A method and system for analyzing the initial value information loss of a linear discrete system source

Abstract

The present invention discloses a method and system for analyzing the initial value information loss of a linear discrete system source. The method comprises establishing a linear discrete system model; establishing and optimizing the objective function of a linear discrete system minimum information loss dynamic state estimation based on the linear discrete system model; optimizing the objective function in combination with the characteristics of the linear discrete system, and outputting a state initial value source loss function model; analyzing the initial value information loss of the source of the state initial value source loss function model under preset state conditions; the present invention is based on a linear discrete system minimum information loss dynamic state estimation model, and is optimized in combination with the characteristics of the linear discrete system to obtain a state initial value source loss function; and analyzing the state initial value source loss function of the linear discrete system; the derivation process of the present invention quantifies the initial value part of the source loss of the linear discrete system, so as to facilitate the study of the initial value information loss of the source of the linear discrete system according to the minimum information loss state estimation model.

Description

Technical Field

[0001] The present invention belongs to the field of integrated energy systems, and in particular relates to a method and system for analyzing initial value information loss of a linear discrete system information source. Background Art

[0002] The integrated energy system has huge advantages in improving energy utilization efficiency, promoting the consumption of new energy, and reducing user energy consumption costs through the deep coupling of multiple energy forms such as electricity, heat, cold, and gas. It is the development trend of future energy systems.

[0003] In the field of power systems, the research and application of energy management systems (EMS) have been very mature. For integrated energy systems, in order to ensure that the energy system can operate safely, economically, green and efficiently, it is also necessary to establish a multi-energy flow integrated energy management system (IEMS) to achieve intelligent regulation of energy in the system.

[0004] In the field of integrated energy systems, for static state estimation methods, the minimum information loss state estimation of power systems can be imitated to give it informatics significance. However, for dynamic multi-section state estimation, the existing minimum information loss state estimation model research has not yet revealed its theoretical basis. It is impossible to study the initial value information loss of the source of linear discrete systems based on the existing minimum information loss state estimation model. Summary of the invention

[0005] In view of the above problems, on the one hand, the present invention discloses a method for analyzing the initial value information loss of a linear discrete system source, the method comprising:

[0006] Establishing the linear discrete system model;

[0007] Based on the linear discrete system model, the objective function of the dynamic state estimation of the linear discrete system with minimum information loss is established and optimized;

[0008] Combined with the characteristics of the linear discrete system, the objective function is optimized and a state initial value source loss function model is output;

[0009] The state condition is preset, and the information loss of the initial value of the state source loss function model is analyzed.

[0010] Furthermore, the step of establishing the linear discrete system model specifically includes:

[0011] A linear discrete system model is established, wherein the linear discrete system model is:

[0012]

[0013] in, They are the state quantity of the system, external disturbance, true value of measurement, and quantity measurement; To measure noise;

[0014] Define the initial time t0 to the current time t n The discrete time parameter set is T = {t0, t1, …, t n}, and set {x n}=x0,x1,…,x n , {ξ n}=ξ0,…,ξ n 、{z n}=z0,…,z n 、{v n}=v0,…,v n are respectively the set of state quantity, external interference, quantity measurement and measurement true value corresponding to the time parameter set T; n}=η0,…,η n is the set of measurement noises corresponding to the time parameter set T; the information source {u n}=u0,u1,…,u n It is the minimum set of unknown quantities at each moment that determines the true value of the system measurement.

[0015] Furthermore, the steps of establishing and optimizing the objective function of the linear discrete system minimum information loss dynamic state estimation based on the linear discrete system model specifically include:

[0016] Set a vector model, the vector model is:

[0017]

[0018] Based on the vector model, for all moments in T, we have:

[0019]

[0020] The values ​​of G and H are as follows:

[0021]

[0022] H=diag{C0,…,C n}.

