CN116319377B - Distributed dynamic state estimation method for power distribution network for resisting network attack - Google Patents
Distributed dynamic state estimation method for power distribution network for resisting network attack Download PDFInfo
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- H—ELECTRICITY
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Abstract
The invention belongs to the field of power distribution network state estimation, and discloses a distributed dynamic state estimation method of a power distribution network for resisting network attack, which comprises the steps of dividing a large-scale power distribution network into a plurality of overlapped subareas by utilizing excellent searching capability of a network; and secondly, establishing a local prediction auxiliary state estimation model considering network attack for the subareas, and finally, adopting a boundary interaction method of adjacent subareas of the power distribution network to enable state estimation calculation results of boundary nodes in the adjacent subareas to be consistent, thereby outputting a global state estimation result of the power distribution network. The invention provides an effective coping method for network attacks which are increasingly increased in the running and controlling processes of the power distribution network, and improves the capability of the dynamic state estimation flow of the power distribution network to resist the network attacks.
Description
Technical Field
The invention belongs to the field of power distribution network state estimation, and particularly relates to a distributed dynamic state estimation method for a power distribution network for resisting network attacks.
Background
In recent years, the national energy structure is also changed greatly, and the wide use of clean energy sources such as photovoltaic power generation, wind power generation and the like greatly increases the complexity of a power distribution network system, so that the difficulty of detection and control of the power system is also increased linearly. Furthermore, with the continuous development of the power distribution network, the transmission distance and the network scale are continuously enlarged, the information network scale of the power system is greatly increased, the number of decision units and sensors is rapidly increased, and the interaction mechanism of the power system control decision units, the power grid and the information network is also more and more complex. Modern power systems are no longer power equipment networks in the traditional sense, but have evolved into power systems featuring various network physical systems.
The power distribution network is huge in scale, the distributed power supply is widely used, the power distribution network model is more complicated due to the factors, the data volume collected by the device is rapidly increased, a large amount of data is easily influenced by factors such as user response demands, customer daily demands, hacker malicious attacks and the like, and therefore the stability of the whole system is influenced. The traditional large-scale power distribution network is difficult to find out attacks in the face of false data injection network attacks, the robustness of the system is poor, and the authenticity of a state estimation result is difficult to guarantee.
At present, related technical researches aiming at the state estimation of a power distribution network and being carried out under network attack have achieved a certain effect, but are limited by the research thinking of a power transmission network, and the built attack model is mostly based on a single-phase or three-phase symmetrical power distribution network structure, which is not in accordance with the actual three-phase asymmetrical power distribution network structure; in addition, most of the prior studies focused on network attacks in the centralized distribution network, such as those described in the literature (Junjun Xu, zaijun Wu, tengfei Zhang, qinran Hu, qiawei Wu. A secure forecasting-aided state estimation framework for power distribution systems against false data injection attacks [ J ]. Applied Energy, 2022, 328:120107.), based on the working freshness of distributed solutions. However, the centralized network attack mode requires an attacker to grasp the topology structure and parameter configuration of the whole power distribution network system, which makes the set network attack reach the expected effect. Although the related literature (Cheng Yan. Consider the three-phase unbalanced distribution network state estimation [ D ] of false data injection attack, university of southeast, south kyo, 2021.) is a distributed network attack study performed on a distribution network, the study object is distribution network static distributed state estimation, and only a distributed attack means is detected, but the attack area is not effectively repaired, so that the reliability of the output state estimation result is not high.
Disclosure of Invention
In order to solve the technical problems, the invention provides a distributed dynamic state estimation method for a power distribution network for resisting network attacks, which aims to improve the capability of the large-scale power distribution network for resisting network attacks, enhance the robustness of the system and improve the authenticity of a state estimation result.
The invention discloses a distributed state estimation method of a power distribution network for resisting network attack, which comprises the following steps:
step 1, dividing a large-scale power distribution network into a plurality of overlapped subareas;
step 2, a local state estimation model is established for the subareas, partial system information is mastered by an attacker, and a sparse false data injection attack model under the condition of mastering partial system information is established;
step 3, designing an improved noise recurrence estimator, and constructing a historical state variable data set of a power distribution network subarea by combining an unscented Kalman filtering algorithm;
step 4, based on a sliding time window theory, a robustness method for enhancing the local state estimation of the power distribution network subarea to resist network attack is adopted, and the influence of the network attack in the local state estimation process of the power distribution network subarea is processed, so that a normal local state estimation result is output;
And 5, adopting an adjacent sub-region boundary interaction method to enable the state estimation results of the boundary nodes in the adjacent sub-regions to be consistent, and then outputting a global state estimation result.
Further, the step 1 specifically includes:
step 1-1, constructing a link table showing the relevance among nodes according to network wiring data of a power distribution network system; wherein, the nodeA i ，i=1, 2 …, representing a common node in the system; superior nodeS i ，i=1, 2 …, representing and nodeA i ，iNodes connected near the power supply end, =1, 2, …; lower nodeM i ，i=1, 2 …, representing and nodeA i ，i=1, 2 …, nodes connected near the end side; node lower connection numberFRepresenting the number of lower nodes of the node, which represents the number of connected branches of the node; number of subsequent nodesZRepresenting all node numbers of the subsequent connection of the nodes; paragraph number from node to root nodeLRepresenting the distance of the node from the primary root node;
step 1-2, comprehensively considering the scale of the power distribution network and the thread number of a calculation program, determining the number C of network partitions, and obtaining the maximum node number H of the partitions by a formula (1);
，
wherein: h is the maximum node number of the subareas, T is the total node number of the power distribution network, C is the subarea number, and e is the adjustment coefficient;
step 1-3, partitioning each feeder line of the power distribution network according to the following rules;
(1a) From the end node to the power source end, the partition task is executed when the partition task is executed to the nodeA i ，i=1, 2, …, continue searching its upper nodesS i ，i=1, 2, …, if the upper nodeS i ，i=1, 2, …, all subsequent node numbersZThe difference between the number of the nodes and all the subsequent nodes of all the end nodes of the area is greater than or equal to the maximum number of the nodes of the partitionHIf the number of nodes in the partition reaches the maximum value, stopping searching, and at the moment, obtaining the nodeA i ，i=1, 2 …, as root node of partition;
(2a) In the process of partitioning from the end node to the power source end, when proceeding to the nodeA i ，i=1, 2, …, continue searching its upper nodesS i ，i=1, 2 …, if nodeS i ，i=1, 2 …, already in the other partitions, search is stopped, at which point the nodeA i ，i=1, 2 …, as root node of partition;
(3a) When the nodeA i ，iWhen the number of segments reaching the primary root node is smaller than the set value, =1, 2, …, the search is stopped, and the node is at this timeA i ，i=1, 2 …, as root node of partition;
(4a) In the process of searching the node towards the power end, when encountering a node with a branch, all subsequent node numbers of the node comprise the node numbers on the branch;
step 1-4, after the partition of the feeder line is completed, starting from the main root node, connecting the empty nodes forward to form a main root node area, and adjusting according to the following principle:
(1b) When the number of the partitions is more than a specified value, the areas with the number of partial nodes less than the average value are merged into the adjacent areas, and the adjusting coefficient e is increased at the moment so as to ensure that the calculated amounts of the partitions are similar;
(2b) When the node number of the root node area is more than a specified value, partial nodes are divided into adjacent partitions, so that the calculated amount of each partition is ensured to be similar.
