A Method for Parameter Identification of Second-Order Model of Distributed Electric Heating Load

Abstract

This invention relates to a method for identifying parameters of a second-order model of a decentralized electric heating load. Its key feature is that it obtains the wall temperature T for model parameter identification through a second-order equivalent thermal parameter model equation. e (t) and indoor temperature T i The calculation formula for (t) was derived, and model parameters were identified. Through the determination and acquisition of model parameters, setting constraints and initializing model parameters, calculating fitness, and updating the particle swarm population, the globally optimal parameters were determined. This model has the advantages of good stability and high accuracy, and can obtain relatively accurate model parameters in a short time. It establishes a decentralized electric heating load model that can accurately predict users' indoor temperatures, providing a good model foundation for decentralized electric heating loads to participate in grid regulation.

Description

Technical Field

[0001] This invention pertains to electric heating and is a method for identifying parameters of a second-order model of a decentralized electric heating load. Background Technology

[0002] Electric heating loads, as clean heating devices, account for a large proportion of daily life. They are easy to control, have a fast response time, and changes in their operating state on a short timescale do not affect user comfort. Therefore, they have significant potential to participate in grid regulation and represent a high-quality demand response resource. Accurately identifying their model parameters can improve the accuracy of the established decentralized electric heating load model, thereby enabling the formulation of reasonable control strategies. Existing research commonly uses the first-order equivalent thermal parameter (ETP) model for decentralized electric heating loads. However, the parameters of the first-order model are overly simplified, making it difficult to accurately describe changes in indoor temperature. Furthermore, the adjustability of the decentralized electric heating load assessed using this model has low accuracy, failing to meet the accuracy requirements of the power grid. In addition, the second-order model has more parameters and more complex equations than the first-order model, making parameter identification more difficult. Considering the problems in current research, this invention proposes a method for identifying the parameters of the second-order equivalent model of decentralized electric heating loads based on an improved particle swarm optimization algorithm. By leveraging the advantages of improved particle swarm optimization (PSO) algorithm, such as good stability and short convergence time, model parameter identification is effectively solved, thus addressing the difficulty of model parameter identification. Summary of the Invention

[0003] The technical problem to be solved by the present invention is to overcome the shortcomings of the prior art and provide an accurate method for identifying second-order model parameters of distributed electric heating loads, which effectively solves the problem of difficulty in identifying model parameters.

[0004] The solution adopted by this invention to solve the technical problem is: a method for identifying second-order model parameters of decentralized electric heating load, characterized in that: the wall temperature T used for model parameter identification is obtained through the second-order equivalent thermal parameter model equation. e (t) and indoor temperature T i The calculation formula for (t) is then used to identify the model parameters. The specific steps are as follows:

[0005] 1) Obtain the wall temperature T for model parameter identification using the second-order equivalent thermal parameter model equation. e (t) and indoor temperature T i Formula for calculating (t)

[0006] ① The second-order equivalent thermal parameter model of the decentralized electric heating load is represented by a set of differential equations, as shown in formula (1):

[0007]

[0008] In the formula, T i Indoor temperature, unit: °C; T o Outdoor ambient temperature, unit: °C; T e Indicates wall temperature, unit: °C; R io Indicates the thermal resistance of indoor and outdoor air heat exchange, unit: ℃ / W; R oe R represents the thermal resistance between outdoor air and the wall, measured in °C / W. ie Indicates the thermal resistance between indoor air and the wall, unit: ℃ / W; C e This indicates the wall's heat capacity, measured in J / ℃; C. i Indicates the heat capacity of indoor air, unit: J / ℃; P h This indicates the operating power of the decentralized electric heating system, in watts (W).

[0009] ②The differential equation formula (1) has a state-space expression in continuous time, as shown in formula (2):

[0010]

[0011] In the formula: x(t) is T e (t) and T i The model state vector consists of u(t) and u(t) is T. o (t) and P h The model input vector consists of (t), where A and B are R. io R oe R ie C e C i The model parameter matrix is ​​composed of;

[0012] ③ Discretize equation (2) to obtain the state-space equation as shown in equation (3):

[0013] x(t+Δt)-x(t)=[Ax(t)+Bu(t)]Δt (3)

[0014] In the formula: x(t+Δt) is T e (t+Δt) and T i The model state vector consists of (t+Δt), where Δt is the sampling period.

