Power distribution network load flow calculation method and system based on incomplete measurement

Abstract

The invention discloses a power distribution network load flow calculation method and system based on incomplete measurement, and the method comprises the steps: building an incomplete measurement linear load flow model based on a preset full measurement linear load flow model through a measurable node set and an unmeasurable node set of a power distribution network; according to a preset double-layer multiple linear regression framework, optimizing the incomplete measurement linear power flow model, and constructing a double-layer power flow model representing a linear relationship between measurable nodes and non-measurable nodes of the power distribution network; and acquiring load flow data of measurable nodes in the power distribution network in real time, inputting the acquired load flow data of the measurable nodes into the double-layer load flow model, calculating load flow data of non-measurable nodes, and obtaining load flow states of all the nodes of the power distribution network. According to the invention, the complete and accurate power flow state of the power distribution network can be obtained without measuring all nodes of the power distribution network, and the measurement cost is saved.

Description

Technical Field

[0001] This application belongs to the technical field of power flow analysis in distribution systems, and particularly relates to a method and system for calculating power flow in a distribution network based on incomplete measurements. Background Art

[0002] In a new type of distribution system, accurate power flow analysis is the key to the operation, planning, and fault diagnosis of the distribution system. Among them, real-time voltage, current, and power distribution information helps operators understand the operating status of the system in a timely manner; predicting the power flow distribution under different load growth scenarios can help planners evaluate the feasibility and economy of different planning schemes; by performing a benchmark analysis on the power flow data during normal operation, abnormal current and voltage changes can be quickly detected, and the fault point can be accurately located.

[0003] Traditional power flow equations must be formed based on accurate topologies and line parameters. However, the distribution network has a wide coverage area and numerous devices, and it is difficult to obtain accurate line parameters. Moreover, the non-linearity of power flow equations usually leads to difficulties in the convergence of optimization and control algorithms, resulting in a high computational burden. Although artificial intelligence methods provide the possibility for non-linear regression of power flow calculation in distribution systems, such data-driven methods assume that the measurements of all nodes and devices in the system are available. In fact, due to the limitation of the deployment cost of measurement devices and communication infrastructure, measurement devices often can only cover some measurable nodes of the system and cannot provide the power flow data of other unmeasurable nodes, resulting in the inability to accurately calculate the power flow state variables of the new type of distribution system, which brings certain difficulties to detecting the fault risks of the new type of distribution system. Summary of the Invention

[0004] This application proposes a method and system for calculating power flow in a distribution network based on incomplete measurements, which can obtain a complete and accurate power flow state of the distribution network without measuring all nodes of the distribution network, saving measurement costs.

[0005] The first aspect of this application provides a method for calculating power flow in a distribution network based on incomplete measurements, and the method includes:

[0006] Based on a preset full-measurement linear power flow model, an incomplete-measurement linear power flow model is constructed through the set of measurable nodes and the set of unmeasurable nodes of the distribution network;

[0007] According to a preset double-layer multiple linear regression framework, the incomplete-measurement linear power flow model is optimized to construct a double-layer power flow model representing the linear relationship between the measurable nodes and the unmeasurable nodes of the distribution network;

[0008] Real-time collect the power flow data of measurable nodes in the distribution network, and input the collected power flow data of the measurable nodes into the double-layer power flow model to calculate the power flow data of the unmeasurable nodes, so as to obtain the power flow states of all nodes in the distribution network.

[0009] The above solution divides all nodes in the distribution network into measurable nodes and unmeasurable nodes according to the actual situation, and then substitutes them into a preset full-measurement linear power flow model that assumes all nodes can be fully measured to construct an incomplete-measurement linear power flow model that contains information about unmeasurable nodes. Since the model contains multiple linear relationships and the power flow data of nodes also contains various data, a linear relationship between the power flow data of measurable nodes and unmeasurable nodes is constructed respectively on the basis of the incomplete-measurement linear power flow model through a double-layer multiple linear regression framework. These two linear relationships are used to construct the upper-layer model and the lower-layer model respectively to obtain the double-layer power flow model. Then collect the power flow data of measurable nodes in the distribution network, use these data as input values to solve the linear relationship of the upper-layer model first to obtain partial power flow data of unmeasurable nodes; then solve the lower-layer model through the partial power flow data of unmeasurable nodes to obtain the full power flow of unmeasurable nodes, realizing the acquisition of a complete and accurate power flow state of the distribution network without measuring all nodes in the distribution network, saving the measurement cost and measurement complexity.

[0010] In a possible implementation method of the first aspect, based on a preset full-measurement linear power flow model, an incomplete-measurement linear power flow model is constructed through the set of measurable nodes and the set of unmeasurable nodes in the distribution network, specifically:

[0011] Input the power flow data of the preset fully measured nodes into a preset non-linear power flow model to construct the full-measurement linear power flow model;

[0012] Divide all nodes in the distribution network into the set of measurable nodes and the set of unmeasurable nodes;

[0013] According to the set of measurable nodes and the set of unmeasurable nodes, pairwise combine the measurable nodes and unmeasurable nodes in the full-measurement linear power flow model to construct a corresponding coefficient matrix to obtain the incomplete-measurement linear power flow model.

[0014] The above solution first assumes the existence of a distribution network with fully measurable nodes, and inputs relevant data into a preset non-linear power flow model to construct a full-measurement linear power flow model based on fully measurable nodes. Then, adapting to the actual situation, all nodes of the target distribution network are divided into measurable nodes and unmeasurable nodes, and the full-measurement linear power flow model is optimized through these nodes to construct an incomplete-measurement linear power flow model that conforms to the actual measurement situation.

[0015] In a possible implementation method of the first aspect, the incomplete measurement linear power flow model is specifically as follows:

[0016] The incomplete measurement linear power flow model has the following specific expression:

[0017]

[0018] In the formula, is the voltage vector of the measurable nodes at time t, is the voltage vector of the unmeasurable nodes at time t, Φ oo is the coefficient matrix of measurable node - measurable node, Φ ou is the coefficient matrix of measurable node - unmeasurable node, Φ uo is the coefficient matrix of unmeasurable node - measurable node, Φ uu is the coefficient matrix of unmeasurable node - unmeasurable node, is the injection power of the unmeasurable nodes at time t, is the injection power of the measurable nodes at time t, o is the set of measurable nodes, and u is the set of unmeasurable nodes.