[0023] Furthermore, the step of establishing and optimizing the objective function of the linear discrete system minimum information loss dynamic state estimation based on the linear discrete system model also includes:

[0024] Based on formula (1), combined with the maximum a posteriori probability estimate P(U n |Zn )Get X n The best estimate of :

[0025]

[0026] According to information theory, the optimal estimate is equivalent to minimizing conditional information:

[0027]

[0028] According to the principle of minimum information loss, the base value of conditional information is defined as given source The value of

[0029] The objective function of the dynamic state estimation of the linear discrete system with minimum information loss is obtained as follows:

[0030]

[0031] Furthermore, the step of optimizing the objective function in combination with the characteristics of the linear discrete system and outputting the state initial value source loss function model specifically includes:

[0032] According to the conditional probability density formula, calculate the source information loss function;

[0033] Based on the initial state value x0 and t n External disturbance at the moment W n The value characteristics of the source information loss function are optimized, and the optimized function is output;

[0034] Based on the optimization function, a state initial value source loss function model is output.

[0035] Furthermore, the step of calculating the source information loss function according to the conditional probability density formula specifically includes:

[0036] Define P(U n ∩Z n ) is U n and Z n The joint probability of

[0037] According to the conditional probability density formula for the joint probability conversion, the conditional probability density formula after conversion is set to formula (2), which is:

[0038]

[0039] According to formula (2), the source information loss function of the linear discrete system is defined as:

[0040]

[0041] Among them, P(U n ) and P(Z n ) are U n and Z n The marginal probability distribution of .

[0042] Furthermore, the initial state value x0 and t n External disturbance at the moment W n The steps of optimizing the objective function and outputting the optimized function specifically include:

[0043] According to the initial state value x0 and t n External disturbance at the moment W n The values ​​of are independent of each other, so we set the source U n The marginal probability distribution P(U n ) is: P(U n )=P(W n-1 )·P(x0);

[0044] The marginal probability distribution P(U n ) is substituted into the source information loss function, and the output optimization function is:

[0045]

[0046] Furthermore, the step of outputting the state initial value source loss function model based on the optimization function specifically includes:

[0047] Based on the optimization function, the state initial value source loss function of the linear discrete system is defined as:

[0048]

[0049] In the process of optimizing the state initial value source loss function, since the numerator of the logarithmic term of the state initial value source loss function is a constant, the value does not affect the optimization result, so the value is 1;

[0050] Since the state values ​​of linear discrete systems are all continuous, the probability density of the state is used instead of the probability of the state, and the output state initial value source loss function model is:

[0051] Furthermore, the preset state condition, the step of analyzing the information loss of the initial value source of the state initial value source loss function model specifically includes:

[0052] When the initial value x0 of the state satisfies the following conditions:

[0053] ④The initial value of the state x0 is unknown;

[0054] ⑤The initial state value x0 obeys uniform distribution;

[0055] ⑥The initial state value x0 is a given value;

[0056] Then the initial value loss of the source is IL SI =0;

[0057] When the initial state value x0 is a normally distributed random variable with a mean of The covariance matrix is ​​P0, and the initial value information loss of the source after ignoring the constant term is:

[0058]

[0059] On the other hand, the present invention also discloses a linear discrete system source initial value information loss analysis system, the system comprising:

[0060] A first building module is used to build the linear discrete system model;

[0061] The second establishment module is used to establish and optimize the objective function of the linear discrete system minimum information loss dynamic state estimation based on the linear discrete system model;

[0062] An optimization module, used to optimize the objective function in combination with the characteristics of the linear discrete system, and output a state initial value source loss function model;

[0063] The analysis module is used to preset state conditions and analyze the information loss of the initial value of the state source loss function model.

[0064] The present invention studies the basic theoretical problems of slow dynamic system state estimation in integrated energy systems from the perspective of information science. First, a source channel model of a linear discrete system is established, and a minimum information loss dynamic state estimation model is established; and based on the minimum information loss dynamic state estimation model of a linear discrete system, the linear discrete system characteristics are optimized to obtain the state initial value source loss function of the linear discrete system. The state initial value source loss function of the linear discrete system is analyzed; the derivation process of the present invention quantifies the initial value part of the source loss of the linear discrete system, which is convenient for studying the source initial value information loss of the linear discrete system according to the minimum information loss state estimation model.

