Smart grid economic dispatch method based on single-point feedback and differential privacy mechanism

Abstract

The application discloses a kind of intelligent power grid economic dispatching methods based on single-point feedback and differential privacy mechanism, comprising: establishing intelligent power grid economic dispatching model;Intelligent power grid economic dispatching model is further converted into corresponding minimization problem;Individual regret is constructed as distributed online economic dispatching method performance evaluation index for distributed online economic dispatching problem;Individual regret is used to reflect the difference between the total cost of power generation and the total cost of optimal power generation;Single-point feedback and differential privacy mechanism are introduced to design distributed economic dispatching method based on surplus variable, and the intelligent power grid economic dispatching model is iteratively solved according to the designed economic dispatching method.The present application can solve the problem of online economic dispatching in uncertain environment, while effectively protecting the privacy information of power generator.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of smart grid economic dispatch, and particularly relates to a smart grid economic dispatch method based on a differential privacy mechanism. BACKGROUND

[0002] Economic dispatch problem is one of the basic problems in power grid operation, and the goal is to dispatch generators to meet the total demand at the minimum cost under the premise of meeting supply and demand balance and various constraint conditions. At present, quite a number of centralized methods have been proposed to solve the economic dispatch problem, such as particle swarm algorithm, differential evolution algorithm and quasi-Newton method. However, in the above centralized control framework, all generators need a central controller to collect information and calculate the optimal solution. The existence of the controller puts requirements on the communication and computing capacity of the power grid, and at the same time easily leads to single point failure and privacy leakage and other problems. Distributed economic dispatch method only needs to exchange information with neighbors, so it is easy to handle single point failure and reduces the computing and communication cost.

[0003] At present, most of the existing distributed economic dispatch algorithms are based on the distributed optimization algorithm of multi-agent system. Since the Lagrange multiplier method can convert the economic dispatch problem into a constraint problem characterized by the Lagrange multiplier, the distributed economic dispatch method based on the Lagrange multiplier method has been widely studied. In the economic dispatch problem, the Lagrange multiplier is usually referred to as the incremental cost. By selecting the incremental cost as the consensus variable, when the incremental cost of all generators achieves consensus, the total generation cost will reach the minimum, and the economic dispatch problem is solved. The existing algorithms can solve the economic dispatch problem when the cost function of the generator is known.

[0004] The invention with publication number CN115473286A provides a distributed economic dispatch optimization method based on constraint projection reinforcement learning, which includes: based on the operation constraints, combining the generation cost function and the feasible power output of the generating unit to construct a distributed economic dispatch mathematical model; implementing the average consistency method for each generator in the regional communication network to obtain the global information in the microgrid in a distributed manner; using the Actor-Critic algorithm to convert the distributed economic dispatch mathematical model into a distributed economic dispatch optimization problem based on constraint projection; combining the Lagrange multiplier method with the penalty function method to obtain the augmented Lagrange dual form of the optimization problem, and based on the KKT condition to obtain the optimal power output of the distributed economic dispatch optimization problem. The invention can effectively coordinate the power output of the generators in the microgrid without worrying about the construction of the cost function, and can complete the distributed scheduling task through feedback interaction with the unknown load bus. The invention with publication number CN105809297A provides a thermal power plant environmental economic dispatch method based on a multi-objective differential evolution algorithm, which includes the following steps: establishing a thermal power plant environmental economic dispatch model with the lowest generation cost and the smallest pollutant emission as the dispatch target, and the generator capacity and power balance as the constraint condition; then using a multi-objective differential evolution algorithm to optimize and solve the model to obtain an optimal Pareto solution set, wherein the multi-objective differential evolution algorithm uses a differential mutation operator to search, selects a mutation operator based on the usage frequency and cumulative performance of each operator in the last several mutation operations each time, and uses methods such as non-dominated sorting, dominance frequency, and hyper-volume contribution to ensure the convergence and uniformity of the solution set; finally, using fuzzy set theory to make decisions and selecting a compromise solution from the Pareto solution set as the final scheduling scheme. The invention method has the characteristics of high precision, uniform distribution of Pareto frontier solution set, and fast convergence speed, and is easy to implement in engineering.