[0019] In a possible implementation method of the first aspect, according to the preset double - layer multiple linear regression framework, the incomplete measurement linear power flow model is optimized to construct a double - layer power flow model representing the linear relationship between the measurable nodes and unmeasurable nodes of the distribution network, specifically as follows:

[0020] Based on the double - layer multiple linear regression framework, the first linear relationship and the second linear relationship between the measurable nodes and the unmeasurable nodes are respectively constructed; among them, the power flow data includes injection power and voltage vector;

[0021] According to the first linear relationship, the incomplete measurement linear power flow model is optimized to construct the upper - layer power flow model;

[0022] According to the second linear relationship, the incomplete measurement linear power flow model is optimized to construct the lower - layer power flow model;

[0023] According to the upper - layer power flow model and the lower - layer power flow model, the double - layer power flow model is constructed.

[0024] In the above solution, the voltage vector and injection power of the nodes are used as the information characterizing the power flow of the distribution network. Therefore, there is more than one unknown in the incomplete measurement linear power flow model. So, constructing different linear relationships for multiple unknowns facilitates solving them one by one.

[0025] In a possible implementation method of the first aspect, the first linear relationship and the second linear relationship are specifically as follows:

[0026] Taking the injection power of the unmeasurable nodes as the solution target, a linear relationship among the voltage vector of the measurable nodes, the injection power of the measurable nodes, and the injection power of the unmeasurable nodes is constructed to obtain the first linear relationship;

[0027] Taking the voltage vector of the unmeasurable nodes as the solution target, a linear relationship among the voltage vector of the unmeasurable nodes, the injection power of the measurable nodes, and the injection power of the unmeasurable nodes is constructed to obtain the second linear relationship.

[0028] In a possible implementation method of the first aspect, it further includes:

[0029] The coefficient matrices of the upper-layer power flow model and the lower-layer power flow model are regularized respectively by the L2 norm to construct the two-layer power flow model.

[0030] The above solution regularizes the coefficient matrix of the model by the L2 norm to prevent overfitting of the model and improve the calculation accuracy.

[0031] In a possible implementation method of the first aspect, the two-layer power flow model is specifically:

[0032] Among them, the specific expression of the upper-layer power flow model of the two-layer power flow model is:

[0033]

[0034] In the formula, Φ oo is the coefficient matrix of measurable node-measurable node, Φ ou is the coefficient matrix of measurable node-unmeasurable node, is the injection power of the unmeasurable nodes at time t, T is the measurement period, is the injection power of the measurable nodes at time t, is, is, and λ, α, and β are all regularization coefficients.

[0035] The specific expression of the lower-layer power flow model of the two-layer power flow model is:

[0036]

[0037] In the formula, Φ uo is the coefficient matrix of unmeasurable node-measurable node, Φ uu is the coefficient matrix of unmeasurable node-unmeasurable node, is the injection power of the unmeasurable nodes at time t, T is the measurement period, is the injection power of the measurable nodes at time t, For where λ, α, and β are all regularization coefficients.

[0038] In a possible implementation of the first aspect, power flow data of measurable nodes in the distribution network is collected in real time, and the collected power flow data of the measurable nodes is input into the double-layer power flow model to calculate the power flow data of the unmeasurable nodes, obtaining the power flow states of all nodes in the distribution network. Specifically:

[0039] Collect the power flow data of the measurable nodes in the distribution network according to the set of measurable nodes;

[0040] Input the power flow data of the measurable nodes into the upper-layer power flow model of the double-layer power flow model for solution to obtain the injection power of the unmeasurable nodes;

[0041] Input the injection power of the unmeasurable nodes into the lower-layer power flow model of the double-layer power flow model for solution to obtain the voltage vector of the unmeasurable nodes.

[0042] The above solution uses the actually collected power flow data of the measurable nodes as the input quantity to calculate the power flow data of the unmeasurable nodes. The voltage vector and injection power of the unmeasurable nodes are partitioned through the upper and lower layers of the model, and the solution of the upper-layer model is used as the input quantity of the lower-layer model to obtain accurate calculation data.

[0043] In a possible implementation of the first aspect, it further includes:

[0044] Adopt the alternating minimization method to calculate the injection power of the unmeasurable nodes and the voltage vector of the unmeasurable nodes by fixing any quantity to be solved in the double-layer power flow model, obtaining the power flow data of the unmeasurable nodes.

[0045] In the above solution, because there are multiple unknowns in the coefficient matrix, it is difficult to solve the model. Therefore, the alternating minimization method is used to fix the unknowns in the model in turn, simplifying the multi-linear problem into an ordinary linear regression problem and reducing the computational complexity.

[0046] The second aspect of the present application provides a distribution network power flow calculation system based on incomplete measurement. The system includes: a linear model construction module, a double-layer model construction module, and a power flow data calculation module;

[0047] Among them, the linear model construction module is used to construct an incomplete measurement linear power flow model based on a preset full-measurement linear power flow model through the set of measurable nodes and the set of unmeasurable nodes in the distribution network;

[0048] The double - layer model construction module is used to optimize the incomplete measurement linear power flow model according to a preset double - layer multiple linear regression framework, and construct a double - layer power flow model representing the linear relationship between the measurable nodes and unmeasurable nodes in the distribution network;

[0049] The power flow data calculation module is used to collect the power flow data of the measurable nodes in the distribution network in real - time, and input the collected power flow data of the measurable nodes into the double - layer power flow model to calculate the power flow data of the unmeasurable nodes, so as to obtain the power flow state of all nodes in the distribution network. Brief Description of the Drawings

[0050] In order to more clearly illustrate the technical solutions of the present application, the drawings required for implementation will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present application. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0051] Figure 1 It is a schematic flowchart of the specific process of a power flow calculation method for a distribution network based on incomplete measurement provided by an embodiment of the present application;

[0052] Figure 2 It is a structural diagram of a power flow calculation system for a distribution network based on incomplete measurement provided by an embodiment of the present application. Detailed Embodiments

[0053] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only some of the embodiments of the present application, rather than all of them. All other embodiments obtained by those of ordinary skill in the art without creative efforts based on the embodiments of the present application belong to the scope of protection of the present application.

