A data-driven carbon dioxide refrigeration data center temperature control method

Abstract

The application discloses a data-driven carbon dioxide refrigeration data center temperature control method, and belongs to the technical field of carbon dioxide refrigeration data center temperature control, which comprises the following steps: combining the control target of a carbon dioxide refrigeration and temperature control system of a data center, establishing an augmented system, and establishing a performance function, an HJB equation and an integral Bellman equation; approximating the performance function and the control strategy through an evaluation network and an action network to obtain an approximate value, replacing the performance function and the control strategy of the integral Bellman equation, and defining a residual error to obtain a weight updating law; given an input signal, collecting state information and input information of the augmented system, and iteratively solving optimal weights based on the weight updating law; and obtaining an optimal control strategy by using the optimal weights, and applying the optimal control strategy to the carbon dioxide refrigeration and temperature control system of the data center. The method does not depend on the dynamic model of the carbon dioxide refrigeration system, and significantly improves the practicability and adaptability of the control scheme.

Description

Technical Field

[0001] This application relates to the field of carbon dioxide refrigeration data center temperature control technology, and in particular to a data-driven carbon dioxide refrigeration data center temperature control method. Background Technology

[0002] With the continuous development of modern information technology, the scale and number of data centers are also increasing, and their cooling demand is also growing rapidly. With its significant advantages such as being non-toxic, non-corrosive, and having good phase change heat transfer, carbon dioxide has been gradually applied to the cooling systems of data centers.

[0003] However, the carbon dioxide cooling system of a data center is extremely complex, including numerous components such as compressors, gas coolers, expansion valves, evaporators, internal heat exchangers, and connecting pipes. Modeling the system requires not only a deep understanding of the physical characteristics of each component but also parameter identification, making it difficult to obtain an accurate model of the system. Furthermore, inaccurate modeling leading to parameter deviations can affect the temperature control precision, thus highlighting the significant limitations of model-based control methods.

[0004] Therefore, a control scheme is needed that eliminates the complex modeling process of carbon dioxide refrigeration systems and uses only the input and status information of the carbon dioxide refrigeration system to achieve precise temperature control of the data center in a data-driven manner. Summary of the Invention

[0005] To address the aforementioned shortcomings in existing technologies, this application provides a data-driven method for controlling the temperature of carbon dioxide refrigeration data centers. This method offers a model-free approach for precise temperature control of carbon dioxide refrigeration systems in data centers, solving the problem that existing model-based control methods can affect the accuracy of temperature control. It also provides technical support for improving energy efficiency and promoting green refrigeration in data centers.

[0006] To achieve the aforementioned objectives, the technical solution adopted in this application is as follows:

[0007] This application provides a data-driven method for temperature control of a carbon dioxide-cooled data center, including:

[0008] S1: Based on the control objectives of the carbon dioxide cooling and temperature control system of the data center, establish an augmented system concerning the state error and the target state, and establish the performance function, HJB equation and integral Bellman equation of the augmented system.

[0009] S2: By approximating the performance function and control strategy of the augmented system through the evaluation network and action network, approximate values ​​of the performance function and control strategy are obtained. Based on the approximate values ​​of the performance function and control strategy, the performance function and control strategy of the integral Bellman equation are replaced, and the residuals are defined. Based on the residuals, the weight update law of the augmented weights is obtained.

[0010] S3: Given an input signal, collect the state information and input information of the augmented system, and iteratively solve for the optimal augmented weights based on the weight update law of the augmented weights;

[0011] S4: The optimal control strategy is calculated using the solved optimal augmented weights, and the optimal control strategy is used as the input signal to apply to the carbon dioxide cooling and temperature control system of the data center.

[0012] Further, S1 includes:

[0013] S101: Combining the control objectives of the data center's carbon dioxide cooling and temperature control system, construct the target state and tracking error, and build the performance function;

[0014] S102: Construct augmented vectors for the target state and tracking error, build an augmented system based on the augmented vectors, and construct the performance function of the augmented system based on the performance function;

[0015] S103: Based on the augmented system and its performance function, construct the optimal performance function and HJB equation, and obtain the optimal control strategy based on the HJB equation;

[0016] S104: Based on the optimal control strategy, rewrite the augmented system, and construct the integral Bellman equation based on the optimal performance function, the optimal control strategy, and the rewritten augmented system.

