A thermal storage heat pump system control method based on a physical information neural network

Abstract

The application provides a kind of heat storage heat pump system control method based on physical information neural network, belongs to the technical field of intelligent control of heat pump system;For the problems that the algorithm in the prior art is difficult to adapt to dynamic energy demand, the model is difficult to apply to engineering due to building space heterogeneity, the prediction credibility of high-order RC model is weak, and the engineering feasibility is poor, etc., a solution combining physical information sequence-to-sequence neural network technology and finite state machine control strategy is proposed.In the model level, a 2R2C RC model of building temperature change is established, and then a PI-Seq2seq prediction model based on the physical model is proposed.In the control process optimization level, based on the time-of-use electricity price policy for industry and commerce, a FSM control model is designed, the system state set, input parameters and conversion function are defined, and the control rules are constructed combined with the building heat pump working period and the characteristics of the heat storage tank.Finally, the energy cost optimization and indoor temperature stability under peak-valley electricity price are realized.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of intelligent control of heat storage pump systems, and particularly relates to a heat storage heat pump system control method based on a physical information neural network. BACKGROUND

[0002] The comprehensive performance of a heat storage heat pump is affected by the type of heat pump and the control strategy; the prerequisite for achieving precise and efficient regulation and control of a heat pump system is to obtain a dynamic and accurate load side model. The prediction method for building room temperature load can be divided into three categories: black box, gray box and white box models. Gray box models are the preferred solution for building heat load modeling due to their strong explainability and real-time operating adaptability. Among them, the RC model is often used for internal thermal environment modeling of buildings due to its simple and efficient fitting performance. Chen et al. analyzed the 2R2C physical information PINN model embedded therein, which is superior to pure neural networks in multi-step prediction of temperature load demand, emphasizing the importance of introducing physical knowledge into traditional data-driven models. The research results of Saeed et al. show that the sampling efficiency of Dyna-PINN is 50% higher than that of DQN, and it is superior to rule-based control in terms of thermal comfort. Due to the introduction of physical principles, Dyna-PINN realizes a more logical and interpretable control strategy. Liu et al. proposed a hierarchical model predictive control framework that uses an improved RC model to reduce energy consumption by 3% to 12%. As the core framework of gray box models, the RC model has shown high accuracy in small-scale building load prediction, but still has limitations in large-scale building scenarios: first, the model parameters depend on physical properties such as wall structure and thermal and humid environment, and the spatial heterogeneity of large-scale buildings makes parameter measurement costly and low-precision, making it difficult to meet the needs of engineering applications; second, although high-order RC models can theoretically improve prediction accuracy, the rapid increase in parameter dimensions not only raises engineering feasibility issues, but also amplifies parameter coupling errors, making it difficult for the model to obtain stable regularization correction parameters, ultimately weakening the credibility of the prediction results.

[0003] Compared with the traditional heat pump control strategy, the optimization direction of the heat storage heat pump combined system focuses more on achieving the optimal economy of the whole cycle operation. This goal orientation puts higher requirements on the realizability and accuracy of the control algorithm, that is, the dynamic energy balance and real-time optimization allocation among load demand, energy storage state and energy supply need to be achieved through algorithm design. Klingebiel et al. developed a data-driven MPC heat pump system control method, which optimized the energy efficiency of the air source heat pump, and maintained thermal comfort by utilizing the flexibility of the system. Chae et al. focused on the water supply flow of the heat pump, and applied a clustering-based regression method to improve the prediction accuracy of flow control. Taking a two-story office area as the application scene, the simulation model and the actual application effect were verified, and under the optimized condition, the cost was reduced by 4% and the COP was improved by 4.4%. Bhadra et al. explored the actual control effect of air source heat pump-solar air collector in cold climate. However, most of the existing researches are theoretically based on high complexity algorithms for predictive control of combined systems, and considering the engineering feasibility on site, there is a lack of control methods with clear constraint conditions, explicit logic conditions and various execution modes.

[0004] Although the existing research has broken through the limitations of single heat pump from the aspects of system integration, cost optimization, etc., there are still unsolved core difficulties. Under the dual background of rapid penetration of new energy and widespread implementation of peak-valley time-of-use electricity price policy, the optimization logic in the traditional mode which focuses on the improvement of system energy efficiency is no longer suitable for the current background, and instead, there is a higher priority for the comprehensive economy of the system. The coordinated optimization of energy efficiency and economy has become a key bottleneck in the industry. SUMMARY

[0005] In view of the above problems, the present application provides a heat storage heat pump system control method based on physical information neural network, comprising the following processes:

[0006] S1, collecting data related to the operation of the heat storage heat pump system and the building environment, including time variable, water supply temperature, heat pump power consumption, solar radiation intensity, indoor temperature and outdoor temperature;

[0007] S2, preprocessing the collected data to obtain standard input data for the prediction model;

[0008] S3, constructing and training a PI-Seq2seq prediction model, inputting the preprocessed data of S2, and the model outputting predicted hourly water supply temperature, hourly power consumption and hourly indoor temperature; the prediction model adopts a unified framework integrating physical information neural network PINN and sequence-to-sequence neural network Seq2seq, including physical information embedding module, sequence time processing module and hybrid loss function module;

[0009] S4, real-time peak-valley electricity price period, real-time temperature of heat storage tank, standby power and rated maximum power of heat pump are acquired, the prediction output results of the PI-Seq2seq prediction model are combined and input into a finite state machine FSM control model, system operation parameters including heat pump operation mode, outlet water temperature control value and heat storage / heat release rate are obtained through three-level architecture operation of the FSM control model, i.e., global optimization-state matching-state execution.

[0010] Preferably, the preprocessing in S2 includes converting time variables into time sequence characteristic variables through sine coding, and performing smoothing, normalization and compensation on the supply water temperature, heat pump power consumption, sunlight intensity, indoor temperature and outdoor temperature.

[0011] Preferably, the physical information embedding module in the PI-Seq2seq prediction model is based on the building RC resistance-capacitance model, and embeds the building heat transfer physical mechanism, specifically including: establishing an indoor and outdoor heat loss differential equation based on Newton's cooling law, deriving a building time constant by solving a temperature exponential decay model with input heat being 0, correcting the thermal resistance by time using a Zhukovskiy cylinder disturbance heat dissipation empirical formula, and using corresponding Nusselt number calculation formulas to derive the convective heat transfer coefficient under natural convection and forced convection conditions, and then correcting the RC model thermal resistance parameter.

