A semi-homomorphic encryption power system distributed economic dispatch method

Abstract

The application discloses a kind of semi-homomorphic encryption power system distributed economic dispatching methods, comprising: obtaining the undirected weighted graph of distributed power system, the weight of each edge is split into two positive integer factors, and one of them is allocated to each of the two generators associated with the edge as a decomposition weight;Each generator as a transmission initiator and neighbor generator based on its own state information and decomposition weight, using the information transmission method based on semi-homomorphic encryption Paillier algorithm to perform information encryption transmission step, obtain the weighted difference value of the state information of each neighbor generator;Each generator uses the pre-constructed new distributed economic dispatching algorithm model to perform economic dispatching step: the generator as the transmission initiator uses the weighted difference value of the state information of all neighbor generators and the new distributed economic dispatching algorithm model to determine its own updated state information and determine the power generation;The application can realize the distributed security economic dispatching of power system.

Description

Technical Field

[0001] This invention belongs to the field of power system security resource allocation, specifically involving a semi-homomorphic encrypted distributed economic dispatch method for power systems. Background Technology

[0002] Economic dispatch is one of the key issues in the operation and control of power systems. With the continuous development of network technology, advanced information technology is being rapidly applied in power systems, gradually forming a new ecosystem of energy interconnection. Centralized methods can no longer meet the needs of economic dispatch in the context of informatization. Distributed economic dispatch schemes emphasize that each participating unit makes independent decisions. Each unit exchanges information with its neighbors through the network according to a preset protocol, compares and adjusts its own output, and collaboratively minimizes the generation cost of the power system. Distributed economic dispatch utilizes a sparse communication structure to achieve decentralized cooperation among units in the network, and has advantages such as flexibility, efficiency, strong scalability, and strong robustness. With distributed generation as the object of regulation, more and more new third-party entities such as virtual power plants or load aggregators are emerging on the demand side, and their control is mostly realized through open information environments. With the widespread access of new third-party regulation entities, some control of the future new power system will be built on open cyberspace, making it more vulnerable to malicious network attacks.

[0003] On the other hand, new demand-side regulation entities in the future will involve a large amount of user privacy information. Optimized scheduling will involve collaborative computing and data analysis across multiple entities. To achieve the economic scheduling goal of minimizing costs, generators typically transmit important and sensitive information to their neighbors for distributed computing. During this process, if an attacker intrudes into the communication link, they can easily steal transmitted information, posing a significant threat to system security and easily leading to the leakage of privacy information, resulting in even greater economic losses. In addition, improper behavior by neighbors can also lead to the leakage of privacy information. Therefore, in an environment where power system regulation entities are becoming increasingly complex and diverse, the separation of user data usage rights and ownership, and the separation of information resources and computing resources, makes privacy protection issues in multi-entity collaborative processes increasingly prominent. Network security and privacy protection, as important components of information security, will directly affect the safe and stable operation of the power system.

[0004] To address the aforementioned privacy concerns, popular existing technologies include noise-injection-based data obfuscation and blockchain-based security measures. However, noise-injection-based data obfuscation only considers external threats to distributed power systems; neighbors can still access the state information of adjacent nodes, leaving the privacy issue unresolved. Furthermore, this method trades accuracy for security, potentially impacting data accuracy. Blockchain-based security measures, due to inherent technological limitations, are currently not feasible for large-scale implementation. Each information assessment in a blockchain requires approval from a majority of nodes, leading to significant delays. Additionally, blockchain requires each node to maintain a complete ledger, incurring additional costs for distributed power systems. Therefore, a satisfactory solution for effectively protecting privacy in distributed economic dispatch of power systems remains elusive. Summary of the Invention

[0005] To address the aforementioned problems in existing technologies, this invention provides a semi-homomorphic encryption-based distributed economic dispatch method for power systems. The technical problem to be solved by this invention is achieved through the following technical solution:

[0006] A semi-homomorphic encryption distributed economic dispatch method for power systems is applied to a distributed power system composed of multiple nodes, each node containing independent generators and loads; the method includes:

[0007] Obtain the undirected weighted graph of the distributed power system;

[0008] For each edge in the undirected weighted graph, the weight of the edge is split into two positive integer factors, and one of these positive integer factors is assigned as the decomposition weight to each of the two generators associated with the edge.

[0009] Each generator performs an encrypted information transmission step, including: each generator, as the transmission initiator, transmits encrypted information with its neighboring generators based on their respective state information and decomposition weights, using a Paillier algorithm-based semi-homomorphic encryption method, so that the generator acting as the transmission initiator obtains a weighted difference in state information with each of its neighboring generators; wherein, the state information includes the generator's incremental cost at each time point, and the local mismatch between power generation and power consumption.

[0010] Each generator executes economic scheduling steps using a pre-built new distributed economic scheduling algorithm model, including: the generator that initiates the transmission uses the weighted difference between its state information and that of all neighboring generators and the new distributed economic scheduling algorithm model to determine its updated state information, and uses its updated state information to determine the amount of electricity generated.

[0011] The new distributed economic dispatch algorithm model is designed to address the optimization problem of minimizing generation costs in the economic dispatch of distributed power systems. It utilizes generator state information to determine the initial distributed economic dispatch algorithm model. Each generator performs an information encryption transmission step. After each generator performs the economic dispatch step using the initial distributed economic dispatch algorithm model, the impact of information encryption transmission on the initial distributed economic dispatch algorithm model is modeled as a time delay effect. The algorithm model is updated after analyzing the impact of the time delay on the initial distributed economic dispatch algorithm model.

[0012] In one embodiment of the present invention, the process of constructing the initial distributed economic scheduling algorithm model includes:

[0013] For the aforementioned distributed power system, the generator generation cost function is determined as follows: Among them, C i (p i ) represents the power generation cost of generator i; p i α represents the amount of electricity generated by generator i; i β i γ i represents the cost coefficient fitted for generator i; N represents the total number of nodes in the distributed power system; i = 1, 2, ..., N;

[0014] Using the aforementioned generation cost function, the optimization problem for minimizing generation costs in the economic dispatch of the distributed power system is as follows:

[0015]

[0016] The communication topology of the distributed power system is represented by an undirected weighted graph; P d This represents the total load power demand of the distributed power system; and These represent the lower limit and upper limit of generator i's power output, respectively;

[0017] The iterative formula for determining the incremental cost of the generator is: Where, N i Let L represent the set of neighboring generators of generator i; ∈1 denotes a constant first step length, ∈1≤1 / q, where q represents the largest eigenvalue of the Laplace matrix L; when i≠j, the element in the i-th row and j-th column of L is -a. ij When i = j, the element in the i-th row and j-th column of L is the sum of the remaining elements in that row, a. ij The sum of; a ij λ represents the weight of the edge connecting generators i and j in the undirected weighted graph; i (k) represents the incremental cost of generator i at time k;

[0018] The formula for adjusting power generation based on the incremental cost of the generator is: p(k+1)=Bλ(k+1)-[σ1,σ2,...,σ N ] T Where, p(k) = col{p1(k), p2(k), ..., p N (k)};p i (k) represents the power generation of generator i at time k; λ(k) = col{λ1(k),λ2(k),...,λ N (k)};col represents a column vector;σ i =β i / 2γ i B = diag(1 / 2γ) i ); diag represents a diagonal matrix; when season when season

[0019] To ensure that the system's power generation matches the load's power consumption, a partial mismatch between power generation and power consumption is introduced: m(k)=col{m1(k),m2(k),...,m N (k)}; and determine the iterative expression for the local mismatch between power generation and power consumption as: m(k+1)=m(k)-∈2Lm(k)-[p(k+1)-p(k)]; where m(k) represents the local mismatch between power generation and power consumption at time k; ∈2 represents the constant second step size, ∈2≤1 / q;

[0020] The local mismatch between the power generation and the power consumption is introduced into the iterative formula of the incremental cost of the generator as feedback for the adjustment of the total power generation. The updated iterative formula of the incremental cost of the generator is: λ(k+1)=λ(k)-∈1Lλ(k)+ιm(k); where ι is the feedback coefficient;

[0021] By simultaneously solving the formula for adjusting power generation based on the incremental cost of generators, the iterative expression for the local mismatch between power generation and electricity consumption, and the iterative formula for the incremental cost of updated generators, the initial distributed economic scheduling algorithm model is obtained as follows: Where I represents the identity matrix.