[0017] Furthermore, the control objective of the combined data center carbon dioxide cooling and temperature control system is used to construct the target state and tracking error, and a performance function is constructed, including:

[0018] A1: Model the carbon dioxide cooling and temperature control system of the data center as a general nonlinear system:

[0019]

[0020] In the formula, Let be the actual state vector of the system. and These are the system drift dynamics and the input dynamics, respectively. For system input, For the current moment The derivative, The number of system states. The number of inputs from the system. For the current moment, Represents the set of real numbers;

[0021] A2: Set the target superheat at the evaporator outlet and the target temperature inside the data center as the target state. , The dynamic characteristics are:

[0022]

[0023] In the formula, For the target state generator function, The target state at the current moment The derivative;

[0024] A3: Construct tracking error based on actual state and target state. :

[0025]

[0026] Among them, tracking error The dynamic equation is:

[0027]

[0028] In the formula, The tracking error at the current moment The derivative;

[0029] A4: Based on tracking error and system input Construct the performance function:

[0030]

[0031] In the formula, Let be the state at any time within the integration interval. For any time interval within the integration interval, the superscript is used as the input. For the transpose of a vector or matrix, As a discount factor, and It is a symmetric positive definite matrix. It is the integral variable.

[0032] Furthermore, the augmented vector for:

[0033]

[0034] The augmentation system is:

[0035]

[0036] in, Augmented vector at the current time step The derivative, To augment the drift state of the system, To enhance the input dynamics of the system, Input for the system;

[0037] The performance function of the augmented system is:

[0038]

[0039] in, Let be the augmented state at any time within the integration interval. For any time interval within the integration interval, the system input is given. It is a symmetric matrix.

[0040] Furthermore, the optimal performance function for:

[0041]

[0042] in, The set of real numbers The allowable control set on, Indicates allowable control set The smallest ;

[0043] The HJB equation is:

[0044]

[0045] in, This is the optimal control strategy. Represents the optimal performance function right The derivative, To find the partial derivative operator;

[0046] The optimal control strategy for:

[0047]

[0048] Among them, superscript Represents the inverse matrix. This indicates taking the minimum value.

[0049] Furthermore, the rewritten augmentation system is as follows:

[0050]

[0051] in, For the control strategy iteration The control strategy obtained from this calculation. This represents the number of iterations.

[0052] Furthermore, the construction of the integral Bellman equation based on the optimal performance function, optimal control strategy, and the rewritten augmented system includes:

[0053] Combining the optimal performance function and the optimal control strategy, the control strategy is iterated in the 1st... The performance function obtained from the calculation Along the rewritten augmented system dynamic trajectory with respect to time Taking the derivative, we get Compared to The derivative:

[0054]

[0055] in, Representing the The performance function obtained from the calculation State The derivative, For the control strategy iteration The control strategy obtained from this calculation;

[0056] In time interval Integrating internally, we obtain the integral Bellman equation:

[0057]

[0058] in, Indicates the integration time. express At this moment The performance function of the next iteration and For the first Second and third Control strategy for the next iteration For the corresponding number The performance function for each iteration.

[0059] Further, S2 includes:

[0060] S201: Utilizing the universal approximation property of neural networks, the control policy is iterated through the evaluation network and the action network respectively. The performance function obtained from the calculation and control strategies :

[0061]

[0062]

[0063] in, and They are respectively and Approximate value, and These are the weights for the evaluation network and the action network, respectively. and These are the basis functions for linearly uncorrelated neural networks. and These represent the number of hidden neurons in the two networks, respectively.

