A closed-loop feedback-based active power distribution network robust optimization operation method

Abstract

The application is suitable for the technical field of active power distribution network operation optimization, and provides a kind of active power distribution network robust optimization operation method based on closed loop feedback. Firstly, a power prediction model based on convolutional neural network and long short term memory network is constructed to complete the time series prediction of source and load power. A centralized-just-in-place collaborative second order cone convex programming (SOCP) model physical control layer is established and robustified. The system scheduling is realized through SOCP optimization method and segmented droop control strategy. A correction feedback layer is established to optimize the parameters of the prediction model according to the comprehensive loss function, improve the prediction accuracy and optimize the active power loss and voltage safety of the system. The results show that the method can significantly reduce the system operation loss and node total voltage out-of-limit rate under the condition of source and load uncertainty while ensuring the prediction accuracy, and has high solving efficiency. The method relies on the "prediction-control-correction" collaborative optimization mechanism to improve the robustness, stability and economy of the power distribution network.

Description

Technical Field

[0001] This invention belongs to the field of active distribution network operation optimization technology, and particularly relates to a robust optimization operation method for active distribution networks based on closed-loop feedback. Background Technology

[0002] With the rapid development of renewable energy power generation technologies, distributed photovoltaic (PV) power generation, with its advantages of being clean, low-carbon, and flexible in installation, has seen its penetration rate in distribution networks continuously increase, gradually becoming an important component of the distribution network's energy supply. While this transformation has injected momentum into the green development of distribution networks, it has also brought significant challenges: the output of distributed PV is highly volatile due to natural conditions such as sunlight and temperature, which may directly lead to frequent voltage exceedances, significant increases in system active power losses, and excessive equipment operation frequency during distribution network operation. These issues seriously threaten the safe, stable, and economically efficient operation of the distribution network, necessitating breakthroughs in optimized dispatching technologies.

[0003] To address these challenges, industry and academia have conducted extensive research on distribution network optimization and scheduling, but various technologies have significant shortcomings. Traditional distribution network optimization methods typically ignore the impact of source load uncertainty on the optimization model, relying directly on prediction results for scheduling. This lacks robustness and dynamic adjustment capabilities, making it difficult to effectively address problems caused by source load fluctuations. To solve these problems, existing research has attempted to introduce robust optimization and distributed control technologies into distribution network optimization and scheduling, but issues such as separation of prediction and decision-making and insufficient control precision still exist. Furthermore, traditional data-based end-to-end models are often "black box" models, focusing only on the mapping from input parameters to decision variables, ignoring intermediate physical constraints or dynamic changes in system operating states, and lacking engineering interpretability. While some improved end-to-end learning methods construct a complete model from input to decision output, considering the reverse impact of prediction errors on decision quality, they are prone to optimization strategy failure and safety hazards such as voltage exceeding limits due to amplified prediction errors. Therefore, this invention proposes an active distribution network robust optimization operation method based on closed-loop feedback. Summary of the Invention

[0004] The purpose of this invention is to provide a robust optimization method for active distribution network operation based on closed-loop feedback, which aims to solve the problems mentioned in the background art.

[0005] The objective of this invention is achieved through the following technical solution:

[0006] A robust optimization operation method for active distribution networks based on closed-loop feedback includes the following steps:

[0007] A closed-loop feedback mechanism of "prediction-control-correction" is established, which integrates machine learning prediction, physical system regulation and decision quality assessment to form a closed-loop iterative process. The closed-loop feedback mechanism outputs the optimized decision results through the power prediction layer, and iteratively feeds them back through the physical control layer and the correction feedback layer to gradually optimize the prediction model parameters.

[0008] A power prediction model is constructed, and a CNN-LSTM hybrid neural network is used to extract and predict the spatiotemporal features of the source load power. The feedback signal of the physical control layer is used to correct the model parameters in reverse.

[0009] A centralized optimization model for the active distribution network in the physical control layer is constructed with the goal of minimizing the active power loss of the system during the control cycle. It comprehensively considers the Dist-Flow power flow constraints, the safety constraints of node voltage and branch current, the operation constraints of photovoltaic inverters, the operation constraints of on-load tap-changing transformers, and the operation constraints of capacitor banks in the three-phase balanced distribution network.

[0010] A local droop control model for photovoltaic inverters in the physical control layer is constructed to form a centralized-local collaborative second-order conical convex programming model. A segmented voltage / reactive power droop control strategy is introduced to mitigate the impact of distributed photovoltaic and load fluctuations on voltage security.

[0011] A correction feedback layer model is established, and an explicit hybrid loss function that integrates prediction error, voltage limit penalty and system network loss is constructed. The gradient of the loss function is passed to the power prediction layer through the backpropagation mechanism to correct the CNN-LSTM model parameters to complete the closed-loop feedback.

[0012] A two-stage robust optimization model is established, taking into account the uncertainty of source load power. The centralized optimization model of the active distribution network is decomposed into a main problem and sub-problems, and a column constraint generation algorithm is used to solve them alternately.

[0013] Furthermore, in the step of constructing the power prediction model, the prediction result is evaluated using the backpropagation algorithm according to the following formula. With real data The root mean square error is iteratively trained:

[0014] ;

[0015] In the formula: This represents the set of CNN-LSTM parameters in the prediction model o; is the total number of nodes in the system; n is the number of nodes; t is time t; o is the prediction model; T is the prediction period; The unified representation of the day-ahead predicted power of the source load at node n output by the prediction model o; A unified representation of the actual source load power of node n; This represents the total number of prediction models.

[0016] Furthermore, the objective function of the active distribution network centralized optimization model is as follows:

[0017] ;

[0018] In the formula: i represents node i; j represents node j; t represents time t; T represents the prediction period; This represents the total number of nodes in the system. Let be the resistance of branch ij; Let be the square of the current flowing through branch ij at time t.