[0015] ④ The second-order model equations are transformed to obtain the discretized formulas for the wall temperature change and indoor temperature change in the second-order equivalent thermal model of the distributed electric heating load, as shown in formula (4):

[0016]

[0017] ⑤ At the same time, the wall temperature T e(t) and indoor temperature T i The recursive formula for (t) is expressed in the form of formula (5):

[0018]

[0019] ⑥ Substitute formula (4) into formula (5) to obtain the wall temperature T used for model parameter identification. e (t) and indoor temperature T i The formula for calculating (t) is shown in formula (6):

[0020]

[0021] 2) Model parameter identification

[0022] ① Determining model parameters

[0023] The model parameters are determined based on the second-order equivalent thermal parameter model of the decentralized electric heating load:

[0024] The model input data is the measured initial indoor temperature T. ia (1) Initial temperature of the wall T e (1) Outdoor ambient temperature T o (t), Distributed electric heating operating power P h ;

[0025] The model outputs indoor temperature T. i (t), wall temperature T e (t);

[0026] The parameter to be identified in the model is the thermal resistance R of indoor and outdoor air heat exchange. io Thermal resistance R between outdoor air and wall oe Thermal resistance R between indoor air and walls ie Wall heat capacity C e Indoor air heat capacity C i ;

[0027] ② Model parameter acquisition

[0028] Use smart devices to acquire model parameters to identify the required data, and preprocess the data;

[0029] ③ Initialize the model parameters

[0030] a) Determine the thermal resistance R of indoor and outdoor air heat exchange based on the actual physical properties of the building. io Thermal resistance R between outdoor air and wall oe Thermal resistance R between indoor air and walls ie Wall heat capacity C e Indoor air heat capacity C i The range of parameter values;

[0031] b) Use the upper and lower limits of the value range as the upper and lower limits of the solution interval for the parameters of the improved particle swarm optimization algorithm, respectively;

[0032] c) Assign values ​​to the number of particles, population size, and initial velocity of the particle swarm, and provide a set of random values ​​as the initial positions of the particles within the solution interval;

[0033] ④ Calculation of fitness

[0034] a) Based on randomly generated parameters to be identified, the indoor and outdoor air heat exchange thermal resistance R io Thermal resistance R between outdoor air and wall oe Thermal resistance R between indoor air and walls ie Wall heat capacity C e Indoor air heat capacity C i The simulated temperature T is obtained using the second-order equivalent thermal parameter model equation. i (t);

[0035] b) Collect the user's actual indoor temperature T through smart devices ia (t);

[0036] c) Combine the optimization objective function based on the least squares criterion to calculate the particle fitness, as shown in formula (7):

[0037]

[0038] ⑤ Particle Swarm Population Update

[0039] a) If the number of iterations does not reach the maximum number of iterations, the particle swarm inertia weights are updated according to formula (8);

[0040]

[0041] In the formula: k represents the iteration number, w(k) represents the inertia weight at the k-th iteration, w max and w min T represents the maximum and minimum inertia weights, respectively. max Indicates the maximum number of iterations;

[0042] b) Update the particle velocity, calculated according to formula (9):

[0043]

[0044] In the formula: v i (k) represents the velocity of particle i in the k-th iteration, x i (k) represents the position of particle i in the k-th iteration, c1 and c2 are non-negative constants, and rand1 and rand2 are random numbers between 0 and 1; pbesti represents the optimal position of particle i, and gbest represents the global optimal position of particle i;

[0045] c) Update particle positions according to formula (10):

[0046] x i (k+1)=x i (k)+v i (k) (10)

[0047] ⑥ Determine the globally optimal parameters

[0048] The optimal particle position and the global optimal position are updated by combining the fitness function. It is then determined whether a pre-set termination condition is met. If the termination condition is met, the optimal parameters are output. If the termination condition is not met, steps 3 and 4 are returned to continue the optimization process to generate the optimal parameters for the simulation temperature T. i (t) and measured temperature T ia Particles with smaller errors between (t) are selected until the termination condition is met, and the globally optimal indoor-outdoor air heat exchange thermal resistance R is output. io Thermal resistance R between outdoor air and wall oe Thermal resistance R between indoor air and walls ie Wall heat capacity C e Indoor air heat capacity C i until.

[0049] The beneficial effects of this invention are: the proposed second-order decentralized electric heating load model parameter identification method has good stability and high accuracy, and can obtain relatively accurate model parameters in a short time, establishing a decentralized electric heating load model that can accurately predict users' indoor temperature, providing a good model foundation for decentralized electric heating loads to participate in grid regulation. Attached Figure Description

[0050] Figure 1 This is a flowchart of the method for identifying parameters of a second-order model of a distributed electric heating load according to the present invention.

[0051] Figure 2 This is a flowchart of the model parameter identification method for the second-order model parameter identification method of the decentralized electric heating load of the present invention;

[0052] Figure 3 The figure shows a comparison between the simulation results of the equivalent thermal parameter model and the measured temperature at an outdoor temperature of -10℃.

