A high-performance power grid monitoring method with differential privacy protection function

Abstract

The application discloses a kind of high-performance power grid monitoring methods with differential privacy protection function.First, the direct current flow model of power grid is established, and then the model of the voltage phase angle of other busbars except the reference bus and the active power measurement value of transmission line is established;Subsequently, on the basis of generating noise protection power grid structure, element configuration and the differential privacy of the active power measurement value of each node to transmission line, the mean consensus is used to independently solve the bus voltage phase angle of each node, combined with the direct measurement of bus voltage amplitude, to determine whether the abnormal state of power system operation occurs, to achieve the monitoring of power grid under the condition of protecting the differential privacy of user electricity data.The method proposed in the application can quickly solve the bus phase angle, generate noise protection power grid topology, element configuration and transmission line active power, etc.User privacy security, effectively solves the problem of large-scale power grid operation state monitoring with privacy protection requirements.

Description

TECHNICAL FIELD

[0001] The application belongs to the cross field of distributed framework, power grid state estimation and privacy protection, and particularly relates to a high-performance power grid monitoring method with differential privacy protection function. BACKGROUND

[0002] With the development of science and technology and the improvement of people's living standards, users' requirements for power stability and the like are also increasing. Meanwhile, the addition of new energy such as wind energy and solar energy makes the power grid scale continuously expand, increasing the difficulty of power grid operation state monitoring. In the power system, a major support for ensuring the safety and stability of the power grid is to determine whether the power grid operation is abnormal by the bus voltage amplitude and phase angle in the network. The voltage amplitude is relatively easy to measure; the voltage phase angle often needs to be estimated by multiple nodes, and a major problem faced is the leakage of privacy data such as real-time power consumption data and power grid configuration parameters in information interaction. Existing privacy protection usually needs the participation of a trusted third party or uses homomorphic encryption algorithm to encrypt data, however, these methods have limitations: accidental collapse or attack on the third party will make the computing network unable to operate or leak all nodes' privacy data, and bring higher management difficulty in large-scale power grids, and using homomorphic encryption in distributed iteration operation without the participation of the third party will bring heavy operation burden. SUMMARY

[0003] Therefore, in order to solve the problems in the background art, for the application scenarios with large network scale and high privacy protection requirements, the application proposes a distributed bus voltage phase angle estimation method based on high-performance differential privacy protection, which further becomes a high-performance power grid monitoring method.

[0004] The technical scheme adopted by the application is as follows:

[0005] Step 1: establishing a direct current flow model of the power grid;

[0006] Step 2: based on the direct current flow model of the power grid, selecting a reference bus and recording its voltage phase angle as zero, establishing a model of the voltage phase angle of other buses except the reference bus and the actual value of the transmission line active power, and further establishing a model of the voltage phase angle of other buses except the reference bus and the measured value of the transmission line active power;

[0007] Step 3: After each node respectively synthesizes the power grid structure, element configuration data and the active power of the transmission line measured by the node itself, the intermediate data corresponding to each node is obtained, and then the mean value of the intermediate data of all nodes is obtained by using the distributed high-performance differential privacy mean consensus algorithm to process the intermediate data of all nodes, and then the bus voltage phase angle is obtained by combining the model of the voltage phase angle and the active power measurement value of the transmission line of the bus except the reference bus.

[0008] Step 4: According to the bus voltage phase angle obtained by solving and the directly measured bus voltage amplitude, it is judged whether the power grid operation is in an abnormal state.

[0009] In step 1, the formula of the direct current flow model of the power grid is as follows:

[0010] P=Bθ

[0011] Wherein, P is the active power vector of all transmission lines in the power grid, θ is the voltage phase angle vector of all buses in the power grid, and B is the admittance matrix.

[0012] In step 2, the formula of the model of the voltage phase angle of the bus except the reference bus and the active power measurement value of the transmission line is as follows:

[0013] z=Hx+v

[0014] E[v]=0

[0015] Wherein, x is the vector obtained by removing the voltage phase angle of the reference bus in θ, H is the matrix obtained by removing the column corresponding to the reference bus in the admittance matrix B, which is called the measurement coefficient matrix, and the measurement coefficient matrix H is composed of the power grid structure and the element configuration data; v is the observation noise, z is the measurement value of the active power of all transmission lines, and E[] is the expected value.

