Security constraint unit commitment method based on tensor completion approximate dynamic programming

Abstract

The invention discloses a security constraint unit commitment method based on tensor completion approximate dynamic programming, and the method comprises the following steps: firstly, building a security constraint unit commitment model based on a Markov decision process; secondly, decoupling the multi-period security constraint unit commitment model into a single-period sub; then, obtaining a value function and a decision function by adopting an approximate dynamic programming algorithm based on tensor completion; according to the approximate dynamic programming algorithm based on tensor completion, the approximate dynamic programming algorithm is improved from the angle of tensor completion, and all value functions and decision functions are approximately obtained by sampling a small number of state variables and decision variables. Decision is made from the angle of tensor complementation, in the face of a discrete state space, the value function of the whole state space can be approximated only by sampling a small number of state points, the calculation burden of an approximate dynamic programming algorithm in the aspect of value function approximation is effectively relieved, and the calculation efficiency of the algorithm can be greatly improved.

Description

Technical Field

[0001] This invention belongs to the field of power system dispatching, and specifically relates to a safety-constrained unit combination method based on tensor completion approximate dynamic programming. Background Technology

[0002] Safety-constrained unit configuration, as a crucial link connecting day-ahead planning and real-time operation, is increasingly essential. It is not only a vital tool for achieving system economy but also an indispensable and rigid line of defense for ensuring power grid security. However, the safety-constrained unit configuration model is a mixed-integer programming problem with extremely high computational complexity. Its massive scale and the "curse of dimensionality" make solving it very time-consuming. Currently, obtaining a scheduling scheme that strictly satisfies safety requirements while being economically optimal within a finite timeframe remains a significant challenge for the industry. Therefore, researching efficient methods for solving the safety-constrained unit configuration problem is essential.

[0003] Currently, commonly used methods for solving safety-constrained unit combinations mainly fall into two categories: classical mathematical optimization algorithms and heuristic optimization algorithms. Among them, classical mathematical optimization methods such as the Lagrange relaxation method and the alternating direction multiplier method require model simplification and use rigorous mathematical theoretical foundations for solving, which have considerable effectiveness and stability. However, they have problems with accuracy and convergence when facing accurate and complex models. Heuristic algorithms such as genetic algorithms and particle swarm optimization algorithms find optimal solutions by simulating certain natural behaviors and can consider complex operational constraints. However, their solution quality is unstable and their computational efficiency is low (Li Yingliang, Gao Zhaodi, Wang Kang, et al. Uncertainty Unit Combination Optimization Method Based on Clean Development Mechanism [J]. Acta Energiae Solaris Sinica, 2023, 44(03):368-375.).

[0004] Approximate dynamic programming (APP) is an emerging algorithm that has been successfully applied in various fields in recent years. Within the framework of PAP, complex multi-time-period optimization problems can be decomposed into a series of solvable single-time-period subproblems. Value functions characterize the interactions between these subproblems, thus significantly reducing computational complexity. Since value functions lack explicit expressions, the core issue in PAP lies in how to approximate them. Existing PAP algorithms typically approximate value functions using piecewise linear functions, Benders cut functions, or table functions. However, PAP methods based on piecewise linear functions and Benders cut functions can only handle continuous variables and cannot handle discrete variables in safety-constrained unit combinations. Table-based PAP methods store the value function values ​​for each state in a table, making them naturally suitable for handling discrete variables. However, current table-based PAP methods still face two problems: 1) In terms of value function approximation, existing table-based PAP algorithms require large-scale sampling of the state space, leading to unnecessary computational burden; 2) In terms of decision-making, existing table-based PAP algorithms need to traverse the entire decision space to obtain the optimal decision, further reducing solution efficiency. Summary of the Invention

[0005] This invention addresses the low computational efficiency of existing approximate dynamic programming algorithms in both value function approximation and decision-making. It proposes an approximate dynamic programming algorithm based on tensor completion and applies it to solve the safety-constrained unit combination problem. Based on the practical requirements of safety-constrained unit combination, this invention improves existing approximate dynamic programming algorithms by sampling a small number of state points to approximate the value functions of all state spaces, thereby reducing the computation time for value function approximation. It also samples a small number of decision predictions to obtain the results of all decisions, avoiding traversing the entire decision space, thus improving computational efficiency in both value function approximation and decision-making. This solves the problem that traditional methods cannot solve safety-constrained unit combination problems within a reasonable timeframe. The method of this invention is applicable to power system dispatching problems involving renewable energy, energy storage systems, and complex power grid safety constraints.