[0053] Figure 4 The figure shows a comparison between the simulation results of the equivalent thermal parameter model and the measured temperature at an outdoor temperature of -15℃.

[0054] Figure 5Comparison of simulated and measured temperatures under different outdoor temperatures using equivalent thermal parameter models. Detailed Implementation

[0055] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0056] See Figures 1-5 Example 1: To verify the effectiveness and feasibility of the second-order model parameter identification method for decentralized electric heating loads of the present invention, a decentralized electric heating load operation simulation experimental platform was built for collecting parameter identification data. The experimental platform was arranged to resemble a real-life scenario, and the main equipment included a thermostat, an operation status recorder, a wireless temperature sensor, a WiFi transmitter, a smart switch, an outdoor environment simulation device, and a room model.

[0057] The simulation experiment conditions are set as follows: the outdoor temperature is set to -15℃ and -10℃ respectively, and the indoor temperature control range is set to 18℃~22℃.

[0058] This embodiment presents a method for identifying second-order model parameters of a decentralized electric heating load. It obtains the wall temperature T for model parameter identification through a second-order equivalent thermal parameter model equation. e (t) and indoor temperature T i The calculation formula for (t) is then used to identify the model parameters. The specific steps are as follows:

[0059] 1) Obtain the wall temperature T for model parameter identification using the second-order equivalent thermal parameter model equation. e (t) and indoor temperature T i Formula for calculating (t)

[0060] ① The second-order equivalent thermal parameter model of the decentralized electric heating load is represented by a set of differential equations, as shown in formula (1):

[0061]

[0062] In the formula, T i Indoor temperature, unit: °C; T o Outdoor ambient temperature, unit: °C; T e Indicates wall temperature, unit: °C; R io Indicates the thermal resistance of indoor and outdoor air heat exchange, unit: ℃ / W; R oe R represents the thermal resistance between outdoor air and the wall, measured in °C / W. ie Indicates the thermal resistance between indoor air and the wall, unit: ℃ / W; C e This indicates the wall's heat capacity, measured in J / ℃; C. i Indicates the heat capacity of indoor air, unit: J / ℃; P h Indicates the operating power of decentralized electric heating;

[0063] ②The differential equation formula (1) has a state-space expression in continuous time, as shown in formula (2):

[0064]

[0065] In the formula: x(t) is T e (t) and T i The model state vector consists of u(t) and u(t) is T. o (t) and P h The model input vector consists of (t), where A and B are R. io R oe R ie C e C i The model parameter matrix is ​​composed of;

[0066] ③ Discretize equation (2) to obtain the state-space equation as shown in equation (3):

[0067] x(t+Δt)-x(t)=[Ax(t)+Bu(t)]Δt (3)

[0068] In the formula: x(t+Δt) is T e (t+Δt) and T i The model state vector consists of (t+Δt), where Δt is the time interval.

[0069] ④ The second-order model equations are transformed to obtain the discretized formulas for the wall temperature change and indoor temperature change in the second-order equivalent thermal model of the distributed electric heating load, as shown in formula (4):

[0070]

[0071] ⑤ At the same time, the wall temperature T e (t) and indoor temperature T i The recursive formula for (t) is expressed in the form of formula (5):

[0072]

[0073] ⑥ Substitute formula (4) into formula (5) to obtain the wall temperature T used for model parameter identification. e (t) and indoor temperature T i The formula for calculating (t) is shown in formula (6):

[0074]

[0075] 2) Model parameter identification

[0076] ① Determining model parameters

[0077] The model parameters are determined based on the second-order equivalent thermal parameter model of the decentralized electric heating load:

[0078] The model input data is the measured initial indoor temperature T. ia (1) Initial temperature of the wall T e (1) Outdoor ambient temperature T o (t), Distributed electric heating operating power P h ;

[0079] The model outputs indoor temperature T. i (t), wall temperature T e (t);

[0080] The parameter to be identified in the model is the thermal resistance R of indoor and outdoor air heat exchange. io Thermal resistance R between outdoor air and wall oe Thermal resistance R between indoor air and walls ie Wall heat capacity C e Indoor air heat capacity C i ;

[0081] ② Model parameter acquisition

[0082] Use smart devices to acquire model parameters to identify the required data, and preprocess the data;

[0083] ③ Initialize the model parameters

[0084] a) Determine the thermal resistance R of indoor and outdoor air heat exchange based on the actual physical properties of the building. io Thermal resistance R between outdoor air and wall oe Thermal resistance R between indoor air and walls ie Wall heat capacity C e Indoor air heat capacity C i The range of parameter values;

