A PMU configuration method for distribution networks that takes both observability and FDIA defense into consideration

Abstract

The present invention relates to a distribution network PMU configuration method that takes into account both observability and FDIA defensiveness, including constructing a connection matrix according to the network topology structure of the distribution network; pre-configuring PMUs at specific positions according to the characteristics of the network topology structure of the distribution network to achieve the purpose of fully utilizing the PMUs; obtaining an iterative Jacobian matrix from a DC model of state estimation; performing elementary matrix transformation on the iterative Jacobian matrix according to a simplified row ladder algorithm to obtain vulnerable areas of the distribution network and find the most labor-saving attack area; formulating a defense countermeasure for the most labor-saving attack model of network attacks, configuring PMUs at the defended nodes to defend against false data injection attacks; and comprehensively considering the observability and defensiveness of the distribution network to generate a final PMU configuration scheme. The present invention can take into account both the observability and defensiveness of the distribution network, and the number of configured PMU nodes is less than that of a scheme that only considers the configuration of PMUs for attacks, thereby improving the defense effect, reducing costs, and having good engineering feasibility.

Description

Technical Field

[0001] The invention relates to a network topology algorithm for a power distribution system, and in particular to a synchronous phasor measurement device configuration method for improving system observability and defending against false data injection attacks. Background Art

[0002] With the continuous development and application of smart distribution network technology, the operation monitoring level of distribution network has been greatly improved. Traditional state estimation uses the measurement data provided by the Supervisory Control and Data Acquisition (SCADA) system as the data source, but its accuracy is low and it is impossible to monitor the distribution network with high precision. At present, synchronous phasor measurement units (PMU) have begun to be configured in the distribution network. The synchronous phasor measurement unit can collect the measurement data of node voltage and branch current in the distribution network, realize the synchronous measurement of measurement amplitude and phase angle, and has higher accuracy than traditional measurement. Therefore, configuring a certain number of synchronous phasor measurement devices in the distribution network can further improve the measurement level of the distribution network and provide data support for solving problems such as operation control and energy management of the distribution network.

[0003] In addition, although most existing technologies for protecting distribution networks are designed to ensure system reliability, in recent years, there has been increasing attention to preventing malicious cyber attacks in distribution networks. Because the operation and control of distribution networks depend on a complex network space of computers, software, and communication technologies, and because the measurement components supported by smart devices (e.g., smart meters and sensors) play an important role, it may become a target of attack. Since these measurement devices may be connected through open network interfaces and the lack of tamper-proof hardware increases the possibility of being compromised by adversaries. In the presence of infected devices in the network, the adversary can inject false measurement reports into the controller. This will cause the controller to estimate the wrong system state, posing a dangerous threat to the operation of the distribution system.

[0004] PMU uses the signal provided by GPS as the time standard of the system, which can ensure the accurate synchronization of the clocks of each node. Since the PMU clock has high accuracy, large synchronization range, and is not interfered by the external environment and natural conditions, we can assume that the measurements obtained from the PMU are safe and cannot be manipulated by the adversary. When the PMU is placed on a given node, it can measure both the node voltage angle and the power flow on the branch incident to the node, and it is difficult for the adversary to manipulate.

[0005] Based on the above analysis, configuring PMUs on the nodes of the distribution network can not only improve the observability of the system but also play a role in defending against network attacks. However, due to the high price of PMUs, configuring PMUs on all nodes will incur a lot of costs, so it is impractical to configure PMUs on all nodes of the distribution network. Existing research on PMU configuration to improve the observability of the system and PMU configuration for network attacks has been relatively mature. The PMU configuration method that considers improving the observability of the system is based on the principle of minimizing the number of PMUs, but has not yet considered the defense measures against network attacks. Although the PMU configuration considering network attacks can play a good defense effect, it uses a large number of PMUs and has a high cost.