Further, in step 2, a local state estimation model is established for the sub-region:
，
wherein, the liquid crystal display device comprises a liquid crystal display device,is a state variable of the system in the local sub-area at time k,/for the system at time k>，、/>Is the corresponding voltage amplitude vector and phase angle vector, < >>Then it is the measured variable of the system in the local sub-area at time k,/>Is Gaussian process noise of the system in the local sub-area at time k-1, +.>Is the measurement noise of the system in the local sub-area at time k,/>Is a state variable +.>Is a nonlinear state transfer function of +.>Is a state variable +.>Is a measurement function of (2);
nonlinear state transfer functionDesigned according to a Holt-windows double-parameter exponential smoothing method,
，
in the above-mentioned method, the step of,is->The local subsystem at the moment predicts the system variable prediction quantity at the moment k; />Is the horizontal component of the state variable at time k-1,/->Is the vertical component of the state variable at time k-1; />Is the state quantity of the system variable of the local subsystem at the time of k-1; / >The method is that a local subsystem at the time of k-2 predicts the system variable prediction quantity at the time of k-1; />And->The method is a smoothing parameter in a Holt-windows double-parameter exponential smoothing method, and represents weights of variables with different distances on time scales; />Is the horizontal component of the state variable at time k-2; />Is the vertical component of the state variable at time k-2;
measuring functionThe measurement vector design is relied on, and in a state estimation model of a three-phase unbalanced distribution network subarea, the measurement variable of a node j at the moment k is +.>The method comprises the following steps:
，
in the above-mentioned method, the step of,active injection power for node j, +.>Reactive power injection for node j, +.>Active injection power for branch j-r, < >>Reactive injection power for branch j-r, < >>Assignment of line current for branch j-r,then it is a node set of the distribution network; />Is a node;
in combination with the data of the measurement vector, the measurement function is obtained by neglecting the admittances of the nodes in parallelThe method comprises the following steps:
，
，，
，
，
，
wherein the method comprises the steps of；/>And->Is the phase +.>The voltage amplitude and phase angle at time k; />And->Is the phase +.>Voltage amplitude at time kAnd phase angle; />And->Is the phase of the j-r branch>Voltage and current at time k; />Is the phase of the j-r branch>Apparent power at time k; />And->Phase ∈zero node >Active and reactive power at time k; />，/>Is the active and reactive power of node j at time k; />And->Is the phase of the j-r branch>Active and reactive power at time k; />And->Is the first node admittance matrixNo. 2 of sub-matrix>Conductance and susceptance of the individual elements; />Is the phase +.>And phase of node r>Phase angle difference between times k; />Is the phase +.>And (2) sum phase->Phase angle difference between times k.
Further, in step 2, a sparse false data injection attack model is established under the condition of grasping part of system information:
assuming that an attacker only knows part of line parameters and topology structures of an attack area;
(1c) State variables of sub-area system at k momentInitializing:
，
in the above-mentioned method, the step of,for the initial value of the node voltage amplitude, +.>An initial value of a node voltage phase angle; />Is the node voltage amplitude at time k, +.>Is the node voltage phase angle at time k;
(2c) Designing attack vectors: the attack vector attacks in a mode of injecting offset, and the set of nodes in an attack area I of the attack is set asBoundary node set of attack area I and non-attack area II is +.>Attack vector for node j at time k>The method comprises the following steps:
，
In the above-mentioned method, the step of,attack offset for node j active power, +.>Is the attack offset for the reactive power of node j, < >>Attack offset for active power of branch between nodes j and r, +.>Attack offset for reactive power of branch between nodes j, r, < >>Attack offset for branch current amplitude values between nodes j and r; />Is a set of n nodes of the complete power distribution network;
(3c) Attack vector sparsification: since the attack assumption is that an attacker grasps part of system information, the attack vector shown in the formula (12) is subjected to thinning processing, and the processed attack vector is:
，
the treatment process is as follows: equation (14) is sparse processing of attack vectors, equation (15) is to ensure that the states of boundary nodes before and after attack are unchanged, and equation (16) -equation (19) is a constraint condition of various variables:
，
，
，
，
，
，
in the above-mentioned method, the step of,attack offset for active power of node j at time k>The value of the change in the iteration,、/>、/>、/>、 />、/>、/>、/>similarly, let go of>Is the variation of the voltage amplitude; />Is the variation of the voltage phase angle; />Is the active power of node j at time k before the false data injection attack,is the active power of node j at k time after the false data injection attack, < >>Is that node j does not exist at k moment before false data injection attack Work power,/->Is the reactive power of node j at k time after the false data injection attack, < >>Is the active power of the branch between nodes j and r at k moment before the false data injection attack, +.>The active power of the branch between the nodes j and r at the moment k after the false data injection attack; />The reactive power of the branch between the nodes j and r at the moment k after the false data injection attack; />The current of the branch circuit between the nodes j and r at the moment k after the false data injection attack; />The state variables of the boundary node set sub-region system of the attack region I and the non-attack region II at the moment k; />，/>Is the upper and lower limits of the active power of node j; />，/>Is the upper and lower reactive power limits of node j; />Is the upper limit of the active power of the branch circuit between the nodes j and r; />Is a sectionAn upper limit of apparent power between points j, r;is the absolute value of apparent power between nodes j and r at k time after the false data injection attack;
(4c) Attack vector effect evaluation: state offset when an attacked node、/>Satisfying equation (20), it indicates: the power distribution network sub-area system suffers from false data injection network attack, and has remarkable attack effect, and the attack vector is +.>，/>；/>Is the variation of the attack vector in two attack iterations; if the state of the attacked node is offset +.>、/>If the equation (20) is not satisfied, the attack effect is poor, and the calculation should be returned to (2 c);
，
In the above-mentioned method, the step of,represents the voltage amplitude offset for node j, < +.>And->Representing the upper and lower limits of the voltage amplitude,represents +.A. for the voltage phase angle offset between nodes j, r>And->Represents the voltage phase angle offset for nodes j and r, < >>，/>Representing the upper and lower limits of the voltage phase angle.
