CN114925537A - Non-initialization smart power grid economic dispatching method based on designated time consistency - Google Patents

Non-initialization smart power grid economic dispatching method based on designated time consistency Download PDF

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CN114925537A
CN114925537A CN202210611030.0A CN202210611030A CN114925537A CN 114925537 A CN114925537 A CN 114925537A CN 202210611030 A CN202210611030 A CN 202210611030A CN 114925537 A CN114925537 A CN 114925537A
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纪良浩
余林华
杨莎莎
李华青
郭兴
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Chongqing University of Post and Telecommunications
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Abstract

The invention discloses a non-initialization intelligent power grid economic dispatching method based on specified time consistency, and belongs to the field of power system economic dispatching. The method is based on a designated time consistency principle, the increment cost of a power generation unit in a power grid system is used as a consistency variable, and the total power generation cost is minimized within designated time under the constraints of a supply and demand balance equation and the constraints of a power generation capacity inequality. The algorithm provided by the invention can uniformly pre-specify the system convergence time without considering the initial state and any other parameters, does not need any initialization, allows the participation of nodes and the load demand to be dynamically changed, and effectively improves the control precision and the flexibility of the intelligent power grid system.

Description

Non-initialization smart power grid economic dispatching method based on designated time consistency
Technical Field
The invention belongs to the field of economic dispatching of smart power grids, and relates to a non-initialization economic dispatching method based on designated time consistency under directed topology.
Background
As the smart grid is applied more and more widely in the scientific and engineering fields, it has received more and more attention. The economic dispatching problem is one of important optimization problems in the field of smart power grids, and aims to minimize the total power generation cost under certain constraint conditions (such as equal constraints of supply and demand, unequal constraints of capacity of a single generator and the like). The cost calculation method for each generator is usually modeled by a respective quadratic convex function. Early economic scheduling problems could be solved by various traditional centralized methods, including lambda iteration, particle swarm optimization, gradient descent, dynamic programming, lagrangian relaxation, etc. However, the centralized architecture requires a powerful central controller, its reliance on global information and limited communication capabilities making the grid vulnerable to single point failures and also reducing the privacy level of the grid.
In order to overcome the shortcomings of the centralized algorithm, in recent years, a distributed algorithm based on a multi-agent system consistency theory has received much attention. The distributed economic scheduling algorithm only needs to calculate the optimal decision by exchanging information between neighbors. On the one hand, the method avoids single point of failure caused by global information, and reduces communication and calculation burden of the system. On the other hand, the method provides the plug and play capability, and improves the flexibility and expansibility of the system to a great extent. However, many distributed algorithms require some initial set-up procedure and cannot handle the time-varying demands and intermittent power generation caused by the addition or withdrawal of a generator set. In addition, the convergence rates of the asymptotic and exponential types are not suitable for the case of frequent changes in the power grid.
To increase convergence speed, finite time and fixed time methods have been developed. The finite time method greatly improves the convergence speed of the system, but is limited by the initial state of the consistency variable, and the convergence time of the finite time method changes along with the change of the initial state. However, in practical applications, the initial state of the system is difficult to collect. The fixed time method is no longer affected by the initial state settings of the consistency variables, but the convergence time cannot be specified in advance due to certain limitations, such as design parameters of the protocol or network topology.
