CN116937536A - Micro-grid optimal scheduling method based on consistency and gradient descent method - Google Patents
Micro-grid optimal scheduling method based on consistency and gradient descent method Download PDFInfo
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
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- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
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- H02J3/46—Controlling of the sharing of output between the generators, converters, or transformers
- H02J3/466—Scheduling the operation of the generators, e.g. connecting or disconnecting generators to meet a given demand
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Abstract
The invention relates to a micro-grid optimal scheduling method based on a consistency and gradient descent method, which comprises the following steps of: researching a complete distributed optimal scheduling strategy of the micro-grid in an island operation mode, and firstly giving a scheduling model of the micro-grid; introducing a graph theory basis, configuring an agent for each power element, and constructing a fully distributed optimal scheduling system of the micro-grid by taking the agent as a framework; providing a complete distributed algorithm based on a consistency principle and a gradient descent method; the optimization of the generation cost of the micro-grid and the improvement of the convergence speed are realized by combining a gradient descent method and a consistency principle, and the flexible change of the topological structure is dealt with by updating parameters through local information interaction between the controllable units and adjacent controllable units; simulation calculation analysis; the invention has the advantages of only needing local and adjacent controllable unit information, realizing optimal scheduling by utilizing local information and being capable of coping with flexible change of the topological structure.
Description
Technical Field
The invention belongs to the technical field of micro-grids, and particularly relates to a micro-grid optimal scheduling method based on a consistency and gradient descent method.
Background
The increasingly depleted fossil energy sources and the increasingly worsened environmental pollution problems lead the students at home and abroad to study low-carbon power generation technology and more efficient equipment in electric power systems, leading to diversified development of distributed power generation (Distributed Generation, DG), including renewable power generation and distributed energy storage systems (Energy Storage System, ESS), meanwhile, due to the increase of load types in the electric power systems, flexible load plays an important role in maintaining power balance, so that the concept of micro-grid is generated, the micro-grid is in an island mode, in order to ensure safe and economic operation of the micro-grid, a large number of distributed power generation units are fused inside the micro-grid, due to the fact that the power generation characteristic diversity of various power generation units is different, the control characteristic and the power generation cost characteristic are different, the goal of micro-grid operation scheduling is to reduce the economic cost of the whole micro-grid while guaranteeing the whole real-time power balance of the micro-grid and meeting the safety constraint, the economic cost of the whole micro-grid is changed into a uniform consumption micro-rate increasing criterion according to the power distribution problem, the fact that the micro-grid is in a uniform, however, the micro-grid control unit is not required to be in a uniform and the form of the optimal computing and the optimal control information is based on the principle of the current principle of the distributed power distribution, the current principle of the distributed power control units, the micro-grid has the need of the optimal information, the optimal information is calculated and the optimal and the principle is based on the principle of the current information-based on the incremental and the principle of the distributed power control, the energy-transfer, the main-control unit has the high-control information, and the energy has the optimal performance, and the optimal control has the advantages of the energy-control system has the optimal performance, updating local parameters, wherein the convergence condition is total power deviation, and solving the problem that the power deviation is unavoidable and the output power of the controllable unit needs to be summed; therefore, it is very necessary to provide a micro grid optimization scheduling method based on a consistency and gradient descent method, which only needs local and adjacent controllable unit information, realizes optimization scheduling by using local information, and can cope with flexible topological structure changes.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, and provides a micro-grid optimal scheduling method based on a consistency and gradient descent method, which only needs local and adjacent controllable unit information, utilizes local information to realize optimal scheduling and can cope with flexible change of a topological structure.
The purpose of the invention is realized in the following way: the micro-grid optimal scheduling method based on the consistency and gradient descent method comprises the following steps of:
step 1: micro-grid scheduling model: researching a complete distributed optimal scheduling strategy of the micro-grid in an island operation mode, and firstly giving a scheduling model of the micro-grid;
step 2: graph theory basis: introducing a graph theory basis, configuring an agent for each power element, and constructing a fully distributed optimal scheduling system of the micro-grid by taking the agent as a framework;
step 3: fully distributed optimized scheduling: providing a complete distributed algorithm based on a consistency principle and a gradient descent method;
step 4: the optimization of the generation cost of the micro-grid and the improvement of the convergence speed are realized by combining a gradient descent method and a consistency principle, and the flexible change of the topological structure is dealt with by updating parameters through local information interaction between the controllable units and adjacent controllable units;
Step 5: simulation calculation analysis: the validity and feasibility of the fully distributed optimal scheduling strategy are verified based on the system simulation of the IEEE-14 node and the IEEE-39 node.
The dispatching model of the micro-grid in the step 1 specifically comprises the following steps: the economic dispatch problem is to maintain the active power balance of the generator, the energy storage unit, the flexible load and the non-adjustable load, so that the system can realize the maximization of economic benefit; the objective function is:
the objective function may be converted to a minimum:
wherein r, m and s are the numbers of the generator, the energy storage unit and the flexible load respectively; c (C) i (P Gi ) Is a cost function of the generator i; c (C) j (P Bj ) For forming the energy-storage unit jA present function; c (C) x (P Lx ) Is a benefit function of the flexible load x; the benefit function is defined by the total load of the different tasks rather than the power consumption of the individual devices:
wherein a is Gi 、b Gi 、c Gi Is a cost coefficient of the generator i; p (P) Gi To which an active force is applied; a, a Bj The cost coefficient of the energy storage unit j; p (P) Bj To which an active force is applied; a, a Lx 、b Lx Is the cost factor of the flexible load x; p (P) Lx For which power is dissipated.