[0054] It should be understood that the step numbers used in the text are only for convenient description and are not used to limit the execution order of the steps.

[0055] First Embodiment

[0056] Accurate power flow analysis is the key to the operation, planning, and fault diagnosis of distribution systems. However, the distribution network has a wide coverage area and numerous devices. If power flow data is collected for each node in the distribution network using measurement devices, the measurement cost will increase significantly. Moreover, the existing communication infrastructure does not allow covering all nodes in the distribution network, and there are still some unmeasurable nodes that cannot be covered. Therefore, how to accurately estimate the power flow data of unmeasurable nodes under the limitations of measurement cost and communication conditions is the technical problem to be solved in the embodiments of the present application.

[0057] As Figure 1 shown Figure 1 Figure 1 is a schematic diagram of the specific process of a method for calculating the power flow of a distribution network based on incomplete measurements provided by an embodiment of the present application. The method for calculating the power flow of the distribution network based on incomplete measurements in this embodiment includes steps S1 to S3, which are described in detail as follows:

[0058] Step S1: Based on a preset full-measurement linear power flow model, an incomplete-measurement linear power flow model is constructed through the set of measurable nodes and the set of unmeasurable nodes of the distribution network.

[0059] In the embodiment of the present application, an incomplete-measurement linear power flow model is constructed based on a preset full-measurement linear power flow model, and the full-measurement linear power flow model is derived based on a non-linear power flow model under the assumption that all nodes in the distribution network are measurable.

[0060] Specifically, the essence of the non-linear power flow model is Kirchhoff's Current Law (abbreviated as KCL), that is, the injected power of a certain node is equal to the sum of the voltage vector of the node multiplied by the injected current vector of the node. The specific expression of the KCL equation of that node is:

[0061] S = UI * ;

[0062] In the formula, S is the injected power of the node, including active power and reactive power; U is the voltage vector of the node, including voltage amplitude and phase angle; I is the injected current vector of the node.

[0063] Assume that a distribution network system has n nodes and all nodes are measurable. The specific expression of the KCL equation of the i-th node is:

[0064]

[0065] In the formula, p i and q i are the injected active power and injected reactive power of node i respectively, g ij and b ij are the line conductance and susceptance on branch i-j respectively, v i is the voltage vector of node i, v j is the voltage vector of node j, and ()* is the conjugate of the voltage vector of the node.

[0066] Write the voltage vector of node i in polar coordinate form:

[0067]

[0068] In the formula, θ ij is the phase angle between node i and node j.

[0069] Let the real and imaginary parts on both sides of the above formula in polar coordinate form be equal respectively, and the following two equality relations can be obtained:

[0070]

[0071] Among them, the first formula represents the active power injection of node i, and the second formula represents the reactive power injection of node i. Taking the first formula as an example, since the phase angle difference between the nodes in the distribution system is very small and the voltage amplitude is approximately 1, the following approximate relationship can be obtained:

[0072]

[0073] Also, according to the equality relationship between the self-admittance and mutual admittance of nodes in the power system: The above formula can be simplified to:

[0074]

[0075] In the formula, y ii and sub y ij are the self-admittance and mutual admittance of node i respectively.

[0076] By analogy with the derivation process of the simplified formula for the active power injection of node i above, the simplified formula for the reactive power injection of node i can be derived:

[0077]

[0078] Then, the expressions of the active power injection and reactive power injection of node i and the relationships with the node voltage amplitude and phase angle are written in a compact matrix form:

[0079]

[0080] In the formula, P and Q are the injection power vectors of the nodes, V and θ are the node voltage amplitude and phase angle vectors respectively, and G and B are the node conductance matrix and susceptance matrix respectively.

[0081] Using the Gaussian decomposition method to decompose the above matrix formula, and let L = (G + BG -1 B) -1 , R = BG -1 , an explicit mapping relationship between the node voltage amplitude and phase angle and the node active power injection and reactive power injection can be obtained:

[0082]

[0083] Written in a compact matrix form:

[0084]

[0085] Among them, H, K, M, and N respectively correspond to the coefficient matrices in the above formula.

[0086] For a determined distribution network system, the injection power and voltage vector of nodes can be used as the only description of the power flow state of the distribution network. Therefore, it is assumed that the nodes of the distribution network are measured at time t, and the following data are obtained:

[0087]

[0088] In the formula, U t is the voltage vector of the node at time t, and S t is the injection power of the node at time t.

[0089] Assume that a distribution network system can measure all nodes. Then, based on the above formula, a full-measurement linear power flow model can be constructed, and the specific expression is:

[0090]

[0091] In the formula, Φ is the coefficient matrix, and T is the measurement period. By minimizing the error of the fitting model, the coefficient matrix Φ is solved, and the model solution is transformed into an ordinary least squares problem.

[0092] However, in fact, the distribution network system cannot achieve full coverage of all nodes. The assumption that a distribution network system can measure all nodes does not hold in actual situations. Therefore, it is necessary to improve the full-measurement linear power flow model.

[0093] Furthermore, all nodes of the distribution network are divided into the measurable node set and the unmeasurable node set. Then, based on the measurable node set and the unmeasurable node set, a coefficient matrix between the two types of nodes is constructed to construct an incomplete measurement linear power flow model.