Further, in the step 3, an improved noise recurrence estimator is designed, and a historical state variable data set of a power distribution network subarea is built by combining an unscented Kalman filtering algorithm;
(1d) When the covariance matrix of the noise is semi-positive, the unbiased noise recursive estimator as in equation (21) is used in combination with the unscented Kalman filtering algorithm to update the noise based on the principle of Sage-Husa maximum a posteriori estimation：
，
，
，
In the above-mentioned method, the step of,for the moment k, error covariance moment,>is an estimate of the k-1 time error covariance,for the process noise covariance matrix at time k, < +.>Process noise covariance matrix for time k+1,>kalman gain at time k +.>A variable representing the weight, wherein->Is a forgetting variable which is used to change the state of the device,is a forgetting variable at time k+1, < >>Is the measured true value at time k, +.>Is the measurement prediction value at time k, +.>Is the difference between the measured real value at time k and the measured predicted value at time k, +. >Is->Is a transposed matrix of (a);is a momentMatrix->Is a transpose of (2);
(2d) Updating the biased noise recurrence estimator as in equation (24) when the covariance matrix of the noise is not semi-positive：
，
And according to the noise recurrence estimator and by combining a local state estimation model, carrying out local state estimation calculation on the three-phase power distribution network by using an unscented Kalman filtering algorithm, so as to obtain a historical state variable data set B of each subarea of the power distribution network under the normal operation condition.
Further, in the step 4, a robustness method for enhancing the local state estimation of the power distribution network subarea to resist network attack is specifically:
(1e) Arranging the state variables in the historical data set B according to time sequence to obtainIs +.>Where n represents the number of samples in the matrix, the matrix is +.>The successive R columns in (a) are called the system state matrix +.>Wherein R represents the length of the time window;
let the column vector at time f beSliding the obtained system state matrix c times with the time window length of RExpressed as formula (25):
in the above-mentioned method, the step of,is the basic sliding unit of the sliding window, +.>；,/>，/>，/>Is the system state at different moments; performing a limited number of slides to divide the historical dataset B into a plurality of system state matrices of time window length R, as in equation (26):
，
In the above-mentioned method, the step of,,/>,/>,/>is a system state matrix;
(2e) False or falseIf the system is not attacked by the network before the time f+1, the node at the time f is based on the system state matrixHistorical data set of the partition, construction (26), development and matrix +.>Most similar matrix->And matrixThe state matrix of the next moment of (a) is called optimal prediction matrix +.>The method comprises the steps of carrying out a first treatment on the surface of the When the state variable of the local subsystem +.>If the formula (20) is not satisfied, an optimal prediction matrix is obtained>Corresponding local subsystem state variable +.>If the optimal prediction matrixCorresponding state variable +.>If the equation (20) is satisfied, the local subsystem is proved to be under network attack, and the local subsystem state variable corresponding to the optimal prediction matrix is used for +.>Replacement of the system state variable which has been attacked +.>To reduceLess local subsystem is subject to network attack; if the optimal prediction matrix->Corresponding state variable +.>If equation (20) is not satisfied, the optimal prediction matrix should be recalculated;
to find the optimal prediction matrixIntroducing definition indexes of similarity:
existing two system state matricesAnd->Similarity->The method comprises the following steps:
，
wherein m and R represent a state matrixRow and column numbers of (a); />Is a matrix- >Elements of row i and column j; />Is a matrix->Elements of row i and column j;
(3e) By arranging phasesSimilarity thresholdJudging whether two system state matrixes are similar, if so, judging whether the two system state matrixes are similarThe two matrixes are considered to be similar matrixes meeting the conditions; in searching for the similarity matrix, to obtain the most suitable sliding unit and sliding window length, +.>And->Satisfy formula (28):
，
in the above-mentioned method, the step of,is a sliding window parameter; />Is the sliding window parameter in the optimal case;then it is satisfied->Is the number of matrices; argmax () is a function; />Is a sliding window parameter +.>Most similar matrix, < >>Is a system state matrix at the time f;
the matrix satisfying the condition of formula (28) is represented as a setSelecting the most preferable by using a clustering algorithm with noise and based on density;
parameters of the density-based clustering algorithm with noise are set as follows:
，
in the above-mentioned method, the step of,is the radius of the smallest core constituting a cluster,/->Then the minimum number of sample points that make up a cluster; />，/>And->Then the maximum mahalanobis distance, the minimum mahalanobis distance between different sample points within a cluster, respectively +.>Is the total number of sample points in a cluster; />Is->Weight parameters of (a) are reduced, and (b) is increased>Is->The reduced weight parameter of (2); [ ]Is a rounding function;
assume that a total of h clusters are generated, whose core point setsSatisfying the formula (30), and then calculating the similarity between the state matrix at the moment f and the core point by using the formula (27), wherein the most similar matrix is the most similar matrix with the highest similarity;
，
in the above-mentioned method, the step of,is the total number of sample points in cluster l, < >>The number of the representative cluster I is +.>Sample points of->Is the mahalanobis distance; h represents a total of h clusters; />Representing the set of all sample points in the cluster.