[0022] In one embodiment of the present invention, the step of decomposing the weight of each edge in the undirected weighted graph into two positive integer factors, and assigning one of these positive integer factors as the decomposed weight to each of the two generators associated with that edge, includes:

[0023] For the weight a of an edge connecting generator i and generator j in the undirected weighted graph ij According to formula a ij =a i-j ×a j-i a ij Split into a i-j and a j-i Two positive integer factors; where × represents the multiplication sign; i and j are the generator numbers;

[0024] a i-j Assigning a to generator i as a decomposition weight j-i The weights are assigned to generator j as decomposition weights.

[0025] In one embodiment of the present invention, the step of each generator performing encrypted information transmission includes:

[0026] Generator i, acting as the transmission initiator, generates public key k using the Paillier algorithm with semi-homomorphic encryption. pi and private key k si and broadcast the public key k to the neighbor's generator. pi ;

[0027] The generator i uses the public key k pi Regarding its own state information x i Encrypting the initiator's state information ψ(-x) using the opposite of the initiator's state information data. i ); and encrypt the initiator's state information data ψ(-x) i Transmitted to neighboring generator j;

[0028] The neighboring generator j uses the public key k pi Encrypt its own state information x j , obtain encrypted neighbor state information data ψ(x) j );

[0029] The neighbor generator j uses the neighbor status information to encrypt data ψ(x). j ) and the received encrypted data ψ(-x) of the initiator's state information i Based on the semi-homomorphic additive property of the Paillier algorithm for semi-homomorphic encryption, the state information difference is used to encrypt the data ψ(x). j -x i );

[0030] The neighboring generator j utilizes its own decomposition weight a j-i Encrypt the difference data ψ(x) in the state information j -x iPerform cumulative multiplication to obtain encrypted data ψ[a], which is the product of the difference between the neighbor decomposition weight state information and the neighbor decomposition weight state information. j-i (x j -x i )], and transmit to the generator i;

[0031] The generator i uses its private key k si Decrypt the encrypted data ψ[a] of the neighbor decomposition weight state information difference product j-i (x j -x i The decomposition weight a of the neighboring generator j is obtained. j-i The difference between the two state information (x) j -x i The product of ) a j-i (x j -x i The initiator decrypts the data;

[0032] The generator i utilizes its own decomposition weight a i-j The decrypted data from the initiator is weighted to obtain a weighted difference 'a' between the data and the state information of the neighboring generator j. i-j a j-i (x j -x i ).

[0033] In one embodiment of the present invention, when generator i, as the initiator of the transmission, performs the information encryption transmission step again, it updates its own public key k. pi And initiate a public key update operation to the neighbor generator j, so that the neighbor generator j can update its public key using the original public key of generator i;

[0034] In this context, generator i, acting as the transmission initiator, updates its own public key k. pi The process includes:

[0035] The generator i determines whether a preset condition is met; wherein the preset condition includes: the time interval between the moment when the generator i first performs the information encryption transmission step and the current moment has reached a preset time length; or, the total amount of data sent by the generator i up to the current moment has reached a preset data amount;

[0036] If at least one preset condition is met, the public key of generator i is updated using its original public key; if no preset condition is met, the original public key of generator i remains unchanged.

[0037] In one embodiment of the present invention, the process of updating the public key of the neighboring generator j using the original public key of generator i includes:

[0038] Generator j selects the basic operation method and operands based on the information of multiple bytes in the pre-agreed transmission data packet that serve as information update flags;

[0039] Using the aforementioned basic operation method and operands, perform basic operations on the original public key of generator i to obtain the updated public key of generator i.

[0040] In one embodiment of the present invention, before splitting the weight of each edge in the undirected weighted graph into two positive integer factors, the method further includes:

[0041] When the preset conditions are met, the weight of the edge is updated; otherwise, the weight of the edge remains unchanged.

[0042] In one embodiment of the present invention, each generator performs economic scheduling steps using the initial distributed economic scheduling algorithm model, including:

[0043] The generator that initiates the transmission uses the weighted difference between its state information and that of all neighboring generators, along with the initial distributed economic scheduling algorithm model, to determine its updated state information, and then uses this updated state information to determine the amount of electricity generated.

[0044] In one embodiment of the present invention, the process of analyzing the impact of latency on the initial distributed economic scheduling algorithm model and updating the algorithm model to obtain the new distributed economic scheduling algorithm model includes:

[0045] The impact of the information transmission method based on the Paillier algorithm with semi-homomorphic encryption on the initial distributed economic scheduling algorithm model is modeled as a time-varying delay d(k); where d(k) represents the delay at time k. d and These represent the maximum allowable lower limit and the maximum allowable upper limit of latency, respectively.

[0046] Introducing a time-varying delay d(k) updates the initial distributed economic scheduling algorithm model to a new distributed economic scheduling algorithm model:

[0047] In one embodiment of the present invention, the novel distributed economic scheduling algorithm model has undergone convergence performance verification in advance; wherein, the convergence performance verification process includes:

[0048] The novel distributed economic scheduling algorithm model is simplified, and a Lyapunov-Krasovskii functional with multiple summation is constructed.

[0049] The functional is subjected to forward difference, analysis and scaling to obtain a new convergence condition for the time-delay-dependent algorithm that balances conservatism and complexity.

[0050] Based on the convergence condition of the new time-delay dependent algorithm, determine the tolerance of the new distributed economic scheduling algorithm model to time delay;

[0051] Using a pre-set simulation platform, the average computation time of encryption / decryption and computation operations during the process of obtaining the weighted difference of state information through a single encrypted transmission between neighboring generators was simulated and obtained.

[0052] Based on the tolerance level and the numerical magnitude, the time required for one iteration is determined in order to achieve convergence in a shorter time.

[0053] In the distributed economic dispatch method for power systems with semi-homomorphic encryption provided in this invention, each generator in the distributed power system performs an encrypted information transmission step with its neighboring generators to obtain a weighted difference in state information with each neighboring generator. Then, a pre-constructed new distributed economic dispatch algorithm model is used to execute economic dispatch steps. Specifically, by using the weighted difference in state information with all neighboring generators and the new distributed economic dispatch algorithm model, the generator determines its own updated state information and uses this updated state information to determine power generation, thereby achieving economic dispatch. This invention provides a simple, highly applicable, and secure economic dispatch scheme for distributed power systems. In this process, the information transmission method based on the Paillier algorithm with semi-homomorphic encryption enables secure and private information exchange, ensuring that information is not stolen or tampered with externally, while also guaranteeing that the privacy of any node is confidential to other nodes.

[0054] Furthermore, the novel distributed economic dispatch algorithm model pre-constructed in this embodiment of the invention is redesigned based on the characteristics of the Paillier algorithm with semi-homomorphic encryption. The construction process involves first addressing the optimization problem of minimizing generation costs in the economic dispatch of distributed power systems. An initial distributed economic dispatch algorithm model is determined using generator state information. Then, based on the properties of the Paillier algorithm with semi-homomorphic encryption, an information exchange scheme is designed to enable each generator to perform encrypted information transmission steps. The initial distributed economic dispatch algorithm model is then used to execute economic dispatch steps to complete the economic dispatch. To analyze the impact of encrypted information transmission on the initial distributed economic dispatch algorithm model, it is modeled as a time delay effect. The impact of time delay on the initial distributed economic dispatch algorithm model is then analyzed to update the algorithm model, thereby obtaining the new distributed economic dispatch algorithm model. This embodiment of the invention fully considers the impact of privacy protection schemes on the proposed initial distributed economic dispatch algorithm model, modeling it as a time-varying time delay with greater practical significance in engineering applications. Finally, a new distributed economic dispatch algorithm model under privacy protection is presented.

