A method for predicting thermal load by combining building thermal processes and subspace identification models

Abstract

The application discloses a heat load prediction method combining a building heat process and a subspace identification model, and belongs to the field of heat load prediction. The method firstly constructs a state space model of the building according to a building heat process mechanism, takes the outdoor temperature, instantaneous heat supply and the indoor temperature of the observable room in the building as historical data, and identifies the coefficient matrix in the state space model by using a subspace identification model. The state space model with the identified coefficient matrix is a prediction model, and the heat load of the building and the indoor average temperature can be predicted according to the predicted value of the outdoor temperature. The application combines the mechanism model of the building heat process and the subspace identification model, identifies the parameters in the mechanism model by using the latter, and specifies the state variable as the indoor average temperature of the building, so that the heat load and the indoor average temperature of the building can be predicted according to the predicted value of the outdoor temperature.

Description

Technical Field

[0001] This invention belongs to the field of heat load prediction, specifically relating to a method for predicting building heat load by combining building thermal processes and subspace identification models. This method is also applicable to predicting the heat load of regional heat exchange stations that serve multiple buildings. Background Technology

[0002] Heating systems play a crucial role in my country's efforts to achieve carbon emission reduction goals. On the one hand, the proportion of renewable energy in the heating energy structure is gradually increasing, raising the instability of heating supply. On the other hand, user-controlled adjustment equipment is becoming increasingly sophisticated, and the demand for self-regulation is constantly rising, increasing demand-side flexibility. To save energy, one of the goals of intelligent heating is to mitigate the contradiction between the instability of heat supply and the high flexibility of demand, achieving a dynamic balance between supply and demand. Due to the thermal inertia of heat users, heating networks, and heat sources, to achieve this dynamic balance, the heating regulation and control system must rely on predicting future heat loads and adjusting the heat supply in advance, thereby reducing the impact of thermal inertia on the supply-demand balance. Therefore, heat load forecasting is a prerequisite for supply-demand balance and one of the fundamental tasks for achieving carbon reduction in heating systems.

[0003] Existing building heat load prediction methods can be categorized into two types: mechanistic models and data-driven models. Mechanistic models rely on the accuracy of their model parameters, but the theoretical values ​​of these parameters often deviate significantly from actual values, leading to high prediction distortion. Data-driven models, on the other hand, depend on the completeness of historical data; if unexpected stimuli or disturbances occur, the predictions may be misleading. Combining the approaches of mechanistic and data-driven models can leverage their respective strengths. Current integrated methods suffer from drawbacks such as the complexity of mechanistic models and the cumbersome parameter identification process, while subspace identification algorithms, with their relatively simpler identification processes, only predict output variables while state variables lack physical meaning. Summary of the Invention

[0004] This invention addresses the need for heat load prediction in heating systems by providing a building heat load prediction method that combines building thermal processes and a subspace identification model. The method first constructs a state-space model of the building based on the building thermal process mechanism, with the average indoor temperature as the state variable. Historical data are used, including outdoor temperature, instantaneous heat supply, and the indoor temperature of observable rooms within the building. A subspace identification model is then used to identify the coefficient matrix in the state-space model. Substituting the identified coefficient matrix into the state-space model yields the prediction model. Based on the predicted outdoor temperature, the building's heat load and average indoor temperature can be predicted. The required duration of historical data for the prediction period of i future cycles is specified.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] A method for predicting heat load that combines building thermal processes and subspace identification models, the method being as follows:

[0007] Step 1: Constructing a state-space model based on building thermal processes

[0008] The thermal process of a heated building is described using the lumped parameter method of a single mass point. The increase in the internal energy of a building mass point equals the net heat gain, as shown in the following equation:

[0009]

[0010] Where I represents the building complex heat capacity, including the heat capacity of indoor air, building envelope, and household appliances, in J / K; t in τ is the average indoor temperature of the building complex, in °C; Q is the heat supply of the building complex per unit time, in W; W is the net heat loss of the building complex per unit time under a unit temperature difference between indoors and outdoors, including heat transfer from the building envelope, heat loss due to cold air infiltration, and heat gain due to solar radiation, in W; t out Outdoor temperature, °C;

