Distributed economic dispatching method for smart power grid

Abstract

The invention discloses a distributed economic dispatching method for a smart power grid, and belongs to the field of energy-saving and environment-friendly economic dispatching of the smart power grid. Firstly, an intelligent power grid distributed economic dispatching model is constructed; secondly, combining a dynamic gain coefficient and local weighted average estimation, and designing a finite time consistency economic dispatching algorithm; then, initializing relevant parameters; and finally, updating the output power of the generator by using the finite time consistency economic dispatching algorithm, and outputting related parameters. According to the method, finite time convergence of the dynamic increment cost of the generator can be realized under the conditions of supply and demand balance constraint conditions of the total output power of the generator and upper and lower limit constraint conditions of the output power of the generator, the consumption of communication resources is reduced while the dependence of centralized communication is avoided, and the method is suitable for rapid economic dispatching of a smart power grid.

Description

Technical Field

[0001] The present invention belongs to the field of energy conservation, environmental protection and economic dispatch of smart grids, and in particular to a distributed economic dispatch method for smart grids. Background Art

[0002] With the transformation of the global energy structure and the continuous growth of power demand, the economy and stability of smart grids, as the core of modern power systems, have received extensive attention. Traditional power grids mainly rely on centralized dispatching and depend on centralized control units for global optimization. However, with the large-scale access of distributed energy sources (such as wind energy, solar energy, etc.), the grid structure has become increasingly complex, and the limitations of centralized dispatching methods in terms of real-time performance, flexibility and scalability have become increasingly prominent. In addition, traditional dispatching algorithms usually require high-frequency global communication, which not only increases the burden on the communication network, but also may lead to high latency and resource waste, making it difficult to meet the rapid response requirements of smart grids.

[0003] In the economic dispatch problem of smart grids, the core goal is to minimize the total generation cost under the conditions of meeting the power supply-demand balance and generator output power constraints. Traditional economic dispatch methods usually adopt centralized optimization algorithms, such as linear programming, quadratic programming, etc. Although these methods can achieve global optimality, they rely on the powerful computing power of the central node and global information sharing, and it is difficult to adapt to the dynamic changes in the distributed environment. Especially in the scenario of large-scale distributed energy access, centralized methods face problems such as high computational complexity, large communication overhead, and poor real-time performance, which seriously restrict the operation efficiency of smart grids.

[0004] To solve these problems, distributed economic dispatch methods have gradually become a research hotspot. Distributed methods achieve global optimization through local information interaction, avoiding the communication bottleneck of centralized dispatching. Among them, the consensus algorithm has been widely applied to distributed optimization problems due to its simplicity and scalability. However, traditional consensus algorithms usually require infinite time to converge, making it difficult to meet the rapid dispatch requirements of smart grids. In addition, existing consensus algorithms lack flexibility in terms of dynamic gain and constraint handling, which may lead to slow convergence or inability to meet strict constraint conditions.

[0005] In recent years, the finite-time consensus algorithm has received extensive attention because it can achieve the convergence of the system state within a finite time. Compared with traditional consensus algorithms, the finite-time consensus algorithm has a faster convergence speed and stronger robustness, and is suitable for scenarios with high real-time requirements. However, existing research still has deficiencies in the design of dynamic gain coefficients and the application of local weighted average estimation. Especially when dealing with the upper and lower limits of the generator output power, the algorithm complexity and convergence performance still need to be improved. In addition, how to achieve fast consensus convergence of dynamic incremental costs without relying on global communication is still a key problem to be solved in the field of distributed economic dispatch.

[0006] To address the above challenges, the present invention proposes an intelligent grid distributed economic dispatch method. By combining dynamic gain coefficients with local weighted average estimation, this method designs an efficient finite-time consensus economic dispatch algorithm. The dynamic gain coefficients can be adaptively adjusted according to the system state, significantly improving the convergence speed of the algorithm; the local weighted average estimation realizes global optimization through local information interaction, avoiding the dependence on centralized communication. At the same time, by introducing a second-order smooth penalty function to handle the constraint conditions of the generator output power, it ensures the efficiency of the algorithm while satisfying the constraints. The present invention can achieve the consensus convergence of the generator dynamic incremental cost within a finite time, providing a practical solution for the fast economic dispatch of the intelligent grid.