[0019] Furthermore, when constructing the local droop control model of the photovoltaic inverter, the segmented voltage / reactive power droop control strategy satisfies the following equation:

[0020] ;

[0021] In the formula: Let be the reactive power output of the photovoltaic inverter connected to node i at time t; Let be the initial reactive power of the inverter at node i at time t during the local droop control phase; For droop gain, and ; This represents the sensitivity of the voltage magnitude at node i at time t to the injected reactive power, and ,in Let i be the reactive power injected into node i at time t. Let be the voltage at node i at time t; and These are the upper and lower limits of the node voltage, respectively.

[0022] Furthermore, the explicit hybrid loss function in the modified feedback layer model is as follows:

[0023] ;

[0024] In the formula: It is an explicit mixture loss function; For prediction accuracy indicators; This is a voltage deviation penalty term; This is an indicator of active power loss. , and They are respectively , , The corresponding indicator weights.

[0025] Furthermore, the compact form of the two-stage robust optimization model is as follows:

[0026] ;

[0027] ;

[0028] In the formula: x is a discrete variable, including the tap position of the on-load tap-changing transformer and the switching state of the capacitor bank; Source load power; y represents the set of source and load scenarios; y represents variables, including inverter reactive power output and optimal power flow results; b represents the set of source and load scenarios. T Let f be the transpose of the coefficient matrix b of variable y; A, B, and C are the coefficient matrices of the corresponding variables; f is a constant vector; This is the predicted value of source load power; and These are the influence matrix of node i perturbation on the system under robust constraints during time period t, and the system's tolerance boundary matrix, respectively. and These represent the upper and lower bounds of the variable y, respectively. , , , and These are the dual variables of each constraint.

[0029] Furthermore, when establishing the two-stage robust optimization model, the uncertainty of the source load power is addressed through a box set. The description satisfies the following formula:

[0030] ;

[0031] In the formula: Represents a set of uncertain source loads; | is a condition separator used to connect elements of the set and filter conditions; , and These represent the PV active power output, the active power vector of the load, and the reactive power vector, respectively, considering uncertainties. , and These represent the PV active power output, the active power vector of the load, and the reactive power vector of the power prediction layer, respectively. , and , representing the interval boundary value obtained in the corresponding time period; , and These represent the maximum permissible deviation vectors for PV active power output, active power, and reactive power of the load, respectively.

[0032] A robust optimization operation system for an active distribution network based on closed-loop feedback includes a processor and a memory. The memory stores computer program instructions, which, when executed by the processor, implement the robust optimization operation method for an active distribution network based on closed-loop feedback as described above.

[0033] Compared with the prior art, the beneficial effects of the present invention are:

[0034] This invention provides a robust optimization operation method for active distribution networks based on a "prediction-control-correction" closed-loop feedback. First, a power prediction model combining a convolutional neural network (CNN) and a long short-term memory (LSTM) network is constructed to perform time-series prediction of source load power. Second, a centralized-local collaborative second-order conical convex programming (SOCP) model physical control layer is established, and robustness processing is applied to address source load uncertainties. Simultaneously, system scheduling is achieved through SOCP optimization and a piecewise droop control strategy. Finally, a correction feedback layer is established to optimize the parameters of the prediction model based on a comprehensive loss function, thereby improving prediction accuracy and optimizing the system's active power loss and voltage safety. Test results based on an improved IEEE 33-node distribution network show that this method, while ensuring prediction accuracy, can significantly reduce system operating losses and node total voltage exceedance rate under source load uncertainty conditions, and possesses high solution efficiency. To address the issues of increased grid losses and voltage exceeding limits caused by large fluctuations in photovoltaic / load, this method relies on a three-level collaborative optimization mechanism of "prediction-control-correction" to effectively improve the robustness, stability, and economy of the distribution network under uncertain source-load scenarios. Attached Figure Description

[0035] Figure 1 This is a diagram illustrating the closed-loop feedback mechanism architecture of the "prediction-control-correction" method of the present invention.

[0036] Figure 2 This is a segmented droop control diagram for a photovoltaic inverter.

[0037] Figure 3 Construct a logic graph for SOCP demapping and gradient functions.

[0038] Figure 4 Diagram of the improved IEEE 33-node test system.

[0039] Figure 5 Initialize the PV and load power prediction curves; where (a) is the PV power prediction and (b) is the load power prediction.

[0040] Figure 6The diagram shows the PV and load power ranges; where (a) is the PV curve and (b) is the load curve.

[0041] Figure 7 The diagrams show the network loss for different schemes; where (a) represents the optimization process for scheme 1, and (b) represents the optimization processes for schemes 2 and 3.

[0042] Figure 8 The diagrams show the voltage distribution for different schemes; (a) shows the voltage distribution for scheme 1, (b) shows the voltage distribution for scheme 2, and (c) shows the voltage distribution for scheme 3.

[0043] Figure 9 The graph shows the total voltage over-limit rate for different schemes.

[0044] Figure 10 The voltage distribution diagrams for node 16 under schemes 2 and 3 are shown.

[0045] Figure 11 The diagram shows the U / Q droop characteristics of the 16-node inverter at different times. Detailed Implementation

[0046] In order to provide a clearer understanding of the technical features, objectives and beneficial effects of the present invention, the technical solution of the present invention will now be described in detail below, but it should not be construed as limiting the scope of implementation of the present invention.

[0047] This invention provides a robust optimization operation method for active distribution networks based on closed-loop feedback, and the specific implementation steps are as follows:

[0048] (i) Establish a closed-loop feedback mechanism of "prediction-control-correction";

[0049] This invention proposes for the first time a three-layer closed-loop feedback mechanism of "prediction-control-correction", which integrates machine learning prediction, physical system regulation and decision quality assessment, and realizes differentiable, trainable and interpretable collaborative optimization of the entire process from data to decision.

[0050] In the design of the mechanism architecture, emphasis should be placed on the organic integration of optimization modeling and physical laws (such as...). Figure 1 As shown, the traditional blind-box end-to-end serial process of "prediction-optimization" in power grid dispatching is improved into a closed-loop iterative process of "prediction-control-evaluation-re-prediction". Through the deep coupling design of optimization control and machine learning, the source-load prediction model is guided to not only focus on prediction accuracy during training, but also actively learn its impact on the quality of the final system optimization decision, achieving efficient closed-loop feedback and iterative optimization. The above process can be expressed mathematically as follows:

[0051] (1);

[0052] In the formula: x is the input feature set (such as historical power data, weather information, etc.); θ represents the final optimization decision result, that is, mapping x to the solution of the optimization problem; θ represents the parameter set of the prediction layer neural network; k is the number of iterations.