[0085] b) Use the upper and lower limits of the value range as the upper and lower limits of the solution interval for the parameters of the improved particle swarm optimization algorithm, respectively;

[0086] c) Assign values ​​to the number of particles, population size, and initial velocity of the particle swarm, and provide a set of random values ​​as the initial positions of the particles within the solution interval;

[0087] ④ Calculation of fitness

[0088] a) Based on randomly generated parameters to be identified, the indoor and outdoor air heat exchange thermal resistance R io Thermal resistance R between outdoor air and wall oe Thermal resistance R between indoor air and walls ie Wall heat capacity C e Indoor air heat capacity C iThe simulated temperature T is obtained using the second-order equivalent thermal parameter model equation. i (t);

[0089] b) Collect the user's actual indoor temperature T through smart devices ia (t);

[0090] c) Combine the optimization objective function based on the least squares criterion to calculate the particle fitness, as shown in formula (7):

[0091]

[0092] ⑤ Particle Swarm Population Update

[0093] a) If the number of iterations does not reach the maximum number of iterations, the particle swarm inertia weights are updated according to formula (8);

[0094]

[0095] In the formula: k represents the iteration number, w(k) represents the inertia weight at the k-th iteration, w max and w min T represents the maximum and minimum inertia weights, respectively. max Indicates the maximum number of iterations;

[0096] b) Update the particle velocity, calculated according to formula (9):

[0097]

[0098] In the formula: v i (k) represents the velocity of particle i in the k-th iteration, x i (k) represents the position of particle i in the k-th iteration, c1 and c2 are non-negative constants, and rand1 and rand2 are random numbers between 0 and 1; pbest i represents the optimal position of particle i, and gbest represents the global optimal position of particle i;

[0099] c) Update particle positions according to formula (10):

[0100] x i (k+1)=x i (k)+v i (k) (10)

[0101] ⑥ Determine the globally optimal parameters

[0102] The optimal particle position and the global optimal position are updated by combining the fitness function. It is then determined whether a pre-set termination condition is met. If the termination condition is met, the optimal parameters are output. If the termination condition is not met, steps 3 and 4 are returned to continue the optimization process to generate the optimal parameters for the simulation temperature T. i (t) and measured temperature T ia Particles with smaller errors between (t) are selected until the termination condition is met, and the globally optimal indoor-outdoor air heat exchange thermal resistance R is output. io Thermal resistance R between outdoor air and wall oe Thermal resistance R between indoor air and walls ie Wall heat capacity C e Indoor air heat capacity C i until.

[0103] The experimental data required for parameter identification in this embodiment were obtained through the experimental platform. Based on the improved particle swarm optimization algorithm, the model parameters were identified, and a second-order model of the distributed electric heating load was established. Two sets of temperature curves were simulated using the second-order model at outdoor temperatures of -10℃ and -15℃, and compared with the measured temperatures. The results are as follows: Figure 3-4 As shown.

[0104] The mean absolute error (MAE) of the equivalent thermal parameter model simulation temperature compared with the measured temperature under different outdoor temperatures is calculated using equation (11). The calculation results are as follows: Figure 5 As shown.

[0105]

[0106] pass Figures 3-5 It can be seen that the error between the simulated indoor temperature and the measured temperature of the second-order equivalent thermal parameter model is small, which proves the accuracy of the second-order model parameter identification method for decentralized electric heating load of the present invention, and further proves the accuracy of the improved particle swarm algorithm in identifying model parameters.