[0005] However, in actual application scenarios, economic dispatch problems usually occur in uncertain environments, and the cost function of the generator is unknown, which makes it difficult to obtain the gradient or subgradient information of the cost function. Such problems can be regarded as distributed online economic dispatch problems, and static regret is often used to measure the performance of online economic dispatch algorithms.

[0006] In addition, with the increasing number of generators and power users in the smart grid, the amount of data in the power system has significantly increased. Therefore, the problem of privacy protection in economic dispatch also needs to be paid attention to. SUMMARY

[0007] The technical problem solved by the present application is that the present application discloses a smart grid economic dispatch method based on a differential privacy mechanism, which can solve the online economic dispatch problem in an uncertain environment, and can effectively protect the privacy information of the generator.

[0008] Technical scheme:

[0009] An intelligent power grid economic dispatch method based on single-point feedback and differential privacy mechanism, the intelligent power grid economic dispatch method comprising the following steps:

[0010] S1, establishing an intelligent power grid economic dispatch model, the intelligent power grid economic dispatch model comprising total generation cost constraints of generators in the intelligent power grid, generation constraints and supply-demand balance constraints;

[0011] S2, further converting the intelligent power grid economic dispatch model established in step S1 into a corresponding minimization problem;

[0012] S3, constructing individual regret for distributed online economic dispatch problem as a performance evaluation index of the distributed online economic dispatch method; individual regret for reflecting the difference between the total cost of the power generation of the generator j and the total cost of the optimal power generation;

[0013] S4, introducing single-point feedback and differential privacy mechanism to design a distributed economic dispatch method based on surplus variables, and iteratively solving the intelligent power grid economic dispatch model according to the designed economic dispatch method.

[0014] Further, in step S1, the intelligent power grid economic dispatch model is:

[0015]

[0016] wherein N is the number of generators in the intelligent power grid, is the power generation of the i-th generator at time t, represents the generation cost of the i-th generator at time t, and respectively represent the upper limit and the lower limit of the power generation of the i-th generator, P D is the total demand including the load demand P d and the line loss P loss , i.e. P D =P d +P loss .

[0017] Further, in step S2, the process of further converting the intelligent power grid economic dispatch model established in step S1 into a corresponding minimization problem comprises the following steps:

[0018] S21, calculating the line loss by using the following formula:

[0019]

[0020] wherein φ i is the loss coefficient;

[0021] S22, restate the economic dispatch model as

[0022] max F= p d P d -C

[0023]

[0024] where F represents the total revenue of the power grid, C represents the total cost of power generation, p d represents the electricity price;

[0025] S23, adopt a variable vector to represent the power generation vector of the generator where and respectively represent the upper and lower limits of the variable; the balance constraint of active power is represented as:

[0026]

[0027] The smart grid economic dispatch problem of step S1 is converted into:

[0028]

[0029] S24, when p d is a fixed value, the size of F is only related to ; let the original smart grid economic dispatch problem be transformed into the corresponding minimization problem:

[0030]

[0031] where represents the power generation constraint.

[0032] Further, in step S3, the individual regret is defined as:

[0033]

[0034] where T represents the total time, is the optimal power generation after iteration.