[0053] (ii) Constructing a power prediction model;

[0054] This invention introduces a CNN-LSTM hybrid neural network into the power prediction layer to capture the spatiotemporal characteristics of source load power, and corrects the prediction model parameters in reverse through feedback signals from the downstream physical control layer, making the prediction results more "decision sensitive" and improving the robustness and economy of the overall system.

[0055] The prediction results are obtained by backpropagation algorithm according to equation (2). With real data The root mean square error (MSE) is continuously used for iterative training to improve the accuracy and generalization ability of the source load prediction model.

[0056] (2);

[0057] In the formula: This represents the set of CNN-LSTM parameters in the prediction model o; is the total number of nodes in the system; n is the number of nodes; t is time t; o is the prediction model; T is the prediction period; The predicted power of the source load of node n before the day of the prediction model o is uniformly represented and determined by the prediction model shown in equation (3); A unified representation of the actual source load power of node n; This represents the total number of prediction models.

[0058] (3);

[0059] In the formula: This represents the feature set of the prediction model o; Indicates by The parameters of the determined prediction model o.

[0060] (III) Constructing a centralized optimization model for the active distribution network in the physical control layer;

[0061] Extract prediction results A centralized optimization model for the active distribution network in the physical control layer is established. This model aims to minimize the active power loss of the system during the control period T, and can be specifically described as follows:

[0062] (4);

[0063] In the formula: i represents node i; j represents node j; Let be the resistance of branch ij; Let be the square of the current flowing through branch ij at time t.

[0064] The constraints are as follows:

[0065] 1. Dist-Flow Constraints in Three-Phase Balanced Distribution Networks:

[0066] (5);

[0067] (6);

[0068] (7);

[0069] In the formula: Let be the active power flowing through line jk at time t; Let be the reactive power flowing through line jk at time t; and let i be node i. , Let each node represent the set of the end node and the set of the beginning node of a branch with node j as the beginning node and the end node, respectively. , Let be the active and reactive power transmitted by branch ij at time t, respectively; The reactance of branch ij; Let be the predicted value of the active power output of the photovoltaic system connected to node j at time t; , These represent the reactive power outputs of the photovoltaic inverter and CBs (capacitor bank) connected to node j, respectively. , These are the predicted active and reactive power values ​​of the load connected to node j at time t, respectively. Let be the square of the voltage at node j at time t; Let be the square of the voltage at node i at time t.

[0070] 2. Safety constraints on node voltage and branch current:

[0071] (8);

[0072] (9);

[0073] In the formula: , and , These are the upper and lower limits of the node voltage and branch current, respectively.

[0074] 3. Operating constraints of photovoltaic inverters:

[0075] (10);

[0076] In the formula: , These represent the reactive power output of the photovoltaic inverter connected to node i at time t and its maximum value, respectively. The apparent capacity of the photovoltaic inverter connected to node i; Let t be the predicted value of the active power output of the photovoltaic system connected to node i at time t.

[0077] 4. OLTC (On-Load Tap Changing Transformer) Operating Constraints:

[0078] (11);

[0079] In the formula: Let be the voltage at node i at time t; , These are the OLTC gears at time t and the initial time, respectively. Let be the voltage at node j at time t; Let t be the contact position of the OLTC; This represents the difference in gear ratio between two adjacent gears. This represents the maximum adjustable position of the OLTC contact. This is a binary variable. A value of 1 indicates a change in the OLTC tap position, and a value of 0 indicates no change in the tap position. The position of the OLTC contact at time t+1; This represents the maximum number of adjustments that the OLTC can make within the scheduling period.

[0080] 5. CBs (Capacitor Banks) Operating Constraints:

[0081] (12);

[0082] In the formula: Let be the reactive power output of CBs at node i at time t; , These are the number of CBs connected to node i and the maximum number of CBs connected to it, respectively. The reactive power output per unit number of CB groups; This is a binary variable that characterizes the change in the number of CBs switching groups. A value of 1 indicates a change in the number of groups, and a value of 0 indicates a change in the number of groups. This represents the maximum number of times CBs can be switched. The number of CBs connected to node i at time t+1.

[0083] (iv) Establish a local vertical control model for the PV inverter in the physical control layer;

[0084] This invention constructs a centralized-local collaborative second-order cone programming (SOCP) model at the control layer and introduces a segmented droop control strategy for photovoltaic inverters. By connecting the droop characteristics with the centralized optimization results, multi-timescale collaborative control is achieved.

[0085] See Figure 2 A segmented voltage / reactive power droop control strategy for PV inverters is introduced to further mitigate the impact of real-time random fluctuations in distributed PV and load power on system voltage safety.

[0086] (13);

[0087] In the formula: For droop gain, and The present invention takes ; This represents the sensitivity of the voltage magnitude at node i at time t to the injected reactive power, and ,in The reactive power injected into node i at time t; Let be the initial reactive power of the inverter at node i at time t during the local droop control phase.

[0088] Available reactive power reserve of PV inverter at any time during local droop control phase It should be the total capacity. The difference between the reactive power output and the previous moment. In fact, its droop characteristic is centrally optimized only at the initial moment of local inverter control enable. The reactive power is used as the initial value, and then the reactive power output of the previous moment is used as the initial value to execute subsequent voltage control.