[0055] Furthermore, this embodiment of the invention pre-verifies the convergence performance of the novel distributed economic scheduling algorithm model. By performing forward differencing and other processing on the constructed multi-sum Lyapunov-Krasovskii functional, a new time-delay-dependent algorithm convergence condition that balances conservatism and complexity is obtained. This condition can be used to determine the latency tolerance of the novel distributed economic scheduling algorithm model. During the process of obtaining the weighted difference of state information through a single encrypted transmission between neighboring generators, the average computation time of encryption / decryption and arithmetic operations is obtained through simulation. Combined with the obtained latency tolerance, the sampling interval time, i.e., the time required for one iteration, is determined to achieve a faster convergence speed. Experiments have confirmed that, within the allowable latency range, the novel distributed economic scheduling algorithm model of this invention can guarantee convergence and converges to the global optimum of the optimization problem under normal operation, thus exhibiting good performance. Attached Figure Description

[0056] Figure 1 A flowchart illustrating a semi-homomorphic encryption method for distributed economic dispatching of power systems provided in an embodiment of the present invention;

[0057] Figure 2 This is an interactive diagram illustrating the generator's execution of the information encryption transmission step in the information transmission method based on the Paillier algorithm with semi-homomorphic encryption provided in an embodiment of the present invention.

[0058] Figure 3 This is a distributed power system communication topology diagram provided in the experiments of this embodiment of the invention;

[0059] Figure 4 This is a diagram showing the local mismatch variation under a fixed time delay in an experiment according to an embodiment of the present invention.

[0060] Figure 5 This is a graph showing the incremental cost variation under a fixed delay in the experiments of this embodiment of the invention;

[0061] Figure 6 This is a diagram showing the local mismatch variation under time-varying delay conditions in an experiment according to an embodiment of the present invention;

[0062] Figure 7 This is a graph showing the incremental cost variation under time-varying delay conditions in an experiment according to an embodiment of the present invention.

[0063] Figure 8 This is a time-varying delay variation diagram in the experiment of an embodiment of the present invention. Detailed Implementation

[0064] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0065] like Figure 1 As shown in the figure, the distributed economic dispatch method for power systems with semi-homomorphic encryption provided by this invention is applied to a distributed power system composed of multiple nodes, each node containing independent generators and loads; the method may include the following steps:

[0066] S1, obtain the undirected weighted graph of the distributed power system;

[0067] Specifically, based on the characteristics and distances of each generator in a distributed power system, an undirected weighted graph of the distributed power system can be obtained, where edges in the undirected weighted graph connect two generators.

[0068] S2, for each edge in the undirected weighted graph, decompose the weight of the edge into two positive integer factors, and assign one of these positive integer factors as the decomposed weight to each of the two generators associated with the edge; wherein, S2 may include:

[0069] S21, for the weight a corresponding to an edge connecting generator i and generator j in the undirected weighted graph. ij According to formula a ij =a i-j ×a j-i a ij Split into a i-j and a j-i Two positive integer factors;

[0070] Where × represents the multiplication sign; i and j are the generator numbers, both of which are natural numbers greater than 0.

[0071] S22, a i-j Assigning weights to generator i as decomposition weights, and then... j-i Assign the weights to generator j as decomposition weights.

[0072] Among them, generator i and generator j can only obtain one of the positive integer factors.

[0073] S3, Each generator performs the information encryption transmission step, including: Each generator, as the transmission initiator, transmits information encrypted with its neighboring generators based on their respective state information and decomposition weights, using the Paillier algorithm based on semi-homomorphic encryption, so that the generator as the transmission initiator obtains the weighted difference between the state information of each neighboring generator.

[0074] The state information includes the incremental cost of the generator at each moment, and the local mismatch between power generation and power consumption, also known as the local mismatch between power supply and demand. "Local" refers to generator i and the generators connected to it; local mismatch refers to the weighted sum of the differences between power generation and power consumption within the corresponding local area.

[0075] S4, each generator executes economic scheduling steps using a pre-built new distributed economic scheduling algorithm model, including: the generator that initiates the transmission uses the weighted difference between its state information and that of all neighboring generators and the new distributed economic scheduling algorithm model to determine its updated state information, and uses its updated state information to determine the amount of electricity generated.

[0076] Among them, the new distributed economic dispatch algorithm model is an optimization problem for minimizing generation costs in the economic dispatch of distributed power systems. It uses the state information of generators to determine the initial distributed economic dispatch algorithm model, and each generator performs information encryption transmission steps. After each generator performs the economic dispatch steps using the initial distributed economic dispatch algorithm model, in order to analyze the impact of information encryption transmission on the initial distributed economic dispatch algorithm model, it is modeled as a time delay effect. After analyzing the impact of time delay on the initial distributed economic dispatch algorithm model, the algorithm model is updated.

[0077] For clarity, steps S3 and S4 will be explained later.

[0078] To facilitate understanding of the embodiments of the present invention, the construction process of the new distributed economic scheduling algorithm model will first be explained. Furthermore, for clarity, the explanation will be divided into the following steps.

[0079] (i) To address the optimization problem of minimizing generation costs in the economic dispatch of distributed power systems, the initial distributed economic dispatch algorithm model is determined using generator state information;

[0080] The process of constructing the initial distributed economic scheduling algorithm model includes the following steps:

[0081] S101, For distributed power systems, the generator generation cost function is determined as follows:

[0082]

[0083] Among them, C i (p i ) represents the power generation cost of generator i; p i α represents the amount of electricity generated by generator i; i β i γ i represents the cost coefficient fitted for generator i; N represents the total number of nodes in the distributed power system; i = 1, 2, ..., N.

[0084] As those skilled in the art will understand, the goal of economic dispatch in a distributed power system is to minimize generation costs by adjusting the generation of each generator while satisfying the balance between power supply and demand. This process usually also needs to consider the generation constraints of the generators, so it is necessary to construct an optimization problem in a reasonable way.

[0085] S102, using the generation cost function, constructs the optimization problem of minimizing generation cost in the economic dispatch of a distributed power system as follows:

[0086]

[0087] In this system, the communication topology of the distributed power system is represented by an undirected weighted graph; P d This represents the total load power demand of a distributed power system; and These represent the lower limit and upper limit of generator i's power output, respectively;

[0088] In this embodiment of the invention, the economic dispatch problem of a distributed power system is described as above. Furthermore, to ensure that the economic dispatch does not lose generality, the following assumptions are given: 1) The optimization problem (2) has a feasible solution, that is, it satisfies 2) The communication topology of a distributed power system is an undirected connected graph.

[0089] S103, the iterative formula for determining the incremental cost of the generator is:

[0090]

[0091] Since the embodiments of the present invention require the establishment of a state iteration algorithm for a distributed power system to minimize costs, the algorithm is iterated according to the common rules in multi-agent systems to obtain formula (3).

[0092] Where, N i Let L represent the set of neighboring generators of generator i; ∈1 denotes a constant first step length, ∈1≤1 / q, where q represents the largest eigenvalue of the Laplace matrix L; when i≠j, the element in the i-th row and j-th column of L is -a. ij When i = j, the element in the i-th row and j-th column of L is the sum of the remaining elements in that row, a. ij The sum of; a ij This represents the weight of the edge connecting generators i and j in an undirected weighted graph, that is, a ij λ represents the weight between generators i and j; i (k) represents the incremental cost of generator i at time k.

[0093] S104, the formula for adjusting power generation based on the incremental cost of the generator is determined as follows:

[0094] p(k+1)=Bλ(k+1)-[σ1,σ2,...,σ N ] T (4)

[0095] According to formula (4), each generator can adjust its power generation p(k+1) based on its own incremental cost λ(k+1).