Further, in the step 4, the robustness thought may be used to process the influence of network attack in the estimation process of the local state of the power distribution network subarea, so as to output a normal local state estimation result:
(1) Assuming that the system is not attacked by the network before the time f+1, obtaining an optimal prediction matrix at the time f+1 according to the historical data set of the partition where the system is located and the nodes in the sub-region I at the time f；
(2) If at time f+1, the local subsystem state variableDoes not meet the condition of the formula (20), and at this time, an optimal prediction matrix is obtained>Corresponding local subsystem state variable +.>If the optimal prediction matrix->Corresponding state variable +.>Satisfying equation (20), the local subsystem state variable corresponding to the optimal prediction matrix is +. >Replacement of the system state variable which has been attacked +.>The method comprises the steps of carrying out a first treatment on the surface of the If the optimal prediction matrix->If the corresponding state does not satisfy equation (20), the optimal prediction matrix is recalculated.
Further, in the step 5, a boundary interaction method of the adjacent subareas is provided, so that the state estimation results of the boundary nodes in the adjacent subareas tend to be consistent, and then, a global state estimation result is output;
assuming that the attacked sub-region I has a boundary node v with the non-attacked sub-region II,
(1) Carrying out primary convergence accuracy judgment on boundary nodes of the sub-region I and the sub-region II, taking S as a basis for judging whether the region is converged, wherein S=0, the region is not converged, S=1 and the region is converged;
(2) Exchanging boundary node information between the region I and the region II; convergence accuracy criterion S of sub-area I I =1, indicating that region I converges, at which time region II may use the boundary node information pair of region ICarrying out iterative processing on boundary node information of the region II; convergence accuracy criterion S of sub-zone II II =1, indicating that the region II converges, where the region I may iterate the boundary node information of the region I using the boundary node information of the region II; if the convergence accuracy criterion S=0 of the subareas, the subareas are not converged, the adjacent subareas do not use the information of the subareas, and the subareas interact with the adjacent subarea again until the subareas are converged;
(3) If the boundary node is subjected to iterative processing and accords with the formula (31), the boundary node represents global convergence, and then a global state estimation result is output:
，
in the above-mentioned method, the step of,indicating the passing +.>V node state variable after iterative processing, < ->Indicating the passing +.>V node state variable after iterative processing, < ->And judging convergence criteria after the adjacent subareas are interactively processed.
The beneficial effects of the invention are as follows:
1) The method is used for constructing a typical power distribution network attacked scene set containing single-area and multi-area network attacks based on an attacker view angle, and providing a distributed network attack sparse modeling and solving method for a large-scale power distribution network, so that the maximization of an attack effect is ensured; compared with the existing centralized network attack model, the distributed attack model provided by the invention is more in line with the limit of the attacker on limited attack resourcesAnd the attack vector is in L 1 Sparse optimization is realized in the form of norms, so that the cost of constructing the attack vector is effectively reduced;
2) The invention designs an improved process noise recurrence estimator combined with the unscented Kalman filtering algorithm, which overcomes the defect of numerical stability of the current local estimation algorithm of the power distribution network, improves the reliability of a state estimation result, and can provide data support for the subsequent operation and maintenance regulation of the power distribution network;
3) The invention designs a distributed local state estimation method of a three-phase power distribution network for resisting network attack, which can keep the robustness of a local estimation algorithm and the reliability of a state estimation result under various attack scenes.
Drawings
FIG. 1 is a flow chart of a method according to the present invention;
FIG. 2 is a schematic linking diagram of the relevance of nodes in a power distribution network system;
FIG. 3 is a diagram of an IEEE 123 node power distribution network test system including PMU and FTU measurement devices;
FIG. 4 is a graph showing reliability comparisons of calculation results of different dynamic state estimation methods;
fig. 5 is an algorithmic calculation efficiency comparison graph of different dynamic state estimation methods for different scale power distribution networks.
Detailed Description
In order that the invention may be more readily understood, a more particular description of the invention will be rendered by reference to specific embodiments that are illustrated in the appended drawings.
As shown in fig. 1, the distributed state estimation method for the power distribution network for resisting network attack according to the invention comprises the following steps:
step 1, dividing a large-scale power distribution network into a plurality of overlapped subareas by utilizing excellent searching capability of a network; as shown in fig. 2, a link table showing the relevance between nodes is first constructed according to network connection data of a power distribution network system, wherein node a i I=1, 2 …, representing a common node in the system; superior nodeS i ，i=1, 2 …, representing and node A i I=1, 2 …, nodes connected to and near the power supply terminal; lower nodeM i ，i=1, 2 …, representing and node a i I=1, 2 …, nodes connected and near the end side; the node lower connection number F represents the number of lower nodes of the node and represents the number of connected branches of the node; the subsequent node number Z represents all node numbers of subsequent connection of the nodes; the paragraph number L from the node to the main root node represents the distance between the node and the main root node; then comprehensively considering the scale of the distribution network and the thread number of the calculation program, determining the number C of network partitions, and according to the number C of the network partitionsCalculating the maximum node number H of the partition; partitioning each feeder line of the power distribution network according to the related rule; after the partitioning of the feeder line is completed, starting from a main root node, connecting the empty nodes positively to form a main root node area, and adjusting according to a related principle to obtain a finally partitioned sub-area;
step 2, a local state estimation model is established for the subareas, partial system information is mastered by an attacker, and a sparse false data injection attack model under the condition of mastering partial system information is established;
step 3, providing an improved noise recurrence estimator, and constructing a historical state variable data set of a power distribution network subarea by combining an unscented Kalman filtering algorithm;
Step 4, based on a sliding time window theory, a robustness method for enhancing the local state estimation of the power distribution network subarea to resist network attack is adopted, and the influence of the network attack in the local state estimation process of the power distribution network subarea can be processed by the method, so that a normal local state estimation result is output;
and 5, adopting an adjacent sub-region boundary interaction method to enable the state estimation results of the boundary nodes in the adjacent sub-regions to be consistent, and then outputting a global state estimation result.
The invention provides an effective coping method for network attacks which are increasingly increased in the running and controlling processes of the power distribution network, and improves the capability of the dynamic state estimation flow of the power distribution network to resist the network attacks.
