CN116388183B - Designated time distributed economic scheduling method under directed unbalanced network - Google Patents
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Abstract
The invention discloses a distributed economic scheduling method for designated time under a directed unbalanced network, which comprises the following steps: setting system parameters including the number n of all generator sets participating in scheduling, and the expected generation power of each generator setSetting convergence timeAccording to the communication network topological graph, a weighted adjacent matrix A is set, and each generator set selects initial decision behaviors according to the decision feasible region of each generator setAnd to error vectorPenalty factor variableSum weight gain variableInitializing to obtain initial values of all variables; and transferring the local constraint of the generator set to a cost function by using a penalty function method so as to convert the mathematical model. Compared with the current fixed time economic scheduling algorithm, the specified time economic scheduling algorithm provided by the invention can ensure that the convergence time is specified by a user; compared with the secondary economic dispatch problem, the economic dispatch algorithm provided by the invention is more flexible and practical, and can solve the more general economic dispatch problem.
Description
Technical Field
The invention relates to the field of intelligent power grid economic dispatch, in particular to a specified time distributed economic dispatch method under a directed unbalanced network.
Background
With the development of smart grids in recent years, economic dispatch problems of power systems are receiving more and more attention. Economic dispatch is one of the most fundamental problems in power grid systems. The economic dispatch problem aims to solve the problems of supply and demand balance of the generator set and the minimum total power generation cost in the power system. At present, thermal power generation is still one of the main modes of power production in China, and the running state of a generator set is reasonably regulated, so that the total power generation cost of a power system is reduced while the requirements of a user side are met, and the energy loss can be effectively reduced. As the scale of power systems continues to expand, traditional centralized approaches are unable to effectively address economic dispatch issues in large-scale systems. In addition, the existence of a total control center in the centralized method certainly reduces the robustness of the system, and the error of the information of a single sub-node can cause the deviation of the whole system.
In order to overcome the above-described drawbacks of the centralized approach, various distributed approaches are receiving a great deal of attention. The distributed method only requires local communication and local optimization among neighbors, not only enhances the robustness of the system, but also accords with the characteristics of plug and play in the future. A new set of distributed optimization algorithms, such as a consistency-based algorithm, an original dual algorithm, a nestrov acceleration algorithm, etc., are designed. These algorithms typically have an exponential convergence or a broad range of asymptotic convergence characteristics, and their convergence rate is often not shown, i.e., the algorithm cannot give the desired optimal allocation in a very short time. Therefore, it is of great practical significance to study distributed economic dispatch algorithms that consider fixed time convergence or specified time convergence characteristics.
Through retrieval, application publication number CN115310776, a smart grid economic dispatch method based on fixed time distributed optimization is disclosed, a distributed economic dispatch algorithm capable of converging at fixed time is designed by utilizing a symbol function, the patent can only solve the economic dispatch problem under an undirected network, and the designed algorithm converging time depends on global information such as the minimum positive characteristic root of a Laplace matrix of a communication network. Application publication number CN114881489, which is a smart grid economic dispatch method based on event triggering and fixed time, can only solve the problem of secondary cost function economic dispatch under the undirected network. Application publication number CN114925537, which is a non-initialized smart grid economic dispatch method based on specified time consistency, can only solve the problem of secondary cost function economic dispatch under a directed balanced network. The invention designs a distributed economic dispatch algorithm converging at a designated time based on the directed unbalanced network research intelligent power grid economic dispatch problem, and is suitable for solving the general economic dispatch problem.
Disclosure of Invention
The invention aims to provide a distributed economic scheduling method for designated time under a directed unbalanced network, so as to solve the problems in the background technology.
In order to achieve the above purpose, the present invention provides the following technical solutions: a distributed economic scheduling method for appointed time under a directed unbalanced network comprises the following steps:
s1, establishing an economic dispatch problem mathematical model in a smart grid;
s2, setting system parameters including the number n of all generator sets participating in scheduling, and expected power generation of each generator set, wherein />Indicating the number of the generator set,/->Setting convergence time +.>；
S3, constructing a communication network topological graph between the generator sets according to a communication topological structure of the intelligent power grid system;
s4, setting a weighted adjacent matrix A according to the communication network topological graph;
s5, each generator set selects initial decision behaviors according to the decision feasible region of each generator setAnd to error vectorPenalty factor variable->Sum weight gain variable->Initializing to obtain initial values of all variables;
s6, transferring the local constraint of the generator set to a cost function by using a penalty function method so as to convert the mathematical model;
s7, acquiring left characteristic roots of the weighted adjacent matrix A in a specified time by utilizing the consistency of the multi-agent system, and acquiring left characteristic roots of the directed unbalanced network Laplacian matrix in the specified time by utilizing an updating strategy so as to update the weight gain variableSo that the weight gain variable +.>Converging to a stable value at a specified time;
s8, updating the error variable by utilizing the proportional-integral control ideaSo that the error variable +.>Converging to zero in a designated time to realize the supply and demand balance of economic dispatching problems;
and S9, acquiring the optimal output power of each generator set in the economic dispatch problem by utilizing the consistency of the multi-agent system, and acquiring the optimal output power of each generator set at the appointed time to obtain an optimal power distribution scheme.