[0016] In step 3, the mean value of the intermediate data of all nodes is obtained by using the distributed high-performance differential privacy mean consensus algorithm to process the intermediate data of all nodes, which is specifically:

[0017] Firstly, the generation of the confusion quantity of all nodes is performed to obtain the initial state quantity corresponding to all nodes; then, according to the power grid structure, the iteration of the state quantity is performed by using the initial state quantity corresponding to all nodes to obtain the final state quantity corresponding to all nodes and record it as the mean value of the intermediate data of all nodes obtained by each node, and the iteration formula is as follows:

[0018]

[0019] Wherein, y i (t+1) is the state quantity of node i at t+1 iteration, yi (t) represents the state variable of node i at iteration t, w ij Let N be the weight between node i and its neighboring node j. i Let y be the set of all nodes adjacent to node i. j (t) represents the state of node j, which is adjacent to node i, at iteration t;

[0020] Then, the sum of intermediate data is calculated using the average of the intermediate data from all nodes; finally, the bus voltage phase angle is obtained by solving the model based on the phase angle of other bus voltages and the measured active power of the transmission line, as well as the sum of the obtained intermediate data. The solution formula is as follows:

[0021]

[0022] in, Let H be the sum of intermediate data obtained from each node, H be the measurement coefficient matrix, ∑ be the weight matrix, and T be the matrix transpose.

[0023] The process of generating confusion amounts from the intermediate data of all nodes to obtain the initial state quantities for node i includes the following steps:

[0024] S1: Node i generates its own first noise η i , will the intermediate data β i Add the corresponding first noise η i Then the corresponding noisy data was obtained. Use the self-generated public key k pi Noisy data of itself The first ciphertext is generated after Paillier homomorphic encryption. and the first ciphertext and public key k pi Send it to all its neighboring nodes j;

[0025] S2: Node i based on the first ciphertext sent by all its neighboring nodes j and public key k pj Calculate and obtain the encrypted interaction data corresponding to all its neighboring nodes j. And send it to the corresponding node, where, a i→j To obfuscate the weights, To obfuscate the upper limit of weights;

[0026] S3: Node i based on the encrypted interactive data sent by all its neighboring nodes j Calculate its confusion level Δ i According to its intermediate data β iand confusion quantity Δ i The initial state quantity of node i is calculated by the following formula:

[0027] y i (0) = β i + ζΔ i + γ i

[0028]

[0029]

[0030] g > 0, μ > 0, ∈ > 0, 0 < δ < 1

[0031]

[0032]

[0033] wherein y i (0) is the initial state quantity of node i, ζ is a confusion coefficient, γ i is a second noise, represents an independent and identically distributed Gaussian distribution with a mean of 0 and a standard deviation of σ γ , g is a noise parameter, μ is a middle data sensitivity, ∈ and δ are a first differential privacy protection parameter and a second differential privacy protection parameter, p is the number of power grid nodes, k ∈，δ is a differential privacy comprehensive parameter; Φ() is a modified error function, and x represents a middle parameter.

[0034] The first noise η i is an independent and identically distributed Gaussian noise, satisfying wherein the standard deviation σ η of the first noise satisfies the following formula:

[0035]

[0036] wherein, represents an independent and identically distributed Gaussian distribution with a mean of 0 and a standard deviation of σ η .

[0037] In the S2, the node i respectively performs Paillier homomorphic encryption on its own noisy data using the public key k pj sent by each adjacent node j, to obtain second ciphertext After respectively multiplying the second ciphertext and the first ciphertext sent by each adjacent node j, encrypted interaction data corresponding to each adjacent node j is respectively obtained

[0038] The S3 is specifically:

[0039] The node i uses its own private key k si Respectively to all adjacent nodes j sent by the encrypted interaction data After decryption, the corresponding confusion interaction data of all adjacent nodes j of node i is obtained And the confusion amount Δ is calculated by the following formula i :

[0040]

[0041] Where, N i Is the set of all adjacent nodes of node i.