[0006] Therefore, it is hoped that there is a PMU configuration method that takes into account both the observability of the distribution network system and network attacks, so as to take into account the advantages of the two PMU configuration methods and avoid their disadvantages. Summary of the invention

[0007] The technical problem to be solved by the present invention is to provide a configuration method for PMU of the defense against FDIA from the distribution network while minimizing the number of synchronous phasor measurement devices under the premise of ensuring complete observation of the distribution network.

[0008] The technical solution adopted by the present invention is as follows:

[0009] The distribution network PMU configuration method that takes into account both observability and FDIA defense includes the following steps:

[0010] Step 1: According to the network topology of the distribution network, a distribution network connection matrix is ​​formed;

[0011] Step 2: Determine the nodes where PMU must be configured based on the characteristics of the distribution network topology.

[0012] Step 3, calculating the iterative Jacobian matrix from the DC model of state estimation;

[0013] Step 4: Update the Jacobian matrix;

[0014] Step 5: Determine whether all nodes are protected by PMU. If yes, execute step 8; otherwise, execute step 6.

[0015] Step 6: Determine the most labor-saving attack area by using a simplified trapezoidal algorithm;

[0016] Step 7: Configure the PMU node at the least-strength attack area and execute steps 4 and 8;

[0017] Step 8: Comprehensively consider the observability and defensiveness of the distribution network to form the final PMU configuration plan.

[0018] The distribution network connection matrix formed in step 1 includes the following contents:

[0019] Obtain the topological connection relationship of the distribution network, construct the adjacency matrix T, and the element T in the adjacency matrix T ij The calculation method is:

[0020]

[0021] Among them, i and j are the numbers of the distribution network nodes respectively.

[0022] The determination of the nodes that must be configured with PMU in step 2 is to determine the nodes that must be configured with PMU and the nodes that do not need to be configured with PMU in the current step according to the configuration principle based on the topology of the distribution network. The configuration principle is as follows:

[0023] Principle 1. The structure of the 2-T connection of the distribution network is: the number of nodes connected at both ends is greater than 2; the number of intermediate nodes is 2, and the number of nodes connected to the intermediate nodes is equal to 2; the structure of the 3-T connection of the distribution network is: the number of nodes connected at both ends is greater than 2; the number of intermediate nodes is 3, and the number of nodes connected to the intermediate nodes is equal to 2; for the 3-T connection of the distribution network, the third node must be configured with a PMU, and for the 2-T connection where any node at the two end nodes is unobservable, the two end nodes must be pre-configured with a PMU;

[0024] Principle 2: For nodes with 1 adjacent node number and zero injection nodes with 1 adjacent node number, PMU is not required for the current step;

[0025] Principle 3: If a node is adjacent to a node with 1 adjacent nodes and the node is a load or power generation node, the node must be configured with a PMU. If the node is connected to a node with a T-connection configured with a PMU, the current step does not need to configure a PMU temporarily.

[0026] Principle 4: To make the configured PMU measure as many nodes as possible, calculate the connection matrix T Configure the PMU for the node with the most connected nodes. If the node is connected to a node with T-connection configured PMU, the current step does not need to configure the PMU temporarily.

[0027] The calculation of the iterative Jacobian matrix described in step 3 includes the following:

[0028] Using the state estimation of the DC model, the actual power flow from distribution network node i to distribution network node j can be expressed as:

[0029]

[0030] Where: X ij is the branch reactance between node i and node j;

[0031] The simplified active power injection of node i is:

[0032]

[0033] Where: J represents the node connected to node i, N i is the set of all branches connected to node i, The power of node i is equal to the sum of the powers of the branches adjacent to node i;

[0034] Therefore, the DC state estimation can be expressed as follows

[0035] Z=H·X+e (4)

[0036] where X=(x1,x2,…,x n ) T Represents the state vector, which is composed of the phase angle θ of the system node i Composition, Z=(z1,z2,…z n ) T represents the system measurement vector, Z i Including node voltage V i The magnitude of the node active power and reactive power P i , and branch active and reactive power flows P ij , represents matrix multiplication; e=(e1,e2,…,e n ) T The vector representing the sensor measurement error follows a Gaussian distribution with zero mean, and the measurement matrix H m×n It is called the iterative Jacobian matrix and is given by P i and P ij Partial derivatives with respect to the state vector X.