[0064] S202: Integrating the Bellman equations , , and Use their approximations respectively , , and To replace, and make , To obtain the residual :

[0065]

[0066] in, and Represent Time and time, For the index of the collected dataset, for Approximate value, and They are respectively and Activation function at time step and These are the activation functions of the action network and the evaluation network at any time within the integration interval, respectively. and The first The weights of the evaluation network and action network in the next iteration;

[0067] S203: Setting intermediate parameters and Simplify the expression for the residual:

[0068]

[0069] in, , , For augmented weight vectors, This means straightening the matrix according to the column order;

[0070] S204: Use least squares to minimize The weight update law for augmented weights is obtained as follows:

[0071]

[0072] in, The size of the collected training dataset.

[0073] Further, S3 includes:

[0074] S301: The set expansion valve opening and compressor speed are used as the given input signals. In the time interval The state and input data of the augmented system are collected and then obtained. and ;

[0075] in, and These represent the initial and final times of data collection, and the size of the collected training dataset. To satisfy the condition: there exist two positive real numbers. and , such that for any All of them have:

[0076]

[0077] In the formula, yes An identity matrix of 3D;

[0078] S302: Setting Using the initial control strategy Calculate the weights of the corresponding action network. The weight update law of augmented weights is used to calculate the first... Augmented weights in the next iteration ;

[0079] S303: Order Iterative updates Until if When the iteration stops, and the value at this point is... As the optimal augmented weight; otherwise, let Continue iterating ;

[0080] in, The pre-set termination iteration threshold, For the first Augmented weights for the next iteration The Euclidean norm represents the vector.

[0081] Further, S4 includes:

[0082] S401: Solve for the optimal control strategy using the optimal augmented weights obtained through iterative solutions. and optimal performance function ;

[0083] S402: Will Carbon dioxide refrigeration and temperature control systems used as input signals in data centers.

[0084] The beneficial effects of this application are:

[0085] This application provides a data-driven method for controlling the temperature of a carbon dioxide-cooled data center. This method does not rely on the dynamic model of the carbon dioxide-cooled system, significantly improving the practicality and adaptability of the control scheme. Furthermore, this method optimizes the performance indicators of the cooling system and achieves precise control of cooling energy consumption through a data-driven dynamic adjustment mechanism. While achieving temperature control of the data center, it also improves the energy efficiency of the system, which meets the needs of green and low-carbon development. Attached Figure Description

[0086] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other embodiments can be obtained based on these drawings.

[0087] Figure 1 This is a flowchart illustrating a data-driven carbon dioxide refrigeration data center temperature control method provided in an embodiment of this application. Detailed Implementation

[0088] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art based on this application are within the scope of protection of this application.

[0089] This application provides a data-driven method for temperature control in a carbon dioxide-cooled data center, which can be found in [reference needed]. Figure 1 , Figure 1The diagram shown is a schematic flowchart of a data-driven carbon dioxide refrigeration data center temperature control method provided in an embodiment of this application, including:

[0090] S1: Based on the control objectives of the carbon dioxide cooling and temperature control system of the data center, establish an augmented system concerning the state error and the target state, and establish the performance function, HJB equation and integral Bellman equation of the augmented system.

[0091] In one embodiment of this application, the carbon dioxide cooling and temperature control system of the data center is first modeled as a general nonlinear system:

[0092]

[0093] in, Let be the actual state vector of the system. and These are the system drift dynamics and the input dynamics, respectively. For system input, For the current moment The derivative, The number of system states. The number of inputs from the system. For the current moment, It represents the set of real numbers.

[0094] Set the target superheat at the evaporator outlet and the target temperature inside the data center as the target states. , The dynamic characteristics are:

[0095]

[0096] in, For the target state generator function, The target state at the current moment The derivative of .

[0097] Tracking error The difference between the actual state and the target state is:

[0098]

[0099] Tracking error The dynamic equation is:

[0100]

[0101] In the formula, The tracking error at the current moment The derivative of .

[0102] Based on tracking error and system input Construct the following performance function:

[0103]

[0104] in, Let be the state at any time within the integration interval. For any time interval within the integration interval, the superscript is used as the input. For the transpose of a vector or matrix, As a discount factor, and It is a symmetric positive definite matrix. It is the integral variable.