[0011] The building heat load calculation model is as follows:

[0012] H = h(t) in -t out (2)

[0013] Where H is the building group heat load in W; h is the building group heat load per unit temperature difference between indoors and outdoors in W / K;

[0014] Let t in Let x be the state variable, [Q t] out ] T Let u be the input variable and H be the output variable y. The above equations for indoor temperature change and building heat load can be written in state-space model form as follows:

[0015]

[0016] in, It is the differential of the state variable x with respect to time. C0 = h and D0 = [0 - h] are coefficient matrices, where W, I and h can all be obtained from the above coefficient matrices;

[0017] Step 2: Discretize the state-space model

[0018] Before parameter identification, the above continuous state-space model is discretized as follows:

[0019]

[0020] Where A = E + TA0, B = TB0, C = C0, D = D0; T is the sampling period; E is the identity matrix; k is the current time, (k+1) is the predicted future time; the prediction duration t = T; x(k+1) is the x element at time k+1;

[0021] Step 3: Subspace Identification Model

[0022] Different state variables are transformed using non-singular linear transformation. Based on this characteristic and the state-space model (4), the historical time series data of input u and output y are used as known quantities to characterize the coefficient matrix identification of the equivalent building thermal process and building heat transfer. The known quantities include: heat supply Q per unit time of the building complex and outdoor temperature t. out Building complex heat load H;

[0023] Step 4: Heat Load Forecast

[0024] Substituting the identification result (18) into the state space model (4) yields the heat load prediction model;

[0025]

[0026] Based on the current state variable x(2M+N-2) and the input u(2M+N-2), the indoor average temperature x(2M+N-1) for the next period is predicted through the state equation, and the building heat load y(2M+N-1) for the next period is predicted through the output equation. This process is repeated iteratively to obtain the indoor average temperature and heat load of the building for the next i periods.

[0027] Furthermore, in step three, the identification steps for the coefficient matrix characterizing the equivalent building thermal process and building heat transfer are as follows:

[0028] (1) Reconstruction of state-space model

[0029] Based on equation (4), a state-space model is established, where x is the state variable specified by the model, and its physical meaning is the average indoor temperature of the building. Let the state variable x′ be the identified state variable of the reconstructed model, and the system output y′ be the average indoor temperature and heat load of the building complex, i.e., y′=[xy]. T As shown in the following formula:

[0030]

[0031] Among them, A1, B1, C1, and D1 are the coefficient matrices of the new state-space model (5);

[0032] Identify the mutual transformation between the state variable x and the model-specified state variable x′ through a non-singular linear transformation, i.e.

[0033] x′=Px (6)

[0034] Where P is the transformation matrix;

[0035] (2) Definition of a matrix

[0036] Using outdoor temperature, instantaneous heating, and indoor temperature of observable rooms in the building as historical data, the coefficient matrix in the state space (5) is identified.

[0037] The generalized observable matrix Γ′ can be obtained from the relationship between the coefficient matrices A1 and C1 of the state-space model. M And define the lower triangular Toeplitz matrix H′ M As follows, where Γ′ M and H′ M The right subscript M represents the row number of the matrix equation;

[0038]

[0039] Based on the input u and the output y′, construct the M×N dimensional Hankel matrix Y′. p U p and Y′ f U f M must be at least greater than the order of the system. Since equation (1) is a first-order differential equation, this invention takes M = 2; N is determined according to the training sample size, as follows:

[0040]

[0041]

[0042] Among them, U p and Y′ p These are referred to as past inputs and outputs, U f and Y′ f These are referred to as future inputs and outputs;

[0043] Define the future state variable X′ f for:

[0044] X′ f =[x′(M) x′(M+1) … x′(M+N-1)] (10)

[0045] Combining equations (5), (7), (9), and (10), we can obtain the matrix equation:

[0046] Y f ′=Γ′ M X′ f +H′ M U′ f (11)

[0047] (3) Trigonometric (LQ) decomposition

[0048] make For U p 、Y′ p U f and Y′ f The LQ decomposition is performed as follows:

[0049]

[0050] According to the theory of zero-input response of a system, R... 33 =0, therefore, from equation (12) we can obtain

[0051]

[0052] Where the superscript + denotes the Moore-Penrose generalized inverse of the matrix;

[0053] Combining equations (11) and (13) yields the state variable matrix X′. f The calculation formula is as follows:

[0054]

[0055] (4) Singular Value Decomposition (SVD)

[0056] From the relationship between a matrix and its rank, we know that Γ′ M The column space is equal to R 32 The column space for R 32 Γ′ can be obtained by performing SVD decomposition. M As shown in the following formula:

[0057]

[0058] According to the theory of oblique projection, the column space of U1 is related to Γ′. M The column spaces are consistent, therefore Γ′ M =U1;

[0059] The future state variable X′ can be calculated using equation (14). f ,Right now:

[0060] X′ f =[x′(M) x′(M+1) … x′(M+N-1)]

[0061] At this point, by identifying the state variable x′ and the building average temperature x, the non-odd anomaly transformation matrix P can be calculated according to equation (6);

[0062] (5) System matrix identification

[0063] Identify the coefficient matrix, let

[0064] X′ f,M+1 =[x′(M+1) … x′(M+N-1)]

[0065] X′ f,M =[x′(M) … x′(M+N-2)]

[0066] U M =[u(M) … u(M+N-2)]

[0067] U M+1 =[u(M+1) … u(M+N-1)]

[0068] Y′ M+1 =[y′(M+1) … y′(M+N-1)]

[0069] get:

[0070]

[0071] Among them, D 1,2 =[0 -h′ s ];C1=[C 1,1 C 1,2 ] T ;D1=[D 1,1 D 1,2 ] T ;

[0072] Solving equation (16) using the least squares method yields the system matrix in the state-space model (5).

[0073] Therefore, the state-space model (5) can be written in the following form:

[0074]

[0075] Combining equations (4) and (17), the coefficient matrix of the state-space model (4) is obtained as follows:

[0076]

[0077] The advantages of this invention over the prior art are as follows:

[0078] (1) The method of combining the mechanism model and the data-driven model not only reduces the distortion caused by the inaccuracy of the mechanism model parameters, but also avoids the erroneous prediction caused by the incomplete historical data of the data-driven model. Moreover, the mechanism model is simple, the model parameter identification process is concise and clear, and the predicted output variables and state variables correspond one-to-one with the building heat load and the building indoor average temperature, respectively, with clear physical meaning.

[0079] (2) Using a subspace identification model, the average indoor temperature of the building can be predicted at the same time as the building heat load.

[0080] (3) This method can predict the heat load and average indoor temperature of a single building or building complex in the next i-th period. It can be used as the set value of the heat load in the heating regulation and control system of a single building heating system, a building heating station in a centralized heating system, and a district heating station in the future to evaluate the living comfort.

[0081] (4) Combine the mechanism model and subspace identification model of building thermal process, and use the latter to identify the parameters in the mechanism model;

[0082] (5) The subspace identification model specifies the state variable as the building's indoor average temperature, and can predict the heat load and the building's indoor average temperature based on the predicted outdoor temperature. Attached Figure Description

[0083] Figure 1 This is a flowchart of the method of the present invention. Detailed Implementation

[0084] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments, but it is not limited thereto. Any modifications or equivalent substitutions to the technical solution of the present invention that do not depart from the spirit and scope of the technical solution of the present invention should be covered within the protection scope of the present invention.