[0035] Further, in step S4, a single-point feedback and differential privacy mechanism is introduced to design a distributed economic dispatch method based on surplus variables, and the process of iteratively solving the smart grid economic dispatch model according to the designed economic dispatch method includes the following steps:

[0036] S41, design a distributed algorithm based on surplus variables to solve the smart grid economic dispatch problem in step S2:

[0037]

[0038] where, is the updated generated power; denotes the projection of x on the set Ω; ∈ is a positive number to make the algorithm converge; α t denotes the step size, satisfying is the designed single-point feedback gradient estimator to avoid the displayed subgradient calculation, d represents the dimension, and δ is the exploration parameter, is a unit random variable with zero mean; is the auxiliary variable of node i at time t, and its iterative rule is as follows:

[0039]

[0040] [A r ] ij and [A c ] ij is an element in the row random adjacency matrix A r and the column random adjacency matrix A c , and the construction rule is as follows:

[0041]

[0042] where is the number of in-neighbors of node i, is the number of out-neighbors of node j, and ε is the edge set;

[0043] S42, the differential privacy mechanism is introduced to protect the privacy information, and the adjusted distributed algorithm iteration formula is as follows:

[0044]

[0045]

[0046] where, is random noise conforming to Laplace distribution, is the state perturbed by noise .

[0047] Advantages:

[0048] ​Firstly, the smart grid economic dispatch method based on single-point feedback and differential privacy mechanism of the present application firstly attempts to combine differential privacy mechanism with single-point feedback to solve the online economic dispatch problem. When the cost function of the generator is unknown, the single-point feedback mechanism is used to estimate the real gradient information, thereby guiding the update of the decision variable. Only the state information of one node is needed, thereby effectively reducing the calculation cost and improving the calculation efficiency.

[0049] Secondly, the smart grid economic dispatch method based on single-point feedback and differential privacy mechanism of the present application introduces the differential privacy mechanism in the distributed optimization algorithm of online economic dispatch, which can effectively protect the privacy information of the generator. BRIEF DESCRIPTION OF DRAWINGS

[0050] Figure 1 is the single-line diagram of the improved 6-bus system;

[0051] Figure 2 is the communication topology structure diagram of the schedulable agent;

[0052] Figure 3 is the simulation result diagram of the smart grid economic dispatch method of the present embodiment running on the 6-bus system;

[0053] Figure 4 is the simulation result diagram of the supply-demand balance constraint of the smart grid economic dispatch method of the present embodiment running on the 6-bus system;

[0054] Figure 5 is the simulation result diagram of the smart grid economic dispatch method of the present embodiment running on the IEEE162-bus system;

[0055] Figure 6 is the simulation result diagram of the supply-demand balance constraint of the smart grid economic dispatch method of the present embodiment running on the IEEE162-bus system;

[0056] Figure 7 is the flow chart of the smart grid economic dispatch method based on single-point feedback and differential privacy mechanism of the present embodiment. DETAILED DESCRIPTION

[0057] The following embodiments can enable the person skilled in the art to more comprehensively understand the present application, but do not limit the present application in any way.

[0058] Reference Figure 7 The smart grid economic dispatch method based on single-point feedback and differential privacy mechanism in the present embodiment comprises the following steps:

[0059] (1) In this embodiment, we consider the economic dispatch problem on the improved 6-bus system and the improved IEEE 162-bus system, respectively. The single-line diagram of the improved 6-bus system is shown in FIG. 1. The system includes 2 distributed generators (DGs), 1 renewable energy (RG), 1 energy storage system (ESS), 3 loads and 11 transmission lines. The communication topology of the dispatchable agents is shown in FIG. 2. According to the total generation cost of the generators in the smart grid, the generation constraints and the supply-demand balance, the economic dispatch model of the smart grid is established as follows: Figure 1 Figure 2

[0060]

[0061] where N is the number of generators in the smart grid, is the power generation of the i-th generator at time t, represents the generation cost of the i-th generator at time t, and represent the upper and lower limits of the power generation of the i-th generator, respectively, P D is the total demand including the load demand P d and the line loss P loss , i.e. P D = P d + P loss , where the line loss can be calculated by the following formula:

[0062]

[0063] where φ i is the loss coefficient.

[0064] (2) On the basis of the established economic dispatch model, the economic dispatch model is further converted; the economic dispatch model can be re-expressed as:

[0065] max F = ρ d P d - C

[0066]

[0067] where F represents the total income of the grid, C represents the total generation cost, and ρ d represents the electricity price.