[0094] Among them, the specific expression of the incomplete measurement linear power flow model is:

[0095]

[0096] In the formula, is the voltage vector of the measurable nodes at time t, is the voltage vector of the unmeasurable nodes at time t, Φ oo is the coefficient matrix of measurable node - measurable node, Φ ou is the coefficient matrix of measurable node - unmeasurable node, Φ uo is the coefficient matrix of unmeasurable node - measurable node, Φ uu is the coefficient matrix of unmeasurable node - unmeasurable node, The injection power of the unmeasurable nodes at time t is the injection power of the measurable nodes at time t, o is the set of measurable nodes, and u is the set of unmeasurable nodes.

[0097] Step S2: Optimize the incomplete measurement linear power flow model according to a preset two - layer multiple linear regression framework, and construct a two - layer power flow model representing the linear relationship between the measurable nodes and unmeasurable nodes of the distribution network.

[0098] In the embodiment of the present application, since the power flow data of the measurable nodes can be collected by detection devices, while the power flow data of the unmeasurable nodes is unknown. Therefore, by taking the voltage vector and injection power of the unmeasurable nodes as unknowns, and solving the incomplete measurement linear power flow model through a multiple linear regression method in two layers, the power flow data of the unmeasurable nodes can be accurately inferred.

[0099] First, based on the preset two - layer multiple linear regression framework and different types of node information in the incomplete measurement linear power flow model, respectively construct a first linear relationship and a second linear relationship between the measurable nodes and the unmeasurable nodes, specifically: taking the injection power of the unmeasurable nodes as the solution target, construct a linear relationship between the voltage vector of the measurable nodes, the injection power of the measurable nodes, and the injection power of the unmeasurable nodes to obtain the first linear relationship; taking the voltage vector of the unmeasurable nodes as the solution target, construct a linear relationship between the voltage vector of the unmeasurable nodes, the injection power of the measurable nodes, and the injection power of the unmeasurable nodes to obtain the second linear relationship.

[0100] Then, construct an upper - layer power flow model with the first linear relationship and a lower - layer power flow model with the second linear relationship; through the upper - layer power flow model and the lower - layer power flow model, construct a two - layer power flow model representing the linear relationship between the measurable nodes and unmeasurable nodes of the distribution network.

[0101] Among them, the specific expression of the upper - layer power flow model is:

[0102]

[0103] Furthermore, in the upper - layer power flow model, the voltage vector and injection power of the measurable nodes can be collected in real - time, which can be used to solve the unknown quantity of the injection power of the unmeasurable nodes. Therefore, in the above formula is the unknown quantity to be solved. Therefore, the solution of the above formula is transformed into a multiple linear regression problem with high identifiability. And to prevent over - fitting of the model, the embodiment of the present application also regularizes the upper - layer power flow model through the L2 norm, specifically:

[0104]

[0105] In the formula, Φ oo is the coefficient matrix of measurable node - measurable node, and Φ ou is the coefficient matrix of measurable node - unmeasurable node. is the injection power of the unmeasurable node at time t, T is the measurement period, is the injection power of the measurable node at time t, is the voltage vector of the measurable node at time t, is the voltage vector of the unmeasurable node at time t, and λ, α, and β are all regularization coefficients.

[0106] The coefficient matrix is also regularized by the L2 norm, specifically:

[0107]

[0108] In the formula, are all the injection powers of the unmeasurable nodes.

[0109] Among them, these regularization coefficients are usually adjusted using cross - validation. This method solves the performance of the above - mentioned model on the test data set through the training data set to determine the optimal regularization coefficients (λ, α, β).

[0110] Exemplarily, in the embodiments of the present application, the optimal regularization coefficients are determined through K - fold cross - validation. Specifically: the entire data set is divided into K groups of equal size. The model is trained on (K - 1) groups and verified on the remaining groups by calculating the model accuracy (root mean square error). This process is repeated K times, and each time a different group is used to verify the model, generating K accuracy estimates, and the highest accuracy is given for selecting the optimal regularization coefficients.

[0111] Similarly, the injection power of the measurable node is collectable, and the injection power of the unmeasurable node can be solved through the upper - layer power flow model. Therefore, the unknown quantity to be solved in the lower - layer power flow model is the voltage vector of the unmeasurable node. Therefore, the specific expression of the lower - layer power flow model regularized by the L2 norm is:

[0112]

[0113] In the formula, Φ uo is the coefficient matrix of unmeasurable node - measurable node, and Φ uu is the coefficient matrix of unmeasurable node - unmeasurable node. is the injection power of the unmeasurable node at time t, T is the measurement period, The injection power of the measurable node at time t The injection power of the measurable node at time t is the voltage vector of the unmeasurable node at time t, and λ, α, and β are all regularization coefficients.

[0114] Among them, the regularized coefficient matrix is:

[0115]

[0116] In the formula, are all voltage vectors of unmeasurable nodes.

[0117] Finally, based on the regularized upper-layer power flow model and the lower-layer power flow model, a two-layer power flow model characterizing the linear relationship between the measurable nodes and unmeasurable nodes of the distribution network can be constructed.

[0118] In the embodiment of the present application, by constructing a two-layer model, the power flow data of complex unmeasurable nodes are solved separately through the upper and lower layers, and accurate power flow information of the entire distribution network can be obtained without prior knowledge, that is, the topological information and line parameters of the distribution network.

[0119] Step S3, collect the power flow data of the measurable nodes in the distribution network in real time, and input the collected power flow data of the measurable nodes into the two-layer power flow model to calculate the power flow data of the unmeasurable nodes, so as to obtain the power flow states of all nodes in the distribution network.

[0120] In the embodiment of the present application, the power flow data of the measurable nodes in the distribution network are collected in real time. First, the voltage vector and injection power of the measurable nodes are input into the upper-layer power flow model to solve the injection power of the unmeasurable nodes; then, the injection power of the unmeasurable nodes and the injection power of the measurable nodes are input into the lower-layer power flow model for solution to calculate the voltage vector of the unmeasurable nodes, so as to obtain the power flow data of all nodes in the distribution network.

[0121] Specifically, because there are multiple unknowns in the two-layer power flow model, the model itself is non-convex, making it difficult to solve the multiple linear relationships between the unknowns. Therefore, in the embodiment of the present application, by fixing any set of unknowns, the multiple linear regression problem is equivalent to an ordinary linear regression problem and is effectively solved.