In the prior art, for example, in a patent of 'an economic dispatching method of a distributed smart power grid based on finite time consistency under directed topology', the problem of economic dispatching in the smart power grid is solved by applying the finite time consistency method, and compared with gradual convergence, the method can obtain an upper bound of system convergence time. However, the upper bound of the convergence time is influenced by the initial value of the state, and the initial value of the system is difficult to obtain in practical application, which results in that the estimation of the convergence time is still limited. The method overcomes the problems, solves the economic dispatching problem by using a method of specifying time consistency, not only ensures that the convergence time is not influenced by the initial state, but also can specify the convergence time in advance, so that the convergence time of the system is not limited by 'estimation' any more, but can be accurately specified in advance. The flexibility and the expandability of the system are improved.
Disclosure of Invention
The present invention is directed to solving the above problems of the prior art. A method is presented. The technical scheme of the invention is as follows:
a non-initialization intelligent power grid economic dispatching method based on designated time consistency comprises the following steps:
step 1, establishing a mathematical model of an economic dispatching problem of the smart power grid: the method comprises the steps that each distributed power generation unit, a power generation cost function, a minimum total cost of economic dispatch, a supply and demand balance and a power limit constraint function of a power generator are included;
step 2, converting into dual problems: the problem of solving the minimum value of the objective function in the economic dispatching mathematical model established in the step 1 is converted into the problem of solving the corresponding maximum value of the dual function, so that the power generation units in the system and the neighbor nodes of the power generation units only need to exchange Lagrange multipliers lambda without exposing respective local power generation quantities, and the privacy protection effect is achieved;
step 3, according to the hairThe generator set layout of the electrical system establishes a directed balanced topological graph structure for representing the communication relationship among the power generation units. According to the communication topological diagram, the state variable lambda in the step 2 can be obtained i The exchange range of (1);
and 4, giving the physical time necessary for the system to operate to determine a lower time limit which can be specified in advance, and then obtaining the optimal incremental cost and the optimal generated power by adopting a specified time consistency control algorithm.
Further, the establishing of the mathematical model of the economic dispatching problem of the smart grid in the step 1 specifically includes:
Figure BDA0003671995440000031
Figure BDA0003671995440000032
wherein N represents the number of generators, P i Representing the generated power of the i-th generator, C i (p i ) A coefficient α in equation (2) representing a power generation cost function of the i-th power generator i ,β i ,γ i > 0 represents the cost parameter for the ith generator;
Figure BDA0003671995440000033
Figure BDA0003671995440000034
wherein d is i In order to locally demand the amount of electricity,
Figure BDA0003671995440000035
is a node set of a communication topology, P d In order to obtain the total power demand,
Figure BDA0003671995440000036
and
Figure BDA0003671995440000037
representing the upper and lower limits of the power generation of the ith generator.
Further, the specific steps of converting into dual problems in step 2 are as follows:
before converting the dual problem, the following lagrangian function needs to be defined:
Figure BDA0003671995440000038
