Completely distributed economic dispatching optimization method for smart power grid based on fixed time

Abstract

The invention belongs to the field of energy-saving and environment-friendly economic dispatching of a smart power grid, and particularly relates to a fully-distributed economic dispatching optimization method for the smart power grid based on fixed time. The method comprises the steps that firstly, an intelligent power grid economic dispatching model is established, and relevant parameters are initialized; secondly, designing a fixed-time completely distributed consistency algorithm, updating power increment cost based on the algorithm, then processing the power increment cost, updating power output power, judging whether an upper limit of convergence time of the algorithm is reached or not, introducing an intermediate variable if the upper limit of the convergence time of the algorithm is reached, and setting an initial value of the intermediate variable; and finally, designing a fixed-time intermediate variable consistency algorithm, updating and processing related parameters based on the algorithm, judging whether the convergence time upper limit of the algorithm is reached or not, and if the convergence time upper limit of the algorithm is reached, outputting electric power increment cost and electric power output power. The method is completely distributed, and economic dispatching of the intelligent power grid can be achieved within fixed time.

Description

Technical Field

[0001] The present invention relates to the field of smart grid energy conservation and environmental protection economic dispatch, and in particular to a fixed-time based smart grid fully distributed economic dispatch optimization method. Background Art

[0002] With the rapid growth of energy demand and the increasing requirements for environmental protection, smart grid, as an upgraded form of traditional power grid, has gradually become an important research direction in the energy field. Smart grid realizes the two-way interaction of information flow and power flow through the deep integration of modern communication technology and power system, thereby effectively improving energy utilization efficiency and the reliability of power grid operation. In smart grid, economic dispatch problem is one of its core research contents. Its goal is to minimize the operating cost of the system by reasonably allocating the power output power of each generator, while meeting the power supply and demand balance constraints and power output power limit constraints.

[0003] Traditional economic dispatch methods mainly adopt centralized dispatch strategies, that is, the central control center collects data from the entire network and performs optimization calculations. Although this method can provide a global optimal solution, it often faces problems such as heavy computing burden, high communication overhead, and poor robustness when facing large-scale smart grids with complex topologies. Once the central control node fails, the dispatching capacity of the entire system will be seriously affected. In addition, with the widespread access to renewable energy and the rapid development of distributed power generation, the grid structure is becoming increasingly complex, and traditional centralized methods are difficult to adapt to the needs of distributed resource coordination.

[0004] Distributed dispatching methods have gradually become a research hotspot for solving the economic dispatch problem of smart grids because they do not rely on a central control center. Existing distributed methods mainly rely on iterative algorithms to achieve coordinated optimization among generators, but their convergence time usually increases significantly with changes in network scale and topology, making it difficult to meet the requirements for fast dispatch in actual projects.

[0005] Based on the above background, a distributed economic dispatch optimization method is needed which can achieve fast convergence within a fixed time and is suitable for large-scale smart grids with complex topology structures, so as to further improve the dispatch efficiency and reliability of system operation. Summary of the invention

[0006] In view of this, the purpose of the present invention is to provide a fixed-time based fully distributed economic dispatch optimization method for smart grids, which can perform economic dispatch on smart grids.

[0007] The present invention is implemented by the following scheme: a fixed-time smart grid fully distributed economic dispatch optimization method, comprising the following steps:

[0008] Step 1: Establish a smart grid economic dispatch model; determine the adjacency matrix based on the smart grid communication topology, and calculate the Laplace matrix based on the adjacency matrix; initialize relevant parameters;

[0009] Step 2: Design a fixed-time fully distributed consensus algorithm;

[0010] Step 3: Update the incremental electricity cost and power output power based on a fixed-time fully distributed consensus algorithm;

[0011] Step 4: Determine whether the fixed-time fully distributed consistency algorithm convergence time limit has been reached; if the fixed-time fully distributed consistency algorithm convergence time limit has not been reached, return to step 3; if the fixed-time fully distributed consistency algorithm convergence time limit has been reached, proceed to step 5;

[0012] Step 5: Introduce intermediate variables and set their initial values;

[0013] Step 6: Design a fixed-time intermediate variable consistency algorithm;

[0014] Step 7: Update the intermediate variables based on the fixed time intermediate variable consistency algorithm; update the incremental power cost; process the incremental power cost and update the power output power;

[0015] Step 8: Determine whether the upper limit of the convergence time of the fixed-time intermediate variable consistency algorithm has been reached; if the upper limit of the convergence time of the fixed-time intermediate variable consistency algorithm has not been reached, return to step 7; if the upper limit of the convergence time of the fixed-time intermediate variable consistency algorithm has been reached, output the incremental power cost and the power output power.