The feasibility and effectiveness of the proposed unbalanced distribution network distributed state estimation method for resisting network attacks are tested and verified based on an improved IEEE 123 node test system. The test system rated voltage is 4.16kV, and the total capacity of the three-phase load is 1420+j775kVA (a-phase), 915+j515kVA (b-phase) and 1155+j635kVA (c-phase) respectively. Rated power and rated value references for network parameters for each phase of each load (Cheng Yan. Three-phase unbalanced distribution network state estimation considering false data injection attacks [ D ]. University of southeast, south kyo, 2021.) are shown. The system consists of 123 load node buses and 122 lines (without connecting lines). The test system is divided into 4 mutually overlapped subareas by adopting a network searching method, as shown in fig. 3, wherein boundary nodes of a subarea I and a subarea II are nodes 152, boundary nodes of the subarea I and the subarea III are nodes 135, and boundary nodes of the subarea II and the subarea IV are nodes 160. High precision synchrophasor unit (phasor measurement units, PMU) measurement devices are installed on both these border nodes and loose busbar nodes, and multiple termination unit (feeder terminal units, FTU) measurement devices are installed on the other lines, as shown in fig. 3, which provide measurement data to the distribution network state estimation process. In addition, in order to intuitively analyze the distributed dynamic state estimation result of the power distribution network under the network attack, the nodes in 4 sub-areas divided by the IEEE 123 node test network are numbered again according to the sequence numbers from small to large, namely 39 nodes in the sub-area I, 32 nodes in the sub-area II, 23 nodes in the sub-area III and 29 nodes in the sub-area IV.
(1) Reliability test comparison of distributed state estimation results considering network attack
In order to verify the advantages of the method proposed by the invention compared with the prior art, a literature (Cheng Yan) is selected for case analysis and comparison by a distributed state estimation method (weighted least square based state estimation, WLS-SE) of the distribution network proposed by three-phase unbalanced distribution network state estimation [ D ] of southeast university, nanj, 2021 ] taking into account false data injection attacks. It should be noted that, although the distributed state estimation method disclosed in this document relates to the network attack situation, because the method belongs to the static state estimation category of the power distribution network, the continuous processing of the static method by adopting the monte carlo sampling mode needs to be implemented, that is, the state estimation method is continuously operated for 24 times with 0.02 seconds as 1 time scale, so as to obtain a dynamic state estimation result. Assuming that the node 5 in the sub-area I is under a network attack with an attack intensity of 0.1 p.u. at the 13 th time sampling point, the calculation result of the system state estimation given by the two state estimation methods is shown in fig. 4.
As can be seen from fig. 4, before an attack is not started, the state estimation results given by the existing WLS-SE method and the method provided by the present invention can both perform a certain estimation on the real state of the system operation, but because the WLS-SE method artificially and continuously performs the static state estimation after the monte carlo sampling simulation, the dynamic state estimation result given by the method cannot accurately track the change of the system operation state, and the dynamic state estimation method provided by the present invention is based on the idea of kalman filtering, compared with the existing WLS-SE method, the method provided by the present invention can accurately track the real operation state of the system; in addition, when the voltage amplitude estimated value given based on WLS-SE exceeds the allowable lower limit value of the system voltage by 0.95 p.u. in a few sampling periods after attack start-up, more serious, the method only detects the existence of false data injection attack and does not give corresponding remedial measures, so that the real running state of the system cannot be tracked at the later running stage. In contrast, the dynamic estimation method provided by the invention relieves the jump of the voltage amplitude to a certain extent through the real-time updating of the process noise, more importantly, the method provided by the invention replaces the attacked measurement value with the normal measurement value, and effectively inhibits the state deviation after attack with the assistance of the improved noise estimator, thereby obtaining the robust estimation result capable of effectively resisting the network attack.
(2) Comparison of calculation efficiency tests of distributed state estimation algorithm
The state estimation is a basic link of advanced application deployment of the power distribution network, so that besides the reliability of a state estimation result, the calculation efficiency of a state estimation algorithm is another focus, and particularly, the state estimation algorithm is aimed at a future large-scale town power distribution network. Compared with the existing power distribution network dynamic state estimation method considering network attack, the method designs a power distribution network distributed dynamic state estimation calculation frame oriented to improving algorithm calculation efficiency, establishes a local dynamic state estimation model through optimal partitioning of a large-scale power distribution network, accurately solves each sub-region dynamic state estimation model, and simultaneously completes effective interaction of boundary information of adjacent sub-regions.
In order to verify the advantages of the method provided by the invention compared with the existing dynamic state estimation technology of the power distribution network, the centralized dynamic state estimation method of the power distribution network provided by the literature (Junjun Xu, zaijun Wu, tengfei Zhang, qinran Hu, qiawei Wu. A secure forecasting-aided state estimation framework for power distribution systems against false data injection attacks [ J ]. Applied Energy,2022, 328:120107.) is selected for carrying out analysis and comparison on the calculation efficiency of the algorithm. Distribution network test cases of 3 different network scales (IEEE 13 node, IEEE 37 node and IEEE 123 node) are selected, wherein distribution network test data of the IEEE 13 node and the IEEE 37 node can be found in documents (Junjun Xu, zaijun Wu, tengafei Zhang, qinran Hu, qiawei Wu. A secure forecasting-aided state estimation framework for power distribution systems against false data injection attacks [ J ]. Applied Energy,2022, 328:120107 ]) and the time consumption and the iterative convergence times of an algorithm for calculating one centralized dynamic estimation and one distributed dynamic state estimation are shown in figure 5 on the premise that all test parameters are the same.