[0006] The present invention is achieved by at least one of the following technical solutions.

[0007] A safety-constrained unit combination method based on tensor completion approximate dynamic programming includes the following steps: (1) Establish a safety-constrained unit combination model based on Markov decision process; (2) Decouple the multi-period safety constraint unit combination model into a single-period sub-problem; (3) The approximate dynamic programming algorithm based on tensor completion is used to obtain the value function and decision function. After obtaining the value function and decision function, the optimal combination of unit start-up and shutdown state and active power output is obtained through optimization and screening.

[0008] Furthermore, the safety-constrained unit combination model based on Markov decision processes includes: State variables include the unit start-up and shutdown times for the current time period, the unit start-up and shutdown status and power generation for the previous time period; Decision variables include unit start-up and shutdown status, active power output, reactive power output, energy storage charging and discharging, node voltage and phase angle; State transition equations describe the state transition process of the unit between different time periods; The objective function is to minimize the operating cost of the unit throughout the entire cycle.

[0009] Furthermore, step (2) decouples the multi-period safety-constrained unit combination model into a single-period sub-problem based on the Bellman optimality principle.

[0010] Furthermore, the approximate dynamic programming algorithm based on tensor completion in step (3) includes reconstructing the state space into tensor form, sampling a small number of state points, and using tensor completion technology to approximate the value function of the entire state space.

[0011] Furthermore, the tensor completion process of the value function includes: representing the value function as a tensor, constructing a rank minimization problem based on Tucker decomposition, and solving the approximate value function by alternately minimizing the core tensor and the factor matrix.

[0012] Furthermore, the approximate dynamic programming algorithm based on tensor completion also includes: reconstructing the decision space into tensor form, sampling a small number of decision points, and using tensor completion technology to approximate the decision function of the entire decision space.

[0013] Furthermore, the tensor completion process of the decision function includes: representing the decision function as a tensor, constructing a rank minimization problem based on Tucker decomposition, and solving the approximate decision function by alternately minimizing the core tensor and the factor matrix.

[0014] Furthermore, the optimal combination of unit start-up and shutdown states and active power output is obtained through optimization and screening using the following formula:

[0015] in, Indicates the first i Start-up and shutdown of individual generating units and active power output; Represents the decision function. Indicates the first t Time periodi The start-up and shutdown status of each generating unit; and the t Time period i Active power generation of each unit; For state In the The value function for a time period represents the state. Impact on subsequent periods.

[0016] A computer device according to the present invention includes a memory and a processor, the memory being electrically connected to the processor, the memory storing a computer program, which, when executed by the processor, causes the processor to implement the method described herein.

[0017] The present invention provides a computer-readable storage medium storing a computer program, wherein when the computer program is executed by a processor, the processor implements the method described herein.

[0018] Compared with existing technologies, the beneficial effects of the present invention are as follows: This invention addresses the inefficiency of approximate dynamic programming in solving value function approximation and decision-making problems. It proposes a tensor completion approximate dynamic programming algorithm and applies it to solving the safety-constrained unit combination problem. The research content is closely related to practical needs, and there is currently no mature experience to draw upon, making its significance self-evident. Compared with existing approximate dynamic programming algorithms, this invention mainly has the following advantages: (1) This invention improves the approximate dynamic programming algorithm from the perspective of tensor completion for the first time. When facing a discrete state space, the value function of the entire state space can be approximated by sampling only a small number of state points, which effectively reduces the computational burden of the approximate dynamic programming algorithm in terms of value function approximation, thereby avoiding extensive exploration of the state space and decision space, and greatly improving the computational efficiency of the algorithm.