[0012] Preferably, the sequence time sequence processing module in the PI-Seq2seq prediction model adopts a Seq2seq neural network structure to extract time sequence dependency of the input time sequence characteristic data, and outputs preliminary per-hour supply water temperature, power consumption and indoor temperature prediction values.

[0013] Preferably, the hybrid loss function module in the PI-Seq2seq prediction model is composed of a data fitting error term and a physical constraint penalty term, wherein the data fitting error term is used to measure the deviation of the model output from the training sample, and the physical constraint penalty term embeds the control equation residual of the building RC resistance-capacitance model, including the room temperature change differential equation residual and the pipeline heat dissipation equation residual, and dynamically optimizes the regularization factor λ in the loss function through Kalman filtering algorithm.

[0014] Preferably, the three-level architecture of the FSM control model is specifically:

[0015] Global optimization layer: combining the prediction results and the peak-valley electricity price period division, quantifying the system heat demand in peak period and the heat storage potential in valley period, calculating the difference hdf between deep valley electricity storage energy and all-day heat consumption, and the difference hhf between total energy consumption in peak electricity period and current heat storage amount, and determining control flag parameters valley electricity heat storage determination F1 and peak electricity heat release determination F2;

[0016] State matching layer: Based on the current electricity price period and F1 and F2 parameters, and referring to the preset FSM control matrix, adaptively match the system operation mode, including direct supply mode, thermal storage mode, and heat release mode;

[0017] State execution layer: Based on the matching relationship between heat pump heating capacity and power consumption, heat storage tank temperature constraint, and heat pump power constraint, the heat pump outlet water temperature is adjusted to dynamically adjust the actual operating load of the heat pump, and finally outputs system operating parameters, including: heat pump operating mode, heat pump outlet water temperature control value, and heat storage / release rate of heat storage tank.

[0018] Preferably, the empirical formula for heat dissipation by turbulence in the Jucauskas cylinder, the formula for calculating the Nusselt number under natural convection conditions and the formula for calculating the Nusselt number under forced convection conditions, are used to derive the convective heat transfer coefficient under the corresponding conditions. The convective heat transfer coefficient is calculated by the Nusselt number, the characteristic scale, and the thermal conductivity when the fluid is at rest.

[0019] Preferably, the matching logic of the FSM control matrix is ​​as follows: during deep valley periods and valley periods, the thermal storage mode is matched first; during peak periods and peak hours, the thermal release mode is matched first; during normal periods, valley periods and peak hours, the direct supply mode is matched first, and the thermal storage mode and thermal release mode are not triggered during normal periods.

[0020] Preferably, the optimization objective of the control strategy of the FSM control model is:

[0021] ;

[0022] The unit electricity price at time i is expressed in yuan / kWh. For a moment i The amount of lost electricity costs is in yuan. The power consumption of the heat pump at time i is expressed in kWh.

[0023] When setting control parameters, use the following conditions for constraints:

[0024] ;

[0025] In the formula, The heating capacity of the heat pump is expressed in kW. The unit of power consumption of the heat pump is kWh. This is the coefficient of performance (COP) of the heat pump.

[0026] Preferably, to achieve optimal economic efficiency, F1 and F2 are used to control whether energy storage and heat release occur during off-peak and peak electricity periods; the judgment criteria are as follows:

[0027] ;

[0028] wherein, h df is the difference between the total energy stored in the valley electricity and the total heat consumption in the whole day. When the value is positive, it means that the energy increment stored at the valley electricity time can cover the heat demand in the whole day, and there is no need to store energy at the valley electricity time. If the value is negative, the valley electricity charging needs to be started, is the duration of the valley electricity time; is the running power consumption in the state of the highest outlet water setting temperature of the heat pump;

[0029] The heat stored in the heat storage tank is preferentially supplied at the peak electricity time, and the judgment basis is the difference between the total energy consumption at the peak electricity time and the current heat storage h hf According to the difference, it is judged whether to release heat at the peak electricity time:

[0030] ;

[0031] In the formula, is the end time of the peak electricity, is the start time of the peak electricity, is the specific heat capacity of the liquid in the heat storage tank, is the mass of the liquid.

[0032] Compared with the prior art, the present application has the following beneficial effects:

[0033] The application is applied to the control of a thermal storage heat pump system, and aims at the problems in the prior art that the algorithm is difficult to adapt to dynamic energy demand, the model is difficult to be applied in engineering due to the heterogeneity of building space, the prediction credibility of the high-order RC model is weak and the engineering feasibility is poor, and there is a lack of practical control method, and proposes a solution combining physical information sequence to sequence (PI-Seq2seq) neural network technology and finite state machine (FSM) control strategy, wherein the PI-Seq2seq model is a unified framework integrating physical information neural network (PINN) and sequence to sequence neural network (Seq2seq), the heat transfer physical mechanism of the building RC resistance and capacitance model is embedded, a mixed loss function containing a data fitting error term and a physical constraint penalty term and optimized by Kalman filtering is designed, the preprocessed heat pump operation parameters, building environment parameters, time variables and heat storage system parameters are used as inputs, the hourly water supply temperature, power consumption and indoor temperature are predicted, the Adam optimizer is used for model training, and the training set is trained and the test set is verified; meanwhile, a three-level FSM control strategy of “global optimization - state matching - state execution” is designed, the PI-Seq2seq prediction result and the peak-valley electricity price are combined in the global optimization layer to determine F1 (valley electricity heat storage determination) and F2 (peak electricity heat release determination) parameters, the FSM control matrix is referred to in the state matching layer to adaptively match the direct supply, heat storage and heat release modes, and the heat pump COP, the heat storage tank temperature (40-60 DEG C) and the heat pump power (standby to rated interval) are used as constraint regulation operation parameters in the state execution layer, so that the model prediction accuracy is improved (the accuracy is improved by 18%-22% compared with the traditional LSTM model, the prediction MAE is 0.8 DEG C for water supply temperature, 0.3 kWh for power consumption and 0.5 DEG C for indoor temperature), the physical consistency is enhanced, the parameter acquisition cost is reduced by 80%, the daily electricity cost is reduced by 13.5% compared with the traditional mode, and the engineering landing cost is low and the response speed is fast (≤10s), so that the core pain points of the prior art are solved. BRIEF DESCRIPTION OF DRAWINGS

[0034] Figure 1 It is a hardware structure schematic diagram in the embodiment.