As can be seen from fig. 5, the size of the network scale of the power distribution network has a large influence on the calculation efficiency of the centralized dynamic state estimation algorithm, but has a small influence on the calculation efficiency of the distributed dynamic state estimation algorithm provided by the invention. In particular, when the network scale is smaller (13 load nodes or 37 load nodes), the calculation efficiency of the centralized dynamic estimation method is slightly better than that of the distributed dynamic estimation method provided by the invention, but the calculation efficiency of the network scale and the calculation efficiency of the distributed dynamic estimation method are not quite different, and the calculation efficiency of the network scale and the calculation efficiency of the distributed dynamic estimation method are both at a higher level. This is because the distributed dynamic estimation algorithm proposed by the present invention requires interaction involving information between different sub-regions, which can be time consuming. However, once the network scale increases to 123 load nodes, the centralized dynamic estimation method has a significant exponential increase in both calculation time consumption and iteration number, which undoubtedly affects the real-time and effectiveness of power distribution network scheduling and control. In contrast, the core idea of the distributed dynamic state estimation algorithm provided by the invention is to split a large-scale complex calculation problem into a plurality of subtasks for parallel calculation, so that even if the network scale is increased, the algorithm calculation time consumption and the iteration times are not exponentially increased, and the higher calculation efficiency level is still maintained. Therefore, compared with the existing centralized dynamic state estimation method, the distributed dynamic state estimation method provided by the invention has higher algorithm calculation efficiency, and is more suitable for the online application of a state estimation program of a large-scale power distribution network in the future.
The above embodiments are provided to illustrate the technical concept and features of the present invention and are intended to enable those skilled in the art to understand the content of the present invention and implement the same, and are not intended to limit the scope of the present invention. All equivalent changes or modifications made in accordance with the spirit of the present invention should be construed to be included in the scope of the present invention.
Claims (5)
1. A method for estimating distributed dynamic state of a power distribution network against network attacks, the method comprising the steps of:
step 1, dividing a large-scale power distribution network into a plurality of overlapped subareas;
step 2, a local state estimation model is established for the subareas, partial system information is mastered by an attacker, and a sparse false data injection attack model under the condition of mastering partial system information is established;
the local state estimation model is established for the subareas as follows:
，
wherein, the liquid crystal display device comprises a liquid crystal display device,is a state variable of the system in the local sub-area at time k,/for the system at time k>，/>、Is the corresponding voltage amplitude vector and phase angle vector, < >>Then it is a measured variable of the system in the local sub-area at time k,is Gaussian process noise of the system in the local sub-area at time k-1, +.>Is the measurement noise of the system in the local sub-area at time k,/ >Is a state variable +.>Is a nonlinear state transfer function of +.>Is a state variable +.>Is a measurement function of (2)A number;
establishing a sparse false data injection attack model under the condition of grasping part of system information:
assuming that an attacker only knows part of line parameters and topology structures of an attack area;
(1c) State variables of sub-area system at k momentInitializing:
，
in the above-mentioned method, the step of,for the initial value of the node voltage amplitude, +.>An initial value of a node voltage phase angle; />Is the node voltage amplitude at time k, +.>Is the node voltage phase angle at time k;
(2c) Designing attack vectors: the attack vector attacks in a mode of injecting offset, and the set of nodes in an attack area I of the attack is set asBoundary node set of attack area I and non-attack area II is +.>Attack vector for node j at time k>The method comprises the following steps:
，
in the above-mentioned method, the step of,attack offset for node j active power, +.>Is the attack offset for the reactive power of node j, < >>Attack offset for active power of branch between nodes j and r, +.>Attack offset for reactive power of branch between nodes j, r, < >>Attack offset for branch current amplitude values between nodes j and r; / >Is a set of n nodes of the complete power distribution network;
(3c) Attack vector sparsification: since the attack assumption is that an attacker grasps part of system information, the attack vector shown in the formula (12) is subjected to thinning processing, and the processed attack vector is:
；
(4c) Attack vector effect evaluation: state offset when an attacked node、/>Satisfying equation (20), it indicates: the power distribution network sub-area system suffers from false data injection network attack, and has remarkable attack effect, and the attack vector is，/>；/>Is the variation of the attack vector in two attack iterations; if the state of the attacked node is offset +.>、/>If the equation (20) is not satisfied, the attack effect is poor, and the calculation should be returned to (2 c);
，
in the above-mentioned method, the step of,represents the voltage amplitude offset for node j, < +.>And->Representing the upper and lower limits of the voltage amplitude,represents +.A. for the voltage phase angle offset between nodes j, r>And->Represents the voltage phase angle offset for nodes j and r, < >>，/>Representing upper and lower limits of the voltage phase angle;
step 3, designing an improved noise recurrence estimator, and constructing a historical state variable data set of a power distribution network subarea by combining an unscented Kalman filtering algorithm; the method comprises the following steps:
(1d) When the covariance matrix of the noise is semi-positive, the unbiased noise recursive estimator as in equation (21) is used in combination with the unscented Kalman filtering algorithm to update the noise based on the principle of Sage-Husa maximum a posteriori estimation：
，
，
，
In the above-mentioned method, the step of,for the moment k, error covariance moment,>pre-determination of k-1 time error covarianceValuation (I)>For the process noise covariance matrix at time k, < +.>Process noise covariance matrix for time k+1,>kalman gain at time k +.>A variable representing the weight, wherein->Is a forgetting variable which is used to change the state of the device,is a forgetting variable at time k+1, < >>Is the measured true value at time k, +.>Is the measurement prediction value at time k, +.>Is the difference between the measured real value at time k and the measured predicted value at time k, +.>Is->Is a transposed matrix of (a);is a matrix->Is a transpose of (2);
(2d) Updating the biased noise recurrence estimator as in equation (24) when the covariance matrix of the noise is not semi-positive：
，
According to the noise recurrence estimator and by combining a local state estimation model, carrying out local state estimation calculation on the three-phase power distribution network by using an unscented Kalman filtering algorithm to obtain a historical state variable data set B of each subarea of the power distribution network under the normal operation condition;
Step 4, based on a sliding time window theory, a robustness method for enhancing the local state estimation of the power distribution network subarea to resist network attack is adopted, and the influence of the network attack in the local state estimation process of the power distribution network subarea is processed, so that a normal local state estimation result is output;
the robustness method for enhancing the local state estimation of the power distribution network subarea to resist network attack specifically comprises the following steps:
(1e) Arranging the state variables in the historical data set B according to time sequence to obtainIs +.>Where n represents the number of samples in the matrix, the matrix is +.>The successive R columns in a column are called a system state matrixWherein R representsThe length of the time window;
let the column vector at time f beSliding the obtained system state matrix c times with the time window length of RExpressed as formula (25):
in the above-mentioned method, the step of,is the basic sliding unit of the sliding window, +.>；/>,，/>，/>Is the system state at different moments; performing a limited number of slides to divide the historical dataset B into a plurality of system state matrices of time window length R, as in equation (26):