[0065] Other features and advantages of the present invention will be described in the following description, and partly become apparent from the description, or understood by practicing the present invention. The purpose and other advantages of the present invention can be realized and obtained by the structures pointed out in the description, claims and drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0067] Figure 1 A schematic diagram of a process for calculating the initial value information loss of a linear discrete system information source according to an embodiment of the present invention is shown;

[0068] Figure 2 A source channel model of a linear discrete system according to an embodiment of the present invention is shown. DETAILED DESCRIPTION

[0069] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0070] The present invention proposes a method for analyzing the initial value information loss of a linear discrete system source. The flow chart of the method is as follows: Figure 1 As shown, the method includes:

[0071] Step 1: Establish the linear discrete system model;

[0072] The step 1 specifically includes the following contents:

[0073] Step 1.1: Establish a linear discrete system model, the linear discrete system model is:

[0074]

[0075] in, They are the state quantity of the system, external disturbance, i.e., the true value of the measurement, and the quantity measured; To measure noise;

[0076] Step 1.2: Define the initial time t0 to the current time t n The discrete time parameter set is T = {t0, t1, …, t n}, and set {x n}=x0,x1,…,x n , {ξ n}=ξ0,…,ξ n 、{z n}=z0,…,z n 、{v n}=v0,…,v n are respectively the set of state quantity, external interference, quantity measurement and measurement true value corresponding to the time parameter set T; n}=η0,…,η n is the set of measurement noises corresponding to the time parameter set T; the information source {u n}=u0,u1,…,u n To determine the minimum set of unknown quantities at each moment of the system measurement true value, refer to Figure 2 shown.

[0077] Step 2: Based on the linear discrete system model, establish and optimize the objective function of the linear discrete system minimum information loss dynamic state estimation;

[0078] The step 2 specifically includes the following contents:

[0079] Step 2.1: Set a vector model, the vector model is:

[0080]

[0081] Step 2.2: Based on the vector model, for all moments in T, we have:

[0082]

[0083] The values ​​of G and H are as follows:

[0084]

[0085] H=diag{C0,…,C n}

[0086] Step 2.3: Based on formula (1), combine the maximum a posteriori probability estimate P(U n |Z n )Get X n The best estimate of :

[0087]

[0088] Step 2.4: According to information theory, the optimal estimate is equivalently optimized to minimize conditional information:

[0089]

[0090] Step 2.5: According to the principle of minimum information loss, define the base value of conditional information as a given source The value of

[0091] Step 2.6: The objective function of the dynamic state estimation of the linear discrete system with minimum information loss is obtained as:

[0092]

[0093] Step 3: In combination with the characteristics of the linear discrete system, the objective function is optimized and the state initial value source loss function model is output;

[0094] The step 3 specifically includes the following contents:

[0095] Step 3.1: Calculate the source information loss function according to the conditional probability density formula;

[0096] Specifically,

[0097] Step 3.1.1: Define P(U n ∩Z n ) is U n and Z n The joint probability of

[0098] Step 3.1.2: According to the conditional probability density formula for the joint probability conversion, the converted conditional probability density formula is set to formula (2), and the formula (2) is:

[0099]

[0100] Step 3.1.3: According to formula (2), the source information loss function of the linear discrete system is defined as:

[0101]

[0102] Among them, P(U n ) and P(Z n ) are U n and Z n The marginal probability distribution of .

[0103] The step 3.1.3 specifically also includes:

[0104] Substituting formula (2) into the objective function, we can obtain the information loss function:

[0105]

[0106] in, It is only related to the information source, and the information loss function of the linear discrete system is defined as:

[0107]

[0108] Step 3.2: Based on the initial state values ​​x0 and t n External disturbance at the moment Wn The value characteristics of the target function are optimized, and the optimized function is output;

[0109] Specifically,

[0110] Step 3.2.1: According to the initial state value x0 and t n External disturbance at the moment W n The values ​​of are independent of each other. n The marginal probability distribution P(U n ) is: P(U n )=P(W n-1 )·P(x0);

[0111] Step 3.2.2: Substitute the marginal probability distribution P(U n ) is substituted into the source information loss function, and the output optimization function is:

[0112]

[0113] Step 3.3: Based on the optimization function, output the state initial value source loss function model.