[0037] In step 4, the Jacobian matrix is ​​updated, including the following: the sub-matrices of the iterative Jacobian matrix H are defined as H P and H P represents the matrix composed of nodes protected by PMU, H P The complement matrix of H represents the matrix of nodes not protected by PMU. When a PMU is placed on a given node i, the nodes j, k, …, m connected to node i are considered safe and observable. The matrix H is updated according to the position of the configured PMU node in the matrix H. P and matrix Delete the columns corresponding to the configured PMU and the nodes adjacent to the configured PMU node in the matrix H, and add the deleted elements to H P The remaining part of the matrix H is

[0038] The step 6 described in which the simplified trapezoidal algorithm is used to determine the least-effort attack area refers to the simplified row trapezoidal algorithm performing elementary matrix transformation on the iterative Jacobian matrix to obtain the vulnerable area of ​​the distribution network and find the least-effort attack area. The least-effort attack vector is constructed based on the simplified row ladder algorithm, including the following steps:

[0039] (1) Define the tracking matrix B to track the matrix The basic row transformation of the matrix is ​​then used to transform Simplify into a row echelon matrix, defined as matrix A;

[0040] (2) Define a tracking matrix C to track the basic column transformation of the matrix A. By exchanging columns, all non-zero elements in the Ith row of the matrix A are exchanged to the last m columns, and the matrix is ​​obtained.

[0041] (3) Matrix The non-zero element in the lower right corner The corresponding node is the most vulnerable area of ​​the distribution network at present;

[0042] (4) Tracked by tracking matrix B and tracking matrix C In the matrix The corresponding position before elementary transformation The corresponding node is the attack area where FDIA saves the most effort. Configuring PMU in this area can achieve the best defense effect against FDIA.

[0043] Repeat steps 4 and 5 until all elements of matrix H are protected and placed in H P middle.

[0044] The configuration of the PMU node at the least-effort attack area described in step 7 is to formulate a defense countermeasure for the least-effort attack model of the network attack, and configure the PMU at the defended node to defend against the false data injection attack.

[0045] The final PMU configuration scheme in step 8 is a superposition of the nodes configured with the PMU in step 2) and the nodes configured with the PMU in step 5).

[0046] Compared with the prior art, the advantages of the present invention are:

[0047] For the IEEE14-node distribution network, the number of PMUs configured for the observability of the distribution network is 3, but the FDIA defense is not considered. The number of PMUs configured for the FDIA defense is at least 4. The configuration method of the present invention configures the number of PMUs to 3, which can take into account the observability and defense of the distribution network. In addition, the number of configured PMU nodes is less than that of the solution that only considers the attack configuration of PMU, which reduces the cost and has better engineering feasibility. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 The present invention is a distribution network PMU configuration method based on both observability and FDIA defensiveness;

[0049] Figure 2 This is a schematic diagram of 2-T wiring and 3-T wiring;

[0050] Figure 3 is a flowchart of the simplified row ladder algorithm. DETAILED DESCRIPTION

[0051] To make the technical solutions and advantages of the present invention more clear, the following is a description of the technical solutions and advantages of the present invention in combination with the embodiments of the present invention. Figure 1-Figure 3 , a clear and complete description of the technical solutions in the embodiments of the present invention is given:

[0052] Example 1

[0053] The distribution network PMU configuration method that takes into account both observability and FDIA defense is as follows:

[0054] 1) Obtain the topological connection relationship of the distribution network and construct the adjacency matrix T. The element T in the adjacency matrix T ij The calculation method is

[0055]

[0056] Among them, i and j are the numbers of the distribution network nodes respectively.