[0019] (2) This invention makes decisions from the perspective of tensor completion. By sampling a small number of decision results, the results of all decisions can be directly inferred, thereby avoiding traversing all decision spaces. It can support the efficient solution of safety-constrained unit combination problems, which is conducive to improving the safety margin and economic benefits of large-scale power grid operation, thus bringing good social and economic benefits. Attached Figure Description

[0020] Figure 1 This is a flowchart illustrating the steps of a safety-constrained unit combination method based on tensor completion approximate dynamic programming, as an example.

[0021] Figure 2 This is a flowchart illustrating a safety-constrained unit combination method based on tensor completion approximate dynamic programming, as an example.

[0022] Figure 3 The diagram shows the results of the unit start-up and shutdown plan in the example.

[0023] Figure 4 This is a stacked diagram of the generator set power generation process as an example. Detailed Implementation

[0024] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0025] like Figure 1 , Figure 2 As shown in the figure, a safety-constrained unit combination method based on tensor completion approximate dynamic programming in this embodiment includes the following steps: First, establish a safety-constrained unit combination model based on Markov decision processes; This embodiment considers the actual operating conditions of power system units and establishes a safety-constrained unit combination model based on Markov decision processes. In one embodiment, the Markov decision process can be described by basic elements such as state variables, decision variables, state transition equations, and objective functions.

[0026] (a) State variables State variables of safety-constrained unit combinations This includes the unit start-up and shutdown times for the current period, the unit start-up and shutdown status and power generation for the previous period, i.e. (1) In the formula, and These represent sets of nodes and sets of times, respectively. Indicates a time interval; and Represents a node i No. t Unit start-up and shutdown times for each time period; Represents a node i No. Start-up and shutdown status of the generator units during specific time periods; Represents a node i No. Active power generation of the unit during a given time period.

[0027] (b) Decision variables Decision variables This represents the variable that needs to be optimized in the safety-constrained unit combination problem, namely: (2) To ensure the safe operation of the system, all decision variables must satisfy the following constraints: (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) In the formula, Represents the set of nodes of the generator unit; G ij and B ij The nodal admittance matrix represents the first... i row and number j The real and imaginary parts of a column; Indicates the first t Time period nodes i Voltage amplitude; Indicates the first t Time period nodes i With nodes j The voltage phase angle difference; and Indicates the first t Time period nodes i The active and reactive loads; and Indicates the first t Time period nodes i The active and reactive power generation of the generating unit; and express t Time period nodes i The amount of energy discharged and charged; Indicates the upper limit of energy storage charging and discharging capacity; Indicates the efficiency of energy storage charging and discharging; and Represents a node i Upper and lower limits of the state of charge of energy storage; Indicates the time period t node i Active power generation from renewable energy sources; and Represents a node i Upper and lower limits of voltage amplitude; and Indicates the first t Time period nodes i and j The active and reactive power of the branches between them; Represents a node i and nodes j The apparent power limit of the path between them; and Represents a node i The unit's maximum gradeability and landslide rate; and These represent the upper spinning reserve capacity and the lower spinning reserve capacity of the system, respectively. Indicates the first t Time period nodes i The start-up and shutdown status of the generating units; and Represents a node i Upper and lower limits of the unit's active power generation capacity; and Represents a node i Upper and lower limits of the unit's reactive power generation; and Indicates the first t Time period nodes i Unit start-up and shutdown times; and Represents a node i Minimum start-up and shutdown time limits for the generating unit.

[0028] (c) The transition function, i.e., the state transition equation The transfer function explains the state transition process of the system between different time periods, that is: (17) (18) (d) Objective function The objective of the safety-constrained unit combination problem is to minimize the operating cost over the entire cycle, i.e.: (19) In the formula, Indicates the first t The operating cost of the time-of-use unit can be calculated using the following formula: (20) In the formula, , and Represents a node i Unit operating cost coefficient; and Represents a node i Unit start-up and shutdown costs.

[0029] Secondly, the multi-period safety constraint unit combination model is decoupled into a single-period sub-problem of a single-period model to reduce computational complexity.