[0114] Specifically,

[0115] Step 3.3.1: Based on the optimization function, define the state initial value source loss function of the linear discrete system as:

[0116]

[0117] In the process of optimizing the state initial value source loss function, since the numerator of the logarithmic term of the state initial value source loss function is a constant, the value does not affect the optimization result, so the value is 1;

[0118] Step 3.3.2: Since the state values ​​of linear discrete systems are all continuous quantities, the probability density of the state quantity is used instead of the probability of the state quantity, and the state initial value source loss function model is rewritten as:

[0119] Step 4: Preset state conditions and analyze the source initial value information loss of the state initial value source loss function model.

[0120] The step 4 specifically includes the following contents:

[0121] When the initial value x0 of the state satisfies the following conditions:

[0122] ⑦The initial value of the state x0 is unknown;

[0123] ⑧The initial state value x0 obeys uniform distribution;

[0124] ⑨The initial state value x0 is a given value;

[0125] Then the initial value loss of the source is IL SI =0;

[0126] When the initial state value x0 is a normally distributed random variable with a mean of The covariance matrix is ​​P0, and the initial value information loss of the source after ignoring the constant term is:

[0127]

[0128] In one embodiment of the present invention, the present invention further proposes a linear discrete system source initial value information loss analysis system, the system comprising:

[0129] A first building module is used to build the linear discrete system model;

[0130] The second establishment module is used to establish and optimize the objective function of the linear discrete system minimum information loss dynamic state estimation based on the linear discrete system model;

[0131] An optimization module, used to optimize the objective function in combination with the characteristics of the linear discrete system, and output a state initial value source loss function model;

[0132] The analysis module is used to preset state conditions and analyze the information loss of the initial value of the state source loss function model.

[0133] Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent substitutions for some of the technical features therein; and these modifications or substitutions do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A linear discrete system source initial value information loss analysis method for slow dynamic system state estimation in integrated energy systems, characterized in that: The method comprises: Establishing the linear discrete system model, the steps of establishing the linear discrete system model specifically include: A linear discrete system model is established, wherein the linear discrete system model is: in, They are the system state quantity, external interference, measurement truth value, and quantity measurement. To measure the noise, represents an n-dimensional real number, represents an m-dimensional real number, represents an l-dimensional real number, A k is the state matrix, F k is the input matrix, C k is the output matrix, The discrete time parameter set from the initial time t0 to the current time tn is defined as T = {t0, t1, ..., t n }, and set {x n }=x0,x1,…,x n , {ξ n }=ξ0,…,ξ n 、{z n }=z0,…,z n 、{v n }=v0,…,v n are the state quantity, external interference, quantity measurement and measurement true value corresponding to the time parameter set T, respectively, n }=η0,…,η n is the set of measurement noises corresponding to the time parameter set T, the source {u n }=u0,u1,…,u n The minimum set of unknown quantities at each moment that determines the true value of the system measurement; Based on the linear discrete system model, an objective function of the linear discrete system minimum information loss dynamic state estimation is established and optimized. The steps of establishing and optimizing the objective function of the linear discrete system minimum information loss dynamic state estimation based on the linear discrete system model specifically include: Set a vector model, the vector model is: Based on the vector model, for all moments in T, we have: The values ​​of G and H are as follows: H=diag{C0,…,C n } Among them, C0, C1...C n ∈C k ; A0, A1, ... A n ∈A k , I is the identity matrix, Based on formula (1), combined with the maximum a posteriori probability estimate P(U n |Z n )Get X n The best estimate of : According to information theory, the optimal estimate is equivalent to minimizing conditional information: According to the principle of minimum information loss, the base value of conditional information is defined as given source The value of The objective function of the dynamic state estimation of the linear discrete system with minimum information loss is obtained as follows: Combined with the characteristics of the linear discrete system, the objective function is optimized and a state initial value source loss function model is output; The state condition is preset, and the information loss of the initial value of the state source loss function model is analyzed.