[0122] Optionally, in the embodiment of the present application, the upper-layer power flow model is solved by using the alternating minimization method to iteratively update multiple groups of variables. The variables that need to be iterated include the coefficient matrix Φ of measurable node-measurable node oo and the coefficient matrix Φ of measurable node-unmeasurable node ou and the injection power of the unmeasurable node at time t

[0123] Specifically, the alternating minimization method is used to fix any one of the above three variables and perform iterative solution. When the preset iteration number threshold is exceeded or the preset convergence condition is met, the injection power of the unmeasurable node is solved. Among them, the iteration number threshold is set according to the requirement for prediction accuracy.

[0124] Similarly, the voltage vector of the unmeasurable node is also calculated by the alternating minimization method for the lower-layer power flow model.

[0125] Implementing the embodiments of the present application has the following beneficial effects:

[0126] In the embodiments of the present application, all nodes in the distribution network are divided into measurable nodes and unmeasurable nodes according to the actual situation, and then substituted into a preset full-measurement linear power flow model that assumes all nodes can be fully measured to construct an incomplete-measurement linear power flow model containing the information of unmeasurable nodes. Because the model contains multiple linear relationships and the power flow data of the nodes also contains various data, linear relationships between the power flow data of the measurable nodes and the unmeasurable nodes are respectively constructed on the basis of the incomplete-measurement linear power flow model through a two-layer multiple linear regression framework. These two linear relationships are respectively used to construct the upper-layer model and the lower-layer model to obtain the two-layer power flow model. Then, the power flow data of the measurable nodes in the distribution network is collected, and these data are used as input values to first solve the linear relationship of the upper-layer model to obtain partial power flow data of the unmeasurable nodes; then, the lower-layer model is solved through the partial power flow data of the unmeasurable nodes to obtain the complete power flow of the unmeasurable nodes, realizing the acquisition of the complete and accurate power flow state of the distribution network without measuring all nodes of the distribution network, saving the measurement cost and measurement complexity.

[0127] Further, in order to execute the distribution network power flow calculation system based on incomplete measurement corresponding to the above method embodiments to achieve the corresponding functions and technical effects, Figure 2 A structure diagram of a distribution network power flow calculation system based on incomplete measurement is provided. For the convenience of description, only the parts related to this embodiment are shown. The distribution network power flow calculation system based on incomplete measurement provided by the embodiments of the present application includes:

[0128] A linear model construction module 201, configured to construct an incomplete-measurement linear power flow model based on a preset full-measurement linear power flow model through the set of measurable nodes and the set of unmeasurable nodes of the distribution network.

[0129] In the embodiments of the present application, the power flow data of the preset fully measured nodes is input into a preset non-linear power flow model to construct the full-measurement linear power flow model.

[0130] All nodes of the distribution network are divided into the measurable node set and the unmeasurable node set.

[0131] According to the measurable node set and the unmeasurable node set, the measurable nodes and unmeasurable nodes in the full-measurement linear power flow model are combined in pairs to construct a corresponding coefficient matrix, and the incomplete-measurement linear power flow model is obtained.

[0132] The two-layer model construction module 202 is configured to optimize the incomplete-measurement linear power flow model according to a preset two-layer multiple linear regression framework, and construct a two-layer power flow model representing the linear relationship between the measurable nodes and unmeasurable nodes of the distribution network.

[0133] In the embodiment of the present application, based on the two-layer multiple linear regression framework, a first linear relationship and a second linear relationship are respectively constructed between the measurable nodes and the unmeasurable nodes; wherein, the power flow data includes injection power and voltage vector.

[0134] Optimize the incomplete-measurement linear power flow model according to the first linear relationship to construct an upper-layer power flow model.

[0135] Optimize the incomplete-measurement linear power flow model according to the second linear relationship to construct a lower-layer power flow model.

[0136] Construct the two-layer power flow model according to the upper-layer power flow model and the lower-layer power flow model.

[0137] The power flow data calculation module 203 is configured to collect the power flow data of the measurable nodes in the distribution network in real time, and input the collected power flow data of the measurable nodes into the two-layer power flow model to calculate the power flow data of the unmeasurable nodes, and obtain the power flow state of all nodes of the distribution network.

[0138] In the embodiment of the present application, according to the measurable node set, the power flow data of the measurable nodes in the distribution network is collected.

[0139] Input the power flow data of the measurable nodes into the upper-layer power flow model of the two-layer power flow model to solve, and obtain the injection power of the unmeasurable nodes.

[0140] Input the injection power of the unmeasurable nodes into the lower-layer power flow model of the two-layer power flow model to solve, and obtain the voltage vector of the unmeasurable nodes.

[0141] In some embodiments, the linear model construction module 201 further includes:

[0142] An incomplete measurement linear power flow model is constructed based on a preset full measurement linear power flow model, and the full measurement linear power flow model is derived from a non-linear power flow model under the assumption that all nodes in the distribution network can be measured.

[0143] Specifically, the essence of the non-linear power flow model is Kirchhoff's Current Law (abbreviated as KCL), that is, the injection power of a certain node is equal to the sum of the voltage vector of the node multiplied by the injection current vector of the node. The specific expression of the KCL equation of that node is:

[0144] S = UI * ;

[0145] In the formula, S is the injection power of the node, including active power and reactive power; U is the voltage vector of the node, including voltage amplitude and phase angle; I is the injection current vector of the node.

[0146] Assume that a distribution network system has n nodes and all nodes can be measured. The specific expression of the KCL equation of the i-th node is:

[0147]

[0148] In the formula, p i and q i are the injection active power and injection reactive power of node i respectively, g ij and b ij are the line conductance and susceptance on the branch i-j respectively, v i is the voltage vector of node i, v j is the voltage vector of node j, and ()* is the conjugate of the voltage vector of the node.