[0035] Figure 2 It is a Seq2seq model architecture diagram.

[0036] Figure 3 It is a building water supply system time constant trend graph in the embodiment.

[0037] Figure 4 It is a building room temperature time constant trend graph in the embodiment.

[0038] Figure 5 It is a FSM-based heat storage heat pump control model principle diagram.

[0039] Figure 6 This is a comparison chart of the normal strategy and the PI-seq2seq-FSM control strategy under high load conditions in the embodiment.

[0040] Figure 7 This is a graph showing the trend of heat pump power consumption under high load conditions after the application of the FSM strategy.

[0041] Figure 8 This is a comparison chart of the normal strategy and the PI-seq2seq-FSM control strategy under low load conditions in the example.

[0042] Figure 9 This is a graph showing the trend of heat pump power consumption under low load conditions after the application of the FSM strategy.

[0043] Figure 10 The diagram shows the power consumption rate at each stage in the example.

[0044] Figure 11 This is a diagram showing the total power consumption in the energy storage state in the embodiment. Detailed Implementation

[0045] The invention will be further described below with reference to specific embodiments.

[0046] This invention conducts research on model construction and control process optimization. First, it constructs a prediction model that integrates physical mechanisms and data-driven approaches. Second, it designs a state switching control strategy based on a finite state machine. Finally, it forms a coupled control process driven by a physical information neural network.

[0047] The system structure in this embodiment is as follows: Figure 1 As shown in the figure, this is an integrated heat pump heating system combining heat pump, thermal storage, and automatic control. It includes core components such as a heat pump unit, heat exchanger, thermal storage tank, pump, bypass, and proportional flow control valve, as well as temperature and flow sensors for parameter acquisition, and a measurement and control system consisting of a PLC, switch, and computer. The temperature and flow sensors transmit measurement data to the control system, which then sends control data to actuators such as valves and pumps for regulation. During operation, the heat energy generated by the heat pump is transferred to the heat carrier fluid via the heat exchanger. After being monitored by sensors, the fluid enters the thermal storage tank for storage or is directly transported. Subsequently, the pump drives the flow, distributing the flow through the proportional flow control valve and bypass branches, ultimately delivering the heat energy to the building's end. The control system optimizes the thermal storage and release process in real time based on the collected temperature, flow, and other parameters.

[0048] At the model level, a 2R2C resistance-capacitance (RC) model for building temperature changes is established, and then a PI-Seq2seq prediction model is proposed based on this physical model.

[0049] At the control process optimization level, based on the time-of-use electricity pricing policy for industrial and commercial users, an FSM control model is designed, defining the system state set, input parameters, and transformation functions. Control rules are constructed by combining the operating periods of the building heat pump and the characteristics of the thermal storage tank. Ultimately, this achieves energy cost optimization and indoor temperature stability under peak-valley electricity pricing.

[0050] 1. Data Acquisition and Preprocessing

[0051] For an air-source heat storage heat pump system in an office building with a floor area of ​​10,000 square meters, multiple types of sensors were deployed to collect the following core data over a continuous 30-day period, covering both weekdays and holidays to ensure data diversity:

[0052] Heat pump operating parameters: The heat pump supply water temperature is collected using a PT100 platinum resistance temperature sensor. (Unit: °C), sampling period 10 minutes; heat pump power consumption is collected using a three-phase power sensor. (Unit: kWh), sampling period 10 minutes; Indoor temperature (unit: °C) was collected using a DHT11 sensor, sampling period 10 minutes;

[0053] Building environmental parameters: Outdoor temperature and solar radiation data from weather stations were used. Data collection was conducted every hour.

[0054] Electricity Price and Time Parameters: Record local peak and off-peak electricity price periods (Deep Valley: 00:00-06:00, price 0.3 yuan / kWh; Valley: 06:00-08:00, 22:00-24:00, price 0.5 yuan / kWh; Flat: 08:00-12:00, 14:00-18:00, price 0.7 yuan / kWh; Peak: 12:00-14:00, 18:00-20:00, price 1.0 yuan / kWh; High Peak: 20:00-22:00, price 1.2 yuan / kWh).

[0055] All sensor analog signals are converted into digital signals via a USB-6210 data acquisition card (DAQ).

[0056] 2. Preprocess the acquired data.

[0057] For the date and time items in the original data, considering their periodic fluctuations, a sinusoidal encoding method is used for processing, and the time data is normalized.

[0058] ;

[0059] For the other data in the dataset, a mean-variance normalization method is used:

[0060] ;

[0061] in, The original data, The sample mean. denoted as the standard deviation of the sample.

[0062] 3. Construct a prediction model

[0063] The building RC resistance-capacitance model is a simplified thermodynamic analysis model that simulates the heat transfer characteristics of a building envelope by using the thermal resistance and thermal capacity during the heat pump's heat transfer from the interior to the exterior and from the interior to the exterior. It is used to calculate or predict the heat exchange between the interior and exterior of a building and the building's thermal dynamic response.

[0064] In this process, the heat input from the heat source (heat pump or heating system) is The specific heat capacity of the pipeline system is The heat loss rate of indoor heating is:

[0065] (1)

[0066] The temperature of the water in the heating pipes, expressed in °C. Indoor temperature, in °C. This refers to the amount of heat dissipated into the room through the heating pipes, measured in J. The thermal resistance between the pipe and the indoor air is expressed in °C / W. When the heat exchanger exchanges heat with the indoor air, there is a significant difference in thermal resistance between natural convection and forced convection. To improve the accuracy of the heat exchange process modeling, the thermal resistance coefficient needs to be corrected. The correction factor is [value missing]. . It can be represented as:

[0067] (2)

[0068] Substituting (2) into (1), we obtain the following differential equation:

[0069] (3)

[0070] In the formula, indoor air receives heat from the air conditioning ducts and radiators, as well as energy from solar radiation, and also dissipates heat to the outside through the building envelope. Therefore, the change in room temperature can be expressed as:

[0071] (4)

[0072] In the formula, Outdoor temperature, in °C. Indoor air temperature, in °C. and These represent the heat capacity of the interior building envelope and the air system, respectively, and their thermal resistance to heat dissipation to the outside, in °C / W. It is a correction factor for solar radiation. The solar direct radiation at time t is expressed in W / m². 2 The specific values ​​can be indexed based on time.