[0042] The beneficial effects of the present application are:

[0043] The present application adopts a complete distributed operation method, without the participation of a trusted third party, avoiding the risk of operation collapse and privacy leakage caused by accidental collapse or attack of the third party. The present application adopts a differential privacy protection algorithm to ensure strict and effective data privacy protection, effectively avoiding the risk of privacy leakage caused by eavesdropping of communication content, and reducing the calculation amount of data protection in the iteration process. The present application only performs information exchange under homomorphic encryption once in the whole iteration process, effectively reducing the calculation and communication burden. The present application adopts a high-performance distributed mean consensus algorithm with higher calculation accuracy under the same differential privacy protection degree, so that it can also maintain high calculation accuracy and monitoring effectiveness in a larger network. BRIEF DESCRIPTION OF DRAWINGS

[0044] Figure 1 The present application relates to a power grid monitoring method flowchart.

[0045] Figure 2 The present application relates to a bus voltage phase angle differential privacy distributed solution result verification diagram. DETAILED DESCRIPTION

[0046] The present application will be further described below in combination with the drawings and specific embodiments, but the protection scope of the present application is not limited thereto.

[0047] As Figure 1 shown, the present application comprises the following steps:

[0048] Step 1: Establish a direct current flow model of the power grid to represent the relationship between bus phase angle and transmission line active power;

[0049] The formula of the direct current flow model of the power grid is as follows:

[0050] P=Bθ

[0051] Where P is the active power vector of all transmission lines in the power grid, θ is the voltage phase angle vector of all buses in the power grid, and B is the susceptance matrix containing the topology and admittance information of the power grid, P∈R n , θ∈R m , B∈R n×m And n≥m, where n and m are the number of active power measurements and the number of buses of the transmission line, respectively.

[0052] Step 2: Based on the DC power flow model of the power grid, select a reference bus and set its voltage phase angle to zero. Establish a model of the voltage phase angle of other buses besides the reference bus and the actual value of active power of the transmission line. Then, establish a model of the voltage phase angle of other buses besides the reference bus and the measured value of active power of the transmission line. This model allows a set of estimated bus voltage phase angle values ​​that minimize the sum of squares of the errors between all measured values ​​and the true values.

[0053] The models for the voltage phase angles of busbars other than the reference bus and the actual values ​​of active power in the transmission line are as follows:

[0054] P = Hx

[0055] Therefore, the formulas for the model of the voltage phase angle of buses other than the reference bus and the measured active power of the transmission line are as follows:

[0056] z = Hx + v

[0057] E[v]=0

[0058] Where x is the vector after removing the reference bus voltage phase angle from θ, H is the matrix after removing the column corresponding to the reference bus from the susceptance matrix B, denoted as the measurement coefficient matrix, and the measurement coefficient matrix H is composed of power grid structure and component configuration data; v is the observation noise, z is the measured value of active power of all transmission lines, E[] is the expected value, x∈R m-1 H∈R n ×(m-1) ,v∈R n , z∈R n .

[0059] To minimize the sum of squares of the errors between all measured values ​​and the true values ​​of the active power of the transmission line, the bus voltage phase angle estimate, excluding the reference bus, is as follows:

[0060] x * =(H T ∑ -1 H) -1 H T Σ -1 z

[0061]

[0062] where x * is the estimation of the true value of the phase angle of the bus voltage except for the reference bus, z is the measured value of the active power of all transmission lines; ∑ is the weight matrix, T is the matrix transpose, denotes the variance of each observation noise.

[0063] Each node i holds the measurement coefficient matrix H, i∈{1, 2, …, p}, p represents the number of nodes of the power grid; and each node i measures the active power of the transmission line The corresponding observation noise variance constitutes the corresponding local weight matrix n i denotes the number of active power measurement values of the transmission line held by each node i. H, z and ∑ have the following forms:

[0064]

[0065] where, and denotes the active power measurement value z i of the transmission line held by node i. i The n ij row matrix or vector of the corresponding measurement coefficient matrix H.