[0149] Write the voltage vector of node i in polar coordinate form:

[0150]

[0151] In the formula, θ ij is the phase angle between node i and node j.

[0152] Let the real and imaginary parts on both sides of the equal sign in the above formula in polar coordinate form be equal respectively, and the following two equal relationships can be obtained:

[0153]

[0154] Among them, the first formula represents the injection active power of node i, and the second formula represents the injection reactive power of node i. Taking the first formula as an example, since the phase angle difference between the nodes in the distribution system is very small and the voltage amplitude is approximately 1, the following approximate relationship can be obtained:

[0155]

[0156] According to the equality relationship between the self-admittance and mutual admittance of nodes in the power system: The above formula can be simplified to:

[0157]

[0158] In the formula, y ii and the split y ij are the self-admittance and mutual admittance of node i respectively.

[0159] By analogy with the derivation process of the simplified formula for the active power injection of node i above, the simplified formula for the reactive power injection of node i can be derived:

[0160]

[0161] Then, the expressions of the active power injection and reactive power injection of node i and the relationship between the node voltage amplitude and phase angle are written in a compact matrix form:

[0162]

[0163] In the formula, P and Q are the injection power vectors of the nodes, V and θ are the node voltage amplitude and phase angle vectors respectively, and G and B are the node conductance matrix and susceptance matrix respectively.

[0164] Using the Gaussian decomposition method to decompose the above matrix formula, and letting L = (G + BG -1 B) -1 , R = BG -1 , an explicit mapping relationship between the node voltage amplitude and phase angle and the node active power injection and reactive power injection can be obtained:

[0165]

[0166] Written in a compact matrix form:

[0167]

[0168] Among them, H, K, M, and N correspond to the coefficient matrices in the above formula respectively.

[0169] For a determined distribution network system, the injection power and voltage vector of the nodes can be used as the only description of the distribution network power flow state. Therefore, it is assumed that the distribution network nodes are measured at time t, and the following data are obtained:

[0170]

[0171] In the formula, U t is the voltage vector of the nodes at time t, St is the injection power of the node at time t.

[0172] Assume that a distribution network system can measure all nodes. Then, based on the above formula, a full-measurement linear power flow model can be constructed, and its specific expression is:

[0173]

[0174] In the formula, Φ is the coefficient matrix, and T is the measurement period. By minimizing the error of the fitting model, the coefficient matrix Φ is solved, and the model solution is transformed into an ordinary least squares problem.

[0175] However, in reality, a distribution network system cannot achieve full coverage of measuring all nodes. The assumption that a distribution network system can measure all nodes does not hold in actual situations. Therefore, it is necessary to improve the full-measurement linear power flow model.

[0176] Furthermore, all nodes of the distribution network are divided into the measurable node set and the unmeasurable node set. Then, based on the measurable node set and the unmeasurable node set, a coefficient matrix between the two types of nodes is constructed to build an incomplete-measurement linear power flow model.

[0177] Among them, the specific expression of the incomplete-measurement linear power flow model is:

[0178]

[0179] In the formula, is the voltage vector of the measurable nodes at time t, is the voltage vector of the unmeasurable nodes at time t, Φ oo is the coefficient matrix of measurable node - measurable node, Φ ou is the coefficient matrix of measurable node - unmeasurable node, Φ uo is the coefficient matrix of unmeasurable node - measurable node, Φ uu is the coefficient matrix of unmeasurable node - unmeasurable node, is the injection power of the unmeasurable nodes at time t, is the injection power of the measurable nodes at time t, o is the set of measurable nodes, and u is the set of unmeasurable nodes.

[0180] In some embodiments, the double-layer model construction module 202 further includes:

[0181] Since the power flow data of measurable nodes can be collected by detection devices, while the power flow data of unmeasurable nodes is unknown. Therefore, by treating the voltage vector and injection power of unmeasurable nodes as unknowns and solving the incomplete measurement linear power flow model through a multi-linear regression method in two layers, the power flow data of unmeasurable nodes can be accurately inferred.

[0182] First, based on a preset two-layer multi-linear regression framework and different types of node information in the incomplete measurement linear power flow model, a first linear relationship and a second linear relationship are respectively constructed between the measurable nodes and the unmeasurable nodes, specifically: taking the injection power of the unmeasurable nodes as the solution target, a linear relationship is constructed among the voltage vector of the measurable nodes, the injection power of the measurable nodes, and the injection power of the unmeasurable nodes to obtain the first linear relationship; taking the voltage vector of the unmeasurable nodes as the solution target, a linear relationship is constructed among the voltage vector of the unmeasurable nodes, the injection power of the measurable nodes, and the injection power of the unmeasurable nodes to obtain the second linear relationship.

[0183] Then, an upper-layer power flow model is constructed based on the first linear relationship, and a lower-layer power flow model is constructed based on the second linear relationship; through the upper-layer power flow model and the lower-layer power flow model, a two-layer power flow model is constructed to represent the linear relationship between the measurable nodes and the unmeasurable nodes of the distribution network.

[0184] Among them, the specific expression of the upper-layer power flow model is:

[0185]

[0186] Further, in the upper-layer power flow model, the voltage vector and injection power of the measurable nodes can be collected in real time, which can be used to solve the unknown injection power of the unmeasurable nodes. Therefore, in the above formula is the unknown to be solved. Therefore, the solution of the above formula is transformed into a multi-linear regression problem with high identifiability. In order to prevent overfitting of the model, the upper-layer power flow model is regularized by the L2 norm in this embodiment of the present application, specifically:

[0187]

[0188] In the formula, Φ oo is the coefficient matrix of measurable node - measurable node, Φ ou is the coefficient matrix of measurable node - unmeasurable node, is the injection power of the unmeasurable nodes at time t, T is the measurement period, is the injection power of the measurable nodes at time t, is the voltage vector of measurable nodes at time t, is the voltage vector of unmeasurable nodes at time t, and λ, α, and β are all regularization coefficients.

[0189] It also uses an L2 norm regularization coefficient matrix, specifically:

[0190]

[0191] In the formula, are all the injection powers of unmeasurable nodes.