[0057] 2) According to the topology of the distribution network, determine the nodes that must be configured with PMU and the nodes that do not need to be configured with PMU in the current step according to the configuration principles. The configuration principles are as follows:

[0058] Principle 1: The 2-T and 3-T wiring structures of the distribution network are as follows: Figure 2As shown in the figure, the structure of the 2-T connection of the distribution network is: the number of nodes connected at both ends is greater than 2; the number of intermediate nodes is 2, and the number of nodes connected to the intermediate nodes is equal to 2. The structure of the 3-T connection of the distribution network is: the number of nodes connected at both ends is greater than 2; the number of intermediate nodes is 3, and the number of nodes connected to the intermediate nodes is equal to 2. For the 3-T connection of the distribution network, the third node must be configured with a PMU. For the 2-T connection where any node at the two end nodes is unobservable, the nodes at both ends must be pre-configured with PMUs;

[0059] Principle 2: For nodes with 1 adjacent node number, such as the generator end node of the generator-transformer group, and zero injection nodes with 1 adjacent node number, such as a pure switch station with only two lines, the current step does not need to be equipped with a PMU;

[0060] Principle 3: If a node is adjacent to a node with 1 adjacent nodes, and the node is a load or power generation node, such as a node on the high-voltage side of a power plant, the node must be configured with a PMU. If the node is connected to a node with a T-connection configured with a PMU, the current step does not need to configure a PMU temporarily.

[0061] Principle 4: To make the configured PMU measure as many nodes as possible, the connection matrix T is calculated Configure the PMU for the node with the most connected nodes. If the node is connected to a node with a T-connection configured PMU, there is no need to configure the PMU.

[0062] 3) To simplify the calculation, the outflow and inflow of reactive power and the parallel admittance and loss are not considered. The state estimation of the DC model is adopted. The actual power flow from distribution network node i to distribution network node j can be expressed as

[0063]

[0064] The simplified active power injection of node i is

[0065]

[0066] Where X ij is the branch reactance between node i and node j, N i is the set of all branches connected to node i.

[0067] Therefore, the DC state estimation can be expressed as follows

[0068] Z=H·X+e (8)

[0069] where X=(x1,x2,…,x n ) T represents the state vector, and is composed of the phase angle θ of the system node i Composition. Z=(z1,z2,…z n )T Represents the system measurement vector, where for the DC model considered in the present invention, Z i Including node voltage V i The magnitude of the node active power and reactive power P i , and branch active and reactive power flows P ij , represents matrix multiplication. In addition, e=(e1,e2,…,e n ) T represents the vector of sensor measurement errors, which follows a Gaussian distribution with zero mean. The measurement matrix H m×n It is called the iterative Jacobian matrix and is given by P i and P ij Partial derivatives with respect to the state vector X.

[0070] 4) Define the sub-matrices of the iterative Jacobian matrix H as H P and H P represents the matrix composed of nodes protected by PMU, H P The complement matrix of H represents the matrix of nodes not protected by PMU. When a PMU is placed on a given node i, the nodes j, k, …, m connected to node i are considered safe and observable. The matrix H is updated according to the position of the configured PMU node in the matrix H. P and matrix Delete the columns corresponding to the configured PMU and the nodes adjacent to the configured PMU node in the H matrix, and add the deleted elements to H P The remaining part of the H matrix is

[0071] 5) Utilize Based on the simplified ladder algorithm (see the algorithm flow chart Figure 3 )Construct the most labor-saving attack vector. The specific steps are:

[0072] (1) Define the tracking matrix B to track the matrix The basic row transformation of the matrix is ​​then used to transform Simplify into a row echelon matrix, defined as matrix A;

[0073] (2) Define a tracking matrix C to track the basic column transformation of the matrix A. By exchanging columns, all non-zero elements in the Ith row of the matrix A are exchanged to the last m columns, and the matrix is ​​obtained.

[0074] (3) Matrix The non-zero element in the lower right corner The corresponding node is the weakest area of ​​the distribution network at present;

[0075] (4) Tracked by tracking matrix B and tracking matrix C In the matrix The corresponding position before elementary transformation The corresponding node is the attack area where FDIA saves the most effort. Configuring PMU in this area can achieve the best defense effect against FDIA.

[0076] 6) Repeat steps 4) and 5) until all elements in matrix H are protected and placed in H P middle.