The dispatching model of the micro-grid in the step 1 comprises power balance constraint and upper and lower limit constraints of output, wherein the power balance constraint is as follows:
wherein W is a non-schedulable load; the upper and lower limits of the force are constrained as follows:
P Gimin (k)＝max(P Gimin ,P Gi (k-1)-ΔD Gi )(6)，
P Gimax (k)＝min(P Gimax ,P Gi (k-1)+ΔU Gi )(7)，
P Bjmin (k)＝max(P Bjmin ,P Bj (k-1)-ΔD Bj )(8)，
P Bjmax (k)＝min(P Bjmax ,P Bj (k-1)+ΔU Bj )(9)，
Wherein P is Gi (k)、P Bj (k) The active output of the generator i and the energy storage unit j at the moment k are respectively; p (P) Gi (k-1)、P Bj (k-1) is the active output of the generator i and the energy storage unit j at the moment k-1 respectively; p (P) Gimin (k)、P Bjmin (k) Active power-adjustable at time k for generator i and energy storage unit j respectivelyA lower limit; p (P) Gimax (k)、P Bjmax (k) The upper limit of the power generator i and the energy storage unit j which are adjustable in the active power at the moment k is respectively set; ΔD of Gi 、ΔD Bj Respectively a generator i and an energy storage unit j in [ k-1, k ]]Maximum value of power reducible in time period; deltaU Gi 、ΔU Bj Respectively a generator i and an energy storage unit j in [ k-1, k ]]Maximum value of power that can be increased during a period of time; p (P) Gimin 、P Bjmin The lower limits of the active output of the generator i and the energy storage unit j are respectively set; p (P) Gimax 、P Bjmax The upper limits of the active output of the generator i and the energy storage unit j are respectively set; p (P) Lxmin 、P Lxmax The upper and lower limits of the power dissipated by the flexible load x, respectively.
The graph theory basis in the step 2 is specifically as follows: based on the dispatching model of the micro-grid in the step 1, configuring an agent for each electric power element, constructing a fully distributed dispatching system of the micro-grid by taking multiple agents as a framework, and carrying out information interaction by a communication network, so that the communication relationship among the agents in the dispatching system of the micro-grid can be represented by a graph G= (V, E), wherein a finite non-empty vertex set V= {1, 2..N } is an agent set of a directed graph G, and the elements thereof are called vertices and represent actual electric power elements; the edge set E is all unordered connections of vertices, the elements of which are called edges, representing the communication channels between the power elements; for each edge, a real weight graph is assigned, a matrix A is defined as an adjacent matrix, diagonal elements of the adjacent matrix A are all 0, and non-diagonal elements a ij Is the number of edges from agent i to agent j; in order to deeply quantify the communication degree of each intelligent agent in a communication network, a Laplace matrix L= [ L ] is introduced ij ]Wherein, the method comprises the steps of, wherein,
the fully distributed algorithm based on the consistency principle and the gradient descent method in the step 3 is specifically: in the consistency principle used, the consistency variable is set as the consumption micro-increment rate of each adjustable unit, so according to the 'equal consumption micro-increment rate criterion': when all the consistent variables are converged to the same value, the obtained result is an optimal solution, and the calculation result is required to meet the necessary constraint conditions, so that the deviation adjustment item is added to correct the calculation result on the basis of the constraint conditions, and the feasibility of the calculation result is ensured; on the other hand, the gradient descent concept can optimize continuous and tiny objective functions, so that the calculation process of the consistency algorithm is further optimized through a random gradient descent optimization method-RMSprop algorithm, and the overall convergence speed is accelerated.
The consistency principle in the step 3 is specifically as follows: the essence of the consistency algorithm is that the local node and the adjacent node in the distributed system carry out information interaction, and the consistency variable of the local node is updated, so that the consistency variable of each node in the communication network is converged to a stable common value; definition x i E R represents a consistent state quantity for node i, and the state information for the node may represent some physical quantity, such as: output power, incremental cost; for all nodes i, j, if and only if x i ＝x j When the consistency variable of the nodes in the network is consistent, namely: x is x 1 ＝x 2 ＝...＝x n (11) The first order continuous consistency algorithm can be expressed as:wherein: a, a ij Is the j-th column element of the i-th row of the adjacency matrix A; considering that a certain time is required for communication transmission between distributed power sources, a discrete consistency algorithm is used to describe the dynamic characteristics of the micro-grid, and the discrete consistency algorithm can be expressed as: />Wherein: k is an iterative sequence; d, d ij The elements of the j-th column of the i-th row of the state transition matrix D can be expressed as: />The slope of a tangent line at a certain point on the consumption characteristic curve is the consumption micro increment rate of the point, namely the increment cost, the increment cost is selected as a consistency variable, and the expression of the increment cost is as follows:from formula (3): />For simplicity, P is used respectively i 、λ i Representing the active force and incremental cost of element i, the incremental cost consistency update rule is, according to equation (13):after a sufficient number of iterations, the incremental cost of all controllable elements in the system will converge to a fixed value: / >Wherein lambda is i (0) Is the initial incremental cost of the controllable element j.
The consistency principle in the step 3 adopts an incremental cost consistency algorithm, which possibly leads the power of a certain controllable unit to exceed the power limit, and when the power limit is reached, the incremental cost of the unit i and the incremental cost lambda of the system are calculated * The relation is:
according to the update rule, the incremental cost lambda is selected i As state variables of the consistency algorithm, a 'consistency term' is formed, and in the iterative process, lambda is known from the formula (18) i Will gradually approach a "fixed value" which is not necessarily lambda when the power balance is not met * Therefore, an adjustment term is added to perform feedback correction to accurately solve the problem, so that the result approaches lambda * The iterative formula of the consistent term + the adjustment term is:
in phi i (k) To adjust items; the matrix V is the transposed matrix of the matrix D; μ is a power balance adjustment coefficient; p (P) i (k+1) performing a calculation of k+1 iterations for element i; in the iterative calculation processWherein, the power adjustment term determines the convergence direction of the consistency variable by using a formula (21) so that the active force of each unit meets the constraint condition of an equation, and an optimal solution is obtained, which is proved as follows: for simplicity, formula (21) is written in vector form: phi (k+1) =vphi (k) - (P (k+1) -P (k)) (22), 1 T φ(k+1)＝1 T Vφ(k)-1 T [P(k+1)-P(k)](23) Wherein, the matrix V is a non-negative column random matrix, namely, the sum of column vectors of V is 1;1 T Is a unit row vector, thus 1 T V＝1 T ；1 T φ(k+1)＝1 T φ(k)-1 T [P(k+1)-P(k)](24)，1 T [P(k+1)+φ(k+1)]＝1 T [P(k)+φ(k)](25) Reducing formula (25) to a variable form, namely: />Wherein N is the total set of the generator, the energy storage unit and the flexible load; thus, the initial value is set to satisfy +.>So thatFor active absence of system, in iteration, phi i Will converge to 0 when all phi in the system i Upon convergence to 0, the active deficit in the system is 0, the equality constraint is satisfied, and the incremental cost λ of each element in the system i Convergence to system delta cost lambda under inequality constraint * 。
The gradient descent method in the step 3 specifically comprises the following steps: the gradient descent method is an optimization algorithm based on the first-order property of the function, has the advantages of small storage capacity, simple structure and easiness in implementation, the gradient direction is the direction in which the function ascends most rapidly at a given point, then the opposite direction of the gradient is the direction in which the function descends most rapidly at the given point, when the objective function is minimized, the gradient descent method can be used for carrying out one-step iterative solution, and for a convex function in the objective function, the result obtained by the gradient descent method is necessarily a global optimal solution; in order to optimize the problem that the swing amplitude of an objective function is overlarge in the iteration process by using a gradient descent optimization algorithm-RMSprop algorithm, the algorithm combines the square root of the square sum of historical gradients controlled by attenuation coefficients, so that the learning rate of each parameter is different, the effect is that the gradient descent optimization algorithm-RMSprop algorithm obtains a larger progress in the direction of a more gentle parameter space, and the steep direction is gentle, so that the iteration speed is increased.