[0085] Example 1:

[0086] A method for predicting heat load that combines building thermal processes and subspace identification models, the method being as follows:

[0087] Step 1: Constructing a state-space model based on building thermal processes

[0088] The thermal process of a heated building is described using the lumped parameter method of a single mass point. The increase in the internal energy of a building mass point equals the net heat gain, as shown in the following equation:

[0089]

[0090] Where I represents the building complex heat capacity, including the heat capacity of indoor air, building envelope, and household appliances, in J / K; t in τ is the average indoor temperature of the building complex, in °C; Q is the heat supply of the building complex per unit time, in W; W is the net heat loss of the building complex per unit time under a unit temperature difference between indoors and outdoors, including heat transfer from the building envelope, heat loss due to cold air infiltration, and heat gain due to solar radiation, in W; t out Outdoor temperature, °C;

[0091] The building heat load calculation model is as follows:

[0092] H = h(t) in -t out (2)

[0093] Where H is the building group heat load in W; h is the building group heat load per unit temperature difference between indoors and outdoors in W / K;

[0094] Let t in Let x be the state variable, [Q t] out ] T Let u be the input variable and H be the output variable y. The above equations for indoor temperature change and building heat load can be written in state-space model form as follows:

[0095]

[0096] in, It is the differential of the state variable x with respect to time. C0 = h and D0 = [0 - h] are coefficient matrices, where W, I and h can all be obtained from the above coefficient matrices;

[0097] Step 2: Discretize the state-space model

[0098] Before parameter identification, the above continuous state-space model is discretized as follows:

[0099]

[0100] Where A = E + TA0, B = TB0, C = C0, D = D0; T is the sampling period; E is the identity matrix; k is the current time, (k+1) is the predicted future time; the prediction duration t = T; x(k+1) is the x element at time k+1;

[0101] Step 3: Subspace Identification Model

[0102] Different state variables are transformed using non-singular linear transformation. Based on this characteristic and the state-space model (4), the historical time series data of input u and output y are used as known quantities to characterize the coefficient matrix of equivalent building thermal process and building heat transfer. The known quantities include: heat supply Q per unit time of the building complex and outdoor temperature t. out The heat load H of the building complex; the identification steps are as follows:

[0103] (1) Reconstruction of state-space model

[0104] Based on equation (4), a state-space model is established, where x is the state variable specified by the model, and its physical meaning is the average indoor temperature of the building. Let the state variable x′ be the identified state variable of the reconstructed model, and the system output y′ be the average indoor temperature and heat load of the building complex, i.e., y′=[xy]. TAs shown in the following formula:

[0105]

[0106] Among them, A1, B1, C1, and D1 are the coefficient matrices of the new state-space model (5);

[0107] Identify the mutual transformation between the state variable x and the model-specified state variable x′ through a non-singular linear transformation, i.e.

[0108] x′=Px (6)

[0109] Where P is the transformation matrix;

[0110] (2) Definition of a matrix

[0111] Using outdoor temperature, instantaneous heating, and indoor temperature of observable rooms in the building as historical data, the coefficient matrix in the state space (5) is identified.

[0112] The generalized observable matrix Γ′ can be obtained from the relationship between the coefficient matrices A1 and C1 of the state-space model. M And define the lower triangular Toeplitz matrix H′ M As follows, where Γ′ M and H′ M The right subscript M represents the row number of the matrix equation;

[0113]

[0114] Based on the input u and the output y′, construct the M×N dimensional Hankel matrix Y′. p U p and Y′ f U f M must be at least greater than the order of the system. Since equation (1) is a first-order differential equation, this invention takes M = 2; N is determined according to the training sample size, as follows:

[0115]

[0116]

[0117] Among them, U p and Y′ p These are referred to as past inputs and outputs, U f and Y′ f These are referred to as future inputs and outputs;

[0118] Define the future state variable X′ f for:

[0119] X′ f=[x′(M) x′(M+1) … x′(M+N-1)] (10)

[0120] Combining equations (5), (7), (9), and (10), we can obtain the matrix equation:

[0121] Y f ′=Γ′ M X′ f +H′ M U′ f (11)

[0122] (3) Trigonometric (LQ) decomposition

[0123] make For U p 、Y′ p U f and Y′ f The LQ decomposition is performed as follows:

[0124]

[0125] According to the theory of zero-input response of a system, R... 33 =0, therefore, from equation (12) we can obtain

[0126]

[0127] Where the superscript + denotes the Moore-Penrose generalized inverse of the matrix;

[0128] Combining equations (11) and (13) yields the state variable matrix X′. f The calculation formula is as follows:

[0129]

[0130] (4) Singular Value Decomposition (SVD)

[0131] From the relationship between a matrix and its rank, we know that Γ′ M The column space is equal to R 32 The column space for R 32 Γ′ can be obtained by performing SVD decomposition. M As shown in the following formula:

[0132]

[0133] According to the theory of oblique projection, the column space of U1 is related to Γ′. M The column spaces are consistent, therefore Γ′ M =U1;

[0134] The future state variable X′ can be calculated using equation (14). f,Right now:

[0135] X′ f =[x′(M) x′(M+1) … x′(M+N-1)]

[0136] At this point, by identifying the state variable x′ and the building average temperature x, the non-odd anomaly transformation matrix P can be calculated according to equation (6);

[0137] (5) System matrix identification

[0138] Identify the coefficient matrix, let

[0139] X′ f,M+1 =[x′(M+1) … x′(M+N-1)]

[0140] X′ f,M =[x′(M) … x′(M+N-2)]

[0141] U M =[u(M) … u(M+N-2)]

[0142] U M+1 =[u(M+1) … u(M+N-1)]

[0143] Y′ M+1 =[y′(M+1) … y′(M+N-1)]

[0144] get:

[0145]

[0146] Among them, D 1,2 =[0 -h′ s ];C1=[C 1,1 C 1,2 ] T ;D1=[D 1,1 D 1,2 ] T ;

[0147] Solving equation (16) using the least squares method yields the system matrix in the state-space model (5).

[0148] Therefore, the state-space model (5) can be written in the following form:

[0149]

[0150] Combining equations (4) and (17), the coefficient matrix of the state-space model (4) is obtained as follows:

[0151]

[0152] Step 4: Heat Load Forecast

[0153] Substituting the identification result (18) into the state space model (4) yields the heat load prediction model;

[0154]

[0155] Based on the current state variable x(2M+N-2) and the input u(2M+N-2), the indoor average temperature x(2M+N-1) for the next period is predicted through the state equation, and the building heat load y(2M+N-1) for the next period is predicted through the output equation. This process is repeated iteratively to obtain the indoor average temperature and heat load of the building for the next i periods.

Claims

1. A method for predicting heat load by combining building thermal processes and subspace identification models, characterized in that: The method is as follows: Step 1: Constructing a state-space model based on building thermal processes The thermal process of a heated building is described using the lumped parameter method of a single mass point. The increase in the internal energy of a building mass point equals the net heat gain, as shown in the following equation: Where I represents the building complex heat capacity, including the heat capacity of indoor air, building envelope, and household appliances, in J / K; t in τ is the average indoor temperature of the building complex, in °C; Q is the heat supply of the building complex per unit time, in W; W is the net heat loss of the building complex per unit time under a unit temperature difference between indoors and outdoors, including heat transfer from the building envelope, heat loss due to cold air infiltration, and heat gain due to solar radiation, in W; t out Outdoor temperature, °C; The building heat load calculation model is as follows: H=h(t in -t out ) (2) Where H is the building group heat load in W; h is the building group heat load per unit temperature difference between indoors and outdoors in W / K; Let t in Let x be the state variable, [Q t] out ] T Let u be the input variable and H be the output variable y. The above equations for indoor temperature change and building heat load can be written in state-space model form as follows: in, It is the differential of the state variable x with respect to time. C0 = h and D0 = [0-h] are coefficient matrices, where W, I and h can all be obtained from the above coefficient matrices; Step 2: Discretize the state-space model Before parameter identification, the above continuous state-space model is discretized as follows: Where A = E + TA0, B = TB0, C = C0, D = D0; T is the sampling period; E is the identity matrix; k is the current time, (k+1) is the predicted future time; the prediction duration t = T; Step 3: Subspace Identification Model Different state variables are transformed using non-singular linear transformation. Based on this characteristic and the state-space model (4), the historical time series data of input u and output y are used as known quantities to characterize the coefficient matrix identification of the equivalent building thermal process and building heat transfer. The known quantities include: heat supply Q per unit time of the building complex and outdoor temperature t. out Building complex heat load H; Step 4: Heat Load Forecast Substituting the identification results into the state-space model (4) yields the heat load prediction model; Based on the current state variable x(2M+N-2) and the input u(2M+N-2), the indoor average temperature x(2M+N-1) for the next period is predicted through the state equation, and the building heat load y(2M+N-1) for the next period is predicted through the output equation. This process is repeated iteratively to obtain the indoor average temperature and heat load of the building for the next i periods.