[0068] The generation vector of the generator can be represented by the variable vector . Wherein, and represent the upper and lower limits of the variable, respectively. Therefore, the active power balance constraint can be expressed as: ​​

[0069]

[0070] The economic dispatch problem can be further converted into:

[0071]

[0072] When ρ d is a fixed value, the size of F is only related to Let The original economic dispatch problem can be transformed into a minimization problem:

[0073]

[0074] where denotes the power generation constraint.

[0075] (3) Construct performance evaluation indexes of distributed online economic dispatch methods for distributed online economic dispatch problems;

[0076] Define individual regret of online economic dispatch method performance evaluation index It reflects the difference between the total cost of the power generation of generator j and the total cost of the optimal power generation. In form, individual regret is defined as:

[0077]

[0078] where, is the optimal power generation after iteration. If the individual regret of an online economic dispatch method as a function of T is sublinear, i.e. This means that the method can effectively solve the economic dispatch problem, and T represents the total time.

[0079] (4) Introduce single-point feedback and differential privacy mechanism to design distributed economic dispatch methods, and solve the smart grid economic dispatch model according to the designed economic dispatch methods.

[0080] Design a distributed algorithm based on surplus variable to solve the above optimization problem:

[0081]

[0082] where, is the updated power generation; denotes the projection of x on the set Ω; ∈ is a small positive number, which plays a key role in the convergence of the algorithm; α t denotes the step size, which satisfies where, is the designed single-point feedback gradient estimator to avoid explicit subgradient calculation, where d represents the dimension, and δ is the exploration parameter, is a unit random variable with zero mean. In addition, is an auxiliary variable for node i at time t, whose iteration rule is as follows:

[0083]

[0084] [A r ] ij and [A c ] ij is the element in row random adjacency matrix A r and column random adjacency matrix A c , whose construction rule is as follows:

[0085]

[0086] where is the number of inner neighbors of node i, is the number of outer neighbors of node j.

[0087] The differential privacy mechanism is introduced to achieve privacy information protection, specifically adjusting the iteration rule of the distributed algorithm. The iteration formula of the adjusted distributed algorithm is as follows:

[0088]

[0089] Based on the above proposed distributed online economic dispatch method, the privacy information of the node can be effectively protected. In addition, with the increase of the number of iterations, the economic dispatch problem can be effectively solved ultimately.

[0090] The parameter settings of the 6-bus system and the IEEE 162-bus system of this embodiment 6 are as follows:

[0091] The cost function of each schedulable agent in the 6-bus system is quadratic, that is, Table 1 gives the cost coefficients and generation capacity of each schedulable agent. In addition, d = 1, δ = 0.4, ∈ = 0.0001 and ε = 15.

[0092] Table 1 Parameters of three schedulable agents

[0093]

[0094] In the IEEE 162-bus system, the cost function of the system is the same as that of the 6-bus system, where the parameters of the schedulable agent are from the interval a i ∈ [0.45, 0.75], b i ∈ [0.15, 0.25], c i ∈ [0.0035, 0.0078], and The total demand P D = 1350, and the rest of the parameters are the same as the 6-bus system.

[0095] Under the above given conditions, the method proposed in the present application is simulated and verified in the simulink environment, and the simulation results are analyzed, as shown in the attached Figure 2 -Appendix Figure 5 The simulation results are shown in the attached Figure 3 , and the results show that the optimal output power of each schedulable agent is 44.2 MW, 43.3 MW and 17.5 MW, respectively, which meets the capacity constraint. The attached Figure 4 reflects the supply-demand balance constraint in the smart grid, and the results show that the supply-demand balance has been achieved. Therefore, the algorithm can solve the economic dispatching problem with a quadratic cost function on the 6-bus system. Then, the effectiveness of the algorithm on large-scale network systems is verified on the IEEE162-bus system. The simulation results are shown in the attached Figure 5 and the attached Figure 6 . The attached Figure 5 shows that the state of all generators converges to the optimal value under the algorithm. As can be seen from the attached Figure 6 , after a period of iteration, the supply-demand balance is finally met, which shows that the algorithm is still effective for large-scale systems.