[0096] Where p(k)=col{p1(k),p2(k),...,p N (k)};p i (k) represents the power generation of generator i at time k; λ(k) = col{λ1(k),λ2(k),...,λ N (k)};col represents a column vector;σ i =β i / 2γ i B = diag(1 / 2γ) i ); diag represents a diagonal matrix; because the generator has generation constraints, therefore, we set: when season when season

[0097] S105, to ensure that the system's power generation matches the load's power consumption, the expression for the local mismatch between the generator's power generation and power consumption is introduced as follows:

[0098] m(k)=col{m1(k), m2(k), ... , m N (k)} (5)

[0099] The iterative expression for the local mismatch between power generation and power consumption is determined as follows:

[0100] m(k+1)=m(k)-∈2Lm(k)-[p(k+1)-p(k)] (6)

[0101] Where m(k) represents the local mismatch between power generation and power consumption at time k; ∈2 represents a constant second step size, ∈2≤1 / q.

[0102] Specifically, the communication topology considered in this embodiment of the invention is an undirected connected graph, so the minimum eigenvalue of matrix L is 0, and therefore formula (3) is convergent. However, formula (3) can only achieve consistency of system incremental cost, and cannot guarantee that the system power generation matches the load power consumption. It is only applicable to systems where the initial power generation is equal to the power consumption. Therefore, a function m(k) is introduced, as shown in formula (5), to represent the local mismatch between power generation and power consumption. For each generator, the iteration of m(k) is specified by formula (6).

[0103] S106, incorporating the local mismatch between power generation and power consumption into the iterative formula for the incremental cost of generators as feedback for the adjustment of total power generation, yields the updated iterative formula for the incremental cost of generators as follows:

[0104] λ(k+1)=λ(k)-∈1Lλ(k)+ιm(k) (7)

[0105] Where ι is the feedback coefficient, which can be a small positive number.

[0106] S107, by simultaneously solving the formula for adjusting power generation based on the incremental cost of generators, the iterative expression for the local mismatch between power generation and consumption, and the iterative formula for the incremental cost of updated generators, the initial distributed economic dispatch algorithm model is obtained as follows:

[0107]

[0108] Formula (8) is specifically derived from formulas (4) to (7) above; I represents the identity matrix.

[0109] (ii) Each generator performs encrypted information transmission steps;

[0110] To ensure the security of information transmission during economic dispatch of distributed power systems, this invention proposes an information transmission method based on the Paillier algorithm with semi-homomorphic encryption for weighted distributed generation systems, and constructs a privacy-protected transmission scheme for distributed systems.

[0111] It should be noted that the information encryption transmission steps performed by each generator are completely consistent in the process of constructing the new distributed economic dispatch algorithm model and in step S3 of the actual semi-homomorphic encrypted power system distributed economic dispatch method. In addition, all generators need to complete the preparatory work before the information encryption transmission steps. The specific preparatory work is shown in S1 and S2, and will not be repeated here.

[0112] For details on the process of encrypting and transmitting information, please refer to [link / reference]. Figure 2 The diagram illustrates the interactive process of encrypting and transmitting information during generator operation. Figure 2 The corresponding steps have been simplified in text.

[0113] Specifically, taking a single encrypted information transmission between generator i and a neighboring generator j as an example, the encrypted information transmission steps performed by each generator include:

[0114] S201, generator i, as the transmission initiator, generates public key k using the Paillier algorithm with semi-homomorphic encryption. pi and private key k si and broadcast the public key k to the neighbor's generator. pi ;

[0115] In a transmission initiated by generator i, generator i broadcasts its public key to all neighboring generators, and stops propagating the public key after all neighboring generators have received it. Figure 2 In this case, it is indicated by "only once". At this time, all neighboring generators of generator i can receive generator i's public key k. pi For details on the Paillier algorithm for semi-homomorphic encryption, please refer to the relevant technical explanations; it will not be described in detail here.

[0116] S202, Generator i uses public key k pi Regarding its own state information x i Encrypting the initiator's state information ψ(-x) using the opposite of the initiator's state information data. i ); and encrypt the initiator's state information data ψ(-x) i Transmitted to neighboring generator j;

[0117] Among them, the state information x of generator i i Including λ(k) and m(k); during the encryption process, by first obtaining... Modulo inverse, then perform the modulo multiplication. Obtained by modulo; r represents a randomly selected value. gcd(z,k pi () indicates the search for z and k pi The greatest common divisor.

[0118] S203, Neighbor generator j uses public key k pi Encrypt its own state information x j , obtain encrypted neighbor state information data ψ(x) j );

[0119] in,

[0120] S204, Neighbor generator j uses neighbor state information to encrypt data ψ(x) j ) and the received initiator state information encrypted data ψ(-x i Based on the semi-homomorphic additive property of the Paillier algorithm for semi-homomorphic encryption, the state information difference is used to encrypt the data ψ(x). j -x i );

[0121] Specifically, ψ(-x) is calculated based on the semi-homomorphic additivity. i )×ψ(x j ) to obtain ψ(x j -x i ).

[0122] S205, Neighbor generator j utilizes its own decomposition weight a j-i Encrypt data ψ(x) based on the difference in state information j -x i Perform cumulative multiplication to obtain encrypted data ψ[a], which is the product of the difference between the neighbor decomposition weight state information and the neighbor decomposition weight state information. j-i (x j -x i )]ψ[a j-i (x j -x i )], and transmit it to generator i;

[0123] Specifically, based on the scalar cumulative multiplication property of the Paillier algorithm for semi-homomorphic encryption, ψ(x) j -x i (cumulative multiplication of a) j-i Next, we obtain ψ[a] j-i (x j -x i )).

[0124] S206, Generator i uses its own private key k si Decrypting neighbor decomposition weight state information difference product encrypted data ψ[a j-i (x j -x i )]ψ[a j-i (x j -x i[ ], obtain the decomposition weight a of neighbor generator j. j-i The difference between the two state information (x) j -x i The product of ) a j-i (x j -x i The initiator decrypts the data;

[0125] For details on key generation and decryption, please refer to the relevant information on the Paillier algorithm for semi-homomorphic encryption; it will not be explained in detail here.

[0126] S207, generator i utilizes its own decomposition weight a i-j The decrypted data from the initiator is weighted to obtain a weighted difference a between the state information of the initiator and that of the neighboring generator j. i-j a j-i (x j -x i ).

[0127] It is understandable that generator i can obtain the weighted difference of its state information with each neighboring generator by transmitting the aforementioned encrypted information to each neighboring generator.

[0128] Figure 2 This demonstrates how generator i obtains the weighted difference in state information with its neighbor generator j without causing information leakage. After each state update, generator i needs to perform the above information exchange process (number of neighboring generators * number of states) times, but these exchanges can be performed in parallel. As seen in the encrypted information transmission process, all generators share their public keys with their neighboring generators in plaintext; thereafter, data is only exchanged in ciphertext. Therefore, data privacy can be protected through encryption.

[0129] In one optional implementation, the generator initiating the transmission may also include a public key update step during multiple encrypted information transmissions. Specifically, taking any encrypted information transmission after the initial transmission as an example, when generator i, as the transmission initiator, executes the encrypted information transmission step again, it updates its own public key k. pi Then initiate a public key update operation to neighbor generator j, so that neighbor generator j can update its public key using the original public key of generator i.

[0130] In this process, generator i, acting as the transmission initiator, updates its own public key k. pi The process includes:

[0131] Generator i determines whether preset conditions are met; the preset conditions include: the time interval between the moment when generator i first performs the information encryption transmission step and the current moment has reached a preset time length; or, the total amount of data sent by generator i up to the current moment has reached a preset data amount; the preset time length and preset data amount can be set according to needs or experience values, and no specific restrictions are imposed here.

[0132] If at least one preset condition is met, the public key of generator i is updated using its original public key; if no preset condition is met, the original public key of generator i remains unchanged.

[0133] The original public key is the most recently used public key by generator i. In actual processing, generator i can set a public key update flag, allowing generator j to update generator i's public key according to the actual situation.