[0066] Step 3: After each node respectively synthesizes the power grid structure, element configuration data and the active power of the transmission line measured by the node itself, the intermediate data corresponding to each node is obtained, and then the intermediate data of all nodes is processed by using the distributed high-performance differential privacy mean consensus algorithm, the mean of the intermediate data of all nodes is obtained, and then the bus voltage phase angle is solved by combining the model of the bus voltage phase angle and the active power measurement value of the transmission line except for the reference bus; specifically, the sum of the intermediate data is calculated according to the mean of the intermediate data of all nodes, and the bus voltage phase angle is solved based on the model of the bus voltage phase angle and the active power measurement value of the transmission line and the sum of the intermediate data.

[0067] In step 3, after the intermediate data of all nodes is processed by using the distributed high-performance differential privacy mean consensus algorithm, the mean of the intermediate data of all nodes is obtained, which is specifically:

[0068] Assuming that the communication network between all nodes forms a connected weighted undirected graph, the weight between two adjacent nodes i and j that can exchange information is w ij >0 and for any i∈{1, 2, …, p} has N i is the set of all nodes adjacent to node i.

[0069] First, the confusion quantity of all nodes is generated respectively to obtain the initial state quantity corresponding to all nodes; then, according to the power grid structure, the iteration of the state quantity is carried out by using the initial state quantity corresponding to all nodes, and finally the final state quantity corresponding to all nodes is obtained and recorded as the mean value y c，i of the intermediate data of all nodes obtained by each node i

[0070]

[0071] wherein, y i (t+1) is the state quantity of node i at t+1 iteration, y i (t) is the state quantity of node i at t iteration, w ij is the weight between node i and adjacent node j, N i is the set of all adjacent nodes of node i, y j (t) is the state quantity of adjacent node j of node i at t iteration;

[0072] Each node calculates the sum of the intermediate data by using the mean value of the intermediate data of all nodes obtained that is Finally, each node solves the bus voltage phase angle based on the model of other bus voltage phase angle and transmission line active power measurement value and the sum of the intermediate data obtained The solving formula is as follows:

[0073]

[0074] wherein, is the sum of the intermediate data obtained by each node, H is the measurement coefficient matrix, Σ is the weight matrix, and T is the matrix transpose.

[0075] The confusion quantity of all nodes is generated to obtain the initial state quantity corresponding to all nodes, and for the generation of the initial state quantity of node i, the following steps are included:

[0076] S1: node i generates a first noise η i The intermediate data is added to the corresponding first noise η i to obtain the corresponding noise-added data that is The public key k pi generated by itself is used to perform Paillier homomorphic encryption on the noise-added data of itself to generate a first ciphertext and send the first ciphertext and the public key k pi to all adjacent nodes j of the node;

[0077] Wherein, the first noise η i For independent and identically distributed Gaussian noise, satisfying Where the standard deviation of the first noise is σ η The formula is as follows:

[0078]

[0079] g>0, μ>0, ∈>0, 0<δ<1

[0080] in, This indicates that the mean is 0 and the standard deviation is σ. η Independent and identically distributed Gaussian distributions, To obfuscate the weight cap, g is the noise parameter, μ is the intermediate data sensitivity, ∈, δ is the first and second differential privacy protection parameters, p is the number of grid nodes, κ ∈，δ The differential privacy synthesis parameters are calculated using a formula that makes the following equation hold:

[0081]

[0082] Where Φ() is a correction error function of the following form:

[0083]

[0084] Where x represents an intermediate parameter. In this embodiment, g = 0.01 is selected.