[0089] Set the critical voltage safety range as The minimum linear droop control region in which the photovoltaic inverter actually performs local control ( Figure 2 The pink shaded area is and The corresponding drooping curve is Figure 2 The purple curve represents the reactive power dispatchable range of the photovoltaic inverter during the centralized voltage / reactive power regulation phase. During the local voltage / reactive power droop control phase, any voltage increment Required inverter output reactive power increment It should meet the following requirements:

[0090] (14);

[0091] Therefore, within the minimum linear droop control region, the inverter has available reactive power reserves during the droop control phase. It can be described as:

[0092] (15);

[0093] Maximum reactive power capacity of photovoltaic inverters Under constraints, its available reactive power reserve during the local sagging control phase It can be represented as:

[0094] (16);

[0095] Finally, the physical control layer transmits the active distribution network operation parameters optimized by the combined action of centralized optimization and inverter local droop control to the downstream correction feedback layer. This serves the correction feedback layer's assessment of the system's operating status and the optimization of the CNN-LSTM parameters in the power prediction layer.

[0096] (v) Establish a corrective feedback layer model;

[0097] This invention constructs an explicit hybrid loss function in the modified feedback layer, fusing prediction error (MSE), voltage over-limit penalty (ReLU activation), and system network loss (differentiable through SOCP demapping). The SOCP physical model is embedded in a CNN-LSTM, and a data-physical fusion active distribution network "grey box" operation optimization model is constructed through the integrated loss function, SOCP demapping, and its partial derivatives. This achieves rigid coupling between prediction results and system operation mechanisms, and allows for tracing the decision-making process between the physical model and numerical logic, effectively improving the model's interpretability.

[0098] The explicit mixed loss function with multi-objective weighting, as shown in Equation (17), comprehensively considers the influence of the above three aspects under the corresponding decision-making process. The data is then fed back to the power prediction layer to correct the CNN-LSTM parameters, thus completing the closed-loop feedback and achieving coordinated optimization of source-load prediction accuracy and node voltage while minimizing network loss.

[0099] (17);

[0100] In the formula: The prediction accuracy index can be directly calculated and determined by equation (2); The voltage deviation penalty term is used to improve the voltage safety level of the decision. It can be compared with the node voltage result after optimization of the physical control layer model and the set voltage safety threshold, and the deviation penalty is implemented by the equation (18) defined by the ReLU linear activation function. The result also has explicit differentiability and can be directly back-propagated to the power prediction layer model. It is an active power loss indicator used to quantify the energy efficiency of system operation; , and They are respectively , , The corresponding indicator weights.

[0101] (18).

[0102] In particular, although In the loss function The active power loss index is explicitly introduced as a variable, but its value is indirectly determined by the SOCP convex optimization problem, and there is no clear analytical relationship between it and the source load prediction results. Therefore, the active power loss index needs to be further clarified. The quantization calculation and SOCP mapping mechanism are used to establish the differentiability and gradient backpropagation model of the implicit optimization result, so as to realize the availability of the overall explicit loss function in the CNN-LSTM training process.

[0103] Based on the optimization results obtained from the centralized-local coordinated regulation of the physical control layer, the optimal power flow calculation is still performed with Equation (4) as the objective, in order to obtain the active power loss index of the active distribution network under the corresponding decision. The corresponding constraints are shown in equations (19) to (22).

[0104] (19);

[0105] (20);

[0106] (twenty one);

[0107] st Equation (6) - Equation (7) (22);

[0108] In the formula: , These are the reactive power outputs of the photovoltaic inverter and CBs connected to node j, which are optimized by the physical control layer, respectively. The contact position of the OLTC at time t is optimized by the physical control layer.

[0109] It should be noted that the function of equation (19) in the model is to optimize the... Transform it into the form of explicit variables to achieve control. Tracking and supporting the backpropagation of gradients to ensure The differentiability of [the property]. We will further examine this using implicit differentiation. The demapping and gradient transfer machine construction are described in detail.

[0110] use Figure 3 SOCP demapping and gradient function construction guarantees Differentiability and gradient backpropagation. The specific steps are as follows:

[0111] First, the optimization models shown in equations (4) and (19)-(22) are converted into the standard forms shown in equations (23) and (24), namely:

[0112] (twenty three);

[0113] (twenty four);

[0114] In the formula: x is the variable to be optimized, representing the reactive power decision result; This is the transpose of the variable to be optimized; is the transpose of the linear term in the objective function; W and c represent the quadratic and linear terms in the objective function, respectively; A is the constraint parameter matrix, which is affected by the source load prediction results; Let be a closed convex cone, representing a set of second-order cone constraints; Let it be a relaxation vector; It is a coefficient matrix.

[0115] To facilitate subsequent reverse updating of source load prediction layer parameters To extract the implicit function derivatives of the optimization problem, we need to perform dual decomposition on equations (23) and (24). The decomposed principal problem and its corresponding dual problem are shown in equations (25), (26) and (27), (28), respectively.

[0116] (25);

[0117] (26);

[0118] (27);

[0119] (28);

[0120] In the formula: , These represent the original variable and the dual variable, respectively. , Represents a real number vector; for The dual cone; This is the transpose of the constraint parameter matrix.

[0121] The relationship between the original and dual variables mentioned above can be established by the (Karush-Kuhn-Tucker, KKT) conditions of the SOCP problem, namely:

[0122] (29);

[0123] In the formula: This is the transpose of the relaxation vector.

[0124] Furthermore, the construction of oblique symmetric mappings, homotopy self-dual embeddings, and optimal dual solution mappings is then utilized to achieve... Differentiability and gradient backpropagation.

[0125] 1) Oblique symmetric mapping: This maps the input variables... Mapped to the corresponding skew-symmetric matrix Q:

[0126] (30);

[0127] In the formula: b T Let b be the transpose of the coefficient matrix of variable y; For (n+m+1) 2 The real number field of dimension.

[0128] 2) Homotopy self-dual embedding: utilizing residual functions The graph zero-point solution equations (25)-(28) are used to construct a self-dual embedding model, and the intermediate variables are used as solution vectors. The normalized residual plot should then satisfy:

[0129] (31);

[0130] In the formula: I is the identity matrix; For projection operator The derivative of . Only if And the third part of the solution vector z When z is used, the optimal solution to the primal-dual optimization problem given Q can be established. ,as well as The partial derivatives with respect to z and Q are:

[0131] (32);

[0132] (33);

[0133] In the formula: for The partial derivative with respect to Q; for The partial derivative with respect to z.