The objective function C (P) of the gradient descent method in the step 3 is a convex function, and the gradient can be expressed asThe variable v (k) of the RMSprop algorithm is the square term +.>Compared with the AdaGrad algorithm, the learning rate of each element of the independent variable is not always reduced or unchanged in the iterative process, the acquisition of attenuation coefficient control history information is increased, the RMSprop algorithm readjusts the learning rate of each element in the independent variable of the objective function through element operation, and then the updated independent variable meets the following formula:
P(k+1)＝P(k)-η(k+1)g k (29) Wherein, beta is an attenuation coefficient; delta is the learning rate; the constant of ε added to maintain numerical stability is usually 10 -8 The method comprises the steps of carrying out a first treatment on the surface of the Since equation (29) is a centralized controllable unit power update principle, and does not belong to a fully distributed algorithm, a distributed improvement of equation (29) is required: /> Wherein N is i A collection of agents that are in communication with agent i; w (w) ij Is an element in the weight matrix; n is n i Number of agents communicating for agent i; by improved formulas (30) - (31), the complete distributed form of the RMSprop algorithm is realized, and the gradient descent principle of the RMSprop algorithm is integrated into the consistency principle The convergence speed of the algorithm is improved, and the calculation time of the algorithm is reduced.
The fully distributed optimal scheduling algorithm flow based on the consistency principle and the RMSprop algorithm in the step 3 comprises the following steps:
step (1): initial value of input system is satisfied
Step (2): forming a Laplace matrix according to the topological network diagram, and acquiring a state transition matrix and a w matrix;
step (3): updating the output and incremental cost of the controllable unit using RMSprop algorithm;
step (4): updating a consistency state variable, namely an incremental cost, of each controllable unit by using a consistency algorithm according to a formula (20); if the convergence condition is met, obtaining an optimal solution; and otherwise, updating the variables again.
The invention has the beneficial effects that: the invention is a micro-grid optimizing and dispatching method based on consistency and gradient descent method, in use, the invention provides a completely distributed optimizing and dispatching strategy based on consistency principle and gradient descent method, which is a distributed energy management method based on consistency + innovation term, used for coordinating controllable units in micro-grid, eliminating centralized processor and leader, compared with centralized regulation mode, the optimizing and dispatching strategy provided by the invention only needs information of local and adjacent controllable units in completely distributed regulation, realizes optimizing and dispatching by using local information, and can cope with flexible change of topological structure; by combining the gradient descent method with the consistency principle, the iteration times are effectively reduced, and the convergence efficiency of the algorithm is improved; the incremental cost of the controllable units is used as a consistency variable to design a complete distributed algorithm, so that the output power of the controllable units is reasonably distributed on the basis of ensuring the power balance (namely, the micro-grid realizes reasonable power distribution under the condition of keeping the power balance in an island mode), the running cost of the micro-grid is optimized, and the method has important significance for improving the economy of the micro-grid; the invention has the advantages of only needing local and adjacent controllable unit information, realizing optimal scheduling by utilizing local information and being capable of coping with flexible change of the topological structure.
Drawings
FIG. 1 is a flow chart of an improved fully distributed algorithm of the present invention.
Fig. 2 is a schematic diagram of an IEEE-14 node system of the present invention.
FIG. 3 is a schematic diagram of the power output of a controllable unit of the incremental cost uniformity convergence process of the present invention.
FIG. 4 is a schematic diagram of the system imbalance power of the incremental cost uniformity convergence process of the present invention.
FIG. 5 is a schematic diagram of the power output of a controllable unit of the incremental cost uniformity convergence process when the controllable unit power is over time in accordance with the present invention.
FIG. 6 is a system imbalance power schematic diagram of an incremental cost uniformity convergence process at a time when the controllable unit power is over-time in accordance with the present invention.
FIG. 7 is a schematic diagram of the power output of a controllable unit of the incremental cost uniformity convergence process at the time of power plug and play of the controllable unit according to the present invention.
FIG. 8 is a schematic diagram of the system imbalance power of the incremental cost uniformity convergence process at plug and play of the controllable unit power of the present invention.
FIG. 9 is a schematic diagram of the power output of a controllable unit of the incremental cost uniformity convergence process at the time of a controllable unit power failure of the present invention.
FIG. 10 is a system imbalance power schematic diagram of an incremental cost uniformity convergence process at the time of a controllable unit power failure of the present invention.
FIG. 11 is a schematic diagram of the power output of a controllable unit of the incremental cost uniformity convergence process of the multiple dispatch instruction of the present invention.
FIG. 12 is a system unbalanced power diagram illustrating an incremental cost uniformity convergence procedure for multiple dispatch instructions according to the present invention.
FIG. 13 is a graph showing unbalanced power for three algorithms of the present invention.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
Example 1
As shown in fig. 1-13, the micro-grid optimization scheduling method based on the consistency and gradient descent method comprises the following steps:
step 1: micro-grid scheduling model: researching a complete distributed optimal scheduling strategy of the micro-grid in an island operation mode, and firstly giving a scheduling model of the micro-grid;
step 2: graph theory basis: introducing a graph theory basis, configuring an agent for each power element, and constructing a fully distributed optimal scheduling system of the micro-grid by taking the agent as a framework;
step 3: fully distributed optimized scheduling: providing a complete distributed algorithm based on a consistency principle and a gradient descent method;
step 4: the optimization of the generation cost of the micro-grid and the improvement of the convergence speed are realized by combining a gradient descent method and a consistency principle, and the flexible change of the topological structure is dealt with by updating parameters through local information interaction between the controllable units and adjacent controllable units;
Step 5: simulation calculation analysis: the validity and feasibility of the fully distributed optimal scheduling strategy are verified based on the system simulation of the IEEE-14 node and the IEEE-39 node.