[0134] Correspondingly, the process of neighboring generator j updating its public key using generator i's existing public key includes:

[0135] ① Generator j selects the basic operation method and operands based on the information of multiple bytes in the pre-agreed data packet that serve as information update flags;

[0136] Each generator can pre-agree with its neighboring generators on several bytes at predetermined positions in the transmitted data packet as information update flags. For example, the first 5 bytes can be designated as information update flags. Specifically, the first byte of these 5 bytes can be 0 to indicate no public key update and 1 to indicate a public key update. The second and third bytes, when combined in the form of 00, 01, 10, and 11 respectively, represent addition, subtraction, multiplication, and division. The fourth and fifth bytes constitute the operands for the basic operations, specifically corresponding to the four types of operations mentioned above as addends, subtractions, multipliers, and divisors.

[0137] After receiving the data packet, the neighboring generator will select a basic operation method and the corresponding operands based on the 5 bytes of information.

[0138] ② Using basic arithmetic methods and operands, perform basic arithmetic operations on the original public key of generator i to obtain the updated public key of generator i.

[0139] Specifically, generator i's original public key is used as the addend, subtrahend, multiplicand, and divisor in basic operations. Neighboring generators perform numerical operations on generator i's original public key according to the selected basic operation method and corresponding operands. The calculated value becomes generator i's updated public key. In this way, after generator i updates its own public key, neighboring generator j also updates generator i's public key accordingly.

[0140] The basic operations can be represented by the formula: k p (k+1)=Y(k p (k)); where k p (k) represents the original public key of the generator; k p (k+1) represents the updated public key of the generator. Here, k and k+1 are used only as an example to distinguish the time corresponding to two different public keys, but do not mean that the two time points are adjacent; Y(k p (k) represents the relationship between k and k. p (k) performs basic operations. It is evident that this public key update method does not infringe on the privacy of other generators.

[0141] Similarly, other information that needs updating in this embodiment of the invention can also be updated using the public key update method. For example, in one optional implementation, before splitting the weight of each edge in the undirected weighted graph into two positive integer factors, the method further includes:

[0142] If the preset conditions are met, the weight of the edge is updated; otherwise, the weight of the edge remains unchanged.

[0143] The updated weight of this edge is obtained by performing basic calculations based on the original weight.

[0144] (iii) Execute the economic scheduling steps using the initial distributed economic scheduling algorithm model;

[0145] Specifically, (iii) may include the following steps:

[0146] S301, the generator that initiates the transmission uses the weighted difference between its state information and that of all neighboring generators, as well as the initial distributed economic scheduling algorithm model, to determine its updated state information.

[0147] Specifically, generator i obtains a weighted difference 'a' between its state information and that of all its neighboring generators j. i-j a j-i (x j -x i After that, it can utilize its original state information λ i (k), m i (k), obtain its updated state information λ according to formula (8). i (k+1), m i (k+1).

[0148] S302 determines the amount of electricity generated using its updated status information.

[0149] Specifically, it utilizes its own updated state information λ i(k+1), m i (k+1), the power generation p can be obtained according to formula (4). i (k+1).

[0150] Once each generator determines its own power generation according to the above process, the economic dispatch of the distributed power system is completed.

[0151] As can be seen, the embodiments of the present invention protect data privacy through encryption and enable generators to be economically dispatched normally without directly obtaining neighbor information through a special information exchange mechanism, effectively improving information security and privacy. During the implementation of this scheme, information encryption prevents external attackers from knowing the specific status of the generators; because of the existence of the key, attackers cannot forge erroneous data that could deceive the generators, making the distributed generation system immune to deception attacks to a certain extent.

[0152] (iv) Analyze the impact of latency on the initial distributed economic scheduling algorithm model, and update the algorithm model to obtain a new distributed economic scheduling algorithm model;

[0153] The privacy protection scheme based on the Paillier algorithm with semi-homomorphic encryption designed in step (ii) of this embodiment of the invention is highly feasible and has high value for data security; however, encrypted transmission introduces a time delay into the system. Figure 2 As can be seen from this, compared to plaintext transmission, this scheme requires a series of actions such as encryption / decryption and ciphertext operations to obtain a weighted difference of state information.

[0154] Therefore, in this embodiment of the invention, step (iv) models the impact of privacy protection schemes on data real-time performance as time delay, and analyzes the impact of delay on the convergence of the initial distributed economic scheduling algorithm model. Considering the complex working environment, this step focuses on the study of time-varying delays, which have greater practical significance in engineering applications.

[0155] Specifically, this step may include:

[0156] S401, the impact of the information transmission method based on the Paillier algorithm of semi-homomorphic encryption on the initial distributed economic scheduling algorithm model is modeled as a time-varying delay d(k);

[0157] Specifically, regarding the aforementioned information transmission method based on the Paillier algorithm with semi-homomorphic encryption as a privacy protection scheme to protect the transmission information of the distributed power system, its impact on the initial distributed economic dispatch algorithm model is first modeled as a time-varying delay d(k); where d(k) represents the delay at time k. d and These represent the lower and upper limits of the maximum allowable delay, respectively. Based on the preceding text, it can be understood that, for generator i, the state information λ... i (k) and m i (k) Iterates based on its own state information and the weighted difference between the state information of its neighboring generators. The weighted difference between the state information of its neighboring generators needs to be obtained through interaction.

[0158] Since the initial distributed economic scheduling algorithm model, i.e., formula (8), uses matrix L to describe the weighted difference of state information, the embodiments of the present invention need to adjust the initial distributed economic scheduling algorithm model in a manner such as S402 after considering the use of privacy protection schemes.

[0159] S402 introduces a time-varying delay d(k) to update the initial distributed economic scheduling algorithm model to a new distributed economic scheduling algorithm model:

[0160]

[0161] The meaning of each parameter is explained in the previous text and will not be repeated here.

[0162] In one optional implementation, the new distributed economic scheduling algorithm model has undergone convergence performance verification beforehand. The following describes this process using step (v).

[0163] (v) Verify the convergence performance of the new distributed economic scheduling algorithm model;

[0164] The convergence performance verification process includes:

[0165] S501 simplifies the new distributed economic scheduling algorithm model and constructs a Lyapunov-Krasovskii functional with multiple summation.

[0166] Specifically, for ease of analysis, formula (9) is simplified to:

[0167] x(k+1)=Ax(k)+A d x(kd(k)) (10)

[0168] in, The initial state of a distributed power system is defined as follows: This represents the state of x(k) when -d≤k≤0.

[0169] For the model represented by the above formula (10), the Lyapunov method is used to determine whether the model converges, and the Lyapunov-Krasovskii functional is constructed as follows:

[0170]

[0171] Among them, V, V i They are V(k) and V i (k) is an abbreviation.

[0172] ①V1=ζ T (k)Pζ(k),

[0173] ②

[0174] ③

[0175] ④

[0176] ⑤

[0177] S502, by performing forward difference, analysis and scaling on the functional, obtains a new convergence condition for the time-delay-dependent algorithm that balances conservatism and complexity.

[0178] For formula (11), in V(k), y(k):=x(k+1)-x(k); calculating the forward difference of V(k) yields:

[0179] ΔV1=ζ T (k+1)Pζ(k+1)-ζ T (k)Pζ(k)

[0180]

[0181]

[0182]

[0183]

[0184] First, in ΔV3 Split:

[0185]

[0186] In ΔV5 Split into separate parts:

[0187]

[0188]

[0189] Equation (A1) is obtained by using inequality scaling techniques:

[0190]

[0191] Where d1 = d(k) - d;

[0192]

[0193]

[0194]

[0195]

[0196] For equation (A2) With equation (A3) After processing, we can obtain:

[0197]

[0198] Add equations (A4) and (A5) together, and determine which contains... By merging the terms and then applying the inverse convex combination property, we can obtain:

[0199]

[0200] Furthermore, due to the use of the reciprocal convex combination property, the above inequality must satisfy the following conditions to hold:

[0201]

[0202] Then, scaling the remaining summation terms of ΔV, for ΔV3... After processing, we can obtain:

[0203]

[0204] For ΔV4 After processing, we can obtain:

[0205] For equation (A2) After processing, we can obtain:

[0206] For equation (A3) After processing, we can obtain:

[0207]

[0208]

[0209] Then, by uniformly representing the remaining summation terms of ΔV using the variables in ξ(k), we can obtain the following inequality relationship:

[0210] ΔV≤ξ T (k)(Ω1+Ω2-Γ)ξ(k)

[0211] According to Lyapunov stability theory, when ΔV < 0, i.e., there exists a negative time matrix (Ω1 + Ω2 - Γ), the system is asymptotically stable, meaning the distributed economic scheduling algorithm converges. In other words, this step, through forward differencing, analysis, and scaling of the aforementioned V(k), yields a new convergence condition for the time-delay-dependent algorithm that balances conservatism and complexity. Specifically,

[0212] Assuming conditions 1) and 2) hold, for a time-varying delay d(k), Model (10), if d exists, With positive definite matrix Q1, Q2, R1, R2, Z1, Z2, Z3, Make When equations (12) and (13) hold simultaneously with d(k) = d, the new distributed economic scheduling algorithm model converges, where w is the order of the system matrix A; Q1~S are matrices to be determined.