[0016] Furthermore, the step 1 is specifically as follows:

[0017] Establish a smart grid economic dispatch model, specifically:

[0018]

[0019] p i_min ≤p i (t)≤p i_max

[0020] Wherein, i = 1, 2, ... n; n is the number of generators in the smart grid; is the objective function of the economic dispatch problem, C i (p i (t)) is the electricity cost function of the i-th generator at time t and p i (t) is the power output of the i-th generator at time t, α pi >0,β pi>0 and γ pi >0 is the electricity cost coefficient of the i-th generator; is the power supply and demand balance constraint; p i_min ≤p i (t)≤p i_max is the power output power limit constraint; is the total power demand; p i_min is the minimum output power of the i-th generator; p i_max is the maximum output power of the i-th generator;

[0021] The adjacency matrix A is determined according to the smart grid communication topology, specifically:

[0022]

[0023] Among them, a ij represents the element in the i-th row and j-th column of the adjacency matrix A, where j = 1, 2, ... n; N i represents the set of generators communicating with the i-th generator;

[0024] The Laplace matrix L is calculated based on the adjacency matrix, specifically:

[0025]

[0026] Among them, l ij represents the i-th row and j-th column element of the Laplace matrix L;

[0027] Initialize related parameters, specifically:

[0028] Set the initial value of the power output of the i-th generator to p i (0), and satisfies The initial value of the incremental electricity cost of the i-th generator is λ pi (0) = 2α pi p i (0)+β pi .

[0029] Furthermore, the step 2 is specifically as follows:

[0030] Design a fixed-time fully distributed consensus algorithm, specifically:

[0031]

[0032] Among them, λ pi (t) is the incremental electricity cost of the i-th generator at time t, λ pj (t) is the incremental electricity cost of the jth generator at time t; Denoted as λ pi(t) is the derivative of time t; u(t) is the controller function; sig h (·)=|·|gsign(·), h is a positive constant, sign(·) is the sign function; C 1 , C 2 , C 3 All are greater than 0; m, n, p, q are all positive odd numbers, and m>m and p <q;σ∈(0,1)。

[0033] Furthermore, the fixed-time fully distributed consensus algorithm in step 2 can converge within a fixed time, specifically:

[0034] when hour, The upper limit of convergence time is in Indicated as T 0 The maximum value of the incremental electricity cost of all generators at the moment, Indicated as T 0 The minimum value of the incremental power cost of all generators at the moment; hour, The upper limit of convergence time is in Indicated as T 1 The maximum value of the incremental electricity cost of all generators at the moment, Indicated as T 1 The minimum value of the incremental electricity cost of all generators at that moment.

[0035] Furthermore, the step five is specifically as follows:

[0036] Introduce intermediate variable XX i (t), YY i (t), and set the initial value of the intermediate variable, specifically:

[0037]

[0038] Among them, XX i (0) is the intermediate variable XX i (t) Initial value; YY i (0) is the intermediate variable YY i (t) initial value; if the power output of the i-th generator at time t is p i (t) exceeds the maximum output power p of its generator i_max ,make If the power output of the i-th generator at time t is pi (t) is lower than the minimum output power p of its generator i_min ,make

[0039] Furthermore, the step six is ​​specifically as follows:

[0040] Design a fixed-time intermediate variable consistency algorithm, specifically:

[0041]

[0042]

[0043] in, and Represents the intermediate variable XX i (t) and YY i (t) is the derivative of time t; the algorithm can converge in a fixed time when hour, and The upper limit of convergence time is when hour, and The upper limit of convergence time is λ 2 (L) is the second smallest eigenvalue of the Laplace matrix L.