2. The heat load prediction method combining building thermal processes and subspace identification models according to claim 1, characterized in that: In step three, the identification steps for the coefficient matrix characterizing the equivalent building thermal process and building heat transfer are as follows: (1) Reconstruction of state-space model Based on equation (4), a state-space model is established, where x is the state variable specified by the model, and its physical meaning is the average indoor temperature of the building. Let the state variable x′ be the identified state variable of the reconstructed model, and the system output y′ be the average indoor temperature and heat load of the building complex, i.e., y′=[xy]. T As shown in the following formula: Among them, A1, B1, C1, and D1 are the coefficient matrices of the new state-space model (5); Identify the mutual transformation between the state variable x and the model-specified state variable x′ through a non-singular linear transformation, i.e. x′=Px (6) Where P is the transformation matrix; (2) Definition of a matrix Using outdoor temperature, instantaneous heating, and indoor temperature of observable rooms in the building as historical data, the coefficient matrix in the state space (5) is identified. The generalized observable matrix Γ′ can be obtained from the relationship between the coefficient matrices A1 and C1 of the state-space model. M And define the lower triangular Toeplitz matrix H′ M As follows, where Γ′ M and H′ M The right subscript M is the row number of the matrix equation; Based on the input u and the output y′, construct the M×N dimensional Hankel matrix Y′. p U p and Y′ f U f Where M must be at least greater than the order of the system, and N is determined based on the training sample size, as shown in the following formula: Among them, U p and Y′ p These are referred to as past inputs and outputs, U f and Y′ f These are referred to as future inputs and outputs; Define the future state variable X′ f for: X′ f =[x′(M) x′(M+1) … x′(M+N-1)] (10) Combining equations (5), (7), (9), and (10), we can obtain the matrix equation: Y f ′=Γ′ M X′ f +H′ M U′ f (11) (3) Trigonometric (LQ) decomposition make For U p 、Y′ p U f and Y′ f The LQ decomposition is performed as follows: According to the theory of zero-input response of a system, R... 33 =0, therefore, from equation (12) we can obtain Where the superscript + denotes the Moore-Penrose generalized inverse of the matrix; Combining equations (11) and (13) yields the state variable matrix X′. f The calculation formula is as follows: (4) Singular Value Decomposition (SVD) From the relationship between a matrix and its rank, we know that Γ′ M The column space is equal to R 32 The column space for R 32 Γ′ can be obtained by performing SVD decomposition. M As shown in the following formula: According to the theory of oblique projection, the column space of U1 is related to Γ′. M The column spaces are consistent, therefore Γ′ M =U1; The future state variable X′ can be calculated using equation (14). f ,Right now: X′ f =[x′(M) x′(M+1) … x′(M+N-1)] At this point, by identifying the state variable x′ and the building average temperature x, the non-odd anomaly transformation matrix P can be calculated according to equation (6); (5) System matrix identification Identify the coefficient matrix, let X′ f,M+1 =[x′(M+1) … x′(M+N-1)] X′ f,M =[x′(M) … x′(M+N-2)] U M = [u(M) … u(M+N-2)] U M+1 = [u(M+1) … u(M+N-1)] AND' M+1 =[y′(M+1) … y′(M+N-1)] get: Among them, D 1,2 =[0 -h′ s ];C1=[C 1,1 C 1,2 ] T ;D1=[D 1,1 D 1,2 ] T ; Solving equation (16) using the least squares method yields the system matrix in the state-space model (5). Therefore, the state-space model (5) can be written in the following form: Combining equations (4) and (17), the coefficient matrix of the state-space model (4) is obtained as follows:

Images