Preferably, in step S1, the mathematical model of the economic dispatch problem is as follows:
；
wherein ,for output power +.>Respectively +.>The lower and upper limits of the output power of the generator sets,is->Generating cost function of each generator set, +.>Is->Local constraint functions of the individual generator sets.
Preferably, in step S4, the acquiring manner of the weighted adjacency matrix a specifically includes:
if generating set in systemCan receive neighbor generator set->Is set to->, wherein />Representing a generator set->The number of the neighbor nodes;
if the generator setCannot receive neighbor genset->Is set to->The method comprises the steps of carrying out a first treatment on the surface of the Furthermore, due to the generator set->Self data are also available, so set +.>。
Preferably, each generator set in step S5 selects an initial decision action according to its own decision feasible regionIn the time of this, the generator set can be taken at will>, wherein />The set of all gensets is numbered.
Preferably, the method for obtaining the initial values of the variables in step S5 specifically includes:，the method comprises the steps of carrying out a first treatment on the surface of the Weight gain variable +.>The initial value is set to +.>I.e.>The individual elements are->Other elements are 0 +.>And (5) a dimension vector.
Preferably, the specific conversion mode of the conversion mathematical model in the step S6 is as follows:
；
wherein ,for a new cost function->For the penalty factor, the gradient function corresponding to the new cost function is defined as +.>，/>Representing the function +.>Regarding variables->Is a gradient function of (a).
Preferably, the specific updating manner of the updating policy in step S7 is as follows:
；
wherein the Laplace matrix is defined as，/>Is a unit array, and the non-periodic sampling time is defined as，/>Is a small positive number; />Respectively represent the generator set-> and />At non-periodic sampling instants->Time gain variable +.>Value of->Representing a generator set->Weight gain variable of (2) at the current moment +.>Is a value of (2).
Preferably, in step S8, the error variable is updated by using the proportional-integral control conceptThe specific updating mode of (a) is as follows: />；
wherein ,for aperiodic sampling instants +.>Is a small positive number, and controls parameters/>；/>For the weight gain variable->Is>Steady state values obtained at the end of the first phase for the individual components; />Representing a generator set->At the present moment +.>Is>Respectively represent generator setsError variable +.>At the present moment +.>And aperiodic sampling instant->Is a value of (2); />Respectively represent the generator set-> and />At non-periodic sampling instants->A gradient value of time; />Representing the integral variable.
Preferably, the specific update manner of the optimal output power in step S9 is as follows:；
wherein ,for aperiodic sampling time, the control parameters are as followsMatrix->Is a diagonal matrix>Representation matrix->Is a second small feature root of (2); />Respectively represent the generator set->Penalty factor->At the current momentAnd aperiodic sampling instant->Values at that time.
Compared with the prior art, the invention has the beneficial effects that:
compared with the current fixed time economic scheduling algorithm, the specified time economic scheduling algorithm provided by the invention can ensure that the convergence time is specified by a user; compared with the secondary economic scheduling problem, the economic scheduling algorithm provided by the invention can solve the more general economic scheduling problem, so that the economic scheduling algorithm for the appointed time provided by the invention is more flexible and practical;
compared with the current economic scheduling algorithm of the designated time, the method can solve the more general economic scheduling problem, and the economic scheduling problem under the directed unbalanced network, and has wider application range.
Drawings
FIG. 1 is a main step diagram of a distributed economic dispatch method for a designated time in a directional unbalanced network according to an embodiment of the present invention;
FIG. 2 is a topology diagram of a communication network between generator sets of a specified time distributed economic dispatch method in a directed unbalanced network according to an embodiment of the present invention;
FIG. 3 is a graph of the weight gain variation of each generator set of the distributed economic dispatch method for a given time in a directed unbalanced network according to an embodiment of the present invention;
FIG. 4 is a diagram of the variation of the error variables of each generator set of a method for distributed economic dispatch of a given time in a directed unbalanced network according to an embodiment of the present invention;
fig. 5 is a graph of power generation change of each generator set according to another method for distributed economic dispatch of designated time in a directed unbalanced network according to an embodiment of the present invention.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The main execution body of the method in this embodiment is a terminal, and the terminal may be a device such as a mobile phone, a tablet computer, a PDA, a notebook or a desktop, or may be other devices with similar functions, which is not limited in this embodiment.