The dispatching model of the micro-grid in the step 1 specifically comprises the following steps: the economic dispatch problem is to maintain the active power balance of the generator, the energy storage unit, the flexible load and the non-adjustable load, so that the system can realize the maximization of economic benefit; the objective function is:the objective function may be converted to a minimum:wherein r, m and s are the numbers of the generator, the energy storage unit and the flexible load respectively; c (C) i (P Gi ) Cost function for generator i；C j (P Bj ) Is a cost function of the energy storage unit j; c (C) x (P Lx ) Is a benefit function of the flexible load x; the benefit function is defined by the total load of the different tasks rather than the power consumption of the individual devices:wherein a is Gi 、b Gi 、c Gi Is a cost coefficient of the generator i; p (P) Gi To which an active force is applied; a, a Bj The cost coefficient of the energy storage unit j; p (P) Bj To which an active force is applied; a, a Lx 、b Lx Is the cost factor of the flexible load x; p (P) Lx For which power is dissipated.
The dispatching model of the micro-grid in the step 1 comprises power balance constraint and upper and lower limit constraints of output, wherein the power balance constraint is as follows:wherein W is a non-schedulable load; the upper and lower limits of the force are constrained as follows: / >P Gimin (k)＝max(P Gimin ,P Gi (k-1)-ΔD Gi )(6)，P Gimax (k)＝min(P Gimax ,P Gi (k-1)+ΔU Gi )(7)，P Bjmin (k)＝max(P Bjmin ,P Bj (k-1)-ΔD Bj )(8)，P Bjmax (k)＝min(P Bjmax ,P Bj (k-1)+ΔU Bj ) (9) wherein, P Gi (k)、P Bj (k) The active output of the generator i and the energy storage unit j at the moment k are respectively; p (P) Gi (k-1)、P Bj (k-1) is the active output of the generator i and the energy storage unit j at the moment k-1 respectively; p (P) Gimin (k)、P Bjmin (k) The lower limit of the power of the generator i and the energy storage unit j at the moment k is respectively adjustable; p (P) Gimax (k)、P Bjmax (k) The upper limit of the power generator i and the energy storage unit j which are adjustable in the active power at the moment k is respectively set; ΔD of Gi 、ΔD Bj Respectively a generator i and an energy storage unit j in [ k-1, k ]]Maximum value of power reducible in time period; deltaU Gi 、ΔU Bj Respectively a generator i and an energy storage unit j in [ k-1, k ]]Maximum value of power that can be increased during a period of time; p (P) Gimin 、P Bjmin The lower limits of the active output of the generator i and the energy storage unit j are respectively set; p (P) Gimax 、P Bjmax The upper limits of the active output of the generator i and the energy storage unit j are respectively set; p (P) Lxmin 、P Lxmax The upper and lower limits of the power dissipated by the flexible load x, respectively.
The graph theory basis in the step 2 is specifically as follows: based on the dispatching model of the micro-grid in the step 1, configuring an agent for each electric power element (a generator, an energy storage unit and a flexible load), constructing a fully distributed dispatching system of the micro-grid by taking a plurality of agents as a framework, and carrying out information interaction by a communication network, so that the communication relationship among the agents in the dispatching system of the micro-grid can be represented by a graph G= (V, E), wherein a finite non-empty vertex set V= {1,2., N } is an agent set of a directed graph G, and the elements thereof are called vertexes and represent actual electric power elements; the edge set E is all unordered connections of vertices, the elements of which are called edges, representing the communication channels between the power elements; for each edge, a real weight graph is assigned, a matrix A is defined as an adjacent matrix, diagonal elements of the adjacent matrix A are all 0, and non-diagonal elements a ij Is the number of edges from agent i to agent j; to more deeply quantify the degree of communication of each agent in a communication network, a Laplace matrix is introducedWherein, the liquid crystal display device comprises a liquid crystal display device,
the fully distributed algorithm based on the consistency principle and the gradient descent method in the step 3 is specifically: in the consistency principle used, the consistency variable is set as the consumption micro-increment rate of each adjustable unit, so according to the 'equal consumption micro-increment rate criterion': when all the consistent variables are converged to the same value, the obtained result is an optimal solution, and the calculation result is required to meet the necessary constraint conditions, so that the deviation adjustment item is added to correct the calculation result on the basis of the constraint conditions, and the feasibility of the calculation result is ensured; on the other hand, the gradient descent concept can optimize continuous and tiny objective functions, so that the calculation process of the consistency algorithm is further optimized through a random gradient descent optimization method-RMSprop algorithm, and the overall convergence speed is accelerated.
The consistency principle in the step 3 is specifically as follows: the essence of the consistency algorithm is that the local node and the adjacent node in the distributed system carry out information interaction, and the consistency variable of the local node is updated, so that the consistency variable of each node in the communication network is converged to a stable common value; definition x i E R represents a consistent state quantity for node i, and the state information for the node may represent some physical quantity, such as: output power, incremental cost; for all nodes i, j, if and only if x i ＝x j When the consistency variable of the nodes in the network is consistent, namely: x is x 1 ＝x 2 ＝...＝x n (11) The first order continuous consistency algorithm can be expressed as:wherein: a, a ij Is the j-th column element of the i-th row of the adjacency matrix A; considering that a certain time is required for communication transmission between distributed power sources, a discrete consistency algorithm is used to describe the dynamic characteristics of the micro-grid, and the discrete consistency algorithm can be expressed as: />Wherein: k is an iterative sequence; d, d ij The elements of the j-th column of the i-th row of the state transition matrix D can be expressed as: />The slope of a tangent line at a certain point on the consumption characteristic curve is the consumption micro increment rate of the point, namely the increment cost, the increment cost is selected as a consistency variable, and the expression of the increment cost is as follows: />From formula (3): />For simplicity, P is used respectively i 、λ i Representing the active force and incremental cost of element i, the incremental cost consistency update rule is, according to equation (13): />After a sufficient number of iterations, the incremental cost of all controllable elements in the system will converge to a fixed value: / >Wherein lambda is i (0) Is the initial incremental cost of the controllable element j.