[0030] Since the aforementioned safety-constrained unit combination model is a multi-time-period, non-convex, and nonlinear optimization model, solving it using traditional methods is extremely time-consuming. To reduce the solution complexity, in one embodiment, the problem is first decomposed into multiple single-time-period sub-problems based on the Bellman optimality principle: (twenty one) In the formula, and They represent the first t and The value function of a time period, i.e., the state and Impact on subsequent periods; This indicates that the optimization problem is subject to constraints (1)-(18).

[0031] Note that once the unit starts or stops and contribution It is determined that other decision variables can be obtained by solving the optimal power flow problem. Therefore, equation (21) can be further transformed into:

[0032] (twenty two) In the formula, Indicates time period t In addition to unit start-up and shutdown and unit output Other decision variables besides; The decision function is used to represent the combination of unit start-up and shutdown. and the active power output of the unit Down The value; Indicates the state and decision Cost of time.

[0033] Then, an approximate dynamic programming algorithm based on tensor completion is used to obtain the value function and decision function.

[0034] Traditional approximate dynamic programming methods are extremely time-consuming, requiring the exploration of numerous states and decisions to obtain value and decision functions. This invention, based on tensor completion, improves upon this approach by sampling a small number of states and decisions to approximate all value and decision functions. Through optimization and selection, the optimal combination of unit start-up / shutdown states and active power output is obtained, significantly improving computational efficiency. The details are as follows: Although the complex multi-period safety-constrained unit combination problem can be decomposed into a single-period problem for solution, existing approximate dynamic programming methods still face two key challenges in handling the problem (Equation (22)): First, the algorithm needs to explore a large state space to obtain the value function (i.e. Secondly, an enumeration search must be performed across the entire decision space to determine the optimal decision (i.e., resolving the optimal power flow problem under each unit combination). However, the size of the state space and decision space increases exponentially with the number of groups, leading to a sharp increase in computational complexity for the safety-constrained unit combinatorial problem in large-scale systems. To address this issue, this invention proposes an approximate dynamic programming algorithm based on tensor completion: for the former, a value function approximation technique based on tensor completion is used to efficiently approximate the value function; for the latter, a decision method based on tensor completion is introduced to quickly approximate the optimal decision, thereby significantly improving the solution efficiency of the safety-constrained unit combinatorial problem.

[0035] (a) The value function approximation technique based on tensor completion can be used to sample a small number of states to approximate the complete value function.

[0036] To avoid extensive exploration of the state space, a value function approximation technique based on tensor completion is proposed. This technique only requires sampling a small number of states to approximately complete the value function, thus significantly improving the computational efficiency of value function acquisition.

[0037] First, due to the large dimension of the state variables, this invention uses a state space... Reconstructed into tensor form:

[0038] (twenty three) In the formula, Indicates the first Taiwan unit The state space of a time period.

[0039] By reconstructing the state space, the value function It can also be further written in tensor form. .

[0040] Value function in a finite number of sampled states This can be approximated using tensor completion. This can be represented as a rank minimization problem: (twenty four) In the formula, express G 3D real space, the first g The size of the space is ; This represents an incomplete value function (i.e., a value function obtained by sampling only a small number of states). Tensor rank; Represents the set of sampled states; Value function The projection tensor can be obtained through equation (25); express The projection tensor can also be obtained similarly.

[0041] (25) Since the rank minimization problem formula (24) is an NP-hard problem, this invention further transforms it into the form of Tucker decomposition as follows: (26) In the formula, The core tensor representing the approximation of the value function; Representing the state space rank; The factor matrix representing the approximation of the value function; This represents G modulus multiplication.

[0042] Then, equation (26) can be minimized by alternation. and The solution is shown in Equations (27) and (28).

[0043] (27) (28) In the formula, k Indicates the number of iterations; g express Index; and Indicates the first k In the next iteration and The value of .

[0044] The termination condition for this alternating minimization can be expressed as the core tensor and factor matrix changing sufficiently before and after the update during the iteration, as shown in Equations (29) and (30).

[0045] (29) (30) In the formula, Indicates the iteration termination coefficient; This represents the Frobenius norm of the tensor.

[0046] Once the termination conditions (29) and (30) are satisfied, the approximate value function can be obtained, as shown in formula (31).