[0007] The economic dispatch of the intelligent grid is not only related to the stable operation of the power system, but also of great significance for improving energy utilization efficiency and reducing operating costs. With the popularization of distributed energy and the expansion of the grid scale, traditional dispatch methods are difficult to meet the actual needs. By innovatively combining the finite-time consensus theory with dynamic gain technology, the present invention provides an efficient, flexible and economic solution for the distributed economic dispatch of the intelligent grid, with important theoretical value and broad application prospects. Summary of the Invention

[0008] The technical problem to be solved by the present invention is to provide an intelligent grid distributed economic dispatch method in view of the defects of the above-mentioned existing technologies.

[0009] The present invention is implemented as follows: An intelligent grid distributed economic dispatch method includes the following steps:

[0010] Step S1: Construct an intelligent grid distributed economic dispatch model;

[0011] Step S2: Combine dynamic gain coefficients with local weighted average estimation to design a finite-time consensus economic dispatch algorithm;

[0012] Step S3: Initialize the output power of each generator and calculate the initial values of the dynamic incremental cost of each generator and the initial value of the total power generation cost of the smart grid;

[0013] Step S4: Update the output power of the generator by using the finite-time consensus economic dispatch algorithm, and determine whether the dynamic incremental costs of all generators reach the consensus condition. If the consensus condition is reached, end the dispatch process and output the output power of each generator; otherwise, continue to execute Step S4.

[0014] Furthermore, the specific steps of Step S1 are as follows:

[0015] Construct a distributed economic dispatch model for the smart grid, and the model includes: the economic dispatch objective function of the smart grid and the supply-demand balance constraint condition of the total output power of the generator, which are respectively:

[0016]

[0017] where i = 1, 2,..., n; n is the number of generators in the smart grid; is the optimization cost function of the i-th generator, and c i (p i (t)) is the power generation cost function of the i-th generator, and p i (t) is the output power of the i-th generator at time t; α i > 0, β i > 0 and γ i > 0 are the power generation cost coefficients of the i-th generator; h(g i,1 (t)) and h(g i,2 (t)) are second-order smooth penalty functions, which are defined as follows:

[0018]

[0019] ρ > 0, ε > 0, m > 0 and k > 0 are smooth parameters; is the minimum output power of the i-th generator, is the maximum output power of the i-th generator; P D is the total demand power.

[0020] Furthermore, the specific steps of Step S2 are as follows:

[0021] Design a finite-time consensus economic dispatch algorithm by combining the dynamic gain coefficient and the local weighted average estimation, specifically:

[0022] The design of the finite-time consensus economic dispatch algorithm is as follows:

[0023]

[0024] Among them, is the derivative of the output power of the i-th generator with respect to time t; d > 0 is the convergence coefficient; a ij is the element in the i-th row and j-th column of the adjacency matrix A = (a ij ) ∈ R n×n of the communication topology of the generators; sign(·) is the sign function; ξ i (t) is the dynamic incremental cost of the i-th generator at time t, and p and q are positive odd numbers satisfying p < q; is the dynamic gain coefficient, and and are the gain coefficients; is the local weighted average estimate, and is the set of adjacent generators that can communicate with the i-th generator, b i is the number of adjacent generators that can communicate with the i-th generator.

[0025] Furthermore, the specific steps of step S3 are as follows:

[0026] The initial value of the output power of the i-th generator is set to p i (0), and it satisfies Calculate the initial value of its dynamic incremental cost from the initial value of the output power of the i-th generator as: Calculate the initial value of the total power generation cost of the smart grid from the initial value of the output power of the i-th generator as:

[0027] Furthermore, in step S4, it is judged whether the dynamic incremental costs of all generators reach the consensus condition, and this condition is specifically:

[0028]

[0029] Among them, υ > 0 is the dynamic incremental cost convergence threshold.

[0030] The present invention provides a distributed economic dispatch method for a smart grid. Compared with the prior art, the beneficial effects of the present invention are:

[0031] 1. The present invention designs a finite-time consensus economic dispatch algorithm by combining a dynamic gain coefficient with local weighted average estimation, which can achieve finite-time convergence of the dynamic incremental cost of generators while satisfying the supply-demand balance constraint of the total output power of generators and the upper and lower limit constraints of the output power of generators. This method significantly improves the convergence speed of the dispatch process, avoids the defect of long convergence time of traditional consensus algorithms, makes power distribution more efficient and accurate, and greatly improves the economic dispatch efficiency and real-time response ability of the smart grid.