，
in the above-mentioned method, the step of,,/>,/>,/>is a system state matrix;
(2e) Assuming that the system is not attacked by the network before the time f+1, the node at the time f is based on the system state matrix Historical data set of the partition, construction (26), development and matrix +.>Most similar matrix->And>the state matrix of the next moment of (a) is called optimal prediction matrix +.>The method comprises the steps of carrying out a first treatment on the surface of the When the state variable of the local subsystem +.>If the formula (20) is not satisfied, an optimal prediction matrix is obtained>Corresponding local subsystem state variable +.>If the optimal prediction matrix->Corresponding state variable +.>If the equation (20) is satisfied, the local subsystem is proved to be under network attack, and the local subsystem state variable corresponding to the optimal prediction matrix is used for +.>Replacement of the system state variable which has been attacked +.>To reduce the impact of network attacks on the local subsystem; if the optimal prediction matrix->Corresponding state variable +.>If equation (20) is not satisfied, the optimal prediction matrix should be recalculated;
to find the optimal prediction matrixIntroducing definition indexes of similarity:
existing two system state matricesAnd->Similarity->The method comprises the following steps:
，
wherein m and R are substitutedMeter state matrixRow and column numbers of (a); />Is a matrix->Elements of row i and column j; />Is a matrixElements of row i and column j;
(3e) By setting a similarity thresholdJudging whether two system state matrixes are similar, if so, judging whether the two system state matrixes are similar The two matrixes are considered to be similar matrixes meeting the conditions; in searching for the similarity matrix, to obtain the most suitable sliding unit and sliding window length, +.>And->Satisfy formula (28):
，
in the above-mentioned method, the step of,is a sliding window parameter; />Is the sliding window parameter in the optimal case; />Then it is satisfied->Is the number of matrices; argmax () is a function; />Is a sliding window parameter ofMost similar matrix, < >>Is a system state matrix at the time f;
the matrix satisfying the condition of formula (28) is represented as a setSelecting the most preferable by using a clustering algorithm with noise and based on density;
parameters of the density-based clustering algorithm with noise are set as follows:
，
in the above-mentioned method, the step of,is the radius of the smallest core constituting a cluster,/->Then the minimum number of sample points that make up a cluster; />，/>And->The maximum mahalanobis distance and the minimum mahalanobis distance between different sample points in a cluster,is the total number of sample points in a cluster; />Is->Weight parameters of (a) are reduced, and (b) is increased>Is->The reduced weight parameter of (2); []Is a rounding function;
assume that a total of h clusters are generated, whose core point setsSatisfying the formula (30), and then calculating the similarity between the state matrix at the moment f and the core point by using the formula (27), wherein the most similar matrix is the most similar matrix with the highest similarity;
，
In the above-mentioned method, the step of,is the total number of sample points in cluster l, < >>The number of the representative cluster I is +.>Is used for the measurement of the sample points of (a),is the mahalanobis distance; h represents a total of h clusters; />Representing a set of all sample points in the cluster;
step 5, adopting an adjacent sub-area boundary interaction method to enable the state estimation results of boundary nodes in the adjacent sub-areas to be consistent, and then outputting a global state estimation result; the method comprises the following steps:
assuming that the attacked sub-region I has a boundary node v with the non-attacked sub-region II,
(1) Carrying out primary convergence accuracy judgment on boundary nodes of the sub-region I and the sub-region II, taking S as a basis for judging whether the region is converged, wherein S=0, the region is not converged, S=1 and the region is converged;
(2) Exchanging boundary node information between the region I and the region II; convergence accuracy criterion S of sub-area I I =1, indicating that the region I converges, where the region II may iterate the boundary node information of the region II using the boundary node information of the region I; convergence accuracy criterion S of sub-zone II II =1, indicating that the region II converges, where the region I may iterate the boundary node information of the region I using the boundary node information of the region II; if the convergence accuracy criterion S=0 of the subareas, the subareas are not converged, the adjacent subareas do not use the information of the subareas, and the subareas interact with the adjacent subarea again until the subareas are converged;
(3) If the boundary node is subjected to iterative processing and accords with the formula (31), the boundary node represents global convergence, and then a global state estimation result is output:
，
in the above-mentioned method, the step of,indicating the passing +.>V node state variable after iterative processing, < ->Indicating the passing +.>V node state variable after iterative processing, < ->And judging convergence criteria after the adjacent subareas are interactively processed.
2. The method for estimating distributed dynamic state of a power distribution network against network attack according to claim 1, wherein step 1 specifically comprises:
step 1-1, constructing a link table showing the relevance among nodes according to network wiring data of a power distribution network system; wherein, the nodeA i ，i=1, 2 …, representing a common node in the system; superior nodeS i ，i=1, 2 …, representing and node A i ，iNodes connected near the power supply end, =1, 2, …; lower nodeM i ，i=1, 2 …, representing and node A i ，i=1, 2 …, nodes connected near the end side; node lower connection numberFRepresenting the number of lower nodes of the node, which represents the number of connected branches of the node; number of subsequent nodesZRepresenting all node numbers of the subsequent connection of the nodes; paragraph number from node to root nodeLRepresenting the distance of the node from the primary root node;
Step 1-2, comprehensively considering the scale of the power distribution network and the thread number of a calculation program, determining the number C of network partitions, and obtaining the maximum node number H of the partitions by a formula (1);
，
wherein: h is the maximum node number of the subareas, T is the total node number of the power distribution network, C is the subarea number, and e is the adjustment coefficient;
step 1-3, partitioning each feeder line of the power distribution network according to the following rules;
(1a) From the end node to the power source end, the partition task is executed when the partition task is executed to the nodeA i ，i=1, 2, …, continue searching its upper nodesS i ，i=1, 2, …, if the upper nodeS i ，i=1, 2, …, all subsequent node numbersZThe difference between the number of the nodes and all the subsequent nodes of all the end nodes of the area is greater than or equal to the maximum number of the nodes of the partitionHIf the number of nodes in the partition reaches the maximum value, stopping searching, and at the moment, obtaining the nodeA i ，i=1, 2 …, as root node of partition;
(2a) In the process of partitioning from the end node to the power source end, when proceeding to the nodeA i ，i=1, 2, …, continue searching its upper nodesS i ，i=1, 2 …, if nodeS i ，i=1, 2 …, already in the other partitions, search is stopped, at which point the nodeA i ，i=1, 2 …, as root node of partition;
(3a) When the nodeA i ，iWhen the number of segments reaching the primary root node is smaller than the set value, =1, 2, …, the search is stopped, and the node is at this time A i ，i=1, 2 …, as root node of partition;
(4a) In the process of searching the node towards the power end, when encountering a node with a branch, all subsequent node numbers of the node comprise the node numbers on the branch;
step 1-4, after the partition of the feeder line is completed, starting from the main root node, connecting the empty nodes forward to form a main root node area, and adjusting according to the following principle:
(1b) When the number of the partitions is more than a specified value, the areas with the number of partial nodes less than the average value are merged into the adjacent areas, and the adjusting coefficient e is increased at the moment so as to ensure that the calculated amounts of the partitions are similar;
(2b) When the node number of the root node area is more than a specified value, partial nodes are divided into adjacent partitions, so that the calculated amount of each partition is ensured to be similar.
