unchanged, as time goes by, the system reaches an equilibrium state, and the probability of each state in the system remains unchanged. (k+1) =S k When , the calculation in matrix form is completed: Among them, the equilibrium state of the system will be obtained, and the probability of each state of the system in the stable state will be determined.
8. A power consumption prediction system based on a grey Markov model, based on the power consumption prediction method based on a grey Markov model according to any one of claims 1 to 7, characterized in that: include, Establishing module, which establishes grey model, generates variables by accumulation, estimates model parameters by using square method, and solves differential equations to obtain prediction model; The prediction module establishes a Markov model, determines the state transition probability matrix, calculates the equilibrium state probability, and uses the Markov model to correct the prediction error of the grey model; The correction module uses the prediction error result of the corrected grey model to establish the grey model process and complete the electricity consumption prediction of the grey Markov model.
9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the method for predicting electricity consumption based on the grey Markov model described in any one of claims 1 to 7 are implemented.
10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method for predicting electricity consumption based on a grey Markov model described in any one of claims 1 to 7 are implemented.