[0213] Ω1+Ω2-Γ<0 (12)

[0214]

[0215] in,

[0216] Ω1 = (Π1 - Π2) T PF(d(k))+F(d(k)) T P(Π1-Π2)

[0217]

[0218]

[0219] e0 = Ae1 - A d e3

[0220] e θ =[0 w×[w×(θ-1)] I w×w 0 w×[w×(13-θ)] ] T ,θ=1,2,...,13

[0221]

[0222]

[0223]

[0224] Π1=col{e0(d+1)e5-e2-e3-e4}

[0225] Π2=col{e1(d+1)e5-e1-e2-e3}

[0226] M1=col{e1-e2e1+e2-2e5e1-e2+6e5-6e8}

[0227] M2=col{e2-e3e2+e3-2e6e2-e3+6e6-6e9}

[0228] M3=col{e3-e4e3+e4-2e7e3-e4+6e7-6e 10}

[0229] M4=col{e1-e5e1+2e5-3e8e1-3e5+12e8-10e 11}

[0230] M5=col{e2-e5e2-4e5+3e8e2-9e5+18e8-10e 11}

[0231] M6=col{e2-e6e2+2e6-3e9e2-3e6+12e9-10e 12}

[0232] M7=col{e3-e7e3+2e7-3e 10 e3-3e7+12e 10 -10e 13}

[0233] M8=col{e3-e6e3-4e6+3e9e3-9e6+18e9-10e 12}

[0234] M9=col{e4-e7e4-4e7+3e 10 e4-9e7+18e 10 -10e 13}

[0235] F(d(k))=col{0 13w×w 0 13w×w (d1+1)e6+(d2+1)e7}

[0236] Regarding the matrix settings throughout the embodiments of this invention, it is necessary to add that, Let represent the set of all real matrices p × q. Let p represent the set of all symmetric positive definite real matrices.

[0237] Through S502, a new convergence condition for time-delay-dependent algorithms that balances conservatism and complexity can be obtained, so as to provide a time-delay-dependent convergence criterion for time-delay-dependent algorithms such as the new distributed economic scheduling algorithm model.

[0238] S503, based on the convergence conditions of the new time-delay-dependent algorithm, determines the tolerance of the new distributed economic scheduling algorithm model to time delay.

[0239] Specifically, the latency tolerance of the new distributed economic scheduling algorithm model can be judged based on the aforementioned convergence conditions. For example, based on the convergence conditions, the latency that the new distributed economic scheduling algorithm model can withstand when d=1 can be calculated, and so on. Within the allowable latency range, the new distributed economic scheduling algorithm model can guarantee convergence.

[0240] Furthermore, it allows for the assessment of the convergence of the optimal solution to the new distributed economic scheduling algorithm model. Specifically, the optimal solution to the optimization problem can be obtained using the Lagrange multiplier method. When a distributed power system reaches equilibrium under a new distributed economic dispatch algorithm model, it has... Therefore, we can obtain ∈1Lλ(k)=ιm(k), by using the Laplace matrix property. We can conclude that at this point, the local power mismatch m(k) = 0, which means the system's power supply and demand are balanced. Multiplying equation (4) by... You can obtain the total power generation (total load demand) and The relationship between them is because the incremental cost of each node is consistent when the algorithm converges, i.e., λ1 = λ2 = ... = λ N Therefore, we can conclude that the incremental cost at this point is equal to λ. * Under the premise of algorithm convergence, the semi-homomorphic encrypted distributed economic dispatch method for power systems proposed in this embodiment of the invention can achieve consistency of incremental costs and ensure that the total power generation of the system is equal to the total load demand. The algorithm converges to the optimal solution of optimization problem (2).

[0241] S504, using a preset simulation platform, simulates the average computation time of encryption / decryption and computation operations during the process of obtaining the weighted difference of state information through a single encrypted transmission between neighboring generators.

[0242] Please see the experimental section below for this part.

[0243] S505 determines the time required for one iteration based on tolerance and numerical magnitude in order to achieve convergence in a shorter time.

[0244] It can be understood that the latency tolerance of the new distributed economic scheduling algorithm model can be expressed as the maximum allowable upper bound of latency that the new distributed economic scheduling algorithm model can withstand in steps, such as 7 steps. The sampling interval time represents the step size of each step, that is, the time required for one iteration. In this embodiment of the invention, the range of total latency can be estimated by referring to the obtained numerical magnitude, and an appropriate sampling interval time can be selected according to the obtained tolerance level, so that the total latency does not exceed the maximum allowable upper bound of latency, so as to achieve the convergence of the algorithm in a shorter time.

[0245] To facilitate understanding, the following example illustrates this: Assume the numerical magnitude is 1 second, the tolerance is 10 steps, and convergence is achieved in 60 steps. The estimated total delay is approximately 4 seconds. Therefore, the algorithm can iterate every 0.5 seconds, resulting in a maximum tolerance of 10 * 0.5 = 5 seconds. It's clear that the estimated total delay does not exceed the upper limit represented by this maximum tolerance, and convergence is achieved in 0.5 * 60 = 300 seconds. However, if the algorithm iterates every 1 second, convergence would require 1 second * 60 = 600 seconds. This demonstrates that choosing an appropriate sampling interval can lead to faster convergence.

[0246] The above is a description of the construction and verification process of the new distributed economic scheduling algorithm model.

[0247] For S4, each generator executes the economic scheduling steps using a pre-built new distributed economic scheduling algorithm model, similar to the scheme in (iii) that uses the initial distributed economic scheduling algorithm model to execute the economic scheduling steps. The difference is that the model used is a new distributed economic scheduling algorithm model. The specific process will not be described in detail.

[0248] In the distributed economic dispatch method for power systems with semi-homomorphic encryption provided in this invention, each generator in the distributed power system performs an encrypted information transmission step with its neighboring generators to obtain a weighted difference in state information with each neighboring generator. Then, a pre-constructed new distributed economic dispatch algorithm model is used to execute economic dispatch steps. Specifically, by using the weighted difference in state information with all neighboring generators and the new distributed economic dispatch algorithm model, the generator determines its own updated state information and uses this updated state information to determine power generation, thereby achieving economic dispatch. This invention provides a simple, highly applicable, and secure economic dispatch scheme for distributed power systems. In this process, the information transmission method based on the Paillier algorithm with semi-homomorphic encryption enables secure and private information exchange, ensuring that information is not stolen or tampered with externally, while also guaranteeing that the privacy of any node is confidential to other nodes.