[0073] According to equations (3) and (4), the first-order linear differential equation matrix of the RC model of the building ash box for underfloor heating can be obtained, expressed as:

[0074] (5)

[0075] As can be seen from this formula, solving for the precise indoor temperature requires precise heat capacity and thermal resistance parameters, and the product of these parameters is the time constant for the building's natural cooling. .

[0076] Therefore, in order to obtain the resistive-capacitive physical characteristics of a building, that is, its time constant... This allows the input of heat Given a value of 0, solving this differential equation yields the temperature exponential decay model, expressed as:

[0077] (6)

[0078] (7)

[0079] In equation (7), the time constant is defined as the product of the building's heat capacity and thermal resistance, and is an inherent parameter characterizing the building's thermal inertia; ideally, this time constant does not change with fluctuations in the external environment. However, based on historical operating data, statistical analysis and parameter identification can only obtain the distribution characteristics of the time constant under natural convection conditions; when the system enters forced convection conditions, the process of the heat pump continuously replenishing heat to the working fluid water system will obscure the natural cooling characteristics of the pipes, making it impossible to directly observe the actual cooling law of the pipes, and thus making it difficult to directly obtain the forced convection thermal resistance.

[0080] To address the aforementioned observational limitations, a combination of the controlled variable method and indirect derivation is employed to correct for forced convection thermal resistance. Utilizing the observed RC constant under natural convection conditions, and combining it with the "fixed ratio of forced convection to natural convection heat transfer resistance" determined from experimental or empirical data, the RC constant under system operating conditions is indirectly corrected. This scheme avoids interference from heat compensation on the observation of cooling patterns. By leveraging the known correlation between natural convection thermal resistance and the fixed ratio, the true thermal resistance under forced convection conditions is indirectly derived, ensuring the accuracy of subsequent temperature predictions by the RC model under this condition.

[0081] According to the empirical formula summarized by Jucauskas for fluid sweeping over a pipe, when under natural convection conditions, i.e., when Re is between 1 and 100, Nu can be calculated using the following formula:

[0082] (8)

[0083] Forced convection state, i.e., Re is between 1000 and 2 × 10⁻⁶. 5 When calculating Nu, the following formula needs to be used:

[0084] (9)

[0085] According to Nusel Feature scale Thermal conductivity of the fluid at rest The convective heat transfer coefficient can be calculated and expressed as:

[0086] (10)

[0087] Building heat load is a typical dynamic nonlinear sequence data driven by multiple factors and with strong time dependence. Its prediction task requires the model to fully capture the inherent time dependence of the data and directly generate a continuous output sequence.

[0088] The Seq2seq model is a deep learning framework designed for the task of mapping "input sequence → output sequence". Through its intermediate vector structure, it can retain historical information of the input sequence to the maximum extent, a structural characteristic that highly matches the aforementioned requirements of building heat load prediction. The model architecture is as follows: Figure 2 As shown.

[0089] For a decoder and encoder composed of two RNNs, the input is a sequence and the output is a sequence. That is, the probability of the output sequence being true given that the input sequence is true, and the probability of the entire sequence is:

[0090] (11)

[0091] in It is the input sequence. For the corresponding output sequence, T This is for outputting time steps.

[0092] While the GRU model possesses memory properties, when the encoder's input sequence is long, the decoder's GRU model struggles to effectively decode earlier input sequence information. Therefore, an attention allocation mechanism is proposed to improve this situation. During the decoding phase, the attention mechanism requires that three inputs be received simultaneously at each time step: the hidden state of the previous layer in the decoding phase. The predicted input from the previous stage The context vector of the encoding stage corresponding to this prediction The new state of this decoding phase These three factors are obtained by mapping them through a nonlinear function:

[0093] (12)

[0094] in, and These represent the hidden state and the predicted output value of the previous state in the decoding phase, respectively. The weighted average sum of the output states at each time step during the encoding phase is calculated as follows:

[0095] (13)

[0096] in It is input Corresponding state The weight is calculated using the following formula:

[0097] (14)

[0098] The calculation formula is:

[0099] (15)

[0100] In the formula, This represents the j-th hidden state in the encoding stage at step i of the decoding stage. Previous hidden state in the decoding phase The higher the energy value, the stronger the connection between the two, and the higher the attention weight will be assigned subsequently. express The transpose of is a trainable parameter vector in the attention mechanism, used to perform a linear transformation on the features after tanh activation, thereby capturing key correlation information. It is the hidden state during the decoding phase. The weight matrix (trainable parameters) is used to decode the hidden state. Mapping to encoded hidden state The feature space of computable associations. It is the hidden state during the encoding phase. The weight matrix is ​​used to encode the hidden state. Mapping to the decoded hidden state The feature space of computable associations.

[0101] This embodiment proposes using a PI-seq2seq model to predict building heat load based on building RC physical information and a Seq2seq model. The physical information fusion method is as follows:

[0102] (16)

[0103] (17)

[0104] (18)

[0105] In the formula These represent the neural network loss, the loss calculated using the RC model, and the total loss. These are the actual temperature of the heating pipes, the temperature change calculated using power consumption and energy efficiency coefficient, and the air temperature inside the building, respectively. These are the predicted heating pipe temperature, the temperature change calculated using power consumption and energy efficiency coefficient, and the building's indoor air temperature, respectively. The regularization factor is used to calculate the total loss.

[0106] The input layer of the PI-Seq2seq neural network includes water supply temperature, power consumption, sunlight, indoor temperature, outdoor temperature, and time variables processed by sinusoidal encoding. The output layer consists of water supply temperature, power consumption, and indoor temperature. During model training, the neural network optimizes the global loss functional (18) by minimizing it using an optimization algorithm. The loss function in the optimization process consists of two parts. Equation (16) inherits the standard loss function of traditional data-driven neural networks and is used to measure the fitting error between the model output and the training samples.

[0107] Another part, based on physical information constraints, embeds the residuals of the governing equations to construct a physical consistency penalty term, thereby enhancing the model's fitting effect on the underlying physical laws. During training, Kalman filtering is used... The value of is optimized. The hybrid loss function can effectively realize a collaborative optimization mechanism between data-driven methods and physical prior knowledge.

[0108] To evaluate the predictive performance of PINN on time series data, this study selected mean squared error (MSE), root mean square error (RMSE), and mean absolute error (MAE) as core evaluation indicators.

[0109] (19)

[0110] (20)

[0111] (twenty one)

[0112] In the formula, N is the sample size. This is the actual value. These are predicted values.