[0044] Furthermore, the step seven is specifically as follows:

[0045] Update the intermediate variables based on the fixed-time intermediate variable consistency algorithm; update the incremental electricity cost as follows:

[0046]

[0047] in, It is expressed as the convergence value of the incremental cost of the generator electricity under the fixed-time fully distributed consensus algorithm;

[0048] Processing incremental electricity costs, specifically:

[0049]

[0050] Among them, λ i_min and λ i_max They represent the minimum and maximum values ​​of the incremental cost of electricity of the i-th generator, specifically λ i_min =2α pi p i_min +β pi and λ i_max =2α pi p i_max +β pi;

[0051] Update the power output, specifically:

[0052]

[0053] The present invention provides a fully distributed economic dispatch optimization method for a smart grid based on fixed time. Compared with the prior art, the present invention has the following beneficial effects:

[0054] 1. The fixed-time-based fully distributed economic dispatch optimization method for smart grids proposed in the present invention is fully distributed and more flexible and scalable than the centralized smart grid economic dispatch method.

[0055] 2. The present invention adopts a fixed-time fully distributed consistency algorithm, which can achieve consistency between the incremental cost of electricity and the incremental cost of thermal energy within a fixed time. Compared with the traditional iterative distributed method, it significantly improves the convergence speed and avoids the disadvantage that the convergence time depends on the number of iterations.

[0056] 3. The present invention proposes a fixed-time-based smart grid fully distributed economic dispatch optimization method, which can also make the intermediate variables converge within a fixed time by introducing intermediate variables and using a fixed-time intermediate variable consistency algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 It is a flow chart of a fixed-time-based fully distributed economic dispatch optimization method for smart grids of the present invention;

[0058] Figure 2 The IEEE 30-node standard power network of the present invention;

[0059] Figure 3 The communication topology diagram of the generator of the present invention;

[0060] Figure 4 A graph showing the change of the incremental cost of the power of the generator of the present invention over time;

[0061] Figure 5 A graph showing the variation of the power output of the generator of the present invention with time;

[0062] Figure 6 This is a graph showing the total electrical output power of the present invention changing with time. DETAILED DESCRIPTION

[0063] The embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and cannot be interpreted as limiting the present invention.

[0064] Embodiment 1:

[0065] The process of a fixed-time smart grid fully distributed economic dispatch optimization method provided in this embodiment is as follows: Figure 1 As shown, the specific steps include:

[0066] Step 1: Establish a smart grid economic dispatch model; determine the adjacency matrix based on the smart grid communication topology, and calculate the Laplace matrix based on the adjacency matrix; initialize relevant parameters;

[0067] Step 2: Design a fixed-time fully distributed consensus algorithm;

[0068] Step 3: Update the incremental electricity cost and power output power based on a fixed-time fully distributed consensus algorithm;

[0069] Step 4: Determine whether the fixed-time fully distributed consistency algorithm convergence time limit has been reached; if the fixed-time fully distributed consistency algorithm convergence time limit has not been reached, return to step 3; if the fixed-time fully distributed consistency algorithm convergence time limit has been reached, proceed to step 5;

[0070] Step 5: Introduce intermediate variables and set their initial values;

[0071] Step 6: Design a fixed-time intermediate variable consistency algorithm;

[0072] Step 7: Update the intermediate variables based on the fixed time intermediate variable consistency algorithm; update the incremental power cost; process the incremental power cost and update the power output power;

[0073] Step 8: Determine whether the upper limit of the convergence time of the fixed-time intermediate variable consistency algorithm has been reached; if the upper limit of the convergence time of the fixed-time intermediate variable consistency algorithm has not been reached, return to step 7; if the upper limit of the convergence time of the fixed-time intermediate variable consistency algorithm has been reached, output the incremental power cost and the power output power.