[0032] 2. The present invention adopts a distributed communication architecture to achieve global optimization through local information interaction, avoiding the dependence on global communication of traditional centralized dispatch methods. The introduction of the dynamic gain coefficient further optimizes the utilization rate of communication resources, reduces unnecessary communication overhead, and has higher practicability.

[0033] 3. The present invention introduces a second-order smooth penalty function to handle the upper and lower limit constraints of the output power of generators, optimizing the total generation cost while ensuring that the dispatch result meets strict operating conditions. This method not only improves the economy of the smart grid, but also takes into account the stability and environmental protection of the system, helps to promote the efficient utilization of renewable energy, reduce carbon emissions, conforms to the development trend of green smart grids, and has important social and environmental values. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 is a flowchart of a distributed economic dispatch method for a smart grid according to the present invention;

[0035] Figure 2 is the IEEE 24-node standard power network according to the present invention;

[0036] Figure 3 is the communication topology diagram of each generator according to the present invention;

[0037] Figure 4 is the output power p i (t) versus time graph of each generator according to the present invention;

[0038] Figure 5 is the total output power of the generators according to the present invention versus time graph;

[0039] Figure 6 is the total generation cost of the smart grid according to the present invention versus time graph;

[0040] Figure 7 is the dynamic incremental cost ξ i (t) versus time graph of each generator according to the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0041] The embodiments of the present invention will be described in detail below. Examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention and should not be construed as limiting the present invention.

[0042] Example 1:

[0043] The flow of an intelligent grid distributed economic dispatch method provided in this embodiment is as Figure 1 shown, and specifically includes the following steps:

[0044] Step S1: Construct an intelligent grid distributed economic dispatch model;

[0045] Step S2: Design a finite-time consensus economic dispatch algorithm by combining a dynamic gain coefficient and local weighted average estimation;

[0046] Step S3: Initialize the output power of each generator and calculate the initial value of the dynamic incremental cost of each generator and the initial value of the total power generation cost of the intelligent grid;

[0047] Step S4: Use the finite-time consensus economic dispatch algorithm to update the output power of the generator, and determine whether the dynamic incremental costs of all generators meet the consensus condition. If the consensus condition is met, end the dispatch process and output the output power of each generator; otherwise, continue to execute Step S4.

[0048] In this embodiment, in Step S1 of constructing an intelligent grid distributed economic dispatch model, specifically:

[0049] Construct an intelligent grid distributed economic dispatch model, and the model includes: the economic dispatch objective function of the intelligent grid and the supply-demand balance constraint condition of the total output power of the generator, which are respectively:

[0050]

[0051] where i = 1, 2,..., n; n is the number of generators in the intelligent grid; is the optimization cost function of the i-th generator, and c i (p i (t)) is the power generation cost function of the i-th generator, and p i (t) is the output power of the i-th generator at time t; α i > 0, β i > 0, and γ i > 0 are the power generation cost coefficients of the i-th generator; h(g i,1(t)) and h(g i,2 (t)) is a second-order smooth penalty function, defined as follows:

[0052]

[0053] ρ > 0, ε > 0, m > 0, and k > 0 are smoothing parameters; is the minimum output power of the i-th generator, is the maximum output power of the i-th generator; P D is the total demand power.

[0054] In this embodiment, step S2 combines a dynamic gain coefficient with local weighted average estimation to design a finite-time consensus economic dispatch algorithm, specifically:

[0055] The finite-time consensus economic dispatch algorithm is designed as follows:

[0056]

[0057] where, is the derivative of the output power of the i-th generator with respect to time t; d > 0 is the convergence coefficient; a ij is the (i, j)-th element of the adjacency matrix A = (a ij ) ∈ R n×n of the communication topology of the generators; sign(·) is the sign function; ξ i (t) is the dynamic incremental cost of the i-th generator at time t, and p and q are positive odd numbers satisfying p < q; is the dynamic gain coefficient, and and are gain coefficients; is the local weighted average estimation, and is the set of adjacent generators that can communicate with the i-th generator, b i is the number of adjacent generators that can communicate with the i-th generator;