λ is the lagrange multiplier corresponding to the constraint in the equation, called the incremental cost.
For the lagrangian function defined in step three, it can be obtained by the lagrangian multiplier method:
Figure BDA0003671995440000039
can be obtained when λ is satisfied 1 ＝λ 2 ＝…＝λ N And when the total cost function is minimum, the system reaches an optimal state.
Then, the dual function is converted into a corresponding dual function according to the following method:
Figure BDA00036719954400000310
wherein order
Figure BDA0003671995440000041
D i A gradient of (lambda)
Figure BDA0003671995440000042
Figure BDA0003671995440000043
The optimal solution may be represented by the following sub-formula:
Figure BDA0003671995440000044
wherein
Figure BDA0003671995440000045
Is that
Figure BDA0003671995440000046
Is limited to the upper and lower limits of individual power generation
Figure BDA0003671995440000047
The inverse function within.
Further, step 3, according to the layout of the generator sets of the power generation system, establishing a directed balanced topological graph structure for representing the communication relationship between the power generation units, specifically including:
the communication topology for the power generation unit is represented as follows:
by using
Figure BDA0003671995440000048
Representing a topological relation, treating each power generating unit as a node, wherein
Figure BDA0003671995440000049
The node is a set of nodes, and the node is a node,
Figure BDA00036719954400000410
is an adjacency matrix of the topological graph,
Figure BDA00036719954400000411
a ij 、
Figure BDA00036719954400000412
representing a set of real numbers, elements of the adjacency matrix, and a set of all N × N (i.e., N rows and N columns) real matrices, respectively.
Figure BDA00036719954400000413
Is a laplacian matrix. When the in-degree and out-degree of each node in the graph are equal, the method is implementedReferred to as a directed equilibrium graph.
Further, in the step 4, an optimal incremental cost and an optimal generated power are obtained by adopting a specified time consistency control algorithm.
Wherein
Figure BDA00036719954400000414
Is the derivative thereof. t is t h ＝t 0 +T，
Figure BDA00036719954400000415
Indicating the start time. T > 0 is a convergence time that can be specified in advance and must be greater than the physical time of the system. k > 2 is a regulating parameter selected in advance.
The designed designated time consistency control algorithm is as follows:
Figure BDA00036719954400000416
p i (t)＝ψ i (λ i (t)), (7)
wherein b > 0, c > 0, θ > 0, η > 0 are design parameters, α i Coefficient of quadratic term, ψ, for the ith generator i (. is) defined in formula (5);
Figure BDA0003671995440000051
representing control input, λ, in a multi-agent system j And λ i Representing the lagrangian multipliers of agent i and agent j, respectively, i.e., the location state information in a multi-agent system. And (4) obtaining the optimal incremental cost by the formula (8), and obtaining the optimal power generation amount by the formula (7).
The invention has the following advantages and beneficial effects:
(1) the invention is different from a finite time/fixed time control method, the specified time ED algorithm provided by the invention can uniformly and pre-specify the convergence time without considering the initial state and other parameters, namely, the convergence time is taken as a parameter which can be defined by self, and the extra expenses caused by initialization preparation and calculation of the upper bound of the convergence time are reduced.
(2) The algorithm eliminates the constraint of keeping supply and demand balance in the initial state, the system can respond adaptively without any additional operation (such as adjusting related parameters or state values) after local change, and the incremental cost is reconciled in a specified time.
Drawings
FIG. 1 is a flow chart of a non-initialized economic dispatch method based on specified time consistency under directed topology according to a preferred embodiment of the present invention;
FIG. 2 is a schematic diagram of a power generation unit communication topology in an embodiment of the present invention;
FIG. 3 is a schematic diagram of the variation of the cost of a specified time increment of a power generation unit in an embodiment of the invention. (ii) a