[0085] S2: Node i based on the first ciphertext sent by all its neighboring nodes j and public key k pj Calculate and obtain the encrypted interaction data corresponding to all its neighboring nodes j. And send it to the corresponding node, where, a i→j The confusion index is a positive integer. To obfuscate the upper limit of weights;

[0086] In this process, node i utilizes the public key k sent by each of its neighboring nodes j. pj The noisy data of itself After performing Paillier homomorphic encryption, the second ciphertext is obtained. The second ciphertext The first ciphertext sent with each neighboring node j After multiplication, the encrypted interaction data corresponding to each adjacent node j is obtained. Right now

[0087] S3: Node i obtains all the encrypted interaction data sent by its all adjacent nodes j The confusion quantity Δ is calculated i According to the intermediate data β i and the confusion quantity Δ i The initial state quantity of node i is calculated by the following formula:

[0088] y i (0) = β i + ζΔ i + γ i

[0089]

[0090]

[0091] Wherein, y i (0) is the initial state quantity of node i, ζ is the confusion coefficient, γ i is the second noise, which represents the independent and identically distributed Gaussian distribution with mean 0 and standard deviation σ γ .

[0092] S3 is specifically:

[0093] Node i uses its own private key k si to respectively decrypt the encrypted interaction data sent by its all adjacent nodes j, and obtains the confusion interaction data corresponding to its all adjacent nodes j. i The confusion quantity Δ is calculated by the following formula:

[0094]

[0095] Note that the Paillier homomorphic encryption method can only be used for integers and is involved in S1-S3 for data that may contain decimals; the solution is to multiply the intermediate data β i by a large enough auxiliary parameter C and take the integer part for subsequent processing, and divide the confusion interaction data obtained by decryption by the auxiliary parameter C for subsequent confusion quantity calculation. In this embodiment, C = 10000 is selected.

[0096] Step 4: According to the bus voltage phase angle obtained by solving and the directly measured bus voltage amplitude, compare the bus voltage phase angle difference range limit and the amplitude limit to determine whether the power grid operation is in an abnormal state.

[0097] In the simulation, all nodes are set to have n i=1, i.e., n=p. The (m, n) values ​​for the three embodiments are set to (26, 30), (26, 41), and (118, 186), respectively. The differential privacy parameter is (∈, δ) = (10, 0.1) for all embodiments, and the intermediate data sensitivity μ = 20. The relative errors of the three embodiments in 100 simulations are... The mean values ​​were 0.0106, 0.0029, and 0.0019, respectively. Figure 2 The distribution of the relative error is given. From Figure 2 It can be seen that, with a fixed number of buses m, the larger the number of measurements n, the higher the accuracy of the bus voltage phase angle estimation proposed in this invention. Under the same ratio of the number of measurements to the number of buses n / m, the method proposed in this invention can still maintain the accuracy of bus voltage phase angle estimation as the power grid scale expands, thereby ensuring the effectiveness of power grid monitoring.

[0098] Finally, it should be noted that the above embodiments and descriptions are only used to illustrate the technical solutions of the present invention and not to limit it. Those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the disclosure of the technical solutions of the present invention, and all such modifications and substitutions should be covered within the protection scope of the claims of the present invention.