[0047] (31) After the above improvements, a value function approximation technique based on tensor completion can be formed. For value functions... This allows for the approximation of the entire value function by sampling only a finite set of states Ω, thereby greatly improving sampling and computation efficiency. The specific steps are as follows: 1) Input: Sampled state set Ω and termination coefficient .

[0048] 2) Initialization: Randomly initialize the factor matrix. .

[0049] 3) for k =1, 2,…do.

[0050] 4) Fix all Solve equation (27) to obtain .

[0051] 5) Fixed Solve formula (28) to obtain .

[0052] 6) If the termination conditions formulas (29) and (30) are satisfied, exit the loop.

[0053] 7) Obtain the value function through equation (31) .

[0054] 8) end for.

[0055] (b) Decision-making method based on tensor completion As can be seen from equation (22), besides the value acquisition function Furthermore, it is necessary to resolve the optimal power flow problem for each unit start-stop combination. (i.e., obtaining the decision function) To avoid this traversal process, this invention proposes a decision-making method based on tensor completion, as follows: First, similar to value function approximation techniques, the decision space related to unit start-up and shutdown and active power output can be represented in tensor form: (32) In the formula, Represents the decision tensor; Indicates the first i g Start-up and shutdown of individual generating units and active power output; Indicates time period t No. i g The decision-making space of each unit.

[0056] By reconstructing the decision space, the decision function can be further represented in tensor form. .

[0057] Under a finite number of sampling decisions, the decision function This can be approximated using tensor completion. This can also be represented as a rank minimization problem: (33) In the formula, This represents an incomplete decision function (i.e., a decision function obtained by sampling only a small number of decisions). Tensor rank; Represents the set of sampled states; and Representing the decision function and The projection tensor can be obtained similarly using equation (25).

[0058] Similar to the value function approximation technique, this invention further transforms equation (33) into the form of Tucker decomposition as follows: (34) In the formula This represents the core tensor in the decision function approximation; This represents the factor matrix in the decision function approximation.

[0059] Then, formula (34) can be minimized by alternation. and The solution is shown in equations (35) and (36).

[0060] (35) (36) In the formula, and Indicates the first k The next iteration and ; Indicates the first G Factor matrix .

[0061] The termination condition for this alternating minimization can be expressed as the core tensor and factor matrix changing sufficiently before and after the update during the iteration, as shown in equations (37) and (38).

[0062] (37) (38) In the formula, This represents the iteration termination coefficient.

[0063] Once the termination conditions (37) and (38) are satisfied, the decision function can be approximated, such as... (39)

[0064] After the above improvements, a decision approximation technique based on tensor completion can be formed. For the decision function... It is possible to sample only a finite number of decision Ω D The entire decision function is approximated, thereby greatly improving decision-making efficiency. The specific steps are as follows: (1) Input: Sampled state set Ω D and termination coefficient .

[0065] (2) Initialization: Randomly initialize the factor matrix .

[0066] (3) for k =1, 2,…do.

[0067] (4) Fix all Solve formula (35) to obtain .

[0068] (5) Fixed Solve formula (36) to obtain .

[0069] (6) If the termination conditions formulas (37) and (38) are satisfied, exit the loop.

[0070] (7) The decision function is obtained through formula (39). .

[0071] (8) end for.

[0072] (c) Solution steps for the safety-constrained unit combination problem By combining the value function approximation technique and decision-making technique described above using tensor completion, an approximate dynamic programming algorithm based on tensor completion can be formed to solve the safety-constrained unit combination problem of power systems. The specific steps are as follows: (1) for t = T , ,…, do (2) Input: Sampled state set Ω and termination coefficient .

[0073] (3) Initialization: Randomly initialize the factor matrix .

[0074] (4) for k =1, 2,…do.

[0075] (5) Fix all Solve formula (27) to obtain .

[0076] (6) Fixed Solve equation (28) to obtain .

[0077] (7) If the termination conditions (29) and (30) are satisfied, exit the loop.

[0078] (8) The value function is obtained through equation (31). .

[0079] (9) end for.

[0080] (10) for t = , ,…, T do.

[0081] (11) Input: Sampled state set Ω D Termination coefficient Sum function .