FIG. 4 is a diagram illustrating the variation of the power demand and the power generation amount of the power generation unit according to the embodiment of the present invention.
Fig. 5 is a diagram showing a change in the amount of power generation by the power generation unit at a specified time in the embodiment of the invention.
FIG. 6 is a schematic diagram of the variation of the total cost of the power generation unit for a given time in the embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be described in detail and clearly with reference to the accompanying drawings. The described embodiments are only some of the embodiments of the present invention.
The technical scheme for solving the technical problems is as follows:
step 1: this example was analyzed with a 5-bus microgrid with one generator and one load on each bus. Assume that the specified convergence time T is 2 s. The following economic dispatching mathematical model is established:
Figure BDA0003671995440000061
Figure BDA0003671995440000062
wherein N represents the number of generators, the generated power of i generators, C i (p i ) Coefficient α in equation (2) representing power generation cost function of i-th power generator i ,β i ,γ i > 0 denotes the cost parameter for the ith generator.
Figure BDA0003671995440000063
Figure BDA0003671995440000064
The two equations are respectively the power generation capacity inequality constraint and the supply and demand balance equality constraint. Wherein d is i For local power demand, P d The total amount of electricity required is,
Figure BDA0003671995440000065
and
Figure BDA0003671995440000066
representing the upper and lower limits of the power generation of the ith generator.
Cost factor α per generator i ,β i ,γ i And specific values of the upper and lower limits of the generated energy are shown in table 1:
TABLE 1
Figure BDA0003671995440000067
Assuming that the initial power of each generator is 0, the virtual demand of each load is d 1 ＝90kW,d 2 ＝110kW,d 3 ＝90kW,d 4 100kW, and d 5 110kW, initial total demand electric quantity is 500 KW. The initial value of the increment cost obtained after calculation is lambda 1 (0)＝1.22,λ 2 (0)＝3.41,λ 3 (0)＝2.53,λ 4 (0) 4.02,. and λ 5 (0)＝2.90。
Step 2: conversion to a dual problem:
Figure BDA0003671995440000071
Figure BDA0003671995440000072
wherein order
Figure BDA0003671995440000073
D i A gradient of (λ)
Figure BDA0003671995440000074
The optimal solution may be represented by the following sub-formula:
Figure BDA0003671995440000075
wherein
Figure BDA0003671995440000076
Is that
Figure BDA0003671995440000077
Is limited to the upper and lower limits of individual power generation
Figure BDA0003671995440000078
The inverse function within.
And step 3: the communication topology for the power generating unit is shown in figure 2. By using
Figure BDA0003671995440000079
Representing a topological relation, treating each power generating unit as a node, wherein
Figure BDA00036719954400000710
Is a set of nodes.
Figure BDA00036719954400000711
Is an adjacency matrix of the topological graph. Laplace matrix
Figure BDA00036719954400000712
Is defined as:
Figure BDA00036719954400000713
when the read-in degree and the read-out degree of each node in the graph are equal, the graph is called a directed balanced graph.
And 4, step 4: the control protocol of the appointed time provided by the invention is as follows:
Figure BDA00036719954400000714
p i (t)＝ψ i (λ i (t)),
using the protocol, the optimal incremental cost is 19.87, and then the respective optimal power generation power is calculated according to the local parameters of each power generation unit:
Figure BDA0003671995440000081
and
Figure BDA0003671995440000082
the variation of all the above processes is shown in fig. 3-6.
It should also be noted that the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other identical elements in the process, method, article, or apparatus that comprises the element.
The above examples are to be construed as merely illustrative and not limitative of the remainder of the disclosure. After reading the description of the invention, the skilled person can make various changes or modifications to the invention, and these equivalent changes and modifications also fall into the scope of the invention defined by the claims.