[0077] 7) The final PMU configuration scheme is the superposition of the nodes configured with PMU in step 2) and the nodes configured with PMU in step 5).

[0078] Example 2

[0079] The present invention uses the IEEE 14-node distribution network to verify the proposed PMU configuration scheme. According to the configuration principle, nodes 6 and 9 are nodes at both ends of the 2-T connection, so PMUs are configured at nodes 6 and 9. Since node 5 and node 2 are connected to node 6 and node 9 respectively, PMUs are not configured at nodes 5 and 2 temporarily. After configuring PMUs at nodes 6 and 9, the observable and protectable nodes are nodes 6, 11, 12, 13, 9, 7, 14, and 10, respectively, thereby achieving the purpose of fully utilizing PMUs.

[0080] By using the simplified line ladder algorithm, we can get that the area of ​​nodes 2, 3, and 4 is the area where the network attacker can attack with the least effort using FDIA. Configuring PMU at node 2 can protect nodes 2, 3, and 4 while making them observable.

[0081] According to Kirchhoff's law, after nodes 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, and 13 are observable, node 1 can be observed based on the data of nodes 2 and 5, and node 8 can be observed based on the data of nodes 4, 7, and 9, thereby protecting nodes 1 and 8.

[0082] In summary, the PMU configuration scheme for the IEEE14 nodes of the distribution network is to configure PMUs at nodes 6, 9, and 3.

[0083] It can be seen that the PMU configuration scheme solved by the method proposed in the present invention can take into account the observability and defensiveness of the distribution network, and the number of configured PMU nodes is less than that of the scheme that only considers attack configuration of PMU, which verifies the effectiveness of the present invention.

[0084] The above-described embodiments merely express the implementation methods of the present invention, but they cannot be understood as limiting the scope of the patent of the present invention. It should be pointed out that for those skilled in the art, several modifications and improvements can be made without departing from the concept of the present invention, which all belong to the protection scope of the present invention.

Claims

1. A distribution network PMU configuration method that takes into account both observability and FDIA defense, characterized in that: The steps include: Step 1. According to the network topology of the distribution network, a distribution network connection matrix is ​​formed; Step 2. According to the characteristics of the distribution network topology, determine the nodes that must be configured with PMU. The nodes that must be configured with PMU and the nodes that do not need to be configured with PMU in the current step are determined according to the configuration principles based on the distribution network topology. The configuration principles are as follows: Principle 1. The structure of the 2-T connection of the distribution network is: the number of nodes connected to the nodes at both ends is greater than 2; the number of intermediate nodes is 2, and the number of nodes connected to the intermediate nodes is equal to 2; the structure of the 3-T connection of the distribution network is: the number of nodes connected to the nodes at both ends is greater than 2; the number of intermediate nodes is 3, and the number of nodes connected to the intermediate nodes is equal to 2; for the 3-T connection of the distribution network, the third node must be equipped with a PMU, and for the 2-T connection where any node at the two end nodes is unobservable, the two end nodes must be pre-configured with a PMU; Principle 2: For nodes with 1 adjacent node number and zero injection nodes with 1 adjacent node number, no PMU is needed for the current step; Principle 3. If a node is adjacent to a node with 1 adjacent nodes and the node is a load or power generation node, the node must be configured with a PMU. If the node is connected to a node with a T-connection configured with a PMU, the current step does not need to configure a PMU temporarily. Principle 4: To make the configured PMU measure as many nodes as possible, calculate the connection matrix T , configure the node with the most connected nodes with PMU. If the node is connected to the node with T-connection configured PMU, the current step does not need to configure PMU temporarily; Step 3. Calculate the iterative Jacobian matrix from the DC model of state estimation; Step 4. Update the Jacobian matrix; Step 5. Determine whether all nodes are protected by PMU, if yes, go to step 8, if not, go to step 6; Step 6. Determine the least-effort attack area by using a simplified trapezoidal algorithm; Step 7. Configure the PMU node at the least-strength attack area and execute steps 4 and 8; Step 8. Comprehensively consider the observability and defensiveness of the distribution network to form the final PMU configuration plan; The distribution network connection matrix is ​​formed as described in step 1, including the following contents: obtaining the topological connection relationship of the distribution network, constructing the adjacency matrix T, and the elements in the adjacency matrix T T ij The calculation method is: (1) Among them, i and j are the numbers of the distribution network nodes respectively.