[0058] The communication topology graph of the smart grid with n generators can be represented by a graph G = {V, ε, A}, where V = {1, 2,..., n} is the set of generator nodes, ε ∈ V × V is the set of edges, is the adjacency matrix, satisfying a ij = 1 (indicating that nodes i and j can communicate with each other) when (i, j) ∈ ε, otherwise a ij = 0; for the i-th generator, its set of adjacent generators is denoted as

[0059] In this embodiment, step S3 specifically includes the following steps:

[0060] The initial output power of the i-th generator is set to p i (0), and it satisfies Calculate the initial value of its dynamic incremental cost from the initial output power of the i-th generator as: Calculate the initial value of the total power generation cost of the smart grid from the initial output power of the i-th generator as:

[0061] In this embodiment, step S4 uses the finite-time consensus economic dispatch algorithm to update the output power of the generator, and determines whether the dynamic incremental costs of all generators reach the consensus condition. If the consensus condition is reached, the dispatch process ends and the output power of each generator is output; otherwise, step S4 continues to be executed; in S4, it is determined whether the dynamic incremental costs of all generators reach the consensus condition, and this condition is specifically:

[0062]

[0063] where υ>0 is the dynamic incremental cost convergence threshold.

[0064] Embodiment 2:

[0065] Embodiment 2 uses the proposed distributed economic dispatch method for smart grid to perform numerical simulation on the IEEE 24-node standard power network. There are 10 generators in total, Figure 2 which is the IEEE 24-node standard power network of the present invention; Figure 3 which is the communication topology diagram of each generator of the present invention.

[0066] Initialize the output power of each generator and calculate the initial value of the dynamic incremental cost of each generator and the initial value of the total power generation cost of the smart grid;

[0067] The power generation cost function of each generator in the smart grid is all c i (p i (t)) = α i p i 2 (t) + β i p i (t) + γ i , and Table 1 shows the power generation cost coefficients α i , β i , γ iand the upper and lower limits of the generator output power; the initial values of the output powers of each generator are set to p1(0) = 45 MW, p2(0) = 40 MW, p3(0) = 55 MW, p4(0) = 30 MW, p5(0) = 80 MW, p6(0) = 75 MW, p7(0) = 60 MW, p8(0) = 25 MW, p9(0) = 20 MW and p 10 (0) = 70 MW; the total demand power From the formula calculate the initial values of the dynamic incremental costs of each generator to be ξ1(0) = 9.20 $ / MW, ξ2(0) = 9.50 $ / MW, ξ3(0) = 8.66 $ / MW, ξ4(0) = 7.90 $ / MW, ξ5(0) = 12.60 $ / MW, ξ6(0) = 14 $ / MW, ξ7(0) = 9.46 $ / MW, ξ8(0) = 5.40 $ / MW, ξ9(0) = 6.30 $ / MW and ξ 10 (0) = 8.92 $ / MW; from the formula calculate the initial value of the total power generation cost of the smart grid to be The smoothing parameters are set to ρ = 0.4, ε = 0.009, m = 2 and k = 1; the convergence coefficient is set to d = 10; the gain coefficient is set to and The dynamic incremental cost convergence threshold is set to υ = 0.001; other parameters are set to p = 1 and q = 5; according to the communication topology, b1 = 3, b2 = 3, b3 = 2, b4 = 4, b5 = 2, b6 = 2, b7 = 2, b8 = 2, b9 = 4, b 10 = 2 and the adjacency matrix A is:

[0068]

[0069] Table 1

[0070]

[0071] Substitute the above parameters into the finite-time consensus economic dispatch algorithm, and the specific formula is as follows:

[0072]

[0073] Use the algorithm to update the generator output power, and judge whether the dynamic incremental costs of all generators meet the consensus condition. If the consensus condition is met, end the dispatch process and output the output power p i (t) of each generator, otherwise continue to update the generator output power; judge whether the dynamic incremental costs of all generators meet the consensus condition, and this condition is:

[0074] Finally, based on the given data, the effectiveness of the present invention is verified through numerical simulation. Figure 4 For the output power p i (t) of each generator of the present invention over time, where, from Figure 4 it can be seen that at the convergence time t = 1.7 s, the optimal values of the generator output powers are respectively p1(0) = 44.66 MW, p2(0) = 38.00 MW, p3(0) = 59.32 MW, p4(0) = 39.57 MW, p5(0) = 51.20 MW, p6(0) = 44.66 MW, p7(0) = 57.27 MW, p8(0) = 55.00 MW, p9(0) = 40.31 MW and p 10 (0) = 70.00 MW, satisfying the upper and lower limit constraint conditions of the generator output power; Figure 5 For the total output power of the generators of the present invention over time, where, from Figure 5 it can be seen that the total output power of the generators does not change over time, satisfying the supply-demand balance constraint condition of the total generator output power; Figure 6 For the total power generation cost of the smart grid of the present invention over time, where, from Figure 6 it can be seen that the total power generation cost of the smart grid of the present invention gradually decreases from the initial 3600.15$ to 3380.59$, achieving the goal of minimizing the total power generation cost of the smart grid; Figure 7 For the dynamic incremental cost ξ i (t) of each generator of the present invention over time, where, from Figure 7 it can be seen that at the convergence time t = 1.7 s, the dynamic incremental costs of each generator converge to 9.15 $ / MW.

[0075] It should be noted that: The above are only preferred examples of the present invention and are not used to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, for those skilled in the art, they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements for some of the technical features. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. An intelligent power grid distributed economic dispatch method, characterized in that, It includes the following steps: Step S1: Construct a distributed economic dispatch model for the smart grid; Step S2: Design a finite-time consensus economic dispatch algorithm by combining dynamic gain coefficients with locally weighted average estimation; Step S3: Initialize the output power of each generator and calculate the initial value of the dynamic incremental cost of each generator and the initial value of the total power generation cost of the smart grid; Step S4: Update the output power of the generator by using the finite-time consensus economic dispatch algorithm, and determine whether the dynamic incremental costs of all generators meet the consensus condition. If the consensus condition is met, end the dispatch process and output the output power of each generator; otherwise, continue to execute Step S4.

2. The intelligent grid distributed economic dispatch method according to claim 1, characterized in that, The specific steps of Step S1 include the following steps: Construct a distributed economic dispatch model for the smart grid, and the model includes: the economic dispatch objective function of the smart grid and the supply-demand balance constraint condition of the total output power of the generators, which are respectively: where \(i = 1, 2, \ldots, n\); \(n\) is the number of generators in the smart grid; is the optimization cost function of the \(i\)-th generator, and c i (p i (t)) is the power generation cost function of the \(i\)-th generator, and p i (t) is the output power of the \(i\)-th generator at time \(t\); \(\alpha\) i > 0, \(\beta\) i > 0 and \(\gamma\) i > 0 are the power generation cost coefficients of the \(i\)-th generator; \(h(g\) i,1 (t)) and \(h(g\) i,2 (t)) are second-order smooth penalty functions, defined as follows: ρ > 0, ε > 0, m > 0, and k > 0 are smooth parameters; is the minimum output power of the i-th generator, is the maximum output power of the i-th generator; P D is the total demand power.

3. The intelligent grid distributed economic dispatch method according to claim 2, characterized in that, The specific steps of Step S2 include the following steps: Design a finite-time consensus economic dispatch algorithm by combining dynamic gain coefficients with locally weighted average estimation, specifically: The finite-time consensus economic dispatch algorithm is designed as follows: wherein, is the derivative of the output power of the i-th generator with respect to time t; d > 0 is the convergence coefficient; a ij is the adjacency matrix of the generator communication topology A = (a i j) ∈ R n×n at the i-th row and j-th column; sign(·) is the sign function; ξ i (t) is the dynamic incremental cost of the i-th generator at time t, and p and q are positive odd numbers satisfying p < q; is the dynamic gain coefficient, and and are the gain coefficients; is the local weighted average estimate, and is the set of adjacent generators that can communicate with the i-th generator, b i is the number of adjacent generators that can communicate with the i-th generator.

4. The intelligent grid distributed economic dispatch method according to claim 3, characterized in that, The specific steps of Step S3 include the following steps: The initial value of the output power of the i-th generator is set to p i (0), and it satisfies The initial value of the dynamic incremental cost is calculated from the initial value of the output power of the i-th generator as follows: The initial value of the total power generation cost of the smart grid is calculated from the initial value of the output power of the i-th generator as follows:

5. An intelligent power grid distributed economic dispatch method according to claim 4, characterized in that, In Step S4, determine whether the dynamic incremental costs of all generators meet the consensus condition, and this condition is specifically: where, υ>0 is the convergence threshold of the dynamic incremental cost.

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