[0074] In this embodiment, the step 1 is specifically as follows:

[0075] Establish a smart grid economic dispatch model, specifically:

[0076]

[0077] pi_min ≤p i (t)≤p i_max

[0078] Wherein, i = 1, 2, ... n; n is the number of generators in the smart grid; is the objective function of the economic dispatch problem, C i (p i (t)) is the electricity cost function of the i-th generator at time t and p i (t) is the power output of the i-th generator at time t, α pi >0,β pi >0 and λ pi >0 is the electricity cost coefficient of the i-th generator; is the power supply and demand balance constraint; p i_min ≤p i (t)≤p i_max is the power output power limit constraint; is the total power demand; p i_min is the minimum output power of the i-th generator; p i_max is the maximum output power of the i-th generator;

[0079] The adjacency matrix A is determined according to the smart grid communication topology, specifically:

[0080]

[0081] Among them, a ij represents the element in the i-th row and j-th column of the adjacency matrix A, where j = 1, 2, ... n; N i represents the set of generators communicating with the i-th generator;

[0082] The Laplace matrix L is calculated based on the adjacency matrix, specifically:

[0083]

[0084] Among them, l ij represents the i-th row and j-th column element of the Laplace matrix L;

[0085] Initialize related parameters, specifically:

[0086] Set the initial value of the power output of the i-th generator to p i (0), and satisfies The initial value of the incremental electricity cost of the i-th generator is λ pi (0) = 2α pi p i (0)+βpi .

[0087] In this embodiment, the step 2 is specifically as follows:

[0088] Design a fixed-time fully distributed consensus algorithm, specifically:

[0089]

[0090] Among them, λ pi (t) is the incremental electricity cost of the i-th generator at time t, λ pj (t) is the incremental electricity cost of the jth generator at time t; Denoted as λ pi (t) is the derivative of time t; u(t) is the controller function; sig h (·)=|·| h sign(·), h is a positive constant, sign(·) is the sign function; C 1 , C 2 , C 3 All are greater than 0; m, n, p, q are all positive odd numbers, and m>n and p <q;σ∈(0,1)。

[0091] In this embodiment, the fixed-time fully distributed consensus algorithm in step 2 can converge within a fixed time, specifically:

[0092] when hour, The upper limit of convergence time is in Indicated as T 0 The maximum value of the incremental electricity cost of all generators at the moment, Indicated as T 0 The minimum value of the incremental power cost of all generators at the moment; hour, The upper limit of convergence time is in Indicated as T 1 The maximum value of the incremental electricity cost of all generators at the moment, Indicated as T 1 The minimum value of the incremental electricity cost of all generators at that moment.

[0093] In this embodiment, the step five is specifically as follows:

[0094] Introduce intermediate variable XX i (t), YYi (t), and set the initial value of the intermediate variable, specifically:

[0095]

[0096] Among them, XX i (0) is the intermediate variable XX i (t) Initial value; YY i (0) is the intermediate variable YY i (t) initial value; if the power output of the i-th generator at time t is p i (t) exceeds the maximum output power p of its generator i_max ,make If the power output of the i-th generator at time t is p i (t) is lower than the minimum output power p of its generator i_min ,make

[0097] In this embodiment, the step six is ​​specifically as follows:

[0098] Design a fixed-time intermediate variable consistency algorithm, specifically:

[0099]

[0100] in, and Represents the intermediate variable XX i (t) and YY i (t) is the derivative of time t; the algorithm can converge in a fixed time when hour, and The upper limit of convergence time is when hour, and The upper limit of convergence time is λ 2 (L) is the second smallest eigenvalue of the Laplace matrix L.

[0101] In this embodiment, the step seven is specifically as follows:

[0102] Update the intermediate variables based on the fixed-time intermediate variable consistency algorithm; update the incremental electricity cost as follows:

[0103]

[0104] in, It is expressed as the convergence value of the incremental cost of the generator electricity under the fixed-time fully distributed consensus algorithm;

[0105] Processing incremental electricity costs, specifically:

[0106]

[0107] Among them, λ i_min and λ i_max They represent the minimum and maximum values ​​of the incremental cost of electricity of the i-th generator, specifically λ i_min =2α pi p i_min +β pi and λ i_max =2α pi p i_max +β pi ;

[0108] Update the power output, specifically:

[0109]

[0110] Embodiment 2:

[0111] Example 2 adopts the proposed fixed-time based smart grid fully distributed economic dispatch optimization method to perform numerical simulation on the IEEE 30-node standard power network with a total of 6 generators. Figure 2 It is an IEEE 30-node standard power network; Figure 3 This is the communication topology diagram of the generator of the present invention.