2. The method according to claim 1, characterized in that The step of optimizing the objective function and outputting the state initial value source loss function model in combination with the characteristics of the linear discrete system specifically includes: According to the conditional probability density formula, the source information loss function is obtained; Based on the initial state value x0 and t n External disturbance at the moment W n The value characteristics of the source information loss function are optimized, and the optimized function is output; Based on the optimization function, a state initial value source loss function model is output.

3. The method according to claim 2, characterized in that The step of obtaining the source information loss function according to the conditional probability density formula specifically includes: Define P(U n ∩Z n ) is U n and Z n The joint probability of According to the conditional probability density formula for the joint probability conversion, the conditional probability density formula after conversion is set to formula (2), which is: According to formula (2), the source information loss function of the linear discrete system is defined as: Among them, P(U n ) and P(Z n ) are U n and Z n The marginal probability distribution of .

4. The method according to claim 3, characterized in that The initial state value x0 and t n External disturbance at the moment W n The steps of optimizing the objective function and outputting the optimized function specifically include: According to the initial state value x0 and t n External disturbance at the moment W n The values ​​of are independent of each other, so we set the source U n The marginal probability distribution P(U n ) is: P(U n )=P(W n-1 )·P(x0); The marginal probability distribution P(U n ) is substituted into the source information loss function, and the output optimization function is:

5. The method according to claim 4, characterized in that The step of outputting the state initial value source loss function model based on the optimization function specifically includes: Based on the optimization function, the state initial value source loss function of the linear discrete system is defined as: Among them, in the process of optimizing the state initial value source loss function, the probability density of the state quantity is used instead of the probability of the state quantity, and the output state initial value source loss function model is:

6. The method according to claim 1, characterized in that The step of analyzing the information loss of the initial value of the state source loss function model under the preset state condition specifically includes: When the value of the initial state x0 satisfies any of the following conditions: ①The initial value of the state x0 is unknown; ②The initial state value x0 obeys uniform distribution; ③The initial state value x0 is a given value; Then the initial value loss of the source is IL SI =0; When the initial state value x0 is a normally distributed random variable, the initial value information loss of the source after ignoring the constant term is: in, is the mean of the initial value of the system state, and P0 is the covariance matrix.

7. A linear discrete system source initial value information loss analysis system, used to implement a linear discrete system source initial value information loss analysis method, the method is used for slow dynamic system state estimation in a comprehensive energy system, characterized in that: The system comprises: The first building module is used to build a linear discrete system model, and the linear discrete system model is: in, They are the system state quantity, external interference, measurement truth value, and quantity measurement. To measure the noise, represents an n-dimensional real number, represents an m-dimensional real number, represents an l-dimensional real number, A k is the state matrix, F k is the input matrix, C k is the output matrix; The first establishment module is also used to define the initial time t0 to the current time t n The discrete time parameter set is T = {t0, t1, …, t n }, and set {x n }=x0,x1,…,x n , {ξ n }=ξ0,…,ξ n 、{z n }=z0,…,z n 、{v n }=v0,…,v n are the state quantity, external interference, quantity measurement and measurement true value corresponding to the time parameter set T, respectively, n }=η0,…,η n is the set of measurement noises corresponding to the time parameter set T, the source {u n }=u0,u1,…,u n The minimum set of unknown quantities at each moment that determines the true value of the system measurement; The second establishment module is used to establish and optimize the objective function of the linear discrete system minimum information loss dynamic state estimation based on the linear discrete system model, and is specifically used to set a vector model, and the vector model is: Based on the vector model, for all moments in T, we have: The values ​​of G and H are as follows: H=diag{C0,…,C n } Among them, C0, C1...C n ∈C k ; A0, A1, ... A n ∈A k , I is the identity matrix, Based on formula (1), combined with the maximum a posteriori probability estimate P(U n |Z n )Get X n The best estimate of : According to information theory, the optimal estimate is equivalent to minimizing conditional information: According to the principle of minimum information loss, the base value of conditional information is defined as given source The value of The objective function of the dynamic state estimation of the linear discrete system with minimum information loss is obtained as follows: An optimization module, used to optimize the objective function in combination with the characteristics of the linear discrete system, and output a state initial value source loss function model; The analysis module is used to preset state conditions and analyze the information loss of the initial value of the state source loss function model.

Images