[0113] The air temperature inside the heat exchanger is in the range of 30~40℃, and the kinematic viscosity of the air under the corresponding operating conditions is 16×10⁻⁶. -6 ~17×10 -6 m 2 / s. Based on the parameters determined above, the range of internal Reynolds number under the operating conditions of the heat exchanger can be further calculated, as shown in Table 1.

[0114] Table 1. Correspondence between pipe diameter and Reynolds number for commonly used specifications

[0115]

[0116] Under different convection conditions, assuming that the thermal conductivity remains constant at the characteristic scale and when the fluid is stationary, the thermal conductivity is linearly related to Nu. The increase in thermal conductivity when the indoor heat exchanger switches from natural convection to forced convection is shown in the table below.

[0117] Table 2. Magnitude difference between natural convection and forced convection

[0118]

[0119] Based on the time period of the data and the reference data in Table 2, when the data collection period is from 7:30 to 18:00, the indoor heat exchanger is in a forced convection state, and its thermal resistance is 7.17% to 8.9% of the thermal resistance under natural cooling. Since the building's heat capacity remains constant, and considering the physical definition of the RC time constant, the building's RC time constant drops to 7.17% to 8.9% of that under natural cooling. Using this correction method to calibrate the building's RC time constant for different time periods in the dataset can effectively improve the model's prediction accuracy throughout the entire time period.

[0120] Based on the above construction process, and relying on the input features, network structure, and training strategy defined in the aforementioned process, a PI-seq2seq model was constructed. The output of this model is the time-series prediction results of hourly water supply temperature, hourly power consumption, and hourly indoor temperature, which can directly serve subsequent system energy consumption analysis and indoor thermal environment control optimization.

[0121] 4. Training process

[0122] The hyperparameter combination was optimized using a grid search method. The types of hyperparameters and their optimal value ranges are shown in Table 3.

[0123] Table 3 Parameter Search and Selection during Training Process

[0124]

[0125] In PINN's losses, This is a weighting coefficient between physical loss and data loss, and its value will affect whether the model leans more towards removing physical constraints or data fitting. Kalman filtering automatically balances the relative importance of physical constraints and data fitting by recursively fusing previous estimates of λ with observations of the current loss ratio. The main hyperparameters of Kalman filtering include the initial state estimate. Initial covariance P0, process noise covariance and observation noise covariance .

[0126] Model training under different hyperparameters The sequence distribution and its fluctuation amplitude are analyzed, and the initial hyperparameters of the Kalman filter are set as follows: Take 0.97, Set to 1e-4 to reflect the high confidence level of the initial value and the process noise covariance. Set to 1e-5 to Smooth the response to changes and observe the noise covariance. Set to 1e-4. The above parameters can be fine-tuned based on specific experimental performance to achieve the optimal dynamic weighting effect.

[0127] Table 4 Regularization Parameter Search and Selection

[0128]

[0129] At each training step, the current physical loss and data loss are first calculated, and the observations are constructed accordingly. Subsequently, the Kalman filter recursive formula is used to update... The updated estimate is used for weighted calculation of the loss function in this round, guiding the optimization of neural network parameters. This process continues iterating until training is complete. Through this dynamic mechanism, the model can automatically reduce the physical loss when it is high in the early stages of training. The value of [the value] strengthens physical constraints, but when data loss becomes dominant in the later stages... The value should be increased appropriately to enhance the data fitting ability.

[0130] 5. Output prediction results

[0131] As can be seen from equation (7), the building RC time constant can be solved by using the unheated periods in the existing dataset.

[0132] like Figure 3 As shown, select Figure 3 The data between the start and end points of section (a), combined with... Figure 3The constraints in Part (b) (building time constant driven mode) are used to perform an inverse analysis of the natural cooling characteristics in the temperature time series. The results of the analysis are as follows: Figure 3 As shown in section (c), the results indicate that the time constant of natural cooling of the water supply temperature is affected by random fluctuations in the data, and the shorter the time interval when calculating the time constant, the greater the impact. When the selected temperature point time interval is sufficiently large, the RC time constant of the building converges to 3860, with the time unit being minutes. This part of the research verifies the basic explanatory ability of the RC model for building thermal inertia from the perspective of dynamic thermal response by inverting the time constant through the time series of temperature, providing experimental basis for subsequent research on the time-varying law of the thermal time constant and model correction.

[0133] From equation (1), it can be seen that when the building itself is in thermal equilibrium, that is... When the value is 0, the heat input to the heat pump water supply is equal to the heat dissipated into the room by the heat pump water supply system. Under this condition, the heat capacity will not affect the room temperature. The current room temperature depends on the thermal resistance of indoor air to heat dissipation to the outside, so the thermal resistance during building operation can be calculated using data from this time period.

[0134] according to Figure 4 The data characteristics shown in part (a) are used to identify stable trend signals, filter out the interval of thermal equilibrium period, retain the indoor temperature, water supply temperature and power consumption data in the interval, and solve the thermal resistance of the radiator to dissipate heat to the indoor air based on the data characteristics in the equilibrium period.

[0135] like Figure 4 As shown in section (b), under thermal equilibrium conditions, fluctuations in water supply temperature have a significant interference effect on the thermal resistance inversion results: when the water supply temperature is in a steady state, although there are slight fluctuations between indoor and outdoor temperatures, the calculated thermal resistance value still tends to converge to a constant reference value; however, when the water supply temperature enters a dynamic fluctuation state, the deviation of the thermal resistance inversion results increases significantly. Considering that thermal resistance is an inherent property of the building, in actual calculations, the average value of the thermal resistance when it is stable is taken as the thermal resistance parameter of the building, which is 9.31℃ / kW.

[0136] From the perspective of the dynamic characteristics of the indoor thermal environment, the indoor temperature is inherently difficult to reach a theoretically strict thermal equilibrium state due to the intermittent input of solar radiation and human factors. Even if the water supply temperature remains stable, slight fluctuations in indoor temperature will still drive the building's heat capacity to participate in energy exchange, and the heating output of the heat pump is not strictly equal to the heat dissipation of the indoor space. At this point, the thermal resistance formula derived from the thermal equilibrium assumption is essentially a quasi-steady-state approximation, and its calculated value will have inherent biases due to the dynamic fluctuations in indoor temperature, making it difficult to calculate the true trend of thermal resistance.