[0192] Among them, these regularization coefficients are usually adjusted using cross-validation. This method solves the performance of the above model on the test dataset through the training dataset to determine the optimal regularization coefficients (λ, α, β).

[0193] Exemplarily, in the embodiments of the present application, the optimal regularization coefficients are determined through K-fold cross-validation. Specifically: the entire dataset is divided into K groups of equal size. The model is trained on (K - 1) groups and verified on the remaining groups by calculating the model accuracy (root mean square error). This process is repeated K times, each time using a different group to verify the model, generating K accuracy estimates, and the highest accuracy is given to select the optimal regularization coefficients.

[0194] Similarly, the injection power of measurable nodes is collectable, and the injection power of unmeasurable nodes can be solved through the upper-layer power flow model. Therefore, the unknown quantity to be solved in the lower-layer power flow model is the voltage vector of unmeasurable nodes. Therefore, the specific expression of the lower-layer power flow model after L2 norm regularization is:

[0195]

[0196] In the formula, Φ uo is the coefficient matrix of unmeasurable nodes - measurable nodes, and Φ uu is the coefficient matrix of unmeasurable nodes - unmeasurable nodes, is the injection power of the unmeasurable nodes at time t, T is the measurement period, is the injection power of the measurable nodes at time t, is the injection power of the measurable nodes at time t, is the voltage vector of the unmeasurable nodes at time t, and λ, α, and β are all regularization coefficients.

[0197] Among them, the regularized coefficient matrix is:

[0198]

[0199] In the formula, They are all voltage vectors of immeasurable nodes.

[0200] Finally, based on the regularized upper-layer power flow model and the lower-layer power flow model, a two-layer power flow model characterizing the linear relationship between the measurable nodes and the immeasurable nodes of the distribution network can be constructed.

[0201] In the embodiment of the present application, by constructing a two-layer model, the power flow data of complex immeasurable nodes are solved separately through the upper and lower layers, and accurate power flow information of all parts of the distribution network can be obtained without prior knowledge, that is, the topological information and line parameters of the distribution network.

[0202] In some embodiments, the power flow data calculation module 203 further includes:

[0203] Real-time collect the power flow data of the measurable nodes in the distribution network. First, input the voltage vector and injection power of the measurable nodes into the upper-layer power flow model to solve the injection power of the immeasurable nodes; then input the injection power of the immeasurable nodes and the injection power of the measurable nodes into the lower-layer power flow model for solution, and calculate the voltage vector of the immeasurable nodes, so as to obtain the power flow data of all nodes in the distribution network.

[0204] Specifically, because there are multiple unknowns in the two-layer power flow model, the model itself is non-convex, making it difficult to solve the multiple linear relationships between the unknowns. Therefore, in the embodiment of the present application, by fixing any set of unknowns, the multiple linear regression problem is equivalent to an ordinary linear regression problem and effectively solved.

[0205] Optionally, in the embodiment of the present application, the upper-layer power flow model is solved by using the alternating minimization method to iteratively update multiple groups of variables. The variables that need to be iterated include the coefficient matrix Φ of the measurable node - measurable node oo , the coefficient matrix Φ of the measurable node - immeasurable node ou and the injection power of the immeasurable nodes at time t

[0206] Specifically, the alternating minimization method is used to fix any one of the above 3 variables and perform iterative solution. When the preset iteration number threshold is exceeded or the preset convergence condition is met, the injection power of the immeasurable nodes is solved. Among them, the iteration number threshold is set according to the requirement of prediction accuracy.

[0207] Similarly, the voltage vector of the immeasurable nodes is also calculated by using the alternating minimization method for the lower-layer power flow model.

[0208] Implementing the embodiment of the present application has the following beneficial effects:

[0209] In the embodiment of the present application, all nodes in the distribution network are divided into measurable nodes and unmeasurable nodes according to the actual situation, and then substituted into a preset full-measurement linear power flow model that assumes all nodes can be fully measured, to construct an incomplete-measurement linear power flow model containing information of unmeasurable nodes. Since the model contains multiple linear relationships and the power flow data of nodes also contains various types of data, linear relationships between the power flow data of measurable nodes and unmeasurable nodes are respectively constructed on the basis of the incomplete-measurement linear power flow model through a two-layer multiple linear regression framework. These two linear relationships are respectively used to construct the upper-layer model and the lower-layer model to obtain the two-layer power flow model. Then, the power flow data of measurable nodes in the distribution network is collected, and these data are used as input values to first solve the linear relationship of the upper-layer model to obtain partial power flow data of unmeasurable nodes; then, the lower-layer model is solved through the partial power flow data of unmeasurable nodes to obtain the full power flow of unmeasurable nodes, realizing the acquisition of a complete and accurate power flow state of the distribution network without measuring all nodes of the distribution network, saving the measurement cost and measurement complexity.

[0210] The specific embodiments described above further elaborate on the purpose, technical solutions, and beneficial effects of the present application. It should be understood that the above are only specific embodiments of the present application and are not used to limit the protection scope of the present application. In particular, for those skilled in the art, any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A power flow calculation method for a distribution network based on incomplete measurements, characterized in that, Including: Based on a preset full-measurement linear power flow model, an incomplete-measurement linear power flow model is constructed through the set of measurable nodes and the set of unmeasurable nodes in the distribution network; According to a preset two-layer multiple linear regression framework, the incomplete-measurement linear power flow model is optimized to construct a two-layer power flow model representing the linear relationship between the measurable nodes and the unmeasurable nodes in the distribution network; The power flow data of the measurable nodes in the distribution network is collected in real time, and the collected power flow data of the measurable nodes is input into the two-layer power flow model to calculate the power flow data of the unmeasurable nodes, so as to obtain the power flow state of all nodes in the distribution network.