[0249] Furthermore, the novel distributed economic dispatch algorithm model pre-constructed in this embodiment of the invention is redesigned based on the characteristics of the Paillier algorithm with semi-homomorphic encryption. The construction process involves first addressing the optimization problem of minimizing generation costs in the economic dispatch of distributed power systems. An initial distributed economic dispatch algorithm model is determined using generator state information. Then, based on the properties of the Paillier algorithm with semi-homomorphic encryption, an information exchange scheme is designed to enable each generator to perform encrypted information transmission steps. The initial distributed economic dispatch algorithm model is then used to execute economic dispatch steps to complete the economic dispatch. To analyze the impact of encrypted information transmission on the initial distributed economic dispatch algorithm model, it is modeled as a time delay effect. The impact of time delay on the initial distributed economic dispatch algorithm model is then analyzed to update the algorithm model, thereby obtaining the new distributed economic dispatch algorithm model. This embodiment of the invention fully considers the impact of privacy protection schemes on the proposed initial distributed economic dispatch algorithm model, modeling it as a time-varying time delay with greater practical significance in engineering applications. Finally, a new distributed economic dispatch algorithm model under privacy protection is presented.

[0250] Furthermore, this embodiment of the invention pre-verifies the convergence performance of the novel distributed economic scheduling algorithm model. By performing forward differencing and other processing on the constructed multi-sum Lyapunov-Krasovskii functional, a new time-delay-dependent algorithm convergence condition that balances conservatism and complexity is obtained. This condition can be used to determine the latency tolerance of the novel distributed economic scheduling algorithm model. During the process of obtaining the weighted difference of state information through a single encrypted transmission between neighboring generators, the average computation time of encryption / decryption and arithmetic operations is obtained through simulation. Combined with the obtained latency tolerance, the sampling interval is determined to achieve a faster convergence speed. Experiments have confirmed that, within the allowable latency range, the novel distributed economic scheduling algorithm model of this invention can guarantee convergence and converges to the global optimum of the optimization problem under normal operation, thus exhibiting good performance.

[0251] To facilitate understanding of the effects of the methods in the embodiments of the present invention, the following description uses experimental data from a specific embodiment.

[0252] Consider a distributed power system consisting of 3 nodes, each containing a generator and a load. The communication topology of this system is as follows: Figure 3 As shown, circles represent nodes, and numbers within the circles represent node numbers. The weights of each edge are already specified. Figure 3 The numbers are marked on the sides.

[0253] Table 1 shows the cost function fitting parameters and generation limits for the generators at each node. The node loads are 300MW, 400MW, and 500MW, and the initial generation capacities are 500MW, 450MW, and 360MW, respectively.

[0254] Table 1. Generator Cost Calculation Parameters and Power Generation Limitations

[0255]

[0256] In a distributed power system, the initial distributed economic dispatch algorithm model shown in Equation (8) is used:

[0257]

[0258] The initial parameter settings for the distributed economic scheduling algorithm model are as follows: ι = 8.0 * 10 -4 ∈1=1 / 100, ∈2=1 / 100, the module used to generate the Paillier encryption key is set to 64 bits, the simulation platform is MATLAB, located in a laptop with a 2.2GHz Intel Core i7 and 16GB of memory. According to multiple experiments, the average computation time of encryption, decryption and operation in the process of obtaining the weighted difference value through a single encrypted transmission (i.e., information exchange) between neighbors is on the order of 10ms. This means that the minimum latency of each control moment after removing the time consumed by communication is 10ms. Therefore, the sampling interval is set to 10ms to obtain a faster convergence speed.

[0259] pass Figure 2 The information transmission method based on the Paillier algorithm with semi-homomorphic encryption shown protects the transmission information of the distributed power system. Its impact on the initial distributed economic dispatch algorithm model is modeled as a time-varying delay d(k). For generator i, state λ i (k) and m i (k) Iteration is performed based on the weighted difference between the generator's own information and the state information of neighboring generators, the latter of which needs to be obtained through interaction. The initial distributed economic scheduling algorithm model uses the L matrix to describe the weighted difference of state information. Therefore, after using the privacy protection scheme, the model needs to be adjusted as follows to become the new distributed economic scheduling algorithm model shown in formula (9):

[0260]

[0261] For this system, when the time delay-dependent convergence criterion obtained by the method of the present invention is calculated to d=1, the new distributed economic scheduling algorithm model has a maximum allowable upperbound (MAUBs) of 7 steps, which represents the tolerance of the new distributed economic scheduling algorithm model to time delay.

[0262] Next, we verify the optimality of the new distributed economic dispatch algorithm model. Using the Lagrange multiplier method, we can obtain the optimal value of the incremental cost of the distributed power system as λ. * = $18.4 / MWh. First, let's verify the case with a fixed delay, based on the above calculation results. Set the latency caused by the secure transmission scheme to the maximum allowable value in 7 steps. Figure 4 and Figure 5 They were given respectively This is a graph showing the trajectory of local mismatch in a distributed power system, specifically the local mismatch between power generation and consumption, and the changes in incremental costs. The horizontal axis represents the number of iterations. i IC represents a local mismatch at node i. i Indicates incremental cost. From Figure 4 As can be seen, the local mismatch of each node eventually tends to 0, which means that all the electricity demand of the distributed power system is met. Figure 5 This shows that the incremental cost of each node eventually reaches a consensus, converging at $18.4 / MWh.

[0263] Furthermore, considering the case of time-varying delay, we set d(k) = randi(7,1,1), where the randi(7,1,1) function can generate pseudo-random integers between 1 and 7. The time-varying delay d(k) generated by this function is shown in [link to relevant documentation]. Figure 8 . Figure 6 The graph shows the variation curves of local mismatch. It can be seen that the local mismatch curves all converge to 0, thus achieving a balance between power supply and demand. Figure 7 The graph showing the incremental cost variation indicates that the incremental cost of each node is $18.4 / MWh when the algorithm converges, which is consistent with the calculation results. This shows that the proposed economic dispatch scheme can guarantee the supply and demand balance of the power system and make the incremental cost reach the optimal value, thus achieving the goal of cost minimization.

Claims

1. A semi-homomorphic encrypted distributed economic dispatch method for power systems, characterized in that, Applied to a distributed power system consisting of multiple nodes, each node containing an independent generator and load; the method includes: Obtain the undirected weighted graph of the distributed power system; For each edge in the undirected weighted graph, the weight of the edge is split into two positive integer factors, and one of these positive integer factors is assigned as the decomposition weight to each of the two generators associated with the edge. Each generator performs an encrypted information transmission step, including: each generator, as the transmission initiator, transmits encrypted information with its neighboring generators based on their respective state information and decomposition weights, using a Paillier algorithm-based semi-homomorphic encryption method, so that the generator acting as the transmission initiator obtains a weighted difference in state information with each of its neighboring generators; wherein, the state information includes the generator's incremental cost at each time point, and the local mismatch between power generation and power consumption. Each generator executes economic scheduling steps using a pre-built new distributed economic scheduling algorithm model, including: the generator that initiates the transmission uses the weighted difference between its state information and that of all neighboring generators and the new distributed economic scheduling algorithm model to determine its updated state information, and uses its updated state information to determine the amount of electricity generated. The new distributed economic dispatch algorithm model is designed to address the optimization problem of minimizing generation costs in the economic dispatch of distributed power systems. It utilizes generator state information to determine the initial distributed economic dispatch algorithm model. Each generator performs an information encryption transmission step. After each generator performs the economic dispatch step using the initial distributed economic dispatch algorithm model, in order to analyze the impact of information encryption transmission on the initial distributed economic dispatch algorithm model, it is modeled as a time delay effect. After analyzing the impact of time delay on the initial distributed economic dispatch algorithm model, the algorithm model is updated.