[0134] According to the implicit function theorem, there exists a neighborhood. Make There exists a unique solution. Therefore, when equation (32) is... When the value is 0, equations (25)-(28) yield a unique solution. Its derivative with respect to Q is:

[0135] (34);

[0136] In the formula: Represents a mapping function for variable Q. Perform differentiation; The inverse matrix of the solution mapping function; Let z be the partial derivative of the residual mapping function with respect to z.

[0137] 3) Construction of the optimal dual solution mapping: intermediate variables... Mapping to the optimal solution The process can be represented as:

[0138] (35);

[0139] In the formula: Solve the constructor for variable z; This refers to the first part of the variable z; For variable v to dual cone The projection; For variable v to cone The projection.

[0140] but It is differentiable, and its derivative is:

[0141] (36);

[0142] In the formula: express The derivative function; Construct a dual cone for the solution of variable v. The partial derivatives; Construct a constructor for the solution of the cone with variable v. The partial derivatives; These are the original variables; As dual variables; These are slack variables.

[0143] Furthermore, the total derivative of the demapping can be constructed by superimposing the derivative of equation (30) with equations (34) and (36). ,Right now:

[0144] (37);

[0145] Therefore, the active power loss index in equation (17) can be determined according to equation (37). Rewritten in the following differentiable form:

[0146] (38);

[0147] In the formula: The feature vector input to the prediction model o; the derivative of the power prediction layer. Calculated by PyTorch's automatic differentiation algorithm, used to quantify the accuracy of the prediction results; This represents the predicted source load power, and ; Used for evaluation right Sensitivity; This represents the decision outcome of the physical control model, and , These represent the reactive power output of the photovoltaic inverter and CBs optimized by the physical control layer, as well as the contact position of the OLTC. Used for quantification right Sensitivity.

[0148] Based on this, according to the chain rule, the total gradient of the overall mixed loss function with respect to the parameters of multiple prediction models can be obtained, realizing the integration of the influence of source load prediction results on system operation optimization decision-making, and improving decision quality by coordinating prediction models. In summary, the update rule of the overall mixed explicit loss function is shown in equation (39):

[0149] (39);

[0150] In the formula: The parameters of the prediction model o are the mixed loss function. Find the partial derivative. The parameters of the prediction model o are represented. Find the partial derivative.

[0151] (vi) Establish a two-stage robust optimization model;

[0152] 1. Model Establishment: First, the active distribution network centralized optimization operation model in step (III) can be rewritten into a compact two-stage robust optimization model without considering the uncertainties of PV and load power.

[0153] (40);

[0154] (41);

[0155] Equation (40) represents the objective function, corresponding to equation (4) in step (iii). The first row of equation (41) represents inequality constraints, corresponding to equations (11) and (12); the second row of equation (41) represents equality constraints, corresponding to equations (5) and (6); the third row of equation (41) represents standard second-order cone constraints, corresponding to equation (7); the fourth row of equation (41) represents limit constraints, corresponding to equations (8)-(10).

[0156] In equation (40): the outer "min problem" is the first stage of optimization, optimizing the discrete variable x, including the OLTC gear position and the switching state of CBs; the inner "max min problem" is the second stage of optimization, optimizing the continuous variable And y, where y includes the inverter's reactive power output and the optimal power flow result, This is the predicted value of source load power; A collection of source and load scenes; Source load power; b T Let f be the transpose of the coefficient matrix b of variable y. In equation (41): A, B, and C are the coefficient matrices of the corresponding variables; f is the constant vector; G is the relation matrix of the perturbation effect on y, and g is the direction vector of the perturbation effect. and These are the influence matrix of node i perturbation on the system under robust constraints during time period t, and the system's tolerance boundary matrix, respectively. and These represent the upper and lower bounds of the variable y, respectively. , , , and These are the dual variables of each constraint in the second stage.

[0157] The aforementioned deterministic model heavily relies on high-precision source-load prediction results. However, with the high proportion of distributed generation (DG) and new loads being integrated, their strong randomness and volatility make it difficult to guarantee the accuracy of source-load prediction. Excessive prediction errors can easily lead to voltage fluctuations exceeding limits or frequent equipment malfunctions, posing a serious threat to the safety of distribution network operation. Therefore, optimizing the operating model should comprehensively consider the impact of source-load uncertainties. This invention uses interval uncertainty to describe the prediction error range of photovoltaic and load power, and its box-type set... It can be defined as:

[0158] (42);

[0159] In the formula: Represents the set of uncertainties in source and load; , and These represent the PV active power output, the active power vector of the load, and the reactive power vector, respectively, considering uncertainties. , and These represent the PV active power output, the active power vector of the load, and the reactive power vector of the power prediction layer, respectively. , and These represent the maximum permissible deviation vectors for PV active power output, active power, and reactive power of the load, respectively.

[0160] To avoid overly conservative robust optimization, an uncertain budget is introduced. , and To limit the number of time periods in which the source load power of node i is simultaneously maximized within the entire optimization period T, the conservatism constraint of the model is set as follows:

[0161] (43);

[0162] In the formula: , and This represents the interval boundary value obtained for the corresponding time period. By adjusting... , and The magnitude of can be used to adjust the conservatism of the robust optimization model; the larger the value, the higher the conservatism of the model. Therefore, equation (42) can be rewritten as follows:

[0163] (44);

[0164] In summary, equations (40) to (44) constitute a two-stage centralized robust optimization operation model for the physical control layer of the active distribution network that considers the uncertainty of source load power. The "max problem" in the second stage is applied to determine the worst-case scenario of source load power.

[0165] 2. Model Solving: First, it needs to be decomposed into a master problem (MP) and sub-problems (SP) and solved alternately to obtain the optimal solution to the original problem. The master problem and sub-problems obtained after decomposing equations (40)-(44) are shown in equations (45) and (46), respectively:

[0166] (45);

[0167] (46);

[0168] In the formula: Represent the objective function of the main problem; and These represent the solution to the subproblem after the k-th iteration and the determined adverse scenario, respectively.