[0112] Table 1 shows the electricity cost coefficient α of the i-th generator pi , β pi 、The minimum output power p of the i-th generator i_min and the maximum output power p of the i-th generator i_max ;Total power demand The initial value of the generator power output p 1 (0) = 50 (MW), p 2 (0) = 60 (MW), p 3 (0) = 40 (MW), p 4 (0) = 60 (MW), p 5 (0) = 40 (MW), p 6 (0)=50(MW); m=9, n=7, p=3, q=5, σ=2 / 5, C 1 , C 2 , C 3 The average value is 2; The upper limit of convergence time is 7.20(s); and The upper limit of convergence time is 2.17(s).

[0113] According to the generator communication topology, the adjacency matrix A is determined as:

[0114]

[0115] Table 1

[0116] Generator <![CDATA[α pi ]]> <![CDATA[β pi ]]> <![CDATA[p i_max ]]> <![CDATA[p i_min ]]> 1 0.0485 12.1 80 0 2 0.0385 13.3 75 0 3 0.0495 12.4 40 0 4 0.0450 12.3 100 0 5 0.0380 13.5 80 0 6 0.0385 13.3 75 0

[0117] Finally, the effectiveness of the present invention is verified through numerical simulation based on the given data.

[0118] Figure 4 A graph showing the change of the incremental cost of the power of the generator of the present invention over time; Figure 4 The optimal value of the incremental cost of the generator power changes from 17.12 ($ / MW) to 17.26 ($ / MW), where λ 3 (t) Because it exceeds the maximum value of the incremental cost of the generator electricity, it changes from 17.12 ($ / MW) to 16.36 ($ / MW), resulting in failure to converge to consistency.

[0119] Figure 5 A graph showing the variation of the power output of the generator of the present invention with time; Figure 5 The optimal value of the generator power output p 1 =53.21(MW), p 2 =51.44(MW), p 3 =40(MW), p 4 =55.12(MW), p 5 =49.49(MW), p 6 =51.44(MW).

[0120] Figure 6 This is a graph showing the total electrical output power of the present invention changing with time.

[0121] It should be noted that the above description is only a preferred example of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art can still modify the technical solutions described in the aforementioned embodiments or replace some of the technical features therein by equivalents. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A fixed-time smart grid fully distributed economic dispatch optimization method, characterized in that: The following steps are involved: Step 1: Establish a smart grid economic dispatch model; determine the adjacency matrix based on the smart grid communication topology, and calculate the Laplace matrix based on the adjacency matrix; initialize relevant parameters; Step 2: Design a fixed-time fully distributed consensus algorithm; Step 3: Update the incremental electricity cost and power output power based on a fixed-time fully distributed consensus algorithm; Step 4: Determine whether the fixed-time fully distributed consistency algorithm convergence time limit has been reached; if the fixed-time fully distributed consistency algorithm convergence time limit has not been reached, return to step 3; if the fixed-time fully distributed consistency algorithm convergence time limit has been reached, proceed to step 5; Step 5: Introduce intermediate variables and set their initial values; Step 6: Design a fixed-time intermediate variable consistency algorithm; Step 7: Update the intermediate variables based on the fixed time intermediate variable consistency algorithm; update the incremental power cost; process the incremental power cost and update the power output power; Step 8: Determine whether the upper limit of the convergence time of the fixed-time intermediate variable consistency algorithm has been reached; If the upper limit of the convergence time of the fixed-time intermediate variable consistency algorithm is not reached, return to step seven; if the upper limit of the convergence time of the fixed-time intermediate variable consistency algorithm is reached, output the incremental power cost and the power output power.