3. The method for estimating distributed dynamic state of a power distribution network against network attacks according to claim 1, wherein in step 2, a nonlinear state transfer function is usedDesigned according to a Holt-windows double-parameter exponential smoothing method,
，
in the above-mentioned method, the step of,is->The local subsystem at the moment predicts the system variable prediction quantity at the moment k; />Is the horizontal component of the state variable at time k-1,/->Is the vertical component of the state variable at time k-1; / >Is the state quantity of the system variable of the local subsystem at the time of k-1; />The method is that a local subsystem at the time of k-2 predicts the system variable prediction quantity at the time of k-1; />And->The method is a smoothing parameter in a Holt-windows double-parameter exponential smoothing method, and represents weights of variables with different distances on time scales; />Is the horizontal component of the state variable at time k-2; />Is the vertical component of the state variable at time k-2;
measuring functionThe measurement vector design is relied on, and in a state estimation model of a three-phase unbalanced distribution network subarea, the measurement variable of a node j at the moment k is +.>The method comprises the following steps:
，
in the above-mentioned method, the step of,active injection power for node j, +.>Reactive power injection for node j, +.>Active injection power for branch j-r, < >>Reactive injection power for branch j-r, < >>Assignment of line current for branch j-r, ->Then it is a node set of the distribution network; />Is a node;
in combination with the data of the measurement vector, the measurement function is obtained by neglecting the admittances of the nodes in parallelThe method comprises the following steps:
，
，，
，
，
，
wherein the method comprises the steps of；/>And->Is the phase +.>The voltage amplitude and phase angle at time k; />And->Is the phase +.>The voltage amplitude and phase angle at time k; />And->Is the phase of the j-r branch>Voltage and current at time k; / >Is the phase of the j-r branch>Apparent power at time k; />And->Phase ∈zero node>Active and reactive power at time k; />，/>Is the active and reactive power of node j at time k; />Andis the phase of the j-r branch>Active and reactive power at time k; />And->Is the +.o of the node admittance matrix>No. 2 of sub-matrix>Conductance and susceptance of the individual elements; />Is the phase +.>And phase of node r>Phase angle difference between times k; />Is the phase +.>And (2) sum phase->Phase angle difference between times k.
4. The distributed dynamic state estimation method for a power distribution network against network attacks according to claim 1, wherein in step 2, the process of sparsifying an attack vector is as follows:
equation (14) is sparse processing of attack vectors, equation (15) is to ensure that the states of boundary nodes before and after attack are unchanged, and equation (16) -equation (19) is a constraint condition of various variables:
，
，
，
，
，
，
in the above-mentioned method, the step of,attack offset for active power of node j at time k>The value of the change in the iteration,、/>、/>、/>、 />、/>、/>、/>similarly, let go of>Is the variation of the voltage amplitude; />Is the variation of the voltage phase angle; />Is the active power of node j at time k before the false data injection attack,is the active power of node j at k time after the false data injection attack, < > >Is the reactive power of node j at k moment before the false data injection attack, < >>Is the reactive power of node j at k time after the false data injection attack, < >>Is the active power of the branch between nodes j and r at k moment before the false data injection attack, +.>The active power of the branch between the nodes j and r at the moment k after the false data injection attack; />The reactive power of the branch between the nodes j and r at the moment k after the false data injection attack; />The current of the branch circuit between the nodes j and r at the moment k after the false data injection attack; />The state variables of the boundary node set sub-region system of the attack region I and the non-attack region II at the moment k; />，/>Is a sectionUpper and lower limits of active power for point j; />，/>Is the upper and lower reactive power limits of node j; />Is the upper limit of the active power of the branch circuit between the nodes j and r; />Is the upper limit of apparent power between nodes j, r;is the absolute value of apparent power between nodes j, r at time k after a dummy data injection attack.
5. The distributed dynamic state estimation method for a power distribution network for resisting network attack according to claim 1, wherein in the step 4, the robust method for enhancing the local state estimation of the power distribution network sub-area for resisting network attack is utilized to process the influence of network attack in the process of estimating the local state of the power distribution network sub-area, so that the normal local state estimation result is output:
(1) Assuming that the system is not under network attack before the time f+1, obtaining an optimal prediction matrix at the time f+1 according to a historical data set of a partition where the system is located and a robustness method for enhancing the local state estimation of the power distribution network sub-area to resist the network attack at the time f and the nodes in the sub-area I；
(2) If at time f+1, the local subsystem state variableDoes not satisfy the condition of formula (20)Solving an optimal prediction matrix->Corresponding local subsystem state variable +.>If the optimal prediction matrix->Corresponding state variablesSatisfying equation (20), the local subsystem state variable corresponding to the optimal prediction matrix is +.>Replacement of the system state variable which has been attacked +.>The method comprises the steps of carrying out a first treatment on the surface of the If the optimal prediction matrix->If the corresponding state does not satisfy equation (20), the optimal prediction matrix is recalculated.
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