2. The power flow calculation method for a distribution network based on incomplete measurement according to claim 1, characterized in that, The constructing of the incomplete-measurement linear power flow model based on a preset full-measurement linear power flow model through the set of measurable nodes and the set of unmeasurable nodes in the distribution network is specifically as follows: The power flow data of the preset full-measurement nodes is input into a preset non-linear power flow model to construct the full-measurement linear power flow model; All nodes in the distribution network are divided into the set of measurable nodes and the set of unmeasurable nodes; According to the set of measurable nodes and the set of unmeasurable nodes, the measurable nodes and the unmeasurable nodes in the full-measurement linear power flow model are combined pairwise to construct a corresponding coefficient matrix, so as to obtain the incomplete-measurement linear power flow model.

3. The power flow calculation method for a distribution network based on incomplete measurement according to claim 2, characterized in that, The incomplete-measurement linear power flow model is specifically: The specific expression of the incomplete-measurement linear power flow model is: wherein, is the voltage vector of measurable nodes at time t, is the voltage vector of unmeasurable nodes at time t, Φ oo is the coefficient matrix of measurable node - measurable node, Φ ou is the coefficient matrix of measurable node - unmeasurable node, Φ uo is the coefficient matrix of unmeasurable node - measurable node, Φ uu is the coefficient matrix of unmeasurable node - unmeasurable node, is the injection power of the unmeasurable nodes at time t, is the injection power of the measurable nodes at time t, o is the set of measurable nodes, and u is the set of unmeasurable nodes.

4. The power flow calculation method for a distribution network based on incomplete measurements according to claim 1, characterized in that The optimizing of the incomplete-measurement linear power flow model according to a preset two-layer multiple linear regression framework to construct a two-layer power flow model representing the linear relationship between the measurable nodes and the unmeasurable nodes in the distribution network is specifically as follows: Based on the two-layer multiple linear regression framework, a first linear relationship and a second linear relationship between the measurable nodes and the unmeasurable nodes are respectively constructed; wherein, the power flow data includes injection power and voltage vector; The incomplete-measurement linear power flow model is optimized according to the first linear relationship to construct an upper-layer power flow model; The incomplete-measurement linear power flow model is optimized according to the second linear relationship to construct a lower-layer power flow model; According to the upper-layer power flow model and the lower-layer power flow model, the two-layer power flow model is constructed.

5. The method for calculating the power flow of a distribution network based on incomplete measurement according to claim 4, characterized in that, The first linear relationship and the second linear relationship are specifically: Taking the injection power of the unmeasurable nodes as the solution target, a linear relationship between the voltage vector of the measurable nodes, the injection power of the measurable nodes and the injection power of the unmeasurable nodes is constructed to obtain the first linear relationship; Taking the voltage vector of the unmeasurable nodes as the solution target, a linear relationship between the voltage vector of the unmeasurable nodes, the injection power of the measurable nodes and the injection power of the unmeasurable nodes is constructed to obtain the second linear relationship.

6. The method for calculating the power flow of a distribution network based on incomplete measurements according to claim 4, wherein, Also including: The coefficient matrices of the upper-layer power flow model and the lower-layer power flow model are regularized respectively through the L2 norm to construct the two-layer power flow model.

7. The method for calculating the power flow of a distribution network based on incomplete measurement according to claim 6, wherein The two-layer power flow model is specifically: Among them, the specific expression of the upper-layer power flow model of the two-layer power flow model is: where Φ oo is the coefficient matrix of the measurable node - measurable node, and Φ ou is the coefficient matrix of the measurable node - unmeasurable node, is the injection power of the unmeasurable node at time t, T is the measurement period, is the injection power of the measurable node at time t, is the voltage vector of the measurable node at time t, is the voltage vector of the unmeasurable node at time t, and λ, α, and β are all regularization coefficients; The lower-layer power flow model of the double-layer power flow model has the following specific expression: where Φ uo is the coefficient matrix of the unmeasurable node - measurable node, and Φ uu is the coefficient matrix of the unmeasurable node - unmeasurable node, is the injection power of the unmeasurable node at time t, T is the measurement period, is the injection power of the measurable node at time t, is the voltage vector of the measurable node at time t, is the voltage vector of the unmeasurable node at time t, and λ, α, and β are all regularization coefficients.

8. The method for calculating the power flow of a distribution network based on incomplete measurements according to claim 1, characterized in that Real-time collect the power flow data of the measurable nodes in the distribution network, and input the collected power flow data of the measurable nodes into the double-layer power flow model to calculate the power flow data of the unmeasurable nodes, thereby obtaining the power flow states of all nodes in the distribution network. Specifically: Collect the power flow data of the measurable nodes in the distribution network according to the set of measurable nodes; Input the power flow data of the measurable nodes into the upper-layer power flow model of the double-layer power flow model for solution to obtain the injection power of the unmeasurable nodes; Input the injection power of the unmeasurable nodes into the lower-layer power flow model of the double-layer power flow model for solution to obtain the voltage vector of the unmeasurable nodes.

9. The method for calculating the power flow of a distribution network based on incomplete measurements according to claim 8, wherein It further includes: Adopt the alternating minimization method. By fixing any quantity to be solved in the double-layer power flow model, calculate the injection power of the unmeasurable nodes and the voltage vector of the unmeasurable nodes, thereby obtaining the power flow data of the unmeasurable nodes.

10. A power flow calculation system for a distribution network based on incomplete measurements, characterized in that, It includes: A linear model construction module, a double-layer model construction module, and a power flow data calculation module; Among them, the linear model construction module is used to construct an incomplete measurement linear power flow model based on a preset full-measurement linear power flow model through the set of measurable nodes and the set of unmeasurable nodes in the distribution network; The double-layer model construction module is used to optimize the incomplete measurement linear power flow model according to a preset double-layer multiple linear regression framework to construct a double-layer power flow model representing the linear relationship between the measurable nodes and the unmeasurable nodes in the distribution network; The power flow data calculation module is used to real-time collect the power flow data of the measurable nodes in the distribution network, and input the collected power flow data of the measurable nodes into the double-layer power flow model to calculate the power flow data of the unmeasurable nodes, thereby obtaining the power flow states of all nodes in the distribution network.

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