[0105] Then, an augmented vector of tracking error and target state is constructed. The dynamic equation of the augmented system is then:

[0106]

[0107] in, Augmented vector at the current time step The derivative, To augment the drift state of the system, To enhance the input dynamics of the system, Input for the system.

[0108] Next, the performance function of the augmented system is:

[0109]

[0110] in, Let be the augmented state at any time within the integration interval. For any time interval within the integration interval, the system input is given. It is a symmetric matrix.

[0111] The constructed HJB equation is as follows:

[0112]

[0113] in, This is the optimal control strategy. Represents the optimal performance function right The derivative, To find the partial derivative operator, The form is:

[0114]

[0115] in, The set of real numbers The allowable control set on, Indicates allowable control set The smallest .

[0116] The optimal control strategy can be obtained from the HJB equation. for:

[0117]

[0118] Among them, superscript Represents the inverse matrix. This indicates taking the minimum value.

[0119] Finally, the augmentation system is rewritten as follows:

[0120]

[0121] in, For initial permissive control, For the control strategy iteration The control strategy obtained from this calculation. This represents the number of iterations.

[0122] Combining the optimal performance function and the optimal control strategy, the control strategy is iterated in the 1st... The performance function obtained from the calculation Along the rewritten augmented system dynamic trajectory with respect to time Taking the derivative, we get Compared to The derivative:

[0123]

[0124] in, Representing the The performance function obtained from the calculation State The derivative, For the control strategy iteration The control strategy is obtained from the calculation.

[0125] Then in the time interval Integrating internally, we obtain the integral Bellman equation:

[0126]

[0127] in, Indicates the integration time. express At this moment The performance function of the next iteration and For the first Second and third Control strategy for the next iteration For the corresponding number The performance function for each iteration.

[0128] S2: By approximating the performance function and control strategy of the augmented system through the evaluation network and action network, approximate values ​​of the performance function and control strategy are obtained. Based on the approximate values ​​of the performance function and control strategy, the performance function and control strategy of the integral Bellman equation are replaced, and the residuals are defined. Based on the residuals, the weight update law of the augmented weights is obtained.

[0129] In one embodiment of this application, firstly, utilizing the universal approximation property of neural networks, the control policy is iterated through an evaluation network and an action network to approximate the first iteration. The performance function obtained from the calculation and control strategies :

[0130]

[0131]

[0132] in, and They are respectively and Approximate value, and These are the weights for the evaluation network and the action network, respectively. and These are the basis functions for linearly uncorrelated neural networks. and These represent the number of hidden neurons in the two networks, respectively.

[0133] Integrating the Bellman equation , , and Use their approximation values ​​respectively , , and To replace, and make , To obtain the residual :

[0134]

[0135] Among them, among them, and Represent Time and time, For the index of the collected dataset, for Approximate value, and They are respectively and Activation function at time step and These are the activation functions of the action network and the evaluation network at any time within the integration interval, respectively. and The first The weights of the evaluation network and action network in the next iteration.

[0136] Set intermediate parameters and :

[0137]

[0138] Simplified residuals The expression for:

[0139]

[0140] in, For augmented weight vectors, This means straightening the matrix according to the column order.

[0141] Then, the least squares method is used to minimize We can obtain the weight update law for augmented weights:

[0142]

[0143] in, The size of the collected training dataset.

[0144] S3: Given the input signal Within a certain time interval, the state and input information of the augmented system are collected; based on the weight update law designed by S2, the optimal augmented weights are iteratively solved.

[0145] In one embodiment of this application, firstly, the set expansion valve opening degree and compressor speed are used as given input signals. In the time interval The system collects and establishes the status and input data of the augmented system, including the superheat at the evaporator outlet, the ambient temperature inside the data center, the expansion valve opening, and the compressor speed. With this status and input information of the augmented system, we can obtain... and .

[0146] in, and These represent the initial and final times of data collection, and the size of the collected training dataset. To satisfy the condition: there exist two positive real numbers. and , such that for any All of them have:

[0147]

[0148] in, yes An identity matrix of dimension 1.

[0149] Secondly, let Using the initial control strategy Calculate the weights of the action network at this time. The weight update law of augmented weights is used to calculate the first... Augmented weights in the next iteration .