[0169] Therefore, the dual problem of subproblem SP can be obtained as follows:

[0170] (47);

[0171] In the formula: The selected interval boundary value; For the introduction of continuous auxiliary variables, ,in , and Represents any real matrix of the corresponding order; Let x be the coefficient matrix of the variable x; The solution to the main problem is passed down to the subproblems; This is the transpose of the lower bound of the variable y; This is the transpose of the upper bound of the variable y; This indicates the fluctuation range of the predicted source load power. , The transpose of the predicted range of source load power; This is the transpose of the coefficient matrix of the variable y; and It is represented as the transpose of the matrix of the influence of node i perturbation on the system under robust constraints during time period t, and the transpose of the system's tolerance boundary matrix. dual variables The upper bound of is a sufficiently large positive real number.

[0172] After the above transformation, the decomposed main problem (Equation (45)) and subproblems (Equation (47)) can be robustly optimized and solved using the column constraint generation algorithm (C&CG), as follows:

[0173] 1) Set upper and lower bounds for the target fitness value. , Initial iteration count k=1. Randomly initialize the worst-case source load scenario based on the prediction results. .

[0174] 2) Based on the initial worst-case scenario Solving the main problem equation (45), we obtain the optimal solution for the k-th iteration. and update the lower bound. .

[0175] 3) Solve the main problem Substituting into equation (47) to solve the subproblem yields the objective value of the subproblem. and the corresponding worst-case scenario and update the upper bound. .

[0176] 4) Set the algorithm convergence criteria If satisfied If the iteration stops, the optimal solution is output. Otherwise, let k = k + 1 and increase the variable. Add constraints to the main problem as shown in equation (48), and return to step 2) until the algorithm converges.

[0177] (48);

[0178] In the formula: This represents the worst-case source load scenario obtained after the (k+1)th iteration.

[0179] Example 1: Case Study Analysis;

[0180] Establish an improved IEEE 33-node test system, whose network structure and the access locations of OLTC, PV, and CBs are as follows: Figure 4 As shown. The system reference voltage and reference capacity are taken as 12.66kV and 100MVA, respectively, and the allowable operating voltage range of the system is taken as... =[0.95,1.05]pu, the critical safe voltage range is taken as... =[0.90,1.10]pu; the capacity of each PV inverter is set to [0.90,1.10]pu. =12MVA; OLTC has a total of 16 gears, each adjustable by 0.00625 pu, with an adjustment range of... The maximum number of daily adjustments for PV is 10; the number of CBs installed is 5, with each group having a reactive power compensation capacity of 0.05 MVar and a maximum daily switching frequency of 5. The PV data and associated meteorological information and load data used in the example are derived from historical data of an actual photovoltaic power station and load in Ningxia, my country in 2023. The dataset resolution is 15 minutes. The maximum permissible deviation of source-load power in the uncertainty set is constructed. Each value is taken as ±10% of the corresponding prediction result. The power prediction layer is implemented using a CNN-LSTM built in PyTorch. The hidden layer dimension of the CNN-LSTM is 128, and the learning rate is... The output dimension is 96, and the number of convolutional output channels is 64; the correction feedback layer is built using Cvxpylayers. The weights of each indicator in equation (17) are... The harsh scene identifier in formula (43) is taken as , Convergence criterion of C&CG algorithm .like Figure 5As shown in (a) and (b), the PV and load power prediction models can basically converge within 5 and 30 iteration cycles, respectively. Combined with the set maximum allowable prediction error margin of ±10%, based on... Figure 5 Based on the prediction results, the initial source load power range input into the robust optimization model is determined as follows: Figure 6 As shown in (a) and (b).

[0181] To verify the model's effectiveness, three schemes were designed and compared in four aspects: system active power loss, voltage safety, source-load prediction accuracy, and model solution efficiency. The specific schemes are as follows:

[0182] Option 1: The physical control layer adopts a robust optimization model of centralized-local coordinated regulation, without considering closed-loop feedback mechanism;

[0183] Option 2: The physical control layer only adopts a centralized optimized closed-loop feedback robust optimization model, without considering the local control of the PV inverter;

[0184] Option 3: The physical control layer adopts a closed-loop feedback robust optimization model of centralized-local coordinated regulation (the method of this invention), and sets the maximum number of closed-loop feedback cycles to 200. The network loss at non-integer times is indirectly calculated by the Newton-Layer method based on the local voltage control results.

[0185] (I) System active power loss analysis; the operational optimization process and corresponding results of the three schemes for system active power loss are as follows: Figure 7 As shown in (a) and (b). From Figure 7 The results show that Scheme 1 converged after three iterations, achieving an optimal network loss of 19.638MW. Schemes 2 and 3, which consider closed-loop feedback, achieved final optimization results of 17.264MW and 17.409MW respectively, representing reductions of 2.374MW and 2.229MW compared to Scheme 1, with reductions exceeding 11%. This demonstrates that the "prediction-control-correction" closed-loop feedback mechanism enables the model to proactively adapt to real-time operating state changes in the distribution network under conditions of strong source-load uncertainty. By optimizing CNN-LSTM parameters through hybrid loss function feedback, the overall energy efficiency of the optimization model is improved, offering significant advantages in ensuring the economic efficiency of distribution network operation. Furthermore, a separate comparison of Schemes 2 and 3 reveals that the former achieves better network loss optimization results than the latter. This is because Scheme 3 additionally considers the local control role of the PV inverter, sacrificing some optimization effect on the main problem objective (minimizing network loss) while striving to improve system voltage safety performance. Figure 7As can be seen from (b), the active power loss after optimization of scheme 3 is 0.145MW higher than that of scheme 2, with an increase of only 0.84%. This proves that the closed-loop feedback robust optimization model proposed in this invention can achieve high economic performance of active distribution network global operation optimization under the action of the hybrid loss function shown in equation (17). The optimization effect of the model on voltage safety and prediction accuracy will be specifically analyzed and discussed below.