The consistency principle in the step 3 adopts an incremental cost consistency algorithm, which possibly leads the power of a certain controllable unit to exceed the power limit, and when the power limit is reached, the incremental cost of the unit i and the incremental cost lambda of the system are calculated * The relation is:according to the update rule, the incremental cost lambda is selected i As state variables of the consistency algorithm, a 'consistency term' is formed, and in the iterative process, lambda is known from the formula (18) i Will gradually approach a "fixed value" which is not necessarily lambda when the power balance is not met * Therefore, an adjustment term is added to perform feedback correction to accurately solve the problem, so that the result approaches lambda * The iterative formula of the consistent term + the adjustment term is: /> In phi i (k) To adjust items; the matrix V is the transposed matrix of the matrix D; μ is a power balance adjustment coefficient; p (P) i (k+1) performing a calculation of k+1 iterations for element i; in the iterative calculation process, the power adjustment term determines the convergence direction of the consistency variable by using a formula (21) so that the active force of each unit meets the constraint condition of an equation to obtain an optimal solution, and the method is proved as follows: for simplicity, formula (21) is written in vector form ：φ(k+1)＝Vφ(k)-(P(k+1)-P(k))(22)，1 T φ(k+1)＝1 T Vφ(k)-1 T [P(k+1)-P(k)](23) Wherein, the matrix V is a non-negative column random matrix, namely, the sum of column vectors of V is 1;1 T Is a unit row vector, thus 1 T V＝1 T ；1 T φ(k+1)＝1 T φ(k)-1 T [P(k+1)-P(k)](24)，1 T [P(k+1)+φ(k+1)]＝1 T [P(k)+φ(k)](25) Reducing formula (25) to a variable form, namely:wherein N is the total set of the generator, the energy storage unit and the flexible load; thus, the initial value is set to satisfy +.>Make->For active absence of system, in iteration, phi i Will converge to 0 when all phi in the system i Upon convergence to 0, the active deficit in the system is 0, the equality constraint is satisfied, and the incremental cost λ of each element in the system i Convergence to system delta cost lambda under inequality constraint * 。
The gradient descent method in the step 3 specifically comprises the following steps: the gradient descent method is an optimization algorithm based on the first-order property of the function, has the advantages of small storage capacity, simple structure and easiness in implementation, the gradient direction is the direction in which the function ascends most rapidly at a given point, then the opposite direction of the gradient is the direction in which the function descends most rapidly at the given point, when the objective function is minimized, the gradient descent method can be used for carrying out one-step iterative solution, and for a convex function in the objective function, the result obtained by the gradient descent method is necessarily a global optimal solution; in order to optimize the problem that the swing amplitude of an objective function is overlarge in the iteration process by using a gradient descent optimization algorithm-RMSprop algorithm, the algorithm combines the square root of the square sum of historical gradients controlled by attenuation coefficients, so that the learning rate of each parameter is different, the effect is that the gradient descent optimization algorithm-RMSprop algorithm obtains a larger progress in the direction of a more gentle parameter space, and the steep direction is gentle, so that the iteration speed is increased.
The objective function C (P) of the gradient descent method in the step 3 is a convex function, and the gradient can be expressed asThe variable v (k) of the RMSprop algorithm is the square term +.>Compared with the AdaGrad algorithm, the learning rate of each element of the independent variable is not always reduced or unchanged in the iterative process, the acquisition of attenuation coefficient control history information is increased, the RMSprop algorithm readjusts the learning rate of each element in the independent variable of the objective function through element operation, and then the updated independent variable meets the following formula:
P(k+1)＝P(k)-η(k+1)g k (29) Wherein, beta is an attenuation coefficient; delta is the learning rate; the constant of ε added to maintain numerical stability is usually 10 -8 The method comprises the steps of carrying out a first treatment on the surface of the Since equation (29) is a centralized controllable unit power update principle, and does not belong to a fully distributed algorithm, a distributed improvement of equation (29) is required: /> Wherein N is i A collection of agents that are in communication with agent i; w (w) ij Is an element in the weight matrix; n is n i Number of agents communicating for agent i; through improved formulas (30) - (31), the complete distributed form of the RMSprop algorithm is realized, and meanwhile, the gradient descent principle of the RMSprop algorithm is integrated into the consistency principle, so that the convergence speed of the algorithm is improved, and the calculation time of the algorithm is shortened.
The fully distributed optimal scheduling algorithm flow based on the consistency principle and the RMSprop algorithm in the step 3 comprises the following steps:
step (1): initial value of input system is satisfied
Step (2): forming a Laplace matrix according to the topological network diagram, and acquiring a state transition matrix and a w matrix;
step (3): updating the output and incremental cost of the controllable unit using RMSprop algorithm;
step (4): updating a consistency state variable, namely an incremental cost, of each controllable unit by using a consistency algorithm according to a formula (20); if the convergence condition is met, obtaining an optimal solution; and otherwise, updating the variables again.