[0082] (12) Initialization: Randomly initialize the factor matrix .

[0083] (13) for k =1, 2,…do.

[0084] (14) Fix all Solve equation (35) to obtain .

[0085] (15) Fixed Solve equation (36) to obtain .

[0086] (16) If the termination conditions (37) and (38) are satisfied, exit the loop.

[0087] (17) The decision function is obtained through equation (39). .

[0088] (18) end for.

[0089] (19) The optimal unit combination and active power output are selected by formula (40).

[0090] (40) (20) end for.

[0091] The preferred embodiments of the present invention disclosed above are merely illustrative of the invention. These preferred embodiments do not exhaustively describe all details, nor do they limit the invention to the specific implementations described. Clearly, many modifications and variations can be made based on the content of this specification. This specification selects and specifically describes these embodiments to better explain the principles and practical applications of the invention, enabling those skilled in the art to better understand and utilize the invention.

Claims

1. A method for safety-constrained unit combination based on tensor completion approximate dynamic programming, characterized in that, Includes the following steps: (1) Establish a safety-constrained unit combination model based on Markov decision process; (2) Decouple the multi-period safety constraint unit combination model into a single-period sub-problem; (3) The approximate dynamic programming algorithm based on tensor completion is used to obtain the value function and decision function. After obtaining the value function and decision function, the optimal combination of unit start-up and shutdown state and active power output is obtained through optimization and screening.

2. The safety-constrained unit combination method based on tensor completion approximate dynamic programming according to claim 1, characterized in that, The safety-constrained unit combination model based on Markov decision processes includes: State variables include the unit start-up and shutdown times for the current time period, the unit start-up and shutdown status and power generation for the previous time period; Decision variables include unit start-up and shutdown status, active power output, reactive power output, energy storage charging and discharging, node voltage and phase angle; State transition equations describe the state transition process of the unit between different time periods; The objective function is to minimize the operating cost of the unit throughout the entire cycle.

3. The safety-constrained unit combination method based on tensor completion approximate dynamic programming according to claim 1, characterized in that, Step (2) is to decouple the multi-time period safety constraint unit combination model into a single-time period sub-problem based on the Bellman optimality principle.

4. The safety-constrained unit combination method based on tensor completion approximate dynamic programming according to claim 1, characterized in that, The approximate dynamic programming algorithm based on tensor completion in step (3) includes reconstructing the state space into tensor form, sampling a small number of state points, and using tensor completion technology to approximate the value function of the entire state space.

5. The safety-constrained unit combination method based on tensor completion approximate dynamic programming according to claim 4, characterized in that, The tensor completion process of the value function includes: representing the value function as a tensor, constructing a rank minimization problem based on Tucker decomposition, and solving the approximate value function by alternately minimizing the core tensor and the factor matrix.

6. The safety-constrained unit combination method based on tensor completion approximate dynamic programming according to claim 1, characterized in that, The approximate dynamic programming algorithm based on tensor completion further includes: reconstructing the decision space into tensor form, sampling a small number of decision points, and using tensor completion technology to approximate the decision function of the entire decision space.

7. The safety-constrained unit combination method based on tensor completion approximate dynamic programming according to claim 6, characterized in that, The tensor completion process of the decision function includes: representing the decision function as a tensor, constructing a rank minimization problem based on Tucker decomposition, and solving the approximate decision function by alternately minimizing the core tensor and the factor matrix.

8. The safety-constrained unit combination method based on tensor completion approximate dynamic programming according to claim 1, characterized in that, The optimal combination of unit start-up and shutdown states and active power output is obtained through optimization and screening using the following formula: in, Indicates the first i Start-up and shutdown of individual generating units and active power output; Represents the decision function. Indicates the first t Time period i The start-up and shutdown status of each generating unit; and the t Time period i Active power generation of each unit; For state In the The value function for a time period represents the state. Impact on subsequent periods.

9. A computer device comprising a memory and a processor, the memory being electrically connected to the processor, the memory storing a computer program, characterized in that: When the computer program is executed by the processor, it causes the processor to implement the method as described in any one of claims 1 to 8.

10. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the processor implements the method as described in any one of claims 1 to 8.

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