[0186] It should be noted that Scheme 3 shows a significant overall downward trend in system network loss, with the minimum value of 17.293MW occurring in the 19th feedback loop. However, at this point, voltage optimization and prediction accuracy are sacrificed to some extent, causing the overall loss function of the model to rise in the opposite direction. Therefore, under the synergistic effect of the three indicators in the hybrid loss function, the system active power loss curve fluctuates to varying degrees during the feedback loop until it stabilizes at the optimal value after 50 iterations, which is only 0.67% higher than the minimum value. This achieves the optimality of the main problem in the robust optimization model that coordinates source-load prediction accuracy and node voltage safety.

[0187] (II) Voltage Safety Analysis; While optimizing the main network loss problem, the method of this invention can also achieve node voltage regulation under random fluctuations in PV and load power through physical control layer regulation and correction feedback layer correction. The system node voltage distribution results of the three schemes are as follows: Figure 8 As shown in (a)-(c), the system voltage safety level during the optimization period is quantified based on the total voltage violation rate (TVVR) index shown in Equation (49).

[0188] (49);

[0189] In the formula: This represents the total number of time points within the optimization period T; Denotes a step function, and when hour, ,when hour, .

[0190] according to Figure 8 Equation (49) yields the TVVR comparison results of the example system under different schemes throughout the entire optimization cycle, as shown below. Figure 9 As shown. With Figure 7 The result in (b) is similar, from Figure 9It can be seen that the closed-loop feedback strategy based on "prediction-control-correction" proposed in this invention can improve the sensitivity of centralized voltage regulation of the physical control layer model to source load fluctuations, and significantly optimize the voltage safety performance of the distribution network. Schemes 2 and 3 respectively optimized the system TVVR from 11.050% and 7.292% (optimal value of Scheme 1) at the beginning of the cycle to 6.220% and 2.431%, with reductions of 43.71% and 66.66%, respectively. In addition, Scheme 3 reduced the optimal TVVR by 3.789% compared to Scheme 2, with a reduction of 60.92%. This shows that the centralized-local coordinated regulation strategy constructed by the physical control layer can effectively cope with voltage fluctuations exceeding limits caused by random source load fluctuations and reduce the operational safety risks of the system.

[0191] Taking a 16-node system at the end of the simulation system with PV access as an example, this paper further analyzes the voltage regulation effect of the segmented local droop control of the PV inverter introduced in this invention. A comparison of the voltage distribution of the 16-node system under schemes 2 and 3 is provided. Figure 10 As shown in the figure, under the action of real-time droop control, the voltage over-limit situation at the nodes was significantly alleviated throughout the entire control cycle, with the over-limit rate decreasing from 23.96% to 3.13%. Voltage over-limit only occurred during the period of 13:15–13:45, when PV output was at its peak (red shaded area). The peak voltage occurred at 13:45, decreasing from 1.094 pu in Scheme 2 to 1.070 pu. This indicates that the introduced on-site droop control of the PV inverter can fully exploit the inverter's reactive power regulation potential and effectively improve the model's real-time voltage regulation capability against random fluctuations in source load. However, droop control is a differential regulation and cannot guarantee the complete elimination of voltage over-limit situations. The voltage regulation process of the PV inverter connected to the 16 nodes at three times during this period is shown in the figure. Figure 11 As shown in the figure =-0.0540MVar, obtained through centralized optimization enabled at the hour (13:00). The droop voltage adjustment process at other non-hourly times is similar to the above process, and will not be described in detail here.

[0192] (III) Source-Load Prediction Accuracy Analysis; As mentioned above, the method of this invention corrects the CNN-LSTM parameters embedded in the SOCP physical model through cyclic feedback, which can reverse the sensitivity of the optimization decision problem to the input prediction error to the power prediction layer model, thereby improving the prediction accuracy. The MSE index calculation results of each PV and load under Scheme 1 and Scheme 3 without considering feedback correction are shown in Table 1.

[0193] Table 1. MSE Indicators for Different Schemes

[0194] Predicted object Option 1 Scheme 3 (Method of the present invention) PV1 0.008159 0.008801 PV2 0.008656 0.007292 PV3 0.006597 0.006182 PV4 0.009148 0.009047 PV5 0.009398 0.007542 load 0.000829 0.000836

[0195] As shown in Table 1, the MSE (Mean Sequence of Error) of most PV power prediction results in Scheme 3 is lower than that in Scheme 1, with only PV1 slightly higher, verifying that the method of this invention has higher overall prediction accuracy. In contrast, the MSE of load prediction in Scheme 1 is lower than that in Scheme 3, and its accuracy is slightly better. This is because Scheme 3 sacrifices load prediction accuracy to some extent in order to improve the overall decision quality of the model through the comprehensive loss function. It can be seen that although the prediction error of some nodes in Scheme 3 is slightly higher, the overall prediction is more decision-sensitive, that is, the prediction deviation has a smaller impact on the final operation optimization result.

[0196] (iv) Model Solving Efficiency Analysis; Scheme 3, due to the construction of a closed-loop feedback mechanism based on "prediction-control-correction," has a more complex optimization process for the active distribution network operation compared to Scheme 1, but... Figure 7 (b) and Figure 9 As can be seen, the proposed model has fully converged after 200 offline training iterations, and the trained model can be used for subsequent system optimization. The online solution times for the two schemes are shown in Table 2.

[0197] Table 2 Online solution time for different schemes

[0198] Comparison Plan Option 1 Scheme 3 (Method of the present invention) Solution time / s 1.4094 1.6178

[0199] As shown in Table 2, the model solution time of Scheme 3 is only 0.2084 seconds longer than that of Scheme 1, which is acceptable in practical engineering applications. This indicates that Scheme 3, while ensuring decision quality and security, does not introduce additional real-time computational pressure and has good engineering feasibility.

[0200] Conclusion: The robust optimization operation model for active distribution networks based on "prediction-control-correction" closed-loop feedback proposed in this invention embeds the SOCP convex optimization problem of the physical control layer into the CNN-LSTM of the power prediction layer. Correction feedback is achieved through a comprehensive loss function, which significantly improves the synergy between prediction and optimization decision-making. This allows the training process of the prediction model to not only focus on the prediction accuracy in the traditional sense, but also to perceive the actual impact of its error on the final scheduling decision, thereby improving the global optimization performance of the model.