In this embodiment, in order to verify the validity of the proposed fully distributed algorithm of the micro-grid based on the consistency principle and the gradient descent method, the real-time power distribution of the micro-grid is simulated by using the adjusted IEEE-14 node and IEEE-39 node systems through MATLAB software, and the IEEE-39 node structure diagram is omitted due to space limitation, and the IEEE-14 node is shown in FIG. 2: wherein the dashed line indicates that G15 is used only in example 3, nodes 1, 2, 3 and 6 are generators, node 7 is an energy storage unit, and the remaining nodes are flexible loads; the parameters of each generator, energy storage unit and flexible load in fig. 2 are shown in table 1:
TABLE 1 various types of generators, energy storage units and flexible load parameters
Example one, incremental cost consistency simulation: the present example verifies the power allocation availability of the improved fully distributed algorithm in an IEEE-14 node system; assuming an initial unbalanced power of 20kW and a power balance adjustment coefficient μ=0.01, the controllable element incremental cost consistency convergence procedure in an IEEE-14 node system is as shown in fig. 3-4: as can be seen from fig. 3, after 60 iterations, the algorithm converges, and the consistency variable of the controllable unit in the system: the incremental costs converge to a common value and the resulting solution is the optimal solution according to the "equal consumption micro-rate criterion". As can be seen from fig. 4, when the algorithm converges, the power output of the controllable unit tends to be stable, the unbalanced power of the system converges to 0, the power balance requirement is met, and the output of the controllable unit meets the upper and lower power limit requirements; in summary, the improved fully distributed algorithm provided by the invention can realize power distribution under the condition of reducing the power generation cost of the controllable unit;
incremental cost consistency simulation of case two and beyond the limit of controllable unit power: in order to verify the effectiveness of the proposed algorithm when the power output of the controllable unit in the system reaches a limit; g3 has a maximum output power of 50kW, and assuming an initial imbalance power of 115kW, the incremental cost uniformity convergence process for the controllable unit is shown in FIGS. 5-6: as can be seen from fig. 5, as the number of iterations increases, the output power of the flexible load changes, the output power of the generator and the energy storage unit increases, and when the iteration reaches the 4 th time, the output power of G3 reaches the upper limit 50kW, and as can be seen from equation (16), the incremental cost reaches the maximum value, and in order to maintain the power balance, other generators and energy storage units will bear more power output than when the constraint of the upper limit and the lower limit of the power is not considered; as can be seen from fig. 6, when the algorithm converges, the unbalanced power of the system tends to be 0, and the effectiveness of the proposed algorithm is proved when the power output of the controllable unit in the system reaches the limit;
Thirdly, incremental cost consistency simulation during plug and play of the controllable unit: in order to verify the validity of the proposed algorithm in the system when the controllable units are plug and play; the following scenario is set: the initial environmental condition of the simulation experiment is the same as that of the algorithm 1, when the algorithm iterates to 100 times, the generator G15 is connected into the IEEE-14 node system, the connection position is shown in the figure 2, and the convergence of the algorithm is shown in Cheng Rutu-8: as can be seen from fig. 7, after the generator G15 is connected to the system, since the initial power output is 0, it will have a certain power output during the iterative process of the algorithm, and compared with the output power of other controllable units before being connected, the output power of other controllable units is reduced, and the incremental cost of the controllable units is also reduced; as can be seen from fig. 8, although there is a certain unbalanced power in the iterative process, when the algorithm converges, the unbalanced power tends to 0, and the system power reaches balance, so that the proposed algorithm can reach incremental cost consistency when the controllable unit is plug and play;
fourth, incremental cost consistency simulation when the controllable unit fails: the micro-grid operation needs to continue to run stably after the controllable unit fails and exits, so that the micro-grid operation has certain stability; in order to verify the effectiveness of the proposed algorithm in the event of a failure of a controllable unit, the following scenario is set: the initial conditions are consistent with the previous example, when the algorithm iterates to 100 times, the generator G1 fails to exit operation, and the convergence process is as shown in fig. 9-10: as can be seen from fig. 9, after the generator G1 fails and exits from operation, the power output is reduced from 53.28kW to 0, and 53.28kW of output power is borne by the remaining controllable units, resulting in an increase in output power of the remaining controllable units, and an increase in convergence value of incremental cost of each controllable unit as compared with that in normal operation; FIG. 10 shows that the system active power eventually reaches equilibrium, with an unbalanced power of 0, and the effectiveness of the proposed algorithm at the time of controllable unit failure is demonstrated;
Fifth, multiple scheduling instruction increment cost consistency simulation: in fact, the unbalanced power is changed in real time, and the scheduling instruction is changed; therefore, in order to verify the real-time performance of the algorithm, the unbalanced power is sequentially set to 20kw,36.8kw and 64.2kw, and the convergence process of the algorithm is as shown in fig. 11-12: as can be seen from fig. 11, when the unbalanced power is changed, the incremental cost of all the controllable units can be eventually consistent, and as the unbalanced power is increased, the incremental cost of each controllable unit is gradually increased, and the output of each generator can be stabilized; as can be seen from fig. 12, the unbalanced power eventually converges to 0, and the proposed algorithm can meet the basic multiple scheduling instruction requirement;
comparison simulation of the sixth calculation example and the traditional algorithm: in order to verify that the proposed algorithm is higher in iteration efficiency than the conventional algorithm, the section uses two more common conventional algorithms to solve the problem of the example 1, namely the initial unbalanced power is 20kW, and the convergence condition of the algorithm is unchanged; the iteration efficiency of each algorithm is reflected by comparing the variation of the unbalanced power in the iteration process, and the comparison result is shown in fig. 13: curve 1 represents a convergence graph of unbalanced power solved using a conventional centralized algorithm; curve 2 represents a convergence graph of unbalanced power solved using a classical coherency algorithm; curve 3 represents a convergence graph of unbalanced power solved using a fully distributed algorithm based on the principle of consistency and gradient descent method proposed by the present invention; as can be seen from fig. 13, the curve 1 converges after 100 iterations, and the calculation time is 0.732s; the curve 2 converges after 86 iterations, and the calculation time is 0.623s; the curve 3 converges after iteration for 60 times, and the calculation time is 0.417s; therefore, compared with other algorithms, the completely distributed algorithm based on the consistency principle and the gradient descent method provided by the invention has the advantages that the calculation time is reduced, and the efficiency is higher;
Example seven, IEEE-39 node incremental cost consistency simulation: the purpose of establishing an IEEE-39 node simulation system is to verify the effectiveness of the proposed algorithm in a micro-grid containing a large number of controllable units; assuming that the initial unbalanced power is 170kW, the algorithm converges when iterating 350 times, the incremental cost of each controllable unit in the system converges to a common value, and the common value is the optimal solution according to an equal consumption micro-increment rate criterion; thus, the effectiveness of the proposed algorithm in micro-grids containing a large number of controllable units is demonstrated.
The invention is a micro-grid optimizing and dispatching method based on consistency and gradient descent method, in use, the invention provides a completely distributed optimizing and dispatching strategy based on consistency principle and gradient descent method, which is a distributed energy management method based on consistency + innovation term, used for coordinating controllable units in micro-grid, eliminating centralized processor and leader, compared with centralized regulation mode, the optimizing and dispatching strategy provided by the invention only needs information of local and adjacent controllable units in completely distributed regulation, realizes optimizing and dispatching by using local information, and can cope with flexible change of topological structure; by combining the gradient descent method with the consistency principle, the iteration times are effectively reduced, and the convergence efficiency of the algorithm is improved; the incremental cost of the controllable units is used as a consistency variable to design a complete distributed algorithm, so that the output power of the controllable units is reasonably distributed on the basis of ensuring the power balance (namely, the micro-grid realizes reasonable power distribution under the condition of keeping the power balance in an island mode), the running cost of the micro-grid is optimized, and the method has important significance for improving the economy of the micro-grid; the invention has the advantages of only needing local and adjacent controllable unit information, realizing optimal scheduling by utilizing local information and being capable of coping with flexible change of the topological structure.