2. The fixed-time-based fully distributed economic dispatch optimization method for smart grid according to claim 1 is characterized in that: The step 1 specifically includes the following steps: Establish a smart grid economic dispatch model, specifically: p i_min ≤p i (t)≤p i_max Wherein, i = 1, 2, ... n; n is the number of generators in the smart grid; is the objective function of the economic dispatch problem, C i (p i (t)) is the electricity cost function of the i-th generator at time t and p i (t) is the power output of the i-th generator at time t, α pi >0,β pi >0 and γ pi >0 is the electricity cost coefficient of the i-th generator; is the power supply and demand balance constraint; p i_min ≤p i (t)≤p i_max is the power output power limit constraint; is the total power demand; p i_min is the minimum output power of the i-th generator; p i_max is the maximum output power of the i-th generator; The adjacency matrix A is determined according to the smart grid communication topology, specifically: Among them, a ij represents the element in the i-th row and j-th column of the adjacency matrix A, where j = 1, 2, ... n; N i represents the set of generators communicating with the i-th generator; The Laplace matrix L is calculated based on the adjacency matrix, specifically: Among them, l ij represents the i-th row and j-th column element of the Laplace matrix L; Initialize related parameters, specifically: Set the initial value of the power output of the i-th generator to p i (0), and satisfies The initial value of the incremental electricity cost of the i-th generator is λ pi (0) = 2α pi p i (0)+β pi .

3. The fixed-time-based fully distributed economic dispatch optimization method for smart grid according to claim 2 is characterized in that: The step 2 specifically includes the following steps: Design a fixed-time fully distributed consensus algorithm, specifically: Among them, λ pi (t) is the incremental electricity cost of the i-th generator at time t, λ pj (t) is the incremental electricity cost of the jth generator at time t; Denoted as λ pi (t) is the derivative of time t; u(t) is the controller function; sig h (·)=|·| h sign(·), h is a normal constant, sign(·) is the sign function; C1, C2, c3 are all greater than 0; m, n, p, q are all positive odd numbers, and m>n and p <q;σ∈(0,1)。 4. The fixed-time-based fully distributed economic dispatch optimization method for smart grid according to claim 3 is characterized in that: The fixed-time fully distributed consensus algorithm in step 2 can converge within a fixed time, specifically: when hour, The upper limit of convergence time is in It is expressed as the maximum value of the incremental electricity cost of all generators at time T0, It is expressed as the minimum value of the incremental cost of all generators at time T0; when hour, The upper limit of convergence time is in It is expressed as the maximum value of the incremental electricity cost of all generators at time T1, It is expressed as the minimum value of the incremental electricity cost of all generators at time T1.

5. The fixed-time-based fully distributed economic dispatch optimization method for smart grid according to claim 4 is characterized in that: The step five specifically includes the following steps: Introduce intermediate variable XX i (t), YY i (t), and set the initial value of the intermediate variable, specifically: Among them, XX i (0) is the intermediate variable XX i (t) Initial value; YY i (0) is the intermediate variable YY i (t) initial value; if the power output of the i-th generator at time t is p i (t) exceeds the maximum output power p of its generator i_max ,make If the power output of the i-th generator at time t is p i (t) is lower than the minimum output power p of its generator i_min ,make 6. The method for optimizing fully distributed economic dispatch of a smart grid at a fixed time according to claim 5, characterized in that: The step six specifically includes the following steps: Design a fixed-time intermediate variable consistency algorithm, specifically: in, and Represents the intermediate variable XX i (t) and YY i (t) is the derivative of time t; the algorithm can converge in a fixed time when hour, and The upper limit of convergence time is when hour, and The upper limit of convergence time is λ2(L) is the second smallest eigenvalue of the Laplace matrix L.

7. The fixed-time-based fully distributed economic dispatch optimization method for smart grid according to claim 6 is characterized in that: The step seven specifically includes the following steps: Update the intermediate variables based on the fixed-time intermediate variable consistency algorithm; update the incremental electricity cost as follows: in, It is expressed as the convergence value of the incremental cost of the generator electricity under the fixed-time fully distributed consensus algorithm; Processing incremental electricity costs, specifically: Among them, λ i_min and λ i_max They represent the minimum and maximum values ​​of the incremental cost of electricity of the i-th generator, specifically λ i_min =2α pi p i_min +β pi and λ i_max =2α pi p i_max +β pi ; Update the power output, specifically:

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