[0201] The above are merely preferred embodiments of the present invention. It should be noted that those skilled in the art can make several modifications and improvements without departing from the concept of the present invention, and these should also be considered within the scope of protection of the present invention. These modifications and improvements will not affect the effectiveness of the implementation of the present invention or the practicality of the patent.

Claims

1. A method for robust optimal operation of active power distribution network based on closed-loop feedback, characterized in that, The method comprises the following steps: A "prediction-control-correction" closed-loop feedback mechanism is established to integrate machine learning prediction, physical system regulation and decision quality evaluation, forming a closed-loop iterative process; the closed-loop feedback mechanism outputs an optimized decision result through the power prediction layer, and iteratively feeds back through the physical control layer and the correction feedback layer to gradually optimize the prediction model parameters; A power prediction model is constructed, a CNN-LSTM hybrid neural network is used to extract and predict the temporal and spatial characteristics of source and load power, and the feedback signal of the physical control layer is used to correct the model parameters in reverse; An active distribution network centralized optimization model in the physical control layer is constructed, with the objective of minimizing the active power loss of the system during the regulation period, and comprehensively considering the Dist-Flow power flow constraints of the three-phase balanced distribution network, the safety constraints of node voltage and branch current, the operation constraints of photovoltaic inverters, the operation constraints of on-load voltage regulating transformers, and the operation constraints of capacitor banks; A photovoltaic inverter local droop control model is constructed to form a centralized-local collaborative second-order convex programming model, and a segmented voltage / reactive power droop control strategy is introduced to alleviate the impact of distributed photovoltaic and load fluctuations on voltage safety; A correction feedback layer model is established, an explicit hybrid loss function is constructed by integrating prediction errors, voltage out-of-limit penalties and system loss, the loss function gradient is transmitted to the power prediction layer through a back propagation mechanism, and the CNN-LSTM model parameters are corrected to complete the closed-loop feedback; A two-stage robust optimization model is established, considering the uncertainty of source and load power, the active distribution network centralized optimization model is decomposed into a main problem and a sub-problem, and a column constraint generation algorithm is used for alternative solution.

2. The closed-loop feedback based proactive power distribution network robust optimization operation method according to claim 1, characterized in that, In the step of constructing the power prediction model, the prediction result is iteratively trained according to the following formula by a back propagation algorithm and the root mean square error of the real data is continuously iterated ； In the formula: represents the CNN-LSTM parameter set in the prediction model o; is the total number of nodes contained by the system; n is the node n; t is the t time; o is the prediction model; T is the prediction period; unifies the day-ahead prediction power of the source load of the node n output by the prediction model o; unifies the actual source load power of the node n; is the total number of prediction models.

3. The closed-loop feedback based proactive power distribution network robust optimization operation method according to claim 1, characterized in that, The objective function of the active distribution network centralized optimization model is as follows: ； where: i is node i; j is node j; t is time t; T is the prediction period; is the total number of nodes included in the system; is the resistance of branch ij; is the current squared flowing through branch ij at time t.

4. The closed-loop feedback based proactive power distribution network robust optimization operation method according to claim 1, characterized in that, When constructing the photovoltaic inverter local droop control model, the segmented voltage / reactive power droop control strategy satisfies the following formula: ； wherein: Qi(t) is the reactive power output of the PV inverter connected to node i at time t; Qi0is the initial reactive power of the inverter connected to node i at time t under the droop control phase; Qi0is the initial reactive power of the inverter connected to node i at time t under the droop control phase; Qi0is the initial reactive power of the inverter connected to node i at time t under the droop control phase; Qi0is the initial reactive power of the inverter connected to node i at time t under the droop control phase; Qi0is the initial reactive power of the inverter connected to node i at time t under the droop control phase; Qi0is the initial reactive power of the inverter connected to node i at time t under the droop control phase; Qi0is the initial reactive power of the inverter connected to node i at time t under the droop control phase; Qi0is the initial reactive power of the inverter connected to node i at time t under the droop control phase; Qi0is the initial reactive power of the inverter connected to node i at time t under the droop control phase.

5. The closed-loop feedback based proactive power distribution network robust optimization operation method according to claim 1, characterized in that, The explicit hybrid loss function in the correction feedback layer model is as follows: ； wherein: is the explicit mixing loss function; is the prediction accuracy indicator; is the voltage deviation penalty term; is the active power loss indicator; , and are , , corresponding indicator weights.

6. The closed-loop feedback based proactive power distribution network robust optimization operation method according to claim 1, characterized in that, The compact form of the two-stage robust optimization model is as follows: ； ； wherein: x is a discrete variable including tap positions of on-load tap changer transformers and switching states of capacitor banks; is the source load power; is the set of source load scenarios; y is a variable, including the reactive power output of the inverter, the optimal power flow result; b T is the transpose matrix of the coefficient matrix b of the variable y; A, B and C are respectively the coefficient matrix corresponding to the variable; f is a constant vector; is the source load power prediction value; and are respectively the influence matrix of the node i disturbance on the system and the tolerance boundary matrix of the system under the robust constraint in the t period; and respectively represent the upper and lower bounds of the variable y; , , , and are the dual variables of each constraint.

7. The closed-loop feedback based proactive power distribution network robust optimization operation method according to claim 1, characterized in that, In establishing the two-stage robust optimization model, the uncertainty of the source load power is represented by a box set is described, satisfying the following equation: ； wherein: represents a set of source mass uncertainty; | is the conditional separator used to connect the elements of the set and the filter condition; , and represent the active power output of the PV, the active and reactive power vectors of the load, respectively, considering the uncertainty; , and represent the active power output of the PV, the active and reactive power vectors of the load, respectively, predicted by the power prediction layer; , and represent the interval boundary values taken at the corresponding time period; , and represent the maximum allowed deviation vectors for the active power output of the PV, the active and reactive power of the load, respectively.

8. A closed-loop feedback based active power distribution network robust optimization operation system, characterized in that, It comprises: A processor and a memory, the memory stores computer program instructions, when the computer program instructions are executed by the processor, the method for robust optimization operation of active distribution network based on closed-loop feedback according to any one of claims 1-7 is realized.

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