Claims (10)
1. The micro-grid optimal scheduling method based on the consistency and gradient descent method is characterized by comprising the following steps of: it comprises the following steps:
step 1: micro-grid scheduling model: researching a complete distributed optimal scheduling strategy of the micro-grid in an island operation mode, and firstly giving a scheduling model of the micro-grid;
step 2: graph theory basis: introducing a graph theory basis, configuring an agent for each power element, and constructing a fully distributed optimal scheduling system of the micro-grid by taking the agent as a framework;
step 3: fully distributed optimized scheduling: providing a complete distributed algorithm based on a consistency principle and a gradient descent method;
step 4: the optimization of the generation cost of the micro-grid and the improvement of the convergence speed are realized by combining a gradient descent method and a consistency principle, and the flexible change of the topological structure is dealt with by updating parameters through local information interaction between the controllable units and adjacent controllable units;
step 5: simulation calculation analysis: the validity and feasibility of the fully distributed optimal scheduling strategy are verified based on the system simulation of the IEEE-14 node and the IEEE-39 node.
2. The micro-grid optimization scheduling method based on the consistency and gradient descent method as claimed in claim 1, wherein: the dispatching model of the micro-grid in the step 1 specifically comprises the following steps: the economic dispatch problem is to maintain the active power balance of the generator, the energy storage unit, the flexible load and the non-adjustable load, so that the system can realize the maximization of economic benefit; the objective function is:
The objective function may be converted to a minimum:
wherein r, m and s are the numbers of the generator, the energy storage unit and the flexible load respectively; c (C) i (P Gi ) Is a cost function of the generator i; c (C) j (P Bj ) Is a cost function of the energy storage unit j; c (C) x (P Lx ) Is a benefit function of the flexible load x; the benefit function is defined by the total load of the different tasks rather than the power consumption of the individual devices:
wherein a is Gi 、b Gi 、c Gi Is a cost coefficient of the generator i; p (P) Gi To which an active force is applied; a, a Bj The cost coefficient of the energy storage unit j; p (P) Bj To which an active force is applied; a, a Lx 、b Lx Is the cost factor of the flexible load x; p (P) Lx For which power is dissipated.
3. The micro-grid optimization scheduling method based on the consistency and gradient descent method according to claim 2, wherein the method comprises the following steps: the dispatching model of the micro-grid in the step 1 comprises power balance constraint and upper and lower limit constraints of output, wherein the power balance constraint is as follows:
wherein W is a non-schedulable load; the upper and lower limits of the force are constrained as follows:
P Gimin (k)＝max(P Gimin ,P Gi (k-1)-ΔD Gi )(6)，P Gimax (k)＝min(P Gimax ,P Gi (k-1)+ΔU Gi )( 7)，
P Bjmin (k)＝max(P Bjmin ,P Bj (k-1)-ΔD Bj )(8)，P Bjmax (k)＝min(P Bjmax ,P Bj (k-1)+ΔU Bj ) (9) wherein, P Gi (k)、P Bj (k) The active output of the generator i and the energy storage unit j at the moment k are respectively; p (P) Gi (k-1)、P Bj (k-1) is the active output of the generator i and the energy storage unit j at the moment k-1 respectively; p (P) Gimin (k)、P Bjmin (k) The lower limit of the power of the generator i and the energy storage unit j at the moment k is respectively adjustable; p (P) Gimax (k)、P Bjmax (k) The upper limit of the power generator i and the energy storage unit j which are adjustable in the active power at the moment k is respectively set; ΔD of Gi 、ΔD Bj Respectively a generator i and an energy storage unit j in [ k-1, k ]]Maximum value of power reducible in time period; deltaU Gi 、ΔU Bj Respectively a generator i and an energy storage unit j in [ k-1, k ]]Maximum value of power that can be increased during a period of time; p (P) Gimin 、P Bjmin The lower limits of the active output of the generator i and the energy storage unit j are respectively set; p (P) Gimax 、P Bjmax The upper limits of the active output of the generator i and the energy storage unit j are respectively set; p (P) Lxmin 、P Lxmax The upper and lower limits of the power dissipated by the flexible load x, respectively.
4. The micro-grid optimization scheduling method based on the consistency and gradient descent method as claimed in claim 1, wherein: the graph theory basis in the step 2 is specifically as follows: based on the dispatching model of the micro-grid in the step 1, each power element is configured with an agent, and the micro-grid is built by taking multiple agents as framesThe system is a fully distributed scheduling system and performs information interaction through a communication network, so that the communication relationship among all the agents in the micro-grid scheduling system can be represented by a graph G= (V, E), wherein a finite non-empty vertex set V= {1,2.., N } is an agent set of a directed graph G, and elements of the agent set are called vertices and represent actual power elements; the edge set E is all unordered connections of vertices, the elements of which are called edges, representing the communication channels between the power elements; for each edge, a real weight graph is assigned, a matrix A is defined as an adjacent matrix, diagonal elements of the adjacent matrix A are all 0, and non-diagonal elements a ij Is the number of edges from agent i to agent j; to more deeply quantify the degree of communication of each agent in a communication network, a Laplace matrix is introducedWherein (1)>
5. The micro-grid optimization scheduling method based on the consistency and gradient descent method as claimed in claim 1, wherein: the fully distributed algorithm based on the consistency principle and the gradient descent method in the step 3 is specifically: in the consistency principle used, the consistency variable is set as the consumption micro-increment rate of each adjustable unit, so according to the 'equal consumption micro-increment rate criterion': when all the consistent variables are converged to the same value, the obtained result is an optimal solution, and the calculation result is required to meet the necessary constraint conditions, so that the deviation adjustment item is added to correct the calculation result on the basis of the constraint conditions, and the feasibility of the calculation result is ensured; on the other hand, the gradient descent concept can optimize continuous and tiny objective functions, so that the calculation process of the consistency algorithm is further optimized through a random gradient descent optimization method-RMSprop algorithm, and the overall convergence speed is accelerated.