[0137] Table 5 Prediction accuracy results of the trained model

[0138]

[0139] Under heat pump operation, the PI-Seq2seq model with enhanced physical information consistently converges its prediction error to within 0.5℃, demonstrating an advantage over the Seq2seq model. The difference lies in the fact that PI-Seq2seq, by embedding prior thermodynamic knowledge, achieves more accurate modeling of the fine dynamic features of temperature changes in the dataset, thus improving the fit between the prediction results and the actual values.

[0140] Both LSTM and Transformer models exhibit adaptive limitations to non-stationary abrupt changes, failing to capture the fine dynamic characteristics of temperature changes in the dataset. Both models show sudden error peaks at the moment of operating condition switching, with subsequent error fluctuations continuing. Furthermore, there is a deviation in the dynamic matching between predicted and actual values; LSTM and Transformer models, due to their over-reliance on historical data, exhibit a lag in predicting the rate of temperature rise.

[0141] Pure data-driven models lack prior knowledge of thermodynamics such as thermal resistance. The loop structure of LSTM can only learn temporal correlations at the data level and cannot constrain the exponential decay law of the cooling process. Although the self-attention of Transformer can extract long-range dependencies, the lack of physical constraints on feature aggregation leads to deviations between the predicted trend and the actual thermodynamic law, ultimately resulting in a lack of robustness in trend fitting.

[0142] 6. FSM-based thermal storage heat pump control model

[0143] First, based on the hourly weather forecast, the PINN model predicts and outputs the system energy consumption curve and water supply temperature curve for the day. Then, based on these curves, the daily thermal storage potential and heat load demand are quantitatively analyzed. Following this, based on the predicted curves, the daily system thermal storage potential and heat load demand are quantitatively assessed, and flag parameters are configured to regulate thermal storage and release behavior during off-peak and peak electricity periods. Next, using electricity price periods as the core input variable, a finite state machine (FSM) control model is employed to achieve precise regulation of the switching logic between thermal storage and release behavior. Based on this hierarchical control process, the goal of synergistic optimization of system heat supply and consumption is ultimately achieved.

[0144] A finite state machine is a mathematical and computational model used to describe the behavior of a system transitioning between different states. It is commonly used in embedded systems, communication protocol design, and financial security processes. A standard finite state machine can be represented as:

[0145] (twenty two)

[0146] The system is in a specific and finite "state" at any given time. That is, there exists a set of states. Any state of the system can be used The elements in the table represent the initial state of the system. The set of input parameters is The set of state transition functions is :

[0147] (twenty three)

[0148] The system transitions from its current state to another state or maintains its current state based on the received input parameters. This set of input parameters is represented as... ,in, For each input parameter;

[0149] (twenty four)

[0150] Equation (23) involves a transition process between states, which is the transition function between each state. Its form can be expressed as:

[0151] (25)

[0152] Indicates the system in state Based on input parameters The response in the transformation function Transition to state under the action .

[0153] The optimization objective of the control strategy is:

[0154] (26)

[0155] The unit electricity price at time i is expressed in yuan / kWh. For a moment i The amount of lost electricity costs is in yuan. The power consumption is expressed in kWh.

[0156] When setting control parameters, use the following conditions for constraints:

[0157] (27)

[0158] In the formula, The heating capacity of the heat pump is expressed in kW. The unit of power consumption of the heat pump is kWh. This is the coefficient of performance (COP) of the heat pump.

[0159] Using the temperature inside the thermal storage tank as a capacity indicator, the maximum and minimum heat storage capacity of the thermal storage tank are denoted as 40℃ and 60℃ respectively. The heat capacity inside the tank can be expressed as:

[0160] (28)

[0161] To achieve optimal economic efficiency, the following settings were configured: F1 and F2 Two control flags are used to determine whether energy storage and heat release occur during off-peak and peak electricity periods. The criteria for determining these flags are:

[0162] (29)

[0163] in, h df This is the difference between the total energy stored during off-peak hours and the total daily heat consumption. A positive value indicates that the energy storage increase during off-peak hours can cover the entire day's heat demand, and no energy storage is needed during off-peak hours. If the value is negative, off-peak charging needs to be activated.

[0164] The heat stored in the thermal storage tank is preferentially supplied during peak electricity hours, based on the difference between the total energy consumption during peak hours and the stored heat at the current time. h hf The difference is used to determine whether heat release occurs at the peak power time.

[0165] (30)

[0166] In the formula, This is the end of the peak electricity period. This marks the start of peak electricity demand. This refers to the specific heat capacity of the liquid in the thermal storage tank. The mass of the liquid.

[0167] The operating power of a heat pump falls within the range of its standby power and rated maximum power, and its output power can be dynamically adjusted according to actual heating demand. In practical engineering applications, the maximum outlet water temperature of the heat pump is controlled by a PLC, thereby indirectly changing the actual output power of the heat pump.

[0168] (31)

[0169] The coupled control flow of the thermal storage-heat pump system designed in this embodiment is as follows: Figure 5 As shown, the system is divided into three progressive levels: global optimization, state matching, and state execution. The functions of each level work together with reference to the FSM control method to achieve precise system control.

[0170] The combined thermal storage and heat pump system has three operating modes: direct supply mode, thermal storage mode, and heat release mode. The input condition for triggering mode switching is the peak and off-peak electricity price. A control function matrix can be configured based on different input conditions and the peak and off-peak electricity prices.

[0171] Table 6. Correspondence between various electricity price models and heat pump behavior status

[0172]

[0173] The global optimizer is the core of the control process decision-making. It first inputs the initial operating parameters of the PINN model, and then, relying on the PINN model's ability to predict thermal dynamics and energy consumption, outputs the daily indoor temperature change trend and system power consumption trend. Based on this prediction result, and combined with the peak-valley electricity price period division, it quantifies the system's heat demand during peak electricity price periods and the heat storage potential during valley electricity price periods. Furthermore, by combining the matching degree between the system's real-time actual heat storage and peak heat demand, it determines the specific values ​​of the flag parameters F1 and F2, providing a decision-making basis for subsequent state matching.

[0174] The state matcher receives the flag parameters and time period information output by the global optimizer. As an intermediate hub for control mode switching, it makes collaborative judgments based on the current operating period and flag parameters F1 and F2 to achieve adaptive matching between the system in direct supply mode, thermal storage mode and heat release mode, ensuring that the system operating mode is highly compatible with the current heat demand, electricity price policy and thermal storage status.