[0150] Then, let Iterative updates Until the very end, if If the iteration stops, then the current iteration will be stopped. As the optimal augmentation weight, where The pre-set termination iteration threshold, For the first Augmented weights for the next iteration The Euclidean norm of the vector; otherwise, let Continue iterating .

[0151] S4: Construct the optimal control strategy using the optimal augmented weights obtained from S3, and apply it to the carbon dioxide cooling and temperature control system of the data center as its input signal.

[0152] In one embodiment of this application, the optimal control strategy is first solved using the optimal augmented weights obtained through S3 iteration. and optimal performance function .

[0153] Then, Carbon dioxide refrigeration and temperature control systems used as input signals in data centers.

[0154] By performing the above steps, temperature control of a data-driven carbon dioxide-cooled data center can be achieved.

[0155] This application provides a data-driven method for controlling the temperature of a carbon dioxide-cooled data center. This method does not rely on the dynamic model of the carbon dioxide-cooled system, significantly improving the practicality and adaptability of the control scheme. Furthermore, this method optimizes the performance indicators of the cooling system and achieves precise control of cooling energy consumption through a data-driven dynamic adjustment mechanism. While achieving temperature control of the data center, it also improves the energy efficiency of the system, which meets the needs of green and low-carbon development.

[0156] It should be noted that those skilled in the art will recognize that the embodiments described herein are for the purpose of helping readers understand the principles of this application, and should be understood as not limiting the scope of protection of this application to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this application without departing from the essence of this application, and these modifications and combinations are still within the scope of protection of this application.

Claims

1. A data-driven method for temperature control in a carbon dioxide-cooled data center, characterized in that, include: S1: Based on the control objectives of the carbon dioxide cooling and temperature control system of the data center, establish an augmented system concerning the state error and the target state, and establish the performance function, HJB equation and integral Bellman equation of the augmented system. S2: By approximating the performance function and control strategy of the augmented system through the evaluation network and action network, approximate values ​​of the performance function and control strategy are obtained. Based on the approximate values ​​of the performance function and control strategy, the performance function and control strategy of the integral Bellman equation are replaced, and the residuals are defined. Based on the residuals, the weight update law of the augmented weights is obtained. S3: Given an input signal, collect the state information and input information of the augmented system, and iteratively solve for the optimal augmented weights based on the weight update law of the augmented weights; S4: The optimal control strategy is calculated using the solved optimal augmented weights, and the optimal control strategy is used as the input signal to apply to the carbon dioxide cooling and temperature control system of the data center. S1 includes: S101: Combining the control objectives of the data center's carbon dioxide cooling and temperature control system, construct the target state and tracking error, and build the performance function; S102: Construct augmented vectors for the target state and tracking error, build an augmented system based on the augmented vectors, and construct the performance function of the augmented system based on the performance function; S103: Based on the augmented system and its performance function, construct the optimal performance function and HJB equation, and obtain the optimal control strategy based on the HJB equation; S104: Based on the optimal control strategy, rewrite the augmented system, and based on the optimal performance function, the optimal control strategy, and the rewritten augmented system, construct the integral Bellman equation; The control objective of the combined data center carbon dioxide cooling and temperature control system is used to construct the target state and tracking error, and a performance function is constructed, including: A1: Model the carbon dioxide cooling and temperature control system of the data center as a general nonlinear system: In the formula, Let be the actual state vector of the system. and These are the system drift dynamics and the input dynamics, respectively. For system input, For the current moment The derivative, The number of system states. The number of inputs from the system. For the current moment, Represents the set of real numbers; A2: Set the target superheat at the evaporator outlet and the target temperature inside the data center as the target state. , The dynamic characteristics are: In the formula, For the target state generator function, The target state at the current moment The derivative; A3: Construct tracking error based on actual state and target state. : Among them, tracking error The dynamic equation is: In the formula, The tracking error at the current moment The derivative; A4: Based on tracking error and system input Construct the performance function: In the formula, Let be the state at any time within the integration interval. For any time interval within the integration interval, the superscript is used as the input. For the transpose of a vector or matrix, As a discount factor, and It is a symmetric positive definite matrix. For integration variables; The augmented vector for: The augmentation system is: in, Augmented vector at the current time step The derivative of To augment the drift state of the system, To enhance the input dynamics of the system, Input for the system; The performance function of the augmented system is: in, Let be the augmented state at any time within the integration interval. For any time interval within the integration interval, the system input is given. It is a symmetric matrix; The optimal performance function for: in, The set of real numbers The allowable control set on, Indicates allowable control set The smallest ; The HJB equation is: in, This is the optimal control strategy. Represents the optimal performance function right The derivative, To find the partial derivative operator; The optimal control strategy for: Among them, superscript Represents the inverse matrix. This indicates taking the minimum value.