Claims (5)

1. A non-initialization smart grid economic dispatching method based on designated time consistency is characterized by comprising the following steps:
step 1, establishing a mathematical model of an economic dispatching problem of the smart power grid: the method comprises the steps of generating each distributed power generation unit, a power generation cost function, a minimum total cost of economic dispatch, a supply-demand balance function and a power limit constraint function of a generator;
step 2, converting into dual problems: the problem of solving the minimum value of the objective function in the economic dispatching mathematical model established in the step 1 is converted into the problem of solving the corresponding maximum value of the dual function, so that the power generation units in the system and the neighbor nodes of the power generation units only need to exchange Lagrange multipliers lambda without exposing respective local power generation amount, and the privacy protection effect is achieved;
step 3, constructing a communication topological structure of the power system: and establishing a directed balance topological graph structure for representing the communication relation among the power generation units according to the layout of the generator set of the power generation system. According to the communication topological diagram, the state variable lambda in the step 2 can be obtained i The exchange range of (1);
and 4, giving the physical time necessary for the system to operate to determine a lower time limit which can be specified in advance, and then obtaining the optimal incremental cost and the optimal generated power by adopting a specified time consistency control algorithm.
2. The uninitialized smart grid economic dispatching method based on designated time consistency according to claim 1, wherein the establishing of the mathematical model of the smart grid economic dispatching problem in the step 1 specifically comprises:
Figure FDA0003671995430000011
Figure FDA0003671995430000012
wherein N represents the number of generators, P i Representing the generated power of the i-th generator, C i (p i ) Coefficient α in equation (2) representing power generation cost function of i-th power generator i ,β i ,γ i > 0 represents the cost parameter of the ith generator;
Figure FDA0003671995430000013
Figure FDA0003671995430000014
wherein d is i In order to have a local power demand,
Figure FDA0003671995430000021
is a node set of a communication topology, P d In order to obtain the total power demand,
Figure FDA00036719954300000213
and
Figure FDA00036719954300000212
representing the upper and lower limits of the power generation of the ith generator.
3. The economic dispatching method of the uninitialized smart grid based on the designated time consistency according to claim 2, characterized in that the specific steps converted into dual problems in step 2 are as follows:
before converting the dual problem, the following lagrangian function needs to be defined:
Figure FDA0003671995430000022
λ is the lagrange multiplier corresponding to the constraint in the equation, called the incremental cost;
for the lagrangian function defined in step three, it can be obtained by the lagrangian multiplier method:
Figure FDA0003671995430000023
can be obtained when λ is satisfied 1 ＝λ 2 ＝…＝λ N When the total cost function is minimum, the system reaches an optimal state;
then the dual function is converted into a corresponding dual function according to the following method:
Figure FDA0003671995430000024
wherein order
Figure FDA0003671995430000025
D i A gradient of (lambda)
Figure FDA0003671995430000026
Figure FDA0003671995430000027
The optimal solution may be represented by the following formula:
Figure FDA0003671995430000028
wherein
Figure FDA0003671995430000029
Is that
Figure FDA00036719954300000210
Is limited to the upper and lower limits of individual power generation
Figure FDA00036719954300000211
The inverse function of (c).
4. The economic dispatching method of the uninitialized smart grid based on the designated time consistency according to claim 3, wherein the step 3 of establishing a directed balanced topological graph structure for representing the communication relationship among the power generation units according to the generator set layout of the power generation system specifically comprises:
the communication topology for the power generation unit is represented as follows:
by using
Figure FDA0003671995430000031
Representing a topological relation, treating each power generating unit as a node, wherein
Figure FDA0003671995430000032
The node is a set of nodes, and the node is a node,
Figure FDA0003671995430000033
is an adjacency matrix of the topological graph,
Figure FDA0003671995430000034
a ij 、
Figure FDA0003671995430000035
respectively representing a real number set, elements of an adjacent matrix and a set of all NxN (namely N rows and N columns) real matrixes;
Figure FDA0003671995430000036
is a laplacian matrix. When the in-degree and the out-degree of each node in the graph are equal, the graph is called a directed balanced graph.
5. The economic dispatching method of the uninitialized smart grid based on the designated time consistency according to claim 4, characterized in that in step 4, the designated time consistency control algorithm is then adopted to obtain the optimal incremental cost and the optimal generated power.
A time-varying scalar function is first defined.
Figure FDA0003671995430000037
Figure FDA0003671995430000038
Wherein
Figure FDA0003671995430000039
Is the derivative thereof. t is t h ＝t 0 +T，
Figure FDA00036719954300000310
Indicating the starting time. T > 0 is convergence time which can be specified in advance and must be longer than the physical time of the system, and k > 2 is a regulating parameter which is selected in advance;
the designed designated time consistency control algorithm is as follows:
Figure FDA00036719954300000311
p i (t)＝ψ i (λ i (t)), (7)
wherein b > 0, c > 0, θ > 0, η > 0 are design parameters, α i Coefficient of quadratic term, ψ, for the ith generator i (. is) defined in formula (5);
Figure FDA0003671995430000041
representing control input, λ, in a multi-agent system j And λ i Representing the lagrangian multipliers of agent i and agent j, respectively, i.e., the location state information in a multi-agent system. And (4) obtaining the optimal incremental cost by the formula (8), and obtaining the optimal power generation amount by the formula (7).
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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116388183A (en) * 2023-06-02 2023-07-04 安徽大学 Designated time distributed economic scheduling method under directed unbalanced network

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116388183A (en) * 2023-06-02 2023-07-04 安徽大学 Designated time distributed economic scheduling method under directed unbalanced network
CN116388183B (en) * 2023-06-02 2023-08-18 安徽大学 Designated time distributed economic scheduling method under directed unbalanced network

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