Referring to fig. 1 to 5, the present invention provides a distributed economic dispatch method for a designated time in a directional unbalanced network, which is applied to a distributed economic dispatch for a designated time of a smart grid, and includes the following steps:
s1, establishing an economic dispatch problem mathematical model in a smart grid; in step S1, the mathematical model of the economic dispatch problem of the smart grid is as follows:； wherein ,/>In order to output the power of the power supply,respectively +.>Lower and upper limits of the output power of the individual generator sets,/->Is->Generating cost function of each generator set, +.>Is->Local constraint functions of the individual generator sets.
S2, setting system parameters including the number n of all generator sets participating in scheduling, and expected power generation of each generator set, wherein />Indicating the number of the generator set,/->Setting convergence time +.>The method comprises the steps of carrying out a first treatment on the surface of the The system specifically comprises the system generator sets with the number of +.>The desired power of the generator set is set to +.>Specify convergence time to be set to +.>The method comprises the steps of carrying out a first treatment on the surface of the The cost function form of each generator set is +.>And has，The method comprises the steps of carrying out a first treatment on the surface of the To embody the wider applicability of the patent, an exponential term is added in the cost function of the generator set No. 1>The power generation power of all the generator sets is respectively as follows:。
s3, constructing a communication network topological graph between the generator sets according to a communication topological structure of the intelligent power grid system; the communication network between the generator sets is shown in fig. 1.
S4, setting a weighted adjacent matrix A according to the communication network topological graph; wherein, in step S4, the adjacency matrix is weightedThe acquisition mode of A specifically comprises the following steps: if generating set in systemCan receive neighbor generator set->Is set up, wherein />Representing a generator set->The number of the neighbor nodes; if the generator set is->Cannot receive neighbor genset->Is set to->The method comprises the steps of carrying out a first treatment on the surface of the Furthermore, due to the generator set->Self data is also available, so the arrangement. The weighted adjacency matrix a corresponding to fig. 2 is as follows: />。
S5, each generator set selects initial decision behaviors according to the decision feasible region of each generator setAnd to error vectorPenalty factor variable->Sum weight gain variable->Initializing to obtain initial values of all variables; wherein each generator set selects an initial decision behavior according to its own decision feasible region>In the time of this, the generator set can be taken at will>, wherein />The set of all gensets is numbered.
Specifically, the mode of acquiring the initial values of the variables is specifically as follows:，/>the method comprises the steps of carrying out a first treatment on the surface of the Weight gain variable +.>The initial value is set to +.>I.e.>The individual elements areOther elements are 0 +.>And (5) a dimension vector.
S6, transferring the local constraint of the generator set to a cost function by using a penalty function method so as to convert the mathematical model; the specific conversion mode of the conversion mathematical model is as follows:
； wherein ,/>For a new cost function->As penalty factors, the gradient function corresponding to the new cost function is defined as
，/>Representing functions respectivelyRegarding variables->Is a gradient function of (a).
S7, acquiring left characteristic roots of the weighted adjacent matrix A in a specified time by utilizing the consistency of the multi-agent system, and acquiring left characteristic roots of the directed unbalanced network Laplacian matrix in the specified time by utilizing an updating strategy so as to update the weight gain variableSo that the weight gain variable +.>Converging to a stable value at a specified time; the specific updating mode of the updating strategy is as follows: />The method comprises the steps of carrying out a first treatment on the surface of the Wherein the Laplace matrix is defined as，/>Is a unit array, and the aperiodic sampling time is defined as +.>，/>Is a small positive number; />Respectively represent the generator set-> and />At non-periodic sampling instants->Time gain variable +.>Value of->Representing a generator set->Weight gain variable of (2) at the current moment +.>Is a value of (2). For example: set->，/>The weight gain variable is updated according to the iteration rule, and the change track of the weight gain variable is shown in fig. 2. It can be seen from fig. 2 that the weight gain variable converges to a stable value +.>And is steady stateThe value satisfies。
S8, updating the error variable by utilizing the proportional-integral control ideaSo that the error variable +.>Converging to zero in a designated time to realize the supply and demand balance of economic dispatching problems; wherein the error variable +.>The specific updating mode of (a) is as follows: />； wherein ,
for aperiodic sampling instants +.>For a smaller positive number, the control parameter +.>；/>For the weight gain variable->Is>Steady state values obtained at the end of the first phase for the individual components; />Representing a generator set->At the present moment +.>Is>Respectively represent the generator set->Error variable +.>At the present moment +.>And aperiodic sampling instant->Is a value of (2); />Respectively represent the generator set-> and />At non-periodic sampling instants->A gradient value of time; />Representing the integral variable. For example: set->，According to the iteration rule, error variable +.>The trace over time is shown in figure 3. From FIG. 3, it can be seen thatThe error variable ie converges to zero in a specified time and is one-step convergence. This shows that the algorithm designed by the present invention allows the equality constraint to be established in the economic dispatch problem.