[0175] As the terminal execution unit of control commands, the state actuator, based on the decision of the global optimizer and the mode determination of the state matcher, combined with the system operation constraints, dynamically adjusts the actual operating load of the heat pump by regulating the key operational variable of the unit outlet water temperature, and finally achieves precise control of the system's energy supply status, ensuring the synchronous optimization of indoor temperature stability and energy consumption optimization goals.

[0176] During off-peak or late-peak electricity hours when the future trend of room temperature changes is relatively small, the system preferentially enters thermal storage mode. In this mode, the heat output from the heat pump is directed to the thermal storage device for storage, rather than being directly supplied to the building load. This mode provides energy storage assurance for stable heating during subsequent peak load periods.

[0177] During peak electricity price periods, the heat pump operates at standby power, and the building's heat load is entirely met by the heat released from the thermal storage device. This operating mode releases the heat stored during low electricity price periods during peak electricity price periods, thereby minimizing operating costs.

[0178] When the available heat inside the thermal storage tank is full or depleted, the system triggers the direct energy supply mode. At this time, the heat pump unit starts as the core heat generation unit, and completes heat preparation through working fluid circulation and heat exchanger, which is then directly delivered to the terminal heat dissipation equipment via the power pump unit; the thermal storage device loop is disconnected and does not participate in energy interaction.

[0179] The three operating modes dynamically switch based on changes in electricity prices, significantly reducing power consumption during periods of high electricity prices. This strategy is simple and straightforward, does not rely on manually set optimization hyperparameters, and uses minimizing electricity prices as the primary constraint for system operation. It offers significant cost advantages and is thus an optimization strategy with broad application prospects in energy management and building systems.

[0180] Based on the PI-Seq2seq model, the prediction method can accurately predict future indoor temperature changes, as well as the secondary water supply temperature and system power consumption under corresponding operating conditions. Subsequent steps will involve control simulation of the combined thermal storage and heat pump system, using the all-day heat demand as a constraint and minimizing total electricity costs as the optimization objective.

[0181] During periods when the heat pump system is not in operation, the heat storage tank primarily stores the remaining heat from the previous day. Upon restarting the system, the stored heat in the tank is first depleted, then the system switches to direct heat pump mode, which continues until 10:00 AM. During off-peak hours, the heat pump operates at maximum load, simultaneously providing heating and storing heat. This mode continues until 3:00 PM, after which the heat pump stops, and the system continues heating based on the stored heat in the tank. If the stored heat is insufficient to meet the building's heat load requirements, the system switches to combined heat and power mode until the heating process ends at 6:00 PM that day.

[0182] Compared to the original control strategy, using a combined thermal storage and heat pump system can effectively improve power consumption during off-peak or deep off-peak hours. Here, we define a power consumption rate concept, which is the ratio of actual heating capacity to full-load heating capacity during a given electricity price period, used to represent off-peak electricity utilization efficiency.

[0183] like Figure 6 and Figure 7 As shown, under high load conditions, the combined heat pump and heat storage system has a utilization efficiency of nearly 100% for off-peak electricity, and the power consumption of the heat pump system drops to 0 during peak and high-peak electricity periods.

[0184] like Figure 8 and Figure 9 As shown, under low load conditions, the combined thermal storage and heat pump system can improve the utilization efficiency of electricity during off-peak hours by 81%, and the improvement is even more significant for electricity during deep off-peak hours, with the absorption rate increasing to over 80% in most periods.

[0185] Combination Figures 6-10This indicates that, for both high and low load conditions, the combined heat storage and heat pump system can more efficiently absorb off-peak electricity, thus offering higher economic benefits, far exceeding the situation where off-peak electricity is almost impossible to absorb effectively under the original control strategy.

[0186] from Figure 10 As can be seen, the total power consumption under the thermal storage mode is higher than that under the conventional mode. The increase in power consumption shown by the blue bars further indicates that the use of thermal storage heat pump systems will lead to increased energy consumption. However, thermal storage heat pump systems can consume more electricity during off-peak hours (such as off-peak and deep off-peak periods) to store heat, shifting the heating load to low-priced electricity periods and reducing electricity usage during high-priced periods. Although the total energy consumption increases, it effectively reduces the total cost of electricity consumption by fully utilizing the price difference, ultimately achieving economic optimization.

[0187] from Figure 11 It can be seen that the combined thermal storage and heat pump system, through flexible adjustment of thermal storage and release across time periods, not only enhances the power absorption capacity during off-peak hours, but also greatly taps the potential for power utilization during deep off-peak hours, effectively improving the overall absorption level of off-peak electricity and energy utilization efficiency.

[0188] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the protection scope of this application.