2. The distribution network PMU configuration method taking into account both observability and FDIA defensiveness according to claim 1 is characterized in that: The calculation of the iterative Jacobian matrix in step 3 includes the following contents: Using the state estimation of the DC model, the actual power flow from the distribution network node i to the distribution network node j can be expressed as: (2) in: X ij is the branch reactance between node i and node j; The simplified active power injection of node i is: (3) Where: J represents the node connected to node i, N i is the set of all branches connected to node i, The power of node i is equal to the sum of the powers of the branches adjacent to node i; Therefore, the DC state estimation can be expressed as follows: Z=H•X+e (4) in X =(x1, x2, …, x n ) T Represents the state vector, which is composed of the phase angles of the system nodes θ i Composition, Z = (z1,z2,…z n ) T represents the system measurement vector, Z i Including node voltage V i The amplitude and active power of the node P i and reactive power flow, • represents the matrix multiplication; e = (e1, e2, …, e n ) T The vector representing the sensor measurement error follows a Gaussian distribution with zero mean, and the measurement matrix H m×n It is called the iterative Jacobian matrix and is given by P i and P ij Partial derivatives with respect to the state vector X.

3. The distribution network PMU configuration method taking into account both observability and FDIA defensiveness according to claim 1 is characterized in that: In step 4, the Jacobian matrix is ​​updated, including the following: the sub-matrices of the iterative Jacobian matrix H are defined as H P and , H P represents the matrix composed of nodes protected by PMU, H P The complement matrix of H represents the matrix of nodes not protected by PMU. When a PMU is placed on a given node i, the nodes j, k, …, m connected to node i are considered safe and observable. The matrix H is updated according to the position of the configured PMU node in the matrix H. P and matrix : Delete the columns corresponding to the configured PMU and the nodes adjacent to the configured PMU nodes in the matrix H, and add the deleted elements to H P The remaining part of the matrix H is .

4. The method for configuring a distribution network PMU that takes into account both observability and FDIA defense according to claim 3, characterized in that: The step 6 described in which the simplified trapezoidal algorithm is used to determine the least-effort attack area refers to the simplified row trapezoidal algorithm performing elementary matrix transformation on the iterative Jacobian matrix to obtain the vulnerable area of ​​the distribution network and find the least-effort attack area. The least-effort attack vector is constructed based on the simplified row ladder algorithm, including the following steps: (1) Define the tracking matrix B to track the matrix The basic row transformation of the matrix is ​​then used to transform Simplify into a row echelon matrix, defined as matrix A; (2) Define a tracing matrix C to trace the basic column transformation of the matrix A. By exchanging columns, all non-zero elements in the Ith row of the matrix A are exchanged to the last m columns, and the matrix is ​​obtained. ; (3) Matrix The non-zero element in the lower right corner In the matrix The corresponding position before elementary transformation The corresponding node is the attack area where FDIA saves the most effort. Configuring PMU in this area can achieve the best defense effect against FDIA.

5. The distribution network PMU configuration method taking into account both observability and FDIA defensiveness according to claim 4 is characterized in that: Repeat steps 4 and 5 until all elements of matrix H are protected and placed in H P middle.

6. The distribution network PMU configuration method taking into account both observability and FDIA defense according to claim 1 is characterized in that: The configuration of the PMU node at the least-effort attack area described in step 7 is to formulate a defense countermeasure for the least-effort attack model of the network attack, and configure the PMU at the defended node to defend against the false data injection attack.

7. The method for configuring a distribution network PMU taking into account both observability and FDIA defensiveness according to claim 1, characterized in that: The final PMU configuration scheme described in step 8 is the superposition of the nodes configured with the PMU in step 2 and the nodes configured with the PMU in step 5.

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