2. The semi-homomorphic encryption distributed economic dispatch method for power systems according to claim 1, characterized in that, The construction process of the initial distributed economic scheduling algorithm model includes: For the aforementioned distributed power system, the generator generation cost function is determined as follows: Among them, C i (p i ) represents the power generation cost of generator i; p i α represents the amount of electricity generated by generator i; i β i γ i represents the cost coefficient fitted for generator i; N represents the total number of nodes in the distributed power system; i = 1, 2, ..., N; Using the aforementioned generation cost function, the optimization problem for minimizing generation costs in the economic dispatch of the distributed power system is as follows: The communication topology of the distributed power system is represented by an undirected weighted graph; P d This represents the total load power demand of the distributed power system; and These represent the lower limit and upper limit of generator i's power output, respectively; The iterative formula for determining the incremental cost of the generator is: Where, N i Let L represent the set of neighboring generators of generator i; ∈1 denotes a constant first step length, ∈1≤1 / q, where q represents the largest eigenvalue of the Laplace matrix L; when i≠j, the element in the i-th row and j-th column of L is -a. ij When i = j, the element in the i-th row and j-th column of L is the sum of the remaining elements in that row, a. ij The sum of; a ij λ represents the weight of the edge connecting generators i and j in the undirected weighted graph; i (k) represents the incremental cost of generator i at time k; The formula for adjusting power generation based on the incremental cost of the generator is: p(k+1)=Bλ(k+1)-[σ1,σ2,...,σ N ] T Where, p(k) = col{p1(k), p2(k), ..., p N (k)};p i (k) represents the power generation of generator i at time k; λ(k) = col{λ1(k),λ2(k),...,λ N (k)};col represents a column vector;σ i =β i / 2γ i B = diag(1 / 2γ) i ); diag represents a diagonal matrix; when season when season To ensure that the system's power generation matches the load's power consumption, a partial mismatch between power generation and power consumption is introduced: m(k)=col{m1(k),m2(k),...,m N (k)}; and determine the iterative expression for the local mismatch between power generation and power consumption as: m(k+1)=m(k)-∈2Lm(k)-[p(k+1)-p(k)]; where m(k) represents the local mismatch between power generation and power consumption at time k; ∈2 represents the constant second step size, ∈2≤1 / q; The local mismatch between the power generation and the power consumption is introduced into the iterative formula of the incremental cost of the generator as feedback for the adjustment of the total power generation. The updated iterative formula of the incremental cost of the generator is: λ(k+1)=λ(k)-∈1Lλ(k)+ιm(k); where ι is the feedback coefficient; By simultaneously solving the formula for adjusting power generation based on the incremental cost of generators, the iterative expression for the local mismatch between power generation and electricity consumption, and the iterative formula for the incremental cost of updated generators, the initial distributed economic scheduling algorithm model is obtained as follows: Where I represents the identity matrix.

3. The semi-homomorphic encryption distributed economic dispatch method for power systems according to claim 1, characterized in that, For each edge in the undirected weighted graph, the weight of that edge is decomposed into two positive integer factors, and one of these positive integer factors is assigned as the decomposed weight to each of the two generators associated with that edge. This includes: For the weight a of an edge connecting generator i and generator j in the undirected weighted graph ij According to formula a ij =a i-j ×a j-i a ij Split into a i-j and a j-i Two positive integer factors; where × represents the multiplication sign; i and j are the generator numbers; a i-j Assigning a to generator i as a decomposition weight j-i The weights are assigned to generator j as decomposition weights.

4. The semi-homomorphic encryption distributed economic dispatch method for power systems according to claim 2 or 3, characterized in that, The steps for each generator to perform encrypted information transmission include: Generator i, acting as the transmission initiator, generates public key k using the Paillier algorithm with semi-homomorphic encryption. pi and private key k si and broadcast the public key k to the neighbor's generator. pi ; The generator i uses the public key k pi Regarding its own state information x i Encrypting the initiator's state information ψ(-x) using the opposite of the initiator's state information data. i ); and encrypt the initiator's state information data ψ(-x) i Transmitted to neighboring generator j; The neighboring generator j uses the public key k pi Encrypt its own state information x j , obtain encrypted neighbor state information data ψ(x) j ); The neighbor generator j uses the neighbor status information to encrypt data ψ(x). j ) and the received encrypted data ψ(-x) of the initiator's state information i Based on the semi-homomorphic additive property of the Paillier algorithm for semi-homomorphic encryption, the state information difference is used to encrypt the data ψ(x). j -x i ); The neighboring generator j utilizes its own decomposition weight a j-i Encrypt the difference data ψ(x) in the state information j -x i Perform cumulative multiplication to obtain encrypted data ψ[a], which is the product of the difference between the neighbor decomposition weight state information and the neighbor decomposition weight state information. j-i (x j -x i )], and transmit to the generator i; The generator i uses its private key k si Decrypt the encrypted data ψ[a] of the neighbor decomposition weight state information difference product j-i (x j -x i The decomposition weight a of the neighboring generator j is obtained. j-i The difference between the two state information (x) j -x i The product of ) a j-i (x j -x i The initiator decrypts the data; The generator i utilizes its own decomposition weight a i-j The decrypted data from the initiator is weighted to obtain a weighted difference 'a' between the data and the state information of the neighboring generator j. i-j a j-i (x j -x i ).

5. The semi-homomorphic encryption distributed economic dispatch method for power systems according to claim 4, characterized in that, When generator i, as the initiator of the transmission, performs the information encryption transmission step again, it updates its own public key k. pi And initiate a public key update operation to the neighbor generator j, so that the neighbor generator j can update its public key using the original public key of generator i; In this context, generator i, acting as the transmission initiator, updates its own public key k. pi The process includes: The generator i determines whether a preset condition is met; wherein the preset condition includes: the time interval between the moment when the generator i first performs the information encryption transmission step and the current moment has reached a preset time length; or, the total amount of data sent by the generator i up to the current moment has reached a preset data amount; If at least one preset condition is met, the public key of generator i is updated using its original public key; if no preset condition is met, the original public key of generator i remains unchanged.

6. The semi-homomorphic encryption distributed economic dispatch method for power systems according to claim 5, characterized in that, The process in which the neighbor generator j updates its public key using the original public key of the generator i includes: The generator j selects a basic operation method and an operand according to the information of multiple bytes used as an information update flag bit in a pre-agreed transmission data packet. Using the basic operation method and the operand, a basic operation is performed on the original public key of the generator i to obtain the updated public key of the generator i.

7. The semi-homomorphic encryption distributed economic dispatch method for power systems according to claim 6, characterized in that, Before splitting the weight of each edge in the undirected weighted graph into two positive integer factors, the method further includes: When the preset condition is satisfied, the weight of this edge is updated; otherwise, the weight of this edge remains unchanged.

8. The semi-homomorphic encryption distributed economic dispatch method for power systems according to claim 5, characterized in that, The process in which each generator executes the economic dispatch step using the initial distributed economic dispatch algorithm model includes: The generator acting as the transmission initiator determines its own updated state information using the weighted difference of the state information with all neighbor generators and the initial distributed economic dispatch algorithm model, and determines the power generation amount using its own updated state information.

9. The semi-homomorphic encryption distributed economic dispatch method for power systems according to claim 8, characterized in that, The process of analyzing the influence of time delay on the initial distributed economic dispatch algorithm model and updating the algorithm model to obtain the new distributed economic dispatch algorithm model includes: Modeling the influence of the information transmission method of the Paillier algorithm based on homomorphic encryption on the initial distributed economic dispatch algorithm model as a time-varying delay d(k); where d(k) represents the delay at time k; 0 < d ≤ d(k) ≤ d; d and d respectively represent the lower limit and upper limit of the maximum allowable delay. Introducing a time-varying delay d(k) updates the initial distributed economic scheduling algorithm model to a new distributed economic scheduling algorithm model:

10. The semi-homomorphic encryption distributed economic dispatch method for power systems according to claim 9, characterized in that, The new distributed economic dispatch algorithm model has been pre-verified for convergence performance; where the convergence performance verification process includes: Simplifying the new distributed economic dispatch algorithm model and constructing a Lyapunov-Krasovskii functional with multiple summations. Performing forward difference, analysis, and scaling processing on the functional to obtain a new time-delay dependent algorithm convergence condition that takes into account both conservativeness and complexity. According to the new time-delay dependent algorithm convergence condition, determining the tolerance of the new distributed economic dispatch algorithm model to time delay. Using a preset simulation platform to simulate the numerical magnitude of the average calculation time of encryption, decryption, and operation operations during the process of obtaining the weighted difference of state information through one information encryption transmission between neighbor generators. According to the tolerance and the numerical magnitude, determining the time required for one iteration to achieve convergence in a shorter time.

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