And S9, acquiring the optimal output power of each generator set in the economic dispatch problem by utilizing the consistency of the multi-agent system, and acquiring the optimal output power of each generator set at the appointed time to obtain an optimal power distribution scheme. The specific updating mode of the optimal output power is as follows:
；
wherein ,for aperiodic sampling time, the control parameters are as followsMatrix->Is a diagonal matrix>Representation matrix->Is a second small feature root of (2); />Respectively represent the generator set->Penalty factor->At the current momentAnd aperiodic sampling instant->Values at that time. For example: set->，/>，/>The output power variation trace of each generator set is shown in fig. 4. As can be seen from FIG. 4, the algorithm designed by the invention can realize that each generator set obtains the optimal output power +.>I.e. the optimum output power of the generator set 6 is the upper limit value.
In this embodiment, compared with the current fixed time economic scheduling algorithm, the specified time economic scheduling algorithm provided by the invention can ensure that the convergence time is specified by the user; compared with the existing economic scheduling algorithm with the designated time, the economic scheduling algorithm provided by the invention can solve the more general economic scheduling problem, so that the economic scheduling algorithm with the designated time is more flexible and practical.
On the basis of the above embodiment, the present invention further provides a specified time distributed economic dispatch device under a directional unbalanced network, which is configured to support the specified time distributed economic dispatch method under the directional unbalanced network in the above embodiment, where the specified time distributed economic dispatch device under the directional unbalanced network includes:
a parameter presetting module for setting system parameters including the number n of all generator sets participating in scheduling, the expected generation power of each generator set, wherein />Indicating the number of the generator set,/->Setting convergence time；
A decision selection module for each generator set to select initial decision behavior according to its own decision feasible regionAnd +.>Penalty factor variable->Sum weight gain variable->Initializing to obtain initial values of all variables;
the constraint transfer module is used for transferring the local constraint of the generator set into a cost function by using a penalty function method so as to convert the mathematical model;
the power distribution module is used for acquiring the left characteristic root of the weighted adjacent matrix in a specified time by utilizing the multi-agent system consistency and obtaining an optimal power generation power distribution scheme in the specified time by utilizing the multi-agent system consistency and the proportional integral control idea.
Those of ordinary skill in the art will appreciate that the modules and method steps of the examples described in connection with the embodiments disclosed herein can be implemented as electronic hardware, or as a combination of computer software and electronic hardware. Whether such functionality is implemented as hardware or software depends upon the particular application and design constraints imposed on the solution. Skilled artisans may implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present invention.
In addition, it should be noted that the combination of the technical features described in the present invention is not limited to the combination described in the claims or the combination described in the specific embodiments, and all the technical features described in the present invention may be freely combined or combined in any manner unless contradiction occurs between them. It should be noted that the above-mentioned embodiments are merely examples of the present invention, and it is obvious that the present invention is not limited to the above-mentioned embodiments, and many similar variations are possible. All modifications attainable or obvious from the present disclosure set forth herein should be deemed to be within the scope of the present disclosure.