Claims

1. A high-performance power grid monitoring method with differential privacy protection function, characterized in that, The method comprises the following steps: Step 1: establishing a direct current flow model of the power grid; Step 2: based on the direct current flow model of the power grid, selecting a reference bus and recording the voltage phase angle of the reference bus as zero, establishing a model of the voltage phase angle of other buses except the reference bus and the actual value of the active power of the transmission line, and further establishing a model of the voltage phase angle of other buses except the reference bus and the measured value of the active power of the transmission line; Step 3: after each node respectively synthesizes the power grid structure, element configuration data and the measured active power of the transmission line of the node itself, the intermediate data corresponding to each node is obtained, and after the intermediate data of all nodes is processed by the distributed high-performance differential privacy mean consensus algorithm, the mean value of the intermediate data of all nodes is obtained, and then combined with the model of the voltage phase angle of other buses except the reference bus and the measured value of the active power of the transmission line, the bus voltage phase angle is solved and obtained; In the step 3, after the intermediate data of all nodes is processed by the distributed high-performance differential privacy mean consensus algorithm, the mean value of the intermediate data of all nodes is obtained, and specifically: First, generate the confusion quantity of the intermediate data of all nodes to obtain the initial state quantity corresponding to all nodes; then, according to the power grid structure, the iteration of the state quantity is carried out by using the initial state quantity corresponding to all nodes, and the final state quantity corresponding to all nodes is obtained and recorded as the mean value of the intermediate data of all nodes obtained by each node, and the iteration formula is as follows: wherein, is the state quantity of node at the th iteration, is the state quantity of node at the th iteration, is the weight between node and node adjacent to node , is the state quantity of node adjacent to node at the th iteration; The sum of the intermediate data is obtained by calculating the average of the intermediate data of all nodes; finally, the bus voltage phase angle is obtained by each node based on the model of the bus voltage phase angle and the active power measurement value of the transmission line and the obtained sum of the intermediate data The solving formula is as follows: wherein, is the sum of the intermediate data obtained for each node, is a measurement coefficient matrix, is a weight matrix, is the matrix transpose; The generation of the confusion quantity of the intermediate data of all nodes obtains the initial state quantity corresponding to all nodes, and the generation of the initial state quantity of the node includes the following steps: S1: node generating first noise by itself , obtaining intermediate data , adding corresponding first noise , obtaining corresponding noisy data , using a self-generated public key , performing Paillier homomorphic encryption on the noisy data of itself to generate first ciphertext , and sending the first ciphertext and the public key to all neighboring nodes thereof ; S2: node all its adjacent nodes the first ciphertext sent and the public key all its adjacent nodes the corresponding encrypted interaction data and sent to the corresponding node, wherein, , the confusion weight, the upper limit of the confusion weight; S3: node according to all its adjacent nodes encrypted interaction data transmitted obtained by calculating its obfuscation amount , according to intermediate data and obfuscation amount obtained by calculating the initial state amount of the node using the following formula: ， ， ， ， ， wherein is an initial state quantity of a node , is a confusion coefficient, is a second noise, denotes an independent identically distributed Gaussian distribution with mean 0 and standard deviation , is a noise parameter, is an intermediate data sensitivity, is a first differential privacy protection parameter and a second differential privacy protection parameter, is a number of grid nodes, is a differential privacy synthesis parameter; is a correction error function, denotes an intermediate parameter; The first noise is an independent and identically distributed Gaussian noise satisfying where the standard deviation of the first noise is given by the formula wherein, denotes an independent and identically distributed Gaussian distribution with mean 0 and standard deviation denotes an independent and identically distributed Gaussian distribution with mean 0 and standard deviation In S2, the node Utilize each adjacent node Public key sent The noisy data of itself After performing Paillier homomorphic encryption, the second ciphertext is obtained. The second ciphertext With each adjacent node The first ciphertext sent After multiplication, each adjacent node is obtained. Corresponding encrypted interaction data ; The S3 is specifically: Node Using its own private key Respectively to all its neighboring nodes The encrypted interaction data sent After decryption, it obtains all its neighboring nodes The corresponding obfuscated interaction data And then calculate the obfuscation amount using the following formula : wherein, is a set of all nodes adjacent to the node Step 4: according to the bus voltage phase angle obtained by solving and the directly measured bus voltage amplitude, whether the abnormal state of the power grid operation appears is judged.

2. The high-performance power grid monitoring method based on differential privacy protection according to claim 1, characterized in that, In the step 1, the formula of the direct current flow model of the power grid is as follows: wherein, is the active power vector of all transmission lines in the grid, is the voltage phase angle vector of all buses in the grid, is the susceptance matrix.

3. The high-performance power grid monitoring method with differential privacy protection function according to claim 1, characterized in that, In the step 2, the formula of the model of the voltage phase angle of other buses except the reference bus and the measured value of the active power of the transmission line is as follows: wherein, is the vector after removing the reference bus voltage phase angle in the is the admittance matrix after removing the reference bus corresponding column in the , and is called the measurement coefficient matrix, the measurement coefficient matrix is composed of the power grid structure and element configuration data; is the observation noise, is the measurement value of all transmission line active power, is the expected value.​

Images