6. The uniformity and gradient descent-based micro-device of claim 5 The power grid optimal scheduling method is characterized by comprising the following steps of: the consistency principle in the step 3 is specifically as follows: the essence of the consistency algorithm is that the local node and the adjacent node in the distributed system carry out information interaction, and the consistency variable of the local node is updated, so that the consistency variable of each node in the communication network is converged to a stable common value; definition x i E R represents a consistent state quantity for node i, and the state information for the node may represent some physical quantity, such as: output power, incremental cost; for all nodes i, j, if and only if x i ＝x j When the consistency variable of the nodes in the network is consistent, namely: x is x 1 ＝x 2 ＝...＝x n (11) The first order continuous consistency algorithm can be expressed as:wherein: a, a ij Is the j-th column element of the i-th row of the adjacency matrix A; considering that a certain time is required for communication transmission between distributed power sources, a discrete consistency algorithm is used to describe the dynamic characteristics of the micro-grid, and the discrete consistency algorithm can be expressed as: />Wherein: k is an iterative sequence; d, d ij The elements of the j-th column of the i-th row of the state transition matrix D can be expressed as: />The slope of a tangent line at a certain point on the consumption characteristic curve is the consumption micro increment rate of the point, namely the increment cost, the increment cost is selected as a consistency variable, and the expression of the increment cost is as follows: / >From formula (3): />For simplicity, P is used respectively i 、λ i Representing the active force and increment of unit iCost, according to equation (13), the incremental cost consistency update rule is: />After a sufficient number of iterations, the incremental cost of all controllable elements in the system will converge to a fixed value: />Wherein lambda is i (0) Is the initial incremental cost of the controllable element j.
7. The micro-grid optimization scheduling method based on the consistency and gradient descent method according to claim 6, wherein the method comprises the following steps: the consistency principle in the step 3 adopts an incremental cost consistency algorithm, which possibly leads the power of a certain controllable unit to exceed the power limit, and when the power limit is reached, the incremental cost of the unit i and the incremental cost lambda of the system are calculated * The relation is:according to the update rule, the incremental cost lambda is selected i As state variables of the consistency algorithm, a 'consistency term' is formed, and in the iterative process, lambda is known from the formula (18) i Will gradually approach a "fixed value" which is not necessarily lambda when the power balance is not met * Therefore, an adjustment term is added to perform feedback correction to accurately solve the problem, so that the result approaches lambda * The iterative formula of the consistent term + the adjustment term is: / > In phi i (k) To adjust items; the matrix V is the transposed matrix of the matrix D; μ is a power balance adjustment coefficient; p (P) i (k+1) performing a calculation of k+1 iterations for element i; in the course of the iterative computation process,the power adjustment term determines the convergence direction of the consistency variable using equation (21) so that the active force of each cell satisfies the equality constraint, and obtains the optimal solution, which is demonstrated as follows: for simplicity, formula (21) is written in vector form: phi (k+1) =vphi (k) - (P (k+1) -P (k)) (22), 1 T φ(k+1)＝1 T Vφ(k)-1 T [P(k+1)-P(k)](23) Wherein, the matrix V is a non-negative column random matrix, namely, the sum of column vectors of V is 1;1 T Is a unit row vector, thus 1 T V＝1 T ；1 T φ(k+1)＝1 T φ(k)-1 T [P(k+1)-P(k)] (24)，1 T [P(k+1)+φ(k+1)]＝1 T [P(k)+φ(k)](25) Reducing formula (25) to a variable form, namely:wherein N is the total set of the generator, the energy storage unit and the flexible load; thus, the initial value is set to satisfy +.>Make->For active absence of system, in iteration, phi i Will converge to 0 when all phi in the system i Upon convergence to 0, the active deficit in the system is 0, the equality constraint is satisfied, and the incremental cost λ of each element in the system i Convergence to system delta cost lambda under inequality constraint * 。
8. The micro-grid optimization scheduling method based on the consistency and gradient descent method according to claim 5, wherein the method comprises the following steps: the gradient descent method in the step 3 specifically comprises the following steps: the gradient descent method is an optimization algorithm based on the first-order property of the function, has the advantages of small storage capacity, simple structure and easiness in implementation, the gradient direction is the direction in which the function ascends most rapidly at a given point, then the opposite direction of the gradient is the direction in which the function descends most rapidly at the given point, when the objective function is minimized, the gradient descent method can be used for carrying out one-step iterative solution, and for a convex function in the objective function, the result obtained by the gradient descent method is necessarily a global optimal solution; in order to optimize the problem that the swing amplitude of an objective function is overlarge in the iteration process by using a gradient descent optimization algorithm-RMSprop algorithm, the algorithm combines the square root of the square sum of historical gradients controlled by attenuation coefficients, so that the learning rate of each parameter is different, the effect is that the gradient descent optimization algorithm-RMSprop algorithm obtains a larger progress in the direction of a more gentle parameter space, and the steep direction is gentle, so that the iteration speed is increased.
9. The micro-grid optimization scheduling method based on the consistency and gradient descent method according to claim 8, wherein the method comprises the following steps: the objective function C (P) of the gradient descent method in the step 3 is a convex function, and the gradient can be expressed as g k ＝▽ p C k (P) the variable v (k) of the RMSprop algorithm is the square termCompared with the AdaGrad algorithm, the learning rate of each element of the independent variable is not always reduced or unchanged in the iterative process, the acquisition of attenuation coefficient control history information is increased, the RMSprop algorithm readjusts the learning rate of each element in the independent variable of the objective function through element operation, and then the updated independent variable meets the following formula:
P(k+1)＝P(k)-η(k+1)g k (29) Wherein, beta is an attenuation coefficient; delta is the learning rate; the constant of ε added to maintain numerical stability is usually 10 -8 The method comprises the steps of carrying out a first treatment on the surface of the Since equation (29) is a centralized controllable unit power update principle, and does not belong to a fully distributed algorithm, a distributed improvement of equation (29) is required:
wherein N is i A collection of agents that are in communication with agent i; w (w) ij Is an element in the weight matrix; n is n i Number of agents communicating for agent i; through improved formulas (30) - (31), the complete distributed form of the RMSprop algorithm is realized, and meanwhile, the gradient descent principle of the RMSprop algorithm is integrated into the consistency principle, so that the convergence speed of the algorithm is improved, and the calculation time of the algorithm is shortened.
10. The micro-grid optimization scheduling method based on the consistency and gradient descent method according to claim 5, wherein the method comprises the following steps: the fully distributed optimal scheduling algorithm flow based on the consistency principle and the RMSprop algorithm in the step 3 comprises the following steps:
step (1): initial value of input system is satisfied
Step (2): forming a Laplace matrix according to the topological network diagram, and acquiring a state transition matrix and a w matrix;
step (3): updating the output and incremental cost of the controllable unit using RMSprop algorithm;
step (4): updating a consistency state variable, namely an incremental cost, of each controllable unit by using a consistency algorithm according to a formula (20); if the convergence condition is met, obtaining an optimal solution; and otherwise, updating the variables again.
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