Claims

1. A method for parameter identification of a second-order model of a decentralized electric heating load, characterized by: The wall temperature T, used for model parameter identification, is obtained through the second-order equivalent thermal parameter model equation. e (t) and indoor temperature T i The calculation formula for (t) is then used to identify the model parameters. The specific steps are as follows: 1) Obtain the wall temperature T for model parameter identification using the second-order equivalent thermal parameter model equation. e (t) and indoor temperature T i Formula for calculating (t) ① The second-order equivalent thermal parameter model of the decentralized electric heating load is represented by a set of differential equations, as shown in formula (1): In the formula, T i Indicates indoor temperature, unit: °C; T o This indicates the outdoor ambient temperature, in °C. T e Indicates wall temperature, unit: °C; R io Indicates the thermal resistance of indoor and outdoor air heat exchange, unit: ℃ / W; R oe R represents the thermal resistance between outdoor air and the wall, measured in °C / W. ie Indicates the thermal resistance between indoor air and the wall, unit: ℃ / W; C e This indicates the wall's heat capacity, measured in J / ℃; C. i Indicates the heat capacity of indoor air, unit: J / ℃; P h This indicates the operating power of the decentralized electric heating system, in watts (W). ②The differential equation formula (1) has a state-space expression in continuous time, as shown in formula (2): In the formula: x(t) is T e (t) and T i The model state vector consists of u(t) and u(t) is T. o (t) and P h The model input vector consists of (t), where A and B are R. io R oe R ie C e C i The model parameter matrix is ​​composed of; ③ Discretize equation (2) to obtain the state-space equation as shown in equation (3): x(t+Δt)-x(t)=[Ax(t)+Bu(t)]Δt (3) In the formula: x(t+Δt) is T e (t+Δt) and T i The model state vector consists of (t+Δt), where Δt is the sampling period; ④ The second-order model equations are transformed to obtain the discretized formulas for the wall temperature change and indoor temperature change in the second-order equivalent thermal model of the distributed electric heating load, as shown in formula (4): ⑤ At the same time, the wall temperature T e (t) and indoor temperature T i The recursive formula for (t) is expressed in the form of formula (5): ⑥ Substitute formula (4) into formula (5) to obtain the wall temperature T used for model parameter identification. e (t) and indoor temperature T i The formula for calculating (t) is shown in formula (6): 2) Model parameter identification ① Determining model parameters The model parameters are determined based on the second-order equivalent thermal parameter model of the decentralized electric heating load: The model input data is the measured initial indoor temperature T. ia (1) Initial temperature of the wall T e (1) Outdoor ambient temperature T o (t), Distributed electric heating operating power P h ; The model outputs indoor temperature T. i (t), wall temperature T e (t); The parameter to be identified in the model is the thermal resistance R of indoor and outdoor air heat exchange. io Thermal resistance R between outdoor air and wall oe Thermal resistance R between indoor air and walls ie Wall heat capacity C e Indoor air heat capacity C i ; ② Model parameter acquisition Use smart devices to acquire model parameters to identify the required data, and preprocess the data; ③ Initialize the model parameters a) Determine the thermal resistance R of indoor and outdoor air heat exchange based on the actual physical properties of the building. io Thermal resistance R between outdoor air and wall oe Thermal resistance R between indoor air and walls ie Wall heat capacity C e Indoor air heat capacity C i The range of parameter values; b) Use the upper and lower limits of the value range as the upper and lower limits of the solution interval for the parameters of the improved particle swarm optimization algorithm, respectively; c) Assign values ​​to the number of particles, population size, and initial velocity of the particle swarm, and provide a set of random values ​​as the initial positions of the particles within the solution interval; ④ Calculation of fitness a) Based on randomly generated parameters to be identified, the indoor and outdoor air heat exchange thermal resistance R io Thermal resistance R between outdoor air and wall oe Thermal resistance R between indoor air and walls ie Wall heat capacity C e Indoor air heat capacity C i The simulated temperature T is obtained using the second-order equivalent thermal parameter model equation. i (t); b) Collect the user's actual indoor temperature T through smart devices ia (t); c) Combine the optimization objective function based on the least squares criterion to calculate the particle fitness, as shown in formula (7): ⑤ Particle swarm population update: a) If the number of iterations does not reach the maximum number of iterations, the particle swarm inertia weights are updated according to formula (8); In the formula: k represents the iteration number, w(k) represents the inertia weight at the k-th iteration, w max and w min T represents the maximum and minimum inertia weights, respectively. max Indicates the maximum number of iterations; b) Update the particle velocity, calculated according to formula (9): In the formula: v i (k) represents the velocity of particle i in the k-th iteration, x i (k) represents the position of particle i in the k-th iteration, c1 and c2 are non-negative constants, and rand1 and rand2 are random numbers between 0 and 1; pbest i represents the optimal position of particle i, and gbest represents the global optimal position of particle i; c) Update particle positions according to formula (10): x i (k+1)=x i (k)+v i (k) (10) ⑥ Determine the globally optimal parameters The optimal position of the particle and the global optimal position are updated by combining the fitness function. It is then determined whether the pre-set termination condition is met. If the termination condition is met, the optimal parameters are output. If the termination condition is not met, it is necessary to return to steps 3 and 4 to continue the optimization process and generate the simulation temperature T. i (t) and measured temperature T ia Particles with smaller errors between (t) are selected until the termination condition is met, and the globally optimal indoor-outdoor air heat exchange thermal resistance R is output. io Thermal resistance R between outdoor air and wall oe Thermal resistance R between indoor air and walls ie Wall heat capacity C e Indoor air heat capacity C i until.

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