The foregoing is merely illustrative of the preferred embodiments of the present invention, and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (8)
1. A method for distributed economic dispatch of designated times in a directed unbalanced network, comprising the steps of:
s1, establishing an economic dispatch problem mathematical model in a smart grid;
s2, setting system parameters including the number n of all generator sets participating in scheduling, and the expected power d of each generator set i Where i represents the genset number, i e v= {1, 2..once, n }, where V is the set of all genset numbers, the convergence time is set to 3T 0 ；
S3, constructing a communication network topological graph between the generator sets according to a communication topological structure of the intelligent power grid system;
s4, setting a weighted adjacent matrix A according to the communication network topological graph;
s5, each generator set selects initial decision behavior x according to the decision feasible region of each generator set i (0) And for error vector e i (0) Penalty factor variable c i (0) Sum weight gain variable z i (0) Initializing to obtain initial values of all variables;
s6, transferring local constraint of the generator set to a cost function by using a penalty function method so as to convert a mathematical model, wherein the specific conversion mode of the mathematical model is as follows:
wherein ,fi c (x i )＝f i (x i )+c i g i (x i ) As a new cost function, x i For output power, f i (x i ) G is the generating cost function of the ith generating set i (x i ) C is the local constraint function of the ith generator set i As penalty factors, the gradient function corresponding to the new cost function is defined as Respectively represent the functions f i (x i ),g i (x i ) With respect to variable x i Is a gradient function of (2);
s7, acquiring left characteristic roots of the weighted adjacent matrix A in a specified time by utilizing the consistency of the multi-agent system, and acquiring left characteristic roots of the directed unbalanced network Laplacian matrix in the specified time by utilizing an updating strategy so as to update the weight gain variable z i (0) So that the weight gain variable z i (0) Converging to a stable value at a specified time;
s8, updating the error variable e by utilizing the proportional-integral control idea i So that the error variable e i Converging to zero in a designated time to realize the supply and demand balance of economic dispatching problems;
and S9, acquiring the optimal output power of each generator set in the economic dispatch problem by utilizing the consistency of the multi-agent system, and acquiring the optimal output power of each generator set at the appointed time to obtain an optimal power distribution scheme.
2. The method for distributed economic dispatch of a specified time in a directed unbalanced network according to claim 1, wherein in step S1, the mathematical model of the economic dispatch problem is as follows:
wherein ,xi In order to output the power of the power supply,respectively the lower limit and the upper limit of the output power of the ith generating set, f i (x i ) G is the generating cost function of the ith generating set i (x i ) Is a local constraint function of the ith generator set.
3. The method for distributed economic dispatch of designated time in a directed unbalanced network according to claim 1, wherein the obtaining mode of the weighted adjacency matrix a in step S4 is specifically as follows:
if the generator set i in the system can receive the information of the neighbor generator set j, setting wherein |Ni I represents the ingress neighbor node of genset iThe number of points;
if the generator set i cannot receive the information of the neighbor generator set j, setting a ij ＝0；
In addition, since the data of the generator set i itself is also available, the arrangement is provided
4. The method for distributed economic dispatch of designated time in a directed unbalanced network according to claim 1 wherein each generating set in S5 selects an initial decision behavior x according to its own decision feasible region i (0) When the method is used, the generator sets i and i epsilon V can be arbitrarily selected, wherein V is a set formed by all the generator set numbers.
5. The method for distributed economic dispatch of a specified time in a directed unbalanced network according to claim 1, wherein the method for obtaining the initial values of the variables in S5 is specifically as follows:
the weight gain variable z i (0) The initial value is set asI.e. the n-dimensional vector with the i-th element being n and the other elements being 0.
6. The method for distributed economic dispatch of a specified time in a directed unbalanced network according to claim 1, wherein the specific update mode of the update policy in step S7 is as follows:
wherein the laplace matrix is defined as l=i n -A，I n Is a unit array, and the non-periodic sampling time is defined asDelta is a small positive number; z i (t p ),z j (t p ) Respectively representing the non-periodic sampling time t of the generator sets i and j p Time weight gain variable z i Value of z i (t) represents the value of the weight gain variable of the generator set i at the current time t.
7. The method for distributed economic dispatch of a specified time in a directed unbalanced network according to claim 1, wherein the error variable e is updated by using a proportional-integral control concept in step S8 i The specific updating mode of (a) is as follows:
wherein ,for non-periodic sampling instants delta is a small positive number, control parameter +.> As weight gain variable z i A steady state value obtained at the end of the first phase for the ith component of (a); x is x i (t) represents the power generation value of the generator set i at the current time t, e i (t),e i (t p ) Error variables e each representing a generator set i i At the current momentt and non-periodic sampling instant t p Is a value of (2); />Respectively representing the non-periodic sampling time t of the generator sets i and j p A gradient value of time; τ represents the integral variable.
8. The method for distributed economic dispatch of a specified time in a directed unbalanced network according to claim 1, wherein the specific update mode of the optimal output power in step S9 is as follows:
wherein ,for aperiodic sampling time, the control parameter isMatrix->As a diagonal matrix ρ 2 (ZL+L T Z T ) Representation matrix ZL+L T Z T Is a second small feature root of (2); c i (t),c i (t p ) Respectively represents the punishment factor c of the generator set i i At the current time t and the non-periodic sampling time t p Values at that time.
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