[0096] The above examples only illustrate the technical idea of the present application, and cannot limit the protection scope of the present application. Any modification made according to the technical idea of the present application on the basis of the technical scheme falls within the protection scope of the present application.

Claims

1. A smart grid economic dispatch method based on single-point feedback and differential privacy mechanism, characterized in that, The smart grid economic dispatch method comprises the following steps: S1, establishing a smart grid economic dispatch model, wherein the smart grid economic dispatch model comprises a total generation cost constraint of a generator in the smart grid, a generation constraint and a supply-demand balance constraint; S2, further converting the smart grid economic dispatch model established in step S1 into a corresponding minimization problem; S3, individual regret for distributed online economic dispatch problem as a performance evaluation index of distributed online economic dispatch method; individual regret for reflecting the difference between the total cost of the power generation amount of the generator j and the total cost of the optimal power generation amount S4, introducing a single-point feedback and a differential privacy mechanism to design a distributed economic dispatch method based on a surplus variable, and iteratively solving the smart grid economic dispatch model according to the designed economic dispatch method; In step S4, the process of introducing a single-point feedback and a differential privacy mechanism to design a distributed economic dispatch method based on a surplus variable, and iteratively solving the smart grid economic dispatch model according to the designed economic dispatch method comprises the following steps: S41, designing a distributed algorithm based on a surplus variable to solve the smart grid economic dispatch problem in step S2: where N is the number of generators in the smart grid, to update the generated power after the update; denotes the projection of x on the set Ω; ∈ is a positive number to make the algorithm converge; α t denotes the step size, satisfying is a designed one-point feedback gradient estimator to avoid the displayed sub-gradient calculation, d denotes the dimension, and δ is the exploration parameter, is a unit random variable with zero mean; is the auxiliary variable of node i at time t, and its iterative rule is as follows: [A r ] ij and [A c ] ij for the elements in the row stochastic adjacency matrix A r and the column stochastic adjacency matrix A c are constructed as follows: wherein is the number of in-neighbors of node i, is the number of out-neighbors of node j, and ε is the edge set. S42, introducing a differential privacy mechanism to protect private information, and the adjusted distributed algorithm iterative formula is as follows: wherein, is a random noise following a Laplace distribution, is a noise to perturbed state. 2.The smart grid economic dispatch method based on single-point feedback and differential privacy mechanism according to claim 1, characterized in that, In step S1, the smart grid economic dispatch model is: where N is the number of generators in the smart grid, P t i is the power output of the i-th generator at time t, denotes the generation cost of the i-th generator at time t, and P t denote the upper and lower limits of the power output of the i-th generator, P D is the total demand including the load demand P d and the line loss P loss , i.e., P D = P d + P loss . 3.The smart grid economic dispatch method based on single-point feedback and differential privacy mechanism of claim 2, wherein, In step S2, the process of further converting the smart grid economic dispatch model established in step S1 into a corresponding minimization problem comprises the following steps: S21, calculating the line loss by using the following formula: where φ i is the loss coefficient; S22, restate the economic dispatch model as max F = p d P d -C where F represents the total income of the power grid, C represents the total cost of power generation, and p d represents the electricity price; S23, with variable vector represents the generation vector P of the generator t = [P t 1 , P t 2 ,..., P t N ] T wherein, and represent the upper and lower bounds of the variable, respectively; the balance constraint of the active power is expressed as: The smart grid economic dispatch problem in step S1 is converted into: S24, when p d F is a fixed value, the size of F only with related; let The original smart grid economic dispatch problem is transformed into the corresponding minimum problem: wherein represents the power generation constraint. 4.The smart grid economic dispatch method based on single-point feedback and differential privacy mechanism of claim 3, wherein, In step S3, the individual regrets is defined as: where T denotes the total time, is the optimal generation after iteration.

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