[0189] While the specific embodiments of the present invention have been described above, they are not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A control method for a thermal storage heat pump system based on a physical information neural network, characterized in that, Includes the following processes: S1 collects data related to the operation of the heat storage heat pump system and the building environment, including time variables, water supply temperature, heat pump power consumption, solar radiation intensity, indoor temperature, and outdoor temperature. S2, preprocess the collected data to obtain the standard input data for the prediction model; S3: Construct and train the PI-Seq2seq prediction model. Input the preprocessed data from S2, and the model outputs the predicted hourly water supply temperature, hourly power consumption, and hourly indoor temperature. The prediction model adopts a unified framework that integrates the physical information neural network PINN and the sequence-to-sequence neural network Seq2seq, including a physical information embedding module, a sequence time processing module, and a hybrid loss function module. The physical information embedding module in the PI-Seq2seq prediction model is based on the building RC resistance-capacitance model and embeds the physical mechanism of building heat transfer. Specifically, it includes: establishing the differential equation of indoor and outdoor heat loss based on Newton's law of cooling; deriving the building time constant by solving the temperature exponential decay model when the input heat is 0; correcting the thermal resistance by using the empirical formula of Jukkauskas cylindrical turbulence heat dissipation in a time-sharing manner; and deriving the convective heat transfer coefficient by using the corresponding Nusselt number calculation formula under natural convection and forced convection conditions, thereby correcting the thermal resistance parameters of the RC model. The empirical formula for heat dissipation by turbulence in the Jucauskas cylinder, the formula for calculating the Nusselt number under natural convection conditions and the formula for calculating the Nusselt number under forced convection conditions, are used to derive the convective heat transfer coefficient under the corresponding conditions. The convective heat transfer coefficient is calculated by the Nusselt number, the characteristic scale and the thermal conductivity when the fluid is at rest. The RC (Resistive Capacitive) model for buildings is represented as follows: In the formula, Outdoor temperature, in °C. Indoor air temperature, in °C. and These represent the heat capacity of the interior building envelope and the air system, respectively, and their thermal resistance to heat dissipation, in °C / W. It is a correction factor for solar radiation. The solar direct radiation at time t is expressed in W / m². 2 The specific values ​​can be indexed based on time; The temperature of the water in the heating pipes is expressed in °C, and the heat input from the heat source is... The unit is J; Thermal resistance between the pipe and the indoor air, expressed in °C / W. The heat capacity of the medium inside the heating pipe; when the heat exchanger exchanges heat with the indoor air, the thermal resistance coefficient is corrected, and the correction factor is... ; According to Nusel Feature scale Thermal conductivity of the fluid at rest The convective heat transfer coefficient can be calculated. , is represented as: ； The Nusselt number is used to estimate the multiple difference between natural and forced convection, which serves as a correction factor. This is used to correct the thermal resistance in the two states of heat pump start-up and shutdown. The physical information fusion method of the PI-seq2seq model is as follows: ； ； ； In the formula These represent the neural network loss, the loss calculated using the RC model, and the total loss. These are the actual temperature of the heating pipes, the temperature change calculated from power consumption and energy efficiency coefficient, and the air temperature inside the building, respectively. These are the predicted heating pipe temperature, the temperature change calculated using power consumption and energy efficiency coefficient, and the building air temperature, respectively. To calculate the regularization factor for the total loss; S4 acquires real-time peak and off-peak electricity price periods, real-time temperature of the thermal storage tank, standby power and rated maximum power of the heat pump, and inputs the prediction output of the PI-Seq2seq prediction model into the finite state machine (FSM) control model. The system operating parameters, including the heat pump operating mode, outlet water temperature control value, and thermal storage / release rate, are obtained through the three-level architecture of "global optimization-state matching-state execution" of the FSM control model.

2. The control method for a heat storage heat pump system based on a physical information neural network as described in claim 1, characterized in that: The preprocessing in S2 includes converting time variables into time-series feature variables through sine coding, and performing smooth normalization compensation on water supply temperature, heat pump power consumption, solar radiation intensity, indoor temperature, and outdoor temperature.

3. The control method for a heat storage heat pump system based on a physical information neural network as described in claim 1, characterized in that: The sequence time processing module in the PI-Seq2seq prediction model uses a Seq2seq neural network structure to extract the time-series dependencies from the input time-series feature data and output preliminary hourly predicted values ​​for water supply temperature, power consumption, and indoor temperature.

4. The control method for a heat storage heat pump system based on a physical information neural network as described in claim 3, characterized in that: The hybrid loss function module in the PI-Seq2seq prediction model consists of a data fitting error term and a physical constraint penalty term. The data fitting error term measures the deviation between the model output and the training samples, while the physical constraint penalty term is embedded in the residuals of the control equations of the building's RC (Resistive Capacitor) model, including the residuals of the differential equations for room temperature change and the residuals of the pipe heat dissipation equations. The regularization factor in the loss function is dynamically optimized using a Kalman filter algorithm. .

5. The control method for a heat storage heat pump system based on a physical information neural network as described in claim 1, characterized in that: The three-tier architecture of the FSM control model, namely "global optimization - state matching - state execution", is as follows: Global optimization layer: Combining the prediction results with the division of peak and valley electricity price periods, quantifying the system heat demand during peak electricity price periods and the heat storage potential during valley electricity price periods, calculating the difference between deep valley electricity storage energy and total daily heat consumption hdf, the difference between total energy consumption during peak electricity periods and current heat storage hhf, and determining the control indicator parameters valley electricity heat storage judgment F1 and peak electricity heat release judgment F2. State matching layer: Based on the current electricity price period and F1 and F2 parameters, and referring to the preset FSM control matrix, adaptively match the system operation mode, including direct supply mode, thermal storage mode, and heat release mode; State execution layer: Based on the matching relationship between heat pump heating capacity and power consumption, heat storage tank temperature constraint, and heat pump power constraint, the heat pump outlet water temperature is adjusted to dynamically adjust the actual operating load of the heat pump, and finally outputs system operating parameters, including: heat pump operating mode, heat pump outlet water temperature control value, and heat storage / release rate of heat storage tank.

6. The control method for a thermal storage heat pump system based on a physical information neural network as described in claim 5, characterized in that: The matching logic of the FSM control matrix is ​​as follows: during deep valley periods and valley periods, the thermal storage mode is matched first; during peak periods and peak hours, the heat release mode is matched first; during normal periods, valley periods and peak hours, the direct supply mode is matched first, and the thermal storage mode and heat release mode are not triggered during normal periods.

7. The control method for a heat storage heat pump system based on a physical information neural network as described in claim 5, characterized in that: The optimization objective of the control strategy of the FSM control model is: ； The unit electricity price at time i is expressed in yuan / kWh. For a moment i The amount of lost electricity costs is in yuan. For a moment i Heat pump power consumption, measured in kWh; When setting control parameters, use the following conditions for constraints: ； In the formula, The heating capacity of the heat pump is expressed in kW. For a moment i Heat pump power consumption, in kWh. This is the coefficient of performance (COP) of the heat pump.

8. The control method for a thermal storage heat pump system based on a physical information neural network as described in claim 7, characterized in that: To achieve optimal economic efficiency, F1 and F2 are used to control whether energy storage and heat release occur during off-peak and peak electricity periods; the judgment criteria are as follows: ； in, h df This is the difference between the total energy stored during off-peak hours and the total daily heat consumption. A positive value indicates that the energy storage increase during off-peak hours can cover the entire day's heat demand, and no energy storage is needed during off-peak hours. A negative value indicates that off-peak charging needs to be activated. The duration of off-peak electricity; Power consumption during operation at the highest set outlet water temperature of the heat pump; The heat stored in the thermal storage tank is preferentially supplied during peak electricity hours, based on the difference between the total energy consumption during peak hours and the stored heat at the current time. h hf The difference is used to determine whether heat release occurs at the peak power time. ； In the formula, This is the end of the peak electricity period. This marks the start of peak electricity demand. This refers to the specific heat capacity of the liquid in the thermal storage tank. The mass of the liquid; This represents the current water temperature inside the thermal storage tank.

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