2. The data-driven carbon dioxide refrigerated data center temperature control method according to claim 1, characterized in that, The rewritten augmentation system is as follows: in, For the control strategy iteration The control strategy obtained from this calculation. This represents the number of iterations.

3. The data-driven carbon dioxide refrigeration data center temperature control method according to claim 2, characterized in that, The integral Bellman equations, constructed based on the optimal performance function, optimal control strategy, and the rewritten augmented system, include: Combining the optimal performance function and the optimal control strategy, the control strategy is iterated in the 1st... The performance function obtained from the calculation Along the rewritten augmented system dynamic trajectory with respect to time Taking the derivative, we get Compared to The derivative: in, Representing the The performance function obtained from the calculation State The derivative, For the control strategy iteration The control strategy obtained from this calculation; In the time interval Integrating internally, we obtain the integral Bellman equation: in, Indicates the integration time. express At this moment The performance function of the next iteration and For the first Second and third Control strategy for the next iteration For the corresponding number The performance function for each iteration.

4. The data-driven carbon dioxide refrigerated data center temperature control method according to claim 3, characterized in that, The S2 includes: S201: Utilizing the universal approximation property of neural networks, the control policy is iterated through the evaluation network and the action network respectively. The performance function obtained from the calculation and control strategies : in, and They are respectively and Approximate value, and These are the weights for the evaluation network and the action network, respectively. and For linearly uncorrelated neural network basis functions, and These represent the number of hidden neurons in the two networks, respectively. S202: Integrating the Bellman equation , , and Use their approximations respectively , , and To replace, and make , To obtain the residual : in, and Represent Time and time, For the index of the collected dataset, for Approximate value, and They are respectively and Activation function at time step and These are the activation functions of the action network and the evaluation network at any time within the integration interval, respectively. and The first The weights of the evaluation network and action network in the next iteration; S203: Setting intermediate parameters and Simplify the expression for the residual: in, , , For augmented weight vectors, This means straightening the matrix according to the column order; S204: Use least squares to minimize The weight update law for augmented weights is obtained as follows: in, The size of the collected training dataset.

5. The data-driven carbon dioxide refrigerated data center temperature control method according to claim 4, characterized in that, The S3 includes: S301: The set expansion valve opening and compressor speed are used as the given input signals. In the time interval The state and input data of the augmented system are collected and then obtained. and ; in, and These represent the initial and final times of data collection, and the size of the collected training dataset. To satisfy the condition: there exist two positive real numbers. and , such that for any All of them have: In the formula, yes An identity matrix of 3D; S302: Setting Using the initial control strategy Calculate the weights of the corresponding action network. The weight update law of augmented weights is used to calculate the first... Augmented weights in the next iteration ; S303: Order Iterative updates Until if When the iteration stops, and the value at this point is... As the optimal augmented weight; otherwise, let Continue iterating ; in, The pre-set termination iteration threshold, For the first Augmented weights for the next iteration The Euclidean norm represents the vector.

6. The data-driven carbon dioxide refrigeration data center temperature control method according to claim 5, characterized in that, The S4 includes: S401: Solve for the optimal control strategy using the optimal augmented weights obtained through iterative solutions. and optimal performance function ; S402: Will Carbon dioxide refrigeration and temperature control systems used as input signals in data centers.

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